Finite Group Databasebeta

← #35611719

Subgroups — #35611719

Order 21248.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915758C211yesmaximal, characteristic, complemented
2#24915746C211yesmaximal, characteristic, complemented
3#24914664C211yesmaximal, characteristic, complemented
4#24914560C211yesmaximal, characteristic, complemented
5#24914519C211yesmaximal, characteristic, complemented
6#24914514C211yesmaximal, characteristic, complemented
7#24914303C211yesmaximal, characteristic, complemented
8#24914105C211yesmaximal, characteristic, complemented
9#24914021C211yesmaximal, characteristic, complemented
10#24914006C211yesmaximal, characteristic, complemented
11#24913973C211yesmaximal, characteristic, complemented
12#24913899C211yesmaximal, characteristic, complemented
13#24913873C211yesmaximal, characteristic, complemented
14#24913844C211yesmaximal, characteristic, complemented
15#24913787C211yesmaximal, characteristic, complemented
16#24913711C211yesmaximal, characteristic, complemented
17#24913687C211yesmaximal, characteristic, complemented
18#24913640C211yesmaximal, characteristic, complemented
19#24913596C211yesmaximal, characteristic, complemented
20#24913009C211yesmaximal, characteristic, complemented
21#24912792C211yesmaximal, characteristic, complemented
22#24912568C211yesmaximal, characteristic, complemented
23#24912568C211yesmaximal, characteristic, complemented
24#24911670C211yesmaximal, characteristic, complemented
25#24911647C211yesmaximal, characteristic, complemented
26#24911612C211yesmaximal, characteristic, complemented
27#24911577C211yesmaximal, characteristic, complemented
28#24910256C211yesmaximal, characteristic, complemented
29#24910227C211yesmaximal, characteristic, complemented
30#24909843C211yesmaximal, characteristic, complemented
31C83×#2739C211yesmaximal, characteristic, complemented
32C23×C4×D83C2211yescharacteristic
33C2×#14581780C2211yescharacteristic
34C2×#14581780C2211yescharacteristic
35C2×#14581778C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581777C2211yescharacteristic
38C2×#14581777C2211yescharacteristic
39C2×#14581777C2211yescharacteristic
40C2×#14581777C2211yescharacteristic, complemented
41C2×#14581770C2211yescharacteristic, complemented
42C2×#14581767C2211yescharacteristic
43C2×#14581767C2211yescharacteristic
44C2×#14581766C2211yescharacteristic
45C2×#14581765C2211yescharacteristic
46C2×#14581762C2211yescharacteristic
47C2×#14581762C2211yescharacteristic
48C2×#14581762C2211yescharacteristic
49C2×#14581748C2211yescharacteristic
50C2×#14581748C2211yescharacteristic
51#19127643C2211yescharacteristic, complemented
52#19127642C2211yescharacteristic, complemented
53#19127636C2211yescharacteristic, complemented
54#19127631C2211yescharacteristic, complemented
55#19127630C2211yescharacteristic
56#19127630C2211yescharacteristic, complemented
57#19127630C2211yescharacteristic, complemented
58#19127630C2211yescharacteristic, complemented
59#19127630C2211yescharacteristic, complemented
60#19127630C2211yescharacteristic, complemented
61#19127630C2211yescharacteristic, complemented
62#19127628C2211yescharacteristic
63#19127627C2211yescharacteristic
64#19127627C2211yescharacteristic
65#19127627C2211yescharacteristic, complemented
66#19127625C2211yescharacteristic
67#19127625C2211yescharacteristic, complemented
68#19127623C2211yescharacteristic
69#19127622C2211yescharacteristic, complemented
70#19127621C2211yescharacteristic, complemented
71#19127621C2211yescharacteristic, complemented
72#19127619C2211yescharacteristic
73#19127619C2211yescharacteristic, complemented
74#19127618C2211yescharacteristic
75#19127618C2211yescharacteristic
76#19127618C2211yescharacteristic
77#19127618C2211yescharacteristic, complemented
78#19127617C2211yescharacteristic
79#19127617C2211yescharacteristic
80#19127616C2211yescharacteristic
81#19127616C2211yescharacteristic
82#19127614C2211yescharacteristic
83#19127614C2211yescharacteristic
84#19127614C2211yescharacteristic, complemented
85#19127614C2211yescharacteristic, complemented
86#19127613C2211yescharacteristic
87#19127611C2211yescharacteristic
88#19127611C2211yescharacteristic
89#19127611C2211yescharacteristic
90#19127611C2211yescharacteristic
91#19127611C2211yescharacteristic, complemented
92#19127610C2211yescharacteristic
93#19127605C2211yescharacteristic, complemented
94#19127605C2211yescharacteristic, complemented
