Finite Group Databasebeta

← #21446522

Subgroups — #21446522

Order 7808.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14519703C211yesmaximal, characteristic
2#16839756C211yesmaximal, characteristic
3#16839728C211yesmaximal, characteristic
4C2×C8×Dic61C211yesmaximal, characteristic, complemented
5#16839526C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#424C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C4×Dic61C2211yescharacteristic
12#14519703—22no—
13#14519700C412yescomplemented
14#14519697C412yescomplemented
15#14519689—22no—
16C8×Dic61—22no—
17C2×M16×C61C2211yescharacteristic
18C22×C8×C61C2211yescharacteristic
19#117×C61C2211yescharacteristic
20C4⋊C8×C61—22no—
21C22×C4×C61C2311yescharacteristic
22C2×C22⋊D61—21no—
23C22×Dic61—21no—
24#11758222—21no—
25#11758222—21no—
26#11758222—21no—
27#11758222—21no—
28C2×D244C2×C411yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122C2×C411yescharacteristic
31M16×C61—21no—
32M16×C61—21no—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61D412yes—
37C4⋊C4×C61C2×C412yes—
38C22⋊C4×C61—21no—
39C42×C61—21no—
40C4×Dic61—21no—
41C4×Dic61D412yes—
42#11758194—21no—
43#11758194—21no—
44C2×#92418—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418C2×C412yes—
48C23×C61#4111yescharacteristic
49C22×D61—21no—
50C2×C4×C61—22no—
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61#4111yescharacteristic
55C2×C4×C61#4111yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C22⋊D61—41no—
58C22⋊D61—41no—
59C2×Dic61—24no—
60C2×Dic61—22no—
61C2×Dic61—21no—
62D244—21no—
63D244—21no—
64C4×D61—41no—
65C4×D61—41no—
66Dic122—21no—
67Dic122—21no—
68C8×C61—22no—
69C8×C61—41no—
70#92418—22no—
71#92418—41no—
72C22×C61—22no—
73C22×C61C4×D411yescharacteristic
74C22×C61#12311yescharacteristic
75C22×C61#12611yescharacteristic
76C2×D61—41no—
77C2×D61—42no—
78C4×C61—42no—
79C4×C61#11711yescharacteristic
80C4×C61C4×D411yescharacteristic
81C4×C61#12111yescharacteristic
82C4×C61#12411yescharacteristic
83Dic61—24no—
84Dic61—41no—
85#1937—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—21no—
88C2×C61#38811yescharacteristic
89C2×C61#44312yes—
90D61—81no—
91#424D6111yescharacteristic, complemented
92C2×#104—611no—
93#416—611no—
94#408—611no—
95C2×C4×C8—611no—
96#341—611no—
97#339—611no—
98C61#193711yescharacteristic, complemented, Sylow
99C2×#41—611no—
100C2×M16—611no—
101C2×M16C2×D6111yescharacteristic
102C22×C8—611no—
103C22×C8C2×D6111yescharacteristic
104#117C2×D6111yescharacteristic
105C2×C42—611no—
106C4⋊C8—22no—
107#104—1222no—
108#103—612no—
109#102—612no—
110C22⋊C8—1222no—
111C4×C8—1222no—
112#41—1221no—
113#41—1221no—
114#41—1221no—
115#41—1221no—
116C2×Q8—611no—
117C2×D4—611no—
118C2×D4—1221no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4C22×D6111yescharacteristic
122M16—21no—
123M16—21no—
124M16—1221no—
125M16—1221no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—612no—
130C2×C8—1221no—
131C2×C8—1221no—
132C2×C8—1221no—
133C2×C8C22⋊D6112yes—
134C4⋊C4C4×D6112yes—
135C22⋊C4—21no—
136C42—21no—
137C42—612no—
138C42—1221no—
139C23—1221no—
140C23#1175822211yescharacteristic
141Q8—1221no—
142Q8—1221no—
143D4—1221no—
144D4—1221no—
145D4—2441no—
146D4—2441no—
147C2×C4—22no—
148C2×C4—1224no—
149C2×C4—1222no—
150C2×C4—1221no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4C2×C4×D6111yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C2×C4#1175822411yescharacteristic
156C2×C4#1175822611yescharacteristic
157C2×C4#1175822611yescharacteristic
158C2×C4C2×C22⋊D6111yescharacteristic
159C8—22no—
160C8—41no—
161C8—1222no—
162C8—2441no—
163C22—22no—
164C22—2442no—
165C22—2441no—
166C22C4×C22⋊D6111yescharacteristic
167C22#1451976211yescharacteristic
168C22#1451977211yescharacteristic
169C4—42no—
170C4—1224no—
171C4—2441no—
172C4#1451973511yescharacteristic
173C4#1451973911yescharacteristic
174C4#1451974911yescharacteristic
175C4#1451976611yescharacteristic
176C2—21no—
177C2—21no—
178C2—4881no—
179C2#1683965211yescharacteristic
180C2#1683987712yes—
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#424C2
socleC22×C61C4×D4
hypercenter#424D61
hypocenterC61#1937
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
4. C2×C8×Dic61C2semidirect
5. #16839526C2semidirect
6. #16839521C2semidirect
7. C61×#424C2semidirect
13. #14519700C4semidirect
14. #14519697C4semidirect
91. #424D61semidirect
98. C61#1937semidirect