Finite Group Databasebeta

← C8×C22⋊#157 #11783641

Subgroups — C8×C22⋊#157 #11783641

Order 1152.

722 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 126 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×C8×C3⋊D3C211yesmaximal, characteristic
2C4×C22⋊#157C211yesmaximal, characteristic
3#10593800C211yesmaximal, characteristic
4C2×C8×#157C212yesmaximal, complemented
5#10590181C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157C412yes—
8C2×C4×#157C2212yes—
9C2×#3787C2212yes—
10C22×C32×C8C411yescharacteristic, complemented
11C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
12C2×C8×C3⋊D3—24no—
13C2×C8×C3⋊D3C411yescharacteristic, complemented
14C2×C8×C3⋊D3C411yescharacteristic, complemented
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C22⋊#622C412yescomplemented
18#63781C412yes—
19#63778C412yescomplemented
20C8×#157—24no—
21C22×D3×C8—62no—
22C23×C3⋊D3C2×C411yescharacteristic
23C22×#157C2×C414yes—
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C22⋊#157C818yesdirect product factor
33C2×#622C2×C414yes—
34C4×#157—22no—
35C4×#157—22no—
36#3787—22no—
37#3787—22no—
38C2×C32×C8—22no—
39C2×C32×C8C2×C411yescharacteristic
40C2×C32×C8C2×C411yescharacteristic
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
43C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
44C8×C3⋊D3—22no—
45C8×C3⋊D3—22no—
46C8×C3⋊D3—22no—
47C8×C3⋊D3D414yes—
48C8×C22⋊C4—91nomaximal, Sylow
49C22×C4×D3—62no—
50C22×C3×C8—22no—
51C22×C3⋊C8—62no—
52C2×D3×C8—62no—
53C2×D3×C8—62no—
54C2×D3×C8—62no—
55C2×D3×C8—62no—
56C2×D3×C8—616no—
57C23×C32C4211yescharacteristic
58C22×C3⋊D3—22no—
59C22×C3⋊D3—22no—
60C22×C3⋊D3C4211yescharacteristic
61C22×C3⋊D3C2×C814yes—
62C22×C3⋊D3C22×C411yescharacteristic
63C2×#157—24no—
64C2×#157—24no—
65C2×#157C2×C818yescomplemented
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4C4211yescharacteristic
69C2×C32×C4C22×C411yescharacteristic
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C4211yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—21no—
75C4×C3⋊D3—21no—
76C4×C3⋊D3—22no—
77C4×C3⋊D3C2×D412yes—
78C4×C3⋊D3#4112yes—
79#622—24no—
80C32×C8—21no—
81C32×C8C22⋊C412yescomplemented
82C3⋊(C3⋊C8)—21no—
83C3⋊(C3⋊C8)C22⋊C412yescomplemented
84C23×C8—91no—
85C2×C22⋊C8—91no—
86C2×C4×C8—92no—
87C4×C22⋊C4—91no—
88#336—92no—
89C23×D3—62no—
90C22×C3×C4—22no—
91C22×Dic3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—68no—
97C2×C4×D3—68no—
98C2×C3×C8—28no—
99C2×C3×C8—22no—
100C2×C3×C8—22no—
101C2×C3⋊C8—62no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—68no—
104D3×C8—68no—
105D3×C8—68no—
106D3×C8—68no—
107D3×C8—68no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32C4×C812yescomplemented
111C22×C32C2×C4211yescharacteristic
112C2×C3⋊D3—21no—
113C2×C3⋊D3—21no—
114C2×C3⋊D3—28no—
115C2×C3⋊D3C4×C812yescomplemented
116C2×C3⋊D3C4×D412yes—
117C2×C3⋊D3C22×C812yes—
118C2×C3⋊D3#13112yes—
119#157—28no—
120C32×C4—21no—
121C32×C4C2×C22⋊C411yescharacteristic
122C32×C4#11711yescharacteristic
123C3⋊Dic3—21no—
124C3⋊Dic3C4×D412yes—
125C23×C4—91no—
126C22×C8—91no—
127C22×C8—92no—
128C22×C8—91no—
129C22×C8—91no—
130C22×C8—91no—
131C22×C8—91no—
132C22×C8—184no—
133C22×C8#15711yescharacteristic, complemented
134C2×C22⋊C4—92no—
