Finite Group Databasebeta

← #22610708

Subgroups — #22610708

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#17988630C211yesmaximal, characteristic
3C2×#14556522C211yesmaximal, characteristic
4#17988543C211yesmaximal, characteristic
5#17988356C211yesmaximal, characteristic
6#17988355C211yesmaximal, characteristic
7#428×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12#14556526C414yescomplemented
13#14556524—21no—
14#14556522—21no—
15#14556522—21no—
16#14556522—21no—
17#14556502—21no—
18C4×#10596831—21no—
19C2×M16×C73C2211yescharacteristic
20#117×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22#107×C73—21no—
23#106×C73—21no—
24C22×Dic73—21no—
25#11924012—21no—
26#11924012—21no—
27#11924012C2×C412yes—
28#11924012Q812yes—
29C2×#10596831—21no—
30C2×#10596831—21no—
31C2×#10596831C2×C412yes—
32C2×#10596831D411yescharacteristic
33C2×#10596831D411yescharacteristic
34C2×#10596831Q812yes—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C22×C4×C73—21no—
38C22×C4×C73C2311yescharacteristic
39M16×C73—21no—
40M16×C73C2×C412yes—
41C2×C8×C73—21no—
42C4⋊C4×C73—21no—
43C4⋊C4×C73—21no—
44C4⋊C4×C73D411yescharacteristic
45C4⋊C4×C73D411yescharacteristic
46C22⋊C4×C73—21no—
47C42×C73—21no—
48C23×C73#4111yescharacteristic
49C2×C4×C73—21no—
50C2×C4×C73—21no—
51C2×C4×C73—41no—
52C2×C4×C73—81no—
53C2×C4×C73C22×C411yescharacteristic
54C2×C4×C73C2×D411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×Q811yescharacteristic
57C2×C4×C73C2×Q811yescharacteristic
58C2×C4×C73#4111yescharacteristic
59C2×Dic73—41no—
60C2×Dic73—81no—
61C8×C73—22no—
62#10596831—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—41no—
72C4×C73—41no—
73C4×C73—81no—
74C4×C73C2×C4⋊C411yescharacteristic
75C4×C73C4×D411yescharacteristic
76C4×C73C22⋊Q811yescharacteristic
77C4×C73C4⋊Q811yescharacteristic
78Dic73—81no—
79C2×C73—21no—
80C2×C73—21no—
81C2×C73#38911yescharacteristic
82C2×C73#47111yescharacteristic
83C2×C73#47111yescharacteristic
84#1951—731nomaximal, Sylow
85C73#195111yescharacteristic, complemented, Sylow
86C2×#108—731no—
87#428—731no—
88#428D7311yescharacteristic
89C2×#106—731no—
90#405—731no—
91#343—731no—
92#343—731no—
93C2×M16—731no—
94C2×M16—731no—
95C2×M16C2×D7311yescharacteristic
96C22×C8—731no—
97#117C2×D7311yescharacteristic
98C2×C4⋊C4—731no—
99C2×C4⋊C4C2×D7311yescharacteristic
100#108—734no—
101#107—21no—
102#107—1461no—
103#106—21no—
104#106—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—732no—
114M16—732no—
115M16—1461no—
116M16—1461no—
117M16C4×D7312yes—
118C2×C8—21no—
119C2×C8—732no—
120C2×C8—731no—
121C2×C8—731no—
122C2×C8—732no—
123C2×C8—1461no—
124C2×C8—1461no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4C22⋊D7311yescharacteristic
130C4⋊C4C22⋊D7311yescharacteristic
131C22⋊C4—21no—
132C42—21no—
133C23#1192402711yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—2921no—
139C2×C4—5841no—
140C2×C4C2×C4×D7311yescharacteristic
141C2×C4D4×D7311yescharacteristic
142C2×C4C2×C22⋊D7311yescharacteristic
143C2×C4Q8×D7311yescharacteristic
144C2×C4Q8×D7311yescharacteristic
145C2×C4#1192402811yescharacteristic
146C8—22no—
147C8—732no—
148C8—732no—
149C8—1462no—
150C8—1462no—
151C22—21no—
152C22—21no—
153C22#1455655611yescharacteristic
154C22#1455656311yescharacteristic
155C22#1455658111yescharacteristic
156C4—41no—
157C4—41no—
158C4—81no—
159C4—5841no—
160C4C4⋊C4×D7311yescharacteristic
161C4C4×C22⋊D7311yescharacteristic
162C4#1455656911yescharacteristic
163C4#1455658911yescharacteristic
164C2—21no—
165C2—21no—
166C2#1798848211yescharacteristic
167C2#1798884811yescharacteristic
168C2#1798885211yescharacteristic
subgroupG/H
centerC22#14556563
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#428×C73C2
socleC22×C73#121
hypercenter#428D73
hypocenterC73#1951
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
12. #14556526C4semidirect
85. C73#1951semidirect