Finite Group Databasebeta

← #22618956

Subgroups — #22618956

Order 9344.

456 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
1C4×D4×D73C211yesmaximal, characteristic
2#17988661C211yesmaximal, characteristic, complemented
3#17988660C211yesmaximal, characteristic, complemented
4#17988659C211yesmaximal, characteristic, complemented
5#17988658C211yesmaximal, characteristic, complemented
6#17988657C211yesmaximal, characteristic, complemented
7#17988656C211yesmaximal, characteristic, complemented
8#17988655C211yesmaximal, characteristic, complemented
9#17988643C211yesmaximal, characteristic, complemented
10#17988642C211yesmaximal, characteristic, complemented
11#17988550C211yesmaximal, characteristic, complemented
12#17988549C211yesmaximal, characteristic, complemented
13C2×#14556503C211yesmaximal, characteristic, complemented
14C22⋊C8×D73C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C411yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C2×#11924012C2211yescharacteristic, complemented
20C2×#11924011C2211yescharacteristic, complemented
21C2×#11924011C2211yescharacteristic, complemented
22C22×#10596831C2211yescharacteristic, complemented
23C2×C8×D73C2211yescharacteristic, complemented
24C2×C8×D73C2211yescharacteristic, complemented
25C4×D292C2211yescharacteristic
26D4×Dic73C411yescharacteristic
27#14556553C411yescharacteristic
28C4×C22⋊D73C2211yescharacteristic
29C4×C22⋊D73C2211yescharacteristic
30#14556551C411yescharacteristic
31#14556551C411yescharacteristic
32C4⋊C4×D73C411yescharacteristic
33C22⋊C4×D73C411yescharacteristic
34C22⋊C4×D73C411yescharacteristic
35C42×D73C2211yescharacteristic
36C4⋊#10596831C2211yescharacteristic, complemented
37#14556520C2211yescharacteristic, complemented
38#14556520C2211yescharacteristic, complemented
39C22⋊#10596831C2211yescharacteristic, complemented
40C22⋊#10596831C2211yescharacteristic, complemented
41#14556503C2211yescharacteristic
42#14556503C2211yescharacteristic
43#14556503C2211yescharacteristic
44#14556503C2211yescharacteristic
45#14556503C2211yescharacteristic, complemented
46#14556503C2211yescharacteristic, complemented
47#14556503C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic, complemented
49#14556502C2211yescharacteristic, complemented
50#14556501C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C2×M16×C73C2211yescharacteristic, complemented
53C22×C8×C73C2211yescharacteristic, complemented
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic, complemented
56C22⋊C8×C73C2211yescharacteristic, complemented
57C22⋊C8×C73C2211yescharacteristic, complemented
58#97×C73C2211yescharacteristic, complemented
59C23×D73C2×C411yescharacteristic
60C23×D73C2×C411yescharacteristic
61C2×D292C2×C411yescharacteristic
62C2×C22⋊D73C2×C411yescharacteristic
63C2×C22⋊D73C2×C411yescharacteristic
64D4×D73—24no—
65C22×Dic73C2×C411yescharacteristic
66C22×Dic73C2×C411yescharacteristic
67C2×C4×D73—41no—
68C2×C4×D73—41no—
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C2×C4×D73C2×C411yescharacteristic
72C2×C4×D73C2×C411yescharacteristic
73C2×C4×D73C2×C411yescharacteristic
74C2×C4×D73C2×C411yescharacteristic
75C2×C4×D73C2×C411yescharacteristic
76C2×C4×D73C2×C411yescharacteristic
77C2×C4×D73C2311yescharacteristic
78C2×C4×D73C2311yescharacteristic
79C2×C4×D73C2311yescharacteristic
80#11924012—41no—
81#11924011—41no—
82#11924011—41no—
83C2×#10596831—41no—
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C8×D73—41no—
89C8×D73—41no—
90C4⋊Dic73C2×C411yescharacteristic
91#11924007C2×C411yescharacteristic
92#11924007C2×C411yescharacteristic
93C22⋊Dic73C2×C411yescharacteristic
94C22⋊Dic73C2×C411yescharacteristic
95#11924005C2×C411yescharacteristic
