Finite Group Databasebeta

← #14738474

Subgroups — #14738474

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079623C212yesmaximal, complemented
2#13079195C211yesmaximal, characteristic
3#13068134C212yesmaximal, complemented
4#13068100C212yesmaximal, complemented
5#13068060C214yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067336C212yesmaximal, complemented
8C11×#2960C211yesmaximal, characteristic, complemented
9C11×#533C2211yescharacteristic
10#10623008C2212yes—
11C11×#446—21no—
12C11×#446C2212yes—
13C8×Q8×C11—21no—
14C8×Q8×C11C2212yes—
15C11×#424—21no—
16C11×#423C2211yescharacteristic
17C11×#405—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622728—21no—
20#10622728—21no—
21#10622702—22no—
22#10622699—22no—
23#10622660—24no—
24#10622644C2214yes—
25#10622640C2214yes—
26#10622539C2212yes—
27#10622308C2211yescharacteristic
28#10622307C2212yes—
29C4×D88—21no—
30C4×D88—21no—
31#10622295C2211yescharacteristic
32#10622124C2214yes—
33#10622123C2214yes—
34#10622096C2212yes—
35#10622095C2212yes—
36C2×#4339—22no—
37C2×C11×M16—21no—
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C11×C4⋊Q8D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8D412yes—
45C4×Q8×C11—21no—
46C4×Q8×C11C2312yes—
47C11×#117—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4326—24no—
50C2×#4325—24no—
51#66983—22no—
52#66983—22no—
53C2×D88—21no—
54C2×D88—21no—
55#66928—22no—
56#66927C2312yes—
57C4×D44—22no—
58C4×D44—22no—
59#66922C2312yes—
60C11×C4⋊C8—22no—
61C11×C4⋊C8—22no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8C2312yes—
64C11×#97—22no—
65C4×C8×C11—22no—
66C4×C8×C11D411yescharacteristic
67C4×C8×C11D411yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C22⋊(C11⋊C8)—22no—
71#66885—22no—
72#66885—22no—
73#66882—21no—
74#66882—21no—
75#66874—24no—
76#66873—24no—
77C4⋊(C11⋊C8)C2314yes—
78#66867—22no—
79#19347—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11C2×D412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—42no—
86#4339—84no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×C4×D11—42no—
91C2×Dic22—22no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4C2×D412yes—
106C11×C22⋊C4—22no—
107C42×C11—22no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11C2411yescharacteristic
112#4326—84no—
113#4325—84no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C2×C11⋊C8—24no—
119D88—42no—
120D88—42no—
121#3216—112no—
122#3169—111no—
123#2960D1111yescharacteristic, complemented
124#1694—112no—
125#1688—112no—
126#1682—114no—
127#1568—111no—
128#1557—112no—
129C23×C11#12111yescharacteristic
130C22×D11—42no—
131Q8×C11—24no—
132Q8×C11—42no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C2×#4111yescharacteristic
145C22⋊D11—84no—
146C2×Dic11—42no—
147D44—42no—
148D44—42no—
149D44—44no—
150D44—82no—
151C4×D11—84no—
152Dic22—44no—
153C8×C11—21no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—42no—
157C8×C11#13712yes—
158C11⋊C8—44no—
159#533C2×D1111yescharacteristic
160#532—112no—
161#500—111no—
162#497—222no—
163#493—111no—
164#489—222no—
165#486—112no—
166#466—221no—
167#466—221no—
168#462—114no—
169#460—114no—
170#452—224no—
171#446—21no—
172#446C2×D1112yes—
173C8×Q8—21no—
174C8×Q8C2×D1112yes—
175C4×D8—221no—
176C4×D8—221no—
177#432—112no—
178#424—21no—
179#423C2×D1111yescharacteristic
180#405—21no—
181C2×C4×C8C2×D1111yescharacteristic
182#335—112no—
183#334—112no—
184#332—114no—
185#331—114no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11C2×#12111yescharacteristic
