Finite Group Databasebeta

← #14759522

Subgroups — #14759522

Order 2816.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622851C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic, complemented
4#13071309C211yesmaximal, characteristic, complemented
5#13068971C211yesmaximal, characteristic, complemented
6#13068964C211yesmaximal, characteristic, complemented
7#13068933C211yesmaximal, characteristic, complemented
8#13068870C211yesmaximal, characteristic, complemented
9#13068863C211yesmaximal, characteristic, complemented
10#13068804C211yesmaximal, characteristic, complemented
11#13068556C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic, complemented
13C4×#66899C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C2×C11×#520C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C11×#520—24no—
18C11×#520—24no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C2×C11×#117C2211yescharacteristic
27C22×C11×C4⋊C4—21no—
28C22×C11×C4⋊C4C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33#10622851C418yescomplemented
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622825C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622639—24no—
44C4×#4323—24no—
45#10622603—21no—
46#10622602—21no—
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622570—21no—
52#10622569—21no—
53#10622552C2211yescharacteristic
54C4×C4⋊Dic11C2211yescharacteristic
55#10622541C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57C2×C4×C11⋊C8C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622162C2211yescharacteristic
63#10622162C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41C2×C414yescomplemented
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11D414yescomplemented
85C4×D4×C11—28no—
86C4×D4×C11—28no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11D414yescomplemented
91C11×#117—28no—
92C11×#117—22no—
93C11×#117—22no—
94C2×C11×C4⋊C4—28no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C22⋊Dic11—21no—
113C2×#4325—22no—
114C2×#4325—22no—
115C2×#4325C2×C414yescomplemented
116C2×#4323—22no—
117C2×#4323—22no—
118C2×#4323C2×C414yescomplemented
119#66983—22no—
120#66983C2×C414yescomplemented
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×C4×Dic11—21no—
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C4×D44—22no—
135C4×D44—22no—
136#66899—22no—
137#66899—22no—
138#66899C2×C414yescomplemented
139#66896—22no—
140#66896—22no—
141#66896C2×C414yescomplemented
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)C2×C414yescomplemented
147#66873—22no—
148#66873—22no—
149#66871—22no—
150#66871—22no—
151#66867—22no—
152C4×C11⋊C8—22no—
153#21460—111nomaximal, Sylow
154C24×C11—21no—
155C24×C11C2×D411yescharacteristic
156C23×D11—21no—
157C11×#41—28no—
158C11×#41—28no—
159C11×#41—28no—
160C11×#41—28no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C22×C412yes—
165C2×Q8×C11C2×D412yes—
166C2×Q8×C11#4112yes—
167C2×D4×C11—24no—
168C2×D4×C11—24no—
169C2×D4×C11—24no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11C22×C412yes—
174C2×D4×C11C2×D412yes—
175C2×D4×C11#4112yes—
176C22×C4×C11—24no—
177C22×C4×C11—24no—
178C22×C4×C11—21no—
179C22×C4×C11—24no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—24no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—81no—
190C22×C4×C11—81no—
191C22×C4×C11—81no—
192C22×C4×C11—81no—
193C22×C4×C11—81no—
194C22×C4×C11—81no—
195C22×C4×C11C22×C412yes—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11#4112yes—
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—81no—
205C2×C22⋊D11—81no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44C22×C412yes—
215C2×C4×D11—42no—
216C2×C4×D11—81no—
217C2×C4×D11—81no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4C2×D412yes—
226C11×C4⋊C4C2×D412yes—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C42×C11—24no—
232C42×C11—24no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11C2×D412yes—
236C42×C11C2×D412yes—
237C22⋊Dic11—81no—
238#4325—28no—
239#4323—28no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—42no—
242(C2×D11)⋊C4—81no—
243(C2×D11)⋊C4—81no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11C22×C412yes—
250Dic11⋊C4—81no—
251C4×Dic11—81no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8C22×C412yes—
263C2×C11⋊C8C22×C412yes—
264C2×#520D1111yescharacteristic, complemented
265C2×#449—111no—
266C2×#440—111no—
267C2×C4×D8—111no—
