Finite Group Databasebeta

← #14763145

Subgroups — #14763145

Order 2816.

1442 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2C2×#10622333C211yesmaximal, characteristic, complemented
3#13071223C211yesmaximal, characteristic, complemented
4#13069545C211yesmaximal, characteristic, complemented
5#13069545C211yesmaximal, characteristic, complemented
6#13069541C211yesmaximal, characteristic, complemented
7#13069541C211yesmaximal, characteristic, complemented
8#13069438C211yesmaximal, characteristic, complemented
9#13069429C211yesmaximal, characteristic, complemented
10#13069424C211yesmaximal, characteristic, complemented
11#13069420C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068546C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D44C2211yescharacteristic
18#10623361—24no—
19#10623361C418yescomplemented
20C2×#67000C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#66993C2211yescharacteristic
23C2×#66993C2211yescharacteristic
24C2×#66990—21no—
25C2×#66990—21no—
26C2×#66983—21no—
27C2×#66983—21no—
28C2×#66979C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic, complemented
30C2×C11×#103C2211yescharacteristic, complemented
31C2×C11×#102C2211yescharacteristic, complemented
32C2×C11×#102C2211yescharacteristic, complemented
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C2×#66899C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic, complemented
38C2×#66896C2211yescharacteristic, complemented
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66879C2211yescharacteristic, complemented
46C2×Dic11⋊C8C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48C2×C8×Dic11C2211yescharacteristic, complemented
49#10622590C2211yescharacteristic, complemented
50#10622589C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66873C2211yescharacteristic
57#10622558—21no—
58#10622557—21no—
59#10622333—24no—
60#10622267—21no—
61#10622266—21no—
62C24×D11—21no—
63C2×C11×#41—22no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C2×C11×#41—41no—
68C2×C11×#41C2×C414yes—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—21no—
75C22×C22⋊D11—21no—
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44C2×C414yes—
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11D411yescharacteristic
94C2×C22⋊Dic11D411yescharacteristic
95#67000—22no—
96#67000—22no—
97#67000C2×C414yes—
98#67000C2×C414yes—
99#66993—22no—
100#66993—22no—
101#66993C2×C414yes—
102#66993C2×C414yes—
103#66990—28no—
104#66990—28no—
105#66983—28no—
106#66983—28no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111#66979C2×C414yes—
112#66979D414yes—
113C2×C4⋊Dic11D411yescharacteristic
114C2×C4⋊Dic11D411yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×C4×Dic11—21no—
120C2×C4×Dic11—21no—
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C11×#103—41no—
126C11×#103—41no—
127C11×#102—41no—
128C11×#102—41no—
129C11×C22⋊C8—22no—
130C11×#95—21no—
131#66899—41no—
132#66899—41no—
133#66896—41no—
134#66896—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141#66885—41no—
142#66885—41no—
143#66885—41no—
144#66885—41no—
145#66879—22no—
146Dic11⋊C8—22no—
147Dic11⋊C8—22no—
148C8×Dic11—22no—
149#66873—41no—
150#66873—41no—
151#66873—41no—
152#66873—41no—
153#21813—111nomaximal, Sylow
154C24×C11—21no—
155C24×C11C2×D411yescharacteristic
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—24no—
159C23×D11—42no—
160C23×D11—42no—
161C23×D11—81no—
162C23×D11—81no—
163C23×D11—81no—
164C23×D11—81no—
165C11×#41—44no—
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11C22×C412yes—
