Finite Group Databasebeta

← #18006117

Subgroups — #18006117

Order 4736.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924562C211yesmaximal, characteristic, complemented
2C2×#11924556C211yesmaximal, characteristic, complemented
3#14558188C211yesmaximal, characteristic, complemented
4#14557928C211yesmaximal, characteristic, complemented
5#14557789C211yesmaximal, characteristic, complemented
6#14557760C211yesmaximal, characteristic, complemented
7#14557745C211yesmaximal, characteristic, complemented
8#14557738C211yesmaximal, characteristic, complemented
9#14557695C211yesmaximal, characteristic, complemented
10#14557693C211yesmaximal, characteristic, complemented
11#14557684C211yesmaximal, characteristic, complemented
12#14557676C211yesmaximal, characteristic, complemented
13#14557643C211yesmaximal, characteristic, complemented
14#14557605C211yesmaximal, characteristic, complemented
15C37×#546C211yesmaximal, characteristic, complemented
16C2×#10596962C2211yescharacteristic
17C2×#10596962C2211yescharacteristic, complemented
18#11924562—24no—
19#11924556—24no—
20C2×#10596942C2211yescharacteristic, complemented
21C2×#10596942C2211yescharacteristic, complemented
22C2×#10596940C2211yescharacteristic
23C2×#10596940C2211yescharacteristic
24C2×#10596940C2211yescharacteristic
25C2×#10596940C2211yescharacteristic
26C2×#10596941C2211yescharacteristic, complemented
27C2×#10596939C2211yescharacteristic
28C2×#10596939C2211yescharacteristic
29C2×#10596934C2211yescharacteristic
30C22×#64436C2211yescharacteristic, complemented
31#11924536C2211yescharacteristic, complemented
32#11924518—21no—
33#11924518—21no—
34#11924515C2211yescharacteristic
35#11924515C2211yescharacteristic, complemented
36#11924507—21no—
37C4×D148C2211yescharacteristic, complemented
38C4⋊C4×D37—21no—
39#11924467C2211yescharacteristic, complemented
40C4⋊#64436C2211yescharacteristic, complemented
41#11924460C2211yescharacteristic, complemented
42#11924459C2211yescharacteristic, complemented
43#11924459C2211yescharacteristic, complemented
44#11924457C2211yescharacteristic
45#11924457C2211yescharacteristic
46#11924456C2211yescharacteristic, complemented
47C22⋊#64436C2211yescharacteristic
48C22⋊#64436C2211yescharacteristic, complemented
49#11924447C2211yescharacteristic, complemented
50C2×#41×C37C2211yescharacteristic
51C22×D4×C37C2211yescharacteristic
52#124×C37C2211yescharacteristic
53#123×C37—21no—
54C22⋊Q8×C37C2211yescharacteristic
55#121×C37—21no—
56#121×C37C2211yescharacteristic
57#120×C37—21no—
58C4×D4×C37C2211yescharacteristic
59C4×D4×C37C2211yescharacteristic
60C2×C22⋊C4×C37—21no—
61C24×C37—21no—
62#41×C37—22no—
63#41×C37—41no—
64C2×Q8×C37C2311yescharacteristic
65C2×D4×C37—22no—
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37—41no—
70C2×D4×C37D411yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C2×D4×C37C2311yescharacteristic
73C22×C4×C37—21no—
74C22×C4×C37—21no—
75C22×C4×C37C2311yescharacteristic
76C22×C4×C37C2311yescharacteristic
77C2×C22⋊D37—21no—
78C2×C22⋊D37—21no—
79#10596962—22no—
80#10596962—22no—
81#10596962—41no—
82#10596962—41no—
83C2×D148C2311yescharacteristic
84C2×C4×D37—21no—
85C2×C4×D37—21no—
86C2×C4×D37—21no—
87C2×Dic74C2311yescharacteristic
88C2×Dic74C2311yescharacteristic
89C4⋊C4×C37—21no—
90C4⋊C4×C37D411yescharacteristic
91C4⋊C4×C37C2311yescharacteristic
92C22⋊C4×C37—21no—
93C22⋊C4×C37—21no—
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊C4×C37—21no—
