Finite Group Databasebeta

← #14920199

Subgroups — #14920199

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2#13074533C212yesmaximal, complemented
3#13074500C212yesmaximal, complemented
4#13074453C214yesmaximal, complemented
5#13074429C211yesmaximal, characteristic, complemented
6#13074421C211yesmaximal, characteristic, complemented
7#13074389C212yesmaximal, complemented
8#13074358C211yesmaximal, characteristic, complemented
9#13074350C211yesmaximal, characteristic, complemented
10#13074328C212yesmaximal, complemented
11#13071875C212yesmaximal, complemented
12#13071858C214yesmaximal, complemented
13#13071831C212yesmaximal, complemented
14C4×#66982C212yesmaximal, complemented
15C4×#67006C212yesmaximal, complemented
16#13070999C211yesmaximal, characteristic, complemented
17C22×C4×D4×C11C211yesmaximal, characteristic, complemented
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C22×#4339C2211yescharacteristic, complemented
22C2×C4×D4×C11—28no—
23C2×C4×D4×C11C2212yes—
24C2×C4×D4×C11C2212yes—
25C2×C4×D4×C11C2212yes—
26C2×C4×D4×C11C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C2×#67006C2212yes—
32C2×#67006C2212yes—
33#10623322—28no—
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic, complemented
36C2×#66982C2212yes—
37C2×#66982C2212yescomplemented
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2212yescomplemented
40C2×C4×C22⋊D11C2214yescomplemented
41C2×#66979C2211yescharacteristic, complemented
42C2×#66979C2212yescomplemented
43C2×#66977C2211yescharacteristic
44C2×#66977C2211yescharacteristic, complemented
45#10622860C2212yes—
46#10622860C2212yes—
47#10622836C2214yes—
48#10622836C2214yes—
49#10622835C2214yes—
50#10622835C2214yes—
51#10622826C2212yes—
52#10622826C2212yes—
53#10622826C2214yescomplemented
54#10622825C2211yescharacteristic
55#10622825C2211yescharacteristic
56#10622825C2212yescomplemented
57#10622824C2212yes—
58#10622824C2212yescomplemented
59#10622823C2212yes—
60#10622823C2212yes—
61#10622823C2214yescomplemented
62C4×C22⋊Dic11C2212yes—
63C4×C22⋊Dic11C2214yescomplemented
64C4×C22⋊Dic11C2212yescomplemented
65#10622607C2214yescomplemented
66#10622604C2212yescomplemented
67#10622599C2212yescomplemented
68#10622597C2214yescomplemented
69#10622596C2212yescomplemented
70#10622592C2212yescomplemented
71#10622574C2214yescomplemented
72#10622573C2212yescomplemented
73#10622572C2214yescomplemented
74#10622572C2214yescomplemented
75#10622566C2212yescomplemented
76#10622565C2214yescomplemented
77#10622565C2214yescomplemented
78#10622562C2212yescomplemented
79#10622561C2214yescomplemented
80#10622560C2212yescomplemented
81#10622553C2214yescomplemented
82C4×(C2×D11)⋊C4C2214yescomplemented
83#10622546C2214yescomplemented
84C4×Dic11⋊C4C2214yescomplemented
85C25×C11C2311yescharacteristic
86C25×C11C2311yescharacteristic
87C22×D4×C11—24no—
88C22×D4×C11—24no—
89C22×D4×C11—24no—
90C22×D4×C11C2312yes—
91C22×D4×C11C2312yes—
92C23×C4×C11—24no—
93C23×C4×C11—44no—
94C23×C4×C11—44no—
95C23×C4×C11D418yescomplemented
96C23×C4×C11C2312yes—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2312yes—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C22×C22⋊D11C2312yes—
108C22×C22⋊D11C2312yes—
109C22×C22⋊D11C2314yes—
110C22×C22⋊D11C2312yes—
111C2×#4339—24no—
112C2×#4339—44no—
113C22×D44C2311yescharacteristic
114C22×C4×D11C2312yes—
115C22×Dic22C2311yescharacteristic
116C4×D4×C11—28no—
117C4×D4×C11—28no—
118C4×D4×C11—28no—
119C4×D4×C11—28no—
