Finite Group Databasebeta

← #22620656

Subgroups — #22620656

Order 9344.

370 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989124C211yesmaximal, characteristic, complemented
2#17989119C211yesmaximal, characteristic, complemented
3#17988988C211yesmaximal, characteristic, complemented
4#17988968C211yesmaximal, characteristic, complemented
5#17988943C211yesmaximal, characteristic, complemented
6#17988940C211yesmaximal, characteristic, complemented
7#17988844C211yesmaximal, characteristic, complemented
8#17988839C211yesmaximal, characteristic
9#17988834C211yesmaximal, characteristic, complemented
10#17988830C211yesmaximal, characteristic, complemented
11#17988697C211yesmaximal, characteristic, complemented
12#17988692C211yesmaximal, characteristic, complemented
13#17988689C211yesmaximal, characteristic, complemented
14#17988539C211yesmaximal, characteristic, complemented
15#440×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21#14556586—21no—
22#14556584—21no—
23#14556582C2211yescharacteristic
24#14556582C2211yescharacteristic
25#14556580C2211yescharacteristic
26#14556578C2211yescharacteristic
27#14556576—21no—
28#14556573—21no—
29#14556571C2211yescharacteristic
30#14556567C2211yescharacteristic
31#14556566C2211yescharacteristic
32#14556562C2211yescharacteristic
33C4×Dic146C2211yescharacteristic
34C4×D292—21no—
35C4×D292C2211yescharacteristic
36C4×C22⋊D73—21no—
37#14556550—21no—
38#14556548—21no—
39C42×D73C2211yescharacteristic
40#14556525C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556515C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556502C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C2×D292—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C4×D73—21no—
64C2×C4×D73D411yescharacteristic
65C2×C4×D73D411yescharacteristic
66C2×C4×D73C2311yescharacteristic
67#11924018—22no—
68#11924017—22no—
69#11924013—22no—
70#11924011—22no—
71#11924011—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92C4×Dic73—21no—
93C4×Dic73D411yescharacteristic
94C4×Dic73D411yescharacteristic
95C4×Dic73C2311yescharacteristic
96C2×Q8×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73—21no—
99SD16×C73—22no—
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C22×D73—21no—
110C22×D73C2×D411yescharacteristic
111Q8×C73—21no—
112Q8×C73—21no—
113D4×C73—21no—
114D4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—42no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C22⋊D73—42no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129D292—21no—
130D292—21no—
131D292—42no—
132C4×D73—21no—
133C4×D73—21no—
134C4×D73—41no—
135C4×D73—41no—
136C4×D73—42no—
137Dic146—21no—
138Dic146—21no—
139C8×C73—21no—
140C8×C73#4112yes—
141#10596831—21no—
142#10596831#4112yes—
143C22×C73—41no—
144C22×C73—41no—
145C22×C73—41no—
146C22×C73C22×D411yescharacteristic
147C2×D73—21no—
148C2×D73—21no—
149C2×D73—21no—
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73C2×#4111yescharacteristic
159C4×C73C2×#4111yescharacteristic
160Dic73—21no—
161Dic73—21no—
162Dic73—21no—
163Dic73—41no—
164Dic73—41no—
165Dic73—41no—
166C2×C73—81no—
167C2×C73#53211yescharacteristic
168C2×C73#57511yescharacteristic
169C2×C73#57511yescharacteristic
170D73—41no—
171D73—81no—
172#3183—731nomaximal, Sylow
173C73#318311yescharacteristic, complemented, Sylow
174#529—731no—
175#529—731no—
176#499—731no—
177#495—731no—
178#488—731no—
179#488—731no—
180#470—731no—
181#469—731no—
182#468—731no—
183#468—731no—
184#442—731no—
185#441—731no—
186#440—731no—
187#440D7311yescharacteristic, complemented
188C4×M16—731no—
189C2×Q16—731no—
190C2×SD16—731no—
191C2×SD16C2×D7311yescharacteristic
192C2×D8—731no—
193C2×M16—731no—
194C2×M16—731no—
195#126—1461no—
196#126—1461no—
197#125—731no—
198#125—731no—
199#124—731no—
200#124—731no—
201#123—1461no—
202#123—1461no—
203C22⋊Q8—731no—
204C22⋊Q8—731no—
205#121—731no—
206#121—731no—
207C4×Q8—731no—
208C4×Q8C2×D7311yescharacteristic
209C4×D4—731no—
210C4×D4—1461no—
211C4×D4—1461no—
212C4×D4C2×D7311yescharacteristic
213#117—1461no—
214#117—1461no—
215C2×C42—731no—
216#107—731no—
217#107C2×D7311yescharacteristic
218#106—731no—
219#106—731no—
220#103—731no—
221#103—731no—
222#103—731no—
223#103C2×D7311yescharacteristic
224#102—731no—
225#102—731no—
226#102—731no—
227#102C2×D7311yescharacteristic
228#97—731no—
229#97C2×D7311yescharacteristic
230C4×C8—731no—
231C4×C8—731no—
232C2×Q8—731no—
233C2×Q8C22×D7311yescharacteristic
234C2×D4—731no—
235C2×D4—1461no—
236C2×D4—1461no—
237C2×D4C22×D7311yescharacteristic
238C22×C4—21no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—1461no—
243Q16—1462no—
244SD16—22no—
245SD16—1462no—
246D8—1462no—
247M16—1462no—
248M16—1462no—
249C2×C8—731no—
250C2×C8—731no—
251C2×C8C22×D7311yescharacteristic
252C2×C8C22×D7311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—731no—
255C4⋊C4—731no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4C22×D7311yescharacteristic
264C4⋊C4C22×D7311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—1461no—
267C22⋊C4—1461no—
268C22⋊C4—1461no—
269C22⋊C4—1461no—
270C22⋊C4—1461no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C42—21no—
276C42—731no—
277C42—731no—
278C42—731no—
279C42—1461no—
280C42C22×D7311yescharacteristic
281C23—21no—
282C23—731no—
283C23—1461no—
284Q8—21no—
285Q8—21no—
286Q8—1461no—
287Q8—1461no—
288D4—21no—
289D4—21no—
290D4—2922no—
291D4—2922no—
292D4—1461no—
293D4—1461no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—2922no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—731no—
302C2×C4—731no—
303C2×C4—731no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4D4×D7311yescharacteristic
310C2×C4D4×D7311yescharacteristic
311C2×C4C23×D7311yescharacteristic
312C8—21no—
313C8—732no—
314C8—1461no—
315C8#1192402812yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—2921no—
320C22—2921no—
321C22—2921no—
322C22—1461no—
323C22—1461no—
324C22—1461no—
325C22C2×D4×D7311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2921no—
332C4—2921no—
333C4—2921no—
334C4—1461no—
335C4—1461no—
336C4—1461no—
337C4#41×D7311yescharacteristic
338C4C2×#1192402811yescharacteristic
339C2—81no—
340C2—2921no—
341C2—5841no—
342C2#1798913411yescharacteristic
343C2#1798938311yescharacteristic
344C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#440×C73C2
socleC22×C73C22×D4
hypercenter#440D73
hypocenterC73#3183
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #17989124C2semidirect
2. #17989119C2semidirect
3. #17988988C2semidirect
4. #17988968C2semidirect
5. #17988943C2semidirect
6. #17988940C2semidirect
7. #17988844C2semidirect
9. #17988834C2semidirect
10. #17988830C2semidirect
11. #17988697C2semidirect
12. #17988692C2semidirect
13. #17988689C2semidirect
14. #17988539C2semidirect
15. #440×C73C2semidirect
173. C73#3183semidirect
187. #440D73semidirect