Finite Group Databasebeta

← #17997249

Subgroups — #17997249

Order 4736.

808 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924506C211yesmaximal, characteristic
2C2×#11924498C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D37C211yesmaximal, characteristic, complemented
4#14557435C211yesmaximal, characteristic, complemented
5#14557433C211yesmaximal, characteristic, complemented
6#14557426C211yesmaximal, characteristic, complemented
7#14557423C211yesmaximal, characteristic, complemented
8#14557422C211yesmaximal, characteristic, complemented
9#14557411C211yesmaximal, characteristic, complemented
10#14557411C211yesmaximal, characteristic, complemented
11#14557409C211yesmaximal, characteristic, complemented
12#14557407C211yesmaximal, characteristic, complemented
13#14557388C211yesmaximal, characteristic, complemented
14C4×#10596938C211yesmaximal, characteristic, complemented
15C37×#388C211yesmaximal, characteristic, complemented
16C24×D37C2211yescharacteristic
17C22×D148C2211yescharacteristic
18C22×D148C2211yescharacteristic
19C22×C22⋊D37C2211yescharacteristic
20C22×C4×D37C2211yescharacteristic
21C22×C4×D37C2211yescharacteristic
22C22×C4×D37C2211yescharacteristic, complemented
23#11924506C418yescomplemented
24#11924498—24no—
25C2×C4⋊Dic37C2211yescharacteristic, complemented
26C2×#10596936C2211yescharacteristic, complemented
27C2×C22⋊Dic37C2211yescharacteristic
28C2×C22⋊Dic37C2211yescharacteristic
29C2×#10596938C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C2×#10596938C2211yescharacteristic
37C2×#10596938C2211yescharacteristic, complemented
38C2×#10596938C2211yescharacteristic, complemented
39C2×#10596938C2211yescharacteristic, complemented
40C22⋊C4×D37—24no—
41C2×C4×Dic37C2211yescharacteristic, complemented
42C2×C4×Dic37C2211yescharacteristic, complemented
43#11924443C2211yescharacteristic, complemented
44#11924443C2211yescharacteristic, complemented
45#11924443C2211yescharacteristic, complemented
46#11924443C2211yescharacteristic, complemented
47C2×C4⋊C4×C37C2211yescharacteristic, complemented
48C2×C22⋊C4×C37C2211yescharacteristic
49C2×C22⋊C4×C37C2211yescharacteristic
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C42×C37C2211yescharacteristic, complemented
52#95×C37C2211yescharacteristic, complemented
53#95×C37C2211yescharacteristic, complemented
54C24×C37C2311yescharacteristic
55C23×D37—22no—
56C23×D37—22no—
57C23×D37—41no—
58C23×D37—41no—
59C23×D37—41no—
60C23×D37—41no—
61C23×D37C2×C414yescomplemented
62C23×D37C2311yescharacteristic
63C23×D37C2311yescharacteristic
64C23×D37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C2×C22⋊D37—41no—
72C2×C22⋊D37—41no—
73C2×C22⋊D37C2×C414yescomplemented
74C22×Dic37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C2×D148—22no—
80C2×D148—22no—
81C2×D148—41no—
82C2×D148—41no—
83C2×D148C2×C414yes—
84C2×D148C2×C414yescomplemented
85C2×C4×D37—22no—
86C2×C4×D37—22no—
87C2×C4×D37—41no—
88C2×C4×D37—41no—
89C2×C4×D37—41no—
90C2×C4×D37—41no—
91C2×C4×D37—41no—
92C2×C4×D37—41no—
