Finite Group Databasebeta

← C137×#19457 #46868843

Subgroups — C137×#19457 #46868843

Order 35072.

660 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3206×C137C211yesmaximal, characteristic, complemented
2#3109×C137C211yesmaximal, characteristic
3C2×#474×C137C211yesmaximal, characteristic, complemented
4#2974×C137C211yesmaximal, characteristic, complemented
5#1703×C137C212yesmaximal, complemented
6#1685×C137C212yesmaximal, complemented
7#1683×C137C212yesmaximal, complemented
8#1665×C137C212yesmaximal, complemented
9#1573×C137C211yesmaximal, characteristic, complemented
10#1556×C137C211yesmaximal, characteristic, complemented
11#1551×C137C211yesmaximal, characteristic, complemented
12#532×C137C2211yescharacteristic
13C2×C4⋊Q8×C137C2211yescharacteristic
14C2×C4×D4×C137C2211yescharacteristic
15#492×C137C2212yescomplemented
16#487×C137C2212yescomplemented
17#481×C137—21no—
18#476×C137C2211yescharacteristic
19#476×C137C2211yescharacteristic
20#474×C137—21no—
21#474×C137—21no—
22#474×C137C2212yes—
23#474×C137C2212yes—
24#461×C137—22no—
25#459×C137C2211yescharacteristic
26#459×C137C2211yescharacteristic
27#448×C137—21no—
28#448×C137—21no—
29#447×C137—21no—
30#442×C137—21no—
31#442×C137—21no—
32#436×C137C2212yes—
33#435×C137—22no—
34C8×D4×C137C2212yes—
35#432×C137C2211yescharacteristic
36#432×C137C2211yescharacteristic
37#431×C137C2211yescharacteristic
38C2×#107×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#332×C137C2212yescomplemented
47#332×C137C2212yescomplemented
48#331×C137C2212yescomplemented
49C2×#41×C137—21no—
50C22×Q8×C137—21no—
51C22×D4×C137D411yescharacteristic
52C23×C4×C137—21no—
53C2×SD16×C137—22no—
54C2×SD16×C137—22no—
55C2×D8×C137—21no—
56C2×D8×C137—21no—
57C2×M16×C137—22no—
58C22×C8×C137—21no—
59C22×C8×C137—22no—
60C4⋊Q8×C137—21no—
61C4⋊Q8×C137—21no—
62C4⋊Q8×C137—21no—
63C4⋊Q8×C137C2312yes—
64C4⋊Q8×C137C2311yescharacteristic
65#127×C137C2311yescharacteristic
66#124×C137—21no—
67#121×C137—21no—
68#121×C137—21no—
69C4×D4×C137—21no—
70C4×D4×C137—21no—
71C4×D4×C137—21no—
72C4×D4×C137—21no—
73C4×D4×C137D411yescharacteristic
74C4×D4×C137D411yescharacteristic
75C4×D4×C137C2311yescharacteristic
76C4×D4×C137C2311yescharacteristic
77C2×C4⋊C4×C137—21no—
78C2×C4⋊C4×C137—21no—
79C2×C4⋊C4×C137D411yescharacteristic
80C2×C22⋊C4×C137—21no—
81C2×C42×C137C2311yescharacteristic
82#107×C137—22no—
83#107×C137—22no—
84#106×C137—21no—
85#106×C137—21no—
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#102×C137—22no—
95#102×C137—22no—
96#102×C137—21no—
97#102×C137—21no—
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—
110#41×C137—82no—
111C2×Q8×C137—22no—
112C2×Q8×C137—21no—
113C2×Q8×C137—41no—
114C2×Q8×C137—82no—
115C2×D4×C137—22no—
116C2×D4×C137—21no—
117C2×D4×C137—21no—
118C2×D4×C137—21no—
119C2×D4×C137—21no—
120C2×D4×C137—41no—
121C2×D4×C137—41no—
122C2×D4×C137C2×D411yescharacteristic
123C2×D4×C137C2×D411yescharacteristic
124C22×C4×C137—21no—
125C22×C4×C137—21no—
126C22×C4×C137—21no—
