Finite Group Databasebeta

← #14738490

Subgroups — #14738490

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C212yesmaximal, complemented
2#13079195C211yesmaximal, characteristic
3#13068144C212yesmaximal, complemented
4#13068100C212yesmaximal, complemented
5#13068032C214yesmaximal, complemented
6#13067372C211yesmaximal, characteristic, complemented
7#13067349C212yesmaximal, 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#10622700—22no—
22#10622696—22no—
23#10622662—24no—
24#10622640C2214yes—
25#10622634C2214yes—
26#10622537C2212yes—
27#10622308C2211yescharacteristic
28#10622307C2212yes—
29C4×D88—21no—
30C4×D88—21no—
31#10622295C2211yescharacteristic
32#10622123C2214yes—
33#10622119C2214yes—
34#10622095C2212yes—
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×#4325—24no—
50#66983—22no—
51#66983—22no—
52C2×#4318—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
70#66899—24no—
71#66885—22no—
72#66885—22no—
73#66882—21no—
74#66882—21no—
75#66873—24no—
76#66871—24no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2314yes—
79#19349—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#4325—84no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117#4318—82no—
118C2×C11⋊C8—24no—
119D88—42no—
120D88—42no—
121#3254—112no—
122#3169—111no—
123#2960D1111yescharacteristic, complemented
124#1696—112no—
125#1688—112no—
126#1678—114no—
127#1566—111no—
128#1560—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—22no—
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—42no—
150D44—42no—
151D44—82no—
152C4×D11—84no—
153Dic22—82no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—42no—
158C8×C11#13712yes—
159C11⋊C8—44no—
160#533C2×D1111yescharacteristic
161#532—112no—
162#500—111no—
163#493—111no—
164#486—112no—
165#477—114no—
166#474—222no—
167#468—224no—
168#466—221no—
169#466—221no—
170#461—222no—
171#460—114no—
172#446—21no—
173#446C2×D1112yes—
174C8×Q8—21no—
175C8×Q8C2×D1112yes—
176C4×D8—221no—
177C4×D8—221no—
178#424—21no—
179#423—112no—
180#423C2×D1111yescharacteristic
181#405—21no—
182C2×C4×C8C2×D1111yescharacteristic
183#334—112no—
184#334—112no—
185#333—114no—
186#331—114no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11C2×#12111yescharacteristic
191C2×D11—82no—
192C2×D11—82no—
193C2×D11—82no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11—42no—
199C4×C11#47212yes—
200C4×C11C2×#13711yescharacteristic
201C4×C11#57511yescharacteristic
202C4×C11#57712yes—
203Dic11—82no—
204C2×#41—222no—
205C2×SD16—224no—
206C2×D8—221no—
207C2×D8—221no—
208C2×M16—21no—
209C2×M16—222no—
210C22×C8C22⋊D1111yescharacteristic
211C22×C8C22⋊D1111yescharacteristic
212C4⋊Q8—112no—
213C4⋊Q8D4411yescharacteristic
214C4⋊Q8D4411yescharacteristic
215#127—112no—
216#125—21no—
217#124—222no—
218C22⋊Q8—21no—
219C22⋊Q8D4412yes—
220#121—222no—
221#121—222no—
222C4×Q8—21no—
223C4×Q8C22×D1112yes—
224C4×D4—222no—
225C4×D4—222no—
226#117—21no—
227C2×C42C22×D1111yescharacteristic
228#107—221no—
229#107—221no—
230#107—224no—
231C4⋊C8—22no—
232C4⋊C8—22no—
233C4⋊C8—21no—
234C4⋊C8—114no—
235C4⋊C8—222no—
236C4⋊C8C22×D1112yes—
237#103—224no—
238#102—222no—
239#102—222no—
240#102—224no—
241#97—22no—
242C4×C8—22no—
243C4×C8C22⋊D1111yescharacteristic
244C4×C8C22⋊D1111yescharacteristic
245C4×C8C22×D1111yescharacteristic
246C4×C8C22×D1111yescharacteristic
247C2×C11—41no—
248C2×C11#303711yescharacteristic
249C2×C11#306011yescharacteristic
250C2×C11C2×#47211yescharacteristic
251D11—162no—
252#41—884no—
253C2×Q8—21no—
254C2×Q8—222no—
255C2×Q8C2×D4412yes—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—222no—
259C2×D4—442no—
260C22×C4—442no—
261C22×C4C2×D4411yescharacteristic
262C22×C4#433911yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264SD16—884no—
265D8—442no—
266D8—442no—
267M16—42no—
268M16—882no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—224no—
273C2×C8C2×C22⋊D1111yescharacteristic
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C2×C8C2×C22⋊D1111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4C2×D4412yes—
285C22⋊C4—22no—
286C22⋊C4—442no—
287C22⋊C4—442no—
288C42—22no—
289C42C2×D4411yescharacteristic
290C42#433911yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C42C23×D1111yescharacteristic
293C11#1934911yescharacteristic, complemented, Sylow
294C23—442no—
295C23#6698311yescharacteristic
296Q8—24no—
297Q8—42no—
298Q8—882no—
299D4—442no—
300D4—442no—
301D4—442no—
302D4—442no—
303D4—882no—
304D4—884no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—442no—
312C2×C4—884no—
313C2×C4#6698311yescharacteristic
314C2×C4#6698311yescharacteristic
315C2×C4#6698311yescharacteristic
316C2×C4C22×D4411yescharacteristic
317C2×C4C2×#433911yescharacteristic
318C2×C4C22×C22⋊D1111yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—42no—
323C8—444no—
324C8#6699512yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22C2×#6698311yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—42no—
336C4—42no—
337C4—882no—
338C4#1062275512yes—
339C4#1062328212yes—
340C4C2×#6699511yescharacteristic
341C4#1062335311yescharacteristic
342C2—41no—
343C2—1762no—
344C2#1307808811yescharacteristic
345C2#1307827811yescharacteristic
346C2C2×#1062275511yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×#121
prime radical#13079195C2
hypercenter#2960D11
hypocenterC11#19349
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. #13079999C2semidirect
3. #13068144C2semidirect
4. #13068100C2semidirect
5. #13068032C2semidirect
6. #13067372C2semidirect
7. #13067349C2semidirect
8. C11×#2960C2semidirect
123. #2960D11semidirect
293. C11#19349semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130791952
#130681442
#130681002
#130680322
#130673722
#130673492
C11×#29602
#1934911