Finite Group Databasebeta

← #35568966

Subgroups — #35568966

Order 21248.

2500 conjugacy classes of subgroups.

The subgroup lattice has 1560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128380C211yesmaximal, characteristic
2#24910653C211yesmaximal, characteristic, complemented
3#24910652C211yesmaximal, characteristic, complemented
4#24910632C211yesmaximal, characteristic, complemented
5#24910607C211yesmaximal, characteristic, complemented
6#24910471C211yesmaximal, characteristic, complemented
7#24910466C211yesmaximal, characteristic, complemented
8#24910461C211yesmaximal, characteristic, complemented
9#24910454C211yesmaximal, characteristic, complemented
10#24910443C211yesmaximal, characteristic
11D4×C4⋊Dic83C211yesmaximal, characteristic, complemented
12#24910359C211yesmaximal, characteristic, complemented
13#24910321C211yesmaximal, characteristic, complemented
14#24910320C211yesmaximal, characteristic, complemented
15#24910315C211yesmaximal, characteristic, complemented
16#24910310C211yesmaximal, characteristic, complemented
17#24910243C211yesmaximal, characteristic, complemented
18#24910234C211yesmaximal, characteristic, complemented
19#24910196C211yesmaximal, characteristic, complemented
20#24910190C211yesmaximal, characteristic, complemented
21#24910172C211yesmaximal, characteristic, complemented
22#24910137C211yesmaximal, characteristic, complemented
23#24910133C211yesmaximal, characteristic, complemented
24#24910129C211yesmaximal, characteristic, complemented
25#24910092C211yesmaximal, characteristic, complemented
26#24910088C211yesmaximal, characteristic, complemented
27#24910082C211yesmaximal, characteristic, complemented
28#24909968C211yesmaximal, characteristic
29C2×#19127575C211yesmaximal, characteristic, complemented
30#385×D83C211yesmaximal, characteristic, complemented
31C83×#2318C211yesmaximal, characteristic, complemented
32C23×C4×D83C2211yescharacteristic
33#19128380C4116yescomplemented
34C2×#14581787C2211yescharacteristic
35C2×#14581786C2211yescharacteristic
36C2×#14581778C2211yescharacteristic
37C2×#14581775C2211yescharacteristic
38C2×#14581774C2211yescharacteristic
39C2×#14581773C2211yescharacteristic
40C2×#14581771C2211yescharacteristic
41C2×#14581770C2211yescharacteristic
42C2×#14581760C2211yescharacteristic
43C2×C4×Dic166C2211yescharacteristic, complemented
44C2×D4×Dic83C2211yescharacteristic
45C2×D4×Dic83C2211yescharacteristic
46C2×C4×C22⋊D83C2211yescharacteristic
47C2×(C22⋊D83)⋊C4C2211yescharacteristic
48C2×(C22⋊D83)⋊C4C2211yescharacteristic
49C2×(C22⋊D83)⋊C4C2211yescharacteristic
50C2×#14581750C2211yescharacteristic
51C2×#14581749C2211yescharacteristic
52C2×#14581748C2211yescharacteristic
53C2×#14581748C2211yescharacteristic
54C22×C4⋊Dic83C2211yescharacteristic
55C22×C4⋊Dic83C2211yescharacteristic, complemented
56C22×Dic83⋊C4C2211yescharacteristic
57C2×C4⋊C4×D83C2211yescharacteristic
58C2×C4⋊C4×D83C2211yescharacteristic
59C22×(C2×D83)⋊C4C2211yescharacteristic
60C22×(C2×D83)⋊C4C2211yescharacteristic
61C2×C22⋊C4×D83C2211yescharacteristic
62C2×C22⋊C4×D83C2211yescharacteristic
63#19127607C2211yescharacteristic, complemented
64#19127605C2211yescharacteristic, complemented
65#19127605C2211yescharacteristic, complemented
66#19127601C2211yescharacteristic
67#19127600C2211yescharacteristic, complemented
68#19127600C2211yescharacteristic, complemented
69#19127599C2211yescharacteristic, complemented
70#19127598C2211yescharacteristic, complemented
71#19127598C2211yescharacteristic, complemented
72#19127598C2211yescharacteristic, complemented
73#19127598C2211yescharacteristic, complemented
74#19127598C2211yescharacteristic, complemented
75#19127598C2211yescharacteristic, complemented
76#19127598C2211yescharacteristic, complemented
77#19127598C2211yescharacteristic, complemented
78#19127598C2211yescharacteristic, complemented
79#19127596C2211yescharacteristic, complemented
80#19127596C2211yescharacteristic, complemented
81#19127595C2211yescharacteristic, complemented
82#19127593C2211yescharacteristic
83#19127593C2211yescharacteristic
84#19127593C2211yescharacteristic
85#19127593C2211yescharacteristic
86#19127593C2211yescharacteristic
87#19127592C2211yescharacteristic
88#19127592C2211yescharacteristic
89#19127591C2211yescharacteristic
90#19127591C2211yescharacteristic
91#19127590C2211yescharacteristic
92#19127589C2211yescharacteristic, complemented
93#19127589C2211yescharacteristic, complemented
94#19127589C2211yescharacteristic, complemented
95#19127588C2211yescharacteristic, complemented
96#19127588C2211yescharacteristic, complemented
97#19127588C2211yescharacteristic, complemented
98#19127588C2211yescharacteristic, complemented
99#19127588C2211yescharacteristic, complemented
100#19127588C2211yescharacteristic, complemented
101#19127588C2211yescharacteristic, complemented
