Finite Group Databasebeta

← #49170616

Subgroups — #49170616

Order 37504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036814C211yesmaximal, characteristic, complemented
2#34036773C211yesmaximal, characteristic
3#34036482C211yesmaximal, characteristic, complemented
4#34036459C211yesmaximal, characteristic, complemented
5#34036451C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036370C211yesmaximal, characteristic, complemented
8#34036357C211yesmaximal, characteristic, complemented
9#34036350C211yesmaximal, characteristic, complemented
10#34036292C211yesmaximal, characteristic, complemented
11#34036280C211yesmaximal, characteristic, complemented
12#34036220C211yesmaximal, characteristic, complemented
13C8×C22⋊D293C211yesmaximal, characteristic, complemented
14#34036122C211yesmaximal, characteristic, complemented
15C2×#102×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×Dic1172C2211yescharacteristic, complemented
18C2×#17989790C2211yescharacteristic
19C2×#17989790C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic, complemented
21#22627619—21no—
22#22627615C2211yescharacteristic, complemented
23#22627614—21no—
24#22627611C2211yescharacteristic
25#22627607—21no—
26#22627605—21no—
27#22627604C2211yescharacteristic, complemented
28#22627603C2211yescharacteristic
29#22627603C2211yescharacteristic
30#22627596—21no—
31#22627595C2211yescharacteristic
32#22627593—21no—
33#22627589C2211yescharacteristic, complemented
34D4×Dic293C2211yescharacteristic
35C4×C22⋊D293C2211yescharacteristic
36#22627583—21no—
37#22627582C2211yescharacteristic, complemented
38C2×C22⋊Dic293—21no—
39#22627558C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627555C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627549C2211yescharacteristic, complemented
45#22627547C2211yescharacteristic, complemented
46#22627547C2211yescharacteristic, complemented
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C22×D4×C293C2211yescharacteristic
53C22×C8×C293C2211yescharacteristic
54C2×C4⋊C4×C293C2211yescharacteristic
55#102×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58#102×C293C2211yescharacteristic
59#17989801—22no—
60#17989801—41no—
61C2×Dic586C2311yescharacteristic
62C2×Dic586C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293D411yescharacteristic
66C22×Dic293—21no—
67C22×Dic293—21no—
68C2×C4×D293C2311yescharacteristic
69Dic1172—41no—
70#17989790—22no—
71#17989790—41no—
72C2×#14556873C2311yescharacteristic
73C2×#14556873C2311yescharacteristic
74C8×D293—41no—
75C4⋊Dic293—21no—
76C4⋊Dic293—21no—
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80#17989781—21no—
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293—21no—
87C22⋊Dic293—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90C22⋊Dic293D411yescharacteristic
91#17989779—21no—
92#17989779—21no—
93#17989779D411yescharacteristic
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293C2311yescharacteristic
97C24×C293—21no—
98C2×D4×C293—22no—
99C2×D4×C293—21no—
100C2×D4×C293—41no—
101C2×D4×C293C2311yescharacteristic
102C2×D4×C293C2311yescharacteristic
103C22×C4×C293—21no—
104C22×C4×C293C2311yescharacteristic
105C2×C8×C293—41no—
106C2×C8×C293C2311yescharacteristic
107C2×C8×C293C2311yescharacteristic
108C4⋊C4×C293—21no—
109C4⋊C4×C293C2311yescharacteristic
110C4⋊C4×C293C2311yescharacteristic
111C22×D293C2×D411yescharacteristic
112Dic586—21no—
113Dic586—21no—
114Dic586—21no—
115Dic586—21no—
116C22⋊D293—22no—
117C22⋊D293—42no—
118C22⋊D293—81no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—42no—
124C2×Dic293—81no—
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—21no—
129C4×D293—21no—
130#14556873—21no—
131#14556873—21no—
132C23×C293—21no—
133C23×C293—21no—
134C23×C293—42no—
135C23×C293—42no—
136C23×C293—81no—
137C23×C293C2×D411yescharacteristic
138D4×C293—21no—
139D4×C293—21no—
140D4×C293—21no—
141D4×C293—42no—
142D4×C293#4112yes—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293—42no—
148C2×C4×C293C2×D411yescharacteristic
149C2×C4×C293C2411yescharacteristic
150C8×C293—21no—
151C8×C293—21no—
152C22×C293—21no—
153C22×C293—21no—
154C22×C293—22no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293—41no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—84no—
161C22×C293#13512yes—
162C22×C293C22×D411yescharacteristic
163C2×D293—21no—
164C2×D293—21no—
165C2×D293—21no—
166C4×C293—21no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293C2×#4111yescharacteristic
170C4×C293H(5,𝔽2)11yescharacteristic
171Dic293—21no—
172Dic293—21no—
173Dic293—21no—
174Dic293—41no—
175Dic293—41no—
176Dic293—41no—
177Dic293—41no—
178C2×C293—22no—
179C2×C293—42no—
180C2×C293—81no—
181C2×C293#54611yescharacteristic
