Finite Group Databasebeta

← #22620789

Subgroups — #22620789

Order 9344.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989167C211yesmaximal, characteristic, complemented
2#17989156C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic, complemented
4#17988907C211yesmaximal, characteristic, complemented
5#17988902C211yesmaximal, characteristic, complemented
6#17988841C211yesmaximal, characteristic, complemented
7#17988836C211yesmaximal, characteristic, complemented
8#17988824C211yesmaximal, characteristic, complemented
9#17988819C211yesmaximal, characteristic, complemented
10#17988737C211yesmaximal, characteristic, complemented
11#17988735C211yesmaximal, characteristic, complemented
12#17988735C211yesmaximal, characteristic, complemented
13#17988723C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#485×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic, complemented
17C2×#11924028C2211yescharacteristic
18C22×D292C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21C2×D584C2211yescharacteristic
22C2×D584C2211yescharacteristic
23C2×#11924011C2211yescharacteristic, complemented
24C2×C8×D73C2211yescharacteristic, complemented
25#14556588—21no—
26#14556579—21no—
27#14556569—21no—
28#14556567C2211yescharacteristic, complemented
29#14556566—21no—
30#14556566C2211yescharacteristic
31#14556566C2211yescharacteristic
32#14556566C2211yescharacteristic
33#14556566C2211yescharacteristic
34#14556566C2211yescharacteristic, complemented
35#14556565C2211yescharacteristic
36#14556564—21no—
37#14556564—21no—
38#14556561—21no—
39#14556561—21no—
40C4⋊C4×D73C2211yescharacteristic, complemented
41#14556524C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556511C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52C22⋊Q8×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#103×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic
59C23×D73—21no—
60#11924029—41no—
61#11924029—41no—
62#11924028—41no—
63#11924028—41no—
64C2×Dic146D411yescharacteristic
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292—21no—
70C2×D292—21no—
71C2×D292—21no—
72C2×D292—41no—
73C2×D292—41no—
74C2×D292D411yescharacteristic
75C2×D292C2311yescharacteristic
76C2×D292C2311yescharacteristic
77C2×D292C2311yescharacteristic
78C2×C22⋊D73—21no—
79C2×C22⋊D73D411yescharacteristic
80C2×C22⋊D73D411yescharacteristic
81C2×C4×D73—21no—
82C2×C4×D73—21no—
83C2×C4×D73C2311yescharacteristic
84C2×C4×D73C2311yescharacteristic
85#11924015—41no—
86#11924015—41no—
87D584—41no—
88D584—41no—
89#11924011—41no—
90C2×#10596831C2311yescharacteristic
91C2×#10596831C2311yescharacteristic
92C8×D73—41no—
93C4⋊Dic73C2311yescharacteristic
94#11924007—21no—
95#11924007—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102#11924005—21no—
103C2×Q8×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C42×C73—21no—
114C23×C73C2×D411yescharacteristic
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—42no—
119C22×D73—81no—
120C22×D73—81no—
121C22×D73C2×D411yescharacteristic
122C22×D73C2×D411yescharacteristic
123Q8×C73—21no—
124Q8×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—41no—
134C22⋊D73—41no—
135C22⋊D73—81no—
136C2×Dic73—21no—
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139D292—21no—
140D292—21no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—21no—
145D292—41no—
146D292—42no—
147D292—42no—
148D292—81no—
149D292—81no—
150D292—81no—
151D292—81no—
152D292—81no—
153C4×D73—21no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—21no—
157C4×D73—42no—
158C4×D73—81no—
159Dic146—41no—
160C8×C73—21no—
161C8×C73—21no—
162#10596831—21no—
163#10596831—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73C22×D411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—41no—
178C2×D73—41no—
179C2×D73—41no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—84no—
184C4×C73—21no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73—41no—
188C4×C73—41no—
189C4×C73H(5,𝔽2)11yescharacteristic
190C4×C73H(5,𝔽2)11yescharacteristic
191Dic73—21no—
192Dic73—21no—
193Dic73—41no—
194C2×C73—41no—
195C2×C73#53411yescharacteristic
196C2×C73#57611yescharacteristic
197C2×C73#57711yescharacteristic
198D73—41no—
199D73—41no—
200D73—81no—
201D73—81no—
202D73—81no—
203#3198—731nomaximal, Sylow
204C73#319811yescharacteristic, complemented, Sylow
205#537—731no—
206#535—731no—
207#485D7311yescharacteristic, complemented
208#482—731no—
209#481—731no—
210#480—731no—
211#469—731no—
212#468—731no—
