Finite Group Databasebeta

← #14765115

Subgroups — #14765115

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×#10622769C211yesmaximal, characteristic
2#13071312C211yesmaximal, characteristic, complemented
3#13071195C211yesmaximal, characteristic, complemented
4#13069481C211yesmaximal, characteristic, complemented
5#13069313C211yesmaximal, characteristic, complemented
6#13069302C211yesmaximal, characteristic, complemented
7#13069242C211yesmaximal, characteristic, complemented
8#13069239C211yesmaximal, characteristic, complemented
9#13068966C211yesmaximal, characteristic, complemented
10#13068962C211yesmaximal, characteristic, complemented
11#13068935C211yesmaximal, characteristic, complemented
12#13068814C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068385C211yesmaximal, characteristic, complemented
15C11×#1972C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic, complemented
20C22×#4323C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic, complemented
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic, complemented
26C2×C11×#97C2211yescharacteristic, complemented
27C11×#390C2211yescharacteristic
28C11×#390C2211yescharacteristic, complemented
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic, complemented
33#10622769C418yescomplemented
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38#10622601C2211yescharacteristic
39#10622600C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic, complemented
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic, complemented
43#10622571—21no—
44#10622570—21no—
45#10622570—21no—
46#10622570—21no—
47#10622568—21no—
48#10622568—21no—
49#10622559—21no—
50#10622557—21no—
51#10622552C2211yescharacteristic
52#10622541C2211yescharacteristic, complemented
53C2×C4×C11⋊C8C2211yescharacteristic, complemented
54#10622189C2211yescharacteristic, complemented
55#10622189C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60C24×D11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C2×D4×D11—22no—
67C2×D4×D11—41no—
68C2×D4×D11—41no—
69C2×D4×D11—41no—
70C2×D4×D11—41no—
71C2×D4×D11C2×C414yescomplemented
72C22×D44C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C2×C11×D8—41no—
75C2×C11×D8—41no—
76C2×C11×D8C2×C414yes—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90#66991—22no—
91#66991C2×C414yes—
92D4×Dic11—41no—
93D4×Dic11—41no—
94C2×#4323—41no—
95C2×#4323—41no—
96C2×#4323C2×C414yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4D411yescharacteristic
104C2×(C2×D11)⋊C4D411yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4D411yescharacteristic
110C2×Dic11⋊C4D411yescharacteristic
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116#66945—41no—
117#66945—41no—
118#66925—41no—
119#66925—41no—
120C11×#106—41no—
121C11×#102—41no—
122C11×#102—41no—
123C11×#97—41no—
124#66896—41no—
125#66896—41no—
126#66896C2×C414yescomplemented
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66885—41no—
131#66885C2×C414yescomplemented
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8C2×C414yescomplemented
134#66873—41no—
135#66871—41no—
136C4×C11⋊C8—41no—
137#22056—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C23×D11—21no—
141C23×D11—24no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11—81no—
145C23×D11—81no—
146C23×D11—81no—
147C23×D11—81no—
148C23×D11C2×D411yescharacteristic
149C2×D4×C11—21no—
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×C11C22×C412yes—
160C2×D4×C11C22×C412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—24no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—81no—
171C2×C22⋊D11—81no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—42no—
176C22×Dic11—81no—
177C22×Dic11—81no—
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
181D4×D11—44no—
182D4×D11—44no—
183D4×D11—44no—
184D4×D11—44no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44C22×C412yes—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11C22×C412yes—
196C2×C4×D11#4112yes—
197C11×D8—44no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11C22×C412yes—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C42×C11—21no—
213C42×C11—21no—
214C22⋊Dic11—24no—
