Finite Group Databasebeta

← #21461935

Subgroups — #21461935

Order 7808.

200 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 72 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×#14519848C211yesmaximal, characteristic
2C2×#14519847C211yesmaximal, characteristic
3#16840767C211yesmaximal, characteristic
4C4×#11758213C211yesmaximal, characteristic
5#16840638C211yesmaximal, characteristic
6#16840638C211yesmaximal, characteristic
7C4⋊C8×D61C211yesmaximal, characteristic
8C2×#11758213C2211yescharacteristic
9C2×#11758213C2211yescharacteristic
10C2×#11758213C2211yescharacteristic
11C2×#11758213C2211yescharacteristic
12#14519848—22no—
13#14519847—22no—
14#14519844—21no—
15#14519844—21no—
16#14519832—21no—
17C4×#92420—21no—
18C2×C8×D61C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20C42×D61C2211yescharacteristic
21C4⋊#92418C411yescharacteristic
22#14519706C411yescharacteristic
23#14519706C411yescharacteristic
24C4⋊C8×C61C411yescharacteristic
25C2×C4×D61Q811yescharacteristic
26C2×C4×D61Q811yescharacteristic
27C2×C4×D61C2311yescharacteristic
28C2×#92420—21no—
29C2×#92420—21no—
30C2×#92420—21no—
31C2×#92420—21no—
32#11758213—21no—
33#11758213—21no—
34#11758213—21no—
35#11758213—21no—
36#11758213—21no—
37#11758213—21no—
38#11758213D412yes—
39#11758213Q812yes—
40C2×C8×C61C2×C411yescharacteristic
41C2×C8×C61C2×C411yescharacteristic
42C42×C61C2×C411yescharacteristic
43C4×Dic61C2×C411yescharacteristic
44C4×Dic61D411yescharacteristic
45C4×Dic61D411yescharacteristic
46C2×#92418C2×C411yescharacteristic
47C2×#92418C2×C411yescharacteristic
48C8×D61—21no—
49C8×D61—21no—
50C8×D61—21no—
51C8×D61—21no—
52C22×D61C2×Q811yescharacteristic
53C2×C4×C61C4⋊C411yescharacteristic
54C2×C4×C61C4⋊C411yescharacteristic
55C2×C4×C61C22×C411yescharacteristic
56C2×Dic61C4⋊C411yescharacteristic
57C2×Dic61C4⋊C411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59C4×D61—22no—
60C4×D61—41no—
61C4×D61C2×D411yescharacteristic
62C4×D61C2×Q811yescharacteristic
63C4×D61#4111yescharacteristic
64C4×D61#4111yescharacteristic
65#92420—22no—
66#92420—22no—
67#92420—41no—
68#92420—41no—
69C8×C61—21no—
70C8×C61—21no—
71#92418—21no—
72#92418—21no—
73C22×C61C2×C4⋊C411yescharacteristic
74C2×D61—21no—
75C2×D61—21no—
76C2×D61#12511yescharacteristic
77C2×D61C4⋊Q811yescharacteristic
78C4×C61—21no—
79C4×C61—21no—
80C4×C61C4×D411yescharacteristic
81C4×C61C4×Q811yescharacteristic
82Dic61—21no—
83Dic61#10812yescomplemented
84Dic61#12111yescharacteristic
85Dic61C22⋊Q811yescharacteristic
86#1950—611nomaximal, Sylow
87C2×C61#38911yescharacteristic
88C2×C61C2×#10811yescharacteristic
89C2×C61#43011yescharacteristic
90D61—21no—
91D61—21no—
92C2×#108—611no—
93C2×#108—611no—
94#423—611no—
95C2×C4⋊C8—611no—
96C4×M16—611no—
97#341—611no—
98#341—611no—
99C61#195011yescharacteristic, complemented, Sylow
100C2×M16—611no—
101C2×M16—611no—
102C2×M16—611no—
103C2×M16—611no—
104C22×C8—611no—
105C22×C8—611no—
106C2×C42—611no—
107#108—1222no—
108#108—1222no—
109C4⋊C8—611no—
110C4⋊C8—611no—
111C4⋊C8—611no—
112C4⋊C8—1221no—
113C4⋊C8—1221no—
114C4⋊C8#692311yescharacteristic
115#97—1221no—
116C4×C8—1221no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—611no—
120M16—612no—
121M16—612no—
122M16—1221no—
123M16—1221no—
124M16—1221no—
125M16—1221no—
126M16—1221no—
127M16—1221no—
128C2×C8—611no—
129C2×C8—611no—
130C2×C8—1221no—
131C2×C8—1221no—
132C2×C8—1221no—
133C2×C8—1221no—
134C2×C8—1221no—
135C2×C8—1221no—
136C2×C8—1221no—
137C2×C8—1221no—
138C2×C8C2×#692311yescharacteristic
139C2×C8C2×#692311yescharacteristic
140C42—611no—
141C42—611no—
142C42—611no—
143C42C2×#692311yescharacteristic
144C23—611no—
145C2×C4—611no—
146C2×C4—611no—
147C2×C4—611no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—1222no—
153C2×C4—2441no—
154C2×C4C4⋊#692311yescharacteristic
155C2×C4C4⋊#692311yescharacteristic
156C2×C4C22×#692311yescharacteristic
157C8—21no—
158C8—21no—
159C8—1222no—
160C8—1222no—
161C8—1221no—
162C8—1221no—
163C8—2441no—
164C8—2441no—
165C22—611no—
166C22—611no—
167C22—1221no—
168C22—1221no—
169C22C2×C4⋊#692311yescharacteristic
170C4—21no—
171C4—21no—
172C4—611no—
173C4—611no—
174C4—612no—
175C4—1221no—
176C4D4×#692311yescharacteristic
177C4Q8×#692311yescharacteristic
178C2—1221no—
179C2—1221no—
180C2#1684071311yescharacteristic
181C2D61⋊#10811yescharacteristic
182C2#1684077711yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC4⋊C8#6923
hypocenterC61#1950
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
83. Dic61#108semidirect
99. C61#1950semidirect