127C22×C4×C137—21no—
128C22×C4×C137—21no—
129C22×C4×C137—41no—
130C22×C4×C137—41no—
131C22×C4×C137—82no—
132C22×C4×C137C2×D411yescharacteristic
133C22×C4×C137C2×D411yescharacteristic
134C22×C4×C137#4111yescharacteristic
135SD16×C137—82no—
136SD16×C137—82no—
137D8×C137—42no—
138D8×C137—42no—
139M16×C137—82no—
140C2×C8×C137—22no—
141C2×C8×C137—21no—
142C2×C8×C137—21no—
143C2×C8×C137—22no—
144C2×C8×C137—42no—
145C2×C8×C137—82no—
146C2×C8×C137C2×D412yes—
147C2×C8×C137C2×D412yes—
148C4⋊C4×C137—21no—
149C4⋊C4×C137—21no—
150C4⋊C4×C137—22no—
151C4⋊C4×C137—21no—
152C4⋊C4×C137—22no—
153C4⋊C4×C137—41no—
154C4⋊C4×C137—41no—
155C4⋊C4×C137C2×D411yescharacteristic
156C4⋊C4×C137C2×D411yescharacteristic
157C22⋊C4×C137—21no—
158C22⋊C4×C137—21no—
159C22⋊C4×C137—21no—
160C22⋊C4×C137—21no—
161C22⋊C4×C137—41no—
162C22⋊C4×C137—41no—
163C42×C137C2×D411yescharacteristic
164C42×C137C2×D411yescharacteristic
165C42×C137#4111yescharacteristic
166C42×C137C2411yescharacteristic
167C23×C137—21no—
168C23×C137—21no—
169C23×C137—42no—
170C23×C137—42no—
171C23×C137—41no—
172C23×C137—81no—
173C23×C137#12111yescharacteristic
174Q8×C137—42no—
175Q8×C137—42no—
176Q8×C137—81no—
177Q8×C137—82no—
178D4×C137—21no—
179D4×C137—21no—
180D4×C137—21no—
181D4×C137—42no—
182D4×C137—41no—
183D4×C137—41no—
184D4×C137—42no—
185D4×C137—81no—
186D4×C137—82no—
187D4×C137#13712yes—
188C2×C4×C137—22no—
189C2×C4×C137—21no—
190C2×C4×C137—21no—
191C2×C4×C137—22no—
192C2×C4×C137—21no—
193C2×C4×C137—21no—
194C2×C4×C137—42no—
195C2×C4×C137—42no—
196C2×C4×C137—41no—
197C2×C4×C137—42no—
198C2×C4×C137—81no—
199C2×C4×C137—81no—
200C2×C4×C137—82no—
201C2×C4×C137—81no—
202C2×C4×C137—82no—
203C2×C4×C137#12111yescharacteristic
204C2×C4×C137#12111yescharacteristic
205C2×C4×C137#12111yescharacteristic
206C2×C4×C137C22×D411yescharacteristic
207C2×C4×C137C22×D411yescharacteristic
208C2×C4×C137C2×#4111yescharacteristic
209C8×C137—22no—
210C8×C137—22no—
211C8×C137—41no—
212C8×C137—42no—
213C8×C137—41no—
214C8×C137—42no—
215C22×C137—21no—
216C22×C137—21no—
217C22×C137—22no—
218C22×C137—41no—
219C22×C137—41no—
220C22×C137—41no—
221C22×C137—41no—
222C22×C137—41no—
223C22×C137—84no—
224C22×C137—81no—
225C22×C137—81no—
226C22×C137—81no—
227C22×C137#47112yes—
228C22×C137C2×#12111yescharacteristic
229C4×C137—21no—
230C4×C137—21no—
231C4×C137—21no—
232C4×C137—21no—
233C4×C137—41no—
234C4×C137—41no—
235C4×C137—82no—
236C4×C137—81no—
237C4×C137C2×#13711yescharacteristic
238C4×C137#57511yescharacteristic
239C4×C137#57612yes—
240C2×C137—22no—
241C2×C137—42no—
242C2×C137—81no—
243C2×C137—161no—
244C2×C137#304111yescharacteristic
245C2×C137#305611yescharacteristic
246C2×C137C2×#47111yescharacteristic
247#19457C13711yesmaximal, characteristic, direct product factor, Sylow
248C137#1945711yescharacteristic, direct product factor, Sylow
249#3206C2×C13711yescharacteristic, complemented
250#3109C2×C13711yescharacteristic
251C2×#474C2×C13711yescharacteristic, complemented