95#19127603C2211yescharacteristic
96#19127602C2211yescharacteristic
97#19127602C2211yescharacteristic
98#19127602C2211yescharacteristic
99#19127602C2211yescharacteristic, complemented
100#19127602C2211yescharacteristic, complemented
101#19127601C2211yescharacteristic
102#19127595C2211yescharacteristic
103#19127593C2211yescharacteristic
104#19127593C2211yescharacteristic, complemented
105#19127592C2211yescharacteristic
106#19127592C2211yescharacteristic, complemented
107#19127591C2211yescharacteristic
108#19127591C2211yescharacteristic, complemented
109#19127591C2211yescharacteristic, complemented
110#19127591C2211yescharacteristic, complemented
111#19127591C2211yescharacteristic, complemented
112#19127590C2211yescharacteristic
113#19127590C2211yescharacteristic, complemented
114#19127590C2211yescharacteristic, complemented
115#19127590C2211yescharacteristic, complemented
116#19127587C2211yescharacteristic, complemented
117#19127587C2211yescharacteristic, complemented
118#19127586C2211yescharacteristic, complemented
119#19127586C2211yescharacteristic, complemented
120#19127585C2211yescharacteristic, complemented
121#19127583C2211yescharacteristic, complemented
122#19127582C2211yescharacteristic, complemented
123#19127582C2211yescharacteristic, complemented
124#19127582C2211yescharacteristic, complemented
125#19127580C2211yescharacteristic
126#19127579C2211yescharacteristic
127#19127579C2211yescharacteristic
128#19127579C2211yescharacteristic
129#19127579C2211yescharacteristic
130#19127579C2211yescharacteristic
131#19127579C2211yescharacteristic
132#19127579C2211yescharacteristic
133#19127579C2211yescharacteristic
134#19127579C2211yescharacteristic
135#19127579C2211yescharacteristic
136#19127579C2211yescharacteristic, complemented
137#19127579C2211yescharacteristic, complemented
138#19127579C2211yescharacteristic, complemented
139#19127579C2211yescharacteristic, complemented
140#19127578C2211yescharacteristic
141#19127578C2211yescharacteristic
142#19127578C2211yescharacteristic
143#19127577C2211yescharacteristic
144#19127577C2211yescharacteristic
145#19127575C2211yescharacteristic, complemented
146#19127575C2211yescharacteristic, complemented
147#19127573C2211yescharacteristic
148#19127572C2211yescharacteristic
149#19127572C2211yescharacteristic
150#19127568C2211yescharacteristic, complemented
151#19127564C2211yescharacteristic
152#19127563C2211yescharacteristic
153#19127563C2211yescharacteristic
154#19127560C2211yescharacteristic
155#19127560C2211yescharacteristic
156#19127560C2211yescharacteristic
157#19127560C2211yescharacteristic
158#19127558C2211yescharacteristic
159#19127558C2211yescharacteristic
160#19127558C2211yescharacteristic, complemented
161#19127556C2211yescharacteristic
162#19127556C2211yescharacteristic
163#19127556C2211yescharacteristic
164#19127552C2211yescharacteristic, complemented
165C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
166C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
167#19127548C2211yescharacteristic
168#19127548C2211yescharacteristic
169#19127548C2211yescharacteristic
170#19127548C2211yescharacteristic
171#19127548C2211yescharacteristic, complemented
172#400×C83C2211yescharacteristic, complemented
173#400×C83C2211yescharacteristic, complemented
174#400×C83C2211yescharacteristic, complemented
175#398×C83C2211yescharacteristic, complemented
176#397×C83C2211yescharacteristic
177#396×C83C2211yescharacteristic
178#389×C83C2211yescharacteristic, complemented
179#388×C83C2211yescharacteristic
180#388×C83C2211yescharacteristic
181#387×C83C2211yescharacteristic, complemented
182#387×C83C2211yescharacteristic, complemented
183#387×C83C2211yescharacteristic, complemented
184#385×C83C2211yescharacteristic
185#381×C83C2211yescharacteristic
186#380×C83C2211yescharacteristic
187C24×D83C2311yescharacteristic
188C22×Dic166C2311yescharacteristic
189C22×Dic166C2311yescharacteristic
190C22×D332C2311yescharacteristic
191C22×D332C2311yescharacteristic
192C22×D332C2311yescharacteristic
193C22×D332C2311yescharacteristic
194C22×D332C2311yescharacteristic
195C22×D332C2311yescharacteristic
196C22×D332C2311yescharacteristic
197C22×D332C2311yescharacteristic
198C22×D332C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C23×Dic83C2311yescharacteristic
203C22×C4×D83—24no—
204C22×C4×D83—42no—
205C22×C4×D83—42no—
206C22×C4×D83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213#14581780—42no—
