Finite Group Databasebeta

← #22621892

Subgroups — #22621892

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#17988946C211yesmaximal, characteristic, complemented
3#17988915C211yesmaximal, characteristic, complemented
4#17988903C211yesmaximal, characteristic, complemented
5#17988877C211yesmaximal, characteristic, complemented
6#17988838C211yesmaximal, characteristic, complemented
7#17988818C211yesmaximal, characteristic, complemented
8#17988799C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic, complemented
10#17988721C211yesmaximal, characteristic, complemented
11#17988697C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988588C211yesmaximal, characteristic, complemented
14C2×#14556512C211yesmaximal, characteristic, complemented
15#546×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×#11924015C2211yescharacteristic, complemented
18C2×#11924013C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924012C2211yescharacteristic, complemented
21C22×#10596831C2211yescharacteristic
22#14556591C2211yescharacteristic, complemented
23#14556575—21no—
24#14556575—21no—
25#14556571—21no—
26#14556565C2211yescharacteristic
27#14556565C2211yescharacteristic, complemented
28C4×D292C2211yescharacteristic, complemented
29C2×C4⋊Dic73C2211yescharacteristic
30C2×C4⋊Dic73C2211yescharacteristic, complemented
31#14556522C2211yescharacteristic, complemented
32#14556522C2211yescharacteristic, complemented
33#14556522C2211yescharacteristic, complemented
34C4⋊#10596831C2211yescharacteristic, complemented
35#14556515C2211yescharacteristic, complemented
36#14556515C2211yescharacteristic, complemented
37#14556515C2211yescharacteristic, complemented
38#14556512C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556511C2211yescharacteristic, complemented
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic, complemented
47#14556502C2211yescharacteristic, complemented
48C2×#41×C73C2211yescharacteristic
49C22×D4×C73C2211yescharacteristic
50#124×C73C2211yescharacteristic
51#123×C73—21no—
52C22⋊Q8×C73C2211yescharacteristic
53#121×C73—21no—
54#121×C73C2211yescharacteristic
55#120×C73—21no—
56C4×D4×C73C2211yescharacteristic
57C4×D4×C73C2211yescharacteristic
58C2×C22⋊C4×C73—21no—
59#11924027—44no—
60C2×Dic146—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×C4×D73—21no—
67#11924015—41no—
68#11924013—22no—
69#11924013—41no—
70#11924012—41no—
71C2×#10596831—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924005—21no—
83#11924005—21no—
84#11924005—21no—
85C24×C73—21no—
86#41×C73—22no—
87#41×C73—41no—
88C2×Q8×C73C2311yescharacteristic
89C2×D4×C73—22no—
90C2×D4×C73—21no—
91C2×D4×C73—21no—
92C2×D4×C73—21no—
93C2×D4×C73—41no—
94C2×D4×C73D411yescharacteristic
95C2×D4×C73C2311yescharacteristic
96C2×D4×C73C2311yescharacteristic
97C22×C4×C73—21no—
98C22×C4×C73—21no—
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C4⋊C4×C73—21no—
102C4⋊C4×C73D411yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C22⋊C4×C73—21no—
109C22⋊C4×C73D411yescharacteristic
110C22⋊C4×C73D411yescharacteristic
111C42×C73C2311yescharacteristic
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—42no—
115C23×C73—42no—
116C23×C73—81no—
117C23×C73C2×D411yescharacteristic
118C23×C73C2×D411yescharacteristic
119C22×D73—21no—
120Q8×C73—21no—
121Q8×C73—21no—
122D4×C73—22no—
123D4×C73—21no—
124D4×C73—21no—
125D4×C73—21no—
126D4×C73—42no—
127D4×C73—42no—
128D4×C73—81no—
129D4×C73#4112yescomplemented
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—42no—
137C2×C4×C73—81no—
138C2×C4×C73C2×D411yescharacteristic
139C2×C4×C73C2×D411yescharacteristic
140C2×C4×C73C2×D411yescharacteristic
141C2×C4×C73C2×D411yescharacteristic
142C2×C4×C73C2411yescharacteristic
143C22⋊D73—42no—
144C22⋊D73—42no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—42no—
149C2×Dic73—42no—
150D292—21no—
151D292—21no—
152C4×D73—42no—
153Dic146—42no—
154#10596831—21no—
155#10596831—21no—
156#10596831—21no—
157#10596831—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—22no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—84no—
170C22×C73AGL(1,ℤ/8)12yes—
171C22×C73C22×D411yescharacteristic
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C4×C73—21no—
176C4×C73—21no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73C2×#4111yescharacteristic
