Finite Group Databasebeta

← #14762897

Subgroups — #14762897

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623160C211yesmaximal, characteristic
2C2×#10622340C211yesmaximal, characteristic, complemented
3#13071204C211yesmaximal, characteristic, complemented
4#13069053C211yesmaximal, characteristic, complemented
5#13069046C211yesmaximal, characteristic, complemented
6#13069043C211yesmaximal, characteristic, complemented
7#13069036C211yesmaximal, characteristic, complemented
8#13068938C211yesmaximal, characteristic, complemented
9#13068931C211yesmaximal, characteristic, complemented
10#13068924C211yesmaximal, characteristic, complemented
11#13068705C211yesmaximal, characteristic, complemented
12#13068701C211yesmaximal, characteristic, complemented
13#13068555C211yesmaximal, characteristic, complemented
14#13068555C211yesmaximal, characteristic, complemented
15C11×#1873C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C22×C8×D11C2211yescharacteristic
25#10623160—24no—
26#10623160C418yescomplemented
27C2×#66949—21no—
28C2×#66948—21no—
29C2×#66948C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66937—21no—
32C2×#66937—21no—
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622600C2211yescharacteristic
46#10622600C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49#10622571—21no—
50#10622571—21no—
51#10622552—21no—
52#10622542—21no—
53#10622340—24no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11D411yescharacteristic
66C22×C22⋊D11D411yescharacteristic
67C23×Dic11—21no—
68C2×#4343—22no—
69C2×#4343—41no—
70C2×#4343—41no—
71C2×#4343—41no—
72C2×#4343—41no—
73C2×#4343C2×C414yescomplemented
74C2×#4339—41no—
75C2×#4339—41no—
76C2×#4339—41no—
77C2×#4339—41no—
78C2×#4339C2×C414yes—
79C2×#4339D414yes—
80C22×D44—21no—
81C22×D44—21no—
82C22×D44D411yescharacteristic
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22D411yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8C2×C414yes—
93C11×#117—41no—
94C11×#117—41no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102#66999—22no—
103#66999C2×C414yescomplemented
104#66983—22no—
105#66983C2×C414yes—
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—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11—41no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C2×#4313—22no—
124C2×#4313—41no—
125C2×#4313—41no—
126C2×C8×D11—22no—
127C2×C8×D11—41no—
128C2×C8×D11—41no—
129#66949—28no—
130#66948—28no—
131#66948—22no—
132#66948C2×C414yescomplemented
133C4⋊C4×D11—22no—
134C4⋊C4×D11C2×C414yescomplemented
135#66937—28no—
136#66937—28no—
137C11×#103—41no—
138C11×#103—41no—
139C11×C22⋊C8—22no—
140#66899—41no—
141#66899—41no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C22⋊(C11⋊C8)—22no—
147#66885—41no—
148#66885—41no—
149(C2×D11)⋊C8—22no—
150(C2×D11)⋊C8—22no—
151#66873—41no—
152#66873—41no—
153#21772—111nomaximal, Sylow
154C24×C11C2×D411yescharacteristic
155C23×D11—21no—
156C23×D11C2×D411yescharacteristic
157C23×D11C2×D411yescharacteristic
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11C22×C412yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11C22×C412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—24no—
177C2×C22⋊D11—41no—
178C2×C22⋊D11—41no—
179C2×C22⋊D11—41no—
180C2×C22⋊D11—41no—
181C2×C22⋊D11—81no—
182C2×C22⋊D11—81no—
183C2×C22⋊D11C22⋊C414yes—
184C2×C22⋊D11C22⋊C414yes—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—42no—
189C22×Dic11—81no—
190C22×Dic11—81no—
191C22×Dic11C2×D411yescharacteristic
192C22×Dic11C2×D411yescharacteristic
193#4343—44no—
194#4343—44no—
