Finite Group Databasebeta

← #22625770

Subgroups — #22625770

Order 9344.

592 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#14556654C214yesmaximal, complemented
2#17989555C211yesmaximal, characteristic
3#17989529C211yesmaximal, characteristic
4C22×Q8×D73C211yesmaximal, characteristic
5C2×#11924036C2212yes—
6C2×C4⋊#64408C2212yes—
7C2×C22⋊#64408—21no—
8#14556654—28no—
9#14556648—21no—
10C22⋊#10596833—21no—
11(C2×#64408)⋊C4—21no—
12C22×Dic146—21no—
13C22×Dic146C411yescharacteristic, complemented
14C2×Q8×D73—28no—
15C2×Q8×D73—21no—
16C2×Q8×D73—21no—
17C2×Q8×D73C412yescomplemented
18C2×Q8×D73C2212yes—
19C22×C4×D73—21no—
20C22×C4×D73C2211yescharacteristic
21C22×Q8×C73C411yescharacteristic, complemented
22C22×#64408—22no—
23#11924036—24no—
24C2×#10596833—22no—
25C4⋊#64408—24no—
26C22⋊#64408—42no—
27C23×D73D411yescharacteristic
28C2×Dic146—28no—
29C2×Dic146—21no—
30C2×Dic146—22no—
31C2×Dic146—22no—
32C2×Dic146—24no—
33C2×Dic146C2×C412yes—
34Q8×D73—28no—
35Q8×D73—28no—
36Q8×D73—24no—
37Q8×D73—24no—
38Q8×D73—24no—
39Q8×D73D418yes—
40C22×Dic73—21no—
41C22×Dic73D411yescharacteristic
42C2×C4×D73—28no—
43C2×C4×D73—22no—
44C2×C4×D73—22no—
45C2×C4×D73—24no—
46C2×C4×D73C2×C411yescharacteristic
47C2×C4×D73D411yescharacteristic
48C2×C4×D73D411yescharacteristic
49C2×C4×D73C2311yescharacteristic
50C2×Q8×C73—24no—
51C2×Q8×C73—21no—
52C2×Q8×C73C2×C412yes—
53C22×C4×C73—21no—
54C22×C4×C73C2×C411yescharacteristic
55C23×C73C22⋊C411yescharacteristic
56C22×D73—22no—
57C22×D73—22no—
58C22×D73C22⋊C411yescharacteristic
59C22×D73SD1612yes—
60C22×D73Q1612yes—
61C22×D73C2×D411yescharacteristic
62C2×#64408—42no—
63C2×#64408—42no—
64C2×#64408—42no—
65Q8×C73—24no—
66Q8×C73—22no—
67Q8×C73C22⋊C414yescomplemented
68C2×C4×C73—24no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73C22⋊C411yescharacteristic
72C2×C4×C73C22×C411yescharacteristic
73C2×Dic73—24no—
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73C22⋊C411yescharacteristic
77C2×Dic73C2×D411yescharacteristic
78C4×D73—28no—
79C4×D73—28no—
80C4×D73—22no—
81C4×D73—22no—
82C4×D73—22no—
83C4×D73C2×D414yes—
84Dic146—28no—
85Dic146—24no—
86Dic146—22no—
87Dic146—28no—
88Dic146C22⋊C414yescomplemented
89#10596833—42no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73#10312yescomplemented
93C22×C73C2×C22⋊C411yescharacteristic
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—24no—
97C2×D73—24no—
98C2×D73#10312yescomplemented
99C2×D73#12012yes—
100C2×D73C2×SD1611yescharacteristic
101C2×D73C2×Q1611yescharacteristic
102C2×D73#13712yes—
103#64408—82no—
104C4×C73—24no—
105C4×C73—21no—
106C4×C73C2×C22⋊C412yes—
107Dic73—21no—
108Dic73—24no—
109Dic73#12012yes—
110C2×C73—22no—
111C2×C73#37911yescharacteristic
