Finite Group Databasebeta

← C137×#24142 #46873528

Subgroups — C137×#24142 #46873528

Order 35072.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C137C211yesmaximal, characteristic, complemented
2#2626×C137C211yesmaximal, characteristic, complemented
3#2617×C137C211yesmaximal, characteristic, complemented
4#2321×C137C211yesmaximal, characteristic, complemented
5#2044×C137C212yesmaximal, complemented
6#2021×C137C212yesmaximal, complemented
7#1996×C137C211yesmaximal, characteristic, complemented
8#1964×C137C211yesmaximal, characteristic, complemented
9#1889×C137C212yesmaximal, complemented
10#1867×C137C212yesmaximal, complemented
11#1799×C137C211yesmaximal, characteristic, complemented
12#553×C137—22no—
13#553×C137—21no—
14#552×C137—21no—
15#551×C137—22no—
16#548×C137—21no—
17#546×C137—21no—
18#539×C137—21no—
19#538×C137—21no—
20#534×C137C2212yes—
21#529×C137—21no—
22#525×C137—21no—
23C2×C22⋊Q8×C137C2211yescharacteristic
24C2×#121×C137C2211yescharacteristic
25C2×#120×C137C2211yescharacteristic
26C2×#120×C137C2212yes—
27#518×C137C2212yes—
28C2×C4×D4×C137C2211yescharacteristic
29C22×C22⋊C4×C137C2211yescharacteristic
30C2×#99×C137C2212yes—
31C2×#99×C137C2212yes—
32C2×#99×C137C2212yes—
33#399×C137—21no—
34#397×C137—21no—
35#396×C137—22no—
36#394×C137—22no—
37#393×C137—21no—
38#392×C137—21no—
39#390×C137—21no—
40#388×C137—21no—
41#388×C137—21no—
42#386×C137—21no—
43#386×C137C2211yescharacteristic
44#386×C137C2212yes—
45#385×C137C2212yes—
46#385×C137C2211yescharacteristic
47#380×C137C2211yescharacteristic
48#380×C137C2211yescharacteristic
49#379×C137C2212yes—
50#379×C137C2211yescharacteristic
51C4×C22⋊C4×C137C2211yescharacteristic
52#342×C137C2212yes—
53#342×C137C2212yes—
54#342×C137C2212yes—
55C25×C137C2311yescharacteristic
56C2×#41×C137—21no—
57C22×Q8×C137D411yescharacteristic, complemented
58C22×D4×C137—21no—
59C22×D4×C137—22no—
60C22×D4×C137D411yescharacteristic, complemented
61C22×D4×C137C2311yescharacteristic
62C22×D4×C137C2312yes—
63C23×C4×C137D411yescharacteristic, complemented
64C23×C4×C137C2311yescharacteristic
65C23×C4×C137C2311yescharacteristic
66#126×C137—22no—
67#126×C137—22no—
68#126×C137—22no—
69#125×C137—21no—
70#125×C137—22no—
71#124×C137—21no—
72#124×C137—22no—
73#123×C137—22no—
74#123×C137—22no—
75#123×C137—22no—
76#123×C137—22no—
77#123×C137—22no—
78C22⋊Q8×C137—21no—
79C22⋊Q8×C137—22no—
80C22⋊Q8×C137—21no—
81C22⋊Q8×C137—21no—
82C22⋊Q8×C137—21no—
83C22⋊Q8×C137—21no—
84#121×C137—21no—
85#121×C137—22no—
86#121×C137—21no—
87#121×C137—21no—
88#121×C137—21no—
89#121×C137—21no—
90#121×C137—22no—
91#121×C137—22no—
92#120×C137—22no—
93#120×C137—22no—
94#120×C137—22no—
95#120×C137—22no—