195#4343—44no—
196#4343—44no—
197#4339—44no—
198#4339—44no—
199#4339—44no—
200#4339—44no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—41no—
209C2×D44—41no—
210C2×D44—42no—
211C2×D44—42no—
212C2×D44—81no—
213C2×D44—81no—
214C2×D44C22⋊C414yes—
215C2×D44C22×C412yes—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—21no—
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—42no—
227C2×C4×D11—42no—
228C2×C4×D11—81no—
229C2×C4×D11—81no—
230C2×C4×D11C22×C412yes—
231C2×C4×D11C22×C412yes—
232C2×C4×D11C2×D412yes—
233C2×C4×D11C2×D412yes—
234C2×Dic22—41no—
235C2×Dic22—41no—
236C2×Dic22C22⋊C414yes—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4C22×C412yes—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—42no—
252C42×C11—42no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—81no—
257(C2×D11)⋊C4—81no—
258(C2×D11)⋊C4—81no—
259(C2×D11)⋊C4—81no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—42no—
266C4⋊Dic11C22×C412yes—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275#4313—44no—
276C8×D11—44no—
277C2×#537—111no—
278C2×#408—111no—
279#2311—111no—
280#1895—111no—
281#1894—111no—
282#1893—111no—
283#1892—111no—
284#1875—111no—
285#1874—111no—
286#1873D1111yescharacteristic, complemented
287#1872—111no—
288#1824—111no—
289#1823—111no—
290#1788—111no—
291#1788—111no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11C2×C22⋊C412yes—
299C23×C11C22×D411yescharacteristic
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—22no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11C2×C22⋊C412yes—
320C22×D11C2×C22⋊C412yes—
321Q8×C11—22no—
322Q8×C11—22no—
323Q8×C11—41no—
324Q8×C11—41no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11C2×C22⋊C412yes—
344C2×C4×C11C23×C411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11H(5,𝔽2)11yescharacteristic
347C2×C4×C11H(5,𝔽2)11yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C2×C4×C11H(5,𝔽2)11yescharacteristic
350C22⋊D11—44no—
351C22⋊D11—44no—
352C22⋊D11—84no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—22no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—84no—
367C2×Dic11C2×C22⋊C412yes—
368C2×Dic11C2×C22⋊C412yes—
369D44—22no—
370D44—22no—
371D44—44no—
372D44—48no—
373D44—41no—
374D44—41no—
375D44—84no—
376C4×D11—22no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—48no—
385C4×D11—84no—
386Dic22—44no—
387C8×C11—41no—
388C8×C11—41no—
389C11⋊C8—41no—
390C11⋊C8—41no—
391C22×#41—111no—
392C22×#41—111no—
393C22×M16—111no—
394C23×C8—111no—
395#537—118no—
396#537—224no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—221no—
399C2×C22⋊Q8C2×D1111yescharacteristic
400C2×#121—111no—
401C2×#121—111no—
402C2×#121—221no—
403C2×#121—221no—
404C2×#121—221no—
405C2×#117C2×D1111yescharacteristic
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103C2×D1111yescharacteristic
411C2×#103C2×D1111yescharacteristic
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416#408—224no—
417C2×C22⋊C8—111no—
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×C22⋊C8C2×D1111yescharacteristic
421#391—221no—
422#390—221no—
423#386—221no—
424#386—221no—
425#380—111no—
426#380—111no—
427#380—111no—
428#380—111no—
429#340—111no—
430#340—111no—
431#340—111no—
432#340—111no—
433#340—111no—
434#340—111no—
435#340C2×D1111yescharacteristic
436#340C2×D1111yescharacteristic
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11C22×C22⋊C411yescharacteristic
445C22×C11#53411yescharacteristic
446C22×C11#53411yescharacteristic
447C22×C11#57611yescharacteristic
448C22×C11#57711yescharacteristic
