Finite Group Databasebeta

← #21446211

Subgroups — #21446211

Order 7808.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14519777C211yesmaximal, characteristic
2#16840239C211yesmaximal, characteristic
3#16839772C211yesmaximal, characteristic
4#16839770C211yesmaximal, characteristic
5C2×#14519695C211yesmaximal, characteristic
6#16839522C211yesmaximal, characteristic
7C61×#339C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519777—22no—
12#14519777C414yescomplemented
13C4×Dic122—22no—
14#14519742—22no—
15#14519736C2211yescharacteristic
16#14519733—22no—
17C2×C4⋊Dic61—22no—
18#14519702—22no—
19#14519700—22no—
20#14519695—22no—
21C2×M16×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23C2×C42×C61C2211yescharacteristic
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61D412yes—
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122C2×C412yes—
38C2×Dic122C2×C412yes—
39C2×Dic122D412yes—
40M16×C61—21no—
41M16×C61—21no—
42C2×C8×C61—21no—
43C4⋊C4×C61D412yes—
44C22⋊C4×C61—21no—
45C42×C61—21no—
46C42×C61—21no—
47C42×C61C2×C412yes—
48C22⋊Dic61—21no—
49C4⋊Dic61—28no—
50C4⋊Dic61D412yes—
51#11758196—24no—
52C4×Dic61—24no—
53C4×Dic61—21no—
54#11758194—21no—
55#11758194—21no—
56C2×#92418—21no—
57C23×C61C2×D411yescharacteristic
58C2×C4×C61—24no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61C22⋊C414yes—
74Dic122—22no—
75Dic122—22no—
76Dic122—22no—
77Dic122—22no—
78Dic122—22no—
79Dic122—22no—
80Dic122—41no—
81Dic122—41no—
82C8×C61—41no—
83#92418—41no—
84C22×C61—22no—
85C22×C61C2×C22⋊C411yescharacteristic
86C22×C61#12011yescharacteristic
87C22×C61#12311yescharacteristic
88C4×C61—24no—
89C4×C61—42no—
90C4×C61C4×D411yescharacteristic
91C4×C61C4×D411yescharacteristic
92C4×C61#12111yescharacteristic
93C4×C61#12111yescharacteristic
94Dic61—24no—
95Dic61—42no—
96Dic61—42no—
97#1886—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—21no—
100C2×C61#38611yescharacteristic
101C2×C61#45612yes—
102C2×C4⋊Q8—611no—
103#519—611no—
104#419—611no—
105#419—611no—
106C2×#101—611no—
107#339—611no—
108#339D6111yescharacteristic
109C61#188611yescharacteristic, complemented, Sylow
110C22×Q8—611no—
111C22×Q8—611no—
112C2×M16—611no—
113C2×M16C2×D6111yescharacteristic
114C4⋊Q8—614no—
115C4⋊Q8—1222no—
116C4×Q8—1222no—
117C4×Q8—1222no—
118#117—611no—
119#117—1222no—
120#117C2×D6111yescharacteristic
121C2×C4⋊C4—1222no—
122C2×C42C2×D6111yescharacteristic
123#103—1222no—
124#103—1222no—
125#101—1222no—
126C2×Q8—612no—
127C2×Q8—612no—
128C2×Q8—612no—
129C2×Q8—1221no—
130C2×Q8—1221no—
131C2×Q8—1221no—
132C2×Q8—1221no—
133C2×Q8—1221no—
134C2×Q8—1221no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C22×C4—21no—
139C22×C4—612no—
140C22×C4—1221no—
141C22×C4C22×D6111yescharacteristic
142M16—21no—
143M16—21no—
144M16—1221no—
145M16—1221no—
146C2×C8—21no—
147C2×C8—1221no—
148C4⋊C4—612no—
149C4⋊C4—1228no—
150C4⋊C4—1224no—
151C4⋊C4D24412yes—
152C22⋊C4—21no—
153C22⋊C4—1221no—
154C42—21no—
155C42—21no—
156C42—1224no—
157C42—1221no—
158C42C4×D6112yes—
159C23D4×D6111yescharacteristic
160Q8—1222no—
161Q8—1222no—
162Q8—1222no—
163Q8—1222no—
164Q8—1222no—
165Q8—1222no—
166Q8—2441no—
167Q8—2441no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—614no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4C2×C4×D6111yescharacteristic
179C2×C4C2×D24411yescharacteristic
180C2×C4#1175822211yescharacteristic
181C2×C4D4×D6111yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4#1175822611yescharacteristic
184C8—41no—
185C8—2441no—
186C22—22no—
187C22C22⋊C4×D6111yescharacteristic
188C22#1451974711yescharacteristic
189C22#1451976211yescharacteristic
190C4—24no—
191C4—42no—
192C4—1224no—
193C4—2442no—
194C4—2442no—
195C4#1451973911yescharacteristic
196C4C4×D24411yescharacteristic
197C4#1451975011yescharacteristic
198C4#1451975211yescharacteristic
199C2—21no—
200C2—21no—
201C2#1683964011yescharacteristic
202C2#1683994612yes—
subgroupG/H
centerC22#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#1886
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #14519777C4semidirect
109. C61#1886semidirect