Finite Group Databasebeta

← #388×D37 #17997024

Subgroups — #388×D37 #17997024

Order 4736.

928 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D37C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D37C211yesmaximal, characteristic
3C2×C22⋊C4×D37C211yesmaximal, characteristic
4C2×C22⋊C4×D37C211yesmaximal, characteristic
5C2×C42×D37C211yesmaximal, characteristic, complemented
6#14557427C211yesmaximal, characteristic, complemented
7#14557426C211yesmaximal, characteristic, complemented
8#14557425C211yesmaximal, characteristic, complemented
9#14557424C211yesmaximal, characteristic, complemented
10#14557423C211yesmaximal, characteristic, complemented
11#14557422C211yesmaximal, characteristic, complemented
12#14557421C211yesmaximal, characteristic, complemented
13#95×D37C211yesmaximal, characteristic, complemented
14#95×D37C211yesmaximal, characteristic, complemented
15C37×#388C211yesmaximal, characteristic, complemented
16C24×D37C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18C22×C4×D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20C22×C4×D37C2211yescharacteristic
21C22×C4×D37C2211yescharacteristic
22C22×C4×D37C2211yescharacteristic
23C2×C4⋊Dic37C2211yescharacteristic, complemented
24C2×#10596936C2211yescharacteristic, complemented
25C2×#10596936C2211yescharacteristic, complemented
26C4⋊C4×D37—24no—
27C2×C22⋊Dic37C2211yescharacteristic
28C2×C22⋊Dic37C2211yescharacteristic
29C2×C22⋊Dic37C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C22⋊C4×D37—24no—
37C22⋊C4×D37—24no—
38C22⋊C4×D37C418yescomplemented
39C2×C4×Dic37C2211yescharacteristic, complemented
40C2×C4×Dic37C2211yescharacteristic, complemented
41C2×C4×Dic37C2211yescharacteristic, complemented
42C42×D37—24no—
43#11924443C2211yescharacteristic, complemented
44#11924443C2211yescharacteristic, complemented
45#11924443C2211yescharacteristic, complemented
46#11924443C2211yescharacteristic, complemented
47#11924443C2211yescharacteristic, complemented
48#11924443C2211yescharacteristic, complemented
49C2×C4⋊C4×C37C2211yescharacteristic, complemented
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52C2×C22⋊C4×C37C2211yescharacteristic
53C2×C42×C37C2211yescharacteristic, complemented
54#95×C37C2211yescharacteristic, complemented
55#95×C37C2211yescharacteristic, complemented
56C24×C37C2311yescharacteristic
57C23×D37—22no—
58C23×D37—22no—
59C23×D37—22no—
60C23×D37—22no—
61C23×D37—22no—
62C23×D37—22no—
63C23×D37C2×C414yes—
64C23×D37C2311yescharacteristic
65C23×D37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C22×C4×C37C2311yescharacteristic
72C22×Dic37C2311yescharacteristic
73C22×Dic37C2311yescharacteristic
74C22×Dic37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C2×C4×D37—22no—
79C2×C4×D37—22no—
80C2×C4×D37—22no—
81C2×C4×D37—22no—
82C2×C4×D37—22no—
83C2×C4×D37—22no—
84C2×C4×D37—22no—
