Finite Group Databasebeta

← #22621118

Subgroups — #22621118

Order 9344.

368 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 113 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#17989132C211yesmaximal, characteristic
2C2×#14556582C211yesmaximal, characteristic, complemented
3#17988995C212yesmaximal, complemented
4#17988950C212yesmaximal, complemented
5#17988906C211yesmaximal, characteristic, complemented
6#17988903C211yesmaximal, characteristic, complemented
7#17988900C211yesmaximal, characteristic, complemented
8#17988890C212yesmaximal, complemented
9#17988889C212yesmaximal, complemented
10#17988641C211yesmaximal, characteristic, complemented
11#480×C73C211yesmaximal, characteristic, complemented
12C2×#11924027—21no—
13#14556590C2211yescharacteristic
14#14556587C2211yescharacteristic
15#14556582—21no—
16#14556582—21no—
17#14556582C2212yes—
18#14556582C2212yes—
19#14556577—21no—
20#14556565C2211yescharacteristic
21#14556563—21no—
22D4×Dic73C2211yescharacteristic
23#14556553C2211yescharacteristic
24#14556551—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2211yescharacteristic
27C2×#11924007—21no—
28C2×C4×Dic73C2211yescharacteristic
29#14556524C2212yes—
30#14556523C2212yes—
31#14556522C2212yes—
32#14556520C2212yes—
33#14556513C2212yes—
34#14556512C2212yes—
35#14556511C2212yes—
36C22⋊#10596831C2211yescharacteristic
37#14556501C2212yes—
38#121×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#107×C73C2212yes—
41#102×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43#11924027—44no—
44C2×Dic146—21no—
45C2×D292C2311yescharacteristic
46C2×C22⋊D73—21no—
47C2×C22⋊D73—21no—
48C2×C22⋊D73—21no—
49C22×Dic73—21no—
50C22×Dic73—21no—
51C22×Dic73D411yescharacteristic
52C22×Dic73D411yescharacteristic
53C2×C4×D73—21no—
54C2×#10596831C2312yes—
55C4⋊Dic73—21no—
56C4⋊Dic73—22no—
57C4⋊Dic73—22no—
58C4⋊Dic73C2312yes—
59C4⋊Dic73C2311yescharacteristic
60#11924007—22no—
61#11924007—22no—
62#11924007—21no—
63C22⋊Dic73—21no—
64#11924005—21no—
65#11924005—21no—
66C4×Dic73D411yescharacteristic
67C4×Dic73D411yescharacteristic
68C4×Dic73C2311yescharacteristic
69C4×Dic73C2311yescharacteristic
70C2×D4×C73—21no—
71C2×D4×C73C2311yescharacteristic
72C22×C4×C73—21no—
73C22×C4×C73C2311yescharacteristic
74C2×C8×C73C2312yes—
75C4⋊C4×C73—21no—
76C4⋊C4×C73C2312yes—
77C4⋊C4×C73C2311yescharacteristic
78C22⋊C4×C73—21no—
79C23×C73—21no—
80C23×C73C2×D411yescharacteristic
81C22×D73—21no—
82D4×C73—22no—
83D4×C73—42no—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—42no—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C22⋊D73—42no—
91C22⋊D73—42no—
92C22⋊D73—42no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—41no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C2×Dic73C2×D411yescharacteristic
100C2×Dic73C2×D411yescharacteristic
101C2×Dic73C2×D411yescharacteristic
102C2×Dic73C2×D411yescharacteristic
103D292—22no—
104C4×D73—42no—
105Dic146—42no—
106C8×C73—22no—
107#10596831—22no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73—41no—
113C22×C73AGL(1,ℤ/8)12yes—
114C22×C73C22×D411yescharacteristic
115C2×D73—41no—
116C2×D73—41no—
117C2×D73—41no—
118C4×C73—21no—
119C4×C73—41no—
120C4×C73—42no—
