Finite Group Databasebeta

← C2×#20265492 #27181005

Subgroups — C2×#20265492 #27181005

Order 12928.

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×#15692230C211yesmaximal, characteristic
2C2×C4⋊C4×D101C211yesmaximal, characteristic, complemented
3#20265492C218yesmaximal, direct product factor
4C2×#15692188C211yesmaximal, characteristic, complemented
5C2×#15692177C211yesmaximal, characteristic, complemented
6C2×#15692175C211yesmaximal, characteristic, complemented
7C2×#15692167C211yesmaximal, characteristic, complemented
8C2×#107×C101C211yesmaximal, characteristic, complemented
9C22×D404—21no—
10C22×D404C2211yescharacteristic
11C22×C4×D101—21no—
12C22×C4×D101C2211yescharacteristic
13C22×#11717579C2211yescharacteristic
14#15692230—22no—
15#15692230C2214yes—
16C2×C4⋊Dic101C2211yescharacteristic
17C2×#13108053—21no—
18C4⋊C4×D101—22no—
19C4⋊C4×D101C2214yescomplemented
20C2×#13108051—21no—
21#15692188C2214yescomplemented
22#15692177C2214yescomplemented
23#15692175C2214yescomplemented
24#15692167C2214yescomplemented
25C22×C8×C101C2211yescharacteristic
26C2×C4⋊C4×C101C2211yescharacteristic
27C2×C4⋊C4×C101C2211yescharacteristic
28#107×C101C2214yescomplemented
29C23×D101—21no—
30C23×D101D411yescharacteristic
31C2×D404—22no—
32C2×D404—22no—
33C2×D404—24no—
34C2×D404—21no—
35C2×D404—44no—
36C2×D404C2312yes—
37C22×Dic101—21no—
38C22×Dic101D411yescharacteristic
39C2×C4×D101—22no—
40C2×C4×D101—22no—
41C2×C4×D101—24no—
42C2×C4×D101—44no—
43C2×C4×D101D412yes—
44C2×C4×D101C2312yes—
45C2×#11717579—22no—
46C2×#11717579C2312yes—
47C4⋊Dic101—21no—
48C4⋊Dic101C2312yes—
49#13108053—24no—
50#13108051—24no—
51C22×C4×C101—21no—
52C22×C4×C101—21no—
53C22×C4×C101C2311yescharacteristic
54C2×C8×C101—22no—
55C2×C8×C101C2312yes—
56C4⋊C4×C101—21no—
57C4⋊C4×C101—21no—
58C4⋊C4×C101C2312yes—
59C4⋊C4×C101C2312yes—
60C23×C101C2×D411yescharacteristic
61C22×D101—22no—
62C22×D101—22no—
63C22×D101—22no—
64C22×D101—42no—
65C22×D101—42no—
66C22×D101—42no—
67C22×D101D814yes—
68C22×D101C2×D412yes—
69C2×C4×C101—22no—
70C2×C4×C101—22no—
71C2×C4×C101—42no—
72C2×C4×C101—42no—
73C2×C4×C101C2×D411yescharacteristic
74C2×C4×C101#4112yes—
75C2×C4×C101#4112yes—
76C2×C4×C101C2411yescharacteristic
77C2×Dic101—22no—
78C2×Dic101—22no—
79C2×Dic101—42no—
80C2×Dic101C2×D412yes—
81D404—22no—
82D404—22no—
83D404—48no—
84D404—42no—
85C4×D101—24no—
86C4×D101—22no—
87C4×D101—22no—
88C4×D101—48no—
89C8×C101—22no—
90#11717579—22no—
91C22×C101#12312yes—
92C22×C101C2×D812yes—
93C22×C101#13712yes—
94C22×C101C22×D411yescharacteristic
95C2×D101—22no—
96C2×D101—22no—
97C2×D101—28no—
98C2×D101—42no—
99C2×D101—42no—
100C2×D101—42no—
101C2×D101—84no—
102C2×D101C2×D814yes—
103C4×C101—42no—
104C4×C101—42no—
105C4×C101#12312yes—
106C4×C101C2×#4111yescharacteristic
107C4×C101C2×#4111yescharacteristic
108Dic101—22no—
109Dic101—42no—
110C2×C101#48014yescomplemented
111C2×C101C2×#12311yescharacteristic
112C2×C101C22×D811yescharacteristic
113C2×C101C2×#13711yescharacteristic
114D101—24no—
115D101—82no—
116C2×#480—1011nomaximal, Sylow
117C101C2×#48011yescharacteristic, complemented, Sylow
118C2×#121—1011no—
119C22×C4⋊C4—1011no—
