Finite Group Databasebeta

← C2×#22625587 #34019787

Subgroups — C2×#22625587 #34019787

Order 18688.

1614 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989546C211yesmaximal, characteristic
2C22×#14556645C212yesmaximal
3C22×C8×#64408C212yesmaximal
4C2×#17989523C211yesmaximal, characteristic
5#22625587C218yesmaximal, direct product factor
6C2×C4×C8×D73C211yesmaximal, characteristic
7C22×#11924036C2212yes—
8C22×C4×#64408C2212yes—
9#17989546C414yescomplemented
10#17989546C2214yes—
11C2×#14556646C414yescomplemented
12C2×#14556645C4116yescomplemented
13C2×#14556645C2218yes—
14C2×C8×#64408C4116yescomplemented
15C2×C8×#64408C2218yes—
16#17989523C414yes—
17#17989523C2214yes—
18C2×(C2×#64408)⋊C4C414yes—
19C22×C8×D73C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21C2×C42×D73C2211yescharacteristic
22C2×C4×#10596831C411yescharacteristic, complemented
23C2×C8×Dic73C411yescharacteristic, complemented
24C2×C8×Dic73C411yescharacteristic, complemented
25C4×C8×D73C414yescomplemented
26C4×C8×D73C2214yes—
27C2×C4×C8×C73C411yescharacteristic, complemented
28C23×#64408C2×C414yes—
29C2×#11924036C2×C418yes—
30C2×#11924036C2×C418yes—
31C2×#11924036C2×C414yes—
32C2×#11924036C2314yes—
33C22×#10596833C2×C414yes—
34C2×C4×#64408C2×C414yes—
35C2×C4×#64408C2×C418yes—
36C2×C4×#64408C2×C418yes—
37C2×C4×#64408C2314yes—
38#14556646C2×C4116yescomplemented
39#14556645C2×C4132yescomplemented
40C8×#64408C2×C4132yescomplemented
41(C2×#64408)⋊C4C2×C4116yes—
42C22×C4×D73C2×C412yes—
43C22×C4×D73C2311yescharacteristic
44C22×#10596831C2×C411yescharacteristic
45C22×#10596831C2×C411yescharacteristic
46C2×C8×D73C2×C418yes—
47C2×C8×D73C2×C418yes—
48C2×C8×D73C2×C412yes—
49C2×C8×D73C2×C412yes—
50C2×C8×D73C2312yes—
51C2×C8×D73C2312yes—
52C2×C4×Dic73C2×C412yes—
53C2×C4×Dic73C2×C411yescharacteristic
54C42×D73C2×C412yes—
55C42×D73C2×C412yes—
56C42×D73C2×C412yes—
57C42×D73C2312yes—
58C4×#10596831C2×C414yescomplemented
59C8×Dic73C2×C414yescomplemented
60C8×Dic73C2×C414yescomplemented
61C22×C8×C73C2×C411yescharacteristic
62C22×C8×C73C2×C411yescharacteristic
63C2×C42×C73C2×C411yescharacteristic
64C4×C8×C73C2×C414yescomplemented
65C22×#64408—216no—
66C22×#64408C42116yes—
67C22×#64408C22×C418yes—
68#11924036C42116yes—
69#11924036C22×C418yes—
70#11924036C22×C418yes—
71C2×#10596833C42116yes—
72C2×#10596833C22×C418yes—
73C4×#64408C42116yes—
74C4×#64408C22×C418yes—
75C4×#64408C22×C418yes—
76C23×D73C22×C411yescharacteristic
77C22×Dic73C4212yes—
78C22×Dic73C22×C411yescharacteristic
79C2×C4×D73—28no—
80C2×C4×D73C4214yes—
81C2×C4×D73C22×C414yes—
82C2×C4×D73C22×C411yescharacteristic
83C2×C4×D73C22×C411yescharacteristic
84C2×C4×D73C22×C411yescharacteristic
85C2×C4×D73C22×C414yes—
86C2×C4×D73C22×C414yes—
87C2×C4×D73C2411yescharacteristic
88C2×#10596831C4214yes—
89C2×#10596831C4214yes—
90C2×#10596831C22×C412yes—
91C2×#10596831C22×C412yes—
92C8×D73C4218yes—
93C8×D73C4218yes—
94C8×D73C22×C418yes—
95C8×D73C22×C418yes—
