Finite Group Databasebeta

← C2×#20261050 #27151609

Subgroups — C2×#20261050 #27151609

Order 12416.

512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690785C211yesmaximal, characteristic
2C2×C4⋊C4×D97C211yesmaximal, characteristic, complemented
3#20261050C218yesmaximal, direct product factor
4C2×#15690743C211yesmaximal, characteristic, complemented
5C2×#15690732C211yesmaximal, characteristic, complemented
6C2×#15690730C211yesmaximal, characteristic, complemented
7C2×#15690722C211yesmaximal, characteristic, complemented
8C2×#107×C97C211yesmaximal, characteristic, complemented
9C22×D388—21no—
10C22×D388C2211yescharacteristic
11C22×C4×D97—21no—
12C22×C4×D97C2211yescharacteristic
13C22×#11715895C2211yescharacteristic
14#15690785—22no—
15#15690785C2214yes—
16C2×C4⋊Dic97C2211yescharacteristic
17C2×#13095490—21no—
18C4⋊C4×D97—22no—
19C4⋊C4×D97C2214yescomplemented
20C2×#13095488—21no—
21#15690743C2214yescomplemented
22#15690732C2214yescomplemented
23#15690730C2214yescomplemented
24#15690722C2214yescomplemented
25C22×C8×C97C2211yescharacteristic
26C2×C4⋊C4×C97C2211yescharacteristic
27C2×C4⋊C4×C97C2211yescharacteristic
28#107×C97C2214yescomplemented
29C23×D97—21no—
30C23×D97D411yescharacteristic
31C2×D388—22no—
32C2×D388—22no—
33C2×D388—24no—
34C2×D388—21no—
35C2×D388—44no—
36C2×D388C2312yes—
37C22×Dic97—21no—
38C22×Dic97D411yescharacteristic
39C2×C4×D97—22no—
40C2×C4×D97—22no—
41C2×C4×D97—24no—
42C2×C4×D97—44no—
43C2×C4×D97D412yes—
44C2×C4×D97C2312yes—
45C2×#11715895—22no—
46C2×#11715895C2312yes—
47C4⋊Dic97—21no—
48C4⋊Dic97C2312yes—
49#13095490—24no—
50#13095488—24no—
51C22×C4×C97—21no—
52C22×C4×C97—21no—
53C22×C4×C97C2311yescharacteristic
54C2×C8×C97—22no—
55C2×C8×C97C2312yes—
56C4⋊C4×C97—21no—
57C4⋊C4×C97—21no—
58C4⋊C4×C97C2312yes—
59C4⋊C4×C97C2312yes—
60C23×C97C2×D411yescharacteristic
61C22×D97—22no—
62C22×D97—22no—
63C22×D97—22no—
64C22×D97—42no—
65C22×D97—42no—
66C22×D97—42no—
67C22×D97D814yes—
68C22×D97C2×D412yes—
69C2×C4×C97—22no—
70C2×C4×C97—22no—
71C2×C4×C97—42no—
72C2×C4×C97—42no—
73C2×C4×C97C2×D411yescharacteristic
74C2×C4×C97#4112yes—
75C2×C4×C97#4112yes—
76C2×C4×C97C2411yescharacteristic
77C2×Dic97—22no—
78C2×Dic97—22no—
79C2×Dic97—42no—
80C2×Dic97C2×D412yes—
81D388—22no—
82D388—22no—
83D388—48no—
84D388—42no—
85C4×D97—24no—
86C4×D97—22no—
87C4×D97—22no—
88C4×D97—48no—
89C8×C97—22no—
90#11715895—22no—
91C22×C97#12312yes—
92C22×C97C2×D812yes—
93C22×C97#13712yes—
94C22×C97C22×D411yescharacteristic
95C2×D97—22no—
96C2×D97—22no—
97C2×D97—28no—
98C2×D97—42no—
99C2×D97—42no—
100C2×D97—42no—
101C2×D97—84no—
102C2×D97C2×D814yes—
103C4×C97—42no—
104C4×C97—42no—
105C4×C97#12312yes—
106C4×C97C2×#4111yescharacteristic
107C4×C97C2×#4111yescharacteristic
108Dic97—22no—
109Dic97—42no—
110C2×C97#48014yescomplemented
111C2×C97C2×#12311yescharacteristic
112C2×C97C22×D811yescharacteristic
113C2×C97C2×#13711yescharacteristic
114D97—24no—
115D97—82no—
116C2×#480—971nomaximal, Sylow
117C97C2×#48011yescharacteristic, complemented, Sylow
118C2×#121—971no—
119C22×C4⋊C4—971no—
120#480—978no—
121C2×#107—971no—
