Finite Group Databasebeta

← C137×#18130 #46867516

Subgroups — C137×#18130 #46867516

Order 35072.

964 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3461×C137C211yesmaximal, characteristic, complemented
2#3105×C137C212yesmaximal, complemented
3#2398×C137C211yesmaximal, characteristic, complemented
4#1617×C137C211yesmaximal, characteristic, complemented
5#1616×C137C211yesmaximal, characteristic, complemented
6#1615×C137C212yesmaximal, complemented
7#1599×C137C211yesmaximal, characteristic, complemented
8#1598×C137C211yesmaximal, characteristic
9#1597×C137C212yesmaximal, complemented
10#1500×C137C212yesmaximal, complemented
11#1461×C137C211yesmaximal, characteristic, complemented
12#544×C137C2211yescharacteristic
13#542×C137—22no—
14#541×C137—22no—
15#539×C137—21no—
16#539×C137C2212yes—
17#537×C137C2211yescharacteristic
18#536×C137—21no—
19#533×C137—22no—
20#529×C137—22no—
21#529×C137—21no—
22#529×C137C2212yes—
23C4×#41×C137—21no—
24C2×C4×Q8×C137C2211yescharacteristic
25C2×C4×D4×C137C2211yescharacteristic
26#484×C137C2212yes—
27#481×C137C2212yes—
28#478×C137—22no—
29#463×C137—22no—
30#450×C137C2212yes—
31#447×C137C2212yes—
32C4×SD16×C137—22no—
33C4×D8×C137—22no—
34#431×C137C2212yes—
35#400×C137C2211yescharacteristic
36#400×C137C2211yescharacteristic
37#397×C137—21no—
38#394×C137C2211yescharacteristic
39#394×C137C2211yescharacteristic
40#393×C137—21no—
41C4×C22⋊C4×C137—21no—
42C4×C22⋊C4×C137—21no—
43#376×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—
52C22×Q8×C137D411yescharacteristic
53C22×D4×C137C2311yescharacteristic
54C23×C4×C137—21no—
55C2×SD16×C137—22no—
56C2×D8×C137—22no—
57C4⋊Q8×C137—22no—
58C4⋊Q8×C137—22no—
59#126×C137—22no—
60#126×C137—22no—
61#126×C137—22no—
62#126×C137—22no—
63#125×C137—21no—
64#125×C137—22no—
65#125×C137—22no—
66#125×C137—22no—
67#125×C137D412yes—
68#124×C137—22no—
69#124×C137—21no—
70#124×C137D412yes—
71#123×C137—22no—
72#123×C137—22no—
73#123×C137—22no—
74#123×C137—22no—
75C22⋊Q8×C137—22no—
76C22⋊Q8×C137—22no—
77C22⋊Q8×C137—22no—
78C22⋊Q8×C137—22no—
79C22⋊Q8×C137—21no—
80C22⋊Q8×C137—22no—
81C22⋊Q8×C137C2312yes—
82#121×C137—22no—
83#121×C137—21no—
84#121×C137C2312yes—
85C4×Q8×C137—21no—
86C4×Q8×C137—21no—
87C4×Q8×C137—21no—
88C4×Q8×C137—22no—
89C4×Q8×C137—22no—
90C4×Q8×C137D412yes—
91C4×D4×C137—21no—
92C4×D4×C137—21no—
93C4×D4×C137—21no—
94C4×D4×C137—22no—
95C4×D4×C137—22no—
96C4×D4×C137—22no—
97C4×D4×C137—22no—
98C4×D4×C137D412yes—
99#117×C137—22no—
100#117×C137—22no—
101#117×C137—21no—
102#117×C137—22no—
103C2×C4⋊C4×C137D411yescharacteristic
104C2×C4⋊C4×C137C2311yescharacteristic
105C2×C4⋊C4×C137C2311yescharacteristic
106C2×C4⋊C4×C137C2311yescharacteristic
107C2×C22⋊C4×C137—21no—
108C2×C22⋊C4×C137—21no—
109C2×C22⋊C4×C137—21no—
110C2×C22⋊C4×C137—21no—
111C2×C22⋊C4×C137—21no—
112C2×C42×C137—22no—
113C2×C42×C137—21no—
114C2×C42×C137D411yescharacteristic
115C2×C42×C137D411yescharacteristic
116C2×C42×C137C2311yescharacteristic
117#107×C137—22no—
118#106×C137—22no—
119C4⋊C8×C137—22no—
120#103×C137—22no—
121#102×C137—22no—
122#102×C137—22no—
123#102×C137—22no—
124C22⋊C8×C137C2312yes—
125C22⋊C8×C137C2312yes—
126C4×C8×C137—22no—
