Finite Group Databasebeta

← C137×#19032 #46868418

Subgroups — C137×#19032 #46868418

Order 35072.

896 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3561×C137C211yesmaximal, characteristic
2#3218×C137C211yesmaximal, characteristic, complemented
3#3165×C137C211yesmaximal, characteristic, complemented
4C2×#489×C137C211yesmaximal, characteristic, complemented
5#1664×C137C214yesmaximal, complemented
6#1661×C137C214yesmaximal, complemented
7#1531×C137C211yesmaximal, characteristic, complemented
8#1527×C137C211yesmaximal, characteristic, complemented
9#1524×C137C211yesmaximal, characteristic, complemented
10#563×C137C2212yes—
11#562×C137C2212yes—
12#556×C137—21no—
13#551×C137—22no—
14D4×Q8×C137—21no—
15#548×C137—21no—
16#546×C137—21no—
17#543×C137—21no—
18#542×C137—21no—
19#542×C137—22no—
20#538×C137—21no—
21#536×C137—21no—
22#533×C137C2211yescharacteristic
23C2×C4⋊Q8×C137C2211yescharacteristic
24#529×C137C2211yescharacteristic
25C2×#124×C137C2211yescharacteristic
26#501×C137C2214yescomplemented
27#500×C137—21no—
28#498×C137—21no—
29#497×C137C2212yescomplemented
30#491×C137C2212yescomplemented
31#489×C137—22no—
32#489×C137C2214yes—
33#462×C137—21no—
34#461×C137—21no—
35#451×C137—21no—
36#448×C137—21no—
37#432×C137C2211yescharacteristic
38#428×C137—22no—
39C2×#103×C137—21no—
40C2×#102×C137—21no—
41C4×M16×C137C2211yescharacteristic
42C2×#97×C137C2211yescharacteristic
43#330×C137C2212yescomplemented
44#330×C137C2214yescomplemented
45#329×C137C2214yes—
46#329×C137C2212yescomplemented
47C2×#41×C137—21no—
48C22×Q8×C137—21no—
49C22×Q8×C137—21no—
50C22×Q8×C137D411yescharacteristic
51C22×D4×C137D411yescharacteristic
52C2×Q16×C137—22no—
53C2×SD16×C137—22no—
54C2×M16×C137—21no—
55C22×C8×C137—21no—
56C4⋊Q8×C137—21no—
57C4⋊Q8×C137—22no—
58C4⋊Q8×C137—21no—
59C4⋊Q8×C137—21no—
60C4⋊Q8×C137—21no—
61C4⋊Q8×C137D411yescharacteristic
62C4⋊Q8×C137D411yescharacteristic
63C4⋊Q8×C137C2312yes—
64#126×C137—22no—
65#126×C137—22no—
66#126×C137—22no—
67#126×C137—21no—
68#125×C137C2311yescharacteristic
69#125×C137C2312yes—
70#124×C137—21no—
71#124×C137—22no—
72#124×C137—22no—
73#124×C137—21no—
74#124×C137—21no—
75#124×C137D412yes—
76#124×C137C2312yes—
77#124×C137C2311yescharacteristic
78#123×C137—22no—
79#123×C137—22no—
80#123×C137—21no—
81#123×C137—22no—
82#123×C137—22no—
83C22⋊Q8×C137—22no—
84C22⋊Q8×C137—22no—
85C22⋊Q8×C137—21no—
86C22⋊Q8×C137—22no—
87C22⋊Q8×C137—22no—
88C22⋊Q8×C137—22no—
89C22⋊Q8×C137—21no—
90C22⋊Q8×C137—21no—
91C22⋊Q8×C137—22no—
92C22⋊Q8×C137—22no—
93C22⋊Q8×C137D411yescharacteristic
94#121×C137—21no—
95#121×C137—22no—
96#121×C137—22no—
97#121×C137D411yescharacteristic
98#120×C137—22no—
99C4×Q8×C137—21no—
100C4×Q8×C137—21no—
101C4×Q8×C137—21no—
102C4×Q8×C137D411yescharacteristic
103C4×D4×C137—22no—
104C4×D4×C137—21no—
105C4×D4×C137—22no—
106C4×D4×C137—21no—
107C4×D4×C137D411yescharacteristic
108#117×C137—22no—
109#117×C137—21no—
110#117×C137D412yes—
111C2×C4⋊C4×C137—21no—
112C2×C4⋊C4×C137—21no—
113C2×C22⋊C4×C137—22no—
114C2×C22⋊C4×C137—21no—
115C2×C22⋊C4×C137—21no—
116C2×C42×C137C2311yescharacteristic
117#107×C137—24no—
118#106×C137—24no—
119C4⋊C8×C137—21no—