96#120×C137—24no—
97#120×C137—42no—
98C4×Q8×C137—21no—
99C4×D4×C137—22no—
100C4×D4×C137—21no—
101C4×D4×C137—21no—
102C4×D4×C137—21no—
103C4×D4×C137—21no—
104C4×D4×C137—21no—
105C4×D4×C137—22no—
106C4×D4×C137—22no—
107C4×D4×C137—22no—
108C4×D4×C137—22no—
109#117×C137—21no—
110#117×C137—22no—
111#117×C137—22no—
112C2×C4⋊C4×C137—21no—
113C2×C4⋊C4×C137—21no—
114C2×C4⋊C4×C137—21no—
115C2×C4⋊C4×C137—22no—
116C2×C4⋊C4×C137D411yescharacteristic, complemented
117C2×C4⋊C4×C137D412yescomplemented
118C2×C4⋊C4×C137D411yescharacteristic, complemented
119C2×C4⋊C4×C137D411yescharacteristic, complemented
120C2×C22⋊C4×C137—22no—
121C2×C22⋊C4×C137—21no—
122C2×C22⋊C4×C137—21no—
123C2×C22⋊C4×C137—21no—
124C2×C22⋊C4×C137—21no—
125C2×C22⋊C4×C137—21no—
126C2×C22⋊C4×C137—21no—
127C2×C22⋊C4×C137—22no—
128C2×C22⋊C4×C137—21no—
129C2×C22⋊C4×C137—21no—
130C2×C22⋊C4×C137—22no—
131C2×C22⋊C4×C137—21no—
132C2×C22⋊C4×C137—21no—
133C2×C22⋊C4×C137—22no—
134C2×C22⋊C4×C137—22no—
135C2×C22⋊C4×C137D411yescharacteristic, complemented
136C2×C22⋊C4×C137D412yescomplemented
137C2×C22⋊C4×C137C2311yescharacteristic
138C2×C22⋊C4×C137C2312yes—
139C2×C22⋊C4×C137C2312yes—
140C2×C22⋊C4×C137C2311yescharacteristic
141C2×C22⋊C4×C137C2312yes—
142C2×C22⋊C4×C137C2311yescharacteristic
143C2×C42×C137—21no—
144C2×C42×C137D411yescharacteristic, complemented
145#99×C137—24no—
146#99×C137—42no—
147#99×C137—42no—
148#95×C137—21no—
149#95×C137—21no—
150#95×C137—21no—
151#95×C137—21no—
152#95×C137—22no—
153#95×C137—21no—
154#95×C137—22no—
155C24×C137—21no—
156C24×C137—21no—
157C24×C137—21no—
158C24×C137—21no—
159C24×C137—21no—
160C24×C137—21no—
161C24×C137—81no—
162C24×C137—81no—
163C24×C137C2×D412yes—
164C24×C137C2×D411yescharacteristic
165C24×C137#4112yescomplemented
166C24×C137C2411yescharacteristic
167#41×C137—82no—
168C2×Q8×C137—21no—
169C2×Q8×C137—21no—
170C2×Q8×C137—81no—
171C2×D4×C137—21no—
172C2×D4×C137—22no—
173C2×D4×C137—21no—
174C2×D4×C137—22no—
175C2×D4×C137—22no—
176C2×D4×C137—21no—
177C2×D4×C137—21no—
178C2×D4×C137—22no—
179C2×D4×C137—21no—
180C2×D4×C137—22no—
181C2×D4×C137—21no—
182C2×D4×C137—22no—
183C2×D4×C137—22no—
184C2×D4×C137—22no—
185C2×D4×C137—24no—
186C2×D4×C137—21no—
187C2×D4×C137—21no—
188C2×D4×C137—44no—
189C2×D4×C137—81no—
190C2×D4×C137—81no—
191C2×D4×C137—81no—
192C2×D4×C137—82no—
193C2×D4×C137—82no—
194C22×C4×C137—21no—
195C22×C4×C137—22no—
196C22×C4×C137—22no—
197C22×C4×C137—21no—
198C22×C4×C137—21no—
199C22×C4×C137—21no—
200C22×C4×C137—21no—
201C22×C4×C137—21no—
202C22×C4×C137—22no—
203C22×C4×C137—22no—
204C22×C4×C137—21no—
205C22×C4×C137—81no—
206C22×C4×C137—81no—
207C22×C4×C137—81no—
208C22×C4×C137C2×D411yescharacteristic
209C22×C4×C137C2×D412yes—