268#2324—111no—
269#1880—111no—
270#1879—111no—
271#1874—111no—
272#1863—111no—
273#1862—111no—
274#1852—111no—
275#1788—111no—
276#1762—111no—
277C4×#103—111no—
278#1750—111no—
279C23×C11—22no—
280C23×C11—21no—
281C23×C11—22no—
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11C4×D412yes—
293C23×C11C22×D411yescharacteristic
294C22×D11—22no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11C4×D414yes—
305D4×C11—216no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11C4×D414yes—
310C2×C4×C11—216no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—84no—
337C2×C4×C11—84no—
338C2×C4×C11—84no—
339C2×C4×C11C4×D412yes—
340C2×C4×C11#12012yes—
341C2×C4×C11#12012yes—
342C2×C4×C11C23×C411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C2×#4111yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C22⋊D11—84no—
349C2×Dic11—22no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358D44—22no—
359D44—22no—
360D44—41no—
361D44—41no—
362C4×D11—84no—
363C11⋊C8—22no—
364C11⋊C8—22no—
365C11⋊C8—41no—
366C11⋊C8—41no—
367C22×#41C2×D1111yescharacteristic
368C22×SD16—111no—
369C22×D8—111no—
370C2×#121—111no—
371#520—24no—
372#520—24no—
373C2×C4×Q8C2×D1111yescharacteristic
374C2×C4×Q8C2×D1111yescharacteristic
375C2×C4×D4—21no—
376C2×C4×D4—21no—
377C2×C4×D4—111no—
378C2×C4×D4C2×D1111yescharacteristic
379C2×C4×D4C2×D1111yescharacteristic
380C2×#117—21no—
381C2×#117C2×D1111yescharacteristic
382C22×C4⋊C4—21no—
383C22×C4⋊C4C2×D1111yescharacteristic
384#449—118no—
385#440—224no—
386C4×D8—224no—
387C2×#107—111no—
388C2×#107—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×#97—111no—
400C2×C4×C8—111no—
401#390—111no—
402#390—221no—
403#389—111no—
404#388—221no—
405#386—221no—
406#385—221no—
407#380—111no—
408C4×C4⋊C4—111no—
409#340—111no—
410#340—111no—
411#340—111no—
412#340—111no—
413#336—111no—
414#336—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—24no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—41no—
428C22×C11—42no—
429C22×C11C2×C4×D411yescharacteristic
430C22×C11C2×#12011yescharacteristic
431C22×C11#52511yescharacteristic
432C22×C11#57611yescharacteristic
433C22×C11#57611yescharacteristic
434C22×C11#57711yescharacteristic
435C22×C11#57811yescharacteristic
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—81no—
440C2×D11—81no—
441C2×D11—81no—
442C2×D11—81no—
443C4×C11—22no—
444C4×C11—22no—
445C4×C11—22no—
446C4×C11—24no—
447C4×C11—41no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—41no—
451C4×C11C2×C4×D411yescharacteristic
452C4×C11C2×C4×D411yescharacteristic
453C4×C11#52511yescharacteristic
454C4×C11#52511yescharacteristic
455Dic11—42no—
456Dic11—81no—
457Dic11—81no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41C4×D1114yescomplemented
464C22×Q8C22×D1111yescharacteristic
465C22×D4—21no—
466C22×D4—111no—
467C22×D4—221no—
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—221no—
474C23×C4C22×D1111yescharacteristic
475C2×SD16—114no—
476C2×SD16—222no—
477C2×SD16—222no—
478C2×D8—114no—
479C2×D8—222no—
480C2×D8—222no—
481C22×C8—111no—
482C22×C8—111no—
483C22×C8—111no—
484C22×C8—111no—
485#121—114no—
486#121—222no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8C22⋊D1114yescomplemented
491C4×D4—28no—
492C4×D4—28no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—222no—
497C4×D4—222no—
498C4×D4C22⋊D1114yescomplemented
499#117—28no—
500#117—22no—
501#117—22no—
502C2×C4⋊C4—28no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22⋊D1111yescharacteristic
513C2×C4⋊C4C22⋊D1111yescharacteristic
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4C22⋊D1111yescharacteristic
524C2×C22⋊C4C22⋊D1111yescharacteristic
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—221no—
528C2×C42C22×D1111yescharacteristic
529C2×C42C22×D1111yescharacteristic
530#107—222no—
531#107—222no—
532#103—114no—
533#103—222no—
534#103—222no—
535#102—114no—
536#102—222no—
537#102—222no—
538#102—222no—
539#102—222no—
540C22⋊C8—114no—
541C22⋊C8—222no—
542#97—222no—
543C4×C8—222no—
544#95—221no—
545#95—221no—
546#95—221no—
547C2×C11—42no—
548C2×C11—44no—
549C2×C11C4×#12011yescharacteristic
550C2×C11#294611yescharacteristic
551C2×C11#295111yescharacteristic
552C2×C11#300811yescharacteristic
553C2×C11#301311yescharacteristic
554C2×C11#311911yescharacteristic
555C2×C11#312411yescharacteristic
556D11—82no—
557C24—21no—
558C24—221no—
559C24C2×C22⋊D1111yescharacteristic
