Finite Group Databasebeta

← #35569060

Subgroups — #35569060

Order 21248.

2368 conjugacy classes of subgroups.

The subgroup lattice has 1544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128400C211yesmaximal, characteristic
2#24910652C211yesmaximal, characteristic, complemented
3#24910650C211yesmaximal, characteristic, complemented
4#24910610C211yesmaximal, characteristic, complemented
5#24910607C211yesmaximal, characteristic, complemented
6#24910556C211yesmaximal, characteristic, complemented
7#24910477C211yesmaximal, characteristic, complemented
8#24910476C211yesmaximal, characteristic, complemented
9#24910474C211yesmaximal, characteristic, complemented
10#24910474C211yesmaximal, characteristic, complemented
11D4×C4⋊Dic83C211yesmaximal, characteristic, complemented
12#24910361C211yesmaximal, characteristic, complemented
13#24910361C211yesmaximal, characteristic, complemented
14#24910359C211yesmaximal, characteristic, complemented
15#24910351C211yesmaximal, characteristic, complemented
16#24910341C211yesmaximal, characteristic, complemented
17#24910245C211yesmaximal, characteristic, complemented
18#24910234C211yesmaximal, characteristic, complemented
19#24910199C211yesmaximal, characteristic, complemented
20#24910166C211yesmaximal, characteristic, complemented
21#24910164C211yesmaximal, characteristic, complemented
22#24910151C211yesmaximal, characteristic, complemented
23#24910136C211yesmaximal, characteristic, complemented
24#24910129C211yesmaximal, characteristic, complemented
25#24910103C211yesmaximal, characteristic, complemented
26#24910091C211yesmaximal, characteristic, complemented
27#24910088C211yesmaximal, characteristic, complemented
28#24909973C211yesmaximal, characteristic, complemented
29C2×#19127598C211yesmaximal, characteristic, complemented
30#24909899C211yesmaximal, characteristic, complemented
31C83×#2318C211yesmaximal, characteristic, complemented
32#19128400C4116yescomplemented
33C2×#14581786C2211yescharacteristic
34C2×#14581785C2211yescharacteristic
35C2×#14581782C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581775C2211yescharacteristic
38C2×#14581766C2211yescharacteristic
39C2×#14581765C2211yescharacteristic
40C2×#14581764C2211yescharacteristic
41C2×#14581764C2211yescharacteristic
42C2×C4×D332C2211yescharacteristic
43C2×D4×Dic83C2211yescharacteristic
44C2×D4×Dic83C2211yescharacteristic
45C2×C4×C22⋊D83C2211yescharacteristic
46C2×C4×C22⋊D83C2211yescharacteristic
47C2×C4×C22⋊D83C2211yescharacteristic
48C2×(C22⋊D83)⋊C4C2211yescharacteristic
49C2×(C22⋊D83)⋊C4C2211yescharacteristic
50C2×(C22⋊D83)⋊C4C2211yescharacteristic
51C2×(C22⋊D83)⋊C4C2211yescharacteristic
52C2×(C22⋊D83)⋊C4C2211yescharacteristic
53C2×(C22⋊D83)⋊C4C2211yescharacteristic
54C2×(C22⋊D83)⋊C4C2211yescharacteristic
55C2×#14581750C2211yescharacteristic
56C2×#14581749C2211yescharacteristic
57C22×C4⋊Dic83C2211yescharacteristic
58C22×C4⋊Dic83C2211yescharacteristic
59C22×Dic83⋊C4C2211yescharacteristic
60C22×Dic83⋊C4C2211yescharacteristic
61C22×Dic83⋊C4C2211yescharacteristic
62C2×C4⋊C4×D83C2211yescharacteristic
63C2×C4⋊C4×D83C2211yescharacteristic
64C22×C4×Dic83C2211yescharacteristic
65#19127603C2211yescharacteristic
66#19127601C2211yescharacteristic
67#19127601C2211yescharacteristic
68#19127601C2211yescharacteristic
69#19127600C2211yescharacteristic
70#19127600C2211yescharacteristic
71#19127599C2211yescharacteristic
72#19127598C2211yescharacteristic
73#19127598C2211yescharacteristic
74#19127598C2211yescharacteristic
75#19127598C2211yescharacteristic
76#19127598C2211yescharacteristic
77#19127598C2211yescharacteristic