214#14581780—42no—
215#14581778—42no—
216#14581777—24no—
217#14581777—42no—
218#14581777—42no—
219#14581777—42no—
220#14581777—42no—
221#14581770—42no—
222#14581767—24no—
223#14581767—42no—
224#14581766—42no—
225#14581765—42no—
226#14581762—42no—
227#14581762—42no—
228#14581762—42no—
229#14581748—42no—
230#14581748—42no—
231C2×C4⋊Dic83C2311yescharacteristic
232C2×C4⋊Dic83C2311yescharacteristic
233C2×C4⋊Dic83C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×Dic83⋊C4C2311yescharacteristic
238C2×Dic83⋊C4C2311yescharacteristic
239C2×Dic83⋊C4C2311yescharacteristic
240C2×Dic83⋊C4C2311yescharacteristic
241C2×Dic83⋊C4C2311yescharacteristic
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×C22⋊Dic83C2311yescharacteristic
246C2×C22⋊Dic83C2311yescharacteristic
247C2×C22⋊Dic83C2311yescharacteristic
248C2×(C2×D83)⋊C4C2311yescharacteristic
249C2×(C2×D83)⋊C4C2311yescharacteristic
250C2×(C2×D83)⋊C4C2311yescharacteristic
251C2×(C2×D83)⋊C4C2311yescharacteristic
252C2×(C2×D83)⋊C4C2311yescharacteristic
253C2×(C2×D83)⋊C4C2311yescharacteristic
254C2×(C2×D83)⋊C4C2311yescharacteristic
255C2×(C2×D83)⋊C4C2311yescharacteristic
256C2×(C2×D83)⋊C4C2311yescharacteristic
257C2×(C2×D83)⋊C4C2311yescharacteristic
258C2×(C2×D83)⋊C4C2311yescharacteristic
259C2×(C2×D83)⋊C4C2311yescharacteristic
260C2×(C2×D83)⋊C4C2311yescharacteristic
261C2×(C2×D83)⋊C4C2311yescharacteristic
262C2×(C2×D83)⋊C4C2311yescharacteristic
263C2×(C2×D83)⋊C4C2311yescharacteristic
264C2×(C2×D83)⋊C4C2311yescharacteristic
265C2×(C2×D83)⋊C4C2311yescharacteristic
266C2×(C2×D83)⋊C4C2311yescharacteristic
267C2×(C2×D83)⋊C4C2311yescharacteristic
268C2×(C2×D83)⋊C4C2311yescharacteristic
269C2×(C2×D83)⋊C4C2311yescharacteristic
270C2×(C2×D83)⋊C4C2311yescharacteristic
271C2×(C2×D83)⋊C4C2311yescharacteristic
272C2×(C2×D83)⋊C4C2311yescharacteristic
273C2×(C2×D83)⋊C4C2311yescharacteristic
274C2×(C2×D83)⋊C4C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
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×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
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
328C23×C4×C83C2311yescharacteristic
329C2×C4⋊C4×C83C2311yescharacteristic
330C2×C4⋊C4×C83C2311yescharacteristic
331C2×C4⋊C4×C83C2311yescharacteristic
332C2×C4⋊C4×C83C2311yescharacteristic
333C2×C4⋊C4×C83C2311yescharacteristic
334C2×C4⋊C4×C83C2311yescharacteristic
335C2×C4⋊C4×C83C2311yescharacteristic
336C2×C4⋊C4×C83C2311yescharacteristic
337C2×C4⋊C4×C83C2311yescharacteristic
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C22⋊C4×C83C2311yescharacteristic
340C2×C22⋊C4×C83C2311yescharacteristic
341C2×C22⋊C4×C83C2311yescharacteristic
342C2×C22⋊C4×C83C2311yescharacteristic
343C2×C22⋊C4×C83C2311yescharacteristic
344C2×C22⋊C4×C83C2311yescharacteristic
345C2×C42×C83C2311yescharacteristic
346C2×C42×C83C2311yescharacteristic
347#95×C83C2311yescharacteristic
348#95×C83C2311yescharacteristic
349#95×C83C2311yescharacteristic
350#95×C83C2311yescharacteristic
351#95×C83C2311yescharacteristic
352#95×C83C2311yescharacteristic
353#95×C83C2311yescharacteristic
354#95×C83C2311yescharacteristic
355#95×C83C2311yescharacteristic
356#95×C83C2311yescharacteristic
357#95×C83C2311yescharacteristic
358#95×C83C2311yescharacteristic
359#95×C83C2311yescharacteristic
360#95×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363C23×D83—22no—
364C23×D83—22no—
365C23×D83—22no—
366C23×D83—41no—
367C23×D83—41no—
368C23×D83—41no—
369C23×D83—41no—
370C23×D83C2411yescharacteristic
371C23×D83C2411yescharacteristic
372C23×D83C2411yescharacteristic
373C23×D83C2411yescharacteristic
374C23×D83C2411yescharacteristic
375C2×Dic166—41no—
376C2×Dic166—41no—
377C2×Dic166—41no—
378C2×Dic166—41no—
379C2×Dic166—41no—
380C2×Dic166—41no—
381C2×D332—22no—
382C2×D332—22no—
383C2×D332—22no—
384C2×D332—22no—
385C2×D332—22no—
386C2×D332—22no—
387C2×D332—22no—
388C2×D332—41no—
389C2×D332—41no—
390C2×D332—41no—
391C2×D332—41no—
392C2×D332—41no—
393C2×D332—41no—
394C2×D332—41no—
395C2×D332—41no—
396C2×D332—41no—
397C2×D332—41no—
398C2×D332—41no—
399C2×D332—41no—
400C2×D332—41no—
401C2×D332—41no—
402C2×D332—41no—
403C2×D332—41no—
404C2×D332—41no—
405C2×D332—41no—
406C2×D332—41no—
407C2×D332—41no—
408C2×C22⋊D83—22no—
409C2×C22⋊D83—22no—
410C2×C22⋊D83—22no—
411C2×C22⋊D83—41no—
412C2×C22⋊D83—41no—
413C2×C22⋊D83—41no—
414C2×C22⋊D83—41no—
415C2×C22⋊D83—41no—
416C2×C22⋊D83—41no—
417C22×Dic83—22no—
418C22×Dic83—22no—
419C22×Dic83—22no—
