Finite Group Databasebeta

← #14765119

Subgroups — #14765119

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×#10622386C211yesmaximal, characteristic
2#13071310C211yesmaximal, characteristic, complemented
3#13071195C211yesmaximal, characteristic, complemented
4#13069489C211yesmaximal, characteristic, complemented
5#13069480C211yesmaximal, characteristic, complemented
6#13069314C211yesmaximal, characteristic, complemented
7#13069301C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic, complemented
11#13068937C211yesmaximal, characteristic, complemented
12#13068812C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068381C211yesmaximal, characteristic, complemented
15C11×#1925C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C22×D88C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic, complemented
22C2×#66925C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic, complemented
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic, complemented
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic, complemented
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66879C2211yescharacteristic, complemented
35C2×C8×Dic11C2211yescharacteristic, complemented
36#10622601C2211yescharacteristic
37#10622601C2211yescharacteristic, complemented
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic, complemented
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic, complemented
43C2×#66872C2211yescharacteristic, complemented
44#10622570—21no—
45#10622570—21no—
46#10622568—21no—
47#10622568—21no—
48#10622553—21no—
49#10622552—21no—
50#10622552C2211yescharacteristic
51#10622386C418yescomplemented
52#10622281—21no—
53#10622278—21no—
54C11×#340C2211yescharacteristic, complemented
55C11×#336C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60C24×D11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×D4×D11—22no—
64C2×D4×D11—41no—
65C2×D4×D11—41no—
66C2×D4×D11—41no—
67C2×D4×D11—41no—
68C2×D4×D11C2×C414yescomplemented
69C22×D44—21no—
70C22×D44C2311yescharacteristic
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×#4323—41no—
86C2×#4323—41no—
87C2×#4323C2×C414yes—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4D411yescharacteristic
99C2×(C2×D11)⋊C4D411yescharacteristic
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4D411yescharacteristic
104C2×Dic11⋊C4D411yescharacteristic
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×D88—41no—
110C2×D88—41no—
111C2×D88C2×C414yes—
112#66948—22no—
113#66948C2×C414yes—
114#66945—41no—
115#66945—41no—
116C4×D44—41no—
117C4×D44—41no—
118#66925—41no—
119#66925—41no—
120C11×#107—41no—
121C11×#102—41no—
122C11×#102C2×C414yescomplemented
123C11×#95—21no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66885—41no—
128#66885—41no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8C2×C414yescomplemented
131#66879—41no—
132C8×Dic11—41no—
133#66873—41no—
134#66873—41no—
135#66873C2×C414yescomplemented
136#66872—41no—
137#22056—111nomaximal, Sylow
138C24×C11—21no—
139C23×D11—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×C11C22×C412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—42no—
163C2×C22⋊D11—42no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169D4×D11—44no—
170D4×D11—44no—
171D4×D11—44no—
172D4×D11—44no—
173C2×D44—24no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—81no—
185C2×D44—81no—
186C2×D44C22×C412yes—
187C2×D44C22×C412yes—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—42no—
193C2×C4×D11—81no—
194C2×C4×D11—81no—
195C2×C4×D11C22×C412yes—
196C2×C4×D11#4112yes—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11C22×C412yes—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4C22×C412yes—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—81no—
214C22⋊Dic11—81no—
215C22⋊Dic11—81no—
216#4323—44no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—41no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—42no—
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—
227(C2×D11)⋊C4—81no—
