Finite Group Databasebeta

← #22625839

Subgroups — #22625839

Order 9344.

306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989558C211yesmaximal, characteristic
2C4×C22⋊#64408C211yesmaximal, characteristic
3#17989457C212yesmaximal, complemented
4#17989457C212yesmaximal, complemented
5#117×D73C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7C2×C22⋊#64408—21no—
8C2×C4×#64408C2212yes—
9#14556648—21no—
10C22⋊#10596833—21no—
11(C2×#64408)⋊C4—21no—
12C22×C4×D73C2211yescharacteristic
13#14556550C411yescharacteristic, complemented
14#14556549C2211yescharacteristic
15#14556549C2211yescharacteristic
16#14556548—21no—
17#14556547—21no—
18C4⋊C4×D73C411yescharacteristic, complemented
19C4⋊C4×D73C411yescharacteristic, complemented
20C22⋊C4×D73—21no—
21C42×D73—21no—
22#117×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924038—24no—
25C2×#10596833—22no—
26C22⋊#64408—24no—
27C4×#64408—24no—
28C23×D73D411yescharacteristic
29C22×Dic73D411yescharacteristic
30C2×C4×D73—24no—
31C2×C4×D73—21no—
32C2×C4×D73—21no—
33C2×C4×D73C2×C411yescharacteristic
34C2×C4×D73D411yescharacteristic
35C2×C4×D73D411yescharacteristic
36C2×C4×D73C2311yescharacteristic
37C4⋊Dic73C2×C411yescharacteristic
38C4⋊Dic73C2×C411yescharacteristic
39#11924007—21no—
40#11924007—21no—
41C22⋊Dic73—21no—
42#11924005—21no—
43#11924005—21no—
44C4×Dic73—21no—
45C4×Dic73—21no—
46C4×Dic73—21no—
47C22×C4×C73C2×C411yescharacteristic
48C4⋊C4×C73C2×C411yescharacteristic
49C4⋊C4×C73C2×C411yescharacteristic
50C22⋊C4×C73—21no—
51C42×C73—21no—
52C23×C73C22⋊C411yescharacteristic
53C22×D73—22no—
54C22×D73—22no—
55C22×D73—41no—
56C22×D73C22⋊C411yescharacteristic
57C22×D73C2×D411yescharacteristic
58C2×#64408—24no—
59C2×#64408—42no—
60C2×#64408—42no—
61C2×C4×C73—22no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73C22⋊C411yescharacteristic
65C2×C4×C73C22×C411yescharacteristic
66C2×Dic73—22no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C2×D411yescharacteristic
71C4×D73—22no—
72C4×D73—22no—
73C4×D73—22no—
74C4×D73—42no—
75C4×D73—42no—
76C4×D73#4114yes—
77#10596833—42no—
78C22×C73—21no—
79C22×C73—21no—
80C22×C73—21no—
81C22×C73C2×C22⋊C411yescharacteristic
82C2×D73—21no—
83C2×D73—21no—
84C2×D73—21no—
85C2×D73—21no—
86C2×D73—44no—
87C2×D73#10412yes—
88C2×D73#12312yes—
89#64408—44no—
90C4×C73—21no—
91C4×C73—41no—
92C4×C73—41no—
93C4×C73#11712yes—
94Dic73—21no—
95Dic73—41no—
96Dic73—41no—
97Dic73#12312yes—
98C2×C73—41no—
99C2×C73#38111yescharacteristic
100C2×C73C2×#10411yescharacteristic
101C2×C73#42111yescharacteristic
102D73—22no—
103D73—22no—
104#1826—731nomaximal, Sylow
105C73#182611yescharacteristic, complemented, Sylow
106C2×#117—731no—
107#407—731no—
108C4×C22⋊C4—731no—
109#339—732no—
110#339—732no—
111C23×C4—731no—
112C2×M16—732no—
113#117—731no—
114#117—731no—
115#117—731no—
116#117—1461no—
117#117—1461no—
118#117#6440811yescharacteristic, complemented
119C2×C4⋊C4—731no—
120C2×C4⋊C4—731no—
121C2×C22⋊C4—1461no—
122C2×C22⋊C4—1461no—
123C2×C42—732no—
124C2×C42—1461no—
125C22⋊C8—1461no—
126C22⋊C8—1461no—
127#95—1461no—
128C24—731no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—731no—
134C22×C4—1461no—
135C22×C4—1461no—
136C22×C4—1464no—
137C22×C4—1462no—
138C22×C4C2×#6440811yescharacteristic
139M16—1464no—
140C2×C8—1462no—
141C4⋊C4—731no—
142C4⋊C4—731no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C4⋊C4C2×#6440811yescharacteristic
146C4⋊C4C2×#6440811yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—1461no—
149C22⋊C4—1461no—
150C22⋊C4—1464no—
151C22⋊C4—1461no—
152C42—21no—
153C42—1461no—
154C42—1461no—
155C42—1464no—
156C42—1461no—
157C23—2921no—
158C23—731no—
159C23—731no—
160C23—1462no—
161C23—1462no—
162C23C22⋊#6440811yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—2922no—
167C2×C4—2922no—
168C2×C4—2922no—
169C2×C4—2922no—
170C2×C4—731no—
171C2×C4—734no—
172C2×C4—731no—
173C2×C4—1462no—
174C2×C4—1462no—
175C2×C4—1464no—
176C2×C4—1461no—
177C2×C4—1461no—
178C2×C4—1462no—
179C2×C4—1462no—
180C2×C4C22⋊#6440811yescharacteristic
181C2×C4C22×#6440811yescharacteristic
182C8—2922no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—2924no—
187C22—732no—
188C22—732no—
189C22—1461no—
190C22—1461no—
191C22—1461no—
192C22—1461no—
193C22C2×C22⋊#6440811yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—2924no—
198C4—2921no—
199C4—2921no—
200C4—732no—
201C4—1461no—
202C4#1455667012yes—
203C2—41no—
204C2—1462no—
205C2—1462no—
206C2#1798953011yescharacteristic
207C2D73⋊#10411yescharacteristic
208C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#117×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#117#64408
hypocenterC73#1826
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #17989457C2semidirect
4. #17989457C2semidirect
13. #14556550C4semidirect
18. C4⋊C4×D73C4semidirect
19. C4⋊C4×D73C4semidirect
22. #117×C73C4semidirect
105. C73#1826semidirect
118. #117#64408semidirect