Finite Group Databasebeta

← C137×#25880 #46875266

Subgroups — C137×#25880 #46875266

Order 35072.

1242 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3500×C137C211yesmaximal, characteristic
2#3141×C137C211yesmaximal, characteristic, complemented
3#3079×C137C211yesmaximal, characteristic, complemented
4#2640×C137C211yesmaximal, characteristic, complemented
5#2038×C137C212yesmaximal, complemented
6#2037×C137C212yesmaximal, complemented
7#1967×C137C211yesmaximal, characteristic, complemented
8#1963×C137C211yesmaximal, characteristic, complemented
9#1793×C137C212yesmaximal, complemented
10#1792×C137C212yesmaximal, complemented
11#1759×C137C211yesmaximal, characteristic, complemented
12C2×2−1+4×C137C2211yescharacteristic
13C2×H(5,𝔽2)×C137C2211yescharacteristic
14#548×C137—21no—
15#548×C137—21no—
16#546×C137—21no—
17#546×C137—21no—
18#546×C137—22no—
19#546×C137—22no—
20#536×C137—21no—
21#536×C137C2211yescharacteristic
22#535×C137—21no—
23#535×C137C2211yescharacteristic
24#532×C137—21no—
25#532×C137C2211yescharacteristic
26C2×C4⋊Q8×C137C2211yescharacteristic, complemented
27C2×#124×C137—21no—
28C2×#124×C137C2211yescharacteristic
29C4×#41×C137C2211yescharacteristic
30#489×C137—21no—
31#489×C137—21no—
32#487×C137—21no—
33#486×C137—21no—
34#477×C137—21no—
35#476×C137—21no—
36#475×C137—21no—
37#474×C137—21no—
38#428×C137C2212yescomplemented
39#423×C137C2211yescharacteristic, complemented
40C2×#104×C137C2212yes—
41C2×#104×C137C2212yes—
42C2×#104×C137C2212yescomplemented
43#417×C137C2212yes—
44#417×C137C2212yes—
45#417×C137C2212yescomplemented
46C2×#101×C137C2212yescomplemented
47C2×#100×C137C2212yes—
48C4×M16×C137C2211yescharacteristic, complemented
49#397×C137—22no—
50#393×C137—22no—
51#391×C137C2212yescomplemented
52#390×C137C2212yes—
53#376×C137C2211yescharacteristic, complemented
54#339×C137C2212yescomplemented
552−1+4×C137—24no—
562−1+4×C137—42no—
57H(5,𝔽2)×C137—24no—
58H(5,𝔽2)×C137—42no—
59C2×#41×C137—21no—
60C2×#41×C137—21no—
61C2×#41×C137—21no—
62C2×#41×C137—21no—
63C2×#41×C137—22no—
64C2×#41×C137C2311yescharacteristic
65C2×#41×C137C2311yescharacteristic
66C2×#41×C137C2311yescharacteristic
67C22×Q8×C137—21no—
68C22×Q8×C137—21no—
69C22×Q8×C137—21no—
70C22×Q8×C137C2311yescharacteristic
71C22×D4×C137—22no—
72C22×D4×C137—21no—
73C22×D4×C137—21no—
74C22×D4×C137C2311yescharacteristic
75C2×M16×C137C2312yes—
76C2×M16×C137C2312yes—
77C4⋊Q8×C137—21no—
78C4⋊Q8×C137—21no—
79C4⋊Q8×C137—21no—
80C4⋊Q8×C137—21no—
81C4⋊Q8×C137—21no—
82C4⋊Q8×C137D411yescharacteristic
83#127×C137—21no—
84#127×C137D411yescharacteristic
85#124×C137—22no—
86#124×C137—22no—
87#124×C137—21no—
88#124×C137—21no—
89#124×C137—21no—
90#124×C137—21no—
91#124×C137—21no—
92#124×C137—21no—
93#124×C137D411yescharacteristic
94#124×C137D411yescharacteristic
95#123×C137—22no—
96#123×C137—22no—
97#123×C137—22no—
98C22⋊Q8×C137—22no—
99C22⋊Q8×C137—22no—
100C22⋊Q8×C137—21no—
101C22⋊Q8×C137—21no—
102#121×C137—22no—
103#121×C137—22no—
104#121×C137—22no—
105#121×C137—22no—
106#121×C137—21no—
107#121×C137—21no—
108#121×C137—21no—
109#121×C137—21no—
110#120×C137—22no—
111#120×C137—22no—
112#120×C137—22no—
113C4×Q8×C137D411yescharacteristic
114C4×Q8×C137D411yescharacteristic
115C4×D4×C137—22no—
116C4×D4×C137—22no—
117C4×D4×C137—21no—
118C4×D4×C137—21no—
