Finite Group Databasebeta

← #49170739

Subgroups — #49170739

Order 37504.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036779C211yesmaximal, characteristic, complemented
2#34036767C211yesmaximal, characteristic, complemented
3#34036490C211yesmaximal, characteristic, complemented
4#34036458C211yesmaximal, characteristic, complemented
5#34036448C211yesmaximal, characteristic, complemented
6#34036417C211yesmaximal, characteristic, complemented
7#34036380C211yesmaximal, characteristic, complemented
8#34036355C211yesmaximal, characteristic, complemented
9#34036346C211yesmaximal, characteristic, complemented
10#34036261C211yesmaximal, characteristic, complemented
11#34036241C211yesmaximal, characteristic, complemented
12#34036203C211yesmaximal, characteristic, complemented
13#34036130C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15#449×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C2×D4×D293C2211yescharacteristic
18C2×#17989787C2211yescharacteristic
19C2×#17989786C2211yescharacteristic, complemented
20C2×C8×D293C2211yescharacteristic
21#22627623C2211yescharacteristic, complemented
22#22627613C2211yescharacteristic
23#22627607—21no—
24#22627606—21no—
25#22627605—21no—
26#22627601—21no—
27#22627600C2211yescharacteristic
28#22627598C2211yescharacteristic
29#22627596—21no—
30#22627595C2211yescharacteristic
31#22627592—21no—
32D4×Dic293C2211yescharacteristic
33D4×Dic293C2211yescharacteristic, complemented
34C4×C22⋊D293C2211yescharacteristic
35C2×C4⋊Dic293C2211yescharacteristic, complemented
36C4⋊C4×D293C2211yescharacteristic
37C2×#17989779—21no—
38#22627556C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627548C2211yescharacteristic, complemented
43#22627548C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic, complemented
49#22627544C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627534C2211yescharacteristic, complemented
52C2×#41×C293C2211yescharacteristic
53C2×SD16×C293C2211yescharacteristic, complemented
54C2×D8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic, complemented
56#103×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60#17989801—44no—
61C2×Dic586—21no—
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293D411yescharacteristic
67D4×D293—22no—
68D4×D293—41no—
69C22×Dic293—21no—
70C22×Dic293—21no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73C2×C4×D293C2311yescharacteristic
74#17989787—41no—
75#17989786—41no—
76C2×#14556873C2311yescharacteristic
77C2×#14556873C2311yescharacteristic
78C8×D293—41no—
79C4⋊Dic293—21no—
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781D411yescharacteristic
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293D411yescharacteristic
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95#17989779D411yescharacteristic
96C4×Dic293C2311yescharacteristic
97#41×C293—22no—
98#41×C293—41no—
99C2×Q8×C293C2311yescharacteristic
100C2×D4×C293—21no—
101C2×D4×C293—21no—
102C2×D4×C293C2311yescharacteristic
103C2×D4×C293C2311yescharacteristic
104C22×C4×C293—21no—
105C22×C4×C293C2311yescharacteristic
106SD16×C293—41no—
107D8×C293—22no—
108C2×C8×C293C2311yescharacteristic
109C2×C8×C293C2311yescharacteristic
110C4⋊C4×C293C2311yescharacteristic
111C22⋊C4×C293—21no—
112C22×D293—21no—
113C22×D293—42no—
114C22×D293—42no—
115C22×D293—81no—
116C22×D293C2×D411yescharacteristic
