Finite Group Databasebeta

← #14922659

Subgroups — #14922659

Order 2816.

3390 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×#10623008C211yesmaximal, characteristic, complemented
2C2×#10623322C211yesmaximal, characteristic, complemented
3C2×#10623322C211yesmaximal, characteristic, complemented
4C2×C4×#4339C211yesmaximal, characteristic, complemented
5#13072215C212yesmaximal, complemented
6#13072204C212yesmaximal, complemented
7#13072193C212yesmaximal, complemented
8#13072182C212yesmaximal, complemented
9#13072167C214yesmaximal, complemented
10#13072152C214yesmaximal, complemented
11#13071860C214yesmaximal, complemented
12C4×#66937C214yesmaximal, complemented
13#13071106C211yesmaximal, characteristic, complemented
14#13071099C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C42×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C2×#67006C2212yes—
23C2×#67006C2212yes—
24#10623322—28no—
25#10623322—28no—
26C2×#66983C2212yes—
27C2×#66983C2212yes—
28C2×#66983C2214yes—
29C2×#66982C2212yes—
30C2×#66982C2212yes—
31C2×C4×C22⋊D11C2214yes—
32C2×C4×C22⋊D11C2214yes—
33C2×C4×C22⋊D11C2214yes—
34C2×#66979C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36C2×#66977C2212yes—
37C2×#66977C2212yes—
38C2×#66937C2214yes—
39#10623008—28no—
40C2×#66928C2211yescharacteristic, complemented
41C2×#66928C2211yescharacteristic, complemented
42C2×#66927C2211yescharacteristic, complemented
43C4×#4339—28no—
44C2×C4×D44C2214yescomplemented
45C2×C4×D44C2212yescomplemented
46C2×#66925C2212yescomplemented
47C2×C42×D11C2212yescomplemented
48C2×#66922C2211yescharacteristic, complemented
49C2×C4×Dic22C2212yescomplemented
50C4×C11×C22⋊C4C2212yes—
51C4×C11×C22⋊C4C2212yes—
52C4×C11×C22⋊C4C2212yes—
53C4×C11×C22⋊C4C2212yes—
54C2×C11×#95C2212yes—
55#10622826C2214yes—
56#10622823C2214yes—
57#10622573C2214yes—
58#10622572C2214yes—
59#10622572C2214yes—
60#10622570C2214yes—
61#10622569C2214yes—
62#10622564C2214yes—
63#10622561C2214yes—
64#10622552C2212yescomplemented
65C4×(C2×D11)⋊C4C2212yescomplemented
66C4×(C2×D11)⋊C4C2212yescomplemented
67C4×Dic11⋊C4C2214yescomplemented
68#10622542C2212yescomplemented
69#10622541C2212yescomplemented
70#10622541C2212yescomplemented
71#10622289C2214yescomplemented
72#10622288C2214yescomplemented
73#10622285C2214yescomplemented
74#10622282C2214yescomplemented
75#10622280C2214yescomplemented
76#10622278C2214yescomplemented
77#10622270C2214yescomplemented
78#10622260C2214yescomplemented
79C25×C11C2311yescharacteristic
80C23×C4×C11—24no—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11C2312yes—
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2312yes—
87C23×C4×C11C2312yes—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2314yes—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2312yes—
93C2×#4339—24no—
94C2×#4339—24no—
95C2×#4339—24no—
96C2×#4339—24no—
97C2×#4339—24no—
98C2×#4339D418yescomplemented
99C22×D44C2311yescharacteristic
100C22×D44C2314yes—
101C22×D44C2311yescharacteristic
102C22×C4×D11C2312yes—
103C22×C4×D11C2314yes—
104C22×C4×D11C2312yes—
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2311yescharacteristic
107C2×C11×C22⋊C4—28no—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C42×C11—24no—
113C2×C42×C11—24no—
114C2×C42×C11C2312yes—