210C22×C4×C137C2×D411yescharacteristic
211C22×C4×C137C2×D412yes—
212C22×C4×C137C2×D411yescharacteristic
213C22×C4×C137C2×D412yes—
214C22×C4×C137C2×D411yescharacteristic
215C22×C4×C137C2×D411yescharacteristic
216C22×C4×C137C2×D411yescharacteristic
217C22×C4×C137C2×D411yescharacteristic
218C22×C4×C137C2×D411yescharacteristic
219C22×C4×C137C2×D411yescharacteristic
220C4⋊C4×C137—22no—
221C4⋊C4×C137—22no—
222C4⋊C4×C137—22no—
223C4⋊C4×C137—22no—
224C4⋊C4×C137—21no—
225C4⋊C4×C137—22no—
226C4⋊C4×C137—21no—
227C4⋊C4×C137—21no—
228C4⋊C4×C137—21no—
229C4⋊C4×C137—21no—
230C4⋊C4×C137—22no—
231C4⋊C4×C137—21no—
232C4⋊C4×C137—81no—
233C4⋊C4×C137—81no—
234C4⋊C4×C137—81no—
235C4⋊C4×C137—82no—
236C22⋊C4×C137—22no—
237C22⋊C4×C137—22no—
238C22⋊C4×C137—24no—
239C22⋊C4×C137—22no—
240C22⋊C4×C137—22no—
241C22⋊C4×C137—22no—
242C22⋊C4×C137—22no—
243C22⋊C4×C137—21no—
244C22⋊C4×C137—22no—
245C22⋊C4×C137—21no—
246C22⋊C4×C137—22no—
247C22⋊C4×C137—21no—
248C22⋊C4×C137—22no—
249C22⋊C4×C137—21no—
250C22⋊C4×C137—21no—
251C22⋊C4×C137—22no—
252C22⋊C4×C137—22no—
253C22⋊C4×C137—22no—
254C22⋊C4×C137—21no—
255C22⋊C4×C137—22no—
256C22⋊C4×C137—22no—
257C22⋊C4×C137—21no—
258C22⋊C4×C137—44no—
259C22⋊C4×C137—41no—
260C22⋊C4×C137—41no—
261C22⋊C4×C137—41no—
262C22⋊C4×C137—41no—
263C22⋊C4×C137—81no—
264C22⋊C4×C137—82no—
265C22⋊C4×C137—81no—
266C22⋊C4×C137—82no—
267C22⋊C4×C137—81no—
268C22⋊C4×C137—82no—
269C22⋊C4×C137#4112yescomplemented
270C42×C137—22no—
271C42×C137—22no—
272C42×C137—21no—
273C42×C137—21no—
274C42×C137—81no—
275C23×C137—21no—
276C23×C137—22no—
277C23×C137—22no—
278C23×C137—21no—
279C23×C137—22no—
280C23×C137—22no—
281C23×C137—21no—
282C23×C137—22no—
283C23×C137—22no—
284C23×C137—41no—
285C23×C137—41no—
286C23×C137—41no—
287C23×C137—41no—
288C23×C137—42no—
289C23×C137—41no—
290C23×C137—42no—
291C23×C137—41no—
292C23×C137—41no—
293C23×C137—42no—
294C23×C137—41no—
295C23×C137—42no—
296C23×C137—42no—
297C23×C137—42no—
298C23×C137—41no—
299C23×C137—41no—
300C23×C137—41no—
301C23×C137—41no—
302C23×C137—82no—
303C23×C137—82no—
304C23×C137—82no—
305C23×C137—82no—
306C23×C137C22×D411yescharacteristic
307C23×C137C22×D411yescharacteristic
308C23×C137C22×D411yescharacteristic
309C23×C137C2×#4111yescharacteristic
310C23×C137C2×#4111yescharacteristic
311C23×C137H(5,𝔽2)11yescharacteristic
312C23×C1372−1+411yescharacteristic
313Q8×C137—42no—
314Q8×C137—81no—
315D4×C137—42no—
316D4×C137—42no—
317D4×C137—42no—
318D4×C137—41no—
319D4×C137—41no—
320D4×C137—41no—
321D4×C137—42no—
322D4×C137—42no—
323D4×C137—41no—
324D4×C137—81no—
325D4×C137—82no—
326D4×C137—84no—
327D4×C137—82no—
328D4×C137—88no—
329C2×C4×C137—21no—
330C2×C4×C137—22no—
