Finite Group Databasebeta

← #14655525

Subgroups — #14655525

Order 2816.

604 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079564C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic
5#13067072C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#492C211yesmaximal, characteristic
8C22×C11×SD16—22no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#492—22no—
13C11×#492—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622841—22no—
16#10622828—22no—
17#10622705—21no—
18#10622703—22no—
19#10622694—21no—
20#10622684—22no—
21#10622683—21no—
22#10622683—21no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622182—22no—
27#10622168—22no—
28#10622094—22no—
29C22×Q8×C11D412yes—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C2×C11×SD16—28no—
34C2×C11×SD16—48no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127D412yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4326—24no—
48#66979—21no—
49#66977—21no—
50#66977—21no—
51C2×#4318—21no—
52C2×#4318D412yes—
53#66923—21no—
54#66922D411yescharacteristic
55#66922D411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×C8×C11—21no—
59C4×C8×C11D412yes—
60#66899—24no—
61#66896—24no—
62#66896—24no—
63C22⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10147—111nomaximal, Sylow
71C24×C11—41no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—44no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—44no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—82no—
85C22×C4×C11—22no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×Dic22—21no—
90C2×Dic22—21no—
91C11×SD16—416no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—41no—
103#4326—84no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111#4318—22no—
112#4318—22no—
113#4318—42no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3209—111no—
118C2×#492D1111yescharacteristic
119#3138—111no—
120#1997—111no—
121#1545—111no—
122#1493—111no—
123#1278—111no—
124C23×C11—42no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11—82no—
128C23×C11#12111yescharacteristic
129Q8×C11—44no—
130Q8×C11—44no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11#13512yes—
149C2×C4×C11#13712yes—
150C2×Dic11—41no—
151C2×Dic11—41no—
152Dic22—42no—
153Dic22—42no—
154C8×C11—24no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C22×SD16—22no—
159#533—111no—
160C2×C4⋊Q8C2×D1111yescharacteristic
161C2×#127C2×D1111yescharacteristic
162#494—221no—
163#492—22no—
164#492—22no—
165#490—222no—
166#487—221no—
167#486—221no—
168#486—221no—
169#462—222no—
170#451—222no—
171#431—111no—
172#423—111no—
173#418—222no—
174C4×M16—111no—
175C2×C4×C8C2×D1111yescharacteristic
176#343—222no—
177#331—222no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—164no—
185C22×C11#39211yescharacteristic
186C22×C11#46412yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11#45212yes—
191C4×C11#45312yes—
192C4×C11#47112yes—
193C4×C11#49511yescharacteristic
194C4×C11#49711yescharacteristic
195Dic11—81no—
196Dic11—81no—
197C22×Q8C22⋊D1112yes—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C2×Q16—224no—
202C2×SD16—28no—
203C2×SD16—48no—
204C2×M16—112no—
205C2×M16—221no—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—111no—
212C4⋊Q8—111no—
213#127—21no—
214#127—21no—
215#127—21no—
216#127C22⋊D1112yes—
217#125—221no—
218C22⋊Q8—221no—
219C22⋊Q8—221no—
220C4×Q8—221no—
221C4×Q8—221no—
222#117—221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—112no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229#103—224no—
230#102—224no—
231#102—224no—
232C22⋊C8—221no—
233#97—221no—
234C4×C8—21no—
235C4×C8—221no—
236C4×C8—221no—
237C4×C8C22⋊D1112yes—
238C2×C11—22no—
239C2×C11—162no—
240C2×C11#200211yescharacteristic
241C2×C11#201511yescharacteristic
242C2×C11#201911yescharacteristic
243C24—41no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—44no—
247C2×Q8—221no—
248C2×Q8—221no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—44no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—82no—
259C22×C4—22no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—884no—
264SD16—416no—
265M16—222no—
266M16—222no—
267M16—442no—
268C2×C8—24no—
269C2×C8—22no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—441no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—441no—
284C42—441no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1014711yescharacteristic, complemented, Sylow
290C23—42no—
291C23—82no—
292C23—82no—
293C23—82no—
294C23#6699211yescharacteristic
295Q8—44no—
296Q8—44no—
297Q8—442no—
298Q8—442no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—81no—
303D4—81no—
304D4—82no—
305D4—82no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4#6696812yes—
313C2×C4#6696912yes—
314C2×C4#6699011yescharacteristic
315C2×C4#6699011yescharacteristic
316C2×C4#6699111yescharacteristic
317C2×C4#6699211yescharacteristic
318C2×C4#6699311yescharacteristic
319C2×C4#6700611yescharacteristic
320C8—24no—
321C8—442no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22#1062277912yes—
331C22#1062283611yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—881no—
336C4—881no—
337C4#1062269012yes—
338C4#1062278011yescharacteristic
339C4#1062278111yescharacteristic
340C4#1062278612yes—
341C4#1062279012yes—
342C2—22no—
343C2—162no—
344C2#1306963111yescharacteristic
345C2#1306970811yescharacteristic
346C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#492C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenterC2×#492D11
hypocenterC11#10147
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
3. #13069606C2semidirect
5. #13067072C2semidirect
6. #13066453C2semidirect
289. C11#10147semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130789902
#130696062
#130672842
#130670722
#130664532
C2×C11×#4922
#1014711