135C2×C42—92no—
136C22⋊C8—92no—
137C22⋊C8—92no—
138C4×C8—184no—
139#95—92no—
140C23×C3—22no—
141C22×D3—62no—
142C22×D3—68no—
143C22×D3—62no—
144C22×D3—68no—
145C22×D3—68no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—68no—
153C4×D3—64no—
154C4×D3—64no—
155C4×D3—64no—
156C4×D3—68no—
157C4×D3—68no—
158C4×D3—64no—
159C3×C8—24no—
160C3×C8—24no—
161C3⋊C8—64no—
162C3⋊C8—64no—
163C2×C32—22no—
164C2×C32C4×C22⋊C411yescharacteristic
165C2×C32C2×C4×C811yescharacteristic
166C2×C32#40511yescharacteristic
167C3⋊D3—22no—
168C3⋊D3C8×D414yes—
169C24—91no—
170C22×C4—91no—
171C22×C4—94no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—182no—
177C22×C4—182no—
178C22×C4C2×#15711yescharacteristic
179C2×C8—22no—
180C2×C8—91no—
181C2×C8—94no—
182C2×C8—94no—
183C2×C8—91no—
184C2×C8—182no—
185C2×C8—182no—
186C2×C8—182no—
187C2×C8—182no—
188C2×C8—182no—
189C2×C8—182no—
190C2×C8C2×#15711yescharacteristic
191C2×C8C2×#15711yescharacteristic
192C22⋊C4—98no—
193C42—182no—
194C42—182no—
195C22×C3—24no—
196C22×C3—24no—
197C22×C3—24no—
198C22×C3—22no—
199C2×D3—64no—
200C2×D3—64no—
201C2×D3—64no—
202C2×D3—64no—
203C2×D3—64no—
204C2×D3—632no—
205C2×D3—64no—
206C3×C4—24no—
207C3×C4—22no—
208C3×C4—22no—
209Dic3—64no—
210Dic3—64no—
211C32C8×C22⋊C411yescharacteristic, complemented, Sylow
212C23—91no—
213C23—94no—
214C23—91no—
215C23—182no—
216C23—182no—
217C23C4×#15711yescharacteristic
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—91no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—98no—
224C2×C4—91no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4—182no—
228C2×C4—184no—
229C2×C4—184no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4C4×#15711yescharacteristic
233C2×C4C22×#15711yescharacteristic
234C8—21no—
235C8—92no—
236C8—184no—
237C8—181no—
238C8C22⋊#15712yesdirect product factor
239C2×C3—28no—
240C2×C3—22no—
241C2×C3—22no—
242C2×C3—22no—
243D3—68no—
244D3—68no—
245C22—21no—
246C22—21no—
247C22—92no—
248C22—92no—
249C22—92no—
250C22—92no—
251C22—188no—
252C22—181no—
253C22—181no—
254C22C8×#15712yescomplemented
255C22C2×C4×#15711yescharacteristic
256C4—21no—
257C4—92no—
258C4—188no—
259C4—181no—
260C4#6428611yescharacteristic
261C4C2×C22⋊#15711yescharacteristic
262C3—22no—
263C2—22no—
264C2—94no—
265C2—182no—
266C2C2×C8×#15711yescharacteristic
267C2#1059376511yescharacteristic
268C2C4×C22⋊#15711yescharacteristic
subgroupG/H
centerC2×C8C2×#157
commutatorC2×C32C2×C4×C8
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC22×C32C2×C42
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C8#157
hypocenterC32C8×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C8×#157C2semidirect
5. #10590181C2semidirect
10. C22×C32×C8C4semidirect
11. C22×C3⋊(C3⋊C8)C4semidirect
13. C2×C8×C3⋊D3C4semidirect
14. C2×C8×C3⋊D3C4semidirect
17. C22⋊#622C4semidirect
19. #63778C4semidirect
32. C22⋊#157C8direct (N × H)
65. C2×#157C2×C8semidirect
81. C32×C8C22⋊C4semidirect
83. C3⋊(C3⋊C8)C22⋊C4semidirect
110. C22×C32C4×C8semidirect
115. C2×C3⋊D3C4×C8semidirect
133. C22×C8#157semidirect
211. C32C8×C22⋊C4semidirect
238. C8C22⋊#157direct (N × H)
254. C22C8×#157semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
C4×C22⋊#1572
#105938002
C2×C8×#1572
#105901812
C8×C22⋊C49