331C2×C4×C137—21no—
332C2×C4×C137—21no—
333C2×C4×C137—22no—
334C2×C4×C137—22no—
335C2×C4×C137—21no—
336C2×C4×C137—22no—
337C2×C4×C137—21no—
338C2×C4×C137—22no—
339C2×C4×C137—22no—
340C2×C4×C137—41no—
341C2×C4×C137—41no—
342C2×C4×C137—41no—
343C2×C4×C137—41no—
344C2×C4×C137—41no—
345C2×C4×C137—41no—
346C2×C4×C137—42no—
347C2×C4×C137—41no—
348C2×C4×C137—41no—
349C2×C4×C137—41no—
350C2×C4×C137—42no—
351C2×C4×C137—41no—
352C2×C4×C137—42no—
353C2×C4×C137—41no—
354C2×C4×C137—41no—
355C2×C4×C137—42no—
356C2×C4×C137—42no—
357C2×C4×C137—41no—
358C2×C4×C137—42no—
359C2×C4×C137—42no—
360C2×C4×C137—42no—
361C2×C4×C137—41no—
362C2×C4×C137—42no—
363C2×C4×C137—41no—
364C2×C4×C137—41no—
365C2×C4×C137—42no—
366C2×C4×C137—42no—
367C2×C4×C137—81no—
368C2×C4×C137—82no—
369C2×C4×C137—82no—
370C2×C4×C137#12011yescharacteristic
371C2×C4×C137#12011yescharacteristic
372C2×C4×C137#12011yescharacteristic
373C2×C4×C137#12011yescharacteristic
374C22×C137—21no—
375C22×C137—21no—
376C22×C137—21no—
377C22×C137—21no—
378C22×C137—21no—
379C22×C137—21no—
380C22×C137—41no—
381C22×C137—41no—
382C22×C137—41no—
383C22×C137—41no—
384C22×C137—42no—
385C22×C137—42no—
386C22×C137—44no—
387C22×C137—42no—
388C22×C137—44no—
389C22×C137—41no—
390C22×C137—42no—
391C22×C137—42no—
392C22×C137—41no—
393C22×C137—42no—
394C22×C137—42no—
395C22×C137—41no—
396C22×C137—82no—
397C22×C137—81no—
398C22×C137—82no—
399C22×C137—82no—
400C22×C137—81no—
401C22×C137—81no—
402C22×C137—82no—
403C22×C137—81no—
404C22×C137—81no—
405C22×C137C2×#12011yescharacteristic
406C22×C137#52511yescharacteristic
407C22×C137#53711yescharacteristic
408C22×C137#54611yescharacteristic
409C22×C137#54711yescharacteristic
410C22×C137#54811yescharacteristic
411C22×C137#55011yescharacteristic
412C4×C137—21no—
413C4×C137—21no—
414C4×C137—21no—
415C4×C137—21no—
416C4×C137—42no—
417C4×C137—41no—
418C4×C137—42no—
419C4×C137—41no—
420C4×C137—42no—
421C4×C137—41no—
422C4×C137—42no—
423C4×C137—82no—
424C4×C137—81no—
425C4×C137—82no—
426C4×C137—81no—
427C2×C137—21no—
428C2×C137—21no—
429C2×C137—21no—
430C2×C137—21no—
431C2×C137—21no—
432C2×C137—21no—
433C2×C137—82no—
434C2×C137—81no—
435C2×C137—82no—
436C2×C137#240711yescharacteristic
437C2×C137#302611yescharacteristic
438C2×C137#302711yescharacteristic
439#24142C13711yesmaximal, characteristic, direct product factor, Sylow
440C137#2414211yescharacteristic, direct product factor, Sylow
441#3505C2×C13711yescharacteristic, complemented
442#2626C2×C13711yescharacteristic, complemented
443#2617C2×C13711yescharacteristic, complemented
444#2321C2×C13711yescharacteristic, complemented
445#2044C2×C13712yescomplemented
446#2021C2×C13712yescomplemented
