Finite Group Databasebeta

← C137×#19463 #46868849

Subgroups — C137×#19463 #46868849

Order 35072.

626 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3229×C137C211yesmaximal, characteristic, complemented
2#3110×C137C211yesmaximal, characteristic
3C2×#476×C137C211yesmaximal, characteristic
4#2974×C137C211yesmaximal, characteristic
5#1703×C137C212yesmaximal, complemented
6#1691×C137C212yesmaximal, complemented
7#1683×C137C212yesmaximal, complemented
8#1671×C137C212yesmaximal, complemented
9#1573×C137C211yesmaximal, characteristic, complemented
10#1558×C137C211yesmaximal, characteristic, complemented
11#1552×C137C211yesmaximal, characteristic, complemented
12#533×C137C2211yescharacteristic
13C2×C4⋊Q8×C137C2211yescharacteristic
14C2×C4×D4×C137C2211yescharacteristic
15#498×C137C2212yescomplemented
16#487×C137C2212yescomplemented
17#484×C137—21no—
18#483×C137—21no—
19#483×C137—21no—
20#476×C137—21no—
21#476×C137—21no—
22#476×C137C2212yes—
23#476×C137C2212yes—
24#475×C137—22no—
25#474×C137C2211yescharacteristic
26#474×C137C2211yescharacteristic
27#461×C137C2211yescharacteristic
28#461×C137C2211yescharacteristic
29#450×C137—21no—
30#440×C137—21no—
31#440×C137—21no—
32#436×C137C2212yes—
33#435×C137—22no—
34C8×D4×C137C2212yes—
35#432×C137C2211yescharacteristic
36#432×C137C2211yescharacteristic
37#431×C137C2211yescharacteristic
38C2×#106×C137—21no—
39C2×C4⋊C8×C137C2211yescharacteristic
40C2×#102×C137—21no—
41#407×C137—21no—
42C2×C22⋊C8×C137—21no—
43#335×C137C2212yescomplemented
44#334×C137C2212yescomplemented
45#333×C137C2212yescomplemented
46#333×C137C2212yescomplemented
47#332×C137C2212yescomplemented
48#332×C137C2212yescomplemented
49C22×Q8×C137—21no—
50C22×D4×C137D411yescharacteristic
51C23×C4×C137—21no—
52C2×SD16×C137—21no—
53C2×SD16×C137—21no—
54C2×M16×C137—22no—
55C22×C8×C137—21no—
56C22×C8×C137—22no—
57C4⋊Q8×C137—21no—
58C4⋊Q8×C137—21no—
59C4⋊Q8×C137—21no—
60C4⋊Q8×C137C2311yescharacteristic
61C4⋊Q8×C137C2311yescharacteristic
62C4⋊Q8×C137C2312yes—
63#125×C137—21no—
64C22⋊Q8×C137—21no—
65C22⋊Q8×C137—21no—
66C4×Q8×C137—21no—
67C4×Q8×C137—21no—
68C4×D4×C137—21no—
69C4×D4×C137—21no—
70C4×D4×C137D411yescharacteristic
71C4×D4×C137D411yescharacteristic
72C4×D4×C137C2311yescharacteristic
73C4×D4×C137C2311yescharacteristic
74#117×C137—21no—
75C2×C4⋊C4×C137—21no—
76C2×C4⋊C4×C137—21no—
77C2×C4⋊C4×C137D411yescharacteristic
78C2×C22⋊C4×C137—21no—
79C2×C42×C137C2311yescharacteristic
80#107×C137—21no—
81#107×C137—21no—
82#106×C137—22no—
83#106×C137—22no—
84#106×C137—22no—
85#106×C137—22no—
86C4⋊C8×C137—21no—
87C4⋊C8×C137D412yes—
88C4⋊C8×C137C2312yes—
89C4⋊C8×C137C2312yes—
90C4⋊C8×C137C2311yescharacteristic
91C4⋊C8×C137C2311yescharacteristic
92#103×C137—22no—
93#103×C137—22no—
94#103×C137—21no—
95#103×C137—21no—
96#102×C137—22no—
97#102×C137—22no—
98#102×C137—21no—
99#102×C137—21no—
100C22⋊C8×C137—21no—
101C22⋊C8×C137—21no—
102C22⋊C8×C137—22no—
103C22⋊C8×C137—22no—
104C22⋊C8×C137D411yescharacteristic
