Finite Group Databasebeta

← #22611849

Subgroups — #22611849

Order 9344.

226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D73C211yesmaximal, characteristic, complemented
2C2×#14556536C211yesmaximal, characteristic, complemented
3C2×#14556534C211yesmaximal, characteristic, complemented
4#17988824C211yesmaximal, characteristic
5#17988390C211yesmaximal, characteristic, complemented
6#17988366C211yesmaximal, characteristic, complemented
7#358×C73C211yesmaximal, characteristic, complemented
8C2×Q8×D73—21no—
9C2×Dic292C2211yescharacteristic
10C2×#11924018—21no—
11Q16×D73—22no—
12Q16×D73—22no—
13C2×D584C2211yescharacteristic
14C2×C8×D73C2211yescharacteristic
15#14556566—21no—
16#14556536—22no—
17#14556534—22no—
18C2×#11924003C2211yescharacteristic
19#14556511—21no—
20C2×Q16×C73C2211yescharacteristic
21C2×C16×C73C2211yescharacteristic
22#107×C73C2211yescharacteristic
23C2×Dic146—21no—
24C2×Dic146—41no—
25Q8×D73—24no—
26Q8×D73—42no—
27C2×D292—21no—
28C2×D292—41no—
29C2×C4×D73—41no—
30C2×C4×D73D411yescharacteristic
31Dic292—21no—
32Dic292D412yescomplemented
33#11924018—24no—
34D584—21no—
35D584—21no—
36C2×#10596831D411yescharacteristic
37C8×D73—21no—
38C8×D73—21no—
39#11924005—41no—
40#11924003—21no—
41C2×Q8×C73—21no—
42Q16×C73—21no—
43Q16×C73D412yescomplemented
44C2×C8×C73C2311yescharacteristic
45C4⋊C4×C73—21no—
46C16×C73—21no—
47C22×D73—41no—
48C22×D73D811yescharacteristic
49Q8×C73—22no—
50Q8×C73—41no—
51C2×C4×C73—41no—
52C2×C4×C73—41no—
53C2×C4×C73C2×D411yescharacteristic
54C2×Dic73—41no—
55C2×Dic73D811yescharacteristic
56D292—41no—
57D292—41no—
58D292—82no—
59C4×D73—21no—
60C4×D73—21no—
61C4×D73—44no—
62Dic146—22no—
63Dic146—44no—
64Dic146—41no—
65C8×C73C2×D411yescharacteristic
66C8×C73C2×D411yescharacteristic
67#10596831—21no—
68C22×C73C2×D811yescharacteristic
69C2×D73—21no—
70C2×D73—21no—
71C2×D73—81no—
72C2×D73—81no—
73C2×D73—81no—
74C2×D73SD3212yescomplemented
75C4×C73—42no—
76C4×C73—81no—
77C4×C73#12011yescharacteristic
78C4×C73AGL(1,ℤ/8)11yescharacteristic
79Dic73—21no—
80Dic73—42no—
81C2×C73#44711yescharacteristic
82C2×C73C2×SD3211yescharacteristic
83C2×C73#51011yescharacteristic
84D73—22no—
85D73—161no—
86#2185—731nomaximal, Sylow
87C73#218511yescharacteristic, complemented, Sylow
88C22×Q16—731no—
89C2×SD32—731no—
90C2×SD32—731no—
91#466—731no—
92#358—731no—
93#358D7311yescharacteristic, complemented
94C22⋊C16—731no—
95C22×Q8—1461no—
96C2×Q16—731no—
97C2×Q16—1461no—
98C2×Q16—1462no—
99C2×Q16—1462no—
100C2×Q16C2×D7311yescharacteristic
101C2×D8—731no—
102C22×C8—731no—
103#121—1461no—
104SD32—1462no—
105SD32—1462no—
106C2×C16—731no—
107C2×C16C2×D7311yescharacteristic
108#107C2×D7311yescharacteristic
109#102—1461no—
110C2×Q8—21no—
111C2×Q8—2921no—
112C2×Q8—2922no—
113C2×Q8—1464no—
114C2×Q8—1461no—
115C2×D4—2921no—
116C2×D4—1461no—
117C22×C4—2921no—
118C22×C4—731no—
119Q16—21no—
120Q16—732no—
121Q16—1464no—
122Q16—1461no—
123Q16D29212yescomplemented
124D8—1461no—
125D8—1461no—
126C2×C8—731no—
127C2×C8—1461no—
128C2×C8—1461no—
129C2×C8C22×D7311yescharacteristic
130C4⋊C4—21no—
131C22⋊C4—2921no—
132C16—21no—
133C16—1461no—
134C23—2921no—
135C23—731no—
136Q8—22no—
137Q8—41no—
138Q8—2924no—
139Q8—2921no—
140Q8—1462no—
141D4—2921no—
142D4—2921no—
143D4—5842no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—2924no—
147C2×C4—2921no—
148C2×C4—731no—
149C2×C4—1461no—
150C2×C4—1461no—
151C2×C4D4×D7311yescharacteristic
152C8—1461no—
153C8D4×D7311yescharacteristic
154C8C2×D29211yescharacteristic
155C22—5841no—
156C22—5841no—
157C22—5841no—
158C22—732no—
159C22—1461no—
160C22—1461no—
161C22D8×D7311yescharacteristic
162C4—42no—
163C4—81no—
164C4—2922no—
165C4—1461no—
166C4#1455656111yescharacteristic
167C4#1455661811yescharacteristic
168C2—11681no—
169C2—1462no—
170C2#1798872211yescharacteristic
171C2SD32×D7311yescharacteristic
172C2#1798902911yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#358×C73C2
socleC22×C73C2×D8
hypercenter#358D73
hypocenterC73#2185
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D73C2semidirect
2. C2×#14556536C2semidirect
3. C2×#14556534C2semidirect
5. #17988390C2semidirect
6. #17988366C2semidirect
7. #358×C73C2semidirect
32. Dic292D4semidirect
43. Q16×C73D4semidirect
74. C2×D73SD32semidirect
87. C73#2185semidirect
93. #358D73semidirect
123. Q16D292semidirect