Finite Group Databasebeta

← #482×D293 #49168665

Subgroups — #482×D293 #49168665

Order 37504.

468 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D293C211yesmaximal, characteristic
2#117×D293C211yesmaximal, characteristic, complemented
3#34036456C211yesmaximal, characteristic, complemented
4#34036455C211yesmaximal, characteristic, complemented
5#34036454C211yesmaximal, characteristic, complemented
6#34036453C211yesmaximal, characteristic, complemented
7#34036452C211yesmaximal, characteristic, complemented
8#34036451C211yesmaximal, characteristic, complemented
9#34036450C211yesmaximal, characteristic, complemented
10#107×D293C211yesmaximal, characteristic, complemented
11#106×D293C211yesmaximal, characteristic, complemented
12#102×D293C211yesmaximal, characteristic, complemented
13#102×D293C211yesmaximal, characteristic, complemented
14C22⋊C8×D293C211yesmaximal, characteristic, complemented
15#482×C293C211yesmaximal, characteristic, complemented
16C2×D4×D293—21no—
17C2×D4×D293C2211yescharacteristic
18C22×C4×D293C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21#22627599C2211yescharacteristic
22#22627598C2211yescharacteristic
23#22627597—21no—
24#22627596—21no—
25#22627595C2211yescharacteristic
26#22627583C2211yescharacteristic, complemented
27#22627582C2211yescharacteristic, complemented
28#22627582C2211yescharacteristic, complemented
29#22627581—21no—
30#22627580—21no—
31C4⋊C4×D293C2211yescharacteristic
32C4⋊C4×D293C2211yescharacteristic
33C4⋊C4×D293C2211yescharacteristic
34C22⋊C4×D293—21no—
35C22⋊C4×D293—21no—
36C42×D293—21no—
37#22627558C2211yescharacteristic, complemented
38#22627557C2211yescharacteristic, complemented
39#22627557C2211yescharacteristic, complemented
40#22627556C2211yescharacteristic, complemented
41#22627555C2211yescharacteristic, complemented
42#22627555C2211yescharacteristic, complemented
43#22627546C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic, complemented
46#22627545C2211yescharacteristic, complemented
47#22627544C2211yescharacteristic, complemented
48#22627544C2211yescharacteristic, complemented
49C22⋊#14556873C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic, complemented
51#22627536C2211yescharacteristic, complemented
52#121×C293C2211yescharacteristic
53#117×C293C2211yescharacteristic, complemented
54#107×C293C2211yescharacteristic, complemented
55#106×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C23×D293D411yescharacteristic
61C2×D1172—21no—
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66D4×D293—22no—
67D4×D293—22no—
68D4×D293—44no—
69C22×Dic293D411yescharacteristic
70C2×C4×D293—22no—
71C2×C4×D293—22no—
72C2×C4×D293—21no—
73C2×C4×D293—21no—
74C2×C4×D293—21no—
75C2×C4×D293D411yescharacteristic
76C2×C4×D293D411yescharacteristic
77C2×C4×D293C2311yescharacteristic
78C2×C4×D293C2311yescharacteristic
79C2×#14556873C2311yescharacteristic
80C2×#14556873C2311yescharacteristic
81C8×D293—22no—
82C8×D293—22no—
83C4⋊Dic293C2311yescharacteristic
84C4⋊Dic293C2311yescharacteristic
85C4⋊Dic293C2311yescharacteristic
86#17989781—21no—
87#17989781—21no—
88#17989781—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C4×Dic293—21no—
98C2×D4×C293—21no—
99C2×D4×C293C2311yescharacteristic
100C22×C4×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C22⋊C4×C293—21no—
107C22⋊C4×C293—21no—
108C42×C293—21no—
109C22×D293—22no—
110C22×D293—22no—
111C22×D293—22no—
112C22×D293—21no—
113C22×D293—42no—
114C22×D293—42no—
115C22×D293—42no—
