Finite Group Databasebeta

← C137×#19382 #46868768

Subgroups — C137×#19382 #46868768

Order 35072.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3251×C137C211yesmaximal, characteristic
2#3238×C137C211yesmaximal, characteristic, complemented
3#3141×C137C211yesmaximal, characteristic, complemented
4#2969×C137C211yesmaximal, characteristic, complemented
5#1704×C137C211yesmaximal, characteristic, complemented
6#1703×C137C211yesmaximal, characteristic, complemented
7#1698×C137C211yesmaximal, characteristic, complemented
8#1697×C137C211yesmaximal, characteristic, complemented
9#1684×C137C211yesmaximal, characteristic, complemented
10#1683×C137C211yesmaximal, characteristic, complemented
11#1678×C137C211yesmaximal, characteristic, complemented
12#1677×C137C211yesmaximal, characteristic, complemented
13#1569×C137C211yesmaximal, characteristic, complemented
14#1553×C137C211yesmaximal, characteristic, complemented
15#1548×C137C211yesmaximal, characteristic, complemented
16#532×C137C2211yescharacteristic
17C2×C4⋊Q8×C137C2211yescharacteristic
18#529×C137C2211yescharacteristic
19#501×C137—21no—
20#489×C137—21no—
21#489×C137—21no—
22#489×C137—21no—
23#487×C137C2211yescharacteristic
24#487×C137C2211yescharacteristic
25#486×C137C2211yescharacteristic
26#486×C137C2211yescharacteristic
27#483×C137—21no—
28#480×C137—21no—
29#478×C137—21no—
30#477×C137C2211yescharacteristic
31#477×C137C2211yescharacteristic
32#476×C137C2211yescharacteristic
33#476×C137C2211yescharacteristic
34#475×C137C2211yescharacteristic
35#474×C137C2211yescharacteristic
36#469×C137—21no—
37#468×C137—21no—
38#463×C137—21no—
39#460×C137C2211yescharacteristic
40#459×C137C2211yescharacteristic
41#446×C137C2211yescharacteristic
42C8×Q8×C137C2211yescharacteristic
43#436×C137—21no—
44#436×C137C2211yescharacteristic
45#435×C137—21no—
46C8×D4×C137C2211yescharacteristic
47#433×C137—21no—
48#432×C137C2211yescharacteristic
49#431×C137C2211yescharacteristic
50#423×C137C2211yescharacteristic
51#417×C137—21no—
52#417×C137—21no—
53#405×C137—21no—
54C4×M16×C137C2211yescharacteristic
55#335×C137C2211yescharacteristic
56#335×C137C2211yescharacteristic
57#334×C137C2211yescharacteristic
58#334×C137C2211yescharacteristic
59#333×C137C2211yescharacteristic
60#333×C137C2211yescharacteristic
61#333×C137C2211yescharacteristic
62#333×C137C2211yescharacteristic
63#332×C137C2211yescharacteristic
64#332×C137C2211yescharacteristic
65#331×C137C2211yescharacteristic
66#331×C137C2211yescharacteristic
67C2×#41×C137—21no—
68C22×Q8×C137—21no—
69C2×SD16×C137—21no—
70C2×D8×C137—21no—
71C2×M16×C137—21no—
72C2×M16×C137—21no—
73C2×M16×C137D411yescharacteristic
74C2×M16×C137D411yescharacteristic
75C22×C8×C137—21no—
76C4⋊Q8×C137—21no—
77C4⋊Q8×C137—21no—
78C4⋊Q8×C137—21no—
79C4⋊Q8×C137C2311yescharacteristic
80C4⋊Q8×C137C2311yescharacteristic
81C4⋊Q8×C137C2311yescharacteristic
82#127×C137C2311yescharacteristic
83#126×C137—21no—
84#125×C137D411yescharacteristic
85#124×C137—21no—
86#124×C137D411yescharacteristic
87#123×C137—21no—
88C22⋊Q8×C137D411yescharacteristic
89#121×C137—21no—
90#121×C137—21no—
91#121×C137D411yescharacteristic
92C4×Q8×C137C2311yescharacteristic
93C4×D4×C137—21no—
94C4×D4×C137—21no—
95C4×D4×C137—21no—
96C4×D4×C137C2311yescharacteristic
97#117×C137—21no—
98C2×C4⋊C4×C137—21no—
99C2×C4⋊C4×C137—21no—
100C2×C42×C137C2311yescharacteristic
101#107×C137—21no—
102#107×C137—21no—
103#107×C137—21no—