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2312yes—
119C2×C42×C11C2311yescharacteristic
120#67006—28no—
121#67006—28no—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126#66983—216no—
127#66983—28no—
128#66983—28no—
129#66982—28no—
130#66982—28no—
131C4×C22⋊D11—216no—
132C4×C22⋊D11—216no—
133C4×C22⋊D11—216no—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×(C2×D11)⋊C4C2314yes—
141#66979—24no—
142#66979D418yescomplemented
143C2×C4⋊Dic11C2314yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146#66977—28no—
147#66977—28no—
148C2×Dic11⋊C4C2314yes—
149C2×Dic11⋊C4C2314yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×C4×Dic11C2314yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156#66937—216no—
157#66928—24no—
158#66928—24no—
159#66927—24no—
160C4×D44—216no—
161C4×D44—28no—
162#66925—28no—
163C42×D11—28no—
164#66922—24no—
165C4×Dic22—28no—
166C11×#95C2312yes—
167C11×#95C2312yes—
168C11×#95C2312yes—
169C11×#95C2312yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174#34743—111nomaximal, Sylow
175C24×C11—24no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—42no—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11C2412yes—
183C23×D11C2412yes—
184C22×C4×C11—24no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—24no—
188C22×C4×C11—22no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—24no—
192C22×C4×C11—24no—
193C22×C4×C11—24no—
194C22×C4×C11—24no—
195C22×C4×C11—24no—
196C22×C4×C11—24no—
197C22×C4×C11—42no—
198C22×C4×C11—42no—
199C22×C4×C11—416no—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11#4114yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—28no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11C2×D418yes—
222C22×Dic11C2414yes—
223C22×Dic11C2412yes—
224C22×Dic11C2414yes—
225C22×Dic11C2412yes—
226#4339—232no—
227#4339—416no—
228C2×D44—28no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44—28no—
234C2×D44—22no—
235C2×D44—44no—
236C2×D44C2×D414yes—
237C2×C4×D11—28no—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—28no—
243C2×C4×D11—24no—
244C2×C4×D11—44no—
245C2×C4×D11C2×D418yes—
246C2×Dic22—22no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22C2×D414yes—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4#4118yescomplemented
256C42×C11—24no—
257C42×C11—22no—
258C42×C11—22no—
259C42×C11—22no—
260C42×C11—24no—
261C42×C11—22no—
262C22⋊Dic11—28no—
263C22⋊Dic11—28no—
264C22⋊Dic11—24no—
265C22⋊Dic11C2×D418yes—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—28no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—28no—
272(C2×D11)⋊C4—44no—
273C4⋊Dic11—28no—
274C4⋊Dic11—24no—
275C4⋊Dic11C2×D418yes—
276Dic11⋊C4—28no—
277Dic11⋊C4—28no—
278Dic11⋊C4—28no—
279Dic11⋊C4—28no—
280Dic11⋊C4—44no—
281C4×Dic11—28no—
282C4×Dic11—24no—
283C4×Dic11C2×D418yes—
284C2×#532—111no—
285C2×#525—111no—
286C2×#525—111no—
287C2×C4×#41—111no—
288#2429—112no—
289#2428—112no—
290#2427—112no—
291#2426—112no—
292#2425—114no—
293#2424—114no—
294#2392—114no—
295C4×#121—114no—
296#2297—111no—
297#2296—111no—
298C2×C4×C22⋊C4D1111yescharacteristic, complemented
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—28no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—48no—
309C23×C11—48no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11C22×D412yes—
