Finite Group Databasebeta

← C37×#24056 #22645309

Subgroups — C37×#24056 #22645309

Order 9472.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3484C211yesmaximal, characteristic
2C37×#2849C212yesmaximal, complemented
3C2×C37×#386C211yesmaximal, characteristic, complemented
4C37×#2044C214yesmaximal, complemented
5C37×#1898C212yesmaximal, complemented
6C37×#1867C212yesmaximal, complemented
7C37×#1790C212yesmaximal, complemented
8C37×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C37C2211yescharacteristic
10C23×D4×C37C2211yescharacteristic
11C24×C4×C37C2211yescharacteristic, complemented
12C37×#546—22no—
13C37×#546—22no—
14D42×C37—22no—
15D42×C37—22no—
16C37×#535—21no—
17C37×#534—21no—
18C37×#534C2212yes—
19C37×#525—21no—
20C2×#123×C37—22no—
21C2×#120×C37—21no—
22C2×#120×C37C2212yes—
23C37×#518C2211yescharacteristic
24C22×C22⋊C4×C37—21no—
25C22×C22⋊C4×C37C2211yescharacteristic, complemented
26C2×#99×C37C2212yes—
27C2×#99×C37C2214yescomplemented
28C2×#99×C37C2212yescomplemented
29C37×#386—21no—
30C37×#386—21no—
31C37×#386—22no—
32C37×#386C2212yes—
33C37×#386C2212yescomplemented
34C37×#386C2214yescomplemented
35C37×#385—22no—
36C37×#385C2214yescomplemented
37C37×#381—22no—
38C37×#379C2212yescomplemented
39C2×#95×C37—21no—
40C37×#342C2214yescomplemented
41C25×C37D411yescharacteristic
42C25×C37C2311yescharacteristic
43H(5,𝔽2)×C37—24no—
44H(5,𝔽2)×C37—42no—
45C2×#41×C37—21no—
46C2×#41×C37—22no—
47C22×D4×C37—21no—
48C22×D4×C37—22no—
49C22×D4×C37—22no—
50C22×D4×C37—22no—
51C22×D4×C37—21no—
52C22×D4×C37—21no—
53C22×D4×C37—24no—
54C22×D4×C37—42no—
55C22×D4×C37D411yescharacteristic
56C22×D4×C37D411yescharacteristic
57C22×D4×C37D412yes—
58C22×D4×C37D412yes—
59C22×D4×C37C2312yes—
60C22×D4×C37C2311yescharacteristic
61C22×D4×C37C2311yescharacteristic
62C23×C4×C37—22no—
63C23×C4×C37—21no—
64C23×C4×C37—22no—
65C23×C4×C37—21no—
66C23×C4×C37—21no—
67C23×C4×C37—44no—
68C23×C4×C37D411yescharacteristic
69C23×C4×C37C2312yes—
70#127×C37—22no—
71#124×C37—22no—
72#123×C37—22no—
73#123×C37—22no—
74#123×C37—22no—
75#123×C37—48no—
76C22⋊Q8×C37—21no—
77C22⋊Q8×C37—21no—
78#121×C37—21no—
79#121×C37—21no—
80#121×C37—22no—
81#121×C37—22no—
82#121×C37—22no—
83#121×C37—22no—
84#121×C37—22no—
85#121×C37—22no—
86#120×C37—22no—
87#120×C37—22no—
88#120×C37—22no—
89#120×C37—22no—
90#120×C37—22no—
91#120×C37—22no—
92#120×C37—22no—
93#120×C37—22no—
94#120×C37—22no—
95C4×D4×C37—22no—
96C4×D4×C37—22no—
97C4×D4×C37—22no—
98C4×D4×C37—22no—
99#117×C37—21no—
100C2×C4⋊C4×C37—24no—
101C2×C22⋊C4×C37—21no—
102C2×C22⋊C4×C37—21no—
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37—22no—
105C2×C22⋊C4×C37—24no—
106C2×C22⋊C4×C37—22no—
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—22no—
109C2×C22⋊C4×C37—22no—
110C2×C22⋊C4×C37—42no—
111C2×C22⋊C4×C37—44no—
112C2×C22⋊C4×C37D412yes—
113C2×C22⋊C4×C37D412yes—
114C2×C22⋊C4×C37C2312yes—
115C2×C22⋊C4×C37C2314yes—
116C2×C22⋊C4×C37C2312yes—
117#99×C37—24no—
118#99×C37—42no—
119#99×C37—44no—
120#95×C37—22no—
121#95×C37—22no—
122#95×C37—24no—
123#95×C37—24no—
124C24×C37—22no—
125C24×C37—22no—
126C24×C37—21no—
127C24×C37—22no—
128C24×C37—21no—
129C24×C37—21no—
130C24×C37—42no—
131C24×C37—42no—
