Finite Group Databasebeta

← C137×#19491 #46868877

Subgroups — C137×#19491 #46868877

Order 35072.

614 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3226×C137C211yesmaximal, characteristic, complemented
2#3106×C137C211yesmaximal, characteristic
3#3079×C137C211yesmaximal, characteristic, complemented
4#2990×C137C211yesmaximal, characteristic, complemented
5#1698×C137C212yesmaximal, complemented
6#1696×C137C212yesmaximal, complemented
7#1677×C137C212yesmaximal, complemented
8#1675×C137C212yesmaximal, complemented
9#1574×C137C211yesmaximal, characteristic, complemented
10#1560×C137C211yesmaximal, characteristic, complemented
11#1548×C137C211yesmaximal, characteristic, complemented
12#532×C137C2211yescharacteristic
13C2×C4⋊Q8×C137C2211yescharacteristic
14C4×#41×C137C2211yescharacteristic
15#500×C137C2212yes—
16#486×C137C2212yes—
17#482×C137—21no—
18#480×C137—22no—
19#477×C137C2212yes—
20#477×C137C2211yescharacteristic
21#476×C137C2212yes—
22#476×C137C2211yescharacteristic
23#475×C137—21no—
24#474×C137—21no—
25#474×C137—21no—
26#474×C137—21no—
27#460×C137C2211yescharacteristic
28#459×C137C2211yescharacteristic
29#449×C137—21no—
30#446×C137C2212yes—
31C4×SD16×C137—21no—
32C4×D8×C137—21no—
33#435×C137—22no—
34C8×D4×C137C2212yes—
35#432×C137—21no—
36#431×C137C2211yescharacteristic
37#431×C137C2211yescharacteristic
38#428×C137—21no—
39#423×C137C2211yescharacteristic
40#423×C137C2211yescharacteristic
41C2×C4⋊C8×C137—21no—
42#417×C137—21no—
43#335×C137C2212yes—
44#334×C137C2212yes—
45#333×C137C2212yes—
46#333×C137C2212yes—
47#333×C137C2212yes—
48#331×C137C2212yes—
49C2×#41×C137—21no—
50C2×#41×C137D411yescharacteristic
51C22×Q8×C137—21no—
52C2×SD16×C137—21no—
53C2×D8×C137—21no—
54C2×M16×C137—21no—
55C2×M16×C137—21no—
56C22×C8×C137—22no—
57C4⋊Q8×C137—21no—
58C4⋊Q8×C137—21no—
59C4⋊Q8×C137—21no—
60C4⋊Q8×C137C2312yes—
61C4⋊Q8×C137C2311yescharacteristic
62#127×C137C2311yescharacteristic
63#124×C137—21no—
64#121×C137—21no—
65#121×C137—21no—
66C4×Q8×C137D411yescharacteristic
67C4×Q8×C137C2311yescharacteristic
68C4×D4×C137—21no—
69C4×D4×C137—21no—
70C4×D4×C137—21no—
71C4×D4×C137—21no—
72C4×D4×C137D411yescharacteristic
73C4×D4×C137C2311yescharacteristic
74#117×C137—21no—
75#117×C137D411yescharacteristic
76C2×C4⋊C4×C137—21no—
77C2×C4⋊C4×C137—21no—
78C2×C42×C137—21no—
79C2×C42×C137C2311yescharacteristic
80#107×C137—22no—
81#107×C137—22no—
82#107×C137—22no—
83#107×C137—21no—
84#106×C137—22no—
85#106×C137—21no—
86C4⋊C8×C137—22no—
87C4⋊C8×C137—21no—
88C4⋊C8×C137—21no—
89C4⋊C8×C137D411yescharacteristic
90C4⋊C8×C137D411yescharacteristic
91C4⋊C8×C137C2312yes—
92C4⋊C8×C137C2312yes—
93C4⋊C8×C137C2311yescharacteristic
94C4⋊C8×C137C2311yescharacteristic
95#103×C137—22no—
96#103×C137—21no—
97#102×C137—22no—
98#102×C137—21no—
99#102×C137—22no—
100#102×C137—22no—
101#102×C137—21no—
102#102×C137—21no—
103C22⋊C8×C137—21no—
104C22⋊C8×C137—22no—
105C22⋊C8×C137D412yes—
106#97×C137—22no—
107C4×C8×C137—21no—
108C4×C8×C137C2312yes—
109#41×C137—22no—
110#41×C137—41no—
111#41×C137—82no—
112C2×Q8×C137—21no—
113C2×Q8×C137—22no—
114C2×Q8×C137—41no—
115C2×Q8×C137—82no—
116C2×Q8×C137C2×D411yescharacteristic
117C2×D4×C137—21no—
118C2×D4×C137—21no—
119C2×D4×C137—21no—
120C2×D4×C137—21no—
121C2×D4×C137—41no—
122C2×D4×C137C2×D411yescharacteristic
123C22×C4×C137—21no—
124C22×C4×C137—21no—
125C22×C4×C137—21no—
126C22×C4×C137—41no—
127C22×C4×C137—41no—
128C22×C4×C137C2×D411yescharacteristic
129C22×C4×C137C2×D411yescharacteristic
130C22×C4×C137#4111yescharacteristic
131SD16×C137—42no—
132D8×C137—42no—
133M16×C137—42no—
134M16×C137—81no—
135C2×C8×C137—21no—
136C2×C8×C137—21no—
137C2×C8×C137—22no—
138C2×C8×C137—22no—
139C2×C8×C137—82no—
140C2×C8×C137C2×D412yes—
141C2×C8×C137C2×D412yes—
142C4⋊C4×C137—21no—
143C4⋊C4×C137—21no—
144C4⋊C4×C137—22no—
