Finite Group Databasebeta

← C137×#13080 #46862466

Subgroups — C137×#13080 #46862466

Order 35072.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C137C211yesmaximal, characteristic
2#2405×C137C211yesmaximal, characteristic
3C2×#352×C137C212yesmaximal, complemented
4#1781×C137C211yesmaximal, characteristic
5#1390×C137C212yesmaximal, complemented
6C23×D4×C137C2211yescharacteristic
7C22×M16×C137—21no—
8C2×#123×C137C411yescharacteristic, complemented
9C2×#123×C137C2211yescharacteristic
10C22×C22⋊C4×C137C411yescharacteristic, complemented
11C2×#100×C137—21no—
12C2×#100×C137—24no—
13C2×#100×C137C2212yes—
14C2×#99×C137—21no—
15C2×#99×C137C2212yes—
16#394×C137—21no—
17#394×C137—21no—
18#386×C137C411yescharacteristic, complemented
19#386×C137C2211yescharacteristic
20#385×C137—21no—
21#379×C137—21no—
22#379×C137—21no—
23#379×C137C411yescharacteristic, complemented
24#352×C137—24no—
25C25×C137C2×C411yescharacteristic
26C25×C137D411yescharacteristic
27C22×D4×C137—22no—
28C22×D4×C137—22no—
29C22×D4×C137—42no—
30C22×D4×C137—41no—
31C22×D4×C137—41no—
32C22×D4×C137C2×C411yescharacteristic
33C22×D4×C137D411yescharacteristic
34C22×D4×C137D411yescharacteristic
35C22×D4×C137C2311yescharacteristic
36C23×C4×C137C2×C411yescharacteristic
37C23×C4×C137C2×C411yescharacteristic
38C23×C4×C137D411yescharacteristic
39C2×M16×C137—24no—
40C2×M16×C137—22no—
41C2×M16×C137—41no—
42C2×M16×C137—42no—
43C22×C8×C137—41no—
44#123×C137—22no—
45#123×C137—22no—
46#123×C137—42no—
47C2×C4⋊C4×C137—21no—
48C2×C4⋊C4×C137—21no—
49C2×C22⋊C4×C137—21no—
50C2×C22⋊C4×C137—21no—
51C2×C22⋊C4×C137—21no—
52C2×C22⋊C4×C137—21no—
53C2×C22⋊C4×C137—21no—
54C2×C22⋊C4×C137—22no—
55C2×C22⋊C4×C137—21no—
56C2×C22⋊C4×C137—21no—
57C2×C22⋊C4×C137—21no—
58C2×C22⋊C4×C137—41no—
59C2×C22⋊C4×C137—41no—
60C2×C22⋊C4×C137—41no—
61C2×C22⋊C4×C137—41no—
62C2×C22⋊C4×C137C2×C411yescharacteristic
63C2×C22⋊C4×C137C2×C411yescharacteristic
64#100×C137—24no—
65#100×C137—22no—
66#100×C137D414yes—
67#99×C137—22no—
68#99×C137—22no—
69#99×C137—42no—
70#95×C137—21no—
71#95×C137—21no—
72C24×C137—21no—
73C24×C137—21no—
74C24×C137—21no—
75C24×C137—21no—
76C24×C137—22no—
77C24×C137—22no—
78C24×C137—41no—
79C24×C137—41no—
80C24×C137—42no—
81C24×C137—42no—
82C24×C137—81no—
83C24×C137—81no—
84C24×C137C22⋊C411yescharacteristic
85C24×C137C22⋊C411yescharacteristic
86C24×C137C22⋊C411yescharacteristic
87C24×C137C22×C411yescharacteristic
88C24×C137C2×D411yescharacteristic
89C2×D4×C137—22no—
90C2×D4×C137—22no—
91C2×D4×C137—22no—
92C2×D4×C137—22no—
93C2×D4×C137—21no—
94C2×D4×C137—21no—
95C2×D4×C137—41no—
96C2×D4×C137—41no—
97C2×D4×C137—41no—
98C2×D4×C137—41no—
99C2×D4×C137—41no—
100C2×D4×C137—41no—
101C2×D4×C137—44no—
102C2×D4×C137—44no—
103C2×D4×C137—44no—
104C2×D4×C137—44no—
105C2×D4×C137C2×D412yes—
106C2×D4×C137#4112yes—
107C22×C4×C137—21no—
108C22×C4×C137—21no—
109C22×C4×C137—22no—
110C22×C4×C137—21no—
111C22×C4×C137—21no—
112C22×C4×C137—21no—
113C22×C4×C137—21no—
114C22×C4×C137—21no—
115C22×C4×C137—21no—
116C22×C4×C137—22no—
117C22×C4×C137—41no—
118C22×C4×C137—41no—
119C22×C4×C137—41no—
120C22×C4×C137—42no—
121C22×C4×C137—81no—
122C22×C4×C137C22⋊C411yescharacteristic
