Finite Group Databasebeta

← #21444966

Subgroups — #21444966

Order 7808.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840477C211yesmaximal, characteristic
2#16840142C211yesmaximal, characteristic, complemented
3#16840053C211yesmaximal, characteristic, complemented
4#16840052C211yesmaximal, characteristic, complemented
5#16839510C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×Dic244—22no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519763—22no—
12#14519751—21no—
13#14519748—21no—
14C4×D244C2211yescharacteristic
15#14519736—21no—
16#14519735—21no—
17#14519709—21no—
18#14519708—21no—
19C4⋊#92418C2211yescharacteristic
20#14519699—21no—
21#14519698—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C2×C22⋊D61—22no—
28C2×D244D411yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122—21no—
31C2×Dic122D412yes—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C4⋊C4×C61D411yescharacteristic
35C22⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37C22⋊Dic61—22no—
38#11758198—22no—
39#11758198—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61D411yescharacteristic
45C4×Dic61—22no—
46C2×#92418—21no—
47Dic244—44no—
48C23×C61—21no—
49C22×D61—21no—
50D4×C61—21no—
51D4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C22⋊D61—82no—
59C2×Dic61—21no—
60C2×Dic61—22no—
61C2×Dic61—41no—
62D244—21no—
63D244—21no—
64C4×D61—41no—
65C4×D61—41no—
66Dic122—42no—
67Dic122—42no—
68C8×C61—22no—
69C8×C61—41no—
70#92418—41no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61#12011yescharacteristic
75C2×D61—41no—
76C2×D61—41no—
77C2×D61—41no—
78C4×C61—21no—
79C4×C61—41no—
80C4×C61#13511yescharacteristic
81C4×C61#13511yescharacteristic
82C4×C61#13711yescharacteristic
83C4×C61#13711yescharacteristic
84Dic61—41no—
85Dic61—42no—
86Dic61—81no—
87#1634—611nomaximal, Sylow
88C2×C61—81no—
89C2×C61#45211yescharacteristic
90C2×C61#45211yescharacteristic
91C2×C61#45311yescharacteristic
92D61—81no—
93#555—611no—
94#494—611no—
95#476—611no—
96#476—611no—
97#333—611no—
98D4⋊C8—611no—
99D4⋊C8D6111yescharacteristic, complemented
100C61#163411yescharacteristic, complemented, Sylow
101C2×Q16—1222no—
102C4⋊Q8—611no—
103C4⋊Q8—611no—
104#124—1222no—
105#121—1221no—
106#121—1221no—
107C4×D4—611no—
108C4×D4C2×D6111yescharacteristic
109#117—1221no—
110#117—1221no—
111#106—1221no—
112#106—1221no—
113C4⋊C8—611no—
114C4⋊C8C2×D6111yescharacteristic
115#102—1221no—
116#102—1221no—
117C4×C8C2×D6111yescharacteristic
118C2×Q8—612no—
119C2×Q8—1221no—
120C2×D4—611no—
121C2×D4—1222no—
122C2×D4D24411yescharacteristic
123C22×C4—21no—
124C22×C4—1221no—
125Q16—2444no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—1221no—
129C4⋊C4—611no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4D24411yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—1222no—
137C22⋊C4—1222no—
138C22⋊C4—1221no—
139C42—1222no—
140C42C22×D6111yescharacteristic
141C23—21no—
142C23—1221no—
143Q8—2442no—
144Q8—2442no—
145D4—21no—
146D4—21no—
147D4—1221no—
148D4—1221no—
149D4—4882no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—1221no—
154C2×C4—1222no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4C2×D24411yescharacteristic
159C2×C4D4×D6111yescharacteristic
160C2×C4D4×D6111yescharacteristic
161C8—22no—
162C8—41no—
163C8—2441no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—2441no—
168C22—2441no—
169C22—2441no—
170C22#1451974711yescharacteristic
171C4—21no—
172C4—41no—
173C4—4881no—
174C4—2441no—
175C4—2442no—
176C4#1451979611yescharacteristic
177C4#1451979911yescharacteristic
178C4#1451980611yescharacteristic
179C4#1451981011yescharacteristic
180C2—81no—
181C2—4881no—
182C2#1683992511yescharacteristic
183C2#1683992611yescharacteristic
184C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1634
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
2. #16840142C2semidirect
3. #16840053C2semidirect
4. #16840052C2semidirect
5. #16839510C2semidirect
6. #16839491C2semidirect
7. C61×D4⋊C8C2semidirect
99. D4⋊C8D61semidirect
100. C61#1634semidirect