215C22⋊Dic11—42no—
216C22⋊Dic11—81no—
217C22⋊Dic11—81no—
218#4323—44no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—41no—
221(C2×D11)⋊C4—42no—
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—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11C22×C412yes—
233Dic11⋊C4—41no—
234Dic11⋊C4—41no—
235Dic11⋊C4—81no—
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⋊C8—21no—
245C2×C11⋊C8C22×C412yes—
246C2×#447—111no—
247#2324—111no—
248#2309—111no—
249#1972D1111yescharacteristic, complemented
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—22no—
262C23×C11—22no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11C22×D411yescharacteristic
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—22no—
283C22×D11—48no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—84no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C22×D11C4×D412yes—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304D4×C11—41no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11C23×C411yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C22⋊D11—48no—
324C22⋊D11—84no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—22no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—84no—
343C2×Dic11C4×D412yes—
344D44—22no—
345D44—22no—
346D44—41no—
347D44—41no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—22no—
352C8×C11—22no—
353C8×C11—41no—
354C11⋊C8—22no—
355C11⋊C8—41no—
356C23×D4—111no—
357C22×D8—111no—
358C22×D8C2×D1111yescharacteristic
359C2×#121—111no—
360C2×C4×D4—111no—
361C2×#117—111no—
362C2×#117—111no—
363#447—118no—
364C2×#107—111no—
365C2×#106C2×D1111yescharacteristic, complemented
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102C2×D1111yescharacteristic
373C2×#102C2×D1111yescharacteristic, complemented
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×#97C2×D1111yescharacteristic, complemented
377C2×C4×C8—111no—
378#390—111no—
379#390—111no—
380#390—111no—
381#390—221no—
382#390—221no—
383#390—221no—
384#390C2×D1111yescharacteristic
385#390C2×D1111yescharacteristic, complemented
386#389—111no—
387#388—221no—
388#386—221no—
389#385—221no—
390#380—111no—
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—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
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—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—41no—
425C2×D11—41no—
426C2×D11—41no—
427C2×D11—41no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—816no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—41no—
437C4×C11—41no—
438C4×C11—81no—
439C4×C11—81no—
440C4×C11#51811yescharacteristic
441C4×C11#51811yescharacteristic
442C4×C11#53811yescharacteristic
443C4×C11#53811yescharacteristic
444Dic11—22no—
445Dic11—41no—
446Dic11—41no—
447Dic11—42no—
448Dic11—81no—
449Dic11—81no—
450C25—221no—
451C22×D4—114no—
452C22×D4—111no—
453C22×D4—222no—
454C22×D4—221no—
455C22×D4—221no—
456C22×D4—441no—
457C22×D4—441no—
458C22×D4—441no—
459C22×D4—441no—
460C22×D4C22×D1111yescharacteristic
461C22×D4C22×D1111yescharacteristic
462C23×C4—111no—
463C23×C4—221no—
464C2×D8—41no—
465C2×D8—41no—
466C2×D8—114no—
467C2×D8—441no—
468C2×D8—441no—
469C2×D8C4×D1114yes—
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—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—111no—
495C2×C22⋊C4—111no—
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—221no—
508C2×C42—221no—
509C2×C42C22×D1111yescharacteristic
510#107—441no—
511#106—41no—
512#102—41no—
513#102—41no—
514#102—114no—
515#102—114no—
516#102—441no—
517#102—441no—
518#102—441no—
519#102—441no—
520C22⋊C8—114no—
521C22⋊C8—222no—
522#97—41no—
523C4×C8—441no—
524#95—221no—
525#95—221no—
526#95—221no—
527C2×C11—82no—
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—42no—
537D11—82no—
538C24—21no—
539C24—21no—
540C24—111no—
541C24—224no—
542C24—221no—
543C24—442no—
544C24—442no—
545C24—881no—
546C24—881no—
547C24—881no—
548C24—881no—
549C2×D4—21no—
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—112no—
560C2×D4—224no—
561C2×D4—224no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—444no—
568C2×D4—444no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—442no—
