Finite Group Databasebeta

← #22622089

Subgroups — #22622089

Order 9344.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989302C211yesmaximal, characteristic, complemented
2#17989233C211yesmaximal, characteristic, complemented
3#17988947C211yesmaximal, characteristic, complemented
4#17988929C211yesmaximal, characteristic, complemented
5#17988912C211yesmaximal, characteristic, complemented
6#17988868C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic, complemented
8#17988823C211yesmaximal, characteristic, complemented
9#17988803C211yesmaximal, characteristic, complemented
10#17988734C211yesmaximal, characteristic, complemented
11#17988723C211yesmaximal, characteristic, complemented
12#17988700C211yesmaximal, characteristic, complemented
13#17988593C211yesmaximal, characteristic, complemented
14#17988584C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×#11924017C2211yescharacteristic, complemented
19C2×D584C2211yescharacteristic
20C2×D584C2211yescharacteristic
21#14556591C2211yescharacteristic, complemented
22#14556579C2211yescharacteristic
23#14556577—21no—
24#14556577—21no—
25#14556576—21no—
26#14556570C2211yescharacteristic
27#14556565C2211yescharacteristic
28#14556565C2211yescharacteristic
29#14556565C2211yescharacteristic, complemented
30#14556564—21no—
31#14556562—21no—
32#14556559—21no—
33C4×D292C2211yescharacteristic
34C4×D292C2211yescharacteristic, complemented
35#14556550C2211yescharacteristic
36#14556550C2211yescharacteristic, complemented
37#14556549—21no—
38C22⋊C4×D73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556525C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic, complemented
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic, complemented
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic, complemented
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic, complemented
58#97×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—22no—
61#11924028—41no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×D292—22no—
65C2×D292—21no—
66C2×D292—41no—
67C2×D292C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77#11924017—41no—
78D584—22no—
79D584—41no—
80C4⋊Dic73—21no—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85#11924007—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73—21no—
88C22⋊Dic73—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C2×D4×C73D411yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101M16×C73—41no—
102C2×C8×C73—41no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—42no—
117C22×D73—42no—
118C22×D73—81no—
119D4×C73—41no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—42no—
130C22⋊D73—81no—
131C22⋊D73—81no—
132C22⋊D73—81no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138D292—21no—
139D292—21no—
140D292—21no—
141D292—21no—
142D292—21no—
143D292—42no—
144D292#4112yes—
145C4×D73—42no—
146C4×D73—42no—
147C4×D73—81no—
148Dic146—21no—
149Dic146—21no—
150Dic146—81no—
151C8×C73—21no—
152C8×C73—21no—
153C8×C73—21no—
154C8×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73C22×D411yescharacteristic
162C2×D73—22no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—84no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—21no—
175C4×C73—21no—
176C4×C73C2×#4111yescharacteristic
177C4×C73H(5,𝔽2)11yescharacteristic
178Dic73—41no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—41no—
184C2×C73—41no—
185C2×C73#54611yescharacteristic
186C2×C73#57511yescharacteristic
187C2×C73#57611yescharacteristic
188D73—42no—
189D73—81no—
190D73—81no—
191#3319—731nomaximal, Sylow
192C73#331911yescharacteristic, complemented, Sylow
193#555—731no—
194#546—731no—
195#489—731no—
196#485—731no—
197#482—731no—
198#474—731no—
199#468—731no—
200#466—731no—
201#463—731no—
202#449—731no—
203#447—731no—
204#442—731no—
205#435D7311yescharacteristic, complemented
206#418—731no—
207#416—731no—
208C2×#41—731no—
209C22×D4—731no—
210C2×SD16—731no—