120C2×C11×C4⋊C4—24no—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C22⋊C4—24no—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C42×C11—24no—
130C2×C42×C11C2312yes—
131C2×C42×C11C2312yes—
132#67006—28no—
133#67006—28no—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144#66983—24no—
145#66983—24no—
146#66982—28no—
147#66982—28no—
148C4×C22⋊D11—28no—
149C4×C22⋊D11—28no—
150C4×C22⋊D11—48no—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156#66979—24no—
157#66979—44no—
158C2×C4⋊Dic11C2311yescharacteristic
159C2×C4⋊Dic11C2311yescharacteristic
160C2×C4⋊Dic11C2312yes—
161C2×C4⋊Dic11C2312yes—
162#66977—24no—
163#66977—24no—
164C2×Dic11⋊C4C2314yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2314yes—
168C2×Dic11⋊C4C2314yes—
169C2×C4×Dic11C2312yes—
170C2×C4×Dic11C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2312yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2312yes—
180#34562—111nomaximal, Sylow
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—42no—
186C24×C11—42no—
187C24×C11—42no—
188C24×C11—42no—
189C24×C11C2×D414yes—
190C24×C11#4114yescomplemented
191C24×C11C2411yescharacteristic
192C24×C11C2411yescharacteristic
193C24×C11C2412yes—
194C24×C11C2411yescharacteristic
195C23×D11C2412yes—
196C2×D4×C11—232no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—24no—
202C2×D4×C11—24no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—24no—
211C22×C4×C11—24no—
212C22×C4×C11—28no—
213C22×C4×C11—416no—
214C22×C4×C11—42no—
215C22×C4×C11—42no—
216C22×C4×C11—42no—
217C22×C4×C11—44no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—416no—
221C22×C4×C11C2×D414yes—
222C22×C4×C11C2×D414yes—
223C22×C4×C11C2×D414yes—
224C22×C4×C11C2×D414yes—
225C22×C4×C11C2×D414yes—
226C22×C4×C11C2×D414yes—
227C22×C4×C11#4114yescomplemented
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C22×C4×C11C2411yescharacteristic
233C22×C4×C11C2412yes—
234C22×C4×C11C2411yescharacteristic
235C2×C22⋊D11—24no—
236C2×C22⋊D11—24no—
237C2×C22⋊D11—24no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C22×Dic11C2414yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2414yes—
249C22×Dic11C2412yes—
250#4339—416no—
251C2×D44—22no—
252C2×D44—42no—
253C2×C4×D11—24no—
254C2×C4×D11—28no—
255C2×Dic22—22no—
256C2×Dic22—42no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C11×C22⋊C4—24no—
263C42×C11—24no—
264C42×C11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—28no—
270C22⋊Dic11—24no—
271C22⋊Dic11—44no—
272C22⋊Dic11—44no—
273C22⋊Dic11—44no—
274C22⋊Dic11—44no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280C4⋊Dic11—22no—
281C4⋊Dic11—22no—
282C4⋊Dic11—42no—
283C4⋊Dic11—42no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—28no—
287Dic11⋊C4—44no—
288Dic11⋊C4—44no—
289C4×Dic11—24no—
290C4×Dic11—28no—
291C2×#525—111no—
292C22×C4×D4D1111yescharacteristic, complemented
293#2638—112no—
294#2635—112no—
295#2630—114no—
296#2627—111no—
297#2626—111no—
298#2622—112no—
299#2618—111no—
300#2617—111no—
301#2613—112no—
302#2395—112no—
303#2392—114no—
304#2388—112no—
305C4×#123—112no—
306C4×#120—112no—
307#2280—111no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—28no—
311C23×C11—28no—
312C23×C11—22no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—24no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—24no—
323C23×C11—22no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—48no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—48no—
330C23×C11—48no—
331C23×C11—48no—
332C23×C11C22×D412yes—
333C23×C11C22×D412yes—