78#19127598C2211yescharacteristic
79#19127598C2211yescharacteristic
80#19127598C2211yescharacteristic
81#19127598C2211yescharacteristic
82#19127598C2211yescharacteristic
83#19127598C2211yescharacteristic
84#19127598C2211yescharacteristic
85#19127598C2211yescharacteristic
86#19127598C2211yescharacteristic
87#19127596C2211yescharacteristic
88#19127596C2211yescharacteristic
89#19127595C2211yescharacteristic
90#19127595C2211yescharacteristic
91#19127595C2211yescharacteristic
92#19127593C2211yescharacteristic
93#19127593C2211yescharacteristic
94#19127593C2211yescharacteristic
95#19127593C2211yescharacteristic
96#19127593C2211yescharacteristic
97#19127593C2211yescharacteristic
98#19127593C2211yescharacteristic
99#19127591C2211yescharacteristic
100#19127591C2211yescharacteristic
101#19127590C2211yescharacteristic
102#19127590C2211yescharacteristic
103#19127590C2211yescharacteristic
104#19127589C2211yescharacteristic
105#19127588C2211yescharacteristic
106#19127588C2211yescharacteristic
107#19127588C2211yescharacteristic
108#19127588C2211yescharacteristic
109#19127588C2211yescharacteristic
110#19127586C2211yescharacteristic
111#19127586C2211yescharacteristic
112#19127585C2211yescharacteristic
113#19127585C2211yescharacteristic
114#19127583C2211yescharacteristic
115#19127582C2211yescharacteristic
116#19127582C2211yescharacteristic
117#19127580C2211yescharacteristic
118#19127580C2211yescharacteristic
119#19127579C2211yescharacteristic
120#19127579C2211yescharacteristic
121#19127578C2211yescharacteristic
122#19127578C2211yescharacteristic
123#19127578C2211yescharacteristic
124#19127577C2211yescharacteristic
125#19127576C2211yescharacteristic
126#19127576C2211yescharacteristic
127#19127576C2211yescharacteristic
128#19127576C2211yescharacteristic
129#19127575C2211yescharacteristic
130#19127575C2211yescharacteristic
131#19127575C2211yescharacteristic
132#19127575C2211yescharacteristic
133#19127575C2211yescharacteristic
134#19127575C2211yescharacteristic
135#19127575C2211yescharacteristic
136#19127575C2211yescharacteristic
137#19127575C2211yescharacteristic
138#19127573C2211yescharacteristic
139#19127573C2211yescharacteristic
140#19127573C2211yescharacteristic
141#19127572C2211yescharacteristic
142#19127572C2211yescharacteristic
143#19127571C2211yescharacteristic
144#19127570C2211yescharacteristic
145#19127570C2211yescharacteristic
146#19127568C2211yescharacteristic
147#19127566C2211yescharacteristic
148#19127563C2211yescharacteristic
149#19127561C2211yescharacteristic
150#19127561C2211yescharacteristic
151#19127560C2211yescharacteristic
152#19127560C2211yescharacteristic
153#19127559C2211yescharacteristic
154#19127559C2211yescharacteristic
155#19127558C2211yescharacteristic
156C4⋊C4×Dic83C2211yescharacteristic
157C4×Dic83⋊C4C2211yescharacteristic
158C4×Dic83⋊C4C2211yescharacteristic
159C4×C4⋊Dic83C2211yescharacteristic
160C4×C4⋊Dic83C2211yescharacteristic
161#19127552C2211yescharacteristic
162#19127552C2211yescharacteristic
163#19127552C2211yescharacteristic
164#19127552C2211yescharacteristic
165#19127552C2211yescharacteristic
166C22⋊C4×Dic83C2211yescharacteristic
167C22⋊C4×Dic83C2211yescharacteristic
168C22⋊C4×Dic83C2211yescharacteristic
169#19127548C2211yescharacteristic
170#19127548C2211yescharacteristic
171#19127546C2211yescharacteristic
172C2×C83⋊#95C2211yescharacteristic
173C2×C4×D4×C83C2211yescharacteristic
174#388×C83C2211yescharacteristic
175#388×C83C2211yescharacteristic
176#387×C83C2211yescharacteristic
177#387×C83C2211yescharacteristic
178#386×C83C2211yescharacteristic
179#386×C83C2211yescharacteristic