123C22×C4×C137C2×D411yescharacteristic
124M16×C137—24no—
125M16×C137—44no—
126M16×C137—42no—
127C2×C8×C137—44no—
128C2×C8×C137—42no—
129C4⋊C4×C137—42no—
130C4⋊C4×C137—41no—
131C4⋊C4×C137—41no—
132C22⋊C4×C137—22no—
133C22⋊C4×C137—42no—
134C22⋊C4×C137—42no—
135C22⋊C4×C137—42no—
136C22⋊C4×C137—41no—
137C22⋊C4×C137—41no—
138C22⋊C4×C137—42no—
139C22⋊C4×C137—41no—
140C22⋊C4×C137—42no—
141C22⋊C4×C137—42no—
142C22⋊C4×C137—81no—
143C22⋊C4×C137—81no—
144C22⋊C4×C137—81no—
145C22⋊C4×C137—82no—
146C22⋊C4×C137—82no—
147C23×C137—22no—
148C23×C137—21no—
149C23×C137—21no—
150C23×C137—21no—
151C23×C137—21no—
152C23×C137—21no—
153C23×C137—21no—
154C23×C137—21no—
155C23×C137—21no—
156C23×C137—21no—
157C23×C137—21no—
158C23×C137—21no—
159C23×C137—21no—
160C23×C137—41no—
161C23×C137—42no—
162C23×C137—42no—
163C23×C137—42no—
164C23×C137—42no—
165C23×C137—41no—
166C23×C137—41no—
167C23×C137—41no—
168C23×C137—41no—
169C23×C137—41no—
170C23×C137—41no—
171C23×C137—42no—
172C23×C137—42no—
173C23×C137—41no—
174C23×C137—41no—
175C23×C137—42no—
176C23×C137—42no—
177C23×C137—81no—
178C23×C137—81no—
179C23×C137—81no—
180C23×C137—81no—
181C23×C137—84no—
182C23×C137—84no—
183C23×C137—84no—
184C23×C137—84no—
185C23×C137#9911yescharacteristic
186C23×C137#9911yescharacteristic
187C23×C137C2×C22⋊C411yescharacteristic
188C23×C137C4×D412yes—
189C23×C137#12112yes—
190D4×C137—42no—
191D4×C137—42no—
192D4×C137—44no—
193D4×C137—44no—
194D4×C137—42no—
195D4×C137—42no—
196C2×C4×C137—22no—
197C2×C4×C137—22no—
198C2×C4×C137—22no—
199C2×C4×C137—22no—
200C2×C4×C137—21no—
201C2×C4×C137—21no—
202C2×C4×C137—21no—
203C2×C4×C137—21no—
204C2×C4×C137—41no—
205C2×C4×C137—41no—
206C2×C4×C137—41no—
207C2×C4×C137—41no—
208C2×C4×C137—41no—
209C2×C4×C137—41no—
210C2×C4×C137—41no—
211C2×C4×C137—41no—
212C2×C4×C137—41no—
213C2×C4×C137—41no—
214C2×C4×C137—41no—
215C2×C4×C137—41no—
216C2×C4×C137—82no—
217C2×C4×C137—82no—
218C2×C4×C137—82no—
219C2×C4×C137—82no—
220C2×C4×C137—82no—
221C2×C4×C137#9912yes—
222C2×C4×C137#12011yescharacteristic
223C2×C4×C137#12311yescharacteristic
224C8×C137—44no—
225C22×C137—21no—
226C22×C137—21no—
227C22×C137—21no—
228C22×C137—21no—
229C22×C137—21no—
230C22×C137—21no—
231C22×C137—21no—
232C22×C137—22no—
233C22×C137—22no—
234C22×C137—42no—
235C22×C137—42no—
236C22×C137—42no—
237C22×C137—42no—
238C22×C137—42no—
239C22×C137—42no—
240C22×C137—41no—
241C22×C137—41no—
242C22×C137—41no—
243C22×C137—41no—
244C22×C137—41no—
245C22×C137—41no—
246C22×C137—41no—
247C22×C137—41no—
248C22×C137—41no—
249C22×C137—41no—
250C22×C137—81no—
251C22×C137—84no—
252C22×C137—84no—
253C22×C137—81no—
254C22×C137—81no—
255C22×C137—81no—
256C22×C137—84no—
257C22×C137—84no—
258C22×C137#35212yescomplemented
259C22×C137#38611yescharacteristic
260C22×C137C2×#9911yescharacteristic
261C22×C137C2×#9911yescharacteristic
262C4×C137—21no—
263C4×C137—22no—
264C4×C137—21no—
265C4×C137—81no—
266C4×C137—81no—
267C4×C137—81no—
268C4×C137—81no—
269C4×C137—162no—
270C2×C137—21no—
271C2×C137—21no—
272C2×C137—22no—
273C2×C137—42no—
274C2×C137—41no—
275C2×C137—42no—
276C2×C137—81no—
277C2×C137—81no—
278C2×C137#189811yescharacteristic
279C2×C137C2×#35211yescharacteristic