96C4×Dic73C4212yes—
97C4×Dic73C4214yes—
98C4×Dic73C22×C412yes—
99C4×Dic73C22×C414yes—
100C22×C4×C73C4212yes—
101C22×C4×C73C22×C411yescharacteristic
102C2×C8×C73C4214yes—
103C2×C8×C73C4214yes—
104C2×C8×C73C22×C412yes—
105C2×C8×C73C22×C412yes—
106C42×C73C4212yes—
107C42×C73C22×C412yes—
108C23×C73C2×C4211yescharacteristic
109C22×D73C2×C4211yescharacteristic
110C22×D73C2×C4214yes—
111C22×D73#13118yes—
112C22×D73C23×C411yescharacteristic
113C2×#64408—216no—
114C2×#64408—232no—
115C2×#64408C2×C42116yes—
116C2×C4×C73—24no—
117C2×C4×C73C2×C4214yes—
118C2×C4×C73C2×C4211yescharacteristic
119C2×C4×C73C2×C4212yes—
120C2×C4×C73C2×C4212yes—
121C2×C4×C73C23×C411yescharacteristic
122C2×Dic73—24no—
123C2×Dic73C2×C4214yes—
124C2×Dic73C2×C4211yescharacteristic
125C2×Dic73C2×C4214yes—
126C2×Dic73C23×C411yescharacteristic
127C4×D73—28no—
128C4×D73—28no—
129C4×D73C2×C4214yes—
130C4×D73C2×C4212yes—
131C4×D73C2×C4212yes—
132C4×D73C2×C4214yes—
133C4×D73C23×C412yes—
134C4×D73C23×C412yes—
135#10596833C2×C42116yes—
136C8×C73C2×C4214yes—
137C8×C73C2×C4214yes—
138#10596831C2×C4214yes—
139#10596831C2×C4214yes—
140C22×C73C4312yes—
141C22×C73#40514yes—
142C22×C73C22×C4211yescharacteristic
143C2×D73C4312yes—
144C2×D73#405116yes—
145C2×D73#40514yes—
146C2×D73C22×C4212yes—
147C2×D73C2×#13114yes—
148#64408—216no—
149C4×C73—24no—
150C4×C73C4312yes—
151C4×C73C22×C4211yescharacteristic
152C4×C73C22×C4211yescharacteristic
153Dic73—24no—
154Dic73C4312yes—
155Dic73C22×C4212yes—
156C2×#1726—731nomaximal, Sylow
157C2×C73#172614yescomplemented
158C2×C73C2×C4311yescharacteristic
159C2×C73C2×#40512yes—
160D73#172614yescomplemented
161D73C2×#40514yes—
162C22×#97—732no—
163C22×#97—731no—
164C22×C4×C8—732no—
165C22×C4×C8—731no—
166C2×#376—731no—
167#1726—738no—
168C73C2×#172611yescharacteristic, complemented, Sylow
169C23×C8—732no—
170C23×C8—731no—
171C23×C8—731no—
172C22×C42—732no—
173C22×C42—731no—
174C2×#97—7316no—
175C2×#97—738no—
176C2×#97—734no—
177C2×#97—734no—
178C2×#97—734no—
179C2×C4×C8—7316no—
180C2×C4×C8—738no—
181C2×C4×C8—731no—
182C2×C4×C8—731no—
183C2×C4×C8—731no—
184C2×C4×C8—734no—
185C2×C4×C8—734no—
186C2×C4×C8#6440811yescharacteristic, complemented
187#376—734no—
188#376—734no—
189C2×#95—734no—
190C23×C4—731no—
191C23×C4—734no—
192C23×C4—732no—
193C22×C8—734no—
194C22×C8—738no—
195C22×C8—738no—
196C22×C8—734no—
197C22×C8—734no—
198C22×C8—731no—
199C22×C8—731no—
200C22×C8—738no—
201C22×C8—738no—
202C22×C8—732no—
203C22×C8—732no—
204C22×C8—732no—
205C22×C8—732no—
206C22×C8C2×#6440811yescharacteristic
207C22×C8C2×#6440811yescharacteristic
208C2×C42—734no—
209C2×C42—734no—
210C2×C42—738no—
211C2×C42—738no—
212C2×C42—732no—
213C2×C42—731no—
214C2×C42—732no—
215C2×C42—732no—
216C2×C42—732no—
217C2×C42—732no—
218C2×C42C2×#6440811yescharacteristic
219#97—7332no—
220#97—7316no—
221C4×C8—7332no—
222C4×C8—734no—
223C4×C8—734no—
224C4×C8—734no—
225C4×C8C2×#6440814yescomplemented
226#95—7316no—
227C24—731no—
