Finite Group Databasebeta

← #22620864

Subgroups — #22620864

Order 9344.

438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989137C211yesmaximal, characteristic, complemented
2#17988963C211yesmaximal, characteristic, complemented
3#17988961C211yesmaximal, characteristic, complemented
4#17988937C211yesmaximal, characteristic, complemented
5#17988933C211yesmaximal, characteristic, complemented
6#17988799C214yesmaximal, complemented
7#17988732C214yesmaximal, complemented
8#17988640C211yesmaximal, characteristic, complemented
9#532×C73C211yesmaximal, characteristic, complemented
10C2×#11924028—21no—
11C2×#11924015C2214yes—
12C2×#11924013C2214yes—
13#14556591C2211yescharacteristic
14#14556588C2211yescharacteristic
15#14556579—21no—
16#14556565—21no—
17#14556565C2212yes—
18C4×D292—21no—
19C4×D292C2212yes—
20C4⋊#10596831C2212yes—
21#14556515C2214yes—
22#14556512C2214yes—
23C22⋊#10596831C2212yes—
24C4×#10596831C2211yescharacteristic
25C4×#10596831C2211yescharacteristic
26C2×#41×C73C2212yes—
27C4⋊Q8×C73C2211yescharacteristic
28#127×C73C2211yescharacteristic
29#124×C73C2212yes—
30#121×C73—21no—
31#121×C73—21no—
32C4×D4×C73—21no—
33C4×D4×C73—21no—
34C2×C42×C73C2211yescharacteristic
35#11924028—44no—
36C2×Dic146—21no—
37C2×D292—21no—
38C2×D292—21no—
39C2×D292C2312yes—
40C2×C22⋊D73—22no—
41C2×C4×D73—22no—
42#11924015—44no—
43#11924013—44no—
44C2×#10596831C2312yes—
45C2×#10596831C2312yes—
46C4⋊Dic73—21no—
47C4⋊Dic73C2312yes—
48#11924005—22no—
49#11924005—22no—
50#41×C73—44no—
51C2×Q8×C73C2312yes—
52C2×D4×C73—22no—
53C2×D4×C73—21no—
54C2×D4×C73—21no—
55C2×D4×C73C2312yes—
56C22×C4×C73—22no—
57C22×C4×C73D411yescharacteristic
58C22×C4×C73D411yescharacteristic
59C22×C4×C73C2311yescharacteristic
60C4⋊C4×C73—21no—
61C4⋊C4×C73—21no—
62C22⋊C4×C73—22no—
63C22⋊C4×C73—22no—
64C42×C73D411yescharacteristic
65C42×C73D411yescharacteristic
66C42×C73C2311yescharacteristic
67C42×C73C2311yescharacteristic
68C23×C73—22no—
69C23×C73C2×D411yescharacteristic
70C22×D73—22no—
71Q8×C73—24no—
72D4×C73—24no—
73D4×C73—44no—
74D4×C73—42no—
75D4×C73—42no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—44no—
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2411yescharacteristic
87C22⋊D73—44no—
88C2×Dic73—22no—
89D292—24no—
90D292—42no—
91D292—42no—
92C4×D73—44no—
93Dic146—42no—
94#10596831—22no—
95#10596831—22no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73—42no—
100C22×C73—42no—
101C22×C73—42no—
102C22×C73C22×D411yescharacteristic
103C2×D73—42no—
104C2×D73—42no—
105C2×D73—42no—
106C4×C73—21no—
107C4×C73—21no—
108C4×C73—21no—
109C4×C73—42no—
110C4×C73#13512yes—
111C4×C73AGL(1,ℤ/8)12yes—
112C4×C73H(5,𝔽2)12yes—
113Dic73—42no—
114C2×C73—41no—
115C2×C73—82no—
116C2×C73#53511yescharacteristic
117C2×C73C2×#13511yescharacteristic
118C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
119D73—82no—
120#3207—731nomaximal, Sylow
121C73#320711yescharacteristic, complemented, Sylow
122#532—731no—
123#532D7311yescharacteristic, complemented
124#493—731no—
125#492—731no—
126#487—731no—
127#486—731no—
128#463—734no—
129#449—734no—
130#431—731no—
131C2×#41—1461no—
132C2×#41C2×D7312yes—
133C2×SD16—734no—
134C2×D8—734no—
135C4⋊Q8—731no—
136C4⋊Q8C2×D7311yescharacteristic
137#127—731no—
138#127C2×D7311yescharacteristic
139#124—1461no—
140#124C2×D7312yes—
141#121—21no—
142#121—21no—
143#121—732no—
144#121—1461no—
145C4×D4—21no—
146C4×D4—21no—
147C4×D4—732no—
148C4×D4—1461no—
149C2×C42C2×D7311yescharacteristic
150C4⋊C8—732no—
151#103—734no—
152#102—734no—
153C22⋊C8—732no—
154C4×C8—731no—
155C4×C8—731no—
156#41—44no—
157#41—2924no—
158C2×Q8—1461no—
159C2×Q8C22×D7312yes—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—732no—
164C2×D4—1462no—
165C2×D4—1461no—
166C2×D4—1461no—
167C2×D4C22×D7312yes—
168C22×C4—22no—
169C22×C4—1462no—
170C22×C4C22⋊D7311yescharacteristic
171C22×C4C22⋊D7311yescharacteristic
172C22×C4C22×D7311yescharacteristic
173SD16—2924no—
174D8—2924no—
175C2×C8—732no—
176C2×C8—732no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—732no—
180C4⋊C4—1461no—
181C22⋊C4—22no—
182C22⋊C4—22no—
183C22⋊C4—1462no—
184C22⋊C4—1462no—
185C42C22⋊D7311yescharacteristic
186C42C22⋊D7311yescharacteristic
187C42C22×D7311yescharacteristic
188C42C22×D7311yescharacteristic
189C23—22no—
190C23—1462no—
191C23C2×C22⋊D7311yescharacteristic
192Q8—24no—
193Q8—2922no—
194D4—24no—
195D4—44no—
196D4—42no—
197D4—42no—
198D4—2924no—
199D4—2922no—
200D4—2922no—
201D4—1464no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—44no—
207C2×C4—2924no—
208C2×C4—1462no—
209C2×C4C2×C22⋊D7311yescharacteristic
210C2×C4C2×C22⋊D7311yescharacteristic
211C2×C4C2×C22⋊D7311yescharacteristic
212C2×C4C2×C22⋊D7311yescharacteristic
213C2×C4C2×C22⋊D7311yescharacteristic
214C2×C4C23×D7311yescharacteristic
215C8—1462no—
216C8—1462no—
217C22—21no—
218C22—21no—
219C22—21no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—2922no—
224C22—2922no—
225C22—2922no—
226C22C22×C22⋊D7311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—42no—
231C4—2922no—
232C4#1455661112yes—
233C4#1455661612yes—
234C4#1455663612yes—
235C2—41no—
236C2—82no—
237C2—5842no—
238C2#1798915411yescharacteristic
239C2C2×#1455661111yescharacteristic
240C2C2×#1455661611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3207
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #17989137C2semidirect
2. #17988963C2semidirect
3. #17988961C2semidirect
4. #17988937C2semidirect
5. #17988933C2semidirect
6. #17988799C2semidirect
7. #17988732C2semidirect
8. #17988640C2semidirect
9. #532×C73C2semidirect
121. C73#3207semidirect
123. #532D73semidirect