Finite Group Databasebeta

← C137×#14188 #46863574

Subgroups — C137×#14188 #46863574

Order 35072.

1894 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C137C211yesmaximal, characteristic, complemented
2C2×#393×C137C211yesmaximal, characteristic
3C2×#388×C137C211yesmaximal, characteristic
4C2×#388×C137C212yesmaximal
5#1446×C137C211yesmaximal, characteristic, complemented
6#1442×C137C211yesmaximal, characteristic, complemented
7#1439×C137C211yesmaximal, characteristic
8#1437×C137C212yesmaximal
9#1436×C137C212yesmaximal, complemented
10#1436×C137C212yesmaximal, complemented
11C4×#95×C137C211yesmaximal, characteristic, complemented
12C23×Q8×C137C2211yescharacteristic
13C2×C4×Q8×C137—28no—
14C2×C4×Q8×C137—24no—
15C22×C4⋊C4×C137C2211yescharacteristic
16C22×C4⋊C4×C137C2211yescharacteristic
17C22×C4⋊C4×C137C2212yes—
18C22×C22⋊C4×C137C2211yescharacteristic
19C22×C22⋊C4×C137C2211yescharacteristic
20C22×C22⋊C4×C137C2212yes—
21C22×C22⋊C4×C137C2212yes—
22C22×C22⋊C4×C137C2211yescharacteristic
23C22×C42×C137C2212yes—
24C22×C42×C137C2212yes—
25C22×C42×C137C2211yescharacteristic
26#393×C137C418yescomplemented
27#388×C137—28no—
28#388×C137—24no—
29C2×#95×C137C2211yescharacteristic
30C2×#95×C137C2212yes—
31C2×#95×C137C2212yes—
32C2×#95×C137C2211yescharacteristic
33C2×#95×C137C2212yes—
34C2×#95×C137C2211yescharacteristic
35C2×#95×C137C2212yes—
36C2×#95×C137C2212yes—
37C2×#95×C137C2212yes—
38C2×#95×C137C2211yescharacteristic
39C2×#95×C137C2212yes—
40C25×C137C2311yescharacteristic
41C22×Q8×C137—24no—
42C22×Q8×C137—22no—
43C22×Q8×C137—22no—
44C22×Q8×C137—24no—
45C22×Q8×C137C2×C414yes—
46C23×C4×C137C2311yescharacteristic
47C23×C4×C137C2311yescharacteristic
48C23×C4×C137C2312yes—
49C23×C4×C137C2311yescharacteristic
50C23×C4×C137C2312yes—
51C23×C4×C137C2312yes—
52C23×C4×C137C2312yes—
53C23×C4×C137C2311yescharacteristic
54C23×C4×C137C2311yescharacteristic
55C23×C4×C137C2311yescharacteristic
56C4×Q8×C137—232no—
57C2×C4⋊C4×C137—24no—
58C2×C4⋊C4×C137—22no—
59C2×C4⋊C4×C137—24no—
60C2×C4⋊C4×C137—24no—
61C2×C4⋊C4×C137—22no—
62C2×C4⋊C4×C137—24no—
63C2×C4⋊C4×C137D418yes—
64C2×C22⋊C4×C137—24no—
65C2×C22⋊C4×C137—22no—
66C2×C22⋊C4×C137—24no—
67C2×C22⋊C4×C137—22no—
68C2×C22⋊C4×C137—24no—
69C2×C22⋊C4×C137—24no—
70C2×C22⋊C4×C137—22no—
71C2×C22⋊C4×C137—22no—
72C2×C22⋊C4×C137—24no—
73C2×C22⋊C4×C137—24no—
74C2×C22⋊C4×C137—42no—
75C2×C22⋊C4×C137C2×C418yes—
76C2×C22⋊C4×C137C2×C414yes—
77C2×C42×C137—24no—
78C2×C42×C137—24no—
79C2×C42×C137—24no—
80C2×C42×C137—24no—
81C2×C42×C137—24no—
82C2×C42×C137—24no—
83C2×C42×C137—42no—
84C2×C42×C137D414yes—
85#95×C137—24no—
86#95×C137—24no—
87#95×C137—22no—
88#95×C137—22no—
89#95×C137—24no—
90#95×C137—22no—
91#95×C137—24no—
92#95×C137—24no—
93#95×C137—42no—
94#95×C137C2×C414yes—