117Dic586—42no—
118D1172—21no—
119D1172—21no—
120C22⋊D293—22no—
121C22⋊D293—42no—
122C22⋊D293—42no—
123C22⋊D293—81no—
124C2×Dic293—21no—
125C2×Dic293—21no—
126C2×Dic293—21no—
127C2×Dic293—42no—
128C2×Dic293—42no—
129C2×Dic293—81no—
130C2×Dic293C2×D411yescharacteristic
131C2×Dic293C2×D411yescharacteristic
132C2×Dic293C2×D411yescharacteristic
133C4×D293—21no—
134C4×D293—21no—
135C4×D293—42no—
136#14556873—21no—
137#14556873—21no—
138C23×C293—21no—
139C23×C293—21no—
140C23×C293C2×D411yescharacteristic
141Q8×C293—21no—
142Q8×C293—21no—
143D4×C293—21no—
144D4×C293—21no—
145D4×C293—21no—
146D4×C293—42no—
147D4×C293—42no—
148D4×C293#4112yescomplemented
149C2×C4×C293—21no—
150C2×C4×C293—21no—
151C2×C4×C293—21no—
152C2×C4×C293—21no—
153C2×C4×C293—42no—
154C2×C4×C293C2×D411yescharacteristic
155C2×C4×C293C2411yescharacteristic
156C8×C293—21no—
157C8×C293—21no—
158C22×C293—21no—
159C22×C293—22no—
160C22×C293—21no—
161C22×C293—21no—
162C22×C293—41no—
163C22×C293—41no—
164C22×C293—41no—
165C22×C293—41no—
166C22×C293—41no—
167C22×C293C22×D411yescharacteristic
168C2×D293—21no—
169C2×D293—21no—
170C2×D293—41no—
171C2×D293—41no—
172C2×D293—41no—
173C2×D293—84no—
174C2×D293AGL(1,ℤ/8)12yes—
175C4×C293—21no—
176C4×C293—41no—
177C4×C293—41no—
178C4×C293C2×#4111yescharacteristic
179C4×C293H(5,𝔽2)11yescharacteristic
180Dic293—21no—
181Dic293—21no—
182Dic293—21no—
183Dic293—41no—
184Dic293—41no—
185Dic293—41no—
186C2×C293—42no—
187C2×C293—41no—
188C2×C293—81no—
189C2×C293#54611yescharacteristic
190C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C293#57711yescharacteristic
192D293—22no—
193D293—81no—
194C293#330611yescharacteristic, complemented, Sylow
195#3306—2931nomaximal, Sylow
196#547—2931no—
197#546—2931no—
198#489—2931no—
199#483—2931no—
200#481—2931no—
201#476—2931no—
202#469—2931no—
203#465—2931no—
204#463—2931no—
205#449D29311yescharacteristic, complemented
206#447—2931no—
207#442—2931no—
208#435—2931no—
209#417—2931no—
210C2×#102—2931no—
211C2×#41—5861no—
212C2×#41C2×D29311yescharacteristic
213C22×D4—2931no—
214C2×SD16C2×D29311yescharacteristic, complemented
215C2×D8—2931no—
216C2×D8C2×D29311yescharacteristic
217C2×M16—2931no—
218C22×C8—2931no—
219C4⋊Q8—2931no—
220#124—2931no—
221#123—5861no—
222#123—5861no—
223#123—5861no—
224C22⋊Q8—2931no—
225C22⋊Q8—5861no—
226#121—2931no—
227#121—2931no—
228#121—5861no—
229#121C2×D29311yescharacteristic, complemented
230#120—5861no—
231C4×D4—2931no—
232C4×D4—2931no—
233C4×D4—2931no—
234C2×C4⋊C4—2931no—
235C2×C4⋊C4—2931no—
236C2×C22⋊C4—5861no—
237#106—2931no—
238#106—2931no—
239#106—2931no—
240C4⋊C8—2931no—
241#103—2931no—
242#103—2931no—
243#103C2×D29311yescharacteristic, complemented
244#102—2931no—
245#102—2931no—
246#102—2931no—
247#102—2931no—
248#102—2931no—
249#102—2931no—
250#102C2×D29311yescharacteristic
251C22⋊C8—2931no—
252C22⋊C8C2×D29311yescharacteristic, complemented
253#97—2931no—
254C24—5861no—
255#41—22no—
256#41—41no—
257#41—11724no—
258C2×Q8—5861no—
259C2×Q8C22×D29311yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—2931no—
263C2×D4—2931no—
264C2×D4—5861no—
265C2×D4—5861no—
266C2×D4—5862no—
267C2×D4—5861no—
268C2×D4—11721no—
269C2×D4C22×D29311yescharacteristic
270C2×D4C22×D29311yescharacteristic
271C22×C4—21no—
272C22×C4—2931no—
273C22×C4—5861no—
274C22×C4—5861no—