132C24×C37—41no—
133C24×C37—42no—
134C24×C37—42no—
135C24×C37C2×D411yescharacteristic
136C24×C37C2×D412yes—
137C24×C37C2×D412yes—
138C24×C37C2×D411yescharacteristic
139C24×C37C2×D412yes—
140C24×C37C2×D411yescharacteristic
141C24×C37C2×D411yescharacteristic
142C24×C37C2411yescharacteristic
143#41×C37—48no—
144#41×C37—42no—
145#41×C37—42no—
146C2×Q8×C37—21no—
147C2×D4×C37—22no—
148C2×D4×C37—22no—
149C2×D4×C37—22no—
150C2×D4×C37—21no—
151C2×D4×C37—22no—
152C2×D4×C37—22no—
153C2×D4×C37—22no—
154C2×D4×C37—22no—
155C2×D4×C37—22no—
156C2×D4×C37—22no—
157C2×D4×C37—22no—
158C2×D4×C37—22no—
159C2×D4×C37—22no—
160C2×D4×C37—24no—
161C2×D4×C37—22no—
162C2×D4×C37—24no—
163C2×D4×C37—22no—
164C2×D4×C37—22no—
165C2×D4×C37—22no—
166C2×D4×C37—22no—
167C2×D4×C37—22no—
168C2×D4×C37—41no—
169C2×D4×C37—41no—
170C2×D4×C37—48no—
171C2×D4×C37—48no—
172C2×D4×C37—48no—
173C2×D4×C37—42no—
174C2×D4×C37—42no—
175C2×D4×C37—44no—
176C2×D4×C37—44no—
177C2×D4×C37—82no—
178C2×D4×C37—82no—
179C2×D4×C37#4114yes—
180C22×C4×C37—21no—
181C22×C4×C37—24no—
182C22×C4×C37—22no—
183C22×C4×C37—28no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—22no—
187C22×C4×C37—24no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—22no—
191C22×C4×C37—24no—
192C22×C4×C37—22no—
193C22×C4×C37—44no—
194C22×C4×C37—41no—
195C22×C4×C37—44no—
196C22×C4×C37—48no—
197C22×C4×C37—42no—
198C22×C4×C37—44no—
199C22×C4×C37—42no—
200C22×C4×C37—41no—
201C22×C4×C37—41no—
202C22×C4×C37—42no—
203C22×C4×C37—42no—
204C22×C4×C37—42no—
205C22×C4×C37C2×D412yes—
206C22×C4×C37C2×D411yescharacteristic
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D412yes—
209C22×C4×C37C2×D412yes—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—21no—
212C4⋊C4×C37—22no—
213C4⋊C4×C37—22no—
214C4⋊C4×C37—48no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—22no—
218C22⋊C4×C37—22no—
219C22⋊C4×C37—22no—
220C22⋊C4×C37—22no—
221C22⋊C4×C37—22no—
222C22⋊C4×C37—22no—
223C22⋊C4×C37—22no—
224C22⋊C4×C37—22no—
225C22⋊C4×C37—22no—
226C22⋊C4×C37—24no—
227C22⋊C4×C37—24no—
228C22⋊C4×C37—24no—
229C22⋊C4×C37—44no—
230C22⋊C4×C37—44no—
231C22⋊C4×C37—48no—
232C22⋊C4×C37—44no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—44no—
235C42×C37—22no—
236C23×C37—21no—
237C23×C37—21no—
238C23×C37—22no—
239C23×C37—22no—
240C23×C37—21no—
241C23×C37—21no—
242C23×C37—21no—
243C23×C37—24no—
244C23×C37—24no—
245C23×C37—24no—
246C23×C37—24no—
247C23×C37—21no—
248C23×C37—21no—
249C23×C37—22no—
250C23×C37—21no—
251C23×C37—21no—
252C23×C37—24no—
253C23×C37—42no—
254C23×C37—41no—
255C23×C37—41no—
256C23×C37—42no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—42no—
260C23×C37—42no—
261C23×C37—48no—
262C23×C37—48no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—48no—
268C23×C37—42no—
269C23×C37—42no—
270C23×C37—42no—
271C23×C37—42no—
272C23×C37—42no—
273C23×C37—81no—
274C23×C37—81no—
275C23×C37—84no—
276C23×C37—81no—
277C23×C37—81no—
278C23×C37#12012yes—
279C23×C37#12011yescharacteristic
280C23×C37#12011yescharacteristic
281C23×C37#12312yescomplemented
282C23×C37C22×D411yescharacteristic
283C23×C37C22×D412yes—
284C23×C37C2×#4112yes—
285C23×C37H(5,𝔽2)12yes—
286Q8×C37—42no—
287D4×C37—28no—
288D4×C37—44no—
