Finite Group Databasebeta

← C2×#10590222 #11773713

Subgroups — C2×#10590222 #11773713

Order 1152.

1130 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C22×#3757C211yesmaximal, characteristic
2C2×C22⋊#622C212yesmaximal, complemented
3#10590222C214yesmaximal, direct product factor
4C25×C32C411yescharacteristic
5C23×C3⋊Dic3C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C22×#622—22no—
8C2×#3757—22no—
9C2×#3757—22no—
10C2×#3757C412yes—
11C2×#3757C2212yes—
12C22⋊#622—22no—
13C22⋊#622C2214yescomplemented
14C22×#217—62no—
15C24×C32—21no—
16C24×C32—21no—
17C24×C32—22no—
18C24×C32—42no—
19C24×C32—42no—
20C24×C32C814yescomplemented
21C24×C32C2×C411yescharacteristic
22C24×C32C2×C412yes—
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3—21no—
25C22×C3⋊Dic3—42no—
26C22×C3⋊Dic3—42no—
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3D412yes—
30C22×C3⋊Dic3D412yes—
31C22×C3⋊Dic3C2311yescharacteristic
32C2×#622—24no—
33C2×#622—44no—
34#3757—24no—
35#3757—24no—
36C2×#323—91nomaximal, Sylow
37C25×C3—22no—
38C23×Dic3—62no—
39C23×Dic3—62no—
40C2×#217—64no—
41C2×#217—64no—
42C2×#217—68no—
43C2×#217—68no—
44C23×C32—22no—
45C23×C32—22no—
46C23×C32—24no—
47C23×C32—24no—
48C23×C32—22no—
49C23×C32—22no—
50C23×C32—48no—
51C23×C32—42no—
52C23×C32—42no—
53C23×C32—48no—
54C23×C32—42no—
55C23×C32—42no—
56C23×C32—42no—
57C23×C32—42no—
58C23×C32C22⋊C411yescharacteristic
59C23×C32C22⋊C411yescharacteristic
60C23×C32C2×C812yes—
61C23×C32C2×C814yescomplemented
62C23×C32M1612yes—
63C23×C32C22×C411yescharacteristic
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—24no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3—42no—
68C2×C3⋊Dic3—41no—
69C2×C3⋊Dic3—42no—
70C2×C3⋊Dic3—42no—
71C2×C3⋊Dic3—42no—
72C2×C3⋊Dic3C22⋊C412yes—
73C2×C3⋊Dic3C2×D412yes—
74#622—44no—
75C22×C22⋊C4—91no—
76C2×C22⋊C8—92no—
77#323—94no—
78C24×C3—28no—
79C24×C3—24no—
80C24×C3—24no—
81C24×C3—28no—
82C24×C3—24no—
83C24×C3—22no—
84C24×C3—48no—
85C24×C3—48no—
86C22×Dic3—62no—
87C22×Dic3—64no—
88C22×Dic3—64no—
89C22×Dic3—64no—
90C22×Dic3—62no—
91C22×Dic3—64no—
92C22×Dic3—64no—
93C22×Dic3—128no—
94C22×Dic3—128no—
95#217—616no—
96#217—616no—
97C22×C32—24no—
98C22×C32—24no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32—21no—
102C22×C32—21no—
103C22×C32—24no—
104C22×C32—44no—
105C22×C32—48no—
106C22×C32—44no—
107C22×C32—48no—
108C22×C32—42no—
109C22×C32—42no—
110C22×C32C22⋊C812yes—
111C22×C32C22⋊C812yes—
112C22×C32#9912yes—
113C22×C32#10012yes—
114C22×C32C2×C22⋊C411yescharacteristic
115C22×C32C22×C811yescharacteristic
116C22×C32C2×M1611yescharacteristic
117C3⋊Dic3—22no—
118C3⋊Dic3—22no—
119C3⋊Dic3—42no—
120C25#15711yescharacteristic
121C23×C4—91no—
122C23×C4—91no—
123C22×C8—182no—
124C2×C22⋊C4—92no—
125C2×C22⋊C4—92no—
126C2×C22⋊C4—182no—
127C2×C22⋊C4—182no—
128C22⋊C8—94no—
129C22⋊C8—182no—
130C23×C3—28no—
131C23×C3—28no—
132C23×C3—28no—
133C23×C3—28no—
134C23×C3—216no—
135C23×C3—216no—
136C23×C3—22no—
137C23×C3—24no—
138C23×C3—28no—
139C23×C3—24no—
140C23×C3—22no—
141C23×C3—22no—
142C23×C3—432no—
143C23×C3—48no—
144C23×C3—48no—
145C23×C3—48no—
