Finite Group Databasebeta

← #21444930

Subgroups — #21444930

Order 7808.

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

normal subgroups only

This group has 216 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#16840486C211yesmaximal, characteristic, complemented
2#16840110C211yesmaximal, characteristic, complemented
3#16839963C211yesmaximal, characteristic, complemented
4#16839958C211yesmaximal, characteristic
5#16839492C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#332C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9C2×D488—21no—
10#14519774C2211yescharacteristic
11#14519772—22no—
12#14519766—21no—
13#14519757—21no—
14Q8×Dic61—21no—
15C4×Dic122C2211yescharacteristic
16C4×D244C2211yescharacteristic
17#14519735—21no—
18#14519699—21no—
19#14519699—21no—
20#14519697—22no—
21C4×#92418C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244D411yescharacteristic
30C2×C4×D61—21no—
31C2×Dic122D411yescharacteristic
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61D412yes—
36C42×C61C2311yescharacteristic
37#11758198—22no—
38#11758198—22no—
39#11758198—21no—
40C4⋊Dic61—22no—
41C4⋊Dic61D411yescharacteristic
42C4⋊Dic61D411yescharacteristic
43#11758196—21no—
44C4×Dic61—22no—
45C4×Dic61—21no—
46C2×#92418—21no—
47D488—42no—
48#11758190—42no—
49C22×D61—21no—
50C22×D61—41no—
51Q8×C61—41no—
52Q8×C61—41no—
53C2×C4×C61—22no—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—21no—
60D244—21no—
61D244—21no—
62D244—42no—
63D244—41no—
64D244—41no—
65D244—41no—
66D244—41no—
67C4×D61—41no—
68C4×D61—41no—
69Dic122—21no—
70Dic122—21no—
71C8×C61—41no—
72C8×C61—41no—
73#92418—41no—
74C22×C61#12011yescharacteristic
75C2×D61—41no—
76C2×D61—41no—
77C2×D61—41no—
78C2×D61—81no—
79C2×D61—81no—
80C2×D61—81no—
81C4×C61—21no—
82C4×C61—42no—
83C4×C61#13511yescharacteristic
84C4×C61#13511yescharacteristic
85C4×C61AGL(1,ℤ/8)11yescharacteristic
86C4×C61AGL(1,ℤ/8)11yescharacteristic
87Dic61—41no—
88Dic61—41no—
89Dic61—41no—
90#1628—611nomaximal, Sylow
91C2×C61#44911yescharacteristic
92C2×C61#44911yescharacteristic
93C2×C61#45411yescharacteristic
94D61—81no—
95D61—161no—
96#556—611no—
97#486—611no—
98#460—611no—
99#459—611no—
100#332D6111yescharacteristic, complemented
101Q8⋊C8—611no—
102D4⋊C8—611no—
103C61#162811yescharacteristic, complemented, Sylow
104C2×SD16—1221no—
105C2×D8—1221no—
106C4⋊Q8C2×D6111yescharacteristic
107#127—611no—
108#126—1222no—
109#124—1221no—
110C22⋊Q8—1221no—
111C4×Q8—611no—
112C4×Q8—1221no—
113C4×D4—611no—
114#117—1221no—
115C4⋊C8C2×D6111yescharacteristic
116C4⋊C8C2×D6111yescharacteristic
117#102—1221no—
118#102—1221no—
119#102—1222no—
120C4×C8—611no—
121C2×Q8—21no—
122C2×Q8—611no—
123C2×D4—611no—
124C2×D4—1221no—
125C2×D4—1221no—
126C2×D4—1221no—
127C22×C4—1221no—
128SD16—2442no—
129D8—2442no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—1221no—
133C4⋊C4—21no—
134C4⋊C4—611no—
135C4⋊C4—611no—
136C4⋊C4—1222no—
137C4⋊C4—1221no—
138C4⋊C4D24412yes—
139C22⋊C4—1222no—
140C22⋊C4—1222no—
141C22⋊C4—1221no—
142C42—1222no—
143C42—1221no—
144C42C22×D6111yescharacteristic
145C23—1221no—
146C23—2441no—
147Q8—41no—
148Q8—41no—
149Q8—1221no—
150Q8—1221no—
151D4—1221no—
152D4—1221no—
153D4—2442no—
154D4—2441no—
155D4—2441no—
156D4—2441no—
157D4—2441no—
158C2×C4—22no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—2441no—
163C2×C4—2441no—
164C2×C4C2×D24411yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C2×C4D4×D6111yescharacteristic
167C8—41no—
168C8—41no—
169C8—2441no—
170C22—4881no—
171C22—4881no—
172C22—4881no—
173C22—2441no—
174C22—2441no—
175C22—2441no—
176C22#1451974711yescharacteristic
177C4—21no—
178C4—42no—
179C4—2441no—
180C4—2441no—
181C4—2441no—
182C4#1451979811yescharacteristic
183C4#1451980011yescharacteristic
184C4#1451980111yescharacteristic
185C4#1451980411yescharacteristic
186C2—9761no—
187C2—4881no—
188C2#1683990811yescharacteristic
189C2#1683991011yescharacteristic
190C2#1683993711yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#332C2
socleC22×C61#120
hypercenter#332D61
hypocenterC61#1628
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #16840486C2semidirect
2. #16840110C2semidirect
3. #16839963C2semidirect
5. #16839492C2semidirect
6. #16839489C2semidirect
7. C61×#332C2semidirect
100. #332D61semidirect
103. C61#1628semidirect