Finite Group Databasebeta

← #22620865

Subgroups — #22620865

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#17989135C211yesmaximal, characteristic, complemented
3#17988963C211yesmaximal, characteristic, complemented
4#17988960C211yesmaximal, characteristic, complemented
5#17988939C211yesmaximal, characteristic, complemented
6#17988801C214yesmaximal, complemented
7#17988733C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#486×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—21no—
11C2×#11924027C2212yes—
12C2×#11924017C2214yes—
13C2×#11924013C2214yes—
14#14556591C2211yescharacteristic
15#14556588C2211yescharacteristic
16#14556580—21no—
17#14556578C2212yes—
18#14556566—21no—
19#14556566C2212yes—
20#14556562—21no—
21#14556562—21no—
22D4×Dic73—21no—
23D4×Dic73—21no—
24#14556553—21no—
25#14556553C2212yes—
26C42×D73C2211yescharacteristic
27#14556520C2212yes—
28#14556514C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32#127×C73C2211yescharacteristic
33#102×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35#11924029—44no—
36#11924027—44no—
37C2×Dic146C2312yes—
38C2×D292—22no—
39C2×D292—21no—
40C2×D292—21no—
41C2×D292C2312yes—
42C2×C22⋊D73—22no—
43C22×Dic73—22no—
44C2×C4×D73—22no—
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47C2×C4×D73C2311yescharacteristic
48#11924017—44no—
49#11924013—44no—
50C2×#10596831C2312yes—
51C4⋊Dic73—21no—
52C4⋊Dic73—21no—
53C22⋊Dic73—22no—
54C22⋊Dic73—22no—
55#11924005—22no—
56#11924005—22no—
57C4×Dic73D411yescharacteristic
58C4×Dic73D411yescharacteristic
59C4×Dic73C2311yescharacteristic
60C2×Q8×C73—21no—
61C2×D4×C73—21no—
62C2×D4×C73—21no—
63C2×D4×C73C2312yes—
64C2×C8×C73C2312yes—
65C4⋊C4×C73—21no—
66C4⋊C4×C73C2312yes—
67C42×C73C2311yescharacteristic
68C23×C73—22no—
69C22×D73—22no—
70C22×D73C2×D411yescharacteristic
71Q8×C73—42no—
72D4×C73—24no—
73D4×C73—42no—
74D4×C73—42no—
75C2×C4×C73—22no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2411yescharacteristic
79C22⋊D73—44no—
80C2×Dic73—22no—
81C2×Dic73—44no—
82C2×Dic73C2×D411yescharacteristic
83C2×Dic73C2×D411yescharacteristic
84C2×Dic73C2×D411yescharacteristic
85D292—24no—
86D292—44no—
87D292—42no—
88D292—42no—
89C4×D73—22no—
90C4×D73—22no—
91C4×D73—22no—
92C4×D73—44no—
93Dic146—24no—
94C8×C73—22no—
95#10596831—22no—
96C22×C73—42no—
97C22×C73—42no—
98C22×C73—42no—
99C22×C73C22×D411yescharacteristic
100C2×D73—21no—
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—42no—
104C2×D73—42no—
105C2×D73—42no—
106C4×C73—42no—
107C4×C73#13512yes—
108C4×C73AGL(1,ℤ/8)12yes—
109C4×C73H(5,𝔽2)12yes—
110Dic73—21no—
111Dic73—21no—
112Dic73—21no—
113Dic73—42no—
114C2×C73—82no—
115C2×C73#53511yescharacteristic
116C2×C73C2×#13511yescharacteristic
117C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
118D73—41no—
119D73—82no—
120#3207—731nomaximal, Sylow
121C73#320711yescharacteristic, complemented, Sylow
122#532—731no—
123#532—731no—
124#493—731no—
125#492—731no—
126#487—731no—
127#486D7311yescharacteristic, complemented
128#463—734no—
129#449—734no—
130#431—731no—
131C2×#41—732no—
132C2×#41—1461no—
133C2×SD16—734no—
134C2×D8—734no—
135C4⋊Q8—731no—
136C4⋊Q8C2×D7311yescharacteristic
137#127—731no—
138#127C2×D7311yescharacteristic
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#103—734no—
152#102C2×D7314yes—
153C22⋊C8—732no—
154C4×C8—731no—
155C4×C8C2×D7311yescharacteristic
156#41—2924no—
157#41—2924no—
158C2×Q8—21no—
159C2×Q8—732no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—732no—
163C2×D4—1462no—
164C2×D4—1462no—
165C2×D4—1461no—
166C2×D4—1461no—
167C2×D4C22×D7312yes—
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—1461no—
179C4⋊C4—1461no—
180C4⋊C4C22×D7312yes—
181C22⋊C4—1462no—
182C22⋊C4—1462no—
183C22⋊C4—1462no—
184C22⋊C4—1462no—
185C42—731no—
186C42—731no—
187C42—731no—
188C42C22×D7311yescharacteristic
189C23—22no—
190C23—731no—
191C23—1462no—
192Q8—42no—
193Q8—1464no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—2924no—
198D4—2924no—
199D4—2922no—
200D4—2922no—
201D4—1464no—
202C2×C4—22no—
203C2×C4—2924no—
204C2×C4—2924no—
205C2×C4—731no—
206C2×C4—731no—
207C2×C4—731no—
208C2×C4—1462no—
209C2×C4—1462no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4D4×D7311yescharacteristic
213C2×C4D4×D7311yescharacteristic
214C2×C4C23×D7311yescharacteristic
215C8—22no—
216C8—1462no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—2922no—
221C22—2922no—
222C22—2922no—
223C22—1461no—
224C22—1461no—
225C22—1461no—
226C22C2×D4×D7311yescharacteristic
227C4—42no—
228C4—2922no—
229C4—1461no—
230C4—1461no—
231C4—1461no—
232C4#1455661212yes—
233C4#1455661512yes—
234C4#1455663712yes—
235C2—82no—
236C2—2921no—
237C2—5842no—
238C2#1798915511yescharacteristic
239C2C2×#1455661211yescharacteristic
240C2C2×#1455661511yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#486×C73C2
socleC22×C73C22×D4
hypercenter#486D73
hypocenterC73#3207
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #17989138C2semidirect
2. #17989135C2semidirect
3. #17988963C2semidirect
4. #17988960C2semidirect
5. #17988939C2semidirect
6. #17988801C2semidirect
7. #17988733C2semidirect
8. #17988638C2semidirect
9. #486×C73C2semidirect
121. C73#3207semidirect
127. #486D73semidirect