Finite Group Databasebeta

← C137×#14669 #46864055

Subgroups — C137×#14669 #46864055

Order 35072.

1342 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C137C211yesmaximal, characteristic
2#1445×C137C212yesmaximal, complemented
3#1443×C137C212yesmaximal, complemented
4#1442×C137C212yesmaximal, complemented
5#1441×C137C212yesmaximal, complemented
6#1440×C137C212yesmaximal
7#1439×C137C211yesmaximal, characteristic
8#1439×C137C211yesmaximal, characteristic
9C22⋊#95×C137C212yesmaximal
10C24×C4×C137C2211yescharacteristic
11C22×C4⋊C4×C137C2211yescharacteristic
12C22×C4⋊C4×C137C2211yescharacteristic
13C22×C4⋊C4×C137C2212yes—
14C22×C22⋊C4×C137C2211yescharacteristic
15C22×C22⋊C4×C137C2212yes—
16C22×C22⋊C4×C137C2212yes—
17C22×C22⋊C4×C137C2211yescharacteristic
18#385×C137C418yescomplemented
19C2×#95×C137C2212yes—
20C2×#95×C137C2212yes—
21C2×#95×C137C2212yes—
22C2×#95×C137C2212yes—
23C2×#95×C137C2212yes—
24C2×#95×C137C2212yes—
25C2×#95×C137C2211yescharacteristic
26C2×#95×C137C2211yescharacteristic
27C2×#95×C137C2212yes—
28C2×#95×C137C2212yes—
29C2×#95×C137C2212yes—
30C2×#95×C137C2212yes—
31C2×#95×C137C2212yes—
32C25×C137C2311yescharacteristic
33C23×C4×C137—41no—
34C23×C4×C137—41no—
35C23×C4×C137—42no—
36C23×C4×C137—42no—
37C23×C4×C137C2×C414yes—
38C23×C4×C137C2312yes—
39C23×C4×C137C2312yes—
40C23×C4×C137C2312yes—
41C23×C4×C137C2312yes—
42C23×C4×C137C2312yes—
43C23×C4×C137C2311yescharacteristic
44C23×C4×C137C2312yes—
45C23×C4×C137C2311yescharacteristic
46C2×C4⋊C4×C137—42no—
47C2×C4⋊C4×C137—42no—
48C2×C4⋊C4×C137—42no—
49C2×C4⋊C4×C137—41no—
50C2×C4⋊C4×C137—41no—
51C2×C4⋊C4×C137—42no—
52C2×C4⋊C4×C137C2×C418yes—
53C2×C22⋊C4×C137—22no—
54C2×C22⋊C4×C137—22no—
55C2×C22⋊C4×C137—24no—
56C2×C22⋊C4×C137—24no—
57C2×C22⋊C4×C137—41no—
58C2×C22⋊C4×C137—41no—
59C2×C22⋊C4×C137—42no—
60C2×C22⋊C4×C137—42no—
61C2×C22⋊C4×C137—42no—
62C2×C22⋊C4×C137—42no—
63C2×C22⋊C4×C137C2×C414yes—
64C2×C22⋊C4×C137C2×C414yes—
65#95×C137—42no—
66#95×C137—42no—
67#95×C137—41no—
68#95×C137—41no—
69#95×C137—42no—
70#95×C137—42no—
71#95×C137—42no—
72#95×C137—42no—
73#95×C137—42no—
74#95×C137—42no—
75#95×C137—42no—
76#95×C137—42no—
77#95×C137C2×C418yes—
78C24×C137—22no—
79C24×C137—21no—
80C24×C137—21no—
81C24×C137—22no—
82C24×C137—22no—
83C24×C137—21no—
84C24×C137—21no—
85C24×C137—22no—
86C24×C137C22×C412yes—
87C24×C137#4112yes—
88C24×C137#4112yes—
89C24×C137C2411yescharacteristic
90C22×C4×C137—22no—
91C22×C4×C137—22no—
92C22×C4×C137—22no—
93C22×C4×C137—21no—
94C22×C4×C137—21no—
95C22×C4×C137—22no—
96C22×C4×C137—22no—
97C22×C4×C137—22no—
98C22×C4×C137—22no—
99C22×C4×C137—22no—
100C22×C4×C137—22no—
101C22×C4×C137—22no—
102C22×C4×C137—22no—
103C22×C4×C137—21no—
104C22×C4×C137—21no—
105C22×C4×C137—22no—
106C22×C4×C137—22no—
107C22×C4×C137—22no—
108C22×C4×C137—22no—
109C22×C4×C137—22no—
110C22×C4×C137—22no—
