Finite Group Databasebeta

← #14816694

Subgroups — #14816694

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622504C211yesmaximal, characteristic, complemented
2#13072323C211yesmaximal, characteristic, complemented
3#13071632C211yesmaximal, characteristic
4#13070146C211yesmaximal, characteristic, complemented
5#13070115C211yesmaximal, characteristic, complemented
6#13069999C211yesmaximal, characteristic, complemented
7#13069952C211yesmaximal, characteristic, complemented
8#13069376C211yesmaximal, characteristic, complemented
9#13069189C211yesmaximal, characteristic, complemented
10#13069054C211yesmaximal, characteristic
11#13068938C211yesmaximal, characteristic
12#13068874C211yesmaximal, characteristic, complemented
13#13068809C211yesmaximal, characteristic, complemented
14#13068799C211yesmaximal, characteristic, complemented
15C2×C11×#428C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×#66946C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C11×#428—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28#10622826—21no—
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622603—21no—
37#10622602—21no—
38#10622601C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48#10622562—21no—
49#10622561—21no—
50#10622546—21no—
51#10622541—21no—
52#10622504—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#117—22no—
72C11×#117—41no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85#66983—22no—
86#66983Q814yes—
87C4×C22⋊D11—44no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66946—22no—
108#66946—41no—
109#66943—22no—
110#66943—41no—
111C11×#107—22no—
112C11×#107D414yescomplemented
113C11×#106—22no—
114C11×#106—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122C22⋊(C11⋊C8)—22no—
123#66885—22no—
124#66885—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8—22no—
127#66873—22no—
128#66873—41no—
129#66872—22no—
130#66872—41no—
131#26366—111nomaximal, Sylow
132C24×C11C2×D411yescharacteristic
133C23×D11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—81no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×Q812yes—
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—24no—
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C2×Q812yes—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—81no—
168C11×M16—28no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D412yes—
174C2×C8×C11#4112yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4C2×D412yes—
184C11×C22⋊C4—42no—
185C42×C11—42no—
186C22⋊Dic11—22no—
187C22⋊Dic11—41no—
188C22⋊Dic11—81no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11C2×Q812yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205Dic11⋊C4—81no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×#478—111no—
218C2×#428D1111yescharacteristic, complemented
219#2441—111no—
220#2361—111no—
221#2094—111no—
222#2088—111no—
223#2067—111no—
224#2059—111no—
225#1948—111no—
226#1918—111no—
227#1895—111no—
228#1875—111no—
229#1864—111no—
230#1853—111no—
231#1851—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11C22⋊Q812yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—84no—
266C2×C4×C11C22⋊Q812yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×Q811yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C22⋊D11—48no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
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×Dic11AGL(1,ℤ/8)12yes—
295D44—22no—
296D44—22no—
297D44—41no—
298D44—41no—
299C4×D11—84no—
300C8×C11—22no—
301C8×C11—22no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×M16C2×D1111yescharacteristic
305C2×#125—111no—
306C2×#121—111no—
307C2×C4×D4—111no—
308C2×C4×D4—221no—
309C2×#117C2×D1111yescharacteristic
310C22×C4⋊C4C2×D1111yescharacteristic
311#478—224no—
312#428—24no—
313C2×#107C2×D1111yescharacteristic
314C2×#107C2×D1111yescharacteristic
315C2×#106—111no—
316C2×#106—111no—
317C2×#106C2×D1111yescharacteristic
318C2×#106C2×D1111yescharacteristic
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×C22⋊C8—111no—
326#399—221no—
327#396—221no—
328#390—111no—
329#389—111no—
330#389—111no—
331#389—111no—
332#389—221no—
333#388—221no—
334#387—221no—
335#386—221no—
336#385—221no—
337#384—111no—
338#380—111no—
339C4×C4⋊C4—111no—
340C4×C22⋊C4—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336—111no—
348#336—111no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11C2×C22⋊Q811yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57711yescharacteristic
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C4×C11—22no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11#52511yescharacteristic
