Finite Group Databasebeta

← C37×#9914 #22631167

Subgroups — C37×#9914 #22631167

Order 9472.

1356 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#447C211yesmaximal, characteristic, complemented
2C37×#2617C211yesmaximal, characteristic, complemented
3C2×C37×#392C211yesmaximal, characteristic, complemented
4C37×#1786C211yesmaximal, characteristic, complemented
5C2×C37×#327C211yesmaximal, characteristic, complemented
6C2×C37×#323C211yesmaximal, characteristic, complemented
7C37×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C37—21no—
9C23×D4×C37C2211yescharacteristic
10C22×D8×C37—21no—
11C2×#121×C37C2211yescharacteristic
12C2×#120×C37—21no—
13C22×C22⋊C4×C37—21no—
14C22×C22⋊C4×C37C2211yescharacteristic
15C37×#447—22no—
16C37×#447—22no—
17C2×#102×C37—21no—
18C2×#102×C37—22no—
19C2×C22⋊C8×C37C2211yescharacteristic
20C2×C22⋊C8×C37C2211yescharacteristic
21C37×#397—21no—
22C37×#394—22no—
23C37×#392—21no—
24C37×#392—22no—
25C37×#392—22no—
26C37×#386—21no—
27C37×#380C2211yescharacteristic
28C2×#95×C37C2211yescharacteristic
29C37×#327—22no—
30C37×#323—22no—
31C25×C37—21no—
32C25×C37D411yescharacteristic
33C22×D4×C37—24no—
34C22×D4×C37—21no—
35C22×D4×C37—22no—
36C22×D4×C37—21no—
37C22×D4×C37—21no—
38C22×D4×C37—21no—
39C22×D4×C37—21no—
40C22×D4×C37—21no—
41C22×D4×C37—44no—
42C22×D4×C37—44no—
43C22×D4×C37—44no—
44C22×D4×C37—42no—
45C22×D4×C37—42no—
46C22×D4×C37D411yescharacteristic, complemented
47C22×D4×C37D412yescomplemented
48C23×C4×C37—21no—
49C23×C4×C37D411yescharacteristic
50C23×C4×C37C2311yescharacteristic
51C2×D8×C37—24no—
52C2×D8×C37—44no—
53C22×C8×C37—21no—
54C22×C8×C37—21no—
55#121×C37—21no—
56#121×C37—21no—
57#121×C37—21no—
58#121×C37—21no—
59#120×C37—42no—
60#120×C37—42no—
61C2×C4⋊C4×C37D411yescharacteristic, complemented
62C2×C4⋊C4×C37D412yescomplemented
63C2×C22⋊C4×C37—22no—
64C2×C22⋊C4×C37—24no—
65C2×C22⋊C4×C37—21no—
66C2×C22⋊C4×C37—21no—
67C2×C22⋊C4×C37—21no—
68C2×C22⋊C4×C37—21no—
69C2×C22⋊C4×C37—21no—
70C2×C22⋊C4×C37—21no—
71C2×C22⋊C4×C37—21no—
72C2×C22⋊C4×C37—21no—
73C2×C22⋊C4×C37—22no—
74C2×C22⋊C4×C37—44no—
75#102×C37—24no—
76#102×C37—44no—
77C22⋊C8×C37—21no—
78C22⋊C8×C37—21no—
79C22⋊C8×C37—21no—
80C22⋊C8×C37D412yescomplemented
81#95×C37—22no—
82#95×C37—21no—
83#95×C37—21no—
84#95×C37D412yescomplemented
85C24×C37—24no—
86C24×C37—21no—
87C24×C37—22no—
88C24×C37—21no—
89C24×C37—21no—
90C24×C37—21no—
91C24×C37—21no—
92C24×C37—21no—
93C24×C37—21no—
94C24×C37—42no—
95C24×C37—42no—
96C24×C37—42no—
97C24×C37—42no—
98C24×C37—42no—
99C24×C37—41no—
100C24×C37—41no—
101C24×C37—41no—
102C24×C37—41no—
103C24×C37—41no—
104C24×C37—41no—
105C24×C37D812yescomplemented
106C24×C37C2×D411yescharacteristic
107C2×D4×C37—24no—
108C2×D4×C37—24no—
109C2×D4×C37—22no—
110C2×D4×C37—21no—
111C2×D4×C37—22no—
112C2×D4×C37—21no—
113C2×D4×C37—42no—
114C2×D4×C37—42no—
115C2×D4×C37—48no—
116C2×D4×C37—42no—
117C2×D4×C37—44no—
118C2×D4×C37—44no—
119C2×D4×C37—44no—
120C2×D4×C37—44no—
121C2×D4×C37—48no—
122C2×D4×C37—48no—
123C2×D4×C37—416no—
124C2×D4×C37—416no—
125C2×D4×C37—44no—
126C2×D4×C37—41no—
127C2×D4×C37—41no—
128C2×D4×C37—41no—
