Finite Group Databasebeta

← #14674135

Subgroups — #14674135

Order 2816.

312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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#13078996C211yesmaximal, characteristic
2C2×#10622186C211yesmaximal, characteristic
3#13066788C214yesmaximal, complemented
4C2×C11×#356C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C2211yescharacteristic
6#10623001C411yescharacteristic
7C2×C11×#101—21no—
8C2×#66900—21no—
9#10622838—21no—
10#10622838—21no—
11#10622695C412yes—
12#10622695C2212yes—
13#10622694—21no—
14#10622694—21no—
15C4×#4318C411yescharacteristic
16C11×#356—21no—
17C11×#356C2212yes—
18#10622186—21no—
19#10622186C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×Q8×C11D411yescharacteristic
22C2×C11×M16—41no—
23C11×C4⋊Q8—41no—
24C11×C4⋊Q8C2×C411yescharacteristic
25C11×C4⋊Q8D411yescharacteristic
26C11×C4⋊Q8D411yescharacteristic
27C11×C4⋊Q8C2311yescharacteristic
28C2×C11×C4⋊C4—41no—
29C2×C42×C11C2×C411yescharacteristic
30#66979—21no—
31#66977—41no—
32C2×#4318—21no—
33C2×#4318—41no—
34#66923C2×C412yes—
35#66922—21no—
36C4×Dic22—41no—
37C11×#101—22no—
38C11×#101—41no—
39#66900—22no—
40#66900—41no—
41#66899—22no—
42#66899—22no—
43#66899—22no—
44#66899—22no—
45#66867C2×C412yes—
46C4×C11⋊C8—21no—
47#13599—111nomaximal, Sylow
48C2×Q8×C11—21no—
49C2×Q8×C11—21no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11C22⋊C411yescharacteristic
55C2×Q8×C11C22⋊C411yescharacteristic
56C2×Q8×C11C2×D411yescharacteristic
57C2×Q8×C11C2×D411yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22⋊C411yescharacteristic
62C2×Dic22—41no—
63C11×M16—42no—
64C11×M16—81no—
65C2×C8×C11—81no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C42×C11—21no—
71C42×C11C22⋊C411yescharacteristic
72C42×C11C22×C411yescharacteristic
73C22⋊Dic11—41no—
74C4⋊Dic11—22no—
75C4⋊Dic11—41no—
76Dic11⋊C4—42no—
77C4×Dic11—41no—
78#4318—41no—
79#4318—41no—
80#4318—42no—
81#4318—81no—
82C2×C11⋊C8—22no—
83C2×C11⋊C8—81no—
84#3139—111no—
85C2×#356—111no—
86C2×#356D1111yescharacteristic
87#1413—114no—
88C23×C11#9911yescharacteristic
89Q8×C11—41no—
90Q8×C11—41no—
91Q8×C11—41no—
92Q8×C11—41no—
93Q8×C11—81no—
94Q8×C11—81no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11#9911yescharacteristic
109C2×C4×C11C2×C22⋊C411yescharacteristic
110C2×Dic11—42no—
111Dic22—82no—
112C8×C11—82no—
113C11⋊C8—42no—
114C11⋊C8—82no—
115#533—111no—
116C2×C4⋊Q8C2×D1111yescharacteristic
117#491—112no—
118#491—112no—
119#487—221no—
120#487—221no—
121#419—221no—
122#419—221no—
123C2×#101—21no—
124C2×#101—221no—
125C4×M16—111no—
126#356—21no—
127#356—112no—
128#356—221no—
129#356C2×D1112yes—
130C22×C11—41no—
131C22×C11#35411yescharacteristic
132C22×C11#35411yescharacteristic
133C22×C11C2×#9911yescharacteristic
134C4×C11—22no—
135C4×C11—21no—
136C4×C11—21no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—41no—
142Dic11—82no—
143C22×Q8D4411yescharacteristic
144C22×Q8C22⋊D1111yescharacteristic
145C2×M16—41no—
146C2×M16—221no—
147C2×M16—441no—
148C4⋊Q8—41no—
149C4⋊Q8—221no—
150C4⋊Q8C4×D1111yescharacteristic
151C4⋊Q8D4411yescharacteristic
152C4⋊Q8C22⋊D1111yescharacteristic
153C4⋊Q8C22×D1111yescharacteristic
154#125—112no—
155C22⋊Q8—441no—
156C4×Q8—441no—
157#117—221no—
158C2×C4⋊C4—41no—
159C2×C42C4×D1111yescharacteristic
160#103—222no—
161#103—222no—
162#103—222no—
163#103—222no—
164#101—22no—
165#101—41no—
166#101—222no—
167#101—441no—
168#97—112no—
169C4×C8—221no—
170C2×C11—21no—
171C2×C11—21no—
172C2×C11—21no—
173C2×C11C2×#35411yescharacteristic
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—441no—
181C2×Q8(C2×D11)⋊C411yescharacteristic
182C2×Q8(C2×D11)⋊C411yescharacteristic
183C2×Q8C2×D4411yescharacteristic
184C2×Q8C2×C22⋊D1111yescharacteristic
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4(C2×D11)⋊C411yescharacteristic
189M16—42no—
190M16—81no—
191M16—441no—
192M16—441no—
193M16—442no—
194M16—881no—
195C2×C8—81no—
196C2×C8—222no—
197C2×C8—881no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—222no—
203C4⋊C4—442no—
204C4⋊C4—441no—
205C22⋊C4—441no—
206C42—21no—
207C42—441no—
208C42(C2×D11)⋊C411yescharacteristic
209C42C2×C4×D1111yescharacteristic
210C11#1359911yescharacteristic, complemented, Sylow
211C23#6687011yescharacteristic
212Q8—41no—
213Q8—41no—
214Q8—41no—
215Q8—41no—
216Q8—81no—
217Q8—81no—
218Q8—882no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—442no—
233C2×C4#6687011yescharacteristic
234C2×C4C2×(C2×D11)⋊C411yescharacteristic
235C8—82no—
236C8—442no—
237C8—882no—
238C22—41no—
239C22#1062211111yescharacteristic
240C22#1062211111yescharacteristic
241C22C2×#6687011yescharacteristic
242C4—22no—
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—882no—
251C2—21no—
252C2—21no—
253C2—21no—
254C2C2×#1062211111yescharacteristic
subgroupG/H
centerC2C2×#10622111
commutatorC42×C11C22×C4
FrattiniC4⋊Q8C22×D11
FittingC2×C11×#356C2
socleC2×C11C2×#354
prime radicalC23×C11#99
cosocleC11×C4⋊Q8C23
hypercenterC2×#356D11
hypocenterC11#13599
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
3. #13066788C2semidirect
210. C11#13599semidirect

Maximal subgroups

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

subgroupindex
#130789962
C2×#106221862
#130667882
C2×C11×#3562
#1359911