Finite Group Databasebeta

← C137×#19583 #46868969

Subgroups — C137×#19583 #46868969

Order 35072.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3248×C137C211yesmaximal, characteristic
2#3239×C137C211yesmaximal, characteristic
3#3209×C137C211yesmaximal, characteristic, complemented
4#2994×C137C211yesmaximal, characteristic
5#1700×C137C211yesmaximal, characteristic, complemented
6#1699×C137C211yesmaximal, characteristic, complemented
7#1690×C137C211yesmaximal, characteristic, complemented
8#1689×C137C211yesmaximal, characteristic, complemented
9#1680×C137C211yesmaximal, characteristic, complemented
10#1679×C137C211yesmaximal, characteristic, complemented
11#1670×C137C211yesmaximal, characteristic, complemented
12#1669×C137C211yesmaximal, characteristic, complemented
13#1573×C137C211yesmaximal, characteristic, complemented
14#1552×C137C211yesmaximal, characteristic, complemented
15C2×#332×C137C211yesmaximal, characteristic, complemented
16#533×C137C2211yescharacteristic
17C2×C4⋊Q8×C137C2211yescharacteristic
18#529×C137C2211yescharacteristic
19#501×C137—21no—
20#494×C137C2211yescharacteristic
21#494×C137C2211yescharacteristic
22#489×C137—21no—
23#487×C137C2211yescharacteristic
24#487×C137C2211yescharacteristic
25#484×C137—21no—
26#481×C137—21no—
27#479×C137—21no—
28#475×C137C2211yescharacteristic
29#475×C137C2211yescharacteristic
30#475×C137C2211yescharacteristic
31#474×C137C2211yescharacteristic
32#474×C137C2211yescharacteristic
33#474×C137C2211yescharacteristic
34#467×C137—21no—
35#465×C137—21no—
36#464×C137—21no—
37#462×C137—21no—
38#462×C137—21no—
39#462×C137C2211yescharacteristic
40#461×C137C2211yescharacteristic
41#451×C137—21no—
42#451×C137—21no—
43#446×C137C2211yescharacteristic
44C8×Q8×C137C2211yescharacteristic
45#436×C137C2211yescharacteristic
46#435×C137—21no—
47C8×D4×C137—21no—
48C8×D4×C137C2211yescharacteristic
49#433×C137—21no—
50#432×C137C2211yescharacteristic
51#431×C137C2211yescharacteristic
52#424×C137—21no—
53C2×C4⋊C8×C137C2211yescharacteristic
54C2×C4⋊C8×C137C2211yescharacteristic
55#335×C137C2211yescharacteristic
56#335×C137C2211yescharacteristic
57#334×C137C2211yescharacteristic
58#334×C137C2211yescharacteristic
59#332×C137C2211yescharacteristic
60#332×C137C2211yescharacteristic
61#332×C137C2211yescharacteristic
62#332×C137C2211yescharacteristic
63#332×C137C2211yescharacteristic
64#332×C137C2211yescharacteristic
65#332×C137C2211yescharacteristic
66#332×C137C2211yescharacteristic
67C22×Q8×C137—21no—
68C2×Q16×C137—21no—
69C2×Q16×C137—21no—
70C2×Q16×C137—21no—
71C2×Q16×C137—21no—
72C2×Q16×C137—21no—
73C2×SD16×C137—21no—
74C2×M16×C137—21no—
75C22×C8×C137—21no—
76C22×C8×C137—21no—
77C22×C8×C137—21no—
78C4⋊Q8×C137—21no—
79C4⋊Q8×C137—21no—
80C4⋊Q8×C137—21no—
81C4⋊Q8×C137C2311yescharacteristic
82C4⋊Q8×C137C2311yescharacteristic
83C4⋊Q8×C137C2311yescharacteristic
84C4⋊Q8×C137C2311yescharacteristic
85#126×C137—21no—
86#125×C137—21no—
87#125×C137D411yescharacteristic
88#124×C137D411yescharacteristic
89#123×C137—21no—
90C22⋊Q8×C137—21no—
91C22⋊Q8×C137—21no—
92C22⋊Q8×C137D411yescharacteristic
93#121×C137D411yescharacteristic
94C4×Q8×C137—21no—
95C4×Q8×C137—21no—
96C4×Q8×C137C2311yescharacteristic
97C4×D4×C137—21no—
98C4×D4×C137C2311yescharacteristic
99#117×C137—21no—
100#117×C137—21no—
101C2×C4⋊C4×C137—21no—
102C2×C4⋊C4×C137—21no—
103C2×C42×C137C2311yescharacteristic
104#107×C137—21no—
105#107×C137—21no—
106#107×C137—21no—
107#106×C137—21no—
108#106×C137—21no—
109#106×C137—21no—
110C4⋊C8×C137—21no—
