Finite Group Databasebeta

← C2×#13066791 #14674142

Subgroups — C2×#13066791 #14674142

Order 2816.

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

normal subgroups only

This group has 340 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
1C2×#10622180C211yesmaximal, characteristic
2C2×#10622179C211yesmaximal, characteristic
3#13066791C214yesmaximal, direct product factor
4C2×C11×#488C211yesmaximal, characteristic
5C2×C11×#125C411yescharacteristic, complemented
6C2×C11×#124C2211yescharacteristic
7C11×#488—21no—
8C11×#488—21no—
9C11×#488C412yescomplemented
10C11×#488C2212yes—
11C2×C11×#103—21no—
12C2×C11×#102—21no—
13C2×C4×C8×C11C411yescharacteristic, complemented
14C2×#66900—21no—
15C2×#66898—21no—
16#10622180—21no—
17#10622180C2212yes—
18#10622179—21no—
19#10622179C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×D4×C11D411yescharacteristic
22C22×C8×C11—21no—
23C11×#125—21no—
24C11×#125—41no—
25C11×#125C2×C412yescomplemented
26C11×#124—41no—
27C11×#124C2×C411yescharacteristic
28C11×#124D411yescharacteristic
29C11×#124D411yescharacteristic
30C11×#124C2311yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C22⋊C4—41no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C22⋊Dic11—41no—
36C2×#4318—41no—
37C11×#103—22no—
38C11×#103—22no—
39C11×#102—22no—
40C11×#102—22no—
41C4×C8×C11—21no—
42C4×C8×C11C2×C412yescomplemented
43#66900—22no—
44#66900—41no—
45#66898—22no—
46#66898—41no—
47C2×#1414—111nomaximal, Sylow
48C24×C11—21no—
49C2×Q8×C11—21no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C2×Q8×C11C22⋊C411yescharacteristic
53C2×Q8×C11C2×D411yescharacteristic
54C2×D4×C11—21no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11C22⋊C411yescharacteristic
58C2×D4×C11C2×D411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×Dic11—81no—
64C2×C8×C11—22no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C22⋊C4—41no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—41no—
74C11×C22⋊C4—41no—
75C42×C11—21no—
76C42×C11C22⋊C411yescharacteristic
77C42×C11C22×C411yescharacteristic
78C22⋊Dic11—42no—
79C22⋊Dic11—81no—
80#4318—42no—
81#4318—81no—
82C2×C11⋊C8—81no—
83C2×#488D1111yescharacteristic
84C2×#355—111no—
85C2×#354—111no—
86#1414—114no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—41no—
90C23×C11—41no—
91C23×C11—82no—
92C23×C11#9911yescharacteristic
93Q8×C11—41no—
94Q8×C11—41no—
95Q8×C11—81no—
96D4×C11—41no—
97D4×C11—41no—
98D4×C11—81no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—42no—
109C2×C4×C11—82no—
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×Dic11—82no—
113C2×Dic11—162no—
114C8×C11—42no—
115C11⋊C8—82no—
116C2×#125Dic1111yescharacteristic, complemented
117C2×#124C2×D1111yescharacteristic
118#488—21no—
119#488—21no—
120#488Dic1112yescomplemented
121#488C2×D1112yes—
122C2×#103—21no—
123C2×#102—21no—
124C2×#101—221no—
125C2×#99—221no—
126C2×C4×C8Dic1111yescharacteristic, complemented
127#355—112no—
128#355—221no—
129#354—112no—
130#354—221no—
131C22×C11—22no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—81no—
135C22×C11—81no—
136C22×C11—82no—
137C22×C11—161no—
138C22×C11#35411yescharacteristic
139C22×C11#35411yescharacteristic
140C22×C11C2×#9911yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—41no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11—82no—
148Dic11—162no—
149C22×Q8C22⋊D1111yescharacteristic
150C22×D4C22⋊D1111yescharacteristic
151C2×M16—441no—
152C22×C8—21no—
153#125—21no—
154#125—41no—
155#125C2×Dic1112yescomplemented
156#124—41no—
157#124C2×Dic1111yescharacteristic
158#124C22⋊D1111yescharacteristic
159#124C22⋊D1111yescharacteristic
160#124C22×D1111yescharacteristic
161C2×C4⋊C4—21no—
162C2×C4⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C22⋊C4—441no—
165C2×C42C2×Dic1111yescharacteristic
166#103—22no—
167#103—22no—
168#102—22no—
169#102—22no—
170#101—222no—
171#101—441no—
172#99—222no—
173#99—441no—
174C4×C8—21no—
175C4×C8C2×Dic1112yescomplemented
176C2×C11—21no—
177C2×C11—21no—
178C2×C11—81no—
179C2×C11—81no—
180C2×C11#141412yescomplemented
181C2×C11C2×#35411yescharacteristic
182C24—21no—
183C2×Q8—21no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8C22⋊Dic1111yescharacteristic
187C2×Q8C2×C22⋊D1111yescharacteristic
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4C22⋊Dic1111yescharacteristic
192C2×D4C2×C22⋊D1111yescharacteristic
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—881no—
197C22×C4C22⋊Dic1111yescharacteristic
198M16—442no—
199M16—881no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—881no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—41no—
211C22⋊C4—41no—
212C22⋊C4—442no—
213C22⋊C4—881no—
214C42—21no—
215C42C22⋊Dic1111yescharacteristic
216C42C22×Dic1111yescharacteristic
217C11C2×#141411yescharacteristic, complemented, Sylow
218C23—21no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23—82no—
223C23#6689811yescharacteristic
224Q8—41no—
225Q8—41no—
226Q8—81no—
227D4—41no—
228D4—41no—
229D4—81no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—82no—
241C2×C4—882no—
242C2×C4—1762no—
243C2×C4#6689811yescharacteristic
244C2×C4C2×C22⋊Dic1111yescharacteristic
245C8—42no—
246C8—882no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—82no—
253C22—161no—
254C22#1062217911yescharacteristic
255C22#1062217911yescharacteristic
256C22C2×#6689811yescharacteristic
257C4—21no—
258C4—21no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—82no—
264C4—1762no—
265C2—21no—
266C2—21no—
267C2—81no—
268C2—81no—
269C2#1306679112yesdirect product factor
270C2C2×#1062217911yescharacteristic
subgroupG/H
centerC22#10622179
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC2×C11×#488C2
socleC22×C11#354
prime radicalC22×D4×C11D4
cosocleC11×#124C23
hypercenterC2×#488D11
hypocenterC11C2×#1414
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
3. #13066791C2direct (N × H)
5. C2×C11×#125C4semidirect
9. C11×#488C4semidirect
13. C2×C4×C8×C11C4semidirect
25. C11×#125C2×C4semidirect
42. C4×C8×C11C2×C4semidirect
116. C2×#125Dic11semidirect
120. #488Dic11semidirect
126. C2×C4×C8Dic11semidirect
155. #125C2×Dic11semidirect
175. C4×C8C2×Dic11semidirect
180. C2×C11#1414semidirect
217. C11C2×#1414semidirect
269. C2#13066791direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221802
C2×#106221792
#130667912
C2×C11×#4882
C2×#141411