Finite Group Databasebeta

← C2×#21460956 #30608367

Subgroups — C2×#21460956 #30608367

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#21460956C214yesmaximal, direct product factor
3C2×#16840141C211yesmaximal, characteristic
4C2×#14519838—22no—
5#16840673—22no—
6#16840673C2214yes—
7C22×#11758202—22no—
8C2×#14519777C2211yescharacteristic
9#16840141—22no—
10#16840141C412yes—
11#16840141C2212yes—
12C2×C4×#92418C411yescharacteristic
13C2×C4⋊Q8×C61C411yescharacteristic
14C2×#11758217—42no—
15#14519838—24no—
16#14519838—42no—
17C22×Dic122D412yes—
18C2×#11758202—24no—
19C2×#11758202—24no—
20C2×#11758202—44no—
21C2×#11758202—44no—
22C22×#92418—21no—
23#14519777—41no—
24#14519777C2×C411yescharacteristic
25#14519777D412yes—
26#14519777C2311yescharacteristic
27C2×C4⋊Dic61—41no—
28C4×#92418—21no—
29C4×#92418C2×C412yes—
30C22×Q8×C61—21no—
31C4⋊Q8×C61—21no—
32C4⋊Q8×C61—41no—
33C4⋊Q8×C61C2×C412yes—
34C2×C4⋊C4×C61—41no—
35C2×C42×C61C2×C411yescharacteristic
36C2×Q8×C61—22no—
37C2×Q8×C61—42no—
38C2×Q8×C61—42no—
39C2×Q8×C61—41no—
40C22×C4×C61—21no—
41C22×C4×C61—41no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61—22no—
44C2×Dic122—22no—
45C2×Dic122—42no—
46C2×Dic122—42no—
47C2×Dic122C22⋊C412yes—
48C2×Dic122C2×D412yes—
49#11758217—44no—
50#11758217—82no—
51C2×#92420—82no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61—42no—
54C42×C61—21no—
55C42×C61C22⋊C411yescharacteristic
56C42×C61C22×C411yescharacteristic
57#11758202—48no—
58#11758202—48no—
59C4⋊Dic61—41no—
60C4⋊Dic61—42no—
61C4⋊Dic61—41no—
62C2×#92418—22no—
63C2×#92418—22no—
64C2×#92418—22no—
65C23×C61#9911yescharacteristic
66Q8×C61—44no—
67Q8×C61—82no—
68C2×C4×C61—24no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—42no—
74C2×C4×C61—81no—
75C2×C4×C61—81no—
76C2×C4×C61#9911yescharacteristic
77C2×C4×C61C2×C22⋊C411yescharacteristic
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82Dic122—42no—
83Dic122—42no—
84Dic122—82no—
85#92420—84no—
86#92418—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—
96C4×C61—82no—
97Dic61—42no—
98Dic61—42no—
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#692311yescharacteristic
109#494—612no—
110#494—612no—
111#494—1222no—
112C2×#101—1222no—
113C2×C4×C8—611no—
114#356—614no—
115#356—1222no—
116C61C2×#141111yescharacteristic, complemented, Sylow
117C22×Q8—21no—
118C22×Q8—612no—
119C2×Q16—1224no—
120C2×Q16—1224no—
121C2×Q16—2444no—
122C2×Q16—2444no—
123C2×M16—2442no—
124C22×C8—1221no—
125C4⋊Q8—21no—
126C4⋊Q8—41no—
127C4⋊Q8—612no—
128C4⋊Q8—611no—
129C4⋊Q8—611no—
130C4⋊Q8—2441no—
131C4⋊Q8C2×#692312yes—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—2441no—
134C2×C42C2×#692311yescharacteristic
135#101—1224no—
136#101—2442no—
137C4×C8—612no—
138C4×C8—1221no—
139C2×Q8—22no—
140C2×Q8—42no—
141C2×Q8—42no—
142C2×Q8—41no—
143C2×Q8—612no—
144C2×Q8—612no—
145C2×Q8—1222no—
146C2×Q8—2442no—
147C2×Q8—2442no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—1222no—
151C22×C4C22⋊#692311yescharacteristic
152Q16—2448no—
153Q16—2448no—
154M16—4882no—
155M16—2444no—
156C2×C8—1222no—
157C2×C8—1222no—
158C2×C8—1222no—
159C2×C8—4882no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—2442no—
163C4⋊C4—2441no—
164C4⋊C4—2441no—
165C42—21no—
166C42C22⋊#692311yescharacteristic
167C42C22×#692311yescharacteristic
168C23#1451983511yescharacteristic
169Q8—44no—
170Q8—82no—
171Q8—4882no—
172Q8—2442no—
173Q8—2442no—
174C2×C4—24no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4#1451983511yescharacteristic
187C2×C4C2×C22⋊#692311yescharacteristic
188C8—1224no—
189C8—4884no—
190C22—22no—
191C22#1684066611yescharacteristic
192C22#1684066611yescharacteristic
193C22C2×#1451983511yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—82no—
199C4—2442no—
200C4—2442no—
201C2—21no—
202C2—21no—
203C2#2146095612yesdirect product factor
204C2C2×#1684066611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC22×C61#353
prime radicalC23×C61#99
cosocle#14519777C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61C2×#1411
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
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. #21460956C2direct (N × H)
104. C2×C61#1411semidirect
116. C61C2×#1411semidirect
203. C2#21460956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406732
#214609562
C2×#168401412
C2×#141161