Finite Group Databasebeta

← #14667440

Subgroups — #14667440

Order 2816.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#13081190C211yesmaximal, characteristic
2#13070861C211yesmaximal, characteristic, complemented
3#13070663C211yesmaximal, characteristic, complemented
4#13066669C211yesmaximal, characteristic, complemented
5#13066585C211yesmaximal, characteristic, complemented
6#13066574C211yesmaximal, characteristic
7C11×#1689C211yesmaximal, characteristic
8#10623072—21no—
9C11×#494C2211yescharacteristic
10C11×#474—21no—
11C11×#436C2211yescharacteristic
12C2×#66893—21no—
13#10622750—21no—
14#10622734—21no—
15#10622442—21no—
16#10622336—21no—
17#10622335—21no—
18C4×Dic44C2211yescharacteristic
19#10622296C2211yescharacteristic
20C11×#334C2211yescharacteristic
21C11×#332—21no—
22#10622202—21no—
23#10622202—21no—
24#10622202—21no—
25C4⋊(C11⋊C16)C2211yescharacteristic
26#10622099C2211yescharacteristic
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8—21no—
31C4×D4×C11D411yescharacteristic
32#66988—41no—
33#66979—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36#66977—21no—
37C2×Dic44D411yescharacteristic
38#66942—41no—
39#66932—41no—
40#66930—41no—
41#66923—21no—
42C4×Dic22—21no—
43C11×#107—41no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D411yescharacteristic
46C11×#102—41no—
47C11×C22⋊C8—21no—
48C4×C8×C11C2311yescharacteristic
49#66893—42no—
50#66882—21no—
51#66882D411yescharacteristic
52#66882D411yescharacteristic
53#66882D411yescharacteristic
54#66881—21no—
55#66881—21no—
56#66880—21no—
57#66880—21no—
58#66880—21no—
59C2×C11⋊C16—21no—
60C2×C11⋊C16—21no—
61#12351—111nomaximal, Sylow
62C2×Q8×C11—41no—
63C2×D4×C11D811yescharacteristic
64C22×C4×C11—21no—
65C22×Dic11—41no—
66C2×Dic22—21no—
67C11×Q16—42no—
68C11×Q16—41no—
69C11×Q16—41no—
70C11×M16—41no—
71C11×M16—41no—
72C2×C8×C11—21no—
73C2×C8×C11—41no—
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4D811yescharacteristic
79C11×C22⋊C4—21no—
80C42×C11C2×D411yescharacteristic
81C22⋊Dic11—41no—
82C22⋊Dic11—41no—
83C22⋊Dic11—41no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95Dic44—21no—
96Dic44—21no—
97C11⋊C16—41no—
98C11⋊C16—41no—
99#3352—111no—
100#2245—111no—
101#2209—111no—
102#1689D1111yescharacteristic
103#1363—111no—
104#1334—111no—
105#1330—111no—
106C23×C11—21no—
107Q8×C11—81no—
108Q8×C11—81no—
109D4×C11—41no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—81no—
114C2×C4×C11#12011yescharacteristic
115C2×C4×C11C2×D811yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×Dic11—41no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—82no—
122Dic22—41no—
123Dic22—41no—
124C8×C11—21no—
125C8×C11—41no—
126C8×C11—81no—
127C8×C11#13511yescharacteristic
128C8×C11AGL(1,ℤ/8)11yescharacteristic
129#552—221no—
130C2×Q32—221no—
131#499—111no—
132#494C2×D1111yescharacteristic
133#485—221no—
134#484—221no—
135#479—221no—
136#474—21no—
137#470—221no—
138C4×Q16—111no—
139#436C2×D1111yescharacteristic
140#428—221no—
141C4⋊C16—111no—
142#358—221no—
143#358—221no—
144#358—221no—
145#346—111no—
146#334C2×D1111yescharacteristic
147#332—21no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11#44711yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—161no—
156C4×C11#44911yescharacteristic
157C4×C11#45411yescharacteristic
158Dic11—81no—
159Dic11—81no—
160Dic11—81no—
161Dic11—81no—
162C2×Q16—21no—
163C2×Q16—21no—
164C2×Q16—111no—
165C2×M16—21no—
166C4⋊Q8—21no—
167#126—441no—
168#125—221no—
169#125—441no—
170#123—441no—
171C22⋊Q8—221no—
172C22⋊Q8—221no—
173C4×Q8—221no—
174C4×D4C22⋊D1111yescharacteristic
175#117—221no—
176#117—441no—
177C2×C4⋊C4—221no—
178Q32—442no—
179C2×C16—221no—
180C2×C16—221no—
181#107—41no—
182#107—111no—
183#107—111no—
184#107—111no—
185#107—221no—
186#106—221no—
187#106—221no—
188C4⋊C8—21no—
189C4⋊C8C22⋊D1111yescharacteristic
190#103—221no—
191#103—221no—
192#103—221no—
193#102—41no—
194C22⋊C8—21no—
195C4×C8C22×D1111yescharacteristic
196C2×C11—81no—
197C2×C11#162511yescharacteristic
198C2×C11#219111yescharacteristic
199C2×C11#219511yescharacteristic
200C2×Q8—41no—
201C2×Q8—221no—
202C2×D4#432311yescharacteristic
203C22×C4—21no—
204C22×C4—441no—
205Q16—42no—
206Q16—41no—
207Q16—41no—
208Q16—221no—
209Q16—221no—
210M16—41no—
211M16—41no—
212C2×C8—21no—
213C2×C8—41no—
214C2×C8D4×D1111yescharacteristic
215C2×C8D4×D1111yescharacteristic
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—221no—
219C4⋊C4—221no—
220C4⋊C4—221no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4#432311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—441no—
230C22⋊C4—441no—
231C22⋊C4—441no—
232C42—441no—
233C42—441no—
234C42C2×C22⋊D1111yescharacteristic
235C16—441no—
236C16—441no—
237C11#1235111yescharacteristic, complemented, Sylow
238C23—21no—
239Q8—81no—
240Q8—81no—
241Q8—441no—
242Q8—441no—
243D4—41no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—441no—
249C2×C4—441no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—882no—
253C2×C4C2×#432311yescharacteristic
254C2×C4#6699011yescharacteristic
255C2×C4#6700211yescharacteristic
256C8—21no—
257C8—41no—
258C8—81no—
259C8#6696411yescharacteristic
260C8#6696511yescharacteristic
261C22—41no—
262C22—41no—
263C22—41no—
264C22#1062264911yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—161no—
269C4—881no—
270C4—881no—
271C4—881no—
272C4—881no—
273C4#1062277111yescharacteristic
274C4#1062281411yescharacteristic
275C2—81no—
276C2#1306770311yescharacteristic
277C2#1307056611yescharacteristic
278C2#1307059211yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1689C2
socleC22×C11#447
prime radicalC2×D4×C11D8
hypercenter#1689D11
hypocenterC11#12351
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1689

Complements

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

NH ≅ G/Ntype
2. #13070861C2semidirect
3. #13070663C2semidirect
4. #13066669C2semidirect
5. #13066585C2semidirect
237. C11#12351semidirect

Maximal subgroups

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

subgroupindex
#130811902
#130708612
#130706632
#130666692
#130665852
#130665742
C11×#16892
#1235111