Finite Group Databasebeta

← #14925257

Subgroups — #14925257

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic, complemented
3#13074225C214yesmaximal, complemented
4#13074210C214yesmaximal, complemented
5#13073818C211yesmaximal, characteristic, complemented
6#13073804C211yesmaximal, characteristic, complemented
7#13073598C211yesmaximal, characteristic, complemented
8#13073584C211yesmaximal, characteristic, complemented
9#13073080C211yesmaximal, characteristic, complemented
10#13073066C211yesmaximal, characteristic, complemented
11#13072246C211yesmaximal, characteristic, complemented
12#13072232C211yesmaximal, characteristic
13#13071854C214yesmaximal, complemented
14C4×#66922C211yesmaximal, characteristic, complemented
15C4×#66989C211yesmaximal, characteristic, complemented
16C4×#66989C211yesmaximal, characteristic, complemented
17#13071061C214yesmaximal, complemented
18C4×#66925C211yesmaximal, characteristic, complemented
19C4×C11×#127C211yesmaximal, characteristic, complemented
20C22×#4341C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2214yes—
25C2×#66991C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C2×#66989C2211yescharacteristic
28C2×#66989C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C2×C4×C22⋊D11C2212yes—
31C2×C4×C22⋊D11C2212yes—
32C2×#66979C2212yes—
33C22×C4×Dic11C2212yes—
34#10623088—28no—
35C4×#4341—28no—
36C2×#66950C2211yescharacteristic
37C2×#66945C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66936C2212yes—
41C2×(C22⋊D11)⋊C4C2212yes—
42C2×#66932C2212yes—
43C2×#66930C2212yes—
44C2×#66925C2212yes—
45C2×C42×D11C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C2×C4×Dic22C2211yescharacteristic
49C11×#390C2214yes—
50C11×#390C2211yescharacteristic
51C11×#390C2211yescharacteristic
52C11×#384C2211yescharacteristic
53C43×C11C2211yescharacteristic
54#10622836C2214yes—
55#10622835C2214yes—
56#10622834C2211yescharacteristic
57#10622834C2211yescharacteristic
58#10622833C2214yes—
59#10622833C2214yes—
60C4×C22⋊Dic11C2214yes—
61C4×C22⋊Dic11C2214yes—
62#10622606C2214yes—
63#10622594C2214yes—
64#10622594C2214yes—
65#10622593C2214yes—
66#10622590C2211yescharacteristic
67#10622590C2211yescharacteristic
68#10622587C2211yescharacteristic
69#10622587C2211yescharacteristic
70#10622574C2214yes—
71#10622574C2214yes—
72#10622564C2214yes—
73#10622564C2214yes—
74#10622563C2214yes—
75#10622563C2214yes—
76#10622561C2214yes—
77#10622561C2214yes—
78#10622558C2214yes—
79#10622558C2214yes—
80C4×(C2×D11)⋊C4C2212yes—
81C4×(C2×D11)⋊C4C2211yescharacteristic
82C4×(C2×D11)⋊C4C2211yescharacteristic
83#10622548C2211yescharacteristic
84C4×C4⋊Dic11C2214yes—
85#10622545C2212yes—
86C4×Dic11⋊C4C2212yes—
87C4×Dic11⋊C4C2211yescharacteristic
88C4×Dic11⋊C4C2211yescharacteristic
89C42×Dic11C2211yescharacteristic
90#10622542C2211yescharacteristic
91#10622542C2211yescharacteristic
92#10622541C2214yes—
93C22×D4×C11C2311yescharacteristic
94C22×D4×C11C2314yes—
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11C2312yes—
97C23×C4×C11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C23×Dic11C2312yes—
101C23×Dic11C2312yes—
102C2×#4341—24no—
103C2×#4341—24no—
104C2×#4341—24no—
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C11×#127—24no—
111C4×D4×C11—24no—
112C4×D4×C11—24no—
113C4×D4×C11—216no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2312yes—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134#66991—24no—
135#66989—24no—
136#66989—24no—
137#66989—24no—
138D4×Dic11—24no—
139C4×C22⋊D11—28no—
140C4×C22⋊D11—28no—
141C2×(C2×D11)⋊C4C2312yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145#66979—28no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2314yes—
149C2×C4⋊Dic11C2312yes—
150C2×C4⋊Dic11C2312yes—
151C2×C4⋊Dic11C2314yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2312yes—