104#106×C137—21no—
105#106×C137—21no—
106#106×C137—21no—
107C4⋊C8×C137—21no—
108C4⋊C8×C137—21no—
109C4⋊C8×C137—21no—
110C4⋊C8×C137C2311yescharacteristic
111C4⋊C8×C137C2311yescharacteristic
112C4⋊C8×C137C2311yescharacteristic
113C4⋊C8×C137C2311yescharacteristic
114C4⋊C8×C137C2311yescharacteristic
115C4⋊C8×C137C2311yescharacteristic
116#103×C137—21no—
117#103×C137—21no—
118#103×C137—21no—
119#103×C137—21no—
120#103×C137—21no—
121#103×C137—21no—
122#103×C137—21no—
123#102×C137—21no—
124#102×C137—21no—
125#102×C137—21no—
126#102×C137—21no—
127#102×C137—21no—
128#102×C137—21no—
129#102×C137—21no—
130#102×C137—21no—
131#102×C137—21no—
132C22⋊C8×C137—21no—
133C22⋊C8×C137—21no—
134C22⋊C8×C137—21no—
135C22⋊C8×C137—21no—
136#97×C137—21no—
137#97×C137—21no—
138#97×C137D411yescharacteristic
139#97×C137D411yescharacteristic
140C4×C8×C137—21no—
141C4×C8×C137—21no—
142C4×C8×C137C2311yescharacteristic
143C4×C8×C137C2311yescharacteristic
144#41×C137—42no—
145#41×C137—42no—
146C2×Q8×C137—21no—
147C2×Q8×C137—21no—
148C2×Q8×C137—21no—
149C2×Q8×C137—41no—
150C2×Q8×C137—82no—
151C2×Q8×C137C2×D411yescharacteristic
152C2×D4×C137—21no—
153C2×D4×C137—21no—
154C2×D4×C137—21no—
155C2×D4×C137—21no—
156C2×D4×C137—41no—
157C2×D4×C137C2×D411yescharacteristic
158C22×C4×C137—21no—
159C22×C4×C137—41no—
160C22×C4×C137—41no—
161C22×C4×C137C2×D411yescharacteristic
162C22×C4×C137C2×D411yescharacteristic
163C22×C4×C137#4111yescharacteristic
164SD16×C137—81no—
165D8×C137—81no—
166M16×C137—41no—
167M16×C137—41no—
168M16×C137—42no—
169M16×C137—81no—
170C2×C8×C137—21no—
171C2×C8×C137—21no—
172C2×C8×C137—21no—
173C2×C8×C137—21no—
174C2×C8×C137—21no—
175C2×C8×C137—21no—
176C2×C8×C137—42no—
177C2×C8×C137C2×D411yescharacteristic
178C2×C8×C137C2×D411yescharacteristic
179C2×C8×C137C2×D411yescharacteristic
180C2×C8×C137C2×D411yescharacteristic
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×C137C2×D411yescharacteristic
194C4⋊C4×C137C2×D411yescharacteristic
195C22⋊C4×C137—21no—
196C22⋊C4×C137—21no—
197C22⋊C4×C137—21no—
198C22⋊C4×C137—21no—
199C22⋊C4×C137—21no—
200C22⋊C4×C137—41no—
201C22⋊C4×C137—41no—
202C42×C137—21no—
203C42×C137C2×D411yescharacteristic
204C42×C137C2×D411yescharacteristic
205C42×C137#4111yescharacteristic
206C42×C137C2411yescharacteristic
207C23×C137—21no—
208C23×C137—41no—
209C23×C137#12111yescharacteristic
210Q8×C137—21no—
211Q8×C137—21no—
212Q8×C137—41no—
213Q8×C137—41no—
214Q8×C137—81no—
215Q8×C137—81no—
216Q8×C137—82no—
217D4×C137—21no—
218D4×C137—21no—
219D4×C137—41no—
220D4×C137—41no—
221D4×C137—41no—
222D4×C137—41no—
223D4×C137—81no—
224D4×C137—81no—
225D4×C137—82no—
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—82no—
241C2×C4×C137#12111yescharacteristic
242C2×C4×C137#12111yescharacteristic
243C2×C4×C137#12111yescharacteristic
244C2×C4×C137C22×D411yescharacteristic
245C2×C4×C137C22×D411yescharacteristic
246C2×C4×C137C2×#4111yescharacteristic
247C8×C137—21no—
248C8×C137—21no—
249C8×C137—21no—
250C8×C137—21no—
251C8×C137—41no—
252C8×C137—41no—
253C8×C137—41no—
254C8×C137—41no—
255C8×C137—41no—
256C8×C137—41no—
257C22×C137—21no—
258C22×C137—21no—
259C22×C137—21no—
260C22×C137—41no—
261C22×C137—41no—
262C22×C137—41no—
263C22×C137—81no—
264C22×C137—81no—
265C22×C137—81no—
266C22×C137C2×#12111yescharacteristic
267C4×C137—21no—
268C4×C137—21no—
269C4×C137—21no—
270C4×C137—21no—
271C4×C137—41no—
272C4×C137—41no—
273C4×C137—41no—
