Finite Group Databasebeta

← #14913922

Subgroups — #14913922

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2#13071590C212yesmaximal, complemented
3#13071584C212yesmaximal, complemented
4#13071582C212yesmaximal, complemented
5#13071576C212yesmaximal, complemented
6#13071559C212yesmaximal, complemented
7#13071557C212yesmaximal, complemented
8#13071553C212yesmaximal, complemented
9#13071549C212yesmaximal, complemented
10#13071223C212yesmaximal, complemented
11#13071221C212yesmaximal, complemented
12#13071205C212yesmaximal
13#13071022C211yesmaximal, characteristic, complemented
14#13071014C211yesmaximal, characteristic, complemented
15#13071009C211yesmaximal, characteristic, complemented
16#13071009C211yesmaximal, characteristic, complemented
17D11×#382C211yesmaximal, characteristic, complemented
18#13070970C212yesmaximal, complemented
19C11×#2283C211yesmaximal, characteristic, complemented
20C22×#4339C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C2×#66945C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C4×#4339C4116yescomplemented
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2211yescharacteristic
32C2×#66925C2211yescharacteristic
33C2×#66925C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C4×Dic22C2211yescharacteristic
38C11×#383C2212yes—
39C11×#382C2211yescharacteristic
40C11×#382C2211yescharacteristic
41C11×#381C2212yes—
42C11×#380C2212yes—
43C4×C11×C4⋊C4C2212yes—
44C4×C11×C22⋊C4C2212yes—
45C11×#376C2212yes—
46#10622825C2212yes—
47#10622824C2212yes—
48C4×C22⋊Dic11C2212yes—
49#10622600C2212yes—
50#10622600C2212yes—
51#10622590C2212yes—
52#10622589C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2212yes—
55#10622570C2214yes—
56#10622569C2214yes—
57#10622558C2214yes—
58#10622557C2214yes—
59#10622553C2214yes—
60C4×(C2×D11)⋊C4C2214yes—
61#10622550C2212yes—
62#10622549C2211yescharacteristic
63#10622549C2211yescharacteristic
64C4×C4⋊Dic11C2212yes—
65#10622546C2214yes—
66#10622545C2212yes—
67C4×Dic11⋊C4C2214yes—
68#10622282C2214yes—
69#10622280C2212yes—
70#10622280C2212yes—
71#10622279C2214yes—
72#10622279C2212yes—
73#10622279C2212yes—
74#10622278C2214yes—
75#10622277C2212yes—
76#10622277C2212yes—
77D11×#95C2212yes—
78D11×#95C2212yes—
79#10622267C2214yes—
80#10622266C2214yes—
81#10622265C2214yes—
82#10622264C2212yes—
83#10622264C2212yes—
84#10622263C2212yes—
85#10622263C2212yes—
86#10622262C2214yes—
87#10622262C2212yes—
88#10622262C2212yes—
89#10622261C2212yes—
90#10622261C2212yes—
91#10622259C2214yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11C2311yescharacteristic
96C22×C22⋊D11C2311yescharacteristic
97C2×#4339—24no—
98C2×#4339—24no—
99C2×#4339C2×C418yes—
100C22×D44C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×C4×D11C2314yes—
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C42×C11C2×C418yescomplemented
113C2×C42×C11C2314yes—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2311yescharacteristic
120C2×C22⋊Dic11C2311yescharacteristic
121C4×C22⋊D11C2×C418yes—
122C4×C22⋊D11C2×C418yes—
123C4×C22⋊D11C2×C418yescomplemented
124C4×C22⋊D11C2×C418yescomplemented
