Finite Group Databasebeta

← #18006457

Subgroups — #18006457

Order 4736.

420 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
1Q8×C22⋊D37C211yesmaximal, characteristic, complemented
2#14558184C211yesmaximal, characteristic
3#14557882C211yesmaximal, characteristic, complemented
4#14557863C211yesmaximal, characteristic, complemented
5#14557862C211yesmaximal, characteristic, complemented
6#14557816C211yesmaximal, characteristic, complemented
7#14557765C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557737C211yesmaximal, characteristic, complemented
10#14557673C211yesmaximal, characteristic, complemented
11#14557672C211yesmaximal, characteristic, complemented
12#14557618C211yesmaximal, characteristic, complemented
13C8×C22⋊D37C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C2×#103×C37C211yesmaximal, characteristic, complemented
16C2×#10596962—21no—
17C2×Q8×D37C2211yescharacteristic
18C2×#10596930C2211yescharacteristic
19C2×#10596941C2211yescharacteristic
20C2×#10596941C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924535C2211yescharacteristic
23#11924534—21no—
24#11924534C2211yescharacteristic
25#11924521—21no—
26#11924519—21no—
27#11924515—21no—
28#11924515C2211yescharacteristic
29#11924514—21no—
30#11924512—21no—
31#11924512C2211yescharacteristic
32#11924511C2211yescharacteristic
33#11924510C2211yescharacteristic
34Q8×Dic37C2211yescharacteristic
35#11924498C2211yescharacteristic
36C4×C22⋊D37—21no—
37C4×C22⋊D37C2211yescharacteristic
38C4⋊C4×D37C2211yescharacteristic
39#11924468C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924458C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C22×Q8×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54C2×C4⋊C4×C37C2211yescharacteristic
55#103×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×Q8×C37—22no—
61C2×Q8×C37—41no—
62C2×Q8×C37C2311yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C22×C4×C37—21no—
65C22×C4×C37—21no—
66C22×C4×C37C2311yescharacteristic
67C2×C22⋊D37—21no—
68C2×C22⋊D37D411yescharacteristic
69Q8×D37—22no—
70Q8×D37—41no—
71#10596962—44no—
72C2×D148—21no—
73C2×D148C2311yescharacteristic
74C2×C4×D37—21no—
75C2×C4×D37—21no—
76C2×C4×D37—21no—
77C2×C4×D37C2311yescharacteristic
78C2×Dic74—21no—
79C2×Dic74—21no—
80C2×Dic74C2311yescharacteristic
81C2×C8×C37—41no—
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C4⋊C4×C37—21no—
85C4⋊C4×C37C2311yescharacteristic
86C4⋊C4×C37C2311yescharacteristic
87C22⋊Dic37—21no—
88C22⋊Dic37D411yescharacteristic
89#10596941—22no—
90#10596941—41no—
91#10596938—21no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938D411yescharacteristic
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103#10596936—21no—
104#10596936—21no—
105#10596936D411yescharacteristic
106C4×Dic37—21no—
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110#10596930—41no—
111C8×D37—41no—
112C23×C37C2×D411yescharacteristic
113C22×D37—21no—
114C22×D37C2×D411yescharacteristic
115Q8×C37—21no—
116Q8×C37—21no—
117Q8×C37—21no—
118Q8×C37—42no—
119Q8×C37#4112yescomplemented
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—42no—
127C2×C4×C37—42no—
128C2×C4×C37C2×D411yescharacteristic
129C2×C4×C37C2411yescharacteristic
130C22⋊D37—42no—
131C22⋊D37SD1614yescomplemented
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37C2×D411yescharacteristic
136C2×Dic37C2×D411yescharacteristic
137C2×Dic37C2×D411yescharacteristic
138D148—21no—
139D148—21no—
140D148—42no—
141C4×D37—21no—
142C4×D37—21no—
143C4×D37—42no—
144C4×D37—42no—
145C4×D37—42no—
146Dic74—21no—
147Dic74—21no—
148Dic74—42no—
149Dic74—42no—
150C8×C37—21no—
151C8×C37—21no—
152#64436—21no—
153#64436—21no—
154C22×C37—21no—
155C22×C37—21no—
156C22×C37C2×SD1612yes—
157C22×C37C22×D411yescharacteristic
158C2×D37—21no—
159C2×D37—21no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C2×D37C2×SD1612yes—
164C4×C37—22no—
165C4×C37—21no—
166C4×C37—41no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37C2×#4111yescharacteristic
170C4×C37H(5,𝔽2)11yescharacteristic
171Dic37—21no—
172Dic37—21no—
173Dic37—41no—
174Dic37—41no—
175Dic37—41no—
176Dic37C2×SD1612yes—
177#3298—371nomaximal, Sylow
178C2×C37—22no—
179C2×C37#54611yescharacteristic
