Finite Group Databasebeta

← #35611279

Subgroups — #35611279

Order 21248.

2440 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128316C211yesmaximal, characteristic, complemented
2C2×#19128210C211yesmaximal, characteristic, complemented
3#24915756C211yesmaximal, characteristic, complemented
4#24915751C211yesmaximal, characteristic, complemented
5#24914011C211yesmaximal, characteristic, complemented
6#24913996C211yesmaximal, characteristic, complemented
7#24913957C211yesmaximal, characteristic, complemented
8#24913942C211yesmaximal, characteristic, complemented
9#24913912C211yesmaximal, characteristic, complemented
10#24913867C211yesmaximal, characteristic, complemented
11#24913852C211yesmaximal, characteristic, complemented
12#24913842C211yesmaximal, characteristic, complemented
13#24913776C211yesmaximal, characteristic, complemented
14#24913767C211yesmaximal, characteristic, complemented
15#24913747C211yesmaximal, characteristic, complemented
16#24913742C211yesmaximal, characteristic, complemented
17#24913717C211yesmaximal, characteristic, complemented
18#24913697C211yesmaximal, characteristic, complemented
19#24913687C211yesmaximal, characteristic, complemented
20#24913669C211yesmaximal, characteristic, complemented
21#24913383C211yesmaximal, characteristic, complemented
22#24913304C211yesmaximal, characteristic, complemented
23#24913140C211yesmaximal, characteristic, complemented
24#24913069C211yesmaximal, characteristic, complemented
25#24913042C211yesmaximal, characteristic, complemented
26#24913031C211yesmaximal, characteristic, complemented
27#24912822C211yesmaximal, characteristic, complemented
28#24912643C211yesmaximal, characteristic, complemented
29#24911091C211yesmaximal, characteristic, complemented
30#24911073C211yesmaximal, characteristic, complemented
31C83×#2318C211yesmaximal, characteristic, complemented
32C22×#13050590C2211yescharacteristic
33C23×C4×D83C2211yescharacteristic
34#19128316—28no—
35C2×#14581792C2211yescharacteristic, complemented
36C2×#14581791C2211yescharacteristic, complemented
37C2×#14581785C2211yescharacteristic
38C2×#14581785C2211yescharacteristic, complemented
39C2×#14581780C2211yescharacteristic
40C2×#14581779C2211yescharacteristic
41C2×#14581778C2211yescharacteristic
42C2×#14581778C2211yescharacteristic, complemented
43#19128210—28no—
44C2×#14581777C2211yescharacteristic
45C2×#14581776C2211yescharacteristic
46C2×#14581775C2211yescharacteristic
47C2×#14581775C2211yescharacteristic, complemented
48C2×#14581774C2211yescharacteristic
49C2×#14581772C2211yescharacteristic
50C2×#14581772C2211yescharacteristic
51C2×#14581772C2211yescharacteristic, complemented
52C2×#14581771C2211yescharacteristic
53C2×#14581771C2211yescharacteristic, complemented
54C2×#14581770C2211yescharacteristic
55C2×#14581769C2211yescharacteristic
56C2×#14581766C2211yescharacteristic
57C2×#14581766C2211yescharacteristic, complemented
58C2×#14581765C2211yescharacteristic
59C2×#14581764C2211yescharacteristic
60C2×#14581763C2211yescharacteristic
61C2×#14581762C2211yescharacteristic
62C2×#14581762C2211yescharacteristic
63C2×#14581760C2211yescharacteristic
64C2×C4×Dic166C2211yescharacteristic, complemented
65C2×C4×D332C2211yescharacteristic
66C2×C4×C22⋊D83C2211yescharacteristic
67C2×C4×C22⋊D83C2211yescharacteristic
68C2×#14581749C2211yescharacteristic
69C2×#14581749C2211yescharacteristic, complemented
70#19127641C2211yescharacteristic, complemented
71#19127641C2211yescharacteristic, complemented
72#19127638C2211yescharacteristic
73#19127638C2211yescharacteristic
74#19127638C2211yescharacteristic, complemented
75#19127638C2211yescharacteristic, complemented
76#19127633C2211yescharacteristic, complemented
77#19127633C2211yescharacteristic, complemented
78#19127631C2211yescharacteristic, complemented
79#19127631C2211yescharacteristic, complemented
80#19127628C2211yescharacteristic
81#19127628C2211yescharacteristic, complemented
82#19127626C2211yescharacteristic
83#19127626C2211yescharacteristic
84#19127626C2211yescharacteristic
85#19127626C2211yescharacteristic, complemented
86#19127623C2211yescharacteristic
87#19127623C2211yescharacteristic, complemented
88#19127623C2211yescharacteristic, complemented
89#19127623C2211yescharacteristic, complemented
90#19127622C2211yescharacteristic, complemented
91#19127622C2211yescharacteristic, complemented
92#19127622C2211yescharacteristic, complemented
93#19127622C2211yescharacteristic, complemented
94#19127619C2211yescharacteristic
95#19127619C2211yescharacteristic
96#19127618C2211yescharacteristic
97#19127618C2211yescharacteristic, complemented
98#19127617C2211yescharacteristic
99#19127617C2211yescharacteristic
100#19127617C2211yescharacteristic
101#19127617C2211yescharacteristic
102#19127617C2211yescharacteristic
103#19127617C2211yescharacteristic
104#19127617C2211yescharacteristic
105#19127617C2211yescharacteristic, complemented
106#19127617C2211yescharacteristic, complemented
107#19127617C2211yescharacteristic, complemented
108#19127614C2211yescharacteristic
109#19127614C2211yescharacteristic
110#19127614C2211yescharacteristic
111#19127614C2211yescharacteristic, complemented
112#19127614C2211yescharacteristic, complemented