119C4×D4×C137—21no—
120C4×D4×C137—21no—
121C4×D4×C137D411yescharacteristic
122C4×D4×C137D411yescharacteristic
123#117×C137—21no—
124#117×C137C2311yescharacteristic
125C2×C4⋊C4×C137—21no—
126C2×C4⋊C4×C137C2312yes—
127C2×C22⋊C4×C137—22no—
128C2×C22⋊C4×C137—22no—
129C2×C22⋊C4×C137—24no—
130C2×C22⋊C4×C137D412yes—
131C2×C22⋊C4×C137D412yes—
132C2×C42×C137—21no—
133C2×C42×C137C2312yes—
134C2×C42×C137C2311yescharacteristic
135#107×C137—22no—
136#106×C137—22no—
137C4⋊C8×C137—21no—
138C4⋊C8×C137—21no—
139#104×C137—24no—
140#104×C137—42no—
141#104×C137—42no—
142#103×C137—22no—
143#103×C137—22no—
144#103×C137—22no—
145#102×C137—22no—
146#102×C137—22no—
147#102×C137—22no—
148#101×C137—42no—
149#100×C137—42no—
150#97×C137—21no—
151C4×C8×C137—21no—
152#95×C137—21no—
153#95×C137—21no—
154#95×C137—24no—
155C24×C137—22no—
156C24×C137C2×D412yes—
157#41×C137—22no—
158#41×C137—22no—
159#41×C137—22no—
160#41×C137—22no—
161#41×C137—22no—
162#41×C137—44no—
163#41×C137—48no—
164#41×C137—44no—
165#41×C137—42no—
166#41×C137—42no—
167#41×C137—42no—
168#41×C137—42no—
169#41×C137#4114yes—
170C2×Q8×C137—22no—
171C2×Q8×C137—21no—
172C2×Q8×C137—21no—
173C2×Q8×C137—22no—
174C2×Q8×C137—22no—
175C2×Q8×C137—44no—
176C2×Q8×C137—42no—
177C2×Q8×C137—42no—
178C2×Q8×C137—41no—
179C2×Q8×C137—41no—
180C2×Q8×C137—82no—
181C2×Q8×C137C2×D411yescharacteristic
182C2×Q8×C137C2×D411yescharacteristic
183C2×Q8×C137C2×D411yescharacteristic
184C2×D4×C137—21no—
185C2×D4×C137—22no—
186C2×D4×C137—22no—
187C2×D4×C137—22no—
188C2×D4×C137—21no—
189C2×D4×C137—21no—
190C2×D4×C137—22no—
191C2×D4×C137—22no—
192C2×D4×C137—21no—
193C2×D4×C137—21no—
194C2×D4×C137—21no—
195C2×D4×C137—21no—
196C2×D4×C137—22no—
197C2×D4×C137—22no—
198C2×D4×C137—44no—
199C2×D4×C137—48no—
200C2×D4×C137—42no—
201C2×D4×C137—42no—
202C2×D4×C137C2×D411yescharacteristic
203C2×D4×C137C2×D411yescharacteristic
204C2×D4×C137C2×D411yescharacteristic
205C22×C4×C137—21no—
206C22×C4×C137—22no—
207C22×C4×C137—22no—
208C22×C4×C137—22no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—22no—
214C22×C4×C137—22no—
215C22×C4×C137C2×D412yes—
216C22×C4×C137C2×D411yescharacteristic
217C22×C4×C137C2×D411yescharacteristic
218C22×C4×C137C2411yescharacteristic
219M16×C137—22no—
220M16×C137—22no—
221M16×C137—22no—
222M16×C137—22no—
223C2×C8×C137—22no—
224C2×C8×C137—22no—
225C4⋊C4×C137—22no—
226C4⋊C4×C137—22no—
227C4⋊C4×C137—21no—
228C4⋊C4×C137—21no—
229C4⋊C4×C137—21no—
230C4⋊C4×C137—21no—
231C4⋊C4×C137—22no—
232C4⋊C4×C137—22no—
233C4⋊C4×C137—41no—
234C4⋊C4×C137—41no—
235C4⋊C4×C137C2×D411yescharacteristic
236C4⋊C4×C137C2×D411yescharacteristic
237C22⋊C4×C137—22no—
238C22⋊C4×C137—22no—
239C22⋊C4×C137—22no—
240C22⋊C4×C137—22no—
241C22⋊C4×C137—21no—
242C22⋊C4×C137—21no—
243C22⋊C4×C137—21no—
244C22⋊C4×C137—22no—
245C22⋊C4×C137—22no—
246C22⋊C4×C137—22no—
247C22⋊C4×C137—22no—
248C22⋊C4×C137—21no—
249C22⋊C4×C137—21no—
250C22⋊C4×C137—21no—
251C22⋊C4×C137—21no—
252C22⋊C4×C137—84no—
253C42×C137—21no—
254C42×C137—21no—
255C42×C137—21no—
256C42×C137—22no—
257C42×C137—22no—
258C42×C137C2×D411yescharacteristic
259C42×C137C2×D411yescharacteristic
260C42×C137C2×D411yescharacteristic
261C42×C137C2×D411yescharacteristic
262C23×C137—21no—
263C23×C137—22no—
264C23×C137—21no—
265C23×C137—21no—
266C23×C137—24no—
