Finite Group Databasebeta

← #14925845

Subgroups — #14925845

Order 2816.

2634 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3#13073989C211yesmaximal, characteristic, complemented
4#13073986C211yesmaximal, characteristic, complemented
5#13073984C212yesmaximal, complemented
6#13073972C212yesmaximal, complemented
7#13073958C214yesmaximal, complemented
8#13073538C211yesmaximal, characteristic, complemented
9#13072929C212yesmaximal, complemented
10#13071977C212yesmaximal, complemented
11#13071891C214yesmaximal, complemented
12C22⋊Q8×Dic11C212yesmaximal, complemented
13#13071144C212yesmaximal, complemented
14#13071103C212yesmaximal
15#13071097C212yesmaximal, complemented
16#13071021C211yesmaximal, characteristic, complemented
17C11×#2538C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C22×#4341C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C2×C4×C22⋊D11C2212yes—
26C2×#66977C2212yes—
27C22×C4×Dic11C2212yes—
28C4×Q8×D11—28no—
29C4×#4341—28no—
30C2×#66945C2212yes—
31C2×#66945C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×C4⋊C4×D11C2212yes—
34C2×#66940C2212yes—
35C2×#66940C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×#66930C2212yes—
39C2×C42×D11C2212yes—
40C2×C42×D11C2211yescharacteristic
41C2×C4×Dic22C2212yes—
42C2×C4×Dic22C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C11×#396C2214yes—
45C11×#390C2212yes—
46C11×#389C2212yes—
47C11×#384C2211yescharacteristic
48C11×#380C2212yes—
49#10622843C2212yes—
50#10622834C2212yes—
51#10622825C2212yes—
52#10622602C2214yes—
53#10622600C2212yes—
54#10622600C2212yes—
55#10622598C2212yes—
56#10622598C2212yes—
57#10622597C2214yes—
58#10622596C2214yes—
59#10622594C2214yes—
60#10622592C2214yes—
61#10622590C2212yes—
62C4⋊C4×Dic11C2212yes—
63C4⋊C4×Dic11C2214yes—
64C4⋊C4×Dic11C2212yes—
65#10622587C2212yes—
66#10622587C2212yes—
67#10622586C2212yes—
68#10622586C2212yes—
69#10622569C2214yes—
70#10622569C2214yes—
71#10622563C2214yes—
72#10622562C2214yes—
73#10622561C2214yes—
74#10622560C2214yes—
75#10622559C2214yes—
76C22⋊C4×Dic11C2214yes—
77C22⋊C4×Dic11C2214yes—
78#10622548C2211yescharacteristic
79#10622542C2212yes—
80#10622541C2212yes—
81#10622281C2214yes—
82#10622271C2214yes—
83#10622265C2214yes—
84#10622262C2214yes—
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C22×C22⋊D11C2312yes—
89C23×Dic11C2312yes—
90C23×Dic11C2312yes—
91C2×Q8×D11—24no—
92C2×Q8×D11—24no—
93C2×Q8×D11—24no—
94C2×#4341—24no—
95C2×#4341—24no—
96C2×#4341Q818yescomplemented
97C22×C4×D11C2312yes—
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2312yes—
100C22×C4×D11C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×Dic22C2312yes—
103C22×Dic22C2311yescharacteristic
104C22×Dic22C2311yescharacteristic
105C11×C22⋊Q8—28no—
106C4×Q8×C11—24no—
107C4×D4×C11—24no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C42×C11C2312yes—
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123Q8×Dic11—24no—
124D4×Dic11—24no—
125C4×C22⋊D11—28no—
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2314yes—
134C2×C4⋊Dic11C2312yes—
135#66977—28no—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11—28no—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154#66945—24no—
155#66945—28no—
156C4⋊C4×D11—24no—
157C4⋊C4×D11—28no—
158#66940—24no—
159#66940—24no—
160#66940—28no—
161(C22⋊D11)⋊C4—28no—
162#66930—28no—
163C42×D11—28no—
164C42×D11D418yes—
165C4×Dic22—24no—
166C4×Dic22—24no—
167C4×Dic22—28no—
168C11×#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178#34952—111nomaximal, Sylow
179C24×C11C2412yes—
180C23×D11C2411yescharacteristic
181C2×Q8×C11—22no—
182C2×Q8×C11—22no—
183C2×Q8×C11#4114yescomplemented
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11C2×Q814yescomplemented
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—24no—
190C22×C4×C11C2414yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2412yes—
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11C2×Q818yes—
