Finite Group Databasebeta

← #14655646

Subgroups — #14655646

Order 2816.

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

normal subgroups only

This group has 498 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#13079746C211yesmaximal, characteristic
2C2×#10622691C211yesmaximal, characteristic, complemented
3#13079012C211yesmaximal, characteristic
4#13069604C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1548C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622706—21no—
14#10622702—22no—
15#10622701—21no—
16#10622691—22no—
17#10622691—22no—
18#10622579—22no—
19C2×#66871—22no—
20C4×#4318C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622455—22no—
23#10622348—22no—
24#10622307—21no—
25#10622293—21no—
26C11×#333—22no—
27#10622192—22no—
28#10622121—22no—
29C22×Q8×C11—21no—
30C2×#4339—21no—
31C22×Dic22—21no—
32C2×C11×M16—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40#66983—21no—
41#66983—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11D412yes—
44C2×#4318D412yes—
45C22×C11⋊C8—21no—
46#66928—21no—
47#66927D411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66885—24no—
61#66881—24no—
62#66874—24no—
63#66873—24no—
64#66871—28no—
65#66867—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10164—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—82no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×C22⋊D11—41no—
78C22×Dic11—22no—
79#4339—42no—
80#4339—42no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×C4×D11—41no—
85C2×Dic22—21no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—82no—
89C11×M16—42no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
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
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102C4⋊Dic11—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—21no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108#4318—22no—
109#4318—22no—
110C2×C11⋊C8—24no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113#3227—111no—
114C2×#500—111no—
115#3141—111no—
116#1997—111no—
117#1548D1111yescharacteristic, complemented
118#1492—111no—
119#1278—111no—
120C23×C11#12111yescharacteristic
121C22×D11—41no—
122Q8×C11—82no—
123Q8×C11—82no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—42no—
127C2×C4×C11—82no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12711yescharacteristic
134C2×C4×C11#13512yes—
135C2×C4×C11#13712yes—
136C22⋊D11—82no—
137C2×Dic11—42no—
138C2×Dic11—41no—
139C2×Dic11—82no—
140D44—42no—
141D44—42no—
142D44—42no—
143C4×D11—81no—
144C4×D11—81no—
145Dic22—42no—
146Dic22—82no—
147Dic22—82no—
148C8×C11—42no—
149C8×C11—81no—
150C11⋊C8—24no—
151C11⋊C8—42no—
152#532—111no—
153C2×C4⋊Q8—111no—
154C2×C4⋊Q8C2×D1111yescharacteristic
155#500—222no—
156#500—222no—
157#498—221no—
158#489—222no—
159#487—221no—
160#486—221no—
161#486—221no—
162#481—222no—
163#476—222no—
164#431C2×D1111yescharacteristic
165C2×#107—222no—
166#423C2×D1111yescharacteristic
167#417—222no—
168C4×M16—111no—
169C2×C4×C8—111no—
170#343—222no—
171#333—22no—
172D4⋊C8—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#39211yescharacteristic
176C22×C11#46412yes—
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—82no—
183C4×C11#45212yes—
184C4×C11#45612yes—
185C4×C11#47212yes—
186C4×C11#49511yescharacteristic
187C4×C11#49711yescharacteristic
188Dic11—81no—
189Dic11—82no—
190C2×#41—221no—
191C22×Q8—21no—
192C22×Q8—221no—
193C2×M16—21no—
194C2×M16—112no—
195C22×C8—221no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—111no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8D4412yes—
205#127—111no—
206#124—221no—
207#121—221no—
208#121—221no—
209C4×D4—221no—
210C4×D4—221no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—221no—
215C2×C42C22×D1111yescharacteristic
216#107—228no—
217#106—224no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8C22⋊D1112yes—
221#103—224no—
222#102—224no—
223#102—224no—
224C22⋊C8—21no—
225#97—221no—
226C4×C8—21no—
227C4×C8—112no—
228C4×C8—221no—
229C4×C8—221no—
230C2×C11—22no—
231C2×C11#200511yescharacteristic
232C2×C11#201511yescharacteristic
233C2×C11#201811yescharacteristic
234D11—161no—
235#41—442no—
236#41—442no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—82no—
240C2×Q8—221no—
241C2×Q8—441no—
242C2×Q8—441no—
243C2×Q8—882no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—441no—
248C22×C4—41no—
249C22×C4—222no—
250C22×C4—441no—
251C22×C4#433911yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254M16—42no—
255M16—222no—
256M16—222no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—224no—
260C2×C8—222no—
261C2×C8—222no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—222no—
267C4⋊C4—221no—
268C4⋊C4—222no—
269C4⋊C4—221no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C22⋊C4—441no—
273C22⋊C4—441no—
274C42C2×D4411yescharacteristic
275C42D4×D1111yescharacteristic
276C42D4×D1111yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C11#1016411yescharacteristic, complemented, Sylow
279C23—441no—
280C23#6693711yescharacteristic
281Q8—82no—
282Q8—82no—
283Q8—442no—
284Q8—882no—
285Q8—882no—
286D4—442no—
287D4—442no—
288D4—442no—
289D4—882no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—82no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4—882no—
299C2×C4#6693511yescharacteristic
300C2×C4#6693511yescharacteristic
301C2×C4#6693711yescharacteristic
302C2×C4#6696912yes—
303C2×C4#6697112yes—
304C2×C4#6698311yescharacteristic
305C2×C4#6699011yescharacteristic
306C2×C4#6699311yescharacteristic
307C8—42no—
308C8—81no—
309C8—224no—
310C8—442no—
311C22—21no—
312C22—21no—
313C22—881no—
314C22—881no—
315C22—881no—
316C22#1062241112yes—
317C22#1062257311yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—881no—
322C4—882no—
323C4#1062236212yes—
324C4#1062242312yes—
325C4#1062278111yescharacteristic
326C4#1062280311yescharacteristic
327C4#1062281812yes—
328C2—22no—
329C2—1761no—
330C2#1306965311yescharacteristic
331C2#1306971111yescharacteristic
332C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1548D11
hypocenterC11#10164
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
2. C2×#10622691C2semidirect
4. #13069604C2semidirect
6. #13066452C2semidirect
7. C11×#1548C2semidirect
117. #1548D11semidirect
278. C11#10164semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106226912
#130790122
#130696042
#130670662
#130664522
C11×#15482
#1016411