Finite Group Databasebeta

← #21462062

Subgroups — #21462062

Order 7808.

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

normal subgroups only

This group has 220 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×#14519852C211yesmaximal, characteristic, complemented
2D61⋊M32C211yesmaximal, characteristic, complemented
3#16840661C212yesmaximal, complemented
4#16840660C212yesmaximal, complemented
5#131×D61C211yesmaximal, characteristic
6#14519852—21no—
7#14519852—21no—
8#14519852—21no—
9#14519851C2212yescomplemented
10D61⋊C16—21no—
11C2×#11758187C2212yescomplemented
12#41×D61C411yescharacteristic
13#14519785—21no—
14#14519785C2211yescharacteristic
15#14519784C2211yescharacteristic
16#14519783—21no—
17#14519783C411yescharacteristic
18M16×D61—21no—
19M16×D61C411yescharacteristic
20C2×C8×D61—21no—
21C2×C8×D61C2211yescharacteristic
22#131×C61C411yescharacteristic
23#41×C61C2×C411yescharacteristic
24#11758226C811yescharacteristic
25Q8×D61C811yescharacteristic
26#11758224—21no—
27#11758224C811yescharacteristic
28D4×D61—21no—
29D4×D61C811yescharacteristic
30#11758222—21no—
31#11758222C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61C2×C411yescharacteristic
34M16×C61—21no—
35M16×C61C2×C411yescharacteristic
36C2×C8×C61—21no—
37C2×C8×C61C2×C411yescharacteristic
38#11758194—21no—
39#11758194C2×C411yescharacteristic
40C2×#92418—21no—
41C2×#92418C2311yescharacteristic
42#11758189—21no—
43#11758189—21no—
44#11758189—21no—
45C8×D61—21no—
46C8×D61—21no—
47C8×D61—21no—
48C8×D61D411yescharacteristic
49C8×D61D411yescharacteristic
50C8×D61D411yescharacteristic
51C8×D61D411yescharacteristic
52#11758187—22no—
53#11758187—22no—
54C22×D61—21no—
55C22×D61M1611yescharacteristic
56Q8×C61C2×C811yescharacteristic
57D4×C61—21no—
58D4×C61C2×C811yescharacteristic
59C2×C4×C61—21no—
60C2×C4×C61C22×C411yescharacteristic
61C22⋊D61—21no—
62C22⋊D61—21no—
63C22⋊D61—21no—
64C2×Dic61—21no—
65C2×Dic61M1611yescharacteristic
66D244—21no—
67D244C2×C811yescharacteristic
68C4×D61—21no—
69C4×D61—21no—
70C4×D61—21no—
71C4×D61C22⋊C411yescharacteristic
72C4×D61C22⋊C411yescharacteristic
73C4×D61C2×C811yescharacteristic
74C4×D61C2×C811yescharacteristic
75Dic122—21no—
76Dic122C2×C811yescharacteristic
77C8×C61—21no—
78C8×C61C22⋊C411yescharacteristic
79C8×C61C22⋊C411yescharacteristic
80#92418—21no—
81#92418C2×D411yescharacteristic
82#92418C2×D411yescharacteristic
83C22×C61—21no—
84C22×C61C2×M1611yescharacteristic
85C2×D61—21no—
86C2×D61—41no—
87C2×D61—42no—
88C2×D61C22⋊C811yescharacteristic
89C2×D61C22⋊C811yescharacteristic
90C4×C61—21no—
91C4×C61C2×C22⋊C411yescharacteristic
92C4×C61C22×C811yescharacteristic
93Dic61—21no—
94Dic61C22⋊C811yescharacteristic
95Dic61C22⋊C811yescharacteristic
96#2117—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—41no—
99C2×C61C2×C22⋊C811yescharacteristic
100D61—21no—
101D61—21no—
102D61—41no—
103C2×#131—611no—
104C2×M32—611no—
105C2×M32—611no—
106#350—612no—
107#350—612no—
108C61#211711yescharacteristic, complemented, Sylow
109C2×#41—611no—
110#131—611no—
111#131—611no—
112#131—611no—
113#131—1221no—
114#131—1221no—
115#131#692311yescharacteristic
116C2×M16—611no—
117C2×M16—1221no—
118C22×C8—611no—
119C22×C8—1221no—
120M32—612no—
121M32—1221no—
122M32—1221no—
123M32—1221no—
124C2×C16—612no—
125C2×C16—1221no—
126#41—611no—
127#41—611no—
128#41—611no—
129#41—1221no—
130#41—1221no—
131#41C2×#692311yescharacteristic
132C2×Q8—611no—
133C2×D4—611no—
134C2×D4—1221no—
135C22×C4—611no—
136C22×C4—1221no—
137M16—21no—
138M16—611no—
139M16—1221no—
140M16—1221no—
141M16—1221no—
142M16—1221no—
143M16C2×#692311yescharacteristic
144C2×C8—21no—
145C2×C8—611no—
146C2×C8—611no—
147C2×C8—611no—
148C2×C8—611no—
149C2×C8—611no—
150C2×C8—1221no—
151C2×C8—1221no—
152C2×C8—1221no—
153C2×C8—1221no—
154C2×C8C2×#692311yescharacteristic
155C16—1222no—
156C16—1222no—
157C23—611no—
158C23—1221no—
159Q8—611no—
160Q8—1221no—
161Q8D61⋊C811yescharacteristic
162D4—21no—
163D4—611no—
164D4—1221no—
165D4—1221no—
166D4—1221no—
167D4—1221no—
168D4D61⋊C811yescharacteristic
169C2×C4—21no—
170C2×C4—611no—
171C2×C4—611no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—611no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4C22×#692311yescharacteristic
180C8—21no—
181C8—611no—
182C8—611no—
183C8—1221no—
184C8C22⋊#692311yescharacteristic
185C8C22⋊#692311yescharacteristic
186C22—21no—
187C22—611no—
188C22—611no—
189C22—1221no—
190C22—2441no—
191C22—2442no—
192C22D61⋊M1611yescharacteristic
193C4—21no—
194C4—611no—
195C4—611no—
196C4—1221no—
197C4C2×C22⋊#692311yescharacteristic
198C4C2×D61⋊C811yescharacteristic
199C2—21no—
200C2—41no—
201C2—1221no—
202C2—1221no—
203C2—2441no—
204C2D61⋊(C22⋊C8)11yescharacteristic
subgroupG/H
centerC4C2×C22⋊#6923
commutatorC4×C61C22×C8
FrattiniC2×C4C22×#6923
Fitting#131×C61C4
socleC2×C61C2×C22⋊C8
hypercenter#131#6923
hypocenterC61#2117
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C2×#14519852C2semidirect
2. D61⋊M32C2semidirect
3. #16840661C2semidirect
4. #16840660C2semidirect
9. #14519851C22semidirect
11. C2×#11758187C22semidirect
108. C61#2117semidirect