Finite Group Databasebeta

← #14655539

Subgroups — #14655539

Order 2816.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079767C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic
5#13067072C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#486—22no—
12C11×#486—22no—
13C2×C11×#102—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622828—22no—
16#10622706—21no—
17#10622704—22no—
18#10622691—21no—
19#10622684—22no—
20#10622683—21no—
21#10622683—21no—
22#10622583—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622182—22no—
27#10622168—22no—
28#10622094—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127D412yes—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D412yes—
44C2×C42×C11C2311yescharacteristic
45#66979—21no—
46#66977—21no—
47#66977—21no—
48C2×#4318—21no—
49C2×#4318D412yes—
50#66923—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×#102—28no—
56C4×C8×C11—21no—
57C4×C8×C11D412yes—
58#66896—24no—
59#66896—24no—
60C22⋊(C11⋊C8)—21no—
61#66874—24no—
62#66871—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69#10149—111nomaximal, Sylow
70C24×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—82no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—44no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—82no—
84C22×C4×C11—22no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×C8×C11—22no—
91C2×C8×C11—42no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C22⋊Dic11—41no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108#4318—22no—
109#4318—22no—
110#4318—42no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114#3230—111no—
115#3138—111no—
116C2×#486D1111yescharacteristic
117#1997—111no—
118#1545—111no—
119#1493—111no—
120#1278—111no—
121C23×C11—42no—
122C23×C11—82no—
123C23×C11—82no—
124C23×C11—82no—
125C23×C11#12111yescharacteristic
126Q8×C11—82no—
127Q8×C11—82no—
128D4×C11—44no—
129D4×C11—44no—
130D4×C11—82no—
131D4×C11—82no—
132D4×C11—82no—
133D4×C11—81no—
134D4×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11#13512yes—
146C2×C4×C11#13712yes—
147C2×Dic11—41no—
148C2×Dic11—41no—
149Dic22—42no—
150Dic22—42no—
151C8×C11—42no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155#533—111no—
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×#127C2×D1111yescharacteristic
158#500—221no—
159#490—222no—
160#487—221no—
161#486—22no—
162#486—22no—
163#486—221no—
164#486—221no—
165#484—222no—
166#477—222no—
167#431—111no—
168#423—111no—
169#418—222no—
170C2×#102—22no—
171C4×M16—111no—
172C2×C4×C8C2×D1111yescharacteristic
173#343—222no—
174#331—222no—
175Q8⋊C8—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—82no—
179C22×C11—82no—
180C22×C11—82no—
181C22×C11—164no—
182C22×C11#39211yescharacteristic
183C22×C11#46412yes—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—82no—
187C4×C11#45212yes—
188C4×C11#45412yes—
189C4×C11#47212yes—
190C4×C11#49511yescharacteristic
191C4×C11#49711yescharacteristic
192Dic11—81no—
193Dic11—81no—
194C22×Q8—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C2×M16—112no—
199C2×M16—221no—
200C22×C8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—111no—
206C4⋊Q8—111no—
207#127—21no—
208#127—21no—
209#127—21no—
210#127C22⋊D1112yes—
211#125—221no—
212C22⋊Q8—221no—
213C22⋊Q8—221no—
214C4×Q8—221no—
215C4×Q8—221no—
216#117—221no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C22⋊D1112yes—
219C2×C42C22×D1111yescharacteristic
220#107—224no—
221C4⋊C8—112no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224#103—224no—
225#102—28no—
226#102—224no—
227#102—224no—
228C22⋊C8—221no—
229#97—221no—
230C4×C8—21no—
231C4×C8—221no—
232C4×C8—221no—
233C4×C8C22⋊D1112yes—
234C2×C11—22no—
235C2×C11—162no—
236C2×C11#200311yescharacteristic
237C2×C11#201511yescharacteristic
238C2×C11#201811yescharacteristic
239C24—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—82no—
243C2×Q8—221no—
244C2×Q8—221no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—44no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—82no—
255C22×C4—22no—
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259M16—222no—
260M16—222no—
261M16—442no—
262C2×C8—22no—
263C2×C8—42no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—441no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—441no—
278C42—441no—
279C42D4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42C2×C22⋊D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C11#1014911yescharacteristic, complemented, Sylow
284C23—42no—
285C23—82no—
286C23—82no—
287C23—82no—
288C23#6699211yescharacteristic
289Q8—82no—
290Q8—82no—
291Q8—442no—
292Q8—442no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—81no—
298D4—81no—
299D4—82no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—82no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4#6696812yes—
307C2×C4#6696912yes—
308C2×C4#6699011yescharacteristic
309C2×C4#6699011yescharacteristic
310C2×C4#6699111yescharacteristic
311C2×C4#6699211yescharacteristic
312C2×C4#6699311yescharacteristic
313C2×C4#6700611yescharacteristic
314C8—42no—
315C8—442no—
316C8—442no—
317C8—881no—
318C22—21no—
319C22—21no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—164no—
324C22#1062277912yes—
325C22#1062283611yescharacteristic
326C4—21no—
327C4—21no—
328C4—82no—
329C4—881no—
330C4—881no—
331C4#1062267512yes—
332C4#1062277312yes—
333C4#1062278011yescharacteristic
334C4#1062278111yescharacteristic
335C4#1062278612yes—
336C2—22no—
337C2—162no—
338C2#1306963811yescharacteristic
339C2#1306970811yescharacteristic
340C2#1306972311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenterC2×#486D11
hypocenterC11#10149
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13079767C2semidirect
3. #13069606C2semidirect
5. #13067072C2semidirect
6. #13066453C2semidirect
283. C11#10149semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130789902
#130696062
#130672842
#130670722
#130664532
C2×C11×#4862
#1014911