Finite Group Databasebeta

← #14909665

Subgroups — #14909665

Order 2816.

730 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079193C211yesmaximal, characteristic, complemented
2D11×#493C211yesmaximal, characteristic, complemented
3#13070865C211yesmaximal, characteristic, complemented
4#13070840C211yesmaximal, characteristic, complemented
5#13070839C211yesmaximal, characteristic, complemented
6#13070649C214yesmaximal, complemented
7#13070526C214yesmaximal, complemented
8#13070413C211yesmaximal, characteristic, complemented
9C11×#2246C211yesmaximal, characteristic, complemented
10C2×D8×D11—21no—
11C2×D8×D11C2212yes—
12#10623247—21no—
13D11×#127—21no—
14C2×C11×D16C2214yescomplemented
15C11×#493C2211yescharacteristic
16C11×#493C2211yescharacteristic, complemented
17#10622770—21no—
18#10622770C2212yes—
19#10622764—21no—
20#10622764C2212yes—
21D8×Dic11—21no—
22D8×Dic11C2212yescomplemented
23C2×#66890C2214yescomplemented
24#10622686—21no—
25#10622683—21no—
26#10622308C2211yescharacteristic
27C4×C8×D11C2211yescharacteristic
28#10622295C2211yescharacteristic, complemented
29C4×C11×C16C2211yescharacteristic, complemented
30#10622200C2214yescomplemented
31#10622147C2214yescomplemented
32(C2×D11)⋊C16C2212yes—
33Dic11⋊C16C2212yescomplemented
34C4×C11⋊C16C2211yescharacteristic, complemented
35C2×#4341—41no—
36C2×D4×D11—22no—
37C2×D4×D11—41no—
38C2×D4×D11—41no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8C2312yes—
42C2×C11×D8C2312yes—
43C11×#127—21no—
44C11×#127—21no—
45#66993—22no—
46#66993—41no—
47#66993—41no—
48#66991—22no—
49#66991—41no—
50#66989—41no—
51D4×Dic11—22no—
52D4×Dic11—41no—
53C2×#4323—22no—
54C2×#4323—22no—
55D8×D11—44no—
56D8×D11—44no—
57C2×D88—21no—
58C2×D88C2312yes—
59C2×C8×D11D411yescharacteristic
60C2×C8×D11C2311yescharacteristic
61#66927—21no—
62C42×D11D411yescharacteristic
63#66922—21no—
64C11×D16—44no—
65C2×C11×C16C2312yes—
66C4×C8×C11C2311yescharacteristic
67#66896—22no—
68#66896—22no—
69#66890—44no—
70#66882—21no—
71#66882C2312yes—
72C8×Dic11D411yescharacteristic
73C8×Dic11C2311yescharacteristic
74C2×C11⋊C16C2312yes—
75C4×C11⋊C8D411yescharacteristic
76#33771—111nomaximal, Sylow
77C23×D11—42no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—42no—
88C22×Dic11—42no—
89#4341—84no—
90D4×D11—44no—
91D4×D11—44no—
92D4×D11—84no—
93D4×D11—84no—
94C2×D44—22no—
95C2×D44—41no—
96C2×D44—41no—
97C2×C4×D11D811yescharacteristic
98C2×C4×D11D811yescharacteristic
99C2×C4×D11C2×D411yescharacteristic
100C2×Dic22—41no—
101C11×D8—24no—
102C11×D8—24no—
103C11×D8—42no—
104C11×D8—42no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110#4323—44no—
111#4323—44no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114C4×Dic11D811yescharacteristic
115C4×Dic11D811yescharacteristic
116C4×Dic11C2×D411yescharacteristic
117C2×C11⋊C8C2×D411yescharacteristic
118C2×C11⋊C8C2×D411yescharacteristic
119D88—24no—
120D88—42no—
121C8×D11—22no—
122C8×D11—22no—
123C11×C16—22no—
124C11⋊C16—22no—
125#3169—111no—
126C2×#493—111no—
127#2246—111no—
128#2246D1111yescharacteristic, complemented
129#2240—111no—
130#2240—111no—
131#2206—114no—
132#2184—114no—
133#2162—111no—
134C23×C11—42no—
135C23×C11—42no—
136C22×D11—42no—
137C22×D11—84no—
138C22×D11—84no—
139C22×D11—84no—
140C22×D11C2×D811yescharacteristic
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—82no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—82no—
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C22⋊D11—84no—
153C22⋊D11—84no—
154C22⋊D11—84no—
155C22⋊D11—84no—
156C2×Dic11—42no—
157C2×Dic11—84no—
158C2×Dic11C2×D811yescharacteristic
159C2×Dic11C2×D811yescharacteristic
160C2×Dic11C2×D811yescharacteristic
161D44—42no—
162D44—42no—
163D44—82no—
164D44—82no—
165C4×D11—21no—
166C4×D11—21no—
167C4×D11—22no—
168C4×D11D1614yescomplemented
169Dic22—82no—
170C8×C11AGL(1,ℤ/8)12yes—
171C8×C11H(5,𝔽2)12yes—
172C11⋊C8—21no—
173C11⋊C8—21no—
174C22×D8—112no—
175C22×D8—221no—
176#532—221no—
177C2×#127—221no—
178C2×D16—114no—
179C2×D16C2×D1114yescomplemented
180#500—111no—
181#493—112no—
182#493—111no—
183#493—221no—
184#493—221no—
185#493C2×D1111yescharacteristic
186#493C2×D1111yescharacteristic, complemented
187#486—221no—
188#466—112no—
189#466—221no—
190C4×D8—112no—
191C4×D8—221no—
192C2×C4×C8—111no—
193C4⋊C16—112no—
194#357—114no—
195#357—114no—
196C22⋊C16—112no—
197C4×C16—111no—