267C23×C137—44no—
268C23×C137—42no—
269C23×C137—42no—
270C23×C137—82no—
271C23×C137—82no—
272C23×C137C22×D411yescharacteristic
273Q8×C137—21no—
274Q8×C137—22no—
275Q8×C137—22no—
276Q8×C137—44no—
277Q8×C137—41no—
278Q8×C137—41no—
279Q8×C137—42no—
280Q8×C137—82no—
281Q8×C137—82no—
282Q8×C137#12412yes—
283D4×C137—24no—
284D4×C137—21no—
285D4×C137—22no—
286D4×C137—22no—
287D4×C137—44no—
288D4×C137—44no—
289D4×C137—44no—
290D4×C137—42no—
291D4×C137—42no—
292D4×C137—41no—
293D4×C137—41no—
294D4×C137—42no—
295D4×C137—81no—
296D4×C137—81no—
297D4×C137—82no—
298D4×C137—82no—
299D4×C137#12412yes—
300C2×C4×C137—21no—
301C2×C4×C137—24no—
302C2×C4×C137—21no—
303C2×C4×C137—21no—
304C2×C4×C137—21no—
305C2×C4×C137—22no—
306C2×C4×C137—21no—
307C2×C4×C137—24no—
308C2×C4×C137—41no—
309C2×C4×C137—41no—
310C2×C4×C137—44no—
311C2×C4×C137—44no—
312C2×C4×C137—44no—
313C2×C4×C137—41no—
314C2×C4×C137—41no—
315C2×C4×C137—41no—
316C2×C4×C137—41no—
317C2×C4×C137—42no—
318C2×C4×C137—44no—
319C2×C4×C137—42no—
320C2×C4×C137—42no—
321C2×C4×C137—42no—
322C2×C4×C137—81no—
323C2×C4×C137—81no—
324C2×C4×C137#12011yescharacteristic
325C2×C4×C137#12011yescharacteristic
326C2×C4×C137#12011yescharacteristic
327C2×C4×C137#12011yescharacteristic
328C2×C4×C137C22×D411yescharacteristic
329C2×C4×C137C22×D411yescharacteristic
330C2×C4×C137C2×#4112yes—
331C2×C4×C137H(5,𝔽2)12yes—
332C8×C137—42no—
333C8×C137—42no—
334C22×C137—21no—
335C22×C137—21no—
336C22×C137—22no—
337C22×C137—41no—
338C22×C137—41no—
339C22×C137—41no—
340C22×C137—41no—
341C22×C137—42no—
342C22×C137—41no—
343C22×C137—42no—
344C22×C137—41no—
345C22×C137—41no—
346C22×C137—42no—
347C22×C137—41no—
348C22×C137—84no—
349C22×C137—164no—
350C22×C137C2×#12011yescharacteristic
351C22×C137#54612yes—
352C4×C137—22no—
353C4×C137—21no—
354C4×C137—21no—
355C4×C137—21no—
356C4×C137—21no—
357C4×C137—42no—
358C4×C137—41no—
359C4×C137—41no—
360C4×C137—41no—
361C4×C137—41no—
362C4×C137—82no—
363C4×C137—82no—
364C4×C137C2×#12411yescharacteristic
365C4×C137#53511yescharacteristic
366C4×C137#54612yes—
367C2×C137—22no—
368C2×C137—42no—
369C2×C137—81no—
370C2×C137—82no—
371C2×C137—81no—
372C2×C137#243511yescharacteristic
373C2×C137#302111yescharacteristic
374C2×C137#302211yescharacteristic
375#25880C13711yesmaximal, characteristic, direct product factor, Sylow
376C137#2588011yescharacteristic, direct product factor, Sylow
377#3500C2×C13711yescharacteristic
378#3141C2×C13711yescharacteristic, complemented
379#3079C2×C13711yescharacteristic, complemented
380#2640C2×C13711yescharacteristic, complemented
381#2038C2×C13712yescomplemented
382#2037C2×C13712yescomplemented
383#1967C2×C13711yescharacteristic, complemented
384#1963C2×C13711yescharacteristic, complemented
385#1793C2×C13712yescomplemented
386#1792C2×C13712yescomplemented
387#1759C2×C13711yescharacteristic, complemented
388C2×2−1+4C22×C13711yescharacteristic
389C2×H(5,𝔽2)C22×C13711yescharacteristic
390#548—21no—
391#548—21no—
392#546—21no—
393#546—21no—
394#546—22no—
395#546—22no—
396#536—21no—
397#536C22×C13711yescharacteristic
398#535—21no—
399#535C22×C13711yescharacteristic
400#532—21no—
401#532C22×C13711yescharacteristic
402C2×C4⋊Q8C22×C13711yescharacteristic, complemented
403C2×#124—21no—
404C2×#124C22×C13711yescharacteristic
