Finite Group Databasebeta

← #21457209

Subgroups — #21457209

Order 7808.

342 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840046C212yesmaximal, complemented
3#16840045C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic
5#16840018C212yesmaximal
6#16839971C212yesmaximal, complemented
7#16839970C212yesmaximal, complemented
8#16839785C211yesmaximal, characteristic
9C61×#470C211yesmaximal, characteristic
10C2×Dic244C2211yescharacteristic
11C2×#11758202C2212yes—
12C2×#11758194C2211yescharacteristic
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#14519709C2211yescharacteristic
24#14519708C2212yes—
25#14519706C2212yes—
26#14519706C2212yes—
27#14519702C2212yes—
28#14519701C2212yes—
29#14519700C2212yes—
30C2×Q16×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic
32C22⋊Q8×C61C2212yes—
33#106×C61C2211yescharacteristic
34#103×C61C2212yes—
35C2×Q8×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61D412yes—
38C2×Dic122—22no—
39C2×Dic122C2312yes—
40Q16×C61—41no—
41M16×C61—41no—
42C2×C8×C61C2311yescharacteristic
43C2×C8×C61C2311yescharacteristic
44C4⋊C4×C61—22no—
45C4⋊C4×C61C2312yes—
46C22⋊C4×C61—22no—
47C22⋊Dic61—22no—
48#11758202—42no—
49C4⋊Dic61—22no—
50C4⋊Dic61C2312yes—
51#11758196—22no—
52#11758196—22no—
53#11758196—22no—
54#11758196—22no—
55#11758196—22no—
56C4×Dic61—22no—
57C4×Dic61—22no—
58C4×Dic61D411yescharacteristic
59C4×Dic61D411yescharacteristic
60C4×Dic61C2312yes—
61#11758194—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—24no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61C2×D412yes—
77C2×Dic61C2×D412yes—
78Dic122—22no—
79Dic122—22no—
80Dic122—44no—
81C8×C61—21no—
82C8×C61—21no—
83#92418—22no—
84C22×C61—21no—
85C22×C61—22no—
86C22×C61C22×D411yescharacteristic
87C4×C61—21no—
88C4×C61—42no—
89C4×C61—42no—
90C4×C61H(5,𝔽2)11yescharacteristic
91C4×C612−1+411yescharacteristic
92Dic61—22no—
93Dic61—42no—
94Dic61—42no—
95Dic61#13714yes—
96#3255—611nomaximal, Sylow
97C2×C61—41no—
98C2×C61#53711yescharacteristic
99C2×C61C2×#13712yes—
100#533—612no—
101#475—612no—
102#475—612no—
103#470—611no—
104#470—612no—
105#470D6111yescharacteristic
106#462—612no—
107#462—612no—
108#423—611no—
109C61#325511yescharacteristic, complemented, Sylow
110C2×Q16—612no—
111C2×Q16—611no—
112C2×Q16C2×D6111yescharacteristic
113C2×M16—611no—
114C2×M16C2×D6111yescharacteristic
115C4⋊Q8—612no—
116C4⋊Q8—612no—
117#125—1222no—
118C22⋊Q8—612no—
119C22⋊Q8—1222no—
120C22⋊Q8C2×D6112yes—
121C4×Q8—612no—
122C4×Q8—612no—
123C4×Q8—1222no—
124#117—1222no—
125C2×C42—611no—
126#106—611no—
127#106—612no—
128#106C2×D6111yescharacteristic
129C4⋊C8—612no—
130C4⋊C8—612no—
131#103—612no—
132#103—612no—
133#103—612no—
134#103C2×D6112yes—
135C2×Q8—612no—
136C2×Q8—1222no—
137C2×Q8C22×D6112yes—
138C22×C4—612no—
139C22×C4C22×D6111yescharacteristic
140Q16—41no—
141Q16—2441no—
142Q16—2442no—
143M16—41no—
144M16—2441no—
145C2×C8—612no—
146C2×C8C22×D6111yescharacteristic
147C2×C8C22×D6111yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—612no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4C22×D6112yes—
157C22⋊C4—22no—
158C22⋊C4—1222no—
159C42—611no—
160C42—611no—
161C42—612no—
162C42—1222no—
163C42—1222no—
164C23D4×D6111yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—1222no—
168Q8—1222no—
169Q8—2444no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—612no—
175C2×C4—612no—
176C2×C4—1224no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4D4×D6111yescharacteristic
180C2×C4C23×D6111yescharacteristic
181C8—21no—
182C8—21no—
183C8—1222no—
184C22—22no—
185C22—21no—
186C22C2×D4×D6111yescharacteristic
187C4—21no—
188C4—42no—
189C4—42no—
190C4—614no—
191C4—1222no—
192C4—2442no—
193C4—2442no—
194C4#1451982211yescharacteristic
195C4#1451982411yescharacteristic
196C2—41no—
197C2#1684033911yescharacteristic
198C2#137×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3255
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #16840046C2semidirect
3. #16840045C2semidirect
6. #16839971C2semidirect
7. #16839970C2semidirect
109. C61#3255semidirect