376C4×C11#53911yescharacteristic
377C4×C11D4×Q811yescharacteristic
378C4×C11#55411yescharacteristic
379Dic11—22no—
380Dic11—42no—
381Dic11—41no—
382Dic11—41no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—21no—
389C23×C4—221no—
390C23×C4C22×D1111yescharacteristic
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—22no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398#125—222no—
399#125—441no—
400#121—114no—
401#121—222no—
402C4×D4—222no—
403C4×D4—441no—
404C4×D4—444no—
405#117—22no—
406#117—41no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—111no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—21no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—221no—
436#107—22no—
437#107C22⋊D1114yescomplemented
438#106—22no—
439#106—22no—
440#106—222no—
441#106—441no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444#102—222no—
445#102—222no—
446#102—222no—
447#102—441no—
448C22⋊C8—222no—
449#95—111no—
450#95—111no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—42no—
457C2×C11#244911yescharacteristic
458C2×C11#307711yescharacteristic
459C2×C11#308411yescharacteristic
460C2×C11#327111yescharacteristic
461C2×C11#327211yescharacteristic
462C2×C11#334511yescharacteristic
463C2×C11#335111yescharacteristic
464D11—82no—
465C24—221no—
466C24D4×D1111yescharacteristic
467C2×D4—112no—
468C2×D4—224no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—442no—
475C2×D4—442no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—881no—
497C22×C4#433912yes—
498C22×C4D4×D1111yescharacteristic
499C22×C4Q8×D1112yes—
500C22×C4C23×D1111yescharacteristic
501M16—28no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8#433912yes—
513C2×C8C2×C22⋊D1112yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—112no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—881no—
533C4⋊C4—881no—
534C4⋊C4C2×C22⋊D1112yes—
535C4⋊C4C2×C22⋊D1112yes—
536C22⋊C4—42no—
537C22⋊C4—222no—
538C22⋊C4—224no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—441no—
542C22⋊C4—881no—
543C22⋊C4—881no—
544C42—42no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—442no—
550C11#2636611yescharacteristic, complemented, Sylow
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—222no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23#6694912yes—
565C23C2×D4×D1111yescharacteristic
566D4—222no—
567D4—222no—
568D4—448no—
569D4—441no—
570D4—441no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—112no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
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—884no—
612C2×C4#6694912yes—
613C2×C4C2×#433911yescharacteristic
614C2×C4C2×#433911yescharacteristic
615C2×C4#6703711yescharacteristic
616C2×C4C2×Q8×D1111yescharacteristic
617C2×C4#6704011yescharacteristic
618C2×C4C22×C22⋊D1111yescharacteristic
619C8—22no—
620C8—22no—
621C8—441no—
622C8—441no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22#1062303811yescharacteristic
638C22C2×#6694911yescharacteristic
639C22D11×AGL(1,ℤ/8)11yescharacteristic
640C22#1062330611yescharacteristic
641C22#1062330811yescharacteristic
642C22#1062330911yescharacteristic
643C22D4×C22⋊D1111yescharacteristic
644C4—22no—
645C4—42no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4—222no—
650C4—441no—
651C4—441no—
652C4—442no—
653C4—441no—
654C4—881no—
655C4—881no—
656C4#1062304211yescharacteristic
657C4#1062304611yescharacteristic
658C4#1062332211yescharacteristic
659C4Q8×C22⋊D1111yescharacteristic
660C2—42no—
661C2—882no—
662C2#1307242511yescharacteristic
663C2#1307841211yescharacteristic
664C2#1307847711yescharacteristic
665C2#1308019511yescharacteristic
666C2#1308021011yescharacteristic
667C2#1308108711yescharacteristic
668C2#1308117711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#428D11
hypocenterC11#26366
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#10622504C2semidirect
2. #13072323C2semidirect
4. #13070146C2semidirect
5. #13070115C2semidirect
6. #13069999C2semidirect
7. #13069952C2semidirect
8. #13069376C2semidirect
9. #13069189C2semidirect
12. #13068874C2semidirect
13. #13068809C2semidirect
14. #13068799C2semidirect
15. C2×C11×#428C2semidirect
112. C11×#107D4semidirect
218. C2×#428D11semidirect
437. #107C22⋊D11semidirect
550. C11#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#106225042
#130723232
#130716322
#130701462
#130701152
#130699992
#130699522
#130693762
#130691892
#130690542
#130689382
#130688742
#130688092
#130687992
C2×C11×#4282
#2636611