102#19127584C2211yescharacteristic, complemented
103#19127584C2211yescharacteristic, complemented
104#19127583C2211yescharacteristic, complemented
105#19127583C2211yescharacteristic, complemented
106#19127583C2211yescharacteristic, complemented
107#19127582C2211yescharacteristic, complemented
108#19127582C2211yescharacteristic, complemented
109#19127578C2211yescharacteristic
110#19127577C2211yescharacteristic
111#19127577C2211yescharacteristic
112#19127577C2211yescharacteristic
113#19127576C2211yescharacteristic
114#19127576C2211yescharacteristic
115#19127576C2211yescharacteristic, complemented
116#19127576C2211yescharacteristic, complemented
117#19127575C2211yescharacteristic
118#19127575C2211yescharacteristic
119#19127575C2211yescharacteristic
120#19127575C2211yescharacteristic
121#19127575C2211yescharacteristic
122#19127575C2211yescharacteristic
123#19127575C2211yescharacteristic
124#19127575C2211yescharacteristic
125#19127575C2211yescharacteristic
126#19127575C2211yescharacteristic
127#19127575C2211yescharacteristic
128#19127575C2211yescharacteristic
129#19127575C2211yescharacteristic
130#19127575C2211yescharacteristic
131#19127575C2211yescharacteristic
132#19127574C2211yescharacteristic
133#19127574C2211yescharacteristic
134#19127573C2211yescharacteristic
135#19127573C2211yescharacteristic
136#19127573C2211yescharacteristic, complemented
137#19127573C2211yescharacteristic, complemented
138#19127573C2211yescharacteristic, complemented
139#19127572C2211yescharacteristic
140#19127572C2211yescharacteristic
141#19127571C2211yescharacteristic, complemented
142#19127570C2211yescharacteristic, complemented
143#19127570C2211yescharacteristic, complemented
144#19127568C2211yescharacteristic, complemented
145#19127566C2211yescharacteristic, complemented
146#19127565C2211yescharacteristic, complemented
147#19127565C2211yescharacteristic, complemented
148#19127563C2211yescharacteristic
149#19127562C2211yescharacteristic
150#19127561C2211yescharacteristic
151#19127561C2211yescharacteristic, complemented
152#19127558C2211yescharacteristic
153#19127556C2211yescharacteristic
154C4⋊C4×Dic83C2211yescharacteristic, complemented
155C4×C4⋊Dic83C2211yescharacteristic, complemented
156C4×C4⋊Dic83C2211yescharacteristic, complemented
157#19127552C2211yescharacteristic, complemented
158C22⋊C4×Dic83C2211yescharacteristic
159C22⋊C4×Dic83C2211yescharacteristic
160C22⋊C4×Dic83C2211yescharacteristic, complemented
161C4×(C2×D83)⋊C4C2211yescharacteristic
162C4×(C2×D83)⋊C4C2211yescharacteristic
163C4×C22⋊Dic83C2211yescharacteristic
164C4×C22⋊Dic83C2211yescharacteristic
165#19127548C2211yescharacteristic
166#19127548C2211yescharacteristic
167#19127548C2211yescharacteristic
168#19127548C2211yescharacteristic
169#19127546C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic
171#95×D83C2211yescharacteristic
172#95×D83C2211yescharacteristic
173C2×C4×D4×C83C2211yescharacteristic
174#388×C83C2211yescharacteristic, complemented
175#388×C83C2211yescharacteristic, complemented
176#387×C83C2211yescharacteristic, complemented
177#387×C83C2211yescharacteristic, complemented
178#386×C83C2211yescharacteristic
179#386×C83C2211yescharacteristic
180#385×C83C2211yescharacteristic
181#385×C83C2211yescharacteristic
182#383×C83C2211yescharacteristic, complemented
183#382×C83C2211yescharacteristic, complemented
184#381×C83C2211yescharacteristic, complemented
185#380×C83C2211yescharacteristic, complemented
186C4×C22⋊C4×C83C2211yescharacteristic
187C2×#95×C83C2211yescharacteristic
188C24×D83C2311yescharacteristic
189C22×Dic166C2311yescharacteristic
190C22×C22⋊D83C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C22×C4×D83—42no—
198C22×C4×D83—42no—
199C22×C4×D83—42no—
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203C22×C4×D83C2311yescharacteristic
204C22×C4×D83C2311yescharacteristic
205C22×C4×D83C2311yescharacteristic
206C22×C4×D83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208#14581787C2×C418yescomplemented
209#14581786C2×C418yescomplemented
210#14581778C2×C418yescomplemented
211#14581775C2×C418yescomplemented
212#14581774C2×C418yescomplemented
213#14581773C2×C418yescomplemented
214#14581771C2×C418yescomplemented
215#14581770C2×C418yescomplemented
216#14581760C2×C418yes—
217C4×Dic166—42no—
218D4×Dic83—42no—
219D4×Dic83—42no—
220C4×C22⋊D83C2×C418yescomplemented
221(C22⋊D83)⋊C4—42no—
222(C22⋊D83)⋊C4—42no—
223(C22⋊D83)⋊C4—42no—
224#14581750—42no—
225#14581749C2×C418yescomplemented
226#14581748—42no—
227#14581748C2×C418yescomplemented
228C2×C4⋊Dic83—42no—
229C2×C4⋊Dic83—42no—
230C2×C4⋊Dic83C2311yescharacteristic
231C2×C4⋊Dic83C2311yescharacteristic
232C2×C4⋊Dic83C2311yescharacteristic
233C2×C4⋊Dic83C2311yescharacteristic
234C2×C4⋊Dic83C2311yescharacteristic
235C2×C4⋊Dic83C2311yescharacteristic
236C2×C4⋊Dic83C2311yescharacteristic
237C2×C4⋊Dic83C2311yescharacteristic
