Finite Group Databasebeta

← #22626111

Subgroups — #22626111

Order 9344.

260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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#17989588C211yesmaximal, characteristic
2C4×C4⋊#64408C211yesmaximal, characteristic
3#17989460C212yesmaximal
4#17989460C212yesmaximal
5#125×D73C211yesmaximal, characteristic
6C2×#11924036C2212yes—
7C2×C4⋊#64408C2212yes—
8C2×C4×#64408—21no—
9#14556658—21no—
10C4⋊#10596833—21no—
11(C2×#64408)⋊C4—21no—
12#14556583C411yescharacteristic, complemented
13#14556582C411yescharacteristic, complemented
14#14556582C411yescharacteristic, complemented
15#14556581—21no—
16#14556581—21no—
17C4⋊C4×D73—21no—
18C4⋊C4×D73—21no—
19C4⋊C4×D73C2211yescharacteristic
20C4⋊C4×D73C2211yescharacteristic
21C42×D73C2211yescharacteristic
22#125×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924036—24no—
25C2×#10596833—22no—
26C4⋊#64408—22no—
27C4⋊#64408Q814yes—
28C4×#64408—42no—
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73D411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73C2311yescharacteristic
34C4⋊Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73C2×C411yescharacteristic
37C4⋊Dic73C2×C411yescharacteristic
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41#11924007—21no—
42#11924007—21no—
43#11924007—21no—
44C4×Dic73C2×C411yescharacteristic
45C4×Dic73D411yescharacteristic
46C4×Dic73D411yescharacteristic
47C4⋊C4×C73—21no—
48C4⋊C4×C73—21no—
49C4⋊C4×C73C2×C411yescharacteristic
50C4⋊C4×C73C2×C411yescharacteristic
51C42×C73C2×C411yescharacteristic
52C22×D73C2×D411yescharacteristic
53C2×#64408—24no—
54C2×#64408—42no—
55C2×#64408—42no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22×C411yescharacteristic
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C2×D411yescharacteristic
66C4×D73—22no—
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—42no—
70C4×D73—41no—
71C4×D73—41no—
72C4×D73C2×Q812yes—
73C4×D73#4112yes—
74#10596833—42no—
75C22×C73C2×C22⋊C411yescharacteristic
76C2×D73C22⋊Q812yes—
77C2×D73#13512yes—
78C2×D73AGL(1,ℤ/8)11yescharacteristic
79C2×D73#13711yescharacteristic
80#64408—44no—
81C4×C73—21no—
82C4×C73—21no—
83C4×C73—41no—
84C4×C73—41no—
85C4×C73C4×Q812yes—
86Dic73—21no—
87Dic73—21no—
88Dic73—41no—
89Dic73—41no—
90Dic73#12411yescharacteristic
91Dic73C4⋊Q811yescharacteristic
92C2×C73#39111yescharacteristic
93C2×C73#41611yescharacteristic
94C2×C73#41711yescharacteristic
95D73#47812yes—
96D73#47912yes—
97#1989—731nomaximal, Sylow
98C73#198911yescharacteristic, complemented, Sylow
99C2×#125—731no—
100C2×C4⋊C8—731no—
101C4×C4⋊C4—731no—
102#340—732no—
103#340—732no—
104C22×C8—732no—
105#125—731no—
106#125—731no—
107#125—731no—
108#125—1461no—
109#125—1461no—
110#125#6440811yescharacteristic, complemented
111C2×C4⋊C4—732no—
112C2×C4⋊C4—731no—
113C2×C4⋊C4—731no—
114C2×C4⋊C4—1461no—
115C2×C4⋊C4—1461no—
116C2×C42—731no—
117C2×C42—1461no—
118C4⋊C8—1461no—
119C4⋊C8—1461no—
120#95—1461no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—731no—
124C22×C4—1461no—
125C22×C4—1461no—
126C22×C4—1462no—
127C2×C8—1462no—
128C2×C8—1464no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—734no—
132C4⋊C4—731no—
133C4⋊C4—731no—
134C4⋊C4—1461no—
135C4⋊C4—1461no—
136C4⋊C4—1461no—
137C4⋊C4—1461no—
138C4⋊C4—1461no—
139C4⋊C4—1461no—
140C4⋊C4—1462no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C4⋊C4C2×#6440811yescharacteristic
144C4⋊C4C2×#6440811yescharacteristic
145C42—2922no—
146C42—731no—
147C42—731no—
148C42—731no—
149C42C2×#6440811yescharacteristic
150C23—731no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2922no—
154C2×C4—2921no—
155C2×C4—2921no—
156C2×C4—2922no—
157C2×C4—2922no—
158C2×C4—731no—
159C2×C4—732no—
160C2×C4—732no—
161C2×C4—731no—
162C2×C4—731no—
163C2×C4—1461no—
164C2×C4—1462no—
165C2×C4—1461no—
166C2×C4—1464no—
167C2×C4—1461no—
168C2×C4—1461no—
169C2×C4C22⋊#6440811yescharacteristic
170C2×C4C22⋊#6440811yescharacteristic
171C2×C4C22×#6440811yescharacteristic
172C8—2922no—
173C22—732no—
174C22—732no—
175C22—731no—
176C22—731no—
177C22C2×C22⋊#6440811yescharacteristic
178C4—21no—
179C4—21no—
180C4—41no—
181C4—41no—
182C4—2924no—
183C4—2921no—
184C4—2921no—
185C4—731no—
186C4—731no—
187C4—1461no—
188C4—1461no—
189C4Q8×#6440812yes—
190C2—732no—
191C2—732no—
192C2(C2×#64408)⋊Q811yescharacteristic
193C2#1798957711yescharacteristic
194C2#1798957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#125×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#125#64408
hypocenterC73#1989
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #14556583C4semidirect
13. #14556582C4semidirect
14. #14556582C4semidirect
22. #125×C73C4semidirect
98. C73#1989semidirect
110. #125#64408semidirect