Finite Group Databasebeta

← #14655541

Subgroups — #14655541

Order 2816.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079769C211yesmaximal, characteristic, complemented
2#13078990C211yesmaximal, characteristic
3C2×#10622683C211yesmaximal, characteristic
4#13069604C211yesmaximal, characteristic, complemented
5#13067070C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1545C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622828—22no—
14C2×#66896—22no—
15#10622684—22no—
16#10622683—22no—
17#10622683—21no—
18#10622683—21no—
19#10622683—22no—
20C4×#4318C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622463—22no—
23#10622335—22no—
24#10622295—21no—
25#10622294—21no—
26C11×#331—22no—
27#10622192—22no—
28#10622122—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127D412yes—
38C2×C42×C11C2311yescharacteristic
39#66979—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D412yes—
42#66977—21no—
43#66977—21no—
44C2×#4318D412yes—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66896—28no—
61#66896—24no—
62#66896—24no—
63#66882—24no—
64#66880—24no—
65#66867—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10149—111nomaximal, Sylow
70C24×C11—41no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—44no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—82no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—22no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—82no—
90C11×M16—42no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C22⋊Dic11—41no—
98C4⋊Dic11—22no—
99C4⋊Dic11—21no—
100C4⋊Dic11—22no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109#4318—22no—
110#4318—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—42no—
114#3230—111no—
115#3138—111no—
116C2×#486—111no—
117#1997—111no—
118#1545D1111yescharacteristic
119#1493—111no—
120#1278—111no—
121C23×C11—42no—
122C23×C11—82no—
123C23×C11—82no—
124C23×C11—82no—
125C23×C11#12111yescharacteristic
126D4×C11—44no—
127D4×C11—44no—
128D4×C11—82no—
129D4×C11—82no—
130D4×C11—82no—
131D4×C11—81no—
132D4×C11—81no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
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×C4×C11#13512yes—
142C2×C4×C11#13712yes—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—42no—
146C2×Dic11—82no—
147Dic22—42no—
148Dic22—42no—
149Dic22—82no—
150Dic22—82no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155#533—111no—
156C2×C4⋊Q8—111no—
157C2×#127C2×D1111yescharacteristic
158#500—221no—
159#490—222no—
160#487—221no—
161#486—222no—
162#486—221no—
163#486—221no—
164#486—222no—
165#484—222no—
166#477—222no—
167#431C2×D1111yescharacteristic
168#423C2×D1111yescharacteristic
169#418—222no—
170C2×#102—222no—
171C4×M16—111no—
172C2×C4×C8—111no—
173#343—222no—
174#331—22no—
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#45212yes—
187C4×C11#45412yes—
188C4×C11#47212yes—
189C4×C11#49511yescharacteristic
190C4×C11#49711yescharacteristic
191Dic11—81no—
192Dic11—81no—
193Dic11—82no—
194C22×Q8—221no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C2×M16—21no—
199C2×M16—112no—
200C22×C8—221no—
201C4⋊Q8—111no—
202C4⋊Q8—111no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207#127—21no—
208#127—21no—
209#127—21no—
210#127D4412yes—
211#125—221no—
212C22⋊Q8—221no—
213C22⋊Q8—221no—
214C4×Q8—221no—
215C4×Q8—221no—
216#117—221no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—221no—
219C2×C42C22×D1111yescharacteristic
220#107—224no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8C22⋊D1112yes—
224#103—224no—
225#102—228no—
226#102—224no—
227#102—224no—
228C22⋊C8—21no—
229#97—221no—
230C4×C8—21no—
231C4×C8—112no—
232C4×C8—221no—
233C4×C8—221no—
234C2×C11—22no—
235C2×C11—162no—
236C2×C11#200311yescharacteristic
237C2×C11#201511yescharacteristic
238C2×C11#201811yescharacteristic
239C24—41no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—441no—
243C2×Q8—441no—
244C2×Q8—882no—
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—44no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—82no—
255C22×C4—222no—
256C22×C4#433911yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259M16—42no—
260M16—222no—
261M16—222no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—442no—
267C4⋊C4—222no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—222no—
272C4⋊C4—221no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—441no—
278C42—441no—
279C42C2×D4411yescharacteristic
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C11#1014911yescharacteristic, complemented, Sylow
284C23—42no—
285C23—82no—
286C23—82no—
287C23—82no—
288C23#6693711yescharacteristic
289Q8—442no—
290Q8—442no—
291Q8—882no—
292Q8—882no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—81no—
297D4—81no—
298D4—82no—
299D4—82no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—882no—
306C2×C4#6693511yescharacteristic
307C2×C4#6693511yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6696512yes—
310C2×C4#6696812yes—
311C2×C4#6698311yescharacteristic
312C2×C4#6699011yescharacteristic
313C2×C4#6699311yescharacteristic
314C8—42no—
315C8—81no—
316C8—442no—
317C8—442no—
318C22—21no—
319C22—21no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—164no—
324C22#1062238012yes—
325C22#1062257311yescharacteristic
326C4—21no—
327C4—21no—
328C4—881no—
329C4—882no—
330C4—881no—
331C4#1062236212yes—
332C4#1062239612yes—
333C4#1062276811yescharacteristic
334C4#1062278011yescharacteristic
335C4#1062281412yes—
336C2—22no—
337C2—162no—
338C2#1306963911yescharacteristic
339C2#1306971211yescharacteristic
340C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1545C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#1545D11
hypocenterC11#10149
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
1. #13079769C2semidirect
4. #13069604C2semidirect
5. #13067070C2semidirect
6. #13066452C2semidirect
283. C11#10149semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130789902
C2×#106226832
#130696042
#130670702
#130664522
C11×#15452
#1014911