Finite Group Databasebeta

← #18006103

Subgroups — #18006103

Order 4736.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924568C211yesmaximal, characteristic, complemented
2C22×#10596930C211yesmaximal, characteristic, complemented
3#14558196C211yesmaximal, characteristic, complemented
4#14558174C211yesmaximal, characteristic
5#14557926C211yesmaximal, characteristic, complemented
6#14557780C211yesmaximal, characteristic, complemented
7#14557758C211yesmaximal, characteristic, complemented
8#14557737C211yesmaximal, characteristic, complemented
9#14557698C211yesmaximal, characteristic, complemented
10#14557688C211yesmaximal, characteristic, complemented
11#14557683C211yesmaximal, characteristic, complemented
12#14557673C211yesmaximal, characteristic, complemented
13#14557632C211yesmaximal, characteristic, complemented
14#14557604C211yesmaximal, characteristic, complemented
15C37×#467C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C22×Dic74C2211yescharacteristic
18C2×Q8×D37C2211yescharacteristic, complemented
19C22×D148C2211yescharacteristic
20#11924568—24no—
21C2×#10596942C2211yescharacteristic, complemented
22C2×#10596942C2211yescharacteristic, complemented
23C2×#10596930—24no—
24C2×#10596930C2211yescharacteristic
25C2×#10596930C2211yescharacteristic
26C2×#10596930C2211yescharacteristic
27C2×#10596930C2211yescharacteristic
28C2×#10596941C2211yescharacteristic
29C2×#10596941C2211yescharacteristic
30C2×#10596929C2211yescharacteristic, complemented
31#11924535—21no—
32#11924534C2211yescharacteristic, complemented
33#11924525C2211yescharacteristic
34#11924521—21no—
35#11924516C2211yescharacteristic, complemented
36#11924514—21no—
37#11924513—21no—
38#11924511—21no—
39#11924511C2211yescharacteristic
40#11924506—21no—
41#11924501C2211yescharacteristic, complemented
42#11924498C2211yescharacteristic
43C4×C22⋊D37C2211yescharacteristic
44#11924496—21no—
45C22⋊C4×D37—21no—
46#11924465C2211yescharacteristic, complemented
47#11924459C2211yescharacteristic, complemented
48#11924459C2211yescharacteristic, complemented
49#11924456C2211yescharacteristic
50#11924456C2211yescharacteristic
51C22⋊#64436C2211yescharacteristic
52#11924448C2211yescharacteristic, complemented
53#11924446C2211yescharacteristic, complemented
54C2×Q16×C37C2211yescharacteristic, complemented
55C22×C8×C37C2211yescharacteristic
56C22⋊Q8×C37C2211yescharacteristic
57C22⋊Q8×C37C2211yescharacteristic
58#107×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60#103×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×Q8×C37C2311yescharacteristic
63C2×Q8×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37D411yescharacteristic
66C22×Dic37—21no—
67#10596966—22no—
68#10596966—41no—
69Q8×D37—22no—
70Q8×D37—41no—
71C2×D148—22no—
72C2×D148—21no—
73C2×D148—21no—
74C2×D148—21no—
75C2×D148—41no—
76C2×D148C2311yescharacteristic
77C2×D148C2311yescharacteristic
78C2×C4×D37—21no—
79C2×C4×D37—21no—
80C2×C4×D37—21no—
81C2×C4×D37C2311yescharacteristic
82C2×Dic74—22no—
83C2×Dic74—21no—
84C2×Dic74—21no—
85C2×Dic74—41no—
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88Q16×C37—22no—
89C2×C8×C37—22no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C4⋊C4×C37—21no—
93C4⋊C4×C37—21no—
94C4⋊C4×C37C2311yescharacteristic
95C4⋊C4×C37C2311yescharacteristic
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊Dic37D411yescharacteristic
99#10596942—22no—
100#10596942—41no—
101#10596941—22no—
102#10596941—41no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938—21no—
