Finite Group Databasebeta

← #18006109

Subgroups — #18006109

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×#11924567C211yesmaximal, characteristic, complemented
2C2×SD16×D37C211yesmaximal, characteristic, complemented
3Q8×C22⋊D37C211yesmaximal, characteristic, complemented
4#14558180C211yesmaximal, characteristic
5#14557924C211yesmaximal, characteristic, complemented
6#14557777C211yesmaximal, characteristic, complemented
7#14557773C211yesmaximal, characteristic, complemented
8#14557753C211yesmaximal, characteristic, complemented
9#14557737C211yesmaximal, characteristic, complemented
10#14557697C211yesmaximal, characteristic, complemented
11#14557690C211yesmaximal, characteristic, complemented
12#14557682C211yesmaximal, characteristic, complemented
13#14557636C211yesmaximal, characteristic, complemented
14#14557607C211yesmaximal, characteristic, complemented
15C37×#448C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×D4×D37C2211yescharacteristic
19#11924567—24no—
20C2×Dic148C2211yescharacteristic, complemented
21C2×#10596942C2211yescharacteristic, complemented
22C2×#10596942C2211yescharacteristic, complemented
23C2×#10596930C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596941C2211yescharacteristic
26C2×#10596941C2211yescharacteristic
27SD16×D37—24no—
28C2×#10596934C2211yescharacteristic, complemented
29C2×C8×D37C2211yescharacteristic
30#11924534—21no—
31#11924534C2211yescharacteristic, complemented
32#11924523C2211yescharacteristic
33#11924518—21no—
34#11924516C2211yescharacteristic
35#11924515—21no—
36#11924515C2211yescharacteristic, complemented
37#11924512—21no—
38#11924512C2211yescharacteristic
39#11924507—21no—
40#11924504—21no—
41Q8×Dic37C2211yescharacteristic, complemented
42#11924498C2211yescharacteristic
43C4×C22⋊D37—21no—
44C4×C22⋊D37C2211yescharacteristic
45C22⋊C4×D37—21no—
46#11924469C2211yescharacteristic, complemented
47#11924465C2211yescharacteristic, complemented
48#11924461C2211yescharacteristic, complemented
49#11924459C2211yescharacteristic, complemented
50#11924458C2211yescharacteristic
51#11924457C2211yescharacteristic
52#11924448C2211yescharacteristic
53#11924446C2211yescharacteristic, complemented
54C22×Q8×C37C2211yescharacteristic, complemented
55C2×SD16×C37C2211yescharacteristic
56C2×SD16×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic, complemented
59#103×C37C2211yescharacteristic, complemented
60C22⋊C8×C37C2211yescharacteristic, complemented
61C23×D37—21no—
62C2×Q8×C37—21no—
63C2×Q8×C37—22no—
64C2×Q8×C37—41no—
65C2×Q8×C37C2311yescharacteristic
66C2×Q8×C37C2311yescharacteristic
67C2×D4×C37—21no—
68C2×D4×C37C2311yescharacteristic
69C22×C4×C37—21no—
70C22×C4×C37C2311yescharacteristic
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37D411yescharacteristic
74Q8×D37—22no—
75Q8×D37—41no—
76D4×D37—22no—
77D4×D37—41no—
78#10596962—22no—
79#10596962—41no—
80C2×D148C2311yescharacteristic
81C2×C4×D37—21no—
82C2×C4×D37—21no—
83C2×C4×D37—21no—
84C2×C4×D37C2311yescharacteristic
85C2×Dic74—21no—
86C2×Dic74C2311yescharacteristic
87C2×Dic74C2311yescharacteristic
88SD16×C37—22no—
89SD16×C37—41no—
90C2×C8×C37C2311yescharacteristic
91C2×C8×C37C2311yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C22⋊C4×C37—21no—
94C22⋊Dic37—21no—
95C22⋊Dic37—21no—
96C22⋊Dic37—21no—
97C22⋊Dic37D411yescharacteristic
98#10596942—22no—
99#10596942—22no—