313C23×C11C22×D412yes—
314C23×C11C2×#4114yes—
315C23×C11C2×#4112yes—
316C23×C11C2511yescharacteristic
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—24no—
320C22×D11—24no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—24no—
324C22×D11—22no—
325C22×D11—24no—
326C22×D11C22×D414yes—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—48no—
341C2×C4×C11—48no—
342C2×C4×C11—44no—
343C2×C4×C11—48no—
344C2×C4×C11—48no—
345C2×C4×C11#121116yescomplemented
346C2×C4×C11C22×D412yes—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D412yes—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C2×#4114yes—
351C2×C4×C11C2×#4114yes—
352C2×C4×C11C2×#4112yes—
353C2×C4×C11C2×#4112yes—
354C22⋊D11—216no—
355C22⋊D11—416no—
356C22⋊D11—416no—
357C22⋊D11—48no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—22no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—24no—
366C2×Dic11—22no—
367C2×Dic11—24no—
368C2×Dic11C22×D418yes—
369C2×Dic11C22×D414yes—
370D44—28no—
371D44—416no—
372D44—44no—
373C4×D11—216no—
374C4×D11—416no—
375C4×D11—48no—
376Dic22—28no—
377Dic22—44no—
378C22×#41—111no—
379C22×#41—111no—
380C24×C4C2×D1111yescharacteristic
381#532—228no—
382C2×C4⋊Q8—111no—
383C2×#127—111no—
384C2×#124—111no—
385C2×#124—111no—
386#525—228no—
387#525—228no—
388C2×#123—112no—
389C2×#123—112no—
390C2×C22⋊Q8—112no—
391C2×C22⋊Q8—112no—
392C2×#121—112no—
393C2×#121—112no—
394C2×#121—114no—
395C2×#121—114no—
396C2×#120—112no—
397C2×#120—112no—
398C4×#41—228no—
399C2×C4×Q8—112no—
400C2×C4×D4—114no—
401C2×C4×D4—114no—
402C2×C4×D4—114no—
403C2×C4×D4—114no—
404C2×C4×D4—112no—
405C2×#117—111no—
406C2×#117—111no—
407C2×#117—112no—
408C22×C22⋊C4C2×D1112yes—
409C22×C42—112no—
410C22×C42C2×D1111yescharacteristic
411C22×C42C2×D1111yescharacteristic
412#398—114no—
413#397—114no—
414#396—114no—
415#396—114no—
416#394—114no—
417#394—114no—
418#394—114no—
419#392—114no—
420#391—112no—
421#390—114no—
422#390—112no—
423#389—112no—
424#389—112no—
425#389—114no—
426#388—114no—
427#388—114no—
428#386—114no—
429#386—114no—
430#386—114no—
431#385—114no—
432#380—114no—
433C4×C4⋊C4—114no—
434C4×C22⋊C4—112no—
435C4×C22⋊C4—112no—
436C4×C22⋊C4C2×D1112yes—
437C4×C22⋊C4C2×D1112yes—
438C4×C22⋊C4C2×D1112yes—
439C4×C22⋊C4C2×D1112yes—
440C2×#95C2×D1112yes—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—416no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11C2×#12114yes—
454C22×C11C23×D411yescharacteristic
455C22×C11C23×D411yescharacteristic
456C22×C11C22×#4111yescharacteristic
457C22×C11C22×#4112yes—
458C22×C11#58512yes—
459C2×D11—24no—
460C2×D11—28no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—44no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—44no—
468C2×D11—44no—
469C4×C11—24no—
470C4×C11—24no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11C2×#12114yes—
475C4×C11C2×#12114yes—
476Dic11—24no—
477Dic11—28no—
478Dic11—42no—
479Dic11—44no—
480C25C22×D1111yescharacteristic
481C2×#41—118no—
482C2×#41—224no—
483C2×#41—224no—
484C2×#41—224no—
485C2×#41—224no—
486C2×#41—224no—
487C22×Q8—111no—
488C22×Q8—111no—
489C22×D4—112no—
490C22×D4—112no—
491C22×D4—114no—
492C22×D4—114no—
493C22×D4—111no—
494C22×D4—111no—
495C22×D4—114no—
496C23×C4—24no—
497C23×C4—24no—