420C22×Dic83C2411yescharacteristic
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2411yescharacteristic
423C22×Dic83C2411yescharacteristic
424C22×Dic83C2411yescharacteristic
425C22×Dic83C2411yescharacteristic
426C22×Dic83C2411yescharacteristic
427C22×Dic83C2411yescharacteristic
428C22×Dic83C2411yescharacteristic
429C22×Dic83C2411yescharacteristic
430C22×Dic83C2411yescharacteristic
431C2×C4×D83—22no—
432C2×C4×D83—22no—
433C2×C4×D83—22no—
434C2×C4×D83—22no—
435C2×C4×D83—22no—
436C2×C4×D83—41no—
437C2×C4×D83—41no—
438C2×C4×D83—41no—
439C2×C4×D83—41no—
440C2×C4×D83—41no—
441C2×C4×D83—41no—
442C2×C4×D83—416no—
443C2×C4×D83—41no—
444C2×C4×D83—41no—
445C2×C4×D83—41no—
446C2×C4×D83—41no—
447C2×C4×D83—41no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
450C2×C4×D83—41no—
451C2×C4×D83—41no—
452C2×C4×D83#4114yes—
453C4⋊Dic83—41no—
454C4⋊Dic83—41no—
455C4⋊Dic83—41no—
456Dic83⋊C4—22no—
457Dic83⋊C4—22no—
458Dic83⋊C4—22no—
459Dic83⋊C4—22no—
460Dic83⋊C4—41no—
461Dic83⋊C4—41no—
462Dic83⋊C4—41no—
463Dic83⋊C4—41no—
464Dic83⋊C4—41no—
465Dic83⋊C4—41no—
466Dic83⋊C4—41no—
467C22⋊Dic83—22no—
468C22⋊Dic83—41no—
469C22⋊Dic83—41no—
470(C2×D83)⋊C4—22no—
471(C2×D83)⋊C4—22no—
472(C2×D83)⋊C4—22no—
473(C2×D83)⋊C4—22no—
474(C2×D83)⋊C4—22no—
475(C2×D83)⋊C4—22no—
476(C2×D83)⋊C4—22no—
477(C2×D83)⋊C4—22no—
478(C2×D83)⋊C4—22no—
479(C2×D83)⋊C4—22no—
480(C2×D83)⋊C4—22no—
481(C2×D83)⋊C4—22no—
482(C2×D83)⋊C4—22no—
483(C2×D83)⋊C4—41no—
484(C2×D83)⋊C4—41no—
485(C2×D83)⋊C4—41no—
486(C2×D83)⋊C4—41no—
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)⋊C4—41no—
499(C2×D83)⋊C4—41no—
500(C2×D83)⋊C4—41no—
501(C2×D83)⋊C4—41no—
502(C2×D83)⋊C4—41no—
503(C2×D83)⋊C4—41no—
504(C2×D83)⋊C4—41no—
505(C2×D83)⋊C4—41no—
506(C2×D83)⋊C4—41no—
507(C2×D83)⋊C4—41no—
508(C2×D83)⋊C4—41no—
509(C2×D83)⋊C4—41no—
510(C2×D83)⋊C4—41no—
511(C2×D83)⋊C4—41no—
512(C2×D83)⋊C4—41no—
513(C2×D83)⋊C4—41no—
514(C2×D83)⋊C4—41no—
515C4×Dic83—41no—
516C4×Dic83—41no—
517C4×Dic83—41no—
518C4×Dic83—41no—
519C4×Dic83—41no—
520C4×Dic83—41no—
521C4×Dic83—41no—
522C24×C83C2411yescharacteristic
523C22×C4×C83—22no—
524C22×C4×C83—22no—
525C22×C4×C83—41no—
526C22×C4×C83C2411yescharacteristic
527C22×C4×C83C2411yescharacteristic
528C22×C4×C83C2411yescharacteristic
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2411yescharacteristic
531C22×C4×C83C2411yescharacteristic
532C22×C4×C83C2411yescharacteristic
533C22×C4×C83C2411yescharacteristic
534C22×C4×C83C2411yescharacteristic
535C22×C4×C83C2411yescharacteristic
536C22×C4×C83C2411yescharacteristic
537C22×C4×C83C2411yescharacteristic
538C22×C4×C83C2411yescharacteristic
539C22×C4×C83C2411yescharacteristic
540C4⋊C4×C83—22no—
541C4⋊C4×C83—22no—
542C4⋊C4×C83—41no—
543C4⋊C4×C83—41no—
544C4⋊C4×C83—41no—
545C4⋊C4×C83—41no—
546C4⋊C4×C83—41no—
547C4⋊C4×C83—41no—
548C4⋊C4×C83—41no—
549C4⋊C4×C83—41no—
550C22⋊C4×C83—22no—
551C22⋊C4×C83—22no—
552C22⋊C4×C83—41no—
553C22⋊C4×C83—41no—
554C22⋊C4×C83—41no—
555C22⋊C4×C83—41no—
556C42×C83—41no—
557C42×C83—41no—
558C23×C83—21no—
559C23×C83—21no—
560C23×C83—21no—
561C23×C83—21no—
562C23×C83—21no—
563C23×C83—21no—
564C23×C83H(5,𝔽2)12yes—
565C23×C83C2511yescharacteristic
566C22×D83—21no—
567C22×D83—21no—
568C22×D83—21no—
569C22×D83—21no—
570C22×D83—21no—
571C22×D83—21no—
572C22×D83—21no—
573C22×D83—21no—
574C22×D83—21no—
575C22×D83—21no—
576C22×D83—21no—
577C22×D83—21no—
578C22×D83—21no—
579C22×D83—21no—
580C22×D83—21no—
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×D83—21no—
594C22×D83—21no—
595C22×D83—21no—
596C22×D83—21no—
597C22×D83—21no—
598C22×D83—21no—
599C22×D83—44no—
600C22×D83—44no—
601C22×D83—44no—
602C22×D83—44no—
603C22×D83—44no—
604C22×D83—44no—
605C22×D83—44no—
606C22×D83C2×#4112yes—
607C22×D83H(5,𝔽2)12yes—
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—21no—
639C2×C4×C83—21no—
640C2×C4×C83—21no—
641C2×C4×C83—21no—
642C2×C4×C83—21no—
643C2×C4×C83—21no—
644C2×C4×C83—21no—
645C2×C4×C83—21no—
646C2×C4×C83—21no—
647C2×C4×C83—21no—
648C2×C4×C83—21no—
649C2×C4×C83—44no—
650C2×C4×C83C2×#4112yes—
651C22⋊D83—82no—
652C22⋊D83—82no—
653C22⋊D83—82no—
654C2×Dic83—28no—
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—21no—
686C2×Dic83C2×#4112yes—
687C2×Dic83H(5,𝔽2)12yes—
688D332—82no—
689D332—82no—
690D332—82no—
691D332—82no—
692D332—82no—
693D332—82no—
694D332—82no—
695D332—82no—
696D332—82no—
697C4×D83—44no—
698C4×D83—44no—
699C4×D83—44no—
700C4×D83—44no—
701C4×D83—82no—
702C4×D83—82no—