129C2×D4×C37—41no—
130C2×D4×C37—41no—
131C2×D4×C37—41no—
132C2×D4×C37—41no—
133C2×D4×C37—41no—
134C2×D4×C37—82no—
135C2×D4×C37—82no—
136C22×C4×C37—24no—
137C22×C4×C37—22no—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—22no—
142C22×C4×C37—21no—
143C22×C4×C37—42no—
144C22×C4×C37—42no—
145C22×C4×C37—41no—
146C22×C4×C37—41no—
147C22×C4×C37—42no—
148C22×C4×C37C2×D411yescharacteristic
149C22×C4×C37C2×D411yescharacteristic
150C22×C4×C37C2×D411yescharacteristic
151C22×C4×C37C2×D411yescharacteristic
152C22×C4×C37C2×D411yescharacteristic
153C22×C4×C37#4111yescharacteristic
154D8×C37—48no—
155C2×C8×C37—22no—
156C2×C8×C37—42no—
157C2×C8×C37—42no—
158C2×C8×C37—41no—
159C4⋊C4×C37—21no—
160C4⋊C4×C37—21no—
161C4⋊C4×C37—42no—
162C22⋊C4×C37—48no—
163C22⋊C4×C37—44no—
164C22⋊C4×C37—41no—
165C22⋊C4×C37—41no—
166C22⋊C4×C37—41no—
167C22⋊C4×C37—41no—
168C22⋊C4×C37—41no—
169C22⋊C4×C37—41no—
170C22⋊C4×C37—41no—
171C22⋊C4×C37—41no—
172C22⋊C4×C37—82no—
173C23×C37—22no—
174C23×C37—22no—
175C23×C37—24no—
176C23×C37—22no—
177C23×C37—22no—
178C23×C37—22no—
179C23×C37—44no—
180C23×C37—42no—
181C23×C37—44no—
182C23×C37—44no—
183C23×C37—44no—
184C23×C37—42no—
185C23×C37—42no—
186C23×C37—42no—
187C23×C37—42no—
188C23×C37—44no—
189C23×C37—44no—
190C23×C37—44no—
191C23×C37—41no—
192C23×C37—42no—
193C23×C37—42no—
194C23×C37—41no—
195C23×C37—41no—
196C23×C37—42no—
197C23×C37—42no—
198C23×C37—44no—
199C23×C37—42no—
200C23×C37—41no—
201C23×C37—41no—
202C23×C37—41no—
203C23×C37—41no—
204C23×C37—42no—
205C23×C37—42no—
206C23×C37—82no—
207C23×C37—82no—
208C23×C37—81no—
209C23×C37—81no—
210C23×C37—82no—
211C23×C37—82no—
212C23×C37—82no—
213C23×C37—82no—
214C23×C37—82no—
215C23×C37—81no—
216C23×C37—81no—
217C23×C37—82no—
218C23×C37—81no—
219C23×C37—81no—
220C23×C37#12011yescharacteristic
221C23×C37#12011yescharacteristic
222C23×C37#12111yescharacteristic
223C23×C37C2×D811yescharacteristic
224C23×C37#13511yescharacteristic
225C23×C37AGL(1,ℤ/8)11yescharacteristic
226C23×C37AGL(1,ℤ/8)11yescharacteristic
227D4×C37—24no—
228D4×C37—24no—
229D4×C37—42no—
230D4×C37—44no—
231D4×C37—42no—
232D4×C37—44no—
233D4×C37—42no—
234D4×C37—432no—
235D4×C37—81no—
236D4×C37—88no—
237D4×C37—81no—
238D4×C37—81no—
239D4×C37—81no—
240D4×C37—81no—
241C2×C4×C37—22no—
242C2×C4×C37—22no—
243C2×C4×C37—24no—
244C2×C4×C37—41no—
245C2×C4×C37—41no—
246C2×C4×C37—41no—
247C2×C4×C37—41no—
248C2×C4×C37—44no—
249C2×C4×C37—44no—
250C2×C4×C37—42no—
251C2×C4×C37—42no—
252C2×C4×C37—42no—
253C2×C4×C37—41no—
254C2×C4×C37—41no—
255C2×C4×C37—42no—
256C2×C4×C37—41no—
257C2×C4×C37—41no—
258C2×C4×C37—42no—
259C2×C4×C37—42no—
260C2×C4×C37—42no—
261C2×C4×C37—81no—
262C2×C4×C37#12011yescharacteristic
263C2×C4×C37#12111yescharacteristic
264C2×C4×C37#12111yescharacteristic
265C2×C4×C37#12711yescharacteristic
266C8×C37—42no—
267C8×C37—81no—
268#9914C3711yesmaximal, characteristic, direct product factor, Sylow
269C22×C37—22no—
270C22×C37—22no—
271C22×C37—22no—
272C22×C37—22no—
273C22×C37—21no—
274C22×C37—21no—
275C22×C37—21no—
276C22×C37—21no—
277C22×C37—44no—
278C22×C37—44no—
279C22×C37—44no—
280C22×C37—44no—
