Finite Group Databasebeta

← #22620740

Subgroups — #22620740

Order 9344.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989097C211yesmaximal, characteristic, complemented
2#121×D73C211yesmaximal, characteristic, complemented
3#17988919C211yesmaximal, characteristic, complemented
4#17988913C211yesmaximal, characteristic, complemented
5#17988909C211yesmaximal, characteristic, complemented
6#17988899C211yesmaximal, characteristic, complemented
7#17988838C211yesmaximal, characteristic, complemented
8#17988833C211yesmaximal, characteristic, complemented
9#17988831C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988733C211yesmaximal, characteristic, complemented
12#17988729C211yesmaximal, characteristic, complemented
13#17988719C211yesmaximal, characteristic, complemented
14#17988550C211yesmaximal, characteristic, complemented
15#469×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic, complemented
17C2×D4×D73—21no—
18C2×D4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×#11924013C2211yescharacteristic, complemented
23C2×#11924012C2211yescharacteristic, complemented
24#14556573—21no—
25#14556571C2211yescharacteristic
26#14556570C2211yescharacteristic, complemented
27#14556566C2211yescharacteristic
28#14556565C2211yescharacteristic
29#14556564—21no—
30#14556563—21no—
31#14556562C2211yescharacteristic
32#14556562C2211yescharacteristic
33#14556559—21no—
34D4×Dic73—21no—
35#14556551—21no—
36#14556549C2211yescharacteristic, complemented
37C4⋊C4×D73C2211yescharacteristic
38C22⋊C4×D73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556514C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic, complemented
45#14556512C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52C2×D8×C73C2211yescharacteristic, complemented
53C2×M16×C73C2211yescharacteristic, complemented
54#121×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic, complemented
56#106×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58#102×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73D411yescharacteristic
61#11924027—41no—
62#11924027—41no—
63C2×Dic146C2311yescharacteristic
64C2×D292—21no—
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71D4×D73—41no—
72D4×D73—41no—
73D4×D73—44no—
74C22×Dic73—21no—
75C22×Dic73D411yescharacteristic
76C2×C4×D73—21no—
77C2×C4×D73—41no—
78C2×C4×D73—41no—
79C2×C4×D73D411yescharacteristic
80C2×C4×D73D411yescharacteristic
81C2×C4×D73C2311yescharacteristic
82C2×C4×D73C2311yescharacteristic
83#11924017—41no—
84#11924016—41no—
85#11924013—41no—
86#11924012—41no—
87C2×#10596831C2311yescharacteristic
88C2×#10596831C2311yescharacteristic
89C4⋊Dic73—21no—
90C4⋊Dic73C2311yescharacteristic
91C4⋊Dic73C2311yescharacteristic
92#11924007—21no—
93#11924007—21no—
94C22⋊Dic73—21no—
95C22⋊Dic73—21no—
96C22⋊Dic73—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101C4×Dic73—21no—
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C2×D4×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107D8×C73—41no—
108M16×C73—41no—
109C2×C8×C73C2311yescharacteristic
110C2×C8×C73C2311yescharacteristic
111C4⋊C4×C73C2311yescharacteristic
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C22⋊C4×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73C2×D411yescharacteristic
118C22×D73—22no—
119C22×D73—21no—
120C22×D73—41no—
121C22×D73—41no—
122C22×D73—42no—
123C22×D73—42no—
124C22×D73—42no—
125C22×D73C2×D411yescharacteristic
126C22×D73C2×D411yescharacteristic
127D4×C73—21no—
128D4×C73—21no—
129D4×C73—21no—
130D4×C73—21no—
131D4×C73—42no—
132D4×C73—42no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73C2×D411yescharacteristic
138C2×C4×C73C2411yescharacteristic
139C22⋊D73—42no—
140C22⋊D73—42no—
141C22⋊D73—42no—
142C22⋊D73—42no—
143C22⋊D73—42no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—41no—
148C2×Dic73—42no—
149C2×Dic73C2×D411yescharacteristic
150C2×Dic73C2×D411yescharacteristic
151D292—21no—
152D292—21no—
153D292—42no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—21no—
157C4×D73—21no—
158C4×D73—41no—
159C4×D73—41no—
160C4×D73—42no—
161Dic146—21no—
162Dic146—21no—
163C8×C73—21no—
164C8×C73—21no—
165#10596831—21no—
166#10596831—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73C22×D411yescharacteristic
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—44no—
183C2×D73—41no—
184C2×D73—41no—
185C2×D73—41no—
186C2×D73—84no—
187C2×D73AGL(1,ℤ/8)12yes—
188C4×C73—21no—
189C4×C73—41no—
190C4×C73—41no—
191C4×C73H(5,𝔽2)11yescharacteristic
192C4×C73H(5,𝔽2)11yescharacteristic
193Dic73—21no—
194Dic73—21no—
195Dic73—41no—
196Dic73—41no—
197Dic73—41no—
198C2×C73—41no—
199C2×C73—81no—
200C2×C73—81no—
201C2×C73#53411yescharacteristic
202C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C73#57511yescharacteristic
204D73—22no—
205D73—41no—
206D73—81no—
207#3194—731nomaximal, Sylow
208C73#319411yescharacteristic, complemented, Sylow
209#525—731no—