405C4×#41C22×C13711yescharacteristic
406#489—21no—
407#489—21no—
408#487—21no—
409#486—21no—
410#477—21no—
411#476—21no—
412#475—21no—
413#474—21no—
414#428C22×C13712yescomplemented
415#423C22×C13711yescharacteristic, complemented
416C2×#104C22×C13712yes—
417C2×#104C22×C13712yes—
418C2×#104C22×C13712yescomplemented
419#417C22×C13712yes—
420#417C22×C13712yes—
421#417C22×C13712yescomplemented
422C2×#101C22×C13712yescomplemented
423C2×#100C22×C13712yes—
424C4×M16C22×C13711yescharacteristic, complemented
425#397—22no—
426#393—22no—
427#391C22×C13712yescomplemented
428#390C22×C13712yes—
429#376C22×C13711yescharacteristic, complemented
430#339C22×C13712yescomplemented
4312−1+4—24no—
4322−1+4—42no—
433H(5,𝔽2)—24no—
434H(5,𝔽2)—42no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—22no—
440C2×#41C23×C13711yescharacteristic
441C2×#41C23×C13711yescharacteristic
442C2×#41C23×C13711yescharacteristic
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8C23×C13711yescharacteristic
447C22×D4—22no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4C23×C13711yescharacteristic
451C2×M16C23×C13712yes—
452C2×M16C23×C13712yes—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8—21no—
457C4⋊Q8—21no—
458C4⋊Q8D4×C13711yescharacteristic
459#127—21no—
460#127D4×C13711yescharacteristic
461#124—22no—
462#124—22no—
463#124—21no—
464#124—21no—
465#124—21no—
466#124—21no—
467#124—21no—
468#124—21no—
469#124D4×C13711yescharacteristic
470#124D4×C13711yescharacteristic
471#123—22no—
472#123—22no—
473#123—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#120—22no—
487#120—22no—
488#120—22no—
489C4×Q8D4×C13711yescharacteristic
490C4×Q8D4×C13711yescharacteristic
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4D4×C13711yescharacteristic
498C4×D4D4×C13711yescharacteristic
499#117—21no—
500#117C23×C13711yescharacteristic
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C13712yes—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4D4×C13712yes—
507C2×C22⋊C4D4×C13712yes—
508C2×C42—21no—
509C2×C42C23×C13712yes—
510C2×C42C23×C13711yescharacteristic
511#107—22no—
512#106—22no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515#104—24no—
516#104—42no—
517#104—42no—
518#103—22no—
519#103—22no—
520#103—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#101—42no—
525#100—42no—
526#97—21no—
527C4×C8—21no—
528#95—21no—
529#95—21no—
530#95—24no—
531C24—22no—
532C24C2×D4×C13712yes—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—44no—
539#41—48no—
540#41—44no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41—42no—
545#41#41×C13714yes—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—44no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—82no—
557C2×Q8C2×D4×C13711yescharacteristic
558C2×Q8C2×D4×C13711yescharacteristic
559C2×Q8C2×D4×C13711yescharacteristic
560C2×D4—21no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—48no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4C2×D4×C13711yescharacteristic
579C2×D4C2×D4×C13711yescharacteristic
580C2×D4C2×D4×C13711yescharacteristic
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4C2×D4×C13712yes—
592C22×C4C2×D4×C13711yescharacteristic
593C22×C4C2×D4×C13711yescharacteristic
594C22×C4C24×C13711yescharacteristic
595M16—22no—
596M16—22no—
597M16—22no—