703C4×D83—82no—
704Dic166—82no—
705Dic166—82no—
706C22×C83—22no—
707C22×C83—22no—
708C22×C83—22no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83—41no—
712C22×C83—41no—
713C22×C83C22×#4111yescharacteristic
714C22×C83C2×H(5,𝔽2)11yescharacteristic
715C22×C83C2×H(5,𝔽2)11yescharacteristic
716C22×C83C2×H(5,𝔽2)11yescharacteristic
717C22×C83#58511yescharacteristic
718C22×C83#58511yescharacteristic
719C22×C83#58511yescharacteristic
720C2×D83—22no—
721C2×D83—22no—
722C2×D83—22no—
723C2×D83—22no—
724C2×D83—22no—
725C2×D83—22no—
726C2×D83—416no—
727C2×D83—41no—
728C2×D83—41no—
729C2×D83—41no—
730C2×D83—41no—
731C2×D83—41no—
732C2×D83—41no—
733C2×D83—41no—
734C2×D83—41no—
735C2×D83—41no—
736C2×D83—41no—
737C2×D83—41no—
738C2×D83—41no—
739C2×D83—41no—
740C2×D83—41no—
741C2×D83—41no—
742C2×D83—41no—
743C2×D83—41no—
744C2×D83—41no—
745C2×D83—41no—
746C2×D83—41no—
747C2×D83—41no—
748C2×D83—41no—
749C2×D83—41no—
750C2×D83—41no—
751C2×D83—41no—
752C2×D83—41no—
753C2×D83—41no—
754C2×D83—41no—
755C2×D83—41no—
756C4×C83—22no—
757C4×C83—41no—
758C4×C83—41no—
759C4×C83—41no—
760C4×C83—41no—
761C4×C83—41no—
762C4×C83—41no—
763C4×C83—41no—
764C4×C83—41no—
765C4×C83—41no—
766C4×C83—41no—
767C4×C83—41no—
768C4×C83—41no—
769C4×C83—41no—
770Dic83—22no—
771Dic83—22no—
772Dic83—41no—
773Dic83—41no—
774Dic83—41no—
775Dic83—41no—
776Dic83—41no—
777Dic83—41no—
778Dic83—41no—
779Dic83—41no—
780Dic83—41no—
781#36735—831nomaximal, Sylow
782C2×C83—42no—
783C2×C83#345511yescharacteristic
784C2×C83#349011yescharacteristic
785C2×C83#349411yescharacteristic
786C2×C83#353311yescharacteristic
787C2×C83#353411yescharacteristic
788C2×C83#354011yescharacteristic
789C2×C83#354211yescharacteristic
790D83—42no—
791D83—42no—
792D83—81no—
793D83—81no—
794D83—81no—
795#2849—831no—
796#2847—831no—
797#2747—831no—
798#2740—831no—
799#2739D8311yescharacteristic, complemented
800#2737—831no—
801#2737—831no—
802#2717—831no—
803#2703—831no—
804#2697—831no—
805#2696—831no—
806#2693—831no—
807#2688—831no—
808#2686—831no—
809#2684—831no—
810#2678—831no—
811#2672—831no—
812#2670—831no—
813#2665—831no—
814#2661—831no—
815#2597—831no—
816#2578—831no—
817#2557—831no—
818#2557—831no—
819#2477—831no—
820#2476—831no—
821#2474—831no—
822#2471—831no—
823#2335—831no—
824#2333—831no—
825#2280—831no—
826C83#3673511yescharacteristic, complemented, Sylow
827C24×C4—831no—
828C2×#124—831no—
829C2×#124—831no—
830C2×#124—831no—
831C2×#123—831no—
832C2×#123—831no—
833C2×#123—831no—
834C2×#123—831no—
835C2×#123—831no—
836C2×C22⋊Q8—831no—
837C2×#121—831no—
838C2×#121—831no—
839C2×#121—831no—
840C2×#121—831no—
841C2×#120—831no—
842C2×#120—831no—
843C2×#120—831no—
844C2×#117—831no—
845C2×#117—831no—
846#400—831no—
847#400—831no—
848#400C2×D8311yescharacteristic, complemented
849#400C2×D8311yescharacteristic, complemented
850#400C2×D8311yescharacteristic, complemented
851#399—831no—
852#398—831no—
853#398C2×D8311yescharacteristic, complemented
854#397—831no—
855#397—831no—
856#397—831no—
857#397—831no—
858#397—831no—
859#397—831no—
860#397—831no—
861#397—831no—
862#397—831no—
863#397—831no—
864#397—831no—
865#397C2×D8311yescharacteristic
866#396—831no—
867#396—831no—
868#396—831no—
869#396C2×D8311yescharacteristic
870#395—831no—
871#395—831no—
872#395—831no—
873#394—831no—
874#394—831no—
875#394—831no—
876#394—831no—
877#394—831no—
878#394—831no—
879#394—831no—
880#394—831no—
881#394—831no—
882#394—831no—
883#393—831no—
884#393—831no—
885#393—831no—
886#393—831no—
887#393—831no—
888#392—831no—
889#392—831no—
890#392—831no—
891#392—831no—
892#392—831no—
893#392—831no—
894#391—831no—
895#391—831no—
896#390—831no—
897#390—831no—
898#390—831no—
899#390—831no—
900#390—831no—
901#390—831no—
902#390—831no—
903#389C2×D8311yescharacteristic, complemented
904#388—831no—
905#388—831no—
906#388—831no—
907#388—831no—
908#388—831no—
909#388—831no—
910#388—831no—
911#388—831no—
912#388—831no—
913#388—831no—
914#388—831no—
915#388—831no—
916#388—831no—
917#388—831no—
918#388C2×D8311yescharacteristic
919#388C2×D8311yescharacteristic
920#387—831no—
921#387—831no—
922#387—831no—
923#387—831no—
924#387—831no—
925#387—831no—
926#387—831no—
927#387—831no—
928#387—831no—
929#387C2×D8311yescharacteristic, complemented
930#387C2×D8311yescharacteristic, complemented
931#387C2×D8311yescharacteristic, complemented
932#386—831no—
933#386—831no—
934#386—831no—
935#386—831no—
936#386—831no—
937#386—831no—
938#386—831no—