238C2×C4⋊Dic83C2311yescharacteristic
239C2×C4⋊Dic83C2311yescharacteristic
240C2×C4⋊Dic83C2311yescharacteristic
241C2×C4⋊Dic83C2311yescharacteristic
242C2×C4⋊Dic83C2311yescharacteristic
243C2×Dic83⋊C4—42no—
244C2×Dic83⋊C4C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×Dic83⋊C4C2311yescharacteristic
254C2×Dic83⋊C4C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C2×Dic83⋊C4C2311yescharacteristic
257C2×Dic83⋊C4C2311yescharacteristic
258C2×Dic83⋊C4C2311yescharacteristic
259C2×Dic83⋊C4C2311yescharacteristic
260C2×Dic83⋊C4C2311yescharacteristic
261C2×Dic83⋊C4C2311yescharacteristic
262C2×Dic83⋊C4C2311yescharacteristic
263C2×Dic83⋊C4C2311yescharacteristic
264C4⋊C4×D83—42no—
265C4⋊C4×D83—42no—
266C2×C22⋊Dic83C2311yescharacteristic
267C2×C22⋊Dic83C2311yescharacteristic
268C2×C22⋊Dic83C2311yescharacteristic
269C2×C22⋊Dic83C2311yescharacteristic
270C2×C22⋊Dic83C2311yescharacteristic
271C2×C22⋊Dic83C2311yescharacteristic
272C2×C22⋊Dic83C2311yescharacteristic
273C2×C22⋊Dic83C2311yescharacteristic
274C2×(C2×D83)⋊C4—42no—
275C2×(C2×D83)⋊C4C2×C418yescomplemented
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C2×(C2×D83)⋊C4C2311yescharacteristic
283C2×(C2×D83)⋊C4C2311yescharacteristic
284C2×(C2×D83)⋊C4C2311yescharacteristic
285C2×(C2×D83)⋊C4C2311yescharacteristic
286C2×(C2×D83)⋊C4C2311yescharacteristic
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
294C22⋊C4×D83—42no—
295C22⋊C4×D83C2×C418yescomplemented
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C2×C4×Dic83C2311yescharacteristic
304C2×C4×Dic83C2311yescharacteristic
305C2×C4×Dic83C2311yescharacteristic
306C2×C4×Dic83C2311yescharacteristic
307C2×C4×Dic83C2311yescharacteristic
308C2×C4×Dic83C2311yescharacteristic
309C2×C4×Dic83C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
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
340C22×D4×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342C23×C4×C83C2311yescharacteristic
343C23×C4×C83C2311yescharacteristic
344C23×C4×C83C2311yescharacteristic
345C4×D4×C83C2×C418yescomplemented
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C4⋊C4×C83C2311yescharacteristic
350C2×C4⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C42×C83C2311yescharacteristic
360C2×C42×C83C2311yescharacteristic
361C2×C42×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370#95×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83—22no—
377C23×D83—22no—
378C23×D83—22no—
379C23×D83—22no—
380C23×D83—41no—
381C23×D83—41no—
382C23×D83C22×C414yes—
383C23×D83C2411yescharacteristic
384C23×D83C2411yescharacteristic
385C2×Dic166—41no—
386C2×Dic166—41no—
387C2×Dic166C22×C414yescomplemented
388C2×C22⋊D83—22no—
389C2×C22⋊D83—22no—
390C2×C22⋊D83—41no—
391C2×C22⋊D83—41no—
392C2×C22⋊D83C22×C414yes—
393C2×C22⋊D83C22×C414yes—
394C22×Dic83—22no—
395C22×Dic83—22no—
396C22×Dic83—22no—
397C22×Dic83—22no—
398C22×Dic83—22no—
399C22×Dic83—22no—
400C22×Dic83—41no—
401C22×Dic83—41no—
402C22×Dic83—41no—
403C22×Dic83—41no—
404C22×Dic83—41no—
405C22×Dic83—41no—
406C22×Dic83—41no—
407C22×Dic83—41no—
408C22×Dic83C22×C414yes—
409C22×Dic83C2411yescharacteristic
410C22×Dic83C2411yescharacteristic
411C22×Dic83C2411yescharacteristic
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C22×Dic83C2411yescharacteristic
420C22×Dic83C2411yescharacteristic
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2411yescharacteristic
423C2×C4×D83—22no—
424C2×C4×D83—22no—
425C2×C4×D83—22no—
426C2×C4×D83—22no—
427C2×C4×D83—22no—
428C2×C4×D83—22no—
429C2×C4×D83—22no—
430C2×C4×D83—22no—
431C2×C4×D83—41no—
432C2×C4×D83—41no—
433C2×C4×D83—41no—
434C2×C4×D83—41no—
435C2×C4×D83—41no—
436C2×C4×D83—41no—
437C2×C4×D83—41no—
438C2×C4×D83—41no—
439C2×C4×D83—41no—
440C2×C4×D83—41no—
441C2×C4×D83—416no—
442C2×C4×D83—41no—
443C2×C4×D83—41no—
444C2×C4×D83—41no—
445C2×C4×D83—41no—
446C2×C4×D83C22×C414yes—
447C2×C4×D83C22×C414yes—
448C4⋊Dic83—22no—
449C4⋊Dic83—22no—
450C4⋊Dic83—22no—
451C4⋊Dic83—41no—
452C4⋊Dic83—41no—
453C4⋊Dic83—41no—
454C4⋊Dic83—41no—
455C4⋊Dic83—41no—
456C4⋊Dic83—41no—
457C4⋊Dic83—41no—
458C4⋊Dic83—41no—
459C4⋊Dic83—41no—
460C4⋊Dic83C22×C414yescomplemented
461Dic83⋊C4—22no—
462Dic83⋊C4—41no—
463Dic83⋊C4—41no—
464Dic83⋊C4—41no—
465Dic83⋊C4—41no—
466Dic83⋊C4—41no—
467Dic83⋊C4—41no—
468Dic83⋊C4—41no—
469Dic83⋊C4—41no—
470Dic83⋊C4—41no—
471Dic83⋊C4—41no—
472Dic83⋊C4—41no—
473Dic83⋊C4—41no—
474Dic83⋊C4—41no—
475Dic83⋊C4C22×C414yescomplemented
476Dic83⋊C4C22×C414yescomplemented
477Dic83⋊C4C22×C414yescomplemented
478Dic83⋊C4C22×C414yescomplemented
479Dic83⋊C4C22×C414yescomplemented
480Dic83⋊C4C22×C414yescomplemented
481C22⋊Dic83—22no—
482C22⋊Dic83—22no—
483C22⋊Dic83—41no—
484C22⋊Dic83—41no—
485C22⋊Dic83C22×C414yes—
486C22⋊Dic83C22×C414yes—
487C22⋊Dic83C22×C414yescomplemented
488C22⋊Dic83C22×C414yescomplemented
