Finite Group Databasebeta

← #49168970

Subgroups — #49168970

Order 37504.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036752C211yesmaximal, characteristic, complemented
2#34036604C211yesmaximal, characteristic, complemented
3#34036467C211yesmaximal, characteristic, complemented
4#34036454C211yesmaximal, characteristic, complemented
5#34036417C211yesmaximal, characteristic, complemented
6#34036407C211yesmaximal, characteristic, complemented
7#34036346C211yesmaximal, characteristic, complemented
8#34036346C211yesmaximal, characteristic, complemented
9#34036263C211yesmaximal, characteristic
10#34036238C211yesmaximal, characteristic, complemented
11#34036230C211yesmaximal, characteristic, complemented
12SD16×Dic293C211yesmaximal, characteristic, complemented
13#34036209C211yesmaximal, characteristic, complemented
14#34036187C211yesmaximal, characteristic, complemented
15#450×C293C211yesmaximal, characteristic, complemented
16C2×#17989787C2211yescharacteristic
17C2×#17989787C2211yescharacteristic
18#22627623C2211yescharacteristic, complemented
19#22627619—21no—
20#22627613C2211yescharacteristic, complemented
21#22627610—21no—
22#22627606—21no—
23#22627604—21no—
24#22627598C2211yescharacteristic
25Q8×Dic293C2211yescharacteristic, complemented
26D4×Dic293—21no—
27D4×Dic293—21no—
28D4×Dic293C2211yescharacteristic
29D4×Dic293C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31D4×Dic293C2211yescharacteristic
32#22627586C2211yescharacteristic, complemented
33#22627583C2211yescharacteristic
34#22627583C2211yescharacteristic
35C2×C22⋊Dic293—21no—
36C2×C22⋊Dic293—21no—
37#22627558C2211yescharacteristic, complemented
38#22627557C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627548C2211yescharacteristic, complemented
44#22627548C2211yescharacteristic, complemented
45#22627546C2211yescharacteristic, complemented
46#22627546C2211yescharacteristic, complemented
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C22×D4×C293C2211yescharacteristic
53C2×SD16×C293C2211yescharacteristic
54C2×SD16×C293C2211yescharacteristic
55C22⋊Q8×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C2×Dic586—21no—
60C2×D1172C2311yescharacteristic
61C2×C22⋊D293—21no—
62C22×Dic293—21no—
63C22×Dic293—21no—
64C22×Dic293—21no—
65C22×Dic293—21no—
66C2×C4×D293—21no—
67#17989787—22no—
68#17989787—22no—
69C2×#14556873C2311yescharacteristic
70C2×#14556873C2311yescharacteristic
71C4⋊Dic293—21no—
72C4⋊Dic293D411yescharacteristic
73C4⋊Dic293D411yescharacteristic
74C4⋊Dic293C2311yescharacteristic
75C4⋊Dic293C2311yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77#17989781—21no—
78C22⋊Dic293—21no—
79C22⋊Dic293—21no—
80C22⋊Dic293—21no—
81C22⋊Dic293—21no—
82C22⋊Dic293—21no—
83C22⋊Dic293D411yescharacteristic
84C22⋊Dic293D411yescharacteristic
85#17989779—21no—
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89C4×Dic293—21no—
90C4×Dic293—21no—
91C4×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93C24×C293—21no—
94C2×Q8×C293C2311yescharacteristic
95C2×D4×C293—22no—
96C2×D4×C293—22no—
97C2×D4×C293—21no—
98C2×D4×C293C2311yescharacteristic
99C2×D4×C293C2311yescharacteristic
100C22×C4×C293C2311yescharacteristic
101SD16×C293—22no—
102SD16×C293—22no—
103C2×C8×C293C2311yescharacteristic
104C2×C8×C293C2311yescharacteristic
105C4⋊C4×C293—21no—
106C4⋊C4×C293C2311yescharacteristic
107C22⋊C4×C293—21no—
108C22×D293—21no—
109Dic586—81no—
110D1172—21no—
111D1172—21no—
112C22⋊D293—81no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—81no—
117C2×Dic293—81no—
118C2×Dic293—81no—
119C2×Dic293—81no—
120C2×Dic293C2×D411yescharacteristic
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C4×D293—81no—
125#14556873—21no—
126#14556873—21no—
127C23×C293—24no—
128C23×C293—21no—
129C23×C293—21no—
130C23×C293—81no—
131C23×C293—81no—
132C23×C293C2×D411yescharacteristic
133Q8×C293—21no—
134Q8×C293—21no—
135D4×C293—24no—
136D4×C293—21no—
137D4×C293—21no—
138D4×C293#4112yes—
139D4×C293#4112yes—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293—21no—
148C22×C293—21no—
149C22×C293—22no—
150C22×C293—22no—
151C22×C293—21no—
152C22×C293—21no—
153C22×C293—41no—
154C22×C293—41no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293—84no—
158C22×C293C22×D411yescharacteristic
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—41no—
162C4×C293—21no—
163C4×C293—41no—
164C4×C293—41no—
165C4×C293C2×#4111yescharacteristic
166C4×C293C2×#4111yescharacteristic
167Dic293—21no—
168Dic293—21no—
169Dic293—21no—
170Dic293—21no—
171Dic293—41no—
172Dic293—41no—
