Finite Group Databasebeta

← #21457268

Subgroups — #21457268

Order 7808.

322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840372C212yesmaximal
2#16840071C212yesmaximal, complemented
3#16840068C212yesmaximal, complemented
4#16840018C212yesmaximal
5#16840003C211yesmaximal, characteristic
6#16839971C212yesmaximal, complemented
7#16839970C212yesmaximal, complemented
8#16839788C211yesmaximal, characteristic
9C61×#467C211yesmaximal, characteristic
10C2×Dic244C2211yescharacteristic
11C2×#11758202C2212yes—
12C2×#11758194C2211yescharacteristic
13#14519775C2212yes—
14#14519770—22no—
15#14519770—22no—
16#14519768—22no—
17#14519768C2212yes—
18#14519767—22no—
19#14519756C2212yes—
20Q8×Dic61C2212yes—
21#14519742C2212yes—
22#14519736C2211yescharacteristic
23#14519711C2211yescharacteristic
24#14519708C2212yes—
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
37C2×Dic122C2312yes—
38Q16×C61—41no—
39C2×C8×C61—41no—
40C2×C8×C61C2311yescharacteristic
41C2×C8×C61C2311yescharacteristic
42C4⋊C4×C61—22no—
43C4⋊C4×C61C2312yes—
44C22⋊C4×C61—22no—
45C22⋊Dic61—22no—
46C22⋊Dic61D412yes—
47#11758202—42no—
48C4⋊Dic61—22no—
49C4⋊Dic61—22no—
50C4⋊Dic61D411yescharacteristic
51C4⋊Dic61D411yescharacteristic
52C4⋊Dic61C2312yes—
53#11758196—22no—
54#11758196—22no—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58C4×Dic61—22no—
59C4×Dic61—22no—
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—22no—
74C2×Dic61—22no—
75C2×Dic61C2×D412yes—
76C2×Dic61C2×D412yes—
77Dic122—22no—
78Dic122—22no—
79C8×C61—21no—
80C8×C61—21no—
81#92418—22no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61—21no—
85C22×C61C22×D411yescharacteristic
86C4×C61—21no—
87C4×C61—42no—
88C4×C61—42no—
89C4×C61H(5,𝔽2)11yescharacteristic
90C4×C612−1+411yescharacteristic
91Dic61—22no—
92Dic61—22no—
93Dic61—42no—
94Dic61—42no—
95#3261—611nomaximal, Sylow
96C2×C61—41no—
97C2×C61#53711yescharacteristic
98C2×C61#57811yescharacteristic
99C2×C61#57811yescharacteristic
100#541—612no—
101#479—612no—
102#479—612no—
103#470—612no—
104#467—611no—
105#467D6111yescharacteristic
106#462—612no—
107#462—612no—
108#424—611no—
109C61#326111yescharacteristic, complemented, Sylow
110C2×Q16—612no—
111C2×Q16—611no—
112C2×Q16C2×D6111yescharacteristic
113C2×M16—611no—
114C22×C8C2×D6111yescharacteristic
115C4⋊Q8—612no—
116#126—1222no—
117#126—1222no—
118#125—612no—
119#125—1222no—
120#125—1222no—
121C22⋊Q8—612no—
122C22⋊Q8C2×D6112yes—
123C4×Q8—612no—
124C4×Q8—612no—
125#117—611no—
126#107—611no—
127#107C2×D6111yescharacteristic
128#106—612no—
129C4⋊C8—612no—
130C4⋊C8—612no—
131#103—612no—
132#103—612no—
133#103—612no—
134#103C2×D6112yes—
135C2×Q8—612no—
136C2×Q8C22×D6112yes—
137C22×C4C22×D6111yescharacteristic
138Q16—41no—
139Q16—2441no—
140Q16—2442no—
141M16—2441no—
142C2×C8—41no—
143C2×C8—612no—
144C2×C8C22×D6111yescharacteristic
145C2×C8C22×D6111yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—611no—
148C4⋊C4—611no—
149C4⋊C4—612no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4C22×D6112yes—
158C22⋊C4—22no—
159C22⋊C4—612no—
160C22⋊C4—1222no—
161C42—612no—
162C42—1222no—
163C42—1222no—
164C23D4×D6111yescharacteristic
165Q8—22no—
166Q8—22no—
167Q8—1222no—
168Q8—1222no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—612no—
174C2×C4—612no—
175C2×C4—1222no—
176C2×C4—1222no—
177C2×C4D4×D6111yescharacteristic
178C2×C4C23×D6111yescharacteristic
179C8—21no—
180C8—21no—
181C8—1222no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22C2×D4×D6111yescharacteristic
186C4—21no—
187C4—42no—
188C4—42no—
189C4—1222no—
190C4—1222no—
191C4—2442no—
192C4—2442no—
193C4#1451982211yescharacteristic
194C4#1451982411yescharacteristic
195C2—41no—
196C2#1684033911yescharacteristic
197C2#1684057511yescharacteristic
198C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#467C2
socleC22×C61C22×D4
hypercenter#467D61
hypocenterC61#3261
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. #16840071C2semidirect
3. #16840068C2semidirect
6. #16839971C2semidirect
7. #16839970C2semidirect
109. C61#3261semidirect