Finite Group Databasebeta

← #49169138

Subgroups — #49169138

Order 37504.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036759C211yesmaximal, characteristic, complemented
2#34036697C211yesmaximal, characteristic
3#34036495C211yesmaximal, characteristic, complemented
4#34036492C211yesmaximal, characteristic, complemented
5#34036490C211yesmaximal, characteristic, complemented
6#34036488C211yesmaximal, characteristic, complemented
7#34036485C211yesmaximal, characteristic, complemented
8#34036476C211yesmaximal, characteristic, complemented
9#34036474C211yesmaximal, characteristic, complemented
10#34036132C211yesmaximal, characteristic, complemented
11#34036129C211yesmaximal, characteristic, complemented
12#34036124C211yesmaximal, characteristic, complemented
13#102×D293C211yesmaximal, characteristic, complemented
14#34036083C211yesmaximal, characteristic, complemented
15#488×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×D4×D293C2211yescharacteristic
18C2×#17989785C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20#22627624C2211yescharacteristic, complemented
21#22627623—21no—
22#22627623C2211yescharacteristic, complemented
23#22627621C2211yescharacteristic
24#22627620C2211yescharacteristic
25#22627615C2211yescharacteristic, complemented
26#22627614—21no—
27#22627613C2211yescharacteristic
28#22627604—21no—
29#22627602—21no—
30#22627597—21no—
31#22627597—21no—
32#22627594—21no—
33#22627594—21no—
34#22627582C2211yescharacteristic
35#22627581C2211yescharacteristic
36C4⋊C4×D293C2211yescharacteristic
37#22627548C2211yescharacteristic, complemented
38#22627548C2211yescharacteristic, complemented
39#22627546C2211yescharacteristic
40#22627546C2211yescharacteristic
41#22627546C2211yescharacteristic, complemented
42#22627546C2211yescharacteristic, complemented
43#22627545C2211yescharacteristic
44#22627545C2211yescharacteristic
45#22627544C2211yescharacteristic
46#22627544C2211yescharacteristic
47#22627544C2211yescharacteristic, complemented
48#22627544C2211yescharacteristic, complemented
49#22627535C2211yescharacteristic, complemented
50#22627534C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52#125×C293C2211yescharacteristic, complemented
53#124×C293C2211yescharacteristic
54#103×C293C2211yescharacteristic, complemented
55#103×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60#17989803—22no—
61#17989803—22no—
62C2×Dic586—21no—
63C2×Dic586—21no—
64C2×D1172—21no—
65C2×D1172—21no—
66C2×D1172—21no—
67C2×D1172C2311yescharacteristic
68C2×D1172C2311yescharacteristic
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C2×C22⋊D293—21no—
72D4×D293—22no—
73D4×D293—22no—
74C2×C4×D293—21no—
75C2×C4×D293—21no—
76C2×C4×D293C2311yescharacteristic
77#17989785—22no—
78C2×#14556873C2311yescharacteristic
79C2×#14556873C2311yescharacteristic
80C8×D293—22no—
81C4⋊Dic293—21no—
82C4⋊Dic293—21no—
83C4⋊Dic293C2311yescharacteristic
84C4⋊Dic293C2311yescharacteristic
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88#17989781D411yescharacteristic
89#17989781D411yescharacteristic
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779D411yescharacteristic
94#17989779D411yescharacteristic
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293C2311yescharacteristic
98C2×D4×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C4⋊C4×C293—21no—
102C4⋊C4×C293—21no—
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C42×C293C2311yescharacteristic
108C22×D293—21no—
109C22×D293—21no—
110C22×D293—42no—
111C22×D293—81no—
112C22×D293—81no—
113C22×D293C2×D411yescharacteristic
114Dic586—81no—
115Dic586—81no—
116D1172—21no—
117D1172—21no—
118D1172—21no—
119D1172—21no—
120D1172—42no—
121D1172—81no—
122D1172—81no—
123C22⋊D293—42no—
124C22⋊D293—81no—
125C22⋊D293—81no—
126C2×Dic293—21no—
127C2×Dic293—21no—
128C2×Dic293C2×D411yescharacteristic
129C2×Dic293C2×D411yescharacteristic
130C2×Dic293C2×D411yescharacteristic
131C4×D293—42no—
132C4×D293—81no—
133C4×D293#4112yes—
134C4×D293#4112yes—
135#14556873—21no—
136#14556873—21no—
137C23×C293—21no—
138Q8×C293—21no—
139Q8×C293—21no—
140D4×C293—21no—
141D4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293C2×D411yescharacteristic
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2411yescharacteristic
148C8×C293—21no—
149C8×C293—21no—
150C22×C293—41no—
151C22×C293—41no—
152C22×C293—41no—
153C22×C293C22×D411yescharacteristic
154C2×D293—21no—
155C2×D293—21no—
156C2×D293—41no—
157C2×D293—41no—
158C2×D293—41no—
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—41no—
162C2×D293—84no—
163C2×D293#12412yes—
164C4×C293—21no—
165C4×C293—21no—
166C4×C293—41no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293C2×#4111yescharacteristic
170C4×C293C2×#4111yescharacteristic
171Dic293—21no—
172Dic293—21no—
173Dic293—41no—
174Dic293—41no—
175Dic293#12412yes—
176C2×C293—81no—
177C2×C293C2×#12411yescharacteristic