116C22×D293C2×D411yescharacteristic
117C22×D293C2×D411yescharacteristic
118D1172—21no—
119D1172—21no—
120D1172—42no—
121C22⋊D293—42no—
122C22⋊D293—42no—
123C22⋊D293—42no—
124C2×Dic293—22no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293C2×D411yescharacteristic
129C2×Dic293C2×D411yescharacteristic
130C4×D293—22no—
131C4×D293—21no—
132C4×D293—21no—
133C4×D293—22no—
134C4×D293—42no—
135C4×D293—42no—
136C4×D293—42no—
137C4×D293#4112yes—
138C4×D293#4112yes—
139#14556873—21no—
140#14556873—21no—
141C23×C293—21no—
142C23×C293C2×D411yescharacteristic
143D4×C293—21no—
144D4×C293—21no—
145D4×C293—42no—
146C2×C4×C293—21no—
147C2×C4×C293—21no—
148C2×C4×C293—21no—
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293C2×D411yescharacteristic
152C2×C4×C293C2411yescharacteristic
153C8×C293—21no—
154C8×C293—21no—
155C22×C293—21no—
156C22×C293—21no—
157C22×C293—21no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—41no—
161C22×C293C22×D411yescharacteristic
162C2×D293—21no—
163C2×D293—21no—
164C2×D293—21no—
165C2×D293—44no—
166C2×D293—41no—
167C2×D293—41no—
168C2×D293—41no—
169C2×D293—84no—
170C2×D293#12312yes—
171C2×D293#13512yes—
172C2×D293AGL(1,ℤ/8)12yes—
173C4×C293—21no—
174C4×C293—41no—
175C4×C293—41no—
176C4×C293—41no—
177C4×C293C2×#4111yescharacteristic
178C4×C293C2×#4111yescharacteristic
179Dic293—21no—
180Dic293—41no—
181Dic293—41no—
182Dic293—41no—
183Dic293#12312yes—
184C2×C293—41no—
185C2×C293—81no—
186C2×C293C2×#12311yescharacteristic
187C2×C293C2×#13511yescharacteristic
188C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
189D293—41no—
190D293—81no—
191D293#48214yesdirect product factor
192C293C2×#48211yescharacteristic, complemented, Sylow
193C2×#482—2931nomaximal, Sylow
194C2×#121—2931no—
195C2×#117—2931no—
196#482—2931no—
197#482—2931no—
198#482—2931no—
199#482—2931no—
200#482—2931no—
201#482—2931no—
202#482—2931no—
203#482D29311yescharacteristic, direct product factor
204C2×#107—2931no—
205C2×#106—2931no—
206C2×#102—2931no—
207C2×#102—2931no—
208C2×C22⋊C8—2931no—
209C22×D4—2931no—
210C22×D4—5861no—
211C23×C4—2931no—
212C22×C8—2931no—
213C22×C8—2931no—
214#121—2931no—
215#121—2931no—
216#121—2931no—
217#121—5861no—
218#121—5861no—
219#121C2×D29311yescharacteristic
220#117—2931no—
221#117—2931no—
222#117—2931no—
223#117—5861no—
224#117—5861no—
225#117C2×D29311yescharacteristic, complemented
226C2×C4⋊C4—2931no—
227C2×C4⋊C4—2931no—
228C2×C4⋊C4—2931no—
229C2×C22⋊C4—5861no—
230C2×C22⋊C4—5861no—
231C2×C42—5861no—
232#107—2931no—
233#107—2931no—
234#107—2931no—
235#107C2×D29311yescharacteristic, complemented
236#106—2931no—
237#106—2931no—
238#106—2931no—
239#106C2×D29311yescharacteristic, complemented
240#102—2931no—
241#102—2931no—
242#102—2931no—
243#102—2931no—
244#102—2931no—
245#102—2931no—
246#102C2×D29311yescharacteristic, complemented
247#102C2×D29311yescharacteristic, complemented
248C22⋊C8—2931no—
249C22⋊C8—2931no—
250C22⋊C8—2931no—
251C22⋊C8C2×D29311yescharacteristic, complemented
252C24—2931no—
253C24—5861no—
254C2×D4—21no—
255C2×D4—2931no—
256C2×D4—5861no—
257C2×D4—5862no—
258C2×D4—5862no—
259C2×D4—5861no—
260C2×D4—5861no—
261C2×D4—5861no—
262C2×D4—11724no—
263C2×D4C22×D29311yescharacteristic
264C22×C4—2931no—
265C22×C4—2931no—
266C22×C4—2931no—
267C22×C4—2931no—
268C22×C4—2931no—
269C22×C4—5862no—
270C22×C4—5862no—
271C22×C4—5861no—
272C22×C4—5861no—
273C22×C4—5861no—
274C22×C4C22×D29311yescharacteristic
275C2×C8—2931no—
276C2×C8—2931no—
277C2×C8—5862no—
278C2×C8—5862no—
