Finite Group Databasebeta

← C137×#10322 #46859708

Subgroups — C137×#10322 #46859708

Order 35072.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3187×C137C211yesmaximal, characteristic, complemented
2#2848×C137C211yesmaximal, characteristic, complemented
3#2847×C137C211yesmaximal, characteristic
4#1779×C137C211yesmaximal, characteristic, complemented
5#1520×C137C211yesmaximal, characteristic, complemented
6#1519×C137C211yesmaximal, characteristic, complemented
7#1289×C137C211yesmaximal, characteristic, complemented
8C24×C4×C137C2211yescharacteristic
9C2×C22⋊Q8×C137—21no—
10C2×C22⋊Q8×C137C2211yescharacteristic
11C2×#121×C137—21no—
12C2×#121×C137C2211yescharacteristic
13C2×#120×C137—21no—
14#483×C137—21no—
15#481×C137—21no—
16#465×C137—22no—
17#450×C137—21no—
18#448×C137—21no—
19C2×C22⋊C8×C137—22no—
20C2×C22⋊C8×C137C2211yescharacteristic
21C2×C22⋊C8×C137C2211yescharacteristic
22#386×C137—21no—
23#386×C137—22no—
24#385×C137—21no—
25#385×C137—22no—
26#380×C137—21no—
27#380×C137—21no—
28#380×C137C2211yescharacteristic
29#380×C137C2211yescharacteristic
30#379×C137—21no—
31#328×C137—22no—
32#327×C137—22no—
33C25×C137D411yescharacteristic
34C22×Q8×C137D411yescharacteristic, complemented
35C22×D4×C137—22no—
36C22×D4×C137—21no—
37C22×D4×C137D411yescharacteristic
38C23×C4×C137—21no—
39C23×C4×C137—21no—
40C23×C4×C137—21no—
41C23×C4×C137—21no—
42C23×C4×C137—21no—
43C23×C4×C137—21no—
44C23×C4×C137—44no—
45C23×C4×C137D411yescharacteristic
46C23×C4×C137C2311yescharacteristic
47C2×SD16×C137—22no—
48C22×C8×C137—21no—
49C22×C8×C137D412yescomplemented
50C22⋊Q8×C137—21no—
51C22⋊Q8×C137—21no—
52C22⋊Q8×C137—21no—
53C22⋊Q8×C137—21no—
54C22⋊Q8×C137—44no—
55#121×C137—21no—
56#121×C137—21no—
57#121×C137—21no—
58#121×C137—21no—
59#121×C137—44no—
60#120×C137—42no—
61#120×C137—42no—
62C2×C4⋊C4×C137—22no—
63C2×C4⋊C4×C137—21no—
64C2×C4⋊C4×C137—21no—
65C2×C4⋊C4×C137—21no—
66C2×C4⋊C4×C137D411yescharacteristic
67C2×C4⋊C4×C137D411yescharacteristic, complemented
68C2×C22⋊C4×C137—22no—
69C2×C22⋊C4×C137—22no—
70C2×C22⋊C4×C137—22no—
71C2×C22⋊C4×C137—22no—
72C2×C22⋊C4×C137—21no—
73C2×C22⋊C4×C137—21no—
74C2×C22⋊C4×C137—21no—
75C2×C22⋊C4×C137—21no—
76#106×C137—22no—
77#103×C137—22no—
78#102×C137—22no—
79C22⋊C8×C137—21no—
80C22⋊C8×C137—21no—
81C22⋊C8×C137—21no—
82C22⋊C8×C137—21no—
83C22⋊C8×C137—44no—
84#95×C137—22no—
85#95×C137—22no—
86#95×C137D412yes—
87#95×C137D412yescomplemented
88C24×C137—21no—
89C24×C137—21no—
90C24×C137—21no—
91C24×C137—21no—
92C24×C137—21no—
93C24×C137—21no—
94C24×C137—21no—
95C24×C137—42no—
96C24×C137—42no—
97C24×C137SD1612yescomplemented
98C24×C137C2×D411yescharacteristic
99C2×Q8×C137—21no—
100C2×Q8×C137—21no—
101C2×Q8×C137—42no—
102C2×D4×C137—21no—
103C2×D4×C137—21no—
104C2×D4×C137—42no—
105C2×D4×C137—44no—
106C2×D4×C137—44no—
107C2×D4×C137—44no—
108C2×D4×C137—41no—
109C2×D4×C137—41no—
110C2×D4×C137—41no—
111C2×D4×C137—41no—
112C2×D4×C137—41no—
113C2×D4×C137—41no—
114C22×C4×C137—24no—
115C22×C4×C137—24no—
116C22×C4×C137—24no—
117C22×C4×C137—21no—
118C22×C4×C137—21no—
119C22×C4×C137—21no—
120C22×C4×C137—21no—
121C22×C4×C137—21no—
122C22×C4×C137—22no—
123C22×C4×C137—22no—
124C22×C4×C137—21no—
125C22×C4×C137—42no—
126C22×C4×C137—42no—
127C22×C4×C137—42no—
128C22×C4×C137—42no—
129C22×C4×C137—42no—
130C22×C4×C137—42no—
131C22×C4×C137—42no—
132C22×C4×C137—42no—
133C22×C4×C137—42no—
134C22×C4×C137—42no—
135C22×C4×C137—42no—
136C22×C4×C137—41no—
137C22×C4×C137—41no—
138C22×C4×C137—41no—
139C22×C4×C137—41no—
140C22×C4×C137C2×D411yescharacteristic
141C22×C4×C137C2×D411yescharacteristic
142C22×C4×C137C2×D411yescharacteristic
143C22×C4×C137C2×D411yescharacteristic
144C22×C4×C137C2×D411yescharacteristic
