Finite Group Databasebeta

← C2×#20245794 #26374574

Subgroups — C2×#20245794 #26374574

Order 12032.

3854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093982C212yesmaximal
2C22×C42×D47C211yesmaximal, characteristic
3#20245794C2116yesmaximal, direct product factor
4C2×#15688992C212yesmaximal, complemented
5C2×#15688989C211yesmaximal, characteristic, complemented
6C2×#15688982C214yesmaximal
7C2×#15688974C214yesmaximal, complemented
8C2×C47×#382C211yesmaximal, characteristic, complemented
9C23×C4×D47C2212yes—
10C23×C4×D47C2211yescharacteristic
11C2×#13093982—216no—
12C2×#13093982C22116yes—
13C22×C4⋊Dic47C2212yes—
14C22×Dic47⋊C4C2218yes—
15C22×(C2×D47)⋊C4C2214yes—
16C22×C4×Dic47C2214yes—
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19C2×C42×D47C4116yescomplemented
20C2×C42×D47C2218yes—
21#15688992C22116yescomplemented
22#15688989C2218yescomplemented
23#15688982C22132yes—
24#15688974C22132yescomplemented
25C2×C47⋊#95C2214yes—
26C22×C4⋊C4×C47C2212yes—
27C22×C42×C47C2211yescharacteristic
28C47×#382C2218yescomplemented
29C2×#95×C47C2214yes—
30C24×D47C2311yescharacteristic
31C23×Dic47C2314yes—
32C23×Dic47C2311yescharacteristic
33C23×Dic47C2312yes—
34C22×C4×D47—216no—
35C22×C4×D47C2×C4116yes—
36C22×C4×D47C2×C418yes—
37C22×C4×D47D418yes—
38C22×C4×D47Q818yes—
39C22×C4×D47C2318yes—
40C22×C4×D47C2314yes—
41#13093982—264no—
42C2×C4⋊Dic47—28no—
43C2×C4⋊Dic47C2318yes—
44C2×Dic47⋊C4—232no—
45C2×Dic47⋊C4C23132yes—
46C2×(C2×D47)⋊C4—216no—
47C2×(C2×D47)⋊C4C23116yes—
48C2×C4×Dic47—216no—
49C2×C4×Dic47C2×C4116yes—
50C2×C4×Dic47C2×C418yes—
51C2×C4×Dic47C23116yes—
52C2×C4×Dic47C2318yes—
53C2×C4×Dic47C2314yes—
54C42×D47C2×C4164yescomplemented
55C47⋊#95C23116yes—
56C23×C4×C47C2314yes—
57C23×C4×C47C2312yes—
58C23×C4×C47C2311yescharacteristic
59C2×C4⋊C4×C47—28no—
60C2×C4⋊C4×C47C2318yes—
61C2×C42×C47C2×C418yes—
62C2×C42×C47C2314yes—
63#95×C47C23116yes—
64C24×C47C2411yescharacteristic
65C23×D47—28no—
66C23×D47C22×C414yes—
67C23×D47C2×D414yes—
68C23×D47C2×Q814yes—
69C23×D47C2412yes—
70C22×C4×C47—28no—
71C22×C4×C47—28no—
72C22×C4×C47—216no—
73C22×C4×C47C22×C418yes—
74C22×C4×C47C22×C414yes—
75C22×C4×C47C2×D414yes—
76C22×C4×C47C2×Q814yes—
77C22×C4×C47C2418yes—
78C22×C4×C47C2414yes—
79C22×C4×C47C2412yes—
80C22×Dic47—28no—
81C22×Dic47—216no—
82C22×Dic47C22×C414yes—
83C22×Dic47C22×C418yes—
84C22×Dic47C2×D414yes—
85C22×Dic47C2×Q814yes—
86C22×Dic47#41116yes—
87C22×Dic47C2418yes—
88C22×Dic47C2412yes—
89C22×Dic47C2414yes—
90C2×C4×D47—264no—
91C2×C4×D47—232no—
92C2×C4×D47C4⋊C4164yescomplemented
93C2×C4×D47C22×C4132yes—
94C2×C4×D47C22×C4116yes—
95C2×C4×D47C2×D4116yes—
96C2×C4×D47C2×Q8116yes—
97C4⋊C4×C47—216no—
98C42×C47C22×C4116yes—
99(C2×D47)⋊C4—232no—
100C4⋊Dic47—216no—
101Dic47⋊C4—264no—
102C4×Dic47—232no—
103C4×Dic47C22×C4132yes—
104C4×Dic47C22×C4116yes—
