Finite Group Databasebeta

← C137×#10960 #46860346

Subgroups — C137×#10960 #46860346

Order 35072.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C137C212yesmaximal
2C2×#386×C137C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
4C2×#342×C137C212yesmaximal, complemented
5C22⋊#95×C137C211yesmaximal, characteristic, complemented
6C23×D4×C137C2211yescharacteristic
7C24×C4×C137C2211yescharacteristic
8C22×C22⋊C4×C137C412yescomplemented
9C22×C22⋊C4×C137C2211yescharacteristic
10C22×C22⋊C4×C137C2212yes—
11C22×C22⋊C4×C137C2212yes—
12C22×C42×C137—21no—
13C2×#99×C137—24no—
14C2×#99×C137—24no—
15C2×#99×C137C418yescomplemented
16#386×C137—21no—
17#386×C137—22no—
18#386×C137—21no—
19C4×C22⋊C4×C137—24no—
20C2×#95×C137—21no—
21C2×#95×C137—22no—
22C2×#95×C137C412yescomplemented
23#342×C137—24no—
24C25×C137C2×C411yescharacteristic
25C25×C137C2311yescharacteristic
26C22×D4×C137—21no—
27C22×D4×C137—21no—
28C22×D4×C137—22no—
29C22×D4×C137—22no—
30C22×D4×C137—22no—
31C22×D4×C137—22no—
32C22×D4×C137—22no—
33C22×D4×C137C2×C414yes—
34C23×C4×C137—22no—
35C23×C4×C137—22no—
36C23×C4×C137—22no—
37C23×C4×C137—22no—
38C23×C4×C137—44no—
39C23×C4×C137C2×C411yescharacteristic
40C23×C4×C137C2×C412yes—
41C23×C4×C137C2×C412yes—
42C23×C4×C137D411yescharacteristic
43C23×C4×C137D412yes—
44C23×C4×C137D411yescharacteristic
45C2×C22⋊C4×C137—22no—
46C2×C22⋊C4×C137—22no—
47C2×C22⋊C4×C137—22no—
48C2×C22⋊C4×C137—22no—
49C2×C22⋊C4×C137—22no—
50C2×C22⋊C4×C137—22no—
51C2×C22⋊C4×C137—22no—
52C2×C22⋊C4×C137—21no—
53C2×C22⋊C4×C137—21no—
54C2×C22⋊C4×C137—22no—
55C2×C22⋊C4×C137—22no—
56C2×C22⋊C4×C137—22no—
57C2×C22⋊C4×C137—22no—
58C2×C22⋊C4×C137—22no—
59C2×C22⋊C4×C137—44no—
60C2×C22⋊C4×C137C2×C414yes—
61C2×C22⋊C4×C137C2×C414yes—
62C2×C22⋊C4×C137D414yes—
63C2×C22⋊C4×C137D414yes—
64C2×C42×C137—24no—
65C2×C42×C137—44no—
66#99×C137—216no—
67#95×C137—24no—
68#95×C137—22no—
69#95×C137—22no—
70#95×C137—44no—
71C24×C137—21no—
72C24×C137—21no—
73C24×C137—22no—
74C24×C137—22no—
75C24×C137—42no—
76C24×C137—42no—
77C24×C137—42no—
78C24×C137—42no—
79C24×C137C4212yescomplemented
80C24×C137C22×C411yescharacteristic
81C24×C137C22×C412yes—
82C24×C137C2×D411yescharacteristic
83C24×C137C2×D411yescharacteristic
84C24×C137C2×D412yes—
85C24×C137C2×D412yes—
86C24×C137#4112yes—
87C24×C137#4112yes—
88C24×C137#4112yes—
89C2×D4×C137—24no—
90C2×D4×C137—24no—
91C2×D4×C137—24no—
92C2×D4×C137—24no—
93C2×D4×C137—24no—
94C2×D4×C137—24no—
95C2×D4×C137—41no—
96C2×D4×C137—42no—
97C2×D4×C137—42no—
98C2×D4×C137—42no—
99C2×D4×C137—41no—
100C2×D4×C137—42no—
101C2×D4×C137—42no—
102C2×D4×C137—41no—
103C2×D4×C137—42no—
104C2×D4×C137—41no—
105C22×C4×C137—21no—
106C22×C4×C137—21no—
107C22×C4×C137—24no—
108C22×C4×C137—21no—
109C22×C4×C137—21no—
110C22×C4×C137—24no—
111C22×C4×C137—24no—
112C22×C4×C137—22no—
113C22×C4×C137—22no—
114C22×C4×C137—21no—
115C22×C4×C137—24no—
