Finite Group Databasebeta

← C137×#18379 #46867765

Subgroups — C137×#18379 #46867765

Order 35072.

980 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3492×C137C211yesmaximal, characteristic
2#3190×C137C212yesmaximal, complemented
3#2583×C137C211yesmaximal, characteristic, complemented
4#1611×C137C211yesmaximal, characteristic, complemented
5#1610×C137C211yesmaximal, characteristic, complemented
6#1609×C137C212yesmaximal, complemented
7#1605×C137C211yesmaximal, characteristic, complemented
8#1604×C137C211yesmaximal, characteristic, complemented
9#1603×C137C212yesmaximal, complemented
10#1501×C137C212yesmaximal, complemented
11C2×#324×C137C211yesmaximal, characteristic, complemented
12#554×C137—22no—
13#553×C137—22no—
14#552×C137—22no—
15#547×C137—22no—
16#544×C137C2211yescharacteristic
17#539×C137—21no—
18#539×C137C2212yes—
19#537×C137C2211yescharacteristic
20#525×C137—21no—
21#525×C137—21no—
22#525×C137C2212yes—
23C2×C22⋊Q8×C137C2211yescharacteristic
24#520×C137—21no—
25C22×C4⋊C4×C137C2211yescharacteristic
26#485×C137—22no—
27#483×C137C2212yes—
28#480×C137C2212yes—
29#467×C137—22no—
30#465×C137—22no—
31#452×C137—22no—
32#451×C137C2212yes—
33#448×C137C2212yes—
34C2×C22⋊C8×C137C2212yes—
35#398×C137C2211yescharacteristic
36#398×C137C2211yescharacteristic
37#395×C137C2211yescharacteristic
38#395×C137C2211yescharacteristic
39#389×C137—21no—
40#389×C137—21no—
41#385×C137—21no—
42#385×C137—21no—
43C4×C22⋊C4×C137C2211yescharacteristic
44#328×C137C2212yes—
45#328×C137C2212yes—
46#327×C137C2212yes—
47#327×C137C2212yes—
48#324×C137C2212yes—
49#324×C137C2211yescharacteristic
50#324×C137C2211yescharacteristic
51C2×#41×C137—21no—
52C2×#41×C137—21no—
53C2×#41×C137D412yes—
54C22×Q8×C137C2311yescharacteristic
55C23×C4×C137D411yescharacteristic
56C23×C4×C137D411yescharacteristic
57C23×C4×C137C2311yescharacteristic
58C2×Q16×C137—22no—
59C2×SD16×C137—22no—
60C22×C8×C137—22no—
61C4⋊Q8×C137—22no—
62#126×C137—22no—
63#126×C137—22no—
64#125×C137—22no—
65#125×C137—22no—
66#125×C137—22no—
67#123×C137—22no—
68#123×C137—22no—
69#123×C137—22no—
70#123×C137—22no—
71#123×C137—22no—
72C22⋊Q8×C137—21no—
73C22⋊Q8×C137—21no—
74C22⋊Q8×C137—21no—
75C22⋊Q8×C137—22no—
76C22⋊Q8×C137—22no—
77C22⋊Q8×C137—21no—
78C22⋊Q8×C137—22no—
79C22⋊Q8×C137—22no—
80C22⋊Q8×C137—22no—
81C22⋊Q8×C137D412yes—
82C22⋊Q8×C137C2312yes—
83#121×C137—21no—
84#121×C137—21no—
85#121×C137—21no—
86#121×C137—22no—
87#121×C137—21no—
88#121×C137D412yes—
89#121×C137C2312yes—
90#120×C137—22no—
91C4×Q8×C137—22no—
92C4×D4×C137—22no—
93C4×D4×C137—22no—
94C4×D4×C137—22no—
95C4×D4×C137—22no—
96C4×D4×C137—22no—
97C4×D4×C137—22no—
98C4×D4×C137—22no—
99#117×C137—22no—
100#117×C137—21no—
101#117×C137—21no—
102#117×C137D412yes—
103C2×C4⋊C4×C137—22no—
104C2×C4⋊C4×C137—22no—
105C2×C4⋊C4×C137—22no—
106C2×C4⋊C4×C137—21no—
107C2×C4⋊C4×C137—21no—
108C2×C4⋊C4×C137—21no—
109C2×C4⋊C4×C137—21no—
110C2×C4⋊C4×C137—21no—
111C2×C4⋊C4×C137D411yescharacteristic
112C2×C4⋊C4×C137D411yescharacteristic
113C2×C4⋊C4×C137C2311yescharacteristic
114C2×C4⋊C4×C137C2311yescharacteristic
115C2×C4⋊C4×C137C2311yescharacteristic
116C2×C22⋊C4×C137—21no—
117C2×C22⋊C4×C137—21no—
118C2×C42×C137—21no—
