Finite Group Databasebeta

← #14826376

Subgroups — #14826376

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072467C211yesmaximal, characteristic
2#13071711C211yesmaximal, characteristic, complemented
3#13069991C211yesmaximal, characteristic
4#13069952C211yesmaximal, characteristic, complemented
5#13069947C211yesmaximal, characteristic, complemented
6#13069761C211yesmaximal, characteristic
7#13069566C211yesmaximal, characteristic, complemented
8#13069242C211yesmaximal, characteristic
9#13069235C211yesmaximal, characteristic
10#13069199C211yesmaximal, characteristic, complemented
11#13069198C211yesmaximal, characteristic, complemented
12#13069180C211yesmaximal, characteristic, complemented
13#13068876C211yesmaximal, characteristic
14#13068442C211yesmaximal, characteristic
15C11×#1943C211yesmaximal, characteristic, complemented
16C2×#66949—21no—
17C2×#66943C2211yescharacteristic
18C2×#66941C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622602—21no—
29#10622601C2211yescharacteristic
30#10622601C2211yescharacteristic
31C4⋊C4×Dic11—21no—
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622585—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43#10622289—21no—
44#10622286—21no—
45#10622266—21no—
46#10622265—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4D411yescharacteristic
85C2×Dic11⋊C4D411yescharacteristic
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66949—44no—
94#66943—22no—
95#66943—22no—
96#66941—22no—
97#66941—41no—
98C4×D44—22no—
99C4×D44—41no—
100C11×#107—22no—
101C11×#106—41no—
102C11×#97—41no—
103C11×#95—21no—
104C11×#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112#66885—22no—
113#66885Q814yescomplemented
114Dic11⋊C8—41no—
115#66873—22no—
116#66873—41no—
117#66872—22no—
118#66872—22no—
119#27026—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×Q812yes—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—81no—
144C2×Dic22—42no—
145C2×Dic22—42no—
146C2×Dic22—81no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×Q812yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4#4112yes—
163C42×C11—21no—
164C42×C11—21no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—81no—
170C4⋊Dic11—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11C2×Q812yes—
175C4⋊Dic11#4112yes—
176C4⋊Dic11#4112yes—
177Dic11⋊C4—24no—
178Dic11⋊C4—22no—
179Dic11⋊C4—41no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—81no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188C4×Dic11—81no—
189C4×Dic11—81no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196#2452—111no—
197#2370—111no—
198#2065—111no—
199#2059—111no—
200#2058—111no—
201#2025—111no—
202#1988—111no—
203#1943D1111yescharacteristic, complemented
204#1926—111no—
205#1925—111no—
206#1920—111no—
207#1920—111no—
208#1917—111no—
209#1864—111no—
210#1762—111no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
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×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11AGL(1,ℤ/8)12yes—
264D44—22no—
265D44—22no—
266D44—41no—
267D44—41no—
268C4×D11—84no—
269Dic22—84no—
270C8×C11—22no—
271C8×C11—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C2×C4⋊Q8—111no—
275C2×#125—111no—
276C2×C22⋊Q8—221no—
277C2×C4×D4—111no—
278C2×#107C2×D1111yescharacteristic
279C2×#106—111no—
280C2×#106—111no—
281C2×#106C2×D1111yescharacteristic
282C2×C4⋊C8—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#102—111no—
287C2×#97C2×D1111yescharacteristic
288#396—221no—
289#393—221no—
290#390—111no—
291#390—111no—
292#389—111no—
293#389—111no—
294#389—221no—
295#389C2×D1111yescharacteristic
296#389C2×D1111yescharacteristic
297#387—221no—
298#387—221no—
299#385—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—221no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340C2×D1111yescharacteristic
312#340C2×D1111yescharacteristic
313#336—111no—
314#336—111no—
315#336—111no—
316#336—111no—
317C22×C11#52511yescharacteristic
318C22×C11#54611yescharacteristic
319C22×C11D4×Q811yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C11#57511yescharacteristic
322C22×C11#57711yescharacteristic
323C22×C11#57711yescharacteristic
