Finite Group Databasebeta

← C2×D97⋊#99 #27158329

Subgroups — C2×D97⋊#99 #27158329

Order 12416.

1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 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×C22⋊#87604C212yesmaximal, complemented
2C2×#15690869C212yesmaximal, complemented
3D97⋊#99C218yesmaximal, direct product factor
4C2×#15690868C212yesmaximal, complemented
5C22×D4×D97C211yesmaximal, characteristic
6C23×#87604—22no—
7C2×C22⋊#87604—24no—
8C2×C22⋊#87604—22no—
9C2×C22⋊#87604C2214yescomplemented
10C2×C22⋊#87604C2218yescomplemented
11#15690869C2218yescomplemented
12#15690868C2218yescomplemented
13C24×D97C411yescharacteristic, complemented
14C24×D97C2211yescharacteristic
15C22×D388C2211yescharacteristic
16C22×C22⋊D97C411yescharacteristic, complemented
17C22×C22⋊D97C2211yescharacteristic
18C2×D4×D97—22no—
19C2×D4×D97—22no—
20C2×D4×D97—24no—
21C2×D4×D97C414yescomplemented
22C2×D4×D97C2214yes—
23C22×C4×D97C411yescharacteristic, complemented
24C22×D4×C97C411yescharacteristic, complemented
25C22×#87604—28no—
26C22×#87604—24no—
27C22×#87604—48no—
28C22⋊#87604—28no—
29C22⋊#87604—24no—
30C22⋊#87604C2318yescomplemented
31C23×D97—22no—
32C23×D97—21no—
33C23×D97—21no—
34C23×D97—44no—
35C23×D97—44no—
36C23×D97C2×C411yescharacteristic
37C23×D97C2×C412yes—
38C23×D97C2×C414yescomplemented
39C23×D97C2×C411yescharacteristic, complemented
40C23×D97D412yes—
41C23×D97D414yes—
42C23×D97D412yes—
43C23×D97C2312yes—
44C23×D97C2311yescharacteristic
45C2×D388—22no—
46C2×D388—22no—
47C2×D388C2×C412yescomplemented
48C2×D388C2312yes—
49C2×C22⋊D97—22no—
50C2×C22⋊D97—22no—
51C2×C22⋊D97—22no—
52C2×C22⋊D97—22no—
53C2×C22⋊D97C2×C412yescomplemented
54C2×C22⋊D97C2×C414yescomplemented
55C2×C22⋊D97C2312yes—
56D4×D97—28no—
57D4×D97—28no—
58D4×D97—28no—
59D4×D97—28no—
60C22×Dic97C2×C411yescharacteristic, complemented
61C2×C4×D97—22no—
62C2×C4×D97—21no—
63C2×C4×D97—21no—
64C2×C4×D97C2×C414yescomplemented
65C24×C97C2×C411yescharacteristic
66C24×C97C2×C411yescharacteristic, complemented
67C2×D4×C97—22no—
68C2×D4×C97—22no—
69C2×D4×C97C2×C414yescomplemented
70C22×C4×C97C2×C411yescharacteristic, complemented
71C23×C97—21no—
72C23×C97—21no—
73C23×C97—42no—
74C23×C97—42no—
75C23×C97C22⋊C412yes—
76C23×C97C22⋊C412yes—
77C23×C97C22×C411yescharacteristic
78C23×C97C22×C412yes—
79C23×C97C22×C412yescomplemented
80C22×D97—24no—
81C22×D97—28no—
82C22×D97—21no—
83C22×D97—21no—
84C22×D97—24no—
85C22×D97—24no—
86C22×D97—44no—
87C22×D97—48no—
88C22×D97—44no—
89C22×D97—44no—
90C22×D97—42no—
91C22×D97—44no—
92C22×D97—48no—
93C22×D97—48no—
94C22×D97—44no—
95C22×D97—42no—
96C22×D97C22⋊C412yes—
97C22×D97C22⋊C411yescharacteristic
98C22×D97C22⋊C414yes—
99C22×D97C22⋊C414yes—
100C22×D97C22⋊C411yescharacteristic
101C22×D97C22×C412yes—
102C22×D97C22×C411yescharacteristic
103C22×D97C22×C412yescomplemented
104C22×D97C2×D414yes—
105C22×D97C2×D412yes—
106C22×D97C2×D414yes—
107C22×D97C2×D412yes—