275C22×C4—5861no—
276C22×C4—5861no—
277C22×C4C22×D29311yescharacteristic
278SD16—41no—
279D8—22no—
280D8—11721no—
281M16—11721no—
282C2×C8—2931no—
283C2×C8—2931no—
284C2×C8—11721no—
285C2×C8C22×D29311yescharacteristic
286C2×C8C22×D29311yescharacteristic
287C4⋊C4—2931no—
288C4⋊C4—2931no—
289C4⋊C4—2931no—
290C4⋊C4—2931no—
291C4⋊C4—5861no—
292C4⋊C4—5861no—
293C4⋊C4—5861no—
294C4⋊C4—5861no—
295C4⋊C4C22×D29311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—2931no—
298C22⋊C4—2931no—
299C22⋊C4—5861no—
300C22⋊C4—5861no—
301C22⋊C4—5861no—
302C22⋊C4—5861no—
303C22⋊C4—5861no—
304C22⋊C4—5861no—
305C22⋊C4—5861no—
306C42—2931no—
307C23—21no—
308C23—21no—
309C23—2931no—
310C23—23441no—
311C23—5861no—
312C23—11722no—
313C23—11722no—
314C23D4×D29311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—11722no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—23441no—
324D4—5862no—
325D4—5861no—
326D4—5861no—
327D4—11722no—
328D4—11722no—
329D4#1798980112yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—2931no—
336C2×C4—2931no—
337C2×C4—2931no—
338C2×C4—23441no—
339C2×C4—5861no—
340C2×C4—5861no—
341C2×C4—5861no—
342C2×C4—5861no—
343C2×C4—5861no—
344C2×C4—11722no—
345C2×C4—11722no—
346C2×C4—11722no—
347C2×C4D4×D29311yescharacteristic
348C2×C4C23×D29311yescharacteristic
349C8—21no—
350C8—21no—
351C8—5861no—
352C8—5861no—
353C22—21no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—2932no—
363C22—23444no—
364C22—5861no—
365C22—5861no—
366C22—11721no—
367C22—11721no—
368C22—11721no—
369C22C2×D4×D29311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—5861no—
374C4—5861no—
375C4—5861no—
376C4—11721no—
377C4—11721no—
378C4—11721no—
379C4C2×#1798980111yescharacteristic
380C4#2262766911yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—23441no—
385C2—5862no—
386C2#3403676611yescharacteristic
387C2AGL(1,ℤ/8)×D29311yescharacteristic
388C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#449×C293C2
socleC22×C293C22×D4
hypercenter#449D293
hypocenterC293#3306
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #34036779C2semidirect
2. #34036767C2semidirect
3. #34036490C2semidirect
4. #34036458C2semidirect
5. #34036448C2semidirect
6. #34036417C2semidirect
7. #34036380C2semidirect
8. #34036355C2semidirect
9. #34036346C2semidirect
10. #34036261C2semidirect
11. #34036241C2semidirect
12. #34036203C2semidirect
13. #34036130C2semidirect
14. #102×D293C2semidirect
15. #449×C293C2semidirect
19. C2×#17989786C22semidirect
21. #22627623C22semidirect
33. D4×Dic293C22semidirect
35. C2×C4⋊Dic293C22semidirect
38. #22627556C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627548C22semidirect
43. #22627548C22semidirect
48. #22627545C22semidirect
51. #22627534C22semidirect
53. C2×SD16×C293C22semidirect
55. #121×C293C22semidirect
56. #103×C293C22semidirect
58. C22⋊C8×C293C22semidirect
148. D4×C293#41semidirect
194. C293#3306semidirect
205. #449D293semidirect
214. C2×SD16C2×D293semidirect
229. #121C2×D293semidirect
243. #103C2×D293semidirect
252. C22⋊C8C2×D293semidirect
329. D4#17989801semidirect

Maximal subgroups

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

subgroupindex
#340367792
#340367672
#340364902
#340364582
#340364482
#340364172
#340363802
#340363552
#340363462
#340362612
#340362412
#340362032
#340361302
#102×D2932
#449×C2932
#3306293