97C22⋊C4×C37D411yescharacteristic
98C22⋊C4×C37D411yescharacteristic
99C42×C37C2311yescharacteristic
100C22⋊Dic37—21no—
101C22⋊Dic37—21no—
102#10596942—22no—
103#10596942—41no—
104#10596941—22no—
105#10596940—22no—
106#10596940—22no—
107#10596940—22no—
108#10596940—41no—
109#10596939—22no—
110#10596939D414yescomplemented
111#10596938—21no—
112C4⋊Dic37—21no—
113C4⋊Dic37—21no—
114C4⋊Dic37C2311yescharacteristic
115#10596936—21no—
116#10596936—21no—
117#10596934—22no—
118C2×#64436—22no—
119C2×#64436C2311yescharacteristic
120C2×#64436C2311yescharacteristic
121C2×#64436C2311yescharacteristic
122C2×#64436C2311yescharacteristic
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—42no—
126C23×C37—42no—
127C23×C37—81no—
128C23×C37C2×D411yescharacteristic
129C23×C37C2×D411yescharacteristic
130C22×D37—21no—
131Q8×C37—21no—
132Q8×C37—21no—
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—21no—
136D4×C37—41no—
137D4×C37—42no—
138D4×C37—42no—
139D4×C37—81no—
140D4×C37C2×D412yes—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—42no—
148C2×C4×C37—81no—
149C2×C4×C37C2×D411yescharacteristic
150C2×C4×C37C2×D411yescharacteristic
151C2×C4×C37C2×D411yescharacteristic
152C2×C4×C37C2×D411yescharacteristic
153C2×C4×C37C2411yescharacteristic
154C22⋊D37—42no—
155C22⋊D37—42no—
156C2×Dic37—21no—
157C2×Dic37—21no—
158C2×Dic37—21no—
159D148—21no—
160D148C2×D412yes—
161C4×D37—42no—
162C4×D37—42no—
163C4×D37—42no—
164Dic74—21no—
165Dic74—21no—
166Dic74—21no—
167Dic74—21no—
168#64436—21no—
169#64436—21no—
170#64436—21no—
171#64436C2×D412yes—
172C22×C37—21no—
173C22×C37—21no—
174C22×C37—22no—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—21no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—84no—
185C22×C37C22×D411yescharacteristic
186C2×D37—22no—
187C2×D37—41no—
188C2×D37—41no—
189C4×C37—21no—
190C4×C37—21no—
191C4×C37—21no—
192C4×C37—21no—
193C4×C37—41no—
194C4×C37—41no—
195C4×C37C22×D411yescharacteristic
196C4×C37H(5,𝔽2)11yescharacteristic
197Dic37—41no—
198Dic37—41no—
199Dic37—41no—
200#3267—371nomaximal, Sylow
201C2×C37—41no—
202C2×C37—41no—
203C2×C37—42no—
204C2×C37—81no—
205C2×C37D4211yescharacteristic
206C2×C37#57511yescharacteristic
207C2×C37#57711yescharacteristic
208D37—42no—
209C2×AGL(1,ℤ/8)—371no—
210C2×#135—371no—
211#547—371no—
212#546D3711yescharacteristic, complemented
213#497—371no—
214#470—371no—
215#465—371no—
216#463—371no—
217#461—371no—
218#452—371no—
219#452—371no—
220#450—371no—
221#449—371no—
222#442—371no—
223#435—371no—
224C37#326711yescharacteristic, complemented, Sylow
225C2×#41—371no—
226C2×#41—371no—
227C2×#41C2×D3711yescharacteristic
228C22×D4C2×D3711yescharacteristic
229AGL(1,ℤ/8)—744no—
230#135—744no—
231C2×Q16—371no—
232C2×Q16—371no—
233C2×SD16—371no—
234C2×SD16—371no—
235C2×SD16—371no—
236C2×SD16—371no—
237C2×SD16—371no—
238C2×D8—371no—
239C2×D8—371no—
240C2×M16—371no—
241C22×C8—371no—
242C4⋊Q8—371no—
243#124C2×D3711yescharacteristic
244#123—21no—
245#123—741no—
246#123—741no—
247C22⋊Q8—371no—
248C22⋊Q8—371no—
249C22⋊Q8C2×D3711yescharacteristic
250#121—21no—
251#121—741no—
252#121C2×D3711yescharacteristic
253#120—21no—
254C4×D4—371no—
255C4×D4C2×D3711yescharacteristic
256C4×D4C2×D3711yescharacteristic
257C2×C4⋊C4—741no—
258C2×C22⋊C4—21no—
259#106—371no—
260C4⋊C8—371no—
261#103—371no—
262#103—371no—
263#103—371no—
264#102—371no—
265#102—371no—
266#102—371no—
267C22⋊C8—371no—
268C22⋊C8—371no—
269#97—371no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—742no—
