Finite Group Databasebeta

← #21458710

Subgroups — #21458710

Order 7808.

324 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 131 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#16840488C212yesmaximal
2#16840166C211yesmaximal, characteristic
3#16840164C211yesmaximal, characteristic
4#16840163C211yesmaximal, characteristic
5#16840069C212yesmaximal
6#16840067C212yesmaximal
7#16840045C212yesmaximal
8C8×Dic122C211yesmaximal, characteristic
9Q16×Dic61C211yesmaximal, characteristic
10Q16×Dic61C211yesmaximal, characteristic
11C4×Q16×C61C211yesmaximal, characteristic
12#14519776—22no—
13#14519776C2212yes—
14#14519769—22no—
15#14519769C2212yes—
16#14519768—22no—
17#14519768C2212yes—
18Q8×Dic61C2212yes—
19Q8×Dic61C2212yes—
20C4×Dic122—22no—
21C4×Dic122C2211yescharacteristic
22#14519711C2211yescharacteristic
23#14519711C2211yescharacteristic
24#14519710C2212yes—
25#14519709C2212yes—
26#14519708C2212yes—
27C4⋊#92418C2211yescharacteristic
28#14519706C2211yescharacteristic
29#14519706C2211yescharacteristic
30#14519701C2212yes—
31#14519701C2212yes—
32C8×Dic61C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×Q16×C61C2211yescharacteristic
35C4×Q8×C61C2212yes—
36#107×C61C2211yescharacteristic
37#103×C61C2212yes—
38C4×C8×C61C2211yescharacteristic
39C2×Q8×C61C2312yes—
40C2×Dic122—22no—
41C2×Dic122D411yescharacteristic
42Q16×C61Q814yescomplemented
43C2×C8×C61C2311yescharacteristic
44C2×C8×C61C2311yescharacteristic
45C4⋊C4×C61—22no—
46C4⋊C4×C61C2312yes—
47C42×C61—22no—
48C42×C61C2311yescharacteristic
49C4⋊Dic61—22no—
50C4⋊Dic61—22no—
51C4⋊Dic61—22no—
52C4⋊Dic61D411yescharacteristic
53C4⋊Dic61C2312yes—
54C4⋊Dic61C2312yes—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59#11758196D411yescharacteristic
60#11758196D411yescharacteristic
61C4×Dic61—22no—
62C4×Dic61—22no—
63C4×Dic61C2311yescharacteristic
64C4×Dic61C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66C2×#92418C2311yescharacteristic
67Q8×C61—22no—
68Q8×C61C2×Q814yes—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61C2×D411yescharacteristic
78C2×Dic61C2×D411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80Dic122—22no—
81Dic122—44no—
82C8×C61—21no—
83C8×C61C2×Q812yes—
84#92418—21no—
85#92418—21no—
86C22×C61C22×D411yescharacteristic
87C4×C61—24no—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—42no—
91C4×C61C22×Q811yescharacteristic
92C4×C612−1+411yescharacteristic
93Dic61—21no—
94Dic61—21no—
95Dic61—21no—
96Dic61—42no—
97Dic61—42no—
98Dic61#13512yes—
99#3383—611nomaximal, Sylow
100C2×C61D4×Q811yescharacteristic
101C2×C61C2×#13511yescharacteristic
102C2×C61#57811yescharacteristic
103#557—612no—
104#500—611no—
105#499—611no—
106#499—611no—
107#479—612no—
108#479—612no—
109#475—612no—
110C8×Q8—611no—
111C4×Q16—611no—
112C4×Q16—611no—
113C4×Q16D6111yescharacteristic
114C61#338311yescharacteristic, complemented, Sylow
115C2×Q16C2×D6111yescharacteristic
116C4⋊Q8—612no—
117C4⋊Q8—1222no—
118#125—612no—
119#125—612no—
120#125—1222no—
121#125—1222no—
122C4×Q8—611no—
123C4×Q8—612no—
124C4×Q8—612no—
125C4×Q8—1222no—
126C4×Q8C2×D6112yes—
127#107—611no—
128#107—611no—
129#107—612no—
130#107C2×D6111yescharacteristic
131#106—612no—
132#106—612no—
133C4⋊C8—611no—
134C4⋊C8—611no—
135C4⋊C8—611no—
136#103—612no—
137#103—612no—
138#103C2×D6112yes—
139C4×C8—611no—
140C4×C8—611no—
141C4×C8C2×D6111yescharacteristic
142C2×Q8—611no—
143C2×Q8—1222no—
144C2×Q8C22×D6112yes—
145Q16Dic12214yescomplemented
146C2×C8—611no—
147C2×C8—611no—
148C2×C8C22×D6111yescharacteristic
149C2×C8C22×D6111yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—611no—
152C4⋊C4—611no—
153C4⋊C4—611no—
154C4⋊C4—612no—
155C4⋊C4—612no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4—1222no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4C22×D6112yes—
164C42—22no—
165C42—611no—
166C42—611no—
167C42—1222no—
168C42—1222no—
169C42C22×D6111yescharacteristic
170Q8—22no—
171Q8—1222no—
172Q8—2444no—
173Q8C2×Dic12214yes—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—611no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4D4×D6111yescharacteristic
183C2×C4D4×D6111yescharacteristic
184C2×C4C23×D6111yescharacteristic
185C8—21no—
186C8—1221no—
187C8—1221no—
188C8C2×Dic12212yes—
189C22C2×D4×D6111yescharacteristic
190C4—21no—
191C4—21no—
192C4—24no—
193C4—42no—
194C4—612no—
195C4—1221no—
196C4—1221no—
197C4—1221no—
198C4—2442no—
199C4—2442no—
200C4C22×Dic12211yescharacteristic
201C4#1451982411yescharacteristic
202C2D4×Dic12211yescharacteristic
203C2#135×D6111yescharacteristic
204C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61#3383
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
42. Q16×C61Q8semidirect
114. C61#3383semidirect
145. Q16Dic122semidirect