Finite Group Databasebeta

← C137×#25832 #46875218

Subgroups — C137×#25832 #46875218

Order 35072.

954 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C137C211yesmaximal, characteristic
2#3166×C137C211yesmaximal, characteristic, complemented
3#3080×C137C211yesmaximal, characteristic
4#2660×C137C211yesmaximal, characteristic, complemented
5#2061×C137C212yesmaximal, complemented
6#2060×C137C212yesmaximal, complemented
7#1997×C137C211yesmaximal, characteristic, complemented
8#1995×C137C211yesmaximal, characteristic, complemented
9#1860×C137C212yesmaximal
10#1859×C137C212yesmaximal
11#1759×C137C211yesmaximal, characteristic
12Q82×C137—21no—
13#557×C137—21no—
14#554×C137—21no—
15#554×C137—22no—
16D4×Q8×C137—22no—
17D4×Q8×C137—21no—
18#544×C137—22no—
19#544×C137C2212yes—
20#533×C137—21no—
21#533×C137C2211yescharacteristic
22C2×C4⋊Q8×C137—21no—
23C2×C4⋊Q8×C137C2211yescharacteristic
24C2×#125×C137C2211yescharacteristic
25#520×C137C2212yes—
26C4×#41×C137C2211yescharacteristic
27#501×C137—21no—
28#501×C137—21no—
29#499×C137—22no—
30#479×C137—21no—
31#479×C137—21no—
32#478×C137—21no—
33#478×C137—21no—
34#428×C137C2211yescharacteristic
35#428×C137C2211yescharacteristic
36#428×C137C2212yes—
37#428×C137C2212yes—
38#423×C137C2211yescharacteristic
39C2×#104×C137C2212yes—
40#417×C137C2211yescharacteristic
41#417×C137C2211yescharacteristic
42C4×M16×C137C2211yescharacteristic
43#398×C137—22no—
44#395×C137—22no—
45#384×C137C2212yes—
46#382×C137C2212yes—
47#376×C137C2211yescharacteristic
48#343×C137C2212yes—
49#343×C137C2212yes—
50#339×C137C2212yes—
51#339×C137C2212yes—
52#339×C137C2212yes—
53C2×#41×C137C2311yescharacteristic
54C22×Q8×C137—22no—
55C22×Q8×C137D412yes—
56C2×M16×C137C2311yescharacteristic
57C2×M16×C137C2311yescharacteristic
58C2×M16×C137C2312yes—
59C4⋊Q8×C137—22no—
60C4⋊Q8×C137—22no—
61C4⋊Q8×C137—24no—
62C4⋊Q8×C137—22no—
63C4⋊Q8×C137—22no—
64C4⋊Q8×C137—21no—
65C4⋊Q8×C137—21no—
66C4⋊Q8×C137—21no—
67C4⋊Q8×C137—21no—
68C4⋊Q8×C137D411yescharacteristic
69C4⋊Q8×C137D411yescharacteristic
70#125×C137—24no—
71#125×C137—22no—
72#125×C137—22no—
73#125×C137—21no—
74#125×C137—21no—
75#125×C137—21no—
76#125×C137—21no—
77#125×C137D412yes—
78C22⋊Q8×C137—22no—
79C22⋊Q8×C137—22no—
80C22⋊Q8×C137—24no—
81C22⋊Q8×C137—24no—
82C22⋊Q8×C137—21no—
83C22⋊Q8×C137—21no—
84C22⋊Q8×C137—24no—
85C4×Q8×C137—22no—
86C4×Q8×C137—22no—
87C4×Q8×C137—22no—
88C4×Q8×C137—21no—
89C4×Q8×C137—21no—
90C4×Q8×C137D411yescharacteristic
91C4×Q8×C137D411yescharacteristic
92C4×D4×C137—22no—
93C4×D4×C137—21no—
94C4×D4×C137—21no—
95C4×D4×C137—24no—
96C4×D4×C137D411yescharacteristic
97C4×D4×C137D411yescharacteristic
98#117×C137—22no—
99#117×C137—21no—
100#117×C137C2311yescharacteristic
101#117×C137C2312yes—
102C2×C4⋊C4×C137—22no—
103C2×C4⋊C4×C137—22no—
104C2×C4⋊C4×C137—21no—
105C2×C4⋊C4×C137—21no—
106C2×C4⋊C4×C137—24no—
107C2×C4⋊C4×C137D412yes—
108C2×C4⋊C4×C137C2311yescharacteristic
109C2×C4⋊C4×C137C2311yescharacteristic
110C2×C4⋊C4×C137C2312yes—
111C2×C42×C137—21no—
112C2×C42×C137C2312yes—
113C2×C42×C137C2311yescharacteristic
114#107×C137—21no—
115#107×C137—21no—
116#107×C137—22no—
117#107×C137—22no—
118#106×C137—21no—
119#106×C137—21no—
120#106×C137—22no—
