Finite Group Databasebeta

← #17997584

Subgroups — #17997584

Order 4736.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924519C211yesmaximal, characteristic
2C2×C4×C22⋊D37C211yesmaximal, characteristic
3C2×#11924495C211yesmaximal, characteristic, complemented
4#14557430C211yesmaximal, characteristic, complemented
5#14557425C211yesmaximal, characteristic, complemented
6#14557422C211yesmaximal, characteristic, complemented
7#14557420C211yesmaximal, characteristic, complemented
8#14557415C211yesmaximal, characteristic, complemented
9#14557412C211yesmaximal, characteristic
10#14557407C211yesmaximal, characteristic, complemented
11#14557406C211yesmaximal, characteristic, complemented
12#14557384C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic37C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic, complemented
15C2×#95×C37C211yesmaximal, characteristic, complemented
16C22×C22⋊D37C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18#11924519C418yescomplemented
19C4×C22⋊D37—24no—
20#11924495—24no—
21C2×C4⋊Dic37C2211yescharacteristic
22C2×C4⋊Dic37C2211yescharacteristic
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×#10596936C2211yescharacteristic
27C2×#10596936C2211yescharacteristic
28C2×C22⋊Dic37C2211yescharacteristic
29C2×C22⋊Dic37C2211yescharacteristic
30C2×C22⋊Dic37C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C2×C4×Dic37C2211yescharacteristic
37C2×C4×Dic37C2211yescharacteristic
38C2×C4×Dic37C2211yescharacteristic
39C2×C4×Dic37C2211yescharacteristic
40C2×C4×Dic37C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46#11924443C2211yescharacteristic
47C23×C4×C37C2211yescharacteristic
48C23×C4×C37C2211yescharacteristic
49C23×C4×C37C2211yescharacteristic
50#95×C37C2211yescharacteristic
51#95×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53#95×C37C2211yescharacteristic
54C24×C37C2311yescharacteristic
55C23×D37C2311yescharacteristic
56C22×C4×C37—22no—
57C22×C4×C37—22no—
58C22×C4×C37—22no—
59C22×C4×C37—22no—
60C22×C4×C37—22no—
61C22×C4×C37—22no—
62C22×C4×C37—41no—
63C22×C4×C37—41no—
64C22×C4×C37C2×C414yescomplemented
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C2×C22⋊D37—22no—
72C2×C22⋊D37—22no—
73C2×C22⋊D37C2×C414yes—
74C22×Dic37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C22×Dic37C2311yescharacteristic
80C22×Dic37C2311yescharacteristic
81C2×C4×D37—22no—
82C2×C4×D37—22no—
83C2×C4×D37—41no—
84C22⋊Dic37—22no—
85C22⋊Dic37C2×C414yescomplemented
86C22⋊Dic37D414yes—
87#10596938—22no—
88#10596938—22no—
89#10596938—41no—
90#10596938C2×C414yescomplemented
91#10596938C2×C414yescomplemented
92C4⋊Dic37—22no—
93C4⋊Dic37—22no—
94#10596936—22no—
95#10596936—22no—
96#10596936—41no—
97#10596936C2×C414yescomplemented
98#10596936C2×C414yescomplemented
99C4×Dic37—22no—
100C4×Dic37—22no—
101C4×Dic37—22no—
102C4×Dic37—22no—
103C4×Dic37—41no—
104C23×C37—21no—
105C23×C37—21no—
106C23×C37—21no—
107C23×C37—21no—
108C23×C37C22×C412yes—
109C23×C37C2×D412yes—
110C23×C37#4112yes—
111C23×C37C2411yescharacteristic
112C22×D37—21no—
113C22×D37—21no—
114C22×D37—21no—
115C22×D37—21no—
116C22×D37—21no—
