Finite Group Databasebeta

← C137×#15163 #46864549

Subgroups — C137×#15163 #46864549

Order 35072.

1862 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C137C211yesmaximal, characteristic, complemented
2C2×#396×C137C212yesmaximal, complemented
3C2×#394×C137C211yesmaximal, characteristic
4C2×#390×C137C211yesmaximal, characteristic
5C2×#388×C137C212yesmaximal, complemented
6C2×C4×C4⋊C4×C137C211yesmaximal, characteristic, complemented
7#1445×C137C211yesmaximal, characteristic, complemented
8#1439×C137C212yesmaximal, complemented
9#1438×C137C211yesmaximal, characteristic
10#1437×C137C212yesmaximal, complemented
11C4⋊#95×C137C211yesmaximal, characteristic, complemented
12C23×D4×C137C2211yescharacteristic
13C22×C4⋊C4×C137C2212yes—
14C22×C4⋊C4×C137C2211yescharacteristic
15C22×C4⋊C4×C137C2212yes—
16C22×C4⋊C4×C137C2211yescharacteristic
17C22×C4⋊C4×C137C2211yescharacteristic
18C22×C22⋊C4×C137C2212yes—
19C22×C22⋊C4×C137C2212yes—
20C22×C22⋊C4×C137C2212yes—
21C22×C22⋊C4×C137C2212yes—
22C22×C22⋊C4×C137C2212yes—
23C22×C22⋊C4×C137C2212yes—
24C22×C42×C137C2211yescharacteristic
25C22×C42×C137C2211yescharacteristic
26C22×C42×C137C2211yescharacteristic
27#398×C137—24no—
28#396×C137—28no—
29#394×C137—24no—
30#390×C137—24no—
31#388×C137—28no—
32C4×C4⋊C4×C137—24no—
33C2×#95×C137C2211yescharacteristic
34C2×#95×C137C2211yescharacteristic
35C2×#95×C137C2212yes—
36C2×#95×C137C2212yes—
37C2×#95×C137C2211yescharacteristic
38C2×#95×C137C2212yes—
39C2×#95×C137C2211yescharacteristic
40C2×#95×C137C2212yes—
41C25×C137C2312yes—
42C22×D4×C137—24no—
43C22×D4×C137—22no—
44C22×D4×C137—22no—
45C22×D4×C137—22no—
46C22×D4×C137—42no—
47C23×C4×C137C2312yes—
48C23×C4×C137C2312yes—
49C23×C4×C137C2311yescharacteristic
50C23×C4×C137C2311yescharacteristic
51C23×C4×C137C2311yescharacteristic
52C23×C4×C137C2312yes—
53C23×C4×C137C2311yescharacteristic
54C23×C4×C137C2311yescharacteristic
55C23×C4×C137C2311yescharacteristic
56C23×C4×C137C2311yescharacteristic
57C2×C4⋊C4×C137—22no—
58C2×C4⋊C4×C137—22no—
59C2×C4⋊C4×C137—22no—
60C2×C4⋊C4×C137—22no—
61C2×C4⋊C4×C137—24no—
62C2×C4⋊C4×C137—22no—
63C2×C4⋊C4×C137—24no—
64C2×C4⋊C4×C137—24no—
65C2×C4⋊C4×C137—22no—
66C2×C4⋊C4×C137—24no—
67C2×C4⋊C4×C137—24no—
68C2×C4⋊C4×C137—22no—
69C2×C4⋊C4×C137—42no—
70C2×C4⋊C4×C137D414yes—
71C2×C4⋊C4×C137D414yescomplemented
72C2×C22⋊C4×C137—24no—
73C2×C22⋊C4×C137—24no—
74C2×C22⋊C4×C137—24no—
75C2×C22⋊C4×C137—24no—
76C2×C22⋊C4×C137—24no—
77C2×C22⋊C4×C137—24no—
78C2×C22⋊C4×C137—24no—
79C2×C22⋊C4×C137—24no—
80C2×C22⋊C4×C137—24no—
81C2×C22⋊C4×C137—24no—
82C2×C22⋊C4×C137—24no—
83C2×C22⋊C4×C137—24no—
84C2×C22⋊C4×C137—24no—
85C2×C22⋊C4×C137—24no—
86C2×C22⋊C4×C137—24no—
87C2×C22⋊C4×C137—24no—
88C2×C22⋊C4×C137—42no—
89C2×C22⋊C4×C137—42no—
90C2×C42×C137—22no—
91C2×C42×C137—22no—
92C2×C42×C137—22no—
93C2×C42×C137—42no—
94C2×C42×C137—42no—
95C2×C42×C137D414yes—
