Finite Group Databasebeta

← #14646785

Subgroups — #14646785

Order 2816.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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#13077546C211yesmaximal, characteristic
2#13067377C211yesmaximal, characteristic
3#13067377C211yesmaximal, characteristic
4#13067253C211yesmaximal, characteristic
5#13067253C211yesmaximal, characteristic
6#13066527C211yesmaximal, characteristic
7C11×#1307C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622735C412yes—
13#10622732C412yes—
14#10622539C2211yescharacteristic
15#10622539C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622444—21no—
18#10622444—21no—
19#10622443—21no—
20#10622443—21no—
21#10622118—21no—
22#10622118—21no—
23#10622117—21no—
24#10622117—21no—
25#10622103—22no—
26#10622103—22no—
27C2×C11×M16C2×C412yes—
28C2×C42×C11C2311yescharacteristic
29#66979C2×C412yes—
30#66977—21no—
31#66977—21no—
32C22×C11⋊C8C2×C411yescharacteristic
33C22×C11⋊C8C2×C411yescharacteristic
34#66923D412yes—
35#66922Q811yescharacteristic
36#66922Q811yescharacteristic
37C4×Dic22—21no—
38C4×Dic22—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C22⋊C8—21no—
44C11×C22⋊C8—21no—
45C11×#97—21no—
46C11×#97—21no—
47C22⋊(C11⋊C8)—21no—
48C22⋊(C11⋊C8)—21no—
49#66879—22no—
50Dic11⋊C8—22no—
51Dic11⋊C8—22no—
52C8×Dic11—22no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55#66867—21no—
56#66867—21no—
57C4×C11⋊C8D411yescharacteristic
58C4×C11⋊C8D411yescharacteristic
59C4×C11⋊C8D411yescharacteristic
60C4×C11⋊C8D411yescharacteristic
61#8635—111nomaximal, Sylow
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11#4111yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C2×Dic22—21no—
66C2×Dic22—21no—
67C11×M16—42no—
68C2×C8×C11—22no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C42×C11C2×D411yescharacteristic
72C42×C11C2×D411yescharacteristic
73C42×C11C2×D411yescharacteristic
74C42×C11C2×Q811yescharacteristic
75C22⋊Dic11—22no—
76C4⋊Dic11—21no—
77C4⋊Dic11—21no—
78C4⋊Dic11C4⋊C412yes—
79C4⋊Dic11C4⋊C412yes—
80Dic11⋊C4—22no—
81Dic11⋊C4—22no—
82C4×Dic11—22no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8C22⋊C411yescharacteristic
88C2×C11⋊C8C22⋊C411yescharacteristic
89C2×C11⋊C8C22⋊C411yescharacteristic
90C2×C11⋊C8C22⋊C411yescharacteristic
91#2960—111no—
92#1568—111no—
93#1568—111no—
94#1537—111no—
95#1537—111no—
96#1307—111no—
97#1307D1111yescharacteristic
98C23×C11#11711yescharacteristic
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11C2×C22⋊C411yescharacteristic
104C2×C4×C11C2×C4⋊C411yescharacteristic
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11#12111yescharacteristic
107C2×C4×C11C22⋊Q811yescharacteristic
108C2×C4×C11C22⋊Q811yescharacteristic
109C2×Dic11—22no—
110C2×Dic11—22no—
111Dic22—42no—
112Dic22—42no—
113C8×C11—42no—
114C8×C11—81no—
115C8×C11—81no—
116C11⋊C8—21no—
117C11⋊C8—21no—
118C11⋊C8—21no—
119C11⋊C8—81no—
120C11⋊C8—81no—
121C11⋊C8#10112yes—
122#533—111no—
123#446—221no—
124#446—221no—
125C8×Q8—221no—
126C8×Q8—221no—
127#432—111no—
128#432—111no—
129#432C2×D1111yescharacteristic
130#432C2×D1111yescharacteristic
131#424—112no—
132#423C2×D1111yescharacteristic
133#405—112no—
134C2×C4×C8—111no—
135#335—221no—
136#335—221no—
137#334—221no—
138#334—221no—
139#330—222no—
140#330—222no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11#38011yescharacteristic
145C4×C11—21no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11C2×#10111yescharacteristic
151C4×C11#41311yescharacteristic
152Dic11—42no—
153Dic11—42no—
154C2×M16C4×D1112yes—
155C22×C8—111no—
156C22×C8—111no—
157C4⋊Q8—111no—
158C4⋊Q8—111no—
159#125—112no—
160C22⋊Q8—221no—
161C22⋊Q8—221no—
162C4×Q8—221no—
163C4×Q8—221no—
164#117—112no—
165C2×C42C22×D1111yescharacteristic
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—222no—
171C4⋊C8—222no—
172C4⋊C8—221no—
173C4⋊C8—221no—
174C22⋊C8—21no—
175C22⋊C8—21no—
176C22⋊C8—221no—
177C22⋊C8—221no—
178#97—21no—
179#97—21no—
180#97—222no—
181#97—221no—
182#97—221no—
183C4×C8—111no—
184C4×C8—111no—
185C4×C8—111no—
186C4×C8—111no—
187C4×C8—222no—
188C2×C11—41no—
189C2×C11#180111yescharacteristic
190C2×C11#181411yescharacteristic
191C2×C11#181411yescharacteristic
192C2×Q8—221no—
193C2×Q8—221no—
194C22×C4C2×C4×D1111yescharacteristic
195C22×C4#433911yescharacteristic
196C22×C4#433911yescharacteristic
197M16—42no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—111no—
202C2×C8—111no—
203C2×C8—111no—
204C2×C8—111no—
205C2×C8—222no—
206C2×C8—441no—
207C2×C8—441no—
208C2×C8—441no—
209C4⋊C4—112no—
210C4⋊C4—112no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C4⋊C4—221no—
214C4⋊C4—221no—
215C22⋊C4—222no—
216C42—222no—
217C42D4×D1111yescharacteristic
218C42D4×D1111yescharacteristic
219C42D4×D1111yescharacteristic
220C42Q8×D1111yescharacteristic
221C11#863511yescharacteristic, complemented, Sylow
222C23#6692511yescharacteristic
223Q8—442no—
224Q8—442no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4C22⋊C4×D1111yescharacteristic
232C2×C4#6693711yescharacteristic
233C2×C4#6693711yescharacteristic
234C2×C4C4⋊C4×D1111yescharacteristic
235C2×C4#6694911yescharacteristic
236C2×C4#6694911yescharacteristic
237C8—42no—
238C8—81no—
239C8—81no—
240C8—112no—
241C8—221no—
242C8—221no—
243C8—221no—
244C8—881no—
245C8—881no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22#1062228011yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—21no—
255C4—442no—
256C4—442no—
257C4#1062235811yescharacteristic
258C4D11×#10111yescharacteristic
259C2—41no—
260C2#1306861111yescharacteristic
261C2#1306866911yescharacteristic
262C2#1306866911yescharacteristic
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1307C2
socleC22×C11#380
prime radicalC23×C11#117
cosocleC2×C42×C11C23
hypercenter#1307D11
hypocenterC11#8635
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
221. C11#8635semidirect

Maximal subgroups

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

subgroupindex
#130775462
#130673772
#130672532
#130665272
C11×#13072
#863511