449C22×C11#57711yescharacteristic
450C22×C11#57811yescharacteristic
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—22no—
454C2×D11—22no—
455C2×D11—22no—
456C2×D11—22no—
457C2×D11—41no—
458C2×D11—41no—
459C2×D11—41no—
460C2×D11—41no—
461C2×D11—41no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—81no—
469C2×D11—81no—
470C2×D11—81no—
471C2×D11—81no—
472C4×C11—22no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—81no—
476C4×C11—81no—
477C4×C11#51811yescharacteristic
478C4×C11#51811yescharacteristic
479C4×C11#53411yescharacteristic
480C4×C11#53411yescharacteristic
481Dic11—22no—
482Dic11—22no—
483Dic11—42no—
484Dic11—81no—
485Dic11—81no—
486C2×#41—114no—
487C2×#41—114no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—441no—
491C2×#41—441no—
492C2×#41—441no—
493C2×#41—441no—
494C2×#41—441no—
495C2×#41—441no—
496C2×#41—441no—
497C2×#41—441no—
498C22×Q8—111no—
499C22×Q8C22×D1111yescharacteristic
500C22×D4—111no—
501C22×D4—111no—
502C22×D4—111no—
503C22×D4—111no—
504C22×D4—221no—
505C22×D4—221no—
506C22×D4—221no—
507C23×C4—111no—
508C23×C4—111no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4—221no—
512C23×C4C22×D1111yescharacteristic
513C2×M16—222no—
514C2×M16—441no—
515C2×M16—441no—
516C22×C8—111no—
517C22×C8—111no—
518C22×C8—222no—
519C22×C8—441no—
520C22×C8—441no—
521C22×C8C22×D1111yescharacteristic
522C22×C8C22×D1111yescharacteristic
523C22⋊Q8—22no—
524C22⋊Q8—114no—
525C22⋊Q8—228no—
526C22⋊Q8—222no—
527C22⋊Q8C4×D1114yes—
528#121—114no—
529#121—114no—
530#121—228no—
531#121—228no—
532#121—222no—
533#121—228no—
534#121—222no—
535#117—41no—
536#117—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—222no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—441no—
547C2×C4⋊C4—441no—
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C42—21no—
561#103—41no—
562#103—41no—
563#103—441no—
564#103—441no—
565#102—441no—
566#102—441no—
567#102—441no—
568#102—441no—
569C22⋊C8—22no—
570C22⋊C8—222no—
571C22⋊C8—222no—
572C22⋊C8—222no—
573#95—221no—
574#95—221no—
575#95—221no—
576#95—221no—
577C2×C11—42no—
578C2×C11#230811yescharacteristic
579C2×C11#289711yescharacteristic
580C2×C11#289811yescharacteristic
581C2×C11#319811yescharacteristic
582C2×C11#320111yescharacteristic
583C2×C11#320311yescharacteristic
584C2×C11#320411yescharacteristic
585D11—42no—
586D11—42no—
587D11—82no—
588C24—111no—
589C24—111no—
590C24—221no—
591C24D4×D1111yescharacteristic
592#41—444no—
593#41—444no—
594#41—444no—
595#41—444no—
596#41—444no—
597#41—444no—
598#41—444no—
599#41—444no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—114no—
606C2×Q8—441no—
607C2×Q8—441no—
608C2×Q8C2×C4×D1112yes—
609C2×D4—114no—
610C2×D4—114no—
611C2×D4—114no—
612C2×D4—112no—
613C2×D4—224no—
614C2×D4—224no—
615C2×D4—224no—
616C2×D4—221no—
617C2×D4—221no—
618C2×D4—221no—
619C2×D4—221no—
620C2×D4—221no—
621C2×D4—441no—
622C2×D4—441no—
623C2×D4—442no—
624C2×D4—442no—
625C2×D4—441no—
626C2×D4—441no—
627C2×D4—441no—
628C2×D4—441no—
629C2×D4—881no—
630C2×D4—881no—
631C2×D4—881no—
632C2×D4—881no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—442no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—881no—
664C22×C4—881no—
665C22×C4—881no—
666C22×C4—881no—
667C22×C4C2×C4×D1112yes—
668C22×C4D4×D1111yescharacteristic
669C22×C4D4×D1112yes—
670C22×C4C23×D1111yescharacteristic
671M16—444no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—221no—
681C2×C8—221no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—444no—
685C4⋊C4—24no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—442no—
