Finite Group Databasebeta

← #21446485

Subgroups — #21446485

Order 7808.

216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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#16839810C211yesmaximal, characteristic, complemented
2#16839779C211yesmaximal, characteristic
3#16839746C211yesmaximal, characteristic
4C4×#11758194C211yesmaximal, characteristic, complemented
5#16839533C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519712—22no—
13#14519704—22no—
14#14519696C412yescomplemented
15#14519694C412yescomplemented
16#14519688—21no—
17C4×#92418—21no—
18C2×#41×C61C2211yescharacteristic
19C2×M16×C61C2211yescharacteristic
20C2×C42×C61C2211yescharacteristic
21#104×C61—21no—
22#104×C61—21no—
23#41×C61—21no—
24#41×C61—21no—
25#41×C61—21no—
26#41×C61—21no—
27C2×Q8×C61C2×C411yescharacteristic
28C2×D4×C61—21no—
29C2×D4×C61C2×C411yescharacteristic
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33M16×C61—21no—
34M16×C61—21no—
35C2×C8×C61—21no—
36C42×C61—21no—
37C42×C61D411yescharacteristic
38C42×C61D411yescharacteristic
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4×Dic61—21no—
42#11758194—21no—
43#11758194—21no—
44#11758194—21no—
45#11758194C2×C412yes—
46#11758194C2×C412yes—
47#11758194D412yes—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C23×C61—21no—
52C23×C61#4111yescharacteristic
53Q8×C61—21no—
54Q8×C61—21no—
55D4×C61—21no—
56D4×C61—21no—
57D4×C61—41no—
58D4×C61—41no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—42no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×Dic61—41no—
72C8×C61—41no—
73#92418—22no—
74#92418—22no—
75#92418—22no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61—81no—
79C22×C61#11711yescharacteristic
80C22×C61#12311yescharacteristic
81C22×C61#12411yescharacteristic
82C4×C61—22no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61C4×D411yescharacteristic
86C4×C61C4×D411yescharacteristic
87C4×C61#12111yescharacteristic
88C4×C61#12611yescharacteristic
89Dic61—81no—
90#1932—611nomaximal, Sylow
91C2×C61—21no—
92C2×C61—21no—
93C2×C61—21no—
94C2×C61—81no—
95C2×C61#38811yescharacteristic
96#430—611no—
97#421—611no—
98C2×#104D6111yescharacteristic
99#413—611no—
100C4×M16—611no—
101#344—611no—
102#339—611no—
103C61#193211yescharacteristic, complemented, Sylow
104C2×#41C2×D6111yescharacteristic
105C2×M16—611no—
106C2×M16—611no—
107C2×M16—611no—
108C2×M16C2×D6111yescharacteristic
109#117—611no—
110C2×C42C2×D6111yescharacteristic
111#108—1222no—
112#104—21no—
113#104—21no—
114#104—1222no—
115#101—612no—
116#100—612no—
117#97—1221no—
118C4×C8—1221no—
119#41—21no—
120#41—21no—
121#41—21no—
122#41—21no—
123C2×Q8C4×D6111yescharacteristic
124C2×D4—21no—
125C2×D4C4×D6111yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4C22×D6111yescharacteristic
129M16—21no—
130M16—21no—
131M16—612no—
132M16—612no—
133M16—612no—
134M16—1221no—
135M16—1221no—
136M16—1221no—
137C2×C8—21no—
138C2×C8—1221no—
139C2×C8—1221no—
140C2×C8—1221no—
141C4⋊C4—1221no—
142C22⋊C4—1221no—
143C42—21no—
144C42—1221no—
145C42C22⋊D6111yescharacteristic
146C42C22⋊D6111yescharacteristic
147C23—21no—
148C23#1175822411yescharacteristic
149Q8—21no—
150Q8—21no—
151D4—21no—
152D4—21no—
153D4—41no—
154D4—41no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—2441no—
162C2×C4C2×C4×D6111yescharacteristic
163C2×C4#1175822211yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C2×C4#1175822411yescharacteristic
166C2×C4#1175822411yescharacteristic
167C2×C4C2×C22⋊D6111yescharacteristic
168C8—41no—
169C8—1222no—
170C8—1222no—
171C8—1222no—
172C22—41no—
173C22—41no—
174C22—81no—
175C22#1451973311yescharacteristic
176C22#1451975811yescharacteristic
177C22#1451976311yescharacteristic
178C4—22no—
179C4—41no—
180C4—41no—
181C4—4881no—
182C4#1451973711yescharacteristic
183C4C4×C22⋊D6111yescharacteristic
184C4#1451974811yescharacteristic
185C4#1451977011yescharacteristic
186C2—21no—
187C2—21no—
188C2—21no—
189C2—81no—
190C2#1683965011yescharacteristic
subgroupG/H
centerC4#14519748
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC2×C61#388
hypercenterC2×#104D61
hypocenterC61#1932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #16839810C2semidirect
4. C4×#11758194C2semidirect
5. #16839533C2semidirect
6. #16839522C2semidirect
14. #14519696C4semidirect
15. #14519694C4semidirect
103. C61#1932semidirect