Finite Group Databasebeta

← #22625366

Subgroups — #22625366

Order 9344.

340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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×#14556648C211yesmaximal, characteristic, complemented
2#17989529C211yesmaximal, characteristic, complemented
3#17989439C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#121×D73C211yesmaximal, characteristic
6C22×#10596833—21no—
7C2×C4⋊#64408—21no—
8C2×C22⋊#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—
24C2×#10596833—22no—
25C2×#10596833—42no—
26C4⋊#64408—42no—
27C22⋊#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—42no—
37D4×D73—42no—
38C22×Dic73D411yescharacteristic
39C2×C4×D73—21no—
40C2×C4×D73—42no—
41C2×C4×D73C2×C411yescharacteristic
42C2×C4×D73D411yescharacteristic
43C2×C4×D73D411yescharacteristic
44C2×C4×D73C2311yescharacteristic
45C4⋊Dic73C2×C411yescharacteristic
46#11924007—21no—
47C22⋊Dic73—21no—
48#11924005—21no—
49#11924005—21no—
50C2×D4×C73—21no—
51C2×D4×C73C2×C411yescharacteristic
52C22×C4×C73C2×C411yescharacteristic
53C4⋊C4×C73C2×C411yescharacteristic
54C22⋊C4×C73—21no—
55C23×C73—21no—
56C23×C73C22⋊C411yescharacteristic
57C22×D73—21no—
58C22×D73—41no—
59C22×D73—41no—
60C22×D73—42no—
61C22×D73—42no—
62C22×D73—42no—
63C22×D73C22⋊C411yescharacteristic
64C22×D73D812yes—
65C22×D73SD1612yes—
66C22×D73C2×D411yescharacteristic
67C2×#64408—42no—
68C2×#64408—42no—
69C2×#64408—42no—
70D4×C73—41no—
71D4×C73—42no—
72C2×C4×C73—21no—
73C2×C4×C73—41no—
74C2×C4×C73C22⋊C411yescharacteristic
75C2×C4×C73C22×C411yescharacteristic
76C22⋊D73—42no—
77C22⋊D73—41no—
78C22⋊D73—41no—
79C22⋊D73—42no—
80C2×Dic73—22no—
81C2×Dic73—21no—
82C2×Dic73C22⋊C411yescharacteristic
83C2×Dic73C2×D411yescharacteristic
84D292—41no—
85D292—41no—
86D292—41no—
87C4×D73—22no—
88C4×D73—22no—
89C4×D73—41no—
90C4×D73—41no—
91C4×D73—42no—
92#10596833—42no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73—41no—
98C22×C73#10212yes—
99C22×C73C2×C22⋊C411yescharacteristic
100C2×D73—21no—
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—21no—
104C2×D73—42no—
105C2×D73—42no—
106C2×D73—41no—
107C2×D73—41no—
108C2×D73—41no—
109C2×D73—84no—
110C2×D73#10212yes—
111C2×D73C2×D811yescharacteristic
112C2×D73C2×SD1611yescharacteristic
113#64408—82no—
114C4×C73—21no—
115C4×C73—21no—
116C4×C73—41no—
117Dic73—21no—
118Dic73—41no—
119Dic73#9912yes—
120C2×C73—22no—
121C2×C73—81no—
122C2×C73C2×#9911yescharacteristic
123C2×C73C2×#10211yescharacteristic
124C2×C73#42111yescharacteristic
125D73—21no—
126D73—22no—
127D73—21no—
128D73—81no—
129#1519—731nomaximal, Sylow
130C73#151911yescharacteristic, complemented, Sylow
131C2×#121—731no—
132C2×C22⋊C8—731no—
133#380—731no—
134#327—732no—
135#327—732no—
136C22×D4—731no—
137C22×D4—1461no—
138C23×C4—731no—
139C22×C8—1461no—
140#121—731no—
141#121—731no—
142#121—731no—
143#121—1461no—
144#121—1461no—
145#121#6440811yescharacteristic, complemented
146C2×C4⋊C4—731no—
147C2×C4⋊C4—1461no—
148C2×C22⋊C4—1461no—
149C2×C22⋊C4—1461no—
150C22⋊C8—732no—
151C22⋊C8—1461no—
152#95—732no—
153C24—731no—
154C24—1461no—
155C2×D4—21no—
156C2×D4—2922no—
157C2×D4—2922no—
158C2×D4—2922no—
159C2×D4—731no—
160C2×D4—1461no—
161C2×D4—1461no—
162C2×D4—1461no—
163C2×D4—1461no—
164C2×D4C2×#6440811yescharacteristic
165C22×C4—2922no—
166C22×C4—731no—
167C22×C4—731no—
168C22×C4—731no—
169C22×C4—731no—
170C22×C4—731no—
171C22×C4—1461no—
172C22×C4—1462no—
173C22×C4C2×#6440811yescharacteristic
174C2×C8—2922no—
175C2×C8—1462no—
176C4⋊C4—2922no—
177C4⋊C4—731no—
178C4⋊C4—1461no—
179C4⋊C4C2×#6440811yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—2922no—
182C22⋊C4—1461no—
183C22⋊C4—1461no—
184C22⋊C4—1461no—
185C23—21no—
186C23—2921no—
187C23—2921no—
188C23—2922no—
189C23—2922no—
190C23—2922no—
191C23—732no—
192C23—732no—
193C23—731no—
194C23—731no—
195C23—1461no—
196C23C22⋊#6440811yescharacteristic
197D4—41no—
198D4—42no—
199D4—2921no—
200D4—2921no—
201D4—2921no—
202D4—2921no—
203D4—2921no—
204D4—2922no—
205D4—2922no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—2921no—
209C2×C4—2921no—
210C2×C4—2922no—
211C2×C4—2922no—
212C2×C4—2922no—
213C2×C4—2922no—
214C2×C4—731no—
215C2×C4—731no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1461no—
219C2×C4—1462no—
220C2×C4C22⋊#6440811yescharacteristic
221C2×C4C22×#6440811yescharacteristic
222C8—2922no—
223C22—21no—
224C22—21no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—2922no—
229C22—2922no—
230C22—2921no—
231C22—2921no—
232C22—2921no—
233C22—5844no—
234C22—731no—
235C22—732no—
236C22—731no—
237C22—1461no—
238C22—1461no—
239C22—1461no—
240C22—1461no—
241C22#1455665312yes—
242C22C2×C22⋊#6440811yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—2921no—
247C4—5842no—
248C4—732no—
249C4—1461no—
250C2—22no—
251C2—81no—
252C2—5841no—
253C2—1461no—
254C2—1462no—
255C2—1461no—
256C2D73⋊#9911yescharacteristic
257C2C2×#1455665311yescharacteristic
258C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1519
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. C2×#14556648C2semidirect
2. #17989529C2semidirect
3. #17989439C2semidirect
4. #17989438C2semidirect
10. #14556648C22semidirect
11. (C2×#64408)⋊C4C22semidirect
13. C2×D4×D73C4semidirect
16. #14556565C4semidirect
20. C4⋊C4×D73C4semidirect
22. #121×C73C4semidirect
130. C73#1519semidirect
145. #121#64408semidirect