289D4×C37—42no—
290D4×C37—44no—
291D4×C37—44no—
292D4×C37—42no—
293D4×C37—42no—
294D4×C37—44no—
295D4×C37—44no—
296D4×C37—44no—
297D4×C37—44no—
298D4×C37—82no—
299D4×C37—82no—
300D4×C37—82no—
301D4×C37—82no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—24no—
305C2×C4×C37—28no—
306C2×C4×C37—22no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—21no—
310C2×C4×C37—21no—
311C2×C4×C37—21no—
312C2×C4×C37—24no—
313C2×C4×C37—42no—
314C2×C4×C37—42no—
315C2×C4×C37—44no—
316C2×C4×C37—44no—
317C2×C4×C37—42no—
318C2×C4×C37—44no—
319C2×C4×C37—48no—
320C2×C4×C37—42no—
321C2×C4×C37—42no—
322C2×C4×C37—44no—
323C2×C4×C37—42no—
324C2×C4×C37—42no—
325C2×C4×C37—44no—
326C2×C4×C37—42no—
327C2×C4×C37—44no—
328C2×C4×C37—42no—
329C2×C4×C37—42no—
330C2×C4×C37—44no—
331C2×C4×C37—81no—
332C2×C4×C37—81no—
333C2×C4×C37—84no—
334C2×C4×C37#12312yescomplemented
335#24056C3711yesmaximal, characteristic, direct product factor, Sylow
336C22×C37—24no—
337C22×C37—24no—
338C22×C37—21no—
339C22×C37—21no—
340C22×C37—22no—
341C22×C37—21no—
342C22×C37—21no—
343C22×C37—22no—
344C22×C37—21no—
345C22×C37—21no—
346C22×C37—22no—
347C22×C37—22no—
348C22×C37—22no—
349C22×C37—22no—
350C22×C37—42no—
351C22×C37—42no—
352C22×C37—48no—
353C22×C37—48no—
354C22×C37—42no—
355C22×C37—42no—
356C22×C37—42no—
357C22×C37—42no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—42no—
361C22×C37—41no—
362C22×C37—42no—
363C22×C37—41no—
364C22×C37—42no—
365C22×C37—41no—
366C22×C37—81no—
367C22×C37—84no—
368C22×C37—84no—
369C22×C37—84no—
370C22×C37—81no—
371C22×C37—162no—
372C22×C37B(4,𝔽2)12yes—
373C22×C37#45812yes—
374C22×C37C2×#12011yescharacteristic
375C22×C37C2×#12311yescharacteristic
376C22×C37#53411yescharacteristic
377C22×C37#54614yes—
378C4×C37—22no—
379C4×C37—41no—
380C4×C37—42no—
381C4×C37—44no—
382C4×C37—42no—
383C4×C37—42no—
384C4×C37—84no—
385C4×C37—82no—
386#3484C2×C3711yescharacteristic
387#2849C2×C3712yescomplemented
388C2×#386C2×C3711yescharacteristic, complemented
389#2044C2×C3714yescomplemented
390#1898C2×C3712yescomplemented
391#1867C2×C3712yescomplemented
392#1790C2×C3712yescomplemented
393#1781C2×C3711yescharacteristic, complemented
394C2×C37—21no—
395C2×C37—24no—
396C2×C37—21no—
397C2×C37—22no—
398C2×C37—22no—
399C2×C37—42no—
400C2×C37—42no—
401C2×C37—81no—
402C2×C37—82no—
403C2×C37#240511yescharacteristic
404C2×C37C2×B(4,𝔽2)11yescharacteristic
405C2×C37C2×#45811yescharacteristic
406C2×H(5,𝔽2)C22×C3711yescharacteristic
407C23×D4C22×C3711yescharacteristic
408C24×C4C22×C3711yescharacteristic, complemented
409#546—22no—
410#546—22no—
411D42—22no—
412D42—22no—
413#535—21no—
414#534—21no—
415#534C22×C3712yes—
416#525—21no—
417C2×#123—22no—
418C2×#120—21no—
419C2×#120C22×C3712yes—
420#518C22×C3711yescharacteristic
421C22×C22⋊C4—21no—
422C22×C22⋊C4C22×C3711yescharacteristic, complemented
423C2×#99C22×C3712yes—
424C2×#99C22×C3714yescomplemented
425C2×#99C22×C3712yescomplemented
426#386—22no—
427#386—21no—
428#386—21no—
429#386C22×C3712yes—
430#386C22×C3714yescomplemented
431#386C22×C3712yescomplemented
432#385—22no—
433#385C22×C3714yescomplemented
434#381—22no—
435#379C22×C3712yescomplemented
436C2×#95—21no—
437#342C22×C3714yescomplemented