180#385×C83C2211yescharacteristic
181#385×C83C2211yescharacteristic
182#383×C83C2211yescharacteristic
183#382×C83C2211yescharacteristic
184#381×C83C2211yescharacteristic
185#380×C83C2211yescharacteristic
186C4×C22⋊C4×C83C2211yescharacteristic
187C2×#95×C83C2211yescharacteristic
188C22×D332C2311yescharacteristic
189C22×C22⋊D83C2311yescharacteristic
190C22×C22⋊D83C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C22×C22⋊D83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C23×Dic83C2311yescharacteristic
198C23×Dic83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203C22×C4×D83C2311yescharacteristic
204C22×C4×D83C2311yescharacteristic
205#14581786C2×C418yescomplemented
206#14581785C2×C418yescomplemented
207#14581782C2×C418yescomplemented
208#14581777C2×C418yescomplemented
209#14581775C2×C418yescomplemented
210#14581766C2×C418yescomplemented
211#14581765C2×C418yescomplemented
212#14581764C2×C418yescomplemented
213#14581764C2×C418yescomplemented
214C4×D332—42no—
215D4×Dic83—42no—
216D4×Dic83—42no—
217C4×C22⋊D83—42no—
218C4×C22⋊D83—42no—
219C4×C22⋊D83C2×C418yescomplemented
220(C22⋊D83)⋊C4—42no—
221(C22⋊D83)⋊C4—42no—
222(C22⋊D83)⋊C4—42no—
223(C22⋊D83)⋊C4—42no—
224(C22⋊D83)⋊C4—42no—
225(C22⋊D83)⋊C4C2×C418yescomplemented
226(C22⋊D83)⋊C4C2×C418yescomplemented
227#14581750—42no—
228#14581749C2×C418yescomplemented
229C2×C4⋊Dic83—42no—
230C2×C4⋊Dic83—42no—
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×C4⋊Dic83C2311yescharacteristic
244C2×Dic83⋊C4—42no—
245C2×Dic83⋊C4—42no—
246C2×Dic83⋊C4C2×C418yescomplemented
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
264C2×Dic83⋊C4C2311yescharacteristic
265C2×Dic83⋊C4C2311yescharacteristic
266C2×Dic83⋊C4C2311yescharacteristic
267C2×Dic83⋊C4C2311yescharacteristic
268C2×Dic83⋊C4C2311yescharacteristic
269C2×Dic83⋊C4C2311yescharacteristic
270C2×Dic83⋊C4C2311yescharacteristic
271C4⋊C4×D83—42no—
272C4⋊C4×D83—42no—
273C2×C22⋊Dic83C2311yescharacteristic
274C2×C22⋊Dic83C2311yescharacteristic
275C2×C22⋊Dic83C2311yescharacteristic
276C2×C22⋊Dic83C2311yescharacteristic
277C2×C22⋊Dic83C2311yescharacteristic
278C2×C22⋊Dic83C2311yescharacteristic
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
294C2×(C2×D83)⋊C4C2311yescharacteristic
295C2×(C2×D83)⋊C4C2311yescharacteristic
296C2×(C2×D83)⋊C4C2311yescharacteristic
297C2×C4×Dic83—42no—
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
310C2×C4×Dic83C2311yescharacteristic
311C2×C4×Dic83C2311yescharacteristic
312C2×C4×Dic83C2311yescharacteristic
313C2×C4×Dic83C2311yescharacteristic
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×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378C2×D332—41no—
379C2×D332—41no—
380C2×D332C22×C414yes—
381C2×C22⋊D83—22no—
382C2×C22⋊D83—22no—
383C2×C22⋊D83—22no—
384C2×C22⋊D83—22no—
385C2×C22⋊D83—22no—
386C2×C22⋊D83—22no—
387C2×C22⋊D83—41no—
388C2×C22⋊D83—41no—
389C2×C22⋊D83C22×C414yes—
390C2×C22⋊D83C22×C414yes—
391C2×C22⋊D83C22×C414yes—
392C2×C22⋊D83C22×C414yes—
393C22×Dic83—22no—
394C22×Dic83—22no—
395C22×Dic83—22no—
396C22×Dic83—22no—
397C22×Dic83—22no—
398C22×Dic83—22no—
399C22×Dic83—41no—
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×Dic83—41no—
409C22×Dic83C22×C414yes—
410C22×Dic83C22×C414yes—
411C22×Dic83C2411yescharacteristic
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C22×Dic83C2411yescharacteristic
420C22×Dic83C2411yescharacteristic
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2411yescharacteristic
423C22×Dic83C2411yescharacteristic
424C22×Dic83C2411yescharacteristic
425C2×C4×D83—22no—
426C2×C4×D83—22no—
427C2×C4×D83—22no—
