Finite Group Databasebeta

← #14655444

Subgroups — #14655444

Order 2816.

434 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079764C211yesmaximal, characteristic
2C2×#10622682C211yesmaximal, characteristic
3#13067334C211yesmaximal, characteristic
4#13067231C211yesmaximal, characteristic
5#13066972C211yesmaximal, characteristic
6#13066514C211yesmaximal, characteristic
7C11×#3236C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#501—21no—
12C11×#491—21no—
13C11×#484—21no—
14C11×#483—21no—
15C11×#479—22no—
16C11×#432C2211yescharacteristic
17#10622694—21no—
18#10622691—21no—
19#10622682—22no—
20#10622682—22no—
21#10622657—22no—
22#10622634—22no—
23C2×#66874—21no—
24C2×#66874—21no—
25#10622539C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622181—22no—
29#10622166—22no—
30#10622120—22no—
31C22×Dic22—21no—
32C11×C4⋊Q8D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C22×C11⋊C8—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×#107—22no—
57C11×#106—22no—
58C11×C4⋊C8D412yes—
59C11×#103—22no—
60C11×#103—22no—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63#66899—24no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D412yes—
66#66874—24no—
67#66874—24no—
68#66871—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10135—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—41no—
84C2×Dic22—22no—
85C2×Dic22—44no—
86C2×Dic22—41no—
87C2×C8×C11—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C4⋊Dic11—22no—
109C4⋊Dic11—22no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—41no—
116#3236D1111yescharacteristic
117#3230—111no—
118C2×#491—111no—
119#1556—111no—
120#1531—111no—
121#1470—111no—
122#1302—111no—
123C23×C11#12111yescharacteristic
124Q8×C11—42no—
125Q8×C11—42no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—81no—
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×Dic11—42no—
142C2×Dic11—82no—
143Dic22—44no—
144Dic22—82no—
145C8×C11—42no—
146C11⋊C8—42no—
147C11⋊C8—42no—
148C11⋊C8—81no—
149#533C2×D1111yescharacteristic
150C2×C4⋊Q8—111no—
151C2×#125C2×D1111yescharacteristic
152#501—21no—
153#500—221no—
154#491—21no—
155#491—222no—
156#491—222no—
157#487—221no—
158#484—21no—
159#484—222no—
160#483—21no—
161#479—22no—
162#477—222no—
163#432—111no—
164#432C2×D1111yescharacteristic
165#431—111no—
166C2×#103—221no—
167C2×#103—221no—
168C2×#97—111no—
169#332—222no—
170#330—222no—
171#324—222no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#39211yescharacteristic
175C22×C11#47312yes—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—81no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11#45412yes—
186Dic11—82no—
187C22×Q8—221no—
188C22×C8—221no—
189C4⋊Q8—112no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8C22⋊D1111yescharacteristic
194C4⋊Q8C22⋊D1111yescharacteristic
195#125—21no—
196#125—21no—
197#125—21no—
198#125—21no—
199#125—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204#117—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4C22⋊D1111yescharacteristic
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C42C22×D1111yescharacteristic
212#107—22no—
213#107—224no—
214#106—22no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8C22⋊D1112yes—
218#103—22no—
219#103—22no—
220#103—224no—
221#103—224no—
222#103—224no—
223C22⋊C8—21no—
224C22⋊C8—112no—
225C22⋊C8—221no—
226#97—21no—
227#97—112no—
228#97—221no—
229#97—221no—
230C4×C8—221no—
231C2×C11—22no—
232C2×C11#200311yescharacteristic
233C2×C11#200911yescharacteristic
234C2×C11#202011yescharacteristic
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—222no—
238C2×Q8—444no—
239C2×Q8—441no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—441no—
243C22×C4D4×D1111yescharacteristic
244C22×C4#434111yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246C2×C8—22no—
247C2×C8—222no—
248C2×C8—222no—
249C2×C8—442no—
250C2×C8—441no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—222no—
266C4⋊C4—222no—
267C4⋊C4—441no—
268C4⋊C4—441no—
269C22⋊C4—41no—
270C42—41no—
271C42D4×D1111yescharacteristic
272C42D4×D1111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C42C2×C22⋊D1111yescharacteristic
275C11#1013511yescharacteristic, complemented, Sylow
276C23#6699211yescharacteristic
277Q8—42no—
278Q8—42no—
279Q8—444no—
280Q8—882no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—442no—
291C2×C4—882no—
292C2×C4#6699011yescharacteristic
293C2×C4#6699011yescharacteristic
294C2×C4#6699111yescharacteristic
295C2×C4#6699211yescharacteristic
296C2×C4#6699311yescharacteristic
297C2×C4#6700611yescharacteristic
298C8—42no—
299C8—442no—
300C8—442no—
301C8—881no—
302C22—21no—
303C22—21no—
304C22#1062281712yes—
305C22#1062283611yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—882no—
316C4#1062285812yes—
317C2—22no—
318C2#1306963611yescharacteristic
319C2#1306967311yescharacteristic
320C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3236C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3236D11
hypocenterC11#10135
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
275. C11#10135semidirect

Maximal subgroups

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

subgroupindex
#130797642
C2×#106226822
#130673342
#130672312
#130669722
#130665142
C11×#32362
#1013511