Finite Group Databasebeta

← C2×#20265471 #27180902

Subgroups — C2×#20265471 #27180902

Order 12928.

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

normal subgroups only

This group has 416 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×#15692254C211yesmaximal, characteristic
2C2×#15692220C211yesmaximal, characteristic
3#20265471C218yesmaximal, direct product factor
4C2×#15692188C211yesmaximal, characteristic
5C2×#15692184C211yesmaximal, characteristic
6C2×#15692180C211yesmaximal, characteristic
7C2×#15692178C211yesmaximal, characteristic
8C2×#107×C101C211yesmaximal, characteristic
9C22×Dic202—21no—
10C22×Dic202C2211yescharacteristic
11C22×#11717579C2211yescharacteristic
12#15692254—22no—
13#15692254C2214yes—
14#15692220—22no—
15#15692220C2214yes—
16C2×C4⋊Dic101C2211yescharacteristic
17C2×#13108053—21no—
18C2×#13108053—21no—
19C2×C4×Dic101—21no—
20C2×C4×Dic101C2211yescharacteristic
21#15692188C2214yes—
22#15692184C2214yes—
23#15692180C2214yes—
24#15692178C2214yes—
25C22×C8×C101C2211yescharacteristic
26C2×C4⋊C4×C101C2211yescharacteristic
27C2×C4⋊C4×C101C2211yescharacteristic
28#107×C101C2214yes—
29C2×Dic202—21no—
30C2×Dic202—22no—
31C2×Dic202—24no—
32C2×Dic202—44no—
33C2×Dic202Q814yescomplemented
34C2×Dic202C2312yes—
35C22×Dic101—21no—
36C22×Dic101—21no—
37C22×Dic101D411yescharacteristic
38C22×Dic101D411yescharacteristic
39C2×#11717579—22no—
40C2×#11717579C2312yes—
41C4⋊Dic101—21no—
42C4⋊Dic101C2312yes—
43#13108053—24no—
44#13108053—24no—
45C4×Dic101—24no—
46C4×Dic101D412yes—
47C4×Dic101C2312yes—
48C22×C4×C101—21no—
49C22×C4×C101—21no—
50C22×C4×C101C2311yescharacteristic
51C2×C8×C101—22no—
52C2×C8×C101C2312yes—
53C4⋊C4×C101—21no—
54C4⋊C4×C101—21no—
55C4⋊C4×C101C2312yes—
56C4⋊C4×C101C2312yes—
57C23×C101C2×D411yescharacteristic
58C2×C4×C101—22no—
59C2×C4×C101—22no—
60C2×C4×C101—42no—
61C2×C4×C101—42no—
62C2×C4×C101C2×D411yescharacteristic
63C2×C4×C101C2×Q812yes—
64C2×C4×C101#4112yes—
65C2×C4×C101C2411yescharacteristic
66C2×Dic101—24no—
67C2×Dic101—22no—
68C2×Dic101—22no—
69C2×Dic101—22no—
70C2×Dic101—42no—
71C2×Dic101Q1614yes—
72C2×Dic101C2×D412yes—
73C2×Dic101C2×D412yes—
74Dic202—24no—
75Dic202—22no—
76Dic202—48no—
77Dic202C2×Q814yescomplemented
78C8×C101—22no—
79#11717579—22no—
80C22×C101C22⋊Q812yes—
81C22×C101C2×Q1612yes—
82C22×C101AGL(1,ℤ/8)12yes—
83C22×C101C22×D411yescharacteristic
84C4×C101—42no—
85C4×C101—42no—
86C4×C101C22⋊Q812yes—
87C4×C101C22×Q811yescharacteristic
88C4×C101C2×#4111yescharacteristic
89Dic101—24no—
90Dic101—22no—
91Dic101—42no—
92Dic101C2×Q1614yes—
93C2×C101#47714yescomplemented
94C2×C101C2×C22⋊Q811yescharacteristic
95C2×C101C22×Q1611yescharacteristic
96C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
97C2×#477—1011nomaximal, Sylow
98C101C2×#47711yescharacteristic, complemented, Sylow
99C2×C4⋊Q8—1011no—
100C2×C4×Q8—1011no—
101#477—1018no—
102C2×#107—1011no—
103C2×#107D10111yescharacteristic
104C2×C4⋊C8—1011no—
105C2×#103—1011no—
106C2×#103—1011no—
107C22×Q8—1011no—
108C22×Q8—2021no—
109C22×C8—1011no—
110C22×C8C2×D10111yescharacteristic
111C4⋊Q8—1014no—
112C4⋊Q8—2022no—
113C4×Q8—1014no—
114C4×Q8—2022no—
115C2×C4⋊C4—1011no—
116C2×C4⋊C4—2021no—
117C2×C4⋊C4—2021no—
118C2×C4⋊C4C2×D10111yescharacteristic
119C2×C4⋊C4C2×D10111yescharacteristic
120C2×C42—1011no—
121C2×C42—2021no—
122#107—1014no—
123#107C2×D10114yes—
124C4⋊C8—1014no—
125#103—1014no—
126#103—1014no—
127C2×Q8—1014no—
128C2×Q8—1012no—
129C2×Q8—4044no—
130C2×Q8—2024no—
131C2×Q8—2021no—
132C2×Q8—2022no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—1011no—
136C22×C4—1011no—
137C22×C4—2021no—
138C22×C4—2021no—
139C22×C4C22×D10111yescharacteristic
140C2×C8—22no—
141C2×C8—1012no—
142C2×C8—2022no—
143C2×C8C22×D10112yes—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1012no—
147C4⋊C4—2024no—
148C4⋊C4—2024no—
149C4⋊C4—2021no—
150C4⋊C4C22×D10112yes—
151C4⋊C4C22×D10112yes—
152C42—1012no—
153C42—1012no—
154C42—2024no—
155C23D4×D10111yescharacteristic
156Q8—1014no—
157Q8—4048no—
158Q8—2022no—
159Q8—2024no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—1012no—
165C2×C4—1014no—
166C2×C4—1012no—
167C2×C4—4042no—
168C2×C4—2022no—
169C2×C4—2022no—
170C2×C4—2024no—
171C2×C4—2022no—
172C2×C4D4×D10111yescharacteristic
173C2×C4Q8×D10112yes—
174C2×C4#1310807412yes—
175C2×C4C23×D10111yescharacteristic
176C8—22no—
177C8—2022no—
178C22#1569223312yes—
179C22Q16×D10112yes—
180C22#1569227912yes—
181C22C2×D4×D10111yescharacteristic
182C4—42no—
183C4—42no—
184C4—1014no—
185C4—4042no—
186C4—2024no—
187C4—2022no—
188C4#1569223312yes—
189C4C2×Q8×D10111yescharacteristic
190C4C2×#1310807411yescharacteristic
191C2#2026547114yesdirect product factor
192C2C2×#1569223311yescharacteristic
193C2C2×Q16×D10111yescharacteristic
194C2C2×#1569227911yescharacteristic
subgroupG/H
centerC23D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC2×#107×C101C2
socle, prime radicalC23×C101C2×D4
hypercenterC2×#107D101
hypocenterC101C2×#477
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
3. #20265471C2direct (N × H)
33. C2×Dic202Q8semidirect
77. Dic202C2×Q8semidirect
93. C2×C101#477semidirect
98. C101C2×#477semidirect
191. C2#20265471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156922542
C2×#156922202
#202654712
C2×#156921882
C2×#156921842
C2×#156921802
C2×#156921782
C2×#107×C1012
C2×#477101