117C22×D37—21no—
118C22×D37C22×C412yes—
119C2×C4×C37—28no—
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—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—44no—
135C2×C4×C37—44no—
136C2×C4×C37C22×C412yes—
137C2×C4×C37C22×C412yes—
138C2×C4×C37#4112yes—
139C2×C4×C37#4112yes—
140C22⋊D37—28no—
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×Dic37—21no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—21no—
156C2×Dic37—21no—
157C2×Dic37C22×C412yes—
158C2×Dic37C22×C412yes—
159C2×Dic37C22×C412yes—
160C2×Dic37C2×D412yes—
161C2×Dic37C2×D412yes—
162C4×D37—44no—
163C22×C37—22no—
164C22×C37—22no—
165C22×C37—22no—
166C22×C37—22no—
167C22×C37—22no—
168C22×C37—22no—
169C22×C37C4×D414yes—
170C22×C37C23×C411yescharacteristic
171C22×C37C22×D411yescharacteristic
172C22×C37C2×#4111yescharacteristic
173C22×C37C2×#4111yescharacteristic
174C22×C37C2×#4111yescharacteristic
175C22×C37H(5,𝔽2)11yescharacteristic
176C22×C372−1+411yescharacteristic
177C2×D37—22no—
178C2×D37—22no—
179C2×D37—22no—
180C2×D37—41no—
181C2×D37—41no—
182C2×D37—41no—
183C2×D37—41no—
184C4×C37—22no—
185C4×C37—22no—
186C4×C37—22no—
187C4×C37—22no—
188C4×C37—41no—
189C4×C37—41no—
190Dic37—22no—
191Dic37—22no—
192Dic37—22no—
193Dic37—22no—
194Dic37—22no—
195Dic37—41no—
196Dic37—41no—
197#2359—371nomaximal, Sylow
198C2×C37—24no—
199C2×C37C2×C4×D411yescharacteristic
200C2×C37C4×#4111yescharacteristic
201C2×C37#52011yescharacteristic
202C2×C37#54611yescharacteristic
203C2×C37#54711yescharacteristic
204C2×C37#55111yescharacteristic
205C2×C37#55211yescharacteristic
206D37—42no—
207C2×#123—371no—
208C2×C4×D4—371no—
209C2×#117—371no—
210#389—371no—
211#388—371no—
212#388—371no—
213#387—371no—
214#387—371no—
215#386—371no—
216#385—371no—
217#385—371no—
218C4×C4⋊C4—371no—
219C4×C22⋊C4—371no—
220C4×C22⋊C4—371no—
221C2×#95D3711yescharacteristic, complemented
222C37#235911yescharacteristic, complemented, Sylow
223C22×D4—371no—
224C23×C4—371no—
225C23×C4C2×D3711yescharacteristic
226C23×C4C2×D3711yescharacteristic
227C23×C4C2×D3711yescharacteristic
228#123—378no—
229C4×D4—744no—
230#117—744no—
231C2×C4⋊C4—371no—
232C2×C4⋊C4—371no—
233C2×C4⋊C4—371no—
234C2×C4⋊C4—371no—
235C2×C4⋊C4—371no—
236C2×C4⋊C4—371no—
237C2×C4⋊C4—371no—
238C2×C22⋊C4—371no—
239C2×C22⋊C4—371no—
240C2×C22⋊C4—371no—
241C2×C22⋊C4—371no—
242C2×C22⋊C4—371no—
243C2×C22⋊C4—371no—
244C2×C22⋊C4—371no—
245C2×C22⋊C4—371no—
246C2×C42—371no—
247C2×C42—371no—
248C2×C42—371no—
249C2×C42—371no—
250C2×C42—371no—
251#95—371no—
252#95—371no—
253#95—371no—
254#95—371no—
255#95—371no—
256#95—371no—
257#95C2×D3711yescharacteristic
258#95C2×D3711yescharacteristic
259#95C2×D3711yescharacteristic
260#95C2×D3711yescharacteristic
261C24—371no—
262C24C22×D3711yescharacteristic
263C2×D4—374no—
264C2×D4—742no—
265C2×D4—742no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—371no—
275C22×C4—371no—
276C22×C4—371no—
277C22×C4—371no—
278C22×C4—371no—
279C22×C4—371no—
280C22×C4—371no—
281C22×C4—742no—
282C22×C4—742no—
283C22×C4—1481no—
284C22×C4C4×D3714yescomplemented
285C22×C4C22×D3711yescharacteristic
286C22×C4C22×D3711yescharacteristic