180C2×C37C22×SD1611yescharacteristic
181C2×C37#57811yescharacteristic
182D37—22no—
183D37—81no—
184D4×Q8—371no—
185#547—371no—
186#487—371no—
187#483—371no—
188#483—371no—
189#475—371no—
190#465—371no—
191#465—371no—
192#461—371no—
193#448—371no—
194#448—371no—
195C4×SD16—371no—
196C8×D4—371no—
197C2×#103—371no—
198C2×#103D3711yescharacteristic, complemented
199C37#329811yescharacteristic, complemented, Sylow
200C2×#41—741no—
201C22×Q8—371no—
202C22×Q8C2×D3711yescharacteristic
203C2×SD16—371no—
204C2×SD16—371no—
205C2×SD16—371no—
206C22×C8—371no—
207C22×C8C2×D3711yescharacteristic
208C4⋊Q8—371no—
209C4⋊Q8—371no—
210C4⋊Q8—741no—
211#123—741no—
212#123—741no—
213C22⋊Q8—371no—
214C22⋊Q8—371no—
215C22⋊Q8—741no—
216C22⋊Q8—741no—
217C22⋊Q8—741no—
218#121—371no—
219#121—371no—
220C4×Q8—371no—
221C4×D4—371no—
222C4×D4—371no—
223C4×D4—741no—
224C2×C4⋊C4—371no—
225C2×C4⋊C4C2×D3711yescharacteristic
226#106—371no—
227#106—371no—
228#106—371no—
229C4⋊C8—371no—
230#103—371no—
231#103—371no—
232#103—371no—
233#103—371no—
234#103—371no—
235#103C2×D3711yescharacteristic
236#103C2×D3711yescharacteristic
237#103C2×D3711yescharacteristic
238#103C2×D3711yescharacteristic
239#102—371no—
240C22⋊C8—371no—
241C22⋊C8—371no—
242C4×C8—371no—
243#41—1484no—
244C2×Q8—21no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—371no—
248C2×Q8—741no—
249C2×Q8—741no—
250C2×Q8—742no—
251C2×Q8—1481no—
252C2×Q8C22×D3711yescharacteristic
253C2×Q8C22×D3711yescharacteristic
254C2×D4—371no—
255C2×D4—371no—
256C2×D4—741no—
257C2×D4—741no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—371no—
261C22×C4—741no—
262C22×C4—741no—
263C22×C4—741no—
264C22×C4C22×D3711yescharacteristic
265SD16—742no—
266SD16—1481no—
267SD16—1481no—
268C2×C8—41no—
269C2×C8—371no—
270C2×C8—371no—
271C2×C8—1481no—
272C2×C8C22×D3711yescharacteristic
273C2×C8C22×D3711yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—371no—
276C4⋊C4—371no—
277C4⋊C4—371no—
278C4⋊C4—741no—
279C4⋊C4—741no—
280C4⋊C4—741no—
281C4⋊C4—741no—
282C4⋊C4—741no—
283C4⋊C4—741no—
284C4⋊C4—741no—
285C4⋊C4C22×D3711yescharacteristic
286C4⋊C4C22×D3711yescharacteristic
287C22⋊C4—371no—
288C22⋊C4—371no—
289C22⋊C4—741no—
290C22⋊C4—741no—
291C22⋊C4—741no—
292C22⋊C4—741no—
293C22⋊C4—741no—
294C42—371no—
295C42—741no—
296C23—371no—
297C23—741no—
298C23D4×D3711yescharacteristic
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—42no—
303Q8—741no—
304Q8—741no—
305Q8—1482no—
306Q8—1482no—
307Q8#1059696212yescomplemented
308D4—374no—
309D4—741no—
310D4—741no—
311D4—1482no—
312D4—1482no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—371no—
322C2×C4—371no—
323C2×C4—371no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—1482no—
330C2×C4—1482no—
331C2×C4—1482no—
332C2×C4D4×D3711yescharacteristic
333C2×C4C23×D3711yescharacteristic
334C8—21no—
335C8—21no—
336C8—741no—
337C8—741no—
338C22—21no—
339C22—21no—
340C22—372no—
341C22—741no—
342C22—741no—
343C22—1481no—
344C22—1481no—
345C22—1481no—
346C22SD16×D3712yes—
347C22C2×D4×D3711yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—372no—
354C4—741no—
355C4—741no—
356C4—1481no—
357C4—1481no—
358C4—1481no—
359C4C2×#1059696211yescharacteristic
360C4#1192458111yescharacteristic
361C2—22no—
362C2—2961no—
363C2—742no—
364C2#1455817311yescharacteristic
365C2C2×SD16×D3711yescharacteristic
366C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#103×C37C2
socleC22×C37C22×D4
prime radical#14558184C2
hypercenterC2×#103D37
hypocenterC37#3298
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D37C2semidirect
3. #14557882C2semidirect
4. #14557863C2semidirect
5. #14557862C2semidirect
6. #14557816C2semidirect
7. #14557765C2semidirect
8. #14557762C2semidirect
9. #14557737C2semidirect
10. #14557673C2semidirect
11. #14557672C2semidirect
12. #14557618C2semidirect
13. C8×C22⋊D37C2semidirect
14. #103×D37C2semidirect
15. C2×#103×C37C2semidirect
119. Q8×C37#41semidirect
131. C22⋊D37SD16semidirect
198. C2×#103D37semidirect
199. C37#3298semidirect
307. Q8#10596962semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D372
#145581842
#145578822
#145578632
#145578622
#145578162
#145577652
#145577622
#145577372
#145576732
#145576722
#145576182
C8×C22⋊D372
#103×D372
C2×#103×C372
#329837