178C2×C293#57611yescharacteristic
179C2×C293#57711yescharacteristic
180D293—22no—
181D293—81no—
182D293—81no—
183C293#313611yescharacteristic, complemented, Sylow
184#3136—2931nomaximal, Sylow
185#544—2931no—
186#535—2931no—
187#490—2931no—
188#490—2931no—
189#489—2931no—
190#489—2931no—
191#488—2931no—
192#488D29311yescharacteristic, complemented
193#486—2931no—
194#486—2931no—
195#418—2931no—
196#417—2931no—
197#416—2931no—
198C2×#102—2931no—
199#405—2931no—
200C2×#41—2931no—
201C22×D4—2931no—
202C2×M16—2931no—
203C22×C8—2931no—
204C4⋊Q8—2931no—
205C4⋊Q8—2931no—
206C4⋊Q8—5861no—
207#127—2931no—
208#127—2931no—
209#125—2931no—
210#125—5861no—
211#125C2×D29311yescharacteristic, complemented
212#124—2931no—
213#124C2×D29311yescharacteristic
214C22⋊Q8—5861no—
215C22⋊Q8—5861no—
216#121—5861no—
217#121—5861no—
218#120—5861no—
219#120—5861no—
220#117—2931no—
221#117—2931no—
222C2×C4⋊C4—2931no—
223#103—2931no—
224#103—2931no—
225#103C2×D29311yescharacteristic, complemented
226#103C2×D29311yescharacteristic, complemented
227#102—2931no—
228#102—2931no—
229#102—2931no—
230#102—2931no—
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102—2931no—
236#102—2931no—
237#102C2×D29311yescharacteristic
238#102C2×D29311yescharacteristic
239#97—2931no—
240#97—2931no—
241C4×C8—2931no—
242C4×C8C2×D29311yescharacteristic, complemented
243C24—5861no—
244#41—5862no—
245#41—5862no—
246C2×Q8—5861no—
247C2×Q8—5861no—
248C2×Q8C22×D29311yescharacteristic
249C2×D4—2931no—
250C2×D4—2931no—
251C2×D4—5861no—
252C2×D4—5862no—
253C2×D4—5862no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4—5861no—
257C2×D4—5861no—
258C2×D4—5861no—
259C2×D4C22×D29311yescharacteristic
260C22×C4—2931no—
261C22×C4—5861no—
262C22×C4—5861no—
263M16—5862no—
264C2×C8—2931no—
265C2×C8—2931no—
266C2×C8—5862no—
267C2×C8C22×D29311yescharacteristic
268C2×C8C22×D29311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—2931no—
272C4⋊C4—2931no—
273C4⋊C4—2931no—
274C4⋊C4—2931no—
275C4⋊C4—5861no—
276C4⋊C4—5861no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4C22×D29311yescharacteristic
281C4⋊C4C22×D29311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2931no—
285C22⋊C4—2931no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C42—2931no—
290C42—5861no—
291C42C22×D29311yescharacteristic
292C23—21no—
293C23—2931no—
294C23—23441no—
295C23—23441no—
296C23—5861no—
297C23—5861no—
298C23—11722no—
299Q8—21no—
300Q8—21no—
301Q8—23441no—
302Q8—23441no—
303D4—21no—
304D4—21no—
305D4—23441no—
306D4—23441no—
307D4—23441no—
308D4—23441no—
309D4—5861no—
310D4—5861no—
311D4—5861no—
312D4—5861no—
313D4—11722no—
314D4—11722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—2931no—
319C2×C4—2932no—
320C2×C4—2932no—
321C2×C4—2931no—
322C2×C4—2931no—
323C2×C4—23441no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—11722no—
327C2×C4D4×D29311yescharacteristic
328C2×C4D4×D29311yescharacteristic
329C2×C4C23×D29311yescharacteristic
330C8—21no—
331C8—21no—
332C8—5861no—
333C8—5861no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—2932no—
338C22—23444no—
339C22—5861no—
340C22—5861no—
341C22—11721no—
342C22—11721no—
343C22—11721no—
344C22—11721no—
345C22—11721no—
346C22—11721no—
347C22C2×D4×D29311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—2932no—
354C4—5861no—
355C4—5861no—
356C4—11721no—
357C4—11721no—
358C4#41×D29311yescharacteristic
359C4#41×D29311yescharacteristic
360C2—81no—
361C2—23441no—
362C2—23441no—
363C2—5862no—
364C2#124×D29311yescharacteristic
365C2#3403693111yescharacteristic
366C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#488×C293C2
socleC22×C293C22×D4
prime radical#34036697C2
hypercenter#488D293
hypocenterC293#3136
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #34036759C2semidirect
3. #34036495C2semidirect
4. #34036492C2semidirect
5. #34036490C2semidirect
6. #34036488C2semidirect
7. #34036485C2semidirect
8. #34036476C2semidirect
9. #34036474C2semidirect
10. #34036132C2semidirect
11. #34036129C2semidirect
12. #34036124C2semidirect
13. #102×D293C2semidirect
14. #34036083C2semidirect
15. #488×C293C2semidirect
20. #22627624C22semidirect
22. #22627623C22semidirect
25. #22627615C22semidirect
37. #22627548C22semidirect
38. #22627548C22semidirect
41. #22627546C22semidirect
42. #22627546C22semidirect
47. #22627544C22semidirect
48. #22627544C22semidirect
49. #22627535C22semidirect
50. #22627534C22semidirect
51. C8×Dic293C22semidirect
52. #125×C293C22semidirect
54. #103×C293C22semidirect
55. #103×C293C22semidirect
58. C4×C8×C293C22semidirect
183. C293#3136semidirect
192. #488D293semidirect
211. #125C2×D293semidirect
225. #103C2×D293semidirect
226. #103C2×D293semidirect
242. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367592
#340366972
#340364952
#340364922
#340364902
#340364882
#340364852
#340364762
#340364742
#340361322
#340361292
#340361242
#102×D2932
#340360832
#488×C2932
#3136293