85C2×C4×D37—22no—
86C2×C4×D37—22no—
87C2×C4×D37—22no—
88C2×C4×D37—22no—
89C2×C4×D37—22no—
90C2×C4×D37—22no—
91C2×C4×D37—22no—
92C2×C4×D37C2×C414yes—
93C2×C4×D37C2×C414yes—
94C2×C4×D37D414yes—
95C2×C4×D37D414yes—
96C4⋊C4×C37—22no—
97C22⋊C4×C37—22no—
98C22⋊C4×C37—22no—
99C22⋊C4×C37C2×C414yescomplemented
100C42×C37—22no—
101C22⋊Dic37—22no—
102C22⋊Dic37—22no—
103C22⋊Dic37C2×C414yescomplemented
104#10596938—22no—
105#10596938—22no—
106#10596938—22no—
107#10596938—22no—
108#10596938C2×C414yescomplemented
109#10596938C2×C414yescomplemented
110C4⋊Dic37—22no—
111#10596936—22no—
112#10596936—22no—
113C4×Dic37—22no—
114C4×Dic37—22no—
115C4×Dic37—22no—
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—28no—
131C22×D37—28no—
132C22×D37—28no—
133C22×D37—44no—
134C22×D37—44no—
135C22×D37—44no—
136C22×D37—44no—
137C22×D37C22×C412yes—
138C22×D37C22×C412yes—
139C22×D37C2×D412yes—
140C22×D37C2×D412yes—
141C22×D37#4112yes—
142C22×D37#4112yes—
143C22×D37#4112yes—
144C22×D37#4112yes—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—21no—
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×C37C22×C412yes—
160C2×C4×C37C22×C412yes—
161C2×C4×C37C2×D412yes—
162C2×C4×C37C2×D412yes—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—21no—
166C2×Dic37—21no—
167C2×Dic37—21no—
168C2×Dic37—21no—
169C2×Dic37—21no—
170C2×Dic37—21no—
171C2×Dic37—21no—
172C2×Dic37—21no—
173C2×Dic37—21no—
174C2×Dic37—21no—
175C2×Dic37—21no—
176C2×Dic37—21no—
177C2×Dic37C22×C412yes—
178C2×Dic37C22×C412yes—
179C2×Dic37C2×D412yes—
180C2×Dic37C2×D412yes—
181C4×D37—28no—
182C4×D37—28no—
183C4×D37—28no—
184C4×D37—28no—
185C4×D37—44no—
186C4×D37—44no—
187C22×C37—22no—
188C22×C37—22no—
189C22×C37—22no—
190C22×C37—41no—
191C22×C37—41no—
192C22×C37—41no—
193C22×C37—41no—
194C22×C37C23×C411yescharacteristic
195C22×C37C22×D411yescharacteristic
196C22×C37C22×D411yescharacteristic
197C22×C37C2×#4111yescharacteristic
198C22×C37C2×#4111yescharacteristic
199C22×C37C2×#4111yescharacteristic
200C22×C37C2×#4111yescharacteristic
201C2×D37—22no—
202C2×D37—22no—
203C2×D37—22no—
204C2×D37—41no—
205C2×D37—41no—
206C2×D37—41no—
207C2×D37—41no—
208C2×D37—416no—
209C2×D37#11714yes—
210C2×D37C4×D414yes—
211C2×D37C4×D414yes—
212C2×D37#12114yes—
213C2×D37#12314yes—
214C2×D37#12414yes—
215C2×D37#12614yes—
216C4×C37—22no—
217C4×C37—22no—
218C4×C37—22no—
219C4×C37—22no—
220C4×C37—41no—
221C4×C37—41no—
222Dic37—22no—
223Dic37—22no—
224Dic37—22no—
225Dic37—22no—
226Dic37—41no—
227Dic37—41no—
228C2×#388—371nomaximal, Sylow
229C2×C37—42no—
230C2×C37C2×#11711yescharacteristic
231C2×C37C2×C4×D411yescharacteristic
232C2×C37C2×C4×D411yescharacteristic
233C2×C37C2×#12111yescharacteristic
234C2×C37C2×#12311yescharacteristic
235C2×C37C2×#12411yescharacteristic
236C2×C37C2×#12611yescharacteristic
237D37—42no—
238D37#38818yesdirect product factor
239C22×C4⋊C4—371no—