119#107×C137—22no—
120#106×C137—22no—
121#103×C137—22no—
122#103×C137—22no—
123#103×C137—22no—
124#102×C137—22no—
125C22⋊C8×C137—22no—
126C22⋊C8×C137C2312yes—
127C22⋊C8×C137C2312yes—
128#95×C137—21no—
129#95×C137—21no—
130#95×C137—21no—
131#95×C137—21no—
132#95×C137C2311yescharacteristic
133#95×C137C2311yescharacteristic
134C24×C137C2×D411yescharacteristic
135#41×C137—42no—
136#41×C137—42no—
137#41×C137—82no—
138#41×C137—82no—
139C2×Q8×C137—21no—
140C2×Q8×C137—21no—
141C2×Q8×C137—22no—
142C2×Q8×C137—81no—
143C2×Q8×C137C2×D412yes—
144C2×D4×C137—21no—
145C2×D4×C137—22no—
146C2×D4×C137—22no—
147C2×D4×C137—22no—
148C2×D4×C137—21no—
149C2×D4×C137C2×D412yes—
150C22×C4×C137—22no—
151C22×C4×C137—21no—
152C22×C4×C137—21no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—22no—
157C22×C4×C137—21no—
158C22×C4×C137—22no—
159C22×C4×C137—22no—
160C22×C4×C137—21no—
161C22×C4×C137—21no—
162C22×C4×C137—41no—
163C22×C4×C137—81no—
164C22×C4×C137—81no—
165C22×C4×C137C2×D411yescharacteristic
166C22×C4×C137C2×D411yescharacteristic
167C22×C4×C137C2×D411yescharacteristic
168C22×C4×C137C2×D411yescharacteristic
169C22×C4×C137C2×D411yescharacteristic
170C22×C4×C137C2×D412yes—
171C22×C4×C137C2×D412yes—
172C22×C4×C137C2411yescharacteristic
173Q16×C137—82no—
174SD16×C137—82no—
175C2×C8×C137—22no—
176C2×C8×C137—22no—
177C2×C8×C137—82no—
178C4⋊C4×C137—21no—
179C4⋊C4×C137—22no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—21no—
182C4⋊C4×C137—21no—
183C4⋊C4×C137—22no—
184C4⋊C4×C137—22no—
185C4⋊C4×C137—22no—
186C4⋊C4×C137—22no—
187C4⋊C4×C137—22no—
188C4⋊C4×C137—22no—
189C4⋊C4×C137—22no—
190C4⋊C4×C137—22no—
191C4⋊C4×C137—22no—
192C4⋊C4×C137—22no—
193C4⋊C4×C137—42no—
194C4⋊C4×C137—42no—
195C4⋊C4×C137—42no—
196C4⋊C4×C137—81no—
197C4⋊C4×C137—81no—
198C4⋊C4×C137C2×D412yes—
199C4⋊C4×C137C2×D412yes—
200C22⋊C4×C137—24no—
201C22⋊C4×C137—22no—
202C22⋊C4×C137—22no—
203C22⋊C4×C137—22no—
204C22⋊C4×C137—22no—
205C22⋊C4×C137—22no—
206C22⋊C4×C137—22no—
207C22⋊C4×C137—22no—
208C22⋊C4×C137—22no—
209C22⋊C4×C137—22no—
210C22⋊C4×C137—41no—
211C22⋊C4×C137—41no—
212C42×C137—22no—
213C42×C137—22no—
214C42×C137—22no—
215C42×C137—81no—
216C23×C137—21no—
217C23×C137—21no—
218C23×C137—22no—
219C23×C137—22no—
220C23×C137—41no—
221C23×C137#12011yescharacteristic
222C23×C137#12011yescharacteristic
223C23×C137C22×D411yescharacteristic
224Q8×C137—42no—
225Q8×C137—42no—
226Q8×C137—42no—
227Q8×C137—42no—
228Q8×C137—81no—
229D4×C137—42no—
230D4×C137—42no—
231D4×C137—44no—
232D4×C137—42no—
233D4×C137—42no—
234D4×C137—44no—
235D4×C137—81no—
236C2×C4×C137—21no—
237C2×C4×C137—21no—
238C2×C4×C137—22no—
239C2×C4×C137—22no—
240C2×C4×C137—22no—
241C2×C4×C137—22no—
242C2×C4×C137—21no—
243C2×C4×C137—22no—
244C2×C4×C137—21no—
245C2×C4×C137—21no—
246C2×C4×C137—21no—
247C2×C4×C137—21no—
248C2×C4×C137—41no—
249C2×C4×C137—42no—
250C2×C4×C137—42no—
251C2×C4×C137—41no—
252C2×C4×C137—42no—
253C2×C4×C137—42no—
254C2×C4×C137—44no—
255C2×C4×C137—41no—
256C2×C4×C137—41no—
257C2×C4×C137—42no—
258C2×C4×C137—41no—
259C2×C4×C137—41no—
260C2×C4×C137—41no—
261C2×C4×C137—41no—
262C2×C4×C137—41no—
263C2×C4×C137—41no—
264C2×C4×C137—41no—
265C2×C4×C137—41no—
266C2×C4×C137—41no—
267C2×C4×C137—41no—
