Finite Group Databasebeta

← #14655582

Subgroups — #14655582

Order 2816.

552 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079561C211yesmaximal, characteristic
2C2×#10622705C211yesmaximal, characteristic
3#13069605C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic
7C11×#3165C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C22×#4326—22no—
11C2×#66922C2211yescharacteristic
12C11×#501—22no—
13C11×#500—21no—
14C11×#498—21no—
15C11×#428—22no—
16C4×C11×M16C2211yescharacteristic
17#10622706—21no—
18#10622705—21no—
19#10622705—22no—
20#10622705—22no—
21#10622663—22no—
22#10622644—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622192—22no—
27#10622185—22no—
28Q8⋊(C11⋊C8)—22no—
29C22×Q8×C11—21no—
30C22×Dic22D412yes—
31C2×C11×M16D412yes—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D412yes—
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4326—28no—
48C2×#4326—24no—
49C2×#4326—48no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×#4318—21no—
53C22×C11⋊C8—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58C11×#107—24no—
59C11×#106—24no—
60C11×#97—21no—
61C4×C8×C11—21no—
62C22⋊(C11⋊C8)—21no—
63#66874—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10155—111nomaximal, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—44no—
75C2×Q8×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—22no—
81C2×Dic22—22no—
82C2×Dic22—22no—
83C2×Dic22—44no—
84C11×M16—22no—
85C11×M16Q1614yescomplemented
86C2×C8×C11—22no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103#4326—416no—
104#4326—84no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109#4318—42no—
110C2×C11⋊C8—24no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—41no—
114#3209—111no—
115#3165D1111yescharacteristic
116C2×#494—111no—
117#1997—111no—
118#1549—111no—
119#1493—111no—
120#1278—111no—
121C23×C11#12111yescharacteristic
122Q8×C11—44no—
123Q8×C11—42no—
124Q8×C11—42no—
125Q8×C11—82no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—82no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11C2×Q1612yes—
139C2×C4×C11#13712yes—
140C2×Dic11—42no—
141C2×Dic11—82no—
142Dic22—44no—
143Dic22—44no—
144C8×C11—24no—
145C11⋊C8—24no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148C22×Q16—222no—
149#533C2×D1111yescharacteristic
150C2×C4⋊Q8—111no—
151C2×C4⋊Q8C2×D1111yescharacteristic
152#501—22no—
153#500—21no—
154#498—21no—
155#494—222no—
156#494—222no—
157#494—221no—
158#487—221no—
159#462—222no—
160#451—222no—
161#431—111no—
162#428—22no—
163#423—111no—
164C4×M16C2×D1111yescharacteristic
165C2×C4×C8—111no—
166#343—222no—
167#332—222no—
168Q8⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39211yescharacteristic
172C22×C11#46212yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—82no—
176C4×C11—81no—
177C4×C11—81no—
178C4×C11#45112yes—
179C4×C11#45312yes—
180C4×C11#47312yes—
181C4×C11#49411yescharacteristic
182C4×C11#49711yescharacteristic
183Dic11—82no—
184C22×Q8—21no—
185C22×Q8—112no—
186C2×Q16—228no—
187C2×Q16—224no—
188C2×Q16—448no—
189C2×M16—221no—
190C2×M16C22⋊D1112yes—
191C22×C8—221no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4⋊Q8C22⋊D1112yes—
200C4⋊Q8C22⋊D1111yescharacteristic
201C4⋊Q8C22⋊D1111yescharacteristic
202#125—21no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207#117—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C42C22×D1111yescharacteristic
213#107—24no—
214#106—24no—
215C4⋊C8—112no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218#103—224no—
219C22⋊C8—221no—
220#97—21no—
221C4×C8—21no—
222C4×C8—112no—
223C4×C8—221no—
224C4×C8—221no—
225C2×C11—22no—
226C2×C11#200211yescharacteristic
227C2×C11#201611yescharacteristic
228C2×C11#202011yescharacteristic
229C2×Q8—21no—
230C2×Q8—22no—
231C2×Q8—21no—
232C2×Q8—44no—
233C2×Q8—41no—
234C2×Q8—222no—
235C2×Q8—222no—
236C2×Q8—444no—
237C22×C4—41no—
238C22×C4—222no—
239C22×C4D4×D1111yescharacteristic
240C22×C4#434111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242Q16—4416no—
243Q16—884no—
244M16—22no—
245M16—442no—
246M16#432614yescomplemented
247C2×C8—22no—
248C2×C8—224no—
249C2×C8—222no—
250C2×C8—222no—
251C2×C8—441no—
252C4⋊C4—21no—
253C4⋊C4—22no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C22⋊C4—41no—
267C42—41no—
268C42D4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C42C2×C22⋊D1111yescharacteristic
271C42C2×C22⋊D1111yescharacteristic
272C11#1015511yescharacteristic, complemented, Sylow
273C23#6699111yescharacteristic
274Q8—44no—
275Q8—42no—
276Q8—42no—
277Q8—82no—
278Q8—444no—
279Q8—444no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—82no—
286C2×C4—442no—
287C2×C4—882no—
288C2×C4#6699011yescharacteristic
289C2×C4#6699011yescharacteristic
290C2×C4#6699211yescharacteristic
291C2×C4#6699211yescharacteristic
292C2×C4#6699311yescharacteristic
293C2×C4#6699512yes—
294C2×C4C2×#432612yes—
295C2×C4#6700611yescharacteristic
296C8—24no—
297C8—224no—
298C8—442no—
299C8—881no—
300C22—21no—
301C22—21no—
302C22#1062270312yes—
303C22#1062283611yescharacteristic
304C4—21no—
305C4—21no—
306C4—82no—
307C4—81no—
308C4—81no—
309C4—882no—
310C4#1062269911yescharacteristic
311C4#1062270511yescharacteristic
312C4#1062281112yes—
313C4#1062281712yes—
314C4#1062284112yes—
315C2—22no—
316C2#1306962811yescharacteristic
317C2#1306971611yescharacteristic
318C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3165D11
hypocenterC11#10155
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
85. C11×M16Q16semidirect
246. M16#4326semidirect
272. C11#10155semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106227052
#130696052
#130673012
#130670712
#130664542
C11×#31652
#1015511