428C2×C4×D83—41no—
429C2×C4×D83—41no—
430C2×C4×D83—41no—
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×D83C22×C414yes—
442C2×C4×D83C22×C414yes—
443C4⋊Dic83—22no—
444C4⋊Dic83—22no—
445C4⋊Dic83—22no—
446C4⋊Dic83—41no—
447C4⋊Dic83—41no—
448C4⋊Dic83—41no—
449C4⋊Dic83—41no—
450C4⋊Dic83—41no—
451C4⋊Dic83—41no—
452C4⋊Dic83—41no—
453C4⋊Dic83—41no—
454C4⋊Dic83—41no—
455C4⋊Dic83C22×C414yes—
456Dic83⋊C4—22no—
457Dic83⋊C4—22no—
458Dic83⋊C4—22no—
459Dic83⋊C4—22no—
460Dic83⋊C4—22no—
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⋊C4C22×C414yes—
473Dic83⋊C4C22×C414yes—
474Dic83⋊C4C22×C414yes—
475Dic83⋊C4C22×C414yes—
476Dic83⋊C4C22×C414yes—
477Dic83⋊C4C22×C414yes—
478Dic83⋊C4C22×C414yes—
479Dic83⋊C4C22×C414yes—
480C22⋊Dic83—22no—
481C22⋊Dic83—22no—
482C22⋊Dic83—41no—
483C22⋊Dic83—41no—
484C22⋊Dic83C22×C414yes—
485C22⋊Dic83C22×C414yes—
486(C2×D83)⋊C4—22no—
487(C2×D83)⋊C4—41no—
488(C2×D83)⋊C4—41no—
489(C2×D83)⋊C4—41no—
490(C2×D83)⋊C4—41no—
491(C2×D83)⋊C4—41no—
492(C2×D83)⋊C4—41no—
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)⋊C4C22×C414yes—
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—
504C4×Dic83—22no—
505C4×Dic83—22no—
506C4×Dic83—22no—
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×Dic83C22×C414yes—
519C4×Dic83C22×C414yes—
520C24×C83C2411yescharacteristic
521C24×C83C2411yescharacteristic
522C2×D4×C83—22no—
523C2×D4×C83—22no—
524C2×D4×C83C22×C414yes—
525C22×C4×C83—22no—
526C22×C4×C83—22no—
527C22×C4×C83—41no—
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×C83C22×C414yes—
536C22×C4×C83C22×C414yes—
537C22×C4×C83C2411yescharacteristic
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
550C4⋊C4×C83—41no—
551C4⋊C4×C83—41no—
552C4⋊C4×C83—41no—
553C4⋊C4×C83—41no—
554C4⋊C4×C83C22×C414yes—
555C22⋊C4×C83—22no—
556C22⋊C4×C83—22no—
557C22⋊C4×C83—41no—
558C22⋊C4×C83—41no—
559C22⋊C4×C83—41no—
560C22⋊C4×C83—41no—
561C22⋊C4×C83C22×C414yes—
562C22⋊C4×C83C22×C414yes—
563C42×C83—41no—
564C42×C83—41no—
565C42×C83C22×C414yes—
566C23×C83—21no—
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×C83C23×C412yes—
577C23×C83C23×C412yes—
578C23×C83H(5,𝔽2)12yes—
579C23×C832−1+412yes—
580C23×C83C2511yescharacteristic
581C22×D83—21no—
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83—21no—
593C22×D83C23×C412yes—
594C22×D83C23×C412yes—
595D4×C83—28no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
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—44no—
631C2×C4×C83—44no—
632C2×C4×C83—44no—
633C2×C4×C83—82no—
634C2×C4×C83C23×C412yes—
635C2×C4×C83C23×C412yes—
636C2×C4×C83C23×C412yes—
637C2×C4×C83C23×C412yes—
638C2×C4×C83C23×C412yes—
639C22⋊D83—28no—
640C22⋊D83—28no—
641C22⋊D83—28no—
642C22⋊D83—44no—
643C2×Dic83—21no—
644C2×Dic83—21no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—28no—
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—44no—
678C2×Dic83—44no—
679C2×Dic83—82no—
680C2×Dic83—82no—
681C2×Dic83—82no—
682C2×Dic83C23×C412yes—
683C2×Dic83C23×C412yes—
684C2×Dic83C23×C412yes—
685C2×Dic83C23×C412yes—
686C2×Dic83C23×C412yes—
687C2×Dic83C23×C412yes—
688C2×Dic83H(5,𝔽2)12yes—
689C2×Dic83H(5,𝔽2)12yes—
690C2×Dic832−1+412yes—
691D332—44no—
692C4×D83—28no—
693C4×D83—44no—
694C4×D83—82no—
695C4×D83—82no—
696C4×D83—82no—
697C4×D83—82no—
698C22×C83—22no—
699C22×C83—22no—
700C22×C83—22no—
701C22×C83—22no—
702C22×C83—22no—
703C22×C83—22no—
704C22×C83—22no—
705C22×C83—22no—
706C22×C83—22no—
707C22×C83—41no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83#52014yes—
712C22×C83C24×C411yescharacteristic
713C22×C83C2×H(5,𝔽2)11yescharacteristic
714C22×C83C2×H(5,𝔽2)11yescharacteristic