158C2×C4×Dic11—28no—
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2311yescharacteristic
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2311yescharacteristic
168C2×C4×Dic11C2311yescharacteristic
169C2×C4×Dic11C2311yescharacteristic
170#66950—24no—
171#66945—24no—
172#66943—24no—
173#66940—24no—
174#66936—28no—
175(C22⋊D11)⋊C4—28no—
176#66932—28no—
177#66930—28no—
178#66925—28no—
179C42×D11D418yescomplemented
180#66922—24no—
181C4×Dic22—24no—
182C4×Dic22—24no—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2314yes—
190C11⋊#95C2314yes—
191C11⋊#95C2314yes—
192C11⋊#95C2314yes—
193#34910—111nomaximal, Sylow
194C24×C11C2412yes—
195C24×C11C2412yes—
196C23×D11C2411yescharacteristic
197C2×D4×C11—28no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—28no—
203C2×D4×C11—22no—
204C2×D4×C11—44no—
205C2×D4×C11#4114yes—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—28no—
209C22×C4×C11—28no—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2411yescharacteristic
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2411yescharacteristic
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—44no—
222C22×Dic11—24no—
223C22×Dic11—24no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—44no—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2411yescharacteristic
233C22×Dic11C2411yescharacteristic
234C22×Dic11C2411yescharacteristic
235C22×Dic11C2412yes—
236#4341—232no—
237C2×C4×D11—24no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—42no—
241C2×C4×D11C2×D414yes—
242C2×C4×D11C2×D414yes—
243C2×C4×D11C2×D414yes—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22#4114yes—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—28no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—28no—
257C42×C11—22no—
258C42×C11—22no—
259C42×C11—42no—
260C42×C11C2×D414yes—
261C42×C11#4118yescomplemented
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—28no—
267C22⋊Dic11—28no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11—24no—
276C4⋊Dic11—28no—
277C4⋊Dic11—22no—
278C4⋊Dic11—22no—
279C4⋊Dic11—44no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11—24no—
289C4×Dic11—24no—
290C4×Dic11—24no—
291C4×Dic11—22no—
292C4×Dic11—22no—
293C4×Dic11—42no—
294C4×Dic11C2×D414yes—
295C4×Dic11C2×D414yes—
296C4×Dic11C2×D414yes—
297C2×#529—111no—
298C2×C4×#41—111no—
299#2602—114no—
300#2601—114no—
301#2566—111no—
302#2565—111no—
303#2545—111no—
304#2544—111no—
305#2500—111no—
306#2499—111no—
307#2432—111no—
308#2431—111no—
309#2392—114no—
310C4×C4⋊Q8—111no—
311C4×#127D1111yescharacteristic, complemented
312C4×#124—111no—
313C4×#124—111no—
314#2290—114no—
315C4×#117—111no—
316C23×C11—22no—
317C23×C11—24no—
318C23×C11—22no—
319C23×C11—24no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—24no—
323C23×C11—22no—
324C23×C11—24no—
325C23×C11C2×#4114yes—
326C23×C11C2511yescharacteristic
327C22×D11—22no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—22no—
331C22×D11C22×D412yes—
332D4×C11—28no—
333D4×C11—416no—
334D4×C11—44no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
344C2×C4×C11—48no—
345C2×C4×C11—48no—
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D412yes—
349C2×C4×C11C2×#4112yes—
350C2×C4×C11C2×#4114yes—
351C2×C4×C11C2×#4114yes—
352C2×C4×C11C2×#4114yes—
353C2×C4×C11C2×#4112yes—
354C22⋊D11—216no—
355C22⋊D11—48no—
356C2×Dic11—216no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—24no—
375C2×Dic11—24no—
376C2×Dic11—48no—
377C2×Dic11C22×D412yes—
378C2×Dic11C22×D412yes—
379C2×Dic11C22×D412yes—
380C2×Dic11C2×#4114yes—
381C4×D11—28no—
382C4×D11—28no—
383C4×D11—44no—
384Dic22—28no—
385Dic22—44no—
386C22×#41—111no—
387C2×C4⋊Q8—111no—
388C2×#127C2×D1111yescharacteristic
389#529—228no—
390C2×#126—112no—
391C2×#125—111no—
392C2×#124—111no—
393C2×#124—111no—
394C2×#124—111no—
395C2×#123—112no—
