Finite Group Databasebeta

← #99×Dic97 #27141526

Subgroups — #99×Dic97 #27141526

Order 12416.

412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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×D4×Dic97C211yesmaximal, characteristic
2C2×#15690725C211yesmaximal, characteristic
3C22⋊C4×Dic97C212yesmaximal, complemented
4#20260501C212yesmaximal, complemented
5C2×#99×C97C211yesmaximal, characteristic
6C23×Dic97C411yescharacteristic, complemented
7C23×Dic97C2211yescharacteristic
8D4×Dic97—22no—
9D4×Dic97—22no—
10C2×C4⋊Dic97C411yescharacteristic, complemented
11C2×C22⋊Dic97C411yescharacteristic, complemented
12C2×C22⋊Dic97C2211yescharacteristic
13C2×C22⋊Dic97C2212yes—
14C2×C4×Dic97—22no—
15C2×C4×Dic97C411yescharacteristic, complemented
16#15690725C414yescomplemented
17#15690717—22no—
18C22×D4×C97C2211yescharacteristic
19C2×C22⋊C4×C97C2212yes—
20#99×C97C414yescomplemented
21C22×Dic97—22no—
22C22×Dic97—21no—
23C22×Dic97—21no—
24C22×Dic97—42no—
25C22×Dic97—42no—
26C22×Dic97C2×C411yescharacteristic
27C22×Dic97C2×C411yescharacteristic
28C22×Dic97C2×C411yescharacteristic
29C22×Dic97C2×C411yescharacteristic
30C22×Dic97D412yes—
31C22×Dic97D412yes—
32C4⋊Dic97—22no—
33C22⋊Dic97—22no—
34C22⋊Dic97—22no—
35C22⋊Dic97—22no—
36C22⋊Dic97C2×C414yescomplemented
37C4×Dic97—21no—
38C4×Dic97—21no—
39C4×Dic97—44no—
40C24×C97C2×C411yescharacteristic
41C24×C97C2311yescharacteristic
42C2×D4×C97—22no—
43C2×D4×C97—22no—
44C2×D4×C97C2×C412yes—
45C2×D4×C97C2×C412yes—
46C22×C4×C97—22no—
47C22×C4×C97C2×C411yescharacteristic
48C22⋊C4×C97—22no—
49C22⋊C4×C97C2×C414yescomplemented
50C23×C97—21no—
51C23×C97—21no—
52C23×C97—41no—
53C23×C97—41no—
54C23×C97—41no—
55C23×C97—41no—
56C23×C97C4212yescomplemented
57C23×C97C22×C411yescharacteristic
58C23×C97C22×C411yescharacteristic
59C23×C97C22×C411yescharacteristic
60C23×C97C2×D412yes—
61C23×C97#4112yes—
62D4×C97—24no—
63D4×C97—24no—
64C2×C4×C97—21no—
65C2×C4×C97—21no—
66C2×C4×C97—24no—
67C2×C4×C97—42no—
68C2×C4×C97—42no—
69C2×C4×C97C4212yescomplemented
70C2×Dic97—24no—
71C2×Dic97—22no—
72C2×Dic97—21no—
73C2×Dic97—21no—
74C2×Dic97—24no—
75C2×Dic97—41no—
76C2×Dic97—42no—
77C2×Dic97—42no—
78C2×Dic97—42no—
79C2×Dic97—42no—
80C2×Dic97—42no—
81C2×Dic97—41no—
82C2×Dic97—41no—
83C2×Dic97C22⋊C411yescharacteristic
84C2×Dic97C22⋊C412yes—
85C2×Dic97C22⋊C411yescharacteristic
86C22×C97—22no—
87C22×C97—21no—
88C22×C97—22no—
89C22×C97—21no—
90C22×C97—22no—
91C22×C97—41no—
92C22×C97—41no—
93C22×C97—42no—
94C22×C97—42no—
95C22×C97—42no—
96C22×C97—41no—
97C22×C97—41no—
98C22×C97C2×C4211yescharacteristic
99C22×C97C2×C22⋊C411yescharacteristic
100C22×C97#11711yescharacteristic
101C22×C97C4×D412yes—
102C22×C97C4×D412yes—
103C4×C97—22no—
104C4×C97—44no—
105Dic97—21no—
106Dic97—22no—
107Dic97—44no—
108Dic97—41no—
109Dic97—41no—
110Dic97#9912yesdirect product factor
111C2×C97—22no—
112C2×C97—22no—
113C2×C97—21no—
114C2×C97—21no—
115C2×C97—42no—
116C2×C97C4×C22⋊C411yescharacteristic
117C2×C97C2×#9911yescharacteristic
