Finite Group Databasebeta

← C2×#20265482 #27180907

Subgroups — C2×#20265482 #27180907

Order 12928.

384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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×#15692246C211yesmaximal, characteristic
2C2×Q8×Dic101C211yesmaximal, characteristic
3#20265482C218yesmaximal, direct product factor
4C2×#15692188C211yesmaximal, characteristic
5C2×#15692187C211yesmaximal, characteristic
6C2×#15692184C211yesmaximal, characteristic
7C2×#15692179C211yesmaximal, characteristic
8C2×#103×C101C211yesmaximal, characteristic
9C22×#11717579C2211yescharacteristic
10#15692246—22no—
11#15692246C2214yes—
12Q8×Dic101—22no—
13Q8×Dic101C2214yes—
14C2×C4⋊Dic101—21no—
15C2×C4⋊Dic101—21no—
16C2×C4⋊Dic101C2211yescharacteristic
17C2×C4⋊Dic101C2211yescharacteristic
18C2×#13108053—21no—
19C2×C4×Dic101—21no—
20C2×C4×Dic101C2211yescharacteristic
21#15692188C2214yes—
22#15692187C2214yes—
23#15692184C2214yes—
24#15692179C2214yes—
25C22×Q8×C101C2211yescharacteristic
26C22×C8×C101C2211yescharacteristic
27C2×C4⋊C4×C101C2211yescharacteristic
28#103×C101C2214yes—
29C22×Dic101—21no—
30C22×Dic101—21no—
31C22×Dic101D411yescharacteristic
32C22×Dic101D411yescharacteristic
33C2×#11717579—22no—
34C2×#11717579C2312yes—
35C4⋊Dic101—21no—
36C4⋊Dic101—21no—
37C4⋊Dic101—24no—
38C4⋊Dic101—24no—
39C4⋊Dic101C2312yes—
40C4⋊Dic101C2312yes—
41#13108053—24no—
42C4×Dic101—24no—
43C4×Dic101D412yes—
44C4×Dic101C2312yes—
45C2×Q8×C101—21no—
46C2×Q8×C101—22no—
47C2×Q8×C101Q814yes—
48C2×Q8×C101C2312yes—
49C22×C4×C101—21no—
50C22×C4×C101—21no—
51C22×C4×C101C2311yescharacteristic
52C2×C8×C101—22no—
53C2×C8×C101C2312yes—
54C4⋊C4×C101—21no—
55C4⋊C4×C101C2312yes—
56C23×C101C2×D411yescharacteristic
57Q8×C101—24no—
58Q8×C101—22no—
59Q8×C101C2×Q814yes—
60C2×C4×C101—24no—
61C2×C4×C101—22no—
62C2×C4×C101—22no—
63C2×C4×C101—42no—
64C2×C4×C101C2×D411yescharacteristic
65C2×C4×C101C2×Q812yes—
66C2×C4×C101#4112yes—
67C2×C4×C101C2411yescharacteristic
68C2×Dic101—22no—
69C2×Dic101—22no—
70C2×Dic101—22no—
71C2×Dic101—22no—
72C2×Dic101—42no—
73C2×Dic101—42no—
74C2×Dic101C2×D412yes—
75C2×Dic101C2×D412yes—
76C8×C101—22no—
77#11717579—22no—
78C22×C101C22⋊Q812yes—
79C22×C101#13512yes—
80C22×C101#13712yes—
81C22×C101C22×D411yescharacteristic
82C4×C101—24no—
83C4×C101—42no—
84C4×C101C22⋊Q812yes—
85C4×C101C22×Q811yescharacteristic
86C4×C101C2×#4111yescharacteristic
87Dic101—22no—
88Dic101—22no—
89Dic101—42no—
90Dic101—42no—
91C2×C101#47914yescomplemented
92C2×C101C2×C22⋊Q811yescharacteristic
93C2×C101C2×#13511yescharacteristic
94C2×C101C2×#13711yescharacteristic
95C2×#479—1011nomaximal, Sylow
96C101C2×#47911yescharacteristic, complemented, Sylow
97C2×#125—1011no—
98C2×C4×Q8—1011no—
99#479—1018no—
100C2×#107—1011no—
101C2×#106—1011no—
102C2×C4⋊C8—1011no—
103C2×#103—1011no—
104C2×#103D10111yescharacteristic
105C22×Q8C2×D10111yescharacteristic
106C22×C8—1011no—
107C22×C8C2×D10111yescharacteristic
108#125—1014no—
109#125—2022no—
110C4×Q8—1014no—
111C4×Q8—2022no—
112C2×C4⋊C4—1011no—
113C2×C4⋊C4—1011no—
114C2×C4⋊C4—2021no—
115C2×C4⋊C4—2021no—
116C2×C4⋊C4—2021no—
117C2×C4⋊C4C2×D10111yescharacteristic
118C2×C42—1011no—
119C2×C42—2021no—
120#107—1014no—
121#106—1014no—
122C4⋊C8—1014no—
123#103—1014no—
124#103C2×D10114yes—
125C2×Q8—21no—
126C2×Q8—22no—
127C2×Q8Dic20214yes—
128C2×Q8C22×D10112yes—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—1011no—
132C22×C4—1011no—
133C22×C4—2021no—
134C22×C4—2021no—
135C22×C4C22×D10111yescharacteristic
136C2×C8—22no—
137C2×C8—1012no—
138C2×C8—2022no—
139C2×C8C22×D10112yes—
140C4⋊C4—21no—
141C4⋊C4—1012no—
142C4⋊C4—1012no—
143C4⋊C4—2024no—
144C4⋊C4—2024no—
145C4⋊C4—2024no—
146C4⋊C4—2021no—
147C4⋊C4—2021no—
148C4⋊C4C22×D10112yes—
149C42—1012no—
150C42—1012no—
151C42—2024no—
152C23D4×D10111yescharacteristic
153Q8—22no—
154Q8—24no—
155Q8C2×Dic20214yes—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—1012no—
161C2×C4—1012no—
162C2×C4—4042no—
163C2×C4—4042no—
164C2×C4—2022no—
165C2×C4—2022no—
166C2×C4—2022no—
167C2×C4—2022no—
168C2×C4D4×D10111yescharacteristic
169C2×C4C2×Dic20212yes—
170C2×C4#1310807312yes—
171C2×C4C23×D10111yescharacteristic
172C8—22no—
173C8—2022no—
174C22#1569223212yes—
175C22#1569227612yes—
176C22#1569228712yes—
177C22C2×D4×D10111yescharacteristic
178C4—24no—
179C4—42no—
180C4—4042no—
181C4—4042no—
182C4—2022no—
183C4—2022no—
184C4#1569223212yes—
185C4C22×Dic20211yescharacteristic
186C4C2×#1310807311yescharacteristic
187C2#2026548214yesdirect product factor
188C2C2×#1569223211yescharacteristic
189C2C2×#1569227611yescharacteristic
190C2C2×#1569228711yescharacteristic
subgroupG/H
centerC23D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC2×#103×C101C2
socle, prime radicalC23×C101C2×D4
hypercenterC2×#103D101
hypocenterC101C2×#479
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #20265482C2direct (N × H)
91. C2×C101#479semidirect
96. C101C2×#479semidirect
187. C2#20265482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156922462
C2×Q8×Dic1012
#202654822
C2×#156921882
C2×#156921872
C2×#156921842
C2×#156921792
C2×#103×C1012
C2×#479101