240C22×C22⋊C4—371no—
241C22×C22⋊C4—371no—
242C22×C22⋊C4—371no—
243C22×C42—371no—
244#388—371no—
245#388—371no—
246#388—371no—
247#388—371no—
248#388—371no—
249#388—371no—
250#388—371no—
251#388D3711yescharacteristic, direct product factor
252C2×#95—371no—
253C2×#95—371no—
254C37C2×#38811yescharacteristic, complemented, Sylow
255C25—371no—
256C23×C4—371no—
257C23×C4—371no—
258C23×C4—371no—
259C23×C4—371no—
260C23×C4—371no—
261C23×C4—371no—
262C2×C4⋊C4—371no—
263C2×C4⋊C4—371no—
264C2×C4⋊C4—371no—
265C2×C4⋊C4—744no—
266C2×C4⋊C4C2×D3711yescharacteristic, complemented
267C2×C22⋊C4—371no—
268C2×C22⋊C4—371no—
269C2×C22⋊C4—371no—
270C2×C22⋊C4—378no—
271C2×C22⋊C4—371no—
272C2×C22⋊C4—371no—
273C2×C22⋊C4—371no—
274C2×C22⋊C4—371no—
275C2×C22⋊C4—371no—
276C2×C22⋊C4—371no—
277C2×C22⋊C4—744no—
278C2×C22⋊C4—744no—
279C2×C22⋊C4C2×D3711yescharacteristic
280C2×C22⋊C4C2×D3711yescharacteristic
281C2×C22⋊C4C2×D3711yescharacteristic
282C2×C42—371no—
283C2×C42—371no—
284C2×C42—371no—
285C2×C42—744no—
286C2×C42C2×D3711yescharacteristic, complemented
287#95—371no—
288#95—371no—
289#95—371no—
290#95—371no—
291#95—371no—
292#95—371no—
293#95C2×D3711yescharacteristic, complemented
294#95C2×D3711yescharacteristic, complemented
295C24—371no—
296C24—374no—
297C24—371no—
298C24—742no—
299C24—742no—
300C24—742no—
301C24—742no—
302C24—742no—
303C24—742no—
304C24C22×D3711yescharacteristic
305C22×C4—371no—
306C22×C4—371no—
307C22×C4—371no—
308C22×C4—371no—
309C22×C4—374no—
310C22×C4—374no—
311C22×C4—374no—
312C22×C4—374no—
313C22×C4—371no—
314C22×C4—371no—
315C22×C4—742no—
316C22×C4—742no—
317C22×C4—742no—
318C22×C4—742no—
319C22×C4—742no—
320C22×C4—742no—
321C22×C4—742no—
322C22×C4—742no—
323C22×C4—742no—
324C22×C4—742no—
325C22×C4—742no—
326C22×C4—742no—
327C22×C4—742no—
328C22×C4—742no—
329C22×C4C22×D3711yescharacteristic
330C22×C4C22×D3711yescharacteristic
331C22×C4C22×D3711yescharacteristic
332C22×C4C22×D3711yescharacteristic
333C22×C4C22×D3711yescharacteristic
334C22×C4C22×D3711yescharacteristic
335C4⋊C4—22no—
336C4⋊C4—742no—
337C4⋊C4—742no—
338C4⋊C4—742no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—374no—
342C22⋊C4—374no—
343C22⋊C4—374no—
344C22⋊C4—742no—
345C22⋊C4—742no—
346C22⋊C4—742no—
347C22⋊C4—742no—
348C22⋊C4—742no—
349C22⋊C4—742no—
350C22⋊C4C4×D3714yescomplemented
351C42—22no—
352C42—742no—
353C42—742no—
354C42—742no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—372no—
362C23—372no—
363C23—372no—
364C23—372no—
365C23—372no—
366C23—372no—
367C23—372no—
368C23—372no—
369C23—748no—
370C23—748no—
371C23—748no—
372C23—741no—
373C23—741no—
374C23—741no—
375C23—741no—
376C23—741no—
377C23—741no—
378C23—1484no—
379C23—1484no—
380C23—1484no—
381C23—1484no—
382C23C2×C4×D3712yes—
383C23C23×D3711yescharacteristic
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—372no—
399C2×C4—372no—