715C22×C83C2×H(5,𝔽2)11yescharacteristic
716C22×C83C2×2−1+411yescharacteristic
717C22×C83C2×2−1+411yescharacteristic
718C22×C83#58511yescharacteristic
719C2×D83—22no—
720C2×D83—22no—
721C2×D83—22no—
722C2×D83—22no—
723C2×D83—22no—
724C2×D83—22no—
725C2×D83—41no—
726C2×D83—41no—
727C2×D83—41no—
728C2×D83—41no—
729C2×D83—41no—
730C2×D83—41no—
731C2×D83—41no—
732C2×D83—41no—
733C4×C83—22no—
734C4×C83—22no—
735C4×C83—22no—
736C4×C83—22no—
737C4×C83—22no—
738C4×C83—41no—
739C4×C83—41no—
740C4×C83—41no—
741C4×C83—41no—
742C4×C83—41no—
743C4×C83—41no—
744C4×C83—41no—
745C4×C83—41no—
746Dic83—22no—
747Dic83—22no—
748Dic83—22no—
749Dic83—22no—
750Dic83—22no—
751Dic83—22no—
752Dic83—41no—
753Dic83—41no—
754Dic83—41no—
755Dic83—41no—
756Dic83—41no—
757Dic83—41no—
758Dic83—41no—
759Dic83#52014yes—
760#34461—831nomaximal, Sylow
761C2×C83—24no—
762C2×C83—42no—
763C2×C83C2×#52011yescharacteristic
764C2×C83C2×#52011yescharacteristic
765C2×C83C4×H(5,𝔽2)11yescharacteristic
766C2×C83#353711yescharacteristic
767C2×C83#354111yescharacteristic
768C2×C83#355211yescharacteristic
769C2×C83#355911yescharacteristic
770D83—42no—
771D83—42no—
772C2×#553—831no—
773#2383—831no—
774#2383—831no—
775#2376—831no—
776#2376—831no—
777#2370—831no—
778#2361—831no—
779#2361—831no—
780#2361—831no—
781#2361—831no—
782D4×C4⋊C4—831no—
783D4×C4⋊C4—831no—
784D4×C4⋊C4—831no—
785D4×C4⋊C4—831no—
786#2347—831no—
787#2345—831no—
788#2334—831no—
789#2334—831no—
790#2330—831no—
791#2325—831no—
792#2325—831no—
793#2324—831no—
794#2322—831no—
795#2322—831no—
796#2319—831no—
797#2318—831no—
798#2318D8311yescharacteristic, complemented
799#2317—831no—
800C4×#121—831no—
801C2×#389—831no—
802#2290—831no—
803C83#3446111yescharacteristic, complemented, Sylow
804#553—8316no—
805C2×#126—831no—
806C2×#126—831no—
807C2×#125—831no—
808C2×#123—831no—
809C2×#123—831no—
810C2×#121—831no—
811C2×#121—831no—
812C2×#121—831no—
813C2×#121—831no—
814C2×C4×D4—831no—
815C2×C4×D4—831no—
816C2×C4×D4—831no—
817C2×C4×D4—831no—
818C2×C4×D4—831no—
819C2×C4×D4—831no—
820C2×C4×D4—831no—
821C2×C4×D4—831no—
822C2×C4×D4—831no—
823C2×C4×D4—831no—
824C2×C4×D4—831no—
825C2×C4×D4—831no—
826C2×C4×D4—831no—
827C2×C4×D4C2×D8311yescharacteristic
828C2×#117—831no—
829C2×#117—831no—
830C22×C4⋊C4—831no—
831C22×C4⋊C4—831no—
832C22×C4⋊C4—831no—
833C22×C4⋊C4—831no—
834C22×C4⋊C4—831no—
835C22×C4⋊C4—831no—
836C22×C4⋊C4—831no—
837C22×C42—831no—
838#390—831no—
839#390—831no—
840#390—831no—
841#390—831no—
842#389—831no—
843#389—831no—
844#389—831no—
845#389—831no—
846#389—831no—
847#389—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#388—831no—
877#388—831no—
878#388C2×D8311yescharacteristic
879#388C2×D8311yescharacteristic
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
893#387C2×D8311yescharacteristic
894#386—831no—
895#386—831no—
896#386—831no—
897#386—831no—
898#386—831no—
899#386—831no—
900#386—831no—
901#386—831no—
902#386C2×D8311yescharacteristic
903#386C2×D8311yescharacteristic
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#385C2×D8311yescharacteristic
923#385C2×D8311yescharacteristic
924#384—831no—
925#384—831no—
926#384—831no—
927#383—831no—
928#383C2×D8311yescharacteristic
929#382—831no—
930#382C2×D8311yescharacteristic
931#381—831no—
932#381C2×D8311yescharacteristic
933#380—831no—
934#380—831no—
935#380—831no—
936#380—831no—
937#380—831no—
938#380—831no—
939#380—831no—
940#380C2×D8311yescharacteristic
941C4×C4⋊C4—831no—
942C4×C4⋊C4—831no—
943C4×C4⋊C4—831no—
944C4×C4⋊C4—831no—
945C4×C4⋊C4—831no—
946C4×C4⋊C4—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⋊C4C2×D8311yescharacteristic