122C2×#107D9711yescharacteristic, complemented
123C2×#102—971no—
124C2×#102—971no—
125C2×C22⋊C8—971no—
126C22×D4—971no—
127C22×D4—1941no—
128C23×C4—971no—
129C23×C4—1941no—
130C22×C8—971no—
131C22×C8C2×D9711yescharacteristic
132#121—974no—
133#121—1942no—
134C2×C4⋊C4—971no—
135C2×C4⋊C4—974no—
136C2×C4⋊C4—1942no—
137C2×C4⋊C4—1941no—
138C2×C4⋊C4C2×D9711yescharacteristic
139C2×C4⋊C4C2×D9711yescharacteristic
140C2×C22⋊C4—1941no—
141#107—974no—
142#107C2×D9714yescomplemented
143#102—974no—
144#102—974no—
145C22⋊C8—974no—
146C24—971no—
147C24—1941no—
148C2×D4—972no—
149C2×D4—3884no—
150C2×D4—1944no—
151C2×D4—1941no—
152C2×D4—1942no—
153C2×D4—1942no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—971no—
157C22×C4—972no—
158C22×C4—972no—
159C22×C4—3884no—
160C22×C4—1944no—
161C22×C4—1941no—
162C22×C4—1942no—
163C22×C4—1942no—
164C22×C4C22×D9711yescharacteristic
165C2×C8—22no—
166C2×C8—972no—
167C2×C8—1942no—
168C2×C8C22×D9712yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—972no—
172C4⋊C4—1944no—
173C4⋊C4—1941no—
174C4⋊C4C22×D9712yes—
175C4⋊C4C22×D9712yes—
176C22⋊C4—1944no—
177C23—974no—
178C23—972no—
179C23—3882no—
180C23—3882no—
181C23—3882no—
182C23—1942no—
183C23—1942no—
184C23—1942no—
185C23D4×D9711yescharacteristic
186D4—3888no—
187D4—3882no—
188D4—1942no—
189D4—1942no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—972no—
195C2×C4—3888no—
196C2×C4—3882no—
197C2×C4—1942no—
198C2×C4—1942no—
199C2×C4—1944no—
200C2×C4—1942no—
201C2×C4—1942no—
202C2×C4D4×D9711yescharacteristic
203C2×C4#1309551112yes—
204C2×C4#1309551212yes—
205C2×C4C23×D9711yescharacteristic
206C8—22no—
207C8—1942no—
208C22—7764no—
209C22—974no—
210C22—3882no—
211C22—3882no—
212C22—3882no—
213C22—1942no—
214C22—1942no—
215C22—1948no—
216C22#1569079512yes—
217C22D8×D9712yes—
218C22#1569084212yes—
219C22C2×D4×D9711yescharacteristic
220C4—42no—
221C4—42no—
222C4—3882no—
223C4—1942no—
224C4#1569079512yes—
225C4C2×#1309551111yescharacteristic
226C4C2×#1309551211yescharacteristic
227C2—7762no—
228C2—1944no—
229C2#2026105014yesdirect product factor
230C2C2×#1569079511yescharacteristic
231C2C2×D8×D9711yescharacteristic
232C2C2×#1569084211yescharacteristic
subgroupG/H
centerC23D4×D97
commutator, cosocleC2×C4×C97C24
FrattiniC2×C4C23×D97
FittingC2×#107×C97C2
socleC23×C97C2×D4
prime radicalC2×#15690785C2
hypercenterC2×#107D97
hypocenterC97C2×#480
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D97C2semidirect
3. #20261050C2direct (N × H)
4. C2×#15690743C2semidirect
5. C2×#15690732C2semidirect
6. C2×#15690730C2semidirect
7. C2×#15690722C2semidirect
8. C2×#107×C97C2semidirect
19. C4⋊C4×D97C22semidirect
21. #15690743C22semidirect
22. #15690732C22semidirect
23. #15690730C22semidirect
24. #15690722C22semidirect
28. #107×C97C22semidirect
110. C2×C97#480semidirect
117. C97C2×#480semidirect
122. C2×#107D97semidirect
142. #107C2×D97semidirect
229. C2#20261050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156907852
C2×C4⋊C4×D972
#202610502
C2×#156907432
C2×#156907322
C2×#156907302
C2×#156907222
C2×#107×C972
C2×#48097