Finite Group Databasebeta

← C2×#97×#64408 #34019783

Subgroups — C2×#97×#64408 #34019783

Order 18688.

1790 conjugacy classes of subgroups.

The subgroup lattice has 328 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×C42×#64408C211yesmaximal, characteristic
5#97×#64408C218yesmaximal, direct product factor
6C2×#97×D73C211yesmaximal, characteristic
7C22×#11924036C2212yes—
8C22×C4×#64408C414yes—
9C22×C4×#64408C2211yescharacteristic
10C22×C4×#64408C2211yescharacteristic
11#17989546C414yescomplemented
12#17989546C2214yes—
13C2×#14556646C414yescomplemented
14C2×#14556645C4116yescomplemented
15C2×#14556645C2218yes—
16C2×C8×#64408C4116yescomplemented
17C2×C8×#64408C2218yes—
18C42×#64408C414yes—
19C42×#64408C2214yes—
20C22×C8×D73C2212yes—
21C2×C42×D73C2211yescharacteristic
22C2×#14556502C411yescharacteristic, complemented
23C2×#14556501C412yescomplemented
24#97×D73C414yescomplemented
25#97×D73C2214yes—
26C2×#97×C73C411yescharacteristic, complemented
27C23×#64408C2×C412yes—
28C23×#64408C2×C412yes—
29C2×#11924036C2×C418yes—
30C2×#11924036C2×C418yes—
31C2×#11924036C2×C414yes—
32C2×#11924036C2314yes—
33C22×#10596833C2×C414yes—
34C2×C4×#64408—216no—
35C2×C4×#64408C2×C4116yes—
36C2×C4×#64408C2×C412yes—
37C2×C4×#64408C2×C412yes—
38C2×C4×#64408C2×C418yes—
39C2×C4×#64408C2×C418yes—
40C2×C4×#64408C2312yes—
41C2×C4×#64408C2312yes—
42#14556646C2×C4116yescomplemented
43#14556645C2×C4132yescomplemented
44C8×#64408C2×C4132yescomplemented
45C22×C4×D73C2×C412yes—
46C22×C4×D73C2311yescharacteristic
47C22×#10596831C2×C412yes—
48C2×C8×D73C2×C418yes—
49C2×C8×D73C2×C418yes—
50C2×C8×D73C2×C414yes—
51C2×C8×D73C2314yes—
52C2×C4×Dic73C2×C412yes—
53C2×C4×Dic73C2×C411yescharacteristic
54C42×D73C2×C412yes—
55C42×D73C2×C412yes—
56C42×D73C2×C412yes—
57C42×D73C2312yes—
58#14556502C2×C414yescomplemented
59#14556501C2×C418yescomplemented
60C22×C8×C73C2×C412yes—
61C2×C42×C73C2×C411yescharacteristic
62#97×C73C2×C414yescomplemented
63C22×#64408—28no—
64C22×#64408C4218yes—
65C22×#64408C4218yes—
66C22×#64408M16116yes—
67C22×#64408C22×C414yes—
68C22×#64408C22×C414yes—
69#11924036C42116yescomplemented
70#11924036C22×C418yes—
71#11924036C22×C418yes—
72C2×#10596833C42116yescomplemented
73C2×#10596833C22×C418yes—
74C4×#64408—232no—
75C4×#64408C4218yes—
76C4×#64408C4218yes—
77C4×#64408C22×C418yes—
78C4×#64408C22×C418yes—
79C23×D73C22×C411yescharacteristic
80C22×Dic73C4212yes—
81C22×Dic73C22×C411yescharacteristic
82C2×C4×D73—28no—
83C2×C4×D73C4214yes—
84C2×C4×D73C22×C414yes—
85C2×C4×D73C22×C411yescharacteristic
86C2×C4×D73C22×C411yescharacteristic
87C2×C4×D73C22×C411yescharacteristic
88C2×C4×D73C22×C414yes—
89C2×C4×D73C22×C414yes—
90C2×C4×D73C2411yescharacteristic
91C2×#10596831C4218yescomplemented
92C2×#10596831C22×C414yes—
93C8×D73C42116yescomplemented
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×C73C4218yescomplemented
103C2×C8×C73C22×C414yes—
104C42×C73C4212yes—
105C42×C73C22×C412yes—
