Finite Group Databasebeta

← C137×#13885 #46863271

Subgroups — C137×#13885 #46863271

Order 35072.

1342 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#382×C137C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C137C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C137C211yesmaximal, characteristic
4#1445×C137C212yesmaximal
5#1443×C137C212yesmaximal
6#1436×C137C212yesmaximal
7C4⋊#95×C137C211yesmaximal, characteristic
8C4⋊#95×C137C211yesmaximal, characteristic
9C4⋊#95×C137C211yesmaximal, characteristic
10C4⋊#95×C137C211yesmaximal, characteristic
11#1434×C137C212yesmaximal
12C22×C4⋊C4×C137C2211yescharacteristic
13C22×C4⋊C4×C137C2211yescharacteristic
14C22×C4⋊C4×C137C2211yescharacteristic
15C22×C4⋊C4×C137C2211yescharacteristic
16C22×C4⋊C4×C137C2211yescharacteristic
17C22×C4⋊C4×C137C2211yescharacteristic
18C22×C42×C137C2212yes—
19C22×C42×C137C2211yescharacteristic
20C22×C42×C137C2211yescharacteristic
21C22×C42×C137C2211yescharacteristic
22#382×C137—24no—
23C4×C4⋊C4×C137—24no—
24C4×C4⋊C4×C137C418yescomplemented
25C2×#95×C137C2212yes—
26C2×#95×C137C2212yes—
27C2×#95×C137C2212yes—
28C2×#95×C137C2212yes—
29C2×#95×C137C2212yes—
30C2×#95×C137C2212yes—
31C2×#95×C137C2212yes—
32C2×#95×C137C2212yes—
33C2×#95×C137C2212yes—
34C2×#95×C137C2212yes—
35C2×#95×C137C2212yes—
36C2×#95×C137C2211yescharacteristic
37C2×#95×C137C2211yescharacteristic
38C23×C4×C137C2312yes—
39C23×C4×C137C2312yes—
40C23×C4×C137C2311yescharacteristic
41C23×C4×C137C2311yescharacteristic
42C23×C4×C137C2311yescharacteristic
43C23×C4×C137C2311yescharacteristic
44C23×C4×C137C2312yes—
45C23×C4×C137C2312yes—
46C23×C4×C137C2311yescharacteristic
47C23×C4×C137C2311yescharacteristic
48C23×C4×C137C2311yescharacteristic
49C2×C4⋊C4×C137—22no—
50C2×C4⋊C4×C137—22no—
51C2×C4⋊C4×C137—22no—
52C2×C4⋊C4×C137—22no—
53C2×C4⋊C4×C137—22no—
54C2×C4⋊C4×C137—22no—
55C2×C4⋊C4×C137—22no—
56C2×C4⋊C4×C137—22no—
57C2×C4⋊C4×C137—22no—
58C2×C4⋊C4×C137—22no—
59C2×C4⋊C4×C137—22no—
60C2×C4⋊C4×C137—22no—
61C2×C4⋊C4×C137—22no—
62C2×C4⋊C4×C137—22no—
63C2×C4⋊C4×C137C2×C414yes—
64C2×C4⋊C4×C137C2×C414yes—
65C2×C4⋊C4×C137D414yes—
66C2×C4⋊C4×C137Q814yes—
67C2×C42×C137—22no—
68C2×C42×C137—22no—
69C2×C42×C137—22no—
70C2×C42×C137—22no—
71C2×C42×C137—22no—
72C2×C42×C137—22no—
73C2×C42×C137—24no—
74C2×C42×C137—24no—
75C2×C42×C137—42no—
76C2×C42×C137C2×C414yes—
77C2×C42×C137C2×C414yes—
78C2×C42×C137C2×C414yes—
79#95×C137—24no—
80#95×C137—24no—
81#95×C137—24no—
82#95×C137—24no—
83#95×C137—24no—
84#95×C137—24no—
85#95×C137—42no—
86#95×C137—42no—
87#95×C137—42no—
88#95×C137—42no—
89#95×C137—42no—
90#95×C137C2×C414yes—
91#95×C137C2×C414yes—
92C24×C137C2411yescharacteristic
93C22×C4×C137—21no—
94C22×C4×C137—21no—
95C22×C4×C137—21no—
96C22×C4×C137—21no—
97C22×C4×C137—21no—
98C22×C4×C137—21no—
99C22×C4×C137—21no—
100C22×C4×C137—21no—
101C22×C4×C137—21no—
102C22×C4×C137—21no—