939#386—831no—
940#386—831no—
941#386—831no—
942#386—831no—
943#386—831no—
944#386—831no—
945#386—831no—
946#386—831no—
947#386—831no—
948#386—831no—
949#386—831no—
950#386—831no—
951#386—831no—
952#385—831no—
953#385—831no—
954#385—831no—
955#385—831no—
956#385—831no—
957#385C2×D8311yescharacteristic
958#383—831no—
959#381—831no—
960#381—831no—
961#381—831no—
962#381C2×D8311yescharacteristic
963#380—831no—
964#380—831no—
965#380—831no—
966#380—831no—
967#380—831no—
968#380—831no—
969#380—831no—
970#380C2×D8311yescharacteristic
971#379—831no—
972#379—831no—
973#379—831no—
974C4×C4⋊C4—831no—
975C4×C22⋊C4—831no—
976C4×C22⋊C4—831no—
977C4×C22⋊C4—831no—
978C4×C22⋊C4—831no—
979C4×C22⋊C4—831no—
980C4×C22⋊C4—831no—
981C4×C22⋊C4—831no—
982C25—831no—
983C22×Q8—831no—
984C22×Q8—831no—
985C22×D4—831no—
986C22×D4—831no—
987C22×D4—831no—
988C22×D4—831no—
989C22×D4—831no—
990C22×D4—831no—
991C22×D4—831no—
992C22×D4—831no—
993C22×D4—831no—
994C22×D4—831no—
995C22×D4—831no—
996C22×D4—831no—
997C23×C4—3322no—
998C23×C4—3322no—
999C23×C4—831no—
1000C23×C4—831no—
1001C23×C4—831no—
1002C23×C4—831no—
1003C23×C4—831no—
1004C23×C4—831no—
1005C23×C4—831no—
1006C23×C4—831no—
1007C23×C4—1664no—
1008C23×C4C22×D8311yescharacteristic
1009#124—3322no—
1010#124—3322no—
1011#124—3322no—
1012#123—3322no—
1013#123—3322no—
1014#123—3322no—
1015#123—3322no—
1016#123—1664no—
1017C22⋊Q8—3322no—
1018#121—3322no—
1019#121—3322no—
1020#121—3322no—
1021#121—1664no—
1022#120—3322no—
1023#120—3322no—
1024#120—3322no—
1025#117—3322no—
1026#117—3322no—
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⋊C4C22×D8311yescharacteristic
1042C2×C4⋊C4C22×D8311yescharacteristic
1043C2×C4⋊C4C22×D8311yescharacteristic
1044C2×C4⋊C4C22×D8311yescharacteristic
1045C2×C4⋊C4C22×D8311yescharacteristic
1046C2×C4⋊C4C22×D8311yescharacteristic
1047C2×C4⋊C4C22×D8311yescharacteristic
1048C2×C4⋊C4C22×D8311yescharacteristic
1049C2×C4⋊C4C22×D8311yescharacteristic
1050C2×C4⋊C4C22×D8311yescharacteristic
1051C2×C22⋊C4—831no—
1052C2×C22⋊C4—831no—
1053C2×C22⋊C4—831no—
1054C2×C22⋊C4—831no—
1055C2×C22⋊C4—831no—
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⋊C4—831no—
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⋊C4—831no—
1088C2×C22⋊C4—831no—
1089C2×C22⋊C4—831no—
1090C2×C22⋊C4—831no—
1091C2×C22⋊C4—831no—
1092C2×C22⋊C4—831no—
1093C2×C22⋊C4—831no—
1094C2×C22⋊C4—831no—
1095C2×C22⋊C4—831no—
1096C2×C22⋊C4—831no—
1097C2×C22⋊C4—831no—
1098C2×C22⋊C4—831no—
1099C2×C22⋊C4C22×D8311yescharacteristic
1100C2×C22⋊C4C22×D8311yescharacteristic
1101C2×C22⋊C4C22×D8311yescharacteristic
1102C2×C22⋊C4C22×D8311yescharacteristic
1103C2×C22⋊C4C22×D8311yescharacteristic
1104C2×C22⋊C4C22×D8311yescharacteristic
1105C2×C42—831no—
1106C2×C42—831no—
1107C2×C42—831no—
1108C2×C42—831no—
1109C2×C42—831no—
1110C2×C42—831no—
1111C2×C42—831no—
1112C2×C42C22×D8311yescharacteristic
1113C2×C42C22×D8311yescharacteristic
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
1156#95C22×D8311yescharacteristic
1157#95C22×D8311yescharacteristic
1158C24—3321no—
1159C24—3321no—
1160C24—3321no—
1161C24—3321no—
1162C24—831no—
1163C24—831no—
1164C24—831no—
1165C24—831no—
1166C24—831no—
1167C24—1662no—
1168C24—1662no—
1169C24—1662no—
1170C24C23×D8311yescharacteristic
1171C2×Q8—3321no—
1172C2×Q8—3321no—
1173C2×Q8—3321no—
1174C2×Q8—3321no—
1175C2×Q8—3321no—
1176C2×Q8—3321no—
1177C2×D4—3321no—
1178C2×D4—3321no—
1179C2×D4—3321no—
1180C2×D4—3321no—
1181C2×D4—3321no—
1182C2×D4—3321no—
1183C2×D4—3321no—
1184C2×D4—3321no—
1185C2×D4—3321no—
1186C2×D4—3321no—
1187C2×D4—3321no—
1188C2×D4—3321no—
1189C2×D4—3321no—
1190C2×D4—3321no—
1191C2×D4—3321no—
1192C2×D4—3321no—
1193C2×D4—3321no—
1194C2×D4—3321no—
1195C2×D4—3321no—
1196C2×D4—3321no—
1197C2×D4—3321no—
1198C2×D4—3321no—
1199C2×D4—3321no—
1200C2×D4—3321no—
1201C2×D4—3321no—
1202C2×D4—3321no—
1203C2×D4—1662no—
1204C2×D4—1662no—
1205C2×D4—1662no—
1206C2×D4—1662no—
1207C2×D4—1662no—
1208C2×D4—1662no—
1209C2×D4—1662no—
1210C2×D4—1662no—
1211C2×D4—1662no—
1212C2×D4—1662no—
1213C22×C4—22no—
1214C22×C4—22no—
1215C22×C4—41no—
1216C22×C4—3321no—
1217C22×C4—3321no—
1218C22×C4—3321no—
1219C22×C4—3321no—
1220C22×C4—3321no—
1221C22×C4—3321no—
1222C22×C4—3321no—
1223C22×C4—3321no—
1224C22×C4—3321no—
1225C22×C4—3321no—
1226C22×C4—3321no—
1227C22×C4—3321no—
1228C22×C4—3321no—
1229C22×C4—3321no—
1230C22×C4—3321no—
1231C22×C4—33216no—
1232C22×C4—834no—
1233C22×C4—831no—
1234C22×C4—831no—