118C2×C97#41011yescharacteristic
119C4×#99—971nomaximal, Sylow
120C97C4×#9911yescharacteristic, complemented, Sylow
121C2×C4×D4—971no—
122C2×#99—971no—
123C2×#99D9711yescharacteristic
124C4×C22⋊C4—972no—
125#342—972no—
126C22×D4C2×D9711yescharacteristic
127C23×C4—971no—
128C23×C4—971no—
129C4×D4—1942no—
130C4×D4—1942no—
131C2×C4⋊C4—971no—
132C2×C22⋊C4—972no—
133C2×C22⋊C4—971no—
134C2×C22⋊C4—971no—
135C2×C22⋊C4C2×D9712yes—
136C2×C42—971no—
137C2×C42—1942no—
138#99—974no—
139#99Dic9714yesdirect product factor
140#95—1942no—
141C24C4×D9711yescharacteristic
142C24C22×D9711yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C4×D9712yes—
146C2×D4C2×Dic9712yes—
147C22×C4—22no—
148C22×C4—971no—
149C22×C4—972no—
150C22×C4—971no—
151C22×C4—972no—
152C22×C4—971no—
153C22×C4—971no—
154C22×C4—3882no—
155C22×C4—3882no—
156C22×C4—1941no—
157C22×C4—1941no—
158C22×C4—1942no—
159C22×C4C4×D9711yescharacteristic
160C4⋊C4—1942no—
161C22⋊C4—22no—
162C22⋊C4—974no—
163C22⋊C4—1942no—
164C22⋊C4—1942no—
165C22⋊C4—1942no—
166C22⋊C4C2×Dic9714yescomplemented
167C42—3884no—
168C42—1941no—
169C42—1941no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23C4×Dic9712yescomplemented
177C23C2×C4×D9711yescharacteristic
178C23C2×C4×D9711yescharacteristic
179C23C22×Dic9711yescharacteristic
180C23D4×D9712yes—
181C23#1309551012yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—971no—
190C2×C4—971no—
191C2×C4—972no—
192C2×C4—3882no—
193C2×C4—3882no—
194C2×C4—3882no—
195C2×C4—3882no—
196C2×C4—3881no—
197C2×C4—3881no—
198C2×C4—3882no—
199C2×C4—3881no—
200C2×C4—1944no—
201C2×C4—1942no—
202C2×C4—1941no—
203C2×C4—1941no—
204C2×C4—1944no—
205C2×C4C4×Dic9712yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C2×C4×Dic9711yescharacteristic
219C22C22⋊C4×D9711yescharacteristic
220C22#1569076611yescharacteristic
221C22#1569077012yes—
222C22D4×Dic9712yes—
223C4—22no—
224C4—44no—
225C4—972no—
226C4—3884no—
227C4—3881no—
228C4—3881no—
229C4—1941no—
230C4—1942no—
231C2—22no—
232C2—22no—
233C2—21no—
234C2—21no—
235C2—42no—
236C2C22⋊C4×Dic9711yescharacteristic
237C2#99×D9711yescharacteristic
238C2#2026070711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D97
commutatorC22×C97C2×C42
FrattiniC24C22×D97
FittingC2×#99×C97C2
socleC22×C97C2×C22⋊C4
prime radicalC22×D4×C97C22
cosocleC24×C97C23
hypercenterC2×#99D97
hypocenterC97C4×#99
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×Dic97C2semidirect
4. #20260501C2semidirect
6. C23×Dic97C4semidirect
10. C2×C4⋊Dic97C4semidirect
11. C2×C22⋊Dic97C4semidirect
15. C2×C4×Dic97C4semidirect
16. #15690725C4semidirect
20. #99×C97C4semidirect
36. C22⋊Dic97C2×C4semidirect
49. C22⋊C4×C97C2×C4semidirect
56. C23×C97C42semidirect
69. C2×C4×C97C42semidirect
110. Dic97#99direct (N × H)
120. C97C4×#99semidirect
139. #99Dic97direct (N × H)
166. C22⋊C4C2×Dic97semidirect
176. C23C4×Dic97semidirect
205. C2×C4C4×Dic97semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic972
C2×#156907252
C22⋊C4×Dic972
#202605012
C2×#99×C972
C4×#9997