200C22×Dic11—24no—
201C22×Dic11—24no—
202C22×Dic11—24no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11C2×Q818yescomplemented
206C22×Dic11C2414yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2411yescharacteristic
210C22×Dic11C2411yescharacteristic
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2411yescharacteristic
214Q8×D11—232no—
215#4341—232no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—22no—
221C2×C4×D11—22no—
222C2×C4×D11—41no—
223C2×C4×D11—41no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×C4×D11C2×D414yes—
227C2×C4×D11C2×D414yes—
228C2×C4×D11C2×D414yes—
229C2×C4×D11C2×Q814yes—
230C2×C4×D11#4114yes—
231C2×Dic22—24no—
232C2×Dic22—24no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22—22no—
236C2×Dic22—24no—
237C2×Dic22—22no—
238C2×Dic22C2×Q814yescomplemented
239C2×Dic22#4114yescomplemented
240C11×C4⋊C4—24no—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—28no—
246C11×C4⋊C4—42no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—44no—
250C42×C11—24no—
251C42×C11C2×D414yes—
252C22⋊Dic11—24no—
253C22⋊Dic11—28no—
254C22⋊Dic11—44no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—28no—
257C4⋊Dic11—24no—
258C4⋊Dic11—22no—
259C4⋊Dic11—22no—
260C4⋊Dic11—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—42no—
263C4⋊Dic11—44no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—28no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—44no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273C4×Dic11—24no—
274C4×Dic11—24no—
275C4×Dic11—28no—
276C4×Dic11—24no—
277C4×Dic11—24no—
278C4×Dic11C2×D414yes—
279C4×Dic11C2×D414yes—
280C4×Dic11C2×D414yes—
281C2×C4×#41—111no—
282C22×C4×Q8—111no—
283#2582—111no—
284#2582—111no—
285#2581—112no—
286#2580—112no—
287#2579—114no—
288#2538—111no—
289#2538D1111yescharacteristic, complemented
290#2487—112no—
291#2409—112no—
292#2396—114no—
293C4×C22⋊Q8—112no—
294C4×C22⋊Q8—112no—
295#2297—112no—
296#2296—112no—
297#2285—111no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11C22×Q814yes—
305C23×C11C2511yescharacteristic
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11C22×D412yes—
311C22×D11C22×Q812yes—
312C22×D11C2×#4112yes—
313Q8×C11—28no—
314D4×C11—28no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—22no—
328C2×C4×C11—48no—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×Q812yes—
333C2×C4×C11C2×#4114yes—
334C2×C4×C11C2×#4112yes—
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2×#4112yes—
337C22⋊D11—216no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—21no—
341C2×Dic11—22no—
342C2×Dic11—21no—
343C2×Dic11—22no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—216no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—22no—
352C2×Dic11—24no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—48no—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×Q814yes—
361C2×Dic11C22×Q812yes—
362C2×Dic11C2×#4114yes—
363C2×Dic11C2×#4112yes—
364C4×D11—216no—
365C4×D11—28no—
366C4×D11—44no—
367C4×D11—48no—
368C4×D11C22⋊Q8116yescomplemented
369Dic22—216no—
370Dic22—28no—
371Dic22—28no—
372C22×#41—111no—
373C23×Q8—111no—
374C2×C22⋊Q8—112no—
375C2×C22⋊Q8C2×D1112yes—
376C4×#41—228no—
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×Q8—112no—
380C2×C4×Q8—111no—
381C2×C4×Q8—112no—
382C2×C4×Q8—111no—
383C2×C4×Q8—111no—
384C2×C4×Q8—228no—
385C2×C4×Q8C2×D1111yescharacteristic
386C2×C4×D4—111no—
387C2×C4×D4—112no—
388C2×C4×D4—112no—
389C2×C4×D4C2×D1111yescharacteristic
390C2×#117—111no—
391C2×#117—112no—
392C2×#117—112no—
393C22×C4⋊C4—112no—
394C22×C4⋊C4—111no—
395C22×C42—111no—
396C22×C42—112no—
397C22×C42—112no—
398#400—114no—
399#399—114no—
400#398—114no—
401#398—114no—
402#396—114no—
403#396C2×D1114yes—
404#395—114no—
405#393—114no—
406#391—112no—
407#391—112no—
408#391—112no—
409#391—112no—
410#390—112no—
411#390C2×D1112yes—
412#389—112no—
413#389—112no—
414#389—112no—
415#389—112no—
416#389—112no—
417#389C2×D1112yes—