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2311yescharacteristic
129C2×(C2×D11)⋊C4C2311yescharacteristic
130C2×(C2×D11)⋊C4C2311yescharacteristic
131C2×(C2×D11)⋊C4C2311yescharacteristic
132#66979C2×C418yescomplemented
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2311yescharacteristic
141C2×Dic11⋊C4C2311yescharacteristic
142C2×Dic11⋊C4C2311yescharacteristic
143C2×Dic11⋊C4C2311yescharacteristic
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154#66945—28no—
155C4⋊C4×D11—28no—
156C4×D44C2×C418yes—
157C4×D44C2×C418yes—
158#66925C2×C418yes—
159#66925C2×C418yescomplemented
160C42×D11C2×C418yes—
161C42×D11C2×C418yescomplemented
162C4×Dic22C2×C418yescomplemented
163C4×Dic22C2×C418yescomplemented
164C11×#95C2314yes—
165C11×#95C2312yes—
166C11×#95C2312yes—
167C11×#95C2312yes—
168C11×#95C2314yes—
169C11×#95C2312yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2312yes—
174C11⋊#95C2312yes—
175C11⋊#95C2314yes—
176C11⋊#95C2312yes—
177C11⋊#95C2312yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C11⋊#95C2314yes—
182#34189—111nomaximal, Sylow
183C24×C11C2411yescharacteristic
184C23×D11C2411yescharacteristic
185C23×D11C2411yescharacteristic
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C22×C414yes—
193C22×C4×C11C2414yes—
194C22×C4×C11C2414yes—
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—22no—
202C2×C22⋊D11—22no—
203C2×C22⋊D11—22no—
204C2×C22⋊D11—22no—
205C2×C22⋊D11C22×C414yes—
206C2×C22⋊D11C22×C414yes—
207C22×Dic11C2414yes—
208C22×Dic11C2414yes—
209C22×Dic11C2411yescharacteristic
210C22×Dic11C2411yescharacteristic
211C22×Dic11C2411yescharacteristic
212C22×Dic11C2411yescharacteristic
213C22×Dic11C2411yescharacteristic
214C22×Dic11C2411yescharacteristic
215#4339—232no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44C22×C414yes—
219C2×C4×D11—28no—
220C2×C4×D11—22no—
221C2×C4×D11—22no—
222C2×C4×D11—42no—
223C2×C4×D11—42no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11C22×C414yes—
229C2×C4×D11C22×C414yes—
230C2×C4×D11C22×C414yes—
231C2×C4×D11C22×C414yes—
232C2×C4×D11C22×C414yes—
233C2×C4×D11C22×C414yes—
234C2×C4×D11#4114yes—
235C2×C4×D11#4114yes—
236C2×Dic22—22no—
237C2×Dic22—22no—
238C2×Dic22C22×C414yes—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C22⋊C4—44no—
242C42×C11—44no—
243C42×C11C22×C414yes—
244C42×C11C22×C414yes—
245C42×C11C22×C414yes—
246C42×C11C22×C414yes—
247C22⋊Dic11—44no—
248C22⋊Dic11C22×C414yes—
249C22⋊Dic11C22×C414yes—
250(C2×D11)⋊C4—28no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4C22×C414yes—
254(C2×D11)⋊C4C22×C414yes—
255(C2×D11)⋊C4C22×C414yes—
256(C2×D11)⋊C4C22×C414yes—
257C4⋊Dic11—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11C22×C414yes—
260C4⋊Dic11C22×C414yes—
261Dic11⋊C4—28no—
262Dic11⋊C4—44no—
263Dic11⋊C4—44no—
264Dic11⋊C4C22×C414yes—
265Dic11⋊C4C22×C414yes—
266Dic11⋊C4C22×C414yes—
267Dic11⋊C4C22×C414yes—
268C4×Dic11—28no—
269C4×Dic11—44no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C4×Dic11C22×C414yes—
273C4×Dic11C22×C414yes—
274C4×Dic11C22×C414yes—
275C4×Dic11C22×C414yes—
276C4×Dic11C22×C414yes—
277C4×Dic11C22×C414yes—
278C2×C4×#41—111no—
279#2357—112no—