116C22×C4×C137—24no—
117C22×C4×C137—24no—
118C22×C4×C137—21no—
119C22×C4×C137—24no—
120C22×C4×C137—24no—
121C22×C4×C137—22no—
122C22×C4×C137—24no—
123C22×C4×C137—24no—
124C22×C4×C137—42no—
125C22×C4×C137—42no—
126C22×C4×C137—42no—
127C22×C4×C137—48no—
128C22×C4×C137—48no—
129C22×C4×C137—44no—
130C22×C4×C137—44no—
131C22×C4×C137—44no—
132C22×C4×C137—44no—
133C22×C4×C137—42no—
134C22×C4×C137—42no—
135C22×C4×C137—42no—
136C22×C4×C137—42no—
137C22×C4×C137C4212yescomplemented
138C22×C4×C137C22⋊C412yes—
139C22×C4×C137C22⋊C412yes—
140C22⋊C4×C137—24no—
141C22⋊C4×C137—24no—
142C22⋊C4×C137—24no—
143C22⋊C4×C137—24no—
144C22⋊C4×C137—24no—
145C22⋊C4×C137—44no—
146C22⋊C4×C137—42no—
147C22⋊C4×C137—42no—
148C22⋊C4×C137—42no—
149C22⋊C4×C137—41no—
150C22⋊C4×C137—41no—
151C22⋊C4×C137—44no—
152C22⋊C4×C137C22⋊C418yescomplemented
153C42×C137—48no—
154C23×C137—22no—
155C23×C137—22no—
156C23×C137—22no—
157C23×C137—22no—
158C23×C137—22no—
159C23×C137—22no—
160C23×C137—22no—
161C23×C137—24no—
162C23×C137—42no—
163C23×C137—42no—
164C23×C137—44no—
165C23×C137—42no—
166C23×C137—44no—
167C23×C137—42no—
168C23×C137—44no—
169C23×C137—44no—
170C23×C137—44no—
171C23×C137—44no—
172C23×C137—41no—
173C23×C137—42no—
174C23×C137—41no—
175C23×C137—42no—
176C23×C137—42no—
177C23×C137—82no—
178C23×C137—82no—
179C23×C137—84no—
180C23×C137C2×C4211yescharacteristic
181C23×C137C2×C22⋊C412yes—
182C23×C137C2×C22⋊C411yescharacteristic
183C23×C137#11711yescharacteristic
184C23×C137#11712yes—
185C23×C137C4×D412yes—
186C23×C137C4×D412yes—
187C23×C137C4×D412yes—
188C23×C137C4×D412yes—
189C23×C137C4×D412yes—
190C23×C137C4×D412yes—
191C23×C137#12011yescharacteristic
192C23×C137#12112yes—
193C23×C137#12112yes—
194C23×C137#12112yes—
195C23×C137#12311yescharacteristic
196C23×C137#12312yes—
197C23×C137#12411yescharacteristic
198C23×C137#12412yes—
199C23×C137#12612yes—
200C23×C137#12711yescharacteristic
201D4×C137—44no—
202D4×C137—44no—
203D4×C137—44no—
204D4×C137—44no—
205C2×C4×C137—24no—
206C2×C4×C137—24no—
207C2×C4×C137—22no—
208C2×C4×C137—22no—
209C2×C4×C137—24no—
210C2×C4×C137—22no—
211C2×C4×C137—28no—
212C2×C4×C137—22no—
213C2×C4×C137—22no—
214C2×C4×C137—22no—
215C2×C4×C137—48no—
216C2×C4×C137—48no—
217C2×C4×C137—44no—
218C2×C4×C137—44no—
219C2×C4×C137—48no—
220C2×C4×C137—48no—
221C2×C4×C137—42no—
222C2×C4×C137—42no—
223C2×C4×C137—41no—
224C2×C4×C137—42no—
225C2×C4×C137—41no—
226C2×C4×C137—48no—
227C2×C4×C137—44no—
228C2×C4×C137—42no—
229C2×C4×C137—42no—
230C2×C4×C137—42no—
231C2×C4×C137—82no—
232C2×C4×C137—82no—
233C2×C4×C137—84no—
234C2×C4×C137—84no—
235C2×C4×C137#9914yescomplemented
236C22×C137—21no—
237C22×C137—21no—
238C22×C137—22no—
239C22×C137—22no—
240C22×C137—21no—
241C22×C137—22no—
242C22×C137—22no—
243C22×C137—21no—
244C22×C137—24no—
245C22×C137—22no—
246C22×C137—24no—
247C22×C137—22no—
248C22×C137—24no—
249C22×C137—24no—
250C22×C137—22no—