103C22×C4×C137—21no—
104C22×C4×C137—22no—
105C22×C4×C137—22no—
106C22×C4×C137—22no—
107C22×C4×C137—21no—
108C22×C4×C137—21no—
109C22×C4×C137—21no—
110C22×C4×C137—21no—
111C22×C4×C137—21no—
112C22×C4×C137—22no—
113C22×C4×C137—22no—
114C22×C4×C137—21no—
115C22×C4×C137—21no—
116C22×C4×C137—21no—
117C22×C4×C137—21no—
118C22×C4×C137—21no—
119C22×C4×C137—21no—
120C22×C4×C137—22no—
121C22×C4×C137—22no—
122C22×C4×C137—22no—
123C22×C4×C137—21no—
124C22×C4×C137—21no—
125C22×C4×C137—21no—
126C22×C4×C137—21no—
127C22×C4×C137—21no—
128C22×C4×C137—22no—
129C22×C4×C137—22no—
130C22×C4×C137—22no—
131C22×C4×C137—21no—
132C22×C4×C137—21no—
133C22×C4×C137—21no—
134C22×C4×C137—21no—
135C22×C4×C137—21no—
136C22×C4×C137—22no—
137C22×C4×C137—22no—
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—22no—
149C22×C4×C137—22no—
150C22×C4×C137—22no—
151C22×C4×C137C22×C412yes—
152C22×C4×C137C22×C412yes—
153C22×C4×C137C22×C412yes—
154C22×C4×C137C22×C412yes—
155C22×C4×C137C22×C412yes—
156C22×C4×C137C22×C412yes—
157C22×C4×C137C22×C412yes—
158C22×C4×C137C2×D414yes—
159C22×C4×C137C2×D412yes—
160C22×C4×C137C2×Q814yes—
161C22×C4×C137C2×Q812yes—
162C22×C4×C137#4112yes—
163C22×C4×C137#4112yes—
164C22×C4×C137#4112yes—
165C22×C4×C137#4112yes—
166C22×C4×C137#4112yes—
167C22×C4×C137#4112yes—
168C22×C4×C137#4112yes—
169C22×C4×C137#4112yes—
170C4⋊C4×C137—28no—
171C4⋊C4×C137—28no—
172C4⋊C4×C137—28no—
173C4⋊C4×C137—28no—
174C4⋊C4×C137—44no—
175C4⋊C4×C137—44no—
176C42×C137—28no—
177C42×C137—28no—
178C42×C137—28no—
179C42×C137—48no—
180C23×C137C23×C411yescharacteristic
181C23×C137C22×D411yescharacteristic
182C23×C137C22×Q811yescharacteristic
183C23×C137C2×#4111yescharacteristic
184C23×C137C2×#4111yescharacteristic
185C23×C137C2×#4111yescharacteristic
186C23×C137C2×#4111yescharacteristic
187C23×C137C2×#4111yescharacteristic
188C23×C137C2×#4111yescharacteristic
189C23×C137C2×#4111yescharacteristic
190C23×C137C2×#4111yescharacteristic
191C23×C137H(5,𝔽2)11yescharacteristic
192C23×C137H(5,𝔽2)11yescharacteristic
193C23×C1372−1+411yescharacteristic
194C23×C1372−1+411yescharacteristic
195C2×C4×C137—22no—
196C2×C4×C137—22no—
197C2×C4×C137—22no—
198C2×C4×C137—22no—
199C2×C4×C137—22no—
200C2×C4×C137—22no—
201C2×C4×C137—22no—
202C2×C4×C137—22no—
203C2×C4×C137—22no—
204C2×C4×C137—22no—
205C2×C4×C137—22no—
206C2×C4×C137—22no—
207C2×C4×C137—22no—
208C2×C4×C137—22no—
209C2×C4×C137—22no—
210C2×C4×C137—22no—
211C2×C4×C137—22no—
212C2×C4×C137—22no—
213C2×C4×C137—22no—
214C2×C4×C137—22no—
215C2×C4×C137—22no—
216C2×C4×C137—22no—
217C2×C4×C137—22no—
218C2×C4×C137—22no—
219C2×C4×C137—24no—
220C2×C4×C137—24no—
221C2×C4×C137—24no—
222C2×C4×C137—24no—
223C2×C4×C137—24no—
224C2×C4×C137—24no—
225C2×C4×C137—42no—
226C2×C4×C137—42no—
227C2×C4×C137—41no—
228C2×C4×C137—42no—
229C2×C4×C137—41no—
230C2×C4×C137—41no—
231C2×C4×C137—41no—
232C2×C4×C137—42no—
233C2×C4×C137—42no—