572C2×D4—442no—
573C2×D4—881no—
574C2×D4—881no—
575C2×D4C2×C4×D1112yes—
576C2×D4C2×C4×D1112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—111no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—442no—
592C22×C4—881no—
593C22×C4—881no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597D8—44no—
598D8—444no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—112no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8C2×C4×D1112yes—
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—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—224no—
629C22⋊C4—441no—
630C22⋊C4—441no—
631C22⋊C4—442no—
632C22⋊C4—442no—
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—221no—
643C42—221no—
644C42—442no—
645C42—881no—
646C11#2205611yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—112no—
662C23—221no—
663C23—221no—
664C23—221no—
665C23—221no—
666C23—221no—
667C23—221no—
668C23—222no—
669C23—448no—
670C23—441no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—884no—
677C23—884no—
678C23—884no—
679C23—884no—
680C23—884no—
681C23—884no—
682C23C2×D4×D1111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—222no—
692D4—222no—
693D4—448no—
694D4—441no—
695D4—441no—
696D4—884no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—112no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—222no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—884no—
732C2×C4C22×C4×D1111yescharacteristic
733C2×C4#6703711yescharacteristic
734C2×C4#6703711yescharacteristic
735C2×C4#6703711yescharacteristic
736C2×C4#41×D1111yescharacteristic
737C2×C4#6704211yescharacteristic
738C8—22no—
739C8—41no—
740C8—222no—
741C8—441no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—222no—
757C22—222no—
758C22—222no—
759C22—441no—
760C22—441no—
761C22—441no—
762C22—441no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22—8816no—
767C22—881no—
768C22—881no—
769C22—881no—
770C22—881no—
771C22C4×D4×D1111yescharacteristic
772C22#1062313611yescharacteristic
773C22#1062324611yescharacteristic
774C22#1062330511yescharacteristic
775C22#1062330511yescharacteristic
776C22#1062330511yescharacteristic
777C22#1062330611yescharacteristic
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—222no—
783C4—441no—
784C4—441no—
785C4—442no—
786C4—881no—
787C4—881no—
788C4#1062301711yescharacteristic
789C4#1062307611yescharacteristic
790C4#1062314411yescharacteristic
791C4#1062320911yescharacteristic
792C2—82no—
793C2—82no—
794C2—442no—
795C2—882no—
796C2#1307127511yescharacteristic
797C2#1307744511yescharacteristic
798C2#1307746511yescharacteristic
799C2#1307946311yescharacteristic
800C2#1307947811yescharacteristic
801C2#1307966111yescharacteristic
802C2#1307970511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1972C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
cosocleC22×C4×C11C24
hypercenter#1972D11
hypocenterC11#22056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. #13071312C2semidirect
3. #13071195C2semidirect
4. #13069481C2semidirect
5. #13069313C2semidirect
6. #13069302C2semidirect
7. #13069242C2semidirect
8. #13069239C2semidirect
9. #13068966C2semidirect
10. #13068962C2semidirect
11. #13068935C2semidirect
12. #13068814C2semidirect
13. #13068545C2semidirect
14. #13068385C2semidirect
15. C11×#1972C2semidirect
19. C2×D4×Dic11C22semidirect
23. C2×C11×#106C22semidirect
25. C2×C11×#102C22semidirect
26. C2×C11×#97C22semidirect
28. C11×#390C22semidirect
32. C2×#66896C22semidirect
33. #10622769C4semidirect
40. C4⋊C4×Dic11C22semidirect
42. C2×#66871C22semidirect
52. #10622541C22semidirect
53. C2×C4×C11⋊C8C22semidirect
54. #10622189C22semidirect
55. #10622189C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
71. C2×D4×D11C2×C4semidirect
126. #66896C2×C4semidirect
131. #66885C2×C4semidirect
133. (C2×D11)⋊C8C2×C4semidirect
249. #1972D11semidirect
365. C2×#106C2×D11semidirect
373. C2×#102C2×D11semidirect
376. C2×#97C2×D11semidirect
385. #390C2×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×#106227692
#130713122
#130711952
#130694812
#130693132
#130693022
#130692422
#130692392
#130689662
#130689622
#130689352
#130688142
#130685452
#130683852
C11×#19722
#2205611