120#103×C137—24no—
121#103×C137—22no—
122#103×C137—22no—
123#102×C137—24no—
124C22⋊C8×C137—21no—
125#97×C137—21no—
126#97×C137C2312yes—
127#97×C137C2312yes—
128#97×C137C2312yes—
129C4×C8×C137—21no—
130C24×C137—21no—
131#41×C137—82no—
132C2×Q8×C137—22no—
133C2×Q8×C137—21no—
134C2×Q8×C137—21no—
135C2×Q8×C137—21no—
136C2×Q8×C137—22no—
137C2×Q8×C137—42no—
138C2×Q8×C137—41no—
139C2×Q8×C137—82no—
140C2×Q8×C137—82no—
141C2×Q8×C137C2×D412yes—
142C2×Q8×C137C2×D411yescharacteristic
143C2×D4×C137—21no—
144C2×D4×C137—22no—
145C2×D4×C137—22no—
146C2×D4×C137—21no—
147C2×D4×C137—42no—
148C2×D4×C137C2×D412yes—
149C2×D4×C137C2×D411yescharacteristic
150C22×C4×C137—22no—
151C22×C4×C137—22no—
152C22×C4×C137—22no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—41no—
156C22×C4×C137C2×D411yescharacteristic
157C22×C4×C137C2×D411yescharacteristic
158C22×C4×C137C2×D411yescharacteristic
159Q16×C137—82no—
160SD16×C137—82no—
161M16×C137—24no—
162C2×C8×C137—22no—
163C2×C8×C137—22no—
164C2×C8×C137—22no—
165C2×C8×C137—42no—
166C4⋊C4×C137—22no—
167C4⋊C4×C137—22no—
168C4⋊C4×C137—22no—
169C4⋊C4×C137—22no—
170C4⋊C4×C137—21no—
171C4⋊C4×C137—21no—
172C4⋊C4×C137—21no—
173C4⋊C4×C137—21no—
174C4⋊C4×C137—21no—
175C4⋊C4×C137—21no—
176C4⋊C4×C137—22no—
177C4⋊C4×C137—22no—
178C4⋊C4×C137—22no—
179C4⋊C4×C137—22no—
180C4⋊C4×C137—41no—
181C4⋊C4×C137—41no—
182C4⋊C4×C137C2×D411yescharacteristic
183C4⋊C4×C137C2×D411yescharacteristic
184C4⋊C4×C137C2×D412yes—
185C4⋊C4×C137C2×D412yes—
186C22⋊C4×C137—22no—
187C22⋊C4×C137—22no—
188C22⋊C4×C137—22no—
189C22⋊C4×C137—22no—
190C22⋊C4×C137—22no—
191C22⋊C4×C137—21no—
192C22⋊C4×C137—22no—
193C22⋊C4×C137—22no—
194C22⋊C4×C137—22no—
195C22⋊C4×C137—21no—
196C22⋊C4×C137—21no—
197C22⋊C4×C137—22no—
198C22⋊C4×C137—22no—
199C22⋊C4×C137—21no—
200C22⋊C4×C137—21no—
201C42×C137—22no—
202C42×C137—22no—
203C42×C137—21no—
204C42×C137C2×D411yescharacteristic
205C42×C137C2×D411yescharacteristic
206C42×C137C2×D411yescharacteristic
207C42×C137C2411yescharacteristic
208C23×C137—22no—
209C23×C137—21no—
210C23×C137—42no—
211C23×C137—81no—
212C23×C137—81no—
213C23×C137#12011yescharacteristic
214Q8×C137—41no—
215Q8×C137—42no—
216Q8×C137—42no—
217Q8×C137—42no—
218Q8×C137—42no—
219Q8×C137—42no—
220Q8×C137—81no—
221Q8×C137—82no—
222Q8×C137—82no—
223D4×C137—41no—
224D4×C137—42no—
225D4×C137—42no—
226D4×C137—42no—
227D4×C137—82no—
228D4×C137—82no—
229C2×C4×C137—22no—
230C2×C4×C137—22no—
231C2×C4×C137—21no—
232C2×C4×C137—22no—
233C2×C4×C137—21no—
234C2×C4×C137—22no—
235C2×C4×C137—22no—
236C2×C4×C137—21no—
237C2×C4×C137—41no—
238C2×C4×C137—42no—
239C2×C4×C137—42no—
240C2×C4×C137—81no—
241C2×C4×C137—82no—
242C2×C4×C137—82no—
243C2×C4×C137—82no—
244C2×C4×C137—82no—
245C2×C4×C137#12011yescharacteristic
246C2×C4×C137#12011yescharacteristic
247C2×C4×C137#12011yescharacteristic
248C2×C4×C137C22×D411yescharacteristic
249C2×C4×C137C22×D411yescharacteristic
250C2×C4×C137C22×D411yescharacteristic
251C8×C137—24no—
252C8×C137—42no—
253C8×C137—42no—
254C22×C137—21no—
255C22×C137—21no—
256C22×C137—41no—
257C22×C137—42no—
258C22×C137—41no—
259C22×C137—42no—
260C22×C137—42no—
261C22×C137—41no—
262C22×C137—162no—
