Finite Group Databasebeta

← #14765114

Subgroups — #14765114

Order 2816.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622830C211yesmaximal, characteristic
2#13071309C211yesmaximal, characteristic, complemented
3#13069491C211yesmaximal, characteristic, complemented
4#13069481C211yesmaximal, characteristic, complemented
5#13069316C211yesmaximal, characteristic, complemented
6#13069302C211yesmaximal, characteristic, complemented
7#13069240C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic, complemented
11#13068938C211yesmaximal, characteristic, complemented
12#13068815C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C11×#2309C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic, complemented
23C11×#390—21no—
24C11×#390—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#379—21no—
30C11×#379—21no—
31#10622830C418yescomplemented
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622603—21no—
42#10622602—21no—
43C2×#66873C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic, complemented
45C2×#66872C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622570—21no—
48#10622569—21no—
49#10622552C2211yescharacteristic, complemented
50C4×C4⋊Dic11C2211yescharacteristic, complemented
51#10622541C2211yescharacteristic, complemented
52C2×#66867C2211yescharacteristic, complemented
53C2×C4×C11⋊C8C2211yescharacteristic, complemented
54#10622167C2211yescharacteristic, complemented
55#10622167C2211yescharacteristic, complemented
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622162C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60C25×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—22no—
63C22×D4×C11—41no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C22×D4×C11—41no—
67C22×D4×C11C2×C414yescomplemented
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C11×#117—41no—
75C11×#117—41no—
76C11×#117—41no—
77C11×#117—41no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×#4323—41no—
98C2×#4323—41no—
99C2×#4323—41no—
100C2×#4323—41no—
101C2×#4323C2×C414yes—
102C2×#4323C2×C414yes—
103#66983—22no—
104#66983C2×C414yes—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C4×D44—41no—
119C4×D44—41no—
120#66896—41no—
121#66896—41no—
122#66896—41no—
123#66896—41no—
124#66896C2×C414yescomplemented
125#66896C2×C414yescomplemented
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)C2×C414yescomplemented
131#66873—41no—
132#66873—41no—
133#66872—41no—
134#66871—41no—
135#66867—41no—
136C4×C11⋊C8—41no—
137#22056—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—24no—
141C24×C11—42no—
142C24×C11—42no—
143C24×C11—81no—
144C24×C11—81no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11C2×D411yescharacteristic
148C23×D11—21no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—44no—
161C2×D4×C11—44no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—44no—
165C2×D4×C11—44no—
166C2×D4×C11C22×C412yes—
167C2×D4×C11C22×C412yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22×C412yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11#4112yes—
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—24no—
183C2×C22⋊D11—81no—
184C2×C22⋊D11—81no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44C22×C412yes—
194C2×C4×D11—42no—
195C2×C4×D11—81no—
196C2×C4×D11—81no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—81no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C11×C22⋊C4—81no—
213C11×C22⋊C4—81no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—42no—
219C22⋊Dic11—81no—
220#4323—44no—
221#4323—44no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—81no—
225(C2×D11)⋊C4—81no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11C22×C412yes—
232Dic11⋊C4—81no—
233C4×Dic11—81no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C412yes—
245C2×C11⋊C8C22×C412yes—
246C2×#447—111no—
247#2324—111no—
248#2309D1111yescharacteristic, complemented
249#1972—111no—
250#1970—111no—
251#1936—111no—
252#1934—111no—
253#1926—111no—
254#1925—111no—
255#1879—111no—
256#1879—111no—
257#1875—111no—
258#1854—111no—
259#1786—111no—
260#1750—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—48no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—84no—
283C23×C11—84no—
284C23×C11—84no—
285C23×C11—84no—
286C23×C11—84no—
287C23×C11—84no—
288C23×C11C4×D412yes—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—48no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305D4×C11—41no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11C4×D412yes—
331C2×C4×C11C23×C411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C22⋊D11—84no—
338C2×Dic11—22no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347D44—22no—
348D44—22no—
349D44—41no—
350D44—41no—
351C4×D11—84no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—41no—
355C11⋊C8—41no—
356C23×D4C2×D1111yescharacteristic
357C22×D8—111no—
358C22×D8—111no—
359C2×#121—111no—
360C2×C4×D4—111no—
361C2×#117C2×D1111yescharacteristic
362C2×#117C2×D1111yescharacteristic
363#447—118no—
364C2×#107—111no—
365C2×#106—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×#97—111no—
377C2×C4×C8—111no—
378#390—21no—
379#390—21no—
380#390—111no—
381#390—221no—
382#390C2×D1111yescharacteristic
383#390C2×D1111yescharacteristic
384#390C2×D1111yescharacteristic
385#390C2×D1111yescharacteristic
386#389—111no—
387#388—221no—
388#386—221no—
389#385—221no—
390#380—111no—
391#379—21no—
392#379—21no—
393C4×C4⋊C4—111no—
394#340—111no—
395#340—111no—
396#340—111no—
397#340—111no—
398#336—111no—
399#336—111no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—816no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11C2×C4×D411yescharacteristic
423C22×C11#53411yescharacteristic
424C22×C11#53511yescharacteristic
425C22×C11#57611yescharacteristic
426C22×C11#57611yescharacteristic
427C22×C11#57611yescharacteristic
428C22×C11#57711yescharacteristic
