Finite Group Databasebeta

← #22625342

Subgroups — #22625342

Order 9344.

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

normal subgroups only

This group has 222 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#17989531C211yesmaximal, characteristic, complemented
3#17989440C212yesmaximal, complemented
4#17989438C212yesmaximal
5#17989119C211yesmaximal, characteristic
6C2×C4⋊#64408—21no—
7#14556658—21no—
8#14556648C2212yes—
9#14556646—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12#14556584—21no—
13#14556582C411yescharacteristic, complemented
14#14556578C411yescharacteristic, complemented
15#14556573—21no—
16#14556571C2211yescharacteristic
17#14556562C2211yescharacteristic
18C4×Dic146C411yescharacteristic, complemented
19C4×C22⋊D73—21no—
20#14556550—21no—
21C42×D73C2211yescharacteristic
22C4×D4×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C4⋊#64408—42no—
26C2×Dic146C2×C411yescharacteristic
27C2×C22⋊D73—21no—
28C2×C4×D73D411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C2×C4×D73C2311yescharacteristic
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73C2×C411yescharacteristic
34#11924007—21no—
35#11924007—21no—
36C22⋊Dic73—21no—
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C2×D4×C73C2×C411yescharacteristic
45C22×C4×C73—21no—
46C4⋊C4×C73C2×C411yescharacteristic
47C22⋊C4×C73—21no—
48C42×C73C2×C411yescharacteristic
49C23×C73—21no—
50C22×D73C2×D411yescharacteristic
51C2×#64408—42no—
52C2×#64408—42no—
53C2×#64408—42no—
54D4×C73—41no—
55C2×C4×C73—21no—
56C2×C4×C73—42no—
57C2×C4×C73C22⋊C411yescharacteristic
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22×C411yescharacteristic
60C22⋊D73—41no—
61C22⋊D73—41no—
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C22⋊C411yescharacteristic
66C2×Dic73C2×D411yescharacteristic
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—41no—
70C4×D73—41no—
71Dic146—41no—
72#10596833—42no—
73C22×C73—41no—
74C22×C73—41no—
75C22×C73—41no—
76C22×C73C2×C22⋊C411yescharacteristic
77C2×D73—21no—
78C2×D73—21no—
79C2×D73AGL(1,ℤ/8)11yescharacteristic
80C2×D73#13711yescharacteristic
81#64408—82no—
82C4×C73—21no—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—41no—
86Dic73—21no—
87Dic73—21no—
88Dic73—21no—
89Dic73—41no—
90Dic73—41no—
91C2×C73—81no—
92C2×C73#41011yescharacteristic
93C2×C73#41711yescharacteristic
94C2×C73#42111yescharacteristic
95D73—21no—
96D73—21no—
97#1512—731nomaximal, Sylow
98C73#151211yescharacteristic, complemented, Sylow
99#529—731no—
100#432—731no—
101#382—731no—
102#328—732no—
103#327—732no—
104#126—1461no—
105#125—731no—
106#124—731no—
107#123—1461no—
108C22⋊Q8—731no—
109#121—731no—
110C4×Q8—731no—
111C4×D4—1461no—
112C4×D4#6440811yescharacteristic, complemented
113#117—1461no—
114C2×C4⋊C4—1461no—
115C2×C42—731no—
116C4⋊C8—1461no—
117C22⋊C8—732no—
118#97—1461no—
119#95—732no—
120#95—1461no—
121C2×Q8—731no—
122C2×D4—1461no—
123C2×D4C2×#6440811yescharacteristic
124C22×C4—21no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—731no—
128C22×C4—1462no—
129C2×C8—1462no—
130C4⋊C4—2922no—
131C4⋊C4—731no—
132C4⋊C4—1461no—
133C4⋊C4—1461no—
134C4⋊C4—1461no—
135C4⋊C4—1461no—
136C4⋊C4C2×#6440811yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C22⋊C4—1461no—
141C22⋊C4—1461no—
142C42—731no—
143C42—731no—
144C42—731no—
145C42—1461no—
146C42C2×#6440811yescharacteristic
147C23—21no—
148C23—731no—
149Q8—2921no—
150D4—41no—
151D4—2921no—
152D4—2921no—
153C2×C4—21no—
154C2×C4—42no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2922no—
158C2×C4—2922no—
159C2×C4—2922no—
160C2×C4—731no—
161C2×C4—731no—
162C2×C4—731no—
163C2×C4—1461no—
164C2×C4—1461no—
165C2×C4—1461no—
166C2×C4—1461no—
167C2×C4C22⋊#6440811yescharacteristic
168C2×C4C22⋊#6440811yescharacteristic
169C2×C4C22×#6440811yescharacteristic
170C8—2922no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—731no—
175C22—731no—
176C22—1461no—
177C22—1461no—
178C22C2×C22⋊#6440811yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—2921no—
184C4—2921no—
185C4—5842no—
186C4—1461no—
187C4—1461no—
188C4—1461no—
189C2—81no—
190C2—1461no—
191C2—1461no—
192C2#1798956611yescharacteristic
193C2#1798957811yescharacteristic
194C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1512
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989610C2semidirect
2. #17989531C2semidirect
3. #17989440C2semidirect
13. #14556582C4semidirect
14. #14556578C4semidirect
18. C4×Dic146C4semidirect
22. C4×D4×C73C4semidirect
98. C73#1512semidirect
112. C4×D4#64408semidirect