96#11924005C2×C411yescharacteristic
97#11924005C2×C411yescharacteristic
98#11924005C2×C411yescharacteristic
99C4×Dic73C2×C411yescharacteristic
100C4×Dic73C2×C411yescharacteristic
101C4×Dic73C2311yescharacteristic
102C2×D4×C73C2×C411yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105M16×C73—41no—
106C2×C8×C73—41no—
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C2×C8×C73C2311yescharacteristic
110C2×C8×C73C2311yescharacteristic
111C4⋊C4×C73C2×C411yescharacteristic
112C22⋊C4×C73C2×C411yescharacteristic
113C22⋊C4×C73C2×C411yescharacteristic
114C42×C73C2311yescharacteristic
115C23×C73C22×C411yescharacteristic
116C23×C73C22×C411yescharacteristic
117C22×D73—22no—
118C22×D73—41no—
119C22×D73—41no—
120C22×D73—41no—
121C22×D73—41no—
122C22×D73M1614yescomplemented
123C22×D73C22×C411yescharacteristic
124C22×D73C22×C411yescharacteristic
125C22×D73C22×C411yescharacteristic
126D4×C73—22no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73C22×C411yescharacteristic
132C2×C4×C73C22×C411yescharacteristic
133C2×C4×C73C22×C411yescharacteristic
134C2×C4×C73C22×C411yescharacteristic
135C2×C4×C73C2411yescharacteristic
136C22⋊D73—22no—
137C22⋊D73—22no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73C22×C411yescharacteristic
141C2×Dic73C22×C411yescharacteristic
142C2×Dic73C22×C411yescharacteristic
143C2×Dic73C22×C411yescharacteristic
144C2×Dic73C22×C411yescharacteristic
145D292—22no—
146C4×D73—22no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—21no—
153C4×D73—41no—
154C4×D73—41no—
155C4×D73—41no—
156C4×D73—41no—
157C4×D73—41no—
158C8×C73—21no—
159C8×C73—21no—
160C8×C73—21no—
161C8×C73—21no—
162#10596831—21no—
163#10596831—21no—
164#10596831—21no—
165#10596831—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73C2×M1612yes—
172C22×C73C23×C411yescharacteristic
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—44no—
181C2×D73—44no—
182C2×D73C2×M1612yes—
183C2×D73C2×M1612yes—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73H(5,𝔽2)11yescharacteristic
189C4×C73H(5,𝔽2)11yescharacteristic
190Dic73—21no—
191Dic73—21no—
192Dic73—21no—
193Dic73—21no—
194Dic73—21no—
195C2×C73—22no—
196C2×C73—41no—
197C2×C73#51811yescharacteristic
198C2×C73C22×M1611yescharacteristic
199C2×C73#56811yescharacteristic
200D73—22no—
201D73—22no—
202D73—41no—
203#2973—731nomaximal, Sylow
204C73#297311yescharacteristic, complemented, Sylow
205C2×C4×D4—731no—
206#435—731no—
207#435—731no—
208#435—731no—
209#435—731no—
210#435—731no—
211#435—731no—
212#435—731no—
213#435D7311yescharacteristic, complemented
214#432—731no—
215#432—731no—
216#407—731no—
217#407—731no—
218C2×C22⋊C8—731no—
219C2×C22⋊C8—731no—
220C22×D4—731no—
221C23×C4—731no—
222C23×C4—731no—
223C2×M16—731no—
224C2×M16—731no—
225C2×M16—731no—
226C2×M16C2×D7311yescharacteristic, complemented
227C22×C8—731no—
228C22×C8—731no—
229C22×C8—731no—
230C22×C8C2×D7311yescharacteristic, complemented
231C4×D4—731no—
232C4×D4—731no—
233C4×D4—731no—
234C4×D4—731no—
235C4×D4—731no—
236C4×D4—731no—
237C4×D4—731no—
238C4×D4C2×D7311yescharacteristic
239C2×C4⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C42—731no—
243C4⋊C8—731no—
244C4⋊C8—731no—
245C4⋊C8—731no—
246C4⋊C8C2×D7311yescharacteristic, complemented
247C22⋊C8—731no—
248C22⋊C8—731no—
249C22⋊C8—731no—
250C22⋊C8—731no—
251C22⋊C8—731no—
252C22⋊C8—731no—
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256C22⋊C8—731no—
257C22⋊C8C2×D7311yescharacteristic, complemented
258C22⋊C8C2×D7311yescharacteristic, complemented
259#97—731no—
260#97—731no—
261#97—731no—
262#97C2×D7311yescharacteristic, complemented
263C24—731no—
264C24—731no—
265C2×D4—731no—
266C2×D4—731no—
267C2×D4—731no—
268C2×D4—1464no—