107#10596938—21no—
108#10596938D411yescharacteristic
109C4⋊Dic37—21no—
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113#10596936D411yescharacteristic
114C4×Dic37—21no—
115C4×Dic37C2311yescharacteristic
116C2×#64436C2311yescharacteristic
117C2×#64436C2311yescharacteristic
118#10596930—22no—
119#10596930—22no—
120#10596930—22no—
121#10596930D414yescomplemented
122#10596929—22no—
123C23×C37C2×D411yescharacteristic
124C22×D37—21no—
125C22×D37—21no—
126C22×D37—42no—
127C22×D37—42no—
128C22×D37—81no—
129C22×D37C2×D411yescharacteristic
130Q8×C37—21no—
131Q8×C37—21no—
132Q8×C37—21no—
133Q8×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37C2×D411yescharacteristic
141C2×C4×C37C2411yescharacteristic
142C22⋊D37—22no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—42no—
146C2×Dic37C2×D411yescharacteristic
147C2×Dic37C2×D411yescharacteristic
148C2×Dic37C2×D411yescharacteristic
149D148—21no—
150D148—21no—
151D148—21no—
152D148—42no—
153D148—42no—
154D148—81no—
155D148C2×D412yes—
156C4×D37—21no—
157C4×D37—21no—
158C4×D37—42no—
159C4×D37—42no—
160C4×D37—81no—
161Dic74—21no—
162Dic74—21no—
163Dic74—21no—
164Dic74—42no—
165Dic74—42no—
166Dic74C2×D412yes—
167C8×C37—21no—
168C8×C37C2×D412yes—
169#64436—21no—
170#64436—21no—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37#13712yescomplemented
174C22×C37C22×D411yescharacteristic
175C2×D37—21no—
176C2×D37—22no—
177C2×D37—21no—
178C2×D37—21no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—41no—
184C2×D37—84no—
185C4×C37—21no—
186C4×C37—41no—
187C4×C37—41no—
188C4×C37—41no—
189C4×C37—41no—
190C4×C37C22×D411yescharacteristic
191C4×C37H(5,𝔽2)11yescharacteristic
192Dic37—22no—
193Dic37—21no—
194Dic37—21no—
195Dic37—21no—
196Dic37—41no—
197#3266—371nomaximal, Sylow
198C2×C37—22no—
199C2×C37D4211yescharacteristic
200C2×C37C2×#13711yescharacteristic
201C2×C37#57711yescharacteristic
202D37—41no—
203D37—42no—
204D37—81no—
205C2×#137—371no—
206C22×SD16—371no—
207D4×Q8—371no—
208#546—371no—
209#497—371no—
210#468—371no—
211#467D3711yescharacteristic, complemented
212#464—371no—
213#461—371no—
214#452—371no—
215#451—371no—
216#450—371no—
217#448—371no—
218#440—371no—
219#435—371no—
220C37#326611yescharacteristic, complemented, Sylow
221C2×#41—371no—
222C22×Q8—371no—
223C22×Q8—371no—
224C22×D4—371no—
225#137—744no—
226C2×Q16—371no—
227C2×Q16—371no—
228C2×Q16C2×D3711yescharacteristic, complemented
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—744no—
236C2×M16—371no—
237C22×C8C2×D3711yescharacteristic
238C4⋊Q8—371no—
239C4⋊Q8—741no—
240#124—371no—
241#123—741no—
242C22⋊Q8—371no—
243C22⋊Q8—741no—
244C22⋊Q8—741no—
245C22⋊Q8C2×D3711yescharacteristic
246C22⋊Q8C2×D3711yescharacteristic
247#121—371no—
248#121—741no—
249#120—741no—
250C4×Q8—371no—
251C4×D4—371no—
252C4×D4—371no—
253C4×D4—741no—
254C2×C22⋊C4—741no—
255#107C2×D3711yescharacteristic, complemented
256C4⋊C8—371no—
257#103—371no—
258#103—371no—
259#103C2×D3711yescharacteristic, complemented
260#103C2×D3711yescharacteristic, complemented
261#102—371no—
262#102—371no—
263C22⋊C8—371no—
264C22⋊C8—371no—
265#97—371no—
266C24—741no—
267#41—742no—
268#41—1481no—
269C2×Q8—371no—
270C2×Q8—371no—
271C2×Q8—741no—
272C2×Q8—742no—
273C2×Q8—741no—
274C2×Q8—742no—
275C2×Q8—1481no—
276C2×Q8—1481no—
277C2×Q8C22×D3711yescharacteristic
278C2×Q8C22×D3711yescharacteristic
279C2×D4—371no—
280C2×D4—371no—
281C2×D4—371no—
282C2×D4—742no—
283C2×D4—741no—
284C2×D4—741no—