106C23×C73C2×C4211yescharacteristic
107C22×D73C2×C4211yescharacteristic
108C22×D73C2×C4212yes—
109C22×D73C2×C4212yes—
110C22×D73C2×M1618yes—
111C22×D73C23×C411yescharacteristic
112C2×#64408—28no—
113C2×#64408—216no—
114C2×#64408#97132yesdirect product factor
115C2×#64408C2×C4218yes—
116C2×#64408C2×C4218yes—
117C2×#64408C2×M16116yes—
118C2×C4×C73—24no—
119C2×C4×C73C2×C4214yes—
120C2×C4×C73C2×C4211yescharacteristic
121C2×C4×C73C2×C4214yes—
122C2×C4×C73C23×C411yescharacteristic
123C2×Dic73—24no—
124C2×Dic73C2×C4214yes—
125C2×Dic73C2×C4211yescharacteristic
126C2×Dic73C2×C4214yes—
127C2×Dic73C23×C411yescharacteristic
128C4×D73—28no—
129C4×D73—28no—
130C4×D73C2×C4212yes—
131C4×D73C2×C4212yes—
132C4×D73C2×C4214yes—
133C4×D73C2×C4214yes—
134C4×D73C23×C412yes—
135C4×D73C23×C412yes—
136#10596833C2×C42116yescomplemented
137C8×C73C2×C4218yescomplemented
138#10596831C2×C4218yescomplemented
139C22×C73C4312yes—
140C22×C73C4×M1614yes—
141C22×C73C22×C4211yescharacteristic
142C2×D73C4312yes—
143C2×D73C2×#9718yes—
144C2×D73C4×M1618yes—
145C2×D73C4×M1614yes—
146C2×D73C22×C4211yescharacteristic
147C2×D73C22×C4211yescharacteristic
148C2×D73C22×M1614yes—
149#64408—28no—
150#64408C2×#97116yesdirect product factor
151C4×C73—24no—
152C4×C73C4312yes—
153C4×C73C22×C4212yes—
154Dic73—24no—
155Dic73C4312yes—
156Dic73C22×C4212yes—
157C2×C4×#97—731nomaximal, Sylow
158C2×C73C4×#9714yescomplemented
159C2×C73C2×C4311yescharacteristic
160C2×C73C2×C4×M1612yes—
161D73C4×#9714yescomplemented
162D73C22×#9712yes—
163D73C2×C4×M1612yes—
164C22×#97—732no—
165C22×#97—731no—
166C22×#97—731no—
167C22×C4×C8—732no—
168C2×C43—731no—
169C4×#97—738no—
170C73C2×C4×#9711yescharacteristic, complemented, Sylow
171C23×C8—732no—
172C23×C8—732no—
173C22×C42—731no—
174C22×C42—731no—
175C22×C42—731no—
176C22×C42—734no—
177C2×#97—7316no—
178C2×#97—738no—
179C2×#97—734no—
180C2×#97—734no—
181C2×#97—734no—
182C2×#97—732no—
183C2×#97—731no—
184C2×#97—734no—
185C2×#97—734no—
186C2×#97#6440811yescharacteristic, direct product factor
187C2×C4×C8—7316no—
188C2×C4×C8—738no—
189C43—734no—
190C43—734no—
191C23×C4—732no—
192C23×C4—731no—
193C23×C4—732no—
194C23×C4—732no—
195C22×C8—734no—
196C22×C8—738no—
197C22×C8—738no—
198C22×C8—734no—
199C22×C8—734no—
200C22×C8—732no—
201C22×C8—738no—
202C22×C8—738no—
203C22×C8—734no—
204C22×C8—734no—
205C22×C8C2×#6440812yes—
206C2×C42—732no—
207C2×C42—732no—
208C2×C42—732no—
209C2×C42—732no—
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×C42—7316no—
219C2×C42—14616no—
220C2×C42C2×#6440811yescharacteristic
221#97—7332no—
222#97—7316no—
223#97—738no—
224#97—734no—
225#97C2×#6440814yesdirect product factor
226C4×C8—7332no—
227C24—731no—
228C22×C4—738no—
229C22×C4—7316no—
230C22×C4—734no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—731no—
236C22×C4—734no—
237C22×C4—734no—
238C22×C4—738no—
239C22×C4—734no—
240C22×C4—732no—
241C22×C4—734no—
242C22×C4—734no—