489(C2×D83)⋊C4—22no—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—22no—
492(C2×D83)⋊C4—22no—
493(C2×D83)⋊C4—41no—
494(C2×D83)⋊C4—41no—
495(C2×D83)⋊C4—41no—
496(C2×D83)⋊C4—41no—
497(C2×D83)⋊C4—41no—
498(C2×D83)⋊C4—41no—
499(C2×D83)⋊C4C22×C414yes—
500(C2×D83)⋊C4C22×C414yes—
501(C2×D83)⋊C4C22×C414yes—
502(C2×D83)⋊C4C22×C414yes—
503(C2×D83)⋊C4C22×C414yes—
504(C2×D83)⋊C4C22×C414yes—
505(C2×D83)⋊C4C22×C414yes—
506(C2×D83)⋊C4C22×C414yes—
507C4×Dic83—22no—
508C4×Dic83—41no—
509C4×Dic83—41no—
510C4×Dic83—41no—
511C4×Dic83—41no—
512C4×Dic83—41no—
513C4×Dic83—41no—
514C4×Dic83—41no—
515C4×Dic83—41no—
516C4×Dic83—41no—
517C4×Dic83—41no—
518C4×Dic83—41no—
519C4×Dic83C22×C414yescomplemented
520C4×Dic83C22×C414yescomplemented
521C24×C83C2411yescharacteristic
522C24×C83C2411yescharacteristic
523C2×D4×C83—22no—
524C2×D4×C83—22no—
525C2×D4×C83C22×C414yes—
526C22×C4×C83—22no—
527C22×C4×C83—22no—
528C22×C4×C83—41no—
529C22×C4×C83—41no—
530C22×C4×C83—41no—
531C22×C4×C83—41no—
532C22×C4×C83—41no—
533C22×C4×C83—41no—
534C22×C4×C83—41no—
535C22×C4×C83—41no—
536C22×C4×C83C22×C414yes—
537C22×C4×C83C22×C414yescomplemented
538C22×C4×C83C2411yescharacteristic
539C22×C4×C83C2411yescharacteristic
540C22×C4×C83C2411yescharacteristic
541C22×C4×C83C2411yescharacteristic
542C22×C4×C83C2411yescharacteristic
543C22×C4×C83C2411yescharacteristic
544C22×C4×C83C2411yescharacteristic
545C22×C4×C83C2411yescharacteristic
546C22×C4×C83C2411yescharacteristic
547C22×C4×C83C2411yescharacteristic
548C22×C4×C83C2411yescharacteristic
549C22×C4×C83C2411yescharacteristic
550C22×C4×C83C2411yescharacteristic
551C4⋊C4×C83—41no—
552C4⋊C4×C83—41no—
553C4⋊C4×C83—41no—
554C4⋊C4×C83—41no—
555C4⋊C4×C83C22×C414yescomplemented
556C22⋊C4×C83—22no—
557C22⋊C4×C83—22no—
558C22⋊C4×C83—41no—
559C22⋊C4×C83—41no—
560C22⋊C4×C83—41no—
561C22⋊C4×C83—41no—
562C22⋊C4×C83C22×C414yes—
563C22⋊C4×C83C22×C414yescomplemented
564C42×C83—41no—
565C42×C83—41no—
566C42×C83C22×C414yescomplemented
567C23×C83—21no—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83—21no—
575C23×C83—21no—
576C23×C83—21no—
577C23×C83C23×C412yes—
578C23×C83C23×C412yes—
579C23×C83H(5,𝔽2)12yes—
580C23×C832−1+412yes—
581C23×C83C2511yescharacteristic
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—28no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83—28no—
594C22×D83—44no—
595C22×D83—44no—
596C22×D83—44no—
597C22×D83—44no—
598C22×D83—44no—
599C22×D83C23×C412yes—
600C22×D83C23×C412yes—
601C22×D83H(5,𝔽2)12yes—
602C22×D832−1+412yes—
603D4×C83—28no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—21no—
623C2×C4×C83—21no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—21no—
628C2×C4×C83—21no—
629C2×C4×C83—21no—
630C2×C4×C83—21no—
631C2×C4×C83—21no—
632C2×C4×C83—21no—
633C2×C4×C83—21no—
634C2×C4×C83—21no—
635C2×C4×C83—21no—
636C2×C4×C83—21no—
637C2×C4×C83—21no—
638C2×C4×C83—44no—
639C2×C4×C83—44no—
640C2×C4×C83—44no—
641C2×C4×C83—82no—
642C2×C4×C83C23×C412yes—
643C2×C4×C83C23×C412yes—
644C2×C4×C83C23×C412yes—
645C2×C4×C83C23×C412yes—
646C2×C4×C83C23×C412yes—
647C22⋊D83—28no—
648C22⋊D83—44no—
649C2×Dic83—28no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—21no—
674C2×Dic83—21no—
675C2×Dic83—21no—
676C2×Dic83—21no—
677C2×Dic83—21no—
678C2×Dic83—21no—
679C2×Dic83—21no—
680C2×Dic83—21no—
681C2×Dic83—21no—
682C2×Dic83—21no—
683C2×Dic83—21no—
684C2×Dic83—21no—
685C2×Dic83—44no—
686C2×Dic83—82no—
687C2×Dic83—82no—
688C2×Dic83—82no—
689C2×Dic83C23×C412yes—
690C2×Dic83C23×C412yes—
691C2×Dic83C23×C412yes—
692C2×Dic83C23×C412yes—
693C2×Dic83C23×C412yes—
694C2×Dic83C23×C412yes—
695C2×Dic83H(5,𝔽2)12yes—
696C4×D83—28no—
697C4×D83—44no—
698C4×D83—44no—
699C4×D83—44no—
700C4×D83—44no—
701C4×D83—44no—
702C4×D83—82no—
703C4×D83—82no—
704Dic166—44no—
705C22×C83—22no—
706C22×C83—22no—
707C22×C83—22no—
708C22×C83—22no—
709C22×C83—22no—
710C22×C83—22no—
711C22×C83—22no—
712C22×C83—22no—
713C22×C83—22no—
714C22×C83—41no—
715C22×C83—41no—
716C22×C83—41no—
717C22×C83—41no—
718C22×C83#52014yes—
719C22×C83C24×C411yescharacteristic
720C22×C83C2×H(5,𝔽2)11yescharacteristic
721C22×C83C2×H(5,𝔽2)11yescharacteristic
722C22×C83C2×H(5,𝔽2)11yescharacteristic
723C22×C83C2×2−1+411yescharacteristic
724C22×C83C2×2−1+411yescharacteristic
725C22×C83#58511yescharacteristic
726C2×D83—22no—
727C2×D83—22no—
728C2×D83—22no—
729C2×D83—22no—
730C2×D83—22no—
731C2×D83—22no—
732C2×D83—22no—
733C2×D83—22no—
734C2×D83—22no—
735C2×D83—416no—
736C2×D83—41no—
737C2×D83—41no—
738C2×D83—41no—
739C2×D83—41no—
740C2×D83#52014yes—
741C4×C83—22no—
742C4×C83—22no—
743C4×C83—22no—
744C4×C83—22no—
745C4×C83—22no—
746C4×C83—41no—
747C4×C83—41no—
748C4×C83—41no—
749C4×C83—41no—
750C4×C83—41no—
751C4×C83—41no—
752C4×C83—41no—
753C4×C83—41no—
754Dic83—22no—
755Dic83—22no—
756Dic83—22no—
757Dic83—22no—
758Dic83—22no—
759Dic83—22no—
760Dic83—22no—
761Dic83—41no—
762Dic83—41no—
763Dic83—41no—