95#95×C137C2×C418yes—
96C24×C137—21no—
97C24×C137—22no—
98C24×C137—21no—
99C24×C137—22no—
100C24×C137—22no—
101C24×C137—22no—
102C24×C137—21no—
103C24×C137—21no—
104C24×C137—21no—
105C24×C137—21no—
106C24×C137C22×C412yes—
107C24×C137C2411yescharacteristic
108C2×Q8×C137—28no—
109C2×Q8×C137—28no—
110C2×Q8×C137—216no—
111C2×Q8×C137—28no—
112C2×Q8×C137—216no—
113C22×C4×C137—22no—
114C22×C4×C137—22no—
115C22×C4×C137—22no—
116C22×C4×C137—22no—
117C22×C4×C137—22no—
118C22×C4×C137—22no—
119C22×C4×C137—22no—
120C22×C4×C137—22no—
121C22×C4×C137—21no—
122C22×C4×C137—21no—
123C22×C4×C137—21no—
124C22×C4×C137—21no—
125C22×C4×C137—22no—
126C22×C4×C137—22no—
127C22×C4×C137—21no—
128C22×C4×C137—22no—
129C22×C4×C137—22no—
130C22×C4×C137—22no—
131C22×C4×C137—22no—
132C22×C4×C137—22no—
133C22×C4×C137—22no—
134C22×C4×C137—22no—
135C22×C4×C137—22no—
136C22×C4×C137—22no—
137C22×C4×C137—21no—
138C22×C4×C137—22no—
139C22×C4×C137—22no—
140C22×C4×C137—22no—
141C22×C4×C137—22no—
142C22×C4×C137—22no—
143C22×C4×C137—22no—
144C22×C4×C137—22no—
145C22×C4×C137—22no—
146C22×C4×C137—22no—
147C22×C4×C137—22no—
148C22×C4×C137—21no—
149C22×C4×C137—21no—
150C22×C4×C137—22no—
151C22×C4×C137—22no—
152C22×C4×C137—22no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—21no—
157C22×C4×C137C22×C412yes—
158C22×C4×C137C22×C414yes—
159C22×C4×C137C22×C414yes—
160C22×C4×C137C22×C412yes—
161C22×C4×C137C2×D414yes—
162C22×C4×C137C2×D414yes—
163C22×C4×C137C2×D412yes—
164C22×C4×C137C2×D412yes—
165C22×C4×C137C2×D414yes—
166C22×C4×C137C2×D412yes—
167C22×C4×C137#4114yes—
168C22×C4×C137#4112yes—
169C22×C4×C137#4114yes—
170C22×C4×C137#4114yes—
171C4⋊C4×C137—28no—
172C4⋊C4×C137—216no—
173C4⋊C4×C137—44no—
174C22⋊C4×C137—216no—
175C22⋊C4×C137—28no—
176C22⋊C4×C137—48no—
177C22⋊C4×C137—44no—
178C22⋊C4×C137—44no—
179C42×C137—216no—
180C42×C137—28no—
181C42×C137—48no—
182C23×C137—22no—
183C23×C137—24no—
184C23×C137—24no—
185C23×C137—22no—
186C23×C137—22no—
187C23×C137—41no—
188C23×C137—41no—
189C23×C137—42no—
190C23×C137—41no—
191C23×C137—42no—
192C23×C137—41no—
193C23×C137—41no—
194C23×C137—41no—
195C23×C137—41no—
196C23×C137—41no—
197C23×C137—42no—
198C23×C137—42no—
199C23×C137—42no—
200C23×C137—42no—
201C23×C137—42no—
202C23×C137—42no—
203C23×C137—42no—
204C23×C137—42no—
205C23×C137C23×C411yescharacteristic
206C23×C137C22×D411yescharacteristic
207C23×C137C22×D412yes—
208C23×C137C2×#4111yescharacteristic
209C23×C137C2×#4112yes—
210C23×C137C2×#4112yes—
211C23×C137C2×#4112yes—
212C23×C137H(5,𝔽2)11yescharacteristic
213C23×C1372−1+411yescharacteristic
214C23×C1372−1+411yescharacteristic
215C23×C1372−1+411yescharacteristic
216Q8×C137—232no—
217C2×C4×C137—24no—
218C2×C4×C137—24no—
219C2×C4×C137—24no—
220C2×C4×C137—22no—
221C2×C4×C137—24no—