198C4×C16C2×D1111yescharacteristic, complemented
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11—82no—
203C22×C11—82no—
204C22×C11—82no—
205C22×C11C22×D811yescharacteristic
206C2×D11—21no—
207C2×D11—21no—
208C2×D11—82no—
209C2×D11—82no—
210C2×D11—82no—
211C2×D11—168no—
212C2×D11C2×D1612yes—
213C4×C11C2×D1612yes—
214C4×C11#50912yes—
215C4×C11#53511yescharacteristic
216C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
217Dic11—21no—
218Dic11—21no—
219Dic11—82no—
220Dic11C2×D1612yes—
221C2×#41—441no—
222C22×D4—222no—
223C22×D4—441no—
224C22×D4—441no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—112no—
228C2×D8—222no—
229C2×D8—222no—
230C2×D8—221no—
231C2×D8—444no—
232C2×D8—444no—
233C2×D8C22×D1112yes—
234C2×D8C22×D1112yes—
235C22×C8—111no—
236C22×C8—111no—
237C4⋊Q8—221no—
238#127—21no—
239#127—21no—
240#127—222no—
241#127—221no—
242#127—441no—
243#127—441no—
244#124—441no—
245#121—222no—
246#121—441no—
247C4×D4—222no—
248C4×D4—441no—
249C2×C42—111no—
250D16—44no—
251D16—444no—
252C2×C16—112no—
253C2×C16C22×D1112yes—
254#107—112no—
255#107—221no—
256#102—222no—
257#102—222no—
258C4×C8—111no—
259C4×C8—111no—
260C4×C8—111no—
261C4×C8C22×D1111yescharacteristic
262C2×C11—162no—
263C2×C11—162no—
264C2×C11#320511yescharacteristic
265C2×C11C22×D1611yescharacteristic
266C2×C11C2×#50911yescharacteristic
267D11—22no—
268D11—162no—
269C24—442no—
270#41—884no—
271C2×Q8—441no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—222no—
279C2×D4—442no—
280C2×D4—442no—
281C2×D4—442no—
282C2×D4—444no—
283C2×D4—444no—
284C2×D4—442no—
285C2×D4—441no—
286C2×D4—441no—
287C2×D4—884no—
288C2×D4—884no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—111no—
292C22×C4—442no—
293D8—24no—
294D8—24no—
295D8—42no—
296D8—42no—
297D8—224no—
298D8—444no—
299D8—444no—
300D8—442no—
301C2×C8—111no—
302C2×C8—111no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8D4×D1111yescharacteristic
306C2×C8C23×D1111yescharacteristic
307C4⋊C4—222no—
308C4⋊C4—441no—
309C22⋊C4—442no—
310C22⋊C4—442no—
311C42—111no—
312C42—111no—
313C42—111no—
314C42D4×D1111yescharacteristic
315C16—22no—
316C16—222no—
317C11#3377111yescharacteristic, complemented, Sylow
318C23—42no—
319C23—42no—
320C23—111no—
321C23—442no—
322C23—884no—
323C23—884no—
324C23—884no—
325Q8—882no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—82no—
331D4—82no—
332D4—82no—
333D4—82no—
334D4—442no—
335D4—442no—
336D4—884no—
337D4—884no—
338D4—884no—
339D4—884no—
340D4—882no—
341D4—882no—
342C2×C4—111no—
343C2×C4—114no—
344C2×C4—111no—
345C2×C4—111no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—222no—
349C2×C4—442no—
350C2×C4—884no—
351C2×C4D8×D1111yescharacteristic
352C2×C4D8×D1111yescharacteristic
353C2×C4C2×D4×D1111yescharacteristic
354C8—221no—
355C8—221no—
356C8#6696412yes—
357C8#6703712yes—
358C22—82no—
359C22—82no—
360C22—82no—
361C22—82no—
362C22—82no—
363C22—82no—
364C22—112no—
365C22—221no—
366C22—221no—
367C22—882no—
368C22—882no—
369C22—882no—
370C22—1768no—
371C22C2×D8×D1111yescharacteristic
372C4—112no—
373C4—221no—
374C4—221no—
375C4—882no—
376C4D11×D1612yes—
377C4#1062252412yes—
378C4#1062324611yescharacteristic
379C4C2×#6696411yescharacteristic
380C2—162no—
381C2—162no—
382C2—222no—
383C2—1762no—
384C2#1307953011yescharacteristic
385C2C2×D11×D1611yescharacteristic
386C2C2×#1062252411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2246C2
socleC22×C11C22×D8
hypercenter#2246D11
hypocenterC11#33771
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #13079193C2semidirect
2. D11×#493C2semidirect
3. #13070865C2semidirect
4. #13070840C2semidirect
5. #13070839C2semidirect
6. #13070649C2semidirect
7. #13070526C2semidirect
8. #13070413C2semidirect
9. C11×#2246C2semidirect
14. C2×C11×D16C22semidirect
16. C11×#493C22semidirect
22. D8×Dic11C22semidirect
23. C2×#66890C22semidirect
28. #10622295C22semidirect
29. C4×C11×C16C22semidirect
30. #10622200C22semidirect
31. #10622147C22semidirect
33. Dic11⋊C16C22semidirect
34. C4×C11⋊C16C22semidirect
128. #2246D11semidirect
168. C4×D11D16semidirect
179. C2×D16C2×D11semidirect
186. #493C2×D11semidirect
198. C4×C16C2×D11semidirect
317. C11#33771semidirect

Maximal subgroups

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

subgroupindex
#130791932
D11×#4932
#130708652
#130708402
#130708392
#130706492
#130705262
#130704132
C11×#22462
#3377111