Finite Group Databasebeta

← #21444290

Subgroups — #21444290

Order 7808.

202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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#16839818C211yesmaximal, characteristic
3#16839813C211yesmaximal, characteristic
4#16839494C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839492C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8#14519776C411yescharacteristic
9#14519775C411yescharacteristic
10#14519767—21no—
11#14519757C411yescharacteristic
12#14519755—21no—
13#14519753C411yescharacteristic
14C4×Dic122—21no—
15C4×Dic122C2211yescharacteristic
16#14519734—21no—
17C42×D61C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519689—21no—
22#14519687—21no—
23C4×#92418C2211yescharacteristic
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—
54C22×D61C22⋊C411yescharacteristic
55Q8×C61—21no—
56Q8×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61C22×C411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C22⋊C411yescharacteristic
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—21no—
70C4×D61—21no—
71C4×D61—41no—
72Dic122—21no—
73Dic122—21no—
74Dic122—42no—
75C8×C61—41no—
76C8×C61—41no—
77#92418—41no—
78#92418—41no—
79C22×C61C2×C22⋊C411yescharacteristic
80C2×D61—21no—
81C2×D61—21no—
82C2×D61—21no—
83C4×C61—21no—
84C4×C61—41no—
85C4×C61—41no—
86C4×C61#13111yescharacteristic
87C4×C61#13111yescharacteristic
88C4×C61#13711yescharacteristic
89C4×C61#13711yescharacteristic
90Dic61—21no—
91Dic61—21no—
92Dic61—21no—
93Dic61—41no—
94Dic61—41no—
95#1497—611nomaximal, Sylow
96C2×C61#40811yescharacteristic
97C2×C61#41911yescharacteristic
98C2×C61#42111yescharacteristic
99D61—41no—
100#533—611no—
101#432—611no—
102#431—611no—
103Q8⋊C8—611no—
104Q8⋊C8—611no—
105Q8⋊C8—611no—
106Q8⋊C8D6111yescharacteristic, complemented
107C61#149711yescharacteristic, complemented, Sylow
108C4⋊Q8—611no—
109C4⋊Q8—611no—
110#125—1221no—
111C22⋊Q8—611no—
112C22⋊Q8—611no—
113C22⋊Q8—1221no—
114C4×Q8—611no—
115C4×Q8—1221no—
116C4×Q8C2×D6111yescharacteristic
117#117—1221no—
118C2×C42—611no—
119C4⋊C8—611no—
120C4⋊C8—1221no—
121C4⋊C8C2×D6111yescharacteristic
122C22⋊C8—1221no—
123C22⋊C8—1221no—
124#97—1221no—
125C4×C8—611no—
126C4×C8C2×D6111yescharacteristic
127C2×Q8—611no—
128C2×Q8—1221no—
129C2×Q8C4×D6111yescharacteristic
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—1221no—
136C2×C8—1221no—
137C4⋊C4—21no—
138C4⋊C4—611no—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4C4×D6111yescharacteristic
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C42—21no—
149C42—611no—
150C42—611no—
151C42—611no—
152C42—1221no—
153C42C22×D6111yescharacteristic
154C23—611no—
155Q8—21no—
156Q8—21no—
157Q8—1221no—
158Q8—1221no—
159Q8—2442no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—2441no—
172C2×C4C2×C4×D6111yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C2×C4D4×D6111yescharacteristic
175C8—41no—
176C8—41no—
177C8—2441no—
178C8—2441no—
179C22—1221no—
180C22—1221no—
181C22—1221no—
182C22C22⋊C4×D6111yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—1221no—
187C4—1221no—
188C4—1221no—
189C4—2441no—
190C4—2441no—
191C4#1451978311yescharacteristic
192C4#1451978511yescharacteristic
193C4#1451980611yescharacteristic
194C4#1451980911yescharacteristic
195C2—2441no—
196C2#1683972711yescharacteristic
197C2#1683976911yescharacteristic
198C2#1683977711yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterQ8⋊C8D61
hypocenterC61#1497
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
106. Q8⋊C8D61semidirect
107. C61#1497semidirect