Finite Group Databasebeta

← #14655302

Subgroups — #14655302

Order 2816.

466 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 89 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
2#13078998C211yesmaximal, characteristic
3#13069604C211yesmaximal, characteristic
4#13067211C211yesmaximal, characteristic
5#13067037C211yesmaximal, characteristic
6#13066505C211yesmaximal, characteristic
7C11×#3255C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#533C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#475—21no—
12C11×#475—21no—
13C11×#470—22no—
14C11×#462—21no—
15C11×#462—21no—
16C11×#423C2211yescharacteristic
17#10622706—21no—
18#10622706—21no—
19#10622706—21no—
20#10622705—21no—
21#10622682—22no—
22#10622663—22no—
23#10622644—22no—
24#10622617—22no—
25#10622538C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622192—22no—
29#10622181—22no—
30Q8⋊(C11⋊C8)—22no—
31C22×Dic22D412yes—
32C2×C11×Q16—22no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C11×#117—21no—
49C11×#117—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—24no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×#4318—21no—
55C2×#4318—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×#103—22no—
64C11×#103—22no—
65C22⋊(C11⋊C8)—21no—
66#66874—24no—
67#66874—24no—
68#66874—24no—
69C4⋊(C11⋊C8)D412yes—
70#66867—21no—
71#66867D412yes—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10115—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—22no—
84C2×Dic22—22no—
85C2×Dic22—22no—
86C2×Dic22—44no—
87C11×Q16—82no—
88C11×M16—42no—
89C2×C8×C11—22no—
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—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#4326—84no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115#4318—22no—
116#4318—41no—
117#4318—42no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121#3255D1111yescharacteristic
122#3209—111no—
123#3139—111no—
124#1997—111no—
125#1526—111no—
126#1485—111no—
127#1299—111no—
128C23×C11#12111yescharacteristic
129Q8×C11—42no—
130Q8×C11—41no—
131Q8×C11—41no—
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—42no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×Dic11—42no—
150C2×Dic11—82no—
151Dic22—44no—
152Dic22—44no—
153C8×C11—42no—
154C11⋊C8—42no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157#533C2×D1111yescharacteristic
158#533C2×D1111yescharacteristic
159C2×C4⋊Q8—111no—
160#494—221no—
161#491—222no—
162#487—221no—
163#487—221no—
164#487—221no—
165#475—21no—
166#475—21no—
167#470—22no—
168#462—21no—
169#462—21no—
170#462—222no—
171#451—222no—
172#431—111no—
173#423C2×D1111yescharacteristic
174#419—222no—
175C4×M16—111no—
176C4×M16—111no—
177#343—222no—
178#330—222no—
179Q8⋊C8—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#39211yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11#45512yes—
192C4×C11#45511yescharacteristic
193C4×C11#45611yescharacteristic
194C4×C11#47312yes—
195Dic11—82no—
196C22×Q8—112no—
197C2×Q16—22no—
198C2×Q16—224no—
199C2×M16—221no—
200C2×M16—221no—
201C2×M16C22⋊D1112yes—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8C22⋊D1111yescharacteristic
207C4⋊Q8C22⋊D1111yescharacteristic
208C4⋊Q8C22⋊D1111yescharacteristic
209C4⋊Q8C22⋊D1111yescharacteristic
210#125—21no—
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220#117—21no—
221#117—21no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42C22×D1111yescharacteristic
225#106—22no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—112no—
229#103—22no—
230#103—22no—
231#103—224no—
232#103—224no—
233#103—224no—
234C22⋊C8—221no—
235#97—112no—
236#97—221no—
237C4×C8—221no—
238C4×C8—221no—
239C4×C8—221no—
240C2×C11—41no—
241C2×C11#200411yescharacteristic
242C2×C11#200711yescharacteristic
243C2×C11#202011yescharacteristic
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—222no—
249C2×Q8—222no—
250C2×Q8—444no—
251C22×C4—222no—
252C22×C4D4×D1111yescharacteristic
253C22×C4#434111yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255Q16—82no—
256Q16—884no—
257M16—42no—
258M16—222no—
259M16—442no—
260M16—441no—
261C2×C8—22no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8—441no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—41no—
284C42—41no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1011511yescharacteristic, complemented, Sylow
290C23#6699111yescharacteristic
291Q8—42no—
292Q8—42no—
293Q8—41no—
294Q8—41no—
295Q8—41no—
296Q8—41no—
297Q8—444no—
298Q8—444no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—442no—
308C2×C4—882no—
309C2×C4#6699011yescharacteristic
310C2×C4#6699011yescharacteristic
311C2×C4#6699211yescharacteristic
312C2×C4#6699211yescharacteristic
313C2×C4#6699311yescharacteristic
314C2×C4#6700611yescharacteristic
315C8—42no—
316C8—442no—
317C8—442no—
318C8—442no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22#1062283611yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—882no—
331C4#1062281512yes—
332C4#1062281712yes—
333C4#1062285511yescharacteristic
334C4#1062285911yescharacteristic
335C2—41no—
336C2#1306964211yescharacteristic
337C2#1306966311yescharacteristic
338C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3255C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3255D11
hypocenterC11#10115
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
289. C11#10115semidirect

Maximal subgroups

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

subgroupindex
#130795612
#130789982
#130696042
#130672112
#130670372
#130665052
C11×#32552
#1011511