Finite Group Databasebeta

← #17997410

Subgroups — #17997410

Order 4736.

540 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924522C211yesmaximal, characteristic
2#14557438C211yesmaximal, characteristic, complemented
3#14557437C211yesmaximal, characteristic, complemented
4#14557426C211yesmaximal, characteristic, complemented
5#14557423C211yesmaximal, characteristic, complemented
6#14557423C211yesmaximal, characteristic, complemented
7#14557421C211yesmaximal, characteristic, complemented
8#14557412C211yesmaximal, characteristic
9#14557409C211yesmaximal, characteristic
10#14557407C211yesmaximal, characteristic, complemented
11#14557400C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic37C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic, complemented
15C37×#385C211yesmaximal, characteristic, complemented
16C22×Dic74C2211yescharacteristic
17C22×C22⋊D37C2211yescharacteristic
18C22×C4×D37C2211yescharacteristic
19#11924522C418yescomplemented
20C2×C4⋊Dic37C2211yescharacteristic
21C2×#10596936C2211yescharacteristic
22C2×C22⋊Dic37C2211yescharacteristic
23C2×C22⋊Dic37C2211yescharacteristic
24C2×C22⋊Dic37C2211yescharacteristic
25C2×#10596938C2211yescharacteristic
26C2×#10596938C2211yescharacteristic
27C2×#10596938C2211yescharacteristic
28C2×#10596938C2211yescharacteristic
29C2×#10596938C2211yescharacteristic
30C2×C4×Dic37C2211yescharacteristic
31C2×C4×Dic37C2211yescharacteristic
32C2×C4×Dic37C2211yescharacteristic
33C2×C4×Dic37C2211yescharacteristic
34C2×C4×Dic37C2211yescharacteristic
35#11924443C2211yescharacteristic
36#11924443C2211yescharacteristic
37#11924443C2211yescharacteristic
38#11924443C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45C23×C4×C37C2211yescharacteristic
46C2×C4⋊C4×C37C2211yescharacteristic
47C2×C4⋊C4×C37C2211yescharacteristic
48C2×C22⋊C4×C37C2211yescharacteristic
49C2×C22⋊C4×C37C2211yescharacteristic
50#95×C37C2211yescharacteristic
51#95×C37C2211yescharacteristic
52C24×C37C2311yescharacteristic
53C23×D37C2311yescharacteristic
54C22×C4×C37—22no—
55C22×C4×C37—41no—
56C22×C4×C37—41no—
57C22×C4×C37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—41no—
64C2×C22⋊D37—41no—
65C2×C22⋊D37C2×C414yes—
66C22×Dic37C2311yescharacteristic
67C22×Dic37C2311yescharacteristic
68C22×Dic37C2311yescharacteristic
69C22×Dic37C2311yescharacteristic
70C22×Dic37C2311yescharacteristic
71C22×Dic37C2311yescharacteristic
72C22×Dic37C2311yescharacteristic
73C2×C4×D37—22no—
74C2×C4×D37—41no—
75C2×C4×D37—41no—
76C2×Dic74—41no—
77C2×Dic74—41no—
78C2×Dic74C2×C414yescomplemented
79C4⋊C4×C37—22no—
80C4⋊C4×C37—41no—
81C22⋊C4×C37—41no—
82C22⋊C4×C37C2×C414yescomplemented
83C22⋊Dic37—22no—
84C22⋊Dic37—41no—
85C22⋊Dic37C2×C414yescomplemented
86#10596938—22no—
87#10596938—41no—
88#10596938—41no—
89#10596938C2×C414yescomplemented
90#10596938C2×C414yescomplemented
91C4⋊Dic37—22no—
92#10596936—41no—
93C4×Dic37—41no—
94C4×Dic37—41no—
95C4×Dic37—41no—
96C4×Dic37—41no—
97C4×Dic37C2×C414yescomplemented
98C23×C37—21no—
99C23×C37—21no—
100C23×C37—21no—
