Finite Group Databasebeta

← #49168697

Subgroups — #49168697

Order 37504.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036639C211yesmaximal, characteristic
2#117×D293C211yesmaximal, characteristic, complemented
3#34036471C211yesmaximal, characteristic, complemented
4#34036470C211yesmaximal, characteristic, complemented
5#34036466C211yesmaximal, characteristic, complemented
6#34036461C211yesmaximal, characteristic, complemented
7#34036450C211yesmaximal, characteristic, complemented
8#34036446C211yesmaximal, characteristic, complemented
9#34036441C211yesmaximal, characteristic, complemented
10#34036166C211yesmaximal, characteristic, complemented
11#34036164C211yesmaximal, characteristic, complemented
12#34036122C211yesmaximal, characteristic, complemented
13#34036122C211yesmaximal, characteristic, complemented
14C22⋊C8×D293C211yesmaximal, characteristic, complemented
15#482×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C22×C4×D293C2211yescharacteristic
18C2×C8×D293C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20#22627606—21no—
21#22627604C2211yescharacteristic
22#22627603C2211yescharacteristic
23#22627595C2211yescharacteristic
24#22627592—21no—
25D4×Dic293—21no—
26#22627584—21no—
27#22627583C2211yescharacteristic
28#22627582C2211yescharacteristic
29#22627582C2211yescharacteristic
30#22627582C2211yescharacteristic
31#22627581—21no—
32#22627580—21no—
33C4⋊C4×D293C2211yescharacteristic
34C4⋊C4×D293C2211yescharacteristic
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#22627549C2211yescharacteristic, complemented
44#22627549C2211yescharacteristic, complemented
45#22627547C2211yescharacteristic, complemented
46#22627547C2211yescharacteristic, complemented
47#22627545C2211yescharacteristic, complemented
48#22627545C2211yescharacteristic, complemented
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627536C2211yescharacteristic
52#121×C293C2211yescharacteristic
53#117×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic, complemented
55#106×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic
59C23×D293D411yescharacteristic
60#17989801—22no—
61#17989801—22no—
62C2×Dic586C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C22×Dic293—21no—
66C22×Dic293D411yescharacteristic
67C2×C4×D293—22no—
68C2×C4×D293—22no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293D411yescharacteristic
72C2×C4×D293D411yescharacteristic
73C2×C4×D293C2311yescharacteristic
74C2×C4×D293C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C8×D293—22no—
78C8×D293—22no—
79C4⋊Dic293—21no—
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C2×D4×C293—21no—
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C2×C8×C293C2311yescharacteristic
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C42×C293—21no—
108C22×D293—22no—
109C22×D293—22no—
110C22×D293—41no—
111C22×D293C2×D411yescharacteristic
112C22×D293C2×D411yescharacteristic
113Dic586—21no—
114Dic586—21no—
115C22⋊D293—42no—
116C22⋊D293—42no—
117C2×Dic293—22no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—42no—
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C4×D293—22no—
126C4×D293—21no—
127C4×D293—21no—
128C4×D293—22no—
129C4×D293—42no—
130C4×D293—42no—
131C4×D293#4112yes—
132C4×D293#4112yes—
133#14556873—21no—
134#14556873—21no—
135C23×C293—21no—
136C23×C293C2×D411yescharacteristic
137D4×C293—21no—
138D4×C293—21no—
139D4×C293—42no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2411yescharacteristic
147C8×C293—21no—
148C8×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293—21no—
152C22×C293—41no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293C22×D411yescharacteristic
156C2×D293—21no—
157C2×D293—21no—
158C2×D293—21no—
159C2×D293—21no—
160C2×D293—44no—
161C2×D293#12312yes—
162C2×D293#13512yes—
163C4×C293—21no—
164C4×C293—41no—
165C4×C293—41no—
166C4×C293—41no—
167C4×C293C2×#4111yescharacteristic
168C4×C293C2×#4111yescharacteristic
169Dic293—21no—
170Dic293—41no—
171Dic293—41no—
172Dic293—41no—
173Dic293—41no—
174Dic293#12312yes—
175C2×C293—41no—
176C2×C293—81no—
177C2×C293C2×#12311yescharacteristic
178C2×C293C2×#13511yescharacteristic
179C2×C293#57511yescharacteristic
180D293—22no—
181D293—22no—
182C293#309111yescharacteristic, complemented, Sylow
183#3091—2931nomaximal, Sylow
184#525—2931no—
185C2×#117—2931no—
186#485—2931no—
187#485—2931no—
188#484—2931no—
189#483—2931no—
190#482—2931no—