764Dic83—41no—
765Dic83—41no—
766Dic83—41no—
767Dic83—41no—
768#34457—831nomaximal, Sylow
769C2×C83—24no—
770C2×C83—42no—
771C2×C83C2×#52011yescharacteristic
772C2×C83C2×#52011yescharacteristic
773C2×C83C4×H(5,𝔽2)11yescharacteristic
774C2×C83#353211yescharacteristic
775C2×C83#353511yescharacteristic
776C2×C83#353511yescharacteristic
777C2×C83#353811yescharacteristic
778D83—24no—
779D83—42no—
780C2×#551—831no—
781#2383—831no—
782#2383—831no—
783#2379—831no—
784#2376—831no—
785#2360—831no—
786#2360—831no—
787#2359—831no—
788#2359—831no—
789#2358—831no—
790D4×C4⋊C4—831no—
791D4×C4⋊C4—831no—
792#2343—831no—
793#2343—831no—
794#2342—831no—
795#2342—831no—
796#2334—831no—
797#2334—831no—
798#2329—831no—
799#2329—831no—
800#2326—831no—
801#2322—831no—
802#2322—831no—
803#2322—831no—
804#2318—831no—
805#2318D8311yescharacteristic, complemented
806#2317—831no—
807#2317—831no—
808C4×#120—831no—
809C2×#385—831no—
810C2×#385—831no—
811C83#3445711yescharacteristic, complemented, Sylow
812C24×C4—831no—
813#551—8316no—
814C2×#126—831no—
815C2×#126—831no—
816C2×#124—831no—
817C2×#123—831no—
818C2×#123—831no—
819C2×#123—831no—
820C2×C22⋊Q8—831no—
821C2×C22⋊Q8—831no—
822C2×#120—831no—
823C2×C4×Q8—831no—
824C2×C4×D4—831no—
825C2×C4×D4—831no—
826C2×C4×D4—831no—
827C2×C4×D4—831no—
828C2×C4×D4—831no—
829C2×C4×D4—831no—
830C2×C4×D4C2×D8311yescharacteristic
831C2×#117—831no—
832C2×#117—831no—
833C2×#117—831no—
834C2×#117—831no—
835C22×C4⋊C4—831no—
836C22×C4⋊C4—831no—
837C22×C4⋊C4—831no—
838C22×C4⋊C4—831no—
839C22×C4⋊C4—831no—
840C22×C22⋊C4—831no—
841C22×C22⋊C4—831no—
842C22×C22⋊C4—831no—
843C22×C22⋊C4—831no—
844#391—831no—
845#391—831no—
846#391—831no—
847#390—831no—
848#389—831no—
849#389—831no—
850#389—831no—
851#389—831no—
852#389—831no—
853#389—831no—
854#389—831no—
855#389—831no—
856#389—831no—
857#389—831no—
858#389—831no—
859#389—831no—
860#389—831no—
861#389—831no—
862#388—831no—
863#388—831no—
864#388—831no—
865#388—831no—
866#388—831no—
867#388—831no—
868#388—831no—
869#388—831no—
870#388—831no—
871#388—831no—
872#388—831no—
873#388—831no—
874#388—831no—
875#388—831no—
876#388C2×D8311yescharacteristic, complemented
877#388C2×D8311yescharacteristic, complemented
878#387—831no—
879#387—831no—
880#387—831no—
881#387—831no—
882#387—831no—
883#387—831no—
884#387—831no—
885#387—831no—
886#387—831no—
887#387—831no—
888#387—831no—
889#387—831no—
890#387—831no—
891#387—831no—
892#387C2×D8311yescharacteristic, complemented
893#387C2×D8311yescharacteristic, complemented
894#386—831no—
895#386—831no—
896#386—831no—
897#386—831no—
898#386C2×D8311yescharacteristic
899#386C2×D8311yescharacteristic
900#385—831no—
901#385—831no—
902#385—831no—
903#385—831no—
904#385—831no—
905#385—831no—
906#385—831no—
907#385—831no—
908#385—831no—
909#385—831no—
910#385—831no—
911#385—831no—
912#385—831no—
913#385—831no—
914#385—831no—
915#385—831no—
916#385—831no—
917#385—831no—
918#385—831no—
919#385—831no—
920#385—831no—
921#385—831no—
922#385—831no—
923#385—831no—
924#385—831no—
925#385—831no—
926#385—831no—
927#385—831no—
928#385C2×D8311yescharacteristic
929#385C2×D8311yescharacteristic
930#384—831no—
931#384—831no—
932#384—831no—
933#383—831no—
934#383C2×D8311yescharacteristic, complemented
935#382—831no—
936#382—831no—
937#382—831no—
938#382C2×D8311yescharacteristic, complemented
939#381—831no—
940#381—831no—
941#381C2×D8311yescharacteristic, complemented
942#380—831no—
943#380—831no—
944#380—831no—
945#380C2×D8311yescharacteristic, complemented
946#379—831no—
947C4×C4⋊C4—831no—
948C4×C4⋊C4—831no—
949C4×C4⋊C4—831no—
950C4×C4⋊C4—831no—
951C4×C22⋊C4—831no—
952C4×C22⋊C4—831no—
953C4×C22⋊C4—831no—
954C4×C22⋊C4—831no—
955C4×C22⋊C4—831no—
956C4×C22⋊C4—831no—
957C4×C22⋊C4—831no—
958C4×C22⋊C4—831no—
959C4×C22⋊C4—831no—
960C4×C22⋊C4—831no—
961C4×C22⋊C4—831no—
962C4×C22⋊C4C2×D8311yescharacteristic
963#376—831no—
964C2×#95—831no—
965C2×#95—831no—
966C2×#95—831no—
967C2×#95C2×D8311yescharacteristic
968C25—831no—
969C22×Q8—831no—
970C22×D4—831no—
971C22×D4—831no—
972C22×D4C22×D8311yescharacteristic
973C23×C4—3322no—
974C23×C4—3322no—
975C23×C4—3322no—
976C23×C4—831no—
977C23×C4—831no—
978C23×C4—831no—
979C23×C4—831no—
980C23×C4—831no—
981C23×C4—831no—
982C23×C4—831no—
983C23×C4—831no—
984C23×C4—831no—
985C23×C4—831no—
986C23×C4—831no—
987C23×C4—831no—
988C23×C4—831no—
989C23×C4C22×D8311yescharacteristic
990C23×C4C22×D8311yescharacteristic
991C23×C4C22×D8311yescharacteristic
992C23×C4C22×D8311yescharacteristic
993#126—838no—
994#126—838no—
995#124—838no—
996#123—838no—
997#123—838no—
998#123—838no—
999C22⋊Q8—838no—
1000C22⋊Q8—838no—
1001#120—838no—
1002C4×Q8—3322no—
1003C4×D4—3322no—
1004C4×D4—3322no—
1005C4×D4—3322no—
1006C4×D4—3322no—
1007C4×D4—3322no—
1008C4×D4—838no—
1009C4×D4C4×D8318yescomplemented
1010#117—3322no—
1011#117—3322no—
1012#117—838no—
