Finite Group Databasebeta

← #14765110

Subgroups — #14765110

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#13071305C211yesmaximal, characteristic, complemented
3#13071198C211yesmaximal, characteristic, complemented
4#13069489C211yesmaximal, characteristic, complemented
5#13069479C211yesmaximal, characteristic, complemented
6#13069310C211yesmaximal, characteristic, complemented
7#13069296C211yesmaximal, characteristic, complemented
8#13069246C211yesmaximal, characteristic, complemented
9#13069239C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068961C211yesmaximal, characteristic, complemented
12#13068936C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C22×#4323C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66946C2211yescharacteristic, complemented
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622860—21no—
30#10622860—21no—
31#10622834—21no—
32#10622834—21no—
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35#10622834C2211yescharacteristic
36#10622834C2211yescharacteristic
37#10622830C418yescomplemented
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×#66885C2211yescharacteristic, complemented
42C2×#66885C2211yescharacteristic, complemented
43C2×#66879C2211yescharacteristic, complemented
44C2×C8×Dic11C2211yescharacteristic, complemented
45#10622601C2211yescharacteristic, complemented
46C4⋊C4×Dic11C2211yescharacteristic, complemented
47#10622586C2211yescharacteristic, complemented
48C2×#66872C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50#10622570—21no—
51#10622569—21no—
52#10622283—21no—
53#10622281—21no—
54#10622189C2211yescharacteristic, complemented
55#10622189C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, 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—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90C2×#4323—41no—
91C2×#4323—41no—
92C2×#4323—41no—
93C2×#4323—41no—
94C2×#4323C2×C414yes—
95C2×#4323C2×C414yes—
96#66983—22no—
97#66983C2×C414yes—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102#66979—41no—
103#66979—41no—
104#66979—41no—
105#66979—41no—
106C2×C4⋊Dic11D411yescharacteristic
107C2×C4⋊Dic11D411yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118#66946—41no—
119#66946—41no—
120C11×#102—41no—
121C11×#102—41no—
122C11×#102—41no—
123C11×#102—41no—
124C11×C22⋊C8—22no—
125C11×#95—21no—
126#66896C2×C414yescomplemented
127#66896C2×C414yescomplemented
128C11⋊#95—21no—
129C11⋊#95—21no—
130C22⋊(C11⋊C8)C2×C414yescomplemented
131#66885—41no—
132#66885—41no—
133#66879—41no—
134C8×Dic11—41no—
135#66872—41no—
136#66871—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×C11#4112yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—24no—
179C2×C22⋊D11—81no—
180C2×C22⋊D11—81no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
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—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C22⋊C4—81no—
208C22⋊Dic11—41no—
209C22⋊Dic11—41no—
210C22⋊Dic11—42no—
211C22⋊Dic11—81no—
212C22⋊Dic11—81no—
213C22⋊Dic11—81no—
214C22⋊Dic11—81no—
215C22⋊Dic11—81no—
216C22⋊Dic11—81no—
217C22⋊Dic11—81no—
218C22⋊Dic11—81no—
219#4323—44no—
220#4323—44no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—81no—
224(C2×D11)⋊C4—81no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—41no—
231C4⋊Dic11—41no—
232C4⋊Dic11C22×C412yes—
233Dic11⋊C4—81no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—21no—
238C4×Dic11—42no—
239C4×Dic11—81no—
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#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#1786D1111yescharacteristic, complemented
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—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11C4×D412yes—
319C2×C4×C11C23×C411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C22⋊D11—84no—
326C2×Dic11—22no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
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—
352C8×C11—41no—
353C8×C11—41no—
354C11⋊C8—22no—
355C11⋊C8—22no—
356C23×D4C2×D1111yescharacteristic
357C22×D8—111no—
358C22×D8—111no—
359C2×#121—111no—
360C2×C4×D4—111no—
361C2×#117—111no—
362C2×#117—111no—
363#447—118no—
364C2×#107—111no—
365C2×#106—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102C2×D1111yescharacteristic
371C2×#102C2×D1111yescharacteristic
372C2×#102C2×D1111yescharacteristic
373C2×#102C2×D1111yescharacteristic
374C2×C22⋊C8—111no—
375C2×C22⋊C8C2×D1111yescharacteristic
376C2×#97—111no—
377C2×C4×C8—111no—
378#390—111no—
379#390—111no—
380#390—111no—
381#390—111no—
382#390—111no—
383#390—221no—
384#390—221no—
385#390—221no—
386#389—111no—
387#388—221no—
388#386—221no—
389#385—221no—
390#380C2×D1111yescharacteristic
391#379—221no—
392#379—221no—