447#1996C2×C13711yescharacteristic, complemented
448#1964C2×C13711yescharacteristic, complemented
449#1889C2×C13712yescomplemented
450#1867C2×C13712yescomplemented
451#1799C2×C13711yescharacteristic, complemented
452#553—22no—
453#553—21no—
454#552—21no—
455#551—22no—
456#548—21no—
457#546—21no—
458#539—21no—
459#538—21no—
460#534C22×C13712yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C13711yescharacteristic
464C2×#121C22×C13711yescharacteristic
465C2×#120C22×C13711yescharacteristic
466C2×#120C22×C13712yes—
467#518C22×C13712yes—
468C2×C4×D4C22×C13711yescharacteristic
469C22×C22⋊C4C22×C13711yescharacteristic
470C2×#99C22×C13712yes—
471C2×#99C22×C13712yes—
472C2×#99C22×C13712yes—
473#399—21no—
474#397—21no—
475#396—22no—
476#394—22no—
477#393—21no—
478#392—21no—
479#390—21no—
480#388—21no—
481#388—21no—
482#386—21no—
483#386C22×C13711yescharacteristic
484#386C22×C13712yes—
485#385C22×C13711yescharacteristic
486#385C22×C13712yes—
487#380C22×C13711yescharacteristic
488#380C22×C13711yescharacteristic
489#379C22×C13711yescharacteristic
490#379C22×C13712yes—
491C4×C22⋊C4C22×C13711yescharacteristic
492#342C22×C13712yes—
493#342C22×C13712yes—
494#342C22×C13712yes—
495C25C23×C13711yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C13711yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C13711yescharacteristic, complemented
501C22×D4C23×C13711yescharacteristic
502C22×D4C23×C13712yes—
503C23×C4D4×C13711yescharacteristic, complemented
504C23×C4C23×C13711yescharacteristic
505C23×C4C23×C13711yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C13711yescharacteristic, complemented
557C2×C4⋊C4D4×C13711yescharacteristic, complemented
558C2×C4⋊C4D4×C13712yescomplemented
559C2×C4⋊C4D4×C13711yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C13711yescharacteristic, complemented
576C2×C22⋊C4D4×C13712yescomplemented
577C2×C22⋊C4C23×C13712yes—
578C2×C22⋊C4C23×C13711yescharacteristic
579C2×C22⋊C4C23×C13712yes—
580C2×C22⋊C4C23×C13711yescharacteristic
581C2×C22⋊C4C23×C13712yes—
582C2×C22⋊C4C23×C13711yescharacteristic
583C2×C42—21no—
584C2×C42D4×C13711yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C13712yes—
604C24C2×D4×C13711yescharacteristic
605C24#41×C13712yescomplemented
606C24C24×C13711yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C13711yescharacteristic
649C22×C4C2×D4×C13712yes—
650C22×C4C2×D4×C13711yescharacteristic
651C22×C4C2×D4×C13712yes—
652C22×C4C2×D4×C13711yescharacteristic
653C22×C4C2×D4×C13712yes—
654C22×C4C2×D4×C13711yescharacteristic
655C22×C4C2×D4×C13711yescharacteristic
656C22×C4C2×D4×C13711yescharacteristic
657C22×C4C2×D4×C13711yescharacteristic
658C22×C4C2×D4×C13711yescharacteristic
