Finite Group Databasebeta

← D61⋊#356 #21462108

Subgroups — D61⋊#356 #21462108

Order 7808.

240 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D61⋊#101C212yesmaximal
2#16840673C212yesmaximal, complemented
3#16840672C212yesmaximal, complemented
4C4⋊Q8×D61C211yesmaximal, characteristic
5D61⋊M16—22no—
6#14519838—22no—
7#14519838C2214yes—
8C2×Q8×D61C411yescharacteristic
9C2×Q8×D61C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519776—22no—
12#14519775C411yescharacteristic
13#14519775C2211yescharacteristic
14C4⋊C4×D61—22no—
15C42×D61C411yescharacteristic
16C4⋊Q8×C61C411yescharacteristic
17C2×Q8×C61C2×C411yescharacteristic
18C2×Q8×C61C2×C411yescharacteristic
19Q8×D61—41no—
20Q8×D61—41no—
21Q8×D61—41no—
22Q8×D61—41no—
23C2×C4×D61—21no—
24C2×C4×D61—21no—
25C2×C4×D61C2×C411yescharacteristic
26C2×C4×D61D412yes—
27C2×Dic122—21no—
28C2×Dic122C2×C411yescharacteristic
29C2×Dic122D412yes—
30C2×Dic122C2311yescharacteristic
31#11758217—24no—
32#11758213—42no—
33D61⋊C8—42no—
34C4⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic
36C4⋊Dic61—22no—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic
41C22×D61C22⋊C411yescharacteristic
42Q8×C61—41no—
43Q8×C61—41no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61C22⋊C412yes—
47C2×C4×C61C22×C411yescharacteristic
48C2×Dic61—21no—
49C2×Dic61—21no—
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C2×D412yes—
52C4×D61—24no—
53C4×D61—22no—
54C4×D61—22no—
55C4×D61—21no—
56C4×D61—21no—
57C4×D61—41no—
58C4×D61—41no—
59Dic122—42no—
60Dic122—41no—
61Dic122—42no—
62Dic122—41no—
63#92420—44no—
64C22×C61C2×C22⋊C411yescharacteristic
65C2×D61—22no—
66C2×D61#9911yescharacteristic
67C2×D61#9911yescharacteristic
68C4×C61—22no—
69C4×C61—21no—
70C4×C61—22no—
71C4×C61—41no—
72Dic61—22no—
73Dic61—22no—
74Dic61—21no—
75Dic61—41no—
76C2×#356—611nomaximal, Sylow
77C2×C61—21no—
78C2×C61C2×#9911yescharacteristic
79D61—21no—
80D61#35612yescomplemented
81C2×C4⋊Q8—611no—
82C2×#101—612no—
83#356—612no—
84#356—612no—
85C61C2×#35611yescharacteristic, complemented, Sylow
86C22×Q8—611no—
87C22×Q8—611no—
88C2×M16—1222no—
89C4⋊Q8—611no—
90C4⋊Q8—611no—
91C4⋊Q8—611no—
92C4⋊Q8—1222no—
93C4⋊Q8#692311yescharacteristic
94C2×C4⋊C4—1222no—
95C2×C42—611no—
96#101—614no—
97#101—1222no—
98C2×Q8—612no—
99C2×Q8—611no—
100C2×Q8—611no—
101C2×Q8—1221no—
102C2×Q8—2441no—
103C2×Q8—2441no—
104C2×Q8—2441no—
105C2×Q8—2441no—
106C2×Q8C2×#692311yescharacteristic
107C2×Q8C2×#692311yescharacteristic
108C22×C4—612no—
109C22×C4—611no—
110C22×C4—1221no—
111C22×C4—1221no—
112M16—1224no—
113M16—2442no—
114C2×C8—2442no—
115C4⋊C4—22no—
116C4⋊C4—1222no—
117C4⋊C4—1222no—
118C4⋊C4—1222no—
119C42—611no—
120C42—1221no—
121C42C2×#692311yescharacteristic
122C23—611no—
123Q8—41no—
124Q8—41no—
125Q8—2442no—
126Q8—2441no—
127Q8—2441no—
128Q8—2442no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—611no—
132C2×C4—612no—
133C2×C4—1222no—
134C2×C4—1222no—
135C2×C4—1221no—
136C2×C4—1221no—
137C2×C4—1224no—
138C2×C4—1221no—
139C2×C4—1221no—
140C2×C4—2441no—
141C2×C4—2441no—
142C2×C4C22⋊#692312yes—
143C2×C4C22×#692311yescharacteristic
144C8—2444no—
145C22—611no—
146C22—611no—
147C22—1222no—
148C22C2×C22⋊#692311yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—1222no—
154C4—1222no—
155C4—1221no—
156C4—2441no—
157C2—21no—
158C2—612no—
159C2—1221no—
160C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC2×C61C2×#99
hypercenterC4⋊Q8#6923
hypocenterC61C2×#356
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16840673C2semidirect
3. #16840672C2semidirect
80. D61#356semidirect
85. C61C2×#356semidirect