Finite Group Databasebeta

← C137×#19465 #46868851

Subgroups — C137×#19465 #46868851

Order 35072.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3226×C137C211yesmaximal, characteristic, complemented
2#3109×C137C211yesmaximal, characteristic
3C2×#476×C137C211yesmaximal, characteristic, complemented
4#2974×C137C211yesmaximal, characteristic, complemented
5#1697×C137C212yesmaximal, complemented
6#1695×C137C212yesmaximal, complemented
7#1677×C137C212yesmaximal, complemented
8#1675×C137C212yesmaximal, complemented
9#1573×C137C211yesmaximal, characteristic, complemented
10#1558×C137C211yesmaximal, characteristic, complemented
11#1551×C137C211yesmaximal, characteristic, complemented
12#532×C137C2211yescharacteristic
13C2×C4⋊Q8×C137C2211yescharacteristic
14C2×C4×D4×C137C2211yescharacteristic
15#500×C137C2212yescomplemented
16#486×C137C2212yescomplemented
17#481×C137—21no—
18#480×C137—21no—
19#480×C137—21no—
20#476×C137—21no—
21#476×C137—21no—
22#476×C137C2212yes—
23#476×C137C2212yes—
24#476×C137C2211yescharacteristic
25#476×C137C2211yescharacteristic
26#474×C137—22no—
27#459×C137C2211yescharacteristic
28#459×C137C2211yescharacteristic
29#447×C137—21no—
30#442×C137—21no—
31#442×C137—21no—
32#436×C137C2212yes—
33#435×C137—22no—
34C8×D4×C137C2212yes—
35#432×C137C2211yescharacteristic
36#432×C137C2211yescharacteristic
37#431×C137C2211yescharacteristic
38C2×#106×C137—21no—
39C2×C4⋊C8×C137C2211yescharacteristic
40C2×#102×C137—21no—
41#407×C137—21no—
42C2×C22⋊C8×C137—21no—
43#335×C137C2212yescomplemented
44#334×C137C2212yescomplemented
45#333×C137C2212yescomplemented
46#333×C137C2212yescomplemented
47#333×C137C2212yescomplemented
48#331×C137C2212yescomplemented
49C2×#41×C137—21no—
50C22×Q8×C137—21no—
51C22×D4×C137D411yescharacteristic
52C23×C4×C137—21no—
53C2×D8×C137—21no—
54C2×D8×C137—21no—
55C2×M16×C137—22no—
56C22×C8×C137—21no—
57C22×C8×C137—22no—
58C4⋊Q8×C137—21no—
59C4⋊Q8×C137—21no—
60C4⋊Q8×C137—21no—
61C4⋊Q8×C137C2312yes—
62C4⋊Q8×C137C2311yescharacteristic
63#127×C137C2311yescharacteristic
64#124×C137—21no—
65#121×C137—21no—
66#121×C137—21no—
67C4×D4×C137—21no—
68C4×D4×C137—21no—
69C4×D4×C137—21no—
70C4×D4×C137—21no—
71C4×D4×C137D411yescharacteristic
72C4×D4×C137D411yescharacteristic
73C4×D4×C137C2311yescharacteristic
74C4×D4×C137C2311yescharacteristic
75C2×C4⋊C4×C137—21no—
76C2×C4⋊C4×C137—21no—
77C2×C4⋊C4×C137D411yescharacteristic
78C2×C22⋊C4×C137—21no—
79C2×C42×C137C2311yescharacteristic
80#107×C137—22no—
81#107×C137—22no—
82#106×C137—22no—
83#106×C137—22no—
84#106×C137—21no—
85#106×C137—21no—
86C4⋊C8×C137—21no—
87C4⋊C8×C137D412yes—
88C4⋊C8×C137C2312yes—
89C4⋊C8×C137C2312yes—
90C4⋊C8×C137C2311yescharacteristic
91C4⋊C8×C137C2311yescharacteristic
92#102×C137—22no—
93#102×C137—22no—
94#102×C137—21no—
95#102×C137—21no—
96#102×C137—22no—
97#102×C137—22no—
98#102×C137—21no—
99#102×C137—21no—
100C22⋊C8×C137—21no—
101C22⋊C8×C137—21no—
102C22⋊C8×C137—22no—
103C22⋊C8×C137—22no—
104C22⋊C8×C137D411yescharacteristic
105C22⋊C8×C137D411yescharacteristic
106#97×C137—21no—