274C4×C137—81no—
275C4×C137—81no—
276C4×C137—81no—
277C4×C137#57511yescharacteristic
278C4×C137#57511yescharacteristic
279C4×C137#57711yescharacteristic
280C4×C137#57811yescharacteristic
281C2×C137—41no—
282C2×C137—81no—
283C2×C137—161no—
284C2×C137#304011yescharacteristic
285C2×C137#306311yescharacteristic
286C2×C137#306811yescharacteristic
287#19382C13711yesmaximal, characteristic, direct product factor, Sylow
288C137#1938211yescharacteristic, direct product factor, Sylow
289#3251C2×C13711yescharacteristic
290#3238C2×C13711yescharacteristic, complemented
291#3141C2×C13711yescharacteristic, complemented
292#2969C2×C13711yescharacteristic, complemented
293#1704C2×C13711yescharacteristic, complemented
294#1703C2×C13711yescharacteristic, complemented
295#1698C2×C13711yescharacteristic, complemented
296#1697C2×C13711yescharacteristic, complemented
297#1684C2×C13711yescharacteristic, complemented
298#1683C2×C13711yescharacteristic, complemented
299#1678C2×C13711yescharacteristic, complemented
300#1677C2×C13711yescharacteristic, complemented
301#1569C2×C13711yescharacteristic, complemented
302#1553C2×C13711yescharacteristic, complemented
303#1548C2×C13711yescharacteristic, complemented
304#532C22×C13711yescharacteristic
305C2×C4⋊Q8C22×C13711yescharacteristic
306#529C22×C13711yescharacteristic
307#501—21no—
308#489—21no—
309#489—21no—
310#489—21no—
311#487C22×C13711yescharacteristic
312#487C22×C13711yescharacteristic
313#486C22×C13711yescharacteristic
314#486C22×C13711yescharacteristic
315#483—21no—
316#480—21no—
317#478—21no—
318#477C22×C13711yescharacteristic
319#477C22×C13711yescharacteristic
320#476C22×C13711yescharacteristic
321#476C22×C13711yescharacteristic
322#475C22×C13711yescharacteristic
323#474C22×C13711yescharacteristic
324#469—21no—
325#468—21no—
326#463—21no—
327#460C22×C13711yescharacteristic
328#459C22×C13711yescharacteristic
329#446C22×C13711yescharacteristic
330C8×Q8C22×C13711yescharacteristic
331#436—21no—
332#436C22×C13711yescharacteristic
333#435—21no—
334C8×D4C22×C13711yescharacteristic
335#433—21no—
336#432C22×C13711yescharacteristic
337#431C22×C13711yescharacteristic
338#423C22×C13711yescharacteristic
339#417—21no—
340#417—21no—
341#405—21no—
342C4×M16C22×C13711yescharacteristic
343#335C22×C13711yescharacteristic
344#335C22×C13711yescharacteristic
345#334C22×C13711yescharacteristic
346#334C22×C13711yescharacteristic
347#333C22×C13711yescharacteristic
348#333C22×C13711yescharacteristic
349#333C22×C13711yescharacteristic
350#333C22×C13711yescharacteristic
351#332C22×C13711yescharacteristic
352#332C22×C13711yescharacteristic
353#331C22×C13711yescharacteristic
354#331C22×C13711yescharacteristic
355C2×#41—21no—
356C22×Q8—21no—
357C2×SD16—21no—
358C2×D8—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16D4×C13711yescharacteristic
362C2×M16D4×C13711yescharacteristic
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8C23×C13711yescharacteristic
368C4⋊Q8C23×C13711yescharacteristic
369C4⋊Q8C23×C13711yescharacteristic
370#127C23×C13711yescharacteristic
371#126—21no—
372#125D4×C13711yescharacteristic
373#124—21no—
374#124D4×C13711yescharacteristic
375#123—21no—
376C22⋊Q8D4×C13711yescharacteristic
377#121—21no—
378#121—21no—
379#121D4×C13711yescharacteristic
380C4×Q8C23×C13711yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4C23×C13711yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C42C23×C13711yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C13711yescharacteristic
