Finite Group Databasebeta

← #22611461

Subgroups — #22611461

Order 9344.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556522C211yesmaximal, characteristic, complemented
2C2×#14556513C211yesmaximal, characteristic
3C2×#14556511C211yesmaximal, characteristic
4#17988488C211yesmaximal, characteristic
5#17988456C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#106×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C22×#10596831C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924007—22no—
12C2×#11924005—22no—
13C2×C4×Dic73C2211yescharacteristic
14#14556522—22no—
15#14556513—22no—
16#14556511—22no—
17C22×C8×C73C2211yescharacteristic
18C2×C4⋊C4×C73C2211yescharacteristic
19C2×C4⋊C4×C73C2211yescharacteristic
20#106×C73—22no—
21C23×D73—21no—
22C2×D292—21no—
23C2×D292—21no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292—21no—
27C2×D292Q812yes—
28C22×Dic73—21no—
29C22×Dic73D412yes—
30C2×#10596831—21no—
31C2×#10596831—21no—
32C2×#10596831D412yes—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35#11924007—44no—
36#11924005—44no—
37C4×Dic73—21no—
38C4×Dic73—21no—
39C22×C4×C73—21no—
40C22×C4×C73—21no—
41C22×C4×C73C2311yescharacteristic
42C2×C8×C73—21no—
43C2×C8×C73—21no—
44C2×C8×C73D412yes—
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C23×C73C2×D411yescharacteristic
50C22×D73—22no—
51C22×D73—41no—
52C22×D73—41no—
53C22×D73—42no—
54C22×D73—42no—
55C2×C4×C73—41no—
56C2×C4×C73—41no—
57C2×C4×C73—42no—
58C2×C4×C73—42no—
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×Q811yescharacteristic
62C2×C4×C73#4111yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×C4×C73#4111yescharacteristic
65C2×Dic73—22no—
66C2×Dic73—22no—
67C2×Dic73—41no—
68C2×Dic73—42no—
69C2×Dic73SD1614yes—
70D292—22no—
71D292—22no—
72D292—41no—
73D292—41no—
74C8×C73—22no—
75#10596831—22no—
76C22×C73C22⋊Q811yescharacteristic
77C22×C73#12311yescharacteristic
78C22×C73#12711yescharacteristic
79C22×C73C2×SD1612yes—
80C22×C73AGL(1,ℤ/8)12yes—
81C2×D73—42no—
82C2×D73—44no—
83C2×D73—82no—
84C2×D73—81no—
85C2×D73—81no—
86C4×C73—81no—
87C4×C73—81no—
88C4×C73C22⋊Q811yescharacteristic
89C4×C73C22⋊Q811yescharacteristic
90C4×C73#12311yescharacteristic
91C4×C73#12311yescharacteristic
92Dic73—24no—
93Dic73—81no—
94C2×C73#39911yescharacteristic
95C2×C73#47612yes—
96C2×C73#48112yes—
97C2×C73#49211yescharacteristic
98C2×C73#49611yescharacteristic
99D73—82no—
100#2094—731nomaximal, Sylow
101C73#209411yescharacteristic, complemented, Sylow
102C2×#106—731no—
103C2×#106D7311yescharacteristic, complemented
104C2×#102—731no—
105C2×#102—731no—
106#390—731no—
107#384—731no—
108#336—731no—
109C22×D4—731no—
110C22×C8—731no—
111C22×C8C2×D7311yescharacteristic
112C2×C4⋊C4—731no—
113C2×C4⋊C4—1462no—
114C2×C4⋊C4C2×D7311yescharacteristic
115C2×C4⋊C4C2×D7311yescharacteristic
116C2×C22⋊C4—1462no—
117C2×C42—731no—
118#106—22no—
119#106—1462no—
120#102—1462no—
121#102—1462no—
122C24—1461no—
123C2×D4—732no—
124C2×D4—1461no—
125C2×D4—1461no—
126C2×D4—1461no—
127C2×D4—1461no—
128C2×D4—1461no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—732no—
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—21no—
143C4⋊C4—21no—
144C4⋊C4—2924no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C22⋊C4—2924no—
148C42—1461no—
149C42—1461no—
150C23—2921no—
151C23—2921no—
152C23—2922no—
153C23—2922no—
154C23—1462no—
155C23D4×D7311yescharacteristic
156D4—2921no—
157D4—2921no—
158D4—1462no—
159D4—1462no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—2921no—
165C2×C4—2922no—
166C2×C4—734no—
167C2×C4—1462no—
168C2×C4—1462no—
169C2×C4D4×D7311yescharacteristic
170C2×C4C2×C22⋊D7311yescharacteristic
171C2×C4Q8×D7311yescharacteristic
172C2×C4#1192402811yescharacteristic
173C2×C4#1192402811yescharacteristic
174C2×C4#1192402911yescharacteristic
175C8—22no—
176C8—1462no—
177C22—2924no—
178C22—2922no—
179C22—5842no—
180C22—5841no—
181C22—5841no—
182C22#1455656911yescharacteristic
183C22#1455657611yescharacteristic
184C22#1455658711yescharacteristic
185C22SD16×D7312yes—
186C22#1455661812yes—
187C4—81no—
188C4—81no—
189C4—5841no—
190C4—1464no—
191C4#1455656711yescharacteristic
192C4#1455656911yescharacteristic
193C4#1455657411yescharacteristic
194C4#1455657611yescharacteristic
195C2—5842no—
196C2#1798852211yescharacteristic
197C2#1798887612yes—
198C2#1798890712yes—
199C2#1798895811yescharacteristic
200C2#1798897311yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#106×C73C2
socleC23×C73C2×D4
hypercenterC2×#106D73
hypocenterC73#2094
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×#14556522C2semidirect
5. #17988456C2semidirect
6. #17988341C2semidirect
7. C2×#106×C73C2semidirect
101. C73#2094semidirect
103. C2×#106D73semidirect