Finite Group Databasebeta

← #21445922

Subgroups — #21445922

Order 7808.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×#11758222C211yesmaximal, characteristic
2#16839744C211yesmaximal, characteristic
3#16839735C211yesmaximal, characteristic
4#16839522C211yesmaximal, characteristic, complemented
5#16839519C211yesmaximal, characteristic, complemented
6#16839518C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C4×Dic122—21no—
11C4×D244—21no—
12C4×C22⋊D61—22no—
13#14519736C2211yescharacteristic
14#14519736C2211yescharacteristic
15#14519734C412yescomplemented
16C42×D61C412yescomplemented
17#14519695—21no—
18#14519693—21no—
19#14519691—22no—
20C2×M16×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22C2×C42×C61C2211yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C2×C22⋊D61D412yes—
26#11758222—21no—
27#11758222—21no—
28#11758222—21no—
29#11758222—21no—
30C2×D244D411yescharacteristic
31C2×C4×D61—22no—
32C2×C4×D61C2×C412yes—
33C2×Dic122D411yescharacteristic
34M16×C61—21no—
35M16×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C42×C61—21no—
40C42×C61—21no—
41C42×C61C2×C411yescharacteristic
42C42×C61C2×C411yescharacteristic
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45#11758198—22no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48#11758196—22no—
49C4×Dic61—22no—
50C4×Dic61—21no—
51C4×Dic61C2×C412yes—
52#11758194—21no—
53#11758194—21no—
54C2×#92418—21no—
55C23×C61C2×D411yescharacteristic
56C22×D61C22⋊C412yes—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—42no—
60C2×C4×C61—41no—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C22⋊D61—22no—
68C22⋊D61—22no—
69C2×Dic61—22no—
70C2×Dic61—41no—
71C2×Dic61C22⋊C412yes—
72D244—21no—
73D244—21no—
74C4×D61—22no—
75C4×D61—22no—
76C4×D61—44no—
77Dic122—21no—
78Dic122—21no—
79C8×C61—41no—
80#92418—41no—
81C22×C61—41no—
82C22×C61C2×C22⋊C411yescharacteristic
83C22×C61#12311yescharacteristic
84C22×C61#12311yescharacteristic
85C2×D61—22no—
86C2×D61—42no—
87C4×C61—22no—
88C4×C61—41no—
89C4×C61—81no—
90C4×C61#11711yescharacteristic
91C4×C61#11711yescharacteristic
92C4×C61#12311yescharacteristic
93C4×C61#12311yescharacteristic
94Dic61—22no—
95Dic61—42no—
96Dic61—81no—
97#1827—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—21no—
100C2×C61—21no—
101C2×C61#38111yescharacteristic
102D61—42no—
103C4×#41—611no—
104#413—611no—
105#410—611no—
106#339—611no—
107#339D6111yescharacteristic, complemented
108H(3,ℤ/4)—611no—
109H(3,ℤ/4)—611no—
110C61#182711yescharacteristic, complemented, Sylow
111C2×#41—611no—
112C2×M16—611no—
113C2×M16C2×D6111yescharacteristic
114C4×Q8—1221no—
115C4×D4—1221no—
116C4×D4—1222no—
117#117—611no—
118#117—612no—
119#117—611no—
120#117C2×D6111yescharacteristic
121C2×C42—612no—
122C2×C42C2×D6111yescharacteristic
123#101—1221no—
124#100—1221no—
125#99—1222no—
126#41—1221no—
127#41—1221no—
128#41—1221no—
129#41—1221no—
130C2×Q8—611no—
131C2×D4—612no—
132C2×D4—611no—
133C22×C4—21no—
134C22×C4—612no—
135C22×C4—1222no—
136C22×C4C22×D6111yescharacteristic
137M16—21no—
138M16—21no—
139M16—1221no—
140M16—1221no—
141C2×C8—21no—
142C2×C8—1221no—
143C4⋊C4—21no—
144C4⋊C4—1222no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C22⋊C4—21no—
148C22⋊C4—1222no—
149C22⋊C4—1221no—
150C22⋊C4—1221no—
151C42—21no—
152C42—21no—
153C42—612no—
154C42—1222no—
155C42—1221no—
156C42C4×D6111yescharacteristic
157C42C4×D6111yescharacteristic
158C23—612no—
159C23D4×D6111yescharacteristic
160Q8—1221no—
161Q8—1221no—
162D4—1222no—
163D4—1222no—
164D4—1221no—
165D4—1221no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—612no—
171C2×C4—1222no—
172C2×C4—1222no—
173C2×C4—1222no—
174C2×C4—2444no—
175C2×C4—2441no—
176C2×C4C2×C4×D6111yescharacteristic
177C2×C4#1175822211yescharacteristic
178C2×C4#1175822211yescharacteristic
179C2×C4D4×D6111yescharacteristic
180C2×C4#1175822411yescharacteristic
181C2×C4#1175822611yescharacteristic
182C8—41no—
183C8—2441no—
184C22—41no—
185C22—1222no—
186C22—2442no—
187C22C22⋊C4×D6111yescharacteristic
188C22#1451975911yescharacteristic
189C22#1451976211yescharacteristic
190C4—22no—
191C4—41no—
192C4—81no—
193C4—1222no—
194C4—4881no—
195C4—2442no—
196C4#1451973411yescharacteristic
197C4#1451973511yescharacteristic
198C4#1451975911yescharacteristic
199C4#1451976211yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—2442no—
204C2#1683962411yescharacteristic
subgroupG/H
centerC4#14519735
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC2×C61#381
hypercenter#339D61
hypocenterC61#1827
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #16839522C2semidirect
5. #16839519C2semidirect
6. #16839518C2semidirect
7. C61×#339C2semidirect
15. #14519734C4semidirect
16. C42×D61C4semidirect
107. #339D61semidirect
110. C61#1827semidirect