334C23×C11C22×D412yes—
335C23×C11C2×#4114yes—
336C23×C11C2×#4112yes—
337C23×C11C2×#4112yes—
338C23×C11C2511yescharacteristic
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—24no—
343C22×D11—24no—
344D4×C11—216no—
345D4×C11—216no—
346C2×C4×C11—28no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—28no—
353C2×C4×C11—28no—
354C2×C4×C11—28no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—24no—
358C2×C4×C11—24no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—48no—
363C2×C4×C11—44no—
364C2×C4×C11—44no—
365C2×C4×C11—48no—
366C2×C4×C11C22×D412yes—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C2×#4114yes—
371C2×C4×C11H(5,𝔽2)14yes—
372C22⋊D11—48no—
373C22⋊D11—48no—
374C22⋊D11—416no—
375C22⋊D11—48no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—24no—
381C2×Dic11—22no—
382C2×Dic11—24no—
383C2×Dic11—24no—
384C2×Dic11—24no—
385C2×Dic11—24no—
386C2×Dic11—24no—
387C2×Dic11—24no—
388C2×Dic11—24no—
389D44—44no—
390C4×D11—48no—
391Dic22—44no—
392C22×#41—111no—
393C23×D4C2×D1111yescharacteristic
394C24×C4C2×D1111yescharacteristic
395C24×C4C2×D1111yescharacteristic
396#525—228no—
397C2×#123—112no—
398C2×#123—112no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×#121—111no—
402C2×#121—111no—
403C2×#120—112no—
404C2×#120—112no—
405C2×C4×D4—28no—
406C2×C4×D4—112no—
407C2×C4×D4—112no—
408C2×C4×D4—114no—
409C2×C4×D4C2×D1112yes—
410C2×C4×D4C2×D1112yes—
411C2×C4×D4C2×D1112yes—
412C2×C4×D4C2×D1112yes—
413C2×#117—111no—
414C2×#117—112no—
415C22×C4⋊C4C2×D1111yescharacteristic
416C22×C22⋊C4C2×D1111yescharacteristic
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C42C2×D1111yescharacteristic
419#400—112no—
420#399—112no—
421#398—112no—
422#398—114no—
423#397—112no—
424#397—114no—
425#397—114no—
426#396—114no—
427#396—114no—
428#395—112no—
429#394—114no—
430#394—114no—
431#394—112no—
432#394—114no—
433#394—114no—
434#394—114no—
435#393—112no—
436#392—114no—
437#392—114no—
438#392—112no—
439#388—114no—
440#387—114no—
441#386—112no—
442#386—112no—
443#386—114no—
444#385—112no—
445#385—112no—
446#385—114no—
447#381—112no—
448#381—112no—
449#380—111no—
450#380—111no—
451#380—112no—
452#379—112no—
453#379—112no—
454C4×C4⋊C4—114no—
455C4×C22⋊C4—112no—
456C4×C22⋊C4—114no—
457C4×C22⋊C4—112no—
458C4×C22⋊C4—114no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—24no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—28no—
471C22×C11—416no—
472C22×C11—416no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—44no—
479C22×C11—42no—
480C22×C11#52514yes—
481C22×C11C23×D411yescharacteristic
482C22×C11C22×#4111yescharacteristic
483C22×C11C22×#4111yescharacteristic
484C22×C11C2×H(5,𝔽2)12yes—
485C22×C11#58512yes—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—44no—
490C2×D11—44no—
491C4×C11—24no—
492C4×C11—22no—
493C4×C11—22no—
494C4×C11—22no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11#53414yes—
498Dic11—42no—
499Dic11—42no—
500Dic11—42no—
501Dic11—44no—
502Dic11—44no—
503C25C22×D1111yescharacteristic
504C25C22×D1111yescharacteristic
505C2×#41—224no—
506C2×#41—444no—
507C22×Q8—111no—
508C22×D4—24no—
509C22×D4—24no—
510C22×D4—24no—
511C22×D4—112no—
512C22×D4—112no—
513C22×D4—114no—
514C22×D4—112no—
515C22×D4—111no—
516C22×D4C22×D1112yes—
517C22×D4C22×D1112yes—
518C23×C4—24no—
519C23×C4—44no—
520C23×C4—44no—
521C23×C4—112no—
522C23×C4C22⋊D1118yescomplemented
523C23×C4C22×D1112yes—
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1112yes—
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534#123—228no—
