Finite Group Databasebeta

← #14655641

Subgroups — #14655641

Order 2816.

488 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079564C211yesmaximal, characteristic
2#13079162C211yesmaximal, characteristic
3C2×#10622694C211yesmaximal, characteristic
4#13067298C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic
7C11×#1997C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622841—22no—
14C2×#66899—22no—
15#10622734—22no—
16#10622705—21no—
17#10622703—22no—
18#10622694—21no—
19#10622694—22no—
20#10622694—22no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622315—22no—
24#10622295—21no—
25#10622293—21no—
26C11×#343—22no—
27#10622122—22no—
28#10622119—22no—
29C22×Q8×C11D412yes—
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C2×C11×M16D412yes—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4326—24no—
41#66979—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44#66977—21no—
45#66977—21no—
46C22×C11⋊C8—21no—
47#66923—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922D412yes—
52#66922D411yescharacteristic
53#66922D411yescharacteristic
54C4×Dic22—21no—
55C4×Dic22—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×#97—21no—
59C4×C8×C11—21no—
60#66899—28no—
61#66899—24no—
62C22⋊(C11⋊C8)—21no—
63#66882—24no—
64#66881—24no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10163—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—22no—
72C2×Q8×C11—44no—
73C22×C4×C11—22no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—41no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22—22no—
81C2×Dic22—41no—
82C2×Dic22—82no—
83C11×M16—22no—
84C11×M16—42no—
85C11×M16Q1614yescomplemented
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C22⋊Dic11—41no—
97#4326—84no—
98C4⋊Dic11—21no—
99C4⋊Dic11—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—22no—
103C4⋊Dic11—21no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—42no—
112#3209—111no—
113#3165—111no—
114C2×#487—111no—
115#1997D1111yescharacteristic
116#1548—111no—
117#1493—111no—
118#1278—111no—
119C23×C11#12111yescharacteristic
120Q8×C11—44no—
121Q8×C11—44no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—42no—
125C2×C4×C11—82no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12711yescharacteristic
132C2×C4×C11C2×Q1612yes—
133C2×C4×C11#13712yes—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—42no—
137C2×Dic11—82no—
138Dic22—42no—
139Dic22—42no—
140Dic22—82no—
141Dic22—82no—
142C8×C11—24no—
143C8×C11—81no—
144C11⋊C8—42no—
145C11⋊C8—42no—
146#533—111no—
147C2×C4⋊Q8—111no—
148C2×C4⋊Q8C2×D1111yescharacteristic
149#501—222no—
150#500—221no—
151#498—221no—
152#494—221no—
153#487—222no—
154#487—222no—
155#487—221no—
156#462—222no—
157#451—222no—
158#431—111no—
159#428—222no—
160#423C2×D1111yescharacteristic
161C2×#103—222no—
162C4×M16C2×D1111yescharacteristic
163C2×C4×C8—111no—
164#343—22no—
165#333—222no—
166Q8⋊C8—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#39211yescharacteristic
170C22×C11#46212yes—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11#45112yes—
175C4×C11#45512yes—
176C4×C11#47112yes—
177C4×C11#49411yescharacteristic
178C4×C11#49711yescharacteristic
179Dic11—81no—
180Dic11—81no—
181Dic11—82no—
182C22×Q8—221no—
183C22×Q8D4412yes—
184C2×Q16—224no—
185C2×M16—21no—
186C2×M16C22⋊D1112yes—
187C22×C8—221no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—112no—
193C4⋊Q8—111no—
194C4⋊Q8—111no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8—221no—
198#125—221no—
199C22⋊Q8—221no—
200C22⋊Q8—221no—
201C4×Q8—221no—
202C4×Q8—221no—
203#117—221no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C42C22×D1111yescharacteristic
209#107—224no—
210#106—224no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—112no—
214#103—228no—
215#103—224no—
216C22⋊C8—221no—
217#97—21no—
218C4×C8—21no—
219C4×C8—112no—
220C4×C8—221no—
221C4×C8—221no—
222C2×C11—22no—
223C2×C11#200411yescharacteristic
224C2×C11#201611yescharacteristic
225C2×C11#201911yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—44no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—222no—
232C2×Q8—441no—
233C2×Q8—882no—
234C22×C4—22no—
235C22×C4—441no—
236C22×C4C2×D4411yescharacteristic
237C22×C4#433911yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239Q16—884no—
240M16—22no—
241M16—42no—
242M16#432614yescomplemented
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—222no—
246C2×C8—222no—
247C2×C8—442no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—222no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—222no—
257C4⋊C4—221no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—441no—
263C42—441no—
264C42D4×D1111yescharacteristic
265C42D4×D1111yescharacteristic
266C42D4×D1111yescharacteristic
267C42D4×D1111yescharacteristic
268C11#1016311yescharacteristic, complemented, Sylow
269C23#6698311yescharacteristic
270Q8—44no—
271Q8—44no—
272Q8—442no—
273Q8—442no—
274Q8—882no—
275Q8—882no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—82no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—442no—
283C2×C4—882no—
284C2×C4#6693511yescharacteristic
285C2×C4#6693511yescharacteristic
286C2×C4#6693711yescharacteristic
287C2×C4#6693711yescharacteristic
288C2×C4#6699011yescharacteristic
289C2×C4#6699311yescharacteristic
290C2×C4C2×#432612yes—
291C2×C4#6700412yes—
292C8—24no—
293C8—81no—
294C8—442no—
295C8—442no—
296C22—21no—
297C22—21no—
298C22#1062257311yescharacteristic
299C22#1062264412yes—
300C4—21no—
301C4—21no—
302C4—82no—
303C4—881no—
304C4—882no—
305C4—881no—
306C4#1062235912yes—
307C4#1062236712yes—
308C4#1062266312yes—
309C4#1062267311yescharacteristic
310C4#1062270511yescharacteristic
311C2—22no—
312C2#1306964711yescharacteristic
313C2#1306971511yescharacteristic
314C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1997D11
hypocenterC11#10163
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
85. C11×M16Q16semidirect
242. M16#4326semidirect
268. C11#10163semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130791622
C2×#106226942
#130672982
#130670702
#130664542
C11×#19972
#1016311