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—22no—
437C4×C11—41no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—81no—
442C4×C11—81no—
443C4×C11#51811yescharacteristic
444C4×C11#51811yescharacteristic
445C4×C11#53811yescharacteristic
446C4×C11#53811yescharacteristic
447Dic11—42no—
448Dic11—81no—
449Dic11—81no—
450C25—21no—
451C22×D4—22no—
452C22×D4—21no—
453C22×D4—41no—
454C22×D4—41no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4—111no—
458C22×D4—221no—
459C22×D4C4×D1114yescomplemented
460C22×D4C22×D1111yescharacteristic
461C22×D4C22×D1111yescharacteristic
462C23×C4—221no—
463C23×C4C22×D1111yescharacteristic
464C2×D8—114no—
465C2×D8—114no—
466C2×D8—441no—
467C2×D8—441no—
468C2×D8—441no—
469C2×D8—441no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—111no—
474#121—114no—
475#121—222no—
476C4×D4—441no—
477C4×D4—441no—
478#117—41no—
479#117—41no—
480#117—41no—
481#117—41no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4C22⋊D1111yescharacteristic
487C2×C4⋊C4C22⋊D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4C22⋊D1111yescharacteristic
505C2×C22⋊C4C22⋊D1111yescharacteristic
506C2×C42—21no—
507C2×C42—221no—
508C2×C42C22×D1111yescharacteristic
509C2×C42C22×D1111yescharacteristic
510#107—441no—
511#106—441no—
512#102—114no—
513#102—114no—
514#102—441no—
515#102—441no—
516#102—441no—
517#102—441no—
518#102—441no—
519#102—441no—
520C22⋊C8—114no—
521C22⋊C8—222no—
522#97—441no—
523C4×C8—441no—
524#95—221no—
525#95—221no—
526#95—221no—
527C2×C11—42no—
528C2×C11—82no—
529C2×C11—82no—
530C2×C11#232111yescharacteristic
531C2×C11#294611yescharacteristic
532C2×C11#294811yescharacteristic
533C2×C11#319811yescharacteristic
534C2×C11#319911yescharacteristic
535C2×C11#322011yescharacteristic
536C2×C11#322411yescharacteristic
537D11—82no—
538C24—21no—
539C24—21no—
540C24—24no—
541C24—42no—
542C24—42no—
543C24—81no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—221no—
548C24C2×C22⋊D1111yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—112no—
567C2×D4—224no—
568C2×D4—221no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—881no—
574C2×D4—881no—
575C2×D4C2×C4×D1112yes—
576C2×D4C2×C4×D1112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—442no—
587C22×C4—881no—
588C22×C4—881no—
589C22×C4C2×C4×D1112yes—
590C22×C4#433912yes—
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597D8—444no—
598D8—444no—
599C2×C8—112no—
600C2×C8—112no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4—112no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—881no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—224no—
636C22⋊C4—442no—
637C22⋊C4—881no—
638C22⋊C4—881no—
639C22⋊C4—881no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—42no—
645C42—881no—
646C11#2205611yescharacteristic, complemented, Sylow
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—222no—
675C23—441no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23C4×C22⋊D1112yes—
682C23C22×C22⋊D1111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—222no—
693D4—222no—
694D4—441no—
695D4—441no—
696D4—884no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—222no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—884no—
731C2×C4C4×C22⋊D1112yes—
732C2×C4C22×C4×D1111yescharacteristic
733C2×C4C2×#433911yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4#6703711yescharacteristic
736C2×C4#6703711yescharacteristic
737C2×C4#6703711yescharacteristic
738C8—222no—
739C8—222no—
740C8—441no—
741C8—441no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—816no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22—881no—
768C22—881no—
769C22—881no—
770C22—881no—
771C22C2×C4×C22⋊D1111yescharacteristic
772C22#1062333511yescharacteristic
773C22#1062333611yescharacteristic
774C22#1062336611yescharacteristic
775C22#1062336611yescharacteristic
776C22#1062336611yescharacteristic
777C22#1062336711yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—442no—
786C4—881no—
787C4—881no—
788C4#1062301711yescharacteristic
789C4#1062301711yescharacteristic
790C4#1062302511yescharacteristic
791C4#1062302511yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—882no—
796C2#1307127411yescharacteristic
797C2#1307744811yescharacteristic
798C2#1307746611yescharacteristic
799C2#1307946811yescharacteristic
800C2#1307947711yescharacteristic
801C2#1307966611yescharacteristic
802C2#1307971011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2309C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
cosocleC22×C4×C11C24
hypercenter#2309D11
hypocenterC11#22056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #13071309C2semidirect
3. #13069491C2semidirect
4. #13069481C2semidirect
5. #13069316C2semidirect
6. #13069302C2semidirect
7. #13069240C2semidirect
8. #13069233C2semidirect
9. #13068967C2semidirect
10. #13068967C2semidirect
11. #13068938C2semidirect
12. #13068815C2semidirect
13. #13068547C2semidirect
14. #13068382C2semidirect
15. C11×#2309C2semidirect
22. C2×C4×D44C22semidirect
31. #10622830C4semidirect
43. C2×#66873C22semidirect
44. C2×#66873C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
49. #10622552C22semidirect
50. C4×C4⋊Dic11C22semidirect
51. #10622541C22semidirect
52. C2×#66867C22semidirect
53. C2×C4×C11⋊C8C22semidirect
54. #10622167C22semidirect
55. #10622167C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622162C22semidirect
59. #10622162C22semidirect
67. C22×D4×C11C2×C4semidirect
124. #66896C2×C4semidirect
125. #66896C2×C4semidirect
130. C22⋊(C11⋊C8)C2×C4semidirect
248. #2309D11semidirect
459. C22×D4C4×D11semidirect
646. C11#22056semidirect

Maximal subgroups

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

subgroupindex
C2×#106228302
#130713092
#130694912
#130694812
#130693162
#130693022
#130692402
#130692332
#130689672
#130689382
#130688152
#130685472
#130683822
C11×#23092
#2205611