Finite Group Databasebeta

← #14765108

Subgroups — #14765108

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×#10622649C211yesmaximal, characteristic
2#13071196C211yesmaximal, characteristic, complemented
3#13069491C211yesmaximal, characteristic, complemented
4#13069481C211yesmaximal, characteristic, complemented
5#13069312C211yesmaximal, characteristic, complemented
6#13069298C211yesmaximal, characteristic, complemented
7#13069243C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13068964C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C11×#2324C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic, complemented
19C2×C11×#117C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C11×#390—21no—
24C11×#390C2211yescharacteristic, complemented
25C11×#389C2211yescharacteristic, complemented
26C11×#388—21no—
27C11×#386—21no—
28C11×#385—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic, complemented
31C2×#66896C2211yescharacteristic, complemented
32C2×#66896C2211yescharacteristic, complemented
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622649C418yescomplemented
36#10622601—21no—
37#10622601—21no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic, complemented
45C2×#66871C2211yescharacteristic, complemented
46#10622568—21no—
47#10622568—21no—
48#10622552C2211yescharacteristic
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
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
60C24×D11—21no—
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—41no—
68C22×D44—41no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44C2×C414yescomplemented
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C11×#121—22no—
75C11×#121C2×C414yes—
76C4×D4×C11—41no—
77C4×D4×C11—41no—
78C11×#117—41no—
79C11×#117—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
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—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111#66979—41no—
112#66979—41no—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4×Dic11—21no—
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123#66896—41no—
124#66896—41no—
125C22⋊(C11⋊C8)—22no—
126C22⋊(C11⋊C8)C2×C414yescomplemented
127#66873—41no—
128#66873—41no—
129#66873—41no—
130#66873—41no—
131#66873C2×C414yescomplemented
132#66873C2×C414yescomplemented
133#66872—41no—
134#66871—41no—
135#66867—41no—
136C4×C11⋊C8—41no—
137#22056—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—24no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—81no—
146C23×D11—81no—
147C23×D11—81no—
148C23×D11—81no—
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—81no—
156C2×D4×C11—81no—
157C2×D4×C11C22×C412yes—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—42no—
166C22×C4×C11—81no—
167C22×C4×C11—81no—
168C22×C4×C11C22×C412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11#4112yes—
175C22×C4×C11C2411yescharacteristic
176C22×Dic11—21no—
177C22×Dic11—21no—
178C2×D44—24no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—44no—
190C2×D44—44no—
191C2×D44—42no—
192C2×D44—42no—
193C2×D44—44no—
194C2×D44—44no—
195C2×D44C22×C412yes—
196C2×D44C22×C412yes—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4—81no—
205C11×C4⋊C4C22×C412yes—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C11×C22⋊C4—81no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—81no—
218C22⋊Dic11—42no—
219#4323—44no—
220#4323—44no—
221(C2×D11)⋊C4—81no—
222(C2×D11)⋊C4—81no—
223(C2×D11)⋊C4—81no—
224(C2×D11)⋊C4—81no—
225(C2×D11)⋊C4—81no—
226(C2×D11)⋊C4—81no—
227(C2×D11)⋊C4—81no—
228(C2×D11)⋊C4—81no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4×Dic11—42no—
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#2324D1111yescharacteristic, complemented
248#2309—111no—
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—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C4×D412yes—
275C23×C11C22×D411yescharacteristic
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—48no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C22×D11—84no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—41no—
300D4×C11—41no—
301D4×C11—84no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
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—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—84no—
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
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343D44—22no—
344D44—22no—
345D44—22no—
346D44—22no—
347D44—48no—
348D44—41no—
349D44—41no—
350D44—41no—
351D44—41no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—41no—
355C11⋊C8—41no—
356C23×D4—111no—
357C22×D8—111no—
358C22×D8—111no—
359C2×#121C2×D1111yescharacteristic
360C2×C4×D4C2×D1111yescharacteristic, complemented
361C2×#117—111no—
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—111no—
380#390—111no—
381#390—111no—
382#390—111no—
383#390—221no—
384#390—221no—
385#390C2×D1111yescharacteristic, complemented
386#389C2×D1111yescharacteristic, complemented
387#388—21no—
388#386—21no—
389#385—21no—
390#380C2×D1111yescharacteristic
391#379—221no—
392#379—221no—
393C4×C4⋊C4C2×D1111yescharacteristic, complemented
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—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11C2×C4×D411yescharacteristic
415C22×C11#53411yescharacteristic
416C22×C11#53511yescharacteristic
417C22×C11#57611yescharacteristic
418C22×C11#57611yescharacteristic
419C22×C11#57611yescharacteristic
420C22×C11#57711yescharacteristic
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—816no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C2×D11—81no—
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—42no—
