Finite Group Databasebeta

← #22622467

Subgroups — #22622467

Order 9344.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989308C211yesmaximal, characteristic
2#17989271C211yesmaximal, characteristic
3#17988995C211yesmaximal, characteristic, complemented
4#17988927C211yesmaximal, characteristic, complemented
5#17988925C211yesmaximal, characteristic, complemented
6#17988925C211yesmaximal, characteristic, complemented
7#17988921C211yesmaximal, characteristic, complemented
8#17988896C211yesmaximal, characteristic, complemented
9#17988880C211yesmaximal, characteristic, complemented
10#17988842C211yesmaximal, characteristic, complemented
11#17988694C211yesmaximal, characteristic, complemented
12#17988658C211yesmaximal, characteristic
13#17988628C211yesmaximal, characteristic, complemented
14#17988625C211yesmaximal, characteristic, complemented
15#467×C73C211yesmaximal, characteristic, complemented
16C2×#11924011C2211yescharacteristic
17#14556590C2211yescharacteristic
18#14556586—21no—
19#14556584—21no—
20#14556584—21no—
21#14556582C2211yescharacteristic
22#14556581—21no—
23#14556577—21no—
24#14556573—21no—
25#14556567C2211yescharacteristic
26#14556567C2211yescharacteristic
27Q8×Dic73C2211yescharacteristic
28Q8×Dic73C2211yescharacteristic
29#14556556—21no—
30C4×C22⋊D73C2211yescharacteristic
31#14556550C2211yescharacteristic
32#14556550C2211yescharacteristic
33#14556549—21no—
34#14556549C2211yescharacteristic
35C4⋊C4×D73C2211yescharacteristic
36#14556525C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556515C2211yescharacteristic
48#14556515C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C2×Q16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×C22⋊D73D411yescharacteristic
61C2×C4×D73—21no—
62C2×C4×D73C2311yescharacteristic
63#11924011—22no—
64C2×#10596831C2311yescharacteristic
65C2×#10596831C2311yescharacteristic
66C4⋊Dic73—21no—
67C4⋊Dic73—21no—
68C4⋊Dic73—21no—
69C4⋊Dic73C2311yescharacteristic
70C4⋊Dic73C2311yescharacteristic
71C4⋊Dic73C2311yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73#11924007—21no—
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007D411yescharacteristic
79C22⋊Dic73—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73D411yescharacteristic
82#11924005—21no—
83#11924005—21no—
84#11924005—21no—
85#11924005D411yescharacteristic
86C4×Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73C2311yescharacteristic
92C2×Q8×C73C2311yescharacteristic
93C2×Q8×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95Q16×C73—22no—
96C2×C8×C73—22no—
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C23×C73C2×D411yescharacteristic
106C22×D73C2×D411yescharacteristic
107Q8×C73—21no—
108Q8×C73—21no—
109Q8×C73—21no—
110Q8×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2411yescharacteristic
119C22⋊D73—41no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127C4×D73—21no—
128C4×D73—21no—
129C4×D73—42no—
130Dic146—42no—
131C8×C73—21no—
132C8×C73#4112yes—
133#10596831—21no—
134#10596831—21no—
135C22×C73—21no—
136C22×C73—21no—
137C22×C73—21no—
138C22×C73C22×D411yescharacteristic
139C2×D73—21no—
140C2×D73—21no—
141C2×D73—21no—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73—41no—
145C4×C73—41no—
146C4×C73—41no—
147C4×C73C2×#4111yescharacteristic
148C4×C732−1+411yescharacteristic
149Dic73—21no—
150Dic73—21no—
151Dic73—21no—
152Dic73—41no—
153Dic73—41no—
154Dic73—41no—
155Dic73—41no—