228(C2×D11)⋊C4—81no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—81no—
234Dic11⋊C4—41no—
235Dic11⋊C4—41no—
236C4×Dic11—21no—
237C4×Dic11—21no—
238C4×Dic11—42no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C412yes—
245D88—44no—
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#1925D1111yescharacteristic, complemented
255#1879—111no—
256#1879—111no—
257#1875—111no—
258#1854—111no—
259#1786—111no—
260#1750—111no—
261C23×C11—22no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11C22×D411yescharacteristic
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—48no—
278C22×D11—41no—
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—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—41no—
300D4×C11—41no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C22⋊D11—48no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11C4×D412yes—
338D44—22no—
339D44—22no—
340D44—22no—
341D44—22no—
342D44—41no—
343D44—41no—
344D44—41no—
345D44—41no—
346D44—84no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—84no—
352C8×C11—22no—
353C8×C11—41no—
354C11⋊C8—22no—
355C11⋊C8—41no—
356C23×D4—111no—
357C22×D8—111no—
358C22×D8—111no—
359C2×#121—111no—
360C2×C4×D4—111no—
361C2×#117—111no—
362C2×#117—111no—
363#447—118no—
364C2×#107C2×D1111yescharacteristic, complemented
365C2×#106—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102C2×D1111yescharacteristic
373C2×#102C2×D1111yescharacteristic
374C2×C22⋊C8—111no—
375C2×C22⋊C8—111no—
376C2×#97—111no—
377C2×C4×C8—111no—
378#390—111no—
379#390—111no—
380#390—111no—
381#390—111no—
382#390—221no—
383#390—221no—
384#390—221no—
385#390C2×D1111yescharacteristic
386#389—111no—
387#388—221no—
388#386—221no—
389#385—221no—
390#380—111no—
391#379—221no—
392#379—221no—
393C4×C4⋊C4C2×D1111yescharacteristic, complemented
394#340—111no—
395#340—111no—
396#340—111no—
397#340C2×D1111yescharacteristic, complemented
398#336—111no—
399#336C2×D1111yescharacteristic, complemented
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11C2×C4×D411yescharacteristic
408C22×C11#53411yescharacteristic
409C22×C11#53511yescharacteristic
410C22×C11#57611yescharacteristic
411C22×C11#57611yescharacteristic
412C22×C11#57611yescharacteristic
413C22×C11#57711yescharacteristic
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
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—41no—
437C4×C11—41no—
438C4×C11—42no—
439C4×C11—81no—
440C4×C11—81no—
441C4×C11#51811yescharacteristic
442C4×C11#51811yescharacteristic
443C4×C11#53811yescharacteristic
444C4×C11#53811yescharacteristic
445Dic11—22no—
446Dic11—41no—
447Dic11—41no—
448Dic11—81no—
449Dic11—81no—
450C25—221no—
451C22×D4—114no—
452C22×D4—111no—
453C22×D4—111no—
454C22×D4—221no—
455C22×D4—222no—
456C22×D4—221no—
457C22×D4—441no—
458C22×D4—441no—
459C22×D4—441no—
460C22×D4—441no—
461C22×D4C22×D1111yescharacteristic
462C23×C4—111no—
463C23×C4—221no—
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—221no—
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—111no—
493C2×C22⋊C4—111no—
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—21no—
507C2×C42—111no—
508C2×C42—221no—
509C2×C42C22×D1111yescharacteristic
510#107—41no—
511#106—441no—
512#102—41no—
513#102—114no—
514#102—441no—
515#102—441no—
516#102—441no—
517#102—441no—
518#102—441no—
519#102C4×D1114yescomplemented
520C22⋊C8—114no—
521C22⋊C8—222no—
522#97—441no—
523C4×C8—441no—
524#95—21no—
525#95—221no—
526#95—221no—
527C2×C11—82no—
528C2×C11#232111yescharacteristic
529C2×C11#294611yescharacteristic
530C2×C11#294811yescharacteristic
531C2×C11#319811yescharacteristic
532C2×C11#319911yescharacteristic
533C2×C11#322011yescharacteristic
534C2×C11#322411yescharacteristic
535D11—42no—
536D11—82no—
537D11—82no—
538C24—21no—
539C24—111no—
540C24—224no—
541C24—221no—
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—112no—
555C2×D4—112no—
556C2×D4—224no—
557C2×D4—224no—
558C2×D4—221no—
559C2×D4—221no—
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—444no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—442no—