222C2×C4×C137—22no—
223C2×C4×C137—22no—
224C2×C4×C137—24no—
225C2×C4×C137—24no—
226C2×C4×C137—24no—
227C2×C4×C137—24no—
228C2×C4×C137—22no—
229C2×C4×C137—22no—
230C2×C4×C137—22no—
231C2×C4×C137—24no—
232C2×C4×C137—24no—
233C2×C4×C137—24no—
234C2×C4×C137—24no—
235C2×C4×C137—24no—
236C2×C4×C137—22no—
237C2×C4×C137—24no—
238C2×C4×C137—24no—
239C2×C4×C137—24no—
240C2×C4×C137—24no—
241C2×C4×C137—24no—
242C2×C4×C137—24no—
243C2×C4×C137—24no—
244C2×C4×C137—24no—
245C2×C4×C137—24no—
246C2×C4×C137—42no—
247C2×C4×C137—41no—
248C2×C4×C137—42no—
249C2×C4×C137—42no—
250C2×C4×C137—41no—
251C2×C4×C137—42no—
252C2×C4×C137—42no—
253C2×C4×C137—42no—
254C2×C4×C137—42no—
255C2×C4×C137—42no—
256C2×C4×C137—42no—
257C2×C4×C137—42no—
258C2×C4×C137—42no—
259C2×C4×C137—42no—
260C2×C4×C137—42no—
261C2×C4×C137—41no—
262C2×C4×C137—41no—
263C2×C4×C137—41no—
264C2×C4×C137—41no—
265C2×C4×C137—41no—
266C2×C4×C137—41no—
267C2×C4×C137—42no—
268C2×C4×C137—42no—
269C2×C4×C137—42no—
270C2×C4×C137—42no—
271C2×C4×C137C4×D414yes—
272C2×C4×C137C4×D418yes—
273C2×C4×C137#12014yes—
274C2×C4×C137#12414yes—
275C22×C137—42no—
276C22×C137—44no—
277C22×C137—44no—
278C22×C137—42no—
279C22×C137—42no—
280C22×C137—81no—
281C22×C137—81no—
282C22×C137—81no—
283C22×C137—81no—
284C22×C137—82no—
285C22×C137—82no—
286C22×C137C2×C4×D411yescharacteristic
287C22×C137C2×C4×D412yes—
288C22×C137C4×#4112yes—
289C22×C137#51911yescharacteristic
290C22×C137#52011yescharacteristic
291C22×C137C2×#12011yescharacteristic
292C22×C137#52511yescharacteristic
293C22×C137#52512yes—
294C22×C137C2×#12411yescharacteristic
295C22×C137#52912yes—
296C22×C137#53211yescharacteristic
297C22×C137#53611yescharacteristic
298C22×C137#53711yescharacteristic
299C22×C137#54111yescharacteristic
300C22×C137#54211yescharacteristic
301C22×C137#54612yes—
302C22×C137#54712yes—
303C22×C137#54812yes—
304C22×C137#54812yes—
305C22×C137#55212yes—
306C22×C137#55612yes—
307C22×C137#55612yes—
308C22×C137#55912yes—
309C4×C137—24no—
310C4×C137—24no—
311C4×C137—28no—
312C4×C137—24no—
313C4×C137—44no—
314C4×C137—44no—
315C4×C137—44no—
316C4×C137—42no—
317C4×C137—81no—
318C4×C137—81no—
319C2×C137—82no—
320C2×C137C4×#12011yescharacteristic
321C2×C137C4×#12411yescharacteristic
322C2×C137#232311yescharacteristic
323C2×C137#236212yes—
324C2×C137#236712yes—
325C2×C137#243011yescharacteristic
326C2×C137#243611yescharacteristic
327C2×C137#245812yes—
328C2×C137#246912yes—
329C2×C137#259211yescharacteristic
330C2×C137#260411yescharacteristic
331#14188C13711yesmaximal, characteristic, direct product factor, Sylow
332C137#1418811yescharacteristic, direct product factor, Sylow
333C22×C4×Q8C2×C13711yescharacteristic, complemented
334C2×#393C2×C13711yescharacteristic
335C2×#388C2×C13711yescharacteristic