1235C22×C4—831no—
1236C22×C4—831no—
1237C22×C4—831no—
1238C22×C4—831no—
1239C22×C4—831no—
1240C22×C4—831no—
1241C22×C4—831no—
1242C22×C4—831no—
1243C22×C4—831no—
1244C22×C4—1662no—
1245C22×C4—1662no—
1246C22×C4—1662no—
1247C22×C4—1662no—
1248C22×C4—1662no—
1249C22×C4—1662no—
1250C22×C4—1662no—
1251C22×C4—1662no—
1252C22×C4C23×D8311yescharacteristic
1253C22×C4C23×D8311yescharacteristic
1254C22×C4C23×D8311yescharacteristic
1255C22×C4C23×D8311yescharacteristic
1256C22×C4C23×D8311yescharacteristic
1257C22×C4C23×D8311yescharacteristic
1258C22×C4C23×D8311yescharacteristic
1259C22×C4C23×D8311yescharacteristic
1260C22×C4C23×D8311yescharacteristic
1261C22×C4C23×D8311yescharacteristic
1262C22×C4C23×D8311yescharacteristic
1263C22×C4C23×D8311yescharacteristic
1264C22×C4C23×D8311yescharacteristic
1265C22×C4C23×D8311yescharacteristic
1266C4⋊C4—22no—
1267C4⋊C4—22no—
1268C4⋊C4—41no—
1269C4⋊C4—41no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4—41no—
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—41no—
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—3321no—
1285C4⋊C4—3321no—
1286C4⋊C4—1662no—
1287C4⋊C4—1662no—
1288C4⋊C4—1662no—
1289C4⋊C4—1662no—
1290C22⋊C4—22no—
1291C22⋊C4—22no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
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—3321no—
1307C22⋊C4—3321no—
1308C22⋊C4—3321no—
1309C22⋊C4—3321no—
1310C22⋊C4—3321no—
1311C22⋊C4—3321no—
1312C22⋊C4—3321no—
1313C22⋊C4—3321no—
1314C22⋊C4—3321no—
1315C22⋊C4—3321no—
1316C22⋊C4—3321no—
1317C22⋊C4—3321no—
1318C22⋊C4—3321no—
1319C22⋊C4—3321no—
1320C22⋊C4—3321no—
1321C22⋊C4—3321no—
1322C22⋊C4—3321no—
1323C22⋊C4—3321no—
1324C22⋊C4—3321no—
1325C22⋊C4—3321no—
1326C22⋊C4—3321no—
1327C22⋊C4—3321no—
1328C22⋊C4—3321no—
1329C22⋊C4—3321no—
1330C22⋊C4—1662no—
1331C22⋊C4—1662no—
1332C22⋊C4—1662no—
1333C22⋊C4—1662no—
1334C22⋊C4—1662no—
1335C22⋊C4—1662no—
1336C22⋊C4—1662no—
1337C22⋊C4—1662no—
1338C22⋊C4—1662no—
1339C22⋊C4—1662no—
1340C22⋊C4—1662no—
1341C22⋊C4—1662no—
1342C22⋊C4—1662no—
1343C22⋊C4—1662no—
1344C42—41no—
1345C42—41no—
1346C42—3321no—
1347C42—3321no—
1348C42—3321no—
1349C42—3321no—
1350C42—3321no—
1351C42—3321no—
1352C42—3321no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—3324no—
1360C23—3324no—
1361C23—3324no—
1362C23—3324no—
1363C23—3324no—
1364C23—3324no—
1365C23—3324no—
1366C23—832no—
1367C23—832no—
1368C23—1661no—
1369C23—1661no—
1370C23—1661no—
1371C23—1661no—
1372C23—1661no—
1373C23—1661no—
1374C23—1661no—
1375C23—1661no—
1376C23—1661no—
1377C23—1661no—
1378C23—1661no—
1379C23—1661no—
1380C23—1661no—
1381C23—1661no—
1382C23—1661no—
1383C23—1661no—
1384C23—1661no—
1385C23—1661no—
1386C23—1661no—
1387C23—1661no—
1388C23—1661no—
1389C23—1661no—
1390C23—1661no—
1391C23—1661no—
1392C23—1661no—
1393C23—1661no—
1394C23—1661no—
1395C23—1661no—
1396C23—1661no—
1397C23—1661no—
1398C23—1661no—
1399C23—1661no—
1400C23—1661no—
1401C23#1458183812yes—
1402C23C24×D8311yescharacteristic
1403Q8—6642no—
1404Q8—6642no—
1405D4—6642no—
1406D4—6642no—
1407D4—6642no—
1408D4—6642no—
1409D4—6642no—
1410D4—6642no—
1411D4—6642no—
1412D4—6642no—
1413D4—6642no—
1414D4—6642no—
1415D4—6642no—
1416D4—6642no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—44no—
1459C2×C4—3324no—
1460C2×C4—3324no—
1461C2×C4—3324no—
1462C2×C4—3324no—
1463C2×C4—832no—
1464C2×C4—832no—
1465C2×C4—6642no—
1466C2×C4—6642no—
1467C2×C4—6642no—
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×C4—1661no—
1481C2×C4—1661no—
1482C2×C4—1661no—
1483C2×C4—1661no—
1484C2×C4—1661no—
1485C2×C4—1661no—
1486C2×C4—1661no—
1487C2×C4—1661no—
1488C2×C4—1661no—
1489C2×C4—1661no—
1490C2×C4—1661no—
1491C2×C4—1661no—
1492C2×C4—1661no—
1493C2×C4—1661no—
1494C2×C4—1661no—
1495C2×C4—1668no—
1496C2×C4—1661no—
1497C2×C4—1661no—
1498C2×C4—1661no—
1499C2×C4—1661no—
1500C2×C4#41×D8312yes—
1501C22—22no—
1502C22—22no—
1503C22—22no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—33216no—
1509C22—3321no—
1510C22—3321no—
1511C22—3321no—
1512C22—3321no—
1513C22—3321no—
1514C22—3321no—
1515C22—3321no—
1516C22—3321no—
1517C22—3321no—
1518C22—3321no—
1519C22—3321no—
1520C22—3321no—
1521C22—3321no—
1522C22—3321no—
1523C22—3321no—
1524C22—3321no—
1525C22—3321no—
1526C22—3321no—
1527C22—3321no—
1528C22—3321no—
1529C22—3321no—
1530C22—3321no—
1531C22—3321no—
1532C22—3321no—
1533C22—3321no—
1534C22—3321no—
1535C22—3321no—
1536C22—3321no—
1537C22—3321no—
1538C22—1662no—
1539C22—1662no—