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—81no—
438C4×C11—81no—
439C4×C11#51811yescharacteristic
440C4×C11#51811yescharacteristic
441C4×C11#53811yescharacteristic
442C4×C11#53811yescharacteristic
443Dic11—41no—
444Dic11—41no—
445Dic11—41no—
446Dic11—41no—
447Dic11—42no—
448Dic11—81no—
449Dic11—81no—
450C25—21no—
451C22×D4—21no—
452C22×D4—22no—
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×C8C22×D1111yescharacteristic
473C22×C8C22×D1111yescharacteristic
474#121—114no—
475#121—222no—
476C4×D4—441no—
477C4×D4—441no—
478#117—441no—
479#117—441no—
480#117—441no—
481#117—441no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—111no—
492C2×C22⋊C4—111no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
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⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C42—111no—
507C2×C42—111no—
508C2×C42—221no—
509C2×C42—221no—
510#107—441no—
511#106—441no—
512#102—41no—
513#102—41no—
514#102—41no—
515#102—41no—
516#102—114no—
517#102—114no—
518#102—441no—
519#102—441no—
520C22⋊C8—22no—
521C22⋊C8—114no—
522#97—441no—
523C4×C8—441no—
524#95—21no—
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—
548C24D4×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—111no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—442no—
591C22×C4—881no—
592C22×C4—881no—
593C22×C4C2×C4×D1112yes—
594C22×C4D4×D1111yescharacteristic
595C22×C4#434112yes—
596C22×C4C23×D1111yescharacteristic
597D8—444no—
598D8—444no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—112no—
606C2×C8—112no—
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—112no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—441no—
622C4⋊C4—441no—
623C4⋊C4—881no—
624C22⋊C4—81no—
625C22⋊C4—224no—
626C22⋊C4—442no—
627C22⋊C4—441no—
628C22⋊C4—441no—
629C22⋊C4—442no—
630C22⋊C4—881no—
631C22⋊C4—881no—
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—221no—
641C42—221no—
642C42—221no—
643C42—221no—
644C42—442no—
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—
681C23(C22⋊D11)⋊C412yes—
682C23C2×D4×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—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—222no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—221no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
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×C4(C22⋊D11)⋊C412yes—
732C2×C4C22×C4×D1111yescharacteristic
733C2×C4C2×#434111yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4#6703711yescharacteristic
736C2×C4#6703711yescharacteristic
737C2×C4#6703711yescharacteristic
738C8—41no—
739C8—41no—
740C8—222no—
741C8—222no—
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×(C22⋊D11)⋊C411yescharacteristic
772C22#1062312011yescharacteristic
773C22#1062312311yescharacteristic
774C22#1062328811yescharacteristic
775C22#1062329311yescharacteristic
776C22#1062330511yescharacteristic
777C22#1062330511yescharacteristic
778C4—22no—
779C4—81no—
780C4—81no—
781C4—441no—
782C4—441no—
783C4—441no—
784C4—441no—
785C4—442no—
786C4—881no—
787C4—881no—
788C4#1062301711yescharacteristic
789C4#1062301711yescharacteristic
790C4#1062312411yescharacteristic
791C4#1062312411yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—882no—
796C2#1307127111yescharacteristic
797C2#1307744211yescharacteristic
798C2#1307746411yescharacteristic
799C2#1307947211yescharacteristic
800C2#1307947911yescharacteristic
801C2#1307966211yescharacteristic
802C2#1307971411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC2×#10622830C2
cosocleC22×C4×C11C24
hypercenter#1786D11
hypocenterC11#22056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #13071305C2semidirect
3. #13071198C2semidirect
4. #13069489C2semidirect
5. #13069479C2semidirect
6. #13069310C2semidirect
7. #13069296C2semidirect
8. #13069246C2semidirect
9. #13069239C2semidirect
10. #13068961C2semidirect
11. #13068961C2semidirect
12. #13068936C2semidirect
13. #13068813C2semidirect
14. #13068384C2semidirect
15. C11×#1786C2semidirect
22. C2×#66946C22semidirect
37. #10622830C4semidirect
41. C2×#66885C22semidirect
42. C2×#66885C22semidirect
43. C2×#66879C22semidirect
44. C2×C8×Dic11C22semidirect
45. #10622601C22semidirect
46. C4⋊C4×Dic11C22semidirect
47. #10622586C22semidirect
48. C2×#66872C22semidirect
49. C2×#66871C22semidirect
54. #10622189C22semidirect
55. #10622189C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
67. C22×D4×C11C2×C4semidirect
126. #66896C2×C4semidirect
127. #66896C2×C4semidirect
130. C22⋊(C11⋊C8)C2×C4semidirect
259. #1786D11semidirect
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
#130713052
#130711982
#130694892
#130694792
#130693102
#130692962
#130692462
#130692392
#130689612
#130689362
#130688132
#130683842
C11×#17862
#2205611