252#2974C2×C13711yescharacteristic, complemented
253#1703C2×C13712yescomplemented
254#1685C2×C13712yescomplemented
255#1683C2×C13712yescomplemented
256#1665C2×C13712yescomplemented
257#1573C2×C13711yescharacteristic, complemented
258#1556C2×C13711yescharacteristic, complemented
259#1551C2×C13711yescharacteristic, complemented
260#532C22×C13711yescharacteristic
261C2×C4⋊Q8C22×C13711yescharacteristic
262C2×C4×D4C22×C13711yescharacteristic
263#492C22×C13712yescomplemented
264#487C22×C13712yescomplemented
265#481—21no—
266#476C22×C13711yescharacteristic
267#476C22×C13711yescharacteristic
268#474—21no—
269#474—21no—
270#474C22×C13712yes—
271#474C22×C13712yes—
272#461—22no—
273#459C22×C13711yescharacteristic
274#459C22×C13711yescharacteristic
275#448—21no—
276#448—21no—
277#447—21no—
278#442—21no—
279#442—21no—
280#436C22×C13712yes—
281#435—22no—
282C8×D4C22×C13712yes—
283#432C22×C13711yescharacteristic
284#432C22×C13711yescharacteristic
285#431C22×C13711yescharacteristic
286C2×#107—21no—
287C2×C4⋊C8C22×C13711yescharacteristic
288C2×#102—21no—
289#407—21no—
290C2×C22⋊C8—21no—
291#335C22×C13712yescomplemented
292#334C22×C13712yescomplemented
293#333C22×C13712yescomplemented
294#332C22×C13712yescomplemented
295#332C22×C13712yescomplemented
296#331C22×C13712yescomplemented
297C2×#41—21no—
298C22×Q8—21no—
299C22×D4D4×C13711yescharacteristic
300C23×C4—21no—
301C2×SD16—22no—
302C2×SD16—22no—
303C2×D8—21no—
304C2×D8—21no—
305C2×M16—22no—
306C22×C8—21no—
307C22×C8—22no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C23×C13712yes—
312C4⋊Q8C23×C13711yescharacteristic
313#127C23×C13711yescharacteristic
314#124—21no—
315#121—21no—
316#121—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4D4×C13711yescharacteristic
322C4×D4D4×C13711yescharacteristic
323C4×D4C23×C13711yescharacteristic
324C4×D4C23×C13711yescharacteristic
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4D4×C13711yescharacteristic
328C2×C22⋊C4—21no—
329C2×C42C23×C13711yescharacteristic
330#107—22no—
331#107—22no—
332#106—21no—
333#106—21no—
334C4⋊C8—21no—
335C4⋊C8D4×C13712yes—
336C4⋊C8C23×C13712yes—
337C4⋊C8C23×C13712yes—
338C4⋊C8C23×C13711yescharacteristic
339C4⋊C8C23×C13711yescharacteristic
340#103—22no—
341#103—22no—
342#102—22no—
343#102—22no—
344#102—21no—
345#102—21no—
346#102—21no—
347#102—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—22no—
351C22⋊C8—22no—
352C22⋊C8D4×C13711yescharacteristic
353C22⋊C8D4×C13711yescharacteristic
354#97—21no—
355#97—21no—
356C4×C8C23×C13712yes—
357C24—21no—
358#41—82no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—41no—
362C2×Q8—82no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4C2×D4×C13711yescharacteristic
371C2×D4C2×D4×C13711yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—82no—
380C22×C4C2×D4×C13711yescharacteristic
381C22×C4C2×D4×C13711yescharacteristic
382C22×C4#41×C13711yescharacteristic
383SD16—82no—
384SD16—82no—
385D8—42no—
386D8—42no—
387M16—82no—
