Finite Group Databasebeta

← #14674120

Subgroups — #14674120

Order 2816.

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

normal subgroups only

This group has 326 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#13078961C211yesmaximal, characteristic
2#13070281C211yesmaximal, characteristic
3#13066786C214yesmaximal, complemented
4C11×#2126C211yesmaximal, characteristic
5C11×#532C2211yescharacteristic
6#10623001C411yescharacteristic, complemented
7C11×#410—21no—
8#10622853—21no—
9#10622846—21no—
10#10622846—21no—
11#10622695C412yescomplemented
12#10622684C2212yes—
13#10622668—21no—
14#10622668—21no—
15C2×#66867C411yescharacteristic, complemented
16C11×#354—21no—
17C11×#353C2212yes—
18#10622183C2212yes—
19#10622179—21no—
20C2×C11×#41D411yescharacteristic
21C2×C11×#41D411yescharacteristic
22C11×C4⋊Q8C2×C411yescharacteristic
23C11×#127C2311yescharacteristic
24C11×#124D411yescharacteristic
25C11×#124D411yescharacteristic
26C11×#121—41no—
27C4×D4×C11—41no—
28C11×#117—41no—
29C2×C42×C11C2×C411yescharacteristic
30#66979—21no—
31#66979—41no—
32#66977—41no—
33C22×C11⋊C8—21no—
34#66923C2×C412yes—
35#66922—21no—
36C4×Dic22—41no—
37C11×#99—22no—
38C11×#99—41no—
39#66899—22no—
40#66899—22no—
41#66898—22no—
42#66898—41no—
43#66896—22no—
44#66896—22no—
45#66867—21no—
46#66867C2×C412yes—
47#13594—111nomaximal, Sylow
48C11×#41—41no—
49C11×#41—41no—
50C11×#41—41no—
51C11×#41—41no—
52C2×Q8×C11C22⋊C411yescharacteristic
53C2×Q8×C11C22⋊C411yescharacteristic
54C2×D4×C11—21no—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C2×D4×C11C2×D411yescharacteristic
58C2×D4×C11C2×D411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C22⋊C411yescharacteristic
63C2×Dic22—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—81no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—42no—
69C42×C11—21no—
70C42×C11—81no—
71C42×C11C22⋊C411yescharacteristic
72C42×C11C22×C411yescharacteristic
73C22⋊Dic11—42no—
74C22⋊Dic11—41no—
75C4⋊Dic11—22no—
76C4⋊Dic11—41no—
77C4⋊Dic11—81no—
78Dic11⋊C4—42no—
79C4×Dic11—41no—
80C4×Dic11—81no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84#3135—111no—
85#2126—111no—
86#2126D1111yescharacteristic
87#1412—114no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11#9911yescharacteristic
91Q8×C11—41no—
92Q8×C11—41no—
93D4×C11—41no—
94D4×C11—41no—
95D4×C11—81no—
96D4×C11—81no—
97D4×C11—82no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—81no—
109C2×C4×C11—82no—
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×Dic11—42no—
113C2×Dic11—82no—
114Dic22—82no—
115C11⋊C8—42no—
116#533—111no—
117#532C2×D1111yescharacteristic
118#491—112no—
119#490—112no—
120#489—221no—
121#489—221no—
122#416—221no—
123#416—221no—
124#410—21no—
125#410—221no—
126C2×#97—111no—
127#354—21no—
128#354—221no—
129#353—112no—
130#353C2×D1112yes—
131C22×C11—21no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—81no—
136C22×C11—81no—
137C22×C11C2×#9911yescharacteristic
138C4×C11—21no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11—41no—
143C4×C11—162no—
144C4×C11#35411yescharacteristic
145C4×C11#35411yescharacteristic
146Dic11—82no—
147Dic11—162no—
148C2×#41D4411yescharacteristic
149C2×#41C22⋊D1111yescharacteristic
150C22×C8—221no—
151C4⋊Q8—221no—
152C4⋊Q8C4×D1111yescharacteristic
153#127C22×D1111yescharacteristic
154#125—112no—
155#124D4411yescharacteristic
156#124C22⋊D1111yescharacteristic
157C22⋊Q8—441no—
158#121—41no—
159C4×Q8—441no—
160C4×D4—41no—
161#117—41no—
162#117—221no—
163#117—441no—
164C2×C42C4×D1111yescharacteristic
165#103—222no—
166#103—222no—
167#102—222no—
168#102—222no—
169#99—22no—
170#99—41no—
171#99—222no—
172#99—441no—
173#97—112no—
174#97—221no—
175C2×C11—21no—
176C2×C11—41no—
177C2×C11—81no—
178C2×C11—81no—
179C2×C11C2×#35411yescharacteristic
180#41—41no—
181#41—41no—
182#41—41no—
183#41—41no—
184C2×Q8—441no—
185C2×Q8(C2×D11)⋊C411yescharacteristic
186C2×Q8(C2×D11)⋊C411yescharacteristic
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4C2×D4411yescharacteristic
191C2×D4C2×C22⋊D1111yescharacteristic
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4(C2×D11)⋊C411yescharacteristic
196C2×C8—222no—
197C2×C8—441no—
198C2×C8—441no—
199C4⋊C4—41no—
200C4⋊C4—81no—
201C4⋊C4—222no—
202C4⋊C4—442no—
203C4⋊C4—441no—
204C4⋊C4—881no—
205C22⋊C4—41no—
206C22⋊C4—41no—
207C22⋊C4—42no—
208C22⋊C4—441no—
209C22⋊C4—442no—
210C42—21no—
211C42—81no—
212C42—441no—
213C42—881no—
214C42(C2×D11)⋊C411yescharacteristic
215C42C2×C4×D1111yescharacteristic
216C11#1359411yescharacteristic, complemented, Sylow
217C23—21no—
218C23—21no—
219C23#6687011yescharacteristic
220Q8—41no—
221Q8—41no—
222Q8—882no—
223D4—41no—
224D4—41no—
225D4—81no—
226D4—81no—
227D4—82no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—82no—
240C2×C4—442no—
241C2×C4—882no—
242C2×C4#6687011yescharacteristic
243C2×C4C2×(C2×D11)⋊C411yescharacteristic
244C8—442no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—81no—
250C22—81no—
251C22C2×#6687011yescharacteristic
252C4—21no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—41no—
257C4—162no—
258C4—882no—
259C4—1762no—
260C4#1062211111yescharacteristic
261C4#1062211111yescharacteristic
262C2—21no—
263C2—41no—
264C2—81no—
265C2—81no—
266C2C2×#1062211111yescharacteristic
subgroupG/H
centerC4#10622111
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC11×#2126C2
socleC2×C11C2×#354
prime radicalC11×#532C22
cosocleC11×#127C23
hypercenter#2126D11
hypocenterC11#13594
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2126

Complements

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

NH ≅ G/Ntype
3. #13066786C2semidirect
6. #10623001C4semidirect
11. #10622695C4semidirect
15. C2×#66867C4semidirect
216. C11#13594semidirect

Maximal subgroups

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

subgroupindex
#130789612
#130702812
#130667862
C11×#21262
#1359411