Finite Group Databasebeta

← C2×#22612245 #33244118

Subgroups — C2×#22612245 #33244118

Order 18688.

502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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×#17989020C211yesmaximal, characteristic, complemented
2C2×D16×D73C211yesmaximal, characteristic, complemented
3#22612245C218yesmaximal, direct product factor
4C2×#17988424C211yesmaximal, characteristic, complemented
5C2×D2336C211yesmaximal, characteristic, complemented
6C2×#17988422C211yesmaximal, characteristic, complemented
7C2×#17988420C211yesmaximal, characteristic, complemented
8C2×SD64×C73C211yesmaximal, characteristic, complemented
9C2×#14556614—21no—
10C2×D8×D73—21no—
11#17989020—22no—
12#17989020C2214yescomplemented
13C2×#14556534—21no—
14C2×D1168C2211yescharacteristic
15C2×D1168C2211yescharacteristic, complemented
16C2×#14556532—21no—
17D16×D73—22no—
18D16×D73C2214yescomplemented
19C2×C16×D73C2211yescharacteristic
20#17988424C2214yescomplemented
21D2336C2214yescomplemented
22#17988422C2214yescomplemented
23#17988420C2214yescomplemented
24C2×#14556497C2211yescharacteristic, complemented
25C2×Q32×C73C2211yescharacteristic, complemented
26C2×D16×C73C2211yescharacteristic
27SD64×C73C2214yescomplemented
28C2×C32×C73C2211yescharacteristic, complemented
29C2×#11924029—41no—
30C2×D4×D73—41no—
31#14556614—24no—
32#14556614—42no—
33C2×#11924015—41no—
34C2×D584—21no—
35C2×D584—21no—
36C2×#11924013—41no—
37D8×D73—24no—
38D8×D73—42no—
39C2×C8×D73D411yescharacteristic
40#14556534—24no—
41D1168—21no—
42D1168—21no—
43D1168C2312yes—
44D1168C2312yescomplemented
45#14556532—24no—
46C2×#11924003D411yescharacteristic
47C16×D73D412yes—
48C16×D73C2312yes—
49#14556497C2312yescomplemented
50C2×Q16×C73—21no—
51C2×D8×C73—21no—
52Q32×C73—21no—
53Q32×C73C2312yescomplemented
54D16×C73—21no—
55D16×C73C2312yes—
56C2×C16×C73C2311yescharacteristic
57C32×C73C2312yescomplemented
58C23×D73—81no—
59#11924029—44no—
60#11924029—82no—
61C2×D292—41no—
62C2×D292—41no—
63C2×D292—81no—
64C2×C22⋊D73—81no—
65D4×D73—44no—
66D4×D73—82no—
67C2×C4×D73—81no—
68C2×C4×D73D811yescharacteristic
69#11924015—44no—
70D584—22no—
71D584—22no—
72D584—41no—
73D584—41no—
74#11924013—44no—
75C2×#10596831D811yescharacteristic
76C8×D73D812yes—
77C8×D73C2×D412yes—
78#11924003C2×D412yes—
79C2×Q8×C73—41no—
80C2×D4×C73—41no—
81Q16×C73—22no—
82Q16×C73—41no—
83D8×C73—22no—
84D8×C73—41no—
85C2×C8×C73C2×D411yescharacteristic
86C16×C73C2×D411yescharacteristic
87C16×C73C2411yescharacteristic
88C23×C73—81no—
89C22×D73—81no—
90C22×D73—81no—
91C22×D73—84no—
92C22×D73—164no—
93C22×D73D1611yescharacteristic
94Q8×C73—42no—
95Q8×C73—81no—
96D4×C73—42no—
97D4×C73—81no—
98C2×C4×C73—81no—
99C2×C4×C73C2×D811yescharacteristic
100C22⋊D73—84no—
101C2×Dic73D1611yescharacteristic
102D292—42no—
103D292—42no—
104D292—84no—
105D292—81no—
106D292—81no—
107C4×D73—84no—
108C4×D73D1612yes—
109C4×D73C2×D812yes—
110C8×C73C2×D811yescharacteristic
111C8×C73C22×D411yescharacteristic
112#10596831C2×D812yes—
113C22×C73—82no—
114C22×C73—162no—
115C22×C73C2×D1611yescharacteristic
116C2×D73—22no—
117C2×D73—82no—
118C2×D73—82no—
119C2×D73—168no—
120C2×D73—162no—
121C2×D73—162no—
122C2×D73C2×D1612yes—
123C4×C73—82no—
124C4×C73C2×D1611yescharacteristic
125C4×C73C22×D811yescharacteristic
126Dic73C2×D1612yes—
127C2×#2263—731nomaximal, Sylow
128C2×C73—162no—
129C2×C73#226312yescomplemented
130C2×C73C22×D1611yescharacteristic
131D73—22no—
132D73—162no—
133D73—162no—
134C2×#508—731no—
135C22×D16—731no—
136#2263—738no—
137C2×SD64—731no—
138C2×SD64D7311yescharacteristic, complemented
139C2×D32—731no—
