Finite Group Databasebeta

← #14804116

Subgroups — #14804116

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622464C211yesmaximal, characteristic, complemented
2#13073789C211yesmaximal, characteristic
3#13073525C211yesmaximal, characteristic
4#13070049C211yesmaximal, characteristic, complemented
5#13070049C211yesmaximal, characteristic, complemented
6#13069820C211yesmaximal, characteristic, complemented
7#13069813C211yesmaximal, characteristic, complemented
8#13069589C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069049C211yesmaximal, characteristic, complemented
11#13069039C211yesmaximal, characteristic, complemented
12#13068649C211yesmaximal, characteristic, complemented
13#13068641C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#435—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28#10622835—21no—
29#10622834—21no—
30#10622825C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33#10622825C2211yescharacteristic
34#10622825C2211yescharacteristic
35#10622825C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39C2×#66881C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44#10622593—21no—
45#10622590—21no—
46#10622560—21no—
47#10622560—21no—
48#10622557—21no—
49#10622557—21no—
50#10622549C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic
52#10622464—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—41no—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
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⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—22no—
99#66977—22no—
100#66977—41no—
101#66977—41no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107#66922—22no—
108#66922—22no—
109C4×Dic22—22no—
110C4×Dic22—22no—
111C11×C4⋊C8D414yes—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—22no—
114C11×#97—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66882—41no—
125#66881—22no—
126#66881—22no—
127#66881—41no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#25356—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—41no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—42no—
169C2×Dic22—81no—
170C2×Dic22—81no—
171C2×Dic22#4112yes—
172C11×M16—44no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—44no—
183C2×C8×C11C2×D412yes—
184C2×C8×C11C2×D412yes—
185C2×C8×C11#4112yes—
186C11×C4⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C42×C11C2×D412yes—
190C42×C11#4112yes—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C22⋊Dic11—81no—
196C22⋊Dic11—81no—
197C22⋊Dic11—81no—
198C22⋊Dic11—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217C4×Dic11—42no—
218C4×Dic11—42no—
219C2×#475—111no—
220C2×#435D1111yescharacteristic
221#2563—111no—
222#2536—111no—
223#2077—111no—
224#2077—111no—
225#2036—111no—
226#2035—111no—
227#1993—111no—
228#1949—111no—
229#1894—111no—
230#1892—111no—
231#1809—111no—
232#1807—111no—
233#1763—111no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11#13712yes—
248C23×C11C22×D411yescharacteristic
249D4×C11—44no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11#12112yes—
269C2×C4×C11#12112yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300Dic22—22no—
301Dic22—22no—
302Dic22—41no—
303Dic22—41no—
304Dic22—84no—
305C8×C11—22no—
306C8×C11—22no—
307C8×C11—22no—
308C8×C11—41no—
309C22×M16C2×D1111yescharacteristic
310C23×C8C2×D1111yescharacteristic
311C2×C4⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8—111no—
314C2×C4×Q8—111no—
315C2×C4×D4C2×D1111yescharacteristic
316#475—224no—
317#435—24no—
318C2×#107—111no—
319C2×#106—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8C2×D1111yescharacteristic
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×C22⋊C8C2×D1111yescharacteristic
329C2×#97C2×D1111yescharacteristic
330#398—221no—
331#394—221no—
332#393—221no—
333#393—221no—
334#390—221no—
335#388—221no—
336#388—221no—
337#382—111no—
338#382—221no—
339#380—111no—
340#380—111no—
341#380—111no—
342#380—111no—
343#380—111no—
344#380—111no—
345C4×C4⋊C4—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11C2×#12111yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11#54711yescharacteristic
371C22×C11C2×#13711yescharacteristic
372C22×C11#57511yescharacteristic
373C22×C11#57711yescharacteristic