96C2×C42×C137D414yescomplemented
97#95×C137—22no—
98#95×C137—22no—
99#95×C137—24no—
100#95×C137—24no—
101#95×C137—22no—
102#95×C137—24no—
103#95×C137—22no—
104#95×C137—24no—
105C24×C137—22no—
106C24×C137—22no—
107C24×C137—22no—
108C24×C137—22no—
109C24×C137—22no—
110C24×C137—22no—
111C24×C137—22no—
112C24×C137—22no—
113C24×C137—22no—
114C24×C137—22no—
115C24×C137—22no—
116C24×C137—22no—
117C24×C137—22no—
118C24×C137—22no—
119C24×C137#4114yes—
120C24×C137C2411yescharacteristic
121C2×D4×C137—28no—
122C2×D4×C137—48no—
123C2×D4×C137—48no—
124C2×D4×C137—44no—
125C2×D4×C137—44no—
126C22×C4×C137—21no—
127C22×C4×C137—21no—
128C22×C4×C137—21no—
129C22×C4×C137—21no—
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—21no—
137C22×C4×C137—22no—
138C22×C4×C137—21no—
139C22×C4×C137—21no—
140C22×C4×C137—22no—
141C22×C4×C137—22no—
142C22×C4×C137—21no—
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—22no—
154C22×C4×C137—22no—
155C22×C4×C137—22no—
156C22×C4×C137—22no—
157C22×C4×C137—22no—
158C22×C4×C137—22no—
159C22×C4×C137—22no—
160C22×C4×C137—22no—
161C22×C4×C137—22no—
162C22×C4×C137—22no—
163C22×C4×C137—22no—
164C22×C4×C137—22no—
165C22×C4×C137—22no—
166C22×C4×C137—22no—
167C22×C4×C137—22no—
168C22×C4×C137C2×D412yes—
169C22×C4×C137C2×D412yes—
170C22×C4×C137C2×D412yes—
171C22×C4×C137C2×D412yes—
172C22×C4×C137C2×D412yes—
173C22×C4×C137C2×D412yes—
174C22×C4×C137C2×D412yes—
175C22×C4×C137C2×D412yes—
176C22×C4×C137C2×D412yes—
177C22×C4×C137C2×D412yes—
178C22×C4×C137C2×D412yes—
179C22×C4×C137C2×D412yes—
180C22×C4×C137#4114yes—
181C22×C4×C137#4112yes—
182C22×C4×C137#4112yes—
183C22×C4×C137#4112yes—
184C4⋊C4×C137—28no—
185C4⋊C4×C137—28no—
186C4⋊C4×C137—48no—
187C4⋊C4×C137—44no—
188C4⋊C4×C137—48no—
189C22⋊C4×C137—216no—
190C22⋊C4×C137—48no—
191C22⋊C4×C137—48no—
192C22⋊C4×C137—48no—
193C22⋊C4×C137—48no—
194C22⋊C4×C137—48no—
195C42×C137—28no—
196C42×C137—44no—
197C42×C137—44no—
198C23×C137—24no—
199C23×C137—24no—
200C23×C137—24no—
201C23×C137—24no—
202C23×C137—24no—
203C23×C137—24no—
204C23×C137—24no—
205C23×C137—42no—
206C23×C137—42no—
207C23×C137—42no—
208C23×C137—42no—
209C23×C137—42no—
210C23×C137—42no—
211C23×C137—42no—
212C23×C137—42no—
213C23×C137—42no—
214C23×C137—42no—
215C23×C137—42no—
216C23×C137—42no—
217C23×C137—42no—
218C23×C137—42no—
219C23×C137—42no—
220C23×C137—42no—
221C23×C137—42no—
222C23×C137—42no—
223C23×C137—42no—
224C23×C137—42no—
225C23×C137—42no—
226C23×C137—42no—
227C23×C137—42no—
228C23×C137—42no—
229C23×C137—42no—
230C23×C137—42no—
231C23×C137—42no—
232C23×C137—42no—
233C23×C137C22×D411yescharacteristic
234C23×C137C22×D411yescharacteristic
235C23×C137C22×D411yescharacteristic
236C23×C137C22×D411yescharacteristic
237C23×C137C2×#4111yescharacteristic
238C23×C137C2×#4111yescharacteristic
239C23×C137C2×#4111yescharacteristic
240C23×C137C2×#4112yes—
241C23×C137C2×#4112yes—
242C23×C137H(5,𝔽2)12yes—