105C23×C47C23×C412yes—
106C23×C47C22×D412yes—
107C23×C47C22×Q812yes—
108C23×C47C2×#4118yes—
109C23×C47C2511yescharacteristic
110C22×D47—216no—
111C22×D47—216no—
112C22×D47—216no—
113C22×D47—28no—
114C22×D47C2×C4⋊C4116yes—
115C22×D47C23×C414yes—
116C22×D47C22×D414yes—
117C22×D47C22×Q814yes—
118C2×C4×C47—216no—
119C2×C4×C47—28no—
120C2×C4×C47—28no—
121C2×C4×C47—216no—
122C2×C4×C47—416no—
123C2×C4×C47C2×C4⋊C4116yes—
124C2×C4×C47C23×C418yes—
125C2×C4×C47C23×C414yes—
126C2×C4×C47C22×D414yes—
127C2×C4×C47C22×Q814yes—
128C2×Dic47—28no—
129C2×Dic47—216no—
130C2×Dic47—416no—
131C2×Dic47C2×C4⋊C4116yes—
132C2×Dic47#117132yescomplemented
133C2×Dic47C23×C414yes—
134C2×Dic47C23×C418yes—
135C2×Dic47C22×D414yes—
136C2×Dic47C22×Q814yes—
137C2×Dic47C2×#41116yes—
138C4×D47—264no—
139C4×D47C2×C4⋊C4164yescomplemented
140C2×#2285—471nomaximal, Sylow
141C22×C47C22×C4⋊C414yes—
142C22×C47C2×#11718yes—
143C22×C47#53218yes—
144C22×C47#53318yes—
145C22×C47C24×C411yescharacteristic
146C22×C47C23×D411yescharacteristic
147C22×C47C23×Q811yescharacteristic
148C22×C47C22×#4114yes—
149C2×D47—28no—
150C2×D47—28no—
151C2×D47—28no—
152C2×D47—232no—
153C2×D47C22×C4⋊C418yes—
154C4×C47—28no—
155C4×C47—48no—
156C4×C47C22×C4⋊C418yes—
157Dic47—48no—
158Dic47C22×C4⋊C418yes—
159Dic47C2×#117116yescomplemented
160C22×#117—472no—
161C23×C42—471no—
162#2285—4716no—
163C2×#384—472no—
164C2×#382—471no—
165C2×#382D4711yescharacteristic, complemented
166C2×#380—474no—
167C2×C4×C4⋊C4—474no—
168C2×C47#228518yescomplemented
169C2×C47C23×C4⋊C411yescharacteristic
170C2×C47C22×#11712yes—
171C2×C47C2×#53212yes—
172C2×C47C2×#53312yes—
173D47—28no—
174C24×C4—471no—
175C24×C4—472no—
176C2×#117—4716no—
177C2×#117—9416no—
178C22×C4⋊C4—472no—
179C22×C4⋊C4—478no—
180C22×C4⋊C4C2×D4712yes—
181C22×C22⋊C4—474no—
182C22×C42—472no—
183C22×C42—471no—
184C22×C42—4716no—
185C22×C42—478no—
186C22×C42—474no—
187C22×C42C2×D4711yescharacteristic
188#384—4716no—
189#382—478no—
190#382C2×D4718yescomplemented
191#380—4732no—
192C4×C4⋊C4—4732no—
193C2×#95—474no—
194C2×#95C2×D4714yes—
195C47C2×#228511yescharacteristic, complemented, Sylow
196C25—471no—
197C23×C4—472no—
198C23×C4—471no—
199C23×C4—478no—
200C23×C4—478no—
201C23×C4—478no—
202C23×C4—474no—
203C23×C4—4716no—
204C23×C4—478no—
205C23×C4—474no—
206C23×C4—9416no—
207C23×C4C22×D4714yes—
208C23×C4C22×D4712yes—
209C23×C4C22×D4711yescharacteristic
210#117—9464no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4—478no—
213C2×C4⋊C4—4732no—
214C2×C4⋊C4—9432no—
215C2×C4⋊C4—948no—
216C2×C4⋊C4C22×D4718yes—
217C2×C22⋊C4—4716no—
218C2×C22⋊C4—9416no—
219C2×C42—4716no—
220C2×C42—478no—
221C2×C42—478no—
222C2×C42—474no—
223C2×C42—4764no—
224C2×C42—4716no—
225C2×C42—9416no—
226C2×C42C4×D4718yes—
227C2×C42C22×D4714yes—
228#95—4716no—
229#95C22×D47116yes—
230C24—474no—
231C24—474no—
232C24—474no—