190C2×D11—82no—
191C2×D11—82no—
192C2×D11—82no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11—42no—
199C4×C11C2×#13711yescharacteristic
200C4×C11#57511yescharacteristic
201C4×C11#57612yes—
202Dic11—82no—
203C2×#41—222no—
204C2×Q16—224no—
205C2×SD16—224no—
206C2×D8—221no—
207C2×D8—221no—
208C2×M16—21no—
209C22×C8C22⋊D1111yescharacteristic
210C22×C8C22⋊D1111yescharacteristic
211C4⋊Q8—112no—
212C4⋊Q8D4411yescharacteristic
213C4⋊Q8D4411yescharacteristic
214#127—112no—
215#125—21no—
216#124—222no—
217C22⋊Q8—21no—
218C22⋊Q8D4412yes—
219#121—222no—
220#121—222no—
221C4×Q8—21no—
222C4×Q8C22×D1112yes—
223C4×D4—222no—
224C4×D4—222no—
225#117—21no—
226C2×C42C22×D1111yescharacteristic
227#107—221no—
228#107—221no—
229C4⋊C8—22no—
230C4⋊C8—22no—
231C4⋊C8—21no—
232C4⋊C8—114no—
233C4⋊C8C22×D1112yes—
234#103—224no—
235#102—222no—
236#102—222no—
237#102—224no—
238C22⋊C8—222no—
239#97—22no—
240#97—222no—
241C4×C8—22no—
242C4×C8C22⋊D1111yescharacteristic
243C4×C8C22⋊D1111yescharacteristic
244C4×C8C22×D1111yescharacteristic
245C4×C8C22×D1111yescharacteristic
246C2×C11—41no—
247C2×C11#303711yescharacteristic
248C2×C11#305811yescharacteristic
249C2×C11#306711yescharacteristic
250D11—162no—
251#41—884no—
252C2×Q8—21no—
253C2×Q8—222no—
254C2×Q8C2×D4412yes—
255C2×D4—222no—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—442no—
259C22×C4—442no—
260C22×C4C2×D4411yescharacteristic
261C22×C4#433911yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—884no—
264SD16—884no—
265D8—442no—
266D8—442no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—224no—
272C2×C8C2×C22⋊D1111yescharacteristic
273C2×C8C2×C22⋊D1111yescharacteristic
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4C2×D4412yes—
284C22⋊C4—22no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C42—22no—
288C42C2×D4411yescharacteristic
289C42#433911yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C42C23×D1111yescharacteristic
292C11#1934711yescharacteristic, complemented, Sylow
293C23—442no—
294C23#6698311yescharacteristic
295Q8—24no—
296Q8—42no—
297Q8—444no—
298D4—444no—
299D4—442no—
300D4—442no—
301D4—882no—
302D4—884no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—442no—
310C2×C4—884no—
311C2×C4#6698311yescharacteristic
312C2×C4#6698311yescharacteristic
313C2×C4#6698311yescharacteristic
314C2×C4C22×D4411yescharacteristic
315C2×C4C2×#433911yescharacteristic
316C2×C4C22×C22⋊D1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8—42no—
321C8—444no—
322C8#6699512yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22C2×#6698311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—882no—
337C4#1062328312yes—
338C4C2×#6699511yescharacteristic
339C4#1062335311yescharacteristic
340C2—41no—
341C2—1762no—
342C2#1307808811yescharacteristic
343C2#1307826411yescharacteristic
344C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×#121
prime radical#13079195C2
hypercenter#2960D11
hypocenterC11#19347
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960

Complements

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

NH ≅ G/Ntype
1. #13079623C2semidirect
3. #13068134C2semidirect
4. #13068100C2semidirect
5. #13068060C2semidirect
6. #13067379C2semidirect
7. #13067336C2semidirect
8. C11×#2960C2semidirect
123. #2960D11semidirect
292. C11#19347semidirect

Maximal subgroups

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

subgroupindex
#130796232
#130791952
#130681342
#130681002
#130680602
#130673792
#130673362
C11×#29602
#1934711