Finite Group Databasebeta

← #21447839

Subgroups — #21447839

Order 7808.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#16839945C212yesmaximal, complemented
3#16839560C212yesmaximal, complemented
4#16839559C211yesmaximal, characteristic, complemented
5C61×#454C211yesmaximal, characteristic
6#14519807—22no—
7#14519775C2212yes—
8#14519770—22no—
9#14519769—21no—
10#14519758—21no—
11#14519754—22no—
12#14519704—22no—
13#14519696C2212yes—
142−1+4×C61C2211yescharacteristic
15AGL(1,ℤ/8)×C61—21no—
16#124×C61C2211yescharacteristic
17#104×C61—21no—
18#101×C61C2211yescharacteristic
19#41×C61—21no—
20#41×C61—22no—
21#41×C61—41no—
22C2×Q8×C61—41no—
23C2×Q8×C61C2311yescharacteristic
24C2×D4×C61D411yescharacteristic
25C22×Dic61—21no—
26C2×Dic122D412yes—
27SD16×C61—41no—
28D8×C61—41no—
29M16×C61—21no—
30C22⋊C4×C61—22no—
31C42×C61D411yescharacteristic
32C22⋊Dic61—22no—
33C22⋊Dic61—21no—
34#11758202—42no—
35#11758200—42no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38#11758196—22no—
39#11758196—22no—
40#11758196—22no—
41C4×Dic61D412yes—
42#11758194—22no—
43C23×C61—21no—
44Q8×C61—22no—
45Q8×C61—21no—
46Q8×C61—41no—
47D4×C61—22no—
48D4×C61—21no—
49D4×C61—41no—
50D4×C61—41no—
51C2×C4×C61—21no—
52C2×C4×C61—42no—
53C2×C4×C61—41no—
54C2×C4×C61C2×D412yes—
55C2×C4×C61C2×D411yescharacteristic
56C2×Dic61—22no—
57C2×Dic61—22no—
58C2×Dic61—81no—
59Dic122—42no—
60C8×C61—41no—
61#92418—42no—
62C22×C61—42no—
63C22×C61—41no—
64C22×C61—41no—
65C22×C61#12011yescharacteristic
66C4×C61—22no—
67C4×C61—21no—
68C4×C61—41no—
69C4×C61—41no—
70Dic61—42no—
71Dic61—42no—
72#2203—611nomaximal, Sylow
73C2×C61—21no—
74C2×C61—81no—
75C2×C61—81no—
76C2×C61B(4,𝔽2)11yescharacteristic
77#563—611no—
78#456—612no—
79#454D6111yescharacteristic
80#356—612no—
81#355—611no—
82C61#220311yescharacteristic, complemented, Sylow
832−1+4C2×D6111yescharacteristic
84#137—1222no—
85AGL(1,ℤ/8)—21no—
86C4⋊Q8—612no—
87#126—1222no—
88#125—1221no—
89#124C2×D6111yescharacteristic
90#123—1221no—
91C22⋊Q8—1222no—
92#104—21no—
93#104—1222no—
94#101—612no—
95#101C2×D6111yescharacteristic
96#41—22no—
97#41—21no—
98#41—41no—
99C2×Q8—41no—
100C2×Q8—612no—
101C2×Q8C22×D6111yescharacteristic
102C2×D4C22⋊D6111yescharacteristic
103C22×C4—1221no—
104Q16—2442no—
105SD16—41no—
106SD16—2442no—
107D8—41no—
108M16—21no—
109M16—1222no—
110C4⋊C4—1222no—
111C4⋊C4—1221no—
112C4⋊C4—1221no—
113C4⋊C4—1222no—
114C4⋊C4—1222no—
115C22⋊C4—22no—
116C22⋊C4—1222no—
117C22⋊C4—1221no—
118C42—612no—
119C42C22⋊D6111yescharacteristic
120C23—21no—
121Q8—21no—
122Q8—22no—
123Q8—41no—
124Q8—2442no—
125D4—21no—
126D4—22no—
127D4—41no—
128D4—41no—
129C2×C4—21no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—1222no—
133C2×C4—1222no—
134C2×C4—4881no—
135C2×C4D4×D6112yes—
136C2×C4C2×C22⋊D6111yescharacteristic
137C8—41no—
138C8—2442no—
139C22—42no—
140C22—41no—
141C22—41no—
142C22#1451974511yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—41no—
147C4—2442no—
148C4—2442no—
149C2—21no—
150C2—81no—
151C2—81no—
152C2#1683994811yescharacteristic
subgroupG/H
centerC2#16839948
commutatorC2×Q8×C61C23
FrattiniC2×Q8C22×D61
FittingC61×#454C2
socleC2×C61B(4,𝔽2)
hypercenter#454D61
hypocenterC61#2203
LCSG ▷ C2×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #16840512C2semidirect
2. #16839945C2semidirect
3. #16839560C2semidirect
4. #16839559C2semidirect
82. C61#2203semidirect