280#2357—112no—
281#2356—112no—
282#2356—112no—
283#2353—112no—
284#2353—112no—
285#2353—112no—
286#2353—112no—
287#2314—112no—
288#2314—112no—
289#2311—112no—
290#2285—111no—
291#2283—111no—
292#2283—111no—
293#2283—111no—
294#2283D1111yescharacteristic, complemented
295C2×#382—111no—
296#2274—112no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11C23×C412yes—
302C23×C11C2511yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11C23×C412yes—
310C22×D11C23×C412yes—
311C22×D11C2×#4112yes—
312C22×D11C2×#4112yes—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—28no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11C23×C412yes—
329C2×C4×C11C23×C412yes—
330C2×C4×C11C23×C412yes—
331C2×C4×C11C23×C412yes—
332C2×C4×C11C23×C412yes—
333C2×C4×C11C23×C412yes—
334C2×C4×C11C2×#4112yes—
335C2×C4×C11C2×#4112yes—
336C22⋊D11—28no—
337C22⋊D11—28no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11C23×C412yes—
351C2×Dic11C23×C412yes—
352C2×Dic11C23×C412yes—
353C2×Dic11C23×C412yes—
354C2×Dic11C23×C412yes—
355C2×Dic11C23×C412yes—
356C2×Dic11C2×#4112yes—
357C2×Dic11C2×#4112yes—
358D44—28no—
359C4×D11—28no—
360C4×D11—44no—
361C4×D11—44no—
362C4×D11—44no—
363C4×D11—44no—
364C4×D11—88no—
365C4×D11#117116yes—
366Dic22—28no—
367C22×#41—111no—
368C4×#41—1116no—
369C2×C4×Q8—111no—
370C2×C4×Q8—111no—
371C2×C4×D4—111no—
372C2×C4×D4—111no—
373C2×C4×D4—111no—
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×#117—111no—
378C2×#117—112no—
379C2×#117—111no—
380C2×#117—111no—
381C22×C4⋊C4—112no—
382C22×C42—111no—
383C22×C42—111no—
384C22×C42C2×D1111yescharacteristic
385#391—114no—
386#390—114no—
387#388—114no—
388#388—114no—
389#388—114no—
390#388—114no—
391#387—114no—
392#387—114no—
393#387—114no—
394#387—114no—
395#386—114no—
396#386—114no—
397#384—112no—
398#383—112no—
399#383—112no—
400#383—112no—
401#383C2×D1112yes—
402#382—112no—
403#382—111no—
404#382—111no—
405#382—112no—
406#382—112no—
407#382C2×D1111yescharacteristic
408#382C2×D1111yescharacteristic
409#381—112no—
410#381—112no—
411#381—112no—
412#381C2×D1112yes—
413#380—112no—
414#380—112no—
415#380—112no—
416#380—112no—
417#380—112no—
418#380C2×D1112yes—
419C4×C4⋊C4—112no—
420C4×C4⋊C4—112no—
421C4×C4⋊C4—112no—
422C4×C4⋊C4—114no—
423C4×C4⋊C4—114no—
424C4×C4⋊C4—112no—
425C4×C4⋊C4—112no—
426C4×C4⋊C4C2×D1112yes—
427C4×C22⋊C4—112no—
428C4×C22⋊C4—114no—
429C4×C22⋊C4—114no—
430C4×C22⋊C4—112no—
431C4×C22⋊C4—112no—
432C4×C22⋊C4C2×D1112yes—
433#376—112no—
434#376—112no—
435#376—112no—
436#376C2×D1112yes—
437C2×#95—112no—
438C2×#95—112no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11C24×C411yescharacteristic
445C22×C11C22×#4111yescharacteristic
446C22×C11C22×#4111yescharacteristic
447C22×C11#58512yes—
448C22×C11#58512yes—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—24no—
452C2×D11—24no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11C2×#11714yes—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—22no—
464C4×C11—44no—
465C4×C11—44no—
466C4×C11C2×#11714yes—
467Dic11—22no—
468Dic11—22no—
469Dic11—22no—
470Dic11—22no—
471Dic11—22no—
472Dic11—44no—
473Dic11—44no—