113#19127614C2211yescharacteristic, complemented
114#19127611C2211yescharacteristic
115#19127611C2211yescharacteristic
116#19127610C2211yescharacteristic
117#19127610C2211yescharacteristic
118#19127607C2211yescharacteristic, complemented
119#19127603C2211yescharacteristic
120#19127603C2211yescharacteristic
121#19127602C2211yescharacteristic
122#19127602C2211yescharacteristic
123#19127600C2211yescharacteristic, complemented
124#19127600C2211yescharacteristic, complemented
125#19127599C2211yescharacteristic, complemented
126#19127593C2211yescharacteristic
127#19127593C2211yescharacteristic
128#19127593C2211yescharacteristic
129#19127593C2211yescharacteristic
130#19127593C2211yescharacteristic, complemented
131#19127593C2211yescharacteristic, complemented
132#19127592C2211yescharacteristic
133#19127592C2211yescharacteristic, complemented
134#19127586C2211yescharacteristic, complemented
135#19127586C2211yescharacteristic, complemented
136#19127586C2211yescharacteristic, complemented
137#19127586C2211yescharacteristic, complemented
138#19127586C2211yescharacteristic, complemented
139#19127586C2211yescharacteristic, complemented
140#19127580C2211yescharacteristic
141#19127580C2211yescharacteristic
142#19127580C2211yescharacteristic
143#19127580C2211yescharacteristic, complemented
144#19127579C2211yescharacteristic
145#19127579C2211yescharacteristic
146#19127579C2211yescharacteristic
147#19127579C2211yescharacteristic
148#19127579C2211yescharacteristic
149#19127579C2211yescharacteristic
150#19127579C2211yescharacteristic, complemented
151#19127579C2211yescharacteristic, complemented
152#19127576C2211yescharacteristic
153#19127576C2211yescharacteristic
154#19127575C2211yescharacteristic
155#19127575C2211yescharacteristic
156#19127575C2211yescharacteristic
157#19127575C2211yescharacteristic
158#19127575C2211yescharacteristic
159#19127575C2211yescharacteristic
160#19127575C2211yescharacteristic
161#19127575C2211yescharacteristic
162#19127575C2211yescharacteristic, complemented
163#19127575C2211yescharacteristic, complemented
164#19127575C2211yescharacteristic, complemented
165#19127575C2211yescharacteristic, complemented
166#19127562C2211yescharacteristic
167#19127561C2211yescharacteristic, complemented
168#19127561C2211yescharacteristic, complemented
169#19127558C2211yescharacteristic
170#19127558C2211yescharacteristic
171#19127556C2211yescharacteristic
172#19127556C2211yescharacteristic
173#19127556C2211yescharacteristic
174C2×C4×D4×C83C2211yescharacteristic
175#388×C83C2211yescharacteristic
176#388×C83C2211yescharacteristic
177#387×C83C2211yescharacteristic, complemented
178#387×C83C2211yescharacteristic, complemented
179#386×C83C2211yescharacteristic
180#386×C83C2211yescharacteristic
181#385×C83C2211yescharacteristic, complemented
182#385×C83C2211yescharacteristic, complemented
183#383×C83C2211yescharacteristic, complemented
184#382×C83C2211yescharacteristic, complemented
185#381×C83C2211yescharacteristic
186#380×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic, complemented
188C2×#95×C83C2211yescharacteristic, complemented
189C24×D83C2311yescharacteristic
190C2×#13050590—24no—
191C2×#13050590—42no—
192C2×#13050590—42no—
193C22×Dic166C2311yescharacteristic
194C22×Dic166C2311yescharacteristic
195C22×Dic166C2311yescharacteristic
196C22×Dic166C2311yescharacteristic
197C22×D332C2311yescharacteristic
198C22×D332C2311yescharacteristic
199C22×D332C2311yescharacteristic
200C22×D332C2311yescharacteristic
201C22×D332C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C22×C22⋊D83C2311yescharacteristic
204C22×C22⋊D83C2311yescharacteristic
205C22×C22⋊D83C2311yescharacteristic
206C22×C22⋊D83C2311yescharacteristic
207C22×C22⋊D83C2311yescharacteristic
208C23×Dic83C2311yescharacteristic
209C22×C4×D83—24no—
210C22×C4×D83—42no—
211C22×C4×D83—42no—
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216C22×C4×D83C2311yescharacteristic
217C22×C4×D83C2311yescharacteristic
218#14581792—42no—
219#14581791—24no—
220#14581785—24no—
221#14581785—24no—
222#14581780—42no—
223#14581779—24no—
224#14581778—24no—
225#14581778—24no—
226#14581777—24no—
227#14581776—42no—
228#14581775—24no—
229#14581775—24no—
230#14581774—24no—
231#14581772—24no—
232#14581772—42no—
233#14581772—42no—
234#14581771—24no—
235#14581771—24no—
236#14581770—24no—
237#14581769—24no—
238#14581766—42no—
239#14581766—42no—
240#14581765—24no—
241#14581764—24no—
242#14581763—24no—
243#14581762—24no—
244#14581762—42no—
245#14581760—24no—
246C4×Dic166—24no—
247C4×D332—24no—
248C4×C22⋊D83—24no—
249C4×C22⋊D83—24no—
250#14581749—24no—
251#14581749—24no—
252C2×C4⋊Dic83C2311yescharacteristic
253C2×C4⋊Dic83C2311yescharacteristic
254C2×C4⋊Dic83C2311yescharacteristic
255C2×C4⋊Dic83C2311yescharacteristic
256C2×C4⋊Dic83C2311yescharacteristic
257C2×C4⋊Dic83C2311yescharacteristic
258C2×C4⋊Dic83C2311yescharacteristic
259C2×C4⋊Dic83C2311yescharacteristic
260C2×C4⋊Dic83C2311yescharacteristic
261C2×C4⋊Dic83C2311yescharacteristic
262C2×C4⋊Dic83C2311yescharacteristic
263C2×C4⋊Dic83C2311yescharacteristic
264C2×C4⋊Dic83C2311yescharacteristic
265C2×C4⋊Dic83C2311yescharacteristic
266C2×C4⋊Dic83C2311yescharacteristic
267C2×C4⋊Dic83C2311yescharacteristic
268C2×C4⋊Dic83C2311yescharacteristic