374C22×C11#57711yescharacteristic
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11#52911yescharacteristic
380C4×C11#54211yescharacteristic
381C4×C11#54611yescharacteristic
382C4×C11#54811yescharacteristic
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8—221no—
393C22×D4D4411yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1111yescharacteristic
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—41no—
399C22×C8—22no—
400C22×C8—22no—
401C22×C8—41no—
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C4⋊Q8—222no—
407C4⋊Q8—222no—
408C22⋊Q8—222no—
409C22⋊Q8—222no—
410C22⋊Q8—441no—
411C22⋊Q8—441no—
412C4×Q8—222no—
413C4×Q8—222no—
414C4×D4—22no—
415C4×D4—22no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4D4411yescharacteristic
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4D4411yescharacteristic
437C2×C22⋊C4D4411yescharacteristic
438C2×C42—221no—
439C2×C42—221no—
440C2×C42C22×D1111yescharacteristic
441#107—441no—
442#106—222no—
443#106—222no—
444#106—441no—
445C4⋊C8C22⋊D1114yes—
446#103—222no—
447#103—222no—
448#103—222no—
449#103—222no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452#97—22no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11—42no—
463C2×C11—81no—
464C2×C11#242711yescharacteristic
465C2×C11#305611yescharacteristic
466C2×C11#305711yescharacteristic
467C2×C11#331611yescharacteristic
468C2×C11#332111yescharacteristic
469C2×C11#334411yescharacteristic
470C2×C11#334811yescharacteristic
471C24C2×D4411yescharacteristic
472C24C2×D4411yescharacteristic
473C2×Q8—112no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—442no—
480C2×Q8—881no—
481C2×Q8—881no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—41no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×D4411yescharacteristic
509C22×C4C23×D1111yescharacteristic
510M16—44no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—44no—
521C2×C8#434112yes—
522C2×C8C2×C22⋊D1112yes—
523C2×C8C2×C22⋊D1112yes—
524C4⋊C4—22no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—881no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C42—442no—
554C42—442no—
555C42#433912yes—
556C42C2×C22⋊D1112yes—
557C11#2535611yescharacteristic, complemented, Sylow
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23#6696212yes—
572C23C22×D4411yescharacteristic
573Q8—222no—
574Q8—222no—
575Q8—441no—
576Q8—441no—
577Q8—884no—
578D4—44no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—222no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4#6698312yes—
622C2×C4#6698312yes—
623C2×C4C2×#433911yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4#6703711yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#6704311yescharacteristic
628C2×C4C22×C22⋊D1111yescharacteristic
629C8—22no—
630C8—22no—
631C8—22no—
632C8—41no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22#1062308511yescharacteristic
648C22#1062308611yescharacteristic
649C22C2×#6696211yescharacteristic
650C22#1062327911yescharacteristic
651C22#1062328211yescharacteristic
652C22#1062328211yescharacteristic
653C22C2×#6698311yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—442no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4#1062308811yescharacteristic
667C4#1062309211yescharacteristic
668C4#1062333711yescharacteristic
669C4#1062336211yescharacteristic
670C2—42no—
671C2—81no—
672C2#1307218711yescharacteristic
673C2#1307824611yescharacteristic
674C2#1307825511yescharacteristic
675C2#1308072911yescharacteristic
676C2#1308080411yescharacteristic
677C2#1308107311yescharacteristic
678C2#1308113311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#435D11
hypocenterC11#25356
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10622464C2semidirect
4. #13070049C2semidirect
5. #13070049C2semidirect
6. #13069820C2semidirect
7. #13069813C2semidirect
8. #13069589C2semidirect
9. #13069386C2semidirect
10. #13069049C2semidirect
11. #13069039C2semidirect
12. #13068649C2semidirect
13. #13068641C2semidirect
14. #13068447C2semidirect
557. C11#25356semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
#130737892
#130735252
#130700492
#130698202
#130698132
#130695892
#130693862
#130690492
#130690392
#130686492
#130686412
#130684472
C2×C11×#4352
#2535611