336C2×#388C2×C13712yes—
337#1446C2×C13711yescharacteristic, complemented
338#1442C2×C13711yescharacteristic, complemented
339#1439C2×C13711yescharacteristic
340#1437C2×C13712yes—
341#1436C2×C13712yescomplemented
342#1436C2×C13712yescomplemented
343C4×#95C2×C13711yescharacteristic, complemented
344C23×Q8C22×C13711yescharacteristic
345C2×C4×Q8—28no—
346C2×C4×Q8—24no—
347C22×C4⋊C4C22×C13711yescharacteristic
348C22×C4⋊C4C22×C13711yescharacteristic
349C22×C4⋊C4C22×C13712yes—
350C22×C22⋊C4C22×C13711yescharacteristic
351C22×C22⋊C4C22×C13711yescharacteristic
352C22×C22⋊C4C22×C13712yes—
353C22×C22⋊C4C22×C13712yes—
354C22×C22⋊C4C22×C13711yescharacteristic
355C22×C42C22×C13712yes—
356C22×C42C22×C13712yes—
357C22×C42C22×C13711yescharacteristic
358#393C4×C13718yescomplemented
359#388—28no—
360#388—24no—
361C2×#95C22×C13712yes—
362C2×#95C22×C13711yescharacteristic
363C2×#95C22×C13712yes—
364C2×#95C22×C13711yescharacteristic
365C2×#95C22×C13712yes—
366C2×#95C22×C13712yes—
367C2×#95C22×C13712yes—
368C2×#95C22×C13711yescharacteristic
369C2×#95C22×C13712yes—
370C2×#95C22×C13711yescharacteristic
371C2×#95C22×C13712yes—
372C25C23×C13711yescharacteristic
373C22×Q8—24no—
374C22×Q8—22no—
375C22×Q8—22no—
376C22×Q8—24no—
377C22×Q8C2×C4×C13714yes—
378C23×C4C23×C13711yescharacteristic
379C23×C4C23×C13711yescharacteristic
380C23×C4C23×C13711yescharacteristic
381C23×C4C23×C13712yes—
382C23×C4C23×C13712yes—
383C23×C4C23×C13712yes—
384C23×C4C23×C13712yes—
385C23×C4C23×C13711yescharacteristic
386C23×C4C23×C13711yescharacteristic
387C23×C4C23×C13711yescharacteristic
388C4×Q8—232no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4D4×C13718yes—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4C2×C4×C13718yes—
408C2×C22⋊C4C2×C4×C13714yes—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—42no—
416C2×C42D4×C13714yes—
417#95—24no—
418#95—24no—
419#95—22no—
420#95—22no—
421#95—24no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—42no—
426#95C2×C4×C13714yes—
427#95C2×C4×C13718yes—
428C24—21no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24C22×C4×C13712yes—
439C24C24×C13711yescharacteristic
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—216no—
443C2×Q8—28no—
444C2×Q8—216no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4C22×C4×C13712yes—
490C22×C4C22×C4×C13714yes—
491C22×C4C22×C4×C13714yes—
492C22×C4C22×C4×C13712yes—
493C22×C4C2×D4×C13714yes—
494C22×C4C2×D4×C13714yes—
495C22×C4C2×D4×C13712yes—
496C22×C4C2×D4×C13712yes—
497C22×C4C2×D4×C13714yes—
498C22×C4C2×D4×C13712yes—
499C22×C4#41×C13714yes—
500C22×C4#41×C13712yes—
501C22×C4#41×C13714yes—
502C22×C4#41×C13714yes—
503C4⋊C4—28no—
504C4⋊C4—216no—
505C4⋊C4—44no—
506C22⋊C4—28no—
507C22⋊C4—216no—
508C22⋊C4—48no—
509C22⋊C4—44no—
