Finite Group Databasebeta

← #21445115

Subgroups — #21445115

Order 7808.

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

normal subgroups only

This group has 206 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#16840512C211yesmaximal, characteristic, complemented
2#16840126C212yesmaximal, complemented
3#16839503C212yesmaximal, complemented
4#16839502C211yesmaximal, characteristic, complemented
5C61×#496C211yesmaximal, characteristic
6#14519775—21no—
7#14519770—22no—
8#14519769C2212yes—
9#14519758—21no—
10#14519754—22no—
11#14519698—22no—
12#14519698—22no—
13#14519688C2212yes—
14C2×SD16×C61—21no—
15C2×D8×C61—21no—
16#127×C61C2211yescharacteristic
17#124×C61C2211yescharacteristic
18#97×C61C2211yescharacteristic
19C2×Q8×C61D411yescharacteristic
20C2×D4×C61—21no—
21C2×D4×C61—22no—
22C2×D4×C61D411yescharacteristic
23C22×Dic61—21no—
24C2×Dic122—21no—
25SD16×C61—42no—
26D8×C61—42no—
27C2×C8×C61—21no—
28C22⋊C4×C61—22no—
29C42×C61C2311yescharacteristic
30C22⋊Dic61—22no—
31C22⋊Dic61—21no—
32C4⋊Dic61D412yes—
33C4⋊Dic61D412yes—
34#11758196—22no—
35#11758196—22no—
36#11758196—22no—
37C4×Dic61—21no—
38C2×#92418—22no—
39C23×C61—21no—
40C23×C61—41no—
41Q8×C61—41no—
42D4×C61—41no—
43D4×C61—41no—
44D4×C61—41no—
45D4×C61—44no—
46C2×C4×C61—21no—
47C2×C4×C61C2×D412yes—
48C2×C4×C61C2×D411yescharacteristic
49C2×Dic61—22no—
50C2×Dic61—22no—
51C2×Dic61—81no—
52Dic122—81no—
53C8×C61—22no—
54#92418—42no—
55C22×C61—41no—
56C22×C61—42no—
57C22×C61—81no—
58C22×C61—82no—
59C22×C61#12011yescharacteristic
60C4×C61—21no—
61C4×C61—22no—
62C4×C61—41no—
63Dic61—42no—
64Dic61—42no—
65#1657—611nomaximal, Sylow
66C2×C61—81no—
67C2×C61—161no—
68C2×C61#45311yescharacteristic
69C2×C61#45412yes—
70#563—611no—
71#496D6111yescharacteristic
72#490—612no—
73#330—612no—
74#329—611no—
75C61#165711yescharacteristic, complemented, Sylow
76C2×SD16—21no—
77C2×D8—21no—
78C4⋊Q8—1221no—
79#127C2×D6111yescharacteristic
80#126—1222no—
81#125—612no—
82#124C2×D6111yescharacteristic
83#123—1221no—
84C22⋊Q8—1222no—
85#102—1222no—
86#102—1222no—
87#97—612no—
88#97C2×D6111yescharacteristic
89C2×Q8—1221no—
90C2×Q8C22⋊D6111yescharacteristic
91C2×D4—22no—
92C2×D4—21no—
93C2×D4C22⋊D6111yescharacteristic
94C22×C4—1221no—
95SD16—42no—
96D8—42no—
97C2×C8—21no—
98C2×C8—1222no—
99C4⋊C4—612no—
100C4⋊C4—612no—
101C4⋊C4—1222no—
102C4⋊C4—1222no—
103C4⋊C4—1222no—
104C22⋊C4—22no—
105C22⋊C4—1222no—
106C22⋊C4—1221no—
107C42—1221no—
108C42C22×D6111yescharacteristic
109C23—21no—
110C23—41no—
111Q8—41no—
112Q8—4881no—
113D4—41no—
114D4—41no—
115D4—41no—
116D4—44no—
117C2×C4—21no—
118C2×C4—1222no—
119C2×C4—1222no—
120C2×C4—4881no—
121C2×C4D4×D6112yes—
122C2×C4C2×C22⋊D6111yescharacteristic
123C8—22no—
124C8—2442no—
125C22—41no—
126C22—42no—
127C22—81no—
128C22—82no—
129C22#1451974511yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—2442no—
134C4—2442no—
135C2—81no—
136C2—161no—
137C2#1683992911yescharacteristic
138C2#1683993312yes—
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#496C2
socleC22×C61#120
hypercenter#496D61
hypocenterC61#1657
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840512C2semidirect
2. #16840126C2semidirect
3. #16839503C2semidirect
4. #16839502C2semidirect
75. C61#1657semidirect