Finite Group Databasebeta

← #21444686

Subgroups — #21444686

Order 7808.

182 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 61 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×#11758199C211yesmaximal, characteristic
2#16839840C211yesmaximal, characteristic, complemented
3#16839827C211yesmaximal, characteristic, complemented
4#16839512C211yesmaximal, characteristic, complemented
5#16839491C211yesmaximal, characteristic, complemented
6#16839483C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758199C411yescharacteristic
9C2×#11758194—21no—
10C2×C8×D61—21no—
11C4×D244C2211yescharacteristic
12#14519710C411yescharacteristic
13C4⋊#92418C2211yescharacteristic
14#14519698C411yescharacteristic
15#14519697C411yescharacteristic
16C22⋊#92418—21no—
17#14519689—21no—
18C4×#92418C2211yescharacteristic
19C4×#92418C2211yescharacteristic
20C4×D4×C61C2211yescharacteristic
21C4⋊C8×C61C2211yescharacteristic
22C4×C8×C61C2211yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C2×D244C2×C411yescharacteristic
26C2×C4×D61—21no—
27C2×C8×C61—21no—
28C2×C8×C61—21no—
29C4⋊C4×C61C2×C411yescharacteristic
30C22⋊C4×C61—21no—
31C42×C61C2311yescharacteristic
32#11758199—22no—
33#11758198—21no—
34C4⋊Dic61C2×C411yescharacteristic
35#11758194—42no—
36C2×#92418—21no—
37C2×#92418C2×C411yescharacteristic
38C2×#92418C2×C411yescharacteristic
39C2×#92418D411yescharacteristic
40C2×#92418D411yescharacteristic
41C8×D61—42no—
42C23×C61—21no—
43C22×D61—21no—
44D4×C61—21no—
45D4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—41no—
48C2×C4×C61—41no—
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61#4111yescharacteristic
52C2×Dic61—21no—
53D244—21no—
54D244M1612yescomplemented
55C4×D61—41no—
56C4×D61—41no—
57C8×C61—22no—
58C8×C61—41no—
59#92418—21no—
60#92418—21no—
61#92418—21no—
62#92418—21no—
63#92418—41no—
64C22×C61—41no—
65C22×C61—41no—
66C22×C61—41no—
67C22×C61C4×D411yescharacteristic
68C2×D61—22no—
69C2×D61—41no—
70C2×D61—41no—
71C4×C61—21no—
72C4×C61—41no—
73C4×C61C2×M1611yescharacteristic
74C4×C61#13111yescharacteristic
75C4×C61AGL(1,ℤ/8)11yescharacteristic
76C4×C61AGL(1,ℤ/8)11yescharacteristic
77Dic61—41no—
78#1586—611nomaximal, Sylow
79C2×C61—81no—
80C2×C61#43511yescharacteristic
81C2×C61#44211yescharacteristic
82C2×C61#44311yescharacteristic
83D61—42no—
84C4×D8—611no—
85#436—611no—
86C8×D4—611no—
87#334—611no—
88D4⋊C8—611no—
89D4⋊C8D6111yescharacteristic, complemented
90#322—611no—
91C61#158611yescharacteristic, complemented, Sylow
92C2×D8—611no—
93C2×M16—1221no—
94C22×C8—1221no—
95C4×D4—611no—
96C4×D4C2×D6111yescharacteristic
97#107—611no—
98C4⋊C8—611no—
99C4⋊C8C2×D6111yescharacteristic
100#102—611no—
101#102—611no—
102C22⋊C8—1221no—
103C22⋊C8—1221no—
104C4×C8—611no—
105C4×C8—611no—
106C4×C8C2×D6111yescharacteristic
107C2×D4—611no—
108C2×D4C4×D6111yescharacteristic
109C22×C4—21no—
110C22×C4—1221no—
111D8—1222no—
112M16—2442no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—611no—
116C2×C8—611no—
117C2×C8—611no—
118C2×C8—611no—
119C2×C8—1221no—
120C2×C8—2442no—
121C4⋊C4—611no—
122C4⋊C4C4×D6111yescharacteristic
123C22⋊C4—21no—
124C22⋊C4—1221no—
125C42C22×D6111yescharacteristic
126C23—21no—
127C23—1221no—
128D4—21no—
129D4—21no—
130D4—612no—
131D4—1221no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—1221no—
136C2×C4—2441no—
137C2×C4—2441no—
138C2×C4C2×C4×D6111yescharacteristic
139C2×C4D4×D6111yescharacteristic
140C2×C4#1175822411yescharacteristic
141C8—22no—
142C8—41no—
143C8—1221no—
144C8—1221no—
145C8—1221no—
146C8—1221no—
147C8—2441no—
148C22—41no—
149C22—41no—
150C22—41no—
151C22—1222no—
152C22—2441no—
153C22—2441no—
154C22#1451973711yescharacteristic
155C4—21no—
156C4—41no—
157C4—2441no—
158C4M16×D6111yescharacteristic
159C4#1451978311yescharacteristic
160C4#1451980111yescharacteristic
161C4#1451980411yescharacteristic
162C2—81no—
163C2—2442no—
164C2#1683983611yescharacteristic
165C2#1683987111yescharacteristic
166C2#1683987611yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61C4×D4
hypercenterD4⋊C8D61
hypocenterC61#1586
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16839840C2semidirect
3. #16839827C2semidirect
4. #16839512C2semidirect
5. #16839491C2semidirect
6. #16839483C2semidirect
7. C61×D4⋊C8C2semidirect
54. D244M16semidirect
89. D4⋊C8D61semidirect
91. C61#1586semidirect