598M16—22no—
599C2×C8—22no—
600C2×C8—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4C2×D4×C13711yescharacteristic
612C4⋊C4C2×D4×C13711yescharacteristic
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—84no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—22no—
633C42—22no—
634C42C2×D4×C13711yescharacteristic
635C42C2×D4×C13711yescharacteristic
636C42C2×D4×C13711yescharacteristic
637C42C2×D4×C13711yescharacteristic
638C23—21no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—24no—
643C23—44no—
644C23—42no—
645C23—42no—
646C23—82no—
647C23—82no—
648C23C22×D4×C13711yescharacteristic
649Q8—21no—
650Q8—22no—
651Q8—22no—
652Q8—44no—
653Q8—41no—
654Q8—41no—
655Q8—42no—
656Q8—82no—
657Q8—82no—
658Q8#124×C13712yes—
659D4—24no—
660D4—21no—
661D4—22no—
662D4—22no—
663D4—44no—
664D4—44no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—41no—
670D4—42no—
671D4—81no—
672D4—81no—
673D4—82no—
674D4—82no—
675D4#124×C13712yes—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4#120×C13711yescharacteristic
701C2×C4#120×C13711yescharacteristic
702C2×C4#120×C13711yescharacteristic
703C2×C4#120×C13711yescharacteristic
704C2×C4C22×D4×C13711yescharacteristic
705C2×C4C22×D4×C13711yescharacteristic
706C2×C4C2×#41×C13712yes—
707C2×C4H(5,𝔽2)×C13712yes—
708C8—42no—
709C8—42no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—41no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—84no—
725C22—164no—
726C22C2×#120×C13711yescharacteristic
727C22#546×C13712yes—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—82no—
739C4—82no—
740C4C2×#124×C13711yescharacteristic
741C4#535×C13711yescharacteristic
742C4#546×C13712yes—
743C2—22no—
744C2—42no—
745C2—82no—
746C2—81no—
747C2—81no—
748C2#2435×C13711yescharacteristic
749C2#3021×C13711yescharacteristic
750C2#3022×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3500×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3141×C137C2semidirect
3. #3079×C137C2semidirect
4. #2640×C137C2semidirect
5. #2038×C137C2semidirect
6. #2037×C137C2semidirect
7. #1967×C137C2semidirect
8. #1963×C137C2semidirect
9. #1793×C137C2semidirect
10. #1792×C137C2semidirect
11. #1759×C137C2semidirect
26. C2×C4⋊Q8×C137C22semidirect
38. #428×C137C22semidirect
39. #423×C137C22semidirect
42. C2×#104×C137C22semidirect
45. #417×C137C22semidirect
46. C2×#101×C137C22semidirect
48. C4×M16×C137C22semidirect
51. #391×C137C22semidirect
53. #376×C137C22semidirect
54. #339×C137C22semidirect
375. #25880C137direct (N × H)
376. C137#25880direct (N × H)
378. #3141C2×C137semidirect
379. #3079C2×C137semidirect
380. #2640C2×C137semidirect
381. #2038C2×C137semidirect
382. #2037C2×C137semidirect
383. #1967C2×C137semidirect
384. #1963C2×C137semidirect
385. #1793C2×C137semidirect
386. #1792C2×C137semidirect
387. #1759C2×C137semidirect
402. C2×C4⋊Q8C22×C137semidirect
414. #428C22×C137semidirect
415. #423C22×C137semidirect
418. C2×#104C22×C137semidirect
421. #417C22×C137semidirect
422. C2×#101C22×C137semidirect
424. C4×M16C22×C137semidirect
427. #391C22×C137semidirect
429. #376C22×C137semidirect
430. #339C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3500×C1372
#3141×C1372
#3079×C1372
#2640×C1372
#2038×C1372
#2037×C1372
#1967×C1372
#1963×C1372
#1793×C1372
#1792×C1372
#1759×C1372
#25880137