145C22×C4×C137#4111yescharacteristic
146SD16×C137—82no—
147C2×C8×C137—22no—
148C2×C8×C137—42no—
149C2×C8×C137—42no—
150C2×C8×C137—41no—
151C4⋊C4×C137—21no—
152C4⋊C4×C137—21no—
153C4⋊C4×C137—21no—
154C4⋊C4×C137—21no—
155C4⋊C4×C137—42no—
156C4⋊C4×C137—42no—
157C4⋊C4×C137—44no—
158C4⋊C4×C137—41no—
159C4⋊C4×C137—41no—
160C22⋊C4×C137—44no—
161C22⋊C4×C137—44no—
162C22⋊C4×C137—44no—
163C22⋊C4×C137—44no—
164C22⋊C4×C137—41no—
165C22⋊C4×C137—41no—
166C22⋊C4×C137—41no—
167C22⋊C4×C137—41no—
168C22⋊C4×C137—41no—
169C22⋊C4×C137—41no—
170C22⋊C4×C137—41no—
171C22⋊C4×C137—41no—
172C23×C137—22no—
173C23×C137—22no—
174C23×C137—22no—
175C23×C137—22no—
176C23×C137—22no—
177C23×C137—22no—
178C23×C137—22no—
179C23×C137—22no—
180C23×C137—22no—
181C23×C137—41no—
182C23×C137—44no—
183C23×C137—41no—
184C23×C137—41no—
185C23×C137—41no—
186C23×C137—41no—
187C23×C137—41no—
188C23×C137—41no—
189C23×C137—41no—
190C23×C137—44no—
191C23×C137—44no—
192C23×C137—44no—
193C23×C137—42no—
194C23×C137—42no—
195C23×C137—41no—
196C23×C137—41no—
197C23×C137—41no—
198C23×C137—41no—
199C23×C137—41no—
200C23×C137—41no—
201C23×C137—41no—
202C23×C137#12011yescharacteristic
203C23×C137#12011yescharacteristic
204C23×C137#12111yescharacteristic
205C23×C137C2×SD1611yescharacteristic
206C23×C137#13511yescharacteristic
207C23×C137AGL(1,ℤ/8)11yescharacteristic
208C23×C137#13711yescharacteristic
209Q8×C137—42no—
210Q8×C137—81no—
211D4×C137—42no—
212D4×C137—81no—
213D4×C137—88no—
214D4×C137—81no—
215D4×C137—81no—
216D4×C137—81no—
217D4×C137—81no—
218C2×C4×C137—22no—
219C2×C4×C137—22no—
220C2×C4×C137—22no—
221C2×C4×C137—22no—
222C2×C4×C137—22no—
223C2×C4×C137—22no—
224C2×C4×C137—41no—
225C2×C4×C137—41no—
226C2×C4×C137—41no—
227C2×C4×C137—44no—
228C2×C4×C137—44no—
229C2×C4×C137—44no—
230C2×C4×C137—41no—
231C2×C4×C137—41no—
232C2×C4×C137—41no—
233C2×C4×C137—41no—
234C2×C4×C137—44no—
235C2×C4×C137—42no—
236C2×C4×C137—42no—
237C2×C4×C137—42no—
238C2×C4×C137—42no—
239C2×C4×C137—42no—
240C2×C4×C137—42no—
241C2×C4×C137—41no—
242C2×C4×C137—41no—
243C2×C4×C137—41no—
244C2×C4×C137—42no—
245C2×C4×C137—42no—
246C2×C4×C137—41no—
247C2×C4×C137—41no—
248C2×C4×C137#12011yescharacteristic
249C2×C4×C137#12111yescharacteristic
250C2×C4×C137#12111yescharacteristic
251C2×C4×C137#12711yescharacteristic
252C8×C137—42no—
253C8×C137—81no—
254C22×C137—21no—
255C22×C137—21no—
256C22×C137—21no—
257C22×C137—21no—
258C22×C137—21no—
259C22×C137—21no—
260C22×C137—24no—
261C22×C137—24no—
262C22×C137—24no—
263C22×C137—41no—
264C22×C137—41no—
265C22×C137—41no—
266C22×C137—41no—
267C22×C137—42no—
268C22×C137—42no—
269C22×C137—42no—
270C22×C137—42no—
271C22×C137—42no—
272C22×C137—42no—
273C22×C137—42no—
274C22×C137—42no—
275C22×C137—42no—
276C22×C137—42no—
277C22×C137—42no—
278C22×C137—42no—
279C22×C137—82no—
280C22×C137—82no—
281C22×C137—81no—
282C22×C137—81no—
283C22×C137—81no—
284C22×C137#39211yescharacteristic
285C22×C137#44811yescharacteristic
286C22×C137#44911yescharacteristic
287C22×C137#45011yescharacteristic
288C22×C137#45211yescharacteristic
289C22×C137#46511yescharacteristic
290C22×C137#46811yescharacteristic
291C4×C137—21no—
292C4×C137—21no—
293C4×C137—21no—
294C4×C137—42no—
295C4×C137—82no—
296C4×C137—82no—
297C4×C137—81no—
298C4×C137—81no—
299C4×C137—81no—
300C4×C137B(4,𝔽2)12yes—
301C2×C137—21no—
302C2×C137—21no—
303C2×C137—21no—
304C2×C137—21no—
305C2×C137—21no—
306C2×C137—21no—
307C2×C137—44no—
308C2×C137—161no—
309C2×C137#200011yescharacteristic
310C2×C137#201011yescharacteristic
311C2×C137#202111yescharacteristic
312#10322C13711yesmaximal, characteristic, direct product factor, Sylow
313C137#1032211yescharacteristic, direct product factor, Sylow