498C23×C4—24no—
499C23×C4—112no—
500C23×C4—112no—
501C23×C4—114no—
502C23×C4C22×D1112yes—
503C23×C4C22×D1111yescharacteristic
504C23×C4C22×D1112yes—
505C23×C4C22×D1112yes—
506C23×C4C22×D1112yes—
507C23×C4C22×D1111yescharacteristic
508C4⋊Q8—224no—
509#127—224no—
510#124—224no—
511#124—224no—
512#123—228no—
513#123—228no—
514C22⋊Q8—228no—
515C22⋊Q8—228no—
516#121—228no—
517#121—228no—
518#121—2216no—
519#121—2216no—
520#120—228no—
521#120—228no—
522C4×Q8—228no—
523C4×D4—228no—
524C4×D4—2216no—
525C4×D4—2216no—
526C4×D4—2216no—
527C4×D4—2216no—
528#117—118no—
529#117—228no—
530#117—224no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C22⋊C4—28no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4C22×D1112yes—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1112yes—
554C2×C22⋊C4C22×D1112yes—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—112no—
558C2×C42—114no—
559C2×C42—112no—
560C2×C42—228no—
561C2×C42C22×D1112yes—
562C2×C42C22×D1111yescharacteristic
563C2×C42C22×D1111yescharacteristic
564C2×C42C22×D1111yescharacteristic
565C2×C42C22×D1112yes—
566C2×C42C22×D1111yescharacteristic
567#95—114no—
568#95—114no—
569#95—114no—
570#95—114no—
571#95C22×D1112yes—
572#95C22×D1112yes—
573#95C22×D1112yes—
574#95C22×D1112yes—
575C2×C11—24no—
576C2×C11—44no—
577C2×C11C22×#12111yescharacteristic
578C2×C11#344411yescharacteristic
579C2×C11#345511yescharacteristic
580C2×C11D4×#4112yes—
581C2×C11D4×#4112yes—
582D11—44no—
583D11—82no—
584C24—24no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—42no—
589C24—112no—
590C24—112no—
591C24C23×D1112yes—
592C24C23×D1111yescharacteristic
593#41—2232no—
594#41—4416no—
595C2×Q8—114no—
596C2×Q8—222no—
597C2×Q8—222no—
598C2×Q8—222no—
599C2×Q8—222no—
600C2×Q8—222no—
601C2×D4—118no—
602C2×D4—114no—
603C2×D4—228no—
604C2×D4—228no—
605C2×D4—224no—
606C2×D4—224no—
607C2×D4—228no—
608C2×D4—228no—
609C2×D4—228no—
610C2×D4—224no—
611C2×D4—224no—
612C2×D4—224no—
613C2×D4—222no—
614C2×D4—228no—
615C2×D4—222no—
616C2×D4—222no—
617C2×D4—222no—
618C2×D4—222no—
619C2×D4—444no—
620C2×D4—444no—
621C2×D4—444no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—416no—
638C22×C4—114no—
639C22×C4—112no—
640C22×C4—118no—
641C22×C4—114no—
642C22×C4—112no—
643C22×C4—228no—
644C22×C4—224no—
645C22×C4—224no—
646C22×C4—228no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—224no—
650C22×C4—444no—
651C22×C4#433914yes—
652C22×C4D4×D1114yes—
653C22×C4D4×D1114yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C4⋊C4—118no—
662C4⋊C4—228no—
663C4⋊C4—228no—
664C4⋊C4—228no—
665C4⋊C4—228no—
666C4⋊C4—228no—
667C4⋊C4—224no—
668C4⋊C4—444no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—118no—
673C22⋊C4—228no—
674C22⋊C4—228no—
675C22⋊C4—228no—
676C22⋊C4—228no—
677C22⋊C4—228no—
678C22⋊C4—228no—
679C22⋊C4—228no—
680C22⋊C4—224no—
681C22⋊C4—228no—
682C22⋊C4—444no—
683C22⋊C4#433918yescomplemented
684C42—22no—
685C42—22no—
686C42—24no—
687C42—24no—
688C42—22no—
689C42—22no—
690C42—118no—
691C42—228no—
692C42—224no—
693C11#3474311yescharacteristic, complemented, Sylow
694C23—22no—
695C23—22no—
696C23—28no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—48no—
704C23—48no—
705C23—44no—
706C23—44no—
707C23—114no—
708C23—222no—
709C23—224no—
710C23—222no—