573C2×D4—442no—
574C2×D4—881no—
575C2×D4—881no—
576C2×D4C2×C4×D1112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—111no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—111no—
584C22×C4—111no—
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—444no—
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—21no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—441no—
621C4⋊C4—441no—
622C4⋊C4—881no—
623C4⋊C4C2×C4×D1112yes—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—224no—
627C22⋊C4—441no—
628C22⋊C4—441no—
629C22⋊C4—442no—
630C22⋊C4—442no—
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—21no—
641C42—21no—
642C42—81no—
643C42—221no—
644C42—221no—
645C42—442no—
646C11#2205611yescharacteristic, complemented, Sylow
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—112no—
655C23—221no—
656C23—221no—
657C23—221no—
658C23—221no—
659C23—221no—
660C23—221no—
661C23—222no—
662C23—222no—
663C23—448no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23—441no—
668C23—441no—
669C23—441no—
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—41no—
686D4—41no—
687D4—222no—
688D4—222no—
689D4—222no—
690D4—222no—
691D4—448no—
692D4—441no—
693D4—441no—
694D4—441no—
695D4—441no—
696D4—884no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—112no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
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#41×D1111yescharacteristic
735C2×C4#6704211yescharacteristic
736C2×C4#6704211yescharacteristic
737C2×C4#6704211yescharacteristic
738C8—22no—
739C8—41no—
740C8—222no—
741C8—441no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—441no—
753C22—441no—
754C22—441no—
755C22—441no—
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—
771C22C4×D4×D1111yescharacteristic
772C22#1062313811yescharacteristic
773C22#1062318411yescharacteristic
774C22#1062328811yescharacteristic
775C22#1062330011yescharacteristic
776C22#1062330511yescharacteristic
777C22#1062330911yescharacteristic
778C4—41no—
779C4—41no—
780C4—42no—
781C4—81no—
782C4—81no—
783C4—222no—
784C4—441no—
785C4—441no—
786C4—881no—
787C4—881no—
788C4#1062305211yescharacteristic
789C4#1062307611yescharacteristic
790C4#1062320911yescharacteristic
791C4#1062323511yescharacteristic
792C2—82no—
793C2—442no—
794C2—882no—
795C2—882no—
796C2#1307127811yescharacteristic
797C2#1307744711yescharacteristic
798C2#1307746311yescharacteristic
799C2#1307947511yescharacteristic
800C2#1307948011yescharacteristic
801C2#1307966511yescharacteristic
802C2#1307971711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1925C2
socleC23×C11C22×D4
prime radicalC2×#10622386C2
cosocleC22×C4×C11C24
hypercenter#1925D11
hypocenterC11#22056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. #13071310C2semidirect
3. #13071195C2semidirect
4. #13069489C2semidirect
5. #13069480C2semidirect
6. #13069314C2semidirect
7. #13069301C2semidirect
8. #13069243C2semidirect
9. #13068967C2semidirect
10. #13068963C2semidirect
11. #13068937C2semidirect
12. #13068812C2semidirect
13. #13068545C2semidirect
14. #13068381C2semidirect
15. C11×#1925C2semidirect
21. C2×C4×D44C22semidirect
23. C2×C11×#107C22semidirect
27. C4×C11×C4⋊C4C22semidirect
31. C2×#66885C22semidirect
34. C2×#66879C22semidirect
35. C2×C8×Dic11C22semidirect
37. #10622601C22semidirect
39. #10622598C22semidirect
42. C2×#66873C22semidirect
43. C2×#66872C22semidirect
51. #10622386C4semidirect
54. C11×#340C22semidirect
55. C11×#336C22semidirect
56. #10622189C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
68. C2×D4×D11C2×C4semidirect
122. C11×#102C2×C4semidirect
130. (C2×D11)⋊C8C2×C4semidirect
135. #66873C2×C4semidirect
254. #1925D11semidirect
364. C2×#107C2×D11semidirect
393. C4×C4⋊C4C2×D11semidirect
397. #340C2×D11semidirect
399. #336C2×D11semidirect
519. #102C4×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×#106223862
#130713102
#130711952
#130694892
#130694802
#130693142
#130693012
#130692432
#130689672
#130689632
#130689372
#130688122
#130685452
#130683812
C11×#19252
#2205611