Finite Group Databasebeta

← #21444894

Subgroups — #21444894

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#16840472C211yesmaximal, characteristic, complemented
2#16840135C211yesmaximal, characteristic, complemented
3#16839962C211yesmaximal, characteristic, complemented
4#16839958C211yesmaximal, characteristic
5#16839510C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758190—22no—
9C2×#11758201—21no—
10C2×D488—21no—
11#14519777C2211yescharacteristic
12#14519774C2211yescharacteristic
13#14519769—21no—
14#14519755—22no—
15#14519753—21no—
16C4×D244—21no—
17C4×D244C2211yescharacteristic
18C4⋊C4×D61—21no—
19C4⋊#92418C2211yescharacteristic
20#14519699—21no—
21#14519697—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×D244—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244D411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—22no—
32C2×Dic122D412yes—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61D411yescharacteristic
37C42×C61—21no—
38C42×C61C2311yescharacteristic
39#11758201—42no—
40#11758198—22no—
41#11758198—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61D411yescharacteristic
45#11758196—22no—
46#11758196—22no—
47C2×#92418—21no—
48D488—42no—
49#11758190—44no—
50C22×D61—21no—
51C22×D61—41no—
52Q8×C61—21no—
53Q8×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—22no—
61D244—21no—
62D244—42no—
63D244—41no—
64D244—41no—
65D244—41no—
66D244—41no—
67D244SD1612yescomplemented
68C4×D61—41no—
69C4×D61—41no—
70C4×D61—82no—
71Dic122—42no—
72C8×C61—22no—
73C8×C61—41no—
74#92418—41no—
75C22×C61#12011yescharacteristic
76C2×D61—22no—
77C2×D61—41no—
78C2×D61—41no—
79C2×D61—81no—
80C2×D61—81no—
81C2×D61—81no—
82C4×C61—21no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61C2×SD1611yescharacteristic
86C4×C61#13511yescharacteristic
87C4×C61AGL(1,ℤ/8)11yescharacteristic
88C4×C61#13711yescharacteristic
89Dic61—41no—
90Dic61—42no—
91#1622—611nomaximal, Sylow
92C2×C61#44811yescharacteristic
93C2×C61#44911yescharacteristic
94C2×C61#45311yescharacteristic
95D61—42no—
96D61—161no—
97#554—611no—
98#492—611no—
99#460—611no—
100#459—611no—
101#333—611no—
102Q8⋊C8D6111yescharacteristic, complemented
103D4⋊C8—611no—
104C61#162211yescharacteristic, complemented, Sylow
105C2×SD16—1222no—
106C2×SD16—1221no—
107C2×D8—1221no—
108C4⋊Q8—611no—
109#127—611no—
110#125—1221no—
111C22⋊Q8—1222no—
112C22⋊Q8—1221no—
113C4×Q8C2×D6111yescharacteristic
114C4×D4—611no—
115C4×D4—1221no—
116C2×C4⋊C4—1221no—
117C4⋊C8—611no—
118C4⋊C8C2×D6111yescharacteristic
119#102—1221no—
120#102—1221no—
121C4×C8C2×D6111yescharacteristic
122C2×Q8—612no—
123C2×Q8D24411yescharacteristic
124C2×D4—611no—
125C2×D4—1221no—
126C2×D4—1221no—
127C2×D4—1221no—
128C22×C4—1222no—
129C22×C4—1221no—
130SD16—2444no—
131SD16—2442no—
132D8—2442no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—1221no—
136C4⋊C4—21no—
137C4⋊C4—611no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4D24411yescharacteristic
143C22⋊C4—1222no—
144C22⋊C4—1221no—
145C42—21no—
146C42C22×D6111yescharacteristic
147C23—1221no—
148C23—2441no—
149Q8—21no—
150Q8—21no—
151Q8—2442no—
152D4—612no—
153D4—1221no—
154D4—2442no—
155D4—2441no—
156D4—2441no—
157D4—2441no—
158D4—2441no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—1221no—
162C2×C4—1222no—
163C2×C4—4882no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4C2×D24411yescharacteristic
167C2×C4D4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C8—22no—
170C8—41no—
171C8—2441no—
172C22—1222no—
173C22—4881no—
174C22—4881no—
175C22—4881no—
176C22—2441no—
177C22—2441no—
178C22#1451974711yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—2441no—
183C4—2442no—
184C4SD16×D6111yescharacteristic
185C4#1451979911yescharacteristic
186C4#1451980511yescharacteristic
187C4#1451980911yescharacteristic
188C2—9761no—
189C2—2442no—
190C2#1683990211yescharacteristic
191C2#1683990911yescharacteristic
192C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1622
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #16840472C2semidirect
2. #16840135C2semidirect
3. #16839962C2semidirect
5. #16839510C2semidirect
6. #16839491C2semidirect
7. C61×Q8⋊C8C2semidirect
67. D244SD16semidirect
102. Q8⋊C8D61semidirect
104. C61#1622semidirect