93C2×C4×D37D414yescomplemented
94C4⋊C4×C37—22no—
95C22⋊C4×C37—22no—
96C22⋊C4×C37—41no—
97C22⋊C4×C37C2×C414yescomplemented
98C42×C37—41no—
99C22⋊Dic37—22no—
100C22⋊Dic37—41no—
101#10596938—22no—
102#10596938—22no—
103#10596938—22no—
104#10596938—22no—
105#10596938—22no—
106#10596938—41no—
107#10596938—41no—
108#10596938—41no—
109#10596938—41no—
110#10596938C2×C414yescomplemented
111#10596938C2×C414yescomplemented
112C4⋊Dic37—41no—
113#10596936—41no—
114C4×Dic37—22no—
115C4×Dic37—41no—
116C23×C37—21no—
117C23×C37—21no—
118C23×C37—21no—
119C23×C37—21no—
120C23×C37—21no—
121C23×C37—21no—
122C23×C37C22×C412yes—
123C23×C37C2411yescharacteristic
124C22×D37—21no—
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—21no—
130C22×D37—21no—
131C22×D37—21no—
132C22×D37—21no—
133C22×D37—21no—
134C22×D37—21no—
135C22×D37—21no—
136C22×D37—21no—
137C22×D37—21no—
138C22×D37—21no—
139C22×D37—21no—
140C22×D37—28no—
141C22×D37—44no—
142C22×D37—44no—
143C22×D37—44no—
144C22×D37—44no—
145C22×D37—44no—
146C22×D37—44no—
147C22×D37C22×C412yes—
148C22×D37C22×C412yes—
149C22×D37C22×C412yes—
150C22×D37C2×D412yes—
151C22×D37#4112yes—
152C2×C4×C37—21no—
153C2×C4×C37—21no—
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37—21no—
159C2×C4×C37—21no—
160C2×C4×C37—21no—
161C2×C4×C37—21no—
162C2×C4×C37—21no—
163C2×C4×C37—21no—
164C2×C4×C37—21no—
165C2×C4×C37—21no—
166C2×C4×C37—21no—
167C2×C4×C37C22×C412yes—
168C2×C4×C37C22×C412yes—
169C2×C4×C37C2×D412yes—
170C22⋊D37—44no—
171C2×Dic37—21no—
172C2×Dic37—21no—
173C2×Dic37—21no—
174C2×Dic37—21no—
175C2×Dic37—21no—
176C2×Dic37—21no—
177C2×Dic37—21no—
178C2×Dic37—21no—
179C2×Dic37—21no—
180C2×Dic37—21no—
181C2×Dic37—21no—
182C2×Dic37—21no—
183C2×Dic37—21no—
184C2×Dic37C22×C412yes—
185C2×Dic37C2×D412yes—
186D148—28no—
187D148—44no—
188C4×D37—44no—
189C4×D37—44no—
190C4×D37—44no—
191C22×C37—22no—
192C22×C37—22no—
193C22×C37—22no—
194C22×C37—41no—
195C22×C37—41no—
196C22×C37—41no—
197C22×C37—41no—
198C22×C37C23×C411yescharacteristic
199C22×C37C22×D411yescharacteristic
200C22×C37C2×#4111yescharacteristic
201C22×C37H(5,𝔽2)11yescharacteristic
202C22×C37H(5,𝔽2)11yescharacteristic
203C22×C37H(5,𝔽2)11yescharacteristic
204C22×C37H(5,𝔽2)11yescharacteristic
205C2×D37—22no—
206C2×D37—22no—
207C2×D37—22no—
208C2×D37—22no—
209C2×D37—22no—
210C2×D37—22no—
211C2×D37—22no—
212C2×D37—22no—
213C2×D37—22no—
214C2×D37—22no—
215C2×D37—22no—
216C2×D37—22no—
217C2×D37—416no—
218C2×D37—41no—
219C2×D37—41no—
220C2×D37—41no—
221C2×D37—41no—
222C2×D37—41no—
223C2×D37—41no—
224C2×D37—41no—
225C2×D37—41no—
226C2×D37C4×D414yes—
227C4×C37—22no—
228C4×C37—22no—
229C4×C37—22no—
230C4×C37—41no—
231C4×C37—41no—
232C4×C37—41no—
233Dic37—22no—
234Dic37—22no—
235Dic37—41no—
236Dic37—41no—
237Dic37—41no—
238#2321—371nomaximal, Sylow
239C2×C37—42no—
240C2×C37C2×C4×D411yescharacteristic
241C2×C37#51811yescharacteristic
242C2×C37#51811yescharacteristic
243C2×C37#53411yescharacteristic
244C2×C37#53511yescharacteristic
245C2×C37#53811yescharacteristic
246C2×C37#53811yescharacteristic
