Finite Group Databasebeta

← #21461729

Subgroups — #21461729

Order 7808.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840748C211yesmaximal, characteristic
2#16840741C211yesmaximal, characteristic
3#16840633C212yesmaximal, complemented
4#16840629C212yesmaximal, complemented
5#16840230C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7#14519856C2212yes—
8#14519838—21no—
9#14519837—21no—
10#14519836—21no—
11#14519835—21no—
12C2×#11758222C2211yescharacteristic
13#14519742—21no—
14#14519739—21no—
15#14519737—21no—
16#14519737—21no—
17#14519734C411yescharacteristic, complemented
18#14519734C2211yescharacteristic
19C2×C4×Dic61C411yescharacteristic, complemented
20C42×D61C411yescharacteristic, complemented
21C42×D61C2211yescharacteristic
22#117×C61C411yescharacteristic, complemented
23C22×C4×C61C2×C411yescharacteristic
24C2×C22⋊D61D411yescharacteristic
25C2×C22⋊D61D411yescharacteristic
26C22×Dic61—21no—
27#11758222—22no—
28#11758222—22no—
29C2×D244D411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61C2×C411yescharacteristic
33C2×C4×D61C2311yescharacteristic
34C2×Dic122D411yescharacteristic
35C22⋊#6923—22no—
36#11758217—22no—
37C4⋊#6923—22no—
38C4×#6923—22no—
39#11758213—22no—
40D61⋊C8—22no—
41C4⋊C4×C61—21no—
42C22⋊C4×C61—21no—
43C42×C61C2×C411yescharacteristic
44C42×C61C2×C411yescharacteristic
45#11758198—21no—
46#11758198—21no—
47#11758196—21no—
48#11758196—21no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C4×Dic61—21no—
52C4×Dic61C2×C411yescharacteristic
53C4×Dic61C2×C411yescharacteristic
54C23×C61C22⋊C411yescharacteristic
55C22×D61C22⋊C411yescharacteristic
56C22×D61C2×D411yescharacteristic
57C2×#6923—42no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C22×C411yescharacteristic
64C22⋊D61—22no—
65C22⋊D61—22no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—42no—
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C2×D411yescharacteristic
71D244—22no—
72C4×D61—21no—
73C4×D61—21no—
74C4×D61—42no—
75C4×D61—42no—
76C4×D61#4112yes—
77C4×D61#4112yes—
78Dic122—22no—
79#92420—42no—
80C22×C61—21no—
81C22×C61—41no—
82C22×C61C2×C22⋊C411yescharacteristic
83C2×D61—21no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61#12312yes—
87#6923—82no—
88C4×C61—21no—
89C4×C61—41no—
90C4×C61—41no—
91C4×C61#11711yescharacteristic
92C4×C61#11711yescharacteristic
93Dic61—22no—
94Dic61—21no—
95Dic61—41no—
96Dic61#12312yes—
97#1827—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—41no—
100C2×C61#38111yescharacteristic
101D61—22no—
102D61—41no—
103C4×#41—611no—
104#413—611no—
105#410—611no—
106#339—612no—
107H(3,ℤ/4)—612no—
108C61#182711yescharacteristic, complemented, Sylow
109C2×#41—611no—
110C2×M16—612no—
111C4×Q8—1221no—
112C4×D4—1221no—
113C4×D4—1221no—
114C4×D4—1221no—
115#117—611no—
116#117—611no—
117#117—612no—
118#117#692311yescharacteristic, complemented
119C2×C42—611no—
120C2×C42—611no—
121C2×C42—611no—
122#101—1221no—
123#100—1221no—
124#99—1221no—
125#99—1221no—
126#41—1222no—
127#41—1222no—
128C2×Q8—611no—
129C2×D4—611no—
130C2×D4—611no—
131C2×D4—611no—
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4—1221no—
137C22×C4C2×#692311yescharacteristic
138M16—1222no—
139M16—1222no—
140C2×C8—1222no—
141C4⋊C4—21no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1222no—
145C22⋊C4—21no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C22⋊C4—1222no—
149C42—611no—
150C42—611no—
151C42—1221no—
152C42—1221no—
153C42—1222no—
154C42—1221no—
155C42C2×#692311yescharacteristic
156C42C2×#692311yescharacteristic
157C23—611no—
158C23—611no—
159C23C22⋊#692311yescharacteristic
160Q8—1222no—
161D4—1222no—
162D4—1222no—
163D4—1222no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—611no—
169C2×C4—612no—
170C2×C4—612no—
171C2×C4—611no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4C22⋊#692311yescharacteristic
181C2×C4C22×#692311yescharacteristic
182C8—2442no—
183C22—21no—
184C22—41no—
185C22—612no—
186C22—1221no—
187C22—2441no—
188C22—2441no—
189C22C2×C22⋊#692311yescharacteristic
190C4—21no—
191C4—41no—
192C4—41no—
193C4—612no—
194C4—1222no—
195C4—1221no—
196C4—4882no—
197C4—2441no—
198C4#1451985611yescharacteristic
199C4#1451985611yescharacteristic
200C2—21no—
201C2—41no—
202C2—1222no—
203C2—2441no—
204C2#1684070511yescharacteristic
subgroupG/H
centerC4#14519856
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC2×C61#381
hypercenter#117#6923
hypocenterC61#1827
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #16840633C2semidirect
4. #16840629C2semidirect
17. #14519734C4semidirect
19. C2×C4×Dic61C4semidirect
20. C42×D61C4semidirect
22. #117×C61C4semidirect
108. C61#1827semidirect
118. #117#6923semidirect