Finite Group Databasebeta

← #22611457

Subgroups — #22611457

Order 9344.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556525C211yesmaximal, characteristic, complemented
2C2×#14556524C211yesmaximal, characteristic, complemented
3C2×#14556512C211yesmaximal, characteristic
4#17988490C211yesmaximal, characteristic
5#17988456C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#102×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C2×C4⋊Dic73C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924007—22no—
12C2×C22⋊Dic73—22no—
13C2×C4×Dic73C2211yescharacteristic
14#14556525—22no—
15#14556524—22no—
16#14556512—22no—
17C22×D4×C73C2211yescharacteristic
18C22×C8×C73C2211yescharacteristic
19C2×C4⋊C4×C73C2211yescharacteristic
20#102×C73—22no—
21C22×Dic73—21no—
22C22×Dic73—21no—
23C22×Dic73D412yes—
24C2×#10596831—21no—
25C2×#10596831—21no—
26C2×#10596831D412yes—
27C4⋊Dic73—21no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31#11924007—44no—
32C22⋊Dic73—44no—
33C4×Dic73—21no—
34C4×Dic73—21no—
35C24×C73—21no—
36C2×D4×C73—21no—
37C2×D4×C73—21no—
38C2×D4×C73—21no—
39C2×D4×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73Q812yes—
42C22×C4×C73—21no—
43C22×C4×C73C2311yescharacteristic
44C2×C8×C73—21no—
45C2×C8×C73—21no—
46C2×C8×C73D412yes—
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C23×C73—22no—
50C23×C73—41no—
51C23×C73—41no—
52C23×C73—42no—
53C23×C73—42no—
54C23×C73C2×D411yescharacteristic
55D4×C73—22no—
56D4×C73—22no—
57D4×C73—41no—
58D4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73—42no—
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73C2×Q811yescharacteristic
64C2×C4×C73#4111yescharacteristic
65C2×C4×C73#4111yescharacteristic
66C2×C4×C73#4111yescharacteristic
67C2×Dic73—22no—
68C2×Dic73—22no—
69C2×Dic73—41no—
70C2×Dic73—41no—
71C2×Dic73—42no—
72C2×Dic73—42no—
73C2×Dic73D814yes—
74C8×C73—22no—
75#10596831—22no—
76C22×C73—42no—
77C22×C73—44no—
78C22×C73—82no—
79C22×C73—81no—
80C22×C73—81no—
81C22×C73C22⋊Q811yescharacteristic
82C22×C73#12311yescharacteristic
83C22×C73#12711yescharacteristic
84C22×C73C2×D812yes—
85C22×C73#13712yes—
86C4×C73—81no—
87C4×C73C22⋊Q811yescharacteristic
88C4×C73C22⋊Q811yescharacteristic
89C4×C73#12311yescharacteristic
90C4×C73#12311yescharacteristic
91Dic73—24no—
92Dic73—81no—
93Dic73—81no—
94C2×C73—82no—
95C2×C73#39911yescharacteristic
96C2×C73#47412yes—
97C2×C73#48012yes—
98C2×C73#49311yescharacteristic
99C2×C73#49711yescharacteristic
100#2093—731nomaximal, Sylow
101C73#209311yescharacteristic, complemented, Sylow
102C2×#107—731no—
103C2×#107—731no—
104C2×#102—731no—
105C2×#102D7311yescharacteristic
106#390—731no—
107#384—731no—
108#336—731no—
109C22×D4C2×D7311yescharacteristic
110C22×C8—731no—
111C22×C8C2×D7311yescharacteristic
112C2×C4⋊C4—731no—
113C2×C4⋊C4—731no—
114C2×C4⋊C4—1462no—
115C2×C4⋊C4C2×D7311yescharacteristic
116C2×C22⋊C4—1462no—
117C2×C42—731no—
118#107—1462no—
119#107—1462no—
120#102—22no—
121#102—1462no—
122C24—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4Dic14612yes—
129C22×C4—21no—
130C22×C4—732no—
131C22×C4—1461no—
132C22×C4—1461no—
133C22×C4C22×D7311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—732no—
137C2×C8—1461no—
138C2×C8—1461no—
139C2×C8C22⋊D7312yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—2924no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C22⋊C4—2924no—
148C42—1461no—
149C42—1461no—
150C23—22no—
151C23—41no—
152C23—41no—
153C23—42no—
154C23—42no—
155C23D4×D7311yescharacteristic
156D4—22no—
157D4—22no—
158D4—41no—
159D4—41no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—2921no—
163C2×C4—2921no—
164C2×C4—2922no—
165C2×C4—2922no—
166C2×C4—734no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4D4×D7311yescharacteristic
170C2×C4C2×C22⋊D7311yescharacteristic
171C2×C4C2×Dic14611yescharacteristic
172C2×C4#1192402711yescharacteristic
173C2×C4#1192402711yescharacteristic
174C2×C4#1192402811yescharacteristic
175C8—22no—
176C8—1462no—
177C22—44no—
178C22—42no—
179C22—82no—
180C22—81no—
181C22—81no—
182C22#1455656811yescharacteristic
183C22#1455657311yescharacteristic
184C22#1455658711yescharacteristic
185C22D8×D7312yes—
186C22#1455662012yes—
187C4—81no—
188C4—5841no—
189C4—5841no—
190C4—1464no—
191C4#1455656811yescharacteristic
192C4#1455657011yescharacteristic
193C4#1455657211yescharacteristic
194C4#1455657311yescharacteristic
195C2—82no—
196C2#1798852311yescharacteristic
197C2#1798886512yes—
198C2#1798889912yes—
199C2#1798896211yescharacteristic
200C2#1798897811yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#102×C73C2
socleC23×C73C2×D4
hypercenterC2×#102D73
hypocenterC73#2093
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14556525C2semidirect
2. C2×#14556524C2semidirect
5. #17988456C2semidirect
6. #17988341C2semidirect
101. C73#2093semidirect