247D37—24no—
248D37—42no—
249D37—42no—
250C2×#120—371no—
251C2×C4×D4—371no—
252C22×C22⋊C4—371no—
253#390—371no—
254#390—371no—
255#388—371no—
256#388—371no—
257#388—371no—
258#388D3711yescharacteristic, complemented
259#386—371no—
260#386—371no—
261#386—371no—
262#385—371no—
263#379—371no—
264C4×C22⋊C4—371no—
265C37#232111yescharacteristic, complemented, Sylow
266C25—371no—
267C22×D4—371no—
268C22×D4—371no—
269C22×D4—371no—
270C23×C4—371no—
271C23×C4—371no—
272C23×C4—371no—
273#120—378no—
274C4×D4—744no—
275C2×C4⋊C4—371no—
276C2×C4⋊C4—371no—
277C2×C4⋊C4C2×D3711yescharacteristic, complemented
278C2×C22⋊C4—371no—
279C2×C22⋊C4—371no—
280C2×C22⋊C4—371no—
281C2×C22⋊C4—371no—
282C2×C22⋊C4—371no—
283C2×C22⋊C4—371no—
284C2×C22⋊C4—371no—
285C2×C22⋊C4—371no—
286C2×C22⋊C4—371no—
287C2×C22⋊C4—371no—
288C2×C22⋊C4—371no—
289C2×C22⋊C4—371no—
290C2×C22⋊C4—371no—
291C2×C22⋊C4—744no—
292C2×C22⋊C4C2×D3711yescharacteristic
293C2×C22⋊C4C2×D3711yescharacteristic
294C2×C22⋊C4C2×D3711yescharacteristic
295C2×C42—371no—
296C2×C42—371no—
297C2×C42C2×D3711yescharacteristic, complemented
298#95—371no—
299#95—371no—
300#95—371no—
301#95—371no—
302#95C2×D3711yescharacteristic, complemented
303#95C2×D3711yescharacteristic, complemented
304C24—371no—
305C24—371no—
306C24—371no—
307C24—374no—
308C24—742no—
309C24—742no—
310C24—1481no—
311C24—1481no—
312C24—1481no—
313C24—1481no—
314C24C22×D3711yescharacteristic
315C2×D4—374no—
316C2×D4—374no—
317C2×D4—374no—
318C2×D4—742no—
319C2×D4—742no—
320C2×D4—1481no—
321C2×D4—1481no—
322C2×D4—1481no—
323C2×D4—1481no—
324C22×C4—371no—
325C22×C4—371no—
326C22×C4—374no—
327C22×C4—371no—
328C22×C4—371no—
329C22×C4—371no—
330C22×C4—742no—
331C22×C4—742no—
332C22×C4—1481no—
333C22×C4—1481no—
334C22×C4—1481no—
335C22×C4—1481no—
336C22×C4—1481no—
337C22×C4—1481no—
338C22×C4C22×D3711yescharacteristic
339C22×C4C22×D3711yescharacteristic
340C22×C4C22×D3711yescharacteristic
341C22×C4C22×D3711yescharacteristic
342C22×C4C22×D3711yescharacteristic
343C22×C4C22×D3711yescharacteristic
344C4⋊C4—22no—
345C4⋊C4—1481no—
346C4⋊C4—1481no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—374no—
350C22⋊C4—374no—
351C22⋊C4—742no—
352C22⋊C4—742no—
353C22⋊C4—742no—
354C22⋊C4—742no—
355C22⋊C4—742no—
356C22⋊C4—742no—
357C22⋊C4—1481no—
358C22⋊C4—1481no—
359C22⋊C4—1481no—
360C22⋊C4—1481no—
361C22⋊C4—1481no—
362C22⋊C4C4×D3714yescomplemented
363C42—41no—
364C42—742no—
365C42—1481no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—372no—
373C23—372no—
374C23—372no—
375C23—372no—
376C23—372no—
377C23—748no—
378C23—741no—
379C23—741no—
380C23—741no—
381C23—741no—
382C23—741no—
383C23—741no—
384C23—741no—
385C23—741no—
386C23—741no—
387C23—741no—
388C23—741no—
389C23—741no—
390C23—741no—
391C23—741no—
392C23—741no—
393C23—741no—
394C23—1484no—
395C23—1484no—
396C23—1484no—
397C23—1484no—
398C23—1484no—
399C23—1484no—
400C23C2×C4×D3712yes—
401C23C23×D3711yescharacteristic
402D4—748no—
403D4—1484no—
404D4—1484no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—372no—