211C2×D8—731no—
212C2×D8—731no—
213C2×M16C2×D7311yescharacteristic
214C22×C8C2×D7311yescharacteristic, complemented
215C4⋊Q8—731no—
216#124—731no—
217#124—1461no—
218#124—1461no—
219#123—1461no—
220C22⋊Q8—731no—
221#121—731no—
222#121—731no—
223#121—731no—
224#121—1461no—
225#121—1461no—
226#120—1461no—
227C4×D4—731no—
228C4×D4—731no—
229C4×D4C2×D7311yescharacteristic
230#117—731no—
231#117—731no—
232#117—1461no—
233C2×C22⋊C4—1461no—
234#107—731no—
235#107—731no—
236#106—731no—
237C4⋊C8C2×D7311yescharacteristic, complemented
238#103—731no—
239#103—731no—
240#103—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248C22⋊C8C2×D7311yescharacteristic
249C22⋊C8C2×D7311yescharacteristic, complemented
250#97C2×D7311yescharacteristic, complemented
251C24—1461no—
252#41—2921no—
253#41—1462no—
254C2×Q8—731no—
255C2×Q8—1461no—
256C2×D4—2921no—
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—731no—
260C2×D4—1462no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4—1461no—
266C2×D4D29211yescharacteristic
267C22×C4—1461no—
268C22×C4—1461no—
269C22×C4—1461no—
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272SD16—2921no—
273D8—2921no—
274D8—1462no—
275M16—41no—
276C2×C8—41no—
277C2×C8C22×D7311yescharacteristic
278C2×C8C22×D7311yescharacteristic
279C2×C8C22×D7311yescharacteristic
280C2×C8C22×D7311yescharacteristic
281C4⋊C4—731no—
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4D29211yescharacteristic
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4D29211yescharacteristic
299C22⋊C4D29211yescharacteristic
300C42—1461no—
301C42—1461no—
302C42C22×D7311yescharacteristic
303C23—2922no—
304C23—2922no—
305C23—5841no—
306C23—1461no—
307C23—1461no—
308C23—1461no—
309C23C2×D29211yescharacteristic
310C23C2×D29211yescharacteristic
311Q8—5841no—
312Q8—1461no—
313Q8—1461no—
314D4—41no—
315D4—2922no—
316D4—2922no—
317D4—5841no—
318D4—5841no—
319D4—5841no—
320D4—732no—
321D4—1461no—
322D4—1461no—
323D4—1461no—
324D4—1461no—
325D4—1461no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—2922no—
331C2×C4—2922no—
332C2×C4—5841no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4C2×D29211yescharacteristic
339C2×C4C2×D29211yescharacteristic
340C2×C4C2×D29211yescharacteristic
341C2×C4C2×D29211yescharacteristic
342C2×C4C23×D7311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—2921no—
354C22—2921no—
355C22—2921no—
356C22—2921no—
357C22—2921no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22—5844no—
362C22—1462no—
363C22C22×D29211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—2921no—
369C4—2921no—
370C4—2921no—
371C4—2921no—
372C4—2921no—
373C4#41×D7311yescharacteristic
374C4#1455663611yescharacteristic
375C2—41no—
376C2—41no—
377C2—2922no—
378C2—5841no—
379C2—5841no—
380C2#1798923211yescharacteristic
381C2#1798938711yescharacteristic
382C2#1798939211yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3319
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17989302C2semidirect
2. #17989233C2semidirect
3. #17988947C2semidirect
4. #17988929C2semidirect
5. #17988912C2semidirect
6. #17988868C2semidirect
7. #17988833C2semidirect
8. #17988823C2semidirect
9. #17988803C2semidirect
10. #17988734C2semidirect
11. #17988723C2semidirect
12. #17988700C2semidirect
13. #17988593C2semidirect
14. #17988584C2semidirect
15. #435×C73C2semidirect
18. C2×#11924017C22semidirect
21. #14556591C22semidirect
29. #14556565C22semidirect
34. C4×D292C22semidirect
36. #14556550C22semidirect
39. #14556525C22semidirect
40. #14556525C22semidirect
41. #14556523C22semidirect
42. #14556516C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
51. #14556513C22semidirect
53. C22×C8×C73C22semidirect
55. C4⋊C8×C73C22semidirect
57. C22⋊C8×C73C22semidirect
58. #97×C73C22semidirect
192. C73#3319semidirect
205. #435D73semidirect
214. C22×C8C2×D73semidirect
237. C4⋊C8C2×D73semidirect
249. C22⋊C8C2×D73semidirect
250. #97C2×D73semidirect