Finite Group Databasebeta

← #22625338

Subgroups — #22625338

Order 9344.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989559C211yesmaximal, characteristic, complemented
2#17989530C211yesmaximal, characteristic, complemented
3#17989439C214yesmaximal, complemented
4C2×#14556566C211yesmaximal, characteristic
5C2×#11924037—21no—
6C2×C22⋊#64408—21no—
7#14556648—21no—
8#14556648C2212yescomplemented
9(C2×#64408)⋊C4—21no—
10(C2×#64408)⋊C4C2212yescomplemented
11C22×D292—21no—
12C22×D292C411yescharacteristic, complemented
13C22×C4×D73C2211yescharacteristic
14#14556566—21no—
15#14556566—21no—
16#14556566C412yescomplemented
17#14556566C2212yes—
18C2×#11924005—21no—
19C2×C4⋊C4×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21#11924037—42no—
22C2×#10596833—22no—
23C22⋊#64408—42no—
24C23×D73—21no—
25C23×D73D411yescharacteristic
26C2×D292—22no—
27C2×D292—22no—
28C2×D292—21no—
29C2×D292—42no—
30C2×D292—44no—
31C2×D292C2×C412yes—
32C22×Dic73D411yescharacteristic
33C2×C4×D73—42no—
34C2×C4×D73C2×C411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C2×C4×D73C2311yescharacteristic
38#11924005—22no—
39#11924005—22no—
40C22×C4×C73—21no—
41C22×C4×C73C2×C411yescharacteristic
42C4⋊C4×C73—21no—
43C4⋊C4×C73C2×C412yes—
44C23×C73C22⋊C411yescharacteristic
45C22×D73—22no—
46C22×D73—22no—
47C22×D73—22no—
48C22×D73—41no—
49C22×D73—42no—
50C22×D73—42no—
51C22×D73—42no—
52C22×D73C22⋊C411yescharacteristic
53C22×D73C2×D411yescharacteristic
54C2×#64408—42no—
55C2×#64408—42no—
56C2×#64408—42no—
57C2×C4×C73—22no—
58C2×C4×C73—22no—
59C2×C4×C73—42no—
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22×C411yescharacteristic
62C2×Dic73—22no—
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C2×D411yescharacteristic
65D292—42no—
66D292—42no—
67D292—44no—
68D292—44no—
69C4×D73—41no—
70C4×D73—41no—
71C4×D73—41no—
72C4×D73—41no—
73#10596833—42no—
74C22×C73—21no—
75C22×C73—21no—
76C22×C73#9912yes—
77C22×C73C2×C22⋊C411yescharacteristic
78C2×D73—21no—
79C2×D73—21no—
80C2×D73—21no—
81C2×D73—21no—
82C2×D73—21no—
83C2×D73—44no—
84C2×D73—42no—
85C2×D73—42no—
86C2×D73—42no—
87C2×D73—84no—
88C2×D73AGL(1,ℤ/8)12yes—
89#64408—82no—
90C4×C73—21no—
91C4×C73—21no—
92C4×C73—42no—
93Dic73—21no—
94Dic73—21no—
95C2×C73—22no—
96C2×C73C2×#9911yescharacteristic
97C2×C73#41811yescharacteristic
98C2×C73#42111yescharacteristic
99D73—22no—
100D73—41no—
101D73—82no—
102#1510—731nomaximal, Sylow
103C73#151011yescharacteristic, complemented, Sylow
104C2×#121—731no—
105#407—731no—
106#381—731no—
107#327—734no—
108C22×D4—731no—
109C22×D4—1461no—
110C23×C4—731no—
111C2×M16—1461no—
112#121—732no—
113#121—732no—
114#121—1461no—
115#121—1461no—
116C2×C4⋊C4#6440811yescharacteristic, complemented
117C2×C22⋊C4—1461no—
118C2×C22⋊C4—1461no—
119C22⋊C8—732no—
120C22⋊C8—1461no—
121#95—732no—
122#95—1461no—
123C24—731no—
124C24—1461no—
125C2×D4—2922no—
126C2×D4—2924no—
127C2×D4—732no—
128C2×D4—1462no—
129C2×D4—1462no—
130C2×D4—1461no—
131C22×C4—21no—
132C22×C4—2922no—
133C22×C4—731no—
134C22×C4—731no—
135C22×C4—731no—
136C22×C4—731no—
137C22×C4—731no—
138C22×C4—1462no—
139C22×C4C2×#6440811yescharacteristic
140M16—2922no—
141C2×C8—1462no—
142C4⋊C4—21no—
143C4⋊C4C2×#6440812yes—
144C22⋊C4—2922no—
145C22⋊C4—1462no—
146C22⋊C4—1462no—
147C23—2921no—
148C23—2922no—
149C23—2922no—
150C23—2922no—
151C23—731no—
152C23—731no—
153C23—1462no—
154C23—1462no—
155C23—1462no—
156C23C22⋊#6440811yescharacteristic
157D4—2922no—
158D4—2922no—
159D4—2924no—
160D4—2924no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—2921no—
165C2×C4—2921no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2922no—
169C2×C4—2922no—
170C2×C4—2922no—
171C2×C4—731no—
172C2×C4—731no—
173C2×C4—1462no—
174C2×C4C22⋊#6440811yescharacteristic
175C2×C4C22×#6440811yescharacteristic
176C8—2922no—
177C22—21no—
178C22—21no—
179C22—2924no—
180C22—2922no—
181C22—2922no—
182C22—2922no—
183C22—5844no—
184C22—732no—
185C22—1461no—
186C22—1461no—
187C22—1461no—
188C22—1461no—
189C22—1461no—
190C22#1455665012yes—
191C22C2×C22⋊#6440811yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—5842no—
196C4—1461no—
197C4—1461no—
198C2—22no—
199C2—2921no—
200C2—5842no—
201C2—1462no—
202C2C2×#1455665011yescharacteristic
203C2#1798957911yescharacteristic
204C2#1798958611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1510
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #17989559C2semidirect
2. #17989530C2semidirect
3. #17989439C2semidirect
8. #14556648C22semidirect
10. (C2×#64408)⋊C4C22semidirect
12. C22×D292C4semidirect
16. #14556566C4semidirect
19. C2×C4⋊C4×C73C4semidirect
103. C73#1510semidirect
116. C2×C4⋊C4#64408semidirect