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—731no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—734no—
234C22×C4—734no—
235C22×C4—7316no—
236C22×C4—738no—
237C22×C4—732no—
238C22×C4—734no—
239C22×C4—734no—
240C22×C4—1468no—
241C22×C4—14616no—
242C22×C4C4×#6440812yes—
243C22×C4C22×#6440811yescharacteristic
244C2×C8—7316no—
245C2×C8—738no—
246C2×C8—7316no—
247C2×C8—738no—
248C2×C8—738no—
249C2×C8—732no—
250C2×C8—732no—
251C2×C8—734no—
252C2×C8—734no—
253C2×C8—738no—
254C2×C8—738no—
255C2×C8—738no—
256C2×C8—738no—
257C2×C8C4×#6440814yes—
258C2×C8C4×#6440814yes—
259C2×C8C22×#6440812yes—
260C2×C8C22×#6440812yes—
261C42—7316no—
262C42—738no—
263C42—738no—
264C42—732no—
265C42—734no—
266C42—732no—
267C42—734no—
268C42C4×#6440812yes—
269C42C22×#6440812yes—
270C23—731no—
271C23—731no—
272C23—734no—
273C23—738no—
274C23C2×C4×#6440811yescharacteristic
275C2×C4—24no—
276C2×C4—731no—
277C2×C4—731no—
278C2×C4—734no—
279C2×C4—732no—
280C2×C4—732no—
281C2×C4—732no—
282C2×C4—732no—
283C2×C4—734no—
284C2×C4—734no—
285C2×C4—7316no—
286C2×C4—734no—
287C2×C4—1468no—
288C2×C4—1468no—
289C2×C4—14632no—
290C2×C4—14616no—
291C2×C4—1464no—
292C2×C4C2×C4×#6440814yes—
293C2×C4C2×C4×#6440812yes—
294C2×C4C2×C4×#6440812yes—
295C2×C4C2×C4×#6440811yescharacteristic
296C2×C4C23×#6440811yescharacteristic
297C8—7316no—
298C8—734no—
299C8—734no—
300C8C2×C4×#6440814yes—
301C8C2×C4×#6440814yes—
302C22—7316no—
303C22—732no—
304C22—732no—
305C22—734no—
306C22—734no—
307C22C42×#6440812yes—
308C22#1798955014yes—
309C22C22×C4×#6440811yescharacteristic
310C4—24no—
311C4—732no—
312C4—732no—
313C4—14616no—
314C4—1464no—
315C4C42×#6440812yes—
316C4C22×C4×#6440811yescharacteristic
317C4C22×C4×#6440811yescharacteristic
318C2—734no—
319C2—734no—
320C2#2262558714yesdirect product factor
321C2C2×C42×#6440811yescharacteristic
322C2C2×#1798955012yes—
subgroupG/H
centerC22×C8C2×#64408
commutatorC2×C73C2×C43
FrattiniC2×C4C23×#64408
FittingC2×C4×C8×C73C4
socleC23×C73C2×C42
prime radicalC23×D73C22×C4
cosocleC2×C4×D73C24
hypercenterC2×C4×C8#64408
hypocenterC73C2×#1726
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
5. #22625587C2direct (N × H)
9. #17989546C4semidirect
11. C2×#14556646C4semidirect
12. C2×#14556645C4semidirect
14. C2×C8×#64408C4semidirect
22. C2×C4×#10596831C4semidirect
23. C2×C8×Dic73C4semidirect
24. C2×C8×Dic73C4semidirect
25. C4×C8×D73C4semidirect
27. C2×C4×C8×C73C4semidirect
38. #14556646C2×C4semidirect
39. #14556645C2×C4semidirect
40. C8×#64408C2×C4semidirect
58. C4×#10596831C2×C4semidirect
59. C8×Dic73C2×C4semidirect
60. C8×Dic73C2×C4semidirect
64. C4×C8×C73C2×C4semidirect
157. C2×C73#1726semidirect
160. D73#1726semidirect
168. C73C2×#1726semidirect
186. C2×C4×C8#64408semidirect
225. C4×C8C2×#64408semidirect
320. C2#22625587direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179895462
C22×#145566452
C22×C8×#644082
C2×#179895232
#226255872
C2×C4×C8×D732
C2×#172673