Finite Group Databasebeta

← C2×#22625064 #34014318

Subgroups — C2×#22625064 #34014318

Order 18688.

474 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 64 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×#17989492C212yesmaximal
2#22625064C214yesmaximal, direct product factor
3C2×#17988961C211yesmaximal, characteristic
4C2×#14556650—22no—
5#17989492—22no—
6#17989492C2214yes—
7C22×#11924015—22no—
8C2×#14556588C2211yescharacteristic
9#17988961—22no—
10#17988961C412yescomplemented
11#17988961C2212yes—
12C2×C4×#10596831C411yescharacteristic, complemented
13C2×C4⋊Q8×C73C411yescharacteristic, complemented
14C2×C22⋊#64408—42no—
15#14556650—24no—
16#14556650—42no—
17C22×D292—41no—
18C22×D292D412yes—
19C2×#11924015—24no—
20C2×#11924015—24no—
21C2×#11924015—44no—
22C2×#11924015—44no—
23C22×#10596831—21no—
24#14556588—41no—
25#14556588C2×C411yescharacteristic
26#14556588D412yes—
27#14556588C2311yescharacteristic
28C4×#10596831—21no—
29C4×#10596831C2×C412yescomplemented
30C22×Q8×C73—21no—
31C4⋊Q8×C73—21no—
32C4⋊Q8×C73—41no—
33C4⋊Q8×C73C2×C412yescomplemented
34C2×C4⋊C4×C73—41no—
35C2×C42×C73C2×C411yescharacteristic
36C22×#64408—82no—
37C22⋊#64408—44no—
38C22⋊#64408—82no—
39C23×D73—22no—
40C2×D292—22no—
41C2×D292—42no—
42C2×D292—42no—
43C2×D292—41no—
44C2×D292—42no—
45C2×D292—41no—
46C2×D292—84no—
47C2×D292C22⋊C412yes—
48C2×D292C2×D412yes—
49#11924015—48no—
50#11924015—48no—
51C2×#10596831—22no—
52C2×#10596831—22no—
53C2×#10596831—22no—
54C2×Q8×C73—22no—
55C2×Q8×C73—42no—
56C2×Q8×C73—42no—
57C2×Q8×C73—41no—
58C22×C4×C73—21no—
59C22×C4×C73—41no—
60C22×C4×C73C22⋊C411yescharacteristic
61C4⋊C4×C73—42no—
62C4⋊C4×C73—42no—
63C42×C73—21no—
64C42×C73C22⋊C411yescharacteristic
65C42×C73C22×C411yescharacteristic
66C23×C73#9911yescharacteristic
67C22×D73—22no—
68C22×D73—22no—
69C22×D73—42no—
70C22×D73—42no—
71C22×D73—84no—
72C2×#64408—84no—
73C2×#64408—164no—
74Q8×C73—44no—
75Q8×C73—82no—
76C2×C4×C73—24no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—42no—
82C2×C4×C73—81no—
83C2×C4×C73—81no—
84C2×C4×C73#9911yescharacteristic
85C2×C4×C73C2×C22⋊C411yescharacteristic
86D292—42no—
87D292—42no—
88D292—82no—
89D292—82no—
90D292—84no—
91D292—82no—
92#10596831—24no—
93C22×C73—22no—
94C22×C73#35311yescharacteristic
95C22×C73#35311yescharacteristic
96C22×C73C2×#9911yescharacteristic
97C2×D73—42no—
98C2×D73—42no—
99C2×D73—84no—
100C2×D73—82no—
101C2×D73—82no—
102C2×D73—162no—
103#64408—164no—
104C4×C73—22no—
105C4×C73—22no—
106C4×C73—21no—
107C4×C73—21no—
108C4×C73—82no—
109C2×#1409—731nomaximal, Sylow
110C2×C73—21no—
111C2×C73—21no—
112C2×C73#140912yescomplemented
113C2×C73C2×#35311yescharacteristic
114D73—82no—
115D73—82no—
116C2×#492—731no—
117C2×#353—732no—
118#1409—734no—
119C73C2×#140911yescharacteristic, complemented, Sylow
120C22×SD16—1462no—
121C2×C4⋊Q8#6440811yescharacteristic, complemented
122C2×#127—731no—
123#492—732no—
124#492—732no—
125#492—1462no—
126C2×#99—1462no—
127C2×C4×C8—731no—
128#353—734no—
129#353—1462no—
130C22×Q8—21no—
131C22×D4—2921no—
132C22×D4—732no—
133C2×SD16—2924no—
134C2×SD16—2924no—
135C2×SD16—1464no—
136C2×SD16—1464no—
137C22×C8—1461no—
138C4⋊Q8—21no—
139C4⋊Q8—41no—
140C4⋊Q8C2×#6440812yescomplemented
141#127—2921no—
142#127—732no—
143#127—731no—
144#127—731no—
145C2×C4⋊C4—41no—
146C2×C22⋊C4—2922no—
147C2×C42C2×#6440811yescharacteristic
148#99—2922no—
149#99—1464no—
150C4×C8—732no—
151C4×C8—1461no—
152C24—1462no—
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—41no—
157C2×D4—2922no—
158C2×D4—2922no—
159C2×D4—2922no—
160C2×D4—2921no—
161C2×D4—2921no—
162C2×D4—5844no—
163C2×D4—732no—
164C2×D4—732no—
165C2×D4—1462no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—5842no—
169C22×C4C22⋊#6440811yescharacteristic
170SD16—2928no—
171SD16—2928no—
172C2×C8—1462no—
173C2×C8—1462no—
174C2×C8—1462no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C22⋊C4—2924no—
178C22⋊C4—5842no—
179C42—21no—
180C42C22⋊#6440811yescharacteristic
181C42C22×#6440811yescharacteristic
182C23—2922no—
183C23—2922no—
184C23—5844no—
185C23—1462no—
186C23—1462no—
187C23#1455664911yescharacteristic
188Q8—44no—
189Q8—82no—
190D4—2922no—
191D4—2922no—
192D4—5842no—
193D4—5844no—
194D4—5842no—
195D4—5842no—
196C2×C4—24no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—5844no—
205C2×C4—11684no—
206C2×C4#1455664911yescharacteristic
207C2×C4C2×C22⋊#6440811yescharacteristic
208C8—1464no—
209C22—22no—
210C22—2922no—
211C22—2922no—
212C22—5842no—
213C22—5842no—
214C22—5844no—
215C22—11682no—
216C22#1798949111yescharacteristic
217C22#1798949111yescharacteristic
218C22C2×#1455664911yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—11684no—
225C2—21no—
226C2—21no—
227C2—5842no—
228C2—5842no—
229C2#2262506412yesdirect product factor
230C2C2×#1798949111yescharacteristic
subgroupG/H
centerC22#17989491
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
FittingC2×C4⋊Q8×C73C4
socleC22×C73#353
prime radicalC2×#14556588C22
cosocle#14556588C23
hypercenterC2×C4⋊Q8#64408
hypocenterC73C2×#1409
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22625064C2direct (N × H)
10. #17988961C4semidirect
12. C2×C4×#10596831C4semidirect
13. C2×C4⋊Q8×C73C4semidirect
29. C4×#10596831C2×C4semidirect
33. C4⋊Q8×C73C2×C4semidirect
112. C2×C73#1409semidirect
119. C73C2×#1409semidirect
121. C2×C4⋊Q8#64408semidirect
140. C4⋊Q8C2×#64408semidirect
229. C2#22625064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179894922
#226250642
C2×#179889612
C2×#140973