213#466—731no—
214#465—731no—
215#450—731no—
216#449—731no—
217#449—731no—
218#447—731no—
219#408—731no—
220C2×#41—731no—
221C2×#41—731no—
222C22×D4—731no—
223C2×SD16—731no—
224C2×SD16—731no—
225C2×D8—731no—
226C2×D8—731no—
227C2×M16—731no—
228C22×C8—731no—
229#127—1461no—
230#124—1461no—
231C22⋊Q8—731no—
232C22⋊Q8—1461no—
233C22⋊Q8C2×D7311yescharacteristic
234#121—731no—
235#121—731no—
236#121—731no—
237#121—731no—
238#121—731no—
239#121—731no—
240#121—1461no—
241#121—1461no—
242#121—1461no—
243#120—1461no—
244#120—1461no—
245#117C2×D7311yescharacteristic
246C2×C4⋊C4—731no—
247#107—731no—
248#107C2×D7311yescharacteristic, complemented
249#106—731no—
250#106C2×D7311yescharacteristic, complemented
251#103C2×D7311yescharacteristic, complemented
252#103C2×D7311yescharacteristic, complemented
253#102—731no—
254#102—731no—
255#102—731no—
256#102—731no—
257#102—731no—
258#102—731no—
259C22⋊C8—731no—
260C22⋊C8—731no—
261C22⋊C8—731no—
262C22⋊C8C2×D7311yescharacteristic
263C24—1461no—
264#41—2921no—
265#41—2921no—
266#41—2921no—
267#41—2921no—
268C2×Q8—731no—
269C2×Q8C22×D7311yescharacteristic
270C2×D4—2921no—
271C2×D4—2921no—
272C2×D4—731no—
273C2×D4—731no—
274C2×D4—731no—
275C2×D4—731no—
276C2×D4—731no—
277C2×D4—731no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4—1461no—
283C2×D4—1461no—
284C2×D4—1461no—
285C2×D4—1461no—
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—1461no—
289C22×C4—1461no—
290C22×C4C22×D7311yescharacteristic
291SD16—2921no—
292SD16—2921no—
293D8—2921no—
294D8—2921no—
295M16—2921no—
296C2×C8—2921no—
297C2×C8—731no—
298C2×C8—731no—
299C2×C8C22×D7311yescharacteristic
300C2×C8C22×D7311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—731no—
303C4⋊C4—1461no—
304C4⋊C4—1461no—
305C4⋊C4C22×D7311yescharacteristic
306C4⋊C4C22×D7311yescharacteristic
307C4⋊C4C22×D7311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—1461no—
311C22⋊C4—1461no—
312C22⋊C4—1461no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C42—21no—
318C23—2922no—
319C23—5841no—
320C23—5841no—
321C23—731no—
322C23—731no—
323C23—1461no—
324C23—1461no—
325C23—1461no—
326C23D4×D7311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—2921no—
330D4—2922no—
331D4—2921no—
332D4—2922no—
333D4—2921no—
334D4—2921no—
335D4—5841no—
336D4—5841no—
337D4—5841no—
338D4—5841no—
339D4—5841no—
340D4—5841no—
341D4—1461no—
342D4—1461no—
343D4—1461no—
344D4—1461no—
345D4—1461no—
346D4—1461no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—2922no—
354C2×C4—5841no—
355C2×C4—731no—
356C2×C4—731no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4D4×D7311yescharacteristic
363C2×C4C23×D7311yescharacteristic
364C8—21no—
365C8—21no—
366C8—1461no—
367C8—1461no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—2921no—
372C22—2921no—
373C22—2921no—
374C22—2921no—
375C22—2921no—
376C22—2921no—
377C22—2921no—
378C22—2921no—
379C22—2921no—
380C22—5844no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22—1461no—
386C22—1461no—
387C22C2×D4×D7311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—2921no—
394C4—1461no—
395C4—1461no—
396C4#1455663711yescharacteristic
397C4#1455663711yescharacteristic
398C2—41no—
399C2—2921no—
400C2—2921no—
401C2—5841no—
402C2—5841no—
403C2—5841no—
404C2#1798914811yescharacteristic
405C2#1798938911yescharacteristic
406C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#485×C73C2
socleC22×C73C22×D4
hypercenter#485D73
hypocenterC73#3198
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #17989167C2semidirect
2. #17989156C2semidirect
3. #17988911C2semidirect
4. #17988907C2semidirect
5. #17988902C2semidirect
6. #17988841C2semidirect
7. #17988836C2semidirect
8. #17988824C2semidirect
9. #17988819C2semidirect
10. #17988737C2semidirect
11. #17988735C2semidirect
12. #17988735C2semidirect
13. #17988723C2semidirect
14. #17988552C2semidirect
15. #485×C73C2semidirect
16. C2×#11924029C22semidirect
23. C2×#11924011C22semidirect
24. C2×C8×D73C22semidirect
28. #14556567C22semidirect
34. #14556566C22semidirect
40. C4⋊C4×D73C22semidirect
41. #14556524C22semidirect
42. #14556522C22semidirect
47. #14556511C22semidirect
48. #14556511C22semidirect
50. #14556503C22semidirect
51. #14556503C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. #103×C73C22semidirect
57. #103×C73C22semidirect
204. C73#3198semidirect
207. #485D73semidirect
248. #107C2×D73semidirect
250. #106C2×D73semidirect
251. #103C2×D73semidirect
252. #103C2×D73semidirect