Finite Group Databasebeta

← #18004315

Subgroups — #18004315

Order 4736.

452 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558333C211yesmaximal, characteristic, complemented
2#14558331C211yesmaximal, characteristic, complemented
3C2×#11924556C211yesmaximal, characteristic, complemented
4C2×#11924544C211yesmaximal, characteristic, complemented
5#14557807C212yesmaximal, complemented
6#14557802C212yesmaximal, complemented
7#14557799C212yesmaximal, complemented
8#14557795C212yesmaximal, complemented
9C2×#11924471C211yesmaximal, characteristic, complemented
10#14557515C211yesmaximal, characteristic, complemented
11C37×#413C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C2×#10596962C2211yescharacteristic
14#11924569—21no—
15#11924569C2212yes—
16#11924567C2212yes—
17#11924566—21no—
18#11924564—21no—
19#11924564C2212yes—
20#11924562C2212yes—
21#11924561—21no—
22#11924558—22no—
23#11924556—22no—
24#11924556—21no—
25#11924556—21no—
26#11924556—21no—
27#11924556—21no—
28C2×#10596942C2211yescharacteristic, complemented
29C2×#10596940C2211yescharacteristic, complemented
30C2×#10596941C2211yescharacteristic, complemented
31C2×#10596939C2211yescharacteristic, complemented
32#11924544—21no—
33#11924544—21no—
34#11924544C2212yes—
35#11924544C2212yes—
36C2×#10596934C2211yescharacteristic
37C2×#10596929—21no—
38C22×#64436C2211yescharacteristic
39C2×C8×D37—21no—
40#11924471C2212yescomplemented
41#11924471C2212yescomplemented
42#11924454C2212yescomplemented
43#11924452C2212yescomplemented
44C2×#41×C37C2211yescharacteristic
45C2×M16×C37C2211yescharacteristic
46C2×M16×C37C2211yescharacteristic
47#101×C37C2212yescomplemented
48#100×C37C2212yescomplemented
49#41×C37—21no—
50#41×C37—21no—
51#41×C37—21no—
52#41×C37—21no—
53C2×Q8×C37C2311yescharacteristic
54C2×D4×C37—21no—
55C2×D4×C37C2311yescharacteristic
56C22×C4×C37—21no—
57C22×C4×C37C2311yescharacteristic
58C2×C22⋊D37—21no—
59C2×C22⋊D37—21no—
60#10596962—21no—
61#10596962—21no—
62#10596962—21no—
63#10596962—21no—
64#10596962—21no—
65#10596962—21no—
66#10596962D412yes—
67#10596962C2312yes—
68C2×D148D411yescharacteristic
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×Dic74D411yescharacteristic
73C2×Dic74C2311yescharacteristic
74M16×C37—21no—
75M16×C37—21no—
76M16×C37C2312yes—
77M16×C37C2312yes—
78C2×C8×C37—21no—
79C2×C8×C37—21no—
80#10596942—22no—
81#10596942—21no—
82#10596942—21no—
83#10596941—22no—
84#10596941—21no—
85#10596941—21no—
86#10596940—22no—
87#10596940—21no—
88#10596940—21no—
89#10596939—22no—
90#10596939—21no—
91#10596939—21no—
92#10596934—21no—
93#10596934C2312yes—
94C2×#64436—21no—
95C2×#64436D411yescharacteristic
96C2×#64436D411yescharacteristic
97C2×#64436D411yescharacteristic
98C2×#64436D411yescharacteristic
99C2×#64436C2311yescharacteristic
100C2×#64436C2311yescharacteristic
101Dic148—22no—
102D296—22no—
103#10596930—22no—
104#10596930—22no—
105#10596929—22no—
106#10596929—22no—
107C8×D37—22no—
108C8×D37—22no—
109C23×C37—21no—
110C23×C37#4111yescharacteristic
111C22×D37—21no—
112C22×D37—21no—
113Q8×C37—21no—
114Q8×C37—21no—
115D4×C37—21no—
116D4×C37—21no—
117D4×C37—41no—
118D4×C37—41no—
119C2×C4×C37—21no—
120C2×C4×C37—41no—
121C2×C4×C37—41no—
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37#4111yescharacteristic
127C2×C4×C37C2411yescharacteristic
128C22⋊D37—22no—
129C22⋊D37—22no—
130C22⋊D37—41no—
131C22⋊D37—41no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134D148—21no—
135D148—21no—
136D148—21no—
137D148C2×D412yes—
138C4×D37—22no—
139C4×D37—22no—
140C4×D37—41no—
141C4×D37—41no—
142Dic74—21no—
143Dic74—21no—
144Dic74—21no—
145Dic74C2×D412yes—
146C8×C37—22no—
147C8×C37—22no—
148#64436—22no—
149#64436C2×D411yescharacteristic
150#64436C2×D411yescharacteristic
151#64436C2×D411yescharacteristic
152#64436C2×D411yescharacteristic
153C22×C37—41no—
154C22×C37—41no—
155C22×C37—81no—
156C22×C37#12111yescharacteristic
157C22×C37#12111yescharacteristic
158C22×C37C2×#4111yescharacteristic
159C2×D37—22no—
160C2×D37—42no—
161C2×D37—41no—
162C2×D37—81no—
163C4×C37—41no—
164C4×C37#12111yescharacteristic
165C4×C37#12111yescharacteristic
166C4×C37C22×D411yescharacteristic
167C4×C37C22×D411yescharacteristic
168Dic37—22no—
169Dic37—41no—
170#3067—371nomaximal, Sylow
171C2×C37—21no—
172C2×C37—21no—
173C2×C37—21no—
174C2×C37—81no—