105C22⋊C8×C137D411yescharacteristic
106#97×C137—21no—
107#97×C137—21no—
108C4×C8×C137C2312yes—
109C24×C137—21no—
110C2×Q8×C137—21no—
111C2×Q8×C137—21no—
112C2×Q8×C137—22no—
113C2×Q8×C137—41no—
114C2×Q8×C137—82no—
115C2×D4×C137—22no—
116C2×D4×C137—21no—
117C2×D4×C137—41no—
118C2×D4×C137C2×D411yescharacteristic
119C2×D4×C137C2×D411yescharacteristic
120C22×C4×C137—21no—
121C22×C4×C137—21no—
122C22×C4×C137—21no—
123C22×C4×C137—21no—
124C22×C4×C137—21no—
125C22×C4×C137—41no—
126C22×C4×C137—82no—
127C22×C4×C137C2×D411yescharacteristic
128C22×C4×C137C2×D411yescharacteristic
129C22×C4×C137#4111yescharacteristic
130SD16×C137—42no—
131SD16×C137—42no—
132M16×C137—82no—
133C2×C8×C137—22no—
134C2×C8×C137—21no—
135C2×C8×C137—21no—
136C2×C8×C137—22no—
137C2×C8×C137—42no—
138C2×C8×C137—82no—
139C2×C8×C137C2×D412yes—
140C2×C8×C137C2×D412yes—
141C4⋊C4×C137—21no—
142C4⋊C4×C137—22no—
143C4⋊C4×C137—21no—
144C4⋊C4×C137—22no—
145C4⋊C4×C137—21no—
146C4⋊C4×C137—21no—
147C4⋊C4×C137—21no—
148C4⋊C4×C137—41no—
149C4⋊C4×C137—41no—
150C4⋊C4×C137—41no—
151C4⋊C4×C137—41no—
152C4⋊C4×C137C2×D411yescharacteristic
153C4⋊C4×C137C2×D411yescharacteristic
154C22⋊C4×C137—21no—
155C22⋊C4×C137—21no—
156C22⋊C4×C137—21no—
157C22⋊C4×C137—21no—
158C22⋊C4×C137—41no—
159C42×C137—41no—
160C42×C137C2×D411yescharacteristic
161C42×C137C2×D411yescharacteristic
162C42×C137#4111yescharacteristic
163C42×C137C2411yescharacteristic
164C23×C137—21no—
165C23×C137—21no—
166C23×C137—42no—
167C23×C137—42no—
168C23×C137—81no—
169C23×C137#12111yescharacteristic
170Q8×C137—41no—
171Q8×C137—41no—
172Q8×C137—42no—
173Q8×C137—82no—
174Q8×C137—82no—
175D4×C137—21no—
176D4×C137—21no—
177D4×C137—21no—
178D4×C137—42no—
179D4×C137#13712yes—
180C2×C4×C137—22no—
181C2×C4×C137—21no—
182C2×C4×C137—21no—
183C2×C4×C137—22no—
184C2×C4×C137—21no—
185C2×C4×C137—21no—
186C2×C4×C137—42no—
187C2×C4×C137—42no—
188C2×C4×C137—41no—
189C2×C4×C137—41no—
190C2×C4×C137—42no—
191C2×C4×C137—81no—
192C2×C4×C137—81no—
193C2×C4×C137—81no—
194C2×C4×C137—82no—
195C2×C4×C137#12111yescharacteristic
196C2×C4×C137#12111yescharacteristic
197C2×C4×C137#12111yescharacteristic
198C2×C4×C137C22×D411yescharacteristic
199C2×C4×C137C22×D411yescharacteristic
200C2×C4×C137C2×#4111yescharacteristic
201C8×C137—22no—
202C8×C137—22no—
203C8×C137—41no—
204C8×C137—42no—
205C8×C137—41no—
206C8×C137—42no—
207C22×C137—21no—
208C22×C137—21no—
209C22×C137—22no—
210C22×C137—41no—
211C22×C137—41no—
212C22×C137—41no—
213C22×C137—41no—
214C22×C137—41no—
215C22×C137—84no—
216C22×C137#47112yes—
217C22×C137C2×#12111yescharacteristic
218C4×C137—21no—
219C4×C137—21no—
220C4×C137—21no—
221C4×C137—21no—
222C4×C137—41no—
223C4×C137—41no—
224C4×C137—81no—
225C4×C137—81no—
226C4×C137—82no—
227C4×C137C2×#13711yescharacteristic
228C4×C137#57511yescharacteristic
229C4×C137#57712yes—
230C2×C137—22no—
231C2×C137—42no—
232C2×C137—81no—
233C2×C137#304211yescharacteristic
234C2×C137#305611yescharacteristic
235C2×C137C2×#47111yescharacteristic
