Finite Group Databasebeta

← #22625326

Subgroups — #22625326

Order 9344.

346 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989559C211yesmaximal, characteristic, complemented
2C4×C22⋊#64408C211yesmaximal, characteristic, complemented
3#17989439C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#121×D73C211yesmaximal, characteristic
6C2×#11924037—21no—
7C2×C22⋊#64408—21no—
8C2×C4×#64408—21no—
9#14556648—21no—
10#14556648C2212yescomplemented
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#11924037—42no—
25C2×#10596833—22no—
26C22⋊#64408—24no—
27C4×#64408—42no—
28C23×D73—21no—
29C23×D73D411yescharacteristic
30C2×D292—21no—
31C2×D292C2×C411yescharacteristic
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C2×C22⋊D73—21no—
35D4×D73—42no—
36D4×D73—44no—
37C22×Dic73D411yescharacteristic
38C2×C4×D73—21no—
39C2×C4×D73—42no—
40C2×C4×D73C2×C411yescharacteristic
41C2×C4×D73D411yescharacteristic
42C2×C4×D73D411yescharacteristic
43C2×C4×D73C2311yescharacteristic
44C4⋊Dic73C2×C411yescharacteristic
45#11924007—21no—
46C22⋊Dic73—21no—
47#11924005—21no—
48#11924005—21no—
49C2×D4×C73—21no—
50C2×D4×C73C2×C411yescharacteristic
51C22×C4×C73C2×C411yescharacteristic
52C4⋊C4×C73C2×C411yescharacteristic
53C22⋊C4×C73—21no—
54C23×C73—21no—
55C23×C73C22⋊C411yescharacteristic
56C22×D73—22no—
57C22×D73—22no—
58C22×D73—21no—
59C22×D73—41no—
60C22×D73—42no—
61C22×D73—42no—
62C22×D73—42no—
63C22×D73C22⋊C411yescharacteristic
64C22×D73C2×D411yescharacteristic
65C2×#64408—24no—
66C2×#64408—42no—
67C2×#64408—42no—
68D4×C73—41no—
69D4×C73—42no—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C2×C4×C73C22⋊C411yescharacteristic
73C2×C4×C73C22×C411yescharacteristic
74C22⋊D73—42no—
75C22⋊D73—42no—
76C22⋊D73—42no—
77C2×Dic73—22no—
78C2×Dic73—21no—
79C2×Dic73C22⋊C411yescharacteristic
80C2×Dic73C2×D411yescharacteristic
81D292—41no—
82D292—42no—
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—41no—
86C4×D73—41no—
87C4×D73—42no—
88#10596833—42no—
89C22×C73—21no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73C2×C22⋊C411yescharacteristic
96C2×D73—21no—
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—44no—
101C2×D73—41no—
102C2×D73—41no—
103C2×D73—41no—
104C2×D73—84no—
105C2×D73#10412yes—
106C2×D73AGL(1,ℤ/8)12yes—
107#64408—44no—
108C4×C73—21no—
109C4×C73—21no—
110C4×C73—41no—
111Dic73—21no—
112Dic73—41no—
113Dic73#9912yes—
114C2×C73—41no—
115C2×C73—81no—
116C2×C73C2×#9911yescharacteristic
117C2×C73#41811yescharacteristic
118C2×C73C2×#10411yescharacteristic
119D73—22no—
120D73—22no—
121D73—81no—
122#1507—731nomaximal, Sylow
123C73#150711yescharacteristic, complemented, Sylow
124C2×#121—731no—
125#407—731no—
126C4×C22⋊C4—731no—
127#327—732no—
128#327—732no—
129C22×D4—731no—
130C22×D4—1461no—
131C23×C4—731no—
132C2×M16—1461no—
133#121—731no—
134#121—731no—
135#121—731no—
136#121—1461no—
137#121—1461no—
138#121#6440811yescharacteristic, complemented
139C2×C4⋊C4—731no—
140C2×C22⋊C4—1461no—
141C2×C22⋊C4—1461no—
142C2×C42—1461no—
143C22⋊C8—732no—
144C22⋊C8—1461no—
145#95—732no—
146C24—731no—
147C24—1461no—
148C2×D4—21no—
149C2×D4—2924no—
150C2×D4—2922no—
151C2×D4—731no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4—1461no—
155C2×D4—1461no—
156C2×D4C2×#6440811yescharacteristic
157C22×C4—2922no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—1461no—
164C22×C4—1462no—
165C22×C4C2×#6440811yescharacteristic
166M16—2922no—
167C2×C8—1462no—
168C4⋊C4—731no—
169C4⋊C4—1461no—
170C4⋊C4C2×#6440811yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—1461no—
173C22⋊C4—1461no—
174C22⋊C4—1464no—
175C22⋊C4—1461no—
176C42—2922no—
177C23—21no—
178C23—2921no—
179C23—2922no—
180C23—2922no—
181C23—2922no—
182C23—731no—
183C23—731no—
184C23—1462no—
185C23—1462no—
186C23—1461no—
187C23C22⋊#6440811yescharacteristic
188D4—41no—
189D4—42no—
190D4—2921no—
191D4—2922no—
192D4—2922no—
193D4—2922no—
194D4—2922no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—2921no—
198C2×C4—2921no—
199C2×C4—2922no—
200C2×C4—2922no—
201C2×C4—2922no—
202C2×C4—731no—
203C2×C4—731no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1464no—
207C2×C4—1461no—
208C2×C4—1462no—
209C2×C4C22⋊#6440811yescharacteristic
210C2×C4C22×#6440811yescharacteristic
211C8—2922no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—2924no—
219C22—2921no—
220C22—2921no—
221C22—2921no—
222C22—5844no—
223C22—732no—
224C22—732no—
225C22—1461no—
226C22—1461no—
227C22—1461no—
228C22—1461no—
229C22C2×C22⋊#6440811yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—2924no—
234C4—2921no—
235C4—732no—
236C4—1461no—
237C2—41no—
238C2—81no—
239C2—5841no—
240C2—1462no—
241C2—1462no—
242C2D73⋊#9911yescharacteristic
243C2#1798957911yescharacteristic
244C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1507
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. #17989559C2semidirect
2. C4×C22⋊#64408C2semidirect
3. #17989439C2semidirect
4. #17989438C2semidirect
10. #14556648C22semidirect
11. (C2×#64408)⋊C4C22semidirect
13. C2×D4×D73C4semidirect
16. #14556565C4semidirect
20. C4⋊C4×D73C4semidirect
22. #121×C73C4semidirect
123. C73#1507semidirect
138. #121#64408semidirect