234C2×C4×C137—41no—
235C2×C4×C137—41no—
236C2×C4×C137—41no—
237C2×C4×C137—41no—
238C2×C4×C137—41no—
239C2×C4×C137—41no—
240C2×C4×C137—42no—
241C2×C4×C137—41no—
242C2×C4×C137—41no—
243C2×C4×C137—41no—
244C2×C4×C137—41no—
245C2×C4×C137—41no—
246C2×C4×C137—41no—
247C2×C4×C137—42no—
248C2×C4×C137—42no—
249C2×C4×C137—42no—
250C2×C4×C137—42no—
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—42no—
262C2×C4×C137—42no—
263C2×C4×C137#11714yes—
264C2×C4×C137#11714yes—
265C2×C4×C137#11714yes—
266C2×C4×C137C4×D414yes—
267C2×C4×C137C4×Q814yes—
268C2×C4×C137C22⋊Q814yes—
269C2×C4×C137#12314yes—
270C2×C4×C137#12514yes—
271C2×C4×C137#12614yes—
272C22×C137C2×#11711yescharacteristic
273C22×C137C2×#11711yescharacteristic
274C22×C137C2×#11711yescharacteristic
275C22×C137C2×C4×D411yescharacteristic
276C22×C137C2×C4×Q811yescharacteristic
277C22×C137#52011yescharacteristic
278C22×C137#52011yescharacteristic
279C22×C137C2×C22⋊Q811yescharacteristic
280C22×C137C2×#12311yescharacteristic
281C22×C137C2×#12511yescharacteristic
282C22×C137C2×#12611yescharacteristic
283C22×C137#52911yescharacteristic
284C22×C137#52911yescharacteristic
285C22×C137#52911yescharacteristic
286C22×C137#52911yescharacteristic
287C22×C137#54011yescharacteristic
288C22×C137#54111yescharacteristic
289C22×C137#54211yescharacteristic
290C22×C137#54211yescharacteristic
291C22×C137#54611yescharacteristic
292C22×C137#54711yescharacteristic
293C22×C137#54811yescharacteristic
294C22×C137#55011yescharacteristic
295C22×C137#55211yescharacteristic
296C22×C137#55311yescharacteristic
297C22×C137#55411yescharacteristic
298C22×C137#55411yescharacteristic
299C22×C137#55511yescharacteristic
300C22×C137#55611yescharacteristic
301C22×C137#55611yescharacteristic
302C22×C137#55611yescharacteristic
303C22×C137#55711yescharacteristic
304C22×C137#55711yescharacteristic
305C22×C137#55911yescharacteristic
306C22×C137#55911yescharacteristic
307C4×C137—24no—
308C4×C137—24no—
309C4×C137—42no—
310C4×C137—42no—
311C4×C137—42no—
312C4×C137—42no—
313C4×C137—44no—
314C4×C137—44no—
315C4×C137—82no—
316C4×C137—82no—
317C4×C137#38718yes—
318C2×C137#228311yescharacteristic
319C2×C137C2×#38711yescharacteristic
320C2×C137#231411yescharacteristic
321C2×C137#235211yescharacteristic
322C2×C137#235411yescharacteristic
323C2×C137#235511yescharacteristic
324C2×C137#235511yescharacteristic
325C2×C137#244711yescharacteristic
326C2×C137#244811yescharacteristic
327C2×C137#245311yescharacteristic
328C2×C137#245411yescharacteristic
329C2×C137#250811yescharacteristic
330C2×C137#250911yescharacteristic
331C2×C137#251311yescharacteristic
332C2×C137#251411yescharacteristic
333#13885C13711yesmaximal, characteristic, direct product factor, Sylow
334C137#1388511yescharacteristic, direct product factor, Sylow
335C2×#382C2×C13711yescharacteristic
336C2×C4×C4⋊C4C2×C13711yescharacteristic
337C2×C4×C4⋊C4C2×C13711yescharacteristic
