Finite Group Databasebeta

← #22619724

Subgroups — #22619724

Order 9344.

440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×D292C211yesmaximal, characteristic
2#17988884C214yesmaximal, complemented
3#17988874C212yesmaximal, complemented
4#17988864C212yesmaximal, complemented
5#17988630C212yesmaximal, complemented
6#17988611C211yesmaximal, characteristic, complemented
7#17988591C212yesmaximal
8#533×C73C211yesmaximal, characteristic, complemented
9C22×D292C2211yescharacteristic
10C22×C4×D73—21no—
11C2×#11924012C2212yes—
12C4×D292—21no—
13C4×D292—21no—
14C4×D292C2212yes—
15C4×D292C2212yes—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924005—21no—
18#14556524C2214yescomplemented
19#14556522C2214yescomplemented
20C4⋊#10596831C2212yescomplemented
21C4⋊#10596831C2212yescomplemented
22#14556511C2214yes—
23#14556511C2214yes—
24C4⋊Q8×C73C2211yescharacteristic, complemented
25C4⋊Q8×C73C2211yescharacteristic, complemented
26#125×C73C2212yescomplemented
27C22⋊Q8×C73—21no—
28C22⋊Q8×C73—21no—
29C4×Q8×C73—21no—
30C4×Q8×C73—21no—
31#117×C73C2212yes—
32C2×C42×C73C2211yescharacteristic
33C23×D73—21no—
34C2×D292—21no—
35C2×D292—22no—
36C2×D292Q814yescomplemented
37C2×D292C2312yes—
38C22×Dic73—21no—
39C2×C4×D73—22no—
40C2×C4×D73—22no—
41C2×C4×D73—44no—
42#11924012—24no—
43C2×#10596831C2314yes—
44C4⋊Dic73—21no—
45C4⋊Dic73C2312yes—
46#11924005—22no—
47#11924005—22no—
48C2×Q8×C73—21no—
49C2×Q8×C73—21no—
50C22×C4×C73D411yescharacteristic
51C22×C4×C73D411yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—22no—
54C4⋊C4×C73—22no—
55C4⋊C4×C73—21no—
56C4⋊C4×C73—21no—
57C4⋊C4×C73C2312yes—
58C4⋊C4×C73C2312yes—
59C22⋊C4×C73—22no—
60C42×C73—22no—
61C42×C73D411yescharacteristic
62C42×C73D411yescharacteristic
63C42×C73C2311yescharacteristic
64C42×C73C2311yescharacteristic
65C23×C73C2×D411yescharacteristic
66C22×D73—24no—
67C22×D73—22no—
68C22×D73—42no—
69C22×D73—42no—
70Q8×C73—42no—
71Q8×C73—42no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73—41no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×Q812yes—
82C2×C4×C73#4112yes—
83C2×C4×C73C2411yescharacteristic
84C2×Dic73—22no—
85C2×Dic73—42no—
86D292—24no—
87D292—22no—
88D292C2×Q814yes—
89C4×D73—44no—
90C4×D73—44no—
91#10596831—24no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73C22⋊Q812yes—
95C22×C73C22×D411yescharacteristic
96C2×D73—24no—
97C2×D73—48no—
98C2×D73—42no—
99C2×D73—42no—
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—42no—
104C4×C73—42no—
105C4×C73C22⋊Q812yes—
106C4×C73AGL(1,ℤ/8)12yes—
107C4×C73C22×Q811yescharacteristic
108C4×C73C2×#4111yescharacteristic
109Dic73—42no—
110C2×C73—22no—
111C2×C73C2×C22⋊Q811yescharacteristic
112C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
113C2×C73#57511yescharacteristic
114D73—44no—
115#3077—731nomaximal, Sylow
116C73#307711yescharacteristic, complemented, Sylow
117#533D7311yescharacteristic, complemented