396C2×C22⋊Q8—111no—
397C2×#121—111no—
398C4×#41—228no—
399C2×C4×Q8—111no—
400C2×C4×Q8—111no—
401C2×C4×Q8—111no—
402C2×C4×D4—111no—
403C2×C4×D4—112no—
404C2×C4×D4—112no—
405C2×C4×D4—112no—
406C2×C4×D4C2×D1114yes—
407C2×C4×D4C2×D1111yescharacteristic
408C2×C4×D4C2×D1111yescharacteristic
409C2×#117—112no—
410C2×#117—111no—
411C2×#117—112no—
412C2×#117—112no—
413C22×C42—111no—
414C22×C42—112no—
415#398—114no—
416#397—114no—
417#396—114no—
418#396—114no—
419#394—114no—
420#394—114no—
421#394—114no—
422#392—114no—
423#391—111no—
424#391—111no—
425#391—111no—
426#391—111no—
427#390—111no—
428#390—111no—
429#390C2×D1111yescharacteristic
430#390C2×D1114yes—
431#390C2×D1111yescharacteristic
432#389—114no—
433#388—114no—
434#388—114no—
435#388—114no—
436#388—114no—
437#387—114no—
438#387—114no—
439#386—114no—
440#386—114no—
441#385—114no—
442#385—114no—
443#384—111no—
444#384C2×D1111yescharacteristic
445#382—111no—
446#382—111no—
447C4×C4⋊C4—114no—
448C4×C4⋊C4—111no—
449C4×C4⋊C4—111no—
450C4×C4⋊C4—112no—
451C4×C22⋊C4—114no—
452C4×C22⋊C4—114no—
453C4×C22⋊C4—112no—
454C4×C22⋊C4—111no—
455C4×C22⋊C4—111no—
456#376—112no—
457C43—111no—
458C43C2×D1111yescharacteristic
459C22×C11—24no—
460C22×C11—28no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—44no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—44no—
468C22×C11—44no—
469C22×C11C23×D411yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4112yes—
472C22×C11C22×#4111yescharacteristic
473C22×C11#58512yes—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—42no—
478C2×D11—42no—
479C4×C11—22no—
480C4×C11—24no—
481C4×C11—24no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11#52514yes—
485C4×C11#53214yes—
486Dic11—24no—
487Dic11—22no—
488Dic11—22no—
489Dic11—22no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C2×#41—224no—
496C2×#41—224no—
497C2×#41—224no—
498C22×Q8—111no—
499C22×Q8—111no—
500C22×D4—112no—
501C22×D4—112no—
502C22×D4C22×D1111yescharacteristic
503C22×D4C22×D1114yes—
504C22×D4C22×D1111yescharacteristic
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—112no—
509C23×C4—112no—
510C23×C4C22×D1112yes—
511C23×C4C22×D1112yes—
512C4⋊Q8—224no—
513#127—24no—
514#126—228no—
515#125—224no—
516#124—224no—
517#124—224no—
518#124—224no—
519#123—228no—
520C22⋊Q8—224no—
521#121—224no—
522C4×Q8—224no—
523C4×Q8—224no—
524C4×Q8—224no—
525C4×D4—24no—
526C4×D4—24no—
527C4×D4—216no—
528C4×D4—224no—
529C4×D4—228no—
530C4×D4—228no—
531C4×D4—228no—
532#117—228no—
533#117—228no—
534#117—224no—
535#117—228no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—112no—
546C2×C4⋊C4—114no—
547C2×C4⋊C4—114no—
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1114yes—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4C22×D1112yes—
564C2×C22⋊C4C22×D1112yes—
565C2×C22⋊C4C22×D1114yes—
566C2×C22⋊C4C22×D1114yes—
567C2×C42—111no—
568C2×C42—111no—
569C2×C42—111no—
570C2×C42—118no—
571C2×C42—112no—
572C2×C42—112no—
573C2×C42—111no—
574C2×C42—111no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—112no—
578C2×C42—112no—
579C2×C42—228no—
580C2×C42C22×D1111yescharacteristic
581C2×C42C22×D1111yescharacteristic
582C2×C42C22×D1112yes—
583C2×C42C22×D1111yescharacteristic
584C2×C42C22×D1112yes—
585#95—112no—
586#95—112no—
587#95—112no—
588#95—112no—
589#95—114no—
590#95—114no—
591#95—114no—
592#95—114no—
593#95—114no—
594#95—114no—
595C2×C11—44no—
596C2×C11—82no—
597C2×C11C2×#52511yescharacteristic
598C2×C11C2×#53211yescharacteristic
599C2×C11#344911yescharacteristic
600C2×C11#347512yes—
601C2×C11#348012yes—
602D11—42no—
603C24—111no—
604C24C23×D1112yes—
605C24C23×D1112yes—
606#41—2232no—
607C2×Q8—114no—
608C2×Q8—222no—
609C2×Q8—222no—
610C2×Q8—222no—
611C2×Q8—222no—
612C2×Q8—222no—
613C2×D4—28no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—28no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—444no—
