Finite Group Databasebeta

← #14813250

Subgroups — #14813250

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073857C211yesmaximal, characteristic, complemented
2#13071525C211yesmaximal, characteristic
3#13070187C211yesmaximal, characteristic, complemented
4#13070184C211yesmaximal, characteristic, complemented
5#13070120C211yesmaximal, characteristic, complemented
6#13069381C211yesmaximal, characteristic, complemented
7#13069336C211yesmaximal, characteristic, complemented
8#13068876C211yesmaximal, characteristic
9#13068860C211yesmaximal, characteristic
10#13068748C211yesmaximal, characteristic, complemented
11#13068627C211yesmaximal, characteristic
12#13068625C211yesmaximal, characteristic
13#13068615C211yesmaximal, characteristic
14#13068440C211yesmaximal, characteristic
15C11×#2086C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622602—21no—
29#10622600—21no—
30#10622598C2211yescharacteristic
31#10622595—21no—
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622585—21no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622549C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43#10622281—21no—
44D11×#95—21no—
45#10622271—21no—
46#10622263—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4D411yescharacteristic
83C2×Dic11⋊C4D411yescharacteristic
84C2×C4×Dic11—21no—
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89#66946—22no—
90#66946—22no—
91#66946—41no—
92#66946Q814yes—
93C4×D44—22no—
94C4×D44—41no—
95C11×#107—41no—
96C11×C4⋊C8—41no—
97C11×#95—21no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—22no—
111#66885—22no—
112#66879—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—41no—
115#66873—22no—
116#66873—22no—
117#66872—41no—
118#26125—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44C2×Q812yes—
138C2×D44#4112yes—
139C2×D44#4112yes—
140C2×C4×D11—24no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—81no—
146C2×C4×D11—81no—
147C2×C4×D11—81no—
148C2×C4×D11—81no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—81no—
163C11×C4⋊C4—81no—
164C11×C4⋊C4C2×Q812yes—
165C42×C11—21no—
166C42×C11—21no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—42no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—81no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—42no—
185C4×Dic11C2×Q812yes—
186C4×Dic11#4112yes—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193#2571—111no—
194#2349—111no—
195#2101—111no—
196#2101—111no—
197#2088—111no—
198#2086D1111yescharacteristic, complemented
199#1949—111no—
200#1940—111no—
201#1864—111no—
202#1862—111no—
203#1836—111no—
204#1804—111no—
205#1804—111no—
206#1802—111no—
207#1762—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11C22⋊Q812yes—
260C2×Dic11C22⋊Q812yes—
261D44—22no—
262D44—22no—
263D44—22no—
264D44#12514yes—
265C4×D11—84no—
266C4×D11—84no—
267C4×D11—84no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C2×C4×D4—111no—
273C2×C4×D4—111no—
274C2×C4×D4—111no—
275C2×#107C2×D1111yescharacteristic
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#97—111no—
285#400—221no—
286#400—221no—
287#389—111no—
288#389—111no—
289#389—221no—
290#389C2×D1111yescharacteristic
291#389C2×D1111yescharacteristic
292#385—221no—
293#385—221no—
294#384—111no—
295#382—111no—
296#382—111no—
297#382—111no—
298#382—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C2×#95—221no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#340C2×D1111yescharacteristic
313#336—111no—
314#336—111no—
315C22×C11C2×C22⋊Q811yescharacteristic
316C22×C11#54611yescharacteristic
317C22×C11#54811yescharacteristic
318C22×C11#57511yescharacteristic
319C22×C11#57511yescharacteristic
320C22×C11#57611yescharacteristic
321C22×C11#57711yescharacteristic
322C2×D11—24no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—42no—
329C4×C11—42no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11C2×#12511yescharacteristic
336C4×C11#54411yescharacteristic
337C4×C11#55211yescharacteristic
338C4×C11#55311yescharacteristic
339Dic11—22no—
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346C22×D4—111no—
347C23×C4—221no—
348C23×C4—221no—
349C23×C4—221no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C4×D4—114no—
355C4×D4—222no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4—441no—
359C4×D4—441no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382#107—41no—
383#106—441no—
384C4⋊C8—41no—
385C4⋊C8—222no—
386C4⋊C8—441no—
387#102—222no—
388#102—222no—
389#102—222no—
390#102—222no—
391#97—222no—
392#95—21no—
393#95—21no—
394#95—111no—
395#95—111no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405C2×C11#244211yescharacteristic
406C2×C11#308011yescharacteristic
407C2×C11#308111yescharacteristic
408C2×C11#331111yescharacteristic
409C2×C11#331911yescharacteristic
410C2×C11#337011yescharacteristic
411C2×C11#337611yescharacteristic
412D11—44no—
413C24—221no—
414C2×D4—112no—
415C2×D4—112no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—224no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—442no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4—881no—
437C22×C4—881no—
438C22×C4—881no—
439C22×C4—881no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—441no—
471C4⋊C4—441no—
472C4⋊C4—442no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C4⋊C4Q8×D1112yes—
477C22⋊C4—224no—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C42—21no—
481C42—21no—
482C42—112no—
483C42—112no—
484C42—221no—
485C42—221no—
486C42—442no—
487C11#2612511yescharacteristic, complemented, Sylow
488C23—222no—
489C23—222no—
490C23—222no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23C2×D4×D1111yescharacteristic
496D4—114no—
497D4—222no—
498D4—222no—
499D4—222no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—884no—
540C2×C4—884no—
541C2×C4—884no—
542C2×C4#6703711yescharacteristic
543C2×C4C2×Q8×D1111yescharacteristic
544C2×C4#6704011yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C8—41no—
549C8—41no—
550C8—441no—
551C8—441no—
552C22—224no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22#1062314111yescharacteristic
560C22D11×C22⋊Q811yescharacteristic
561C22#1062316411yescharacteristic
562C22#1062328811yescharacteristic
563C22#1062329911yescharacteristic
564C22#1062330811yescharacteristic
565C22#1062330911yescharacteristic
566C4—41no—
567C4—42no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—222no—
573C4—222no—
574C4—441no—
575C4—441no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4#1062319211yescharacteristic
580C4D11×#12511yescharacteristic
581C4#1062322411yescharacteristic
582C4#1062326011yescharacteristic
583C2—444no—
584C2#1307233511yescharacteristic
585C2#1307843511yescharacteristic
586C2#1307844011yescharacteristic
587C2#1308064711yescharacteristic
588C2#1308077811yescharacteristic
589C2#1308137611yescharacteristic
590C2#1308144111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2086C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2086D11
hypocenterC11#26125
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2086

Complements

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

NH ≅ G/Ntype
1. #13073857C2semidirect
3. #13070187C2semidirect
4. #13070184C2semidirect
5. #13070120C2semidirect
6. #13069381C2semidirect
7. #13069336C2semidirect
10. #13068748C2semidirect
15. C11×#2086C2semidirect
198. #2086D11semidirect
487. C11#26125semidirect

Maximal subgroups

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

subgroupindex
#130738572
#130715252
#130701872
#130701842
#130701202
#130693812
#130693362
#130688762
#130688602
#130687482
#130686272
#130686252
#130686152
#130684402
C11×#20862
#2612511