269C2×D4C4×D7311yescharacteristic
270C22×C4—2921no—
271C22×C4—2921no—
272C22×C4—2921no—
273C22×C4—2921no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—731no—
285C22×C4C22×D7311yescharacteristic
286C22×C4C22×D7311yescharacteristic
287M16—41no—
288M16—2921no—
289M16—2921no—
290M16—2921no—
291C2×C8—41no—
292C2×C8—2921no—
293C2×C8—2921no—
294C2×C8—2921no—
295C2×C8—731no—
296C2×C8—731no—
297C2×C8—731no—
298C2×C8—731no—
299C2×C8C22×D7311yescharacteristic
300C2×C8C22×D7311yescharacteristic
301C2×C8C22×D7311yescharacteristic
302C2×C8C22×D7311yescharacteristic
303C4⋊C4—731no—
304C4⋊C4—731no—
305C4⋊C4—731no—
306C4⋊C4C4×D7311yescharacteristic
307C22⋊C4—731no—
308C22⋊C4—731no—
309C22⋊C4—731no—
310C22⋊C4—731no—
311C22⋊C4—731no—
312C22⋊C4—731no—
313C22⋊C4C4×D7311yescharacteristic
314C22⋊C4C4×D7311yescharacteristic
315C42—731no—
316C42—731no—
317C42—731no—
318C42C22×D7311yescharacteristic
319C23—2921no—
320C23—2921no—
321C23—2921no—
322C23—2921no—
323C23—734no—
324C23—731no—
325C23—731no—
326C23—731no—
327C23—1462no—
328C23C2×C4×D7311yescharacteristic
329C23C2×C4×D7311yescharacteristic
330D4—22no—
331D4—1462no—
332D4—1462no—
333D4—1462no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—2921no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—731no—
348C2×C4—731no—
349C2×C4—731no—
350C2×C4—1462no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4C2×C4×D7311yescharacteristic
358C2×C4C2×C4×D7311yescharacteristic
359C2×C4C2×C4×D7311yescharacteristic
360C2×C4C2×C4×D7311yescharacteristic
361C2×C4C23×D7311yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—21no—
366C8—1461no—
367C8—1461no—
368C8—1461no—
369C8—1461no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—2924no—
376C22—2924no—
377C22—732no—
378C22—732no—
379C22—1461no—
380C22—1461no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22—1461no—
386C22M16×D7312yes—
387C22C22×C4×D7311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—1461no—
393C4—1461no—
394C4—1461no—
395C4—1461no—
396C4—1461no—
397C4#1455663611yescharacteristic
398C4#1455663711yescharacteristic
399C2—22no—
400C2—41no—
401C2—2921no—
402C2—1462no—
403C2—1462no—
404C2#1798905911yescharacteristic
405C2C2×M16×D7311yescharacteristic
406C2#1798935211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D73
commutator, socleC22×C73C23×C4
Fitting#435×C73C2
hypercenter#435D73
hypocenterC73#2973
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #17988661C2semidirect
3. #17988660C2semidirect
4. #17988659C2semidirect
5. #17988658C2semidirect
6. #17988657C2semidirect
7. #17988656C2semidirect
8. #17988655C2semidirect
9. #17988643C2semidirect
10. #17988642C2semidirect
11. #17988550C2semidirect
12. #17988549C2semidirect
13. C2×#14556503C2semidirect
14. C22⋊C8×D73C2semidirect
15. #435×C73C2semidirect
19. C2×#11924012C22semidirect
20. C2×#11924011C22semidirect
21. C2×#11924011C22semidirect
22. C22×#10596831C22semidirect
23. C2×C8×D73C22semidirect
24. C2×C8×D73C22semidirect
36. C4⋊#10596831C22semidirect
37. #14556520C22semidirect
38. #14556520C22semidirect
39. C22⋊#10596831C22semidirect
40. C22⋊#10596831C22semidirect
45. #14556503C22semidirect
46. #14556503C22semidirect
47. #14556503C22semidirect
48. #14556503C22semidirect
49. #14556502C22semidirect
50. #14556501C22semidirect
51. #14556501C22semidirect
52. C2×M16×C73C22semidirect
53. C22×C8×C73C22semidirect
55. C4⋊C8×C73C22semidirect
56. C22⋊C8×C73C22semidirect
57. C22⋊C8×C73C22semidirect
58. #97×C73C22semidirect
122. C22×D73M16semidirect
204. C73#2973semidirect
213. #435D73semidirect
226. C2×M16C2×D73semidirect
230. C22×C8C2×D73semidirect
246. C4⋊C8C2×D73semidirect
257. C22⋊C8C2×D73semidirect
258. C22⋊C8C2×D73semidirect
262. #97C2×D73semidirect