243C22×C4—1468no—
244C22×C4—1468no—
245C22×C4C4×#6440812yes—
246C22×C4C22×#6440811yescharacteristic
247C2×C8—7316no—
248C2×C8—738no—
249C2×C8—7316no—
250C2×C8—738no—
251C2×C8—738no—
252C2×C8—734no—
253C2×C8—738no—
254C2×C8—7316no—
255C2×C8—738no—
256C2×C8—738no—
257C2×C8C4×#6440818yescomplemented
258C2×C8C22×#6440814yes—
259C42—738no—
260C42—738no—
261C42—738no—
262C42—738no—
263C42—732no—
264C42—734no—
265C42—732no—
266C42—734no—
267C42—14632no—
268C42C4×#6440812yes—
269C42C22×#6440812yes—
270C23—731no—
271C23—731no—
272C23—732no—
273C23—732no—
274C23—738no—
275C23C2×C4×#6440811yescharacteristic
276C2×C4—24no—
277C2×C4—738no—
278C2×C4—7316no—
279C2×C4—7332no—
280C2×C4—731no—
281C2×C4—731no—
282C2×C4—734no—
283C2×C4—732no—
284C2×C4—732no—
285C2×C4—734no—
286C2×C4—732no—
287C2×C4—732no—
288C2×C4—734no—
289C2×C4—738no—
290C2×C4—734no—
291C2×C4—1468no—
292C2×C4—1468no—
293C2×C4—1468no—
294C2×C4—14616no—
295C2×C4—1464no—
296C2×C4C2×C4×#6440814yes—
297C2×C4C2×C4×#6440814yes—
298C2×C4C2×C4×#6440811yescharacteristic
299C2×C4C23×#6440811yescharacteristic
300C8—7316no—
301C8—738no—
302C8C2×C4×#6440818yescomplemented
303C22—738no—
304C22—738no—
305C22—731no—
306C22—731no—
307C22—732no—
308C22—734no—
309C22—734no—
310C22C42×#6440812yes—
311C22M16×#6440814yes—
312C22C22×C4×#6440811yescharacteristic
313C4—24no—
314C4—7316no—
315C4—732no—
316C4—732no—
317C4—1468no—
318C4—1464no—
319C4C42×#6440812yes—
320C4C22×C4×#6440812yes—
321C2—732no—
322C2—732no—
323C2—734no—
324C2#97×#6440814yesdirect product factor
325C2C2×C42×#6440811yescharacteristic
326C2C2×M16×#6440812yes—
subgroupG/H
centerC22×C4C22×#64408
commutatorC2×C73C2×C43
FrattiniC2×C4C23×#64408
FittingC2×#97×C73C4
socleC23×C73C2×C42
prime radicalC23×D73C22×C4
cosocleC2×C4×D73C24
hypercenterC2×#97#64408
hypocenterC73C2×C4×#97
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
5. #97×#64408C2direct (N × H)
11. #17989546C4semidirect
13. C2×#14556646C4semidirect
14. C2×#14556645C4semidirect
16. C2×C8×#64408C4semidirect
22. C2×#14556502C4semidirect
23. C2×#14556501C4semidirect
24. #97×D73C4semidirect
26. C2×#97×C73C4semidirect
42. #14556646C2×C4semidirect
43. #14556645C2×C4semidirect
44. C8×#64408C2×C4semidirect
58. #14556502C2×C4semidirect
59. #14556501C2×C4semidirect
62. #97×C73C2×C4semidirect
69. #11924036C42semidirect
72. C2×#10596833C42semidirect
91. C2×#10596831C42semidirect
93. C8×D73C42semidirect
102. C2×C8×C73C42semidirect
114. C2×#64408#97direct (N × H)
136. #10596833C2×C42semidirect
137. C8×C73C2×C42semidirect
138. #10596831C2×C42semidirect
150. #64408C2×#97direct (N × H)
158. C2×C73C4×#97semidirect
161. D73C4×#97semidirect
170. C73C2×C4×#97semidirect
186. C2×#97#64408direct (N × H)
225. #97C2×#64408direct (N × H)
257. C2×C8C4×#64408semidirect
302. C8C2×C4×#64408semidirect
324. C2#97×#64408direct (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×C42×#644082
#97×#644082
C2×#97×D732
C2×C4×#9773