Finite Group Databasebeta

← #21456203

Subgroups — #21456203

Order 7808.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840315C211yesmaximal, characteristic, complemented
2C2×#14519764C211yesmaximal, characteristic
3#16840120C214yesmaximal, complemented
4#16840115C214yesmaximal, complemented
5#16839772C211yesmaximal, characteristic, complemented
6#16839770C211yesmaximal, characteristic, complemented
7#16839767C211yesmaximal, characteristic
8M16×Dic61C211yesmaximal, characteristic, complemented
9C61×#418C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×#11758194C2211yescharacteristic
12#14519776C2212yescomplemented
13#14519768C2212yescomplemented
14#14519764—22no—
15#14519764C2212yes—
16#14519764C2212yes—
17#14519754—22no—
18C4×Dic122—22no—
19#14519736C2211yescharacteristic
20C2×C22⋊Dic61—22no—
21C2×C4×Dic61C2211yescharacteristic
22#14519702C2214yescomplemented
23#14519700C2214yescomplemented
24#14519698C2214yes—
25#14519687C2212yescomplemented
26C8×Dic61C2212yescomplemented
27C22×D4×C61C2211yescharacteristic
28C2×M16×C61C2211yescharacteristic
29#117×C61C2211yescharacteristic
30#102×C61C2214yes—
31C24×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—22no—
34C2×D4×C61—22no—
35C2×D4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—21no—
38C22×Dic61D412yes—
39C2×Dic122—22no—
40C2×Dic122—22no—
41C2×Dic122—21no—
42C2×Dic122—22no—
43C2×Dic122C2312yes—
44M16×C61—22no—
45C2×C8×C61C2312yes—
46C4⋊C4×C61C2312yes—
47C22⋊C4×C61—21no—
48C42×C61—21no—
49C22⋊Dic61—21no—
50C22⋊Dic61—24no—
51C22⋊Dic61—24no—
52C4⋊Dic61—22no—
53C4⋊Dic61C2312yes—
54#11758196—22no—
55#11758196—22no—
56C4×Dic61—21no—
57C4×Dic61D412yes—
58C4×Dic61C2311yescharacteristic
59C4×Dic61C2311yescharacteristic
60#11758194—22no—
61C2×#92418C2312yes—
62C23×C61—22no—
63C23×C61—44no—
64C23×C61—42no—
65C23×C61C2×D411yescharacteristic
66D4×C61—22no—
67D4×C61—22no—
68D4×C61—42no—
69C2×C4×C61—22no—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61#4112yes—
72C2×C4×C61#4112yes—
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61C2×D412yes—
79C2×Dic61C2×D412yes—
80Dic122—22no—
81Dic122—22no—
82Dic122—44no—
83Dic122—42no—
84C8×C61—22no—
85#92418—22no—
86C22×C61—22no—
87C22×C61—42no—
88C22×C61—44no—
89C22×C61—84no—
90C22×C61#12412yes—
91C22×C61C22×D411yescharacteristic
92C4×C61—42no—
93C4×C61#12412yes—
94C4×C61C2×#4111yescharacteristic
95C4×C61C2×#4111yescharacteristic
96Dic61—22no—
97Dic61—22no—
98Dic61—42no—
99Dic61—42no—
100#3140—611nomaximal, Sylow
101C2×C61—22no—
102C2×C61—82no—
103C2×C61C2×#12411yescharacteristic
104C2×C61#57512yes—
105#533—611no—
106C2×#124—611no—
107#489—614no—
108#488—614no—
109#419—611no—
110#419—611no—
111#418—611no—
112#418D6111yescharacteristic
113C4×M16—611no—
114C61#314011yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C22×D4C2×D6111yescharacteristic
117C2×M16—611no—
118C2×M16C2×D6111yescharacteristic
119C4⋊Q8—612no—
120#125—612no—
121#124—612no—
122#124—612no—
123#124—1222no—
124C22⋊Q8—1222no—
125C4×Q8—1222no—
126#117—611no—
127#117C2×D6111yescharacteristic
128C2×C22⋊C4—1222no—
129C2×C42—611no—
130#103—614no—
131#103—614no—
132#102—614no—
133#102C2×D6114yes—
134#97—612no—
135C4×C8—612no—
136C24—21no—
137C2×Q8—612no—
138C2×Q8—1222no—
139C2×Q8—1221no—
140C2×Q8—1222no—
141C2×Q8—1222no—
142C2×D4—22no—
143C2×D4—21no—
144C2×D4—22no—
145C2×D4C22×D6112yes—
146C22×C4—612no—
147C22×C4—1221no—
148C22×C4C22×D6111yescharacteristic
149M16—22no—
150M16—1222no—
151C2×C8—612no—
152C2×C8C22×D6112yes—
153C4⋊C4—612no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1222no—
157C4⋊C4C22×D6112yes—
158C22⋊C4—21no—
159C22⋊C4—1224no—
160C22⋊C4—1224no—
161C22⋊C4—1221no—
162C42—21no—
163C42—612no—
164C42—611no—
165C42—611no—
166C42—1221no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D6111yescharacteristic
171Q8—1222no—
172Q8—1222no—
173Q8—2444no—
174Q8—2442no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—612no—
180C2×C4—612no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4#1175822212yes—
186C2×C4D4×D6111yescharacteristic
187C2×C4#1175822412yes—
188C2×C4C23×D6111yescharacteristic
189C8—22no—
190C8—1222no—
191C22—22no—
192C22—42no—
193C22—44no—
194C22—84no—
195C22#1451976312yes—
196C22C2×D4×D6111yescharacteristic
197C4—42no—
198C4—1222no—
199C4—1222no—
200C4—2442no—
201C4—2442no—
202C4#1451976312yes—
203C4C2×#1175822411yescharacteristic
204C4C2×#1175822211yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#1451976311yescharacteristic
208C2#1684055812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#418C2
socleC22×C61C22×D4
hypercenter#418D61
hypocenterC61#3140
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16840315C2semidirect
3. #16840120C2semidirect
4. #16840115C2semidirect
5. #16839772C2semidirect
6. #16839770C2semidirect
8. M16×Dic61C2semidirect
12. #14519776C22semidirect
13. #14519768C22semidirect
22. #14519702C22semidirect
23. #14519700C22semidirect
25. #14519687C22semidirect
26. C8×Dic61C22semidirect
114. C61#3140semidirect