700C4⋊C4C2×C4×D1112yes—
701C22⋊C4—24no—
702C22⋊C4—42no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—881no—
707C22⋊C4—881no—
708C22⋊C4—881no—
709C22⋊C4—881no—
710C42—42no—
711C11#2177211yescharacteristic, complemented, Sylow
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—112no—
719C23—112no—
720C23—221no—
721C23—221no—
722C23—221no—
723C23—221no—
724C23—221no—
725C23—221no—
726C23—221no—
727C23—221no—
728C23—221no—
729C23—221no—
730C23—221no—
731C23—221no—
732C23—222no—
733C23—441no—
734C23—441no—
735C23—441no—
736C23—441no—
737C23—441no—
738C23—441no—
739C23C22⋊C4×D1112yes—
740C23C2×D4×D1111yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—41no—
744Q8—41no—
745Q8—444no—
746D4—222no—
747D4—222no—
748D4—444no—
749D4—448no—
750D4—444no—
751D4—444no—
752D4—441no—
753D4—441no—
754D4—884no—
755D4—884no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—112no—
775C2×C4—112no—
776C2×C4—221no—
777C2×C4—221no—
778C2×C4—221no—
779C2×C4—221no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—448no—
790C2×C4—441no—
791C2×C4—441no—
792C2×C4—441no—
793C2×C4—441no—
794C2×C4—441no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—884no—
799C2×C4—884no—
800C2×C4C22⋊C4×D1112yes—
801C2×C4C22×C4×D1111yescharacteristic
802C2×C4C2×D4×D1111yescharacteristic
803C2×C4#6703711yescharacteristic
804C2×C4#6703711yescharacteristic
805C2×C4#6704211yescharacteristic
806C2×C4#6704211yescharacteristic
807C8—41no—
808C8—41no—
809C8—441no—
810C8—441no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—222no—
819C22—222no—
820C22—222no—
821C22—222no—
822C22—222no—
823C22—222no—
824C22—441no—
825C22—441no—
826C22—441no—
827C22—441no—
828C22—441no—
829C22—441no—
830C22—441no—
831C22—441no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—881no—
836C22—881no—
837C22—881no—
838C22—881no—
839C22C2×C22⋊C4×D1111yescharacteristic
840C22#1062312011yescharacteristic
841C22#1062318411yescharacteristic
842C22#1062330011yescharacteristic
843C22#1062330111yescharacteristic
844C22#1062330911yescharacteristic
845C22#1062331011yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—81no—
850C4—81no—
851C4—222no—
852C4—222no—
853C4—442no—
854C4—881no—
855C4—881no—
856C4#1062307611yescharacteristic
857C4#1062307611yescharacteristic
858C4#1062313611yescharacteristic
859C4#1062313611yescharacteristic
860C2—42no—
861C2—442no—
862C2—442no—
863C2—882no—
864C2#1307119011yescharacteristic
865C2#1307713811yescharacteristic
866C2#1307714811yescharacteristic
867C2#1307947411yescharacteristic
868C2#1307950411yescharacteristic
869C2#1307951711yescharacteristic
870C2#1307952411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#10623160C2
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#21772
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#10622340C2semidirect
3. #13071204C2semidirect
4. #13069053C2semidirect
5. #13069046C2semidirect
6. #13069043C2semidirect
7. #13069036C2semidirect
8. #13068938C2semidirect
9. #13068931C2semidirect
10. #13068924C2semidirect
11. #13068705C2semidirect
12. #13068701C2semidirect
13. #13068555C2semidirect
14. #13068555C2semidirect
15. C11×#1873C2semidirect
26. #10623160C4semidirect
73. C2×#4343C2×C4semidirect
103. #66999C2×C4semidirect
132. #66948C2×C4semidirect
134. C4⋊C4×D11C2×C4semidirect
286. #1873D11semidirect
711. C11#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#106231602
C2×#106223402
#130712042
#130690532
#130690462
#130690432
#130690362
#130689382
#130689312
#130689242
#130687052
#130687012
#130685552
C11×#18732
#2177211