210C2×#121—731no—
211#483—731no—
212#482—731no—
213#482—731no—
214#480—731no—
215#469—731no—
216#469D7311yescharacteristic, complemented
217#468—731no—
218#468—731no—
219#450—731no—
220#449—731no—
221#449—731no—
222#447—731no—
223#407—731no—
224C2×#41—731no—
225C22×D4—731no—
226C22×D4—1461no—
227C23×C4—731no—
228C2×SD16—731no—
229C2×SD16—731no—
230C2×D8—731no—
231C2×D8C2×D7311yescharacteristic, complemented
232C2×M16—731no—
233C2×M16C2×D7311yescharacteristic, complemented
234#123—1461no—
235C22⋊Q8—731no—
236C22⋊Q8—731no—
237#121—731no—
238#121—731no—
239#121—731no—
240#121—731no—
241#121—1461no—
242#121—1461no—
243#121C2×D7311yescharacteristic
244#121C2×D7311yescharacteristic, complemented
245#120—1461no—
246C4×D4—1461no—
247C4×D4—1461no—
248#117—731no—
249C2×C4⋊C4—731no—
250C2×C22⋊C4—1461no—
251#107—731no—
252#107—731no—
253#106—731no—
254#106C2×D7311yescharacteristic, complemented
255#103—731no—
256#103—731no—
257#102—731no—
258#102—731no—
259#102—731no—
260#102—731no—
261#102C2×D7311yescharacteristic, complemented
262#102C2×D7311yescharacteristic, complemented
263C22⋊C8—731no—
264C22⋊C8—731no—
265C22⋊C8—731no—
266C22⋊C8—731no—
267C24—731no—
268C24—1461no—
269#41—2921no—
270#41—2921no—
271C2×Q8—731no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—2924no—
275C2×D4—2921no—
276C2×D4—2921no—
277C2×D4—731no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4—1461no—
283C2×D4—1461no—
284C2×D4C22×D7311yescharacteristic
285C2×D4C22×D7311yescharacteristic
286C22×C4—2921no—
287C22×C4—2921no—
288C22×C4—731no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—1461no—
294C22×C4—1461no—
295C22×C4C22×D7311yescharacteristic
296SD16—2921no—
297SD16—2921no—
298D8—41no—
299D8—2921no—
300M16—41no—
301M16—2921no—
302C2×C8—731no—
303C2×C8—731no—
304C2×C8C22×D7311yescharacteristic
305C2×C8C22×D7311yescharacteristic
306C4⋊C4—731no—
307C4⋊C4—731no—
308C4⋊C4—1461no—
309C4⋊C4—1461no—
310C4⋊C4—1461no—
311C4⋊C4C22×D7311yescharacteristic
312C4⋊C4C22×D7311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C22⋊C4—1461no—
318C22⋊C4—1461no—
319C22⋊C4—1461no—
320C22⋊C4—1461no—
321C22⋊C4—1461no—
322C42—1461no—
323C23—21no—
324C23—21no—
325C23—2921no—
326C23—2921no—
327C23—2922no—
328C23—2922no—
329C23—2922no—
330C23—731no—
331C23—731no—
332C23—1462no—
333C23—1461no—
334C23D4×D7311yescharacteristic
335Q8—1461no—
336Q8—1461no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—2922no—
344D4—2922no—
345D4—2922no—
346D4—2922no—
347D4—2922no—
348D4—2922no—
349D4—1461no—
350D4—1461no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—2921no—
356C2×C4—2921no—
357C2×C4—2922no—
358C2×C4—2922no—
359C2×C4—2921no—
360C2×C4—731no—
361C2×C4—731no—
362C2×C4—1461no—
363C2×C4—1461no—
364C2×C4—1461no—
365C2×C4—1461no—
366C2×C4—1461no—
367C2×C4—1461no—
368C2×C4—1461no—
369C2×C4D4×D7311yescharacteristic
370C2×C4C23×D7311yescharacteristic
371C8—21no—
372C8—21no—
373C8—1461no—
374C8—1461no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—2924no—
385C22—2921no—
386C22—2921no—
387C22—2921no—
388C22—5844no—
389C22—732no—
390C22—1461no—
391C22—1461no—
392C22—1461no—
393C22—1461no—
394C22—1461no—
395C22C2×D4×D7311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—2921no—
400C4—2921no—
401C4—2921no—
402C4—1461no—
403C4—1461no—
404C4#1455663611yescharacteristic
405C4#1455663711yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—2921no—
410C2—5841no—
411C2—1462no—
412C2#1798914511yescharacteristic
413C2AGL(1,ℤ/8)×D7311yescharacteristic
414C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#469×C73C2
socleC22×C73C22×D4
hypercenter#469D73
hypocenterC73#3194
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #17989097C2semidirect
2. #121×D73C2semidirect
3. #17988919C2semidirect
4. #17988913C2semidirect
5. #17988909C2semidirect
6. #17988899C2semidirect
7. #17988838C2semidirect
8. #17988833C2semidirect
9. #17988831C2semidirect
10. #17988739C2semidirect
11. #17988733C2semidirect
12. #17988729C2semidirect
13. #17988719C2semidirect
14. #17988550C2semidirect
15. #469×C73C2semidirect
16. C2×#11924027C22semidirect
20. C2×#11924017C22semidirect
21. C2×#11924016C22semidirect
22. C2×#11924013C22semidirect
23. C2×#11924012C22semidirect
26. #14556570C22semidirect
36. #14556549C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556522C22semidirect
42. #14556516C22semidirect
43. #14556514C22semidirect
44. #14556513C22semidirect
45. #14556512C22semidirect
46. #14556512C22semidirect
47. #14556511C22semidirect
50. #14556503C22semidirect
51. #14556503C22semidirect
52. C2×D8×C73C22semidirect
53. C2×M16×C73C22semidirect
55. #121×C73C22semidirect
56. #106×C73C22semidirect
57. #102×C73C22semidirect
58. #102×C73C22semidirect
208. C73#3194semidirect
216. #469D73semidirect
231. C2×D8C2×D73semidirect
233. C2×M16C2×D73semidirect
244. #121C2×D73semidirect
254. #106C2×D73semidirect
261. #102C2×D73semidirect
262. #102C2×D73semidirect