Finite Group Databasebeta

← #22622575

Subgroups — #22622575

Order 9344.

350 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989306C211yesmaximal, characteristic, complemented
2#17989296C211yesmaximal, characteristic, complemented
3#17988941C211yesmaximal, characteristic, complemented
4#17988940C211yesmaximal, characteristic, complemented
5#17988936C211yesmaximal, characteristic, complemented
6#17988896C211yesmaximal, characteristic, complemented
7#17988895C211yesmaximal, characteristic, complemented
8#17988875C211yesmaximal, characteristic, complemented
9#17988800C211yesmaximal, characteristic
10#17988790C211yesmaximal, characteristic, complemented
11#17988711C211yesmaximal, characteristic, complemented
12SD16×Dic73C211yesmaximal, characteristic, complemented
13C4×#11924016C211yesmaximal, characteristic, complemented
14D8×Dic73C211yesmaximal, characteristic
15#463×C73C211yesmaximal, characteristic
16C2×#11924016C2211yescharacteristic
17#14556590C2211yescharacteristic
18#14556589C2211yescharacteristic
19#14556584—21no—
20#14556584—21no—
21#14556583C2211yescharacteristic
22#14556582C2211yescharacteristic
23#14556578C2211yescharacteristic
24#14556570—21no—
25#14556568—21no—
26#14556568—21no—
27#14556568—21no—
28Q8×Dic73C2211yescharacteristic
29C4×Dic146C2211yescharacteristic
30C4×Dic146C2211yescharacteristic
31D4×Dic73C2211yescharacteristic
32D4×Dic73C2211yescharacteristic
33D4×Dic73C2211yescharacteristic
34#14556547—21no—
35C2×#11924007—21no—
36#14556525C2211yescharacteristic
37#14556523C2211yescharacteristic
38#14556522C2211yescharacteristic
39#14556520C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556516C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C4×#10596831C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×D8×C73C2211yescharacteristic
54#124×C73C2211yescharacteristic
55C4×D4×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146D411yescharacteristic
61C2×Dic146C2311yescharacteristic
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65#11924016—22no—
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C4⋊Dic73—21no—
69C4⋊Dic73—21no—
70C4⋊Dic73D411yescharacteristic
71C4⋊Dic73C2311yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007D411yescharacteristic
82#11924007D411yescharacteristic
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73C2311yescharacteristic
91C4×Dic73C2311yescharacteristic
92C2×Q8×C73C2311yescharacteristic
93C2×D4×C73C2311yescharacteristic
94C2×D4×C73C2311yescharacteristic
95C22×C4×C73—21no—
96SD16×C73—22no—
97D8×C73—22no—
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73C2311yescharacteristic
101C22⋊C4×C73—21no—
102C22⋊C4×C73—21no—
103C22⋊C4×C73—21no—
104C42×C73C2311yescharacteristic
105C23×C73—21no—
106C23×C73—21no—
107Q8×C73—21no—
108Q8×C73—21no—
109D4×C73—21no—
110D4×C73—21no—
111D4×C73—21no—
112D4×C73#4112yes—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—81no—
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2411yescharacteristic
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—42no—
124C2×Dic73—42no—
125C2×Dic73—81no—
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130Dic146—22no—
131Dic146—21no—
132Dic146—21no—
133Dic146—81no—
134C8×C73—21no—
135C8×C73—21no—
136#10596831—21no—
137#10596831—21no—
138C22×C73—22no—
139C22×C73—41no—
140C22×C73—41no—
141C22×C73—41no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73C22×D411yescharacteristic
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73C2×#4111yescharacteristic
150C4×C732−1+411yescharacteristic
151Dic73—21no—
152Dic73—21no—
