Finite Group Databasebeta

← C22⋊C8×#157 #11783556

Subgroups — C22⋊C8×#157 #11783556

Order 1152.

638 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 136 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×C4×#157C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic
3C2×C8×#157C212yesmaximal, complemented
4C3⋊D3×C22⋊C8C211yesmaximal, characteristic
5#10590181C212yesmaximal, complemented
6C23×#157C412yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C4×#157—24no—
9C2×C4×#157C412yes—
10C2×C4×#157C2211yescharacteristic
11C2×C4×#157C2211yescharacteristic
12C2×#3787C2212yes—
13C2×C8×C3⋊D3C2212yes—
14C22⋊#622C412yescomplemented
15#63778C412yescomplemented
16C8×#157—24no—
17C32×C22⋊C8C411yescharacteristic, complemented
18#63657C411yescharacteristic, complemented
19#63647C412yescomplemented
20D3×C22⋊C8—62no—
21C23×C3⋊D3C2×C411yescharacteristic
22C22×#157—24no—
23C22×#157—24no—
24C22×#157C818yescomplemented
25C22×#157C2×C412yes—
26C22×#157C2×C412yes—
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×#622C2×C414yescomplemented
36C4×#157—24no—
37C4×#157—22no—
38C4×#157D414yes—
39#3787—22no—
40#3787—22no—
41C2×C32×C8C2×C412yescomplemented
42C2×C3⋊(C3⋊C8)C2×C412yescomplemented
43C8×C3⋊D3—22no—
44C8×C3⋊D3—22no—
45C4×C22⋊C8—91nomaximal, Sylow
46C22×C4×D3—62no—
47C2×D3×C8—64no—
48C3×C22⋊C8—22no—
49#830—62no—
50(C2×D3)⋊C8—64no—
51C23×C32C4211yescharacteristic
52C22×C3⋊D3—21no—
53C22×C3⋊D3—21no—
54C22×C3⋊D3—22no—
55C22×C3⋊D3C4211yescharacteristic
56C22×C3⋊D3C2×C814yes—
57C22×C3⋊D3C22×C411yescharacteristic
58C2×#157—22no—
59C2×#157—22no—
60C2×#157—216no—
61C2×#157C22⋊C414yes—
62C2×#157C2×C814yes—
63C2×#157C2×C814yes—
64C2×#157M1614yes—
65C2×C32×C4—22no—
66C2×C32×C4C4211yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3C4211yescharacteristic
70C2×C3⋊Dic3C22×C411yescharacteristic
71C4×C3⋊D3—21no—
72C4×C3⋊D3—21no—
73C4×C3⋊D3—22no—
74C4×C3⋊D3—22no—
75C4×C3⋊D3C2×D412yes—
76C4×C3⋊D3#4112yes—
77#622—24no—
78C32×C8—22no—
79C3⋊(C3⋊C8)—22no—
80C22×C42—91no—
81C2×C22⋊C8—91no—
82C2×C22⋊C8—91no—
83C2×C4×C8—92no—
84#336—92no—
85C23×D3—62no—
86C22×C3×C4—22no—
87C22×Dic3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—124no—
93C2×C4×D3—124no—
94C2×C3×C8—24no—
95C2×C3⋊C8—64no—
96D3×C8—124no—
97D3×C8—124no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32C4×C812yescomplemented
101C22×C32C2×C4211yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—21no—
104C2×C3⋊D3—24no—
105C2×C3⋊D3—24no—
106C2×C3⋊D3C4×C812yescomplemented
107C2×C3⋊D3C2×C22⋊C411yescharacteristic
108C2×C3⋊D3#11711yescharacteristic
109C2×C3⋊D3C22×C812yes—
110C2×C3⋊D3C2×M1612yes—
111#157—24no—
112#157C22⋊C818yesdirect product factor
113C32×C4—21no—
114C32×C4C4×D412yes—
115C3⋊Dic3—21no—
116C3⋊Dic3C4×D412yes—
117C23×C4—92no—
118C23×C4—91no—
119C22×C8—92no—
120C22×C8—92no—
121C2×C42—91no—
122C2×C42—92no—
123C2×C42—91no—
124C2×C42—184no—
125C22⋊C8—92no—
126C22⋊C8—92no—
127C22⋊C8—91no—
128C22⋊C8—92no—
129C22⋊C8#15711yescharacteristic, direct product factor
130C4×C8—184no—
131C23×C3—22no—
132C22×D3—62no—
133C22×D3—62no—
134C22×D3—68no—