173Dic293—41no—
174C2×C293—41no—
175C2×C293—42no—
176C2×C293—42no—
177C2×C293#52511yescharacteristic
178C2×C293#57611yescharacteristic
179C2×C293#57711yescharacteristic
180D293—81no—
181C293#311811yescharacteristic, complemented, Sylow
182#3118—2931nomaximal, Sylow
183#542—2931no—
184#518—2931no—
185#485—2931no—
186#482—2931no—
187#476—2931no—
188#474—2931no—
189#463—2931no—
190#463—2931no—
191#450D29311yescharacteristic, complemented
192#447—2931no—
193#442—2931no—
194#440—2931no—
195C4×SD16—2931no—
196C4×D8—2931no—
197#433—2931no—
198C22×D4C2×D29311yescharacteristic
199C2×SD16C2×D29311yescharacteristic
200C2×SD16C2×D29311yescharacteristic
201C2×D8—2931no—
202C2×D8—2931no—
203C4⋊Q8—2931no—
204#126—5861no—
205#124—2931no—
206#124—5861no—
207#123—5861no—
208C22⋊Q8—5861no—
209C22⋊Q8C2×D29311yescharacteristic
210#121—2931no—
211C4×Q8—2931no—
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—2931no—
217C4×D4—5861no—
218C4×D4—5861no—
219#117—2931no—
220#117—2931no—
221C2×C22⋊C4—5861no—
222C2×C22⋊C4—5861no—
223#107—2931no—
224#107—2931no—
225#106—2931no—
226#106—2931no—
227C4⋊C8—2931no—
228C4⋊C8—2931no—
229#103—2931no—
230#103—2931no—
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102C2×D29311yescharacteristic
236#102C2×D29311yescharacteristic
237C22⋊C8—2931no—
238C22⋊C8C2×D29311yescharacteristic
239#97—2931no—
240C4×C8—2931no—
241C24—21no—
242C2×Q8—5861no—
243C2×Q8C22×D29311yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—2931no—
248C2×D4—5861no—
249C2×D4C22×D29311yescharacteristic
250C2×D4C22×D29311yescharacteristic
251C22×C4—5861no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4C22×D29311yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—5862no—
260D8—5862no—
261C2×C8—2931no—
262C2×C8—2931no—
263C2×C8C22×D29311yescharacteristic
264C2×C8C22×D29311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—2931no—
270C4⋊C4—2931no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4C22×D29311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—2931no—
276C22⋊C4—2931no—
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—2931no—
287C42—2931no—
288C42—5861no—
289C42—5861no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—5861no—
296C23D4×D29311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—23441no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—23441no—
304D4—5861no—
305D4—5861no—
306D4#1798980112yes—
307D4#1798980112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—2931no—
313C2×C4—2931no—
314C2×C4—2931no—
315C2×C4—2931no—
316C2×C4—23441no—
317C2×C4—23441no—
318C2×C4—23441no—
319C2×C4—23441no—
320C2×C4—23441no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4D4×D29311yescharacteristic
325C2×C4C23×D29311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5861no—
329C8—5861no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—11721no—
341C22—11721no—
342C22—11721no—
343C22C2×D4×D29311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—5861no—
348C4—5861no—
349C4—5861no—
350C4—5861no—
351C4—11721no—
352C4—11721no—
353C4—11721no—
354C4C2×#1798980111yescharacteristic
355C4C2×#1798980111yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—23441no—
360C2#3403663511yescharacteristic
361C2#3403693311yescharacteristic
362C2#3403693511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#450×C293C2
socleC22×C293C22×D4
prime radical#34036263C2
hypercenter#450D293
hypocenterC293#3118
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #34036752C2semidirect
2. #34036604C2semidirect
3. #34036467C2semidirect
4. #34036454C2semidirect
5. #34036417C2semidirect
6. #34036407C2semidirect
7. #34036346C2semidirect
8. #34036346C2semidirect
10. #34036238C2semidirect
11. #34036230C2semidirect
12. SD16×Dic293C2semidirect
13. #34036209C2semidirect
14. #34036187C2semidirect
15. #450×C293C2semidirect
18. #22627623C22semidirect
20. #22627613C22semidirect
25. Q8×Dic293C22semidirect
32. #22627586C22semidirect
37. #22627558C22semidirect
38. #22627557C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627553C22semidirect
43. #22627548C22semidirect
44. #22627548C22semidirect
45. #22627546C22semidirect
46. #22627546C22semidirect
50. #22627534C22semidirect
51. C8×Dic293C22semidirect
181. C293#3118semidirect
191. #450D293semidirect

Maximal subgroups

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

subgroupindex
#340367522
#340366042
#340364672
#340364542
#340364172
#340364072
#340363462
#340362632
#340362382
#340362302
SD16×Dic2932
#340362092
#340361872
#450×C2932
#3118293