Finite Group Databasebeta

← #22621233

Subgroups — #22621233

Order 9344.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989218C211yesmaximal, characteristic, complemented
2#17989210C211yesmaximal, characteristic
3#17988994C211yesmaximal, characteristic, complemented
4#17988984C211yesmaximal, characteristic, complemented
5#17988948C211yesmaximal, characteristic, complemented
6#17988943C211yesmaximal, characteristic, complemented
7#17988925C211yesmaximal, characteristic, complemented
8#17988912C211yesmaximal, characteristic
9#17988905C211yesmaximal, characteristic
10#17988896C211yesmaximal, characteristic, complemented
11#17988886C211yesmaximal, characteristic, complemented
12#17988876C211yesmaximal, characteristic, complemented
13#17988870C211yesmaximal, characteristic, complemented
14#17988645C211yesmaximal, characteristic, complemented
15#483×C73C211yesmaximal, characteristic, complemented
16#14556590—21no—
17#14556590C2211yescharacteristic
18#14556590C2211yescharacteristic
19#14556590C2211yescharacteristic
20#14556586—21no—
21#14556582—21no—
22#14556582C2211yescharacteristic
23#14556582C2211yescharacteristic
24#14556580C2211yescharacteristic
25#14556577—21no—
26#14556573—21no—
27#14556571—21no—
28#14556570—21no—
29#14556570—21no—
30#14556565C2211yescharacteristic
31Q8×Dic73C2211yescharacteristic
32#14556553C2211yescharacteristic
33#14556550C2211yescharacteristic
34#14556550C2211yescharacteristic
35#14556525C2211yescharacteristic
36#14556524C2211yescharacteristic
37#14556523C2211yescharacteristic
38#14556522C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic
54#106×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C4×D73—21no—
65C2×#10596831C2311yescharacteristic
66C2×#10596831C2311yescharacteristic
67C4⋊Dic73—21no—
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73D411yescharacteristic
71C4⋊Dic73D411yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73D411yescharacteristic
82C22⋊Dic73D411yescharacteristic
83#11924005—21no—
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73C2311yescharacteristic
90C4×Dic73C2311yescharacteristic
91C2×Q8×C73C2311yescharacteristic
92C22×C4×C73—21no—
93C22×C4×C73C2311yescharacteristic
94C2×C8×C73C2311yescharacteristic
95C2×C8×C73C2311yescharacteristic
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73C2311yescharacteristic
99C4⋊C4×C73C2311yescharacteristic
100C4⋊C4×C73C2311yescharacteristic
101C22⋊C4×C73—21no—
102C23×C73C2×D411yescharacteristic
103C22×D73—21no—
104Q8×C73—21no—
105Q8×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—81no—
113C2×C4×C73C2×D411yescharacteristic
114C2×C4×C73C2411yescharacteristic
115C22⋊D73—81no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73C2×D411yescharacteristic
120C2×Dic73C2×D411yescharacteristic
121C2×Dic73C2×D411yescharacteristic
122C2×Dic73C2×D411yescharacteristic
123D292—21no—
124D292—21no—
125C4×D73—81no—
126Dic146—81no—
127Dic146—81no—
128Dic146—81no—
129C8×C73—21no—
130C8×C73—21no—
131#10596831—21no—
132#10596831—21no—
133C22×C73—21no—
134C22×C73—21no—
135C22×C73—21no—
136C22×C73C22×D411yescharacteristic
137C2×D73—41no—
138C2×D73—41no—
139C2×D73—41no—
140C4×C73—21no—
141C4×C73—41no—
142C4×C73—41no—
143C4×C73—41no—
144C4×C73—41no—
145C4×C732−1+411yescharacteristic
146C4×C732−1+411yescharacteristic
147Dic73—21no—
148Dic73—21no—
149Dic73—21no—
150Dic73—21no—
151Dic73—41no—
152Dic73—41no—
153Dic73—41no—
154C2×C73—41no—
155C2×C73#53611yescharacteristic