1540C22—1662no—
1541C22—1662no—
1542C22—1662no—
1543C22—1662no—
1544C22C2×#41×D8311yescharacteristic
1545C22H(5,𝔽2)×D8311yescharacteristic
1546C22H(5,𝔽2)×D8311yescharacteristic
1547C22C2×#1458183811yescharacteristic
1548C22#1912853711yescharacteristic
1549C22#1912853811yescharacteristic
1550C22#1912853811yescharacteristic
1551C4—22no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—41no—
1557C4—41no—
1558C4—41no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—3321no—
1566C4—3321no—
1567C4—3321no—
1568C4—3321no—
1569C4—3321no—
1570C4—3321no—
1571C4—3321no—
1572C4—3321no—
1573C4—3321no—
1574C4—1662no—
1575C4—1662no—
1576C2—42no—
1577C2—3322no—
1578C2—3322no—
1579C2—6641no—
1580C2—6641no—
1581C2—6641no—
1582C2#2492085411yescharacteristic
1583C2#2492114711yescharacteristic
1584C2#2492119111yescharacteristic
1585C2#2492162911yescharacteristic
1586C2#2492165111yescharacteristic
1587C2#2492172811yescharacteristic
1588C2#2492177611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2739C2
hypercenter#2739D83
hypocenterC83#36735
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2739

Complements

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

NH ≅ G/Ntype
1. #24915758C2semidirect
2. #24915746C2semidirect
3. #24914664C2semidirect
4. #24914560C2semidirect
5. #24914519C2semidirect
6. #24914514C2semidirect
7. #24914303C2semidirect
8. #24914105C2semidirect
9. #24914021C2semidirect
10. #24914006C2semidirect
11. #24913973C2semidirect
12. #24913899C2semidirect
13. #24913873C2semidirect
14. #24913844C2semidirect
15. #24913787C2semidirect
16. #24913711C2semidirect
17. #24913687C2semidirect
18. #24913640C2semidirect
19. #24913596C2semidirect
20. #24913009C2semidirect
21. #24912792C2semidirect
22. #24912568C2semidirect
23. #24912568C2semidirect
24. #24911670C2semidirect
25. #24911647C2semidirect
26. #24911612C2semidirect
27. #24911577C2semidirect
28. #24910256C2semidirect
29. #24910227C2semidirect
30. #24909843C2semidirect
31. C83×#2739C2semidirect
40. C2×#14581777C22semidirect
41. C2×#14581770C22semidirect
51. #19127643C22semidirect
52. #19127642C22semidirect
53. #19127636C22semidirect
54. #19127631C22semidirect
56. #19127630C22semidirect
57. #19127630C22semidirect
58. #19127630C22semidirect
59. #19127630C22semidirect
60. #19127630C22semidirect
61. #19127630C22semidirect
65. #19127627C22semidirect
67. #19127625C22semidirect
69. #19127622C22semidirect
70. #19127621C22semidirect
71. #19127621C22semidirect
73. #19127619C22semidirect
77. #19127618C22semidirect
84. #19127614C22semidirect
85. #19127614C22semidirect
91. #19127611C22semidirect
93. #19127605C22semidirect
94. #19127605C22semidirect
99. #19127602C22semidirect
100. #19127602C22semidirect
104. #19127593C22semidirect
106. #19127592C22semidirect
108. #19127591C22semidirect
109. #19127591C22semidirect
110. #19127591C22semidirect
111. #19127591C22semidirect
113. #19127590C22semidirect
114. #19127590C22semidirect
115. #19127590C22semidirect
116. #19127587C22semidirect
117. #19127587C22semidirect
118. #19127586C22semidirect
119. #19127586C22semidirect
120. #19127585C22semidirect
121. #19127583C22semidirect
122. #19127582C22semidirect
123. #19127582C22semidirect
124. #19127582C22semidirect
136. #19127579C22semidirect
137. #19127579C22semidirect
138. #19127579C22semidirect
139. #19127579C22semidirect
145. #19127575C22semidirect
146. #19127575C22semidirect
150. #19127568C22semidirect
160. #19127558C22semidirect
164. #19127552C22semidirect
165. C4×(C2×D83)⋊C4C22semidirect
166. C4×(C2×D83)⋊C4C22semidirect
171. #19127548C22semidirect
172. #400×C83C22semidirect
173. #400×C83C22semidirect
174. #400×C83C22semidirect
175. #398×C83C22semidirect
178. #389×C83C22semidirect
181. #387×C83C22semidirect
182. #387×C83C22semidirect
183. #387×C83C22semidirect
799. #2739D83semidirect
826. C83#36735semidirect
848. #400C2×D83semidirect
849. #400C2×D83semidirect
850. #400C2×D83semidirect
853. #398C2×D83semidirect
903. #389C2×D83semidirect
929. #387C2×D83semidirect
930. #387C2×D83semidirect
931. #387C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249157582
#249157462
#249146642
#249145602
#249145192
#249145142
#249143032
#249141052
#249140212
#249140062
#249139732
#249138992
#249138732
#249138442
#249137872
#249137112
#249136872
#249136402
#249135962
#249130092
#249127922
#249125682
#249116702
#249116472
#249116122
#249115772
#249102562
#249102272
#249098432
C83×#27392
#3673583