127#95×C137—21no—
128#95×C137—21no—
129#95×C137—21no—
130#95×C137—21no—
131#95×C137—21no—
132#95×C137C2311yescharacteristic
133#95×C137C2311yescharacteristic
134C24×C137—21no—
135#41×C137—42no—
136#41×C137—42no—
137C2×Q8×C137—21no—
138C2×Q8×C137—21no—
139C2×Q8×C137—22no—
140C2×Q8×C137—22no—
141C2×Q8×C137—41no—
142C2×Q8×C137C2×D412yes—
143C2×D4×C137—21no—
144C2×D4×C137—22no—
145C2×D4×C137—21no—
146C2×D4×C137—22no—
147C2×D4×C137—42no—
148C2×D4×C137C2×D412yes—
149C22×C4×C137—22no—
150C22×C4×C137—22no—
151C22×C4×C137—22no—
152C22×C4×C137—21no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—42no—
156C22×C4×C137—42no—
157C22×C4×C137—41no—
158C22×C4×C137—41no—
159C22×C4×C137C2×D411yescharacteristic
160C22×C4×C137C2×D411yescharacteristic
161C22×C4×C137C2×D411yescharacteristic
162C22×C4×C137C2×D411yescharacteristic
163C22×C4×C137C2×D411yescharacteristic
164C22×C4×C137C2×D411yescharacteristic
165C22×C4×C137C2411yescharacteristic
166SD16×C137—44no—
167D8×C137—44no—
168C2×C8×C137—22no—
169C2×C8×C137—22no—
170C4⋊C4×C137—21no—
171C4⋊C4×C137—22no—
172C4⋊C4×C137—21no—
173C4⋊C4×C137—22no—
174C4⋊C4×C137—22no—
175C4⋊C4×C137—21no—
176C4⋊C4×C137—21no—
177C4⋊C4×C137—22no—
178C4⋊C4×C137—22no—
179C4⋊C4×C137—22no—
180C4⋊C4×C137—22no—
181C4⋊C4×C137—22no—
182C4⋊C4×C137—22no—
183C4⋊C4×C137—22no—
184C4⋊C4×C137—22no—
185C4⋊C4×C137—22no—
186C4⋊C4×C137C2×D412yes—
187C4⋊C4×C137C2×D412yes—
188C22⋊C4×C137—22no—
189C22⋊C4×C137—22no—
190C22⋊C4×C137—22no—
191C22⋊C4×C137—22no—
192C22⋊C4×C137—22no—
193C22⋊C4×C137—22no—
194C22⋊C4×C137—22no—
195C22⋊C4×C137—22no—
196C22⋊C4×C137—22no—
197C22⋊C4×C137—42no—
198C22⋊C4×C137—42no—
199C22⋊C4×C137—42no—
200C22⋊C4×C137—42no—
201C22⋊C4×C137—42no—
202C42×C137—22no—
203C42×C137—22no—
204C42×C137—21no—
205C42×C137—21no—
206C42×C137—21no—
207C42×C137—22no—
208C42×C137—21no—
209C42×C137—42no—
210C42×C137C2×D412yes—
211C42×C137C2×D412yes—
212C23×C137—22no—
213C23×C137—22no—
214C23×C137—41no—
215C23×C137—41no—
216C23×C137—41no—
217C23×C137—41no—
218C23×C137—41no—
219C23×C137—41no—
220C23×C137C22×D411yescharacteristic
221Q8×C137—44no—
222Q8×C137—42no—
223Q8×C137—42no—
224Q8×C137—81no—
225D4×C137—24no—
226D4×C137—42no—
227D4×C137—42no—
228D4×C137—42no—
229D4×C137—42no—
230D4×C137—42no—
231D4×C137—81no—
232C2×C4×C137—21no—
233C2×C4×C137—21no—
234C2×C4×C137—21no—
235C2×C4×C137—21no—
236C2×C4×C137—22no—
237C2×C4×C137—21no—
238C2×C4×C137—22no—
239C2×C4×C137—22no—
240C2×C4×C137—21no—
241C2×C4×C137—21no—
242C2×C4×C137—22no—
243C2×C4×C137—21no—
244C2×C4×C137—21no—
245C2×C4×C137—41no—
246C2×C4×C137—44no—
247C2×C4×C137—44no—
248C2×C4×C137—41no—
249C2×C4×C137—41no—
250C2×C4×C137—41no—
251C2×C4×C137—41no—
252C2×C4×C137—41no—
253C2×C4×C137—41no—
254C2×C4×C137—41no—
255C2×C4×C137—41no—
256C2×C4×C137—41no—
257C2×C4×C137—41no—
258C2×C4×C137—41no—
259C2×C4×C137—82no—
260C2×C4×C137—82no—
261C2×C4×C137—82no—
262C2×C4×C137#12011yescharacteristic
263C2×C4×C137#12012yes—
264C2×C4×C137#12011yescharacteristic
265C2×C4×C137#13512yes—
266C2×C4×C137C22×D412yes—
267C8×C137—42no—
268C8×C137—42no—
269C22×C137—21no—
270C22×C137—21no—
271C22×C137—42no—
272C22×C137—42no—
273C22×C137—42no—