175C2×C37C2×#12111yescharacteristic
176D37—42no—
177D37—81no—
178#575—371no—
179#575—371no—
180C2×#135—371no—
181C2×#131—371no—
182#473—372no—
183#472—372no—
184#471—372no—
185#471—372no—
186C2×#108—371no—
187#413—371no—
188#413D3711yescharacteristic, complemented
189C37#306711yescharacteristic, complemented, Sylow
190C2×#41—371no—
191C2×#41—371no—
192C2×#41C2×D3711yescharacteristic
193#137—372no—
194#137—372no—
195#137—741no—
196#137—741no—
197AGL(1,ℤ/8)—372no—
198AGL(1,ℤ/8)—372no—
199AGL(1,ℤ/8)—741no—
200AGL(1,ℤ/8)—741no—
201#135—742no—
202#135—741no—
203#135—741no—
204#135—741no—
205#135—741no—
206#135—742no—
207C2×Q16—371no—
208C2×SD16—371no—
209C2×SD16—371no—
210C2×D8—371no—
211#131—372no—
212#131—372no—
213#131—741no—
214#131—741no—
215C2×M16—371no—
216C2×M16—741no—
217C2×M16C2×D3711yescharacteristic
218C2×M16C2×D3711yescharacteristic
219C22×C8—371no—
220C22×C8—741no—
221#108—372no—
222#108—372no—
223#101—372no—
224#101C2×D3712yescomplemented
225#100—372no—
226#100C2×D3712yescomplemented
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—372no—
232#41—372no—
233#41—741no—
234#41—741no—
235#41—741no—
236#41—741no—
237#41—741no—
238#41—741no—
239C2×Q8—371no—
240C2×Q8—371no—
241C2×Q8C22×D3711yescharacteristic
242C2×D4—21no—
243C2×D4—371no—
244C2×D4—371no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4C22×D3711yescharacteristic
248C22×C4—21no—
249C22×C4—741no—
250C22×C4—741no—
251C22×C4C22×D3711yescharacteristic
252Q16—742no—
253Q16—741no—
254Q16—741no—
255Q16—742no—
256SD16—742no—
257SD16—742no—
258SD16—741no—
259SD16—741no—
260SD16—741no—
261SD16—741no—
262SD16—742no—
263SD16—742no—
264D8—742no—
265D8—741no—
266D8—741no—
267D8—742no—
268M16—21no—
269M16—21no—
270M16—372no—
271M16—742no—
272M16—742no—
273M16—741no—
274M16C22×D3712yes—
275M16C22×D3712yes—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—371no—
279C2×C8—371no—
280C2×C8—371no—
281C2×C8—371no—
282C2×C8—371no—
283C2×C8—371no—
284C2×C8—742no—
285C2×C8—742no—
286C2×C8—741no—
287C23—21no—
288C23—741no—
289C23—741no—
290C23#1059696211yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—372no—
294Q8—741no—
295Q8—741no—
296Q8—741no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301D4—372no—
302D4—742no—
303D4—742no—
304D4—741no—
305D4—741no—
306D4—741no—
307D4—1481no—
308D4—1481no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—741no—
313C2×C4—742no—
314C2×C4—742no—
315C2×C4—741no—
316C2×C4—1481no—
317C2×C4—1481no—
318C2×C4#1059696211yescharacteristic
319C2×C4D4×D3711yescharacteristic
320C2×C4D4×D3711yescharacteristic
321C2×C4D4×D3711yescharacteristic
322C2×C4D4×D3711yescharacteristic
323C2×C4C23×D3711yescharacteristic
324C8—22no—
325C8—22no—
326C8—371no—
327C8—371no—
328C8—371no—
329C8—371no—
330C8—742no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—2961no—
335C22—742no—
336C22—1482no—
337C22—1481no—
338C22#1192450911yescharacteristic
339C22#1192450911yescharacteristic
340C22C2×#1059696211yescharacteristic
341C4—41no—
342C4—742no—
343C4—1481no—
344C4#1192450911yescharacteristic
345C4#1192450911yescharacteristic
346C4C2×D4×D3711yescharacteristic
347C4C2×D4×D3711yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—81no—
352C2—2961no—
353C2—1482no—
354C2C2×#1192450911yescharacteristic
subgroupG/H
centerC4#11924509
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#413C2
socleC2×C37C2×#121
hypercenter#413D37
hypocenterC37#3067
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #14558333C2semidirect
2. #14558331C2semidirect
3. C2×#11924556C2semidirect
4. C2×#11924544C2semidirect
5. #14557807C2semidirect
6. #14557802C2semidirect
7. #14557799C2semidirect
8. #14557795C2semidirect
9. C2×#11924471C2semidirect
10. #14557515C2semidirect
11. C37×#413C2semidirect
28. C2×#10596942C22semidirect
29. C2×#10596940C22semidirect
30. C2×#10596941C22semidirect
31. C2×#10596939C22semidirect
40. #11924471C22semidirect
41. #11924471C22semidirect
42. #11924454C22semidirect
43. #11924452C22semidirect
47. #101×C37C22semidirect
48. #100×C37C22semidirect
188. #413D37semidirect
189. C37#3067semidirect
224. #101C2×D37semidirect
226. #100C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145583332
#145583312
C2×#119245562
C2×#119245442
#145578072
#145578022
#145577992
#145577952
C2×#119244712
#145575152
C37×#4132
#306737