101C23×C37—21no—
102C23×C37—21no—
103C23×C37—21no—
104C23×C37C22×C412yes—
105C23×C37C2411yescharacteristic
106C22×D37—21no—
107C22×D37—21no—
108C22×D37—21no—
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—21no—
112C22×D37C22×C412yes—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
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—21no—
127C2×C4×C37—21no—
128C2×C4×C37—44no—
129C2×C4×C37C22×C412yes—
130C2×C4×C37C22×C412yes—
131C2×C4×C37#4112yes—
132C22⋊D37—44no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37C22×C412yes—
151C2×Dic37C22×C412yes—
152C2×Dic37C22×C412yes—
153C2×Dic37#4112yes—
154C4×D37—44no—
155Dic74—44no—
156C22×C37—22no—
157C22×C37—22no—
158C22×C37—22no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37C23×C411yescharacteristic
164C22×C37C2×#4111yescharacteristic
165C22×C37C2×#4111yescharacteristic
166C22×C37H(5,𝔽2)11yescharacteristic
167C22×C37H(5,𝔽2)11yescharacteristic
168C22×C37H(5,𝔽2)11yescharacteristic
169C22×C372−1+411yescharacteristic
170C2×D37—22no—
171C2×D37—22no—
172C2×D37—22no—
173C2×D37—41no—
174C2×D37—41no—
175C2×D37—41no—
176C2×D37—41no—
177C4×C37—22no—
178C4×C37—22no—
179C4×C37—22no—
180C4×C37—41no—
181C4×C37—41no—
182C4×C37—41no—
183Dic37—22no—
184Dic37—22no—
185Dic37—22no—
186Dic37—22no—
187Dic37—41no—
188Dic37—41no—
189Dic37—41no—
190#2337—371nomaximal, Sylow
191C2×C37—42no—
192C2×C37C4×#4111yescharacteristic
193C2×C37#51811yescharacteristic
194C2×C37#52011yescharacteristic
195C2×C37#53811yescharacteristic
196C2×C37#53811yescharacteristic
197C2×C37#54211yescharacteristic
198C2×C37#54211yescharacteristic
199D37—42no—
200C2×#124—371no—
201#391—371no—
202#391—371no—
203#388—371no—
204#388—371no—
205#388—371no—
206#388—371no—
207#386—371no—
208#386—371no—
209#385—371no—
210#385D3711yescharacteristic, complemented
211#383—371no—
212C4×C4⋊C4—371no—
213C4×C22⋊C4—371no—
214C4×C22⋊C4—371no—
215C37#233711yescharacteristic, complemented, Sylow
216C22×Q8—371no—
217C22×D4—371no—
218C23×C4—371no—
219C23×C4C2×D3711yescharacteristic
220#124—378no—
221C2×C4⋊C4—371no—
222C2×C4⋊C4—371no—
223C2×C4⋊C4C2×D3711yescharacteristic
224C2×C4⋊C4C2×D3711yescharacteristic
225C2×C22⋊C4—371no—
226C2×C22⋊C4—371no—
227C2×C22⋊C4—371no—
228C2×C22⋊C4—371no—
229C2×C22⋊C4—371no—
230C2×C22⋊C4—371no—
231C2×C22⋊C4—371no—
232C2×C22⋊C4—371no—
233C2×C22⋊C4C2×D3711yescharacteristic
234C2×C22⋊C4C2×D3711yescharacteristic
235C2×C42—371no—
236C2×C42—371no—
237C2×C42—371no—
238C2×C42—371no—
239C2×C42—371no—
240#95—371no—
241#95—371no—
242#95—371no—
243#95—371no—
244#95—371no—
245#95—371no—
246#95—371no—
247#95—371no—
248#95—371no—
249#95—371no—
250#95C2×D3711yescharacteristic
251#95C2×D3711yescharacteristic
252C24—371no—
253C24C22×D3711yescharacteristic
254C2×Q8—374no—
255C2×Q8—1481no—
256C2×Q8—1481no—
257C2×D4—374no—
258C2×D4—1481no—
259C2×D4—1481no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—371no—
264C22×C4—371no—
265C22×C4—371no—
266C22×C4—371no—
267C22×C4—371no—
268C22×C4—371no—
269C22×C4—371no—
270C22×C4—742no—
271C22×C4—1481no—
