Finite Group Databasebeta

← #14658279

Subgroups — #14658279

Order 2816.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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#13076891C211yesmaximal, characteristic
2#13068785C211yesmaximal, characteristic
3#13068784C211yesmaximal, characteristic
4#13068750C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×C11×#97C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66882—21no—
12C2×#66881—21no—
13#10622597—21no—
14#10622597—21no—
15C2×#66872—21no—
16C2×#66871—21no—
17#10622549C2211yescharacteristic
18#10622549C2211yescharacteristic
19#10622548C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622274—21no—
22#10622274—21no—
23#10622270—21no—
24#10622270—21no—
25#10622189—21no—
26#10622189—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C22×C11⋊C8—21no—
46C11×#97—21no—
47C11×#97—21no—
48C11×#97Q812yes—
49C11×#97Q812yes—
50C11×#95—21no—
51C11×#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58#66882—42no—
59#66881—42no—
60#66872—42no—
61#66871—42no—
62#66867—21no—
63#66867Q812yes—
64#10585—111nomaximal, Sylow
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—41no—
75C2×C8×C11—22no—
76C2×C8×C11—22no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11C2×Q811yescharacteristic
84C42×C11C2×Q811yescharacteristic
85C42×C11C2×Q811yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—42no—
96C4⋊Dic11—81no—
97C4⋊Dic11—81no—
98Dic11⋊C4—81no—
99Dic11⋊C4—81no—
100Dic11⋊C4—81no—
101Dic11⋊C4—81no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105#2845—111no—
106#1847—111no—
107#1847—111no—
108#1836—111no—
109#1295—111no—
110#1295—111no—
111#1295D1111yescharacteristic
112C23×C11#12011yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11C22⋊Q811yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C4⋊Q811yescharacteristic
129C2×C4×C11C4⋊Q811yescharacteristic
130C2×C4×C11C4⋊Q811yescharacteristic
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C8×C11—24no—
147C8×C11—42no—
148C11⋊C8—24no—
149C2×#107—221no—
150C2×#107—221no—
151C2×#106—221no—
152C2×#106—221no—
153C2×#97—111no—
154C2×#97C2×D1111yescharacteristic
155C2×#97C2×D1111yescharacteristic
156#398—221no—
157#398—221no—
158#398—221no—
159#398—221no—
160#398—221no—
161#398—221no—
162#384—111no—
163#382—111no—
164#382—111no—
165#382C2×D1111yescharacteristic
166#340—221no—
167#340—221no—
168C22×C11#39511yescharacteristic
169C22×C11#45311yescharacteristic
170C22×C11#45311yescharacteristic
171C22×C11#45411yescharacteristic
172C22×C11#45511yescharacteristic
173C22×C11#45611yescharacteristic
174C22×C11#45611yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—81no—
182C4×C11—81no—
183Dic11—81no—
184Dic11—81no—
185Dic11—81no—
186Dic11—81no—
187Dic11—161no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—221no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4D4411yescharacteristic
205C2×C4⋊C4D4411yescharacteristic
206C2×C42C22×D1111yescharacteristic
207#107—442no—
208#107—442no—
209#106—442no—
210#106—442no—
211#97—21no—
212#97—21no—
213#97—112no—
214#97—221no—
215#97Dic2212yes—
216#97Dic2212yes—
217#95—21no—
218#95—21no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11#165611yescharacteristic
226C2×C11#166111yescharacteristic
227C2×C11#166111yescharacteristic
228C2×C11#166311yescharacteristic
229C2×C11#206011yescharacteristic
230C2×C11#206011yescharacteristic
231C2×C11#206111yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—441no—
239C22×C4C2×D4411yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—222no—
249C2×C8—222no—
250C2×C8—222no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—442no—
262C4⋊C4—881no—
263C4⋊C4—881no—
264C4⋊C4—881no—
265C4⋊C4—881no—
266C4⋊C4—881no—
267C4⋊C4—881no—
268C42C2×Dic2211yescharacteristic
269C42C2×Dic2211yescharacteristic
270C42#434111yescharacteristic
271C42Q8×D1111yescharacteristic
272C11#1058511yescharacteristic, complemented, Sylow
273C23#6693511yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4#6692211yescharacteristic
302C2×C4#6693111yescharacteristic
303C2×C4#6693111yescharacteristic
304C2×C4#6694111yescharacteristic
305C2×C4#6694111yescharacteristic
306C2×C4#6695011yescharacteristic
307C8—24no—
308C8—42no—
309C8—224no—
310C22#1062226911yescharacteristic
311C22#1062236011yescharacteristic
312C22#1062236511yescharacteristic
313C22#1062243511yescharacteristic
314C22#1062243811yescharacteristic
315C22#1062243911yescharacteristic
316C22#1062244011yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—881no—
326C4—881no—
327C4—881no—
328C4—881no—
329C4—1761no—
330C2#1306791011yescharacteristic
331C2#1306793411yescharacteristic
332C2#1306793511yescharacteristic
333C2#1306794611yescharacteristic
334C2#1306996011yescharacteristic
335C2#1306996211yescharacteristic
336C2#1306996511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10585
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
272. C11#10585semidirect

Maximal subgroups

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

subgroupindex
#130768912
#130687852
#130687842
#130687502
#130664982
C11×#12952
#1058511