Finite Group Databasebeta

← #21446601

Subgroups — #21446601

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#16839805C211yesmaximal, characteristic
3C2×#14519710C211yesmaximal, characteristic
4#16839718C211yesmaximal, characteristic
5#16839531C211yesmaximal, characteristic
6#16839530C211yesmaximal, characteristic
7C61×#428C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12#14519712C414yescomplemented
13#14519710—21no—
14#14519710—21no—
15#14519710—21no—
16#14519708—21no—
17#14519688—21no—
18C4×#92418—21no—
19C2×M16×C61C2211yescharacteristic
20#117×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22#107×C61—21no—
23#106×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27M16×C61—21no—
28M16×C61C2×C412yes—
29C2×C8×C61—21no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61D411yescharacteristic
33C4⋊C4×C61D411yescharacteristic
34C22⋊C4×C61—21no—
35C42×C61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38#11758194—21no—
39#11758194—21no—
40#11758194C2×C412yes—
41#11758194Q812yes—
42C2×#92418—21no—
43C2×#92418—21no—
44C2×#92418C2×C412yes—
45C2×#92418D411yescharacteristic
46C2×#92418D411yescharacteristic
47C2×#92418Q812yes—
48C23×C61#4111yescharacteristic
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61—41no—
52C2×C4×C61—81no—
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×Q811yescharacteristic
57C2×C4×C61C2×Q811yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×Dic61—41no—
60C2×Dic61—81no—
61C8×C61—22no—
62#92418—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—41no—
72C4×C61—41no—
73C4×C61—81no—
74C4×C61C2×C4⋊C411yescharacteristic
75C4×C61C4×D411yescharacteristic
76C4×C61C22⋊Q811yescharacteristic
77C4×C61C4⋊Q811yescharacteristic
78Dic61—81no—
79#1952—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—21no—
82C2×C61#38911yescharacteristic
83C2×C61#47211yescharacteristic
84C2×C61#47311yescharacteristic
85C2×#108—611no—
86#428—611no—
87#428D6111yescharacteristic
88C2×#107—611no—
89#405—611no—
90#343—611no—
91#343—611no—
92C61#195211yescharacteristic, complemented, Sylow
93C2×M16—611no—
94C2×M16—611no—
95C2×M16C2×D6111yescharacteristic
96C22×C8—611no—
97#117C2×D6111yescharacteristic
98C2×C4⋊C4—611no—
99C2×C4⋊C4C2×D6111yescharacteristic
100#108—614no—
101#107—21no—
102#107—1221no—
103#107—1221no—
104#107—1221no—
105#106—21no—
106#106—1221no—
107#97—1221no—
108C4×C8—1221no—
109C22×C4—21no—
110C22×C4—1221no—
111C22×C4C22×D6111yescharacteristic
112M16—21no—
113M16—612no—
114M16—612no—
115M16—1221no—
116M16—1221no—
117M16C4×D6112yes—
118C2×C8—21no—
119C2×C8—612no—
120C2×C8—611no—
121C2×C8—611no—
122C2×C8—612no—
123C2×C8—1221no—
124C2×C8—1221no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4C22⋊D6111yescharacteristic
130C4⋊C4C22⋊D6111yescharacteristic
131C22⋊C4—21no—
132C42—21no—
133C23#1175822411yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—4881no—
139C2×C4—2441no—
140C2×C4C2×C4×D6111yescharacteristic
141C2×C4#1175822211yescharacteristic
142C2×C4D4×D6111yescharacteristic
143C2×C4Q8×D6111yescharacteristic
144C2×C4Q8×D6111yescharacteristic
145C2×C4C2×C22⋊D6111yescharacteristic
146C8—22no—
147C8—612no—
148C8—612no—
149C8—1222no—
150C8—1222no—
151C22—21no—
152C22—21no—
153C22#1451974211yescharacteristic
154C22#1451974911yescharacteristic
155C22#1451976711yescharacteristic
156C4—41no—
157C4—41no—
158C4—81no—
159C4—4881no—
160C4C4⋊C4×D6111yescharacteristic
161C4C4×C22⋊D6111yescharacteristic
162C4#1451975511yescharacteristic
163C4#1451977511yescharacteristic
164C2—21no—
165C2—21no—
166C2#1683965711yescharacteristic
167C2#1684003011yescharacteristic
168C2#1684003511yescharacteristic
subgroupG/H
centerC22#14519749
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#428C2
socleC22×C61#121
hypercenter#428D61
hypocenterC61#1952
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
12. #14519712C4semidirect
92. C61#1952semidirect