251C22×C137—22no—
252C22×C137—42no—
253C22×C137—42no—
254C22×C137—42no—
255C22×C137—42no—
256C22×C137—42no—
257C22×C137—42no—
258C22×C137—42no—
259C22×C137—42no—
260C22×C137—42no—
261C22×C137—44no—
262C22×C137—84no—
263C22×C137—84no—
264C22×C137—81no—
265C22×C137—81no—
266C22×C137—82no—
267C22×C137C4×C22⋊C412yes—
268C22×C137C4×C22⋊C411yescharacteristic
269C22×C137#38612yes—
270C22×C137#38611yescharacteristic
271C22×C137#38812yes—
272C22×C137#38812yes—
273C22×C137#38812yes—
274C22×C137#39012yes—
275C22×C137#39011yescharacteristic
276C22×C137C2×#9912yes—
277C22×C137#41012yes—
278C4×C137—24no—
279C4×C137—48no—
280C4×C137—42no—
281C4×C137—42no—
282C4×C137—84no—
283C4×C137—82no—
284C2×C137—22no—
285C2×C137—22no—
286C2×C137—22no—
287C2×C137—22no—
288C2×C137—22no—
289C2×C137—22no—
290C2×C137—82no—
291C2×C137#143711yescharacteristic
292C2×C137C4×#9912yes—
293C2×C137#189811yescharacteristic
294C2×C137#189911yescharacteristic
295C2×C137#196412yes—
296#10960C13711yesmaximal, characteristic, direct product factor, Sylow
297C137#1096011yescharacteristic, direct product factor, Sylow
298C22×#99C2×C13712yes—
299C2×#386C2×C13711yescharacteristic
300C2×C4×C22⋊C4C2×C13711yescharacteristic, complemented
301C2×#342C2×C13712yescomplemented
302C22⋊#95C2×C13711yescharacteristic, complemented
303C23×D4C22×C13711yescharacteristic
304C24×C4C22×C13711yescharacteristic
305C22×C22⋊C4C4×C13712yescomplemented
306C22×C22⋊C4C22×C13711yescharacteristic
307C22×C22⋊C4C22×C13712yes—
308C22×C22⋊C4C22×C13712yes—
309C22×C42—21no—
310C2×#99—24no—
311C2×#99—24no—
312C2×#99C4×C13718yescomplemented
313#386—21no—
314#386—22no—
315#386—21no—
316C4×C22⋊C4—24no—
317C2×#95—21no—
318C2×#95—22no—
319C2×#95C4×C13712yescomplemented
320#342—24no—
321C25C2×C4×C13711yescharacteristic
322C25C23×C13711yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4C2×C4×C13714yes—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—44no—
336C23×C4C2×C4×C13711yescharacteristic
337C23×C4C2×C4×C13712yes—
338C23×C4C2×C4×C13712yes—
339C23×C4D4×C13711yescharacteristic
340C23×C4D4×C13712yes—
341C23×C4D4×C13711yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×C4×C13714yes—
358C2×C22⋊C4C2×C4×C13714yes—
359C2×C22⋊C4D4×C13714yes—
360C2×C22⋊C4D4×C13714yes—
361C2×C42—24no—
362C2×C42—44no—
363#99—216no—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—44no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24C42×C13712yescomplemented
377C24C22×C4×C13711yescharacteristic
378C24C22×C4×C13712yes—
379C24C2×D4×C13711yescharacteristic
380C24C2×D4×C13711yescharacteristic
381C24C2×D4×C13712yes—
382C24C2×D4×C13712yes—
383C24#41×C13712yes—
384C24#41×C13712yes—
385C24#41×C13712yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C42×C13712yescomplemented
435C22×C4C22⋊C4×C13712yes—
436C22×C4C22⋊C4×C13712yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—44no—