121C4×C732−1+412yes—
122Dic73—21no—
123Dic73—21no—
124Dic73—21no—
125Dic73—21no—
126Dic73—41no—
127Dic73—42no—
128C2×C73—22no—
129C2×C73—81no—
130C2×C73#53611yescharacteristic
131C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C73#57511yescharacteristic
133D73—81no—
134#3234—731nomaximal, Sylow
135C73#323411yescharacteristic, complemented, Sylow
136#532—731no—
137C2×#125—731no—
138#501—732no—
139#490—732no—
140#481—731no—
141#481—731no—
142#480—731no—
143#480D7311yescharacteristic, complemented
144#478—732no—
145#478—732no—
146#432—731no—
147C2×#41—1461no—
148C4⋊Q8—731no—
149#127—731no—
150#125—732no—
151#125—732no—
152#125—1461no—
153#125—1461no—
154#124—1461no—
155#121—731no—
156#121—1461no—
157#121C2×D7311yescharacteristic
158C4×D4—731no—
159C4×D4—731no—
160C4×D4—1461no—
161C2×C4⋊C4—731no—
162C2×C4⋊C4—1461no—
163C2×C4⋊C4—1461no—
164C2×C4⋊C4C2×D7311yescharacteristic
165C2×C42—731no—
166#107—732no—
167#107C2×D7312yes—
168#106—732no—
169#106—732no—
170C4⋊C8—732no—
171#102—732no—
172#102—732no—
173#102—732no—
174#102C2×D7312yes—
175C22⋊C8—731no—
176C22⋊C8C2×D7311yescharacteristic
177#97—732no—
178#41—2924no—
179C2×Q8—1461no—
180C2×D4—21no—
181C2×D4—731no—
182C2×D4—1461no—
183C2×D4—1461no—
184C2×D4—1461no—
185C2×D4C22×D7311yescharacteristic
186C22×C4—21no—
187C22×C4—731no—
188C22×C4—731no—
189C22×C4—1461no—
190C22×C4—1461no—
191C22×C4—1461no—
192C22×C4C22×D7311yescharacteristic
193C2×C8—732no—
194C2×C8C22×D7312yes—
195C4⋊C4—21no—
196C4⋊C4—732no—
197C4⋊C4—731no—
198C4⋊C4—1462no—
199C4⋊C4—1462no—
200C4⋊C4—1461no—
201C4⋊C4—1462no—
202C4⋊C4—1462no—
203C4⋊C4—1461no—
204C4⋊C4C22×D7312yes—
205C4⋊C4C22×D7311yescharacteristic
206C22⋊C4—21no—
207C22⋊C4—1461no—
208C22⋊C4—1461no—
209C22⋊C4—1461no—
210C42—731no—
211C42—731no—
212C42—731no—
213C42—731no—
214C23—21no—
215C23—1461no—
216C23D4×D7311yescharacteristic
217Q8—2922no—
218D4—22no—
219D4—42no—
220D4—2922no—
221D4—2922no—
222D4—2922no—
223D4—1462no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—2922no—
229C2×C4—2922no—
230C2×C4—2922no—
231C2×C4—2921no—
232C2×C4—731no—
233C2×C4—731no—
234C2×C4—731no—
235C2×C4—731no—
236C2×C4—1461no—
237C2×C4—1462no—
238C2×C4—1462no—
239C2×C4D4×D7311yescharacteristic
240C2×C4C23×D7311yescharacteristic
241C8—22no—
242C8—1462no—
243C22—21no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—2921no—
249C22—2921no—
250C22—2921no—
251C22#1455661512yes—
252C22C2×D4×D7311yescharacteristic
253C4—21no—
254C4—42no—
255C4—41no—
256C4—2922no—
257C4—2921no—
258C4—1461no—
259C4—1461no—
260C4—1461no—
261C4—1461no—
262C4#1455663812yes—
263C2—22no—
264C2—81no—
265C2—5841no—
266C2#1798915911yescharacteristic
267C2C2×#1455661511yescharacteristic
268C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#480×C73C2
socleC22×C73C22×D4
hypercenter#480D73
hypocenterC73#3234
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#14556582C2semidirect
3. #17988995C2semidirect
4. #17988950C2semidirect
5. #17988906C2semidirect
6. #17988903C2semidirect
7. #17988900C2semidirect
8. #17988890C2semidirect
9. #17988889C2semidirect
10. #17988641C2semidirect
11. #480×C73C2semidirect
135. C73#3234semidirect
143. #480D73semidirect