263C22×C137#45612yes—
264C22×C137C2×#12011yescharacteristic
265C4×C137—21no—
266C4×C137—21no—
267C4×C137—21no—
268C4×C137—21no—
269C4×C137—21no—
270C4×C137—41no—
271C4×C137—42no—
272C4×C137—42no—
273C4×C137—41no—
274C4×C137—41no—
275C4×C137—42no—
276C4×C137—82no—
277C4×C137#45512yes—
278C2×C137—22no—
279C2×C137—81no—
280C2×C137—82no—
281C2×C137C2×#45511yescharacteristic
282C2×C137C2×#45611yescharacteristic
283C2×C137#302111yescharacteristic
284#19032C13711yesmaximal, characteristic, direct product factor, Sylow
285C137#1903211yescharacteristic, direct product factor, Sylow
286#3561C2×C13711yescharacteristic
287#3218C2×C13711yescharacteristic, complemented
288#3165C2×C13711yescharacteristic, complemented
289C2×#489C2×C13711yescharacteristic, complemented
290#1664C2×C13714yescomplemented
291#1661C2×C13714yescomplemented
292#1531C2×C13711yescharacteristic, complemented
293#1527C2×C13711yescharacteristic, complemented
294#1524C2×C13711yescharacteristic, complemented
295#563C22×C13712yes—
296#562C22×C13712yes—
297#556—21no—
298#551—22no—
299D4×Q8—21no—
300#548—21no—
301#546—21no—
302#543—21no—
303#542—21no—
304#542—22no—
305#538—21no—
306#536—21no—
307#533C22×C13711yescharacteristic
308C2×C4⋊Q8C22×C13711yescharacteristic
309#529C22×C13711yescharacteristic
310C2×#124C22×C13711yescharacteristic
311#501C22×C13714yescomplemented
312#500—21no—
313#498—21no—
314#497C22×C13712yescomplemented
315#491C22×C13712yescomplemented
316#489—22no—
317#489C22×C13714yes—
318#462—21no—
319#461—21no—
320#451—21no—
321#448—21no—
322#432C22×C13711yescharacteristic
323#428—22no—
324C2×#103—21no—
325C2×#102—21no—
326C4×M16C22×C13711yescharacteristic
327C2×#97C22×C13711yescharacteristic
328#330C22×C13714yescomplemented
329#330C22×C13712yescomplemented
330#329C22×C13714yes—
331#329C22×C13712yescomplemented
332C2×#41—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8D4×C13711yescharacteristic
336C22×D4D4×C13711yescharacteristic
337C2×Q16—22no—
338C2×SD16—22no—
339C2×M16—21no—
340C22×C8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—22no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8D4×C13711yescharacteristic
347C4⋊Q8D4×C13711yescharacteristic
348C4⋊Q8C23×C13712yes—
349#126—22no—
350#126—22no—
351#126—22no—
352#126—21no—
353#125C23×C13711yescharacteristic
354#125C23×C13712yes—
355#124—21no—
356#124—22no—
357#124—22no—
358#124—21no—
359#124—21no—
360#124D4×C13712yes—
361#124C23×C13712yes—
362#124C23×C13711yescharacteristic
363#123—22no—
364#123—22no—
365#123—21no—
366#123—22no—
367#123—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8D4×C13711yescharacteristic
379#121—21no—
380#121—22no—
381#121—22no—
382#121D4×C13711yescharacteristic
383#120—22no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8D4×C13711yescharacteristic
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—22no—
391C4×D4—21no—
392C4×D4D4×C13711yescharacteristic
393#117—22no—
394#117—21no—
395#117D4×C13712yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42C23×C13711yescharacteristic
402#107—24no—
403#106—24no—
404C4⋊C8—21no—
405#103—24no—
406#103—22no—
407#103—22no—
408#102—24no—
409C22⋊C8—21no—