474Dic11C2×#11714yes—
475C2×#41—118no—
476C2×#41—224no—
477C2×#41—224no—
478C22×Q8—111no—
479C22×D4—111no—
480C22×D4—111no—
481C22×D4—111no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—114no—
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1111yescharacteristic
492C4×Q8—118no—
493C4×Q8—118no—
494C4×D4—118no—
495C4×D4—118no—
496C4×D4—118no—
497C4×D4—118no—
498C4×D4—118no—
499C4×D4—118no—
500#117—118no—
501#117—118no—
502#117—118no—
503#117—228no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—112no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—228no—
516C2×C4⋊C4C22×D1112yes—
517C2×C4⋊C4C22×D1112yes—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—111no—
522C2×C22⋊C4—111no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4C22×D1114yes—
529C2×C42—111no—
530C2×C42—111no—
531C2×C42—111no—
532C2×C42—111no—
533C2×C42—111no—
534C2×C42—111no—
535C2×C42—118no—
536C2×C42—118no—
537C2×C42—114no—
538C2×C42—114no—
539C2×C42—114no—
540C2×C42—114no—
541C2×C42C4×D1118yescomplemented
542C2×C42C22×D1114yes—
543C2×C42C22×D1111yescharacteristic
544C2×C42C22×D1111yescharacteristic
545C2×C42C22×D1111yescharacteristic
546C2×C42C22×D1111yescharacteristic
547#95—112no—
548#95—112no—
549#95—114no—
550#95—114no—
551#95—112no—
552#95—114no—
553#95—114no—
554#95—114no—
555#95—112no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95C22×D1112yes—
560#95C22×D1112yes—
561#95C22×D1112yes—
562#95C22×D1114yes—
563#95C22×D1112yes—
564#95C22×D1114yes—
565C2×C11—42no—
566C2×C11C22×#11711yescharacteristic
567C2×C11#342811yescharacteristic
568C2×C11#342811yescharacteristic
569C2×C11#351012yes—
570C2×C11#351212yes—
571D11—24no—
572D11—42no—
573C24—111no—
574C24—111no—
575C24C23×D1111yescharacteristic
576#41—2232no—
577C2×Q8—114no—
578C2×Q8—222no—
579C2×Q8—222no—
580C2×D4—114no—
581C2×D4—114no—
582C2×D4—114no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—222no—
587C2×D4—222no—
588C2×D4—222no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—111no—
594C22×C4—114no—
595C22×C4—114no—
596C22×C4—114no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—114no—
603C22×C4—114no—
604C22×C4—114no—
605C22×C4—114no—
606C22×C4—114no—
607C22×C4—114no—
608C22×C4—114no—
609C22×C4—228no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4—444no—
617C22×C4—444no—
618C22×C4C2×C4×D1114yes—
619C22×C4C2×C4×D1114yes—
620C22×C4C2×C4×D1114yes—
621C22×C4C23×D1114yes—
622C22×C4C23×D1114yes—
623C22×C4C23×D1111yescharacteristic
624C22×C4C23×D1111yescharacteristic
625C22×C4C23×D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627C22×C4C23×D1111yescharacteristic
628C22×C4C23×D1111yescharacteristic
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—114no—
632C4⋊C4—114no—
633C4⋊C4—114no—
634C4⋊C4—114no—
635C4⋊C4—114no—
636C4⋊C4—114no—
637C4⋊C4—228no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—444no—
641C4⋊C4—444no—
642C22⋊C4—44no—
643C22⋊C4—114no—
644C22⋊C4—114no—
645C22⋊C4—114no—
646C22⋊C4—114no—
647C22⋊C4—114no—
648C22⋊C4—114no—
649C22⋊C4—228no—
650C22⋊C4—444no—
651C22⋊C4—444no—
652C22⋊C4—444no—
653C42—44no—
654C42—114no—
655C42—114no—
656C42—114no—