156C2×C73#57711yescharacteristic
157C2×C73#57711yescharacteristic
158D73—81no—
159#3244—731nomaximal, Sylow
160C73#324411yescharacteristic, complemented, Sylow
161#544—731no—
162#542—731no—
163#501—731no—
164#498—731no—
165#489—731no—
166#488—731no—
167#485—731no—
168#483D7311yescharacteristic, complemented
169#482—731no—
170#481—731no—
171#479—731no—
172#478—731no—
173#476—731no—
174#475—731no—
175#433—731no—
176C4⋊Q8—731no—
177C4⋊Q8—731no—
178C4⋊Q8—731no—
179C4⋊Q8—1461no—
180#126—1461no—
181#125—731no—
182#125—731no—
183#125—1461no—
184#124—731no—
185#124—1461no—
186#123—1461no—
187C22⋊Q8—1461no—
188C22⋊Q8—1461no—
189C22⋊Q8—1461no—
190C22⋊Q8C2×D7311yescharacteristic
191#121—731no—
192C4×Q8—731no—
193C4×D4—731no—
194#117—731no—
195#117—731no—
196C2×C4⋊C4C2×D7311yescharacteristic
197#107—731no—
198#107—731no—
199#106—731no—
200#106—731no—
201#106—731no—
202#106—731no—
203#106C2×D7311yescharacteristic
204#106C2×D7311yescharacteristic
205C4⋊C8—731no—
206C4⋊C8—731no—
207#103—731no—
208#103—731no—
209#103C2×D7311yescharacteristic
210#103C2×D7311yescharacteristic
211#102—731no—
212#102—731no—
213#102—731no—
214#102—731no—
215C22⋊C8—731no—
216C22⋊C8C2×D7311yescharacteristic
217#97—731no—
218C4×C8—731no—
219C2×Q8—1461no—
220C2×Q8—1461no—
221C2×Q8—1461no—
222C2×Q8C22×D7311yescharacteristic
223C2×D4—731no—
224C2×D4—1461no—
225C22×C4—21no—
226C22×C4—1461no—
227C22×C4C22×D7311yescharacteristic
228C2×C8—731no—
229C2×C8—731no—
230C2×C8C22×D7311yescharacteristic
231C2×C8C22×D7311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—731no—
235C4⋊C4—731no—
236C4⋊C4—731no—
237C4⋊C4—731no—
238C4⋊C4—731no—
239C4⋊C4—1461no—
240C4⋊C4—1461no—
241C4⋊C4—1461no—
242C4⋊C4—1461no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4C22×D7311yescharacteristic
248C4⋊C4C22×D7311yescharacteristic
249C4⋊C4C22×D7311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—731no—
252C22⋊C4—731no—
253C22⋊C4—1461no—
254C22⋊C4—1461no—
255C22⋊C4—1461no—
256C22⋊C4—1461no—
257C22⋊C4—1461no—
258C42—731no—
259C42—731no—
260C42—1461no—
261C42—1461no—
262C23—1461no—
263C23D4×D7311yescharacteristic
264Q8—21no—
265Q8—21no—
266Q8—5841no—
267Q8—5841no—
268Q8—5841no—
269D4—5841no—
270D4—1461no—
271D4—1461no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—81no—
279C2×C4—5841no—
280C2×C4—731no—
281C2×C4—731no—
282C2×C4—731no—
283C2×C4—731no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4D4×D7311yescharacteristic
288C2×C4C23×D7311yescharacteristic
289C8—21no—
290C8—21no—
291C8—1461no—
292C8—1461no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—2921no—
297C22—2921no—
298C22—2921no—
299C22C2×D4×D7311yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—2921no—
306C4—2921no—
307C4—2921no—
308C4—1461no—
309C4—1461no—
310C4—1461no—
311C4—1461no—
312C4#1455663811yescharacteristic
313C4#1455663811yescharacteristic
314C2—41no—
315C2—5841no—
316C2#1798915911yescharacteristic
317C2#1798939311yescharacteristic
318C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#483×C73C2
socleC22×C73C22×D4
hypercenter#483D73
hypocenterC73#3244
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #17989218C2semidirect
3. #17988994C2semidirect
4. #17988984C2semidirect
5. #17988948C2semidirect
6. #17988943C2semidirect
7. #17988925C2semidirect
10. #17988896C2semidirect
11. #17988886C2semidirect
12. #17988876C2semidirect
13. #17988870C2semidirect
14. #17988645C2semidirect
15. #483×C73C2semidirect
160. C73#3244semidirect
168. #483D73semidirect