100#10596941—22no—
101#10596941D414yescomplemented
102#10596940—22no—
103#10596938—21no—
104#10596938—21no—
105#10596938—21no—
106#10596938D411yescharacteristic
107C4⋊Dic37—21no—
108C4⋊Dic37—21no—
109C4⋊Dic37C2311yescharacteristic
110#10596936—21no—
111#10596936—21no—
112#10596936—21no—
113#10596936—21no—
114#10596936D411yescharacteristic
115C4×Dic37—21no—
116C4×Dic37C2311yescharacteristic
117#10596934—22no—
118C2×#64436C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120Dic148—41no—
121#10596930—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37C2×D411yescharacteristic
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—42no—
134Q8×C37C2×D412yes—
135D4×C37—21no—
136D4×C37—21no—
137D4×C37—81no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—42no—
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2411yescharacteristic
146C22⋊D37—22no—
147C22⋊D37—42no—
148C22⋊D37—42no—
149C2×Dic37—21no—
150C2×Dic37—21no—
151C2×Dic37—21no—
152C2×Dic37C2×D411yescharacteristic
153C2×Dic37C2×D411yescharacteristic
154C2×Dic37C2×D411yescharacteristic
155D148—21no—
156D148C2×D412yes—
157C4×D37—21no—
158C4×D37—21no—
159C4×D37—42no—
160C4×D37—42no—
161C4×D37—81no—
162Dic74—21no—
163Dic74—21no—
164Dic74—21no—
165Dic74—21no—
166Dic74—42no—
167C8×C37—21no—
168C8×C37—21no—
169#64436—21no—
170#64436C2×D412yes—
171C22×C37—21no—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37—41no—
177C22×C37C22×D411yescharacteristic
178C2×D37—21no—
179C2×D37—21no—
180C2×D37—22no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—84no—
184C2×D37#13712yescomplemented
185C4×C37—22no—
186C4×C37—21no—
187C4×C37—41no—
188C4×C37—41no—
189C4×C37C22×D411yescharacteristic
190C4×C37H(5,𝔽2)11yescharacteristic
191Dic37—21no—
192Dic37—21no—
193Dic37—21no—
194Dic37—41no—
195Dic37—41no—
196Dic37—41no—
197#3266—371nomaximal, Sylow
198C2×C37—41no—
199C2×C37—81no—
200C2×C37D4211yescharacteristic
201C2×C37C2×#13711yescharacteristic
202C2×C37#57711yescharacteristic
203D37—22no—
204D37—42no—
205C2×#137—371no—
206C22×SD16—371no—
207D4×Q8—371no—
208#546—371no—
209#497—371no—
210#468—371no—
211#467—371no—
212#464—371no—
213#461—371no—
214#452—371no—
215#451—371no—
216#450—371no—
217#448D3711yescharacteristic, complemented
218#440—371no—
219#435—371no—
220C37#326611yescharacteristic, complemented, Sylow
221C2×#41—371no—
222C22×Q8—371no—
223C22×Q8C2×D3711yescharacteristic, complemented
224C22×D4—371no—
225#137—744no—
226C2×Q16—371no—
227C2×Q16—371no—
228C2×Q16—371no—
229C2×SD16—371no—
230C2×SD16—371no—
231C2×SD16—371no—
232C2×SD16—371no—
233C2×SD16—744no—
234C2×SD16C2×D3711yescharacteristic
235C2×SD16C2×D3711yescharacteristic
236C2×M16—371no—
237C22×C8—371no—
238C4⋊Q8—371no—
239C4⋊Q8—741no—
240#124—371no—
241#123—741no—
242C22⋊Q8—371no—
243C22⋊Q8—371no—
244C22⋊Q8—371no—
245C22⋊Q8—741no—
246C22⋊Q8—741no—
247#121—741no—
248#121C2×D3711yescharacteristic
249#120—741no—
250C4×Q8—371no—
251C4×D4—371no—
252C4×D4—371no—
253C4×D4—741no—
254C2×C22⋊C4—741no—
255#107—371no—
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⋊C8C2×D3711yescharacteristic, complemented
265#97—371no—
266C24—741no—
267#41—742no—
268#41—1481no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—371no—
273C2×Q8—371no—
274C2×Q8—741no—
275C2×Q8—742no—
276C2×Q8—1481no—
277C2×Q8C22×D3711yescharacteristic
278C2×Q8C22×D3711yescharacteristic
279C2×D4—21no—
280C2×D4—371no—