957#376—831no—
958C2×#95—831no—
959C2×#95C2×D8311yescharacteristic
960C22×D4—831no—
961C22×D4—831no—
962C22×D4—831no—
963C22×D4—831no—
964C22×D4—831no—
965C22×D4C22×D8311yescharacteristic
966C23×C4—831no—
967C23×C4—831no—
968C23×C4—831no—
969C23×C4—831no—
970C23×C4—831no—
971C23×C4—831no—
972C23×C4—831no—
973C23×C4—831no—
974C23×C4—831no—
975C23×C4—831no—
976C23×C4—831no—
977C23×C4—831no—
978C23×C4C22×D8311yescharacteristic
979C23×C4C22×D8311yescharacteristic
980C23×C4C22×D8311yescharacteristic
981C23×C4C22×D8311yescharacteristic
982#126—838no—
983#126—838no—
984#125—838no—
985#123—838no—
986#123—838no—
987#121—838no—
988#121—838no—
989#121—838no—
990#121—838no—
991C4×D4—3322no—
992C4×D4—3322no—
993C4×D4—3322no—
994C4×D4—3322no—
995C4×D4—3322no—
996C4×D4—3322no—
997C4×D4—3322no—
998C4×D4—3322no—
999C4×D4—3322no—
1000C4×D4—3322no—
1001C4×D4—838no—
1002C4×D4—838no—
1003C4×D4—838no—
1004C4×D4C4×D8318yescomplemented
1005#117—3322no—
1006#117—838no—
1007C2×C4⋊C4—3322no—
1008C2×C4⋊C4—3322no—
1009C2×C4⋊C4—3322no—
1010C2×C4⋊C4—3322no—
1011C2×C4⋊C4—3322no—
1012C2×C4⋊C4—3322no—
1013C2×C4⋊C4—831no—
1014C2×C4⋊C4—831no—
1015C2×C4⋊C4—831no—
1016C2×C4⋊C4—831no—
1017C2×C4⋊C4—831no—
1018C2×C4⋊C4—831no—
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—838no—
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⋊C4C22×D8311yescharacteristic
1052C2×C4⋊C4C22×D8311yescharacteristic
1053C2×C4⋊C4C22×D8311yescharacteristic
1054C2×C4⋊C4C22×D8311yescharacteristic
1055C2×C4⋊C4C22×D8311yescharacteristic
1056C2×C22⋊C4—831no—
1057C2×C22⋊C4—831no—
1058C2×C22⋊C4—831no—
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—831no—
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⋊C4C22×D8311yescharacteristic
1081C2×C22⋊C4C22×D8311yescharacteristic
1082C2×C22⋊C4C22×D8311yescharacteristic
1083C2×C22⋊C4C22×D8311yescharacteristic
1084C2×C22⋊C4C22×D8311yescharacteristic
1085C2×C22⋊C4C22×D8311yescharacteristic
1086C2×C22⋊C4C22×D8311yescharacteristic
1087C2×C22⋊C4C22×D8311yescharacteristic
1088C2×C42—3322no—
1089C2×C42—831no—
1090C2×C42—831no—
1091C2×C42—831no—
1092C2×C42—831no—
1093C2×C42—831no—
1094C2×C42—831no—
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×C42C22×D8311yescharacteristic
1106C2×C42C22×D8311yescharacteristic
1107C2×C42C22×D8311yescharacteristic
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
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#95C22×D8311yescharacteristic
1135#95C22×D8311yescharacteristic
1136#95C22×D8311yescharacteristic
1137#95C22×D8311yescharacteristic
1138#95C22×D8311yescharacteristic
1139#95C22×D8311yescharacteristic
1140#95C22×D8311yescharacteristic
1141#95C22×D8311yescharacteristic
1142#95C22×D8311yescharacteristic
1143#95C22×D8311yescharacteristic
1144#95C22×D8311yescharacteristic
1145#95C22×D8311yescharacteristic
1146#95C22×D8311yescharacteristic
1147#95C22×D8311yescharacteristic
1148C24—831no—
1149C24—831no—
1150C24C23×D8311yescharacteristic
1151C24C23×D8311yescharacteristic
1152C2×D4—22no—
1153C2×D4—22no—
1154C2×D4—3321no—
1155C2×D4—3321no—
1156C2×D4—3321no—
1157C2×D4—3321no—
1158C2×D4—834no—
1159C2×D4—834no—
1160C2×D4—834no—
1161C2×D4—834no—
1162C2×D4—834no—
1163C2×D4—1662no—
1164C2×D4—1662no—
1165C2×D4—1662no—
1166C2×D4—1662no—
1167C2×D4—1662no—
1168C2×D4—1662no—
1169C2×D4C2×C4×D8314yes—
1170C22×C4—22no—
1171C22×C4—22no—
1172C22×C4—41no—
1173C22×C4—41no—
1174C22×C4—41no—
1175C22×C4—41no—
1176C22×C4—41no—
1177C22×C4—41no—
1178C22×C4—41no—
1179C22×C4—41no—
1180C22×C4—3321no—
1181C22×C4—3321no—
1182C22×C4—3321no—
1183C22×C4—3321no—
1184C22×C4—3321no—