108C22×D97C2411yescharacteristic
109C2×#87604—28no—
110C2×#87604—48no—
111C2×#87604—416no—
112D4×C97—28no—
113C2×C4×C97—21no—
114C2×C4×C97—21no—
115C2×C4×C97C22×C412yescomplemented
116C22⋊D97—28no—
117C22⋊D97—24no—
118C22⋊D97—24no—
119C2×Dic97—21no—
120C2×Dic97—21no—
121C2×Dic97C22×C412yescomplemented
122D388—24no—
123D388—24no—
124C4×D97—24no—
125C4×D97—24no—
126C22×C97—22no—
127C22×C97—24no—
128C22×C97—22no—
129C22×C97—42no—
130C22×C97—42no—
131C22×C97—42no—
132C22×C97—42no—
133C22×C97—42no—
134C22×C97C2×C22⋊C411yescharacteristic
135C22×C97C2×C22⋊C414yes—
136C22×C97C2×C22⋊C411yescharacteristic
137C22×C97C23×C411yescharacteristic
138C2×D97—24no—
139C2×D97—22no—
140C2×D97—28no—
141C2×D97—24no—
142C2×D97—24no—
143C2×D97—28no—
144C2×D97—22no—
145C2×D97—44no—
146C2×D97—41no—
147C2×D97—44no—
148C2×D97—42no—
149C2×D97—41no—
150C2×D97—48no—
151C2×D97—42no—
152C2×D97—42no—
153C2×D97—48no—
154C2×D97—42no—
155C2×D97#9914yescomplemented
156C2×D97C2×C22⋊C412yes—
157C2×D97C2×C22⋊C412yes—
158C2×D97C2×C22⋊C412yes—
159C2×D97C22×D412yes—
160#87604—48no—
161C4×C97—22no—
162Dic97—22no—
163C2×C97—21no—
164C2×C97—21no—
165C2×C97—24no—
166C2×C97—42no—
167C2×C97C2×#9912yescomplemented
168C2×C97C22×C22⋊C411yescharacteristic
169D97—22no—
170D97—22no—
171D97—22no—
172D97—42no—
173D97C2×#9914yescomplemented
174C22×#99—971nomaximal, Sylow
175C97C22×#9911yescharacteristic, complemented, Sylow
176C23×D4—971no—
177C22×C22⋊C4—972no—
178C2×#99—972no—
179C2×#99—978no—
180C2×#99—972no—
181C25—971no—
182C25—971no—
183C22×D4—971no—
184C22×D4—971no—
185C22×D4—974no—
186C22×D4—974no—
187C22×D4—971no—
188C22×D4—1944no—
189C22×D4—1942no—
190C22×D4—1942no—
191C22×D4#8760411yescharacteristic, complemented
192C23×C4—971no—
193C23×C4—1942no—
194C2×C22⋊C4—974no—
195C2×C22⋊C4—978no—
196C2×C22⋊C4—1944no—
197C2×C22⋊C4—1942no—
198#99—978no—
199#99—978no—
200C24—972no—
201C24—974no—
202C24—972no—
203C24—971no—
204C24—972no—
205C24—972no—
206C24—971no—
207C24—971no—
208C24—974no—
209C24—3884no—
210C24—3884no—
211C24—1942no—
212C24—1941no—
213C24—1941no—
214C24C2×#8760411yescharacteristic
215C24C2×#8760411yescharacteristic, complemented
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—974no—
219C2×D4—972no—
220C2×D4—972no—
221C2×D4—972no—
222C2×D4—972no—
223C2×D4—1942no—
224C2×D4—1942no—
225C2×D4—1948no—
226C2×D4—1948no—
227C2×D4—1948no—
228C2×D4—1948no—
229C2×D4—1942no—
230C2×D4—1942no—
231C2×D4—1942no—
232C2×D4—1942no—
233C2×D4C2×#8760414yescomplemented
234C22×C4—971no—
235C22×C4—974no—
236C22×C4—3888no—
237C22×C4—1942no—
238C22×C4—1941no—
239C22×C4—1941no—
240C22×C4—1948no—
241C22×C4—1944no—
242C22×C4C2×#8760411yescharacteristic, complemented
243C22⋊C4—978no—
244C22⋊C4—1948no—
245C22⋊C4—1944no—
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—971no—
251C23—974no—
252C23—972no—
253C23—974no—
254C23—971no—
255C23—971no—
256C23—974no—
257C23—972no—
258C23—974no—
259C23—972no—
260C23—971no—
