Finite Group Databasebeta

← #22625774

Subgroups — #22625774

Order 9344.

618 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14556656C214yesmaximal, complemented
2#17989558C211yesmaximal, characteristic, complemented
3C4×C22⋊#64408C211yesmaximal, characteristic, complemented
4C22×#11924029C211yesmaximal, characteristic
5C2×#11924038C2212yescomplemented
6C2×C22⋊#64408—21no—
7C2×C4×#64408C2212yescomplemented
8#14556656—28no—
9#14556648—21no—
10C22⋊#10596833—21no—
11(C2×#64408)⋊C4—21no—
12C2×#11924029—28no—
13C2×#11924029—21no—
14C2×#11924029—21no—
15C2×#11924029C412yescomplemented
16C2×#11924029C2212yes—
17C22×D292—21no—
18C22×D292C411yescharacteristic, complemented
19C22×C4×D73—21no—
20C22×C4×D73C2211yescharacteristic
21C22×Q8×C73C411yescharacteristic, complemented
22C22×#64408—22no—
23#11924038—24no—
24C2×#10596833—22no—
25C22⋊#64408—24no—
26C4×#64408—24no—
27C23×D73—21no—
28C23×D73D411yescharacteristic
29#11924029—28no—
30#11924029—28no—
31#11924029—24no—
32#11924029—24no—
33#11924029—24no—
34#11924029D418yes—
35C2×D292—28no—
36C2×D292—22no—
37C2×D292—22no—
38C2×D292—21no—
39C2×D292—24no—
40C2×D292C2×C412yes—
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—24no—
57C22×D73—22no—
58C22×D73—22no—
59C22×D73—22no—
60C22×D73—41no—
61C22×D73—42no—
62C22×D73—42no—
63C22×D73C22⋊C411yescharacteristic
64C22×D73C2×D411yescharacteristic
65C2×#64408—24no—
66C2×#64408—42no—
67C2×#64408—42no—
68Q8×C73—24no—
69Q8×C73—22no—
70Q8×C73C22⋊C414yescomplemented
71C2×C4×C73—24no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73C22⋊C411yescharacteristic
75C2×C4×C73C22×C411yescharacteristic
76C2×Dic73—22no—
77C2×Dic73C22⋊C411yescharacteristic
78C2×Dic73C2×D411yescharacteristic
79D292—28no—
80D292—24no—
81D292—28no—
82D292—22no—
83D292C22⋊C414yescomplemented
84C4×D73—28no—
85C4×D73—22no—
86C4×D73—22no—
87C4×D73—28no—
88C4×D73—22no—
89C4×D73C2×D414yes—
90#10596833—42no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73#10412yescomplemented
94C22×C73C2×C22⋊C411yescharacteristic
95C2×D73—21no—
96C2×D73—21no—
97C2×D73—21no—
98C2×D73—24no—
99C2×D73—21no—
100C2×D73—21no—
101C2×D73—44no—
102C2×D73—48no—
103C2×D73—42no—
104C2×D73—42no—
105C2×D73#12012yes—
106#64408—44no—
107C4×C73—24no—
108C4×C73—21no—
109C4×C73C2×C22⋊C412yes—
110Dic73—21no—
111Dic73#12012yes—
112C2×C73—22no—
113C2×C73#37911yescharacteristic
114C2×C73C2×#10411yescharacteristic
115C2×C73#42111yescharacteristic
116D73—22no—
117D73—41no—
118D73—44no—
119#1789—731nomaximal, Sylow
120C73#178911yescharacteristic, complemented, Sylow
121C22×#41—731no—
122C2×#104—734no—
123#407—731no—
124C4×C22⋊C4—731no—
125C2×#41—732no—
126C2×#41—732no—
127C2×#41—1461no—
128C2×#41—1461no—
129C2×#41—1468no—
130C22×Q8#6440811yescharacteristic, complemented
131C22×D4—731no—
132C22×D4—1461no—
133C23×C4—731no—
134C23×C4—1461no—
135C2×M16—732no—
136C2×C22⋊C4—1461no—
137C2×C42—732no—
138#104—1468no—
139C22⋊C8—1461no—
140C22⋊C8—1461no—
141#95—1461no—
142C24—731no—
143C24—1461no—
144#41—738no—
145#41—1464no—
146#41—1464no—
147#41—1468no—
148#41—1468no—
149#41—1464no—
150C2×Q8—24no—
151C2×Q8—21no—
152C2×Q8C2×#6440812yes—
153C2×D4—732no—
154C2×D4—1464no—
155C2×D4—1462no—
156C2×D4—1462no—
157C2×D4—1468no—
158C2×D4—1461no—
159C22×C4—21no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—731no—
165C22×C4—1464no—
166C22×C4—1462no—
167C22×C4—1462no—
168C22×C4—1468no—
169C22×C4—1462no—
170C22×C4C2×#6440811yescharacteristic
171M16—1464no—
172C2×C8—1462no—
173C22⋊C4—1464no—
174C42—1464no—
175C23—2922no—
176C23—2921no—
177C23—2922no—
178C23—731no—
179C23—731no—
180C23—1462no—
181C23—1464no—
182C23—1462no—
183C23—1462no—
184C23C22⋊#6440811yescharacteristic
185Q8—24no—
186Q8—22no—
187Q8C22⋊#6440814yescomplemented
188D4—734no—
189D4—1468no—
190D4—1468no—
191D4—1464no—
192D4—1462no—
193C2×C4—24no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—2922no—
197C2×C4—2922no—
198C2×C4—731no—
199C2×C4—734no—
200C2×C4—731no—
201C2×C4—1462no—
202C2×C4—1468no—
203C2×C4—1462no—
204C2×C4—1468no—
205C2×C4—1464no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4C22⋊#6440811yescharacteristic
209C2×C4C22×#6440811yescharacteristic
210C8—2922no—
211C22—21no—
212C22—21no—
213C22—2928no—
214C22—2924no—
215C22—2922no—
216C22—2922no—
217C22—732no—
218C22—1464no—
219C22—1461no—
220C22—1461no—
221C22—1461no—
222C22—1461no—
223C22—1461no—
224C22#1455665612yescomplemented
225C22C2×C22⋊#6440811yescharacteristic
226C4—24no—
227C4—21no—
228C4—2924no—
229C4—732no—
230C4—1461no—
231C4C2×C22⋊#6440812yes—
232C2—22no—
233C2—2924no—
234C2—2921no—
235C2—1462no—
236C2#1798952811yescharacteristic
237C2C2×#1455665611yescharacteristic
238C2#1798958611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×Q8#64408
hypocenterC73#1789
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×#14556656C2semidirect
2. #17989558C2semidirect
3. C4×C22⋊#64408C2semidirect
5. C2×#11924038C22semidirect
7. C2×C4×#64408C22semidirect
15. C2×#11924029C4semidirect
18. C22×D292C4semidirect
21. C22×Q8×C73C4semidirect
70. Q8×C73C22⋊C4semidirect
83. D292C22⋊C4semidirect
93. C22×C73#104semidirect
120. C73#1789semidirect
130. C22×Q8#64408semidirect
187. Q8C22⋊#64408semidirect
224. C22#14556656semidirect