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#53311yescharacteristic
338C4×C11#54211yescharacteristic
339C4×C11#55411yescharacteristic
340C4×C11#55611yescharacteristic
341Dic11—22no—
342Dic11—41no—
343Dic11—41no—
344Dic11—42no—
345Dic11—42no—
346Dic11—42no—
347Dic11—41no—
348C22×Q8—221no—
349C22×D4—111no—
350C23×C4—221no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355C4⋊Q8—222no—
356C4⋊Q8—441no—
357#125—222no—
358#125—222no—
359C22⋊Q8—444no—
360C4×D4—222no—
361C4×D4—441no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42—221no—
388C2×C42C22×D1111yescharacteristic
389#107—22no—
390#106—41no—
391#106—222no—
392#106—222no—
393C4⋊C8—441no—
394#102—114no—
395#102—222no—
396#102—222no—
397#102—441no—
398#97—41no—
399#95—21no—
400#95—21no—
401#95—111no—
402#95—111no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11#246511yescharacteristic
409C2×C11#311511yescharacteristic
410C2×C11#312511yescharacteristic
411C2×C11#331011yescharacteristic
412C2×C11#332611yescharacteristic
413C2×C11#338411yescharacteristic
414C2×C11#338811yescharacteristic
415D11—82no—
416C24—221no—
417C2×Q8—442no—
418C2×Q8—442no—
419C2×Q8—881no—
420C2×D4—112no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—221no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—442no—
438C22×C4—442no—
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—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8Q8×D1112yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—112no—
465C4⋊C4—112no—
466C4⋊C4—112no—
467C4⋊C4—222no—
468C4⋊C4—224no—
469C4⋊C4—224no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—441no—
474C4⋊C4—442no—
475C4⋊C4—442no—
476C4⋊C4—881no—
477C4⋊C4#433912yes—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C22⋊C4—442no—
481C22⋊C4—442no—
482C22⋊C4—881no—
483C42—21no—
484C42—21no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—442no—
490C42—881no—
491C42—881no—
492C11#2702611yescharacteristic, complemented, Sylow
493C23—222no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23C2×D4×D1111yescharacteristic
501Q8—884no—
502D4—222no—
503D4—222no—
504D4—441no—
505D4—441no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—112no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—222no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—222no—
537C2×C4—221no—
538C2×C4—222no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—884no—
546C2×C4C2×#433911yescharacteristic
547C2×C4#6703711yescharacteristic
548C2×C4C2×Q8×D1111yescharacteristic
549C2×C4#6704011yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—22no—
553C8—41no—
554C8—441no—
555C8—441no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22—881no—
563C22#1062307811yescharacteristic
564C22#1062314111yescharacteristic
565C22#1062325811yescharacteristic
566C22D11×AGL(1,ℤ/8)11yescharacteristic
567C22#1062330411yescharacteristic
568C22#1062330911yescharacteristic
569C22#1062330911yescharacteristic
570C4—41no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—222no—
577C4—441no—
578C4—442no—
579C4—441no—
580C4—442no—
581C4—442no—
582C4—441no—
583C4#1062304211yescharacteristic
584C4#1062309911yescharacteristic
585C4#1062317111yescharacteristic
586C4#1062321911yescharacteristic
587C2—882no—
588C2#1307264311yescharacteristic
589C2#1307876311yescharacteristic
590C2#1307889111yescharacteristic
591C2#1308063211yescharacteristic
592C2#1308086411yescharacteristic
593C2#1308151211yescharacteristic
594C2#1308155611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1943C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1943D11
hypocenterC11#27026
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
2. #13071711C2semidirect
4. #13069952C2semidirect
5. #13069947C2semidirect
7. #13069566C2semidirect
10. #13069199C2semidirect
11. #13069198C2semidirect
12. #13069180C2semidirect
15. C11×#1943C2semidirect
113. #66885Q8semidirect
203. #1943D11semidirect
492. C11#27026semidirect

Maximal subgroups

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

subgroupindex
#130724672
#130717112
#130699912
#130699522
#130699472
#130697612
#130695662
#130692422
#130692352
#130691992
#130691982
#130691802
#130688762
#130684422
C11×#19432
#2702611