Finite Group Databasebeta

← #21444927

Subgroups — #21444927

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#16840482C211yesmaximal, characteristic, complemented
2#16840108C211yesmaximal, characteristic, complemented
3#16839959C211yesmaximal, characteristic, complemented
4#16839509C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic, complemented
7C61×#459C211yesmaximal, characteristic
8C2×#11758200—21no—
9#14519777C2211yescharacteristic
10#14519770—22no—
11#14519764—21no—
12#14519756—21no—
13C4×Dic122C2211yescharacteristic
14#14519742—21no—
15#14519736—21no—
16C4⋊#92418C2211yescharacteristic
17#14519698—21no—
18#14519698—22no—
19C4×#92418C2211yescharacteristic
20C2×D8×C61—21no—
21#127×C61C2211yescharacteristic
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61D411yescharacteristic
29C22×C4×C61—21no—
30C2×Dic122—21no—
31C2×Dic122D411yescharacteristic
32D8×C61—42no—
33C2×C8×C61—21no—
34C4⋊C4×C61D411yescharacteristic
35C22⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37C22⋊Dic61—22no—
38C22⋊Dic61—22no—
39#11758200—42no—
40C4⋊Dic61—21no—
41C4⋊Dic61D411yescharacteristic
42C4⋊Dic61D412yes—
43#11758196—22no—
44#11758196—21no—
45C4×Dic61—22no—
46C4×Dic61—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C23×C61—21no—
50C23×C61—41no—
51D4×C61—21no—
52D4×C61—21no—
53D4×C61—42no—
54D4×C61—41no—
55D4×C61—41no—
56D4×C61—41no—
57D4×C61—41no—
58C2×C4×C61—21no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—22no—
67Dic122—21no—
68Dic122—21no—
69Dic122—41no—
70Dic122—41no—
71C8×C61—41no—
72#92418—41no—
73#92418—41no—
74C22×C61—41no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61—81no—
78C22×C61—81no—
79C22×C61—81no—
80C22×C61#12011yescharacteristic
81C4×C61—21no—
82C4×C61—41no—
83C4×C61#13511yescharacteristic
84C4×C61#13511yescharacteristic
85C4×C61AGL(1,ℤ/8)11yescharacteristic
86C4×C61AGL(1,ℤ/8)11yescharacteristic
87Dic61—41no—
88Dic61—42no—
89Dic61—41no—
90#1628—611nomaximal, Sylow
91C2×C61—81no—
92C2×C61—161no—
93C2×C61#44911yescharacteristic
94C2×C61#44911yescharacteristic
95C2×C61#45411yescharacteristic
96#556—611no—
97#486—611no—
98#460—611no—
99#459D6111yescharacteristic
100#332—611no—
101Q8⋊C8—611no—
102D4⋊C8—611no—
103C61#162811yescharacteristic, complemented, Sylow
104C2×SD16—1221no—
105C2×D8—21no—
106C4⋊Q8—611no—
107#127C2×D6111yescharacteristic
108#126—1222no—
109#124—1221no—
110C22⋊Q8—1221no—
111C4×Q8—611no—
112C4×Q8—1221no—
113C4×D4C2×D6111yescharacteristic
114#117—1221no—
115C4⋊C8—611no—
116C4⋊C8C2×D6111yescharacteristic
117#102—21no—
118#102—1221no—
119#102—1222no—
120C4×C8—611no—
121C2×Q8—611no—
122C2×Q8—1221no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D6111yescharacteristic
127C22×C4—21no—
128SD16—2442no—
129D8—42no—
130C2×C8—21no—
131C2×C8—1221no—
132C2×C8—1221no—
133C4⋊C4—611no—
134C4⋊C4—612no—
135C4⋊C4—1222no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4C22⋊D6111yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—1222no—
141C22⋊C4—1222no—
142C42—1222no—
143C42—1221no—
144C42C22×D6111yescharacteristic
145C23—21no—
146C23—41no—
147Q8—1221no—
148Q8—1221no—
149Q8—2441no—
150Q8—2441no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—1221no—
162C2×C4—1222no—
163C2×C4—1221no—
164C2×C4D4×D6111yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C2×C4C2×C22⋊D6111yescharacteristic
167C8—41no—
168C8—2441no—
169C8—2441no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#1451974511yescharacteristic
177C4—21no—
178C4—41no—
179C4—2441no—
180C4—2442no—
181C4—2441no—
182C4#1451979611yescharacteristic
183C4#1451979711yescharacteristic
184C4#1451980111yescharacteristic
185C4#1451980311yescharacteristic
186C2—81no—
187C2—161no—
188C2#1683990411yescharacteristic
189C2#1683990511yescharacteristic
190C2#1683993311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#459C2
socleC22×C61#120
hypercenter#459D61
hypocenterC61#1628
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840482C2semidirect
2. #16840108C2semidirect
3. #16839959C2semidirect
4. #16839509C2semidirect
5. #16839492C2semidirect
6. D4⋊#92418C2semidirect
103. C61#1628semidirect