626C2×D4#433914yes—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—111no—
632C22×C4—111no—
633C22×C4—112no—
634C22×C4—111no—
635C22×C4—114no—
636C22×C4—114no—
637C22×C4—114no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—224no—
644C22×C4—224no—
645C22×C4—224no—
646C22×C4—224no—
647C22×C4—222no—
648C22×C4—224no—
649C22×C4—222no—
650C22×C4—442no—
651C22×C4—444no—
652C22×C4C23×D1112yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—28no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—228no—
667C4⋊C4—224no—
668C4⋊C4—222no—
669C4⋊C4—222no—
670C4⋊C4—224no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—444no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—224no—
682C22⋊C4—224no—
683C22⋊C4—224no—
684C22⋊C4—228no—
685C22⋊C4—228no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—444no—
689C22⋊C4—444no—
690C42—22no—
691C42—22no—
692C42—42no—
693C42—114no—
694C42—114no—
695C42—114no—
696C42—224no—
697C42—224no—
698C42—222no—
699C42—224no—
700C42—224no—
701C42—224no—
702C42—222no—
703C42—442no—
704C42D4×D1114yes—
705C42#434118yescomplemented
706C11#3491011yescharacteristic, complemented, Sylow
707C23—22no—
708C23—24no—
709C23—22no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—24no—
716C23—112no—
717C23—221no—
718C23—222no—
719C23—221no—
720C23—222no—
721C23C2×#433914yes—
722C23C24×D1111yescharacteristic
723Q8—228no—
724Q8—444no—
725D4—28no—
726D4—416no—
727D4—44no—
728D4—2216no—
729D4—448no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—48no—
740C2×C4—48no—
741C2×C4—112no—
742C2×C4—112no—
743C2×C4—112no—
744C2×C4—114no—
745C2×C4—2216no—
746C2×C4—221no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—221no—
751C2×C4—222no—
752C2×C4—228no—
753C2×C4—228no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—444no—
768C2×C4—448no—
769C2×C4C2×#433912yes—
770C2×C4C2×D4×D1112yes—
771C2×C4C2×D4×D1112yes—
772C2×C4C2×D4×D1112yes—
773C2×C4C2×#434114yes—
774C2×C4C2×#434114yes—
775C2×C4C2×#434114yes—
776C2×C4#41×D1112yes—
777C22—24no—
778C22—28no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—42no—
786C22—44no—
787C22—222no—
788C22—222no—
789C22—222no—
790C22—442no—
791C22—442no—
792C22C22×#433911yescharacteristic
793C22C22×D4×D1111yescharacteristic
794C22C22×#434112yes—
795C22C2×#41×D1111yescharacteristic
796C22#1062345312yes—
797C4—24no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—222no—
803C4—224no—
804C4—222no—
805C4—222no—
806C4—442no—
807C4—442no—
808C4—442no—
809C4—442no—
810C4—442no—
811C4#1062307814yes—
812C4#1062324714yes—
813C2—44no—
814C2—82no—
815C2—442no—
816C2C2×#1062307811yescharacteristic
817C2C2×#1062324711yescharacteristic
818C2#1308194311yescharacteristic
819C2#1308217412yes—
820C2#1308221312yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#127C2
prime radical#13072232C2
hypercenterC4×#127D11
hypocenterC11#34910
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. C2×#10623088C2semidirect
2. C2×C4×#4341C2semidirect
3. #13074225C2semidirect
4. #13074210C2semidirect
5. #13073818C2semidirect
6. #13073804C2semidirect
7. #13073598C2semidirect
8. #13073584C2semidirect
9. #13073080C2semidirect
10. #13073066C2semidirect
11. #13072246C2semidirect
13. #13071854C2semidirect
14. C4×#66922C2semidirect
15. C4×#66989C2semidirect
16. C4×#66989C2semidirect
17. #13071061C2semidirect
18. C4×#66925C2semidirect
19. C4×C11×#127C2semidirect
179. C42×D11D4semidirect
261. C42×C11#41semidirect
311. C4×#127D11semidirect
705. C42#4341semidirect
706. C11#34910semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
C2×C4×#43412
#130742252
#130742102
#130738182
#130738042
#130735982
#130735842
#130730802
#130730662
#130722462
#130722322
#130718542
C4×#669222
C4×#669892
#130710612
C4×#669252
C4×C11×#1272
#3491011