111C4⋊C8×C137—21no—
112C4⋊C8×C137—21no—
113C4⋊C8×C137—21no—
114C4⋊C8×C137D411yescharacteristic
115C4⋊C8×C137D411yescharacteristic
116C4⋊C8×C137C2311yescharacteristic
117C4⋊C8×C137C2311yescharacteristic
118C4⋊C8×C137C2311yescharacteristic
119C4⋊C8×C137C2311yescharacteristic
120C4⋊C8×C137C2311yescharacteristic
121C4⋊C8×C137C2311yescharacteristic
122#103×C137—21no—
123#103×C137—21no—
124#103×C137—21no—
125#103×C137—21no—
126#103×C137—21no—
127#103×C137—21no—
128#103×C137—21no—
129#103×C137—21no—
130#103×C137—21no—
131#102×C137—21no—
132#102×C137—21no—
133#102×C137—21no—
134C22⋊C8×C137—21no—
135C22⋊C8×C137—21no—
136C22⋊C8×C137—21no—
137C22⋊C8×C137D411yescharacteristic
138C22⋊C8×C137D411yescharacteristic
139#97×C137—21no—
140#97×C137—21no—
141C4×C8×C137—21no—
142C4×C8×C137C2311yescharacteristic
143C4×C8×C137C2311yescharacteristic
144C2×Q8×C137—21no—
145C2×Q8×C137—21no—
146C2×Q8×C137—21no—
147C2×Q8×C137—21no—
148C2×Q8×C137—41no—
149C2×Q8×C137—81no—
150C2×Q8×C137—81no—
151C2×Q8×C137C2×D411yescharacteristic
152C2×D4×C137—21no—
153C2×D4×C137C2×D411yescharacteristic
154C22×C4×C137—21no—
155C22×C4×C137—41no—
156C22×C4×C137C2×D411yescharacteristic
157C22×C4×C137C2×D411yescharacteristic
158C22×C4×C137#4111yescharacteristic
159Q16×C137—81no—
160Q16×C137—81no—
161Q16×C137—81no—
162Q16×C137—81no—
163Q16×C137—81no—
164SD16×C137—81no—
165M16×C137—81no—
166C2×C8×C137—21no—
167C2×C8×C137—21no—
168C2×C8×C137—21no—
169C2×C8×C137—21no—
170C2×C8×C137—21no—
171C2×C8×C137—21no—
172C2×C8×C137—81no—
173C2×C8×C137—81no—
174C2×C8×C137—81no—
175C2×C8×C137C2×D411yescharacteristic
176C2×C8×C137C2×D411yescharacteristic
177C2×C8×C137C2×D411yescharacteristic
178C2×C8×C137C2×D411yescharacteristic
179C4⋊C4×C137—21no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—21no—
182C4⋊C4×C137—21no—
183C4⋊C4×C137—21no—
184C4⋊C4×C137—21no—
185C4⋊C4×C137—21no—
186C4⋊C4×C137—21no—
187C4⋊C4×C137—21no—
188C4⋊C4×C137—21no—
189C4⋊C4×C137—21no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—41no—
192C4⋊C4×C137—41no—
193C4⋊C4×C137—41no—
194C4⋊C4×C137—41no—
195C4⋊C4×C137C2×D411yescharacteristic
196C4⋊C4×C137C2×D411yescharacteristic
197C22⋊C4×C137—21no—
198C22⋊C4×C137—21no—
199C22⋊C4×C137—21no—
200C22⋊C4×C137—21no—
201C22⋊C4×C137—21no—
202C22⋊C4×C137—41no—
203C42×C137—21no—
204C42×C137—41no—
205C42×C137C2×D411yescharacteristic
206C42×C137C2×D411yescharacteristic
207C42×C137#4111yescharacteristic
208C42×C137C2411yescharacteristic
209C23×C137—21no—
210C23×C137#12111yescharacteristic
211Q8×C137—21no—
212Q8×C137—21no—
213Q8×C137—41no—
214Q8×C137—41no—
215Q8×C137—41no—
216Q8×C137—41no—
217Q8×C137—41no—
218Q8×C137—41no—
219Q8×C137—41no—
220Q8×C137—41no—
221Q8×C137—82no—
222D4×C137—21no—
223D4×C137—21no—
224D4×C137—42no—
225C2×C4×C137—22no—
226C2×C4×C137—21no—
227C2×C4×C137—21no—
228C2×C4×C137—21no—
229C2×C4×C137—21no—
230C2×C4×C137—21no—
231C2×C4×C137—21no—
232C2×C4×C137—21no—
233C2×C4×C137—41no—
234C2×C4×C137—41no—
235C2×C4×C137—41no—
236C2×C4×C137—41no—
237C2×C4×C137—41no—
238C2×C4×C137—41no—
239C2×C4×C137—82no—
240C2×C4×C137#12111yescharacteristic
241C2×C4×C137#12111yescharacteristic
242C2×C4×C137#12111yescharacteristic
243C2×C4×C137C22×D411yescharacteristic
244C2×C4×C137C22×D411yescharacteristic
245C2×C4×C137C2×#4111yescharacteristic
246C8×C137—21no—
247C8×C137—21no—
248C8×C137—21no—
249C8×C137—21no—
250C8×C137—41no—
251C8×C137—41no—
252C8×C137—41no—
253C8×C137—41no—
254C8×C137—41no—
255C8×C137—41no—
256C22×C137—21no—
257C22×C137—21no—
258C22×C137—41no—
