Finite Group Databasebeta

← #356×D61 #21447498

Subgroups — #356×D61 #21447498

Order 7808.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C4⋊Q8×D61C211yesmaximal, characteristic
2#101×D61C212yesmaximal
3#16839561C211yesmaximal, characteristic, complemented
4#16839560C212yesmaximal, complemented
5C61×#356C211yesmaximal, characteristic, complemented
6C2×Q8×D61C411yescharacteristic
7C2×Q8×D61C2211yescharacteristic
8M16×D61—22no—
9#14519777C411yescharacteristic
10#14519776—22no—
11#14519775C411yescharacteristic
12#14519775C2211yescharacteristic
13C4⋊C4×D61—22no—
14C42×D61C411yescharacteristic
15#14519696C2212yes—
16#14519695—22no—
17C4⋊Q8×C61C2211yescharacteristic
18#101×C61C2212yes—
19C2×Q8×C61C2×C411yescharacteristic
20C2×Q8×C61C2311yescharacteristic
21Q8×D61—41no—
22Q8×D61—41no—
23Q8×D61—41no—
24Q8×D61—41no—
25C2×C4×D61—21no—
26C2×C4×D61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D412yes—
29C2×Dic122—21no—
30C2×Dic122C2×C411yescharacteristic
31C2×Dic122C2×C411yescharacteristic
32C2×Dic122D412yes—
33M16×C61—22no—
34C4⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic
36C4⋊Dic61—22no—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic
41#11758194—22no—
42#11758189—42no—
43C8×D61—42no—
44C22×D61C22⋊C411yescharacteristic
45Q8×C61—41no—
46Q8×C61—41no—
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C2×D412yes—
51C2×Dic61—21no—
52C2×Dic61—21no—
53C2×Dic61C22⋊C411yescharacteristic
54C2×Dic61C22⋊C412yes—
55C4×D61—24no—
56C4×D61—22no—
57C4×D61—22no—
58C4×D61—21no—
59C4×D61—21no—
60C4×D61—41no—
61C4×D61—41no—
62Dic122—41no—
63Dic122—42no—
64Dic122—42no—
65Dic122—41no—
66C8×C61—42no—
67#92418—42no—
68C22×C61C2×C22⋊C411yescharacteristic
69C2×D61—22no—
70C2×D61#9911yescharacteristic
71C2×D61#9911yescharacteristic
72C4×C61—22no—
73C4×C61—22no—
74C4×C61—21no—
75C4×C61—41no—
76Dic61—22no—
77Dic61—21no—
78Dic61—22no—
79Dic61—41no—
80C2×#356—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61C2×#9911yescharacteristic
83D61—21no—
84D61#35612yesdirect product factor
85C2×C4⋊Q8—611no—
86C2×#101—612no—
87#356—611no—
88#356—612no—
89#356D6111yescharacteristic, direct product factor
90C61C2×#35611yescharacteristic, complemented, Sylow
91C22×Q8—611no—
92C22×Q8—611no—
93C2×M16—1222no—
94C4⋊Q8—611no—
95C4⋊Q8—611no—
96C4⋊Q8—611no—
97C4⋊Q8—1222no—
98C4⋊Q8C2×D6111yescharacteristic
99C2×C4⋊C4—1222no—
100C2×C42—611no—
101#101—612no—
102#101—1222no—
103#101C2×D6112yes—
104C2×Q8—611no—
105C2×Q8—612no—
106C2×Q8—611no—
107C2×Q8—1221no—
108C2×Q8—2441no—
109C2×Q8—2441no—
110C2×Q8—2441no—
111C2×Q8—2441no—
112C2×Q8C4×D6111yescharacteristic
113C2×Q8C22×D6111yescharacteristic
114C22×C4—611no—
115C22×C4—612no—
116C22×C4—1221no—
117C22×C4—1221no—
118M16—22no—
119M16—1222no—
120M16—2442no—
121C2×C8—2442no—
122C4⋊C4—22no—
123C4⋊C4—1222no—
124C4⋊C4—1222no—
125C4⋊C4—1222no—
126C42—611no—
127C42—1221no—
128C42C4×D6111yescharacteristic
129C23—611no—
130Q8—41no—
131Q8—41no—
132Q8—2442no—
133Q8—2441no—
134Q8—2441no—
135Q8—2442no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—611no—
139C2×C4—612no—
140C2×C4—1222no—
141C2×C4—1222no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—1224no—
145C2×C4—1221no—
146C2×C4—1221no—
147C2×C4—2441no—
148C2×C4—2441no—
149C2×C4C2×C4×D6111yescharacteristic
150C2×C4D4×D6112yes—
151C8—42no—
152C8—2442no—
153C22—611no—
154C22—611no—
155C22—1222no—
156C22C22⋊C4×D6111yescharacteristic
157C4—22no—
158C4—22no—
159C4—21no—
160C4—41no—
161C4—1222no—
162C4—1222no—
163C4—1221no—
164C4—2441no—
165C2—21no—
166C2—612no—
167C2—1221no—
168C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#356C2
socleC2×C61C2×#99
hypercenter#356D61
hypocenterC61C2×#356
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #16839561C2semidirect
4. #16839560C2semidirect
5. C61×#356C2semidirect
84. D61#356direct (N × H)
89. #356D61direct (N × H)
90. C61C2×#356semidirect