107#97×C137—21no—
108C4×C8×C137C2312yes—
109C24×C137—21no—
110#41×C137—82no—
111C2×Q8×C137—21no—
112C2×Q8×C137—22no—
113C2×Q8×C137—41no—
114C2×Q8×C137—82no—
115C2×D4×C137—22no—
116C2×D4×C137—21no—
117C2×D4×C137—21no—
118C2×D4×C137—21no—
119C2×D4×C137—21no—
120C2×D4×C137—41no—
121C2×D4×C137—41no—
122C2×D4×C137C2×D411yescharacteristic
123C2×D4×C137C2×D411yescharacteristic
124C22×C4×C137—21no—
125C22×C4×C137—21no—
126C22×C4×C137—21no—
127C22×C4×C137—21no—
128C22×C4×C137—21no—
129C22×C4×C137—41no—
130C22×C4×C137—41no—
131C22×C4×C137—82no—
132C22×C4×C137C2×D411yescharacteristic
133C22×C4×C137C2×D411yescharacteristic
134C22×C4×C137#4111yescharacteristic
135D8×C137—42no—
136D8×C137—42no—
137M16×C137—82no—
138C2×C8×C137—22no—
139C2×C8×C137—21no—
140C2×C8×C137—21no—
141C2×C8×C137—22no—
142C2×C8×C137—42no—
143C2×C8×C137—82no—
144C2×C8×C137C2×D412yes—
145C2×C8×C137C2×D412yes—
146C4⋊C4×C137—21no—
147C4⋊C4×C137—22no—
148C4⋊C4×C137—21no—
149C4⋊C4×C137—22no—
150C4⋊C4×C137—21no—
151C4⋊C4×C137—41no—
152C4⋊C4×C137—41no—
153C4⋊C4×C137C2×D411yescharacteristic
154C4⋊C4×C137C2×D411yescharacteristic
155C22⋊C4×C137—21no—
156C22⋊C4×C137—21no—
157C22⋊C4×C137—21no—
158C22⋊C4×C137—21no—
159C22⋊C4×C137—41no—
160C22⋊C4×C137—41no—
161C42×C137C2×D411yescharacteristic
162C42×C137C2×D411yescharacteristic
163C42×C137#4111yescharacteristic
164C42×C137C2411yescharacteristic
165C23×C137—21no—
166C23×C137—21no—
167C23×C137—42no—
168C23×C137—42no—
169C23×C137—41no—
170C23×C137—81no—
171C23×C137#12111yescharacteristic
172Q8×C137—82no—
173Q8×C137—81no—
174Q8×C137—82no—
175D4×C137—21no—
176D4×C137—21no—
177D4×C137—21no—
178D4×C137—42no—
179D4×C137—41no—
180D4×C137—41no—
181D4×C137—42no—
182D4×C137—81no—
183D4×C137—82no—
184D4×C137#13712yes—
185C2×C4×C137—22no—
186C2×C4×C137—21no—
187C2×C4×C137—21no—
188C2×C4×C137—22no—
189C2×C4×C137—21no—
190C2×C4×C137—21no—
191C2×C4×C137—42no—
192C2×C4×C137—42no—
193C2×C4×C137—41no—
194C2×C4×C137—42no—
195C2×C4×C137—81no—
196C2×C4×C137—81no—
197C2×C4×C137—82no—
198C2×C4×C137—81no—
199C2×C4×C137—82no—
200C2×C4×C137#12111yescharacteristic
201C2×C4×C137#12111yescharacteristic
202C2×C4×C137#12111yescharacteristic
203C2×C4×C137C22×D411yescharacteristic
204C2×C4×C137C22×D411yescharacteristic
205C2×C4×C137C2×#4111yescharacteristic
206C8×C137—22no—
207C8×C137—22no—
208C8×C137—41no—
209C8×C137—42no—
210C8×C137—41no—
211C8×C137—42no—
212C22×C137—21no—
213C22×C137—21no—
214C22×C137—22no—
215C22×C137—41no—
216C22×C137—41no—
217C22×C137—41no—
218C22×C137—41no—
219C22×C137—41no—
220C22×C137—84no—
221C22×C137—81no—
222C22×C137—81no—
223C22×C137—81no—
224C22×C137#47212yes—
225C22×C137C2×#12111yescharacteristic
226C4×C137—21no—
227C4×C137—21no—
228C4×C137—21no—
229C4×C137—21no—
230C4×C137—41no—
231C4×C137—41no—
232C4×C137—81no—
233C4×C137—82no—
234C4×C137C2×#13711yescharacteristic
235C4×C137#57511yescharacteristic
236C4×C137#57712yes—
237C2×C137—22no—
238C2×C137—42no—
239C2×C137—81no—
240C2×C137—161no—
241C2×C137#304211yescharacteristic
242C2×C137#305611yescharacteristic