399C4⋊C8C23×C13711yescharacteristic
400C4⋊C8C23×C13711yescharacteristic
401C4⋊C8C23×C13711yescharacteristic
402C4⋊C8C23×C13711yescharacteristic
403C4⋊C8C23×C13711yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424#97—21no—
425#97—21no—
426#97D4×C13711yescharacteristic
427#97D4×C13711yescharacteristic
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C23×C13711yescharacteristic
431C4×C8C23×C13711yescharacteristic
432#41—42no—
433#41—42no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8—82no—
439C2×Q8C2×D4×C13711yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×D4×C13711yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4C2×D4×C13711yescharacteristic
450C22×C4C2×D4×C13711yescharacteristic
451C22×C4#41×C13711yescharacteristic
452SD16—81no—
453D8—81no—
454M16—41no—
455M16—41no—
456M16—42no—
457M16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
465C2×C8C2×D4×C13711yescharacteristic
466C2×C8C2×D4×C13711yescharacteristic
467C2×C8C2×D4×C13711yescharacteristic
468C2×C8C2×D4×C13711yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C13711yescharacteristic
482C4⋊C4C2×D4×C13711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42C2×D4×C13711yescharacteristic
492C42C2×D4×C13711yescharacteristic
493C42#41×C13711yescharacteristic
494C42C24×C13711yescharacteristic
495C23—21no—
496C23—41no—
497C23#121×C13711yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503Q8—81no—
504Q8—82no—
505D4—21no—
506D4—21no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4—81no—
513D4—82no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4#121×C13711yescharacteristic
530C2×C4#121×C13711yescharacteristic
531C2×C4#121×C13711yescharacteristic
532C2×C4C22×D4×C13711yescharacteristic
533C2×C4C22×D4×C13711yescharacteristic
534C2×C4C2×#41×C13711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×#121×C13711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4#575×C13711yescharacteristic
566C4#575×C13711yescharacteristic
567C4#577×C13711yescharacteristic
568C4#578×C13711yescharacteristic
569C2—41no—
570C2—81no—
571C2—161no—
572C2#3040×C13711yescharacteristic
573C2#3063×C13711yescharacteristic
574C2#3068×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#3251×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
2. #3238×C137C2semidirect
3. #3141×C137C2semidirect
4. #2969×C137C2semidirect
5. #1704×C137C2semidirect
6. #1703×C137C2semidirect
7. #1698×C137C2semidirect
8. #1697×C137C2semidirect
9. #1684×C137C2semidirect
10. #1683×C137C2semidirect
11. #1678×C137C2semidirect
12. #1677×C137C2semidirect
13. #1569×C137C2semidirect
14. #1553×C137C2semidirect
15. #1548×C137C2semidirect
287. #19382C137direct (N × H)
288. C137#19382direct (N × H)
290. #3238C2×C137semidirect
291. #3141C2×C137semidirect
292. #2969C2×C137semidirect
293. #1704C2×C137semidirect
294. #1703C2×C137semidirect
295. #1698C2×C137semidirect
296. #1697C2×C137semidirect
297. #1684C2×C137semidirect
298. #1683C2×C137semidirect
299. #1678C2×C137semidirect
300. #1677C2×C137semidirect
301. #1569C2×C137semidirect
302. #1553C2×C137semidirect
303. #1548C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3251×C1372
#3238×C1372
#3141×C1372
#2969×C1372
#1704×C1372
#1703×C1372
#1698×C1372
#1697×C1372
#1684×C1372
#1683×C1372
#1678×C1372
#1677×C1372
#1569×C1372
#1553×C1372
#1548×C1372
#19382137