281C22×C37—42no—
282C22×C37—44no—
283C22×C37—82no—
284C22×C37—82no—
285C22×C37—82no—
286C22×C37—82no—
287C22×C37—84no—
288C22×C37—82no—
289C22×C37—84no—
290C22×C37—84no—
291C22×C37—82no—
292C22×C37—84no—
293C22×C37—82no—
294C22×C37—81no—
295C22×C37—82no—
296C22×C37—81no—
297C22×C37—82no—
298C22×C37—82no—
299C22×C37—81no—
300C22×C37—81no—
301C22×C37—81no—
302C22×C37#39211yescharacteristic
303C22×C37#44711yescharacteristic
304C22×C37#44711yescharacteristic
305C22×C37#44911yescharacteristic
306C22×C37#44911yescharacteristic
307C22×C37#45312yes—
308C22×C37B(4,𝔽2)12yes—
309C22×C37#46611yescharacteristic
310C22×C37#46911yescharacteristic
311C4×C37—21no—
312C4×C37—21no—
313C4×C37—21no—
314C4×C37—21no—
315C4×C37—44no—
316C4×C37—82no—
317C4×C37—81no—
318C4×C37—81no—
319C2×#447C2×C3711yescharacteristic, complemented
320#2617C2×C3711yescharacteristic, complemented
321C2×#392C2×C3711yescharacteristic, complemented
322#1786C2×C3711yescharacteristic, complemented
323C2×#327C2×C3711yescharacteristic, complemented
324C2×#323C2×C3711yescharacteristic, complemented
325#1294C2×C3711yescharacteristic, complemented
326C2×C37—21no—
327C2×C37—21no—
328C2×C37—21no—
329C2×C37—21no—
330C2×C37—82no—
331C2×C37—84no—
332C2×C37—161no—
333C2×C37#159512yes—
334C2×C37#160012yes—
335C2×C37#199911yescharacteristic
336C2×C37#200211yescharacteristic
337C2×C37#202111yescharacteristic
338C23×D4—21no—
339C23×D4C22×C3711yescharacteristic
340C22×D8—21no—
341C2×#121C22×C3711yescharacteristic
342C2×#120—21no—
343C22×C22⋊C4—21no—
344C22×C22⋊C4C22×C3711yescharacteristic
345#447—22no—
346#447—22no—
347C2×#102—21no—
348C2×#102—22no—
349C2×C22⋊C8C22×C3711yescharacteristic
350C2×C22⋊C8C22×C3711yescharacteristic
351#397—21no—
352#394—22no—
353#392—21no—
354#392—22no—
355#392—22no—
356#386—21no—
357#380C22×C3711yescharacteristic
358C2×#95C22×C3711yescharacteristic
359#327—22no—
360#323—22no—
361C37#991411yescharacteristic, direct product factor, Sylow
362C25—21no—
363C25D4×C3711yescharacteristic
364C22×D4—24no—
365C22×D4—21no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—44no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4D4×C3711yescharacteristic, complemented
378C22×D4D4×C3712yescomplemented
379C23×C4—21no—
380C23×C4D4×C3711yescharacteristic
381C23×C4C23×C3711yescharacteristic
382C2×D8—24no—
383C2×D8—44no—
384C22×C8—21no—
385C22×C8—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121—21no—
390#120—42no—
391#120—42no—
392C2×C4⋊C4D4×C3711yescharacteristic, complemented
393C2×C4⋊C4D4×C3712yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—44no—
406#102—24no—
407#102—44no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8D4×C3712yescomplemented
412#95—22no—
413#95—21no—
414#95—21no—
415#95D4×C3712yescomplemented
416C24—24no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24D8×C3712yescomplemented
437C24C2×D4×C3711yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—82no—
466C2×D4—82no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4C2×D4×C3711yescharacteristic
480C22×C4C2×D4×C3711yescharacteristic
481C22×C4C2×D4×C3711yescharacteristic
