Finite Group Databasebeta

← C2×#21460954 #30608364

Subgroups — C2×#21460954 #30608364

Order 15616.

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

normal subgroups only

This group has 450 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, complemented
2#21460954C214yesmaximal, direct product factor
3C2×#16840134C211yesmaximal, characteristic
4C2×#14519838—22no—
5#16840673—22no—
6#16840673C2214yescomplemented
7C22×#11758200—22no—
8C2×#14519777C2211yescharacteristic
9#16840134—22no—
10#16840134C412yes—
11#16840134C2212yes—
12C2×C4×#92418C411yescharacteristic
13C2×#127×C61C411yescharacteristic
14C2×#11758217—42no—
15#14519838—24no—
16#14519838—42no—
17C22×Dic122D412yes—
18C2×#11758200—24no—
19C2×#11758200—24no—
20C2×#11758200—44no—
21C2×#11758200—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×D4×C61—21no—
31C22×D4×C61—41no—
32#127×C61—21no—
33#127×C61—41no—
34#127×C61C2×C412yes—
35C2×C42×C61C2×C411yescharacteristic
36C24×C61—41no—
37C2×D4×C61—22no—
38C2×D4×C61—42no—
39C2×D4×C61—42no—
40C2×D4×C61—42no—
41C2×D4×C61—42no—
42C2×D4×C61—41no—
43C2×D4×C61—84no—
44C22×C4×C61—21no—
45C22×C4×C61C22⋊C411yescharacteristic
46C22×Dic61—22no—
47C2×Dic122—22no—
48C2×Dic122—42no—
49C2×Dic122—42no—
50C2×Dic122C22⋊C412yes—
51C2×Dic122C2×D412yes—
52#11758217—44no—
53#11758217—82no—
54C2×#92420—82no—
55C42×C61—21no—
56C42×C61C22⋊C411yescharacteristic
57C42×C61C22×C411yescharacteristic
58#11758200—48no—
59#11758200—48no—
60C4⋊Dic61—41no—
61C4⋊Dic61—42no—
62C4⋊Dic61—41no—
63C2×#92418—22no—
64C2×#92418—22no—
65C2×#92418—22no—
66C23×C61—42no—
67C23×C61—84no—
68C23×C61—81no—
69C23×C61—81no—
70C23×C61#9911yescharacteristic
71D4×C61—44no—
72D4×C61—82no—
73D4×C61—84no—
74D4×C61—84no—
75C2×C4×C61—24no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61#9911yescharacteristic
81C2×C4×C61C2×C22⋊C411yescharacteristic
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86Dic122—42no—
87Dic122—42no—
88Dic122—82no—
89#92420—84no—
90#92418—24no—
91C2×#1410—611nomaximal, Sylow
92C22×C61—22no—
93C22×C61—84no—
94C22×C61—82no—
95C22×C61—162no—
96C22×C61—162no—
97C22×C61#35311yescharacteristic
98C22×C61#35311yescharacteristic
99C22×C61C2×#9911yescharacteristic
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—21no—
103C4×C61—21no—
104Dic61—42no—
105Dic61—42no—
106C2×#492—611no—
107C2×#356—612no—
108#1410—614no—
109C2×C61—21no—
110C2×C61—21no—
111C2×C61—162no—
112C2×C61#141012yescomplemented
113C2×C61C2×#35311yescharacteristic
114C22×SD16—1222no—
115C2×C4⋊Q8—611no—
116C2×#127#692311yescharacteristic
117#492—612no—
118#492—612no—
119#492—1222no—
120C2×#101—1222no—
121C2×C4×C8—611no—
122#356—614no—
123#356—1222no—
124C61C2×#141011yescharacteristic, complemented, Sylow
125C22×Q8—612no—
126C22×D4—21no—
127C22×D4—41no—
128C2×SD16—1224no—
129C2×SD16—1224no—
130C2×SD16—2444no—
131C2×SD16—2444no—
132C2×M16—2442no—
133C22×C8—1221no—
134C4⋊Q8—612no—
135C4⋊Q8—611no—
136C4⋊Q8—611no—
137C4⋊Q8—2441no—
138#127—21no—
139#127—41no—
140#127C2×#692312yes—
141C2×C4⋊C4—2441no—
142C2×C42C2×#692311yescharacteristic
143#101—1224no—
144#101—2442no—
145C4×C8—612no—
146C4×C8—1221no—
147C24—41no—
148C2×Q8—612no—
149C2×Q8—612no—
150C2×Q8—1222no—
151C2×Q8—2442no—
152C2×Q8—2442no—
153C2×D4—22no—
154C2×D4—42no—
155C2×D4—42no—
156C2×D4—42no—
157C2×D4—42no—
158C2×D4—41no—
159C2×D4—84no—
160C22×C4—21no—
161C22×C4—1222no—
162C22×C4C22⋊#692311yescharacteristic
163SD16—2448no—
164SD16—2448no—
165M16—4882no—
166M16—2444no—
167C2×C8—1222no—
168C2×C8—1222no—
169C2×C8—1222no—
170C2×C8—4882no—
171C4⋊C4—2442no—
172C4⋊C4—2441no—
173C4⋊C4—2441no—
174C42—21no—
175C42C22⋊#692311yescharacteristic
176C42C22×#692311yescharacteristic
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23#1451983511yescharacteristic
182Q8—4882no—
183Q8—2442no—
184Q8—2442no—
185D4—44no—
186D4—82no—
187D4—84no—
188D4—84no—
189C2×C4—24no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4#1451983511yescharacteristic
199C2×C4C2×C22⋊#692311yescharacteristic
200C8—1224no—
201C8—4884no—
202C22—22no—
203C22—84no—
204C22—82no—
205C22—162no—
206C22—162no—
207C22#1684066611yescharacteristic
208C22#1684066611yescharacteristic
209C22C2×#1451983511yescharacteristic
210C4—22no—
211C4—22no—
212C4—21no—
213C4—21no—
214C4—2442no—
215C4—2442no—
216C2—21no—
217C2—21no—
218C2—162no—
219C2#2146095412yesdirect product factor
220C2C2×#1684066611yescharacteristic
subgroupG/H
centerC22#16840666
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
Fitting, prime radicalC2×#127×C61C4
socleC22×C61#353
cosocle#14519777C23
hypercenterC2×#127#6923
hypocenterC61C2×#1410
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#16840673C2semidirect
2. #21460954C2direct (N × H)
6. #16840673C22semidirect
112. C2×C61#1410semidirect
124. C61C2×#1410semidirect
219. C2#21460954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406732
#214609542
C2×#168401342
C2×#141061