Finite Group Databasebeta

← C2×#21460957 #30608369

Subgroups — C2×#21460957 #30608369

Order 15616.

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

normal subgroups only

This group has 398 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×#16840673C212yesmaximal
2#21460957C214yesmaximal, direct product factor
3C2×#16840142C211yesmaximal, characteristic
4C2×#14519838—22no—
5#16840673—22no—
6#16840673C2214yes—
7C22×Dic244—22no—
8C2×#14519777C411yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840142—22no—
11#16840142C412yes—
12#16840142C2212yes—
13C2×C4×C8×C61C411yescharacteristic
14C2×#11758217—42no—
15#14519838—24no—
16#14519838—42no—
17C22×Dic122—21no—
18C22×Dic122D412yes—
19C2×Dic244—24no—
20C2×Dic244—24no—
21C2×Dic244—44no—
22C2×Dic244—44no—
23#14519777—21no—
24#14519777—41no—
25#14519777—41no—
26#14519777C2×C412yes—
27#14519777C2×C411yescharacteristic
28#14519777D412yes—
29#14519777C2311yescharacteristic
30C2×C4⋊Dic61—41no—
31C2×C4⋊Dic61—41no—
32C22×C8×C61—21no—
33C2×C42×C61C2×C411yescharacteristic
34C4×C8×C61—21no—
35C4×C8×C61C2×C412yes—
36C22×C4×C61—21no—
37C22×C4×C61C22⋊C411yescharacteristic
38C22×Dic61—22no—
39C22×Dic61—41no—
40C2×Dic122—22no—
41C2×Dic122—22no—
42C2×Dic122—42no—
43C2×Dic122—42no—
44C2×Dic122—42no—
45C2×Dic122—42no—
46C2×Dic122—41no—
47C2×Dic122C22⋊C412yes—
48C2×Dic122C2×D412yes—
49#11758217—44no—
50#11758217—82no—
51C2×#92420—82no—
52C2×C8×C61—22no—
53C2×C8×C61—22no—
54C2×C8×C61—22no—
55C42×C61—21no—
56C42×C61C22⋊C411yescharacteristic
57C42×C61C22×C411yescharacteristic
58C4⋊Dic61—41no—
59C4⋊Dic61—42no—
60C4⋊Dic61—41no—
61C4⋊Dic61—42no—
62C4⋊Dic61—42no—
63Dic244—48no—
64Dic244—48no—
65C23×C61#9911yescharacteristic
66C2×C4×C61—24no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61#9911yescharacteristic
72C2×C4×C61C2×C22⋊C411yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—81no—
79C2×Dic61—81no—
80Dic122—42no—
81Dic122—42no—
82Dic122—44no—
83Dic122—82no—
84Dic122—82no—
85#92420—84no—
86C8×C61—24no—
87C2×#1411—611nomaximal, Sylow
88C22×C61—22no—
89C22×C61#35311yescharacteristic
90C22×C61#35311yescharacteristic
91C22×C61C2×#9911yescharacteristic
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—21no—
95C4×C61—21no—
96Dic61—42no—
97Dic61—42no—
98Dic61—82no—
99C2×#494—611no—
100C2×#356—612no—
101#1411—614no—
102C2×C61—21no—
103C2×C61—21no—
104C2×C61#141112yescomplemented
105C2×C61C2×#35311yescharacteristic
106C22×Q16—1222no—
107C2×C4⋊Q8—611no—
108C2×C4⋊Q8—611no—
109#494—612no—
110#494—612no—
111#494—1222no—
112C2×#101—1222no—
113C2×C4×C8#692311yescharacteristic
114#356—614no—
115#356—1222no—
116C61C2×#141111yescharacteristic, complemented, Sylow
117C22×Q8—612no—
118C22×Q8—1221no—
119C2×Q16—1224no—
120C2×Q16—1224no—
121C2×Q16—2444no—
122C2×Q16—2444no—
123C2×M16—2442no—
124C22×C8—21no—
125C4⋊Q8—612no—
126C4⋊Q8—611no—
127C4⋊Q8—611no—
128C4⋊Q8—612no—
129C4⋊Q8—1221no—
130C4⋊Q8—2441no—
131C4⋊Q8—2441no—
132C2×C4⋊C4—2441no—
133C2×C4⋊C4—2441no—
134C2×C42C2×#692311yescharacteristic
135#101—1224no—
136#101—2442no—
137C4×C8—21no—
138C4×C8C2×#692312yes—
139C2×Q8—612no—
140C2×Q8—612no—
141C2×Q8—1222no—
142C2×Q8—1222no—
143C2×Q8—2442no—
144C2×Q8—2442no—
145C2×Q8—2442no—
146C2×Q8—2442no—
147C2×Q8—2441no—
148C22×C4—21no—
149C22×C4—1222no—
150C22×C4—2441no—
151C22×C4C22⋊#692311yescharacteristic
152Q16—2448no—
153Q16—2448no—
154M16—4882no—
155M16—2444no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—4882no—
160C4⋊C4—2442no—
161C4⋊C4—2441no—
162C4⋊C4—2441no—
163C4⋊C4—2442no—
164C4⋊C4—2442no—
165C42—21no—
166C42C22⋊#692311yescharacteristic
167C42C22×#692311yescharacteristic
168C23#1451983611yescharacteristic
169Q8—4882no—
170Q8—4882no—
171Q8—2444no—
172Q8—2442no—
173Q8—2442no—
174C2×C4—24no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—4881no—
182C2×C4—4881no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4#1451983611yescharacteristic
187C2×C4C2×C22⋊#692311yescharacteristic
188C8—24no—
189C8—4884no—
190C22—22no—
191C22#1684066711yescharacteristic
192C22#1684066711yescharacteristic
193C22C2×#1451983611yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—4882no—
199C4—2442no—
200C4—2442no—
201C2—21no—
202C2—21no—
203C2#2146095712yesdirect product factor
204C2C2×#1684066711yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#353
prime radicalC23×C61#99
cosocle#14519777C23
hypercenterC2×C4×C8#6923
hypocenterC61C2×#1411
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #21460957C2direct (N × H)
104. C2×C61#1411semidirect
116. C61C2×#1411semidirect
203. C2#21460957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406732
#214609572
C2×#168401422
C2×#141161