1013#117—838no—
1014C2×C4⋊C4—3322no—
1015C2×C4⋊C4—3322no—
1016C2×C4⋊C4—3322no—
1017C2×C4⋊C4—3322no—
1018C2×C4⋊C4—3322no—
1019C2×C4⋊C4—831no—
1020C2×C4⋊C4—831no—
1021C2×C4⋊C4—831no—
1022C2×C4⋊C4—831no—
1023C2×C4⋊C4—831no—
1024C2×C4⋊C4—831no—
1025C2×C4⋊C4—831no—
1026C2×C4⋊C4—831no—
1027C2×C4⋊C4—831no—
1028C2×C4⋊C4—831no—
1029C2×C4⋊C4—831no—
1030C2×C4⋊C4—831no—
1031C2×C4⋊C4—831no—
1032C2×C4⋊C4—831no—
1033C2×C4⋊C4—831no—
1034C2×C4⋊C4—831no—
1035C2×C4⋊C4—831no—
1036C2×C4⋊C4—831no—
1037C2×C4⋊C4—831no—
1038C2×C4⋊C4—831no—
1039C2×C4⋊C4—831no—
1040C2×C4⋊C4—831no—
1041C2×C4⋊C4—831no—
1042C2×C4⋊C4—831no—
1043C2×C4⋊C4—831no—
1044C2×C4⋊C4—831no—
1045C2×C4⋊C4—831no—
1046C2×C4⋊C4—831no—
1047C2×C4⋊C4—831no—
1048C2×C4⋊C4—831no—
1049C2×C4⋊C4—831no—
1050C2×C4⋊C4—831no—
1051C2×C4⋊C4—831no—
1052C2×C4⋊C4C22×D8311yescharacteristic
1053C2×C4⋊C4C22×D8311yescharacteristic
1054C2×C4⋊C4C22×D8311yescharacteristic
1055C2×C4⋊C4C22×D8311yescharacteristic
1056C2×C4⋊C4C22×D8311yescharacteristic
1057C2×C22⋊C4—3322no—
1058C2×C22⋊C4—3322no—
1059C2×C22⋊C4—831no—
1060C2×C22⋊C4—831no—
1061C2×C22⋊C4—831no—
1062C2×C22⋊C4—831no—
1063C2×C22⋊C4—831no—
1064C2×C22⋊C4—831no—
1065C2×C22⋊C4—831no—
1066C2×C22⋊C4—831no—
1067C2×C22⋊C4—831no—
1068C2×C22⋊C4—831no—
1069C2×C22⋊C4—831no—
1070C2×C22⋊C4—831no—
1071C2×C22⋊C4—838no—
1072C2×C22⋊C4—831no—
1073C2×C22⋊C4—831no—
1074C2×C22⋊C4—831no—
1075C2×C22⋊C4—831no—
1076C2×C22⋊C4—831no—
1077C2×C22⋊C4—831no—
1078C2×C22⋊C4—831no—
1079C2×C22⋊C4—831no—
1080C2×C22⋊C4—838no—
1081C2×C22⋊C4—831no—
1082C2×C22⋊C4—831no—
1083C2×C22⋊C4—831no—
1084C2×C22⋊C4—831no—
1085C2×C22⋊C4—831no—
1086C2×C22⋊C4—831no—
1087C2×C22⋊C4C22×D8311yescharacteristic
1088C2×C22⋊C4C22×D8311yescharacteristic
1089C2×C22⋊C4C22×D8311yescharacteristic
1090C2×C22⋊C4C22×D8311yescharacteristic
1091C2×C22⋊C4C22×D8311yescharacteristic
1092C2×C22⋊C4C22×D8311yescharacteristic
1093C2×C22⋊C4C22×D8311yescharacteristic
1094C2×C22⋊C4C22×D8311yescharacteristic
1095C2×C42—831no—
1096C2×C42—831no—
1097C2×C42—831no—
1098C2×C42—831no—
1099C2×C42—831no—
1100C2×C42—831no—
1101C2×C42—831no—
1102C2×C42—831no—
1103C2×C42—831no—
1104C2×C42—831no—
1105C2×C42—831no—
1106C2×C42—831no—
1107C2×C42—831no—
1108C2×C42—831no—
1109C2×C42C22×D8311yescharacteristic
1110C2×C42C22×D8311yescharacteristic
1111C2×C42C22×D8311yescharacteristic
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95—831no—
1116#95—831no—
1117#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95—831no—
1122#95—831no—
1123#95—831no—
1124#95—831no—
1125#95—831no—
1126#95—831no—
1127#95—831no—
1128#95—831no—
1129#95—831no—
1130#95—831no—
1131#95—831no—
1132#95—831no—
1133#95—831no—
1134#95—831no—
1135#95—831no—
1136#95—831no—
1137#95—831no—
1138#95—831no—
1139#95—831no—
1140#95—831no—
1141#95—831no—
1142#95C22×D8311yescharacteristic
1143#95C22×D8311yescharacteristic
1144#95C22×D8311yescharacteristic
1145#95C22×D8311yescharacteristic
1146#95C22×D8311yescharacteristic
1147#95C22×D8311yescharacteristic
1148#95C22×D8311yescharacteristic
1149#95C22×D8311yescharacteristic
1150#95C22×D8311yescharacteristic
1151#95C22×D8311yescharacteristic
1152#95C22×D8311yescharacteristic
1153#95C22×D8311yescharacteristic
1154#95C22×D8311yescharacteristic
1155#95C22×D8311yescharacteristic
1156C24—3321no—
1157C24—3321no—
1158C24—834no—
1159C24—831no—
1160C24—831no—
1161C24—1662no—
1162C24—1662no—
1163C24—1662no—
1164C24—1662no—
1165C24C23×D8311yescharacteristic
1166C24C23×D8311yescharacteristic
1167C2×Q8—3321no—
1168C2×Q8—3321no—
1169C2×Q8—834no—
1170C2×D4—22no—
1171C2×D4—22no—
1172C2×D4—3321no—
1173C2×D4—3321no—
1174C2×D4—834no—
1175C2×D4—834no—
1176C2×D4—1662no—
1177C2×D4—1662no—
1178C2×D4C2×C4×D8314yes—
1179C22×C4—22no—
1180C22×C4—22no—
1181C22×C4—41no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—3321no—
1190C22×C4—3321no—
1191C22×C4—3321no—
1192C22×C4—3321no—
1193C22×C4—3321no—
1194C22×C4—3321no—
1195C22×C4—3321no—
1196C22×C4—3321no—
1197C22×C4—3321no—
1198C22×C4—3321no—
1199C22×C4—3321no—
1200C22×C4—3321no—
1201C22×C4—3321no—
1202C22×C4—3321no—
1203C22×C4—33216no—
1204C22×C4—3321no—
1205C22×C4—3321no—
1206C22×C4—3321no—
1207C22×C4—3321no—
1208C22×C4—3321no—
1209C22×C4—3321no—
1210C22×C4—3321no—
1211C22×C4—3321no—
1212C22×C4—834no—
1213C22×C4—834no—
1214C22×C4—831no—
1215C22×C4—831no—
1216C22×C4—831no—
1217C22×C4—831no—
1218C22×C4—831no—
1219C22×C4—831no—
1220C22×C4—831no—
1221C22×C4—834no—
1222C22×C4—831no—
1223C22×C4—831no—
1224C22×C4—831no—
1225C22×C4—831no—
1226C22×C4—831no—
1227C22×C4—831no—
1228C22×C4—831no—
1229C22×C4—1662no—
1230C22×C4—1662no—
1231C22×C4—1662no—
1232C22×C4—1662no—
1233C22×C4—1662no—
1234C22×C4—1662no—
1235C22×C4—1662no—
1236C22×C4—1662no—
1237C22×C4—1662no—
1238C22×C4—1662no—
1239C22×C4—1662no—
1240C22×C4—1662no—
1241C22×C4—1662no—
1242C22×C4—1662no—
1243C22×C4C2×C4×D8314yes—
1244C22×C4C2×C4×D8314yescomplemented