279C2×C8C22×D29311yescharacteristic
280C2×C8C22×D29311yescharacteristic
281C4⋊C4—2931no—
282C4⋊C4—2931no—
283C4⋊C4—2931no—
284C4⋊C4—5861no—
285C4⋊C4—5861no—
286C4⋊C4—5861no—
287C4⋊C4C22×D29311yescharacteristic
288C4⋊C4C22×D29311yescharacteristic
289C4⋊C4C22×D29311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—5861no—
293C22⋊C4—5861no—
294C22⋊C4—5861no—
295C22⋊C4—5861no—
296C22⋊C4—5861no—
297C22⋊C4—5861no—
298C42—21no—
299C42—5861no—
300C42—5861no—
301C42—5861no—
302C23—21no—
303C23—2931no—
304C23—2931no—
305C23—5862no—
306C23—5862no—
307C23—5862no—
308C23—5861no—
309C23—11722no—
310C23—11722no—
311C23—11722no—
312C23D4×D29311yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—5861no—
317D4—5861no—
318D4—11722no—
319D4—11722no—
320D4—11722no—
321D4—11722no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—2931no—
328C2×C4—2932no—
329C2×C4—2932no—
330C2×C4—2931no—
331C2×C4—5862no—
332C2×C4—5862no—
333C2×C4—5862no—
334C2×C4—5861no—
335C2×C4—5861no—
336C2×C4—5861no—
337C2×C4—5861no—
338C2×C4—5861no—
339C2×C4—11722no—
340C2×C4—11722no—
341C2×C4—11722no—
342C2×C4D4×D29311yescharacteristic
343C2×C4C23×D29311yescharacteristic
344C8—21no—
345C8—21no—
346C8—5861no—
347C8—5861no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—2932no—
355C22—2932no—
356C22—2932no—
357C22—23444no—
358C22—5861no—
359C22—5861no—
360C22—5861no—
361C22—11724no—
362C22—11721no—
363C22—11721no—
364C22—11721no—
365C22C2×D4×D29311yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—2932no—
371C4—5861no—
372C4—11721no—
373C4—11721no—
374C4—11721no—
375C4#41×D29311yescharacteristic
376C4#41×D29311yescharacteristic
377C2—41no—
378C2—81no—
379C2—2934no—
380C2—23441no—
381C2—11721no—
382C2#123×D29311yescharacteristic
383C2#135×D29311yescharacteristic
384C2AGL(1,ℤ/8)×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#482×C293C2
socleC22×C293C22×D4
prime radical#121×D293C2
hypercenter#482D293
hypocenterC293C2×#482
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D293C2semidirect
3. #34036456C2semidirect
4. #34036455C2semidirect
5. #34036454C2semidirect
6. #34036453C2semidirect
7. #34036452C2semidirect
8. #34036451C2semidirect
9. #34036450C2semidirect
10. #107×D293C2semidirect
11. #106×D293C2semidirect
12. #102×D293C2semidirect
13. #102×D293C2semidirect
14. C22⋊C8×D293C2semidirect
15. #482×C293C2semidirect
26. #22627583C22semidirect
27. #22627582C22semidirect
28. #22627582C22semidirect
37. #22627558C22semidirect
38. #22627557C22semidirect
39. #22627557C22semidirect
40. #22627556C22semidirect
41. #22627555C22semidirect
42. #22627555C22semidirect
43. #22627546C22semidirect
44. #22627546C22semidirect
45. #22627545C22semidirect
46. #22627545C22semidirect
47. #22627544C22semidirect
48. #22627544C22semidirect
49. C22⋊#14556873C22semidirect
50. #22627536C22semidirect
51. #22627536C22semidirect
53. #117×C293C22semidirect
54. #107×C293C22semidirect
55. #106×C293C22semidirect
56. #102×C293C22semidirect
57. #102×C293C22semidirect
58. C22⋊C8×C293C22semidirect
191. D293#482direct (N × H)
192. C293C2×#482semidirect
203. #482D293direct (N × H)
225. #117C2×D293semidirect
235. #107C2×D293semidirect
239. #106C2×D293semidirect
246. #102C2×D293semidirect
247. #102C2×D293semidirect
251. C22⋊C8C2×D293semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#121×D2932
#117×D2932
#340364562
#340364552
#340364542
#340364532
#340364522
#340364512
#340364502
#107×D2932
#106×D2932
#102×D2932
C22⋊C8×D2932
#482×C2932
C2×#482293