Finite Group Databasebeta

← #22620694

Subgroups — #22620694

Order 9344.

472 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#17989094C211yesmaximal, characteristic, complemented
2#121×D73C211yesmaximal, characteristic, complemented
3#17988921C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic, complemented
5#17988908C211yesmaximal, characteristic, complemented
6#17988904C211yesmaximal, characteristic, complemented
7#17988822C211yesmaximal, characteristic, complemented
8#17988820C211yesmaximal, characteristic, complemented
9#17988819C211yesmaximal, characteristic, complemented
10#17988813C211yesmaximal, characteristic, complemented
11#17988736C211yesmaximal, characteristic, complemented
12#17988732C211yesmaximal, characteristic, complemented
13#17988719C211yesmaximal, characteristic, complemented
14C22⋊C8×D73C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73—21no—
17C2×D4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C2×#11924015C2211yescharacteristic, complemented
20C2×#11924013C2211yescharacteristic, complemented
21C2×C8×D73C2211yescharacteristic, complemented
22C2×C8×D73C2211yescharacteristic, complemented
23#14556572—21no—
24#14556567C2211yescharacteristic
25#14556567C2211yescharacteristic, complemented
26#14556566C2211yescharacteristic
27#14556565C2211yescharacteristic
28#14556564—21no—
29#14556563—21no—
30#14556562C2211yescharacteristic
31#14556562C2211yescharacteristic
32#14556562C2211yescharacteristic, complemented
33#14556559—21no—
34C4×C22⋊D73—21no—
35C4×C22⋊D73—21no—
36#14556550C2211yescharacteristic, complemented
37C4⋊C4×D73C2211yescharacteristic
38C22⋊C4×D73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic, complemented
48#14556512C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic, complemented
53C2×SD16×C73C2211yescharacteristic, complemented
54C2×D8×C73C2211yescharacteristic, complemented
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73D411yescharacteristic
61C2×D292—21no—
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68D4×D73—41no—
69D4×D73—41no—
70D4×D73—44no—
71C22×Dic73D411yescharacteristic
72C2×C4×D73—21no—
73C2×C4×D73—41no—
74C2×C4×D73—41no—
75C2×C4×D73D411yescharacteristic
76C2×C4×D73D411yescharacteristic
77C2×C4×D73C2311yescharacteristic
78C2×C4×D73C2311yescharacteristic
79#11924015—41no—
80#11924013—41no—
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C8×D73—41no—
84C8×D73—41no—
85C4⋊Dic73C2311yescharacteristic
86C4⋊Dic73C2311yescharacteristic
87C4⋊Dic73C2311yescharacteristic
88#11924007—21no—
89#11924007—21no—
90#11924007—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93C22⋊Dic73—21no—
94C22⋊Dic73—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99C4×Dic73—21no—
100#41×C73—41no—
101#41×C73—41no—
102C2×Q8×C73C2311yescharacteristic
103C2×D4×C73—21no—
104C2×D4×C73—21no—
105C2×D4×C73C2311yescharacteristic
106C2×D4×C73C2311yescharacteristic
107C22×C4×C73—21no—
108C22×C4×C73C2311yescharacteristic
109SD16×C73—41no—
110D8×C73—41no—
111C2×C8×C73C2311yescharacteristic
112C2×C8×C73C2311yescharacteristic
113C4⋊C4×C73C2311yescharacteristic
114C22⋊C4×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73C2×D411yescharacteristic
118C22×D73—22no—
119C22×D73—22no—
120C22×D73—21no—
121C22×D73—41no—
122C22×D73—42no—
123C22×D73—42no—
124C22×D73—42no—
125C22×D73C2×D411yescharacteristic
126C22×D73C2×D411yescharacteristic
127Q8×C73—21no—
128Q8×C73—21no—
129D4×C73—21no—
130D4×C73—21no—
131D4×C73—21no—
132D4×C73—21no—
133D4×C73—42no—
134D4×C73—42no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—42no—
140C2×C4×C73C2×D411yescharacteristic
141C2×C4×C73C2411yescharacteristic
142C22⋊D73—42no—
143C22⋊D73—42no—
144C22⋊D73—42no—
145C22⋊D73—42no—
146C22⋊D73—42no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—21no—
150C2×Dic73—41no—
151C2×Dic73C2×D411yescharacteristic
152C2×Dic73C2×D411yescharacteristic
153D292—21no—
154D292—21no—
155D292—42no—
156C4×D73—21no—
157C4×D73—21no—
158C4×D73—21no—
159C4×D73—21no—
160C4×D73—41no—
161C4×D73—41no—
162C4×D73—42no—
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—44no—
