Finite Group Databasebeta

← #22620749

Subgroups — #22620749

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#17989099C211yesmaximal, characteristic, complemented
2#121×D73C211yesmaximal, characteristic, complemented
3#17988919C211yesmaximal, characteristic, complemented
4#17988911C211yesmaximal, characteristic, complemented
5#17988902C211yesmaximal, characteristic, complemented
6#17988841C211yesmaximal, characteristic, complemented
7#17988839C211yesmaximal, characteristic, complemented
8#17988834C211yesmaximal, characteristic, complemented
9#17988832C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988734C211yesmaximal, characteristic, complemented
12#17988730C211yesmaximal, characteristic, complemented
13#17988722C211yesmaximal, characteristic, complemented
14#17988549C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic, complemented
17C2×D4×D73—21no—
18C2×D4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×D584C2211yescharacteristic, complemented
23C2×#11924013C2211yescharacteristic, complemented
24C2×#11924011C2211yescharacteristic, complemented
25C2×#11924011C2211yescharacteristic, complemented
26#14556575—21no—
27#14556571C2211yescharacteristic
28#14556571C2211yescharacteristic, complemented
29#14556566C2211yescharacteristic
30#14556566C2211yescharacteristic
31#14556566C2211yescharacteristic, complemented
32#14556565C2211yescharacteristic
33#14556564—21no—
34#14556563—21no—
35#14556562C2211yescharacteristic
36#14556561—21no—
37C4×D292—21no—
38C4×D292—21no—
39C4⋊C4×D73C2211yescharacteristic
40C22⋊C4×D73—21no—
41#14556524C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic, complemented
46#14556511C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic, complemented
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73D411yescharacteristic
61#11924028—41no—
62#11924028—41no—
63C2×Dic146C2311yescharacteristic
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73D4×D73—41no—
74D4×D73—41no—
75D4×D73—44no—
76C22×Dic73D411yescharacteristic
77C2×C4×D73—21no—
78C2×C4×D73—21no—
79C2×C4×D73—41no—
80C2×C4×D73—41no—
81C2×C4×D73D411yescharacteristic
82C2×C4×D73D411yescharacteristic
83C2×C4×D73C2311yescharacteristic
84C2×C4×D73C2311yescharacteristic
85#11924017—41no—
86#11924016—41no—
87D584—41no—
88#11924013—41no—
89#11924011—41no—
90#11924011—41no—
91C2×#10596831C2311yescharacteristic
92C2×#10596831C2311yescharacteristic
93C4⋊Dic73—21no—
94C4⋊Dic73—21no—
95C4⋊Dic73C2311yescharacteristic
96#11924007—21no—
97C22⋊Dic73—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102#11924005—21no—
103#11924005—21no—
104C2×D4×C73—21no—
105C2×D4×C73C2311yescharacteristic
106C22×C4×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C4⋊C4×C73C2311yescharacteristic
112C22⋊C4×C73—21no—
113C22⋊C4×C73—21no—
114C42×C73—21no—
115C23×C73—21no—
116C23×C73C2×D411yescharacteristic
117C22×D73—22no—
118C22×D73—21no—
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—42no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2411yescharacteristic
137C22⋊D73—42no—
138C22⋊D73—42no—
139C22⋊D73—42no—
140C22⋊D73—42no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—41no—
144C2×Dic73C2×D411yescharacteristic
145C2×Dic73C2×D411yescharacteristic
146D292—21no—
147D292—21no—
148D292—21no—
149D292—21no—
150D292—42no—
151D292—42no—
152D292—42no—
153C4×D73—21no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—21no—
157C4×D73—41no—
158C4×D73—41no—
159C4×D73—42no—
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×C73C22×D411yescharacteristic
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—44no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
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×C73—41no—
192C4×C73H(5,𝔽2)11yescharacteristic
193C4×C73H(5,𝔽2)11yescharacteristic
194Dic73—21no—
195Dic73—21no—