338#1445C2×C13712yes—
339#1443C2×C13712yes—
340#1436C2×C13712yes—
341C4⋊#95C2×C13711yescharacteristic
342C4⋊#95C2×C13711yescharacteristic
343C4⋊#95C2×C13711yescharacteristic
344C4⋊#95C2×C13711yescharacteristic
345#1434C2×C13712yes—
346C22×C4⋊C4C22×C13711yescharacteristic
347C22×C4⋊C4C22×C13711yescharacteristic
348C22×C4⋊C4C22×C13711yescharacteristic
349C22×C4⋊C4C22×C13711yescharacteristic
350C22×C4⋊C4C22×C13711yescharacteristic
351C22×C4⋊C4C22×C13711yescharacteristic
352C22×C42C22×C13712yes—
353C22×C42C22×C13711yescharacteristic
354C22×C42C22×C13711yescharacteristic
355C22×C42C22×C13711yescharacteristic
356#382—24no—
357C4×C4⋊C4—24no—
358C4×C4⋊C4C4×C13718yescomplemented
359C2×#95C22×C13712yes—
360C2×#95C22×C13712yes—
361C2×#95C22×C13712yes—
362C2×#95C22×C13712yes—
363C2×#95C22×C13712yes—
364C2×#95C22×C13712yes—
365C2×#95C22×C13712yes—
366C2×#95C22×C13712yes—
367C2×#95C22×C13712yes—
368C2×#95C22×C13712yes—
369C2×#95C22×C13712yes—
370C2×#95C22×C13711yescharacteristic
371C2×#95C22×C13711yescharacteristic
372C23×C4C23×C13712yes—
373C23×C4C23×C13712yes—
374C23×C4C23×C13711yescharacteristic
375C23×C4C23×C13711yescharacteristic
376C23×C4C23×C13711yescharacteristic
377C23×C4C23×C13711yescharacteristic
378C23×C4C23×C13712yes—
379C23×C4C23×C13712yes—
380C23×C4C23×C13711yescharacteristic
381C23×C4C23×C13711yescharacteristic
382C23×C4C23×C13711yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4C2×C4×C13714yes—
398C2×C4⋊C4C2×C4×C13714yes—
399C2×C4⋊C4D4×C13714yes—
400C2×C4⋊C4Q8×C13714yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—42no—
410C2×C42C2×C4×C13714yes—
411C2×C42C2×C4×C13714yes—
412C2×C42C2×C4×C13714yes—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95C2×C4×C13714yes—
425#95C2×C4×C13714yes—
426C24C24×C13711yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
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—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4C22×C4×C13712yes—
486C22×C4C22×C4×C13712yes—
487C22×C4C22×C4×C13712yes—
488C22×C4C22×C4×C13712yes—
489C22×C4C22×C4×C13712yes—
490C22×C4C22×C4×C13712yes—
491C22×C4C22×C4×C13712yes—
492C22×C4C2×D4×C13714yes—
493C22×C4C2×D4×C13712yes—
494C22×C4C2×Q8×C13714yes—
495C22×C4C2×Q8×C13712yes—
496C22×C4#41×C13712yes—
497C22×C4#41×C13712yes—
498C22×C4#41×C13712yes—
499C22×C4#41×C13712yes—
500C22×C4#41×C13712yes—
501C22×C4#41×C13712yes—
502C22×C4#41×C13712yes—
503C22×C4#41×C13712yes—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—28no—
507C4⋊C4—28no—
508C4⋊C4—44no—
509C4⋊C4—44no—
510C42—28no—
511C42—28no—
512C42—28no—
513C42—48no—
514C23C23×C4×C13711yescharacteristic
515C23C22×D4×C13711yescharacteristic
516C23C22×Q8×C13711yescharacteristic
517C23C2×#41×C13711yescharacteristic
518C23C2×#41×C13711yescharacteristic
519C23C2×#41×C13711yescharacteristic
520C23C2×#41×C13711yescharacteristic
521C23C2×#41×C13711yescharacteristic