269C2×Dic83⋊C4C2311yescharacteristic
270C2×Dic83⋊C4C2311yescharacteristic
271C2×Dic83⋊C4C2311yescharacteristic
272C2×Dic83⋊C4C2311yescharacteristic
273C2×Dic83⋊C4C2311yescharacteristic
274C2×Dic83⋊C4C2311yescharacteristic
275C2×Dic83⋊C4C2311yescharacteristic
276C2×Dic83⋊C4C2311yescharacteristic
277C2×Dic83⋊C4C2311yescharacteristic
278C2×Dic83⋊C4C2311yescharacteristic
279C2×C22⋊Dic83C2311yescharacteristic
280C2×C22⋊Dic83C2311yescharacteristic
281C2×C22⋊Dic83C2311yescharacteristic
282C2×C22⋊Dic83C2311yescharacteristic
283C2×C22⋊Dic83C2311yescharacteristic
284C2×C22⋊Dic83C2311yescharacteristic
285C2×C22⋊Dic83C2311yescharacteristic
286C2×C22⋊Dic83C2311yescharacteristic
287C2×(C2×D83)⋊C4C2311yescharacteristic
288C2×(C2×D83)⋊C4C2311yescharacteristic
289C2×(C2×D83)⋊C4C2311yescharacteristic
290C2×(C2×D83)⋊C4C2311yescharacteristic
291C2×(C2×D83)⋊C4C2311yescharacteristic
292C2×(C2×D83)⋊C4C2311yescharacteristic
293C2×(C2×D83)⋊C4C2311yescharacteristic
294C2×(C2×D83)⋊C4C2311yescharacteristic
295C2×(C2×D83)⋊C4C2311yescharacteristic
296C2×(C2×D83)⋊C4C2311yescharacteristic
297C2×(C2×D83)⋊C4C2311yescharacteristic
298C2×(C2×D83)⋊C4C2311yescharacteristic
299C2×(C2×D83)⋊C4C2311yescharacteristic
300C2×(C2×D83)⋊C4C2311yescharacteristic
301C2×(C2×D83)⋊C4C2311yescharacteristic
302C2×(C2×D83)⋊C4C2311yescharacteristic
303C2×(C2×D83)⋊C4C2311yescharacteristic
304C2×(C2×D83)⋊C4C2311yescharacteristic
305C2×(C2×D83)⋊C4C2311yescharacteristic
306C2×(C2×D83)⋊C4C2311yescharacteristic
307C2×(C2×D83)⋊C4C2311yescharacteristic
308C2×(C2×D83)⋊C4C2311yescharacteristic
309C2×(C2×D83)⋊C4C2311yescharacteristic
310C2×(C2×D83)⋊C4C2311yescharacteristic
311C2×(C2×D83)⋊C4C2311yescharacteristic
312C2×(C2×D83)⋊C4C2311yescharacteristic
313C2×(C2×D83)⋊C4C2311yescharacteristic
314C2×(C2×D83)⋊C4C2311yescharacteristic
315C2×(C2×D83)⋊C4C2311yescharacteristic
316C2×(C2×D83)⋊C4C2311yescharacteristic
317C2×(C2×D83)⋊C4C2311yescharacteristic
318C2×(C2×D83)⋊C4C2311yescharacteristic
319C2×(C2×D83)⋊C4C2311yescharacteristic
320C2×(C2×D83)⋊C4C2311yescharacteristic
321C2×(C2×D83)⋊C4C2311yescharacteristic
322C2×(C2×D83)⋊C4C2311yescharacteristic
323C2×C4×Dic83C2311yescharacteristic
324C2×C4×Dic83C2311yescharacteristic
325C2×C4×Dic83C2311yescharacteristic
326C2×C4×Dic83C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C83⋊#95C2311yescharacteristic
337C83⋊#95C2311yescharacteristic
338C83⋊#95C2311yescharacteristic
339C83⋊#95C2311yescharacteristic
340C83⋊#95C2311yescharacteristic
341C83⋊#95C2311yescharacteristic
342C83⋊#95C2311yescharacteristic
343C83⋊#95C2311yescharacteristic
344C83⋊#95C2311yescharacteristic
345C83⋊#95C2311yescharacteristic
346C83⋊#95C2311yescharacteristic
347C83⋊#95C2311yescharacteristic
348C83⋊#95C2311yescharacteristic
349C22×D4×C83C2311yescharacteristic
350C23×C4×C83C2311yescharacteristic
351C23×C4×C83C2311yescharacteristic
352C23×C4×C83C2311yescharacteristic
353C23×C4×C83C2311yescharacteristic
354C4×D4×C83D418yescomplemented
355C2×C4⋊C4×C83C2311yescharacteristic
356C2×C4⋊C4×C83C2311yescharacteristic
357C2×C4⋊C4×C83C2311yescharacteristic
358C2×C4⋊C4×C83C2311yescharacteristic
359C2×C4⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361C2×C22⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C22⋊C4×C83C2311yescharacteristic
365C2×C22⋊C4×C83C2311yescharacteristic
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C22⋊C4×C83C2311yescharacteristic
368C2×C42×C83C2311yescharacteristic
369C2×C42×C83C2311yescharacteristic
370C2×C42×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376#95×C83C2311yescharacteristic
377#95×C83C2311yescharacteristic
378#95×C83C2311yescharacteristic
379#95×C83C2311yescharacteristic
380#95×C83C2311yescharacteristic
381#95×C83C2311yescharacteristic
382#95×C83C2311yescharacteristic
383#95×C83C2311yescharacteristic
384#95×C83C2311yescharacteristic
385C23×D83—22no—
386C23×D83—22no—
387C23×D83—22no—
388C23×D83—41no—
389C23×D83—41no—
390C23×D83—41no—
391C23×D83—41no—
392C23×D83C2411yescharacteristic
393C23×D83C2411yescharacteristic
394C23×D83C2411yescharacteristic
395C23×D83C2411yescharacteristic
396#13050590—416no—
397C2×Dic166—22no—
398C2×Dic166—22no—
399C2×Dic166—22no—
400C2×Dic166—22no—
401C2×Dic166—22no—
402C2×Dic166—41no—
403C2×Dic166—41no—
404C2×Dic166—41no—
405C2×Dic166—41no—
406C2×Dic166—41no—
407C2×Dic166—41no—
408C2×Dic166—41no—
409C2×D332—22no—
410C2×D332—22no—
411C2×D332—22no—
412C2×D332—22no—
413C2×D332—22no—
414C2×D332—22no—
415C2×D332—41no—
416C2×D332—41no—
417C2×D332—41no—
418C2×D332—41no—
419C2×D332—41no—
420C2×D332—41no—
421C2×D332—41no—
422C2×D332—41no—
423C2×D332—41no—
424C2×C22⋊D83—22no—
425C2×C22⋊D83—22no—
426C2×C22⋊D83—22no—
427C2×C22⋊D83—22no—
428C2×C22⋊D83—22no—
429C2×C22⋊D83—22no—
430C2×C22⋊D83—22no—
431C2×C22⋊D83—22no—
432C2×C22⋊D83—22no—
433C2×C22⋊D83—41no—
434C2×C22⋊D83—41no—
435C2×C22⋊D83—41no—
436C2×C22⋊D83—41no—
437C2×C22⋊D83—41no—
438C2×C22⋊D83—41no—
439C2×C22⋊D83—41no—
440C2×C22⋊D83—41no—
441C2×C22⋊D83—41no—
442C22×Dic83—22no—
443C22×Dic83—22no—
444C22×Dic83—41no—
445C22×Dic83C2411yescharacteristic
446C22×Dic83C2411yescharacteristic
447C22×Dic83C2411yescharacteristic
448C22×Dic83C2411yescharacteristic
449C22×Dic83C2411yescharacteristic
450C22×Dic83C2411yescharacteristic
451C22×Dic83C2411yescharacteristic
