Finite Group Databasebeta

← #49168922

Subgroups — #49168922

Order 37504.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036658C211yesmaximal, characteristic, complemented
2C4×D4×D293C211yesmaximal, characteristic, complemented
3#34036458C211yesmaximal, characteristic, complemented
4#34036441C211yesmaximal, characteristic, complemented
5#34036430C211yesmaximal, characteristic, complemented
6#34036429C211yesmaximal, characteristic, complemented
7#34036341C211yesmaximal, characteristic, complemented
8#34036278C211yesmaximal, characteristic, complemented
9#34036261C211yesmaximal, characteristic
10#34036241C211yesmaximal, characteristic, complemented
11#34036238C211yesmaximal, characteristic, complemented
12#34036232C211yesmaximal, characteristic, complemented
13#34036230C211yesmaximal, characteristic, complemented
14#34036185C211yesmaximal, characteristic, complemented
15#463×C293C211yesmaximal, characteristic, complemented
16C2×D4×D293C2211yescharacteristic
17C22×C4×D293—21no—
18C2×#17989789C2211yescharacteristic
19C2×#17989787C2211yescharacteristic
20#22627617—21no—
21#22627616C2211yescharacteristic, complemented
22#22627606—21no—
23#22627600C2211yescharacteristic
24#22627595C2211yescharacteristic
25Q8×Dic293C2211yescharacteristic, complemented
26C4×D1172C2211yescharacteristic
27D4×Dic293C2211yescharacteristic
28D4×Dic293C2211yescharacteristic, complemented
29#22627586C2211yescharacteristic
30C4×C22⋊D293—21no—
31#22627584—21no—
32#22627584—21no—
33#22627580—21no—
34C4⋊C4×D293C2211yescharacteristic
35C22⋊C4×D293—21no—
36C42×D293C2211yescharacteristic
37#22627558C2211yescharacteristic, complemented
38#22627557C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41C4⋊#14556873C2211yescharacteristic, complemented
42#22627548C2211yescharacteristic, complemented
43#22627546C2211yescharacteristic
44#22627546C2211yescharacteristic
45#22627545C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic, complemented
48#22627536C2211yescharacteristic
49#22627536C2211yescharacteristic
50#22627534C2211yescharacteristic, complemented
51#22627534C2211yescharacteristic, complemented
52C2×SD16×C293C2211yescharacteristic
53C2×D8×C293C2211yescharacteristic
54#124×C293C2211yescharacteristic, complemented
55C4×D4×C293C2211yescharacteristic
56C4⋊C8×C293C2211yescharacteristic, complemented
57#103×C293C2211yescharacteristic, complemented
58#102×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C2×D1172C2311yescharacteristic
61C2×C22⋊D293—21no—
62C2×C22⋊D293—21no—
63D4×D293—22no—
64D4×D293—22no—
65C22×Dic293—21no—
66C22×Dic293—21no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—44no—
71C2×C4×D293D411yescharacteristic
72C2×C4×D293D411yescharacteristic
73C2×C4×D293C2311yescharacteristic
74#17989789—22no—
75#17989787—22no—
76C2×#14556873C2311yescharacteristic
77C2×#14556873C2311yescharacteristic
78C4⋊Dic293—21no—
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82#17989781—21no—
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—
92C4×Dic293—21no—
93C4×Dic293D411yescharacteristic
94C4×Dic293D411yescharacteristic
95C4×Dic293C2311yescharacteristic
96C2×Q8×C293C2311yescharacteristic
97C2×D4×C293C2311yescharacteristic
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293—21no—
100SD16×C293—22no—
101D8×C293—22no—
102C2×C8×C293C2311yescharacteristic
103C2×C8×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C22⋊C4×C293—21no—
108C42×C293C2311yescharacteristic
109C22×D293—24no—
110C22×D293—21no—
111C22×D293—42no—
112C22×D293—42no—
113C22×D293C2×D411yescharacteristic
114D1172—21no—
115D1172#4112yes—
116C22⋊D293—24no—
117C22⋊D293—42no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—42no—
122C2×Dic293—42no—
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C4×D293—22no—
127C4×D293—21no—
128C4×D293—21no—
129C4×D293—41no—
130C4×D293—42no—
131C4×D293—42no—
132C4×D293—42no—
133#14556873—21no—
134#14556873—21no—
135C23×C293—21no—
136C23×C293—21no—
137Q8×C293—21no—
138Q8×C293—21no—
139D4×C293—21no—
140D4×C293—21no—
141D4×C293—21no—
142D4×C293#4112yes—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—42no—
146C2×C4×C293C2×D411yescharacteristic
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2411yescharacteristic
149C8×C293—21no—
150C8×C293—21no—
151C22×C293—22no—
152C22×C293—41no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293C22×D411yescharacteristic
158C2×D293—21no—
159C2×D293—21no—
160C2×D293—22no—
161C2×D293—48no—
162C2×D293—41no—
163C2×D293—41no—
164C2×D293AGL(1,ℤ/8)12yes—
165C4×C293—21no—
166C4×C293—21no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293C2×#4111yescharacteristic
170C4×C293C2×#4111yescharacteristic
171Dic293—21no—
172Dic293—21no—
173Dic293—21no—
174Dic293—41no—
175Dic293—41no—
176Dic293—41no—
177C2×C293—42no—
178C2×C293—81no—
179C2×C293#52511yescharacteristic