657C42—114no—
658C42—114no—
659C42—114no—
660C42—228no—
661C42—444no—
662C42—444no—
663C42—444no—
664C42C2×C4×D1114yes—
665C42C2×C4×D1114yes—
666C42C2×C4×D1114yes—
667C42C2×C4×D1114yes—
668C11#3418911yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—112no—
674C23—112no—
675C23—112no—
676C23—112no—
677C23—222no—
678C23—222no—
679C23—221no—
680C23—221no—
681C23—222no—
682C23—222no—
683C23C22×C4×D1112yes—
684C23C24×D1111yescharacteristic
685Q8—228no—
686D4—228no—
687D4—228no—
688D4—228no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—112no—
705C2×C4—112no—
706C2×C4—112no—
707C2×C4—1116no—
708C2×C4—112no—
709C2×C4—112no—
710C2×C4—112no—
711C2×C4—112no—
712C2×C4—112no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—228no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—444no—
727C2×C4—444no—
728C2×C4—444no—
729C2×C4—444no—
730C2×C4—888no—
731C2×C4C22×C4×D1112yes—
732C2×C4C22×C4×D1112yes—
733C2×C4C22×C4×D1112yes—
734C2×C4C22×C4×D1112yes—
735C2×C4C22×C4×D1112yes—
736C2×C4C22×C4×D1112yes—
737C2×C4#41×D1112yes—
738C2×C4#41×D1112yes—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—42no—
743C22—42no—
744C22—114no—
745C22—224no—
746C22—224no—
747C22—222no—
748C22—222no—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—442no—
753C22—442no—
754C22C23×C4×D1111yescharacteristic
755C22C2×#41×D1111yescharacteristic
756C22C2×#41×D1111yescharacteristic
757C22#1062345312yes—
758C22#1062345312yes—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—44no—
765C4—44no—
766C4—114no—
767C4—222no—
768C4—222no—
769C4—222no—
770C4—222no—
771C4—222no—
772C4—444no—
773C4—444no—
774C4D11×#11714yes—
775C2—42no—
776C2—224no—
777C2—442no—
778C2C2×D11×#11711yescharacteristic
779C2#1308181711yescharacteristic
780C2#1308181711yescharacteristic
781C2#1308250512yes—
782C2#1308253112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2283C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2283D11
hypocenterC11#34189
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2283

Complements

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

NH ≅ G/Ntype
2. #13071590C2semidirect
3. #13071584C2semidirect
4. #13071582C2semidirect
5. #13071576C2semidirect
6. #13071559C2semidirect
7. #13071557C2semidirect
8. #13071553C2semidirect
9. #13071549C2semidirect
10. #13071223C2semidirect
11. #13071221C2semidirect
13. #13071022C2semidirect
14. #13071014C2semidirect
15. #13071009C2semidirect
16. #13071009C2semidirect
17. D11×#382C2semidirect
18. #13070970C2semidirect
19. C11×#2283C2semidirect
29. C4×#4339C4semidirect
112. C2×C42×C11C2×C4semidirect
123. C4×C22⋊D11C2×C4semidirect
124. C4×C22⋊D11C2×C4semidirect
132. #66979C2×C4semidirect
159. #66925C2×C4semidirect
161. C42×D11C2×C4semidirect
162. C4×Dic22C2×C4semidirect
163. C4×Dic22C2×C4semidirect
294. #2283D11semidirect
541. C2×C42C4×D11semidirect
668. C11#34189semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130715902
#130715842
#130715822
#130715762
#130715592
#130715572
#130715532
#130715492
#130712232
#130712212
#130712052
#130710222
#130710142
#130710092
D11×#3822
#130709702
C11×#22832
#3418911