452C22×Dic83C2411yescharacteristic
453C22×Dic83C2411yescharacteristic
454C22×Dic83C2411yescharacteristic
455C22×Dic83C2411yescharacteristic
456C22×Dic83C2411yescharacteristic
457C2×C4×D83—22no—
458C2×C4×D83—22no—
459C2×C4×D83—22no—
460C2×C4×D83—22no—
461C2×C4×D83—22no—
462C2×C4×D83—22no—
463C2×C4×D83—22no—
464C2×C4×D83—22no—
465C2×C4×D83—22no—
466C2×C4×D83—22no—
467C2×C4×D83—416no—
468C2×C4×D83—41no—
469C2×C4×D83—41no—
470C2×C4×D83—41no—
471C2×C4×D83—41no—
472C2×C4×D83—41no—
473C2×C4×D83—41no—
474C2×C4×D83—41no—
475C2×C4×D83—41no—
476C4⋊Dic83—22no—
477C4⋊Dic83—22no—
478C4⋊Dic83—22no—
479C4⋊Dic83—22no—
480C4⋊Dic83—22no—
481C4⋊Dic83—22no—
482C4⋊Dic83—22no—
483C4⋊Dic83—41no—
484C4⋊Dic83—41no—
485C4⋊Dic83—41no—
486C4⋊Dic83—41no—
487C4⋊Dic83—41no—
488C4⋊Dic83—41no—
489C4⋊Dic83—41no—
490C4⋊Dic83—41no—
491C4⋊Dic83—41no—
492C4⋊Dic83—41no—
493Dic83⋊C4—22no—
494Dic83⋊C4—22no—
495Dic83⋊C4—22no—
496Dic83⋊C4—22no—
497Dic83⋊C4—22no—
498Dic83⋊C4—22no—
499Dic83⋊C4—22no—
500Dic83⋊C4—22no—
501Dic83⋊C4—22no—
502Dic83⋊C4—22no—
503C22⋊Dic83—22no—
504C22⋊Dic83—22no—
505C22⋊Dic83—22no—
506C22⋊Dic83—22no—
507C22⋊Dic83—22no—
508C22⋊Dic83—22no—
509C22⋊Dic83—22no—
510C22⋊Dic83—22no—
511(C2×D83)⋊C4—22no—
512(C2×D83)⋊C4—22no—
513(C2×D83)⋊C4—22no—
514(C2×D83)⋊C4—22no—
515(C2×D83)⋊C4—22no—
516(C2×D83)⋊C4—22no—
517(C2×D83)⋊C4—22no—
518(C2×D83)⋊C4—22no—
519(C2×D83)⋊C4—22no—
520(C2×D83)⋊C4—22no—
521(C2×D83)⋊C4—22no—
522(C2×D83)⋊C4—22no—
523(C2×D83)⋊C4—22no—
524(C2×D83)⋊C4—22no—
525(C2×D83)⋊C4—22no—
526(C2×D83)⋊C4—41no—
527(C2×D83)⋊C4—41no—
528(C2×D83)⋊C4—41no—
529(C2×D83)⋊C4—41no—
530(C2×D83)⋊C4—41no—
531(C2×D83)⋊C4—41no—
532(C2×D83)⋊C4—41no—
533(C2×D83)⋊C4—41no—
534(C2×D83)⋊C4—41no—
535(C2×D83)⋊C4—41no—
536(C2×D83)⋊C4—41no—
537(C2×D83)⋊C4—41no—
538(C2×D83)⋊C4—41no—
539(C2×D83)⋊C4—41no—
540(C2×D83)⋊C4—41no—
541(C2×D83)⋊C4—41no—
542(C2×D83)⋊C4—41no—
543(C2×D83)⋊C4—41no—
544(C2×D83)⋊C4—41no—
545(C2×D83)⋊C4—41no—
546(C2×D83)⋊C4—41no—
547C4×Dic83—22no—
548C4×Dic83—22no—
549C4×Dic83—22no—
550C4×Dic83—22no—
551C24×C83C2411yescharacteristic
552C24×C83C2411yescharacteristic
553C2×D4×C83—41no—
554C2×D4×C83—41no—
555C2×D4×C83C2×D414yes—
556C22×C4×C83—41no—
557C22×C4×C83—41no—
558C22×C4×C83—41no—
559C22×C4×C83—41no—
560C22×C4×C83—41no—
561C22×C4×C83—41no—
562C22×C4×C83—41no—
563C22×C4×C83—41no—
564C22×C4×C83—41no—
565C22×C4×C83—41no—
566C22×C4×C83C2×D414yes—
567C22×C4×C83C2×D414yes—
568C22×C4×C83C2411yescharacteristic
569C22×C4×C83C2411yescharacteristic
570C22×C4×C83C2411yescharacteristic
571C22×C4×C83C2411yescharacteristic
572C22×C4×C83C2411yescharacteristic
573C22×C4×C83C2411yescharacteristic
574C22×C4×C83C2411yescharacteristic
575C22×C4×C83C2411yescharacteristic
576C22×C4×C83C2411yescharacteristic
577C22×C4×C83C2411yescharacteristic
578C22×C4×C83C2411yescharacteristic
579C22×C4×C83C2411yescharacteristic
580C22×C4×C83C2411yescharacteristic
581C4⋊C4×C83—41no—
582C4⋊C4×C83—41no—
583C4⋊C4×C83—41no—
584C4⋊C4×C83—41no—
585C4⋊C4×C83C2×D414yes—
586C22⋊C4×C83—41no—
587C22⋊C4×C83—41no—
588C22⋊C4×C83—41no—
589C22⋊C4×C83—41no—
590C22⋊C4×C83—41no—
591C22⋊C4×C83—41no—
592C22⋊C4×C83C2×D414yes—
593C22⋊C4×C83C2×D414yes—
594C42×C83—41no—
595C42×C83—41no—
596C42×C83C2×D414yes—
597C23×C83—21no—
598C23×C83—21no—
599C23×C83—21no—
600C23×C83—21no—
601C23×C83—21no—
602C23×C83—21no—
603C23×C83—21no—
604C23×C83—21no—
605C23×C83—21no—
606C23×C83—21no—
607C23×C83—21no—
608C23×C83—21no—
609C23×C83C22×D412yes—
610C23×C83C22×D412yes—
611C23×C83C2511yescharacteristic
612C22×D83—21no—
613C22×D83—21no—
614C22×D83—21no—
615C22×D83—21no—
616C22×D83—21no—
617C22×D83—21no—
618C22×D83—21no—
619C22×D83—21no—
620C22×D83—21no—
621C22×D83—21no—
622C22×D83—21no—
623C22×D83—21no—
624C22×D83—21no—
625C22×D83—21no—
626C22×D83—21no—
627C22×D83—21no—
628C22×D83—21no—
629C22×D83—21no—
630C22×D83—21no—
631C22×D83—21no—
632C22×D83—21no—
633C22×D83—21no—
634C22×D83—21no—
635C22×D83—21no—
636C22×D83—21no—
637C22×D83—21no—
638C22×D83—44no—
639C22×D83—44no—
640C22×D83—44no—
641C22×D83—44no—
642C22×D83—44no—
643C22×D83—44no—
644C22×D83—44no—
645C22×D83H(5,𝔽2)12yes—
646C22×D832−1+412yes—
647D4×C83—44no—
648C2×C4×C83—21no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—21no—
666C2×C4×C83—21no—
667C2×C4×C83—21no—
668C2×C4×C83—21no—
669C2×C4×C83—21no—
670C2×C4×C83—21no—
671C2×C4×C83—21no—
672C2×C4×C83—21no—
673C2×C4×C83—21no—
674C2×C4×C83—21no—
675C2×C4×C83—21no—
676C2×C4×C83—21no—
677C2×C4×C83—21no—
678C2×C4×C83—21no—
679C2×C4×C83—21no—
680C2×C4×C83—21no—
681C2×C4×C83—21no—
682C2×C4×C83—44no—
683C2×C4×C83—44no—
684C2×C4×C83—82no—
685C2×C4×C83—82no—
686C2×C4×C83C22×D412yes—
687C2×C4×C83C22×D412yes—
688C2×C4×C83C22×D412yes—
689C2×C4×C83C22×D412yes—
690C2×C4×C83C22×D412yes—
691C22⋊D83—44no—
692C22⋊D83—44no—
693C22⋊D83—44no—
694C22⋊D83—44no—
695C22⋊D83—82no—
696C22⋊D83—82no—
697C2×Dic83—21no—
698C2×Dic83—21no—
699C2×Dic83—21no—
700C2×Dic83—21no—
701C2×Dic83—21no—
702C2×Dic83—21no—
703C2×Dic83—21no—
704C2×Dic83—21no—
705C2×Dic83—21no—
706C2×Dic83—21no—
707C2×Dic83—21no—
708C2×Dic83—21no—
709C2×Dic83—21no—
710C2×Dic83—21no—
711C2×Dic83—21no—
712C2×Dic83—21no—
713C2×Dic83—21no—
714C2×Dic83—21no—
715C2×Dic83—21no—
716C2×Dic83—21no—
717C2×Dic83—21no—
718C2×Dic83—21no—
719C2×Dic83—21no—