180C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C293#57511yescharacteristic
182D293—22no—
183D293—42no—
184C293#311411yescharacteristic, complemented, Sylow
185#3114—2931nomaximal, Sylow
186#529—2931no—
187C2×C4×D4—2931no—
188#483—2931no—
189#480—2931no—
190#478—2931no—
191#478—2931no—
192#463—2931no—
193#463D29311yescharacteristic, complemented
194#450—2931no—
195#447—2931no—
196#442—2931no—
197#442—2931no—
198#440—2931no—
199#440—2931no—
200#432—2931no—
201C22×D4—2931no—
202C23×C4—5861no—
203C2×SD16—2931no—
204C2×SD16C2×D29311yescharacteristic
205C2×D8—2931no—
206C2×D8C2×D29311yescharacteristic
207#126—5861no—
208#125—2931no—
209#124C2×D29311yescharacteristic, complemented
210#123—5861no—
211C22⋊Q8—2931no—
212#121—2931no—
213C4×Q8—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—2931no—
217C4×D4—2931no—
218C4×D4—5861no—
219C4×D4—5861no—
220C4×D4—5861no—
221C4×D4C2×D29311yescharacteristic
222#117—5861no—
223C2×C4⋊C4—2931no—
224C2×C22⋊C4—5861no—
225C2×C42—2931no—
226#107—2931no—
227#107—2931no—
228#106—2931no—
229#106—2931no—
230C4⋊C8—2931no—
231C4⋊C8C2×D29311yescharacteristic, complemented
232#103—2931no—
233#103C2×D29311yescharacteristic, complemented
234#102—2931no—
235#102—2931no—
236#102—2931no—
237#102—2931no—
238#102—2931no—
239#102C2×D29311yescharacteristic, complemented
240C22⋊C8—2931no—
241C22⋊C8—2931no—
242#97—2931no—
243#97—2931no—
244C24—5861no—
245C2×Q8C22×D29311yescharacteristic
246C2×D4—2931no—
247C2×D4—5861no—
248C2×D4—5862no—
249C2×D4—5862no—
250C2×D4—5861no—
251C2×D4C22×D29311yescharacteristic
252C2×D4C22×D29311yescharacteristic
253C22×C4—21no—
254C22×C4—2931no—
255C22×C4—2931no—
256C22×C4—2931no—
257C22×C4—5861no—
258C22×C4—5861no—
259C22×C4—5861no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4—11724no—
263SD16—22no—
264SD16—5862no—
265D8—22no—
266D8—5862no—
267C2×C8—2931no—
268C2×C8—2931no—
269C2×C8C22×D29311yescharacteristic
270C2×C8C22×D29311yescharacteristic
271C4⋊C4—2931no—
272C4⋊C4—2931no—
273C4⋊C4—2931no—
274C4⋊C4—5861no—
275C4⋊C4—5861no—
276C4⋊C4—5861no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4C22×D29311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C42—2931no—
290C42—2931no—
291C42—2931no—
292C42—5861no—
293C42C22×D29311yescharacteristic
294C23—21no—
295C23—21no—
296C23—2931no—
297C23—5864no—
298C23—5861no—
299C23—11722no—
300C23—11722no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2932no—
307D4—5864no—
308D4—5861no—
309D4—11722no—
310D4#1798980112yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—2931no—
315C2×C4—2931no—
316C2×C4—2931no—
317C2×C4—5862no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—11721no—
324C2×C4—11722no—
325C2×C4—11722no—
326C2×C4—11722no—
327C2×C4—11722no—
328C2×C4—11722no—
329C2×C4D4×D29311yescharacteristic
330C2×C4D4×D29311yescharacteristic
331C2×C4C23×D29311yescharacteristic
332C8—21no—
333C8—21no—
334C8—5861no—
335C8—5861no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—2932no—
343C22—5861no—
344C22—5861no—
345C22—5862no—
346C22—11728no—
347C22—11721no—
348C22—11721no—
349C22C2×D4×D29311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—5861no—
355C4—5861no—
356C4—5861no—
357C4—11721no—
358C4—11721no—
359C4—11721no—
360C4#41×D29311yescharacteristic
361C4C2×#1798980111yescharacteristic
362C2—42no—
363C2—81no—
364C2—5862no—
365C2—11722no—
366C2#3403663911yescharacteristic
367C2AGL(1,ℤ/8)×D29311yescharacteristic
368C2#3403692611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#463×C293C2
socleC22×C293C22×D4
prime radical#34036261C2
hypercenter#463D293
hypocenterC293#3114
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #34036658C2semidirect
2. C4×D4×D293C2semidirect
3. #34036458C2semidirect
4. #34036441C2semidirect
5. #34036430C2semidirect
6. #34036429C2semidirect
7. #34036341C2semidirect
8. #34036278C2semidirect
10. #34036241C2semidirect
11. #34036238C2semidirect
12. #34036232C2semidirect
13. #34036230C2semidirect
14. #34036185C2semidirect
15. #463×C293C2semidirect
21. #22627616C22semidirect
25. Q8×Dic293C22semidirect
28. D4×Dic293C22semidirect
37. #22627558C22semidirect
38. #22627557C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. C4⋊#14556873C22semidirect
42. #22627548C22semidirect
47. #22627545C22semidirect
50. #22627534C22semidirect
51. #22627534C22semidirect
54. #124×C293C22semidirect
56. C4⋊C8×C293C22semidirect
57. #103×C293C22semidirect
58. #102×C293C22semidirect
184. C293#3114semidirect
193. #463D293semidirect
209. #124C2×D293semidirect
231. C4⋊C8C2×D293semidirect
233. #103C2×D293semidirect
239. #102C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366582
C4×D4×D2932
#340364582
#340364412
#340364302
#340364292
#340363412
#340362782
#340362612
#340362412
#340362382
#340362322
#340362302
#340361852
#463×C2932
#3114293