1185C22×C4—3321no—
1186C22×C4—3321no—
1187C22×C4—3321no—
1188C22×C4—3321no—
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—834no—
1204C22×C4—834no—
1205C22×C4—831no—
1206C22×C4—834no—
1207C22×C4—831no—
1208C22×C4—831no—
1209C22×C4—831no—
1210C22×C4—831no—
1211C22×C4—831no—
1212C22×C4—831no—
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—1662no—
1222C22×C4—1662no—
1223C22×C4—1662no—
1224C22×C4—1662no—
1225C22×C4—1662no—
1226C22×C4—1662no—
1227C22×C4—1662no—
1228C22×C4—1662no—
1229C22×C4—1662no—
1230C22×C4C2×C4×D8314yes—
1231C22×C4C2×C4×D8314yes—
1232C22×C4C23×D8311yescharacteristic
1233C22×C4C23×D8311yescharacteristic
1234C22×C4C23×D8311yescharacteristic
1235C22×C4C23×D8311yescharacteristic
1236C22×C4C23×D8311yescharacteristic
1237C22×C4C23×D8311yescharacteristic
1238C22×C4C23×D8311yescharacteristic
1239C22×C4C23×D8311yescharacteristic
1240C22×C4C23×D8311yescharacteristic
1241C22×C4C23×D8311yescharacteristic
1242C22×C4C23×D8311yescharacteristic
1243C22×C4C23×D8311yescharacteristic
1244C22×C4C23×D8311yescharacteristic
1245C4⋊C4—41no—
1246C4⋊C4—41no—
1247C4⋊C4—41no—
1248C4⋊C4—41no—
1249C4⋊C4—3321no—
1250C4⋊C4—3321no—
1251C4⋊C4—3321no—
1252C4⋊C4—3321no—
1253C4⋊C4—3321no—
1254C4⋊C4—3321no—
1255C4⋊C4—3321no—
1256C4⋊C4—3321no—
1257C4⋊C4—3321no—
1258C4⋊C4—3321no—
1259C4⋊C4—3321no—
1260C4⋊C4—3321no—
1261C4⋊C4—3321no—
1262C4⋊C4—3321no—
1263C4⋊C4—3321no—
1264C4⋊C4—3321no—
1265C4⋊C4—3321no—
1266C4⋊C4—3321no—
1267C4⋊C4—3321no—
1268C4⋊C4—834no—
1269C4⋊C4—834no—
1270C4⋊C4—834no—
1271C4⋊C4—834no—
1272C4⋊C4—834no—
1273C4⋊C4—834no—
1274C4⋊C4—834no—
1275C4⋊C4—834no—
1276C4⋊C4—834no—
1277C4⋊C4—1662no—
1278C4⋊C4—1662no—
1279C4⋊C4—1662no—
1280C4⋊C4—1662no—
1281C4⋊C4—1662no—
1282C4⋊C4—1662no—
1283C4⋊C4—1662no—
1284C4⋊C4—1662no—
1285C4⋊C4—1662no—
1286C4⋊C4C2×C4×D8314yes—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—3321no—
1294C22⋊C4—3321no—
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—3321no—
1304C22⋊C4—3321no—
1305C22⋊C4—3321no—
1306C22⋊C4—834no—
1307C22⋊C4—834no—
1308C22⋊C4—834no—
1309C22⋊C4—834no—
1310C22⋊C4—834no—
1311C22⋊C4—834no—
1312C22⋊C4—834no—
1313C22⋊C4—834no—
1314C22⋊C4—1662no—
1315C22⋊C4—1662no—
1316C22⋊C4—1662no—
1317C22⋊C4C2×C4×D8314yes—
1318C22⋊C4C2×C4×D8314yes—
1319C42—41no—
1320C42—41no—
1321C42—3321no—
1322C42—3321no—
1323C42—3321no—
1324C42—3321no—
1325C42—3321no—
1326C42—3321no—
1327C42—3321no—
1328C42—3321no—
1329C42—3321no—
1330C42—3321no—
1331C42—834no—
1332C42—834no—
1333C42—1662no—
1334C42—1662no—
1335C42—1662no—
1336C42—1662no—
1337C42C2×C4×D8314yes—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—832no—
1349C23—832no—
1350C23—1661no—
1351C23—1661no—
1352C23—1661no—
1353C23—1661no—
1354C23—1661no—
1355C23—1661no—
1356C23—1661no—
1357C23—1661no—
1358C23—1661no—
1359C23—1661no—
1360C23—1661no—
1361C23—1661no—
1362C23C22×C4×D8312yes—
1363C23C22×C4×D8312yes—
1364C23#1458183812yes—
1365C23#1458183912yes—
1366C23C24×D8311yescharacteristic
1367D4—28no—
1368D4—3324no—
1369D4—3324no—
1370D4—1668no—
1371D4—1668no—
1372D4—1668no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
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—44no—
1408C2×C4—44no—
1409C2×C4—44no—
1410C2×C4—82no—
1411C2×C4—3324no—
1412C2×C4—3324no—
1413C2×C4—3324no—
1414C2×C4—832no—
1415C2×C4—832no—
1416C2×C4—832no—
1417C2×C4—832no—
1418C2×C4—832no—
1419C2×C4—832no—
1420C2×C4—832no—
1421C2×C4—832no—
1422C2×C4—832no—
1423C2×C4—6642no—
1424C2×C4—6642no—
1425C2×C4—6642no—
1426C2×C4—6642no—
1427C2×C4—6642no—
1428C2×C4—6642no—
1429C2×C4—6642no—
1430C2×C4—1668no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4—1661no—
