Finite Group Databasebeta

← #21456401

Subgroups — #21456401

Order 7808.

368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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#16840319C211yesmaximal, characteristic
2#16840165C211yesmaximal, characteristic, complemented
3#16840141C211yesmaximal, characteristic, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840112C211yesmaximal, characteristic, complemented
6#16840001C214yesmaximal
7C4×#11758202C214yesmaximal, complemented
8C2×C4×#92418C211yesmaximal, characteristic
9C61×#533C211yesmaximal, characteristic
10C2×#11758202C2214yes—
11C22×#92418C2212yes—
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519769—21no—
15#14519756—21no—
16#14519756C2212yes—
17C4×Dic122—21no—
18C4×Dic122C2212yes—
19#14519736—21no—
20#14519710C2214yes—
21#14519701C2214yes—
22#14519700C2214yes—
23C4×#92418C2212yes—
24C4×#92418C2211yescharacteristic
25C4×#92418C2211yescharacteristic
26C4⋊Q8×C61C2211yescharacteristic
27C4⋊Q8×C61C2211yescharacteristic
28#125×C61—21no—
29C22⋊Q8×C61—21no—
30C22⋊Q8×C61C2212yes—
31C4×Q8×C61—21no—
32C4×Q8×C61C2212yes—
33#117×C61—21no—
34C2×C42×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61C2312yes—
37C22×C4×C61D411yescharacteristic
38C22×C4×C61D411yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C2×Dic122—21no—
41C2×Dic122C2312yes—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61C2312yes—
48C22⋊C4×C61—22no—
49C42×C61—22no—
50C42×C61D411yescharacteristic
51C42×C61D411yescharacteristic
52C42×C61C2311yescharacteristic
53C42×C61C2311yescharacteristic
54C22⋊Dic61—22no—
55#11758202—28no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61C2312yes—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61—22no—
63C2×#92418—24no—
64C2×#92418C2312yes—
65C2×#92418C2312yes—
66C23×C61C2×D411yescharacteristic
67Q8×C61—24no—
68Q8×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61Q1614yescomplemented
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—22no—
82Dic122—24no—
83Dic122—42no—
84#92418—22no—
85#92418#4114yes—
86C22×C61—21no—
87C22×C61—21no—
88C22×C61C2×Q1612yes—
89C22×C61C22×D411yescharacteristic
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—42no—
93C4×C61—42no—
94C4×C61C2×Q1612yes—
95C4×C61C2×Q1612yes—
96C4×C61#13512yes—
97C4×C61C2×#4112yes—
98Dic61—42no—
99Dic61—42no—
100#3170—611nomaximal, Sylow
101C2×C61—22no—
102C2×C61#53211yescharacteristic
103C2×C61C22×Q1611yescharacteristic
104C2×C61C2×#13511yescharacteristic
105#533—611no—
106#533D6111yescharacteristic
107#500—611no—
108#494—611no—
109#487—611no—
110#487—611no—
111#467—614no—
112C4×Q16—614no—
113C2×C4×C8—611no—
114C61#317011yescharacteristic, complemented, Sylow
115C2×Q16—614no—
116C22×C8—612no—
117C4⋊Q8—611no—
118C4⋊Q8—611no—
119C4⋊Q8C2×D6111yescharacteristic
120C4⋊Q8C2×D6111yescharacteristic
121#125—21no—
122#125—1221no—
123C22⋊Q8—21no—
124C22⋊Q8—612no—
125C22⋊Q8—1221no—
126C22⋊Q8C2×D6112yes—
127C4×Q8—21no—
128C4×Q8—612no—
129C4×Q8—1221no—
130C4×Q8C2×D6112yes—
131#117—21no—
132#117—1221no—
133C2×C42C2×D6111yescharacteristic
134#107—614no—
135#103—614no—
136#103—614no—
137C4×C8—612no—
138C4×C8—611no—
139C4×C8—611no—
140C2×Q8—21no—
141C2×Q8—612no—
142C2×Q8—1221no—
143C2×Q8C22×D6112yes—
144C22×C4C22⋊D6111yescharacteristic
145C22×C4C22⋊D6111yescharacteristic
146C22×C4C22×D6111yescharacteristic
147Q16—1228no—
148C2×C8—612no—
149C2×C8—612no—
150C2×C8—1224no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—612no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4C22×D6112yes—
163C22⋊C4—22no—
164C22⋊C4—1222no—
165C42—22no—
166C42—1222no—
167C42C22⋊D6111yescharacteristic
168C42C22⋊D6111yescharacteristic
169C42C22×D6111yescharacteristic
170C42C22×D6111yescharacteristic
171C23C2×C22⋊D6111yescharacteristic
172Q8—24no—
173Q8—42no—
174Q8—1224no—
175Q8—2442no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4#1175820214yescomplemented
183C2×C4C2×C22⋊D6111yescharacteristic
184C2×C4C2×C22⋊D6111yescharacteristic
185C2×C4C2×C22⋊D6111yescharacteristic
186C2×C4C2×C22⋊D6111yescharacteristic
187C2×C4C2×C22⋊D6111yescharacteristic
188C2×C4C23×D6111yescharacteristic
189C8—614no—
190C8—1222no—
191C22—21no—
192C22—21no—
193C22C2×#1175820212yes—
194C22C22×C22⋊D6111yescharacteristic
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—2442no—
200C4—2442no—
201C4C2×#1175820212yes—
202C4C2×#1175820212yes—
203C4#1451979712yes—
204C4#41×D6112yes—
205C2—22no—
206C2#1684030811yescharacteristic
207C2C22×#1175820211yescharacteristic
208C2C2×#1451979711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3170
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840165C2semidirect
3. #16840141C2semidirect
4. #16840114C2semidirect
5. #16840112C2semidirect
7. C4×#11758202C2semidirect
73. C2×C4×C61Q16semidirect
114. C61#3170semidirect
182. C2×C4#11758202semidirect