145C4⋊C4×C137—22no—
146C4⋊C4×C137—21no—
147C4⋊C4×C137—21no—
148C4⋊C4×C137—41no—
149C4⋊C4×C137—41no—
150C4⋊C4×C137C2×D411yescharacteristic
151C4⋊C4×C137C2×D411yescharacteristic
152C22⋊C4×C137—21no—
153C22⋊C4×C137—21no—
154C22⋊C4×C137—21no—
155C22⋊C4×C137—41no—
156C22⋊C4×C137—41no—
157C42×C137—21no—
158C42×C137—21no—
159C42×C137—21no—
160C42×C137C2×D411yescharacteristic
161C42×C137C2×D411yescharacteristic
162C42×C137#4111yescharacteristic
163C42×C137C2411yescharacteristic
164C23×C137—21no—
165C23×C137—41no—
166C23×C137#12111yescharacteristic
167Q8×C137—21no—
168Q8×C137—21no—
169Q8×C137—82no—
170Q8×C137—81no—
171Q8×C137—82no—
172D4×C137—21no—
173D4×C137—42no—
174D4×C137—41no—
175D4×C137—41no—
176D4×C137—41no—
177D4×C137—41no—
178D4×C137—81no—
179D4×C137—82no—
180D4×C137#13712yes—
181C2×C4×C137—21no—
182C2×C4×C137—21no—
183C2×C4×C137—21no—
184C2×C4×C137—21no—
185C2×C4×C137—22no—
186C2×C4×C137—21no—
187C2×C4×C137—21no—
188C2×C4×C137—21no—
189C2×C4×C137—42no—
190C2×C4×C137—41no—
191C2×C4×C137—41no—
192C2×C4×C137—42no—
193C2×C4×C137—41no—
194C2×C4×C137—42no—
195C2×C4×C137—82no—
196C2×C4×C137—82no—
197C2×C4×C137#12111yescharacteristic
198C2×C4×C137#12111yescharacteristic
199C2×C4×C137#12111yescharacteristic
200C2×C4×C137C22×D411yescharacteristic
201C2×C4×C137C22×D411yescharacteristic
202C2×C4×C137C2×#4111yescharacteristic
203C8×C137—22no—
204C8×C137—22no—
205C8×C137—41no—
206C8×C137—42no—
207C8×C137—41no—
208C8×C137—42no—
209C22×C137—21no—
210C22×C137—21no—
211C22×C137—22no—
212C22×C137—21no—
213C22×C137—41no—
214C22×C137—41no—
215C22×C137—81no—
216C22×C137—81no—
217C22×C137—81no—
218C22×C137C2×#12111yescharacteristic
219C4×C137—21no—
220C4×C137—21no—
221C4×C137—21no—
222C4×C137—41no—
223C4×C137—41no—
224C4×C137—41no—
225C4×C137—81no—
226C4×C137—82no—
227C4×C137#47212yes—
228C4×C137C2×#13711yescharacteristic
229C4×C137#57511yescharacteristic
230C4×C137#57711yescharacteristic
231C4×C137#57811yescharacteristic
232C2×C137—41no—
233C2×C137—42no—
234C2×C137—161no—
235C2×C137#304611yescharacteristic
236C2×C137#305611yescharacteristic
237C2×C137C2×#47211yescharacteristic
238#19491C13711yesmaximal, characteristic, direct product factor, Sylow
239C137#1949111yescharacteristic, direct product factor, Sylow
240#3226C2×C13711yescharacteristic, complemented
241#3106C2×C13711yescharacteristic
242#3079C2×C13711yescharacteristic, complemented
243#2990C2×C13711yescharacteristic, complemented
244#1698C2×C13712yescomplemented
245#1696C2×C13712yescomplemented
246#1677C2×C13712yescomplemented
247#1675C2×C13712yescomplemented
248#1574C2×C13711yescharacteristic, complemented
249#1560C2×C13711yescharacteristic, complemented
250#1548C2×C13711yescharacteristic, complemented
251#532C22×C13711yescharacteristic
252C2×C4⋊Q8C22×C13711yescharacteristic
253C4×#41C22×C13711yescharacteristic
254#500C22×C13712yes—
255#486C22×C13712yes—
256#482—21no—
257#480—22no—
258#477C22×C13712yes—
259#477C22×C13711yescharacteristic
260#476C22×C13712yes—
261#476C22×C13711yescharacteristic
262#475—21no—
263#474—21no—
264#474—21no—
265#474—21no—
266#460C22×C13711yescharacteristic
267#459C22×C13711yescharacteristic
268#449—21no—
269#446C22×C13712yes—
270C4×SD16—21no—
271C4×D8—21no—
272#435—22no—
273C8×D4C22×C13712yes—
274#432—21no—
275#431C22×C13711yescharacteristic
276#431C22×C13711yescharacteristic
277#428—21no—
278#423C22×C13711yescharacteristic
279#423C22×C13711yescharacteristic
280C2×C4⋊C8—21no—
281#417—21no—
282#335C22×C13712yes—
283#334C22×C13712yes—
284#333C22×C13712yes—
285#333C22×C13712yes—
286#333C22×C13712yes—
287#331C22×C13712yes—
288C2×#41—21no—
289C2×#41D4×C13711yescharacteristic
290C22×Q8—21no—
291C2×SD16—21no—
292C2×D8—21no—
293C2×M16—21no—
294C2×M16—21no—
295C22×C8—22no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8C23×C13712yes—
