Finite Group Databasebeta

← #22621894

Subgroups — #22621894

Order 9344.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989241C211yesmaximal, characteristic, complemented
2#17989233C211yesmaximal, characteristic, complemented
3#17988947C211yesmaximal, characteristic, complemented
4#17988918C211yesmaximal, characteristic, complemented
5#17988906C211yesmaximal, characteristic, complemented
6#17988878C211yesmaximal, characteristic, complemented
7#17988840C211yesmaximal, characteristic, complemented
8#17988816C211yesmaximal, characteristic, complemented
9#17988803C211yesmaximal, characteristic, complemented
10#17988734C211yesmaximal, characteristic, complemented
11#17988723C211yesmaximal, characteristic, complemented
12#17988700C211yesmaximal, characteristic, complemented
13#17988589C211yesmaximal, characteristic, complemented
14C2×#14556513C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027—21no—
18C22×D292C2211yescharacteristic
19C2×#11924017C2211yescharacteristic, complemented
20C2×D584C2211yescharacteristic
21C2×D584C2211yescharacteristic
22#14556591C2211yescharacteristic, complemented
23#14556579C2211yescharacteristic
24#14556576—21no—
25#14556575—21no—
26#14556575—21no—
27#14556571—21no—
28#14556570C2211yescharacteristic
29#14556565C2211yescharacteristic
30#14556565C2211yescharacteristic
31#14556565C2211yescharacteristic, complemented
32#14556564—21no—
33#14556559—21no—
34C4×D292C2211yescharacteristic
35C4×D292C2211yescharacteristic, complemented
36C2×C4⋊Dic73C2211yescharacteristic
37C2×C4⋊Dic73C2211yescharacteristic, complemented
38C22⋊C4×D73—21no—
39#14556523C2211yescharacteristic, complemented
40#14556523C2211yescharacteristic, 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, complemented
53C22×C8×C73C2211yescharacteristic
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—
62#11924027—44no—
63C2×Dic146—21no—
64C2×Dic146C2311yescharacteristic
65C2×D292—22no—
66C2×D292—21no—
67C2×D292—41no—
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×D292C2311yescharacteristic
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C22×Dic73—21no—
76C22×Dic73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—21no—
79C2×C4×D73—21no—
80#11924017—41no—
81D584—22no—
82D584—41no—
83C4⋊Dic73—21no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73C2311yescharacteristic
87C4⋊Dic73C2311yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89C4⋊Dic73C2311yescharacteristic
90#11924007—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99C2×D4×C73D411yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C22×C4×C73C2311yescharacteristic
102M16×C73—41no—
103C2×C8×C73—41no—
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C22⋊C4×C73D411yescharacteristic
111C42×C73C2311yescharacteristic
112C23×C73C2×D411yescharacteristic
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—42no—
118C22×D73—42no—
119C22×D73—81no—
120D4×C73—22no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—42no—
131C22⋊D73—42no—
132C22⋊D73—42no—
133C22⋊D73—81no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—42no—
140C2×Dic73—42no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—21no—
145D292—21no—
146D292—42no—
147D292#4112yescomplemented
148C4×D73—42no—
149C4×D73—42no—
150C4×D73—81no—
151Dic146—21no—
152Dic146—21no—
153Dic146—42no—
154C8×C73—21no—
155C8×C73—21no—
156C8×C73—21no—
157C8×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73AGL(1,ℤ/8)12yes—
164C22×C73C22×D411yescharacteristic
165C2×D73—22no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—84no—
175C4×C73—21no—
176C4×C73—21no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73C2×#4111yescharacteristic
180C4×C73H(5,𝔽2)11yescharacteristic
181Dic73—41no—
182Dic73—41no—
183Dic73—41no—
184Dic73—41no—
185Dic73—41no—
186C2×C73—22no—
187C2×C73—41no—
188C2×C73#54611yescharacteristic
189C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C73#57711yescharacteristic
191D73—42no—
192D73—81no—
193D73—81no—
194#3306—731nomaximal, Sylow
195C73#330611yescharacteristic, complemented, Sylow
196#547—731no—
197#546—731no—
198#489—731no—
199#483—731no—
200#481—731no—
201#476—731no—
202#469—731no—
203#465—731no—
204#463—731no—
205#449—731no—