1439C2×C4—1661no—
1440C2×C4—1661no—
1441C2×C4—1661no—
1442C2×C4—1661no—
1443C2×C4—1661no—
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—1668no—
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×C4C22×C4×D8312yes—
1466C2×C4C22×C4×D8312yes—
1467C2×C4C22×C4×D8312yes—
1468C2×C4C22×C4×D8312yes—
1469C2×C4C22×C4×D8312yes—
1470C22—22no—
1471C22—22no—
1472C22—22no—
1473C22—22no—
1474C22—22no—
1475C22—22no—
1476C22—22no—
1477C22—22no—
1478C22—22no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—3321no—
1484C22—3321no—
1485C22—3321no—
1486C22—3321no—
1487C22—3321no—
1488C22—3321no—
1489C22—3321no—
1490C22—3321no—
1491C22—1662no—
1492C22—1662no—
1493C22—1662no—
1494C22—1662no—
1495C22—1662no—
1496C22—1662no—
1497C22#1912818114yes—
1498C22C23×C4×D8311yescharacteristic
1499C22H(5,𝔽2)×D8311yescharacteristic
1500C22H(5,𝔽2)×D8311yescharacteristic
1501C22C2×#1458183811yescharacteristic
1502C222−1+4×D8311yescharacteristic
1503C22C2×#1458183911yescharacteristic
1504C22#1912853611yescharacteristic
1505C4—22no—
1506C4—22no—
1507C4—22no—
1508C4—22no—
1509C4—22no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C4—41no—
1518C4—3321no—
1519C4—3321no—
1520C4—3321no—
1521C4—3321no—
1522C4—3321no—
1523C4—3321no—
1524C4—3321no—
1525C4—834no—
1526C4—1662no—
1527C4—1662no—
1528C4—1662no—
1529C4—1662no—
1530C4—1662no—
1531C4—1662no—
1532C2—24no—
1533C2—42no—
1534C2—3322no—
1535C2—3322no—
1536C2#520×D8311yescharacteristic
1537C2C2×#1912818111yescharacteristic
1538C2#2492066711yescharacteristic
1539C2#2492169511yescharacteristic
1540C2#2492174311yescharacteristic
1541C2#2492189611yescharacteristic
1542C2#2492199911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2318C2
socle, cosocleC23×C83C25
prime radicalC2×#19128400C2
hypercenter#2318D83
hypocenterC83#34461
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #24910652C2semidirect
3. #24910650C2semidirect
4. #24910610C2semidirect
5. #24910607C2semidirect
6. #24910556C2semidirect
7. #24910477C2semidirect
8. #24910476C2semidirect
9. #24910474C2semidirect
10. #24910474C2semidirect
11. D4×C4⋊Dic83C2semidirect
12. #24910361C2semidirect
13. #24910361C2semidirect
14. #24910359C2semidirect
15. #24910351C2semidirect
16. #24910341C2semidirect
17. #24910245C2semidirect
18. #24910234C2semidirect
19. #24910199C2semidirect
20. #24910166C2semidirect
21. #24910164C2semidirect
22. #24910151C2semidirect
23. #24910136C2semidirect
24. #24910129C2semidirect
25. #24910103C2semidirect
26. #24910091C2semidirect
27. #24910088C2semidirect
28. #24909973C2semidirect
29. C2×#19127598C2semidirect
30. #24909899C2semidirect
31. C83×#2318C2semidirect
32. #19128400C4semidirect
205. #14581786C2×C4semidirect
206. #14581785C2×C4semidirect
207. #14581782C2×C4semidirect
208. #14581777C2×C4semidirect
209. #14581775C2×C4semidirect
210. #14581766C2×C4semidirect
211. #14581765C2×C4semidirect
212. #14581764C2×C4semidirect
213. #14581764C2×C4semidirect
219. C4×C22⋊D83C2×C4semidirect
225. (C22⋊D83)⋊C4C2×C4semidirect
226. (C22⋊D83)⋊C4C2×C4semidirect
228. #14581749C2×C4semidirect
246. C2×Dic83⋊C4C2×C4semidirect
345. C4×D4×C83C2×C4semidirect
798. #2318D83semidirect
803. C83#34461semidirect
1004. C4×D4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191284002
#249106522
#249106502
#249106102
#249106072
#249105562
#249104772
#249104762
#249104742
D4×C4⋊Dic832
#249103612
#249103592
#249103512
#249103412
#249102452
#249102342
#249101992
#249101662
#249101642
#249101512
#249101362
#249101292
#249101032
#249100912
#249100882
#249099732
C2×#191275982
#249098992
C83×#23182
#3446183