Finite Group Databasebeta

← #21446598

Subgroups — #21446598

Order 7808.

196 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14519712C211yesmaximal, characteristic
2#16839804C211yesmaximal, characteristic
3#16839802C211yesmaximal, characteristic
4C2×#14519708C211yesmaximal, characteristic
5#16839720C211yesmaximal, characteristic
6#16839530C211yesmaximal, characteristic
7C61×#343C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519736C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519712C414yescomplemented
13#14519711—21no—
14#14519710—21no—
15#14519709—21no—
16#14519708—21no—
17#14519708—21no—
18#14519708—21no—
19#14519687—21no—
20C8×Dic61—21no—
21C2×M16×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27M16×C61—21no—
28M16×C61—21no—
29M16×C61C2×C412yes—
30M16×C61Q812yes—
31C2×C8×C61—21no—
32C2×C8×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C22⋊Dic61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61D411yescharacteristic
39C4⋊Dic61D411yescharacteristic
40C4×Dic61—21no—
41#11758194—21no—
42#11758194C2×C412yes—
43C2×#92418—21no—
44C2×#92418C2×C412yes—
45C2×#92418D411yescharacteristic
46C2×#92418D411yescharacteristic
47C2×#92418Q812yes—
48C23×C61#4111yescharacteristic
49C2×C4×C61—41no—
50C2×C4×C61—81no—
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×Q811yescharacteristic
55C2×C4×C61C2×Q811yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—41no—
60C2×Dic61—81no—
61C8×C61—22no—
62C8×C61—22no—
63#92418—22no—
64#92418C4⋊C412yes—
65#92418C4⋊C412yes—
66C22×C61—21no—
67C22×C61—21no—
68C22×C61C4×Q811yescharacteristic
69C22×C61#12111yescharacteristic
70C22×C61#12511yescharacteristic
71C4×C61—81no—
72C4×C61C2×C4⋊C411yescharacteristic
73C4×C61C4×D411yescharacteristic
74C4×C61C22⋊Q811yescharacteristic
75C4×C61C4⋊Q811yescharacteristic
76Dic61—41no—
77Dic61—41no—
78Dic61—81no—
79#1951—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—21no—
82C2×C61#38911yescharacteristic
83C2×C61#47111yescharacteristic
84C2×C61#47111yescharacteristic
85C2×#108—611no—
86#428—611no—
87#428—611no—
88C2×#106—611no—
89#405—611no—
90#343—611no—
91#343D6111yescharacteristic
92C61#195111yescharacteristic, complemented, Sylow
93C2×M16—611no—
94C2×M16C2×D6111yescharacteristic
95C2×M16C2×D6111yescharacteristic
96C22×C8—611no—
97#117—611no—
98C2×C4⋊C4—611no—
99C2×C4⋊C4C2×D6111yescharacteristic
100#108—614no—
101#107—1221no—
102#107—1221no—
103#106—1221no—
104#106—1221no—
105#106—1221no—
106#106—1221no—
107#97—1221no—
108C4×C8—1221no—
109C22×C4—21no—
110C22×C4—1221no—
111C22×C4C22×D6111yescharacteristic
112M16—21no—
113M16—21no—
114M16—612no—
115M16—1221no—
116M16Dic12212yes—
117M16C4×D6112yes—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—612no—
121C2×C8—611no—
122C2×C8—611no—
123C2×C8—612no—
124C2×C8—1221no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—611no—
128C4⋊C4—611no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C22⋊C4—1221no—
132C42—1221no—
133C23#1175822211yescharacteristic
134C2×C4—41no—
135C2×C4—81no—
136C2×C4—1221no—
137C2×C4—1221no—
138C2×C4—4881no—
139C2×C4—2441no—
140C2×C4C2×Dic12211yescharacteristic
141C2×C4C2×C4×D6111yescharacteristic
142C2×C4D4×D6111yescharacteristic
143C2×C4D4×D6111yescharacteristic
144C2×C4#1175822411yescharacteristic
145C2×C4Q8×D6111yescharacteristic
146C8—22no—
147C8—22no—
148C8—612no—
149C8—612no—
150C8—1222no—
151C22—21no—
152C22—21no—
153C22C4×Dic12211yescharacteristic
154C22#1451975011yescharacteristic
155C22#1451976711yescharacteristic
156C4—81no—
157C4—4881no—
158C4—2441no—
159C4—2441no—
160C4C4⋊C4×D6111yescharacteristic
161C4#1451973711yescharacteristic
162C4#1451975411yescharacteristic
163C4#1451977611yescharacteristic
164C2—21no—
165C2—21no—
166C2#1683965911yescharacteristic
167C2#1684002411yescharacteristic
168C2#1684002811yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61#121
hypercenter#343D61
hypocenterC61#1951
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
12. #14519712C4semidirect
92. C61#1951semidirect