146C23×C3—48no—
147C23×C3—432no—
148C23×C3—48no—
149C23×C3—48no—
150C2×Dic3—64no—
151C2×Dic3—64no—
152C2×Dic3—68no—
153C2×Dic3—128no—
154C2×Dic3—124no—
155C2×Dic3—128no—
156C2×Dic3—124no—
157C2×Dic3—128no—
158C2×Dic3—128no—
159C2×Dic3—128no—
160C2×C32—22no—
161C2×C32—21no—
162C2×C32—21no—
163C2×C32—44no—
164C2×C32#32314yescomplemented
165C2×C32C2×C22⋊C811yescharacteristic
166C2×C32C2×#9911yescharacteristic
167C2×C32C2×#10011yescharacteristic
168C24—22no—
169C24—21no—
170C24—21no—
171C24—42no—
172C24—42no—
173C24#62214yescomplemented
174C24C2×#15712yes—
175C24C2×#15711yescharacteristic
176C22×C4—92no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4—92no—
180C22×C4—92no—
181C22×C4—181no—
182C22×C4—181no—
183C22×C4—362no—
184C22×C4—362no—
185C2×C8—184no—
186C2×C8—364no—
187C22⋊C4—184no—
188C22⋊C4—184no—
189C22×C3—24no—
190C22×C3—24no—
191C22×C3—24no—
192C22×C3—24no—
193C22×C3—216no—
194C22×C3—216no—
195C22×C3—216no—
196C22×C3—22no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—24no—
200C22×C3—24no—
201C22×C3—24no—
202C22×C3—24no—
203C22×C3—416no—
204C22×C3—416no—
205C22×C3—432no—
206C22×C3—432no—
207C22×C3—48no—
208C22×C3—48no—
209Dic3—124no—
210Dic3—124no—
211Dic3—128no—
212C32C2×#32311yescharacteristic, complemented, Sylow
213C23—22no—
214C23—22no—
215C23—22no—
216C23—22no—
217C23—24no—
218C23—24no—
219C23—48no—
220C23—42no—
221C23—42no—
222C23—48no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23C2×#62212yes—
228C23C2×#62214yescomplemented
229C23#379212yes—
230C23C22⋊#15711yescharacteristic
231C23C22⋊#15711yescharacteristic
232C23C22×#15711yescharacteristic
233C2×C4—92no—
234C2×C4—92no—
235C2×C4—184no—
236C2×C4—182no—
237C2×C4—361no—
238C2×C4—362no—
239C2×C4—361no—
240C2×C4—362no—
241C2×C4—362no—
242C2×C4—362no—
243C8—364no—
244C2×C3—24no—
245C2×C3—24no—
246C2×C3—28no—
247C2×C3—28no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—22no—
251C2×C3—416no—
252C22—24no—
253C22—24no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—24no—
259C22—44no—
260C22—44no—
261C22—48no—
262C22—48no—
263C22—42no—
264C22—42no—
265C22#6378612yes—
266C22C22⋊#62212yes—
267C22C22⋊#62212yes—
268C22#6378812yes—
269C22C22×#62211yescharacteristic
270C22C2×#379211yescharacteristic
271C22C2×C22⋊#15711yescharacteristic
272C4—182no—
273C4—182no—
274C4—362no—
275C3—22no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2—44no—
280C2#1059022214yesdirect product factor
281C2C2×#6378611yescharacteristic
282C2C2×C22⋊#62211yescharacteristic
283C2C2×#6378811yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
Fitting, prime radicalC25×C32C4
socleC23×C32C22⋊C4
cosocleC22×C3⋊Dic3C23
hypercenterC25#157
hypocenterC32C2×#323
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#622C2semidirect
3. #10590222C2direct (N × H)
13. C22⋊#622C22semidirect
20. C24×C32C8semidirect
61. C23×C32C2×C8semidirect
164. C2×C32#323semidirect
173. C24#622semidirect
212. C32C2×#323semidirect
228. C23C2×#622semidirect
280. C2#10590222direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37572
C2×C22⋊#6222
#105902222
C2×#3239