182C2×C293C2×#13511yescharacteristic
183C2×C293#57711yescharacteristic
184D293—41no—
185C293#329611yescharacteristic, complemented, Sylow
186#3296—2931nomaximal, Sylow
187#552—2931no—
188#546—2931no—
189#488—2931no—
190#483—2931no—
191#482—2931no—
192#478—2931no—
193#467—2931no—
194#465—2931no—
195#464—2931no—
196#452—2931no—
197#450—2931no—
198C4×SD16—2931no—
199C8×D4—2931no—
200#416—2931no—
201C2×#102D29311yescharacteristic, complemented
202C2×#41—2931no—
203C22×D4C2×D29311yescharacteristic
204C2×Q16—2931no—
205C2×SD16—2931no—
206C2×SD16—2931no—
207C22×C8—2931no—
208C22×C8C2×D29311yescharacteristic
209#126—5861no—
210#125—2931no—
211#125—5861no—
212#124—2931no—
213#123—5861no—
214#123—5861no—
215C22⋊Q8—2931no—
216C22⋊Q8—2931no—
217C22⋊Q8—2931no—
218#121—2931no—
219#121—5861no—
220#120—5861no—
221C4×Q8—2931no—
222C4×D4—2931no—
223C4×D4—2931no—
224#117—2931no—
225#117—5861no—
226C2×C4⋊C4C2×D29311yescharacteristic
227C2×C22⋊C4—5861no—
228#107—2931no—
229#106—2931no—
230#106—2931no—
231C4⋊C8—2931no—
232#103—2931no—
233#103—2931no—
234#103—2931no—
235#103—2931no—
236#102—2931no—
237#102—2931no—
238#102C2×D29311yescharacteristic
239#102C2×D29311yescharacteristic
240#102C2×D29311yescharacteristic
241#102C2×D29311yescharacteristic
242C22⋊C8—2931no—
243C22⋊C8—2931no—
244C4×C8—2931no—
245C24—21no—
246#41—5862no—
247#41—11721no—
248C2×Q8—2931no—
249C2×Q8—2931no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—2931no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4C22×D29311yescharacteristic
257C2×D4C22×D29311yescharacteristic
258C22×C4—21no—
259C22×C4—2931no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4C22×D29311yescharacteristic
263Q16—11721no—
264SD16—5862no—
265SD16—11721no—
266C2×C8—41no—
267C2×C8—2931no—
268C2×C8—2931no—
269C2×C8—11721no—
270C2×C8C22×D29311yescharacteristic
271C2×C8C22×D29311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2931no—
274C4⋊C4—2931no—
275C4⋊C4—2931no—
276C4⋊C4—5861no—
277C4⋊C4—5861no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4C22×D29311yescharacteristic
283C4⋊C4C22×D29311yescharacteristic
284C22⋊C4—2931no—
285C22⋊C4—2931no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C22⋊C4—5861no—
294C42—2931no—
295C42—5861no—
296C42—5861no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—2931no—
303C23D4×D29311yescharacteristic
304Q8—5861no—
305Q8—5861no—
306Q8—5861no—
307Q8—5861no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—23441no—
313D4—5862no—
314D4—11722no—
315D4#1798980212yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—2931no—
322C2×C4—2931no—
323C2×C4—2931no—
324C2×C4—23441no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—5861no—
329C2×C4—5861no—
330C2×C4—5861no—
331C2×C4—11722no—
332C2×C4D4×D29311yescharacteristic
333C2×C4C23×D29311yescharacteristic
334C8—21no—
335C8—21no—
336C8—5861no—
337C8—5861no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—5861no—
348C22—5861no—
349C22—5861no—
350C22#2262764312yes—
351C22C2×D4×D29311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—5861no—
356C4—5861no—
357C4—5861no—
358C4—11721no—
359C4—11721no—
360C4—11721no—
361C4—11721no—
362C4C2×#1798980211yescharacteristic
363C4#2262766911yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—11721no—
368C2#3403676911yescharacteristic
369C2C2×#2262764311yescharacteristic
370C2#3403693511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#102×C293C2
socleC22×C293C22×D4
prime radical#34036773C2
hypercenterC2×#102D293
hypocenterC293#3296
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #34036814C2semidirect
3. #34036482C2semidirect
4. #34036459C2semidirect
5. #34036451C2semidirect
6. #34036427C2semidirect
7. #34036370C2semidirect
8. #34036357C2semidirect
9. #34036350C2semidirect
10. #34036292C2semidirect
11. #34036280C2semidirect
12. #34036220C2semidirect
13. C8×C22⋊D293C2semidirect
14. #34036122C2semidirect
15. C2×#102×C293C2semidirect
17. C2×Dic1172C22semidirect
20. C2×C8×D293C22semidirect
22. #22627615C22semidirect
27. #22627604C22semidirect
33. #22627589C22semidirect
37. #22627582C22semidirect
39. #22627558C22semidirect
40. #22627555C22semidirect
41. #22627555C22semidirect
42. #22627553C22semidirect
43. #22627549C22semidirect
44. #22627549C22semidirect
45. #22627547C22semidirect
46. #22627547C22semidirect
50. #22627536C22semidirect
51. C8×Dic293C22semidirect
185. C293#3296semidirect
201. C2×#102D293semidirect

Maximal subgroups

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

subgroupindex
#340368142
#340367732
#340364822
#340364592
#340364512
#340364272
#340363702
#340363572
#340363502
#340362922
#340362802
#340362202
C8×C22⋊D2932
#340361222
C2×#102×C2932
#3296293