206#447—731no—
207#442—731no—
208#435D7311yescharacteristic, complemented
209#417—731no—
210C2×#102—731no—
211C2×#41—731no—
212C2×#41—1461no—
213C22×D4—731no—
214C2×SD16—731no—
215C2×D8—731no—
216C2×D8—731no—
217C2×M16C2×D7311yescharacteristic, complemented
218C22×C8C2×D7311yescharacteristic
219C4⋊Q8—731no—
220#124—731no—
221#123—1461no—
222#123—1461no—
223#123—1461no—
224C22⋊Q8—731no—
225C22⋊Q8—1461no—
226#121—731no—
227#121—731no—
228#121—731no—
229#121—1461no—
230#120—1461no—
231C4×D4—731no—
232C4×D4—731no—
233C4×D4C2×D7311yescharacteristic
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C22⋊C4—1461no—
237#106—731no—
238#106—731no—
239#106—731no—
240C4⋊C8C2×D7311yescharacteristic, complemented
241#103—731no—
242#103—731no—
243#103—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102—731no—
249#102—731no—
250#102—731no—
251C22⋊C8C2×D7311yescharacteristic
252C22⋊C8C2×D7311yescharacteristic, complemented
253#97C2×D7311yescharacteristic, complemented
254C24—1461no—
255#41—2921no—
256#41—2924no—
257#41—1462no—
258C2×Q8—731no—
259C2×Q8—1461no—
260C2×D4—2921no—
261C2×D4—731no—
262C2×D4—731no—
263C2×D4—731no—
264C2×D4—1462no—
265C2×D4—1461no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4D29211yescharacteristic
271C22×C4—1461no—
272C22×C4—1461no—
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4C22×D7311yescharacteristic
277C22×C4C22×D7311yescharacteristic
278SD16—2921no—
279D8—2921no—
280D8—1462no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D7311yescharacteristic
284C2×C8C22×D7311yescharacteristic
285C2×C8C22×D7311yescharacteristic
286C2×C8C22×D7311yescharacteristic
287C4⋊C4—731no—
288C4⋊C4—731no—
289C4⋊C4—731no—
290C4⋊C4—731no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4D29211yescharacteristic
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4D29211yescharacteristic
305C22⋊C4D29211yescharacteristic
306C42C22×D7311yescharacteristic
307C23—2922no—
308C23—2922no—
309C23—5841no—
310C23—1461no—
311C23—1461no—
312C23—1461no—
313C23C2×D29211yescharacteristic
314C23C2×D29211yescharacteristic
315Q8—2922no—
316Q8—1461no—
317Q8—1461no—
318D4—22no—
319D4—2922no—
320D4—2922no—
321D4—2922no—
322D4—2922no—
323D4—5841no—
324D4—732no—
325D4—1461no—
326D4—1461no—
327D4—1461no—
328D4—1461no—
329D4—1461no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2922no—
335C2×C4—2922no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—5841no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4C2×D29211yescharacteristic
345C2×C4C2×D29211yescharacteristic
346C2×C4C2×D29211yescharacteristic
347C2×C4C2×D29211yescharacteristic
348C2×C4C23×D7311yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—2921no—
365C22—2921no—
366C22—5844no—
367C22—1462no—
368C22#1455661912yes—
369C22C22×D29211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—2921no—
375C4—2921no—
376C4—2921no—
377C4—2921no—
378C4—2921no—
379C4#41×D7311yescharacteristic
380C4#1455663611yescharacteristic
381C2—22no—
382C2—41no—
383C2—2922no—
384C2—5841no—
385C2—5841no—
386C2#1798923211yescharacteristic
387C2C2×#1455661911yescharacteristic
388C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3306
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. #17989241C2semidirect
2. #17989233C2semidirect
3. #17988947C2semidirect
4. #17988918C2semidirect
5. #17988906C2semidirect
6. #17988878C2semidirect
7. #17988840C2semidirect
8. #17988816C2semidirect
9. #17988803C2semidirect
10. #17988734C2semidirect
11. #17988723C2semidirect
12. #17988700C2semidirect
13. #17988589C2semidirect
14. C2×#14556513C2semidirect
15. #435×C73C2semidirect
19. C2×#11924017C22semidirect
22. #14556591C22semidirect
31. #14556565C22semidirect
35. C4×D292C22semidirect
37. C2×C4⋊Dic73C22semidirect
39. #14556523C22semidirect
40. #14556523C22semidirect
41. #14556523C22semidirect
42. #14556516C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
51. #14556513C22semidirect
52. C2×M16×C73C22semidirect
55. C4⋊C8×C73C22semidirect
57. C22⋊C8×C73C22semidirect
58. #97×C73C22semidirect
147. D292#41semidirect
195. C73#3306semidirect
208. #435D73semidirect
217. C2×M16C2×D73semidirect
240. C4⋊C8C2×D73semidirect
252. C22⋊C8C2×D73semidirect
253. #97C2×D73semidirect