418#387—114no—
419#387—114no—
420#386—114no—
421#386—114no—
422#385—114no—
423#385—114no—
424#385—114no—
425#385—114no—
426#384—111no—
427#384C2×D1111yescharacteristic
428#382—112no—
429#380—112no—
430#380—112no—
431#380—112no—
432#380C2×D1112yes—
433C4×C4⋊C4—112no—
434C4×C4⋊C4—114no—
435C4×C4⋊C4—112no—
436C4×C4⋊C4—114no—
437C4×C22⋊C4—114no—
438C4×C22⋊C4—114no—
439C22×C11—24no—
440C22×C11—24no—
441C22×C11—24no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11C23×D411yescharacteristic
447C22×C11C23×Q811yescharacteristic
448C22×C11C22×#4111yescharacteristic
449C22×C11C22×#4111yescharacteristic
450C22×C11C22×#4111yescharacteristic
451C22×C11#58511yescharacteristic
452C22×C11#58511yescharacteristic
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—22no—
458C2×D11—22no—
459C2×D11C2×C22⋊Q814yes—
460C4×C11—24no—
461C4×C11—22no—
462C4×C11—42no—
463C4×C11—42no—
464C4×C11—44no—
465C4×C11C2×C22⋊Q814yes—
466C4×C11#52514yes—
467Dic11—24no—
468Dic11—22no—
469Dic11—24no—
470Dic11—22no—
471Dic11—42no—
472Dic11—42no—
473Dic11—44no—
474Dic11C2×C22⋊Q814yes—
475C2×#41—118no—
476C2×#41—224no—
477C2×#41—224no—
478C22×Q8—111no—
479C22×Q8—111no—
480C22×Q8—112no—
481C22×Q8—224no—
482C22×Q8—224no—
483C22×Q8—224no—
484C22×Q8C22×D1111yescharacteristic
485C22×D4—112no—
486C22×D4C22×D1111yescharacteristic
487C23×C4—111no—
488C23×C4—112no—
489C23×C4—111no—
490C23×C4—111no—
491C23×C4—112no—
492C23×C4—112no—
493C23×C4—112no—
494C23×C4C22×D1112yes—
495C22⋊Q8—28no—
496C22⋊Q8—228no—
497C4×Q8—24no—
498C4×Q8—228no—
499C4×Q8—224no—
500C4×Q8—228no—
501C4×Q8—224no—
502C4×Q8—224no—
503C4×Q8—224no—
504C4×Q8—224no—
505C4×D4—24no—
506C4×D4—224no—
507C4×D4—228no—
508C4×D4—228no—
509#117—228no—
510#117—224no—
511#117—228no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—112no—
515C2×C4⋊C4—112no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—112no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—112no—
521C2×C4⋊C4—112no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—112no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—228no—
528C2×C4⋊C4C22×D1111yescharacteristic
529C2×C4⋊C4C22×D1112yes—
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C4⋊C4C22×D1112yes—
532C2×C4⋊C4C22×D1112yes—
533C2×C4⋊C4C22×D1114yes—
534C2×C4⋊C4C22×D1112yes—
535C2×C22⋊C4—112no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4C22×D1112yes—
541C2×C22⋊C4C22×D1114yes—
542C2×C22⋊C4C22×D1114yes—
543C2×C42—111no—
544C2×C42—111no—
545C2×C42—111no—
546C2×C42—118no—
547C2×C42—112no—
548C2×C42—114no—
549C2×C42—112no—
550C2×C42—112no—
551C2×C42—112no—
552C2×C42—112no—
553C2×C42—112no—
554C2×C42—228no—
555C2×C42—228no—
556C2×C42C22×D1112yes—
557C2×C42C22×D1111yescharacteristic
558#95—114no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—114no—
563#95—114no—
564#95—114no—
565#95—114no—
566#95—114no—
567#95C22×D1114yes—
568C2×C11—44no—
569C2×C11C22×C22⋊Q811yescharacteristic
570C2×C11C2×#52511yescharacteristic
571C2×C11#344911yescharacteristic
572C2×C11Q8×#4111yescharacteristic
573C2×C11Q8×#4111yescharacteristic
574C2×C11#348011yescharacteristic
575C2×C11#348011yescharacteristic
576D11—24no—
577C24—111no—
578C24C23×D1112yes—
579#41—2232no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—114no—
583C2×Q8—114no—
584C2×Q8—224no—
585C2×Q8—224no—
586C2×Q8—2232no—
587C2×Q8—222no—
588C2×Q8—222no—
589C2×Q8—224no—
590C2×Q8—222no—
591C2×Q8—222no—
592C2×Q8#434114yescomplemented
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—118no—
596C2×D4—224no—
597C2×D4—224no—
598C2×D4Q8×D1114yescomplemented
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—111no—
603C22×C4—114no—
604C22×C4—114no—
605C22×C4—114no—
606C22×C4—118no—
607C22×C4—112no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—112no—
611C22×C4—114no—
612C22×C4—114no—
613C22×C4—114no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—224no—
617C22×C4—224no—
618C22×C4—224no—
619C22×C4—224no—
