Finite Group Databasebeta

← #21446476

Subgroups — #21446476

Order 7808.

212 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 81 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#16839804C211yesmaximal, characteristic
2#16839771C211yesmaximal, characteristic
3C2×#14519701C211yesmaximal, characteristic
4#16839720C211yesmaximal, characteristic
5#16839530C211yesmaximal, characteristic
6#16839526C211yesmaximal, characteristic
7C2×#101×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519736C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519711—21no—
13#14519709—21no—
14#14519701—21no—
15#14519701—21no—
16#14519701—21no—
17#14519701—21no—
18#14519687—21no—
19C8×Dic61—21no—
20C22×Q8×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#101×C61C414yescomplemented
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61C2×C412yes—
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33M16×C61—21no—
34M16×C61—21no—
35M16×C61C2×C412yes—
36M16×C61C2×C412yes—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61D411yescharacteristic
43C4⋊Dic61D411yescharacteristic
44C4×Dic61—21no—
45#11758194—21no—
46#11758194—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418D411yescharacteristic
51C2×#92418D411yescharacteristic
52C23×C61#4111yescharacteristic
53Q8×C61—22no—
54Q8×C61—22no—
55Q8×C61—41no—
56Q8×C61—41no—
57C2×C4×C61—22no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61C22×C411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—41no—
69C2×Dic61—81no—
70C8×C61—22no—
71C8×C61—22no—
72#92418—21no—
73#92418—21no—
74#92418—41no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61#11711yescharacteristic
78C22×C61#12111yescharacteristic
79C22×C61#12611yescharacteristic
80C4×C61—42no—
81C4×C61C4×D411yescharacteristic
82C4×C61C4×D411yescharacteristic
83C4×C61#12311yescharacteristic
84C4×C61#12411yescharacteristic
85Dic61—41no—
86Dic61—41no—
87Dic61—81no—
88#1930—611nomaximal, Sylow
89C2×C61—21no—
90C2×C61—21no—
91C2×C61#38811yescharacteristic
92C2×C61#47111yescharacteristic
93C2×C61#47311yescharacteristic
94#428—611no—
95#419—611no—
96C2×#103—611no—
97C2×#101D6111yescharacteristic
98#405—611no—
99#343—611no—
100#341—611no—
101C61#193011yescharacteristic, complemented, Sylow
102C22×Q8C2×D6111yescharacteristic
103C2×M16—611no—
104C2×M16C2×D6111yescharacteristic
105C2×M16C2×D6111yescharacteristic
106C22×C8—611no—
107#117—611no—
108C2×C4⋊C4—611no—
109#107—1221no—
110#106—1221no—
111#103—1221no—
112#103—1221no—
113#103—1221no—
114#103—1221no—
115#101Dic6114yescomplemented
116#97—1221no—
117C4×C8—1221no—
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—21no—
122C2×Q8—21no—
123C2×Q8C2×Dic6112yes—
124C22×C4—21no—
125C22×C4—1221no—
126C22×C4C22×D6111yescharacteristic
127M16—21no—
128M16—21no—
129M16—1221no—
130M16—1221no—
131M16C2×Dic6112yes—
132M16C2×Dic6112yes—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—611no—
136C2×C8—611no—
137C2×C8—1221no—
138C2×C8—1221no—
139C2×C8—1221no—
140C4⋊C4—611no—
141C4⋊C4—611no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C22⋊C4—1221no—
145C42—1221no—
146C23#1175822211yescharacteristic
147Q8—22no—
148Q8—22no—
149Q8—41no—
150Q8—41no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—4881no—
157C2×C4—2441no—
158C2×C4#1175822211yescharacteristic
159C2×C4D4×D6111yescharacteristic
160C2×C4D4×D6111yescharacteristic
161C2×C4#1175822411yescharacteristic
162C2×C4#1175822411yescharacteristic
163C2×C4C22×Dic6111yescharacteristic
164C8—22no—
165C8—22no—
166C8—1221no—
167C8—1221no—
168C8—2441no—
169C22—21no—
170C22—21no—
171C22#1451973611yescharacteristic
172C22#1451975011yescharacteristic
173C22#1451977011yescharacteristic
174C4—42no—
175C4—4881no—
176C4—2441no—
177C4—2441no—
178C4D4×Dic6111yescharacteristic
179C4D4×Dic6111yescharacteristic
180C4#1451975911yescharacteristic
181C4#1451976311yescharacteristic
182C2—21no—
183C2—21no—
184C2#1683965511yescharacteristic
185C2#1684002811yescharacteristic
186C2#1684003611yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#121
hypercenterC2×#101D61
hypocenterC61#1930
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
23. #101×C61C4semidirect
101. C61#1930semidirect
115. #101Dic61semidirect