535#123—228no—
536C22⋊Q8—224no—
537C22⋊Q8—224no—
538#121—224no—
539#121—224no—
540#120—228no—
541#120—228no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—28no—
546C4×D4—228no—
547C4×D4—228no—
548C4×D4—448no—
549#117—224no—
550#117—444no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—112no—
555C2×C4⋊C4—112no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—112no—
558C2×C4⋊C4—112no—
559C2×C4⋊C4—114no—
560C2×C4⋊C4—114no—
561C2×C4⋊C4C22×D1112yes—
562C2×C4⋊C4C22×D1112yes—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—112no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4—112no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—112no—
571C2×C22⋊C4—112no—
572C2×C22⋊C4—112no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4C22×D1112yes—
581C2×C22⋊C4C22×D1112yes—
582C2×C22⋊C4C22×D1112yes—
583C2×C22⋊C4C22×D1112yes—
584C2×C42—24no—
585C2×C42—112no—
586C2×C42—114no—
587C2×C42C22×D1112yes—
588C2×C42C22×D1112yes—
589#95—114no—
590#95—112no—
591#95—112no—
592#95—114no—
593#95—114no—
594#95—114no—
595#95—114no—
596#95—114no—
597#95—114no—
598C2×C11—24no—
599C2×C11—42no—
600C2×C11—42no—
601C2×C11—44no—
602C2×C11C2×#52511yescharacteristic
603C2×C11C2×#53411yescharacteristic
604C2×C11#344911yescharacteristic
605C2×C11#345912yes—
606C2×C11#346012yes—
607D11—82no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—42no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—112no—
617C24#433914yescomplemented
618C24C2×C22⋊D1114yes—
619C24C23×D1112yes—
620C24C23×D1111yescharacteristic
621C24C23×D1111yescharacteristic
622C24C23×D1111yescharacteristic
623#41—4416no—
624C2×Q8—222no—
625C2×Q8—442no—
626C2×D4—232no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—24no—
633C2×D4—228no—
634C2×D4—224no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—222no—
640C2×D4—442no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—444no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—416no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—44no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—416no—
663C22×C4—114no—
664C22×C4—114no—
665C22×C4—112no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—228no—
669C22×C4—224no—
670C22×C4#433914yescomplemented
671C22×C4C2×C22⋊D1114yes—
672C22×C4C2×C22⋊D1114yes—
673C22×C4C2×C22⋊D1114yes—
674C22×C4C2×C22⋊D1114yes—
675C22×C4C2×C22⋊D1114yes—
676C22×C4C2×C22⋊D1114yes—
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1111yescharacteristic
681C22×C4C23×D1111yescharacteristic
682C22×C4C23×D1111yescharacteristic
683C22×C4C23×D1111yescharacteristic
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—228no—
687C4⋊C4—222no—
688C4⋊C4—222no—
689C4⋊C4—224no—
690C4⋊C4—224no—
691C4⋊C4—442no—
692C4⋊C4—442no—
693C4⋊C4—444no—
694C4⋊C4—444no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—228no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—228no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C22⋊C4—444no—
711C22⋊C4—444no—
712C22⋊C4—444no—
713C22⋊C4—444no—
714C42—24no—
715C42—24no—
716C42—228no—
717C42—224no—
718C11#3456211yescharacteristic, complemented, Sylow
719C23—22no—
720C23—22no—
721C23—28no—
722C23—28no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—24no—
730C23—22no—
731C23—22no—
732C23—24no—
733C23—22no—
734C23—22no—
735C23—44no—
736C23—48no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—48no—
741C23—48no—
742C23—48no—
743C23—222no—
744C23—222no—
745C23—224no—
746C23—224no—
747C23—222no—