280C2×C137#212111yescharacteristic
281#13080C13711yesmaximal, characteristic, direct product factor, Sylow
282C137#1308011yescharacteristic, direct product factor, Sylow
283C22×#100C2×C13711yescharacteristic
284#2405C2×C13711yescharacteristic
285C2×#352C2×C13712yescomplemented
286#1781C2×C13711yescharacteristic
287#1390C2×C13712yescomplemented
288C23×D4C22×C13711yescharacteristic
289C22×M16—21no—
290C2×#123C4×C13711yescharacteristic, complemented
291C2×#123C22×C13711yescharacteristic
292C22×C22⋊C4C4×C13711yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C13712yes—
296C2×#99—21no—
297C2×#99C22×C13712yes—
298#394—21no—
299#394—21no—
300#386C4×C13711yescharacteristic, complemented
301#386C22×C13711yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C13711yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C13711yescharacteristic
308C25D4×C13711yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C13711yescharacteristic
315C22×D4D4×C13711yescharacteristic
316C22×D4D4×C13711yescharacteristic
317C22×D4C23×C13711yescharacteristic
318C23×C4C2×C4×C13711yescharacteristic
319C23×C4C2×C4×C13711yescharacteristic
320C23×C4D4×C13711yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C13711yescharacteristic
345C2×C22⋊C4C2×C4×C13711yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C13714yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C13711yescharacteristic
367C24C22⋊C4×C13711yescharacteristic
368C24C22⋊C4×C13711yescharacteristic
369C24C22×C4×C13711yescharacteristic
370C24C2×D4×C13711yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C13712yes—
388C2×D4#41×C13712yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C13711yescharacteristic
405C22×C4C2×D4×C13711yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C13711yescharacteristic
468C23#99×C13711yescharacteristic
469C23C2×C22⋊C4×C13711yescharacteristic
470C23C4×D4×C13712yes—
471C23#121×C13712yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C13712yes—
504C2×C4#120×C13711yescharacteristic
505C2×C4#123×C13711yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C13712yescomplemented
541C22#386×C13711yescharacteristic
542C22C2×#99×C13711yescharacteristic
543C22C2×#99×C13711yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2#1898×C13711yescharacteristic
561C2C2×#352×C13711yescharacteristic
562C2#2121×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#99
commutatorC24C22×C4×C137
Frattini, cosocleC22×D4C23×C137
prime radicalC23×D4×C137C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C24×C137 ◁ C23×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#352×C137C2semidirect
5. #1390×C137C2semidirect
8. C2×#123×C137C4semidirect
10. C22×C22⋊C4×C137C4semidirect
18. #386×C137C4semidirect
23. #379×C137C4semidirect
258. C22×C137#352semidirect
281. #13080C137direct (N × H)
282. C137#13080direct (N × H)
285. C2×#352C2×C137semidirect
287. #1390C2×C137semidirect
290. C2×#123C4×C137semidirect
292. C22×C22⋊C4C4×C137semidirect
300. #386C4×C137semidirect
305. #379C4×C137semidirect
540. C22#352×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1372
#2405×C1372
C2×#352×C1372
#1781×C1372
#1390×C1372
#13080137