140C2×D32—731no—
141C2×M64—731no—
142C73C2×#226311yescharacteristic, complemented, Sylow
143C2×#135—1461no—
144C22×D8—1461no—
145#508—734no—
146#508—1462no—
147C2×Q32C2×D7311yescharacteristic, complemented
148C2×SD32—1461no—
149C2×D16—734no—
150C2×D16—731no—
151C2×D16—731no—
152C2×D16—1462no—
153C2×D16—1461no—
154C2×D16C2×D7311yescharacteristic
155C22×C16—731no—
156SD64—734no—
157SD64C2×D7314yescomplemented
158D32—734no—
159D32—734no—
160M64—734no—
161C2×C32—731no—
162C2×C32C2×D7311yescharacteristic, complemented
163C2×#41—2921no—
164C22×D4—2921no—
165#135—2922no—
166#135—1464no—
167C2×Q16—21no—
168C2×SD16—2921no—
169C2×D8—21no—
170C2×D8—2922no—
171C2×D8—2921no—
172C2×D8—1464no—
173C2×D8—1461no—
174C2×D8—1461no—
175C22×C8—731no—
176Q32—21no—
177Q32C22×D7312yescomplemented
178SD32—1464no—
179D16—21no—
180D16—732no—
181D16—732no—
182D16—1464no—
183D16—1461no—
184D16—1461no—
185D16C22×D7312yes—
186C2×C16—731no—
187C2×C16—732no—
188C2×C16—732no—
189C2×C16C22×D7311yescharacteristic
190C32—732no—
191C32C22×D7312yescomplemented
192C24—5841no—
193#41—2924no—
194#41—5842no—
195C2×Q8—41no—
196C2×D4—41no—
197C2×D4—2924no—
198C2×D4—2921no—
199C2×D4—2921no—
200C2×D4—5841no—
201C2×D4—5842no—
202C2×D4—5841no—
203C22×C4—5841no—
204C22×C4—731no—
205Q16—22no—
206Q16—41no—
207SD16—2924no—
208D8—22no—
209D8—41no—
210D8—2924no—
211D8—2921no—
212D8—2921no—
213D8—1462no—
214D8—1462no—
215C2×C8—731no—
216C2×C8—732no—
217C2×C8—732no—
218C2×C8D4×D7311yescharacteristic
219C16—732no—
220C16D4×D7311yescharacteristic
221C16C23×D7311yescharacteristic
222C23—81no—
223C23—5844no—
224C23—5841no—
225C23—5841no—
226C23—731no—
227C23—11684no—
228Q8—42no—
229Q8—81no—
230D4—42no—
231D4—81no—
232D4—2922no—
233D4—2922no—
234D4—5844no—
235D4—5844no—
236D4—5841no—
237D4—5841no—
238C2×C4—81no—
239C2×C4—5844no—
240C2×C4—731no—
241C2×C4—732no—
242C2×C4—732no—
243C2×C4D8×D7311yescharacteristic
244C8—732no—
245C8D8×D7311yescharacteristic
246C8C2×D4×D7311yescharacteristic
247C22—82no—
248C22—162no—
249C22—5842no—
250C22—5842no—
251C22—732no—
252C22—11688no—
253C22—11682no—
254C22—11682no—
255C22—1462no—
256C22D16×D7311yescharacteristic
257C4—82no—
258C4—732no—
259C4D16×D7311yescharacteristic
260C4C2×D8×D7311yescharacteristic
261C2—162no—
262C2—11682no—
263C2—11682no—
264C2—1462no—
265C2#2261224512yesdirect product factor
266C2C2×D16×D7311yescharacteristic
subgroupG/H
centerC22D16×D73
commutator, cosocleC16×C73C24
FrattiniC16C23×D73
FittingC2×SD64×C73C2
socleC22×C73C2×D16
hypercenterC2×SD64D73
hypocenterC73C2×#2263
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×#17989020C2semidirect
2. C2×D16×D73C2semidirect
3. #22612245C2direct (N × H)
4. C2×#17988424C2semidirect
5. C2×D2336C2semidirect
6. C2×#17988422C2semidirect
7. C2×#17988420C2semidirect
8. C2×SD64×C73C2semidirect
12. #17989020C22semidirect
15. C2×D1168C22semidirect
18. D16×D73C22semidirect
20. #17988424C22semidirect
21. D2336C22semidirect
22. #17988422C22semidirect
23. #17988420C22semidirect
24. C2×#14556497C22semidirect
25. C2×Q32×C73C22semidirect
27. SD64×C73C22semidirect
28. C2×C32×C73C22semidirect
44. D1168C23semidirect
49. #14556497C23semidirect
53. Q32×C73C23semidirect
57. C32×C73C23semidirect
129. C2×C73#2263semidirect
138. C2×SD64D73semidirect
142. C73C2×#2263semidirect
147. C2×Q32C2×D73semidirect
157. SD64C2×D73semidirect
162. C2×C32C2×D73semidirect
177. Q32C22×D73semidirect
191. C32C22×D73semidirect
265. C2#22612245direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179890202
C2×D16×D732
#226122452
C2×#179884242
C2×D23362
C2×#179884222
C2×#179884202
C2×SD64×C732
C2×#226373