191#482D29311yescharacteristic, complemented
192#481—2931no—
193#480—2931no—
194#427—2931no—
195#427—2931no—
196#416—2931no—
197#416—2931no—
198C2×C22⋊C8—2931no—
199C2×#41—2931no—
200C23×C4—2931no—
201C22×C8—2931no—
202C22×C8—2931no—
203#123—5861no—
204C22⋊Q8—2931no—
205C22⋊Q8—2931no—
206#121—2931no—
207#121C2×D29311yescharacteristic
208#120—5861no—
209C4×D4—5861no—
210C4×D4—5861no—
211#117—2931no—
212#117—2931no—
213#117—2931no—
214#117—2931no—
215#117—5861no—
216#117—5861no—
217#117C2×D29311yescharacteristic
218C2×C4⋊C4—2931no—
219C2×C4⋊C4—2931no—
220C2×C22⋊C4—5861no—
221C2×C42—5861no—
222#107—2931no—
223#107—2931no—
224#107—2931no—
225#107C2×D29311yescharacteristic, complemented
226#106—2931no—
227#106—2931no—
228#106—2931no—
229#106C2×D29311yescharacteristic, complemented
230#103—2931no—
231#103—2931no—
232#103—2931no—
233#103—2931no—
234#102—2931no—
235#102—2931no—
236#102C2×D29311yescharacteristic, complemented
237#102C2×D29311yescharacteristic, complemented
238C22⋊C8—2931no—
239C22⋊C8—2931no—
240C22⋊C8—2931no—
241C22⋊C8C2×D29311yescharacteristic
242C24—2931no—
243#41—5862no—
244#41—5862no—
245C2×Q8—2931no—
246C2×D4—21no—
247C2×D4—5861no—
248C2×D4—5861no—
249C2×D4C22×D29311yescharacteristic
250C22×C4—2931no—
251C22×C4—2931no—
252C22×C4—2931no—
253C22×C4—2931no—
254C22×C4—2931no—
255C22×C4—5862no—
256C22×C4—5862no—
257C22×C4—5861no—
258C22×C4—5861no—
259C22×C4—5861no—
260C22×C4C22×D29311yescharacteristic
261C2×C8—2931no—
262C2×C8—2931no—
263C2×C8—5862no—
264C2×C8—5862no—
265C2×C8C22×D29311yescharacteristic
266C2×C8C22×D29311yescharacteristic
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—2931no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4—5861no—
274C4⋊C4C22×D29311yescharacteristic
275C4⋊C4C22×D29311yescharacteristic
276C4⋊C4C22×D29311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—21no—
287C42—5861no—
288C42—5861no—
289C42—5861no—
290C42—5861no—
291C23—21no—
292C23—2931no—
293C23—2931no—
294C23—5862no—
295C23—5862no—
296C23—11721no—
297C23D4×D29311yescharacteristic
298Q8—5861no—
299Q8—5861no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—11722no—
304D4—11722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—2931no—
311C2×C4—2932no—
312C2×C4—2932no—
313C2×C4—2931no—
314C2×C4—5862no—
315C2×C4—5862no—
316C2×C4—5862no—
317C2×C4—5861no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—11722no—
324C2×C4—11722no—
325C2×C4—11722no—
326C2×C4D4×D29311yescharacteristic
327C2×C4C23×D29311yescharacteristic
328C8—21no—
329C8—21no—
330C8—5861no—
331C8—5861no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2932no—
339C22—2932no—
340C22—5861no—
341C22—5861no—
342C22—5861no—
343C22—5861no—
344C22—11724no—
345C22C2×D4×D29311yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—2932no—
351C4—5861no—
352C4—11721no—
353C4—11721no—
354C4—11721no—
355C4—11721no—
356C4#41×D29311yescharacteristic
357C4#41×D29311yescharacteristic
358C2—41no—
359C2—81no—
360C2—5862no—
361C2—5862no—
362C2#123×D29311yescharacteristic
363C2#135×D29311yescharacteristic
364C2#3403692511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#482×C293C2
socleC22×C293C22×D4
prime radical#34036639C2
hypercenter#482D293
hypocenterC293#3091
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. #34036471C2semidirect
4. #34036470C2semidirect
5. #34036466C2semidirect
6. #34036461C2semidirect
7. #34036450C2semidirect
8. #34036446C2semidirect
9. #34036441C2semidirect
10. #34036166C2semidirect
11. #34036164C2semidirect
12. #34036122C2semidirect
13. #34036122C2semidirect
14. C22⋊C8×D293C2semidirect
15. #482×C293C2semidirect
37. #22627558C22semidirect
38. #22627557C22semidirect
39. #22627557C22semidirect
40. #22627556C22semidirect
41. #22627555C22semidirect
42. #22627555C22semidirect
43. #22627549C22semidirect
44. #22627549C22semidirect
45. #22627547C22semidirect
46. #22627547C22semidirect
47. #22627545C22semidirect
48. #22627545C22semidirect
54. #107×C293C22semidirect
55. #106×C293C22semidirect
56. #102×C293C22semidirect
57. #102×C293C22semidirect
182. C293#3091semidirect
191. #482D293semidirect
225. #107C2×D293semidirect
229. #106C2×D293semidirect
236. #102C2×D293semidirect
237. #102C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366392
#117×D2932
#340364712
#340364702
#340364662
#340364612
#340364502
#340364462
#340364412
#340361662
#340361642
#340361222
C22⋊C8×D2932
#482×C2932
#3091293