Finite Group Databasebeta

← #14665127

Subgroups — #14665127

Order 2816.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079203C211yesmaximal, characteristic
2#13070418C211yesmaximal, characteristic
3#13067363C211yesmaximal, characteristic
4#13066674C211yesmaximal, characteristic, complemented
5#13066666C211yesmaximal, characteristic, complemented
6#13066664C211yesmaximal, characteristic, complemented
7C11×#1365C211yesmaximal, characteristic, complemented
8#10623259—21no—
9C11×#500C2211yescharacteristic
10#10622706—21no—
11#10622500—21no—
12#10622500C412yes—
13#10622486—21no—
14#10622486C412yes—
15#10622446—21no—
16#10622312C2211yescharacteristic
17C4×C8×D11C2211yescharacteristic
18C11×C4⋊C16C2211yescharacteristic
19C11×#335C2211yescharacteristic
20(C2×D11)⋊C16—21no—
21#10622140—21no—
22#10622118—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C11×C4⋊Q8—21no—
26#66999—41no—
27Q8×Dic11—41no—
28C2×Dic44—21no—
29C2×Dic44C2×C412yes—
30C2×C8×D11C2×C411yescharacteristic
31C2×C8×D11D411yescharacteristic
32#66950—22no—
33#66945—41no—
34#66943—41no—
35#66940—22no—
36C42×D11D411yescharacteristic
37#66922—21no—
38C2×C11×C16—21no—
39C11×#107—21no—
40C11×#107C2×C412yes—
41C11×C4⋊C8—21no—
42C4×C8×C11C2311yescharacteristic
43(C2×D11)⋊C8—41no—
44C8×Dic11—41no—
45C8×Dic11C2×C411yescharacteristic
46C8×Dic11D411yescharacteristic
47C2×C11⋊C16—21no—
48#66874—22no—
49#66874—22no—
50C4⋊(C11⋊C8)—21no—
51C4×C11⋊C8D411yescharacteristic
52#11953—111nomaximal, Sylow
53C2×Q8×C11—41no—
54C2×C4×D11C22⋊C411yescharacteristic
55C2×C4×D11D811yescharacteristic
56C2×C4×D11SD1611yescharacteristic
57C2×Dic22—22no—
58C2×C8×C11—41no—
59C2×C8×C11C22×C411yescharacteristic
60C2×C8×C11C2×D411yescharacteristic
61C11×C4⋊C4—22no—
62C11×C4⋊C4—41no—
63C42×C11C2×D411yescharacteristic
64(C2×D11)⋊C4—42no—
65C4⋊Dic11—42no—
66C4⋊Dic11—41no—
67C4⋊Dic11—41no—
68Dic11⋊C4—42no—
69C4×Dic11—42no—
70C4×Dic11C22⋊C411yescharacteristic
71C4×Dic11D811yescharacteristic
72C4×Dic11SD1611yescharacteristic
73C2×C11⋊C8—41no—
74C2×C11⋊C8C22⋊C411yescharacteristic
75C2×C11⋊C8C22⋊C411yescharacteristic
76Dic44—42no—
77Dic44—41no—
78Dic44—41no—
79C8×D11—21no—
80C8×D11—21no—
81C8×D11—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3170—111no—
85#2163—111no—
86#1564—111no—
87#1365—111no—
88#1365D1111yescharacteristic, complemented
89#1362—111no—
90#1362—111no—
91C22×D11#10211yescharacteristic
92Q8×C11—82no—
93C2×C4×C11—42no—
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11C2×D811yescharacteristic
96C2×C4×C11C2×SD1611yescharacteristic
97C2×Dic11—42no—
98C2×Dic11#10211yescharacteristic
99C2×Dic11#10211yescharacteristic
100C2×Dic11#10211yescharacteristic
101C4×D11—21no—
102C4×D11—21no—
103C4×D11—21no—
104C4×D11—21no—
105C4×D11—41no—
106Dic22—42no—
107Dic22—42no—
108C8×C11—21no—
109C8×C11—81no—
110C8×C11#13511yescharacteristic
111C8×C11#13511yescharacteristic
112C11⋊C8—21no—
113C11⋊C8—21no—
114C11⋊C8—81no—
115#533—221no—
116#500C2×D1111yescharacteristic
117#494—111no—
118#487—221no—
119#467—112no—
120#467—221no—
121C4×Q16—112no—
122C4×Q16—221no—
