Finite Group Databasebeta

← #21444888

Subgroups — #21444888

Order 7808.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840473C211yesmaximal, characteristic, complemented
2#16839959C211yesmaximal, characteristic, complemented
3#16839954C211yesmaximal, characteristic
4#16839511C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×#492C211yesmaximal, characteristic, complemented
8C2×#11758200—21no—
9C2×#11758199—21no—
10#14519768—21no—
11#14519757—21no—
12#14519753—22no—
13C4×Dic122C2211yescharacteristic
14C4×D244C2211yescharacteristic
15#14519739—21no—
16C4⋊C4×D61—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519698—21no—
20#14519698—21no—
21C2×SD16×C61—22no—
22C4⋊Q8×C61C2211yescharacteristic
23#127×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D412yes—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D244D411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—22no—
32C2×Dic122D411yescharacteristic
33SD16×C61—44no—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C42×C61C2311yescharacteristic
38#11758200—42no—
39#11758199—42no—
40#11758198—22no—
41#11758198—21no—
42C4⋊Dic61—22no—
43C4⋊Dic61D411yescharacteristic
44C4⋊Dic61D411yescharacteristic
45#11758196—22no—
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61—41no—
51C22×D61—21no—
52Q8×C61—42no—
53D4×C61—42no—
54D4×C61—41no—
55D4×C61—41no—
56D4×C61—41no—
57D4×C61—41no—
58C2×C4×C61—22no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65D244—21no—
66D244SD1612yescomplemented
67C4×D61—41no—
68C4×D61—41no—
69C4×D61—82no—
70Dic122—21no—
71Dic122—21no—
72C8×C61—22no—
73#92418—41no—
74#92418—41no—
75C22×C61—81no—
76C22×C61—81no—
77C22×C61—81no—
78C22×C61#12011yescharacteristic
79C2×D61—22no—
80C2×D61—41no—
81C2×D61—41no—
82C4×C61—21no—
83C4×C61—42no—
84C4×C61C2×SD1611yescharacteristic
85C4×C61#13511yescharacteristic
86C4×C61AGL(1,ℤ/8)11yescharacteristic
87C4×C61#13711yescharacteristic
88Dic61—41no—
89Dic61—41no—
90Dic61—41no—
91#1622—611nomaximal, Sylow
92C2×C61—161no—
93C2×C61#44811yescharacteristic
94C2×C61#44911yescharacteristic
95C2×C61#45311yescharacteristic
96D61—42no—
97#554—611no—
98#492D6111yescharacteristic, complemented
99#460—611no—
100#459—611no—
101#333—611no—
102Q8⋊C8—611no—
103D4⋊C8—611no—
104C61#162211yescharacteristic, complemented, Sylow
105C2×SD16—22no—
106C2×SD16—1221no—
107C2×D8—1221no—
108C4⋊Q8C2×D6111yescharacteristic
109#127C2×D6111yescharacteristic
110#125—1221no—
111C22⋊Q8—1221no—
112C22⋊Q8—1222no—
113C4×Q8—611no—
114C4×D4—611no—
115C4×D4—1221no—
116C2×C4⋊C4—1221no—
117C4⋊C8—611no—
118C4⋊C8—611no—
119#102—1221no—
120#102—1221no—
121C4×C8C2×D6111yescharacteristic
122C2×Q8—611no—
123C2×Q8C22⋊D6112yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—611no—
128C22×C4—1222no—
129C22×C4—1221no—
130SD16—44no—
131SD16—2442no—
132D8—2442no—
133C2×C8—21no—
134C2×C8—1221no—
135C2×C8—1221no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—611no—
139C4⋊C4—611no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4—1221no—
143C22⋊C4—1222no—
144C22⋊C4—1221no—
145C42—1221no—
146C42C22×D6111yescharacteristic
147C23—41no—
148C23—1221no—
149Q8—42no—
150Q8—1221no—
151Q8—1221no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—612no—
158D4—1221no—
159C2×C4—22no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—4882no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4D4×D6111yescharacteristic
167C2×C4D4×D6111yescharacteristic
168C2×C4C2×C22⋊D6111yescharacteristic
169C8—22no—
170C8—2441no—
171C8—2441no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—1222no—
176C22—2441no—
177C22—2441no—
178C22#1451974511yescharacteristic
179C4—21no—
180C4—42no—
181C4—2441no—
182C4—2441no—
183C4—2441no—
184C4SD16×D6111yescharacteristic
185C4#1451979811yescharacteristic
186C4#1451980411yescharacteristic
187C4#1451980611yescharacteristic
188C2—161no—
189C2—2442no—
190C2#1683989911yescharacteristic
191C2#1683990611yescharacteristic
192C2#1683992911yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#492C2
socleC22×C61#120
hypercenter#492D61
hypocenterC61#1622
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16840473C2semidirect
2. #16839959C2semidirect
4. #16839511C2semidirect
5. #16839494C2semidirect
6. #16839491C2semidirect
7. C61×#492C2semidirect
66. D244SD16semidirect
98. #492D61semidirect
104. C61#1622semidirect