421C2×C4—372no—
422C2×C4—741no—
423C2×C4—741no—
424C2×C4—741no—
425C2×C4—741no—
426C2×C4—741no—
427C2×C4—741no—
428C2×C4—741no—
429C2×C4—741no—
430C2×C4—741no—
431C2×C4—741no—
432C2×C4—741no—
433C2×C4—741no—
434C2×C4—741no—
435C2×C4—1484no—
436C2×C4—1484no—
437C2×C4—1484no—
438C2×C4C2×C4×D3712yes—
439C2×C4C2×C4×D3712yes—
440C2×C4D4×D3712yes—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—374no—
449C22—742no—
450C22—742no—
451C22—742no—
452C22—742no—
453C22—742no—
454C22—742no—
455C22—742no—
456C22—742no—
457C22—742no—
458C22—742no—
459C22—742no—
460C22—742no—
461C22—14816no—
462C22—1481no—
463C22—1481no—
464C22—1481no—
465C22—1481no—
466C22—1481no—
467C22—1481no—
468C22—1481no—
469C22—1481no—
470C22C22×C4×D3711yescharacteristic
471C22C2×D4×D3711yescharacteristic
472C22#41×D3711yescharacteristic
473C22#1192458111yescharacteristic
474C22#1192458211yescharacteristic
475C22#1192458211yescharacteristic
476C22#1192458211yescharacteristic
477C4—22no—
478C4—22no—
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—742no—
484C4—742no—
485C4—1481no—
486C4—1481no—
487C4—1481no—
488C2—42no—
489C2—744no—
490C2—1482no—
491C2—1482no—
492C2C4×D4×D3711yescharacteristic
493C2#1455800511yescharacteristic
494C2#1455800711yescharacteristic
495C2#1455809111yescharacteristic
496C2#1455810111yescharacteristic
497C2#1455811911yescharacteristic
498C2#1455812211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#388C2
socle, cosocleC23×C37C24
prime radicalC2×#11924506C2
hypercenter#388D37
hypocenterC37#2321
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#11924498C2semidirect
3. C2×C22⋊C4×D37C2semidirect
4. #14557435C2semidirect
5. #14557433C2semidirect
6. #14557426C2semidirect
7. #14557423C2semidirect
8. #14557422C2semidirect
9. #14557411C2semidirect
10. #14557411C2semidirect
11. #14557409C2semidirect
12. #14557407C2semidirect
13. #14557388C2semidirect
14. C4×#10596938C2semidirect
15. C37×#388C2semidirect
22. C22×C4×D37C22semidirect
23. #11924506C4semidirect
25. C2×C4⋊Dic37C22semidirect
26. C2×#10596936C22semidirect
37. C2×#10596938C22semidirect
38. C2×#10596938C22semidirect
39. C2×#10596938C22semidirect
41. C2×C4×Dic37C22semidirect
42. C2×C4×Dic37C22semidirect
43. #11924443C22semidirect
44. #11924443C22semidirect
45. #11924443C22semidirect
46. #11924443C22semidirect
47. C2×C4⋊C4×C37C22semidirect
51. C2×C42×C37C22semidirect
52. #95×C37C22semidirect
53. #95×C37C22semidirect
61. C23×D37C2×C4semidirect
73. C2×C22⋊D37C2×C4semidirect
84. C2×D148C2×C4semidirect
93. C2×C4×D37D4semidirect
97. C22⋊C4×C37C2×C4semidirect
110. #10596938C2×C4semidirect
111. #10596938C2×C4semidirect
258. #388D37semidirect
265. C37#2321semidirect
277. C2×C4⋊C4C2×D37semidirect
297. C2×C42C2×D37semidirect
302. #95C2×D37semidirect
303. #95C2×D37semidirect
362. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245062
C2×#119244982
C2×C22⋊C4×D372
#145574352
#145574332
#145574262
#145574232
#145574222
#145574112
#145574092
#145574072
#145573882
C4×#105969382
C37×#3882
#232137