153Dic73—21no—
154Dic73—41no—
155Dic73—41no—
156Dic73—41no—
157Dic73—41no—
158Dic73#13512yes—
159C2×C73—42no—
160C2×C73—81no—
161C2×C73#54811yescharacteristic
162C2×C73C2×#13511yescharacteristic
163C2×C73#57711yescharacteristic
164#3360—731nomaximal, Sylow
165C73#336011yescharacteristic, complemented, Sylow
166#556—731no—
167#554—731no—
168#488—731no—
169#488—731no—
170#487—731no—
171#479—731no—
172#479—731no—
173#476—731no—
174#463—731no—
175#463D7311yescharacteristic
176#461—731no—
177C8×Q8—731no—
178C4×SD16—731no—
179C4×SD16—731no—
180C4×D8—731no—
181C2×SD16—731no—
182C2×SD16C2×D7311yescharacteristic
183C2×D8C2×D7311yescharacteristic
184C4⋊Q8—731no—
185C4⋊Q8—731no—
186#126—1461no—
187#126—1461no—
188#125—731no—
189#125—731no—
190#124—731no—
191#124C2×D7311yescharacteristic
192C22⋊Q8—1461no—
193C22⋊Q8—1461no—
194C22⋊Q8—1461no—
195C22⋊Q8—1461no—
196C4×Q8—731no—
197C4×Q8—731no—
198C4×Q8—731no—
199C4×D4—731no—
200C4×D4—731no—
201C4×D4—731no—
202C4×D4C2×D7311yescharacteristic
203#117—1461no—
204C2×C4⋊C4—1461no—
205#107—731no—
206#106—731no—
207#106—731no—
208C4⋊C8—731no—
209C4⋊C8—731no—
210C4⋊C8C2×D7311yescharacteristic
211#103—731no—
212#103—731no—
213#103—731no—
214#103—731no—
215#103—731no—
216#103C2×D7311yescharacteristic
217#102—731no—
218#102—731no—
219#102—731no—
220#102C2×D7311yescharacteristic
221C4×C8—731no—
222C4×C8—731no—
223C4×C8—731no—
224C2×Q8—731no—
225C2×Q8—731no—
226C2×Q8—1461no—
227C2×Q8C22×D7311yescharacteristic
228C2×D4C22×D7311yescharacteristic
229C2×D4C22×D7311yescharacteristic
230C22×C4—21no—
231C22×C4—1461no—
232C22×C4—1461no—
233C22×C4—1461no—
234SD16—22no—
235SD16—1462no—
236D8—22no—
237C2×C8—731no—
238C2×C8—731no—
239C2×C8C22×D7311yescharacteristic
240C2×C8C22×D7311yescharacteristic
241C4⋊C4—731no—
242C4⋊C4—731no—
243C4⋊C4—731no—
244C4⋊C4—731no—
245C4⋊C4—731no—
246C4⋊C4—731no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4C22×D7311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—1461no—
261C22⋊C4—1461no—
262C22⋊C4—1461no—
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C42—731no—
266C42—731no—
267C42—1461no—
268C42—1461no—
269C42C22×D7311yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—5841no—
275Q8—1462no—
276Q8—1461no—
277Q8—1461no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4#1192402712yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—81no—
285C2×C4—2922no—
286C2×C4—2922no—
287C2×C4—5841no—
288C2×C4—731no—
289C2×C4—731no—
290C2×C4—731no—
291C2×C4—731no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4D4×D7311yescharacteristic
297C2×C4D4×D7311yescharacteristic
298C2×C4C23×D7311yescharacteristic
299C8—21no—
300C8—21no—
301C8—1461no—
302C8—1461no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×D4×D7311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—2921no—
315C4—2921no—
316C4—2921no—
317C4—2921no—
318C4—732no—
319C4—1461no—
320C4—1461no—
321C4—1461no—
322C4C2×#1192402711yescharacteristic
323C4#1455663811yescharacteristic
324C2—42no—
325C2—81no—
326C2#1798924311yescharacteristic
327C2#135×D7311yescharacteristic
328C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#463×C73C2
socleC22×C73C22×D4
hypercenter#463D73
hypocenterC73#3360
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #17989306C2semidirect
2. #17989296C2semidirect
3. #17988941C2semidirect
4. #17988940C2semidirect
5. #17988936C2semidirect
6. #17988896C2semidirect
7. #17988895C2semidirect
8. #17988875C2semidirect
10. #17988790C2semidirect
11. #17988711C2semidirect
12. SD16×Dic73C2semidirect
13. C4×#11924016C2semidirect
165. C73#3360semidirect