Finite Group Databasebeta

← #21447288

Subgroups — #21447288

Order 7808.

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

normal subgroups only

This group has 184 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#16839810C211yesmaximal, characteristic
2#16839770C211yesmaximal, characteristic
3#16839770C211yesmaximal, characteristic
4C2×#14519695C211yesmaximal, characteristic
5#16839532C211yesmaximal, characteristic
6#16839532C211yesmaximal, characteristic
7C61×H(3,ℤ/4)C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11C2×#11758194C2211yescharacteristic
12#14519712—22no—
13#14519700—22no—
14#14519700—22no—
15#14519695—22no—
16C2×M16×C61C2211yescharacteristic
17#117×C61C2211yescharacteristic
18#117×C61C2211yescharacteristic
19C22×C4×C61C2311yescharacteristic
20C22×Dic61—21no—
21C2×Dic122—21no—
22C2×Dic122—21no—
23C2×Dic122—21no—
24C2×Dic122—21no—
25C2×Dic122—21no—
26C2×Dic122D412yes—
27M16×C61—21no—
28M16×C61—21no—
29C2×C8×C61—21no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—21no—
32C22⋊C4×C61—21no—
33C22⋊C4×C61—21no—
34C42×C61—21no—
35C42×C61—21no—
36#11758194—21no—
37#11758194—21no—
38#11758194—21no—
39#11758194—21no—
40#11758194—21no—
41#11758194—21no—
42C2×#92418—21no—
43C2×#92418—21no—
44C2×#92418D412yes—
45C23×C61#4111yescharacteristic
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61C2×D411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×C4×C61#4111yescharacteristic
51C2×C4×C61#4111yescharacteristic
52C2×C4×C61#4111yescharacteristic
53C2×C4×C61#4111yescharacteristic
54C2×Dic61—22no—
55C2×Dic61—41no—
56C2×Dic61—41no—
57Dic122—22no—
58Dic122—22no—
59Dic122—41no—
60Dic122—41no—
61C8×C61—41no—
62#92418—22no—
63#92418—41no—
64#92418—41no—
65C22×C61—41no—
66C22×C61#12311yescharacteristic
67C22×C61#12411yescharacteristic
68C22×C61#12611yescharacteristic
69C4×C61—81no—
70C4×C61—81no—
71C4×C61#12111yescharacteristic
72C4×C61#12311yescharacteristic
73C4×C61#12311yescharacteristic
74C4×C61#12611yescharacteristic
75Dic61—42no—
76#2082—611nomaximal, Sylow
77C2×C61—21no—
78C2×C61—21no—
79C2×C61—21no—
80C2×C61#39711yescharacteristic
81#430—611no—
82#419—611no—
83#419—611no—
84C2×#101—611no—
85#344—611no—
86#344—611no—
87H(3,ℤ/4)D6111yescharacteristic
88C61#208211yescharacteristic, complemented, Sylow
89C22×Q8—611no—
90C2×M16—611no—
91C2×M16—611no—
92C2×M16—611no—
93C2×M16C2×D6111yescharacteristic
94#117C2×D6111yescharacteristic
95#117C2×D6111yescharacteristic
96#108—1222no—
97#103—1222no—
98#103—1222no—
99#101—1222no—
100C2×Q8—612no—
101C2×Q8—1221no—
102C2×Q8—1221no—
103C2×Q8—1221no—
104C2×Q8—1221no—
105C2×Q8—1221no—
106C22×C4—1221no—
107C22×C4C22×D6111yescharacteristic
108M16—21no—
109M16—21no—
110M16—1221no—
111M16—1221no—
112M16—1221no—
113M16—1221no—
114M16—1221no—
115M16—1221no—
116C2×C8—21no—
117C2×C8—612no—
118C2×C8—1221no—
119C2×C8—1221no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C22⋊C4—21no—
123C22⋊C4—21no—
124C42—21no—
125C42—21no—
126C23#1175822411yescharacteristic
127Q8—1222no—
128Q8—1222no—
129Q8—2441no—
130Q8—2441no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—1222no—
134C2×C4—2441no—
135C2×C4—2441no—
136C2×C4#1175822211yescharacteristic
137C2×C4#1175822211yescharacteristic
138C2×C4#1175822211yescharacteristic
139C2×C4D4×D6111yescharacteristic
140C2×C4D4×D6111yescharacteristic
141C2×C4#1175822611yescharacteristic
142C8—41no—
143C8—1222no—
144C8—2441no—
145C8—2441no—
146C22—41no—
147C22#1451975911yescharacteristic
148C22#1451976311yescharacteristic
149C22#1451977211yescharacteristic
150C4—81no—
151C4—81no—
152C4—2442no—
153C4#1451975011yescharacteristic
154C4#1451976211yescharacteristic
155C4#1451976211yescharacteristic
156C4#1451977111yescharacteristic
157C2—21no—
158C2—21no—
159C2—21no—
160C2#1683969111yescharacteristic
subgroupG/H
centerC2#16839691
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×H(3,ℤ/4)C2
socleC2×C61#397
hypercenterH(3,ℤ/4)D61
hypocenterC61#2082
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
88. C61#2082semidirect