Finite Group Databasebeta

← #22625836

Subgroups — #22625836

Order 9344.

300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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#17989555C211yesmaximal, characteristic
2#17989529C211yesmaximal, characteristic
3#17989460C212yesmaximal, complemented
4#17989460C212yesmaximal, complemented
5#117×D73C211yesmaximal, characteristic
6C2×#11924036C2212yes—
7C2×C4⋊#64408C2212yes—
8C2×C22⋊#64408—21no—
9#14556648—21no—
10C22⋊#10596833—21no—
11(C2×#64408)⋊C4—21no—
12C22×C4×D73C2211yescharacteristic
13#14556550C411yescharacteristic, complemented
14#14556549C411yescharacteristic, complemented
15#14556549C411yescharacteristic, complemented
16#14556548—21no—
17#14556547—21no—
18C4⋊C4×D73C2211yescharacteristic
19C4⋊C4×D73C2211yescharacteristic
20C22⋊C4×D73—21no—
21C42×D73—21no—
22#117×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924036—24no—
25C2×#10596833—22no—
26C4⋊#64408—24no—
27C22⋊#64408—42no—
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—21no—
56C22×D73—21no—
57C22×D73C22⋊C411yescharacteristic
58C22×D73C2×D411yescharacteristic
59C2×#64408—42no—
60C2×#64408—42no—
61C2×#64408—42no—
62C2×C4×C73—22no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73C22⋊C411yescharacteristic
66C2×C4×C73C22×C411yescharacteristic
67C2×Dic73—22no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73C22⋊C411yescharacteristic
71C2×Dic73C2×D411yescharacteristic
72C4×D73—22no—
73C4×D73—22no—
74C4×D73—22no—
75C4×D73—42no—
76C4×D73—41no—
77C4×D73—41no—
78C4×D73#4114yes—
79#10596833—42no—
80C22×C73—21no—
81C22×C73—21no—
82C22×C73—21no—
83C22×C73C2×C22⋊C411yescharacteristic
84C2×D73—21no—
85C2×D73—21no—
86C2×D73—21no—
87C2×D73—42no—
88C2×D73—42no—
89C2×D73#12312yes—
90C2×D73#13512yes—
91C2×D73AGL(1,ℤ/8)11yescharacteristic
92C2×D73#13711yescharacteristic
93#64408—82no—
94C4×C73—21no—
95C4×C73—41no—
96C4×C73—41no—
97C4×C73#11712yes—
98Dic73—21no—
99Dic73—41no—
100Dic73—41no—
101Dic73#12312yes—
102C2×C73—41no—
103C2×C73#38111yescharacteristic
104C2×C73#41611yescharacteristic
105C2×C73#41711yescharacteristic
106D73—41no—
107D73#48212yes—
108D73#48512yes—
109#1825—731nomaximal, Sylow
110C73#182511yescharacteristic, complemented, Sylow
111C2×#117—731no—
112C2×C22⋊C8—731no—
113#380—731no—
114#340—732no—
115#340—732no—
116C23×C4—731no—
117C22×C8—732no—
118#117—731no—
119#117—731no—
120#117—731no—
121#117—1461no—
122#117—1461no—
123#117#6440811yescharacteristic, complemented
124C2×C4⋊C4—731no—
125C2×C4⋊C4—731no—
126C2×C4⋊C4—732no—
127C2×C22⋊C4—1461no—
128C2×C22⋊C4—1461no—
129C2×C42—1461no—
130C22⋊C8—1461no—
131C22⋊C8—1461no—
132#95—1461no—
133C24—731no—
134C22×C4—731no—
135C22×C4—731no—
136C22×C4—731no—
137C22×C4—731no—
138C22×C4—731no—
139C22×C4—1461no—
140C22×C4—1461no—
141C22×C4—1464no—
142C22×C4—1462no—
143C22×C4C2×#6440811yescharacteristic
144C2×C8—1462no—
145C2×C8—1464no—
146C4⋊C4—731no—
147C4⋊C4—731no—
148C4⋊C4—1461no—
149C4⋊C4—1461no—
150C4⋊C4—1464no—
151C4⋊C4C2×#6440811yescharacteristic
152C4⋊C4C2×#6440811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—2922no—
155C22⋊C4—1461no—
156C22⋊C4—1461no—
157C22⋊C4—1461no—
158C42—21no—
159C42—1461no—
160C42—1461no—
161C42—1461no—
162C23—731no—
163C23—731no—
164C23—1461no—
165C23—1462no—
166C23—1462no—
167C23—1461no—
168C23C22⋊#6440811yescharacteristic
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—2922no—
173C2×C4—2921no—
174C2×C4—2921no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—731no—
179C2×C4—734no—
180C2×C4—731no—
181C2×C4—1462no—
182C2×C4—1462no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4—1462no—
186C2×C4—1462no—
187C2×C4C22⋊#6440811yescharacteristic
188C2×C4C22×#6440811yescharacteristic
189C8—2922no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—2922no—
194C22—2922no—
195C22—732no—
196C22—732no—
197C22—731no—
198C22—731no—
199C22—1461no—
200C22—1461no—
201C22—1461no—
202C22C2×C22⋊#6440811yescharacteristic
203C4—21no—
204C4—41no—
205C4—41no—
206C4—2921no—
207C4—2921no—
208C4—5842no—
209C4—732no—
210C4—1461no—
211C4#1455667012yes—
212C2—41no—
213C2—2921no—
214C2—732no—
215C2—732no—
216C2#1798953011yescharacteristic
217C2#1798957711yescharacteristic
218C2#1798957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#117×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#117#64408
hypocenterC73#1825
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. #17989460C2semidirect
4. #17989460C2semidirect
13. #14556550C4semidirect
14. #14556549C4semidirect
15. #14556549C4semidirect
22. #117×C73C4semidirect
110. C73#1825semidirect
123. #117#64408semidirect