182C2×D73—41no—
183C2×D73—41no—
184C2×D73—41no—
185C2×D73—84no—
186C2×D73#13512yes—
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×#13511yescharacteristic
203C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
204D73—22no—
205D73—22no—
206D73—81no—
207#3188—731nomaximal, Sylow
208C73#318811yescharacteristic, complemented, Sylow
209#525—731no—
210C2×#121—731no—
211#484—731no—
212#482—731no—
213#482—731no—
214#481—731no—
215#466—731no—
216#466—731no—
217#465—731no—
218#465—731no—
219#450—731no—
220#449—731no—
221#449D7311yescharacteristic, complemented
222#447—731no—
223C2×C22⋊C8—731no—
224C2×#41C2×D7311yescharacteristic, complemented
225C22×D4—731no—
226C22×D4—1461no—
227C23×C4—731no—
228C2×SD16—731no—
229C2×SD16C2×D7311yescharacteristic, complemented
230C2×D8—731no—
231C2×D8C2×D7311yescharacteristic, complemented
232C22×C8—731no—
233C22×C8—731no—
234#123—1461no—
235C22⋊Q8—731no—
236C22⋊Q8—731no—
237#121—731no—
238#121—731no—
239#121—731no—
240#121—731no—
241#121—731no—
242#121—1461no—
243#121—1461no—
244#121C2×D7311yescharacteristic
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#106—731no—
255#103—731no—
256#103C2×D7311yescharacteristic, complemented
257#102—731no—
258#102—731no—
259#102—731no—
260#102—731no—
261#102—731no—
262#102C2×D7311yescharacteristic, complemented
263C22⋊C8—731no—
264C22⋊C8—731no—
265C22⋊C8—731no—
266C22⋊C8C2×D7311yescharacteristic, complemented
267C24—731no—
268C24—1461no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D7311yescharacteristic
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—21no—
287C22×C4—2921no—
288C22×C4—2921no—
289C22×C4—731no—
290C22×C4—731no—
291C22×C4—731no—
292C22×C4—731no—
293C22×C4—731no—
294C22×C4—1461no—
295C22×C4C22×D7311yescharacteristic
296SD16—41no—
297SD16—2921no—
298D8—41no—
299D8—2921no—
300C2×C8—2921no—
301C2×C8—2921no—
302C2×C8—731no—
303C2×C8—731no—
304C2×C8C22×D7311yescharacteristic
305C2×C8C22×D7311yescharacteristic
306C4⋊C4—731no—
307C4⋊C4—731no—
308C4⋊C4—731no—
309C4⋊C4—1461no—
310C4⋊C4—1461no—
311C4⋊C4—1461no—
312C4⋊C4C22×D7311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—1461no—
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—2922no—
327C23—2922no—
328C23—2922no—
329C23—731no—
330C23—731no—
331C23—1462no—
332C23—1462no—
333C23—1461no—
334C23D4×D7311yescharacteristic
335Q8—21no—
336Q8—21no—
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—42no—
356C2×C4—2921no—
357C2×C4—2921no—
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—732no—
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#1455663611yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—5841no—
410C2—1462no—
411C2—1462no—
412C2#1798914711yescharacteristic
413C2#135×D7311yescharacteristic
414C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3188
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #17989094C2semidirect
2. #121×D73C2semidirect
3. #17988921C2semidirect
4. #17988912C2semidirect
5. #17988908C2semidirect
6. #17988904C2semidirect
7. #17988822C2semidirect
8. #17988820C2semidirect
9. #17988819C2semidirect
10. #17988813C2semidirect
11. #17988736C2semidirect
12. #17988732C2semidirect
13. #17988719C2semidirect
14. C22⋊C8×D73C2semidirect
15. #449×C73C2semidirect
19. C2×#11924015C22semidirect
20. C2×#11924013C22semidirect
21. C2×C8×D73C22semidirect
22. C2×C8×D73C22semidirect
25. #14556567C22semidirect
32. #14556562C22semidirect
36. #14556550C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556523C22semidirect
42. #14556522C22semidirect
43. #14556515C22semidirect
44. #14556513C22semidirect
45. #14556513C22semidirect
46. #14556512C22semidirect
47. #14556512C22semidirect
48. #14556512C22semidirect
49. C22⋊#10596831C22semidirect
52. C2×#41×C73C22semidirect
53. C2×SD16×C73C22semidirect
54. C2×D8×C73C22semidirect
56. #103×C73C22semidirect
57. #102×C73C22semidirect
58. C22⋊C8×C73C22semidirect
208. C73#3188semidirect
221. #449D73semidirect
224. C2×#41C2×D73semidirect
229. C2×SD16C2×D73semidirect
231. C2×D8C2×D73semidirect
256. #103C2×D73semidirect
262. #102C2×D73semidirect
266. C22⋊C8C2×D73semidirect