281C2×D4—371no—
282C2×D4—741no—
283C2×D4—742no—
284C2×D4—741no—
285C2×D4—1481no—
286C2×D4C22×D3711yescharacteristic
287C22×C4—21no—
288C22×C4—371no—
289C22×C4—741no—
290C22×C4—741no—
291C22×C4—741no—
292C22×C4C22×D3711yescharacteristic
293Q16—742no—
294Q16—742no—
295Q16—1481no—
296SD16—22no—
297SD16—41no—
298SD16—374no—
299SD16—742no—
300SD16—742no—
301SD16—742no—
302M16—742no—
303C2×C8—371no—
304C2×C8—371no—
305C2×C8—742no—
306C2×C8C22×D3711yescharacteristic
307C2×C8C22×D3711yescharacteristic
308C4⋊C4—371no—
309C4⋊C4—371no—
310C4⋊C4—741no—
311C4⋊C4—741no—
312C4⋊C4—741no—
313C4⋊C4—741no—
314C4⋊C4—741no—
315C4⋊C4—741no—
316C4⋊C4C22×D3711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—371no—
319C22⋊C4—371no—
320C22⋊C4—741no—
321C22⋊C4—741no—
322C22⋊C4—741no—
323C22⋊C4—741no—
324C22⋊C4—741no—
325C22⋊C4—741no—
326C42—371no—
327C42—741no—
328C23—21no—
329C23—371no—
330C23—2961no—
331C23—741no—
332C23—1482no—
333C23—1482no—
334C23D4×D3711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—741no—
340Q8—741no—
341Q8—741no—
342Q8—741no—
343Q8—1482no—
344Q8D4×D3712yes—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—372no—
349D4—742no—
350D4—741no—
351D4—1482no—
352D4—1482no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
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—741no—
368C2×C4—1482no—
369C2×C4—1482no—
370C2×C4D4×D3711yescharacteristic
371C2×C4C23×D3711yescharacteristic
372C8—21no—
373C8—21no—
374C8—372no—
375C8—741no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—372no—
383C22—2964no—
384C22—741no—
385C22—741no—
386C22—742no—
387C22—1481no—
388C22—1481no—
389C22C2×D4×D3711yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—741no—
395C4—741no—
396C4—741no—
397C4—1481no—
398C4—1481no—
399C4—1481no—
400C4C2×D4×D3711yescharacteristic
401C4#1192458111yescharacteristic
402C2—41no—
403C2—81no—
404C2—742no—
405C2—1482no—
406C2#1455816511yescharacteristic
407C2#137×D3711yescharacteristic
408C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#448C2
socleC22×C37C22×D4
prime radical#14558180C2
hypercenter#448D37
hypocenterC37#3266
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#11924567C2semidirect
2. C2×SD16×D37C2semidirect
3. Q8×C22⋊D37C2semidirect
5. #14557924C2semidirect
6. #14557777C2semidirect
7. #14557773C2semidirect
8. #14557753C2semidirect
9. #14557737C2semidirect
10. #14557697C2semidirect
11. #14557690C2semidirect
12. #14557682C2semidirect
13. #14557636C2semidirect
14. #14557607C2semidirect
15. C37×#448C2semidirect
20. C2×Dic148C22semidirect
21. C2×#10596942C22semidirect
22. C2×#10596942C22semidirect
28. C2×#10596934C22semidirect
31. #11924534C22semidirect
36. #11924515C22semidirect
41. Q8×Dic37C22semidirect
46. #11924469C22semidirect
47. #11924465C22semidirect
48. #11924461C22semidirect
49. #11924459C22semidirect
53. #11924446C22semidirect
54. C22×Q8×C37C22semidirect
58. #103×C37C22semidirect
59. #103×C37C22semidirect
60. C22⋊C8×C37C22semidirect
101. #10596941D4semidirect
184. C2×D37#137semidirect
217. #448D37semidirect
220. C37#3266semidirect
223. C22×Q8C2×D37semidirect
259. #103C2×D37semidirect
260. #103C2×D37semidirect
264. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245672
C2×SD16×D372
Q8×C22⋊D372
#145581802
#145579242
#145577772
#145577732
#145577532
#145577372
#145576972
#145576902
#145576822
#145576362
#145576072
C37×#4482
#326637