243C2×C137C2×#47211yescharacteristic
244#19465C13711yesmaximal, characteristic, direct product factor, Sylow
245C137#1946511yescharacteristic, direct product factor, Sylow
246#3226C2×C13711yescharacteristic, complemented
247#3109C2×C13711yescharacteristic
248C2×#476C2×C13711yescharacteristic, complemented
249#2974C2×C13711yescharacteristic, complemented
250#1697C2×C13712yescomplemented
251#1695C2×C13712yescomplemented
252#1677C2×C13712yescomplemented
253#1675C2×C13712yescomplemented
254#1573C2×C13711yescharacteristic, complemented
255#1558C2×C13711yescharacteristic, complemented
256#1551C2×C13711yescharacteristic, complemented
257#532C22×C13711yescharacteristic
258C2×C4⋊Q8C22×C13711yescharacteristic
259C2×C4×D4C22×C13711yescharacteristic
260#500C22×C13712yescomplemented
261#486C22×C13712yescomplemented
262#481—21no—
263#480—21no—
264#480—21no—
265#476—21no—
266#476—21no—
267#476C22×C13711yescharacteristic
268#476C22×C13711yescharacteristic
269#476C22×C13712yes—
270#476C22×C13712yes—
271#474—22no—
272#459C22×C13711yescharacteristic
273#459C22×C13711yescharacteristic
274#447—21no—
275#442—21no—
276#442—21no—
277#436C22×C13712yes—
278#435—22no—
279C8×D4C22×C13712yes—
280#432C22×C13711yescharacteristic
281#432C22×C13711yescharacteristic
282#431C22×C13711yescharacteristic
283C2×#106—21no—
284C2×C4⋊C8C22×C13711yescharacteristic
285C2×#102—21no—
286#407—21no—
287C2×C22⋊C8—21no—
288#335C22×C13712yescomplemented
289#334C22×C13712yescomplemented
290#333C22×C13712yescomplemented
291#333C22×C13712yescomplemented
292#333C22×C13712yescomplemented
293#331C22×C13712yescomplemented
294C2×#41—21no—
295C22×Q8—21no—
296C22×D4D4×C13711yescharacteristic
297C23×C4—21no—
298C2×D8—21no—
299C2×D8—21no—
300C2×M16—22no—
301C22×C8—21no—
302C22×C8—22no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C23×C13712yes—
307C4⋊Q8C23×C13711yescharacteristic
308#127C23×C13711yescharacteristic
309#124—21no—
310#121—21no—
311#121—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4D4×C13711yescharacteristic
317C4×D4D4×C13711yescharacteristic
318C4×D4C23×C13711yescharacteristic
319C4×D4C23×C13711yescharacteristic
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C13711yescharacteristic
323C2×C22⋊C4—21no—
324C2×C42C23×C13711yescharacteristic
325#107—22no—
326#107—22no—
327#106—22no—
328#106—22no—
329#106—21no—
330#106—21no—
331C4⋊C8—21no—
332C4⋊C8D4×C13712yes—
333C4⋊C8C23×C13712yes—
334C4⋊C8C23×C13712yes—
335C4⋊C8C23×C13711yescharacteristic
336C4⋊C8C23×C13711yescharacteristic
337#102—22no—
338#102—22no—
339#102—21no—
340#102—21no—
341#102—22no—
342#102—22no—
343#102—21no—
344#102—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—22no—
348C22⋊C8—22no—
349C22⋊C8D4×C13711yescharacteristic
350C22⋊C8D4×C13711yescharacteristic
351#97—21no—
352#97—21no—
353C4×C8C23×C13712yes—
354C24—21no—
355#41—82no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—82no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4C2×D4×C13711yescharacteristic
368C2×D4C2×D4×C13711yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—82no—