438C37#2405611yescharacteristic, direct product factor, Sylow
439C25D4×C3711yescharacteristic
440C25C23×C3711yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C3711yescharacteristic
454C22×D4D4×C3711yescharacteristic
455C22×D4D4×C3712yes—
456C22×D4D4×C3712yes—
457C22×D4C23×C3712yes—
458C22×D4C23×C3711yescharacteristic
459C22×D4C23×C3711yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C3711yescharacteristic
467C23×C4C23×C3712yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C3712yes—
511C2×C22⋊C4D4×C3712yes—
512C2×C22⋊C4C23×C3712yes—
513C2×C22⋊C4C23×C3714yes—
514C2×C22⋊C4C23×C3712yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C3711yescharacteristic
534C24C2×D4×C3712yes—
535C24C2×D4×C3712yes—
536C24C2×D4×C3711yescharacteristic
537C24C2×D4×C3712yes—
538C24C2×D4×C3711yescharacteristic
539C24C2×D4×C3711yescharacteristic
540C24C24×C3711yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C3714yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C3712yes—
604C22×C4C2×D4×C3711yescharacteristic
605C22×C4C2×D4×C3711yescharacteristic
606C22×C4C2×D4×C3712yes—
607C22×C4C2×D4×C3712yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—42no—
632C22⋊C4—44no—
633C42—22no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C3712yes—
677C23#120×C3711yescharacteristic
678C23#120×C3711yescharacteristic
679C23#123×C3712yescomplemented
680C23C22×D4×C3711yescharacteristic
681C23C22×D4×C3712yes—
682C23C2×#41×C3712yes—
683C23H(5,𝔽2)×C3712yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C3712yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C37×B(4,𝔽2)12yes—
770C22C37×#45812yes—
771C22C2×#120×C3711yescharacteristic
772C22C2×#123×C3711yescharacteristic
773C22C37×#53411yescharacteristic
774C22C37×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C37×#240511yescharacteristic
793C2C2×C37×B(4,𝔽2)11yescharacteristic
794C2C2×C37×#45811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
prime radicalC37×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2849C2semidirect
3. C2×C37×#386C2semidirect
4. C37×#2044C2semidirect
5. C37×#1898C2semidirect
6. C37×#1867C2semidirect
7. C37×#1790C2semidirect
8. C37×#1781C2semidirect
11. C24×C4×C37C22semidirect
25. C22×C22⋊C4×C37C22semidirect
27. C2×#99×C37C22semidirect
28. C2×#99×C37C22semidirect
33. C37×#386C22semidirect
34. C37×#386C22semidirect
36. C37×#385C22semidirect
38. C37×#379C22semidirect
40. C37×#342C22semidirect
281. C23×C37#123semidirect
334. C2×C4×C37#123semidirect
335. #24056C37direct (N × H)
387. #2849C2×C37semidirect
388. C2×#386C2×C37semidirect
389. #2044C2×C37semidirect
390. #1898C2×C37semidirect
391. #1867C2×C37semidirect
392. #1790C2×C37semidirect
393. #1781C2×C37semidirect
408. C24×C4C22×C37semidirect
422. C22×C22⋊C4C22×C37semidirect
424. C2×#99C22×C37semidirect
425. C2×#99C22×C37semidirect
430. #386C22×C37semidirect
431. #386C22×C37semidirect
433. #385C22×C37semidirect
435. #379C22×C37semidirect
437. #342C22×C37semidirect
438. C37#24056direct (N × H)
679. C23#123×C37semidirect
732. C2×C4#123×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34842
C37×#28492
C2×C37×#3862
C37×#20442
C37×#18982
C37×#18672
C37×#17902
C37×#17812
#2405637