Finite Group Databasebeta

← #14668973

Subgroups — #14668973

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077332C211yesmaximal, characteristic
2#13070299C211yesmaximal, characteristic
3#13070279C211yesmaximal, characteristic
4#13068416C211yesmaximal, characteristic, complemented
5#13066746C211yesmaximal, characteristic, complemented
6#13066744C211yesmaximal, characteristic, complemented
7C11×#1757C211yesmaximal, characteristic, complemented
8C2×C11×#131C2211yescharacteristic
9#10623363C2211yescharacteristic
10C2×#66954C411yescharacteristic, complemented
11C11×#413C2211yescharacteristic
12C11×#410C2211yescharacteristic
13C11×#405—21no—
14#10622853C2211yescharacteristic
15#10622850C2211yescharacteristic
16#10622847C2211yescharacteristic
17#10622742C411yescharacteristic, complemented
18#10622740—21no—
19#10622740—21no—
20#10622731C411yescharacteristic, complemented
21#10622724—21no—
22#10622724—21no—
23#10622714—21no—
24C2×#66879C411yescharacteristic, complemented
25C11×#344—21no—
26#10622194—21no—
27#10622116C412yescomplemented
28#10622115C412yescomplemented
29#10622112C412yes—
30#10622111C412yes—
31C2×C11×#41C2311yescharacteristic
32C2×#4339C2×C411yescharacteristic
33C11×#131—41no—
34C11×#131—41no—
35C2×C11×M16—21no—
36C2×C11×M16C2×C411yescharacteristic
37C2×C11×M16D411yescharacteristic
38C2×C11×M16D411yescharacteristic
39C22×C8×C11C2×C411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C11×#117—21no—
43#67000C2×C411yescharacteristic
44#66997C2×C411yescharacteristic
45#66993C2×C411yescharacteristic
46#66992—21no—
47#66992—21no—
48#66989C2×C411yescharacteristic
49C4×C22⋊D11—21no—
50C4×C22⋊D11—21no—
51#66979—21no—
52C2×C4×Dic11C2×C411yescharacteristic
53C2×#4318—21no—
54C2×#4318C2×C411yescharacteristic
55C22×C11⋊C8C2×C411yescharacteristic
56#66954—41no—
57#66954—41no—
58C2×#4313—21no—
59C2×C8×D11—21no—
60C11×#101C2×C412yes—
61C11×#100—21no—
62C11×#99—21no—
63C11×#99C2×C412yes—
64C11×#97—41no—
65C4×C8×C11—41no—
66#66900C2×C412yes—
67#66898—21no—
68#66898C2×C412yes—
69#66897—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72(C2×D11)⋊C8—21no—
73(C2×D11)⋊C8—21no—
74#66879—21no—
75#66879—21no—
76#66879—41no—
77Dic11⋊C8—21no—
78Dic11⋊C8—21no—
79C8×Dic11—41no—
80#12634—111nomaximal, Sylow
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11C22×C411yescharacteristic
84C2×D4×C11C22×C411yescharacteristic
85C2×D4×C11#4111yescharacteristic
86C2×D4×C11#4111yescharacteristic
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C2×C22⋊D11—21no—
91C2×C22⋊D11—21no—
92C2×C22⋊D11—21no—
93C22×Dic11—21no—
94#4339—41no—
95#4339—41no—
96C2×D44C4211yescharacteristic
97C2×C4×D11—21no—
98C2×Dic22C4211yescharacteristic
99C11×M16—22no—
100C11×M16—41no—
101C11×M16—41no—
102C11×M16—41no—
103C11×M16—41no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—41no—
111C2×C8×C11C22⋊C411yescharacteristic
112C2×C8×C11C22⋊C411yescharacteristic
113C2×C8×C11C22⋊C411yescharacteristic
114C2×C8×C11C22⋊C411yescharacteristic
115C11×C4⋊C4—41no—
116C11×C22⋊C4—22no—
117C42×C11—41no—
118C22⋊Dic11—21no—
119C22⋊Dic11—21no—
120C22⋊Dic11—22no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—21no—
123C4⋊Dic11—41no—
124Dic11⋊C4—21no—
125Dic11⋊C4—21no—
126C4×Dic11—21no—
127C4×Dic11—41no—
128C4×Dic11C4211yescharacteristic
129C4×Dic11C4211yescharacteristic
130#4318—22no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137#4313—41no—
138#4313—41no—
139C8×D11—42no—
140#2932—111no—
141#2132—111no—
142#2126—111no—
143#1757—111no—
144#1757D1111yescharacteristic, complemented
145#1395—111no—
146#1395—111no—
147C23×C11#11711yescharacteristic
148C23×C11C4×D411yescharacteristic
149C23×C11C4×D411yescharacteristic
150C22×D11—21no—
151Q8×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—41no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—42no—
162C2×C4×C11C2×C4211yescharacteristic
163C2×C4×C11C2×C22⋊C411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C22⋊D11—42no—
167C22⋊D11—81no—
168C22⋊D11—81no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—42no—
173C2×Dic11—81no—
174D44—41no—
175C4×D11—41no—
176C4×D11—41no—
177Dic22—41no—
178C8×C11—21no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11—42no—
182C8×C11#9911yescharacteristic
183C8×C11#9911yescharacteristic
184C11⋊C8—42no—
185C11⋊C8—41no—
186C11⋊C8—41no—
187C2×#131—111no—
188C2×#131C2×D1111yescharacteristic
189#532—111no—
190#435—221no—
191#435—221no—
192#435—221no—
193#435—221no—
194#423—111no—