243C23×C1372−1+412yes—
244D4×C137—416no—
245C2×C4×C137—22no—
246C2×C4×C137—22no—
247C2×C4×C137—22no—
248C2×C4×C137—22no—
249C2×C4×C137—22no—
250C2×C4×C137—22no—
251C2×C4×C137—22no—
252C2×C4×C137—22no—
253C2×C4×C137—22no—
254C2×C4×C137—22no—
255C2×C4×C137—22no—
256C2×C4×C137—22no—
257C2×C4×C137—24no—
258C2×C4×C137—24no—
259C2×C4×C137—24no—
260C2×C4×C137—24no—
261C2×C4×C137—24no—
262C2×C4×C137—24no—
263C2×C4×C137—22no—
264C2×C4×C137—22no—
265C2×C4×C137—22no—
266C2×C4×C137—24no—
267C2×C4×C137—24no—
268C2×C4×C137—24no—
269C2×C4×C137—24no—
270C2×C4×C137—24no—
271C2×C4×C137—24no—
272C2×C4×C137—41no—
273C2×C4×C137—41no—
274C2×C4×C137—42no—
275C2×C4×C137—42no—
276C2×C4×C137—41no—
277C2×C4×C137—41no—
278C2×C4×C137—41no—
279C2×C4×C137—41no—
280C2×C4×C137—42no—
281C2×C4×C137—42no—
282C2×C4×C137—42no—
283C2×C4×C137—42no—
284C2×C4×C137—42no—
285C2×C4×C137—42no—
286C2×C4×C137—42no—
287C2×C4×C137—42no—
288C2×C4×C137—42no—
289C2×C4×C137—42no—
290C2×C4×C137—42no—
291C2×C4×C137—42no—
292C2×C4×C137—42no—
293C2×C4×C137—42no—
294C2×C4×C137—42no—
295C2×C4×C137—42no—
296C2×C4×C137—42no—
297C2×C4×C137—42no—
298C2×C4×C137—42no—
299C2×C4×C137#12114yes—
300C2×C4×C137#12114yes—
301C2×C4×C137#12114yes—
302C2×C4×C137#12714yes—
303C22×C137—44no—
304C22×C137—44no—
305C22×C137—44no—
306C22×C137—44no—
307C22×C137—44no—
308C22×C137—44no—
309C22×C137—44no—
310C22×C137—82no—
311C22×C137—82no—
312C22×C137—82no—
313C22×C137—82no—
314C22×C137—82no—
315C22×C137—82no—
316C22×C137—82no—
317C22×C137—82no—
318C22×C137C2×#12111yescharacteristic
319C22×C137C2×#12111yescharacteristic
320C22×C137C2×#12111yescharacteristic
321C22×C137#52512yes—
322C22×C137#52511yescharacteristic
323C22×C137#52912yes—
324C22×C137C2×#12711yescharacteristic
325C22×C137#53211yescharacteristic
326C22×C137#53211yescharacteristic
327C22×C137#53211yescharacteristic
328C22×C137#53211yescharacteristic
329C22×C137#53411yescharacteristic
330C22×C137#53611yescharacteristic
331C22×C137#53712yes—
332C22×C137#53912yes—
333C22×C137#54612yes—
334C22×C137#54612yes—
335C22×C137#54812yes—
336C22×C137#54812yes—
337C22×C137#55112yes—
338C22×C137#55212yes—
339C22×C137#55312yes—
340C22×C137#55612yes—
341C4×C137—24no—
342C4×C137—24no—
343C4×C137—24no—
344C4×C137—24no—
345C4×C137—42no—
346C4×C137—42no—
347C4×C137—44no—
348C4×C137—42no—
349C4×C137—82no—
350C4×C137—82no—
351C2×C137—84no—
352C2×C137#239211yescharacteristic
353C2×C137#253411yescharacteristic
354C2×C137#253611yescharacteristic
355C2×C137#254012yes—
356C2×C137#254311yescharacteristic
357C2×C137#254511yescharacteristic
358C2×C137#255812yes—
359C2×C137#256012yes—
360C2×C137#260112yes—
361C2×C137#261811yescharacteristic
362C2×C137#285611yescharacteristic
363#15163C13711yesmaximal, characteristic, direct product factor, Sylow
364C137#1516311yescharacteristic, direct product factor, Sylow
365C2×#398C2×C13711yescharacteristic, complemented