720C2×Dic83—21no—
721C2×Dic83—21no—
722C2×Dic83—21no—
723C2×Dic83—21no—
724C2×Dic83—21no—
725C2×Dic83—21no—
726C2×Dic83—21no—
727C2×Dic83—21no—
728C2×Dic83—21no—
729C2×Dic83—21no—
730C2×Dic83—21no—
731C2×Dic83—21no—
732C2×Dic83—44no—
733C2×Dic83H(5,𝔽2)12yes—
734D332—44no—
735D332—44no—
736D332—82no—
737D332—82no—
738D332—82no—
739C4×D83—28no—
740C4×D83—44no—
741C4×D83—44no—
742C4×D83—44no—
743C4×D83—44no—
744C4×D83—44no—
745Dic166—44no—
746Dic166—44no—
747Dic166—82no—
748Dic166—82no—
749C22×C83—22no—
750C22×C83—22no—
751C22×C83—22no—
752C22×C83—22no—
753C22×C83—22no—
754C22×C83—22no—
755C22×C83—41no—
756C22×C83—41no—
757C22×C83—41no—
758C22×C83—41no—
759C22×C83—41no—
760C22×C83—41no—
761C22×C83—41no—
762C22×C83—41no—
763C22×C83C23×D411yescharacteristic
764C22×C83C2×H(5,𝔽2)11yescharacteristic
765C22×C83C2×H(5,𝔽2)11yescharacteristic
766C22×C83C2×2−1+411yescharacteristic
767C22×C83#58511yescharacteristic
768C22×C83#58511yescharacteristic
769C22×C83#58511yescharacteristic
770C2×D83—22no—
771C2×D83—22no—
772C2×D83—22no—
773C2×D83—22no—
774C2×D83—22no—
775C2×D83—22no—
776C2×D83—416no—
777C2×D83—41no—
778C2×D83—41no—
779C2×D83—41no—
780C2×D83—41no—
781C2×D83—41no—
782C2×D83—41no—
783C2×D83—41no—
784C2×D83—41no—
785C2×D83—41no—
786C2×D83—41no—
787C2×D83—41no—
788C2×D83—41no—
789C2×D83—41no—
790C2×D83—41no—
791C2×D83—41no—
792C2×D83—41no—
793C2×D83—41no—
794C2×D83—41no—
795C2×D83—41no—
796C2×D83—41no—
797C2×D83—41no—
798C2×D83—41no—
799C4×C83—22no—
800C4×C83—22no—
801C4×C83—22no—
802C4×C83—22no—
803C4×C83—22no—
804C4×C83—41no—
805C4×C83—41no—
806C4×C83—41no—
807C4×C83—41no—
808C4×C83—41no—
809C4×C83—41no—
810C4×C83—41no—
811C4×C83—41no—
812Dic83—22no—
813Dic83—41no—
814Dic83—41no—
815Dic83—41no—
816Dic83—41no—
817Dic83—41no—
818Dic83—41no—
819Dic83—41no—
820Dic83—41no—
821Dic83—41no—
822Dic83—41no—
823Dic83—41no—
824#36712—831nomaximal, Sylow
825C2×C83—42no—
826C2×C83—42no—
827C2×C83#344911yescharacteristic
828C2×C83#348411yescharacteristic
829C2×C83#348911yescharacteristic
830C2×C83#353311yescharacteristic
831C2×C83#353511yescharacteristic
832C2×C83#354011yescharacteristic
833C2×C83#354111yescharacteristic
834D83—42no—
835D83—42no—
836D83—81no—
837D83—81no—
838C2×#542—831no—
839C2×#525—831no—
840#2849—831no—
841#2848—831no—
842#2696—831no—
843#2695—831no—
844#2692—831no—
845#2691—831no—
846#2689—831no—
847#2686—831no—
848#2685—831no—
849#2684—831no—
850#2677—831no—
851#2676—831no—
852#2674—831no—
853#2674—831no—
854#2672—831no—
855#2671—831no—
856#2670—831no—
857#2668—831no—
858#2638—831no—
859#2630—831no—
860#2609—831no—
861#2602—831no—
862#2599—831no—
863#2598—831no—
864#2580—831no—
865#2564—831no—
866#2432—831no—
867#2430—831no—
868#2318D8311yescharacteristic, complemented
869C83#3671211yescharacteristic, complemented, Sylow
870C22×#41—831no—
871C24×C4—831no—
872#542—1668no—
873C2×C4⋊Q8—831no—
874C2×C4⋊Q8—831no—
875C2×#126—831no—
876C2×#126—831no—
877C2×#124—831no—
878C2×#124—831no—
879C2×#124—831no—
880C2×#124—831no—
881#525—1668no—
882C2×#123—831no—
883C2×#123—831no—
884C2×#123—831no—
885C2×#123—831no—
886C2×#123—831no—
887C2×C22⋊Q8—831no—
888C2×C22⋊Q8—831no—
889C2×C22⋊Q8—831no—
890C2×C22⋊Q8—831no—
891C2×C22⋊Q8—831no—
892C2×C22⋊Q8—831no—
893C2×C22⋊Q8—831no—
894C2×#121—831no—
895C2×#121—831no—
896C2×#121—831no—
897C2×#121—831no—
898C2×#121—831no—
899C2×#120—831no—
900C2×#120—831no—
901C2×#120—831no—
902C2×C4×Q8—831no—
903C2×C4×D4—831no—
904C2×C4×D4—831no—
905C2×C4×D4—831no—
906C2×C4×D4C2×D8311yescharacteristic
907C2×#117—831no—
908C2×#117—831no—
909#400—831no—
910#400—831no—
911#399—831no—
912#399—831no—
913#399—831no—
914#399—831no—
915#398—831no—
916#398—831no—
917#398—831no—
918#398—831no—
919#397—831no—
920#397—831no—
921#397—831no—
922#397—831no—
923#397—831no—
924#397—831no—
925#396—831no—
926#396—831no—
927#396—831no—
928#396—831no—
929#395—831no—
930#395—831no—
931#395—831no—
932#395—831no—
933#394—831no—
934#394—831no—
935#394—831no—
936#394—831no—
937#394—831no—
938#394—831no—
939#394—831no—
940#394—831no—
941#394—831no—
942#394—831no—
943#394—831no—
944#394—831no—
945#394—831no—
946#394—831no—
947#393—831no—
948#393—831no—
949#393—831no—
950#393—831no—
951#393—831no—
952#393—831no—
953#392—831no—
954#392—831no—
955#392—831no—
956#392—831no—
957#391—831no—
958#390—831no—
959#390—831no—
960#390—831no—
961#390—831no—
962#389—831no—
963#389—831no—
964#389—831no—
965#388—831no—
966#388—831no—
967#388—831no—
968#388—831no—
969#388—831no—
970#388—831no—
971#388—831no—
972#388—831no—
973#388C2×D8311yescharacteristic
974#388C2×D8311yescharacteristic
975#387—831no—
976#387—831no—
977#387—831no—
978#387—831no—
979#387—831no—
980#387—831no—
981#387C2×D8311yescharacteristic, complemented
982#387C2×D8311yescharacteristic, complemented
983#386—831no—
984#386—831no—
985#386—831no—
986#386—831no—
987#386—831no—
988#386—831no—
989#386—831no—
990#386—831no—
991#386—831no—
992#386—831no—
993#386—831no—
994#386—831no—
995#386C2×D8311yescharacteristic
996#386C2×D8311yescharacteristic
997#385—831no—
998#385—831no—
999#385—831no—
1000#385—831no—
1001#385—831no—
1002#385—831no—
1003#385—831no—
1004#385—831no—
1005#385—831no—
1006#385—831no—
1007#385—831no—
1008#385—831no—
1009#385—831no—
1010#385—831no—