1245C22×C4C23×D8311yescharacteristic
1246C22×C4C23×D8311yescharacteristic
1247C22×C4C23×D8311yescharacteristic
1248C22×C4C23×D8311yescharacteristic
1249C22×C4C23×D8311yescharacteristic
1250C22×C4C23×D8311yescharacteristic
1251C22×C4C23×D8311yescharacteristic
1252C22×C4C23×D8311yescharacteristic
1253C22×C4C23×D8311yescharacteristic
1254C22×C4C23×D8311yescharacteristic
1255C22×C4C23×D8311yescharacteristic
1256C22×C4C23×D8311yescharacteristic
1257C22×C4C23×D8311yescharacteristic
1258C4⋊C4—41no—
1259C4⋊C4—41no—
1260C4⋊C4—41no—
1261C4⋊C4—41no—
1262C4⋊C4—3321no—
1263C4⋊C4—3321no—
1264C4⋊C4—3321no—
1265C4⋊C4—3321no—
1266C4⋊C4—3321no—
1267C4⋊C4—3321no—
1268C4⋊C4—3321no—
1269C4⋊C4—3321no—
1270C4⋊C4—3321no—
1271C4⋊C4—3321no—
1272C4⋊C4—3321no—
1273C4⋊C4—3321no—
1274C4⋊C4—3321no—
1275C4⋊C4—3321no—
1276C4⋊C4—3321no—
1277C4⋊C4—3321no—
1278C4⋊C4—3321no—
1279C4⋊C4—3321no—
1280C4⋊C4—3321no—
1281C4⋊C4—3321no—
1282C4⋊C4—3321no—
1283C4⋊C4—3321no—
1284C4⋊C4—834no—
1285C4⋊C4—834no—
1286C4⋊C4—834no—
1287C4⋊C4—834no—
1288C4⋊C4—834no—
1289C4⋊C4—834no—
1290C4⋊C4—834no—
1291C4⋊C4—1662no—
1292C4⋊C4—1662no—
1293C4⋊C4—1662no—
1294C4⋊C4—1662no—
1295C4⋊C4C2×C4×D8314yescomplemented
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—3321no—
1303C22⋊C4—3321no—
1304C22⋊C4—3321no—
1305C22⋊C4—3321no—
1306C22⋊C4—3321no—
1307C22⋊C4—3321no—
1308C22⋊C4—3321no—
1309C22⋊C4—3321no—
1310C22⋊C4—834no—
1311C22⋊C4—834no—
1312C22⋊C4—834no—
1313C22⋊C4—834no—
1314C22⋊C4—834no—
1315C22⋊C4—834no—
1316C22⋊C4—834no—
1317C22⋊C4—834no—
1318C22⋊C4—834no—
1319C22⋊C4—834no—
1320C22⋊C4—834no—
1321C22⋊C4—834no—
1322C22⋊C4—1662no—
1323C22⋊C4—1662no—
1324C22⋊C4—1662no—
1325C22⋊C4—1662no—
1326C22⋊C4—1662no—
1327C22⋊C4—1662no—
1328C22⋊C4C2×C4×D8314yes—
1329C22⋊C4C2×C4×D8314yescomplemented
1330C42—41no—
1331C42—41no—
1332C42—3321no—
1333C42—3321no—
1334C42—3321no—
1335C42—3321no—
1336C42—3321no—
1337C42—3321no—
1338C42—3321no—
1339C42—3321no—
1340C42—3321no—
1341C42—3321no—
1342C42—3321no—
1343C42—834no—
1344C42—834no—
1345C42—1662no—
1346C42C2×C4×D8314yescomplemented
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—3324no—
1358C23—3324no—
1359C23—3324no—
1360C23—3324no—
1361C23—3324no—
1362C23—832no—
1363C23—832no—
1364C23—832no—
1365C23—832no—
1366C23—1668no—
1367C23—1668no—
1368C23—1661no—
1369C23—1661no—
1370C23—1661no—
1371C23—1661no—
1372C23—1661no—
1373C23—1661no—
1374C23—1661no—
1375C23—1661no—
1376C23—1661no—
1377C23—1661no—
1378C23C22×C4×D8312yes—
1379C23C22×C4×D8312yes—
1380C23#1458183812yes—
1381C23#1458183912yes—
1382C23C24×D8311yescharacteristic
1383Q8—3324no—
1384D4—28no—
1385D4—3324no—
1386D4—1668no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—44no—
1422C2×C4—44no—
1423C2×C4—44no—
1424C2×C4—82no—
1425C2×C4—3324no—
1426C2×C4—3324no—
1427C2×C4—3324no—
1428C2×C4—3324no—
1429C2×C4—3324no—
1430C2×C4—3324no—
1431C2×C4—832no—
1432C2×C4—832no—
1433C2×C4—832no—
1434C2×C4—832no—
1435C2×C4—832no—
1436C2×C4—832no—
1437C2×C4—832no—
1438C2×C4—6642no—
1439C2×C4—6642no—
1440C2×C4—6642no—
1441C2×C4—6642no—
1442C2×C4—6642no—
1443C2×C4—1668no—
1444C2×C4—1661no—
1445C2×C4—1661no—
1446C2×C4—1661no—
1447C2×C4—1661no—
1448C2×C4—1661no—
1449C2×C4—1661no—
1450C2×C4—1661no—
1451C2×C4—1661no—
1452C2×C4—1661no—
1453C2×C4—1661no—
1454C2×C4—1661no—
1455C2×C4—1661no—
1456C2×C4—1661no—
1457C2×C4—1661no—
1458C2×C4—1661no—
1459C2×C4—1661no—
1460C2×C4—1661no—
1461C2×C4—1661no—
1462C2×C4—1661no—
1463C2×C4—1661no—
1464C2×C4—1661no—
1465C2×C4—1668no—
1466C2×C4—1661no—
1467C2×C4—1661no—
1468C2×C4—1661no—
1469C2×C4—1661no—
1470C2×C4—1661no—
1471C2×C4—1661no—
1472C2×C4—1661no—
1473C2×C4—1661no—
1474C2×C4—1661no—
1475C2×C4—1661no—
1476C2×C4—1661no—
1477C2×C4—1661no—
1478C2×C4—1661no—
1479C2×C4—1661no—
1480C2×C4C22×C4×D8312yes—
1481C2×C4C22×C4×D8312yes—
1482C2×C4C22×C4×D8312yes—
1483C2×C4C22×C4×D8312yes—
1484C2×C4C22×C4×D8312yes—
1485C22—22no—
1486C22—22no—
1487C22—22no—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—41no—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—33216no—
1499C22—3321no—
1500C22—3321no—
1501C22—3321no—
1502C22—3321no—
1503C22—834no—
1504C22—1662no—
1505C22—1662no—
1506C22—1662no—
1507C22—1662no—
1508C22—1662no—
1509C22—1662no—
1510C22—1662no—
1511C22—1662no—
1512C22—1662no—
1513C22#1912818114yes—
1514C22C23×C4×D8311yescharacteristic
1515C22H(5,𝔽2)×D8311yescharacteristic
1516C22H(5,𝔽2)×D8311yescharacteristic
1517C22C2×#1458183811yescharacteristic
1518C222−1+4×D8311yescharacteristic
1519C22C2×#1458183911yescharacteristic
1520C22#1912853611yescharacteristic
1521C4—22no—
1522C4—22no—
1523C4—22no—
1524C4—22no—
1525C4—22no—
1526C4—41no—
1527C4—41no—
1528C4—41no—
1529C4—41no—
1530C4—41no—
1531C4—41no—
1532C4—41no—
1533C4—41no—
1534C4—3321no—
1535C4—3321no—
1536C4—3321no—
1537C4—3321no—
1538C4—3321no—
1539C4—3321no—
1540C4—3321no—
1541C4—1662no—
1542C4—1662no—
