Finite Group Databasebeta

← #14655598

Subgroups — #14655598

Order 2816.

476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079163C211yesmaximal, characteristic
2C2×#10622706C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic
7C11×#3230C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#500—21no—
12C11×#487—21no—
13C11×#484—22no—
14C11×#477—22no—
15C11×#431C2211yescharacteristic
16#10622706—22no—
17#10622706—22no—
18#10622692—21no—
19#10622691—21no—
20#10622678—22no—
21#10622608—22no—
22C2×#66874—22no—
23#10622537C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26Q8⋊(C11⋊C8)—22no—
27#10622168—22no—
28#10622120—22no—
29C22×Q8×C11—21no—
30C22×Dic22—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×#4318—21no—
49C2×#4318D412yes—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55C11×#107—24no—
56C11×C4⋊C8D412yes—
57C11×#103—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66874—28no—
61#66872—24no—
62#66871—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10157—111nomaximal, Sylow
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—82no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—41no—
80C2×Dic22—22no—
81C2×Dic22—44no—
82C2×Dic22—41no—
83C2×C8×C11—22no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C4⋊Dic11—22no—
101C4⋊Dic11—22no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104#4318—22no—
105#4318—42no—
106#4318Q1614yes—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—41no—
111#3230D1111yescharacteristic
112#3165—111no—
113C2×#487—111no—
114#1997—111no—
115#1549—111no—
116#1493—111no—
117#1278—111no—
118C23×C11#12111yescharacteristic
119Q8×C11—42no—
120Q8×C11—42no—
121Q8×C11—82no—
122Q8×C11—82no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—82no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12711yescharacteristic
135C2×C4×C11C2×Q1612yes—
136C2×C4×C11#13712yes—
137C2×Dic11—42no—
138C2×Dic11—82no—
139Dic22—44no—
140Dic22—82no—
141C8×C11—42no—
142C11⋊C8—24no—
143C11⋊C8—42no—
144C11⋊C8—81no—
145#533C2×D1111yescharacteristic
146C2×C4⋊Q8—111no—
147C2×C4⋊Q8C2×D1111yescharacteristic
148#501—222no—
149#500—21no—
150#500—221no—
151#498—221no—
152#487—21no—
153#487—222no—
154#487—222no—
155#484—22no—
156#477—22no—
157#431C2×D1111yescharacteristic
158#428—222no—
159#423—111no—
160C2×#103—222no—
161C4×M16—111no—
162C2×C4×C8—111no—
163#343—222no—
164#332—222no—
165Q8⋊C8—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39211yescharacteristic
169C22×C11#46212yes—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—81no—
173C4×C11—82no—
174C4×C11—81no—
175C4×C11#45112yes—
176C4×C11#45412yes—
177C4×C11#47112yes—
178C4×C11#49411yescharacteristic
179C4×C11#49711yescharacteristic
180Dic11—82no—
181C22×Q8—21no—
182C22×Q8—221no—
183C2×M16—112no—
184C2×M16—221no—
185C22×C8—221no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—112no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8C22⋊D1111yescharacteristic
195C4⋊Q8C22⋊D1111yescharacteristic
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C22⋊D1112yes—
206C2×C42C22×D1111yescharacteristic
207#107—24no—
208#107—224no—
209#106—224no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212C4⋊C8C22⋊D1112yes—
213#103—24no—
214#103—228no—
215C22⋊C8—21no—
216#97—221no—
217C4×C8—21no—
218C4×C8—112no—
219C4×C8—221no—
220C4×C8—221no—
221C2×C11—22no—
222C2×C11#200311yescharacteristic
223C2×C11#201611yescharacteristic
224C2×C11#201911yescharacteristic
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—82no—
230C2×Q8—222no—
231C2×Q8—444no—
232C2×Q8—441no—
233C22×C4—22no—
234C22×C4—441no—
235C22×C4D4×D1111yescharacteristic
236C22×C4#434111yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238M16—114no—
239M16—222no—
240M16—442no—
241C2×C8—22no—
242C2×C8—222no—
243C2×C8—222no—
244C2×C8—442no—
245C2×C8—441no—
246C4⋊C4—22no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—222no—
257C4⋊C4—222no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—41no—
261C42—41no—
262C42D4×D1111yescharacteristic
263C42D4×D1111yescharacteristic
264C42C2×C22⋊D1111yescharacteristic
265C42C2×C22⋊D1111yescharacteristic
266C11#1015711yescharacteristic, complemented, Sylow
267C23#6699211yescharacteristic
268Q8—42no—
269Q8—42no—
270Q8—82no—
271Q8—82no—
272Q8—444no—
273Q8—882no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—82no—
280C2×C4—442no—
281C2×C4—882no—
282C2×C4Q16×D1112yes—
283C2×C4#6697112yes—
284C2×C4#6699011yescharacteristic
285C2×C4#6699011yescharacteristic
286C2×C4#6699111yescharacteristic
287C2×C4#6699211yescharacteristic
288C2×C4#6699311yescharacteristic
289C2×C4#6700611yescharacteristic
290C8—42no—
291C8—224no—
292C8—442no—
293C8—881no—
294C22—21no—
295C22—21no—
296C22#1062279512yes—
297C22#1062283611yescharacteristic
298C4—21no—
299C4—21no—
300C4—81no—
301C4—82no—
302C4—81no—
303C4—882no—
304C4#1062279411yescharacteristic
305C4#1062279912yes—
306C4#1062280311yescharacteristic
307C4#1062281312yes—
308C4#1062285812yes—
309C2—22no—
310C2#1306963611yescharacteristic
311C2#1306971411yescharacteristic
312C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3230C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3230D11
hypocenterC11#10157
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
266. C11#10157semidirect

Maximal subgroups

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

subgroupindex
#130791632
C2×#106227062
#130696062
#130673002
#130670712
#130664522
C11×#32302
#1015711