123#431—221no—
124C2×C4×C8—111no—
125C4⋊C16—111no—
126C4⋊C16C2×D1111yescharacteristic
127C22⋊C16—221no—
128#346—221no—
129#335—111no—
130#335C2×D1111yescharacteristic
131#334—221no—
132C22×C11C2×#10211yescharacteristic
133C2×D11—21no—
134C2×D11—21no—
135C2×D11—21no—
136C4×C11—21no—
137C4×C11—82no—
138C4×C11#41311yescharacteristic
139C4×C11#41611yescharacteristic
140C4×C11#51011yescharacteristic
141C4×C11#51011yescharacteristic
142Dic11—21no—
143Dic11—21no—
144Dic11—21no—
145Dic11—82no—
146C2×Q16—112no—
147C2×Q16—221no—
148C22×C8—111no—
149C22×C8—111no—
150C4⋊Q8—21no—
151C4⋊Q8—221no—
152#125—441no—
153C22⋊Q8—222no—
154C22⋊Q8—441no—
155C4×Q8—222no—
156C4×Q8—441no—
157#117—441no—
158C2×C42—111no—
159C2×C16—21no—
160C2×C16—221no—
161#107—21no—
162#107C4×D1112yes—
163C4⋊C8—21no—
164C4⋊C8—221no—
165#103—222no—
166#103—222no—
167C22⋊C8—441no—
168C4×C8—111no—
169C4×C8—111no—
170C4×C8—111no—
171C4×C8—441no—
172C4×C8C22×D1111yescharacteristic
173C2×C11#154011yescharacteristic
174C2×C11#214111yescharacteristic
175C2×C11#214811yescharacteristic
176D11—41no—
177C2×Q8—41no—
178C2×Q8—222no—
179C22×C4—111no—
180C22×C4—111no—
181C22×C4—111no—
182Q16—442no—
183Q16—441no—
184Q16—441no—
185C2×C8—41no—
186C2×C8—111no—
187C2×C8—111no—
188C2×C8—221no—
189C2×C8—221no—
190C2×C8—441no—
191C2×C8—441no—
192C2×C8C2×C4×D1111yescharacteristic
193C2×C8D4×D1111yescharacteristic
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—442no—
197C4⋊C4—442no—
198C4⋊C4—441no—
199C4⋊C4—441no—
200C22⋊C4—442no—
201C42—111no—
202C42—111no—
203C42—111no—
204C42—442no—
205C42D4×D1111yescharacteristic
206C16—41no—
207C16—441no—
208C11#1195311yescharacteristic, complemented, Sylow
209C23—111no—
210Q8—82no—
211Q8—442no—
212Q8—442no—
213C2×C4—42no—
214C2×C4—111no—
215C2×C4—111no—
216C2×C4—111no—
217C2×C4—221no—
218C2×C4—221no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—441no—
222C2×C4—442no—
223C2×C4C22⋊C4×D1111yescharacteristic
224C2×C4D8×D1111yescharacteristic
225C2×C4SD16×D1111yescharacteristic
226C8—21no—
227C8—81no—
228C8—221no—
229C8—221no—
230C8—881no—
231C8#6696911yescharacteristic
232C8#6697211yescharacteristic
233C22—221no—
234C22—221no—
235C22—221no—
236C22D11×#10211yescharacteristic
237C4—21no—
238C4—82no—
239C4—221no—
240C4—221no—
241C4—221no—
242C4—882no—
243C4#1062236411yescharacteristic
244C4#1062241711yescharacteristic
245C4#1062252811yescharacteristic
246C4#1062253111yescharacteristic
247C2—441no—
248C2#1306726411yescharacteristic
249C2#1307033411yescharacteristic
250C2#1307036211yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1365C2
socleC22×C11C2×#102
prime radicalC22×D11#102
cosocleC4×C8×C11C23
hypercenter#1365D11
hypocenterC11#11953
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
4. #13066674C2semidirect
5. #13066666C2semidirect
6. #13066664C2semidirect
7. C11×#1365C2semidirect
88. #1365D11semidirect
208. C11#11953semidirect

Maximal subgroups

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

subgroupindex
#130792032
#130704182
#130673632
#130666742
#130666662
#130666642
C11×#13652
#1195311