195#413—111no—
196#413C2×D1111yescharacteristic
197#410—111no—
198#410C2×D1111yescharacteristic
199#408—111no—
200#408—111no—
201#405—21no—
202#405—221no—
203C2×#97—111no—
204#356—112no—
205#355—112no—
206#354—112no—
207#353—112no—
208#344—21no—
209#344—221no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11C4×C22⋊C411yescharacteristic
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—41no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—82no—
224C4×C11C2×#9911yescharacteristic
225C4×C11#41011yescharacteristic
226Dic11—41no—
227Dic11—41no—
228Dic11—41no—
229Dic11—82no—
230C2×#41—111no—
231C2×#41C22×D1111yescharacteristic
232#131—41no—
233#131—41no—
234#131—441no—
235#131—441no—
236C2×M16—21no—
237C2×M16—111no—
238C2×M16—221no—
239C2×M16—221no—
240C2×M16C4×D1111yescharacteristic
241C2×M16D4411yescharacteristic
242C2×M16C22⋊D1111yescharacteristic
243C22×C8—111no—
244C22×C8—221no—
245C22×C8C4×D1111yescharacteristic
246C22×C8D4411yescharacteristic
247C22×C8C22⋊D1111yescharacteristic
248C4⋊Q8—111no—
249#127—111no—
250#124—111no—
251#124—111no—
252#121—221no—
253#121—221no—
254C4×D4—221no—
255C4×D4—221no—
256#117—21no—
257#117—221no—
258C2×C42—111no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261#101—112no—
262#101C4×D1112yes—
263#100—21no—
264#100—221no—
265#99—21no—
266#99—112no—
267#99—221no—
268#99C4×D1112yes—
269C22⋊C8—221no—
270C22⋊C8—221no—
271C22⋊C8—221no—
272C22⋊C8—221no—
273#97—41no—
274#97—221no—
275#97—221no—
276#97—441no—
277C4×C8—41no—
278C4×C8—441no—
279C2×C11—21no—
280C2×C11—41no—
281C2×C11—41no—
282C2×C11—41no—
283C2×C11C4×#9911yescharacteristic
284D11—81no—
285#41—41no—
286#41—41no—
287#41—441no—
288#41—441no—
289C2×Q8—111no—
290C2×Q8C2×C4×D1111yescharacteristic
291C2×D4—111no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—221no—
295C2×D4C2×C4×D1111yescharacteristic
296C2×D4#433911yescharacteristic
297C2×D4#433911yescharacteristic
298C22×C4—221no—
299C22×C4—221no—
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C2×D4411yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303M16—22no—
304M16—41no—
305M16—41no—
306M16—41no—
307M16—41no—
308M16—222no—
309M16—441no—
310M16—441no—
311M16—441no—
312M16—441no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—221no—
321C2×C8—221no—
322C2×C8—442no—
323C2×C8—441no—
324C2×C8—441no—
325C2×C8(C2×D11)⋊C411yescharacteristic
326C2×C8(C2×D11)⋊C411yescharacteristic
327C2×C8(C2×D11)⋊C411yescharacteristic
328C2×C8(C2×D11)⋊C411yescharacteristic
329C4⋊C4—41no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—441no—
333C22⋊C4—22no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C22⋊C4—222no—
339C42—41no—
340C42—111no—
341C42—111no—
342C42—221no—
343C42—441no—
344C11#1263411yescharacteristic, complemented, Sylow
345C23—221no—
346C23#6692511yescharacteristic
347C23C4×D4411yescharacteristic
348C23C4×C22⋊D1111yescharacteristic
349Q8—41no—
350Q8—441no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—441no—
355D4—442no—
356D4—881no—
357D4—881no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—442no—
371C2×C4—881no—
372C2×C4C42×D1111yescharacteristic
373C2×C4C4×D4411yescharacteristic
374C2×C4C2×(C2×D11)⋊C411yescharacteristic
375C2×C4C4×C22⋊D1111yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8—42no—
380C8—442no—
381C8—441no—
382C8—441no—
383C8#6687011yescharacteristic
384C8#6687011yescharacteristic
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22C4×(C2×D11)⋊C411yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—441no—
400C4—441no—
401C4—441no—
402C4—882no—
403C4C2×#6687011yescharacteristic
404C4#1062261911yescharacteristic
405C2—21no—
406C2—41no—
407C2—41no—
408C2—41no—
409C2—881no—
410C2C4×#6687011yescharacteristic
subgroupG/H
centerC4C2×#66870
commutatorC2×C4×C11C2×C42
FrattiniC2×#41C22×D11
FittingC11×#1757C2
socleC2×C11C4×#99
prime radical#10623363C22
cosocleC2×C11×#41C23
hypercenter#1757D11
hypocenterC11#12634
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
4. #13068416C2semidirect
5. #13066746C2semidirect
6. #13066744C2semidirect
7. C11×#1757C2semidirect
10. C2×#66954C4semidirect
17. #10622742C4semidirect
20. #10622731C4semidirect
24. C2×#66879C4semidirect
27. #10622116C4semidirect
28. #10622115C4semidirect
144. #1757D11semidirect
344. C11#12634semidirect

Maximal subgroups

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

subgroupindex
#130773322
#130702992
#130702792
#130684162
#130667462
#130667442
C11×#17572
#1263411