Finite Group Databasebeta

← #21445075

Subgroups — #21445075

Order 7808.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840165C211yesmaximal, characteristic, complemented
2#16840047C211yesmaximal, characteristic, complemented
3#16839967C211yesmaximal, characteristic
4#16839508C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic
7C61×#556C211yesmaximal, characteristic
8C2×#11758200—21no—
9#14519777C2211yescharacteristic
10#14519710—22no—
11#14519708—21no—
12C4⋊#92418C2211yescharacteristic
13C4⋊#92418C2211yescharacteristic
14#14519701—21no—
15#14519700—21no—
16C4×#92418C2211yescharacteristic
17C4⋊Q8×C61C2211yescharacteristic
18#126×C61—22no—
19#124×C61—21no—
20C22⋊Q8×C61—21no—
21C4×Q8×C61—21no—
22C4×Q8×C61C2211yescharacteristic
23C4×D4×C61C2211yescharacteristic
24#117×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61D411yescharacteristic
27C2×D4×C61D411yescharacteristic
28C22×C4×C61—21no—
29C2×Dic122—21no—
30C4⋊C4×C61—22no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C4⋊C4×C61D411yescharacteristic
35C4⋊C4×C61D412yes—
36C22⋊C4×C61—22no—
37C22⋊C4×C61—22no—
38C22⋊C4×C61—21no—
39C42×C61—22no—
40C42×C61—21no—
41C42×C61C2311yescharacteristic
42#11758200—42no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C23×C61—21no—
49Q8×C61—21no—
50Q8×C61—21no—
51Q8×C61—41no—
52Q8×C61—41no—
53D4×C61—21no—
54D4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—22no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—41no—
65Dic122—41no—
66Dic122—41no—
67#92418—22no—
68#92418—41no—
69#92418—41no—
70C22×C61—41no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61#12011yescharacteristic
74C4×C61—21no—
75C4×C61—42no—
76C4×C61—41no—
77C4×C61—41no—
78C4×C61—41no—
79C4×C61#13511yescharacteristic
80C4×C61#13511yescharacteristic
81C4×C61AGL(1,ℤ/8)11yescharacteristic
82C4×C61#13711yescharacteristic
83Dic61—81no—
84#1650—611nomaximal, Sylow
85C2×C61—81no—
86C2×C61#44911yescharacteristic
87C2×C61#45211yescharacteristic
88C2×C61#45611yescharacteristic
89#556D6111yescharacteristic
90#500—611no—
91#475—611no—
92#461—611no—
93#332—611no—
94Q8⋊C8—611no—
95D4⋊C8—611no—
96C61#165011yescharacteristic, complemented, Sylow
97C2×SD16—1221no—
98C4⋊Q8—611no—
99C4⋊Q8C2×D6111yescharacteristic
100#126—22no—
101#124—21no—
102C22⋊Q8—21no—
103C4×Q8—21no—
104C4×Q8C2×D6111yescharacteristic
105C4×D4C2×D6111yescharacteristic
106#117—21no—
107#107—1222no—
108#106—1221no—
109C4⋊C8—611no—
110C4⋊C8—611no—
111#103—1221no—
112#103—1221no—
113C4×C8—611no—
114C2×Q8—21no—
115C2×Q8—1221no—
116C2×Q8C22⋊D6111yescharacteristic
117C2×D4C22⋊D6111yescharacteristic
118C22×C4—21no—
119SD16—2442no—
120C2×C8—1221no—
121C2×C8—1221no—
122C2×C8—1221no—
123C4⋊C4—22no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4C22⋊D6111yescharacteristic
129C4⋊C4C22⋊D6111yescharacteristic
130C4⋊C4C22⋊D6112yes—
131C22⋊C4—22no—
132C22⋊C4—22no—
133C22⋊C4—21no—
134C42—22no—
135C42—21no—
136C42C22×D6111yescharacteristic
137C23—21no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—2441no—
143Q8—2441no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—2441no—
153C2×C4C2×C22⋊D6111yescharacteristic
154C2×C4C2×C22⋊D6111yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—1222no—
157C8—2441no—
158C8—2441no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1451974611yescharacteristic
163C4—21no—
164C4—41no—
165C4—42no—
166C4—41no—
167C4—41no—
168C4—4881no—
169C4#1451979711yescharacteristic
170C4#1451979711yescharacteristic
171C4#1451980211yescharacteristic
172C4#1451980711yescharacteristic
173C2—81no—
174C2#1683990711yescharacteristic
175C2#1683992411yescharacteristic
176C2#1683994511yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#556C2
socleC22×C61#120
hypercenter#556D61
hypocenterC61#1650
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #16840165C2semidirect
2. #16840047C2semidirect
4. #16839508C2semidirect
5. Q8⋊#92418C2semidirect
96. C61#1650semidirect