366C2×#396C2×C13712yescomplemented
367C2×#394C2×C13711yescharacteristic
368C2×#390C2×C13711yescharacteristic
369C2×#388C2×C13712yescomplemented
370C2×C4×C4⋊C4C2×C13711yescharacteristic, complemented
371#1445C2×C13711yescharacteristic, complemented
372#1439C2×C13712yescomplemented
373#1438C2×C13711yescharacteristic
374#1437C2×C13712yescomplemented
375C4⋊#95C2×C13711yescharacteristic, complemented
376C23×D4C22×C13711yescharacteristic
377C22×C4⋊C4C22×C13712yes—
378C22×C4⋊C4C22×C13711yescharacteristic
379C22×C4⋊C4C22×C13712yes—
380C22×C4⋊C4C22×C13711yescharacteristic
381C22×C4⋊C4C22×C13711yescharacteristic
382C22×C22⋊C4C22×C13712yes—
383C22×C22⋊C4C22×C13712yes—
384C22×C22⋊C4C22×C13712yes—
385C22×C22⋊C4C22×C13712yes—
386C22×C22⋊C4C22×C13712yes—
387C22×C22⋊C4C22×C13712yes—
388C22×C42C22×C13711yescharacteristic
389C22×C42C22×C13711yescharacteristic
390C22×C42C22×C13711yescharacteristic
391#398—24no—
392#396—28no—
393#394—24no—
394#390—24no—
395#388—28no—
396C4×C4⋊C4—24no—
397C2×#95C22×C13711yescharacteristic
398C2×#95C22×C13712yes—
399C2×#95C22×C13711yescharacteristic
400C2×#95C22×C13712yes—
401C2×#95C22×C13712yes—
402C2×#95C22×C13711yescharacteristic
403C2×#95C22×C13711yescharacteristic
404C2×#95C22×C13712yes—
405C25C23×C13712yes—
406C22×D4—24no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4—22no—
410C22×D4—42no—
411C23×C4C23×C13712yes—
412C23×C4C23×C13712yes—
413C23×C4C23×C13711yescharacteristic
414C23×C4C23×C13711yescharacteristic
415C23×C4C23×C13711yescharacteristic
416C23×C4C23×C13712yes—
417C23×C4C23×C13711yescharacteristic
418C23×C4C23×C13711yescharacteristic
419C23×C4C23×C13711yescharacteristic
420C23×C4C23×C13711yescharacteristic
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4D4×C13714yes—
435C2×C4⋊C4D4×C13714yescomplemented
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—42no—
458C2×C42—42no—
459C2×C42D4×C13714yes—
460C2×C42D4×C13714yescomplemented
461#95—22no—
462#95—22no—
463#95—24no—
464#95—24no—
465#95—22no—
466#95—24no—
467#95—22no—
468#95—24no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24#41×C13714yes—
484C24C24×C13711yescharacteristic
485C2×D4—28no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—44no—
489C2×D4—44no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4C2×D4×C13712yes—
533C22×C4C2×D4×C13712yes—
534C22×C4C2×D4×C13712yes—
535C22×C4C2×D4×C13712yes—
536C22×C4C2×D4×C13712yes—
537C22×C4C2×D4×C13712yes—
538C22×C4C2×D4×C13712yes—
539C22×C4C2×D4×C13712yes—
540C22×C4C2×D4×C13712yes—
541C22×C4C2×D4×C13712yes—
542C22×C4C2×D4×C13712yes—
543C22×C4C2×D4×C13712yes—
544C22×C4#41×C13714yes—
545C22×C4#41×C13712yes—
546C22×C4#41×C13712yes—
547C22×C4#41×C13712yes—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—48no—
551C4⋊C4—44no—
552C4⋊C4—48no—
553C22⋊C4—216no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C42—28no—
