Finite Group Databasebeta

← #22620857

Subgroups — #22620857

Order 9344.

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

normal subgroups only

This group has 428 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#17989138C211yesmaximal, characteristic
2C4⋊Q8×D73C211yesmaximal, characteristic, complemented
3#17988961C211yesmaximal, characteristic, complemented
4#17988960C211yesmaximal, characteristic, complemented
5#17988939C211yesmaximal, characteristic, complemented
6#17988791C214yesmaximal, complemented
7#17988727C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#487×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—21no—
11C2×Q8×D73C2212yes—
12C2×#11924017C2214yes—
13C2×#11924015C2214yes—
14#14556591C2211yescharacteristic
15#14556590—21no—
16#14556590—21no—
17#14556589C2212yes—
18#14556588C2211yescharacteristic
19#14556580—21no—
20#14556566—21no—
21#14556566C2212yes—
22#14556553—21no—
23#14556553C2212yes—
24C4⋊C4×D73—21no—
25C4⋊C4×D73—21no—
26C42×D73C2211yescharacteristic
27#14556520C2212yes—
28#14556514C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#103×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35#11924029—44no—
36C2×Dic146—22no—
37C2×Dic146C2312yes—
38Q8×D73—44no—
39C2×D292—22no—
40C2×D292—21no—
41C2×D292—21no—
42C2×D292C2312yes—
43C2×C4×D73—22no—
44C2×C4×D73—22no—
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47C2×C4×D73C2311yescharacteristic
48#11924017—44no—
49#11924015—44no—
50C2×#10596831C2312yes—
51C4⋊Dic73—21no—
52C4⋊Dic73—21no—
53#11924007—22no—
54#11924007—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×D73C2×D411yescharacteristic
70Q8×C73—24no—
71Q8×C73—42no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2411yescharacteristic
77C2×Dic73—22no—
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80C2×Dic73C2×D411yescharacteristic
81D292—24no—
82D292—44no—
83D292—42no—
84D292—42no—
85C4×D73—22no—
86C4×D73—22no—
87C4×D73—44no—
88C4×D73—44no—
89C4×D73SD1614yescomplemented
90Dic146—24no—
91Dic146—44no—
92C8×C73—22no—
93#10596831—22no—
94C22×C73C22×D411yescharacteristic
95C2×D73—21no—
96C2×D73—21no—
97C2×D73—42no—
98C2×D73—42no—
99C2×D73—42no—
100C2×D73C2×SD1612yes—
101C4×C73—42no—
102C4×C73—42no—
103C4×C73C2×SD1612yes—
104C4×C73#13712yes—
105C4×C73H(5,𝔽2)12yes—
106Dic73—21no—
107Dic73—21no—
108Dic73—42no—
109Dic73C2×SD1612yes—
110C2×C73#53511yescharacteristic
111C2×C73C22×SD1611yescharacteristic
112C2×C73C2×#13711yescharacteristic
113D73—22no—
114D73—82no—
115#3206—731nomaximal, Sylow
116C73#320611yescharacteristic, complemented, Sylow
117#532—731no—
118C2×C4⋊Q8—731no—
119#492—731no—
120#492—731no—
121#487—731no—
122#487D7311yescharacteristic, complemented
123#461—734no—
124#448—734no—
125#431—731no—
126C2×#41—1461no—
127C22×Q8—732no—
128C2×SD16—734no—
129C2×SD16—734no—
130C4⋊Q8—732no—
131C4⋊Q8—731no—
132C4⋊Q8—1461no—
133C4⋊Q8—1461no—
134C4⋊Q8C2×D7311yescharacteristic
135C4⋊Q8C2×D7311yescharacteristic
136#127—731no—
137#124—1461no—
138#121—732no—
139#121—1461no—
140C4×D4—732no—
141C4×D4—1461no—
142C2×C4⋊C4—1461no—
143C2×C4⋊C4—1461no—
144C2×C42—731no—
145C4⋊C8—732no—
146#103—734no—
147#103C2×D7314yes—
148C22⋊C8—732no—
149C4×C8—731no—
150C4×C8C2×D7311yescharacteristic
151#41—2924no—
152C2×Q8—21no—
153C2×Q8—2924no—
154C2×Q8—732no—
155C2×Q8—1462no—
156C2×Q8C22×D7312yes—
157C2×D4—732no—
158C2×D4—1462no—
159C2×D4—1461no—
160C2×D4—1461no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—1462no—
165C22×C4—1462no—
166SD16—2924no—
167SD16—2924no—
168C2×C8—732no—
169C2×C8C22×D7312yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C4⋊C4—1461no—
176C4⋊C4—1461no—
177C4⋊C4C22×D7312yes—
178C22⋊C4—1462no—
179C22⋊C4—1462no—
180C42—731no—
181C42—731no—
182C42—731no—
183C42C22×D7311yescharacteristic
184C23—731no—
185C23—1462no—
186Q8—24no—
187Q8—42no—
188Q8—2924no—
189Q8—1464no—
190D4—2924no—
191D4—2922no—
192D4—2922no—
193D4—1464no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—2924no—
197C2×C4—2924no—
198C2×C4—731no—
199C2×C4—734no—
200C2×C4—731no—
201C2×C4—731no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4D4×D7311yescharacteristic
206C2×C4D4×D7311yescharacteristic
207C2×C4C23×D7311yescharacteristic
208C8—22no—
209C8—1462no—
210C22—2922no—
211C22—2922no—
212C22—2922no—
213C22—732no—
214C22—1461no—
215C22—1461no—
216C22C2×D4×D7311yescharacteristic
217C4—42no—
218C4—42no—
219C4—2922no—
220C4—732no—
221C4—1461no—
222C4—1461no—
223C4SD16×D7312yes—
224C4#1455662312yes—
225C4#1455663712yes—
226C2—5842no—
227C2—1462no—
228C2#1798915511yescharacteristic
229C2C2×SD16×D7311yescharacteristic
230C2C2×#1455662311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#487×C73C2
socleC22×C73C22×D4
hypercenter#487D73
hypocenterC73#3206
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
2. C4⋊Q8×D73C2semidirect
3. #17988961C2semidirect
4. #17988960C2semidirect
5. #17988939C2semidirect
6. #17988791C2semidirect
7. #17988727C2semidirect
8. #17988638C2semidirect
9. #487×C73C2semidirect
89. C4×D73SD16semidirect
116. C73#3206semidirect
122. #487D73semidirect