259C22×C137—41no—
260C22×C137—41no—
261C22×C137#47312yes—
262C22×C137C2×#12111yescharacteristic
263C4×C137—21no—
264C4×C137—21no—
265C4×C137—21no—
266C4×C137—21no—
267C4×C137—41no—
268C4×C137—41no—
269C4×C137—41no—
270C4×C137—81no—
271C4×C137—81no—
272C4×C137—81no—
273C4×C137—81no—
274C4×C137#57611yescharacteristic
275C4×C137#57711yescharacteristic
276C4×C137#57711yescharacteristic
277C4×C137#57811yescharacteristic
278C2×C137—22no—
279C2×C137—81no—
280C2×C137#304511yescharacteristic
281C2×C137#306311yescharacteristic
282C2×C137C2×#47311yescharacteristic
283#19583C13711yesmaximal, characteristic, direct product factor, Sylow
284C137#1958311yescharacteristic, direct product factor, Sylow
285#3248C2×C13711yescharacteristic
286#3239C2×C13711yescharacteristic
287#3209C2×C13711yescharacteristic, complemented
288#2994C2×C13711yescharacteristic
289#1700C2×C13711yescharacteristic, complemented
290#1699C2×C13711yescharacteristic, complemented
291#1690C2×C13711yescharacteristic, complemented
292#1689C2×C13711yescharacteristic, complemented
293#1680C2×C13711yescharacteristic, complemented
294#1679C2×C13711yescharacteristic, complemented
295#1670C2×C13711yescharacteristic, complemented
296#1669C2×C13711yescharacteristic, complemented
297#1573C2×C13711yescharacteristic, complemented
298#1552C2×C13711yescharacteristic, complemented
299C2×#332C2×C13711yescharacteristic, complemented
300#533C22×C13711yescharacteristic
301C2×C4⋊Q8C22×C13711yescharacteristic
302#529C22×C13711yescharacteristic
303#501—21no—
304#494C22×C13711yescharacteristic
305#494C22×C13711yescharacteristic
306#489—21no—
307#487C22×C13711yescharacteristic
308#487C22×C13711yescharacteristic
309#484—21no—
310#481—21no—
311#479—21no—
312#475C22×C13711yescharacteristic
313#475C22×C13711yescharacteristic
314#475C22×C13711yescharacteristic
315#474C22×C13711yescharacteristic
316#474C22×C13711yescharacteristic
317#474C22×C13711yescharacteristic
318#467—21no—
319#465—21no—
320#464—21no—
321#462—21no—
322#462—21no—
323#462C22×C13711yescharacteristic
324#461C22×C13711yescharacteristic
325#451—21no—
326#451—21no—
327#446C22×C13711yescharacteristic
328C8×Q8C22×C13711yescharacteristic
329#436C22×C13711yescharacteristic
330#435—21no—
331C8×D4—21no—
332C8×D4C22×C13711yescharacteristic
333#433—21no—
334#432C22×C13711yescharacteristic
335#431C22×C13711yescharacteristic
336#424—21no—
337C2×C4⋊C8C22×C13711yescharacteristic
338C2×C4⋊C8C22×C13711yescharacteristic
339#335C22×C13711yescharacteristic
340#335C22×C13711yescharacteristic
341#334C22×C13711yescharacteristic
342#334C22×C13711yescharacteristic
343#332C22×C13711yescharacteristic
344#332C22×C13711yescharacteristic
345#332C22×C13711yescharacteristic
346#332C22×C13711yescharacteristic
347#332C22×C13711yescharacteristic
348#332C22×C13711yescharacteristic
349#332C22×C13711yescharacteristic
350#332C22×C13711yescharacteristic
351C22×Q8—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16—21no—
357C2×SD16—21no—
358C2×M16—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C23×C13711yescharacteristic
366C4⋊Q8C23×C13711yescharacteristic
367C4⋊Q8C23×C13711yescharacteristic
368C4⋊Q8C23×C13711yescharacteristic
369#126—21no—
370#125—21no—
371#125D4×C13711yescharacteristic
372#124D4×C13711yescharacteristic
373#123—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8D4×C13711yescharacteristic
377#121D4×C13711yescharacteristic
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C23×C13711yescharacteristic
381C4×D4—21no—
