Finite Group Databasebeta

← #14826374

Subgroups — #14826374

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#13072460C211yesmaximal, characteristic
2#13071711C211yesmaximal, characteristic, complemented
3#13069988C211yesmaximal, characteristic
4#13069953C211yesmaximal, characteristic, complemented
5#13069947C211yesmaximal, characteristic, complemented
6#13069760C211yesmaximal, characteristic
7#13069566C211yesmaximal, characteristic, complemented
8#13069351C211yesmaximal, characteristic, complemented
9#13069246C211yesmaximal, characteristic
10#13069239C211yesmaximal, characteristic
11#13069203C211yesmaximal, characteristic, complemented
12#13069202C211yesmaximal, characteristic, complemented
13#13069178C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic
15C11×#1864C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66977—21no—
18C2×#66943C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#389C2211yescharacteristic
24#10622834C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622823—21no—
29C2×#66881C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622598C2211yescharacteristic
32C4⋊C4×Dic11—21no—
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622585—21no—
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622561—21no—
40#10622560—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622266—21no—
46#10622265—21no—
47C11×#340C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×Dic22—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11—22no—
65C4×D4×C11—41no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82#66977—44no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66943—22no—
97#66943—22no—
98#66941—22no—
99#66941—41no—
100C11×#106—22no—
101C11×#102—22no—
102C11×#102—41no—
103C11×#95—21no—
104#66896—22no—
105#66896Q814yescomplemented
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66881—22no—
115Dic11⋊C8—41no—
116#66872—41no—
117#66871—22no—
118#66867—41no—
119#27026—111nomaximal, Sylow
120C24×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×Q812yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—81no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
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×C11—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4#4112yes—
159C11×C4⋊C4#4112yes—
160C11×C22⋊C4—42no—
161C42×C11—21no—
162C42×C11—21no—
163C22⋊Dic11—42no—
164C22⋊Dic11—42no—
165C22⋊Dic11—42no—
166C22⋊Dic11—81no—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11C2×Q812yes—
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⋊C8C2×Q812yes—
196#2452—111no—
197#2370—111no—
198#2065—111no—
199#2059—111no—
200#2058—111no—
201#2025—111no—
202#1988—111no—
203#1943—111no—
204#1926—111no—
205#1925—111no—
206#1920—111no—
207#1920—111no—
208#1917—111no—
209#1864D1111yescharacteristic
210#1762—111no—
211C23×C11—22no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C22×D411yescharacteristic
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—41no—
222D4×C11—41no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
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×C11—41no—
238C2×C4×C11—84no—
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—21no—
251C2×Dic11—22no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11AGL(1,ℤ/8)12yes—
269Dic22—84no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—22no—
273C11⋊C8—41no—
274C2×C4⋊Q8—111no—
275C2×#125—111no—
276C2×C22⋊Q8—221no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#107—111no—
279C2×#106—111no—
280C2×#106—111no—
281C2×#106C2×D1111yescharacteristic
282C2×C4⋊C8—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102C2×D1111yescharacteristic
286C2×#102C2×D1111yescharacteristic
287C2×#97—111no—
288#396—221no—
289#393—221no—
290#390—111no—
291#390—111no—
292#389—111no—
293#389—111no—
294#389—111no—
295#389—221no—
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#340—111no—
312#340C2×D1111yescharacteristic
313#336—111no—
314#336—111no—
315#336—111no—
316#336C2×D1111yescharacteristic
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11#52511yescharacteristic
325C22×C11#54611yescharacteristic
326C22×C11D4×Q811yescharacteristic
327C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C11#57511yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57711yescharacteristic
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11#53311yescharacteristic
337C4×C11#54211yescharacteristic
338C4×C11#55411yescharacteristic
339C4×C11#55611yescharacteristic
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343Dic11—42no—
344Dic11—42no—
345Dic11—41no—
346Dic11—81no—
347Dic11—81no—
348C22×Q8—221no—
349C22×D4C22×D1111yescharacteristic
350C23×C4—21no—
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—22no—
361C4×D4—41no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—111no—
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⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
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—222no—
390#106—22no—
391#106—222no—
392#106—441no—
393C4⋊C8—441no—
394#102—22no—
395#102—41no—
396#102—114no—
397#102—222no—
398#97—441no—
399#95—21no—
400#95—111no—
401#95—111no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11—82no—
409C2×C11#246511yescharacteristic
410C2×C11#311511yescharacteristic
411C2×C11#312511yescharacteristic
412C2×C11#331011yescharacteristic
413C2×C11#332611yescharacteristic
414C2×C11#338411yescharacteristic
415C2×C11#338811yescharacteristic
416C24—21no—
417C2×Q8—442no—
418C2×Q8—442no—
419C2×Q8—881no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4Q8×D1112yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—81no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
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—112no—
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—42no—
460C4⋊C4—112no—
461C4⋊C4—112no—
462C4⋊C4—222no—
463C4⋊C4—224no—
464C4⋊C4—224no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—441no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4—881no—
476C4⋊C4#433912yes—
477C4⋊C4#434112yes—
478C22⋊C4—42no—
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—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C2×D4×D1111yescharacteristic
501Q8—884no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—84no—
522C2×C4—112no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—222no—
534C2×C4—221no—
535C2×C4—222no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4#6703711yescharacteristic
549C2×C4C2×Q8×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—41no—
553C8—41no—
554C8—222no—
555C8—441no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#1062307811yescharacteristic
564C22#1062312211yescharacteristic
565C22#1062316311yescharacteristic
566C22#1062329311yescharacteristic
567C22#1062330111yescharacteristic
568C22D11×AGL(1,ℤ/8)11yescharacteristic
569C22#1062330411yescharacteristic
570C4—41no—
571C4—41no—
572C4—42no—
573C4—42no—
574C4—81no—
575C4—222no—
576C4—441no—
577C4—441no—
578C4—442no—
579C4—442no—
580C4—441no—
581C4—881no—
582C4—881no—
583C4#1062304211yescharacteristic
584C4#1062307311yescharacteristic
585C4#1062315311yescharacteristic
586C4#1062319311yescharacteristic
587C2—82no—
588C2#1307264111yescharacteristic
589C2#1307876311yescharacteristic
590C2#1307889911yescharacteristic
591C2#1308063011yescharacteristic
592C2#1308086211yescharacteristic
593C2#1308151811yescharacteristic
594C2#1308155411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1864D11
hypocenterC11#27026
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. #13071711C2semidirect
4. #13069953C2semidirect
5. #13069947C2semidirect
7. #13069566C2semidirect
8. #13069351C2semidirect
11. #13069203C2semidirect
12. #13069202C2semidirect
13. #13069178C2semidirect
105. #66896Q8semidirect
492. C11#27026semidirect

Maximal subgroups

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

subgroupindex
#130724602
#130717112
#130699882
#130699532
#130699472
#130697602
#130695662
#130693512
#130692462
#130692392
#130692032
#130692022
#130691782
#130684412
C11×#18642
#2702611