268C2×C4×C137—82no—
269C2×C4×C137—81no—
270C2×C4×C137—82no—
271C2×C4×C137#12012yes—
272C2×C4×C137#13512yes—
273C2×C4×C137C22×D412yes—
274C8×C137—42no—
275C8×C137—42no—
276C22×C137—21no—
277C22×C137—21no—
278C22×C137—21no—
279C22×C137—21no—
280C22×C137—21no—
281C22×C137—21no—
282C22×C137—21no—
283C22×C137—42no—
284C22×C137—42no—
285C22×C137—42no—
286C22×C137—42no—
287C22×C137—42no—
288C22×C137#45612yes—
289C22×C137C2×#12011yescharacteristic
290C22×C137C2×#13511yescharacteristic
291C22×C137#57511yescharacteristic
292C4×C137—22no—
293C4×C137—22no—
294C4×C137—22no—
295C4×C137—42no—
296C4×C137—42no—
297C4×C137—41no—
298C4×C137—42no—
299C4×C137—42no—
300C4×C137—41no—
301C4×C137—41no—
302C4×C137—42no—
303C4×C137—81no—
304C4×C137—81no—
305C2×C137—21no—
306C2×C137—21no—
307C2×C137—22no—
308C2×C137—41no—
309C2×C137—82no—
310C2×C137#300211yescharacteristic
311C2×C137C2×#45611yescharacteristic
312C2×C137#302611yescharacteristic
313#18379C13711yesmaximal, characteristic, direct product factor, Sylow
314C137#1837911yescharacteristic, direct product factor, Sylow
315#3492C2×C13711yescharacteristic
316#3190C2×C13712yescomplemented
317#2583C2×C13711yescharacteristic, complemented
318#1611C2×C13711yescharacteristic, complemented
319#1610C2×C13711yescharacteristic, complemented
320#1609C2×C13712yescomplemented
321#1605C2×C13711yescharacteristic, complemented
322#1604C2×C13711yescharacteristic, complemented
323#1603C2×C13712yescomplemented
324#1501C2×C13712yescomplemented
325C2×#324C2×C13711yescharacteristic, complemented
326#554—22no—
327#553—22no—
328#552—22no—
329#547—22no—
330#544C22×C13711yescharacteristic
331#539—21no—
332#539C22×C13712yes—
333#537C22×C13711yescharacteristic
334#525—21no—
335#525—21no—
336#525C22×C13712yes—
337C2×C22⋊Q8C22×C13711yescharacteristic
338#520—21no—
339C22×C4⋊C4C22×C13711yescharacteristic
340#485—22no—
341#483C22×C13712yes—
342#480C22×C13712yes—
343#467—22no—
344#465—22no—
345#452—22no—
346#451C22×C13712yes—
347#448C22×C13712yes—
348C2×C22⋊C8C22×C13712yes—
349#398C22×C13711yescharacteristic
350#398C22×C13711yescharacteristic
351#395C22×C13711yescharacteristic
352#395C22×C13711yescharacteristic
353#389—21no—
354#389—21no—
355#385—21no—
356#385—21no—
357C4×C22⋊C4C22×C13711yescharacteristic
358#328C22×C13712yes—
359#328C22×C13712yes—
360#327C22×C13712yes—
361#327C22×C13712yes—
362#324C22×C13712yes—
363#324C22×C13711yescharacteristic
364#324C22×C13711yescharacteristic
365C2×#41—21no—
366C2×#41—21no—
367C2×#41D4×C13712yes—
368C22×Q8C23×C13711yescharacteristic
369C23×C4D4×C13711yescharacteristic
370C23×C4D4×C13711yescharacteristic
371C23×C4C23×C13711yescharacteristic
372C2×Q16—22no—
373C2×SD16—22no—
374C22×C8—22no—
375C4⋊Q8—22no—
376#126—22no—
377#126—22no—
378#125—22no—
379#125—22no—
380#125—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8D4×C13712yes—
396C22⋊Q8C23×C13712yes—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—22no—
401#121—21no—
402#121D4×C13712yes—
403#121C23×C13712yes—
404#120—22no—
405C4×Q8—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413#117—22no—
414#117—21no—
415#117—21no—
416#117D4×C13712yes—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4D4×C13711yescharacteristic
