Finite Group Databasebeta

← #21461980

Subgroups — #21461980

Order 7808.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊#108C211yesmaximal, characteristic, complemented
2#16840754C212yesmaximal, complemented
3D61⋊#100C212yesmaximal, complemented
4#16840725C211yesmaximal, characteristic, complemented
5C2×D8×D61C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7D61⋊M16C2211yescharacteristic
8#14519856C2211yescharacteristic
9#14519848—21no—
10#14519847—21no—
11#14519839—24no—
12#14519837—24no—
13#14519831—21no—
14C8×#6923—21no—
15C2×D4×D61C2212yes—
16C2×D488C411yescharacteristic, complemented
17C2×#11758199C412yescomplemented
18D8×D61—21no—
19D8×D61—21no—
20D8×D61—21no—
21D8×D61—21no—
22C2×C8×D61C2211yescharacteristic
23C2×D8×C61C411yescharacteristic, complemented
24C23×D61—22no—
25C2×D4×C61C2×C412yes—
26C2×C22⋊D61—22no—
27D4×D61—22no—
28D4×D61—22no—
29D4×D61—22no—
30D4×D61—22no—
31C2×D244C2×C412yes—
32C2×C4×D61C2311yescharacteristic
33C22⋊#6923—21no—
34#11758217—22no—
35#11758217D412yes—
36C4⋊#6923D412yes—
37C4×#6923—21no—
38#11758213—21no—
39#11758213—22no—
40D61⋊C8—21no—
41D61⋊C8—22no—
42D8×C61—21no—
43D8×C61—21no—
44C2×C8×C61C2×C411yescharacteristic
45#11758199—22no—
46#11758199—22no—
47C2×#92418C2×C411yescharacteristic
48D488—21no—
49D488—21no—
50C8×D61D411yescharacteristic
51C8×D61D411yescharacteristic
52C8×D61D411yescharacteristic
53C8×D61D411yescharacteristic
54C23×C61—22no—
55C22×D61—22no—
56C22×D61—42no—
57C22×D61—42no—
58C22×D61—84no—
59C22×D61#4111yescharacteristic
60C2×#6923—22no—
61D4×C61—22no—
62D4×C61—22no—
63C2×C4×C61C22×C411yescharacteristic
64C22⋊D61—42no—
65C22⋊D61—42no—
66C2×Dic61C2×D411yescharacteristic
67D244—22no—
68D244—22no—
69C4×D61C2×D411yescharacteristic
70C4×D61C2×D411yescharacteristic
71C4×D61C2×D411yescharacteristic
72C4×D61#4111yescharacteristic
73#92420—22no—
74#92420—42no—
75C8×C61C22⋊C411yescharacteristic
76C8×C61C22⋊C411yescharacteristic
77#92418C22⋊C411yescharacteristic
78#92418C22⋊C411yescharacteristic
79C22×C61—42no—
80C22×C61—82no—
81C22×C61C4×D411yescharacteristic
82C2×D61—22no—
83C2×D61—42no—
84C2×D61—84no—
85C2×D61—84no—
86C2×D61—82no—
87C2×D61#12111yescharacteristic
88C2×D61#12411yescharacteristic
89#6923—42no—
90C4×C61C2×C22⋊C411yescharacteristic
91C4×C61C4×D411yescharacteristic
92Dic61#12111yescharacteristic
93Dic61#12711yescharacteristic
94#1978—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—82no—
97C2×C61#39011yescharacteristic
98D61—21no—
99D61—82no—
100D61#47212yes—
101C22×D8—611no—
102C2×#108—611no—
103#418—612no—
104C2×#100—612no—
105#405—611no—
106C61#197811yescharacteristic, complemented, Sylow
107C22×D4—612no—
108C2×D8—612no—
109C2×D8—611no—
110C2×D8—1221no—
111C2×D8—1221no—
112C2×D8—1221no—
113C2×D8—1221no—
114C2×D8#692311yescharacteristic, complemented
115C2×M16—611no—
116C2×M16—612no—
117C22×C8—611no—
118#117—611no—
119#108—1221no—
120#108—1221no—
121#102—1224no—
122#100—1224no—
123#97—1221no—
124C4×C8—1221no—
125C24—1222no—
126C2×D4—612no—
127C2×D4—1222no—
128C2×D4—1222no—
129C2×D4—1222no—
130C2×D4—1222no—
131C2×D4—1222no—
132C2×D4C2×#692312yes—
133C22×C4—611no—
134D8—21no—
135D8—21no—
136D8—1222no—
137D8—1222no—
138D8—1221no—
139D8—1221no—
140M16—612no—
141M16—1221no—
142M16—1222no—
143M16—1222no—
144C2×C8—611no—
145C2×C8—611no—
146C2×C8—611no—
147C2×C8—611no—
148C2×C8—611no—
149C2×C8—1221no—
150C2×C8—1222no—
151C2×C8C2×#692311yescharacteristic
152C4⋊C4—612no—
153C22⋊C4—1221no—
154C42—1221no—
155C23—22no—
156C23—611no—
157C23—1222no—
158C23—4884no—
159C23—2442no—
160C23—2442no—
161D4—22no—
162D4—22no—
163D4—1222no—
164D4—1222no—
165D4—2442no—
166D4—2442no—
167C2×C4—611no—
168C2×C4—611no—
169C2×C4—611no—
170C2×C4—611no—
171C2×C4—611no—
172C2×C4—1222no—
173C2×C4C22×#692311yescharacteristic
174C8—611no—
175C8—611no—
176C8—1222no—
177C8—2442no—
178C8C22⋊#692311yescharacteristic
179C8C22⋊#692311yescharacteristic
180C22—42no—
181C22—82no—
182C22—611no—
183C22—611no—
184C22—1222no—
185C22—4882no—
186C22—4884no—
187C22—4884no—
188C22—2442no—
189C22D4×#692311yescharacteristic
190C4—611no—
191C4—611no—
192C4—2442no—
193C4C2×C22⋊#692311yescharacteristic
194C4D4×#692311yescharacteristic
195C2—21no—
196C2—82no—
197C2—612no—
198C2—1221no—
199C2—4882no—
200C2#1684071411yescharacteristic
subgroupG/H
centerC2#16840714
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×D8×C61C4
socleC2×C61#390
hypercenterC2×D8#6923
hypocenterC61#1978
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D61⋊#108C2semidirect
2. #16840754C2semidirect
3. D61⋊#100C2semidirect
4. #16840725C2semidirect
16. C2×D488C4semidirect
17. C2×#11758199C4semidirect
23. C2×D8×C61C4semidirect
106. C61#1978semidirect
114. C2×D8#6923semidirect