Finite Group Databasebeta

← #14655530

Subgroups — #14655530

Order 2816.

604 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079561C211yesmaximal, characteristic, complemented
2C2×#10622306C211yesmaximal, characteristic
3#13078992C211yesmaximal, characteristic
4#13069604C211yesmaximal, characteristic, complemented
5#13067285C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1493C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C22×#4314—22no—
10C2×#66927C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14#10622706—21no—
15#10622705—21no—
16#10622701—21no—
17#10622701—21no—
18#10622680—22no—
19#10622663—22no—
20#10622644—22no—
21#10622614—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622306—22no—
25#10622306—22no—
26C11×Q8⋊C8—22no—
27#10622192—22no—
28#10622123—22no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×Dic22D412yes—
33C2×C11×M16—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4326—24no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×#4318D412yes—
48C2×#4314—28no—
49C2×#4314—48no—
50#66927—21no—
51#66927—21no—
52#66927—21no—
53#66927D412yes—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62C22⋊(C11⋊C8)—21no—
63#66874—24no—
64#66873—24no—
65#66873—24no—
66C4⋊(C11⋊C8)D412yes—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10147—111nomaximal, Sylow
71C23×D11—41no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—22no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—44no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—42no—
86C2×D44—42no—
87C2×D44—82no—
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—44no—
91C11×M16—42no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107#4326—84no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112#4318—22no—
113#4318—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116#4314—416no—
117#3209—111no—
118C2×#492—111no—
119#3138—111no—
120#1997—111no—
121#1545—111no—
122#1493D1111yescharacteristic, complemented
123#1278—111no—
124C23×C11#12111yescharacteristic
125C22×D11—42no—
126C22×D11—82no—
127C22×D11—82no—
128C22×D11—82no—
129Q8×C11—42no—
130Q8×C11—42no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12711yescharacteristic
141C2×C4×C11#13512yes—
142C2×C4×C11#13712yes—
143C2×Dic11—42no—
144C2×Dic11—82no—
145D44—44no—
146D44—44no—
147D44—82no—
148D44—82no—
149D44—82no—
150D44—81no—
151D44—81no—
152Dic22—44no—
153Dic22—44no—
154C8×C11—24no—
155C8×C11—81no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158C22×SD16—222no—
159#533C2×D1111yescharacteristic
160C2×C4⋊Q8—111no—
161C2×#127—111no—
162#494—221no—
163#492—222no—
164#492—222no—
165#490—222no—
166#487—221no—
167#486—221no—
168#486—221no—
169#462—222no—
170#451—222no—
171#431—111no—
172#423C2×D1111yescharacteristic
173#418—222no—
174C4×M16—111no—
175C2×C4×C8C2×D1111yescharacteristic
176#343—222no—
177#331—222no—
178Q8⋊C8—22no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39211yescharacteristic
182C22×C11#46412yes—
183C2×D11—82no—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—164no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11#45212yes—
192C4×C11#45312yes—
193C4×C11#47112yes—
194C4×C11#49511yescharacteristic
195C4×C11#49711yescharacteristic
196Dic11—82no—
197C22×Q8—112no—
198C22×D4—221no—
199C22×D4—221no—
200C22×D4—221no—
201C2×Q16—224no—
202C2×SD16—228no—
203C2×SD16—448no—
204C2×M16—21no—
205C2×M16—112no—
206C22×C8—21no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8D4411yescharacteristic
212C4⋊Q8D4411yescharacteristic
213#127—112no—
214#127—221no—
215#127—221no—
216#127—221no—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—112no—
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#200211yescharacteristic
240C2×C11#201511yescharacteristic
241C2×C11#201911yescharacteristic
242D11—162no—
243C24—441no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—222no—
247C2×Q8—222no—
248C2×Q8—444no—
249C2×D4—222no—
250C2×D4—222no—
251C2×D4—222no—
252C2×D4—444no—
253C2×D4—441no—
254C2×D4—442no—
255C2×D4—442no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—882no—
259C22×C4—222no—
260C22×C4#433911yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263Q16—884no—
264SD16—4416no—
265M16—42no—
266M16—222no—
267M16—222no—
268C2×C8—24no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—222no—
272C2×C8—222no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—41no—
284C42—41no—
285C42C2×D4411yescharacteristic
286C42D4×D1111yescharacteristic
287C42D4×D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1014711yescharacteristic, complemented, Sylow
290C23—442no—
291C23—882no—
292C23—882no—
293C23—882no—
294C23#6693711yescharacteristic
295Q8—42no—
296Q8—42no—
297Q8—444no—
298Q8—444no—
299D4—444no—
300D4—444no—
301D4—882no—
302D4—882no—
303D4—881no—
304D4—881no—
305D4—882no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—442no—
311C2×C4—882no—
312C2×C4#6693511yescharacteristic
313C2×C4#6693511yescharacteristic
314C2×C4#6693711yescharacteristic
315C2×C4#6696912yes—
316C2×C4#6697112yes—
317C2×C4#6698311yescharacteristic
318C2×C4#6699011yescharacteristic
319C2×C4#6699311yescharacteristic
320C8—24no—
321C8—81no—
322C8—442no—
323C8—442no—
324C22—21no—
325C22—21no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22—1764no—
330C22#1062241112yes—
331C22#1062257311yescharacteristic
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—882no—
337C4#1062242312yes—
338C4#1062243512yes—
339C4#1062275412yes—
340C4#1062278111yescharacteristic
341C4#1062280311yescharacteristic
342C2—22no—
343C2—1762no—
344C2#1306963011yescharacteristic
345C2#1306971111yescharacteristic
346C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1493C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1493D11
hypocenterC11#10147
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
4. #13069604C2semidirect
6. #13066453C2semidirect
7. C11×#1493C2semidirect
122. #1493D11semidirect
289. C11#10147semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106223062
#130789922
#130696042
#130672852
#130664532
C11×#14932
#1014711