659C22×C4C2×D4×C13711yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C13712yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C13711yescharacteristic
747C23C22×D4×C13711yescharacteristic
748C23C22×D4×C13711yescharacteristic
749C23C2×#41×C13711yescharacteristic
750C23C2×#41×C13711yescharacteristic
751C23H(5,𝔽2)×C13711yescharacteristic
752C232−1+4×C13711yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C13711yescharacteristic
811C2×C4#120×C13711yescharacteristic
812C2×C4#120×C13711yescharacteristic
813C2×C4#120×C13711yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C13711yescharacteristic
846C22#525×C13711yescharacteristic
847C22#537×C13711yescharacteristic
848C22#546×C13711yescharacteristic
849C22#547×C13711yescharacteristic
850C22#548×C13711yescharacteristic
851C22#550×C13711yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2#2407×C13711yescharacteristic
877C2#3026×C13711yescharacteristic
878C2#3027×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC24C24×C137
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3505×C137C2semidirect
2. #2626×C137C2semidirect
3. #2617×C137C2semidirect
4. #2321×C137C2semidirect
5. #2044×C137C2semidirect
6. #2021×C137C2semidirect
7. #1996×C137C2semidirect
8. #1964×C137C2semidirect
9. #1889×C137C2semidirect
10. #1867×C137C2semidirect
11. #1799×C137C2semidirect
57. C22×Q8×C137D4semidirect
60. C22×D4×C137D4semidirect
63. C23×C4×C137D4semidirect
116. C2×C4⋊C4×C137D4semidirect
117. C2×C4⋊C4×C137D4semidirect
118. C2×C4⋊C4×C137D4semidirect
119. C2×C4⋊C4×C137D4semidirect
135. C2×C22⋊C4×C137D4semidirect
136. C2×C22⋊C4×C137D4semidirect
144. C2×C42×C137D4semidirect
165. C24×C137#41semidirect
269. C22⋊C4×C137#41semidirect
439. #24142C137direct (N × H)
440. C137#24142direct (N × H)
441. #3505C2×C137semidirect
442. #2626C2×C137semidirect
443. #2617C2×C137semidirect
444. #2321C2×C137semidirect
445. #2044C2×C137semidirect
446. #2021C2×C137semidirect
447. #1996C2×C137semidirect
448. #1964C2×C137semidirect
449. #1889C2×C137semidirect
450. #1867C2×C137semidirect
451. #1799C2×C137semidirect
497. C22×Q8D4×C137semidirect
500. C22×D4D4×C137semidirect
503. C23×C4D4×C137semidirect
556. C2×C4⋊C4D4×C137semidirect
557. C2×C4⋊C4D4×C137semidirect
558. C2×C4⋊C4D4×C137semidirect
559. C2×C4⋊C4D4×C137semidirect
575. C2×C22⋊C4D4×C137semidirect
576. C2×C22⋊C4D4×C137semidirect
584. C2×C42D4×C137semidirect
605. C24#41×C137semidirect
709. C22⋊C4#41×C137semidirect

Maximal subgroups

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

subgroupindex
#3505×C1372
#2626×C1372
#2617×C1372
#2321×C1372
#2044×C1372
#2021×C1372
#1996×C1372
#1964×C1372
#1889×C1372
#1867×C1372
#1799×C1372
#24142137