Finite Group Databasebeta

← #21445019

Subgroups — #21445019

Order 7808.

250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 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#16840108C211yesmaximal, characteristic, complemented
2#16840047C211yesmaximal, characteristic, complemented
3#16839967C211yesmaximal, characteristic, complemented
4#16839506C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic, complemented
7C61×#550C211yesmaximal, characteristic
8C2×#11758200—21no—
9#14519777C2211yescharacteristic
10#14519708—21no—
11C4⋊#92418C2211yescharacteristic
12C4⋊#92418C2211yescharacteristic
13#14519701—21no—
14#14519700—21no—
15#14519698—22no—
16C4×#92418C2211yescharacteristic
17C2×#41×C61—21no—
18#127×C61—21no—
19#127×C61C2211yescharacteristic
20#121×C61—22no—
21#121×C61—21no—
22C4×Q8×C61C2211yescharacteristic
23C4×D4×C61—21no—
24C4×D4×C61C2211yescharacteristic
25#41×C61—42no—
26#41×C61—42no—
27C2×Q8×C61D411yescharacteristic
28C2×D4×C61—22no—
29C2×D4×C61—22no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61D411yescharacteristic
33C2×D4×C61D412yes—
34C22×C4×C61—22no—
35C22×C4×C61—21no—
36C2×Dic122—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61D411yescharacteristic
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—22no—
41C22⋊C4×C61—21no—
42C42×C61—21no—
43C42×C61C2311yescharacteristic
44#11758200—42no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61—21no—
51C23×C61—22no—
52Q8×C61—21no—
53Q8×C61SD1612yescomplemented
54D4×C61—21no—
55D4×C61—21no—
56D4×C61—42no—
57D4×C61—44no—
58D4×C61—41no—
59D4×C61—41no—
60D4×C61—41no—
61D4×C61—41no—
62D4×C61—82no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—44no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×Dic61—41no—
73Dic122—41no—
74Dic122—41no—
75#92418—41no—
76#92418—41no—
77#92418—41no—
78C22×C61—41no—
79C22×C61—42no—
80C22×C61—42no—
81C22×C61—41no—
82C22×C61—42no—
83C22×C61—41no—
84C22×C61#12011yescharacteristic
85C4×C61—22no—
86C4×C61—21no—
87C4×C61—41no—
88C4×C61—41no—
89C4×C61C2×SD1611yescharacteristic
90C4×C61#13511yescharacteristic
91C4×C61AGL(1,ℤ/8)11yescharacteristic
92C4×C61AGL(1,ℤ/8)11yescharacteristic
93Dic61—81no—
94#1642—611nomaximal, Sylow
95C2×C61—81no—
96C2×C61—82no—
97C2×C61#44911yescharacteristic
98C2×C61#45011yescharacteristic
99C2×C61#45511yescharacteristic
100#550D6111yescharacteristic
101#486—611no—
102#475—611no—
103#461—611no—
104#331—611no—
105Q8⋊C8—611no—
106D4⋊C8—611no—
107C61#164211yescharacteristic, complemented, Sylow
108C2×#41—21no—
109C2×SD16—1221no—
110C4⋊Q8—611no—
111#127—21no—
112#127C2×D6111yescharacteristic
113#121—22no—
114#121—21no—
115C4×Q8C2×D6111yescharacteristic
116C4×D4—21no—
117C4×D4C2×D6111yescharacteristic
118#106—1221no—
119C4⋊C8—611no—
120C4⋊C8—611no—
121#103—1221no—
122#103—1221no—
123#102—1222no—
124C4×C8—611no—
125#41—42no—
126#41—42no—
127C2×Q8—1221no—
128C2×Q8C22⋊D6111yescharacteristic
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D6111yescharacteristic
134C2×D4C22⋊D6112yes—
135C22×C4—22no—
136C22×C4—21no—
137SD16—2442no—
138C2×C8—1221no—
139C2×C8—1221no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4C22⋊D6111yescharacteristic
145C4⋊C4C22⋊D6111yescharacteristic
146C22⋊C4—22no—
147C22⋊C4—21no—
148C42—21no—
149C42C22×D6111yescharacteristic
150C23—22no—
151C23—21no—
152Q8—21no—
153Q8—2441no—
154Q8—2441no—
155Q8#1175820012yescomplemented
156D4—21no—
157D4—21no—
158D4—42no—
159D4—44no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—44no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2441no—
172C2×C4C2×C22⋊D6111yescharacteristic
173C2×C4C2×C22⋊D6111yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C8—2441no—
176C8—2441no—
177C8—2441no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22#1451974611yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—41no—
189C4—4881no—
190C4C2×#1175820011yescharacteristic
191C4#1451979711yescharacteristic
192C4#1451980211yescharacteristic
193C4#1451980311yescharacteristic
194C2—82no—
195C2—81no—
196C2#1683990711yescharacteristic
197C2#1683991311yescharacteristic
198C2#1683994011yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#550C2
socleC22×C61#120
hypercenter#550D61
hypocenterC61#1642
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #16840108C2semidirect
2. #16840047C2semidirect
3. #16839967C2semidirect
4. #16839506C2semidirect
5. Q8⋊#92418C2semidirect
6. D4⋊#92418C2semidirect
53. Q8×C61SD16semidirect
107. C61#1642semidirect
155. Q8#11758200semidirect