121#106×C137—22no—
122C4⋊C8×C137—21no—
123C4⋊C8×C137—21no—
124#104×C137Q818yescomplemented
125#103×C137—21no—
126#103×C137—21no—
127#102×C137—21no—
128#102×C137—21no—
129#97×C137—21no—
130C4×C8×C137—21no—
131#95×C137—21no—
132#95×C137—21no—
133#95×C137—24no—
134#41×C137—22no—
135#41×C137C2×Q814yes—
136C2×Q8×C137—24no—
137C2×Q8×C137—21no—
138C2×Q8×C137—22no—
139C2×Q8×C137—21no—
140C2×Q8×C137—22no—
141C2×Q8×C137—82no—
142C2×Q8×C137—84no—
143C2×Q8×C137C2×D411yescharacteristic
144C2×D4×C137—21no—
145C2×D4×C137C2×D411yescharacteristic
146C22×C4×C137—21no—
147C22×C4×C137—22no—
148C22×C4×C137—24no—
149C22×C4×C137—21no—
150C22×C4×C137—21no—
151C22×C4×C137—21no—
152C22×C4×C137—21no—
153C22×C4×C137C2×D414yes—
154C22×C4×C137C2×D411yescharacteristic
155C22×C4×C137C2×D411yescharacteristic
156C22×C4×C137C2411yescharacteristic
157M16×C137—22no—
158M16×C137—22no—
159M16×C137—22no—
160M16×C137C2×Q814yescomplemented
161C2×C8×C137—22no—
162C2×C8×C137—21no—
163C2×C8×C137—21no—
164C4⋊C4×C137—24no—
165C4⋊C4×C137—24no—
166C4⋊C4×C137—24no—
167C4⋊C4×C137—24no—
168C4⋊C4×C137—21no—
169C4⋊C4×C137—22no—
170C4⋊C4×C137—22no—
171C4⋊C4×C137—21no—
172C4⋊C4×C137—21no—
173C4⋊C4×C137—21no—
174C4⋊C4×C137—22no—
175C4⋊C4×C137—22no—
176C4⋊C4×C137—22no—
177C4⋊C4×C137—22no—
178C4⋊C4×C137—21no—
179C4⋊C4×C137—21no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—21no—
182C4⋊C4×C137—41no—
183C4⋊C4×C137—41no—
184C4⋊C4×C137—41no—
185C4⋊C4×C137—41no—
186C4⋊C4×C137—84no—
187C4⋊C4×C137C2×D412yes—
188C4⋊C4×C137C2×D412yes—
189C4⋊C4×C137C2×D411yescharacteristic
190C4⋊C4×C137C2×D411yescharacteristic
191C22⋊C4×C137—24no—
192C22⋊C4×C137—22no—
193C22⋊C4×C137—21no—
194C22⋊C4×C137—21no—
195C22⋊C4×C137—21no—
196C42×C137—24no—
197C42×C137—21no—
198C42×C137—21no—
199C42×C137—21no—
200C42×C137—22no—
201C42×C137—22no—
202C42×C137C2×D411yescharacteristic
203C42×C137C2×D411yescharacteristic
204C42×C137C2×D411yescharacteristic
205C42×C137C2×D411yescharacteristic
206C42×C137C2×Q814yescomplemented
207C23×C137—21no—
208C23×C137C22×D411yescharacteristic
209Q8×C137—21no—
210Q8×C137—42no—
211Q8×C137—44no—
212Q8×C137—42no—
213Q8×C137—82no—
214Q8×C137—84no—
215Q8×C137C4⋊Q812yes—
216D4×C137—24no—
217D4×C137—21no—
218D4×C137C4⋊Q812yes—
219C2×C4×C137—21no—
220C2×C4×C137—24no—
221C2×C4×C137—22no—
222C2×C4×C137—21no—
223C2×C4×C137—21no—
224C2×C4×C137—24no—
225C2×C4×C137—22no—
226C2×C4×C137—24no—
227C2×C4×C137—41no—
228C2×C4×C137—41no—
229C2×C4×C137—42no—
230C2×C4×C137—42no—
231C2×C4×C137—42no—
232C2×C4×C137—42no—
233C2×C4×C137—44no—
234C2×C4×C137—42no—
235C2×C4×C137—42no—
236C2×C4×C137—41no—
237C2×C4×C137—41no—
238C2×C4×C137—84no—
239C2×C4×C137#12011yescharacteristic
240C2×C4×C137#12011yescharacteristic
241C2×C4×C137#12011yescharacteristic
242C2×C4×C137#12011yescharacteristic
243C2×C4×C137C22×D411yescharacteristic
244C2×C4×C137C22×D411yescharacteristic
245C2×C4×C137C22×Q812yes—
246C2×C4×C1372−1+412yes—
247C8×C137—24no—
248C8×C137—41no—
249C8×C137—41no—
250C22×C137—21no—
251C22×C137—21no—
252C22×C137—22no—
253C22×C137—41no—
254C22×C137—41no—
255C22×C137C2×#12011yescharacteristic
256C22×C137D4×Q812yes—
257C4×C137—22no—
258C4×C137—21no—
259C4×C137—21no—
260C4×C137—21no—
261C4×C137—21no—
