Finite Group Databasebeta

← #21444272

Subgroups — #21444272

Order 7808.

232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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#16840316C211yesmaximal, characteristic
2#16839784C211yesmaximal, characteristic
3C4×C8×D61C211yesmaximal, characteristic
4#16839494C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839492C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9C2×C8×D61—21no—
10#14519776C411yescharacteristic
11#14519775C411yescharacteristic
12#14519767—21no—
13#14519757C411yescharacteristic
14#14519755—21no—
15#14519753C411yescharacteristic
16C4×Dic122—21no—
17C4×Dic122C2211yescharacteristic
18#14519734—21no—
19C42×D61C2211yescharacteristic
20C4⋊#92418C2211yescharacteristic
21#14519706—21no—
22C4×#92418C2211yescharacteristic
23C8×Dic61—21no—
24C4×Q8×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×Q8×C61C2×C411yescharacteristic
28C2×C4×D61C2×C411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61D411yescharacteristic
31C2×Dic122—21no—
32C2×Dic122C2×C411yescharacteristic
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C42×C61—21no—
38C42×C61C2311yescharacteristic
39#11758198—21no—
40#11758198—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54#11758189—42no—
55C8×D61—24no—
56C22×D61C22⋊C411yescharacteristic
57Q8×C61—21no—
58Q8×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C22⋊C411yescharacteristic
69C4×D61—21no—
70C4×D61—21no—
71C4×D61—22no—
72C4×D61SD1612yes—
73C4×D61Q1612yes—
74Dic122—21no—
75Dic122—21no—
76Dic122—42no—
77C8×C61—22no—
78C8×C61—41no—
79#92418—22no—
80#92418—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61#10312yes—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61—41no—
88C4×C61#13111yescharacteristic
89C4×C61#13111yescharacteristic
90C4×C61C2×SD1611yescharacteristic
91C4×C61C2×Q1611yescharacteristic
92Dic61—21no—
93Dic61—41no—
94Dic61—41no—
95Dic61#10312yes—
96Dic61#10412yes—
97#1493—611nomaximal, Sylow
98C2×C61#40811yescharacteristic
99C2×C61C2×#10311yescharacteristic
100C2×C61C2×#10411yescharacteristic
101D61—22no—
102#533—611no—
103#423—611no—
104C2×C4×C8—611no—
105Q8⋊C8—611no—
106Q8⋊C8—611no—
107Q8⋊C8—611no—
108Q8⋊C8D6111yescharacteristic, complemented
109C61#149311yescharacteristic, complemented, Sylow
110C2×M16—1221no—
111C22×C8—1221no—
112C4⋊Q8—611no—
113C4⋊Q8—611no—
114#125—1221no—
115C22⋊Q8—611no—
116C22⋊Q8—611no—
117C22⋊Q8—1221no—
118C4×Q8—611no—
119C4×Q8—1221no—
120C4×Q8C2×D6111yescharacteristic
121#117—1221no—
122C2×C42—611no—
123C4⋊C8—611no—
124C4⋊C8—1221no—
125C4⋊C8C2×D6111yescharacteristic
126C4×C8—611no—
127C4×C8—1221no—
128C4×C8C2×D6111yescharacteristic
129C2×Q8—611no—
130C2×Q8—1221no—
131C2×Q8C4×D6111yescharacteristic
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—611no—
135M16—2442no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—1224no—
139C2×C8—1221no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—611no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4C4×D6111yescharacteristic
150C22⋊C4—1221no—
151C22⋊C4—1221no—
152C42—21no—
153C42—611no—
154C42—611no—
155C42—611no—
156C42—1221no—
157C42C22×D6111yescharacteristic
158C23—611no—
159Q8—21no—
160Q8—21no—
161Q8—1221no—
162Q8—1221no—
163Q8—2442no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—611no—
167C2×C4—611no—
168C2×C4—612no—
169C2×C4—612no—
170C2×C4—611no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4C2×C4×D6111yescharacteristic
177C2×C4D4×D6111yescharacteristic
178C2×C4D4×D6111yescharacteristic
179C8—22no—
180C8—41no—
181C8—1222no—
182C8—2441no—
183C22—612no—
184C22—1221no—
185C22—1221no—
186C22C22⋊C4×D6111yescharacteristic
187C4—21no—
188C4—41no—
189C4—41no—
190C4—612no—
191C4—612no—
192C4—1221no—
193C4—2441no—
194C4—2441no—
195C4#1451978311yescharacteristic
196C4#1451978511yescharacteristic
197C4SD16×D6111yescharacteristic
198C4Q16×D6111yescharacteristic
199C2—1222no—
200C2#1683972711yescharacteristic
201C2#103×D6111yescharacteristic
202C2#104×D6111yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterQ8⋊C8D61
hypocenterC61#1493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #16839494C2semidirect
5. Q8⋊#92418C2semidirect
6. #16839492C2semidirect
7. C61×Q8⋊C8C2semidirect
108. Q8⋊C8D61semidirect
109. C61#1493semidirect