274#41—742no—
275#41—1481no—
276#41—1481no—
277C2×Q8—371no—
278C2×Q8—371no—
279C2×Q8C22×D3711yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—371no—
286C2×D4—741no—
287C2×D4—741no—
288C2×D4C22⋊D3711yescharacteristic
289C2×D4C22×D3711yescharacteristic
290C2×D4C22×D3711yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—741no—
294C22×C4—741no—
295C22×C4—741no—
296C22×C4C22×D3711yescharacteristic
297C22×C4C22×D3711yescharacteristic
298Q16—742no—
299Q16—1481no—
300SD16—742no—
301SD16—742no—
302SD16—742no—
303SD16—742no—
304SD16—1481no—
305D8—374no—
306D8—742no—
307M16—742no—
308C2×C8—371no—
309C2×C8—371no—
310C2×C8—371no—
311C2×C8—371no—
312C2×C8—742no—
313C4⋊C4—21no—
314C4⋊C4—371no—
315C4⋊C4—741no—
316C4⋊C4—741no—
317C4⋊C4—741no—
318C4⋊C4—741no—
319C4⋊C4C22⋊D3711yescharacteristic
320C4⋊C4C22×D3711yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—741no—
327C22⋊C4—741no—
328C22⋊C4—741no—
329C22⋊C4C22⋊D3711yescharacteristic
330C22⋊C4C22⋊D3711yescharacteristic
331C42C22×D3711yescharacteristic
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—741no—
338C23C2×C22⋊D3711yescharacteristic
339C23C2×C22⋊D3711yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—741no—
343Q8—741no—
344Q8—741no—
345Q8—741no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—81no—
353D4—372no—
354D4—741no—
355D4—1482no—
356D4—1482no—
357D4D4×D3712yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—741no—
367C2×C4—741no—
368C2×C4—741no—
369C2×C4—1482no—
370C2×C4—1482no—
371C2×C4—1482no—
372C2×C4C2×C22⋊D3711yescharacteristic
373C2×C4C2×C22⋊D3711yescharacteristic
374C2×C4C2×C22⋊D3711yescharacteristic
375C2×C4C2×C22⋊D3711yescharacteristic
376C2×C4C23×D3711yescharacteristic
377C8—372no—
378C8—741no—
379C8—741no—
380C8—741no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—742no—
395C22—1481no—
396C22—1481no—
397C22C22×C22⋊D3711yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—1481no—
405C4—1481no—
406C4—1481no—
407C4C2×D4×D3711yescharacteristic
408C4#1192458111yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—1482no—
414C2D4×C22⋊D3711yescharacteristic
415C2#1455833111yescharacteristic
416C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#546C2
socleC22×C37C22×D4
hypercenter#546D37
hypocenterC37#3267
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#11924562C2semidirect
2. C2×#11924556C2semidirect
3. #14558188C2semidirect
4. #14557928C2semidirect
5. #14557789C2semidirect
6. #14557760C2semidirect
7. #14557745C2semidirect
8. #14557738C2semidirect
9. #14557695C2semidirect
10. #14557693C2semidirect
11. #14557684C2semidirect
12. #14557676C2semidirect
13. #14557643C2semidirect
14. #14557605C2semidirect
15. C37×#546C2semidirect
17. C2×#10596962C22semidirect
20. C2×#10596942C22semidirect
21. C2×#10596942C22semidirect
26. C2×#10596941C22semidirect
30. C22×#64436C22semidirect
31. #11924536C22semidirect
35. #11924515C22semidirect
37. C4×D148C22semidirect
39. #11924467C22semidirect
40. C4⋊#64436C22semidirect
41. #11924460C22semidirect
42. #11924459C22semidirect
43. #11924459C22semidirect
46. #11924456C22semidirect
48. C22⋊#64436C22semidirect
49. #11924447C22semidirect
110. #10596939D4semidirect
212. #546D37semidirect
224. C37#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#119245622
C2×#119245562
#145581882
#145579282
#145577892
#145577602
#145577452
#145577382
#145576952
#145576932
#145576842
#145576762
#145576432
#145576052
C37×#5462
#326737