400C2×C4—372no—
401C2×C4—372no—
402C2×C4—748no—
403C2×C4—748no—
404C2×C4—748no—
405C2×C4—748no—
406C2×C4—741no—
407C2×C4—741no—
408C2×C4—741no—
409C2×C4—741no—
410C2×C4—741no—
411C2×C4—741no—
412C2×C4—741no—
413C2×C4—741no—
414C2×C4—741no—
415C2×C4—741no—
416C2×C4—741no—
417C2×C4—741no—
418C2×C4—741no—
419C2×C4—741no—
420C2×C4—1484no—
421C2×C4—1484no—
422C2×C4C2×C4×D3712yes—
423C2×C4C2×C4×D3712yes—
424C2×C4D4×D3712yes—
425C2×C4D4×D3712yes—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—374no—
434C22—374no—
435C22—374no—
436C22—374no—
437C22—374no—
438C22—374no—
439C22—374no—
440C22—742no—
441C22—742no—
442C22—742no—
443C22—14816no—
444C22—1481no—
445C22—1481no—
446C22—1481no—
447C22—1481no—
448C22C22×C4×D3711yescharacteristic
449C22C2×D4×D3711yescharacteristic
450C22C2×D4×D3711yescharacteristic
451C22#41×D3711yescharacteristic
452C22#41×D3711yescharacteristic
453C22#41×D3711yescharacteristic
454C22#41×D3711yescharacteristic
455C4—22no—
456C4—22no—
457C4—22no—
458C4—22no—
459C4—41no—
460C4—41no—
461C4—742no—
462C4—742no—
463C4—742no—
464C4—742no—
465C4—1481no—
466C4—1481no—
467C2—42no—
468C2—378no—
469C2—1482no—
470C2#117×D3711yescharacteristic
471C2C4×D4×D3711yescharacteristic
472C2C4×D4×D3711yescharacteristic
473C2#121×D3711yescharacteristic
474C2#123×D3711yescharacteristic
475C2#124×D3711yescharacteristic
476C2#126×D3711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#388C2
socle, cosocleC23×C37C24
prime radicalC24×D37C22
hypercenter#388D37
hypocenterC37C2×#388
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D37C2semidirect
5. C2×C42×D37C2semidirect
6. #14557427C2semidirect
7. #14557426C2semidirect
8. #14557425C2semidirect
9. #14557424C2semidirect
10. #14557423C2semidirect
11. #14557422C2semidirect
12. #14557421C2semidirect
13. #95×D37C2semidirect
14. #95×D37C2semidirect
15. C37×#388C2semidirect
23. C2×C4⋊Dic37C22semidirect
24. C2×#10596936C22semidirect
25. C2×#10596936C22semidirect
38. C22⋊C4×D37C4semidirect
39. C2×C4×Dic37C22semidirect
40. C2×C4×Dic37C22semidirect
41. C2×C4×Dic37C22semidirect
43. #11924443C22semidirect
44. #11924443C22semidirect
45. #11924443C22semidirect
46. #11924443C22semidirect
47. #11924443C22semidirect
48. #11924443C22semidirect
49. C2×C4⋊C4×C37C22semidirect
53. C2×C42×C37C22semidirect
54. #95×C37C22semidirect
55. #95×C37C22semidirect
99. C22⋊C4×C37C2×C4semidirect
103. C22⋊Dic37C2×C4semidirect
108. #10596938C2×C4semidirect
109. #10596938C2×C4semidirect
238. D37#388direct (N × H)
251. #388D37direct (N × H)
254. C37C2×#388semidirect
266. C2×C4⋊C4C2×D37semidirect
286. C2×C42C2×D37semidirect
293. #95C2×D37semidirect
294. #95C2×D37semidirect
350. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D372
C2×C22⋊C4×D372
C2×C42×D372
#145574272
#145574262
#145574252
#145574242
#145574232
#145574222
#145574212
#95×D372
C37×#3882
C2×#38837