287C22×C4C22×D3711yescharacteristic
288C22×C4C22×D3711yescharacteristic
289C22×C4C22×D3711yescharacteristic
290C22×C4C22×D3711yescharacteristic
291C4⋊C4—374no—
292C4⋊C4—374no—
293C4⋊C4—742no—
294C4⋊C4—742no—
295C4⋊C4—742no—
296C4⋊C4—742no—
297C4⋊C4—1481no—
298C22⋊C4—374no—
299C22⋊C4—374no—
300C22⋊C4—374no—
301C22⋊C4—374no—
302C22⋊C4—742no—
303C22⋊C4—742no—
304C22⋊C4—742no—
305C22⋊C4—1481no—
306C42—742no—
307C42—742no—
308C42—742no—
309C42—742no—
310C42—1481no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—372no—
316C23—741no—
317C23—741no—
318C23—741no—
319C23—741no—
320C23—741no—
321C23—741no—
322C23C2×C4×D3712yes—
323C23D4×D3712yes—
324C23#1059696412yes—
325C23C23×D3711yescharacteristic
326D4—748no—
327C2×C4—28no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—372no—
345C2×C4—372no—
346C2×C4—372no—
347C2×C4—372no—
348C2×C4—372no—
349C2×C4—741no—
350C2×C4—741no—
351C2×C4—741no—
352C2×C4—741no—
353C2×C4—741no—
354C2×C4—741no—
355C2×C4—741no—
356C2×C4—741no—
357C2×C4—741no—
358C2×C4—741no—
359C2×C4—741no—
360C2×C4—741no—
361C2×C4—741no—
362C2×C4—741no—
363C2×C4—741no—
364C2×C4—741no—
365C2×C4—1484no—
366C2×C4C2×C4×D3712yes—
367C2×C4C2×C4×D3712yes—
368C2×C4#1059696212yes—
369C2×C4#1059696212yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—742no—
377C22—742no—
378C22—742no—
379C22—1481no—
380C22—1481no—
381C22—1481no—
382C22—1481no—
383C22#1192449614yes—
384C22C22×C4×D3711yescharacteristic
385C22C2×D4×D3711yescharacteristic
386C22C2×#1059696411yescharacteristic
387C22C2×#1059696211yescharacteristic
388C22C2×#1059696211yescharacteristic
389C22#1192458111yescharacteristic
390C22#1192458411yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—41no—
396C4—41no—
397C4—742no—
398C4—742no—
399C4—742no—
400C4—742no—
401C4—742no—
402C4—1481no—
403C4—1481no—
404C2—24no—
405C2—1482no—
406C2C2×#1192449611yescharacteristic
407C2C4×#1059696211yescharacteristic
408C2#1455801411yescharacteristic
409C2#1455817311yescharacteristic
410C2#1455818411yescharacteristic
411C2#1455820911yescharacteristic
412C2#1455821811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC2×#95×C37C2
socle, cosocleC23×C37C24
prime radicalC22×C22⋊D37C22
hypercenterC2×#95D37
hypocenterC37#2359
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×#11924495C2semidirect
4. #14557430C2semidirect
5. #14557425C2semidirect
6. #14557422C2semidirect
7. #14557420C2semidirect
8. #14557415C2semidirect
10. #14557407C2semidirect
11. #14557406C2semidirect
12. #14557384C2semidirect
13. C4×C22⋊Dic37C2semidirect
14. #14557380C2semidirect
15. C2×#95×C37C2semidirect
18. #11924519C4semidirect
64. C22×C4×C37C2×C4semidirect
85. C22⋊Dic37C2×C4semidirect
90. #10596938C2×C4semidirect
91. #10596938C2×C4semidirect
97. #10596936C2×C4semidirect
98. #10596936C2×C4semidirect
221. C2×#95D37semidirect
222. C37#2359semidirect
284. C22×C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245192
C2×C4×C22⋊D372
C2×#119244952
#145574302
#145574252
#145574222
#145574202
#145574152
#145574122
#145574072
#145574062
#145573842
C4×C22⋊Dic372
#145573802
C2×#95×C372
#235937