560C42—44no—
561C42—44no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23C22×D4×C13711yescharacteristic
598C23C22×D4×C13711yescharacteristic
599C23C22×D4×C13711yescharacteristic
600C23C22×D4×C13711yescharacteristic
601C23C2×#41×C13711yescharacteristic
602C23C2×#41×C13711yescharacteristic
603C23C2×#41×C13711yescharacteristic
604C23C2×#41×C13712yes—
605C23C2×#41×C13712yes—
606C23H(5,𝔽2)×C13712yes—
607C232−1+4×C13712yes—
608D4—416no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4#121×C13714yes—
664C2×C4#121×C13714yes—
665C2×C4#121×C13714yes—
666C2×C4#127×C13714yes—
667C22—44no—
668C22—44no—
669C22—44no—
670C22—44no—
671C22—44no—
672C22—44no—
673C22—44no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22—82no—
679C22—82no—
680C22—82no—
681C22—82no—
682C22C2×#121×C13711yescharacteristic
683C22C2×#121×C13711yescharacteristic
684C22C2×#121×C13711yescharacteristic
685C22#525×C13711yescharacteristic
686C22#525×C13712yes—
687C22#529×C13712yes—
688C22C2×#127×C13711yescharacteristic
689C22#532×C13711yescharacteristic
690C22#532×C13711yescharacteristic
691C22#532×C13711yescharacteristic
692C22#532×C13711yescharacteristic
693C22#534×C13711yescharacteristic
694C22#536×C13711yescharacteristic
695C22#537×C13712yes—
696C22#539×C13712yes—
697C22#546×C13712yes—
698C22#546×C13712yes—
699C22#548×C13712yes—
700C22#548×C13712yes—
701C22#551×C13712yes—
702C22#552×C13712yes—
703C22#553×C13712yes—
704C22#556×C13712yes—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—24no—
709C4—42no—
710C4—44no—
711C4—42no—
712C4—42no—
713C4—82no—
714C4—82no—
715C2—84no—
716C2#2392×C13711yescharacteristic
717C2#2534×C13711yescharacteristic
718C2#2536×C13711yescharacteristic
719C2#2540×C13712yes—
720C2#2543×C13711yescharacteristic
721C2#2545×C13711yescharacteristic
722C2#2558×C13712yes—
723C2#2560×C13712yes—
724C2#2601×C13712yes—
725C2#2618×C13711yescharacteristic
726C2#2856×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
prime radicalC23×D4×C137C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#398×C137C2semidirect
2. C2×#396×C137C2semidirect
5. C2×#388×C137C2semidirect
6. C2×C4×C4⋊C4×C137C2semidirect
7. #1445×C137C2semidirect
8. #1439×C137C2semidirect
10. #1437×C137C2semidirect
11. C4⋊#95×C137C2semidirect
71. C2×C4⋊C4×C137D4semidirect
96. C2×C42×C137D4semidirect
363. #15163C137direct (N × H)
364. C137#15163direct (N × H)
365. C2×#398C2×C137semidirect
366. C2×#396C2×C137semidirect
369. C2×#388C2×C137semidirect
370. C2×C4×C4⋊C4C2×C137semidirect
371. #1445C2×C137semidirect
372. #1439C2×C137semidirect
374. #1437C2×C137semidirect
375. C4⋊#95C2×C137semidirect
435. C2×C4⋊C4D4×C137semidirect
460. C2×C42D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1372
C2×#396×C1372
C2×#394×C1372
C2×#390×C1372
C2×#388×C1372
C2×C4×C4⋊C4×C1372
#1445×C1372
#1439×C1372
#1438×C1372
#1437×C1372
C4⋊#95×C1372
#15163137