274C22×C137—42no—
275C22×C137—42no—
276C22×C137—42no—
277C22×C137—81no—
278C22×C137—81no—
279C22×C137—81no—
280C22×C137—81no—
281C22×C137C2×#12011yescharacteristic
282C22×C137C2×#13511yescharacteristic
283C22×C137#57511yescharacteristic
284C4×C137—22no—
285C4×C137—22no—
286C4×C137—21no—
287C4×C137—22no—
288C4×C137—41no—
289C4×C137—42no—
290C4×C137—42no—
291C4×C137—41no—
292C4×C137—41no—
293C4×C137—42no—
294C4×C137—81no—
295C4×C137—81no—
296C4×C137—81no—
297C4×C137#45412yes—
298C2×C137—21no—
299C2×C137—21no—
300C2×C137—82no—
301C2×C137—82no—
302C2×C137#300211yescharacteristic
303C2×C137C2×#45411yescharacteristic
304C2×C137#302511yescharacteristic
305#18130C13711yesmaximal, characteristic, direct product factor, Sylow
306C137#1813011yescharacteristic, direct product factor, Sylow
307#3461C2×C13711yescharacteristic, complemented
308#3105C2×C13712yescomplemented
309#2398C2×C13711yescharacteristic, complemented
310#1617C2×C13711yescharacteristic, complemented
311#1616C2×C13711yescharacteristic, complemented
312#1615C2×C13712yescomplemented
313#1599C2×C13711yescharacteristic, complemented
314#1598C2×C13711yescharacteristic
315#1597C2×C13712yescomplemented
316#1500C2×C13712yescomplemented
317#1461C2×C13711yescharacteristic, complemented
318#544C22×C13711yescharacteristic
319#542—22no—
320#541—22no—
321#539—21no—
322#539C22×C13712yes—
323#537C22×C13711yescharacteristic
324#536—21no—
325#533—22no—
326#529—22no—
327#529—21no—
328#529C22×C13712yes—
329C4×#41—21no—
330C2×C4×Q8C22×C13711yescharacteristic
331C2×C4×D4C22×C13711yescharacteristic
332#484C22×C13712yes—
333#481C22×C13712yes—
334#478—22no—
335#463—22no—
336#450C22×C13712yes—
337#447C22×C13712yes—
338C4×SD16—22no—
339C4×D8—22no—
340#431C22×C13712yes—
341#400C22×C13711yescharacteristic
342#400C22×C13711yescharacteristic
343#397—21no—
344#394C22×C13711yescharacteristic
345#394C22×C13711yescharacteristic
346#393—21no—
347C4×C22⋊C4—21no—
348C4×C22⋊C4—21no—
349#376C22×C13711yescharacteristic
350#328C22×C13712yes—
351#328C22×C13712yes—
352#327C22×C13712yes—
353#327C22×C13712yes—
354#324C22×C13712yes—
355#324C22×C13711yescharacteristic
356#324C22×C13711yescharacteristic
357C2×#41—21no—
358C22×Q8D4×C13711yescharacteristic
359C22×D4C23×C13711yescharacteristic
360C23×C4—21no—
361C2×SD16—22no—
362C2×D8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365#126—22no—
366#126—22no—
367#126—22no—
368#126—22no—
369#125—21no—
370#125—22no—
371#125—22no—
372#125—22no—
373#125D4×C13712yes—
374#124—22no—
375#124—21no—
376#124D4×C13712yes—
377#123—22no—
378#123—22no—
379#123—22no—
380#123—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8C23×C13712yes—
388#121—22no—
389#121—21no—
390#121C23×C13712yes—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8D4×C13712yes—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4D4×C13712yes—
405#117—22no—
406#117—22no—
407#117—21no—
408#117—22no—
409C2×C4⋊C4D4×C13711yescharacteristic
410C2×C4⋊C4C23×C13711yescharacteristic
411C2×C4⋊C4C23×C13711yescharacteristic
412C2×C4⋊C4C23×C13711yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C42—22no—
419C2×C42—21no—
420C2×C42D4×C13711yescharacteristic
