Finite Group Databasebeta

← #22625352

Subgroups — #22625352

Order 9344.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#17989610C211yesmaximal, characteristic, complemented
2#17989532C211yesmaximal, characteristic, complemented
3#17989439C214yesmaximal, complemented
4#17989138C211yesmaximal, characteristic
5#14556658—21no—
6#14556648C2212yes—
7#14556646—21no—
8(C2×#64408)⋊C4—21no—
9(C2×#64408)⋊C4—21no—
10(C2×#64408)⋊C4C2212yes—
11C2×#11924029—21no—
12#14556588C411yescharacteristic, complemented
13#14556580—21no—
14#14556566—21no—
15#14556566C2212yes—
16#14556553—21no—
17#14556553C412yescomplemented
18C42×D73C2211yescharacteristic
19C4⋊Q8×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21C2×#10596833—22no—
22#11924029—44no—
23C2×D292—22no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292C2×C412yes—
27C2×C4×D73—22no—
28C2×C4×D73D411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C2×C4×D73C2311yescharacteristic
31#11924005—22no—
32#11924005—22no—
33C4×Dic73C2×C411yescharacteristic
34C4×Dic73D411yescharacteristic
35C4×Dic73D411yescharacteristic
36C2×Q8×C73—21no—
37C4⋊C4×C73—21no—
38C4⋊C4×C73C2×C412yes—
39C42×C73C2×C411yescharacteristic
40C22×D73—22no—
41C22×D73C2×D411yescharacteristic
42C2×#64408—42no—
43C2×#64408—42no—
44C2×#64408—42no—
45Q8×C73—42no—
46C2×C4×C73—22no—
47C2×C4×C73C22⋊C411yescharacteristic
48C2×C4×C73C22⋊C411yescharacteristic
49C2×C4×C73C22×C411yescharacteristic
50C2×Dic73C22⋊C411yescharacteristic
51C2×Dic73C22⋊C411yescharacteristic
52C2×Dic73C2×D411yescharacteristic
53D292—42no—
54D292—42no—
55D292—42no—
56D292—44no—
57C4×D73—22no—
58C4×D73—41no—
59C4×D73—41no—
60C4×D73—44no—
61#10596833—42no—
62C22×C73C2×C22⋊C411yescharacteristic
63C2×D73—21no—
64C2×D73—21no—
65C2×D73—42no—
66C2×D73—42no—
67C2×D73—42no—
68C2×D73AGL(1,ℤ/8)12yes—
69#64408—82no—
70C4×C73—21no—
71C4×C73—21no—
72C4×C73—21no—
73C4×C73—42no—
74Dic73—21no—
75Dic73—21no—
76Dic73—21no—
77C2×C73#41011yescharacteristic
78C2×C73#41811yescharacteristic
79C2×C73#42111yescharacteristic
80D73—22no—
81D73—82no—
82#1514—731nomaximal, Sylow
83C73#151411yescharacteristic, complemented, Sylow
84#532—731no—
85#432—731no—
86#383—731no—
87#327—734no—
88C2×#41—1461no—
89C4⋊Q8#6440811yescharacteristic, complemented
90#127—731no—
91#124—1461no—
92#121—732no—
93#121—1461no—
94C4×D4—732no—
95C4×D4—1461no—
96C2×C42—731no—
97C4⋊C8—1461no—
98C22⋊C8—732no—
99#97—1461no—
100#95—732no—
101#95—1461no—
102#95—1461no—
103#41—2924no—
104C2×Q8—21no—
105C2×D4—732no—
106C2×D4—1462no—
107C2×D4—1461no—
108C2×D4—1461no—
109C22×C4—731no—
110C22×C4—731no—
111C22×C4—731no—
112C22×C4—1462no—
113C22×C4—1462no—
114C2×C8—1462no—
115C4⋊C4—21no—
116C4⋊C4C2×#6440812yes—
117C22⋊C4—1462no—
118C22⋊C4—1462no—
119C42—731no—
120C42—731no—
121C42—731no—
122C42C2×#6440811yescharacteristic
123C23—731no—
124C23—1462no—
125Q8—42no—
126D4—2922no—
127D4—2922no—
128D4—2922no—
129D4—2924no—
130C2×C4—22no—
131C2×C4—2921no—
132C2×C4—2921no—
133C2×C4—2924no—
134C2×C4—2922no—
135C2×C4—2922no—
136C2×C4—2922no—
137C2×C4—731no—
138C2×C4—731no—
139C2×C4—731no—
140C2×C4—1462no—
141C2×C4C22⋊#6440811yescharacteristic
142C2×C4C22⋊#6440811yescharacteristic
143C2×C4C22×#6440811yescharacteristic
144C8—2922no—
145C22—2922no—
146C22—2922no—
147C22—2922no—
148C22—732no—
149C22—1461no—
150C22—1461no—
151C22C2×C22⋊#6440811yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—42no—
156C4—5842no—
157C4—1461no—
158C4—1461no—
159C4—1461no—
160C2—5842no—
161C2—1462no—
162C2#1798956811yescharacteristic
163C2#1798957911yescharacteristic
164C2#1798958611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4⋊Q8#64408
hypocenterC73#1514
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #17989610C2semidirect
2. #17989532C2semidirect
3. #17989439C2semidirect
12. #14556588C4semidirect
17. #14556553C4semidirect
19. C4⋊Q8×C73C4semidirect
83. C73#1514semidirect
89. C4⋊Q8#64408semidirect