182C4×C73H(5,𝔽2)11yescharacteristic
183Dic73—41no—
184Dic73—41no—
185Dic73—41no—
186C2×C73—22no—
187C2×C73—41no—
188C2×C73—42no—
189C2×C73—81no—
190C2×C73#54611yescharacteristic
191C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C73#57711yescharacteristic
193D73—81no—
194#3306—731nomaximal, Sylow
195C73#330611yescharacteristic, complemented, Sylow
196#547—731no—
197#546D7311yescharacteristic, complemented
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#435—731no—
209#417—731no—
210C2×#102—731no—
211C2×#41—1461no—
212C2×#41C2×D7311yescharacteristic
213C22×D4C2×D7311yescharacteristic
214C2×SD16—731no—
215C2×D8—731no—
216C2×D8—731no—
217C2×M16—731no—
218C22×C8—731no—
219C4⋊Q8—731no—
220#124C2×D7311yescharacteristic
221#123—21no—
222#123—1461no—
223#123—1461no—
224C22⋊Q8—1461no—
225C22⋊Q8C2×D7311yescharacteristic
226#121—21no—
227#121—731no—
228#121—731no—
229#121C2×D7311yescharacteristic
230#120—21no—
231C4×D4—731no—
232C4×D4C2×D7311yescharacteristic
233C4×D4C2×D7311yescharacteristic
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C22⋊C4—21no—
237#106—731no—
238#106—731no—
239#106—731no—
240C4⋊C8—731no—
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⋊C8—731no—
252C22⋊C8—731no—
253#97—731no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—2924no—
258C2×Q8—1461no—
259C2×Q8C22×D7311yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—731no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4C22⋊D7311yescharacteristic
269C2×D4C22×D7311yescharacteristic
270C2×D4C22×D7311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4C22×D7311yescharacteristic
277C22×C4C22×D7311yescharacteristic
278SD16—2921no—
279D8—2921no—
280D8—1462no—
281M16—2921no—
282C2×C8—2921no—
283C2×C8—731no—
284C2×C8—731no—
285C2×C8—731no—
286C2×C8—731no—
287C4⋊C4—21no—
288C4⋊C4—731no—
289C4⋊C4—731no—
290C4⋊C4—731no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4C22⋊D7311yescharacteristic
295C4⋊C4C22×D7311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4C22⋊D7311yescharacteristic
305C22⋊C4C22⋊D7311yescharacteristic
306C42C22×D7311yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—1461no—
313C23C2×C22⋊D7311yescharacteristic
314C23C2×C22⋊D7311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—2922no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—2922no—
326D4—2922no—
327D4—1461no—
328D4—1461no—
329D4#1192402712yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—2922no—
339C2×C4—2922no—
340C2×C4—2922no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4C2×C22⋊D7311yescharacteristic
345C2×C4C2×C22⋊D7311yescharacteristic
346C2×C4C2×C22⋊D7311yescharacteristic
347C2×C4C2×C22⋊D7311yescharacteristic
348C2×C4C23×D7311yescharacteristic
349C8—1461no—
350C8—1461no—
351C8—1461no—
352C8—1461no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—2921no—
366C22—2921no—
367C22—2921no—
368C22#1455661612yes—
369C22C22×C22⋊D7311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—2921no—
377C4—2921no—
378C4—2921no—
379C4C2×#1192402711yescharacteristic
380C4#1455663611yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—5841no—
386C2#1798923111yescharacteristic
387C2C2×#1455661611yescharacteristic
388C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#546×C73C2
socleC22×C73C22×D4
hypercenter#546D73
hypocenterC73#3306
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #17989241C2semidirect
2. #17988946C2semidirect
3. #17988915C2semidirect
4. #17988903C2semidirect
5. #17988877C2semidirect
6. #17988838C2semidirect
7. #17988818C2semidirect
8. #17988799C2semidirect
9. #17988732C2semidirect
10. #17988721C2semidirect
11. #17988697C2semidirect
12. #17988659C2semidirect
13. #17988588C2semidirect
14. C2×#14556512C2semidirect
15. #546×C73C2semidirect
17. C2×#11924015C22semidirect
20. C2×#11924012C22semidirect
22. #14556591C22semidirect
27. #14556565C22semidirect
28. C4×D292C22semidirect
30. C2×C4⋊Dic73C22semidirect
31. #14556522C22semidirect
32. #14556522C22semidirect
33. #14556522C22semidirect
34. C4⋊#10596831C22semidirect
35. #14556515C22semidirect
36. #14556515C22semidirect
37. #14556515C22semidirect
44. #14556511C22semidirect
46. C22⋊#10596831C22semidirect
47. #14556502C22semidirect
129. D4×C73#41semidirect
195. C73#3306semidirect
197. #546D73semidirect
329. D4#11924027semidirect