Finite Group Databasebeta

← #22610715

Subgroups — #22610715

Order 9344.

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×#14556526C211yesmaximal, characteristic
2#17988629C211yesmaximal, characteristic
3#17988627C211yesmaximal, characteristic
4C2×#14556524C211yesmaximal, characteristic
5#17988545C211yesmaximal, characteristic
6#17988355C211yesmaximal, characteristic
7#343×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9C22×#10596831C2211yescharacteristic
10#14556550C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12#14556526C414yescomplemented
13#14556525—21no—
14#14556524—21no—
15#14556524—21no—
16#14556524—21no—
17#14556523—21no—
18#14556522—21no—
19#14556501—21no—
20C8×Dic73—21no—
21C2×M16×C73C2211yescharacteristic
22C2×M16×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24C22×Dic73—21no—
25#11924012—21no—
26#11924012C2×C412yes—
27C2×#10596831—21no—
28C2×#10596831C2×C412yes—
29C2×#10596831D411yescharacteristic
30C2×#10596831D411yescharacteristic
31C2×#10596831Q812yes—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73D411yescharacteristic
35C4⋊Dic73D411yescharacteristic
36C22⋊Dic73—21no—
37C4×Dic73—21no—
38C22×C4×C73—21no—
39C22×C4×C73C2311yescharacteristic
40M16×C73—21no—
41M16×C73—21no—
42M16×C73C2×C412yes—
43M16×C73Q812yes—
44C2×C8×C73—21no—
45C2×C8×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C23×C73#4111yescharacteristic
49C2×C4×C73—41no—
50C2×C4×C73—81no—
51C2×C4×C73C22×C411yescharacteristic
52C2×C4×C73C2×D411yescharacteristic
53C2×C4×C73C2×D411yescharacteristic
54C2×C4×C73C2×Q811yescharacteristic
55C2×C4×C73C2×Q811yescharacteristic
56C2×C4×C73#4111yescharacteristic
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73—41no—
60C2×Dic73—81no—
61C8×C73—22no—
62C8×C73—22no—
63#10596831—22no—
64#10596831C4⋊C412yes—
65#10596831C4⋊C412yes—
66C22×C73—21no—
67C22×C73—21no—
68C22×C73C4×Q811yescharacteristic
69C22×C73#12111yescharacteristic
70C22×C73#12511yescharacteristic
71C4×C73—81no—
72C4×C73C2×C4⋊C411yescharacteristic
73C4×C73C4×D411yescharacteristic
74C4×C73C22⋊Q811yescharacteristic
75C4×C73C4⋊Q811yescharacteristic
76Dic73—41no—
77Dic73—41no—
78Dic73—81no—
79C2×C73—21no—
80C2×C73—21no—
81C2×C73#38911yescharacteristic
82C2×C73#47211yescharacteristic
83C2×C73#47311yescharacteristic
84#1952—731nomaximal, Sylow
85C73#195211yescharacteristic, complemented, Sylow
86C2×#108—731no—
87#428—731no—
88#428—731no—
89C2×#107—731no—
90#405—731no—
91#343—731no—
92#343D7311yescharacteristic
93C2×M16—731no—
94C2×M16C2×D7311yescharacteristic
95C2×M16C2×D7311yescharacteristic
96C22×C8—731no—
97#117—731no—
98C2×C4⋊C4—731no—
99C2×C4⋊C4C2×D7311yescharacteristic
100#108—734no—
101#107—1461no—
102#107—1461no—
103#107—1461no—
104#107—1461no—
105#106—1461no—
106#106—1461no—
107#97—1461no—
108C4×C8—1461no—
109C22×C4—21no—
110C22×C4—1461no—
111C22×C4C22×D7311yescharacteristic
112M16—21no—
113M16—21no—
114M16—732no—
115M16—1461no—
116M16Dic14612yes—
117M16C4×D7312yes—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—732no—
121C2×C8—731no—
122C2×C8—731no—
123C2×C8—732no—
124C2×C8—1461no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—731no—
128C4⋊C4—731no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C22⋊C4—1461no—
132C42—1461no—
133C23#1192402811yescharacteristic
134C2×C4—41no—
135C2×C4—81no—
136C2×C4—2921no—
137C2×C4—5841no—
138C2×C4—1461no—
139C2×C4—1461no—
140C2×C4C2×C4×D7311yescharacteristic
141C2×C4D4×D7311yescharacteristic
142C2×C4D4×D7311yescharacteristic
143C2×C4Q8×D7311yescharacteristic
144C2×C4C2×Dic14611yescharacteristic
145C2×C4#1192402711yescharacteristic
146C8—22no—
147C8—22no—
148C8—732no—
149C8—732no—
150C8—1462no—
151C22—21no—
152C22—21no—
153C22C4×Dic14611yescharacteristic
154C22#1455656411yescharacteristic
155C22#1455658111yescharacteristic
156C4—81no—
157C4—2921no—
158C4—2921no—
159C4—5841no—
160C4C4⋊C4×D7311yescharacteristic
161C4#1455655111yescharacteristic
162C4#1455656811yescharacteristic
163C4#1455659011yescharacteristic
164C2—21no—
165C2—21no—
166C2#1798848411yescharacteristic
167C2#1798885611yescharacteristic
168C2#1798886111yescharacteristic
subgroupG/H
centerC22#14556564
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#343×C73C2
socleC22×C73#121
hypercenter#343D73
hypocenterC73#1952
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
12. #14556526C4semidirect
85. C73#1952semidirect