382C4×D4C23×C13711yescharacteristic
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C23×C13711yescharacteristic
388#107—21no—
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8D4×C13711yescharacteristic
399C4⋊C8D4×C13711yescharacteristic
400C4⋊C8C23×C13711yescharacteristic
401C4⋊C8C23×C13711yescharacteristic
402C4⋊C8C23×C13711yescharacteristic
403C4⋊C8C23×C13711yescharacteristic
404C4⋊C8C23×C13711yescharacteristic
405C4⋊C8C23×C13711yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8D4×C13711yescharacteristic
422C22⋊C8D4×C13711yescharacteristic
423#97—21no—
424#97—21no—
425C4×C8—21no—
426C4×C8C23×C13711yescharacteristic
427C4×C8C23×C13711yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×Q8C2×D4×C13711yescharacteristic
436C2×D4—21no—
437C2×D4C2×D4×C13711yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4C2×D4×C13711yescharacteristic
441C22×C4C2×D4×C13711yescharacteristic
442C22×C4#41×C13711yescharacteristic
443Q16—81no—
444Q16—81no—
445Q16—81no—
446Q16—81no—
447Q16—81no—
448SD16—81no—
449M16—81no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—81no—
457C2×C8—81no—
458C2×C8—81no—
459C2×C8C2×D4×C13711yescharacteristic
460C2×C8C2×D4×C13711yescharacteristic
461C2×C8C2×D4×C13711yescharacteristic
462C2×C8C2×D4×C13711yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C13711yescharacteristic
480C4⋊C4C2×D4×C13711yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C42—21no—
488C42—41no—
489C42C2×D4×C13711yescharacteristic
490C42C2×D4×C13711yescharacteristic
491C42#41×C13711yescharacteristic
492C42C24×C13711yescharacteristic
493C23—21no—
494C23#121×C13711yescharacteristic
495Q8—21no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506D4—21no—
507D4—21no—
508D4—42no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4#121×C13711yescharacteristic
525C2×C4#121×C13711yescharacteristic
526C2×C4#121×C13711yescharacteristic
527C2×C4C22×D4×C13711yescharacteristic
528C2×C4C22×D4×C13711yescharacteristic
529C2×C4C2×#41×C13711yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C22—21no—
541C22—21no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#473×C13712yes—
546C22C2×#121×C13711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4#576×C13711yescharacteristic
559C4#577×C13711yescharacteristic
560C4#577×C13711yescharacteristic
561C4#578×C13711yescharacteristic
562C2—22no—
563C2—81no—
564C2#3045×C13711yescharacteristic
565C2#3063×C13711yescharacteristic
566C2C2×#473×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#121×C137D4
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
3. #3209×C137C2semidirect
5. #1700×C137C2semidirect
6. #1699×C137C2semidirect
7. #1690×C137C2semidirect
8. #1689×C137C2semidirect
9. #1680×C137C2semidirect
10. #1679×C137C2semidirect
11. #1670×C137C2semidirect
12. #1669×C137C2semidirect
13. #1573×C137C2semidirect
14. #1552×C137C2semidirect
15. C2×#332×C137C2semidirect
283. #19583C137direct (N × H)
284. C137#19583direct (N × H)
287. #3209C2×C137semidirect
289. #1700C2×C137semidirect
290. #1699C2×C137semidirect
291. #1690C2×C137semidirect
292. #1689C2×C137semidirect
293. #1680C2×C137semidirect
294. #1679C2×C137semidirect
295. #1670C2×C137semidirect
296. #1669C2×C137semidirect
297. #1573C2×C137semidirect
298. #1552C2×C137semidirect
299. C2×#332C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3248×C1372
#3239×C1372
#3209×C1372
#2994×C1372
#1700×C1372
#1699×C1372
#1690×C1372
#1689×C1372
#1680×C1372
#1679×C1372
#1670×C1372
#1669×C1372
#1573×C1372
#1552×C1372
C2×#332×C1372
#19583137