Finite Group Databasebeta

← #21462013

Subgroups — #21462013

Order 7808.

228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840765C211yesmaximal, characteristic
2C4×#11758217C211yesmaximal, characteristic
3#16840642C212yesmaximal
4#16840642C212yesmaximal
5C2×#14519767C211yesmaximal, characteristic
6C2×#11758217C2212yes—
7C2×#11758217C2212yes—
8#14519844—21no—
9C4⋊#92420—21no—
10#14519832—21no—
11C4×#92420—21no—
12#14519767—21no—
13#14519767—21no—
14#14519767—21no—
15#14519767—21no—
16C2×C4⋊Dic61C411yescharacteristic
17C2×#11758196C411yescharacteristic
18C2×#11758196C411yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×C4×Dic61C2211yescharacteristic
22C2×C4⋊C4×C61C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×Dic61C2×C411yescharacteristic
27C22×Dic61C2×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2311yescharacteristic
30#11758217—22no—
31#11758217—24no—
32#11758217Q814yes—
33C2×#92420—22no—
34C2×#92420—22no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—21no—
39#11758196—21no—
40#11758196—21no—
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61D411yescharacteristic
51C23×C61C22×C411yescharacteristic
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—41no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68C2×Dic61C2×Q812yes—
69C2×Dic61#4112yes—
70#92420—24no—
71#92420—42no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61C2×C22⋊C411yescharacteristic
75C22×C61C4×Q812yes—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—41no—
79C4×C61—41no—
80Dic61—21no—
81Dic61—21no—
82Dic61—41no—
83Dic61—41no—
84Dic61C22⋊Q812yes—
85Dic61#12411yescharacteristic
86Dic61C4⋊Q811yescharacteristic
87#1998—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61#39111yescharacteristic
90C2×C61#41311yescharacteristic
91C2×C61#41311yescharacteristic
92C2×#125—611no—
93#423—611no—
94C4×M16—611no—
95#343—612no—
96#343—612no—
97C61#199811yescharacteristic, complemented, Sylow
98C2×M16—612no—
99C2×M16—612no—
100#125—1221no—
101#125—1221no—
102#125—1221no—
103#125—1221no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4—611no—
106C2×C4⋊C4—611no—
107C2×C4⋊C4—611no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4#692311yescharacteristic
110C2×C42—611no—
111C4⋊C8—1221no—
112C4⋊C8—1221no—
113#97—1221no—
114C4×C8—1221no—
115C22×C4—611no—
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4C2×#692311yescharacteristic
120C22×C4C2×#692311yescharacteristic
121C22×C4C2×#692311yescharacteristic
122M16—614no—
123M16—1222no—
124M16—1224no—
125C2×C8—1222no—
126C2×C8—1222no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C42—611no—
140C42—611no—
141C42—611no—
142C42—611no—
143C23C22×#692311yescharacteristic
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—612no—
152C2×C4—612no—
153C2×C4—611no—
154C2×C4—611no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4C22⋊#692311yescharacteristic
161C2×C4C22⋊#692311yescharacteristic
162C8—1224no—
163C8—2442no—
164C22—21no—
165C22—21no—
166C22C2×C22⋊#692311yescharacteristic
167C22Q8×#692312yes—
168C4—21no—
169C4—21no—
170C4—41no—
171C4—41no—
172C4—612no—
173C4—611no—
174C4—611no—
175C4—1221no—
176C4—1221no—
177C4—2441no—
178C4—2441no—
179C2—22no—
180C2(C2×#6923)⋊Q811yescharacteristic
181C2#1684074811yescharacteristic
182C2#1684074911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1998
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
97. C61#1998semidirect