175C2×D4×C11—24no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—42no—
182C2×D4×C11—42no—
183C2×D4×C11C22×C412yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—81no—
203C2×C22⋊D11—81no—
204C2×C22⋊D11—81no—
205C2×C22⋊D11—81no—
206C2×C22⋊D11—81no—
207C2×C22⋊D11—81no—
208C2×C22⋊D11—81no—
209C2×C22⋊D11—81no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C2×D44—24no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44—21no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44—42no—
230C2×D44—42no—
231C2×D44—44no—
232C2×D44—44no—
233C2×D44C22×C412yes—
234C2×D44C22×C412yes—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C22⋊C4—81no—
246C22⋊Dic11—81no—
247C22⋊Dic11C22⋊C414yes—
248C22⋊Dic11C22⋊C414yes—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11C22⋊C414yes—
258C4⋊Dic11C22⋊C414yes—
259Dic11⋊C4—81no—
260Dic11⋊C4—81no—
261C4×Dic11—81no—
262C4×Dic11—81no—
263C4×Dic11C22×C412yes—
264C4×Dic11C22×C412yes—
265C4×Dic11C2×D412yes—
266C4×Dic11C2×D412yes—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×#535—111no—
274C2×#433—111no—
275#2314—111no—
276#1983—111no—
277#1983—111no—
278#1982—111no—
279#1982—111no—
280#1961—111no—
281#1959—111no—
282#1958—111no—
283#1957—111no—
284#1788—111no—
285#1788D1111yescharacteristic, complemented
286#1786—111no—
287#1786—111no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11C2×C22⋊C412yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—48no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—84no—
319C22×D11—84no—
320C22×D11—84no—
321C22×D11—84no—
322C22×D11—84no—
323C22×D11—84no—
324Q8×C11—22no—
325Q8×C11—22no—
326Q8×C11—41no—
327Q8×C11—41no—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—48no—
331D4×C11—41no—
332D4×C11—41no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—48no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11C2×C22⋊C412yes—
350C2×C4×C11C23×C411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C2×C4×C11H(5,𝔽2)11yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C22⋊D11—84no—
357C22⋊D11—84no—
358C22⋊D11—84no—
359C22⋊D11—84no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11C2×C22⋊C412yes—
375C2×Dic11C2×C22⋊C412yes—
376C2×Dic11C2×C22⋊C412yes—
377C2×Dic11C2×C22⋊C412yes—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—48no—
383D44—41no—
384D44—41no—
385D44—41no—
386D44—41no—
387C8×C11—41no—
388C8×C11—41no—
389C11⋊C8—41no—
390C11⋊C8—41no—
391C22×#41C2×D1111yescharacteristic
392C23×D4—111no—
393#535—118no—
394#535—224no—
395C2×#127—111no—
396C2×#127—111no—
397C2×#124—111no—
398C2×#124—111no—
399C2×#121—221no—
400C2×#121—221no—
401C2×#120—221no—
402C2×#120—221no—
403C2×#117—111no—
404#433—224no—
405C2×C4⋊C8—111no—
406C2×C4⋊C8—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103C2×D1111yescharacteristic, complemented
410C2×#103C2×D1111yescharacteristic, complemented
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102C2×D1111yescharacteristic, complemented
422C2×#102C2×D1111yescharacteristic, complemented
423C2×C22⋊C8—111no—
424C2×C22⋊C8C2×D1111yescharacteristic
425C2×#97—111no—
426C2×C4×C8—111no—
427#388—221no—
428#388—221no—
429#387—221no—
430#387—221no—
431#384—111no—
432#382—111no—
433#380—111no—
434#380C2×D1111yescharacteristic
435C4×C4⋊C4—111no—
436C4×C4⋊C4—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11C22×C22⋊C411yescharacteristic
452C22×C11#53511yescharacteristic
453C22×C11#53511yescharacteristic
454C22×C11#57611yescharacteristic
455C22×C11#57611yescharacteristic
456C22×C11#57711yescharacteristic
457C22×C11#57711yescharacteristic