522C23C2×#41×C13711yescharacteristic
523C23C2×#41×C13711yescharacteristic
524C23C2×#41×C13711yescharacteristic
525C23H(5,𝔽2)×C13711yescharacteristic
526C23H(5,𝔽2)×C13711yescharacteristic
527C232−1+4×C13711yescharacteristic
528C232−1+4×C13711yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
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—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4#117×C13714yes—
598C2×C4#117×C13714yes—
599C2×C4#117×C13714yes—
600C2×C4C4×D4×C13714yes—
601C2×C4C4×Q8×C13714yes—
602C2×C4C22⋊Q8×C13714yes—
603C2×C4#123×C13714yes—
604C2×C4#125×C13714yes—
605C2×C4#126×C13714yes—
606C22C2×#117×C13711yescharacteristic
607C22C2×#117×C13711yescharacteristic
608C22C2×#117×C13711yescharacteristic
609C22C2×C4×D4×C13711yescharacteristic
610C22C2×C4×Q8×C13711yescharacteristic
611C22#520×C13711yescharacteristic
612C22#520×C13711yescharacteristic
613C22C2×C22⋊Q8×C13711yescharacteristic
614C22C2×#123×C13711yescharacteristic
615C22C2×#125×C13711yescharacteristic
616C22C2×#126×C13711yescharacteristic
617C22#529×C13711yescharacteristic
618C22#529×C13711yescharacteristic
619C22#529×C13711yescharacteristic
620C22#529×C13711yescharacteristic
621C22#540×C13711yescharacteristic
622C22#541×C13711yescharacteristic
623C22#542×C13711yescharacteristic
624C22#542×C13711yescharacteristic
625C22#546×C13711yescharacteristic
626C22#547×C13711yescharacteristic
627C22#548×C13711yescharacteristic
628C22#550×C13711yescharacteristic
629C22#552×C13711yescharacteristic
630C22#553×C13711yescharacteristic
631C22#554×C13711yescharacteristic
632C22#554×C13711yescharacteristic
633C22#555×C13711yescharacteristic
634C22#556×C13711yescharacteristic
635C22#556×C13711yescharacteristic
636C22#556×C13711yescharacteristic
637C22#557×C13711yescharacteristic
638C22#557×C13711yescharacteristic
639C22#559×C13711yescharacteristic
640C22#559×C13711yescharacteristic
641C4—24no—
642C4—24no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—44no—
648C4—44no—
649C4—82no—
650C4—82no—
651C4#387×C13718yes—
652C2#2283×C13711yescharacteristic
653C2C2×#387×C13711yescharacteristic
654C2#2314×C13711yescharacteristic
655C2#2352×C13711yescharacteristic
656C2#2354×C13711yescharacteristic
657C2#2355×C13711yescharacteristic
658C2#2355×C13711yescharacteristic
659C2#2447×C13711yescharacteristic
660C2#2448×C13711yescharacteristic
661C2#2453×C13711yescharacteristic
662C2#2454×C13711yescharacteristic
663C2#2508×C13711yescharacteristic
664C2#2509×C13711yescharacteristic
665C2#2513×C13711yescharacteristic
666C2#2514×C13711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
24. C4×C4⋊C4×C137C4semidirect
333. #13885C137direct (N × H)
334. C137#13885direct (N × H)
358. C4×C4⋊C4C4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#382×C1372
C2×C4×C4⋊C4×C1372
#1445×C1372
#1443×C1372
#1436×C1372
C4⋊#95×C1372
#1434×C1372
#13885137