388C2×C8—22no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—22no—
392C2×C8—42no—
393C2×C8—82no—
394C2×C8C2×D4×C13712yes—
395C2×C8C2×D4×C13712yes—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×D4×C13711yescharacteristic
404C4⋊C4C2×D4×C13711yescharacteristic
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42C2×D4×C13711yescharacteristic
412C42C2×D4×C13711yescharacteristic
413C42#41×C13711yescharacteristic
414C42C24×C13711yescharacteristic
415C23—21no—
416C23—21no—
417C23—42no—
418C23—42no—
419C23—41no—
420C23—81no—
421C23#121×C13711yescharacteristic
422Q8—42no—
423Q8—42no—
424Q8—81no—
425Q8—82no—
426D4—21no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4—41no—
431D4—41no—
432D4—42no—
433D4—81no—
434D4—82no—
435D4#137×C13712yes—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—82no—
449C2×C4—81no—
450C2×C4—82no—
451C2×C4#121×C13711yescharacteristic
452C2×C4#121×C13711yescharacteristic
453C2×C4#121×C13711yescharacteristic
454C2×C4C22×D4×C13711yescharacteristic
455C2×C4C22×D4×C13711yescharacteristic
456C2×C4C2×#41×C13711yescharacteristic
457C8—22no—
458C8—22no—
459C8—41no—
460C8—42no—
461C8—41no—
462C8—42no—
463C22—21no—
464C22—21no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—84no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22#471×C13712yes—
476C22C2×#121×C13711yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—82no—
484C4—81no—
485C4C2×#137×C13711yescharacteristic
486C4#575×C13711yescharacteristic
487C4#576×C13712yes—
488C2—22no—
489C2—42no—
490C2—81no—
491C2—161no—
492C2#3041×C13711yescharacteristic
493C2#3056×C13711yescharacteristic
494C2C2×#471×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#3109×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. #3206×C137C2semidirect
3. C2×#474×C137C2semidirect
4. #2974×C137C2semidirect
5. #1703×C137C2semidirect
6. #1685×C137C2semidirect
7. #1683×C137C2semidirect
8. #1665×C137C2semidirect
9. #1573×C137C2semidirect
10. #1556×C137C2semidirect
11. #1551×C137C2semidirect
15. #492×C137C22semidirect
16. #487×C137C22semidirect
43. #335×C137C22semidirect
44. #334×C137C22semidirect
45. #333×C137C22semidirect
46. #332×C137C22semidirect
47. #332×C137C22semidirect
48. #331×C137C22semidirect
247. #19457C137direct (N × H)
248. C137#19457direct (N × H)
249. #3206C2×C137semidirect
251. C2×#474C2×C137semidirect
252. #2974C2×C137semidirect
253. #1703C2×C137semidirect
254. #1685C2×C137semidirect
255. #1683C2×C137semidirect
256. #1665C2×C137semidirect
257. #1573C2×C137semidirect
258. #1556C2×C137semidirect
259. #1551C2×C137semidirect
263. #492C22×C137semidirect
264. #487C22×C137semidirect
291. #335C22×C137semidirect
292. #334C22×C137semidirect
293. #333C22×C137semidirect
294. #332C22×C137semidirect
295. #332C22×C137semidirect
296. #331C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3206×C1372
#3109×C1372
C2×#474×C1372
#2974×C1372
#1703×C1372
#1685×C1372
#1683×C1372
#1665×C1372
#1573×C1372
#1556×C1372
#1551×C1372
#19457137