135C22×D3—122no—
136C22×D3—122no—
137C22×D3—124no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—44no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—124no—
144C4×D3—64no—
145C4×D3—64no—
146C4×D3—124no—
147C4×D3—124no—
148C4×D3—122no—
149C4×D3—122no—
150C3×C8—44no—
151C3⋊C8—124no—
152C2×C32—22no—
153C2×C32C4×C22⋊C411yescharacteristic
154C2×C32C2×C4×C811yescharacteristic
155C2×C32C4×M1611yescharacteristic
156C3⋊D3—22no—
157C3⋊D3C2×C22⋊C812yes—
158C3⋊D3#43112yes—
159C24—91no—
160C22×C4—92no—
161C22×C4—91no—
162C22×C4—98no—
163C22×C4—92no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—182no—
169C22×C4—182no—
170C22×C4—184no—
171C22×C4—184no—
172C22×C4C2×#15711yescharacteristic
173C2×C8—94no—
174C2×C8—92no—
175C2×C8—182no—
176C2×C8—182no—
177C2×C8—182no—
178C2×C8—182no—
179C2×C8C2×#15712yescomplemented
180C42—94no—
181C42—184no—
182C42—182no—
183C22×C3—24no—
184C22×C3—22no—
185C22×C3—42no—
186C22×C3—42no—
187C2×D3—62no—
188C2×D3—62no—
189C2×D3—64no—
190C2×D3—64no—
191C2×D3—64no—
192C2×D3—128no—
193C2×D3—128no—
194C2×D3—122no—
195C2×D3—122no—
196C3×C4—24no—
197C3×C4—42no—
198Dic3—64no—
199Dic3—122no—
200C32C4×C22⋊C811yescharacteristic, complemented, Sylow
201C23—91no—
202C23—94no—
203C23—91no—
204C23—181no—
205C23—181no—
206C23—182no—
207C23C4×#15711yescharacteristic
208C2×C4—22no—
209C2×C4—94no—
210C2×C4—94no—
211C2×C4—94no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—94no—
216C2×C4—91no—
217C2×C4—182no—
218C2×C4—181no—
219C2×C4—181no—
220C2×C4—182no—
221C2×C4—1816no—
222C2×C4—182no—
223C2×C4—182no—
224C2×C4—182no—
225C2×C4C4×#15711yescharacteristic
226C2×C4C22×#15711yescharacteristic
227C8—22no—
228C8—184no—
229C8—182no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—22no—
233C2×C3—44no—
234D3—64no—
235D3—64no—
236D3—124no—
237C22—21no—
238C22—21no—
239C22—91no—
240C22—91no—
241C22—92no—
242C22—92no—
243C22—92no—
244C22—184no—
245C22—184no—
246C22—181no—
247C22—181no—
248C22C8×#15712yescomplemented
249C22C2×C4×#15711yescharacteristic
250C4—21no—
251C4—98no—
252C4—92no—
253C4—184no—
254C4—181no—
255C4D4×#15712yes—
256C3—22no—
257C2—22no—
258C2—92no—
259C2—92no—
260C2—182no—
261C2C22⋊C4×#15711yescharacteristic
262C2C2×C8×#15711yescharacteristic
263C2M16×#15711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutatorC2×C32C2×C4×C8
FittingC32×C22⋊C8C4
socleC22×C32C2×C42
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊C8#157
hypocenterC32C4×C22⋊C8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×C8×#157C2semidirect
5. #10590181C2semidirect
14. C22⋊#622C4semidirect
15. #63778C4semidirect
17. C32×C22⋊C8C4semidirect
18. #63657C4semidirect
19. #63647C4semidirect
24. C22×#157C8semidirect
35. C2×#622C2×C4semidirect
41. C2×C32×C8C2×C4semidirect
42. C2×C3⋊(C3⋊C8)C2×C4semidirect
100. C22×C32C4×C8semidirect
106. C2×C3⋊D3C4×C8semidirect
112. #157C22⋊C8direct (N × H)
129. C22⋊C8#157direct (N × H)
179. C2×C8C2×#157semidirect
200. C32C4×C22⋊C8semidirect
248. C22C8×#157semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
#105938002
C2×C8×#1572
C3⋊D3×C22⋊C82
#105901812
C4×C22⋊C89