262C4×C137—44no—
263C4×C137—41no—
264C4×C137—44no—
265C4×C137—42no—
266C4×C137—41no—
267C4×C137—42no—
268C4×C137—81no—
269C4×C137—81no—
270C4×C137C2×C4⋊Q811yescharacteristic
271C4×C137#53611yescharacteristic
272C4×C137D4×Q812yes—
273C2×C137—22no—
274C2×C137—42no—
275C2×C137#243411yescharacteristic
276C2×C137#301911yescharacteristic
277C2×C137#302011yescharacteristic
278#25832C13711yesmaximal, characteristic, direct product factor, Sylow
279C137#2583211yescharacteristic, direct product factor, Sylow
280#3503C2×C13711yescharacteristic
281#3166C2×C13711yescharacteristic, complemented
282#3080C2×C13711yescharacteristic
283#2660C2×C13711yescharacteristic, complemented
284#2061C2×C13712yescomplemented
285#2060C2×C13712yescomplemented
286#1997C2×C13711yescharacteristic, complemented
287#1995C2×C13711yescharacteristic, complemented
288#1860C2×C13712yes—
289#1859C2×C13712yes—
290#1759C2×C13711yescharacteristic
291Q82—21no—
292#557—21no—
293#554—21no—
294#554—22no—
295D4×Q8—22no—
296D4×Q8—21no—
297#544—22no—
298#544C22×C13712yes—
299#533—21no—
300#533C22×C13711yescharacteristic
301C2×C4⋊Q8—21no—
302C2×C4⋊Q8C22×C13711yescharacteristic
303C2×#125C22×C13711yescharacteristic
304#520C22×C13712yes—
305C4×#41C22×C13711yescharacteristic
306#501—21no—
307#501—21no—
308#499—22no—
309#479—21no—
310#479—21no—
311#478—21no—
312#478—21no—
313#428C22×C13711yescharacteristic
314#428C22×C13711yescharacteristic
315#428C22×C13712yes—
316#428C22×C13712yes—
317#423C22×C13711yescharacteristic
318C2×#104C22×C13712yes—
319#417C22×C13711yescharacteristic
320#417C22×C13711yescharacteristic
321C4×M16C22×C13711yescharacteristic
322#398—22no—
323#395—22no—
324#384C22×C13712yes—
325#382C22×C13712yes—
326#376C22×C13711yescharacteristic
327#343C22×C13712yes—
328#343C22×C13712yes—
329#339C22×C13712yes—
330#339C22×C13712yes—
331#339C22×C13712yes—
332C2×#41C23×C13711yescharacteristic
333C22×Q8—22no—
334C22×Q8D4×C13712yes—
335C2×M16C23×C13711yescharacteristic
336C2×M16C23×C13711yescharacteristic
337C2×M16C23×C13712yes—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—24no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8D4×C13711yescharacteristic
348C4⋊Q8D4×C13711yescharacteristic
349#125—24no—
350#125—22no—
351#125—22no—
352#125—21no—
353#125—21no—
354#125—21no—
355#125—21no—
356#125D4×C13712yes—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—24no—
360C22⋊Q8—24no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—24no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8D4×C13711yescharacteristic
370C4×Q8D4×C13711yescharacteristic
371C4×D4—22no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—24no—
375C4×D4D4×C13711yescharacteristic
376C4×D4D4×C13711yescharacteristic
377#117—22no—
378#117—21no—
379#117C23×C13711yescharacteristic
380#117C23×C13712yes—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4D4×C13712yes—
387C2×C4⋊C4C23×C13711yescharacteristic
388C2×C4⋊C4C23×C13711yescharacteristic
389C2×C4⋊C4C23×C13712yes—
390C2×C42—21no—
391C2×C42C23×C13712yes—
392C2×C42C23×C13711yescharacteristic
393#107—21no—
394#107—21no—
395#107—22no—
396#107—22no—
397#106—21no—
398#106—21no—
399#106—22no—
