Finite Group Databasebeta

← C2×#20260944 #27151173

Subgroups — C2×#20260944 #27151173

Order 12416.

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

normal subgroups only

This group has 480 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
1C22×Dic388C211yesmaximal, characteristic
2C22×#13095501C211yesmaximal, characteristic
3C2×#15690808C211yesmaximal, characteristic
4C2×#15690775C211yesmaximal, characteristic
5#20260944C218yesmaximal, direct product factor
6C2×#15690739C211yesmaximal, characteristic
7C2×#15690733C211yesmaximal, characteristic
8C2×#103×C97C211yesmaximal, characteristic
9C22×Dic194C2211yescharacteristic
10C22×Dic194C2211yescharacteristic
11C2×Dic388—24no—
12C2×Dic388C2214yes—
13C2×#13095501—24no—
14C2×#13095501C2214yes—
15C22×#11715895C2211yescharacteristic
16#15690808—22no—
17#15690808C2214yes—
18#15690775—22no—
19#15690775C2214yes—
20C2×#13095490—21no—
21C2×#13095490—21no—
22C2×#13095490—21no—
23C2×C4×Dic97—21no—
24C2×C4×Dic97C2211yescharacteristic
25#15690739C2214yes—
26#15690733C2214yes—
27C22×Q8×C97C2211yescharacteristic
28C22×C8×C97C2211yescharacteristic
29C2×C4⋊C4×C97C2211yescharacteristic
30#103×C97C2214yes—
31C2×Dic194—21no—
32C2×Dic194—22no—
33C2×Dic194—22no—
34C2×Dic194—22no—
35C2×Dic194—21no—
36C2×Dic194D414yes—
37C2×Dic194C2312yes—
38C2×Dic194C2312yes—
39C22×Dic97—21no—
40C22×Dic97—21no—
41C22×Dic97D411yescharacteristic
42C22×Dic97D411yescharacteristic
43Dic388—28no—
44#13095501—28no—
45C2×#11715895—22no—
46C2×#11715895C2312yes—
47#13095490—24no—
48#13095490—24no—
49#13095490—24no—
50C4×Dic97—24no—
51C4×Dic97D412yes—
52C4×Dic97C2312yes—
53C2×Q8×C97—21no—
54C2×Q8×C97—22no—
55C2×Q8×C97—22no—
56C2×Q8×C97C2312yes—
57C22×C4×C97—21no—
58C22×C4×C97—21no—
59C22×C4×C97C2311yescharacteristic
60C2×C8×C97—22no—
61C2×C8×C97C2312yes—
62C4⋊C4×C97—21no—
63C4⋊C4×C97C2312yes—
64C23×C97C2×D411yescharacteristic
65Q8×C97—22no—
66Q8×C97—22no—
67Q8×C97—42no—
68C2×C4×C97—22no—
69C2×C4×C97—22no—
70C2×C4×C97—42no—
71C2×C4×C97—42no—
72C2×C4×C97C2×D411yescharacteristic
73C2×C4×C97C2×D412yes—
74C2×C4×C97#4112yes—
75C2×C4×C97C2411yescharacteristic
76C2×Dic97—24no—
77C2×Dic97—22no—
78C2×Dic97—22no—
79C2×Dic97—22no—
80C2×Dic97—42no—
81C2×Dic97Q1614yescomplemented
82C2×Dic97C2×D412yes—
83C2×Dic97C2×D412yes—
84Dic194—24no—
85Dic194—22no—
86Dic194—22no—
87Dic194—22no—
88Dic194—42no—
89Dic194C2×D414yes—
90C8×C97—22no—
91#11715895—22no—
92C22×C97#12112yes—
93C22×C97C2×Q1612yes—
94C22×C97#13712yes—
95C22×C97C22×D411yescharacteristic
96C4×C97—42no—
97C4×C97—42no—
98C4×C97#12112yes—
99C4×C97C22×D411yescharacteristic
100C4×C97C2×#4111yescharacteristic
101Dic97—24no—
102Dic97—22no—
103Dic97—42no—
104Dic97C2×Q1614yescomplemented
105C2×C97#46214yescomplemented
106C2×C97C2×#12111yescharacteristic
107C2×C97C22×Q1611yescharacteristic
