Finite Group Databasebeta

← #21445009

Subgroups — #21445009

Order 7808.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 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#16840432C211yesmaximal, characteristic
2#16840039C211yesmaximal, characteristic, complemented
3#16839969C211yesmaximal, characteristic, complemented
4#16839506C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×#486C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9C2×#11758202—21no—
10#14519773—21no—
11#14519749—22no—
12#14519748—21no—
13C4×Dic122C2211yescharacteristic
14C4×D244C2211yescharacteristic
15D4×Dic61—21no—
16#14519710—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519701—21no—
20#14519697—21no—
21C4⋊Q8×C61C2211yescharacteristic
22#127×C61C2211yescharacteristic
23#102×C61—22no—
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61D412yes—
29C2×C22⋊D61—22no—
30C2×C22⋊D61—22no—
31C22×Dic61—22no—
32#11758224—42no—
33#11758224—42no—
34C2×D244D411yescharacteristic
35C2×C4×D61—21no—
36C2×Dic122D411yescharacteristic
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C42×C61C2311yescharacteristic
41C22⋊Dic61—22no—
42#11758202—42no—
43#11758198—21no—
44C4⋊Dic61D411yescharacteristic
45C4⋊Dic61D411yescharacteristic
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61—22no—
51C22×D61—21no—
52Q8×C61—41no—
53Q8×C61—41no—
54D4×C61—42no—
55D4×C61—41no—
56D4×C61—41no—
57D4×C61—41no—
58D4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C22⋊D61—44no—
64C22⋊D61—82no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—44no—
69D244—21no—
70D244—21no—
71C4×D61—41no—
72C4×D61—41no—
73Dic122—21no—
74Dic122D812yes—
75C8×C61—41no—
76#92418—41no—
77#92418—41no—
78C22×C61—42no—
79C22×C61—42no—
80C22×C61—42no—
81C22×C61#12011yescharacteristic
82C2×D61—41no—
83C2×D61—41no—
84C2×D61—41no—
85C4×C61—21no—
86C4×C61—81no—
87C4×C61C2×D811yescharacteristic
88C4×C61#13511yescharacteristic
89C4×C61AGL(1,ℤ/8)11yescharacteristic
90C4×C61#13711yescharacteristic
91Dic61—22no—
92Dic61—41no—
93Dic61—41no—
94#1641—611nomaximal, Sylow
95C2×C61—82no—
96C2×C61#44711yescharacteristic
97C2×C61#45211yescharacteristic
98C2×C61#45511yescharacteristic
99D61—81no—
100#550—611no—
101#486D6111yescharacteristic, complemented
102#474—611no—
103#462—611no—
104#331—611no—
105Q8⋊C8—611no—
106D4⋊C8—611no—
107C61#164111yescharacteristic, complemented, Sylow
108C2×#41—1221no—
109C2×Q16—1221no—
110C4⋊Q8C2×D6111yescharacteristic
111#127—1221no—
112#127C2×D6111yescharacteristic
113#121—1221no—
114#121—1222no—
115C4×Q8—611no—
116C4×D4—611no—
117C4×D4—1221no—
118#107—1221no—
119C4⋊C8—611no—
120C4⋊C8—611no—
121#103—1221no—
122#102—22no—
123#102—1221no—
124C4×C8C2×D6111yescharacteristic
125#41—2442no—
126#41—2442no—
127C2×Q8—21no—
128C2×Q8—611no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—611no—
132C2×D4—1222no—
133C2×D4—1222no—
134C2×D4C22⋊D6112yes—
135C22×C4—1222no—
136C22×C4—1221no—
137Q16—2442no—
138C2×C8—21no—
139C2×C8—1221no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—611no—
144C4⋊C4—611no—
145C4⋊C4—1221no—
146C22⋊C4—1222no—
147C22⋊C4—1221no—
148C42—1221no—
149C42C22×D6111yescharacteristic
150C23—22no—
151C23—1221no—
152Q8—41no—
153Q8—41no—
154Q8—612no—
155Q8—1221no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—1221no—
162D4—1221no—
163D4—4882no—
164D4—2444no—
165C2×C4—41no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—2444no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4D4×D6111yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C8—41no—
176C8—2441no—
177C8—2441no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—2441no—
182C22—2441no—
183C22—2441no—
184C22#1451974511yescharacteristic
185C4—21no—
186C4—81no—
187C4—1222no—
188C4—2441no—
189C4—2441no—
190C4D8×D6111yescharacteristic
191C4#1451979811yescharacteristic
192C4#1451980111yescharacteristic
193C4#1451980611yescharacteristic
194C2—82no—
195C2—4881no—
196C2#1683989411yescharacteristic
197C2#1683992111yescharacteristic
198C2#1683993911yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#486C2
socleC22×C61#120
hypercenter#486D61
hypocenterC61#1641
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #16840039C2semidirect
3. #16839969C2semidirect
4. #16839506C2semidirect
5. #16839494C2semidirect
6. #16839491C2semidirect
7. C61×#486C2semidirect
101. #486D61semidirect
107. C61#1641semidirect