1011#385C2×D8311yescharacteristic, complemented
1012#385C2×D8311yescharacteristic, complemented
1013#383C2×D8311yescharacteristic, complemented
1014#382C2×D8311yescharacteristic, complemented
1015#381—831no—
1016#381C2×D8311yescharacteristic
1017#380—831no—
1018#380—831no—
1019#380—831no—
1020#380—831no—
1021#380C2×D8311yescharacteristic
1022#379—831no—
1023#379—831no—
1024#379—831no—
1025C4×C22⋊C4C2×D8311yescharacteristic, complemented
1026C2×#95C2×D8311yescharacteristic, complemented
1027C25—831no—
1028C2×#41—3322no—
1029C2×#41—3322no—
1030C2×#41—1664no—
1031C22×Q8—831no—
1032C22×Q8—831no—
1033C22×Q8—831no—
1034C22×Q8—831no—
1035C22×D4—831no—
1036C22×D4—831no—
1037C22×D4—831no—
1038C22×D4—831no—
1039C22×D4—831no—
1040C22×D4—831no—
1041C22×D4—831no—
1042C22×D4—831no—
1043C22×D4—831no—
1044C22×D4—831no—
1045C22×D4—831no—
1046C22×D4C22×D8311yescharacteristic
1047C23×C4—3322no—
1048C23×C4—3322no—
1049C23×C4—831no—
1050C23×C4—831no—
1051C23×C4—831no—
1052C23×C4—831no—
1053C23×C4—831no—
1054C23×C4—831no—
1055C23×C4—831no—
1056C23×C4—1664no—
1057C23×C4C22×D8311yescharacteristic
1058C23×C4C22×D8311yescharacteristic
1059C23×C4C22×D8311yescharacteristic
1060C23×C4C22×D8311yescharacteristic
1061C4⋊Q8—3322no—
1062C4⋊Q8—1664no—
1063#126—1664no—
1064#126—1664no—
1065#124—3322no—
1066#124—1664no—
1067#124—1664no—
1068#124—1664no—
1069#123—3322no—
1070#123—1664no—
1071#123—1664no—
1072#123—1664no—
1073#123—1664no—
1074C22⋊Q8—3322no—
1075C22⋊Q8—3322no—
1076C22⋊Q8—1664no—
1077C22⋊Q8—1664no—
1078C22⋊Q8—1664no—
1079C22⋊Q8—1664no—
1080C22⋊Q8—1664no—
1081#121—3322no—
1082#121—3322no—
1083#121—1664no—
1084#121—1664no—
1085#121—1664no—
1086#120—3322no—
1087#120—1664no—
1088#120—1664no—
1089C4×Q8—1664no—
1090C4×D4—1664no—
1091C4×D4—1664no—
1092C4×D4—1664no—
1093C4×D4D33218yescomplemented
1094#117—1664no—
1095#117—1664no—
1096C2×C4⋊C4—831no—
1097C2×C4⋊C4—831no—
1098C2×C4⋊C4—831no—
1099C2×C4⋊C4—831no—
1100C2×C4⋊C4—831no—
1101C2×C4⋊C4—831no—
1102C2×C4⋊C4—831no—
1103C2×C4⋊C4—831no—
1104C2×C4⋊C4—831no—
1105C2×C4⋊C4—831no—
1106C2×C4⋊C4—831no—
1107C2×C4⋊C4—831no—
1108C2×C4⋊C4—831no—
1109C2×C4⋊C4—831no—
1110C2×C4⋊C4—831no—
1111C2×C4⋊C4—831no—
1112C2×C4⋊C4—831no—
1113C2×C4⋊C4—831no—
1114C2×C4⋊C4—831no—
1115C2×C4⋊C4—831no—
1116C2×C4⋊C4—831no—
1117C2×C4⋊C4—831no—
1118C2×C4⋊C4—831no—
1119C2×C4⋊C4—831no—
1120C2×C4⋊C4—831no—
1121C2×C4⋊C4—831no—
1122C2×C4⋊C4—831no—
1123C2×C4⋊C4C22×D8311yescharacteristic
1124C2×C4⋊C4C22×D8311yescharacteristic
1125C2×C4⋊C4C22×D8311yescharacteristic
1126C2×C4⋊C4C22×D8311yescharacteristic
1127C2×C4⋊C4C22×D8311yescharacteristic
1128C2×C22⋊C4—831no—
1129C2×C22⋊C4—831no—
1130C2×C22⋊C4—831no—
1131C2×C22⋊C4—831no—
1132C2×C22⋊C4—831no—
1133C2×C22⋊C4—831no—
1134C2×C22⋊C4—831no—
1135C2×C22⋊C4—831no—
1136C2×C22⋊C4—831no—
1137C2×C22⋊C4—831no—
1138C2×C22⋊C4—831no—
1139C2×C22⋊C4—831no—
1140C2×C22⋊C4—831no—
1141C2×C22⋊C4—831no—
1142C2×C22⋊C4—831no—
1143C2×C22⋊C4—831no—
1144C2×C22⋊C4—831no—
1145C2×C22⋊C4—831no—
1146C2×C22⋊C4—831no—
1147C2×C22⋊C4—831no—
1148C2×C22⋊C4—831no—
1149C2×C22⋊C4—831no—
1150C2×C22⋊C4—831no—
1151C2×C22⋊C4—831no—
1152C2×C22⋊C4—831no—
1153C2×C22⋊C4—831no—
1154C2×C22⋊C4—831no—
1155C2×C22⋊C4—831no—
1156C2×C22⋊C4—831no—
1157C2×C22⋊C4—831no—
1158C2×C22⋊C4—831no—
1159C2×C22⋊C4—831no—
1160C2×C22⋊C4—831no—
1161C2×C22⋊C4—831no—
1162C2×C22⋊C4—831no—
1163C2×C22⋊C4—831no—
1164C2×C22⋊C4—831no—
1165C2×C22⋊C4—831no—
1166C2×C22⋊C4—831no—
1167C2×C22⋊C4—831no—
1168C2×C22⋊C4—831no—
1169C2×C22⋊C4—831no—
1170C2×C22⋊C4—831no—
1171C2×C22⋊C4—831no—
1172C2×C22⋊C4C22×D8311yescharacteristic
1173C2×C22⋊C4C22×D8311yescharacteristic
1174C2×C22⋊C4C22×D8311yescharacteristic
1175C2×C22⋊C4C22×D8311yescharacteristic
1176C2×C22⋊C4C22×D8311yescharacteristic
1177C2×C22⋊C4C22×D8311yescharacteristic
1178C2×C22⋊C4C22×D8311yescharacteristic
1179C2×C22⋊C4C22×D8311yescharacteristic
1180C2×C42—831no—
1181C2×C42—831no—
1182C2×C42—831no—
1183C2×C42—831no—
1184C2×C42C22×D8311yescharacteristic
1185C2×C42C22×D8311yescharacteristic
1186C2×C42C22×D8311yescharacteristic
1187#95—831no—
1188#95—831no—
1189#95—831no—
1190#95—831no—
1191#95—831no—
1192#95—831no—
1193#95—831no—
1194#95—831no—
1195#95—831no—
1196#95—831no—
1197#95—831no—
1198#95—831no—
1199#95—831no—
1200#95—831no—
1201#95—831no—
1202#95—831no—
1203#95—831no—
1204#95—831no—
1205#95—831no—
1206#95—831no—
1207#95—831no—
1208#95—831no—
1209#95C22×D8311yescharacteristic
1210#95C22×D8311yescharacteristic
1211#95C22×D8311yescharacteristic
1212#95C22×D8311yescharacteristic
1213#95C22×D8311yescharacteristic
1214#95C22×D8311yescharacteristic
1215#95C22×D8311yescharacteristic
1216#95C22×D8311yescharacteristic
1217#95C22×D8311yescharacteristic
1218#95C22×D8311yescharacteristic
1219#95C22×D8311yescharacteristic
1220#95C22×D8311yescharacteristic
1221#95C22×D8311yescharacteristic
1222#95C22×D8311yescharacteristic
1223C24—3321no—
1224C24—3321no—
1225C24—3321no—
1226C24—3321no—
1227C24—831no—
1228C24—831no—
1229C24—831no—
1230C24—831no—
1231C24—1662no—
1232C24—1662no—
1233C24—1662no—
1234C24C23×D8311yescharacteristic
1235C24C23×D8311yescharacteristic
1236#41—33216no—
1237C2×Q8—3321no—
1238C2×Q8—3321no—
1239C2×Q8—3321no—
1240C2×Q8—3321no—
1241C2×Q8—3321no—
1242C2×Q8—3321no—
1243C2×Q8—3321no—