482C22×C4C2×D4×C3711yescharacteristic
483C22×C4C2×D4×C3711yescharacteristic
484C22×C4#41×C3711yescharacteristic
485D8—48no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—41no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—44no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—82no—
538C23—82no—
539C23—81no—
540C23—81no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23—82no—
546C23—81no—
547C23—81no—
548C23—82no—
549C23—81no—
550C23—81no—
551C23#120×C3711yescharacteristic
552C23#120×C3711yescharacteristic
553C23#121×C3711yescharacteristic
554C23C2×D8×C3711yescharacteristic
555C23#135×C3711yescharacteristic
556C23AGL(1,ℤ/8)×C3711yescharacteristic
557C23AGL(1,ℤ/8)×C3711yescharacteristic
558D4—24no—
559D4—24no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—432no—
566D4—81no—
567D4—88no—
568D4—81no—
569D4—81no—
570D4—81no—
571D4—81no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—81no—
593C2×C4#120×C3711yescharacteristic
594C2×C4#121×C3711yescharacteristic
595C2×C4#121×C3711yescharacteristic
596C2×C4#127×C3711yescharacteristic
597C8—42no—
598C8—81no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—42no—
612C22—44no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—84no—
618C22—82no—
619C22—84no—
620C22—84no—
621C22—82no—
622C22—84no—
623C22—82no—
624C22—81no—
625C22—82no—
626C22—81no—
627C22—82no—
628C22—82no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22C37×#39211yescharacteristic
633C22C37×#44711yescharacteristic
634C22C37×#44711yescharacteristic
635C22C37×#44911yescharacteristic
636C22C37×#44911yescharacteristic
637C22C37×#45312yes—
638C22C37×B(4,𝔽2)12yes—
639C22C37×#46611yescharacteristic
640C22C37×#46911yescharacteristic
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—44no—
646C4—82no—
647C4—81no—
648C4—81no—
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—82no—
654C2—84no—
655C2—161no—
656C2C37×#159512yes—
657C2C37×#160012yes—
658C2C37×#199911yescharacteristic
659C2C37×#200211yescharacteristic
660C2C37×#202111yescharacteristic
subgroupG/H
center, socleC23×C37#120
commutator, Frattini, cosocleC23×C4C23×C37
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#447C2semidirect
2. C37×#2617C2semidirect
3. C2×C37×#392C2semidirect
4. C37×#1786C2semidirect
5. C2×C37×#327C2semidirect
6. C2×C37×#323C2semidirect
7. C37×#1294C2semidirect
46. C22×D4×C37D4semidirect
47. C22×D4×C37D4semidirect
61. C2×C4⋊C4×C37D4semidirect
62. C2×C4⋊C4×C37D4semidirect
80. C22⋊C8×C37D4semidirect
84. #95×C37D4semidirect
105. C24×C37D8semidirect
268. #9914C37direct (N × H)
319. C2×#447C2×C37semidirect
320. #2617C2×C37semidirect
321. C2×#392C2×C37semidirect
322. #1786C2×C37semidirect
323. C2×#327C2×C37semidirect
324. C2×#323C2×C37semidirect
325. #1294C2×C37semidirect
361. C37#9914direct (N × H)
377. C22×D4D4×C37semidirect
378. C22×D4D4×C37semidirect
392. C2×C4⋊C4D4×C37semidirect
393. C2×C4⋊C4D4×C37semidirect
411. C22⋊C8D4×C37semidirect
415. #95D4×C37semidirect
436. C24D8×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4472
C37×#26172
C2×C37×#3922
C37×#17862
C2×C37×#3272
C2×C37×#3232
C37×#12942
#991437