Finite Group Databasebeta

← #21457269

Subgroups — #21457269

Order 7808.

322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840374C211yesmaximal, characteristic
2#16840069C212yesmaximal, complemented
3#16840066C212yesmaximal, complemented
4#16840018C212yesmaximal
5#16840001C212yesmaximal
6#16839972C212yesmaximal, complemented
7#16839969C212yesmaximal, complemented
8#16839789C211yesmaximal, characteristic
9C61×#541C211yesmaximal, characteristic
10C2×#11758202C2212yes—
11C2×#11758202C2212yes—
12C2×#11758194C2211yescharacteristic
13C22×#92418C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519770—22no—
16#14519769C2211yescharacteristic
17#14519767—22no—
18#14519756C2212yes—
19C4×Dic122C2212yes—
20#14519710C2212yes—
21#14519708C2212yes—
22C4⋊#92418C2212yes—
23C4⋊#92418C2212yes—
24#14519701C2212yes—
25#14519701C2212yes—
26#14519700C2212yes—
27#14519700C2212yes—
28C4⋊Q8×C61C2211yescharacteristic
29#126×C61—22no—
30#125×C61—22no—
31#125×C61C2211yescharacteristic
32C22⋊Q8×C61C2212yes—
33C4×Q8×C61C2212yes—
34#117×C61C2211yescharacteristic
35C2×Q8×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C2×Dic122C2312yes—
38C4⋊C4×C61—22no—
39C4⋊C4×C61—22no—
40C4⋊C4×C61—22no—
41C4⋊C4×C61—22no—
42C4⋊C4×C61D412yes—
43C4⋊C4×C61C2312yes—
44C22⋊C4×C61—22no—
45C22⋊C4×C61D412yes—
46C42×C61—22no—
47C42×C61C2311yescharacteristic
48C42×C61C2311yescharacteristic
49C22⋊Dic61—22no—
50#11758202—42no—
51#11758202—42no—
52C4⋊Dic61—22no—
53C4⋊Dic61C2312yes—
54#11758196—22no—
55#11758196—22no—
56#11758196—22no—
57C4×Dic61—22no—
58#11758194—41no—
59C2×#92418—41no—
60C2×#92418C2312yes—
61C2×#92418C2312yes—
62C23×C61C2×D411yescharacteristic
63Q8×C61—22no—
64Q8×C61—22no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D412yes—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2411yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—22no—
75Dic122—22no—
76Dic122—22no—
77#92418—22no—
78#92418—22no—
79C22×C61—21no—
80C22×C61—22no—
81C22×C61C22×D411yescharacteristic
82C4×C61—21no—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—42no—
86C4×C61—42no—
87C4×C61H(5,𝔽2)11yescharacteristic
88C4×C612−1+411yescharacteristic
89Dic61—42no—
90Dic61—42no—
91#3261—611nomaximal, Sylow
92C2×C61—41no—
93C2×C61#53711yescharacteristic
94C2×C61#57812yes—
95#541—611no—
96#541D6111yescharacteristic
97#479—612no—
98#479—612no—
99#470—612no—
100#467—612no—
101#462—612no—
102#462—612no—
103#424—611no—
104C61#326111yescharacteristic, complemented, Sylow
105C2×Q16—612no—
106C2×Q16—612no—
107C2×M16—611no—
108C22×C8—611no—
109C4⋊Q8—611no—
110C4⋊Q8C2×D6111yescharacteristic
111#126—22no—
112#126—1222no—
113#125—22no—
114#125—611no—
115#125—1222no—
116#125C2×D6111yescharacteristic
117C22⋊Q8—612no—
118C22⋊Q8C2×D6112yes—
119C4×Q8—612no—
120C4×Q8C2×D6112yes—
121#117C2×D6111yescharacteristic
122#107—612no—
123#106—612no—
124C4⋊C8—612no—
125C4⋊C8—612no—
126#103—612no—
127#103—612no—
128#103—612no—
129#103—612no—
130C2×Q8—612no—
131C2×Q8C22×D6112yes—
132C22×C4C22×D6111yescharacteristic
133Q16—2442no—
134Q16—2442no—
135M16—2441no—
136C2×C8—612no—
137C2×C8—612no—
138C2×C8—2441no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—612no—
144C4⋊C4—1222no—
145C4⋊C4—1222no—
146C4⋊C4—1222no—
147C4⋊C4—1222no—
148C4⋊C4C22⋊D6112yes—
149C4⋊C4C22×D6112yes—
150C22⋊C4—22no—
151C22⋊C4—1222no—
152C22⋊C4C22⋊D6112yes—
153C42—22no—
154C42—1222no—
155C42C22×D6111yescharacteristic
156C42C22×D6111yescharacteristic
157C23C2×C22⋊D6111yescharacteristic
158Q8—22no—
159Q8—22no—
160Q8—1222no—
161Q8—1222no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4C2×C22⋊D6112yes—
169C2×C4C2×C22⋊D6112yes—
170C2×C4C2×C22⋊D6111yescharacteristic
171C2×C4C23×D6111yescharacteristic
172C8—1222no—
173C8—1222no—
174C22—22no—
175C22—21no—
176C22C22×C22⋊D6111yescharacteristic
177C4—22no—
178C4—22no—
179C4—21no—
180C4—42no—
181C4—42no—
182C4—2442no—
183C4—2442no—
184C4#1451982311yescharacteristic
185C4#1451982411yescharacteristic
186C2—41no—
187C2#1684034011yescharacteristic
188C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#541C2
socleC22×C61C22×D4
hypercenter#541D61
hypocenterC61#3261
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #16840069C2semidirect
3. #16840066C2semidirect
6. #16839972C2semidirect
7. #16839969C2semidirect
104. C61#3261semidirect