120#480—1018no—
121C2×#107—1011no—
122C2×#107D10111yescharacteristic, complemented
123C2×#102—1011no—
124C2×#102—1011no—
125C2×C22⋊C8—1011no—
126C22×D4—1011no—
127C22×D4—2021no—
128C23×C4—1011no—
129C23×C4—2021no—
130C22×C8—1011no—
131C22×C8C2×D10111yescharacteristic
132#121—1014no—
133#121—2022no—
134C2×C4⋊C4—1011no—
135C2×C4⋊C4—1014no—
136C2×C4⋊C4—2022no—
137C2×C4⋊C4—2021no—
138C2×C4⋊C4C2×D10111yescharacteristic
139C2×C4⋊C4C2×D10111yescharacteristic
140C2×C22⋊C4—2021no—
141#107—1014no—
142#107C2×D10114yescomplemented
143#102—1014no—
144#102—1014no—
145C22⋊C8—1014no—
146C24—1011no—
147C24—2021no—
148C2×D4—1012no—
149C2×D4—4044no—
150C2×D4—2024no—
151C2×D4—2021no—
152C2×D4—2022no—
153C2×D4—2022no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—1011no—
157C22×C4—1012no—
158C22×C4—1012no—
159C22×C4—4044no—
160C22×C4—2024no—
161C22×C4—2021no—
162C22×C4—2022no—
163C22×C4—2022no—
164C22×C4C22×D10111yescharacteristic
165C2×C8—22no—
166C2×C8—1012no—
167C2×C8—2022no—
168C2×C8C22×D10112yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—1012no—
172C4⋊C4—2024no—
173C4⋊C4—2021no—
174C4⋊C4C22×D10112yes—
175C4⋊C4C22×D10112yes—
176C22⋊C4—2024no—
177C23—1012no—
178C23—1014no—
179C23—4042no—
180C23—4042no—
181C23—4042no—
182C23—2022no—
183C23—2022no—
184C23—2022no—
185C23D4×D10111yescharacteristic
186D4—4048no—
187D4—4042no—
188D4—2022no—
189D4—2022no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—1012no—
195C2×C4—4048no—
196C2×C4—4042no—
197C2×C4—2022no—
198C2×C4—2022no—
199C2×C4—2022no—
200C2×C4—2022no—
201C2×C4—2024no—
202C2×C4D4×D10111yescharacteristic
203C2×C4#1310807412yes—
204C2×C4#1310807512yes—
205C2×C4C23×D10111yescharacteristic
206C8—22no—
207C8—2022no—
208C22—8084no—
209C22—1014no—
210C22—4042no—
211C22—4042no—
212C22—4042no—
213C22—2028no—
214C22—2022no—
215C22—2022no—
216C22#1569224012yes—
217C22D8×D10112yes—
218C22#1569228712yes—
219C22C2×D4×D10111yescharacteristic
220C4—42no—
221C4—42no—
222C4—4042no—
223C4—2022no—
224C4#1569224012yes—
225C4C2×#1310807411yescharacteristic
226C4C2×#1310807511yescharacteristic
227C2—8082no—
228C2—2024no—
229C2#2026549214yesdirect product factor
230C2C2×#1569224011yescharacteristic
231C2C2×D8×D10111yescharacteristic
232C2C2×#1569228711yescharacteristic
subgroupG/H
centerC23D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC2×#107×C101C2
socleC23×C101C2×D4
prime radicalC2×#15692230C2
hypercenterC2×#107D101
hypocenterC101C2×#480
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D101C2semidirect
3. #20265492C2direct (N × H)
4. C2×#15692188C2semidirect
5. C2×#15692177C2semidirect
6. C2×#15692175C2semidirect
7. C2×#15692167C2semidirect
8. C2×#107×C101C2semidirect
19. C4⋊C4×D101C22semidirect
21. #15692188C22semidirect
22. #15692177C22semidirect
23. #15692175C22semidirect
24. #15692167C22semidirect
28. #107×C101C22semidirect
110. C2×C101#480semidirect
117. C101C2×#480semidirect
122. C2×#107D101semidirect
142. #107C2×D101semidirect
229. C2#20265492direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156922302
C2×C4⋊C4×D1012
#202654922
C2×#156921882
C2×#156921772
C2×#156921752
C2×#156921672
C2×#107×C1012
C2×#480101