Finite Group Databasebeta

← #14655725

Subgroups — #14655725

Order 2816.

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

normal subgroups only

This group has 492 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#13079760C211yesmaximal, characteristic
2C2×#10622691C211yesmaximal, characteristic
3#13078997C211yesmaximal, characteristic
4#13067289C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic
7C11×#1966C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#101—22no—
13C4×C11×M16C2211yescharacteristic
14#10622733—22no—
15#10622707—22no—
16#10622706—21no—
17#10622692—21no—
18#10622691—22no—
19#10622691—22no—
20#10622584—22no—
21C2×#66871—22no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622316—22no—
25#10622294—21no—
26#10622294—21no—
27#10622122—22no—
28#10622120—22no—
29C22×Q8×C11—21no—
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⋊C4D412yes—
39C2×C42×C11C2311yescharacteristic
40#66979—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43#66977—21no—
44#66977—21no—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922D412yes—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#101—44no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C22⋊(C11⋊C8)—21no—
61#66880—24no—
62#66880—24no—
63#66874—24no—
64#66872—24no—
65#66871—28no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10175—111nomaximal, Sylow
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—41no—
80C2×Dic22—21no—
81C2×Dic22—22no—
82C2×Dic22—21no—
83C2×Dic22—41no—
84C2×Dic22—42no—
85C2×Dic22—42no—
86C11×M16—22no—
87C11×M16—22no—
88C11×M16—42no—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C22⋊Dic11—41no—
100C4⋊Dic11—22no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111C2×C11⋊C8—24no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114#3229—111no—
115C2×#500—111no—
116#3139—111no—
117#1966D1111yescharacteristic
118#1546—111no—
119#1493—111no—
120#1278—111no—
121C23×C11#12111yescharacteristic
122Q8×C11—82no—
123Q8×C11—81no—
124Q8×C11—81no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—42no—
128C2×C4×C11—44no—
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×C11#13512yes—
136C2×C4×C11AGL(1,ℤ/8)12yes—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—42no—
140C2×Dic11—82no—
141Dic22—44no—
142Dic22—42no—
143Dic22—42no—
144Dic22—81no—
145Dic22—81no—
146C8×C11—42no—
147C8×C11—81no—
148C11⋊C8—24no—
149C11⋊C8—42no—
150#533—111no—
151C2×C4⋊Q8—111no—
152C2×C4⋊Q8C2×D1111yescharacteristic
153#500—222no—
154#500—222no—
155#498—221no—
156#491—222no—
157#487—221no—
158#487—221no—
159#487—221no—
160#483—222no—
161#475—222no—
162#431—111no—
163C2×#107—222no—
164#423C2×D1111yescharacteristic
165#419—222no—
166C2×#101—22no—
167C4×M16C2×D1111yescharacteristic
168C2×C4×C8—111no—
169#332—222no—
170Q8⋊C8—222no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#39211yescharacteristic
174C22×C11#46312yes—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—82no—
178C4×C11#44912yes—
179C4×C11#45612yes—
180C4×C11#47312yes—
181C4×C11#49511yescharacteristic
182C4×C11#49611yescharacteristic
183Dic11—81no—
184Dic11—82no—
185Dic11—81no—
186C22×Q8—21no—
187C22×Q8—221no—
188C2×M16—21no—
189C2×M16C22⋊D1112yes—
190C22×C8—221no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—112no—
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201#125—221no—
202C22⋊Q8—221no—
203C22⋊Q8—221no—
204C4×Q8—221no—
205C4×Q8—221no—
206#117—221no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4D4412yes—
211C2×C42C22×D1111yescharacteristic
212#107—228no—
213#106—224no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—112no—
217#103—224no—
218#103—224no—
219#103—224no—
220#101—44no—
221C22⋊C8—221no—
222#97—21no—
223C4×C8—21no—
224C4×C8—112no—
225C4×C8—221no—
226C4×C8—221no—
227C2×C11—22no—
228C2×C11#200511yescharacteristic
229C2×C11#201211yescharacteristic
230C2×C11#202011yescharacteristic
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—42no—
235C2×Q8—221no—
236C2×Q8—221no—
237C2×Q8—222no—
238C2×Q8—441no—
239C2×Q8—442no—
240C2×Q8—442no—
241C22×C4—22no—
242C22×C4—441no—
243C22×C4C2×D4411yescharacteristic
244C22×C4#433911yescharacteristic
245C22×C4C2×C22⋊D1111yescharacteristic
246M16—22no—
247M16—22no—
248M16—42no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—224no—
252C2×C8—222no—
253C2×C8—222no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—221no—
259C4⋊C4—222no—
260C4⋊C4—222no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C22⋊C4—441no—
269C42—441no—
270C42D4×D1111yescharacteristic
271C42D4×D1111yescharacteristic
272C42D4×D1111yescharacteristic
273C42D4×D1111yescharacteristic
274C11#1017511yescharacteristic, complemented, Sylow
275C23#6698311yescharacteristic
276Q8—82no—
277Q8—81no—
278Q8—81no—
279Q8—442no—
280Q8—442no—
281Q8—444no—
282Q8—881no—
283Q8—881no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—882no—
292C2×C4#6693511yescharacteristic
293C2×C4#6693511yescharacteristic
294C2×C4#6693711yescharacteristic
295C2×C4#6693711yescharacteristic
296C2×C4#6698512yes—
297C2×C4#6699011yescharacteristic
298C2×C4#6699311yescharacteristic
299C2×C4#6700312yes—
300C8—42no—
301C8—81no—
302C8—224no—
303C8—442no—
304C22—21no—
305C22—21no—
306C22#1062257311yescharacteristic
307C22#1062262912yes—
308C4—21no—
309C4—21no—
310C4—82no—
311C4—881no—
312C4—882no—
313C4—881no—
314C4#1062236512yes—
315C4#1062236812yes—
316C4#1062265012yes—
317C4#1062267211yescharacteristic
318C4#1062268711yescharacteristic
319C2—22no—
320C2#1306965411yescharacteristic
321C2#1306969211yescharacteristic
322C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1966C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1966D11
hypocenterC11#10175
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
274. C11#10175semidirect

Maximal subgroups

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

subgroupindex
#130797602
C2×#106226912
#130789972
#130672892
#130670702
#130664542
C11×#19662
#1017511