449C22⋊C4C22⋊C4×C13718yescomplemented
450C42—48no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—44no—
464C23—42no—
465C23—44no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—41no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23C2×C42×C13711yescharacteristic
478C23C2×C22⋊C4×C13712yes—
479C23C2×C22⋊C4×C13711yescharacteristic
480C23#117×C13711yescharacteristic
481C23#117×C13712yes—
482C23C4×D4×C13712yes—
483C23C4×D4×C13712yes—
484C23C4×D4×C13712yes—
485C23C4×D4×C13712yes—
486C23C4×D4×C13712yes—
487C23C4×D4×C13712yes—
488C23#120×C13711yescharacteristic
489C23#121×C13712yes—
490C23#121×C13712yes—
491C23#121×C13712yes—
492C23#123×C13711yescharacteristic
493C23#123×C13712yes—
494C23#124×C13711yescharacteristic
495C23#124×C13712yes—
496C23#126×C13712yes—
497C23#127×C13711yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—48no—
519C2×C4—48no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—48no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4#99×C13714yescomplemented
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—22no—
540C22—21no—
541C22—24no—
542C22—22no—
543C22—24no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—22no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—44no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C4×C22⋊C4×C13712yes—
565C22C4×C22⋊C4×C13711yescharacteristic
566C22#386×C13712yes—
567C22#386×C13711yescharacteristic
568C22#388×C13712yes—
569C22#388×C13712yes—
570C22#388×C13712yes—
571C22#390×C13712yes—
572C22#390×C13711yescharacteristic
573C22C2×#99×C13712yes—
574C22#410×C13712yes—
575C4—24no—
576C4—48no—
577C4—42no—
578C4—42no—
579C4—84no—
580C4—82no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2#1437×C13711yescharacteristic
589C2C4×#99×C13712yes—
590C2#1898×C13711yescharacteristic
591C2#1899×C13711yescharacteristic
592C2#1964×C13712yes—
subgroupG/H
center, socleC23×C137C2×C22⋊C4
commutatorC23C2×C42×C137
Frattini, cosocleC25C23×C137
prime radicalC23×D4×C137C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C24×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C137C2semidirect
4. C2×#342×C137C2semidirect
5. C22⋊#95×C137C2semidirect
8. C22×C22⋊C4×C137C4semidirect
15. C2×#99×C137C4semidirect
22. C2×#95×C137C4semidirect
79. C24×C137C42semidirect
137. C22×C4×C137C42semidirect
152. C22⋊C4×C137C22⋊C4semidirect
235. C2×C4×C137#99semidirect
296. #10960C137direct (N × H)
297. C137#10960direct (N × H)
300. C2×C4×C22⋊C4C2×C137semidirect
301. C2×#342C2×C137semidirect
302. C22⋊#95C2×C137semidirect
305. C22×C22⋊C4C4×C137semidirect
312. C2×#99C4×C137semidirect
319. C2×#95C4×C137semidirect
376. C24C42×C137semidirect
434. C22×C4C42×C137semidirect
449. C22⋊C4C22⋊C4×C137semidirect
532. C2×C4#99×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C1372
C2×#386×C1372
C2×C4×C22⋊C4×C1372
C2×#342×C1372
C22⋊#95×C1372
#10960137