300C4⋊Q8C23×C13711yescharacteristic
301#127C23×C13711yescharacteristic
302#124—21no—
303#121—21no—
304#121—21no—
305C4×Q8D4×C13711yescharacteristic
306C4×Q8C23×C13711yescharacteristic
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4D4×C13711yescharacteristic
312C4×D4C23×C13711yescharacteristic
313#117—21no—
314#117D4×C13711yescharacteristic
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C42—21no—
318C2×C42C23×C13711yescharacteristic
319#107—22no—
320#107—22no—
321#107—22no—
322#107—21no—
323#106—22no—
324#106—21no—
325C4⋊C8—22no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8D4×C13711yescharacteristic
329C4⋊C8D4×C13711yescharacteristic
330C4⋊C8C23×C13712yes—
331C4⋊C8C23×C13712yes—
332C4⋊C8C23×C13711yescharacteristic
333C4⋊C8C23×C13711yescharacteristic
334#103—22no—
335#103—21no—
336#102—22no—
337#102—21no—
338#102—22no—
339#102—22no—
340#102—21no—
341#102—21no—
342C22⋊C8—21no—
343C22⋊C8—22no—
344C22⋊C8D4×C13712yes—
345#97—22no—
346C4×C8—21no—
347C4×C8C23×C13712yes—
348#41—22no—
349#41—41no—
350#41—82no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×Q8C2×D4×C13711yescharacteristic
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4C2×D4×C13711yescharacteristic
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×D4×C13711yescharacteristic
368C22×C4C2×D4×C13711yescharacteristic
369C22×C4#41×C13711yescharacteristic
370SD16—42no—
371D8—42no—
372M16—42no—
373M16—81no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—82no—
379C2×C8C2×D4×C13712yes—
380C2×C8C2×D4×C13712yes—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
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—41no—
395C22⋊C4—41no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42C2×D4×C13711yescharacteristic
400C42C2×D4×C13711yescharacteristic
401C42#41×C13711yescharacteristic
402C42C24×C13711yescharacteristic
403C23—21no—
404C23—41no—
405C23#121×C13711yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—82no—
409Q8—81no—
410Q8—82no—
411D4—21no—
412D4—42no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—81no—
418D4—82no—
419D4#137×C13712yes—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4#121×C13711yescharacteristic
437C2×C4#121×C13711yescharacteristic
438C2×C4#121×C13711yescharacteristic
439C2×C4C22×D4×C13711yescharacteristic
440C2×C4C22×D4×C13711yescharacteristic
441C2×C4C2×#41×C13711yescharacteristic
442C8—22no—
443C8—22no—
444C8—41no—
445C8—42no—
446C8—41no—
447C8—42no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22C2×#121×C13711yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—81no—
465C4—82no—
466C4#472×C13712yes—
467C4C2×#137×C13711yescharacteristic
468C4#575×C13711yescharacteristic
469C4#577×C13711yescharacteristic
470C4#578×C13711yescharacteristic
471C2—41no—
472C2—42no—
473C2—161no—
474C2#3046×C13711yescharacteristic
475C2#3056×C13711yescharacteristic
476C2C2×#472×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#3106×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
1. #3226×C137C2semidirect
3. #3079×C137C2semidirect
4. #2990×C137C2semidirect
5. #1698×C137C2semidirect
6. #1696×C137C2semidirect
7. #1677×C137C2semidirect
8. #1675×C137C2semidirect
9. #1574×C137C2semidirect
10. #1560×C137C2semidirect
11. #1548×C137C2semidirect
238. #19491C137direct (N × H)
239. C137#19491direct (N × H)
240. #3226C2×C137semidirect
242. #3079C2×C137semidirect
243. #2990C2×C137semidirect
244. #1698C2×C137semidirect
245. #1696C2×C137semidirect
246. #1677C2×C137semidirect
247. #1675C2×C137semidirect
248. #1574C2×C137semidirect
249. #1560C2×C137semidirect
250. #1548C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3226×C1372
#3106×C1372
#3079×C1372
#2990×C1372
#1698×C1372
#1696×C1372
#1677×C1372
#1675×C1372
#1574×C1372
#1560×C1372
#1548×C1372
#19491137