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—816no—
465C2×D11—81no—
466C2×D11—81no—
467C2×D11—81no—
468C2×D11—81no—
469C2×D11—81no—
470C2×D11—81no—
471C2×D11—81no—
472C2×D11—81no—
473C4×C11—22no—
474C4×C11—42no—
475C4×C11—81no—
476C4×C11—81no—
477C4×C11#51811yescharacteristic
478C4×C11#51811yescharacteristic
479C4×C11#53511yescharacteristic
480C4×C11#53511yescharacteristic
481Dic11—22no—
482Dic11—22no—
483Dic11—22no—
484Dic11—22no—
485Dic11—81no—
486Dic11—81no—
487C25—221no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41C4×D1114yes—
494C22×Q8C22×D1111yescharacteristic
495C22×D4—21no—
496C22×D4—114no—
497C22×D4—111no—
498C22×D4—111no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4—222no—
505C22×D4—441no—
506C22×D4—441no—
507C22×D4—441no—
508C22×D4—441no—
509C22×D4C22×D1111yescharacteristic
510C23×C4—21no—
511C23×C4C22×D1111yescharacteristic
512C22×C8—111no—
513C22×C8—111no—
514C22×C8C22×D1111yescharacteristic
515C22×C8C22×D1111yescharacteristic
516#127—114no—
517#127—114no—
518#127—222no—
519#127—222no—
520#124—114no—
521#124—114no—
522#124—222no—
523#124—222no—
524#121—228no—
525#121—228no—
526#120—228no—
527#120—228no—
528#117—114no—
529#117—114no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—111no—
540C2×C22⋊C4—111no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C42—111no—
547C2×C42—111no—
548C2×C42—221no—
549C2×C42—221no—
550C4⋊C8—222no—
551C4⋊C8—222no—
552#103—41no—
553#103—41no—
554#103—441no—
555#103—441no—
556#102—41no—
557#102—41no—
558#102—441no—
559#102—441no—
560#102—441no—
561#102—441no—
562#102—441no—
563#102—441no—
564#102—441no—
565#102—441no—
566#102—441no—
567#102—441no—
568C22⋊C8—22no—
569C22⋊C8—222no—
570#97—222no—
571C4×C8—222no—
572#95—21no—
573#95—221no—
574#95—221no—
575#95—221no—
576#95—221no—
577#95—221no—
578C2×C11—42no—
579C2×C11—82no—
580C2×C11#230911yescharacteristic
581C2×C11#289711yescharacteristic
582C2×C11#289711yescharacteristic
583C2×C11#322011yescharacteristic
584C2×C11#322211yescharacteristic
585C2×C11#322411yescharacteristic
586C2×C11#322411yescharacteristic
587D11—82no—
588D11—82no—
589C24—21no—
590C24—221no—
591C24—221no—
592C24—224no—
593C24—442no—
594C24—442no—
595C24—881no—
596C24—881no—
597C24—881no—
598C24—881no—
599C24D4×D1111yescharacteristic
600#41—44no—
601#41—44no—
602#41—44no—
603#41—44no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8C2×C4×D1112yes—
610C2×D4—24no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—112no—
619C2×D4—112no—
620C2×D4—224no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—444no—
636C2×D4—444no—
637C2×D4—442no—
638C2×D4—442no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—881no—
642C2×D4—881no—
643C2×D4—881no—
644C2×D4—881no—
645C2×D4—881no—
646C2×D4—881no—
647C2×D4—881no—
648C2×D4—881no—
649C2×D4C2×C4×D1112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—111no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4C2×C4×D1112yes—
667C22×C4D4×D1111yescharacteristic
668C22×C4D4×D1112yes—
669C22×C4C23×D1111yescharacteristic
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—221no—
677C2×C8—221no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—221no—
681C2×C8—221no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—114no—
687C4⋊C4—114no—
688C4⋊C4—221no—
689C4⋊C4—221no—
690C4⋊C4—221no—
691C4⋊C4—221no—
692C4⋊C4—881no—
693C4⋊C4—881no—
694C22⋊C4—81no—
695C22⋊C4—114no—
696C22⋊C4—114no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—881no—
702C42—112no—
703C42—112no—
704C42—112no—
705C42—112no—
706C42—881no—
707C42—881no—