1244C2×Q8—1662no—
1245C2×Q8—1662no—
1246C2×Q8—1662no—
1247C2×Q8—1662no—
1248C2×Q8—1662no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—3321no—
1252C2×D4—3321no—
1253C2×D4—3321no—
1254C2×D4—3321no—
1255C2×D4—3321no—
1256C2×D4—3321no—
1257C2×D4—3321no—
1258C2×D4—3321no—
1259C2×D4—3321no—
1260C2×D4—3321no—
1261C2×D4—3321no—
1262C2×D4—3321no—
1263C2×D4—3321no—
1264C2×D4—3321no—
1265C2×D4—3321no—
1266C2×D4—3321no—
1267C2×D4—3321no—
1268C2×D4—3321no—
1269C2×D4—1662no—
1270C2×D4—1662no—
1271C2×D4—1662no—
1272C2×D4—1662no—
1273C2×D4—1662no—
1274C2×D4—1662no—
1275C2×D4—1662no—
1276C2×D4—1662no—
1277C2×D4—1662no—
1278C2×D4—1662no—
1279C2×D4—1662no—
1280C2×D4—1662no—
1281C2×D4—1662no—
1282C2×D4—1662no—
1283C2×D4—1662no—
1284C2×D4C2×D33214yes—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—3321no—
1296C22×C4—3321no—
1297C22×C4—3321no—
1298C22×C4—3321no—
1299C22×C4—3321no—
1300C22×C4—3321no—
1301C22×C4—3321no—
1302C22×C4—3321no—
1303C22×C4—33216no—
1304C22×C4—3321no—
1305C22×C4—831no—
1306C22×C4—831no—
1307C22×C4—831no—
1308C22×C4—831no—
1309C22×C4—831no—
1310C22×C4—831no—
1311C22×C4—831no—
1312C22×C4—831no—
1313C22×C4—831no—
1314C22×C4—831no—
1315C22×C4—831no—
1316C22×C4—831no—
1317C22×C4—1662no—
1318C22×C4—1662no—
1319C22×C4—1662no—
1320C22×C4—1662no—
1321C22×C4—1662no—
1322C22×C4—1662no—
1323C22×C4—1662no—
1324C22×C4—1662no—
1325C22×C4—1662no—
1326C22×C4—1662no—
1327C22×C4—1662no—
1328C22×C4—1662no—
1329C22×C4C2×D33214yes—
1330C22×C4C2×D33214yes—
1331C22×C4C23×D8311yescharacteristic
1332C22×C4C23×D8311yescharacteristic
1333C22×C4C23×D8311yescharacteristic
1334C22×C4C23×D8311yescharacteristic
1335C22×C4C23×D8311yescharacteristic
1336C22×C4C23×D8311yescharacteristic
1337C22×C4C23×D8311yescharacteristic
1338C22×C4C23×D8311yescharacteristic
1339C22×C4C23×D8311yescharacteristic
1340C22×C4C23×D8311yescharacteristic
1341C22×C4C23×D8311yescharacteristic
1342C22×C4C23×D8311yescharacteristic
1343C22×C4C23×D8311yescharacteristic
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—41no—
1347C4⋊C4—41no—
1348C4⋊C4—3321no—
1349C4⋊C4—3321no—
1350C4⋊C4—3321no—
1351C4⋊C4—3321no—
1352C4⋊C4—3321no—
1353C4⋊C4—3321no—
1354C4⋊C4—3321no—
1355C4⋊C4—3321no—
1356C4⋊C4—3321no—
1357C4⋊C4—3321no—
1358C4⋊C4—1662no—
1359C4⋊C4—1662no—
1360C4⋊C4—1662no—
1361C4⋊C4—1662no—
1362C4⋊C4—1662no—
1363C4⋊C4—1662no—
1364C4⋊C4—1662no—
1365C4⋊C4—1662no—
1366C4⋊C4—1662no—
1367C4⋊C4—1662no—
1368C4⋊C4—1662no—
1369C4⋊C4—1662no—
1370C4⋊C4—1662no—
1371C4⋊C4—1662no—
1372C4⋊C4—1662no—
1373C4⋊C4—1662no—
1374C4⋊C4—1662no—
1375C4⋊C4C2×D33214yes—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—3321no—
1383C22⋊C4—3321no—
1384C22⋊C4—3321no—
1385C22⋊C4—3321no—
1386C22⋊C4—3321no—
1387C22⋊C4—3321no—
1388C22⋊C4—3321no—
1389C22⋊C4—3321no—
1390C22⋊C4—3321no—
1391C22⋊C4—3321no—
1392C22⋊C4—3321no—
1393C22⋊C4—3321no—
1394C22⋊C4—3321no—
1395C22⋊C4—3321no—
1396C22⋊C4—3321no—
1397C22⋊C4—3321no—
1398C22⋊C4—3321no—
1399C22⋊C4—3321no—
1400C22⋊C4—3321no—
1401C22⋊C4—3321no—
1402C22⋊C4—3321no—
1403C22⋊C4—1662no—
1404C22⋊C4—1662no—
1405C22⋊C4—1662no—
1406C22⋊C4—1662no—
1407C22⋊C4—1662no—
1408C22⋊C4—1662no—
1409C22⋊C4—1662no—
1410C22⋊C4—1662no—
1411C22⋊C4—1662no—
1412C22⋊C4—1662no—
1413C22⋊C4—1662no—
1414C22⋊C4—1662no—
1415C22⋊C4—1662no—
1416C22⋊C4—1662no—
1417C22⋊C4—1662no—
1418C22⋊C4—1662no—
1419C22⋊C4—1662no—
1420C22⋊C4—1662no—
1421C22⋊C4—1662no—
1422C22⋊C4—1662no—
1423C22⋊C4—1662no—
1424C22⋊C4—1662no—
1425C22⋊C4—1662no—
1426C22⋊C4C2×D33214yes—
1427C22⋊C4C2×D33214yes—
1428C42—41no—
1429C42—41no—
1430C42—1662no—
1431C42—1662no—
1432C42—1662no—
1433C42—1662no—
1434C42C2×D33214yes—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—3324no—
1448C23—3324no—
1449C23—3324no—
1450C23—3324no—
1451C23—3324no—
1452C23—3324no—
1453C23—3324no—
1454C23—832no—
1455C23—832no—
1456C23—1661no—
1457C23—1661no—
1458C23—1661no—
1459C23—1661no—
1460C23—1661no—
1461C23—1661no—
1462C23—1661no—
1463C23—1661no—
1464C23—1661no—
1465C23—1661no—
1466C23—1661no—
1467C23—1661no—
1468C23—1661no—
1469C23—1661no—
1470C23—1661no—
1471C23—1661no—
1472C23—1661no—
1473C23—1661no—
1474C23—1661no—
1475C23—1661no—
1476C23—1661no—
1477C23—1661no—
1478C23—1661no—
1479C23—1661no—
1480C23—1661no—
1481C23—1661no—
1482C23C22×D33212yes—
1483C23C22×D33212yes—
1484C23C24×D8311yescharacteristic
1485Q8—3324no—
1486Q8—3324no—
1487Q8—6642no—
1488Q8—6642no—
1489D4—44no—
1490D4—3324no—
1491D4—3324no—
1492D4—3324no—
1493D4—3324no—
1494D4—3324no—
1495D4—3324no—
1496D4—6642no—
1497D4—6642no—
1498D4—6642no—
1499D4—6642no—
1500D4—6642no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—44no—
1536C2×C4—44no—
1537C2×C4—82no—
1538C2×C4—82no—
1539C2×C4—3324no—
1540C2×C4—3324no—
1541C2×C4—3324no—
1542C2×C4—3324no—
1543C2×C4—3324no—
1544C2×C4—3324no—
1545C2×C4—832no—
1546C2×C4—1668no—
1547C2×C4—1661no—
1548C2×C4—1661no—
1549C2×C4—1661no—
1550C2×C4—1661no—
1551C2×C4—1661no—
1552C2×C4—1661no—
1553C2×C4—1661no—
1554C2×C4—1661no—
1555C2×C4—1661no—
1556C2×C4—1661no—
1557C2×C4—1661no—
1558C2×C4—1661no—
1559C2×C4—1661no—
1560C2×C4—1661no—
1561C2×C4—1661no—
1562C2×C4—1661no—
1563C2×C4—1661no—
1564C2×C4—1661no—
1565C2×C4—1661no—
1566C2×C4—1661no—
1567C2×C4—1661no—
1568C2×C4—1661no—
1569C2×C4—1661no—
1570C2×C4—1661no—
1571C2×C4—1661no—
