Finite Group Databasebeta

← #22620867

Subgroups — #22620867

Order 9344.

438 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989138C211yesmaximal, characteristic, complemented
2#17989138C211yesmaximal, characteristic, complemented
3#17988964C211yesmaximal, characteristic, complemented
4#17988961C211yesmaximal, characteristic, complemented
5#17988935C211yesmaximal, characteristic, complemented
6#17988805C214yesmaximal, complemented
7#17988735C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#487×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—21no—
11C2×#11924029C2212yes—
12C2×#11924015C2214yes—
13C2×D584C2214yes—
14#14556588C2211yescharacteristic
15#14556588C2211yescharacteristic
16#14556580—21no—
17#14556580C2212yes—
18#14556566—21no—
19#14556566—21no—
20#14556566—21no—
21#14556566C2212yes—
22#14556553—21no—
23#14556553—21no—
24#14556553—21no—
25#14556553C2212yes—
26C42×D73C2211yescharacteristic
27#14556520C2212yes—
28#14556511C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#103×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35#11924029—44no—
36#11924029—44no—
37C2×D292—22no—
38C2×D292—22no—
39C2×D292—21no—
40C2×D292—21no—
41C2×D292—21no—
42C2×D292—21no—
43C2×D292C2312yes—
44C2×D292C2312yes—
45C2×C4×D73—22no—
46C2×C4×D73—22no—
47C2×C4×D73D411yescharacteristic
48C2×C4×D73D411yescharacteristic
49C2×C4×D73C2311yescharacteristic
50#11924015—44no—
51D584—44no—
52C2×#10596831C2312yes—
53#11924005—22no—
54#11924005—22no—
55#11924005—22no—
56#11924005—22no—
57C4×Dic73D411yescharacteristic
58C4×Dic73D411yescharacteristic
59C4×Dic73C2311yescharacteristic
60C2×Q8×C73—21no—
61C2×Q8×C73C2312yes—
62C2×C8×C73C2312yes—
63C4⋊C4×C73—21no—
64C4⋊C4×C73—21no—
65C4⋊C4×C73—21no—
66C4⋊C4×C73C2312yes—
67C42×C73C2311yescharacteristic
68C22×D73—22no—
69C22×D73—22no—
70C22×D73C2×D411yescharacteristic
71Q8×C73—24no—
72Q8×C73—42no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2411yescharacteristic
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80C2×Dic73C2×D411yescharacteristic
81D292—24no—
82D292—24no—
83D292—44no—
84D292—44no—
85D292—42no—
86D292—42no—
87D292—42no—
88D292—42no—
89C4×D73—22no—
90C4×D73—22no—
91C4×D73—22no—
92C4×D73—44no—
93C4×D73—44no—
94C8×C73—22no—
95#10596831—22no—
96C22×C73C22×D411yescharacteristic
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—42no—
101C2×D73—42no—
102C2×D73—42no—
103C2×D73—42no—
104C2×D73—42no—
105C2×D73—42no—
106C4×C73—42no—
107C4×C73—42no—
108C4×C73#13512yes—
109C4×C73AGL(1,ℤ/8)12yes—
110C4×C73H(5,𝔽2)12yes—
111Dic73—21no—
112Dic73—21no—
113Dic73—21no—
114C2×C73#53511yescharacteristic
115C2×C73C2×#13511yescharacteristic
116C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
117D73—41no—
118D73—82no—
119D73—82no—
120#3207—731nomaximal, Sylow
121C73#320711yescharacteristic, complemented, Sylow
122#532—731no—
123#532—731no—
124#493—731no—
125#492—731no—
126#487D7311yescharacteristic, complemented
127#486—731no—
128#463—734no—
129#449—734no—
130#431—731no—
131C2×#41—732no—
132C2×#41—1461no—
133C2×SD16—734no—
134C2×D8—734no—
135C4⋊Q8C2×D7311yescharacteristic
136C4⋊Q8C2×D7311yescharacteristic
137#127—731no—
138#127—731no—
139#124—732no—
140#124—1461no—
141#121—732no—
142#121—1461no—
143#121—1461no—
144#121—1461no—
145C4×D4—732no—
146C4×D4—1461no—
147C4×D4—1461no—
148C4×D4—1461no—
149C2×C42—731no—
150C4⋊C8—732no—
151#103C2×D7314yes—
152#102—734no—
153C22⋊C8—732no—
154C4×C8—731no—
155C4×C8C2×D7311yescharacteristic
156#41—2924no—
157#41—2924no—
158C2×Q8—21no—
159C2×Q8C22×D7312yes—
160C2×D4—732no—
161C2×D4—732no—
162C2×D4—1462no—
163C2×D4—1462no—
164C2×D4—1461no—
165C2×D4—1461no—
166C2×D4—1461no—
167C2×D4—1461no—
168C22×C4—731no—
169C22×C4—731no—
170C22×C4—731no—
171C22×C4—1462no—
172C22×C4—1462no—
173SD16—2924no—
174D8—2924no—
175C2×C8—732no—
176C2×C8C22×D7312yes—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4C22×D7312yes—
181C22⋊C4—1462no—
182C22⋊C4—1462no—
183C22⋊C4—1462no—
184C22⋊C4—1462no—
185C42—731no—
186C42—731no—
187C42—731no—
188C42C22×D7311yescharacteristic
189C23—731no—
190C23—1462no—
191C23—1462no—
192Q8—24no—
193Q8—42no—
194D4—2924no—
195D4—2924no—
196D4—2922no—
197D4—2922no—
198D4—2922no—
199D4—2922no—
200D4—1464no—
201D4—1464no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—2924no—
205C2×C4—2924no—
206C2×C4—731no—
207C2×C4—731no—
208C2×C4—731no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4D4×D7311yescharacteristic
213C2×C4D4×D7311yescharacteristic
214C2×C4C23×D7311yescharacteristic
215C8—22no—
216C8—1462no—
217C22—2922no—
218C22—2922no—
219C22—2922no—
220C22—2922no—
221C22—2922no—
222C22—2922no—
223C22—1461no—
224C22—1461no—
225C22—1461no—
226C22C2×D4×D7311yescharacteristic
227C4—42no—
228C4—42no—
229C4—1461no—
230C4—1461no—
231C4—1461no—
232C4#1455661412yes—
233C4#1455661812yes—
234C4#1455663712yes—
235C2—2921no—
236C2—5842no—
237C2—5842no—
238C2#1798915511yescharacteristic
239C2C2×#1455661411yescharacteristic
240C2C2×#1455661811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#487×C73C2
socleC22×C73C22×D4
hypercenter#487D73
hypocenterC73#3207
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #17989138C2semidirect
2. #17989138C2semidirect
3. #17988964C2semidirect
4. #17988961C2semidirect
5. #17988935C2semidirect
6. #17988805C2semidirect
7. #17988735C2semidirect
8. #17988638C2semidirect
9. #487×C73C2semidirect
121. C73#3207semidirect
126. #487D73semidirect