Finite Group Databasebeta

← #22625337

Subgroups — #22625337

Order 9344.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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, complemented
2#17989530C211yesmaximal, characteristic, complemented
3#17989439C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#121×D73C211yesmaximal, characteristic
6C2×#11924038—21no—
7C2×C22⋊#64408—21no—
8#14556648C2212yescomplemented
9C22⋊#10596833—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yescomplemented
12C2×D4×D73—21no—
13C2×D4×D73C411yescharacteristic, complemented
14C22×C4×D73C2211yescharacteristic
15#14556566C2211yescharacteristic
16#14556565C411yescharacteristic, complemented
17#14556564—21no—
18#14556563—21no—
19#14556562C2211yescharacteristic
20C4⋊C4×D73C411yescharacteristic, complemented
21C22⋊C4×D73—21no—
22#121×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924038—42no—
25C2×#10596833—22no—
26C22⋊#64408—42no—
27C23×D73—21no—
28C23×D73D411yescharacteristic
29C2×D292—21no—
30C2×D292C2×C411yescharacteristic
31C2×C22⋊D73—21no—
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34D4×D73—42no—
35D4×D73—44no—
36C22×Dic73D411yescharacteristic
37C2×C4×D73—21no—
38C2×C4×D73—42no—
39C2×C4×D73C2×C411yescharacteristic
40C2×C4×D73D411yescharacteristic
41C2×C4×D73D411yescharacteristic
42C2×C4×D73C2311yescharacteristic
43C4⋊Dic73C2×C411yescharacteristic
44#11924007—21no—
45C22⋊Dic73—21no—
46#11924005—21no—
47#11924005—21no—
48C2×D4×C73—21no—
49C2×D4×C73C2×C411yescharacteristic
50C22×C4×C73C2×C411yescharacteristic
51C4⋊C4×C73C2×C411yescharacteristic
52C22⋊C4×C73—21no—
53C23×C73—21no—
54C23×C73C22⋊C411yescharacteristic
55C22×D73—22no—
56C22×D73—22no—
57C22×D73—21no—
58C22×D73—41no—
59C22×D73—42no—
60C22×D73—42no—
61C22×D73—42no—
62C22×D73C22⋊C411yescharacteristic
63C22×D73C2×D411yescharacteristic
64C2×#64408—42no—
65C2×#64408—42no—
66C2×#64408—42no—
67D4×C73—41no—
68D4×C73—42no—
69C2×C4×C73—21no—
70C2×C4×C73—41no—
71C2×C4×C73C22⋊C411yescharacteristic
72C2×C4×C73C22×C411yescharacteristic
73C22⋊D73—42no—
74C22⋊D73—42no—
75C22⋊D73—42no—
76C2×Dic73—21no—
77C2×Dic73—41no—
78C2×Dic73C22⋊C411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80D292—41no—
81D292—42no—
82C4×D73—22no—
83C4×D73—22no—
84C4×D73—41no—
85C4×D73—41no—
86C4×D73—42no—
87#10596833—42no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73—21no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73C2×C22⋊C411yescharacteristic
95C2×D73—21no—
96C2×D73—21no—
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—44no—
100C2×D73—41no—
101C2×D73—41no—
102C2×D73—41no—
103C2×D73—84no—
104C2×D73#9912yes—
105C2×D73AGL(1,ℤ/8)12yes—
106#64408—82no—
107C4×C73—21no—
108C4×C73—21no—
109C4×C73—41no—
110Dic73—21no—
111Dic73—21no—
112Dic73—41no—
113C2×C73—41no—
114C2×C73—81no—
115C2×C73C2×#9911yescharacteristic
116C2×C73#41811yescharacteristic
117C2×C73#42111yescharacteristic
118D73—22no—
119D73—22no—
120D73—81no—
121#1510—731nomaximal, Sylow
122C73#151011yescharacteristic, complemented, Sylow
123C2×#121—731no—
124#407—731no—
125#381—731no—
126#327—732no—
127#327—732no—
128C22×D4—731no—
129C22×D4—1461no—
130C23×C4—731no—
131C2×M16—1461no—
132#121—731no—
133#121—731no—
134#121—731no—
135#121—1461no—
136#121—1461no—
137#121#6440811yescharacteristic, complemented
138C2×C4⋊C4—731no—
139C2×C22⋊C4—1461no—
140C2×C22⋊C4—1461no—
141C22⋊C8—732no—
142C22⋊C8—1461no—
143#95—732no—
144#95—1461no—
145C24—731no—
146C24—1461no—
147C2×D4—21no—
148C2×D4—2924no—
149C2×D4—2922no—
150C2×D4—731no—
151C2×D4—1461no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4—1461no—
155C2×D4C2×#6440811yescharacteristic
156C22×C4—2922no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—1461no—
163C22×C4—1462no—
164C22×C4C2×#6440811yescharacteristic
165M16—2922no—
166C2×C8—1462no—
167C4⋊C4—731no—
168C4⋊C4—1461no—
169C4⋊C4C2×#6440811yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—2922no—
172C22⋊C4—1461no—
173C22⋊C4—1461no—
174C22⋊C4—1461no—
175C23—21no—
176C23—2921no—
177C23—2922no—
178C23—2922no—
179C23—2922no—
180C23—731no—
181C23—731no—
182C23—1462no—
183C23—1462no—
184C23—1461no—
185C23C22⋊#6440811yescharacteristic
186D4—41no—
187D4—42no—
188D4—2921no—
189D4—2922no—
190D4—2922no—
191D4—2922no—
192D4—2922no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—2921no—
196C2×C4—2921no—
197C2×C4—2922no—
198C2×C4—2922no—
199C2×C4—2922no—
200C2×C4—2922no—
201C2×C4—2921no—
202C2×C4—731no—
203C2×C4—731no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1461no—
207C2×C4C22⋊#6440811yescharacteristic
208C2×C4C22×#6440811yescharacteristic
209C8—2922no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—2924no—
217C22—2921no—
218C22—2921no—
219C22—2921no—
220C22—5844no—
221C22—732no—
222C22—732no—
223C22—1461no—
224C22—1461no—
225C22—1461no—
226C22—1461no—
227C22C2×C22⋊#6440811yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—2921no—
232C4—5842no—
233C4—1461no—
234C4—1461no—
235C2—41no—
236C2—81no—
237C2—5841no—
238C2—1462no—
239C2—1462no—
240C2D73⋊#9911yescharacteristic
241C2#1798957911yescharacteristic
242C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1510
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #17989558C2semidirect
2. #17989530C2semidirect
3. #17989439C2semidirect
4. #17989438C2semidirect
8. #14556648C22semidirect
11. (C2×#64408)⋊C4C22semidirect
13. C2×D4×D73C4semidirect
16. #14556565C4semidirect
20. C4⋊C4×D73C4semidirect
22. #121×C73C4semidirect
122. C73#1510semidirect
137. #121#64408semidirect