118C2×C4×D4—731no—
119#478—734no—
120#476—732no—
121#474—732no—
122#428—732no—
123#423—731no—
124#418—732no—
125C22×D4—731no—
126C23×C4—1461no—
127C2×M16—732no—
128C4⋊Q8C2×D7311yescharacteristic, complemented
129C4⋊Q8C2×D7311yescharacteristic, complemented
130#125C2×D7312yescomplemented
131C22⋊Q8—21no—
132C22⋊Q8—21no—
133C4×Q8—21no—
134C4×Q8—21no—
135C4×D4—732no—
136C4×D4—732no—
137C4×D4—1461no—
138C4×D4—1461no—
139#117C2×D7312yes—
140C2×C4⋊C4—731no—
141C2×C22⋊C4—1461no—
142C2×C42C2×D7311yescharacteristic
143#107—734no—
144#106—734no—
145C4⋊C8—732no—
146C4⋊C8—732no—
147#102—734no—
148#102—734no—
149C24—1461no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×D4—734no—
153C2×D4—732no—
154C2×D4—1461no—
155C2×D4—1462no—
156C22×C4—2924no—
157C22×C4—1461no—
158C22×C4—1462no—
159C22×C4—1462no—
160C22×C4C22⋊D7311yescharacteristic
161C22×C4C22⋊D7311yescharacteristic
162C22×C4C22×D7311yescharacteristic
163M16—1464no—
164C2×C8—734no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—732no—
170C4⋊C4—1461no—
171C4⋊C4C22×D7312yes—
172C4⋊C4C22×D7312yes—
173C22⋊C4—22no—
174C22⋊C4—1462no—
175C22⋊C4—1462no—
176C42—22no—
177C42C22⋊D7311yescharacteristic
178C42C22⋊D7311yescharacteristic
179C42C22×D7311yescharacteristic
180C42C22×D7311yescharacteristic
181C23—2922no—
182C23—2922no—
183C23—1464no—
184C23—1462no—
185C23C2×C22⋊D7311yescharacteristic
186Q8—42no—
187Q8—42no—
188D4—734no—
189D4—1464no—
190D4—1462no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—2924no—
196C2×C4—2922no—
197C2×C4—2924no—
198C2×C4—1462no—
199C2×C4C2×C22⋊D7311yescharacteristic
200C2×C4C2×C22⋊D7311yescharacteristic
201C2×C4C2×C22⋊D7311yescharacteristic
202C2×C4C2×C22⋊D7311yescharacteristic
203C2×C4C2×C22⋊D7311yescharacteristic
204C2×C4Q8×D7312yes—
205C2×C4#1192402912yes—
206C2×C4C23×D7311yescharacteristic
207C8—1464no—
208C22—21no—
209C22—21no—
210C22—2928no—
211C22—2922no—
212C22—2922no—
213C22—1464no—
214C22#1455656712yes—
215C22C22×C22⋊D7311yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—2922no—
222C4#1455656712yes—
223C4#1455661612yes—
224C4C2×Q8×D7311yescharacteristic
225C4C2×#1192402911yescharacteristic
226C2—22no—
227C2—2924no—
228C2C2×#1455656711yescharacteristic
229C2C2×#1455661611yescharacteristic
230C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#533×C73C2
socleC22×C73C22×D4
hypercenter#533D73
hypocenterC73#3077
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17988884C2semidirect
3. #17988874C2semidirect
4. #17988864C2semidirect
5. #17988630C2semidirect
6. #17988611C2semidirect
8. #533×C73C2semidirect
18. #14556524C22semidirect
19. #14556522C22semidirect
20. C4⋊#10596831C22semidirect
21. C4⋊#10596831C22semidirect
24. C4⋊Q8×C73C22semidirect
25. C4⋊Q8×C73C22semidirect
26. #125×C73C22semidirect
36. C2×D292Q8semidirect
116. C73#3077semidirect
117. #533D73semidirect
128. C4⋊Q8C2×D73semidirect
129. C4⋊Q8C2×D73semidirect
130. #125C2×D73semidirect