111C22×C4×C137—22no—
112C22×C4×C137—22no—
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—22no—
122C22×C4×C137—22no—
123C22×C4×C137—22no—
124C22×C4×C137—22no—
125C22×C4×C137—22no—
126C22×C4×C137—22no—
127C22×C4×C137—22no—
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—22no—
138C22×C4×C137—48no—
139C22×C4×C137—44no—
140C22×C4×C137—44no—
141C22×C4×C137—48no—
142C22×C4×C137—44no—
143C22×C4×C137C22×C412yes—
144C22×C4×C137C22×C414yes—
145C22×C4×C137C22×C414yes—
146C22×C4×C137C22×C412yes—
147C4⋊C4×C137—48no—
148C4⋊C4×C137—44no—
149C4⋊C4×C137—44no—
150C22⋊C4×C137—28no—
151C22⋊C4×C137—44no—
152C22⋊C4×C137—48no—
153C22⋊C4×C137—48no—
154C23×C137—22no—
155C23×C137—24no—
156C23×C137—22no—
157C23×C137—24no—
158C23×C137—24no—
159C23×C137—24no—
160C23×C137—22no—
161C23×C137—22no—
162C23×C137—22no—
163C23×C137—22no—
164C23×C137—24no—
165C23×C137—24no—
166C23×C137—41no—
167C23×C137—42no—
168C23×C137—41no—
169C23×C137—41no—
170C23×C137—42no—
171C23×C137—42no—
172C23×C137—42no—
173C23×C137—42no—
174C23×C137—42no—
175C23×C137—41no—
176C23×C137#11714yes—
177C23×C137C23×C411yescharacteristic
178C23×C137C2×#4111yescharacteristic
179C23×C137C2×#4111yescharacteristic
180C23×C137H(5,𝔽2)12yes—
181C23×C137H(5,𝔽2)12yes—
182C23×C137H(5,𝔽2)11yescharacteristic
183C23×C137H(5,𝔽2)11yescharacteristic
184C23×C137H(5,𝔽2)12yes—
185C23×C1372−1+411yescharacteristic
186C23×C1372−1+411yescharacteristic
187C23×C1372−1+412yes—
188C2×C4×C137—24no—
189C2×C4×C137—22no—
190C2×C4×C137—22no—
191C2×C4×C137—24no—
192C2×C4×C137—24no—
193C2×C4×C137—24no—
194C2×C4×C137—24no—
195C2×C4×C137—24no—
196C2×C4×C137—24no—
197C2×C4×C137—24no—
198C2×C4×C137—416no—
199C2×C4×C137—42no—
200C2×C4×C137—42no—
201C2×C4×C137—42no—
202C2×C4×C137—42no—
203C2×C4×C137—41no—
204C2×C4×C137—41no—
205C2×C4×C137—42no—
206C2×C4×C137—42no—
207C2×C4×C137—42no—
208C2×C4×C137—42no—
209C2×C4×C137—41no—
210C2×C4×C137—42no—
211C2×C4×C137—42no—
212C2×C4×C137—41no—
213C2×C4×C137—42no—
214C2×C4×C137—42no—
215C2×C4×C137—42no—
216C2×C4×C137—42no—
217C2×C4×C137—42no—
218C2×C4×C137—42no—
219C2×C4×C137—42no—
220C2×C4×C137—42no—
221C2×C4×C137—42no—
222C2×C4×C137—42no—
223C2×C4×C137—42no—
224C2×C4×C137—42no—
225C2×C4×C137—42no—
226C2×C4×C137—42no—
227C2×C4×C137—42no—
228C2×C4×C137—42no—
229C2×C4×C137—42no—
230C2×C4×C137—42no—
231C2×C4×C137—42no—
232C2×C4×C137—42no—
233C2×C4×C137—42no—
234C2×C4×C137—42no—
235C2×C4×C137—42no—
236C2×C4×C137—42no—
237C2×C4×C137—42no—
238C2×C4×C137—42no—
239C2×C4×C137—42no—
240C2×C4×C137—42no—
241C22×C137—24no—
242C22×C137—28no—
243C22×C137—42no—
244C22×C137—42no—
245C22×C137—44no—
246C22×C137—44no—
247C22×C137—42no—
248C22×C137—42no—
249C22×C137—42no—
250C22×C137—42no—
251C22×C137—44no—
252C22×C137C2×#11711yescharacteristic
253C22×C137#51811yescharacteristic
254C22×C137#51812yes—
255C22×C137#51911yescharacteristic