748C23C2×#433914yes—
749C23C2×#433912yes—
750C23C2×#433912yes—
751C23C22×C22⋊D1112yes—
752C23C22×C22⋊D1112yes—
753C23C22×C22⋊D1112yes—
754C23C24×D1111yescharacteristic
755Q8—444no—
756D4—216no—
757D4—216no—
758D4—444no—
759D4—448no—
760D4—448no—
761D4—4416no—
762D4—448no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—48no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—48no—
783C2×C4—224no—
784C2×C4—222no—
785C2×C4—224no—
786C2×C4—222no—
787C2×C4—224no—
788C2×C4—224no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—224no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—448no—
797C2×C4C2×#433914yes—
798C2×C4#6703714yes—
799C2×C4C22×C22⋊D1112yes—
800C2×C4C22×C22⋊D1112yes—
801C2×C4C22×C22⋊D1112yes—
802C2×C4C22×C22⋊D1112yes—
803C22—22no—
804C22—22no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—28no—
815C22—416no—
816C22—416no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—42no—
824C22—442no—
825C22—442no—
826C22—442no—
827C22—444no—
828C22—444no—
829C22#1062332214yes—
830C22C22×#433911yescharacteristic
831C22C22×#433911yescharacteristic
832C22C2×#6703712yes—
833C22#1062345312yes—
834C22C23×C22⋊D1111yescharacteristic
835C4—24no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—42no—
840C4—42no—
841C4—442no—
842C4—442no—
843C4—442no—
844C4—444no—
845C4—444no—
846C4#1062333514yes—
847C2—24no—
848C2—44no—
849C2—42no—
850C2—42no—
851C2—882no—
852C2C2×#1062332211yescharacteristic
853C2C2×#1062333511yescharacteristic
854C2#1308194511yescharacteristic
855C2#1308202512yes—
856C2#1308203812yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
hypercenterC22×C4×D4D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13074533C2semidirect
3. #13074500C2semidirect
4. #13074453C2semidirect
5. #13074429C2semidirect
6. #13074421C2semidirect
7. #13074389C2semidirect
8. #13074358C2semidirect
9. #13074350C2semidirect
10. #13074328C2semidirect
11. #13071875C2semidirect
12. #13071858C2semidirect
13. #13071831C2semidirect
14. C4×#66982C2semidirect
15. C4×#67006C2semidirect
16. #13070999C2semidirect
17. C22×C4×D4×C11C2semidirect
21. C22×#4339C22semidirect
35. C2×#66983C22semidirect
37. C2×#66982C22semidirect
39. C2×C4×C22⋊D11C22semidirect
40. C2×C4×C22⋊D11C22semidirect
41. C2×#66979C22semidirect
42. C2×#66979C22semidirect
44. C2×#66977C22semidirect
53. #10622826C22semidirect
56. #10622825C22semidirect
58. #10622824C22semidirect
61. #10622823C22semidirect
63. C4×C22⋊Dic11C22semidirect
64. C4×C22⋊Dic11C22semidirect
65. #10622607C22semidirect
66. #10622604C22semidirect
67. #10622599C22semidirect
68. #10622597C22semidirect
69. #10622596C22semidirect
70. #10622592C22semidirect
71. #10622574C22semidirect
72. #10622573C22semidirect
73. #10622572C22semidirect
74. #10622572C22semidirect
75. #10622566C22semidirect
76. #10622565C22semidirect
77. #10622565C22semidirect
78. #10622562C22semidirect
79. #10622561C22semidirect
80. #10622560C22semidirect
81. #10622553C22semidirect
82. C4×(C2×D11)⋊C4C22semidirect
83. #10622546C22semidirect
84. C4×Dic11⋊C4C22semidirect
95. C23×C4×C11D4semidirect
190. C24×C11#41semidirect
227. C22×C4×C11#41semidirect
292. C22×C4×D4D11semidirect
522. C23×C4C22⋊D11semidirect
617. C24#4339semidirect
670. C22×C4#4339semidirect
718. C11#34562semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130745332
#130745002
#130744532
#130744292
#130744212
#130743892
#130743582
#130743502
#130743282
#130718752
#130718582
#130718312
C4×#669822
C4×#670062
#130709992
C22×C4×D4×C112
#3456211