236#19463C13711yesmaximal, characteristic, direct product factor, Sylow
237C137#1946311yescharacteristic, direct product factor, Sylow
238#3229C2×C13711yescharacteristic, complemented
239#3110C2×C13711yescharacteristic
240C2×#476C2×C13711yescharacteristic
241#2974C2×C13711yescharacteristic
242#1703C2×C13712yescomplemented
243#1691C2×C13712yescomplemented
244#1683C2×C13712yescomplemented
245#1671C2×C13712yescomplemented
246#1573C2×C13711yescharacteristic, complemented
247#1558C2×C13711yescharacteristic, complemented
248#1552C2×C13711yescharacteristic, complemented
249#533C22×C13711yescharacteristic
250C2×C4⋊Q8C22×C13711yescharacteristic
251C2×C4×D4C22×C13711yescharacteristic
252#498C22×C13712yescomplemented
253#487C22×C13712yescomplemented
254#484—21no—
255#483—21no—
256#483—21no—
257#476—21no—
258#476—21no—
259#476C22×C13712yes—
260#476C22×C13712yes—
261#475—22no—
262#474C22×C13711yescharacteristic
263#474C22×C13711yescharacteristic
264#461C22×C13711yescharacteristic
265#461C22×C13711yescharacteristic
266#450—21no—
267#440—21no—
268#440—21no—
269#436C22×C13712yes—
270#435—22no—
271C8×D4C22×C13712yes—
272#432C22×C13711yescharacteristic
273#432C22×C13711yescharacteristic
274#431C22×C13711yescharacteristic
275C2×#106—21no—
276C2×C4⋊C8C22×C13711yescharacteristic
277C2×#102—21no—
278#407—21no—
279C2×C22⋊C8—21no—
280#335C22×C13712yescomplemented
281#334C22×C13712yescomplemented
282#333C22×C13712yescomplemented
283#333C22×C13712yescomplemented
284#332C22×C13712yescomplemented
285#332C22×C13712yescomplemented
286C22×Q8—21no—
287C22×D4D4×C13711yescharacteristic
288C23×C4—21no—
289C2×SD16—21no—
290C2×SD16—21no—
291C2×M16—22no—
292C22×C8—21no—
293C22×C8—22no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8C23×C13712yes—
298C4⋊Q8C23×C13711yescharacteristic
299C4⋊Q8C23×C13711yescharacteristic
300#125—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4D4×C13711yescharacteristic
308C4×D4D4×C13711yescharacteristic
309C4×D4C23×C13711yescharacteristic
310C4×D4C23×C13711yescharacteristic
311#117—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C13711yescharacteristic
315C2×C22⋊C4—21no—
316C2×C42C23×C13711yescharacteristic
317#107—21no—
318#107—21no—
319#106—22no—
320#106—22no—
321#106—22no—
322#106—22no—
323C4⋊C8—21no—
324C4⋊C8D4×C13712yes—
325C4⋊C8C23×C13712yes—
326C4⋊C8C23×C13712yes—
327C4⋊C8C23×C13711yescharacteristic
328C4⋊C8C23×C13711yescharacteristic
329#103—22no—
330#103—22no—
331#103—21no—
332#103—21no—
333#102—22no—
334#102—22no—
335#102—21no—
336#102—21no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—22no—
340C22⋊C8—22no—
341C22⋊C8D4×C13711yescharacteristic
342C22⋊C8D4×C13711yescharacteristic
343#97—21no—
344#97—21no—
345C4×C8C23×C13712yes—
346C24—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—22no—
350C2×Q8—41no—
351C2×Q8—82no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4C2×D4×C13711yescharacteristic
356C2×D4C2×D4×C13711yescharacteristic
