Finite Group Databasebeta

← #14658612

Subgroups — #14658612

Order 2816.

298 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 89 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#13068631C211yesmaximal, characteristic
2#13067392C211yesmaximal, characteristic
3#13067011C211yesmaximal, characteristic
4#13066511C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066476C211yesmaximal, characteristic
7C11×#1801C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×#101—21no—
12C2×#66899—21no—
13#10622549C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622538C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C11×#343—21no—
18Q8⋊(C11⋊C8)—22no—
19#10622167—21no—
20#10622117—22no—
21C22×Q8×C11D411yescharacteristic
22C2×C11×M16—21no—
23C2×C11×M16—21no—
24C4×Q8×C11—21no—
25C4×Q8×C11—21no—
26C4×Q8×C11—21no—
27C4×Q8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C22×C11⋊C8—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×#101—42no—
39#66899—42no—
40C11⋊#95—21no—
41C11⋊#95—21no—
42C22⋊(C11⋊C8)—21no—
43C22⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4×C11⋊C8—21no—
49C4×C11⋊C8D412yes—
50#10639—111nomaximal, Sylow
51C2×Q8×C11—21no—
52C2×Q8×C11—21no—
53C2×Q8×C11—21no—
54C2×Q8×C11—21no—
55C2×Q8×C11—21no—
56C2×Q8×C11D812yes—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C22×Dic11—41no—
63C11×M16—41no—
64C11×M16—41no—
65C11×M16—41no—
66C11×M16—41no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C42×C11—41no—
74C42×C11—41no—
75C42×C11C2×D411yescharacteristic
76C42×C11#4111yescharacteristic
77C42×C11#4111yescharacteristic
78C42×C11#4111yescharacteristic
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86#1805—111no—
87#1801D1111yescharacteristic
88#1571—111no—
89#1479—111no—
90#1301—111no—
91#1286—111no—
92#1286—111no—
93C23×C11#12311yescharacteristic
94Q8×C11—22no—
95Q8×C11—22no—
96Q8×C11—41no—
97Q8×C11—41no—
98C2×C4×C11—22no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—81no—
105C2×C4×C11#12111yescharacteristic
106C2×C4×C11#12311yescharacteristic
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11#12411yescharacteristic
109C2×C4×C11#12611yescharacteristic
110C2×C4×C11#12611yescharacteristic
111C2×C4×C11C2×D811yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11#13711yescharacteristic
114C2×C4×C11#13711yescharacteristic
115C2×Dic11—81no—
116C2×Dic11—81no—
117C2×Dic11—81no—
118C8×C11—81no—
119C8×C11—81no—
120C11⋊C8—42no—
121C11⋊C8—81no—
122C11⋊C8—81no—
123C2×C4×Q8C2×D1111yescharacteristic
124#431—111no—
125#431—111no—
126#423C2×D1111yescharacteristic
127#423C2×D1111yescharacteristic
128C2×C4⋊C8—111no—
129C2×#103—221no—
130C2×#101—21no—
131#382—111no—
132#343—21no—
133#340—221no—
134#335—222no—
135Q8⋊C8—222no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11#39711yescharacteristic
139C22×C11#48011yescharacteristic
140C22×C11#48511yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—42no—
146C4×C11—81no—
147C4×C11#46611yescharacteristic
148C4×C11#47011yescharacteristic
149C4×C11#48011yescharacteristic
150C4×C11#48511yescharacteristic
151Dic11—161no—
152C22×Q8C22⋊D1111yescharacteristic
153C2×M16—21no—
154C2×M16—21no—
155C22×C8—221no—
156C4×Q8—21no—
157C4×Q8—21no—
158C4×Q8—21no—
159C4×Q8—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4C22⋊D1111yescharacteristic
163C2×C42—21no—
164C2×C42C22×D1111yescharacteristic
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—21no—
169C4⋊C8—221no—
170C4⋊C8—221no—
171C4⋊C8—221no—
172C4⋊C8—221no—
173#103—442no—
174#101—42no—
175C22⋊C8—221no—
176C22⋊C8—221no—
177C4×C8—112no—
178C4×C8—221no—
179#95—221no—
180#95—221no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11#207511yescharacteristic
184C2×C11#208011yescharacteristic
185C2×C11#208211yescharacteristic
186C2×Q8—21no—
187C2×Q8—21no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8#432312yes—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—441no—
195C22×C4#433911yescharacteristic
196C22×C4#433911yescharacteristic
197C22×C4C2×C22⋊D1111yescharacteristic
198M16—41no—
199M16—41no—
200M16—41no—
201M16—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—222no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—441no—
208C2×C8—441no—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C42—41no—
216C42—41no—
217C42D4×D1111yescharacteristic
218C42#434111yescharacteristic
219C42#434111yescharacteristic
220C42#434111yescharacteristic
221C11#1063911yescharacteristic, complemented, Sylow
222C23#6698211yescharacteristic
223Q8—22no—
224Q8—22no—
225Q8—41no—
226Q8—41no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—81no—
234C2×C4—881no—
235C2×C4—881no—
236C2×C4—881no—
237C2×C4#6693211yescharacteristic
238C2×C4#6693211yescharacteristic
239C2×C4#6693611yescharacteristic
240C2×C4#6693811yescharacteristic
241C2×C4C2×#432311yescharacteristic
242C2×C4#6698811yescharacteristic
243C2×C4#6699211yescharacteristic
244C2×C4#6699511yescharacteristic
245C2×C4#6700311yescharacteristic
246C2×C4#6700411yescharacteristic
247C8—81no—
248C8—81no—
249C8—442no—
250C8—881no—
251C8—881no—
252C22—21no—
253C22—21no—
254C22#1062256511yescharacteristic
255C22#1062258011yescharacteristic
256C22#1062260911yescharacteristic
257C4—21no—
258C4—21no—
259C4—21no—
260C4—21no—
261C4—42no—
262C4—81no—
263C4—1761no—
264C4#1062264611yescharacteristic
265C4#1062265111yescharacteristic
266C4#1062265811yescharacteristic
267C4#1062266511yescharacteristic
268C2—21no—
269C2—21no—
270C2#1307004211yescharacteristic
271C2#1307006911yescharacteristic
272C2#1307008311yescharacteristic
subgroupG/H
centerC22#10622565
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1801C2
socleC22×C11#397
prime radicalC23×C11#123
hypercenter#1801D11
hypocenterC11#10639
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
221. C11#10639semidirect

Maximal subgroups

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

subgroupindex
#130686312
#130673922
#130670112
#130665112
#130664762
C11×#18012
#1063911