560#41—28no—
561#41—28no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C2×C4×D1112yes—
568C2×Q8#433912yes—
569C2×Q8C2×C22⋊D1112yes—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—112no—
577C2×D4—224no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—221no—
583C2×D4—881no—
584C2×D4—881no—
585C2×D4C2×C4×D1112yes—
586C2×D4#433912yes—
587C2×D4C2×C22⋊D1112yes—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—442no—
611C22×C4—881no—
612C22×C4—881no—
613C22×C4C2×C4×D1112yes—
614C22×C4#433912yes—
615C22×C4C2×C22⋊D1111yescharacteristic
616C22×C4C2×C22⋊D1111yescharacteristic
617C22×C4C2×C22⋊D1111yescharacteristic
618C22×C4C2×C22⋊D1111yescharacteristic
619C22×C4C2×C22⋊D1111yescharacteristic
620C22×C4C23×D1111yescharacteristic
621SD16—228no—
622D8—228no—
623C2×C8—112no—
624C2×C8—112no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8—221no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—112no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—221no—
646C4⋊C4—221no—
647C4⋊C4—221no—
648C4⋊C4—881no—
649C4⋊C4C2×C22⋊D1112yes—
650C4⋊C4C2×C22⋊D1112yes—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—224no—
656C22⋊C4—442no—
657C22⋊C4—881no—
658C22⋊C4—881no—
659C22⋊C4—881no—
660C42—24no—
661C42—24no—
662C42—21no—
663C42—21no—
664C42—881no—
665C42C2×C22⋊D1112yes—
666C42C2×C22⋊D1112yes—
667C11#2146011yescharacteristic, complemented, Sylow
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—222no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23C4×C22⋊D1112yes—
689C23C22×C22⋊D1111yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×C22⋊D1114yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—222no—
699D4—222no—
700D4—441no—
701D4—441no—
702D4—884no—
703D4C4×C22⋊D1114yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—222no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—884no—
743C2×C4C4×C22⋊D1112yes—
744C2×C4#6700612yes—
745C2×C4#6700612yes—
746C2×C4C22×C4×D1111yescharacteristic
747C2×C4C2×#433911yescharacteristic
748C2×C4C2×#433911yescharacteristic
749C2×C4C2×#433911yescharacteristic
750C2×C4C22×C22⋊D1111yescharacteristic
751C2×C4C22×C22⋊D1111yescharacteristic
752C8—222no—
753C8—222no—
754C8—441no—
755C8—441no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—442no—
771C22—442no—
772C22—442no—
773C22—881no—
774C22—881no—
775C22—881no—
776C22—881no—
777C22C2×C4×C22⋊D1111yescharacteristic
778C22#1062332211yescharacteristic
779C22#1062336611yescharacteristic
780C22#1062336611yescharacteristic
781C22#1062336811yescharacteristic
782C22#1062336911yescharacteristic
783C22C2×#6700611yescharacteristic
784C4—22no—
785C4—24no—
786C4—22no—
787C4—22no—
788C4—41no—
789C4—42no—
790C4—42no—
791C4—41no—
792C4—442no—
793C4—881no—
794C4—881no—
795C4C2×C4×C22⋊D1111yescharacteristic
796C4C2×C4×C22⋊D1111yescharacteristic
797C4#1062332211yescharacteristic
798C4#1062332211yescharacteristic
799C2—42no—
800C2—44no—
801C2—882no—
802C2C4×#6700611yescharacteristic
803C2#1307744411yescharacteristic
804C2#1307748911yescharacteristic
805C2#1307788411yescharacteristic
806C2#1307793111yescharacteristic
807C2#1307881511yescharacteristic
808C2#1307887811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC2×#10622851C2
cosocleC22×C4×C11C24
hypercenterC2×#520D11
hypocenterC11#21460
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. C2×C4×#4323C2semidirect
4. #13071309C2semidirect
5. #13068971C2semidirect
6. #13068964C2semidirect
7. #13068933C2semidirect
8. #13068870C2semidirect
9. #13068863C2semidirect
10. #13068804C2semidirect
11. #13068556C2semidirect
12. #13068441C2semidirect
13. C4×#66899C2semidirect
14. #13068382C2semidirect
15. C2×C11×#520C2semidirect
33. #10622851C4semidirect
69. C2×C11×#41C2×C4semidirect
84. C4×Q8×C11D4semidirect
90. C4×D4×C11D4semidirect
115. C2×#4325C2×C4semidirect
118. C2×#4323C2×C4semidirect
120. #66983C2×C4semidirect
138. #66899C2×C4semidirect
141. #66896C2×C4semidirect
146. C22⋊(C11⋊C8)C2×C4semidirect
264. C2×#520D11semidirect
463. C2×#41C4×D11semidirect
490. C4×Q8C22⋊D11semidirect
498. C4×D4C22⋊D11semidirect
667. C11#21460semidirect

Maximal subgroups

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

subgroupindex
C2×#106228512
C2×#106226392
C2×C4×#43232
#130713092
#130689712
#130689642
#130689332
#130688702
#130688632
#130688042
#130685562
#130684412
C4×#668992
#130683822
C2×C11×#5202
#2146011