285C2×D4—741no—
286C2×D4—1481no—
287C22×C4—371no—
288C22×C4—741no—
289C22×C4—741no—
290C22×C4—741no—
291C22×C4—741no—
292C22×C4C22×D3711yescharacteristic
293Q16—22no—
294Q16—742no—
295Q16—1481no—
296SD16—374no—
297SD16—742no—
298SD16—742no—
299SD16—742no—
300SD16—742no—
301SD16—1481no—
302M16—742no—
303C2×C8—22no—
304C2×C8—371no—
305C2×C8—371no—
306C2×C8C22×D3711yescharacteristic
307C2×C8C22×D3711yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—371no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4—741no—
314C4⋊C4—741no—
315C4⋊C4C22×D3711yescharacteristic
316C4⋊C4C22×D3711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—371no—
320C22⋊C4—371no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C42—371no—
327C42—741no—
328C23—371no—
329C23—2961no—
330C23—741no—
331C23—741no—
332C23—1482no—
333C23—1482no—
334C23D4×D3711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—372no—
340Q8—741no—
341Q8—741no—
342Q8—741no—
343Q8—1482no—
344Q8—1482no—
345D4—372no—
346D4—2961no—
347D4—742no—
348D4—741no—
349D4—741no—
350D4—741no—
351D4—1482no—
352D4—1482no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—371no—
360C2×C4—371no—
361C2×C4—371no—
362C2×C4—2961no—
363C2×C4—741no—
364C2×C4—741no—
365C2×C4—741no—
366C2×C4—741no—
367C2×C4—1482no—
368C2×C4—1482no—
369C2×C4—1482no—
370C2×C4D4×D3711yescharacteristic
371C2×C4C23×D3711yescharacteristic
372C8—21no—
373C8—741no—
374C8—741no—
375C8D4×D3712yes—
376C22—21no—
377C22—21no—
378C22—2964no—
379C22—741no—
380C22—741no—
381C22—741no—
382C22—742no—
383C22—1481no—
384C22—1481no—
385C22—1481no—
386C22—1481no—
387C22—1481no—
388C22#1192456812yescomplemented
389C22C2×D4×D3711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—741no—
396C4—741no—
397C4—741no—
398C4—742no—
399C4—1481no—
400C4C2×D4×D3711yescharacteristic
401C4#1192458211yescharacteristic
402C2—22no—
403C2—2961no—
404C2—1482no—
405C2—1481no—
406C2#1455816711yescharacteristic
407C2C2×#1192456811yescharacteristic
408C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#467C2
socleC22×C37C22×D4
prime radical#14558174C2
hypercenter#467D37
hypocenterC37#3266
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#11924568C2semidirect
2. C22×#10596930C2semidirect
3. #14558196C2semidirect
5. #14557926C2semidirect
6. #14557780C2semidirect
7. #14557758C2semidirect
8. #14557737C2semidirect
9. #14557698C2semidirect
10. #14557688C2semidirect
11. #14557683C2semidirect
12. #14557673C2semidirect
13. #14557632C2semidirect
14. #14557604C2semidirect
15. C37×#467C2semidirect
18. C2×Q8×D37C22semidirect
21. C2×#10596942C22semidirect
22. C2×#10596942C22semidirect
30. C2×#10596929C22semidirect
32. #11924534C22semidirect
35. #11924516C22semidirect
41. #11924501C22semidirect
46. #11924465C22semidirect
47. #11924459C22semidirect
48. #11924459C22semidirect
52. #11924448C22semidirect
53. #11924446C22semidirect
54. C2×Q16×C37C22semidirect
58. #107×C37C22semidirect
59. #103×C37C22semidirect
60. #103×C37C22semidirect
121. #10596930D4semidirect
173. C22×C37#137semidirect
211. #467D37semidirect
220. C37#3266semidirect
228. C2×Q16C2×D37semidirect
255. #107C2×D37semidirect
259. #103C2×D37semidirect
260. #103C2×D37semidirect
388. C22#11924568semidirect

Maximal subgroups

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

subgroupindex
C2×#119245682
C22×#105969302
#145581962
#145581742
#145579262
#145577802
#145577582
#145577372
#145576982
#145576882
#145576832
#145576732
#145576322
#145576042
C37×#4672
#326637