400#106—22no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403#104Q8×C13718yescomplemented
404#103—21no—
405#103—21no—
406#102—21no—
407#102—21no—
408#97—21no—
409C4×C8—21no—
410#95—21no—
411#95—21no—
412#95—24no—
413#41—22no—
414#41C2×Q8×C13714yes—
415C2×Q8—24no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—82no—
421C2×Q8—84no—
422C2×Q8C2×D4×C13711yescharacteristic
423C2×D4—21no—
424C2×D4C2×D4×C13711yescharacteristic
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4C2×D4×C13714yes—
433C22×C4C2×D4×C13711yescharacteristic
434C22×C4C2×D4×C13711yescharacteristic
435C22×C4C24×C13711yescharacteristic
436M16—22no—
437M16—22no—
438M16—22no—
439M16C2×Q8×C13714yescomplemented
440C2×C8—22no—
441C2×C8—21no—
442C2×C8—21no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—84no—
466C4⋊C4C2×D4×C13712yes—
467C4⋊C4C2×D4×C13712yes—
468C4⋊C4C2×D4×C13711yescharacteristic
469C4⋊C4C2×D4×C13711yescharacteristic
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C42—24no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—22no—
480C42—22no—
481C42C2×D4×C13711yescharacteristic
482C42C2×D4×C13711yescharacteristic
483C42C2×D4×C13711yescharacteristic
484C42C2×D4×C13711yescharacteristic
485C42C2×Q8×C13714yescomplemented
486C23—21no—
487C23C22×D4×C13711yescharacteristic
488Q8—21no—
489Q8—44no—
490Q8—42no—
491Q8—42no—
492Q8—82no—
493Q8—84no—
494Q8C4⋊Q8×C13712yes—
495D4—24no—
496D4—21no—
497D4C4⋊Q8×C13712yes—
498C2×C4—21no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—84no—
518C2×C4#120×C13711yescharacteristic
519C2×C4#120×C13711yescharacteristic
520C2×C4#120×C13711yescharacteristic
521C2×C4#120×C13711yescharacteristic
522C2×C4C22×D4×C13711yescharacteristic
523C2×C4C22×D4×C13711yescharacteristic
524C2×C4C22×Q8×C13712yes—
525C2×C42−1+4×C13712yes—
526C8—24no—
527C8—41no—
528C8—41no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—41no—
533C22—41no—
534C22C2×#120×C13711yescharacteristic
535C22D4×Q8×C13712yes—
536C4—22no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—44no—
542C4—41no—
543C4—44no—
544C4—42no—
545C4—41no—
546C4—42no—
547C4—81no—
548C4—81no—
549C4C2×C4⋊Q8×C13711yescharacteristic
550C4#536×C13711yescharacteristic
551C4D4×Q8×C13712yes—
552C2—22no—
553C2—42no—
554C2#2434×C13711yescharacteristic
555C2#3019×C13711yescharacteristic
556C2#3020×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×#41×C137C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3166×C137C2semidirect
4. #2660×C137C2semidirect
5. #2061×C137C2semidirect
6. #2060×C137C2semidirect
7. #1997×C137C2semidirect
8. #1995×C137C2semidirect
124. #104×C137Q8semidirect
160. M16×C137C2×Q8semidirect
206. C42×C137C2×Q8semidirect
278. #25832C137direct (N × H)
279. C137#25832direct (N × H)
281. #3166C2×C137semidirect
283. #2660C2×C137semidirect
284. #2061C2×C137semidirect
285. #2060C2×C137semidirect
286. #1997C2×C137semidirect
287. #1995C2×C137semidirect
403. #104Q8×C137semidirect
439. M16C2×Q8×C137semidirect
485. C42C2×Q8×C137semidirect

Maximal subgroups

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

subgroupindex
#3503×C1372
#3166×C1372
#3080×C1372
#2660×C1372
#2061×C1372
#2060×C1372
#1997×C1372
#1995×C1372
#1860×C1372
#1859×C1372
#1759×C1372
#25832137