256C22×C137#52012yes—
257C22×C137#53812yes—
258C22×C137#53812yes—
259C22×C137#53911yescharacteristic
260C22×C137#53911yescharacteristic
261C22×C137#53911yescharacteristic
262C22×C137#53911yescharacteristic
263C22×C137#53912yes—
264C22×C137#53912yes—
265C22×C137#56011yescharacteristic
266C22×C137#56011yescharacteristic
267C22×C137#56012yes—
268C22×C137H(3,𝔽4)11yescharacteristic
269C22×C137#56212yes—
270C22×C137#56212yes—
271C22×C137#56212yes—
272C22×C137#56312yes—
273C22×C137#56312yes—
274C22×C137#56311yescharacteristic
275C4×C137—44no—
276C4×C137—42no—
277C4×C137—44no—
278C4×C137—42no—
279C4×C137—82no—
280C4×C137—82no—
281C4×C137—82no—
282C4×C137—82no—
283C2×C137—44no—
284C2×C137#231311yescharacteristic
285C2×C137#231812yes—
286C2×C137#237511yescharacteristic
287C2×C137#237611yescharacteristic
288C2×C137#237812yes—
289C2×C137#282411yescharacteristic
290C2×C137#282611yescharacteristic
291C2×C137#282712yes—
292C2×C137#282712yes—
293C2×C137#283411yescharacteristic
294C2×C137#283511yescharacteristic
295#14669C13711yesmaximal, characteristic, direct product factor, Sylow
296C137#1466911yescharacteristic, direct product factor, Sylow
297C2×#385C2×C13711yescharacteristic
298#1445C2×C13712yescomplemented
299#1443C2×C13712yescomplemented
300#1442C2×C13712yescomplemented
301#1441C2×C13712yescomplemented
302#1440C2×C13712yes—
303#1439C2×C13711yescharacteristic
304#1439C2×C13711yescharacteristic
305C22⋊#95C2×C13712yes—
306C24×C4C22×C13711yescharacteristic
307C22×C4⋊C4C22×C13711yescharacteristic
308C22×C4⋊C4C22×C13711yescharacteristic
309C22×C4⋊C4C22×C13712yes—
310C22×C22⋊C4C22×C13711yescharacteristic
311C22×C22⋊C4C22×C13712yes—
312C22×C22⋊C4C22×C13712yes—
313C22×C22⋊C4C22×C13711yescharacteristic
314#385C4×C13718yescomplemented
315C2×#95C22×C13712yes—
316C2×#95C22×C13712yes—
317C2×#95C22×C13712yes—
318C2×#95C22×C13712yes—
319C2×#95C22×C13712yes—
320C2×#95C22×C13712yes—
321C2×#95C22×C13711yescharacteristic
322C2×#95C22×C13711yescharacteristic
323C2×#95C22×C13712yes—
324C2×#95C22×C13712yes—
325C2×#95C22×C13712yes—
326C2×#95C22×C13712yes—
327C2×#95C22×C13712yes—
328C25C23×C13711yescharacteristic
329C23×C4—41no—
330C23×C4—41no—
331C23×C4—42no—
332C23×C4—42no—
333C23×C4C2×C4×C13714yes—
334C23×C4C23×C13712yes—
335C23×C4C23×C13712yes—
336C23×C4C23×C13712yes—
337C23×C4C23×C13712yes—
338C23×C4C23×C13711yescharacteristic
339C23×C4C23×C13712yes—
340C23×C4C23×C13711yescharacteristic
341C23×C4C23×C13712yes—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4C2×C4×C13718yes—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4C2×C4×C13714yes—
360C2×C22⋊C4C2×C4×C13714yes—
361#95—42no—
362#95—42no—
363#95—41no—
364#95—41no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95C2×C4×C13718yes—
374C24—22no—
375C24—21no—
376C24—21no—
377C24—22no—
378C24—22no—
379C24—21no—
380C24—21no—
381C24—22no—
