Finite Group Databasebeta

← #22610596

Subgroups — #22610596

Order 9344.

232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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#17988630C211yesmaximal, characteristic, complemented
2C2×#14556512C211yesmaximal, characteristic
3C2×#14556508C211yesmaximal, characteristic
4#17988543C211yesmaximal, characteristic, complemented
5#17988355C211yesmaximal, characteristic, complemented
6#17988351C211yesmaximal, characteristic, complemented
7#418×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12#14556524—21no—
13#14556522—21no—
14#14556512—21no—
15#14556512—21no—
16#14556508C414yescomplemented
17#14556502—21no—
18C4×#10596831—21no—
19C22×D4×C73C2211yescharacteristic
20C2×M16×C73C2211yescharacteristic
21#117×C73C2211yescharacteristic
22#102×C73—21no—
23#102×C73—21no—
24C22×Dic73—21no—
25#11924012—21no—
26#11924012—21no—
27#11924012C2×C412yes—
28#11924012C2×C412yes—
29C2×#10596831—21no—
30C2×#10596831—21no—
31C2×#10596831—21no—
32C2×#10596831—21no—
33C2×#10596831D411yescharacteristic
34C2×#10596831D411yescharacteristic
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C24×C73—21no—
38C2×D4×C73—21no—
39C2×D4×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73—21no—
42C2×D4×C73—21no—
43C2×D4×C73C2×C412yes—
44C22×C4×C73C2311yescharacteristic
45M16×C73—21no—
46M16×C73—21no—
47C2×C8×C73—21no—
48C4⋊C4×C73D411yescharacteristic
49C4⋊C4×C73D411yescharacteristic
50C22⋊C4×C73—21no—
51C42×C73—21no—
52C23×C73—22no—
53C23×C73—41no—
54C23×C73—41no—
55C23×C73—81no—
56C23×C73—81no—
57C23×C73#4111yescharacteristic
58D4×C73—22no—
59D4×C73—22no—
60D4×C73—41no—
61D4×C73—41no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73C22×C411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73#4111yescharacteristic
68C2×C4×C73#4111yescharacteristic
69C2×C4×C73#4111yescharacteristic
70C2×Dic73—41no—
71C2×Dic73—81no—
72C8×C73—41no—
73#10596831—22no—
74#10596831—22no—
75#10596831—21no—
76#10596831—21no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73—42no—
80C22×C73—82no—
81C22×C73—82no—
82C22×C73—81no—
83C22×C73—81no—
84C22×C73#11711yescharacteristic
85C22×C73#12111yescharacteristic
86C22×C73#12611yescharacteristic
87C4×C73—41no—
88C4×C73—41no—
89C4×C73C4×D411yescharacteristic
90C4×C73C4×D411yescharacteristic
91C4×C73#12311yescharacteristic
92C4×C73#12411yescharacteristic
93Dic73—81no—
94C2×C73—21no—
95C2×C73—21no—
96C2×C73—82no—
97C2×C73#38811yescharacteristic
98C2×C73#47111yescharacteristic
99C2×C73#47211yescharacteristic
100#1931—731nomaximal, Sylow
101C73#193111yescharacteristic, complemented, Sylow
102#428—731no—
103#418D7311yescharacteristic
104C2×#102—731no—
105C2×#100—731no—
106#405—731no—
107#343—731no—
108#341—731no—
109C22×D4C2×D7311yescharacteristic
110C2×M16—731no—
111C2×M16—731no—
112C2×M16C2×D7311yescharacteristic
113C22×C8—731no—
114#117C2×D7311yescharacteristic
115C2×C4⋊C4—731no—
116#107—1461no—
117#106—1461no—
118#102—21no—
119#102—21no—
120#102—1461no—
121#102—1461no—
122#100—734no—
123#97—1461no—
124C4×C8—1461no—
125C24—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4C4×D7312yes—
132C22×C4—1461no—
133C22×C4C22×D7311yescharacteristic
134M16—21no—
135M16—21no—
136M16—732no—
137M16—732no—
138M16—1461no—
139M16—1461no—
140C2×C8—21no—
141C2×C8—731no—
142C2×C8—731no—
143C2×C8—1461no—
144C2×C8—1461no—
145C2×C8—1461no—
146C2×C8—1461no—
147C4⋊C4—1461no—
148C4⋊C4—1461no—
149C4⋊C4C22⋊D7311yescharacteristic
150C4⋊C4C22⋊D7311yescharacteristic
151C22⋊C4—21no—
152C42—21no—
153C23—22no—
154C23—41no—
155C23—41no—
156C23—81no—
157C23—81no—
158C23#1192402711yescharacteristic
159D4—22no—
160D4—22no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—2921no—
166C2×C4—5841no—
167C2×C4C2×C4×D7311yescharacteristic
168C2×C4D4×D7311yescharacteristic
169C2×C4C2×C22⋊D7311yescharacteristic
170C2×C4#1192402711yescharacteristic
171C2×C4#1192402711yescharacteristic
172C2×C4#1192402811yescharacteristic
173C8—41no—
174C8—1462no—
175C8—1462no—
176C8—1461no—
177C8—1461no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—82no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22#1455654711yescharacteristic
186C22#1455656311yescharacteristic
187C22#1455658411yescharacteristic
188C4—41no—
189C4—41no—
190C4—5841no—
191C4#1455655111yescharacteristic
192C4C4×C22⋊D7311yescharacteristic
193C4#1455657311yescharacteristic
194C4#1455657811yescharacteristic
195C2—21no—
196C2—21no—
197C2—82no—
198C2#1798848111yescharacteristic
199C2#1798884811yescharacteristic
200C2#1798885511yescharacteristic
subgroupG/H
centerC22#14556563
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#418×C73C2
socleC22×C73#121
hypercenter#418D73
hypocenterC73#1931
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17988630C2semidirect
4. #17988543C2semidirect
5. #17988355C2semidirect
6. #17988351C2semidirect
16. #14556508C4semidirect
101. C73#1931semidirect