272C22×C4—1481no—
273C22×C4C22×D3711yescharacteristic
274C22×C4C22×D3711yescharacteristic
275C22×C4C22×D3711yescharacteristic
276C22×C4C22×D3711yescharacteristic
277C22×C4C22×D3711yescharacteristic
278C22×C4C22×D3711yescharacteristic
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—742no—
282C4⋊C4—1481no—
283C22⋊C4—41no—
284C22⋊C4—374no—
285C22⋊C4—374no—
286C22⋊C4—374no—
287C22⋊C4—742no—
288C22⋊C4—742no—
289C22⋊C4—1481no—
290C22⋊C4—1481no—
291C22⋊C4—1481no—
292C22⋊C4C4×D3714yescomplemented
293C42—374no—
294C42—1481no—
295C42—1481no—
296C42—1481no—
297C42—1481no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—372no—
305C23—741no—
306C23—741no—
307C23—741no—
308C23—741no—
309C23—741no—
310C23—741no—
311C23C2×C4×D3712yes—
312C23C23×D3711yescharacteristic
313Q8—1484no—
314D4—1484no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—44no—
331C2×C4—372no—
332C2×C4—372no—
333C2×C4—372no—
334C2×C4—372no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—741no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—741no—
344C2×C4—741no—
345C2×C4—741no—
346C2×C4—741no—
347C2×C4—741no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—741no—
351C2×C4—741no—
352C2×C4—1484no—
353C2×C4C2×C4×D3712yes—
354C2×C4C2×C4×D3712yes—
355C2×C4#1059696412yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—742no—
364C22—742no—
365C22—742no—
366C22—1481no—
367C22—1481no—
368C22—1481no—
369C22—1481no—
370C22C22×C4×D3711yescharacteristic
371C22#41×D3711yescharacteristic
372C22C2×#1059696411yescharacteristic
373C22#1192458111yescharacteristic
374C22#1192458111yescharacteristic
375C22#1192458211yescharacteristic
376C22#1192458411yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—742no—
384C4—742no—
385C4—742no—
386C4—742no—
387C4—1481no—
388C4—1481no—
389C4—1481no—
390C2—42no—
391C2—1482no—
392C2C4×#1059696411yescharacteristic
393C2#1455800511yescharacteristic
394C2#1455801411yescharacteristic
395C2#1455811811yescharacteristic
396C2#1455811911yescharacteristic
397C2#1455815311yescharacteristic
398C2#1455815611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#385C2
socle, cosocleC23×C37C24
prime radicalC22×C22⋊D37C22
hypercenter#385D37
hypocenterC37#2337
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #14557438C2semidirect
3. #14557437C2semidirect
4. #14557426C2semidirect
5. #14557423C2semidirect
6. #14557423C2semidirect
7. #14557421C2semidirect
10. #14557407C2semidirect
11. #14557400C2semidirect
12. C4⋊C4×Dic37C2semidirect
13. C4×C22⋊Dic37C2semidirect
14. #14557380C2semidirect
15. C37×#385C2semidirect
19. #11924522C4semidirect
78. C2×Dic74C2×C4semidirect
82. C22⋊C4×C37C2×C4semidirect
85. C22⋊Dic37C2×C4semidirect
89. #10596938C2×C4semidirect
90. #10596938C2×C4semidirect
97. C4×Dic37C2×C4semidirect
210. #385D37semidirect
215. C37#2337semidirect
292. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245222
#145574382
#145574372
#145574262
#145574232
#145574212
#145574122
#145574092
#145574072
#145574002
C4⋊C4×Dic372
C4×C22⋊Dic372
#145573802
C37×#3852
#233737