156C2×C73—41no—
157C2×C73#54711yescharacteristic
158C2×C73#57511yescharacteristic
159C2×C73#57811yescharacteristic
160D73—41no—
161#3349—731nomaximal, Sylow
162C73#334911yescharacteristic, complemented, Sylow
163#556—731no—
164#552—731no—
165#501—731no—
166#485—731no—
167#485—731no—
168#485—731no—
169#484—731no—
170#479—731no—
171#477—731no—
172#470—731no—
173#467D7311yescharacteristic, complemented
174#441—731no—
175#435—731no—
176#428—731no—
177#427—731no—
178C2×Q16C2×D7311yescharacteristic
179C2×M16—731no—
180C22×C8C2×D7311yescharacteristic
181C4⋊Q8—731no—
182#126—1461no—
183#126—1461no—
184#126—1461no—
185#125—731no—
186#125—1461no—
187#124—1461no—
188#123—1461no—
189C22⋊Q8—731no—
190C22⋊Q8—731no—
191C22⋊Q8C2×D7311yescharacteristic
192C22⋊Q8C2×D7311yescharacteristic
193C4×Q8—731no—
194C4×Q8—731no—
195C4×Q8—1461no—
196C4×D4—731no—
197#117—731no—
198#117—731no—
199#117—731no—
200#117—1461no—
201C2×C4⋊C4—731no—
202#107—731no—
203#107—731no—
204#107—731no—
205#107—731no—
206#107C2×D7311yescharacteristic
207#106—731no—
208#106—731no—
209#106—731no—
210#106—731no—
211C4⋊C8—731no—
212#103—731no—
213#103—731no—
214#103—731no—
215#103—731no—
216#103C2×D7311yescharacteristic
217#103C2×D7311yescharacteristic
218C22⋊C8—731no—
219C22⋊C8—731no—
220#97—731no—
221C2×Q8—1461no—
222C2×Q8C22×D7311yescharacteristic
223C2×Q8C22×D7311yescharacteristic
224C2×D4—731no—
225C22×C4—731no—
226C22×C4—1461no—
227C22×C4C22×D7311yescharacteristic
228Q16—22no—
229M16—1462no—
230C2×C8—22no—
231C2×C8—731no—
232C2×C8—731no—
233C2×C8C22×D7311yescharacteristic
234C2×C8C22×D7311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—731no—
238C4⋊C4—731no—
239C4⋊C4—731no—
240C4⋊C4—731no—
241C4⋊C4—731no—
242C4⋊C4—1461no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4C22×D7311yescharacteristic
251C4⋊C4C22×D7311yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—731no—
255C22⋊C4—731no—
256C22⋊C4—1461no—
257C22⋊C4—1461no—
258C22⋊C4—1461no—
259C22⋊C4—1461no—
260C22⋊C4—1461no—
261C42—731no—
262C42—1461no—
263C42—1461no—
264C42—1461no—
265C42—1461no—
266C42—1461no—
267C23—731no—
268C23D4×D7311yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—2922no—
274D4—2921no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—2922no—
282C2×C4—731no—
283C2×C4—731no—
284C2×C4—731no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4D4×D7311yescharacteristic
292C2×C4C23×D7311yescharacteristic
293C8—21no—
294C8—1461no—
295C8—1461no—
296C8#1192402712yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—1461no—
301C22—1461no—
302C22—1461no—
303C22C2×D4×D7311yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—2921no—
310C4—2921no—
311C4—2921no—
312C4—2921no—
313C4—1461no—
314C4—1461no—
315C4—1461no—
316C4C2×#1192402711yescharacteristic
317C4#1455663811yescharacteristic
318C2—41no—
319C2—2921no—
320C2#1798923711yescharacteristic
321C2#1798938411yescharacteristic
322C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#467×C73C2
socleC22×C73C22×D4
hypercenter#467D73
hypocenterC73#3349
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #17988995C2semidirect
4. #17988927C2semidirect
5. #17988925C2semidirect
6. #17988925C2semidirect
7. #17988921C2semidirect
8. #17988896C2semidirect
9. #17988880C2semidirect
10. #17988842C2semidirect
11. #17988694C2semidirect
13. #17988628C2semidirect
14. #17988625C2semidirect
15. #467×C73C2semidirect
162. C73#3349semidirect
173. #467D73semidirect