Finite Group Databasebeta

← #21447512

Subgroups — #21447512

Order 7808.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#16840337C211yesmaximal, characteristic
2#16839745C212yesmaximal
3#16839561C211yesmaximal, characteristic, complemented
4#16839560C212yesmaximal, complemented
5C61×#356C211yesmaximal, characteristic, complemented
6C2×#11758226C2211yescharacteristic
7C2×Q8×D61C411yescharacteristic
8M16×D61—22no—
9#14519775C2211yescharacteristic
10#14519766C411yescharacteristic
11#14519765C411yescharacteristic
12#14519762—22no—
13#14519755—22no—
14#14519734C411yescharacteristic
15#14519696C2212yes—
16#14519693—22no—
17C4⋊Q8×C61C2211yescharacteristic
18#101×C61C2212yes—
19C2×Q8×C61C2×C411yescharacteristic
20C2×Q8×C61C2311yescharacteristic
21#11758226—42no—
22Q8×D61—42no—
23C2×D244C2×C411yescharacteristic
24C2×D244D412yes—
25C2×C4×D61—21no—
26C2×C4×D61C2×C411yescharacteristic
27C2×C4×D61D412yes—
28C2×Dic122—21no—
29C2×Dic122C2×C411yescharacteristic
30M16×C61—22no—
31C4⋊C4×C61—22no—
32C42×C61C2×C411yescharacteristic
33#11758198—21no—
34#11758198—22no—
35#11758198—22no—
36#11758196—22no—
37#11758196—21no—
38C4×Dic61C2×C411yescharacteristic
39#11758194—22no—
40#11758189—42no—
41C8×D61—42no—
42C22×D61C22⋊C412yes—
43C22×D61C22⋊C411yescharacteristic
44Q8×C61—41no—
45Q8×C61—41no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61C22×C411yescharacteristic
49C2×C4×C61C2×D412yes—
50C2×Dic61—21no—
51C2×Dic61—21no—
52C2×Dic61C22⋊C411yescharacteristic
53D244—41no—
54D244—42no—
55C4×D61—22no—
56C4×D61—22no—
57C4×D61—22no—
58C4×D61—42no—
59Dic122—42no—
60Dic122—41no—
61C8×C61—42no—
62#92418—42no—
63C22×C61C2×C22⋊C411yescharacteristic
64C2×D61—21no—
65C2×D61—22no—
66C2×D61—42no—
67C2×D61—41no—
68C4×C61—22no—
69C4×C61—21no—
70C4×C61—41no—
71C4×C61—41no—
72Dic61—41no—
73Dic61—41no—
74Dic61#9912yes—
75#2135—611nomaximal, Sylow
76C2×C61—21no—
77C2×C61C2×#9911yescharacteristic
78D61—41no—
79D61—42no—
80#536—611no—
81#413—612no—
82#356—611no—
83#356—612no—
84#356D6111yescharacteristic, complemented
85C61#213511yescharacteristic, complemented, Sylow
86C2×#41—611no—
87C22×Q8—611no—
88C2×M16—1222no—
89C4⋊Q8—611no—
90C4⋊Q8C2×D6111yescharacteristic
91#124—611no—
92#124—611no—
93#123—1222no—
94C22⋊Q8—1222no—
95#117—611no—
96#101—612no—
97#101C2×D6112yes—
98#100—1222no—
99#41—2442no—
100C2×Q8—611no—
101C2×Q8—1221no—
102C2×Q8—2442no—
103C2×Q8C4×D6111yescharacteristic
104C2×Q8C22×D6111yescharacteristic
105C2×D4—611no—
106C2×D4—612no—
107C22×C4—611no—
108C22×C4—612no—
109C22×C4—1221no—
110M16—22no—
111M16—1222no—
112M16—2442no—
113C2×C8—2442no—
114C4⋊C4—22no—
115C4⋊C4—1221no—
116C4⋊C4—1222no—
117C22⋊C4—1221no—
118C22⋊C4—1222no—
119C22⋊C4—1222no—
120C42—611no—
121C42C4×D6111yescharacteristic
122C23—612no—
123C23—611no—
124Q8—41no—
125Q8—41no—
126Q8—2441no—
127Q8—2442no—
128D4—2442no—
129D4—2441no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—611no—
133C2×C4—1222no—
134C2×C4—1222no—
135C2×C4—1222no—
136C2×C4—1221no—
137C2×C4—1221no—
138C2×C4—2442no—
139C2×C4C2×C4×D6111yescharacteristic
140C2×C4D4×D6112yes—
141C8—42no—
142C8—2442no—
143C22—1221no—
144C22—1222no—
145C22—2442no—
146C22—2441no—
147C22C22⋊C4×D6111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—612no—
153C4—2441no—
154C4—2441no—
155C2—21no—
156C2—2441no—
157C2—2442no—
158C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#356C2
socleC2×C61C2×#99
hypercenter#356D61
hypocenterC61#2135
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. #356D61semidirect
85. C61#2135semidirect