112C2×C73C2×#10311yescharacteristic
113C2×C73#41911yescharacteristic
114D73—22no—
115D73#44812yes—
116D73#45112yes—
117#1787—731nomaximal, Sylow
118C73#178711yescharacteristic, complemented, Sylow
119C23×Q8—731no—
120C2×#103—734no—
121C2×C22⋊C8—731no—
122#380—731no—
123C22×Q8—732no—
124C22×Q8—732no—
125C22×Q8—731no—
126C22×Q8—1461no—
127C22×Q8—1461no—
128C22×Q8—1461no—
129C22×Q8—1468no—
130C22×Q8#6440811yescharacteristic, complemented
131C23×C4—731no—
132C23×C4—1461no—
133C22×C8—732no—
134C2×C4⋊C4—732no—
135C2×C22⋊C4—1461no—
136#103—1468no—
137C22⋊C8—1461no—
138C22⋊C8—1461no—
139#95—1461no—
140C24—731no—
141C2×Q8—24no—
142C2×Q8—21no—
143C2×Q8—738no—
144C2×Q8—732no—
145C2×Q8—1462no—
146C2×Q8—1462no—
147C2×Q8—1464no—
148C2×Q8—1468no—
149C2×Q8—1464no—
150C2×Q8—1464no—
151C2×Q8—1468no—
152C2×Q8—1468no—
153C2×Q8—1464no—
154C2×Q8—1461no—
155C2×Q8C2×#6440812yes—
156C22×C4—21no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—1464no—
163C22×C4—1462no—
164C22×C4—1462no—
165C22×C4—1468no—
166C22×C4—1462no—
167C22×C4—1461no—
168C22×C4C2×#6440811yescharacteristic
169C2×C8—1462no—
170C2×C8—1464no—
171C4⋊C4—1464no—
172C22⋊C4—2922no—
173C23—731no—
174C23—732no—
175C23—732no—
176C23—731no—
177C23—1462no—
178C23—1462no—
179C23C22⋊#6440811yescharacteristic
180Q8—24no—
181Q8—22no—
182Q8—734no—
183Q8—1468no—
184Q8—1468no—
185Q8—1464no—
186Q8—1462no—
187Q8C22⋊#6440814yescomplemented
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—2922no—
192C2×C4—2922no—
193C2×C4—2922no—
194C2×C4—731no—
195C2×C4—734no—
196C2×C4—731no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1468no—
200C2×C4—1468no—
201C2×C4—1462no—
202C2×C4—1464no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4C22⋊#6440811yescharacteristic
206C2×C4C22×#6440811yescharacteristic
207C8—2922no—
208C22—21no—
209C22—21no—
210C22—732no—
211C22—731no—
212C22—731no—
213C22—732no—
214C22—732no—
215C22—1464no—
216C22—1464no—
217C22—1461no—
218C22—1461no—
219C22#1455665412yescomplemented
220C22C2×C22⋊#6440811yescharacteristic
221C4—24no—
222C4—21no—
223C4—5842no—
224C4—732no—
225C4—1461no—
226C4—1464no—
227C4C2×C22⋊#6440812yes—
228C2—22no—
229C2—732no—
230C2—732no—
231C2—1462no—
232C2#1798952811yescharacteristic
233C2C2×#1455665411yescharacteristic
234C2#1798958011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×Q8#64408
hypocenterC73#1787
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14556654C2semidirect
13. C22×Dic146C4semidirect
17. C2×Q8×D73C4semidirect
21. C22×Q8×C73C4semidirect
67. Q8×C73C22⋊C4semidirect
88. Dic146C22⋊C4semidirect
92. C22×C73#103semidirect
98. C2×D73#103semidirect
118. C73#1787semidirect
130. C22×Q8#64408semidirect
187. Q8C22⋊#64408semidirect
219. C22#14556654semidirect