426C2×C4⋊C4D4×C13711yescharacteristic
427C2×C4⋊C4C23×C13711yescharacteristic
428C2×C4⋊C4C23×C13711yescharacteristic
429C2×C4⋊C4C23×C13711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C42—21no—
433#107—22no—
434#106—22no—
435#103—22no—
436#103—22no—
437#103—22no—
438#102—22no—
439C22⋊C8—22no—
440C22⋊C8C23×C13712yes—
441C22⋊C8C23×C13712yes—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95C23×C13711yescharacteristic
447#95C23×C13711yescharacteristic
448C24C2×D4×C13711yescharacteristic
449#41—42no—
450#41—42no—
451#41—82no—
452#41—82no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—81no—
457C2×Q8C2×D4×C13712yes—
458C2×D4—21no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4C2×D4×C13712yes—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4C2×D4×C13711yescharacteristic
480C22×C4C2×D4×C13711yescharacteristic
481C22×C4C2×D4×C13711yescharacteristic
482C22×C4C2×D4×C13711yescharacteristic
483C22×C4C2×D4×C13711yescharacteristic
484C22×C4C2×D4×C13712yes—
485C22×C4C2×D4×C13712yes—
486C22×C4C24×C13711yescharacteristic
487Q16—82no—
488SD16—82no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—82no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—81no—
511C4⋊C4—81no—
512C4⋊C4C2×D4×C13712yes—
513C4⋊C4C2×D4×C13712yes—
514C22⋊C4—24no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—81no—
530C23—22no—
531C23—21no—
532C23—21no—
533C23—22no—
534C23—41no—
535C23#120×C13711yescharacteristic
536C23#120×C13711yescharacteristic
537C23C22×D4×C13711yescharacteristic
538Q8—42no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543D4—42no—
544D4—42no—
545D4—44no—
546D4—44no—
547D4—42no—
548D4—42no—
549D4—81no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—81no—
584C2×C4—82no—
585C2×C4#120×C13712yes—
586C2×C4#135×C13712yes—
587C2×C4C22×D4×C13712yes—
588C8—42no—
589C8—42no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22#456×C13712yes—
603C22C2×#120×C13711yescharacteristic
604C22C2×#135×C13711yescharacteristic
605C22#575×C13711yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—42no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C2—21no—
620C2—21no—
621C2—22no—
622C2—41no—
623C2—82no—
624C2#3002×C13711yescharacteristic
625C2C2×#456×C13711yescharacteristic
626C2#3026×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3492×C137C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3190×C137C2semidirect
3. #2583×C137C2semidirect
4. #1611×C137C2semidirect
5. #1610×C137C2semidirect
6. #1609×C137C2semidirect
7. #1605×C137C2semidirect
8. #1604×C137C2semidirect
9. #1603×C137C2semidirect
10. #1501×C137C2semidirect
11. C2×#324×C137C2semidirect
313. #18379C137direct (N × H)
314. C137#18379direct (N × H)
316. #3190C2×C137semidirect
317. #2583C2×C137semidirect
318. #1611C2×C137semidirect
319. #1610C2×C137semidirect
320. #1609C2×C137semidirect
321. #1605C2×C137semidirect
322. #1604C2×C137semidirect
323. #1603C2×C137semidirect
324. #1501C2×C137semidirect
325. C2×#324C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3492×C1372
#3190×C1372
#2583×C1372
#1611×C1372
#1610×C1372
#1609×C1372
#1605×C1372
#1604×C1372
#1603×C1372
#1501×C1372
C2×#324×C1372
#18379137