314#3187C2×C13711yescharacteristic, complemented
315#2848C2×C13711yescharacteristic, complemented
316#2847C2×C13711yescharacteristic
317#1779C2×C13711yescharacteristic, complemented
318#1520C2×C13711yescharacteristic, complemented
319#1519C2×C13711yescharacteristic, complemented
320#1289C2×C13711yescharacteristic, complemented
321C24×C4C22×C13711yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8C22×C13711yescharacteristic
324C2×#121—21no—
325C2×#121C22×C13711yescharacteristic
326C2×#120—21no—
327#483—21no—
328#481—21no—
329#465—22no—
330#450—21no—
331#448—21no—
332C2×C22⋊C8—22no—
333C2×C22⋊C8C22×C13711yescharacteristic
334C2×C22⋊C8C22×C13711yescharacteristic
335#386—21no—
336#386—22no—
337#385—21no—
338#385—22no—
339#380—21no—
340#380—21no—
341#380C22×C13711yescharacteristic
342#380C22×C13711yescharacteristic
343#379—21no—
344#328—22no—
345#327—22no—
346C25D4×C13711yescharacteristic
347C22×Q8D4×C13711yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C13711yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C13711yescharacteristic
359C23×C4C23×C13711yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C13712yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C13711yescharacteristic
380C2×C4⋊C4D4×C13711yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C13712yes—
400#95D4×C13712yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C13712yescomplemented
411C24C2×D4×C13711yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C13711yescharacteristic
454C22×C4C2×D4×C13711yescharacteristic
455C22×C4C2×D4×C13711yescharacteristic
456C22×C4C2×D4×C13711yescharacteristic
457C22×C4C2×D4×C13711yescharacteristic
458C22×C4#41×C13711yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C13711yescharacteristic
516C23#120×C13711yescharacteristic
517C23#121×C13711yescharacteristic
518C23C2×SD16×C13711yescharacteristic
519C23#135×C13711yescharacteristic
520C23AGL(1,ℤ/8)×C13711yescharacteristic
521C23#137×C13711yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C13711yescharacteristic
562C2×C4#121×C13711yescharacteristic
563C2×C4#121×C13711yescharacteristic
564C2×C4#127×C13711yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#392×C13711yescharacteristic
598C22#448×C13711yescharacteristic
599C22#449×C13711yescharacteristic
600C22#450×C13711yescharacteristic
601C22#452×C13711yescharacteristic
602C22#465×C13711yescharacteristic
603C22#468×C13711yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4B(4,𝔽2)×C13712yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2#2000×C13711yescharacteristic
623C2#2010×C13711yescharacteristic
624C2#2021×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#392
commutator, Frattini, cosocleC23×C4C23×C137
prime radical#2847×C137C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3187×C137C2semidirect
2. #2848×C137C2semidirect
4. #1779×C137C2semidirect
5. #1520×C137C2semidirect
6. #1519×C137C2semidirect
7. #1289×C137C2semidirect
34. C22×Q8×C137D4semidirect
49. C22×C8×C137D4semidirect
67. C2×C4⋊C4×C137D4semidirect
87. #95×C137D4semidirect
97. C24×C137SD16semidirect
312. #10322C137direct (N × H)
313. C137#10322direct (N × H)
314. #3187C2×C137semidirect
315. #2848C2×C137semidirect
317. #1779C2×C137semidirect
318. #1520C2×C137semidirect
319. #1519C2×C137semidirect
320. #1289C2×C137semidirect
347. C22×Q8D4×C137semidirect
362. C22×C8D4×C137semidirect
380. C2×C4⋊C4D4×C137semidirect
400. #95D4×C137semidirect
410. C24SD16×C137semidirect

Maximal subgroups

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

subgroupindex
#3187×C1372
#2848×C1372
#2847×C1372
#1779×C1372
#1520×C1372
#1519×C1372
#1289×C1372
#10322137