510C22⋊C4—44no—
511C42—216no—
512C42—28no—
513C42—48no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—22no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—41no—
523C23—42no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C23×C4×C13711yescharacteristic
538C23C22×D4×C13711yescharacteristic
539C23C22×D4×C13712yes—
540C23C2×#41×C13711yescharacteristic
541C23C2×#41×C13712yes—
542C23C2×#41×C13712yes—
543C23C2×#41×C13712yes—
544C23H(5,𝔽2)×C13711yescharacteristic
545C232−1+4×C13711yescharacteristic
546C232−1+4×C13711yescharacteristic
547C232−1+4×C13711yescharacteristic
548Q8—232no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4C4×D4×C13714yes—
604C2×C4C4×D4×C13718yes—
605C2×C4#120×C13714yes—
606C2×C4#124×C13714yes—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—44no—
611C22—44no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—82no—
617C22—82no—
618C22C2×C4×D4×C13711yescharacteristic
619C22C2×C4×D4×C13712yes—
620C22C4×#41×C13712yes—
621C22#519×C13711yescharacteristic
622C22#520×C13711yescharacteristic
623C22C2×#120×C13711yescharacteristic
624C22#525×C13711yescharacteristic
625C22#525×C13712yes—
626C22C2×#124×C13711yescharacteristic
627C22#529×C13712yes—
628C22#532×C13711yescharacteristic
629C22#536×C13711yescharacteristic
630C22#537×C13711yescharacteristic
631C22#541×C13711yescharacteristic
632C22#542×C13711yescharacteristic
633C22#546×C13712yes—
634C22#547×C13712yes—
635C22#548×C13712yes—
636C22#548×C13712yes—
637C22#552×C13712yes—
638C22#556×C13712yes—
639C22#556×C13712yes—
640C22#559×C13712yes—
641C4—28no—
642C4—24no—
643C4—24no—
644C4—24no—
645C4—42no—
646C4—44no—
647C4—44no—
648C4—44no—
649C4—81no—
650C4—81no—
651C2—82no—
652C2C4×#120×C13711yescharacteristic
653C2C4×#124×C13711yescharacteristic
654C2#2323×C13711yescharacteristic
655C2#2362×C13712yes—
656C2#2367×C13712yes—
657C2#2430×C13711yescharacteristic
658C2#2436×C13711yescharacteristic
659C2#2458×C13712yes—
660C2#2469×C13712yes—
661C2#2592×C13711yescharacteristic
662C2#2604×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
prime radicalC25×C137C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×Q8×C137C2semidirect
5. #1446×C137C2semidirect
6. #1442×C137C2semidirect
9. #1436×C137C2semidirect
10. #1436×C137C2semidirect
11. C4×#95×C137C2semidirect
26. #393×C137C4semidirect
331. #14188C137direct (N × H)
332. C137#14188direct (N × H)
333. C22×C4×Q8C2×C137semidirect
337. #1446C2×C137semidirect
338. #1442C2×C137semidirect
341. #1436C2×C137semidirect
342. #1436C2×C137semidirect
343. C4×#95C2×C137semidirect
358. #393C4×C137semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1372
C2×#393×C1372
C2×#388×C1372
#1446×C1372
#1442×C1372
#1439×C1372
#1437×C1372
#1436×C1372
C4×#95×C1372
#14188137