108C2×C97C2×#13711yescharacteristic
109C2×#462—971nomaximal, Sylow
110C97C2×#46211yescharacteristic, complemented, Sylow
111C22×Q16—971no—
112C22×Q16—971no—
113C2×C4⋊Q8—971no—
114C2×C4×Q8—971no—
115#462—978no—
116C2×C4⋊C8—971no—
117C2×#103—971no—
118C2×#103D9711yescharacteristic
119C22×Q8—971no—
120C22×Q8—971no—
121C22×Q8C2×D9711yescharacteristic
122C2×Q16—974no—
123C2×Q16—974no—
124C2×Q16—1944no—
125C2×Q16—1944no—
126C22×C8—971no—
127C22×C8C2×D9711yescharacteristic
128C4⋊Q8—974no—
129C4⋊Q8—1942no—
130C4×Q8—974no—
131C4×Q8—1942no—
132C2×C4⋊C4—1941no—
133C2×C4⋊C4—1941no—
134C2×C4⋊C4—1941no—
135C2×C4⋊C4C2×D9711yescharacteristic
136C2×C42—971no—
137C2×C42—1941no—
138C4⋊C8—974no—
139#103—974no—
140#103C2×D9714yes—
141C2×Q8—21no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—974no—
145C2×Q8—972no—
146C2×Q8—972no—
147C2×Q8—1942no—
148C2×Q8—1942no—
149C2×Q8—1941no—
150C2×Q8—1941no—
151C2×Q8—1942no—
152C2×Q8C22×D9712yes—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—971no—
156C22×C4—971no—
157C22×C4—1941no—
158C22×C4—1941no—
159C22×C4C22×D9711yescharacteristic
160Q16—1948no—
161Q16—1948no—
162C2×C8—22no—
163C2×C8—972no—
164C2×C8—1942no—
165C2×C8C22×D9712yes—
166C4⋊C4—21no—
167C4⋊C4—1944no—
168C4⋊C4—1944no—
169C4⋊C4—1944no—
170C4⋊C4C22×D9712yes—
171C42—972no—
172C42—972no—
173C42—1944no—
174C23D4×D9711yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—42no—
178Q8—974no—
179Q8—3882no—
180Q8—1942no—
181Q8—1942no—
182Q8—1944no—
183Q8—1942no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—974no—
189C2×C4—972no—
190C2×C4—972no—
191C2×C4—3882no—
192C2×C4—1942no—
193C2×C4—1944no—
194C2×C4—1942no—
195C2×C4—1942no—
196C2×C4D4×D9711yescharacteristic
197C2×C4D4×D9712yes—
198C2×C4#1309551112yes—
199C2×C4C23×D9711yescharacteristic
200C8—22no—
201C8—1942no—
202C22#1569078312yes—
203C22Q16×D9712yes—
204C22#1569083912yes—
205C22C2×D4×D9711yescharacteristic
206C4—42no—
207C4—42no—
208C4—974no—
209C4—3882no—
210C4—1944no—
211C4—1942no—
212C4#1569078312yes—
213C4C2×D4×D9711yescharacteristic
214C4C2×#1309551111yescharacteristic
215C2#2026094414yesdirect product factor
216C2C2×#1569078311yescharacteristic
217C2C2×Q16×D9711yescharacteristic
218C2C2×#1569083911yescharacteristic
subgroupG/H
centerC23D4×D97
commutator, cosocleC2×C4×C97C24
FrattiniC2×C4C23×D97
FittingC2×#103×C97C2
socle, prime radicalC23×C97C2×D4
hypercenterC2×#103D97
hypocenterC97C2×#462
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
5. #20260944C2direct (N × H)
81. C2×Dic97Q16semidirect
104. Dic97C2×Q16semidirect
105. C2×C97#462semidirect
110. C97C2×#462semidirect
215. C2#20260944direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic3882
C22×#130955012
C2×#156908082
C2×#156907752
#202609442
C2×#156907392
C2×#156907332
C2×#103×C972
C2×#46297