442C4×C11—81no—
443C4×C11—81no—
444C4×C11#51811yescharacteristic
445C4×C11#51811yescharacteristic
446C4×C11#53811yescharacteristic
447C4×C11#53811yescharacteristic
448Dic11—81no—
449Dic11—81no—
450C25—221no—
451C22×D4—21no—
452C22×D4—114no—
453C22×D4—111no—
454C22×D4—111no—
455C22×D4—222no—
456C22×D4—221no—
457C22×D4—441no—
458C22×D4—441no—
459C22×D4—441no—
460C22×D4—441no—
461C22×D4C22×D1111yescharacteristic
462C23×C4—21no—
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—22no—
475#121C4×D1114yes—
476C4×D4—41no—
477C4×D4—41no—
478#117—41no—
479#117—41no—
480#117—441no—
481#117—441no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4C22⋊D1111yescharacteristic
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—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
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—21no—
525#95—21no—
526#95—21no—
527C2×C11—42no—
528C2×C11—82no—
529C2×C11#232111yescharacteristic
530C2×C11#294611yescharacteristic
531C2×C11#294811yescharacteristic
532C2×C11#319811yescharacteristic
533C2×C11#319911yescharacteristic
534C2×C11#322011yescharacteristic
535C2×C11#322411yescharacteristic
536D11—82no—
537D11—82no—
538C24—21no—
539C24—221no—
540C24—221no—
541C24—224no—
542C24—442no—
543C24—442no—
544C24—881no—
545C24—881no—
546C24—881no—
547C24—881no—
548C24C2×C22⋊D1111yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—112no—
558C2×D4—112no—
559C2×D4—224no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—221no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—442no—
573C2×D4—442no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4C2×C4×D1112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—221no—
588C22×C4—221no—
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—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—81no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4C2×C4×D1112yes—
624C22⋊C4—24no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—442no—
632C22⋊C4—881no—
633C22⋊C4—881no—
634C22⋊C4—881no—
635C22⋊C4—881no—
636C22⋊C4—881no—
637C22⋊C4—881no—
638C22⋊C4—881no—
639C22⋊C4—881no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—81no—
645C42—442no—
646C11#2205611yescharacteristic, complemented, Sylow
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—222no—
661C23—222no—
662C23—448no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23—441no—
668C23—441no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—884no—
676C23—884no—
677C23—884no—
678C23—884no—
679C23—884no—
680C23—884no—
681C23C4×C22⋊D1112yes—
682C23C22×C22⋊D1111yescharacteristic
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—222no—
689D4—222no—
690D4—222no—
691D4—222no—
692D4—448no—
693D4—441no—
694D4—441no—
695D4—441no—
696D4—441no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
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—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4C4×C22⋊D1112yes—
732C2×C4C22×C4×D1111yescharacteristic
733C2×C4C2×#433911yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4#6703711yescharacteristic
736C2×C4#6704211yescharacteristic
737C2×C4#6704211yescharacteristic
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—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—442no—
757C22—442no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—442no—
762C22—8816no—
763C22—881no—
764C22—881no—
765C22—881no—
766C22—881no—
767C22—881no—
768C22—881no—
769C22—881no—
770C22—881no—
771C22C2×C4×C22⋊D1111yescharacteristic
772C22#1062333511yescharacteristic
773C22#1062336111yescharacteristic
774C22#1062336611yescharacteristic
775C22#1062336611yescharacteristic
776C22#1062336611yescharacteristic
777C22#1062336811yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—881no—
787C4—881no—
788C4#1062307611yescharacteristic
789C4#1062307611yescharacteristic
790C4#1062309111yescharacteristic
791C4#1062309111yescharacteristic
792C2—42no—
793C2—82no—
794C2—882no—
795C2—882no—
796C2#1307127011yescharacteristic
797C2#1307744411yescharacteristic
798C2#1307746611yescharacteristic
799C2#1307946211yescharacteristic
800C2#1307947711yescharacteristic
801C2#1307966011yescharacteristic
802C2#1307970411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2324C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
cosocleC22×C4×C11C24
hypercenter#2324D11
hypocenterC11#22056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13071196C2semidirect
3. #13069491C2semidirect
4. #13069481C2semidirect
5. #13069312C2semidirect
6. #13069298C2semidirect
7. #13069243C2semidirect
8. #13069236C2semidirect
9. #13068964C2semidirect
10. #13068964C2semidirect
11. #13068939C2semidirect
12. #13068813C2semidirect
13. #13068546C2semidirect
14. #13068382C2semidirect
15. C11×#2324C2semidirect
18. C2×C4×D4×C11C22semidirect
24. C11×#390C22semidirect
25. C11×#389C22semidirect
30. C4×C11×C4⋊C4C22semidirect
31. C2×#66896C22semidirect
32. C2×#66896C22semidirect
35. #10622649C4semidirect
44. C2×#66872C22semidirect
45. C2×#66871C22semidirect
52. C2×#66867C22semidirect
53. C2×C4×C11⋊C8C22semidirect
54. #10622167C22semidirect
55. #10622167C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622162C22semidirect
59. #10622162C22semidirect
71. C22×D44C2×C4semidirect
126. C22⋊(C11⋊C8)C2×C4semidirect
131. #66873C2×C4semidirect
132. #66873C2×C4semidirect
247. #2324D11semidirect
360. C2×C4×D4C2×D11semidirect
385. #390C2×D11semidirect
386. #389C2×D11semidirect
393. C4×C4⋊C4C2×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×#106226492
#130711962
#130694912
#130694812
#130693122
#130692982
#130692432
#130692362
#130689642
#130689392
#130688132
#130685462
#130683822
C11×#23242
#2205611