1572C2×C4—1661no—
1573C2×C4—1661no—
1574C2×C4—1661no—
1575C2×C4—1661no—
1576C2×C4—1661no—
1577C2×C4—1661no—
1578C2×C4—1661no—
1579C2×C4—1661no—
1580C2×C4—1661no—
1581C2×C4—1661no—
1582C2×C4C22×D33212yes—
1583C2×C4C22×D33212yes—
1584C2×C4C22×D33212yes—
1585C2×C4C22×D33212yes—
1586C2×C4C22×D33212yes—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—33216no—
1602C22—3321no—
1603C22—3321no—
1604C22—3321no—
1605C22—3321no—
1606C22—3321no—
1607C22—3321no—
1608C22—3321no—
1609C22—3321no—
1610C22—3321no—
1611C22—3321no—
1612C22—3321no—
1613C22—3321no—
1614C22—3321no—
1615C22—3321no—
1616C22—3321no—
1617C22—3321no—
1618C22—3321no—
1619C22—3321no—
1620C22—3321no—
1621C22—3321no—
1622C22—3321no—
1623C22—3321no—
1624C22—1662no—
1625C22—1662no—
1626C22—1662no—
1627C22—1662no—
1628C22—1662no—
1629C22—1662no—
1630C22C23×D33211yescharacteristic
1631C22H(5,𝔽2)×D8311yescharacteristic
1632C22H(5,𝔽2)×D8311yescharacteristic
1633C222−1+4×D8311yescharacteristic
1634C22#1912853611yescharacteristic
1635C22#1912853711yescharacteristic
1636C22#1912853711yescharacteristic
1637C4—22no—
1638C4—22no—
1639C4—22no—
1640C4—22no—
1641C4—22no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—3321no—
1651C4—3321no—
1652C4—3321no—
1653C4—3321no—
1654C4—3321no—
1655C4—3321no—
1656C4—3321no—
1657C4—3321no—
1658C4—3321no—
1659C4—3321no—
1660C4—3321no—
1661C4—1662no—
1662C2—42no—
1663C2—42no—
1664C2—3322no—
1665C2—3322no—
1666C2—6641no—
1667C2—6641no—
1668C2#2492079611yescharacteristic
1669C2#2492109911yescharacteristic
1670C2#2492114411yescharacteristic
1671C2#2492163011yescharacteristic
1672C2#2492167111yescharacteristic
1673C2#2492173411yescharacteristic
1674C2#2492175511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2318C2
hypercenter#2318D83
hypocenterC83#36712
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2318

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19128316C2semidirect
2. C2×#19128210C2semidirect
3. #24915756C2semidirect
4. #24915751C2semidirect
5. #24914011C2semidirect
6. #24913996C2semidirect
7. #24913957C2semidirect
8. #24913942C2semidirect
9. #24913912C2semidirect
10. #24913867C2semidirect
11. #24913852C2semidirect
12. #24913842C2semidirect
13. #24913776C2semidirect
14. #24913767C2semidirect
15. #24913747C2semidirect
16. #24913742C2semidirect
17. #24913717C2semidirect
18. #24913697C2semidirect
19. #24913687C2semidirect
20. #24913669C2semidirect
21. #24913383C2semidirect
22. #24913304C2semidirect
23. #24913140C2semidirect
24. #24913069C2semidirect
25. #24913042C2semidirect
26. #24913031C2semidirect
27. #24912822C2semidirect
28. #24912643C2semidirect
29. #24911091C2semidirect
30. #24911073C2semidirect
31. C83×#2318C2semidirect
35. C2×#14581792C22semidirect
36. C2×#14581791C22semidirect
38. C2×#14581785C22semidirect
42. C2×#14581778C22semidirect
47. C2×#14581775C22semidirect
51. C2×#14581772C22semidirect
53. C2×#14581771C22semidirect
57. C2×#14581766C22semidirect
64. C2×C4×Dic166C22semidirect
69. C2×#14581749C22semidirect
70. #19127641C22semidirect
71. #19127641C22semidirect
74. #19127638C22semidirect
75. #19127638C22semidirect
76. #19127633C22semidirect
77. #19127633C22semidirect
78. #19127631C22semidirect
79. #19127631C22semidirect
81. #19127628C22semidirect
85. #19127626C22semidirect
87. #19127623C22semidirect
88. #19127623C22semidirect
89. #19127623C22semidirect
90. #19127622C22semidirect
91. #19127622C22semidirect
92. #19127622C22semidirect
93. #19127622C22semidirect
97. #19127618C22semidirect
105. #19127617C22semidirect
106. #19127617C22semidirect
107. #19127617C22semidirect
111. #19127614C22semidirect
112. #19127614C22semidirect
113. #19127614C22semidirect
118. #19127607C22semidirect
123. #19127600C22semidirect
124. #19127600C22semidirect
125. #19127599C22semidirect
130. #19127593C22semidirect
131. #19127593C22semidirect
133. #19127592C22semidirect
134. #19127586C22semidirect
135. #19127586C22semidirect
136. #19127586C22semidirect
137. #19127586C22semidirect
138. #19127586C22semidirect
139. #19127586C22semidirect
143. #19127580C22semidirect
150. #19127579C22semidirect
151. #19127579C22semidirect
162. #19127575C22semidirect
163. #19127575C22semidirect
164. #19127575C22semidirect
165. #19127575C22semidirect
167. #19127561C22semidirect
168. #19127561C22semidirect
177. #387×C83C22semidirect
178. #387×C83C22semidirect
181. #385×C83C22semidirect
182. #385×C83C22semidirect
183. #383×C83C22semidirect
184. #382×C83C22semidirect
187. C4×C22⋊C4×C83C22semidirect
188. C2×#95×C83C22semidirect
354. C4×D4×C83D4semidirect
868. #2318D83semidirect
869. C83#36712semidirect
981. #387C2×D83semidirect
982. #387C2×D83semidirect
1011. #385C2×D83semidirect
1012. #385C2×D83semidirect
1013. #383C2×D83semidirect
1014. #382C2×D83semidirect
1025. C4×C22⋊C4C2×D83semidirect
1026. C2×#95C2×D83semidirect
1093. C4×D4D332semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191283162
C2×#191282102
#249157562
#249157512
#249140112
#249139962
#249139572
#249139422
#249139122
#249138672
#249138522
#249138422
#249137762
#249137672
#249137472
#249137422
#249137172
#249136972
#249136872
#249136692
#249133832
#249133042
#249131402
#249130692
#249130422
#249130312
#249128222
#249126432
#249110912
#249110732
C83×#23182
#3671283