377C22×C4C2×D4×C13711yescharacteristic
378C22×C4C2×D4×C13711yescharacteristic
379C22×C4#41×C13711yescharacteristic
380D8—42no—
381D8—42no—
382M16—82no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—82no—
389C2×C8C2×D4×C13712yes—
390C2×C8C2×D4×C13712yes—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C13711yescharacteristic
399C4⋊C4C2×D4×C13711yescharacteristic
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42C2×D4×C13711yescharacteristic
407C42C2×D4×C13711yescharacteristic
408C42#41×C13711yescharacteristic
409C42C24×C13711yescharacteristic
410C23—21no—
411C23—21no—
412C23—42no—
413C23—42no—
414C23—41no—
415C23—81no—
416C23#121×C13711yescharacteristic
417Q8—82no—
418Q8—81no—
419Q8—82no—
420D4—21no—
421D4—21no—
422D4—21no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—42no—
427D4—81no—
428D4—82no—
429D4#137×C13712yes—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4—81no—
444C2×C4—82no—
445C2×C4#121×C13711yescharacteristic
446C2×C4#121×C13711yescharacteristic
447C2×C4#121×C13711yescharacteristic
448C2×C4C22×D4×C13711yescharacteristic
449C2×C4C22×D4×C13711yescharacteristic
450C2×C4C2×#41×C13711yescharacteristic
451C8—22no—
452C8—22no—
453C8—41no—
454C8—42no—
455C8—41no—
456C8—42no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—84no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22#472×C13712yes—
470C22C2×#121×C13711yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4C2×#137×C13711yescharacteristic
480C4#575×C13711yescharacteristic
481C4#577×C13712yes—
482C2—22no—
483C2—42no—
484C2—81no—
485C2—161no—
486C2#3042×C13711yescharacteristic
487C2#3056×C13711yescharacteristic
488C2C2×#472×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#3109×C137C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3226×C137C2semidirect
3. C2×#476×C137C2semidirect
4. #2974×C137C2semidirect
5. #1697×C137C2semidirect
6. #1695×C137C2semidirect
7. #1677×C137C2semidirect
8. #1675×C137C2semidirect
9. #1573×C137C2semidirect
10. #1558×C137C2semidirect
11. #1551×C137C2semidirect
15. #500×C137C22semidirect
16. #486×C137C22semidirect
43. #335×C137C22semidirect
44. #334×C137C22semidirect
45. #333×C137C22semidirect
46. #333×C137C22semidirect
47. #333×C137C22semidirect
48. #331×C137C22semidirect
244. #19465C137direct (N × H)
245. C137#19465direct (N × H)
246. #3226C2×C137semidirect
248. C2×#476C2×C137semidirect
249. #2974C2×C137semidirect
250. #1697C2×C137semidirect
251. #1695C2×C137semidirect
252. #1677C2×C137semidirect
253. #1675C2×C137semidirect
254. #1573C2×C137semidirect
255. #1558C2×C137semidirect
256. #1551C2×C137semidirect
260. #500C22×C137semidirect
261. #486C22×C137semidirect
288. #335C22×C137semidirect
289. #334C22×C137semidirect
290. #333C22×C137semidirect
291. #333C22×C137semidirect
292. #333C22×C137semidirect
293. #331C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3226×C1372
#3109×C1372
C2×#476×C1372
#2974×C1372
#1697×C1372
#1695×C1372
#1677×C1372
#1675×C1372
#1573×C1372
#1558×C1372
#1551×C1372
#19465137