Finite Group Databasebeta

← #21445138

Subgroups — #21445138

Order 7808.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#16840510C211yesmaximal, characteristic
2#16840172C211yesmaximal, characteristic, complemented
3#16840156C211yesmaximal, characteristic, complemented
4#16840122C211yesmaximal, characteristic, complemented
5#16839501C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#330C211yesmaximal, characteristic, complemented
8C2×Dic244—21no—
9C2×#11758190—21no—
10#14519777C2211yescharacteristic
11#14519765C2211yescharacteristic
12#14519765C2211yescharacteristic
13#14519762—21no—
14#14519762—21no—
15#14519755—21no—
16#14519755—21no—
17#14519752—21no—
18#14519752—21no—
19#14519710—21no—
20#14519708—21no—
21#14519702—21no—
22#14519699—21no—
23#14519688C2211yescharacteristic
24#125×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×D244—21no—
28C2×D244—21no—
29C2×D244D411yescharacteristic
30C2×D244D411yescharacteristic
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122—21no—
34C2×Dic122D411yescharacteristic
35C2×Dic122D411yescharacteristic
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61D411yescharacteristic
41C4⋊C4×C61D411yescharacteristic
42C42×C61C2311yescharacteristic
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51#11758196—21no—
52#11758196—21no—
53C2×#92418—21no—
54Dic244—42no—
55#11758190—42no—
56C22×D61—21no—
57C22×D61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—41no—
66D244—41no—
67D244—41no—
68D244—81no—
69D244—81no—
70C4×D61—81no—
71C4×D61—81no—
72Dic122—41no—
73Dic122—41no—
74Dic122—41no—
75Dic122—41no—
76C8×C61—22no—
77C8×C61—41no—
78#92418—22no—
79C22×C61#12011yescharacteristic
80C2×D61—41no—
81C2×D61—41no—
82C2×D61—41no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—41no—
86C4×C61—21no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—41no—
90C4×C61—41no—
91Dic61—41no—
92Dic61—41no—
93Dic61—81no—
94#1661—611nomaximal, Sylow
95C2×C61#45311yescharacteristic
96C2×C61#45511yescharacteristic
97C2×C61#45611yescharacteristic
98D61—81no—
99D61—81no—
100#562—611no—
101#501—611no—
102#497—611no—
103#489—611no—
104#330D6111yescharacteristic, complemented
105#329—611no—
106#329—611no—
107C61#166111yescharacteristic, complemented, Sylow
108C2×Q16—1221no—
109C2×SD16—1221no—
110C4⋊Q8—611no—
111#125C2×D6111yescharacteristic
112#124—611no—
113#124—611no—
114#123—1221no—
115#123—1221no—
116C22⋊Q8—1221no—
117C22⋊Q8—1221no—
118#121—1221no—
119#121—1221no—
120#107—1221no—
121#106—1221no—
122#103—1221no—
123#102—1221no—
124#97—611no—
125#97C2×D6111yescharacteristic
126#97C2×D6111yescharacteristic
127C2×Q8—611no—
128C2×Q8—611no—
129C2×Q8—1221no—
130C2×D4—611no—
131C2×D4—611no—
132C2×D4—1221no—
133C2×D4—1221no—
134C22×C4—1221no—
135C22×C4—1221no—
136Q16—2442no—
137SD16—2442no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C4⋊C4D24411yescharacteristic
148C4⋊C4D24411yescharacteristic
149C22⋊C4—1221no—
150C22⋊C4—1221no—
151C22⋊C4—1221no—
152C22⋊C4—1221no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C42C22×D6111yescharacteristic
156C23—1221no—
157C23—1221no—
158Q8—2441no—
159Q8—2441no—
160Q8—2441no—
161Q8—2441no—
162D4—4881no—
163D4—4881no—
164D4—2441no—
165D4—2441no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—4881no—
171C2×C4—4881no—
172C2×C4—2441no—
173C2×C4C2×D24411yescharacteristic
174C2×C4D4×D6111yescharacteristic
175C2×C4D4×D6111yescharacteristic
176C8—22no—
177C8—41no—
178C8—1222no—
179C22—2441no—
180C22—2441no—
181C22—2441no—
182C22—2441no—
183C22—2441no—
184C22—2441no—
185C22#1451974711yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—4881no—
192C4—2441no—
193C4—2441no—
194C2—4881no—
195C2—4881no—
196C2#1683993111yescharacteristic
197C2#1683994111yescharacteristic
198C2#1683994711yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#330C2
socleC22×C61#120
hypercenter#330D61
hypocenterC61#1661
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #16840172C2semidirect
3. #16840156C2semidirect
4. #16840122C2semidirect
5. #16839501C2semidirect
6. #16839501C2semidirect
7. C61×#330C2semidirect
104. #330D61semidirect
107. C61#1661semidirect