421C2×C42D4×C13711yescharacteristic
422C2×C42C23×C13711yescharacteristic
423#107—22no—
424#106—22no—
425C4⋊C8—22no—
426#103—22no—
427#102—22no—
428#102—22no—
429#102—22no—
430C22⋊C8C23×C13712yes—
431C22⋊C8C23×C13712yes—
432C4×C8—22no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95C23×C13711yescharacteristic
439#95C23×C13711yescharacteristic
440C24—21no—
441#41—42no—
442#41—42no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—41no—
448C2×Q8C2×D4×C13712yes—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—42no—
454C2×D4C2×D4×C13712yes—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4C2×D4×C13711yescharacteristic
466C22×C4C2×D4×C13711yescharacteristic
467C22×C4C2×D4×C13711yescharacteristic
468C22×C4C2×D4×C13711yescharacteristic
469C22×C4C2×D4×C13711yescharacteristic
470C22×C4C2×D4×C13711yescharacteristic
471C22×C4C24×C13711yescharacteristic
472SD16—44no—
473D8—44no—
474C2×C8—22no—
475C2×C8—22no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4C2×D4×C13712yes—
493C4⋊C4C2×D4×C13712yes—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C42—22no—
509C42—22no—
510C42—21no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42C2×D4×C13712yes—
517C42C2×D4×C13712yes—
518C23—22no—
519C23—22no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23C22×D4×C13711yescharacteristic
527Q8—44no—
528Q8—42no—
529Q8—42no—
530Q8—81no—
531D4—24no—
532D4—42no—
533D4—42no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—81no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4#120×C13711yescharacteristic
569C2×C4#120×C13712yes—
570C2×C4#120×C13711yescharacteristic
571C2×C4#135×C13712yes—
572C2×C4C22×D4×C13712yes—
573C8—42no—
574C8—42no—
575C22—21no—
576C22—21no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×#120×C13711yescharacteristic
588C22C2×#135×C13711yescharacteristic
589C22#575×C13711yescharacteristic
590C4—22no—
591C4—22no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—42no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4#454×C13712yes—
604C2—21no—
605C2—21no—
606C2—82no—
607C2—82no—
608C2#3002×C13711yescharacteristic
609C2C2×#454×C13711yescharacteristic
610C2#3025×C13711yescharacteristic
subgroupG/H
centerC2×C4×C137#120
commutator, Frattini, cosocleC22×C4C24×C137
socleC22×C137C2×#120
prime radical#1598×C137C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3461×C137C2semidirect
2. #3105×C137C2semidirect
3. #2398×C137C2semidirect
4. #1617×C137C2semidirect
5. #1616×C137C2semidirect
6. #1615×C137C2semidirect
7. #1599×C137C2semidirect
9. #1597×C137C2semidirect
10. #1500×C137C2semidirect
11. #1461×C137C2semidirect
305. #18130C137direct (N × H)
306. C137#18130direct (N × H)
307. #3461C2×C137semidirect
308. #3105C2×C137semidirect
309. #2398C2×C137semidirect
310. #1617C2×C137semidirect
311. #1616C2×C137semidirect
312. #1615C2×C137semidirect
313. #1599C2×C137semidirect
315. #1597C2×C137semidirect
316. #1500C2×C137semidirect
317. #1461C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3461×C1372
#3105×C1372
#2398×C1372
#1617×C1372
#1616×C1372
#1615×C1372
#1599×C1372
#1598×C1372
#1597×C1372
#1500×C1372
#1461×C1372
#18130137