Finite Group Databasebeta

← #21444812

Subgroups — #21444812

Order 7808.

228 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 228 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#16840388C211yesmaximal, characteristic
2#16840093C212yesmaximal, complemented
3#16839687C211yesmaximal, characteristic
4#16839500C212yesmaximal, complemented
5C61×#323C211yesmaximal, characteristic
6#14519756—21no—
7#14519756C2212yes—
8#14519754—22no—
9#14519754—22no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C22⋊Dic61—21no—
12C2×C22⋊Dic61—21no—
13#14519709—22no—
14#14519702—22no—
15#14519684—21no—
16#14519684C2211yescharacteristic
17C2×C22⋊C4×C61C2211yescharacteristic
18C22⋊C8×C61C2212yes—
19C24×C61D411yescharacteristic
20C22×C4×C61D411yescharacteristic
21C22×C4×C61C2311yescharacteristic
22C22×Dic61—21no—
23C22×Dic61—21no—
24C22×Dic61—21no—
25C22×Dic61—21no—
26C2×Dic122—21no—
27C2×Dic122D412yes—
28C2×C8×C61—22no—
29C22⋊C4×C61—22no—
30C22⋊Dic61—22no—
31C22⋊Dic61—22no—
32C22⋊Dic61—42no—
33C4⋊Dic61—21no—
34C4⋊Dic61—22no—
35C4⋊Dic61D412yes—
36#11758196—22no—
37#11758196—22no—
38C23×C61—21no—
39C23×C61—21no—
40C23×C61—41no—
41C23×C61—41no—
42C23×C61SD1612yes—
43C23×C61C2×D411yescharacteristic
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61C2×D412yes—
48C2×Dic61—22no—
49C2×Dic61—22no—
50C2×Dic61—41no—
51C2×Dic61—41no—
52C2×Dic61—41no—
53C2×Dic61—41no—
54C2×Dic61—41no—
55C2×Dic61—41no—
56C2×Dic61—81no—
57C2×Dic61—81no—
58Dic122—42no—
59Dic122—81no—
60C8×C61—42no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61—22no—
64C22×C61—42no—
65C22×C61—41no—
66C22×C61—41no—
67C22×C61—81no—
68C22×C61#12011yescharacteristic
69C22×C61C2×SD1611yescharacteristic
70C22×C61#13711yescharacteristic
71C4×C61—22no—
72C4×C61—41no—
73Dic61—42no—
74Dic61—42no—
75Dic61—81no—
76Dic61—81no—
77#1608—611nomaximal, Sylow
78C2×C61—21no—
79C2×C61—21no—
80C2×C61—42no—
81C2×C61#44811yescharacteristic
82C2×C61#45511yescharacteristic
83C2×C61#45811yescharacteristic
84#543—611no—
85#483—612no—
86#397—611no—
87#328—612no—
88#323D6111yescharacteristic
89C61#160811yescharacteristic, complemented, Sylow
90C22⋊Q8—612no—
91C22⋊Q8—1222no—
92C22⋊Q8—1222no—
93C22⋊Q8—1221no—
94C2×C4⋊C4—611no—
95C2×C22⋊C4—1221no—
96C2×C22⋊C4—1221no—
97C2×C22⋊C4C2×D6111yescharacteristic
98#106—1222no—
99#103—1222no—
100C22⋊C8C2×D6112yes—
101#95—611no—
102#95—1221no—
103C24D24411yescharacteristic
104C2×Q8—612no—
105C2×Q8—1221no—
106C22×C4—1221no—
107C22×C4—1221no—
108C22×C4—1221no—
109C22×C4—1221no—
110C22×C4D24411yescharacteristic
111C22×C4C22×D6111yescharacteristic
112C2×C8—22no—
113C4⋊C4—612no—
114C4⋊C4—1222no—
115C4⋊C4—1221no—
116C4⋊C4—1222no—
117C4⋊C4—1222no—
118C22⋊C4—22no—
119C22⋊C4—1222no—
120C22⋊C4—1222no—
121C22⋊C4—2442no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1175819012yes—
127C23C2×D24411yescharacteristic
128Q8—4881no—
129Q8—2442no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—1222no—
134C2×C4—1222no—
135C2×C4—4881no—
136C2×C4—4881no—
137C2×C4—2441no—
138C2×C4—2441no—
139C2×C4—2441no—
140C2×C4—2441no—
141C2×C4—2441no—
142C2×C4—2441no—
143C2×C4D4×D6112yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1451974711yescharacteristic
153C22C2×#1175819011yescharacteristic
154C22#1451981011yescharacteristic
155C4—22no—
156C4—41no—
157C4—4881no—
158C4—4881no—
159C4—2442no—
160C4—2442no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#1683990311yescharacteristic
165C2#1683994211yescharacteristic
166C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#323C2
socleC22×C61#120
hypercenter#323D61
hypocenterC61#1608
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #16840093C2semidirect
4. #16839500C2semidirect
89. C61#1608semidirect