1543C4—1662no—
1544C4—1662no—
1545C4—1662no—
1546C4—1662no—
1547C4—1662no—
1548C2—24no—
1549C2—42no—
1550C2—3322no—
1551C2—1664no—
1552C2#520×D8311yescharacteristic
1553C2C2×#1912818111yescharacteristic
1554C2#2492066711yescharacteristic
1555C2#2492161411yescharacteristic
1556C2#2492166111yescharacteristic
1557C2#2492167011yescharacteristic
1558C2#2492171011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2318C2
socle, cosocleC23×C83C25
prime radicalC2×#14581760C22
hypercenter#2318D83
hypocenterC83#34457
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #24910653C2semidirect
3. #24910652C2semidirect
4. #24910632C2semidirect
5. #24910607C2semidirect
6. #24910471C2semidirect
7. #24910466C2semidirect
8. #24910461C2semidirect
9. #24910454C2semidirect
11. D4×C4⋊Dic83C2semidirect
12. #24910359C2semidirect
13. #24910321C2semidirect
14. #24910320C2semidirect
15. #24910315C2semidirect
16. #24910310C2semidirect
17. #24910243C2semidirect
18. #24910234C2semidirect
19. #24910196C2semidirect
20. #24910190C2semidirect
21. #24910172C2semidirect
22. #24910137C2semidirect
23. #24910133C2semidirect
24. #24910129C2semidirect
25. #24910092C2semidirect
26. #24910088C2semidirect
27. #24910082C2semidirect
29. C2×#19127575C2semidirect
30. #385×D83C2semidirect
31. C83×#2318C2semidirect
33. #19128380C4semidirect
43. C2×C4×Dic166C22semidirect
55. C22×C4⋊Dic83C22semidirect
63. #19127607C22semidirect
64. #19127605C22semidirect
65. #19127605C22semidirect
67. #19127600C22semidirect
68. #19127600C22semidirect
69. #19127599C22semidirect
70. #19127598C22semidirect
71. #19127598C22semidirect
72. #19127598C22semidirect
73. #19127598C22semidirect
74. #19127598C22semidirect
75. #19127598C22semidirect
76. #19127598C22semidirect
77. #19127598C22semidirect
78. #19127598C22semidirect
79. #19127596C22semidirect
80. #19127596C22semidirect
81. #19127595C22semidirect
92. #19127589C22semidirect
93. #19127589C22semidirect
94. #19127589C22semidirect
95. #19127588C22semidirect
96. #19127588C22semidirect
97. #19127588C22semidirect
98. #19127588C22semidirect
99. #19127588C22semidirect
100. #19127588C22semidirect
101. #19127588C22semidirect
102. #19127584C22semidirect
103. #19127584C22semidirect
104. #19127583C22semidirect
105. #19127583C22semidirect
106. #19127583C22semidirect
107. #19127582C22semidirect
108. #19127582C22semidirect
115. #19127576C22semidirect
116. #19127576C22semidirect
136. #19127573C22semidirect
137. #19127573C22semidirect
138. #19127573C22semidirect
141. #19127571C22semidirect
142. #19127570C22semidirect
143. #19127570C22semidirect
144. #19127568C22semidirect
145. #19127566C22semidirect
146. #19127565C22semidirect
147. #19127565C22semidirect
151. #19127561C22semidirect
154. C4⋊C4×Dic83C22semidirect
155. C4×C4⋊Dic83C22semidirect
156. C4×C4⋊Dic83C22semidirect
157. #19127552C22semidirect
160. C22⋊C4×Dic83C22semidirect
169. #19127546C22semidirect
174. #388×C83C22semidirect
175. #388×C83C22semidirect
176. #387×C83C22semidirect
177. #387×C83C22semidirect
182. #383×C83C22semidirect
183. #382×C83C22semidirect
184. #381×C83C22semidirect
185. #380×C83C22semidirect
208. #14581787C2×C4semidirect
209. #14581786C2×C4semidirect
210. #14581778C2×C4semidirect
211. #14581775C2×C4semidirect
212. #14581774C2×C4semidirect
213. #14581773C2×C4semidirect
214. #14581771C2×C4semidirect
215. #14581770C2×C4semidirect
220. C4×C22⋊D83C2×C4semidirect
225. #14581749C2×C4semidirect
227. #14581748C2×C4semidirect
275. C2×(C2×D83)⋊C4C2×C4semidirect
295. C22⋊C4×D83C2×C4semidirect
345. C4×D4×C83C2×C4semidirect
387. C2×Dic166C22×C4semidirect
460. C4⋊Dic83C22×C4semidirect
475. Dic83⋊C4C22×C4semidirect
476. Dic83⋊C4C22×C4semidirect
477. Dic83⋊C4C22×C4semidirect
478. Dic83⋊C4C22×C4semidirect
479. Dic83⋊C4C22×C4semidirect
480. Dic83⋊C4C22×C4semidirect
487. C22⋊Dic83C22×C4semidirect
488. C22⋊Dic83C22×C4semidirect
519. C4×Dic83C22×C4semidirect
520. C4×Dic83C22×C4semidirect
537. C22×C4×C83C22×C4semidirect
555. C4⋊C4×C83C22×C4semidirect
563. C22⋊C4×C83C22×C4semidirect
566. C42×C83C22×C4semidirect
805. #2318D83semidirect
811. C83#34457semidirect
876. #388C2×D83semidirect
877. #388C2×D83semidirect
892. #387C2×D83semidirect
893. #387C2×D83semidirect
934. #383C2×D83semidirect
938. #382C2×D83semidirect
941. #381C2×D83semidirect
945. #380C2×D83semidirect
1009. C4×D4C4×D83semidirect
1244. C22×C4C2×C4×D83semidirect
1295. C4⋊C4C2×C4×D83semidirect
1329. C22⋊C4C2×C4×D83semidirect
1346. C42C2×C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283802
#249106532
#249106522
#249106322
#249106072
#249104712
#249104662
#249104612
#249104542
#249104432
D4×C4⋊Dic832
#249103592
#249103212
#249103202
#249103152
#249103102
#249102432
#249102342
#249101962
#249101902
#249101722
#249101372
#249101332
#249101292
#249100922
#249100882
#249100822
#249099682
C2×#191275752
#385×D832
C83×#23182
#3445783