382C24C22×C4×C13712yes—
383C24#41×C13712yes—
384C24#41×C13712yes—
385C24C24×C13711yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—48no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—48no—
438C22×C4—44no—
439C22×C4C22×C4×C13712yes—
440C22×C4C22×C4×C13714yes—
441C22×C4C22×C4×C13714yes—
442C22×C4C22×C4×C13712yes—
443C4⋊C4—48no—
444C4⋊C4—44no—
445C4⋊C4—44no—
446C22⋊C4—28no—
447C22⋊C4—44no—
448C22⋊C4—48no—
449C22⋊C4—48no—
450C23—22no—
451C23—24no—
452C23—22no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—24no—
461C23—24no—
462C23—41no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23#117×C13714yes—
473C23C23×C4×C13711yescharacteristic
474C23C2×#41×C13711yescharacteristic
475C23C2×#41×C13711yescharacteristic
476C23H(5,𝔽2)×C13712yes—
477C23H(5,𝔽2)×C13712yes—
478C23H(5,𝔽2)×C13711yescharacteristic
479C23H(5,𝔽2)×C13711yescharacteristic
480C23H(5,𝔽2)×C13712yes—
481C232−1+4×C13711yescharacteristic
482C232−1+4×C13711yescharacteristic
483C232−1+4×C13712yes—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—416no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C22—24no—
538C22—28no—
539C22—42no—
540C22—42no—
541C22—44no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—44no—
548C22C2×#117×C13711yescharacteristic
549C22#518×C13711yescharacteristic
550C22#518×C13712yes—
551C22#519×C13711yescharacteristic
552C22#520×C13712yes—
553C22#538×C13712yes—
554C22#538×C13712yes—
555C22#539×C13711yescharacteristic
556C22#539×C13711yescharacteristic
557C22#539×C13711yescharacteristic
558C22#539×C13711yescharacteristic
559C22#539×C13712yes—
560C22#539×C13712yes—
561C22#560×C13711yescharacteristic
562C22#560×C13711yescharacteristic
563C22#560×C13712yes—
564C22H(3,𝔽4)×C13711yescharacteristic
565C22#562×C13712yes—
566C22#562×C13712yes—
567C22#562×C13712yes—
568C22#563×C13712yes—
569C22#563×C13712yes—
570C22#563×C13711yescharacteristic
571C4—44no—
572C4—44no—
573C4—42no—
574C4—42no—
575C4—82no—
576C4—82no—
577C4—82no—
578C4—82no—
579C2—44no—
580C2#2313×C13711yescharacteristic
581C2#2318×C13712yes—
582C2#2375×C13711yescharacteristic
583C2#2376×C13711yescharacteristic
584C2#2378×C13712yes—
585C2#2824×C13711yescharacteristic
586C2#2826×C13711yescharacteristic
587C2#2827×C13712yes—
588C2#2827×C13712yes—
589C2#2834×C13711yescharacteristic
590C2#2835×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
2. #1445×C137C2semidirect
3. #1443×C137C2semidirect
4. #1442×C137C2semidirect
5. #1441×C137C2semidirect
18. #385×C137C4semidirect
295. #14669C137direct (N × H)
296. C137#14669direct (N × H)
298. #1445C2×C137semidirect
299. #1443C2×C137semidirect
300. #1442C2×C137semidirect
301. #1441C2×C137semidirect
314. #385C4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#385×C1372
#1445×C1372
#1443×C1372
#1442×C1372
#1441×C1372
#1440×C1372
#1439×C1372
C22⋊#95×C1372
#14669137