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—82no—
364C22×C4C2×D4×C13711yescharacteristic
365C22×C4C2×D4×C13711yescharacteristic
366C22×C4#41×C13711yescharacteristic
367SD16—42no—
368SD16—42no—
369M16—82no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—42no—
375C2×C8—82no—
376C2×C8C2×D4×C13712yes—
377C2×C8C2×D4×C13712yes—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4C2×D4×C13711yescharacteristic
390C4⋊C4C2×D4×C13711yescharacteristic
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—41no—
396C42—41no—
397C42C2×D4×C13711yescharacteristic
398C42C2×D4×C13711yescharacteristic
399C42#41×C13711yescharacteristic
400C42C24×C13711yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—42no—
405C23—81no—
406C23#121×C13711yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—42no—
410Q8—82no—
411Q8—82no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—42no—
416D4#137×C13712yes—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4#121×C13711yescharacteristic
433C2×C4#121×C13711yescharacteristic
434C2×C4#121×C13711yescharacteristic
435C2×C4C22×D4×C13711yescharacteristic
436C2×C4C22×D4×C13711yescharacteristic
437C2×C4C2×#41×C13711yescharacteristic
438C8—22no—
439C8—22no—
440C8—41no—
441C8—42no—
442C8—41no—
443C8—42no—
444C22—21no—
445C22—21no—
446C22—22no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—84no—
453C22#471×C13712yes—
454C22C2×#121×C13711yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—41no—
460C4—41no—
461C4—81no—
462C4—81no—
463C4—82no—
464C4C2×#137×C13711yescharacteristic
465C4#575×C13711yescharacteristic
466C4#577×C13712yes—
467C2—22no—
468C2—42no—
469C2—81no—
470C2#3042×C13711yescharacteristic
471C2#3056×C13711yescharacteristic
472C2C2×#471×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radicalC22×D4×C137D4
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
1. #3229×C137C2semidirect
5. #1703×C137C2semidirect
6. #1691×C137C2semidirect
7. #1683×C137C2semidirect
8. #1671×C137C2semidirect
9. #1573×C137C2semidirect
10. #1558×C137C2semidirect
11. #1552×C137C2semidirect
15. #498×C137C22semidirect
16. #487×C137C22semidirect
43. #335×C137C22semidirect
44. #334×C137C22semidirect
45. #333×C137C22semidirect
46. #333×C137C22semidirect
47. #332×C137C22semidirect
48. #332×C137C22semidirect
236. #19463C137direct (N × H)
237. C137#19463direct (N × H)
238. #3229C2×C137semidirect
242. #1703C2×C137semidirect
243. #1691C2×C137semidirect
244. #1683C2×C137semidirect
245. #1671C2×C137semidirect
246. #1573C2×C137semidirect
247. #1558C2×C137semidirect
248. #1552C2×C137semidirect
252. #498C22×C137semidirect
253. #487C22×C137semidirect
280. #335C22×C137semidirect
281. #334C22×C137semidirect
282. #333C22×C137semidirect
283. #333C22×C137semidirect
284. #332C22×C137semidirect
285. #332C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3229×C1372
#3110×C1372
C2×#476×C1372
#2974×C1372
#1703×C1372
#1691×C1372
#1683×C1372
#1671×C1372
#1573×C1372
#1558×C1372
#1552×C1372
#19463137