Finite Group Databasebeta

← #14655484

Subgroups — #14655484

Order 2816.

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

normal subgroups only

This group has 472 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#13079615C211yesmaximal, characteristic
2C2×#10622702C211yesmaximal, characteristic
3#13067342C211yesmaximal, characteristic, complemented
4#13067231C211yesmaximal, characteristic, complemented
5#13066967C211yesmaximal, characteristic
6#13066516C211yesmaximal, characteristic, complemented
7C11×#3229C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66928C2211yescharacteristic
11C11×#498—21no—
12C11×#487—21no—
13C11×#483—22no—
14C11×#475—22no—
15C11×#431C2211yescharacteristic
16#10622702—21no—
17#10622702—22no—
18#10622702—22no—
19#10622699—21no—
20#10622663—21no—
21#10622659—21no—
22#10622641—22no—
23C2×#66874—21no—
24C2×#66873—21no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622184—22no—
29#10622181—22no—
30#10622106—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×Dic22D411yescharacteristic
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4326—22no—
50C2×#4325—22no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C22×C11⋊C8—21no—
54#66928—21no—
55#66928—21no—
56#66928—21no—
57#66928—21no—
58C11×#106—24no—
59C11×C4⋊C8—21no—
60C11×#103—24no—
61C11×C22⋊C8D412yes—
62C4×C8×C11—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66#66874—22no—
67#66873—24no—
68#66873—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#66867—21no—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75#10141—111nomaximal, Sylow
76C23×D11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—42no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—42no—
93C2×C8×C11—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110#4326—82no—
111#4325—82no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—41no—
120#3229D1111yescharacteristic, complemented
121#3215—111no—
122C2×#489—111no—
123#1558—111no—
124#1531—111no—
125#1469—111no—
126#1302—111no—
127C23×C11#12111yescharacteristic
128C22×D11—41no—
129C22×D11—42no—
130C22×D11—81no—
131C22×D11—81no—
132Q8×C11—42no—
133Q8×C11—42no—
134Q8×C11—82no—
135Q8×C11—82no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
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—41no—
150C2×Dic11—81no—
151D44—42no—
152D44—42no—
153Dic22—42no—
154Dic22—42no—
155C8×C11—42no—
156C11⋊C8—42no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159#533C2×D1111yescharacteristic
160C2×C4⋊Q8C2×D1111yescharacteristic
161C2×#124—111no—
162#498—21no—
163#497—221no—
164#489—222no—
165#489—222no—
166#489—221no—
167#487—21no—
168#483—22no—
169#475—22no—
170#464—222no—
171#451—221no—
172#450—221no—
173#432—111no—
174#432—111no—
175#431C2×D1111yescharacteristic
176C2×#103—221no—
177C2×#102—221no—
178C2×#97—111no—
179#333—222no—
180#330—222no—
181#323—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#39211yescharacteristic
185C22×C11#47112yes—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—162no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—82no—
198C4×C11#45512yes—
199Dic11—81no—
200C22×Q8—21no—
201C22×Q8—111no—
202C22×D4—111no—
203C2×Q16—222no—
204C2×SD16—222no—
205C22×C8—221no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8C22⋊D1112yes—
210C4⋊Q8C22⋊D1111yescharacteristic
211C4⋊Q8C22⋊D1111yescharacteristic
212#125—21no—
213#124—221no—
214#124—221no—
215#124—221no—
216#124—221no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221#117—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C42C22×D1111yescharacteristic
227#106—24no—
228C4⋊C8—21no—
229C4⋊C8—112no—
230C4⋊C8—221no—
231#103—24no—
232#103—224no—
233#103—222no—
234#102—224no—
235#102—222no—
236C22⋊C8—221no—
237C22⋊C8—221no—
238C22⋊C8C22⋊D1112yes—
239#97—112no—
240#97—221no—
241#97—221no—
242#97—221no—
243C4×C8—21no—
244C2×C11—22no—
245C2×C11#200411yescharacteristic
246C2×C11#200911yescharacteristic
247C2×C11#201911yescharacteristic
248D11—161no—
249C24—221no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—21no—
253C2×Q8—41no—
254C2×Q8—82no—
255C2×Q8—221no—
256C2×Q8—221no—
257C2×Q8—442no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—442no—
261C22×C4—41no—
262C22×C4—221no—
263C22×C4D4×D1111yescharacteristic
264C22×C4#434111yescharacteristic
265C22×C4C2×C22⋊D1111yescharacteristic
266Q16—882no—
267SD16—882no—
268C2×C8—22no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—442no—
272C2×C8—441no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C22⋊C4—441no—
288C42—41no—
289C42D4×D1111yescharacteristic
290C42D4×D1111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C42C2×C22⋊D1111yescharacteristic
293C11#1014111yescharacteristic, complemented, Sylow
294C23—441no—
295C23—442no—
296C23—881no—
297C23—881no—
298C23#6699111yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—82no—
302Q8—82no—
303Q8—442no—
304Q8—442no—
305D4—442no—
306D4—442no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—82no—
314C2×C4—441no—
315C2×C4—881no—
316C2×C4#6699011yescharacteristic
317C2×C4#6699011yescharacteristic
318C2×C4#6699211yescharacteristic
319C2×C4#6699211yescharacteristic
320C2×C4#6699311yescharacteristic
321C2×C4#6700611yescharacteristic
322C8—42no—
323C8—442no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22—1762no—
332C22#1062279012yes—
333C22#1062283611yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—82no—
342C4—881no—
343C4#1062281512yes—
344C2—22no—
345C2—1761no—
346C2#1306964211yescharacteristic
347C2#1306967611yescharacteristic
348C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3229C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#3229D11
hypocenterC11#10141
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
3. #13067342C2semidirect
4. #13067231C2semidirect
6. #13066516C2semidirect
7. C11×#3229C2semidirect
120. #3229D11semidirect
293. C11#10141semidirect

Maximal subgroups

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

subgroupindex
#130796152
C2×#106227022
#130673422
#130672312
#130669672
#130665162
C11×#32292
#1014111