233C24—472no—
234C24—948no—
235C24C23×D4711yescharacteristic
236C22×C4—28no—
237C22×C4—28no—
238C22×C4—216no—
239C22×C4—474no—
240C22×C4—478no—
241C22×C4—474no—
242C22×C4—474no—
243C22×C4—4716no—
244C22×C4—472no—
245C22×C4—474no—
246C22×C4—4764no—
247C22×C4—4716no—
248C22×C4—4716no—
249C22×C4—4716no—
250C22×C4—4732no—
251C22×C4—478no—
252C22×C4—9464no—
253C22×C4—9432no—
254C22×C4—948no—
255C22×C4—9416no—
256C22×C4C2×C4×D4718yes—
257C22×C4C2×C4×D4714yes—
258C22×C4D4×D4714yes—
259C22×C4Q8×D4714yes—
260C22×C4C23×D4718yes—
261C22×C4C23×D4714yes—
262C22×C4C23×D4712yes—
263C4⋊C4—216no—
264C4⋊C4—9464no—
265C4⋊C4—9416no—
266C22⋊C4—9432no—
267C42—4732no—
268C42—4716no—
269C42—9432no—
270C42C2×C4×D47116yes—
271C23—4716no—
272C23—474no—
273C23—474no—
274C23—474no—
275C23—9416no—
276C23—9416no—
277C23—9416no—
278C23—948no—
279C23C22×C4×D4712yes—
280C23C2×D4×D4712yes—
281C23C2×Q8×D4712yes—
282C23#41×D4718yes—
283C23C24×D4711yescharacteristic
284C2×C4—216no—
285C2×C4—28no—
286C2×C4—28no—
287C2×C4—216no—
288C2×C4—416no—
289C2×C4—4716no—
290C2×C4—4732no—
291C2×C4—474no—
292C2×C4—478no—
293C2×C4—474no—
294C2×C4—474no—
295C2×C4—4716no—
296C2×C4—4764no—
297C2×C4—9464no—
298C2×C4—948no—
299C2×C4—9416no—
300C2×C4—18816no—
301C2×C4C4⋊C4×D47116yes—
302C2×C4C22×C4×D4718yes—
303C2×C4C22×C4×D4714yes—
304C2×C4C2×D4×D4714yes—
305C2×C4C2×Q8×D4714yes—
306C22—478no—
307C22—9432no—
308C22—948no—
309C22—948no—
310C22—948no—
311C22C2×C4⋊C4×D4714yes—
312C22#117×D4718yes—
313C22#1568967218yes—
314C22#1568967918yes—
315C22C23×C4×D4711yescharacteristic
316C22C22×D4×D4711yescharacteristic
317C22C22×Q8×D4711yescharacteristic
318C22C2×#41×D4714yes—
319C4—28no—
320C4—48no—
321C4—478no—
322C4—4716no—
323C4—1888no—
324C4C2×C4⋊C4×D4718yes—
325C2—948no—
326C2#2024579418yesdirect product factor
327C2C22×C4⋊C4×D4711yescharacteristic
328C2C2×#117×D4712yes—
329C2C2×#1568967212yes—
330C2C2×#1568967912yes—
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#382C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×#382D47
hypocenterC47C2×#2285
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. #20245794C2direct (N × H)
4. C2×#15688992C2semidirect
5. C2×#15688989C2semidirect
7. C2×#15688974C2semidirect
8. C2×C47×#382C2semidirect
19. C2×C42×D47C4semidirect
21. #15688992C22semidirect
22. #15688989C22semidirect
24. #15688974C22semidirect
28. C47×#382C22semidirect
54. C42×D47C2×C4semidirect
92. C2×C4×D47C4⋊C4semidirect
132. C2×Dic47#117semidirect
139. C4×D47C2×C4⋊C4semidirect
159. Dic47C2×#117semidirect
165. C2×#382D47semidirect
168. C2×C47#2285semidirect
190. #382C2×D47semidirect
195. C47C2×#2285semidirect
326. C2#20245794direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939822
C22×C42×D472
#202457942
C2×#156889922
C2×#156889892
C2×#156889822
C2×#156889742
C2×C47×#3822
C2×#228547