708C11#2181311yescharacteristic, complemented, Sylow
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—222no—
723C23—222no—
724C23—448no—
725C23—441no—
726C23—441no—
727C23—441no—
728C23—441no—
729C23—441no—
730C23—441no—
731C23—441no—
732C23—441no—
733C23—441no—
734C23—441no—
735C23—441no—
736C23—441no—
737C23—884no—
738C23—884no—
739C23—884no—
740C23—884no—
741C23—884no—
742C23—884no—
743C23C22⋊C4×D1112yes—
744C23C2×D4×D1111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—41no—
748Q8—41no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—222no—
755D4—222no—
756D4—222no—
757D4—222no—
758D4—448no—
759D4—441no—
760D4—441no—
761D4—441no—
762D4—441no—
763D4—884no—
764D4—884no—
765D4—884no—
766D4—884no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—112no—
784C2×C4—112no—
785C2×C4—112no—
786C2×C4—112no—
787C2×C4—221no—
788C2×C4—221no—
789C2×C4—221no—
790C2×C4—221no—
791C2×C4—221no—
792C2×C4—221no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4C22⋊C4×D1112yes—
802C2×C4C22×C4×D1111yescharacteristic
803C2×C4C2×D4×D1111yescharacteristic
804C2×C4#6703711yescharacteristic
805C2×C4#6703711yescharacteristic
806C2×C4#6703711yescharacteristic
807C2×C4#6703711yescharacteristic
808C8—41no—
809C8—41no—
810C8—441no—
811C8—441no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—8816no—
833C22—881no—
834C22—881no—
835C22—881no—
836C22—881no—
837C22—881no—
838C22—881no—
839C22—881no—
840C22—881no—
841C22C2×C22⋊C4×D1111yescharacteristic
842C22#1062312311yescharacteristic
843C22#1062312311yescharacteristic
844C22#1062330011yescharacteristic
845C22#1062330111yescharacteristic
846C22#1062330511yescharacteristic
847C22#1062330911yescharacteristic
848C4—22no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—222no—
853C4—222no—
854C4—222no—
855C4—222no—
856C4—881no—
857C4—881no—
858C4#1062301711yescharacteristic
859C4#1062301711yescharacteristic
860C4#1062312311yescharacteristic
861C4#1062312311yescharacteristic
862C2—42no—
863C2—82no—
864C2—882no—
865C2—882no—
866C2#1307119711yescharacteristic
867C2#1307713811yescharacteristic
868C2#1307714011yescharacteristic
869C2#1307966411yescharacteristic
870C2#1307968611yescharacteristic
871C2#1307970811yescharacteristic
872C2#1307971611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623361C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#21813
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622333C2semidirect
3. #13071223C2semidirect
4. #13069545C2semidirect
5. #13069545C2semidirect
6. #13069541C2semidirect
7. #13069541C2semidirect
8. #13069438C2semidirect
9. #13069429C2semidirect
10. #13069424C2semidirect
11. #13069420C2semidirect
12. #13068556C2semidirect
13. #13068548C2semidirect
14. #13068546C2semidirect
15. C11×#1788C2semidirect
19. #10623361C4semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
32. C2×C11×#102C22semidirect
35. C2×#66899C22semidirect
36. C2×#66899C22semidirect
37. C2×#66896C22semidirect
38. C2×#66896C22semidirect
45. C2×#66879C22semidirect
46. C2×Dic11⋊C8C22semidirect
47. C2×Dic11⋊C8C22semidirect
48. C2×C8×Dic11C22semidirect
49. #10622590C22semidirect
50. #10622589C22semidirect
51. C4⋊C4×Dic11C22semidirect
52. C4⋊C4×Dic11C22semidirect
285. #1788D11semidirect
409. C2×#103C2×D11semidirect
410. C2×#103C2×D11semidirect
421. C2×#102C2×D11semidirect
422. C2×#102C2×D11semidirect
708. C11#21813semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106223332
#130712232
#130695452
#130695412
#130694382
#130694292
#130694242
#130694202
#130685562
#130685482
#130685462
C11×#17882
#2181311