Finite Group Databasebeta

← #21457270

Subgroups — #21457270

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#16840072C212yesmaximal, complemented
3#16840067C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic
5#16840001C212yesmaximal
6#16839971C212yesmaximal, complemented
7#16839970C212yesmaximal, complemented
8#16839790C211yesmaximal, characteristic
9C61×#470C211yesmaximal, characteristic
10C2×Dic244C2211yescharacteristic
11C2×#11758202C2212yes—
12C22×#92418C2211yescharacteristic
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#14519710C2212yes—
24#14519709C2211yescharacteristic
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
37C2×Dic122C2312yes—
38Q16×C61—41no—
39M16×C61—41no—
40C2×C8×C61C2311yescharacteristic
41C2×C8×C61C2311yescharacteristic
42C4⋊C4×C61—22no—
43C4⋊C4×C61C2312yes—
44C22⋊C4×C61—22no—
45C22⋊Dic61—22no—
46C22⋊Dic61D411yescharacteristic
47C22⋊Dic61D411yescharacteristic
48#11758202—42no—
49C4⋊Dic61—22no—
50C4⋊Dic61—22no—
51C4⋊Dic61D412yes—
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—
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×Dic61C2×D412yes—
76C2×Dic61C2×D412yes—
77Dic122—22no—
78Dic122—22no—
79C8×C61—21no—
80C8×C61—21no—
81#92418—22no—
82C22×C61—21no—
83C22×C61—22no—
84C22×C61C22×D411yescharacteristic
85C4×C61—21no—
86C4×C61—42no—
87C4×C61—42no—
88C4×C61H(5,𝔽2)11yescharacteristic
89C4×C612−1+411yescharacteristic
90Dic61—22no—
91Dic61—22no—
92Dic61—42no—
93Dic61—42no—
94#3261—611nomaximal, Sylow
95C2×C61—41no—
96C2×C61#53711yescharacteristic
97C2×C61#57812yes—
98#541—612no—
99#479—612no—
100#479—612no—
101#470—611no—
102#470D6111yescharacteristic
103#467—612no—
104#462—612no—
105#462—612no—
106#424—611no—
107C61#326111yescharacteristic, complemented, Sylow
108C2×Q16—612no—
109C2×Q16—611no—
110C2×Q16C2×D6111yescharacteristic
111C2×M16C2×D6111yescharacteristic
112C22×C8—611no—
113C4⋊Q8—612no—
114#126—1222no—
115#126—1222no—
116#125—612no—
117#125—1222no—
118#125—1222no—
119C22⋊Q8—612no—
120C22⋊Q8C2×D6112yes—
121C4×Q8—612no—
122C4×Q8—612no—
123#117—611no—
124#107—612no—
125#106—611no—
126#106C2×D6111yescharacteristic
127C4⋊C8—612no—
128C4⋊C8—612no—
129#103—612no—
130#103—612no—
131#103—612no—
132#103C2×D6112yes—
133C2×Q8—612no—
134C2×Q8C22×D6112yes—
135C22×C4C22×D6111yescharacteristic
136Q16—41no—
137Q16—2441no—
138Q16—2442no—
139M16—41no—
140C2×C8—612no—
141C2×C8—2441no—
142C2×C8C22×D6111yescharacteristic
143C2×C8C22×D6111yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—612no—
146C4⋊C4—612no—
147C4⋊C4—1222no—
148C4⋊C4—1222no—
149C4⋊C4—1222no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4C22×D6112yes—
155C22⋊C4—22no—
156C22⋊C4—611no—
157C22⋊C4—611no—
158C22⋊C4—1222no—
159C42—612no—
160C42—1222no—
161C42—1222no—
162C23D4×D6111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—1222no—
166Q8—1222no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—612no—
172C2×C4—612no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4D4×D6111yescharacteristic
176C2×C4C23×D6111yescharacteristic
177C8—21no—
178C8—21no—
179C8—1222no—
180C22—22no—
181C22—21no—
182C22C2×D4×D6111yescharacteristic
183C4—21no—
184C4—42no—
185C4—42no—
186C4—1222no—
187C4—1222no—
188C4—2442no—
189C4—2442no—
190C4#1451982211yescharacteristic
191C4#1451982411yescharacteristic
192C2—41no—
193C2#1684033911yescharacteristic
194C2#1684057812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3261
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. #16840072C2semidirect
3. #16840067C2semidirect
6. #16839971C2semidirect
7. #16839970C2semidirect
107. C61#3261semidirect