410#97—21no—
411#97C23×C13712yes—
412#97C23×C13712yes—
413#97C23×C13712yes—
414C4×C8—21no—
415C24—21no—
416#41—82no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—22no—
422C2×Q8—42no—
423C2×Q8—41no—
424C2×Q8—82no—
425C2×Q8—82no—
426C2×Q8C2×D4×C13712yes—
427C2×Q8C2×D4×C13711yescharacteristic
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4C2×D4×C13712yes—
434C2×D4C2×D4×C13711yescharacteristic
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441C22×C4C2×D4×C13711yescharacteristic
442C22×C4C2×D4×C13711yescharacteristic
443C22×C4C2×D4×C13711yescharacteristic
444Q16—82no—
445SD16—82no—
446M16—24no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—42no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C13711yescharacteristic
468C4⋊C4C2×D4×C13711yescharacteristic
469C4⋊C4C2×D4×C13712yes—
470C4⋊C4C2×D4×C13712yes—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C42—22no—
487C42—22no—
488C42—21no—
489C42C2×D4×C13711yescharacteristic
490C42C2×D4×C13711yescharacteristic
491C42C2×D4×C13711yescharacteristic
492C42C24×C13711yescharacteristic
493C23—22no—
494C23—21no—
495C23—42no—
496C23—81no—
497C23—81no—
498C23#120×C13711yescharacteristic
499Q8—41no—
500Q8—42no—
501Q8—42no—
502Q8—42no—
503Q8—42no—
504Q8—42no—
505Q8—81no—
506Q8—82no—
507Q8—82no—
508D4—41no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—82no—
513D4—82no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4#120×C13711yescharacteristic
531C2×C4#120×C13711yescharacteristic
532C2×C4#120×C13711yescharacteristic
533C2×C4C22×D4×C13711yescharacteristic
534C2×C4C22×D4×C13711yescharacteristic
535C2×C4C22×D4×C13711yescharacteristic
536C8—24no—
537C8—42no—
538C8—42no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22—42no—
545C22—42no—
546C22—41no—
547C22—162no—
548C22#456×C13712yes—
549C22C2×#120×C13711yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—82no—
562C4#455×C13712yes—
563C2—22no—
564C2—82no—
565C2—81no—
566C2C2×#455×C13711yescharacteristic
567C2C2×#456×C13711yescharacteristic
568C2#3021×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
prime radical#3561×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. #3218×C137C2semidirect
3. #3165×C137C2semidirect
4. C2×#489×C137C2semidirect
5. #1664×C137C2semidirect
6. #1661×C137C2semidirect
7. #1531×C137C2semidirect
8. #1527×C137C2semidirect
9. #1524×C137C2semidirect
26. #501×C137C22semidirect
29. #497×C137C22semidirect
30. #491×C137C22semidirect
43. #330×C137C22semidirect
44. #330×C137C22semidirect
46. #329×C137C22semidirect
284. #19032C137direct (N × H)
285. C137#19032direct (N × H)
287. #3218C2×C137semidirect
288. #3165C2×C137semidirect
289. C2×#489C2×C137semidirect
290. #1664C2×C137semidirect
291. #1661C2×C137semidirect
292. #1531C2×C137semidirect
293. #1527C2×C137semidirect
294. #1524C2×C137semidirect
311. #501C22×C137semidirect
314. #497C22×C137semidirect
315. #491C22×C137semidirect
328. #330C22×C137semidirect
329. #330C22×C137semidirect
331. #329C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3561×C1372
#3218×C1372
#3165×C1372
C2×#489×C1372
#1664×C1372
#1661×C1372
#1531×C1372
#1527×C1372
#1524×C1372
#19032137