Finite Group Databasebeta

← #22611103

Subgroups — #22611103

Order 9344.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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#17989144C211yesmaximal, characteristic, complemented
2#17988604C211yesmaximal, characteristic
3#17988561C211yesmaximal, characteristic
4#17988359C211yesmaximal, characteristic, complemented
5#17988347C211yesmaximal, characteristic, complemented
6#17988344C211yesmaximal, characteristic, complemented
7C2×#104×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9#14556591—21no—
10#14556583—21no—
11#14556570—22no—
12C4×Dic146—22no—
13#14556550C2211yescharacteristic
14#14556550C2211yescharacteristic
15#14556550C2211yescharacteristic
16#14556518—22no—
17#14556506—22no—
18C2×#41×C73C2211yescharacteristic
19C2×M16×C73C2211yescharacteristic
20C2×C42×C73C2211yescharacteristic
21#104×C73—21no—
22#104×C73—21no—
23C2×Dic146—22no—
24#11924012—21no—
25#11924012—21no—
26C2×#10596831—21no—
27C4⋊Dic73—22no—
28C4⋊Dic73—21no—
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31#11924007—24no—
32C22⋊Dic73—21no—
33C22⋊Dic73—21no—
34C22⋊Dic73D412yes—
35C4×Dic73—21no—
36C4×Dic73—21no—
37C4×Dic73D412yes—
38#41×C73—21no—
39#41×C73—21no—
40#41×C73—21no—
41#41×C73—21no—
42C2×Q8×C73Q811yescharacteristic, complemented
43C2×D4×C73—21no—
44C2×D4×C73Q811yescharacteristic, complemented
45C22×C4×C73—21no—
46C22×C4×C73—21no—
47C22×C4×C73C2311yescharacteristic
48M16×C73—21no—
49M16×C73—21no—
50C2×C8×C73—21no—
51C42×C73—21no—
52C42×C73D411yescharacteristic
53C42×C73D411yescharacteristic
54C23×C73—21no—
55C23×C73C2×D411yescharacteristic
56Q8×C73—21no—
57Q8×C73—21no—
58D4×C73—21no—
59D4×C73—21no—
60D4×C73—41no—
61D4×C73—41no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—42no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×Q811yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—41no—
77Dic146—44no—
78C8×C73—41no—
79#10596831—41no—
80C22×C73—41no—
81C22×C73—41no—
82C22×C73—81no—
83C22×C73#12011yescharacteristic
84C22×C73C22⋊Q811yescharacteristic
85C22×C73#12411yescharacteristic
86C4×C73—22no—
87C4×C73—41no—
88C4×C73—41no—
89C4×C73C22⋊Q811yescharacteristic
90C4×C73C22⋊Q811yescharacteristic
91C4×C73#12411yescharacteristic
92C4×C73#12411yescharacteristic
93Dic73—42no—
94Dic73—42no—
95Dic73—81no—
96C2×C73—21no—
97C2×C73—21no—
98C2×C73—21no—
99C2×C73—81no—
100C2×C73#39311yescharacteristic
101#2031—731nomaximal, Sylow
102C73#203111yescharacteristic, complemented, Sylow
103#533—731no—
104#421—731no—
105C2×#104D7311yescharacteristic
106#410—731no—
107#344—731no—
108#339—731no—
109H(3,ℤ/4)—731no—
110C2×#41C2×D7311yescharacteristic
111C2×M16—731no—
112C2×M16C2×D7311yescharacteristic
113C4⋊Q8—1461no—
114#125—1461no—
115C22⋊Q8—1462no—
116C4×Q8—1462no—
117#117—731no—
118#117—731no—
119#117—731no—
120C2×C42C2×D7311yescharacteristic
121#104—21no—
122#104—21no—
123#104—1462no—
124#99—1462no—
125#41—21no—
126#41—21no—
127#41—21no—
128#41—21no—
129C2×Q8—1462no—
130C2×Q8Dic14611yescharacteristic, complemented
131C2×D4—21no—
132C2×D4Dic14611yescharacteristic, complemented
133C22×C4—21no—
134C22×C4—21no—
135C22×C4C22×D7311yescharacteristic
136M16—21no—
137M16—21no—
138M16—1461no—
139M16—1461no—
140C2×C8—21no—
141C2×C8—1461no—
142C4⋊C4—1464no—
143C4⋊C4—1462no—
144C4⋊C4—1461no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C22⋊C4—732no—
148C22⋊C4—1461no—
149C22⋊C4—1461no—
150C42—21no—
151C42—732no—
152C42—1461no—
153C42—1461no—
154C42C22⋊D7311yescharacteristic
155C42C22⋊D7311yescharacteristic
156C23—21no—
157C23D4×D7311yescharacteristic
158Q8—21no—
159Q8—21no—
160Q8—2924no—
161D4—21no—
162D4—21no—
163D4—41no—
164D4—41no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2921no—
172C2×C4—1462no—
173C2×C4—1462no—
174C2×C4D4×D7311yescharacteristic
175C2×C4C2×C22⋊D7311yescharacteristic
176C2×C4C2×Dic14611yescharacteristic
177C2×C4#1192402711yescharacteristic
178C2×C4#1192402711yescharacteristic
179C2×C4#1192402811yescharacteristic
180C8—41no—
181C8—2921no—
182C22—41no—
183C22—41no—
184C22—81no—
185C22#1455655911yescharacteristic
186C22#1455656811yescharacteristic
187C22#1455657711yescharacteristic
188C4—22no—
189C4—41no—
190C4—41no—
191C4—2922no—
192C4—2922no—
193C4—5841no—
194C4#1455656811yescharacteristic
195C4#1455657011yescharacteristic
196C4#1455657711yescharacteristic
197C4#1455657811yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#1798849911yescharacteristic
subgroupG/H
centerC4#14556577
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#104×C73C2
socleC2×C73#393
hypercenterC2×#104D73
hypocenterC73#2031
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
4. #17988359C2semidirect
5. #17988347C2semidirect
6. #17988344C2semidirect
42. C2×Q8×C73Q8semidirect
44. C2×D4×C73Q8semidirect
102. C73#2031semidirect
130. C2×Q8Dic146semidirect
132. C2×D4Dic146semidirect