261C23—972no—
262C23—972no—
263C23—3882no—
264C23—3882no—
265C23—3884no—
266C23—3884no—
267C23—3888no—
268C23—3884no—
269C23—3888no—
270C23—3888no—
271C23—3884no—
272C23—3884no—
273C23—1944no—
274C23—1944no—
275C23—1948no—
276C23—1944no—
277C23—1941no—
278C23—1941no—
279C23C22⋊#8760412yes—
280C23C22⋊#8760412yes—
281C23C22×#8760411yescharacteristic
282C23C22×#8760412yes—
283C23C22×#8760412yescomplemented
284D4—28no—
285D4—1944no—
286D4—1944no—
287D4—1944no—
288D4—1944no—
289D4—1948no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—972no—
293C2×C4—38816no—
294C2×C4—3888no—
295C2×C4—1944no—
296C2×C4—1944no—
297C2×C4—1948no—
298C2×C4—1941no—
299C2×C4—1941no—
300C2×C4C22×#8760412yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—974no—
310C22—972no—
311C22—972no—
312C22—972no—
313C22—972no—
314C22—3882no—
315C22—3882no—
316C22—3882no—
317C22—3881no—
318C22—3881no—
319C22—3884no—
320C22—3884no—
321C22—3888no—
322C22—3888no—
323C22—3882no—
324C22—1948no—
325C22—1944no—
326C22—1944no—
327C22—1948no—
328C22—1942no—
329C22—1944no—
330C22—1942no—
331C22C2×C22⋊#8760411yescharacteristic
332C22C2×C22⋊#8760414yes—
333C22C2×C22⋊#8760411yescharacteristic
334C22C23×#8760411yescharacteristic
335C4—22no—
336C4—3888no—
337C4—1942no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—974no—
343C2—3882no—
344C2—1942no—
345C2—1942no—
346C2—1942no—
347C2D97⋊#9912yesdirect product factor
348C2C22×C22⋊#8760411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87604
commutatorC22×C97C23×C4
FrattiniC22C23×#87604
FittingC22×D4×C97C4
socleC22×C97C2×C22⋊C4
prime radicalC22×D4×D97C2
cosocleC22×D97C24
hypercenterC22×D4#87604
hypocenterC97C22×#99
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#87604C2semidirect
2. C2×#15690869C2semidirect
3. D97⋊#99C2direct (N × H)
4. C2×#15690868C2semidirect
9. C2×C22⋊#87604C22semidirect
10. C2×C22⋊#87604C22semidirect
11. #15690869C22semidirect
12. #15690868C22semidirect
13. C24×D97C4semidirect
16. C22×C22⋊D97C4semidirect
21. C2×D4×D97C4semidirect
23. C22×C4×D97C4semidirect
24. C22×D4×C97C4semidirect
30. C22⋊#87604C23semidirect
38. C23×D97C2×C4semidirect
39. C23×D97C2×C4semidirect
47. C2×D388C2×C4semidirect
53. C2×C22⋊D97C2×C4semidirect
54. C2×C22⋊D97C2×C4semidirect
60. C22×Dic97C2×C4semidirect
64. C2×C4×D97C2×C4semidirect
66. C24×C97C2×C4semidirect
69. C2×D4×C97C2×C4semidirect
70. C22×C4×C97C2×C4semidirect
79. C23×C97C22×C4semidirect
103. C22×D97C22×C4semidirect
115. C2×C4×C97C22×C4semidirect
121. C2×Dic97C22×C4semidirect
155. C2×D97#99semidirect
167. C2×C97C2×#99semidirect
173. D97C2×#99semidirect
175. C97C22×#99semidirect
191. C22×D4#87604semidirect
215. C24C2×#87604semidirect
233. C2×D4C2×#87604semidirect
242. C22×C4C2×#87604semidirect
283. C23C22×#87604semidirect
300. C2×C4C22×#87604semidirect
347. C2D97⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#876042
C2×#156908692
D97⋊#992
C2×#156908682
C22×D4×D972
C22×#9997