Finite Group Databasebeta

← #21446483

Subgroups — #21446483

Order 7808.

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

normal subgroups only

This group has 232 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, complemented
2#16839767C211yesmaximal, characteristic
3C2×#14519698C211yesmaximal, characteristic
4#16839720C211yesmaximal, characteristic, complemented
5#16839530C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C2×#100×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519736C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519711—21no—
13#14519709—21no—
14#14519698—21no—
15#14519698—21no—
16#14519698—21no—
17#14519698—21no—
18#14519687—21no—
19C8×Dic61—21no—
20C22×D4×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#100×C61C414yescomplemented
24C24×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61C2×C412yes—
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—22no—
53C23×C61—41no—
54C23×C61—41no—
55C23×C61—81no—
56C23×C61—81no—
57C23×C61#4111yescharacteristic
58D4×C61—22no—
59D4×C61—22no—
60D4×C61—41no—
61D4×C61—41no—
62C2×C4×C61C22×C411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—41no—
71C2×Dic61—81no—
72C8×C61—22no—
73C8×C61—22no—
74#92418—21no—
75#92418—21no—
76#92418—41no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—42no—
80C22×C61—82no—
81C22×C61—82no—
82C22×C61—81no—
83C22×C61—81no—
84C22×C61#11711yescharacteristic
85C22×C61#12111yescharacteristic
86C22×C61#12611yescharacteristic
87C4×C61C4×D411yescharacteristic
88C4×C61C4×D411yescharacteristic
89C4×C61#12311yescharacteristic
90C4×C61#12411yescharacteristic
91Dic61—41no—
92Dic61—41no—
93Dic61—81no—
94#1931—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—21no—
97C2×C61—82no—
98C2×C61#38811yescharacteristic
99C2×C61#47111yescharacteristic
100C2×C61#47211yescharacteristic
101#428—611no—
102#418—611no—
103C2×#102—611no—
104C2×#100D6111yescharacteristic
105#405—611no—
106#343—611no—
107#341—611no—
108C61#193111yescharacteristic, complemented, Sylow
109C22×D4C2×D6111yescharacteristic
110C2×M16—611no—
111C2×M16C2×D6111yescharacteristic
112C2×M16C2×D6111yescharacteristic
113C22×C8—611no—
114#117—611no—
115C2×C4⋊C4—611no—
116#107—1221no—
117#106—1221no—
118#102—1221no—
119#102—1221no—
120#102—1221no—
121#102—1221no—
122#100Dic6114yescomplemented
123#97—1221no—
124C4×C8—1221no—
125C24—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4C2×Dic6112yes—
132C22×C4—1221no—
133C22×C4C22×D6111yescharacteristic
134M16—21no—
135M16—21no—
136M16—1221no—
137M16—1221no—
138M16C2×Dic6112yes—
139M16C2×Dic6112yes—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—611no—
143C2×C8—611no—
144C2×C8—1221no—
145C2×C8—1221no—
146C2×C8—1221no—
147C4⋊C4—611no—
148C4⋊C4—611no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C22⋊C4—1221no—
152C42—1221no—
153C23—22no—
154C23—41no—
155C23—41no—
156C23—81no—
157C23—81no—
158C23#1175822211yescharacteristic
159D4—22no—
160D4—22no—
161D4—41no—
162D4—41no—
163C2×C4—1221no—
164C2×C4—1221no—
165C2×C4—4881no—
166C2×C4—2441no—
167C2×C4#1175822211yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4#1175822411yescharacteristic
171C2×C4#1175822411yescharacteristic
172C2×C4C22×Dic6111yescharacteristic
173C8—22no—
174C8—22no—
175C8—1221no—
176C8—1221no—
177C8—2441no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—82no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22#1451973611yescharacteristic
186C22#1451975011yescharacteristic
187C22#1451977011yescharacteristic
188C4—4881no—
189C4—2441no—
190C4—2441no—
191C4D4×Dic6111yescharacteristic
192C4D4×Dic6111yescharacteristic
193C4#1451975911yescharacteristic
194C4#1451976311yescharacteristic
195C2—21no—
196C2—21no—
197C2—82no—
198C2#1683965511yescharacteristic
199C2#1684002411yescharacteristic
200C2#1684003111yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#100×C61C2
socleC22×C61#121
hypercenterC2×#100D61
hypocenterC61#1931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. #16839804C2semidirect
4. #16839720C2semidirect
5. #16839530C2semidirect
6. #16839526C2semidirect
23. #100×C61C4semidirect
108. C61#1931semidirect
122. #100Dic61semidirect