Finite Group Databasebeta

← #21457160

Subgroups — #21457160

Order 7808.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840314C212yesmaximal
2#16840056C212yesmaximal, complemented
3#16840055C212yesmaximal, complemented
4#16840003C211yesmaximal, characteristic
5#16840001C212yesmaximal
6#16839971C212yesmaximal, complemented
7#16839970C212yesmaximal, complemented
8C2×#14519706C211yesmaximal, characteristic
9C61×#467C211yesmaximal, characteristic
10C2×Dic244C2211yescharacteristic
11C2×#11758202C2212yes—
12C22×#92418C2211yescharacteristic
13#14519776C2212yes—
14#14519775C2212yes—
15#14519767—22no—
16#14519756C2212yes—
17#14519754—22no—
18Q8×Dic61C2212yes—
19#14519742—22no—
20#14519742C2212yes—
21#14519733—22no—
22C2×C4×Dic61C2211yescharacteristic
23#14519711C2211yescharacteristic
24#14519710C2212yes—
25#14519706C2212yes—
26#14519706C2212yes—
27#14519702C2212yes—
28#14519701C2212yes—
29#14519700C2212yes—
30C2×Q16×C61C2211yescharacteristic
31C22×C8×C61C2211yescharacteristic
32C22⋊Q8×C61C2212yes—
33#107×C61C2211yescharacteristic
34#103×C61C2212yes—
35C2×Q8×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61D411yescharacteristic
38C22×Dic61D411yescharacteristic
39C2×Dic122—22no—
40C2×Dic122C2312yes—
41Q16×C61—41no—
42C2×C8×C61—41no—
43C2×C8×C61C2311yescharacteristic
44C2×C8×C61C2311yescharacteristic
45C4⋊C4×C61—22no—
46C4⋊C4×C61C2312yes—
47C22⋊C4×C61—22no—
48C22⋊Dic61—22no—
49#11758202—42no—
50C4⋊Dic61—22no—
51C4⋊Dic61C2312yes—
52#11758196—22no—
53#11758196—22no—
54#11758196—22no—
55#11758196—22no—
56#11758196—22no—
57C4×Dic61—22no—
58C4×Dic61—22no—
59C4×Dic61D412yes—
60C4×Dic61C2312yes—
61C2×#92418—41no—
62C2×#92418C2312yes—
63Dic244—41no—
64C23×C61C2×D411yescharacteristic
65Q8×C61—22no—
66Q8×C61—22no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2411yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—41no—
76C2×Dic61Q1614yescomplemented
77C2×Dic61C2×D412yes—
78C2×Dic61C2×D412yes—
79Dic122—22no—
80Dic122—22no—
81Dic122—44no—
82C8×C61—21no—
83C8×C61—21no—
84#92418—22no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61C2×Q1612yes—
88C22×C61C22×D411yescharacteristic
89C4×C61—21no—
90C4×C61—42no—
91C4×C61—42no—
92C4×C61H(5,𝔽2)11yescharacteristic
93C4×C612−1+411yescharacteristic
94Dic61—22no—
95Dic61—42no—
96Dic61—42no—
97Dic61C2×Q1614yes—
98#3249—611nomaximal, Sylow
99C2×C61—22no—
100C2×C61#53711yescharacteristic
101C2×C61C22×Q1611yescharacteristic
102C2×C61#57511yescharacteristic
103#533—612no—
104#477—612no—
105#477—612no—
106#467—611no—
107#467—612no—
108#467D6111yescharacteristic
109#462—612no—
110#462—612no—
111C2×C4⋊C8—611no—
112C61#324911yescharacteristic, complemented, Sylow
113C2×Q16—612no—
114C2×Q16—611no—
115C2×Q16C2×D6111yescharacteristic
116C22×C8—611no—
117C22×C8C2×D6111yescharacteristic
118C4⋊Q8—612no—
119C4⋊Q8—612no—
120#125—1222no—
121C22⋊Q8—612no—
122C22⋊Q8—1222no—
123C22⋊Q8C2×D6112yes—
124C4×Q8—612no—
125C4×Q8—612no—
126C4×Q8—1222no—
127#117—1222no—
128C2×C42—611no—
129#107—611no—
130#107—612no—
131#107C2×D6111yescharacteristic
132C4⋊C8—612no—
133C4⋊C8—612no—
134#103—612no—
135#103—612no—
136#103—612no—
137#103C2×D6112yes—
138C2×Q8—612no—
139C2×Q8—1222no—
140C2×Q8C22×D6112yes—
141C22×C4—611no—
142C22×C4—611no—
143C22×C4C22×D6111yescharacteristic
144Q16—41no—
145Q16—2441no—
146Q16—2442no—
147C2×C8—41no—
148C2×C8—612no—
149C2×C8—2441no—
150C2×C8C22×D6111yescharacteristic
151C2×C8C22×D6111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—612no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4C22×D6112yes—
161C22⋊C4—22no—
162C22⋊C4—1222no—
163C42—612no—
164C42—612no—
165C42—1222no—
166C42—1222no—
167C23D4×D6111yescharacteristic
168Q8—22no—
169Q8—22no—
170Q8—1222no—
171Q8—1222no—
172Q8—2444no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—612no—
178C2×C4—614no—
179C2×C4—612no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—2441no—
183C2×C4D4×D6111yescharacteristic
184C2×C4C23×D6111yescharacteristic
185C8—21no—
186C8—21no—
187C8—1222no—
188C22—21no—
189C22—21no—
190C22Q16×D6112yes—
191C22C2×D4×D6111yescharacteristic
192C4—21no—
193C4—42no—
194C4—42no—
195C4—614no—
196C4—1222no—
197C4—2442no—
198C4—2442no—
199C4#1451982211yescharacteristic
200C4#1451982411yescharacteristic
201C2—22no—
202C2#1684033911yescharacteristic
203C2C2×Q16×D6111yescharacteristic
204C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#467C2
socleC22×C61C22×D4
hypercenter#467D61
hypocenterC61#3249
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #16840056C2semidirect
3. #16840055C2semidirect
6. #16839971C2semidirect
7. #16839970C2semidirect
76. C2×Dic61Q16semidirect
112. C61#3249semidirect