711C23—224no—
712C23—224no—
713C23—222no—
714C23—222no—
715C23—222no—
716C23—224no—
717C23C2×#433914yes—
718C23C2×#433912yes—
719C23C2×D4×D1112yes—
720C23C2×D4×D1112yes—
721C23C24×D1111yescharacteristic
722Q8—228no—
723Q8—444no—
724D4—2216no—
725D4—228no—
726D4—4416no—
727D4—4416no—
728D4—4416no—
729D4—448no—
730D4—444no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—48no—
745C2×C4—48no—
746C2×C4—44no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—118no—
750C2×C4—114no—
751C2×C4—224no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—2216no—
756C2×C4—224no—
757C2×C4—222no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—224no—
762C2×C4—4416no—
763C2×C4—448no—
764C2×C4#66937116yescomplemented
765C2×C4C2×#433914yes—
766C2×C4C2×#433914yes—
767C2×C4C2×#433912yes—
768C2×C4C2×#433912yes—
769C2×C4C2×D4×D1112yes—
770C2×C4C2×D4×D1112yes—
771C2×C4C2×D4×D1112yes—
772C2×C4C2×D4×D1112yes—
773C22—22no—
774C22—22no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—416no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—224no—
786C22—228no—
787C22—442no—
788C22—442no—
789C22—444no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—444no—
794C22—444no—
795C22C2×#6693714yes—
796C22C22×#433911yescharacteristic
797C22C22×#433912yes—
798C22C22×D4×D1111yescharacteristic
799C22C22×D4×D1111yescharacteristic
800C22#1062345312yes—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—224no—
807C4—228no—
808C4—442no—
809C4—444no—
810C4C2×#6693714yes—
811C4C2×#6693714yes—
812C2—24no—
813C2—44no—
814C2—444no—
815C2—882no—
816C2C22×#6693711yescharacteristic
817C2#1308191211yescharacteristic
818C2#1308200611yescharacteristic
819C2D4×#433912yes—
820C2D4×#433912yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#34743
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. C2×#10623322C2semidirect
3. C2×#10623322C2semidirect
4. C2×C4×#4339C2semidirect
5. #13072215C2semidirect
6. #13072204C2semidirect
7. #13072193C2semidirect
8. #13072182C2semidirect
9. #13072167C2semidirect
10. #13072152C2semidirect
11. #13071860C2semidirect
12. C4×#66937C2semidirect
13. #13071106C2semidirect
14. #13071099C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
40. C2×#66928C22semidirect
41. C2×#66928C22semidirect
42. C2×#66927C22semidirect
44. C2×C4×D44C22semidirect
45. C2×C4×D44C22semidirect
46. C2×#66925C22semidirect
47. C2×C42×D11C22semidirect
48. C2×#66922C22semidirect
49. C2×C4×Dic22C22semidirect
64. #10622552C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
67. C4×Dic11⋊C4C22semidirect
68. #10622542C22semidirect
69. #10622541C22semidirect
70. #10622541C22semidirect
71. #10622289C22semidirect
72. #10622288C22semidirect
73. #10622285C22semidirect
74. #10622282C22semidirect
75. #10622280C22semidirect
76. #10622278C22semidirect
77. #10622270C22semidirect
78. #10622260C22semidirect
98. C2×#4339D4semidirect
142. #66979D4semidirect
255. C11×C22⋊C4#41semidirect
298. C2×C4×C22⋊C4D11semidirect
345. C2×C4×C11#121semidirect
683. C22⋊C4#4339semidirect
693. C11#34743semidirect
764. C2×C4#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106233222
C2×C4×#43392
#130722152
#130722042
#130721932
#130721822
#130721672
#130721522
#130718602
C4×#669372
#130711062
#130710992
C2×C4×C11×C22⋊C42
#3474311