Finite Group Databasebeta

← #21444893

Subgroups — #21444893

Order 7808.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840469C211yesmaximal, characteristic, complemented
2#16840135C211yesmaximal, characteristic, complemented
3#16839963C211yesmaximal, characteristic, complemented
4#16839957C211yesmaximal, characteristic
5#16839510C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9C2×#11758190—22no—
10C2×#11758199—21no—
11#14519777C2211yescharacteristic
12#14519774C2211yescharacteristic
13#14519768—21no—
14#14519756—21no—
15#14519754—22no—
16C4×Dic122C2211yescharacteristic
17D4×Dic61—21no—
18C2×C4⋊Dic61—21no—
19C4⋊#92418C2211yescharacteristic
20#14519699—21no—
21#14519697—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C22×Dic61—22no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×Dic122D411yescharacteristic
32C2×Dic122D412yes—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C4⋊C4×C61D411yescharacteristic
36C22⋊C4×C61—21no—
37C42×C61C2311yescharacteristic
38C22⋊Dic61—22no—
39#11758199—42no—
40C4⋊Dic61—22no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61D411yescharacteristic
44#11758196—22no—
45#11758196—21no—
46C4×Dic61—21no—
47C2×#92418—21no—
48#11758190—44no—
49#11758190—42no—
50C23×C61—21no—
51C22×D61—41no—
52D4×C61—21no—
53D4×C61SD1612yescomplemented
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—22no—
63C2×Dic61—82no—
64D244—42no—
65D244—41no—
66D244—41no—
67D244—41no—
68D244—41no—
69Dic122—21no—
70Dic122—21no—
71Dic122—42no—
72C8×C61—22no—
73C8×C61—41no—
74#92418—41no—
75C22×C61—22no—
76C22×C61—41no—
77C22×C61—41no—
78C22×C61#12011yescharacteristic
79C2×D61—81no—
80C2×D61—81no—
81C2×D61—81no—
82C4×C61—21no—
83C4×C61—41no—
84C4×C61C2×SD1611yescharacteristic
85C4×C61#13511yescharacteristic
86C4×C61AGL(1,ℤ/8)11yescharacteristic
87C4×C61#13711yescharacteristic
88Dic61—41no—
89Dic61—42no—
90Dic61—41no—
91#1622—611nomaximal, Sylow
92C2×C61—42no—
93C2×C61#44811yescharacteristic
94C2×C61#44911yescharacteristic
95C2×C61#45311yescharacteristic
96D61—161no—
97#554—611no—
98#492—611no—
99#460—611no—
100#459—611no—
101#333—611no—
102Q8⋊C8—611no—
103D4⋊C8D6111yescharacteristic, complemented
104C61#162211yescharacteristic, complemented, Sylow
105C2×SD16—1221no—
106C2×SD16—1222no—
107C2×D8—1221no—
108C4⋊Q8—611no—
109#127—611no—
110#125—1221no—
111C22⋊Q8—1222no—
112C22⋊Q8—1221no—
113C4×Q8—611no—
114C4×D4—1221no—
115C4×D4C2×D6111yescharacteristic
116C2×C4⋊C4—1221no—
117C4⋊C8—611no—
118C4⋊C8C2×D6111yescharacteristic
119#102—1221no—
120#102—1221no—
121C4×C8C2×D6111yescharacteristic
122C2×Q8—611no—
123C2×Q8—612no—
124C2×D4—1221no—
125C2×D4—1221no—
126C2×D4—1221no—
127C2×D4D24411yescharacteristic
128C22×C4—21no—
129C22×C4—1222no—
130SD16—2444no—
131SD16—2442no—
132D8—2442no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—1221no—
136C4⋊C4—611no—
137C4⋊C4—1222no—
138C4⋊C4—1222no—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4D24411yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1222no—
145C42—1221no—
146C42C22×D6111yescharacteristic
147C23—21no—
148C23—2441no—
149Q8—1221no—
150Q8—1221no—
151Q8—2442no—
152D4—21no—
153D4—2442no—
154D4—2441no—
155D4—2441no—
156D4—2441no—
157D4—2441no—
158D4#1175819012yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1221no—
163C2×C4—1221no—
164C2×C4—1222no—
165C2×C4—4882no—
166C2×C4C2×D24411yescharacteristic
167C2×C4D4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C8—22no—
170C8—41no—
171C8—2441no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—4881no—
176C22—4881no—
177C22—4881no—
178C22#1451974711yescharacteristic
179C4—21no—
180C4—41no—
181C4—2441no—
182C4—2441no—
183C4—2442no—
184C4C2×#1175819011yescharacteristic
185C4#1451979811yescharacteristic
186C4#1451980111yescharacteristic
187C4#1451981011yescharacteristic
188C2—42no—
189C2—9761no—
190C2#1683990311yescharacteristic
191C2#1683990811yescharacteristic
192C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1622
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #16840469C2semidirect
2. #16840135C2semidirect
3. #16839963C2semidirect
5. #16839510C2semidirect
6. #16839494C2semidirect
7. C61×D4⋊C8C2semidirect
53. D4×C61SD16semidirect
103. D4⋊C8D61semidirect
104. C61#1622semidirect
158. D4#11758190semidirect