620C22×C4—224no—
621C22×C4—224no—
622C22×C4—224no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—441no—
626C22×C4—441no—
627C22×C4—442no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4C23×D1114yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1112yes—
634C22×C4C23×D1111yescharacteristic
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637C22×C4C23×D1111yescharacteristic
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—28no—
643C4⋊C4—24no—
644C4⋊C4—42no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—228no—
650C4⋊C4—224no—
651C4⋊C4—222no—
652C4⋊C4—224no—
653C4⋊C4—222no—
654C4⋊C4—224no—
655C4⋊C4—224no—
656C4⋊C4—444no—
657C4⋊C4—442no—
658C4⋊C4—444no—
659C22⋊C4—24no—
660C22⋊C4—28no—
661C22⋊C4—44no—
662C22⋊C4—224no—
663C22⋊C4—228no—
664C22⋊C4—224no—
665C22⋊C4—228no—
666C22⋊C4—444no—
667C42—24no—
668C42—114no—
669C42—114no—
670C42—114no—
671C42—224no—
672C42—224no—
673C42—224no—
674C42—224no—
675C42—228no—
676C42—224no—
677C42—224no—
678C42D4×D1114yes—
679C11#3495211yescharacteristic, complemented, Sylow
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—112no—
687C23—112no—
688C23—112no—
689C23—221no—
690C23—221no—
691C23—221no—
692C23—221no—
693C23C2×Q8×D1114yes—
694C23C24×D1111yescharacteristic
695Q8—28no—
696Q8—2216no—
697Q8—228no—
698Q8—228no—
699D4—28no—
700D4—2216no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—48no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—1116no—
719C2×C4—112no—
720C2×C4—112no—
721C2×C4—114no—
722C2×C4—114no—
723C2×C4—2216no—
724C2×C4—2216no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—221no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—228no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—224no—
742C2×C4—222no—
743C2×C4—444no—
744C2×C4—448no—
745C2×C4—448no—
746C2×C4C2×D4×D1112yes—
747C2×C4C2×D4×D1112yes—
748C2×C4C2×D4×D1112yes—
749C2×C4C2×#434114yes—
750C2×C4C2×#434112yes—
751C2×C4C2×Q8×D1112yes—
752C2×C4#41×D1112yes—
753C2×C4#41×D1112yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—114no—
762C22—222no—
763C22—222no—
764C22—222no—
765C22—222no—
766C22—222no—
767C22—222no—
768C22C22×D4×D1111yescharacteristic
769C22C22×#434111yescharacteristic
770C22C22×Q8×D1111yescharacteristic
771C22C2×#41×D1111yescharacteristic
772C22C2×#41×D1111yescharacteristic
773C22#1062345511yescharacteristic
774C22#1062345711yescharacteristic
775C4—24no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—44no—
780C4—114no—
781C4—222no—
782C4—224no—
783C4—222no—
784C4—224no—
785C4—442no—
786C4—442no—
787C4—444no—
788C4#1062313714yes—
789C4D11×C22⋊Q814yes—
790C2—44no—
791C2—224no—
792C2C2×D11×C22⋊Q811yescharacteristic
793C2C2×#1062313711yescharacteristic
794C2#1308194411yescharacteristic
795C2Q8×#434111yescharacteristic
796C2#1308219511yescharacteristic
797C2#1308220811yescharacteristic
798C2#1308221511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2538C2
prime radicalC22×#4341C22
hypercenter#2538D11
hypocenterC11#34952
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
3. #13073989C2semidirect
4. #13073986C2semidirect
5. #13073984C2semidirect
6. #13073972C2semidirect
7. #13073958C2semidirect
8. #13073538C2semidirect
9. #13072929C2semidirect
10. #13071977C2semidirect
11. #13071891C2semidirect
12. C22⋊Q8×Dic11C2semidirect
13. #13071144C2semidirect
15. #13071097C2semidirect
16. #13071021C2semidirect
17. C11×#2538C2semidirect
96. C2×#4341Q8semidirect
183. C2×Q8×C11#41semidirect
186. C2×D4×C11C2×Q8semidirect
205. C22×Dic11C2×Q8semidirect
238. C2×Dic22C2×Q8semidirect
239. C2×Dic22#41semidirect
289. #2538D11semidirect
368. C4×D11C22⋊Q8semidirect
592. C2×Q8#4341semidirect
598. C2×D4Q8×D11semidirect
679. C11#34952semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×C4×Q8×D112
#130739892
#130739862
#130739842
#130739722
#130739582
#130735382
#130729292
#130719772
#130718912
C22⋊Q8×Dic112
#130711442
#130711032
#130710972
#130710212
C11×#25382
#3495211