196Dic73—41no—
197Dic73—41no—
198C2×C73—41no—
199C2×C73—81no—
200C2×C73#53411yescharacteristic
201C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
202C2×C73#57511yescharacteristic
203D73—22no—
204D73—41no—
205D73—81no—
206D73—81no—
207#3194—731nomaximal, Sylow
208C73#319411yescharacteristic, complemented, Sylow
209#525—731no—
210C2×#121—731no—
211#483—731no—
212#482—731no—
213#482D7311yescharacteristic, complemented
214#480—731no—
215#469—731no—
216#469—731no—
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×D8—731no—
232C2×M16—731no—
233C2×M16—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#117C2×D7311yescharacteristic, complemented
249C2×C4⋊C4—731no—
250C2×C22⋊C4—1461no—
251#107—731no—
252#107C2×D7311yescharacteristic, complemented
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⋊C8C2×D7311yescharacteristic, complemented
267C24—731no—
268C24—1461no—
269#41—2921no—
270#41—2921no—
271C2×Q8—731no—
272C2×D4—21no—
273C2×D4—2924no—
274C2×D4—2921no—
275C2×D4—2921no—
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×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—2921no—
299D8—2921no—
300M16—2921no—
301M16—2921no—
302C2×C8—731no—
303C2×C8—731no—
304C2×C8C22×D7311yescharacteristic
305C2×C8C22×D7311yescharacteristic
306C4⋊C4—731no—
307C4⋊C4—1461no—
308C4⋊C4—1461no—
309C4⋊C4—1461no—
310C4⋊C4C22×D7311yescharacteristic
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—21no—
323C23—21no—
324C23—2921no—
325C23—2921no—
326C23—2922no—
327C23—2922no—
328C23—2922no—
329C23—731no—
330C23—731no—
331C23—1462no—
332C23—1461no—
333C23—1461no—
334C23D4×D7311yescharacteristic
335Q8—1461no—
336Q8—1461no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—2922no—
341D4—2922no—
342D4—2922no—
343D4—2922no—
344D4—2922no—
345D4—2922no—
346D4—2922no—
347D4—1461no—
348D4—1461no—
349D4—1461no—
350D4—1461no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—2922no—
357C2×C4—2921no—
358C2×C4—2921no—
359C2×C4—2922no—
360C2×C4—2921no—
361C2×C4—731no—
362C2×C4—731no—
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—2924no—
382C22—2921no—
383C22—2921no—
384C22—2921no—
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—41no—
400C4—2921no—
401C4—2921no—
402C4—1461no—
403C4—1461no—
404C4#1455663711yescharacteristic
405C4#1455663711yescharacteristic
406C2—41no—
407C2—81no—
408C2—2921no—
409C2—5841no—
410C2—5841no—
411C2—1462no—
412C2#1798914811yescharacteristic
413C2AGL(1,ℤ/8)×D7311yescharacteristic
414C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3194
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17989099C2semidirect
2. #121×D73C2semidirect
3. #17988919C2semidirect
4. #17988911C2semidirect
5. #17988902C2semidirect
6. #17988841C2semidirect
7. #17988839C2semidirect
8. #17988834C2semidirect
9. #17988832C2semidirect
10. #17988739C2semidirect
11. #17988734C2semidirect
12. #17988730C2semidirect
13. #17988722C2semidirect
14. #17988549C2semidirect
15. #482×C73C2semidirect
16. C2×#11924028C22semidirect
20. C2×#11924017C22semidirect
21. C2×#11924016C22semidirect
22. C2×D584C22semidirect
23. C2×#11924013C22semidirect
24. C2×#11924011C22semidirect
25. C2×#11924011C22semidirect
28. #14556571C22semidirect
31. #14556566C22semidirect
41. #14556524C22semidirect
42. #14556522C22semidirect
43. #14556516C22semidirect
44. #14556514C22semidirect
45. #14556513C22semidirect
46. #14556511C22semidirect
47. #14556511C22semidirect
48. #14556511C22semidirect
49. C22⋊#10596831C22semidirect
53. #117×C73C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. #102×C73C22semidirect
57. #102×C73C22semidirect
58. C22⋊C8×C73C22semidirect
208. C73#3194semidirect
213. #482D73semidirect
248. #117C2×D73semidirect
252. #107C2×D73semidirect
254. #106C2×D73semidirect
261. #102C2×D73semidirect
262. #102C2×D73semidirect
266. C22⋊C8C2×D73semidirect