Finite Group Databasebeta

← #21447490

Subgroups — #21447490

Order 7808.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840326C211yesmaximal, characteristic
2#16839736C211yesmaximal, characteristic, complemented
3#16839554C214yesmaximal, complemented
4C61×#410C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic, complemented
6#14519773C2212yes—
7#14519766C412yescomplemented
8#14519751—21no—
9#14519751—21no—
10#14519745—21no—
11#14519745—21no—
12#14519736—21no—
13#14519736C411yescharacteristic, complemented
14#14519692—21no—
15#14519692C2212yescomplemented
16C2×#41×C61C2211yescharacteristic
17#117×C61—21no—
18#99×C61—21no—
19#99×C61C2212yescomplemented
20C23×D61—21no—
21#41×C61—41no—
22#41×C61—41no—
23C2×Q8×C61C2×C411yescharacteristic
24C2×D4×C61D411yescharacteristic
25C2×D4×C61D411yescharacteristic
26C2×D4×C61C2311yescharacteristic
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C2×C22⋊D61—22no—
31C2×C22⋊D61—22no—
32C2×D244—21no—
33C2×D244—41no—
34C2×D244—41no—
35C2×D244C2×C412yes—
36C4⋊C4×C61—41no—
37C22⋊C4×C61—22no—
38C42×C61—41no—
39C22⋊Dic61—21no—
40C22⋊Dic61—22no—
41#11758198—22no—
42#11758198—22no—
43C4⋊Dic61—21no—
44C4⋊Dic61—41no—
45C4×Dic61—41no—
46C4×Dic61C2×C412yes—
47C23×C61C22⋊C411yescharacteristic
48C23×C61C2×D411yescharacteristic
49C23×C61C2×D411yescharacteristic
50C22×D61—22no—
51C22×D61—42no—
52C22×D61—82no—
53Q8×C61—41no—
54D4×C61—41no—
55D4×C61—41no—
56D4×C61—41no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—42no—
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C22×C411yescharacteristic
68C22⋊D61—82no—
69C22⋊D61—82no—
70C2×Dic61—22no—
71C2×Dic61—42no—
72D244—42no—
73D244—41no—
74D244—41no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—42no—
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—84no—
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—82no—
90C4×C61#9911yescharacteristic
91C4×C61#9911yescharacteristic
92Dic61—42no—
93Dic61—82no—
94#2128—611nomaximal, Sylow
95C2×C61—21no—
96C2×C61—41no—
97C2×C61—41no—
98C2×C61—41no—
99C2×C61C2×#9911yescharacteristic
100D61—82no—
101#535—611no—
102#410—611no—
103#410D6111yescharacteristic, complemented
104#353—614no—
105C61#212811yescharacteristic, complemented, Sylow
106C2×#41C2×D6111yescharacteristic
107C22×D4—611no—
108#127—612no—
109#124—612no—
110#121—1221no—
111#121—1221no—
112#120—1221no—
113#120—1221no—
114#117—21no—
115#117—611no—
116#117—1221no—
117#99—21no—
118#99—612no—
119#99—1221no—
120#99C2×D6112yescomplemented
121C24—1221no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D6111yescharacteristic
125C2×D4—612no—
126C2×D4—1222no—
127C2×D4—1222no—
128C2×D4—1221no—
129C2×D4—2441no—
130C2×D4—2441no—
131C2×D4D24411yescharacteristic
132C2×D4C22⋊D6111yescharacteristic
133C2×D4C22×D6111yescharacteristic
134C22×C4C4×D6111yescharacteristic
135C22×C4D24411yescharacteristic
136C22×C4C22⋊D6111yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—1221no—
139C4⋊C4—2441no—
140C22⋊C4—22no—
141C22⋊C4—1221no—
142C22⋊C4—1222no—
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C42—41no—
146C42—612no—
147C42—2441no—
148C23—1222no—
149C23—4882no—
150C23—2442no—
151C23#1175819811yescharacteristic
152C23C2×D24411yescharacteristic
153C23C2×C22⋊D6111yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—4882no—
159D4—4882no—
160D4—2442no—
161D4—2441no—
162D4—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—1222no—
171C2×C4—2442no—
172C2×C4#1175819811yescharacteristic
173C2×C4#1175819811yescharacteristic
174C2×C4#1175819811yescharacteristic
175C2×C4C2×C4×D6111yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—4884no—
183C22—2442no—
184C22—2442no—
185C22—2442no—
186C22C2×#1175819811yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—4882no—
192C4—2442no—
193C4#1451969111yescharacteristic
194C4#1451969111yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—4882no—
200C2C2×#1451969111yescharacteristic
subgroupG/H
centerC2C2×#14519691
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#410C2
socleC2×C61C2×#99
hypercenter#410D61
hypocenterC61#2128
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16839736C2semidirect
3. #16839554C2semidirect
4. C61×#410C2semidirect
5. C22×D244C4semidirect
7. #14519766C4semidirect
13. #14519736C4semidirect
15. #14519692C22semidirect
19. #99×C61C22semidirect
103. #410D61semidirect
105. C61#2128semidirect
120. #99C2×D61semidirect