Finite Group Databasebeta

← C37×#24464 #22645717

Subgroups — C37×#24464 #22645717

Order 9472.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3488C211yesmaximal, characteristic, complemented
2C37×#3055C211yesmaximal, characteristic, complemented
3C2×C37×#453C211yesmaximal, characteristic, complemented
4C37×#3006C211yesmaximal, characteristic, complemented
5C22×#104×C37C211yesmaximal, characteristic, complemented
6C37×#2856C211yesmaximal, characteristic, complemented
7C37×#2039C211yesmaximal, characteristic, complemented
8C37×#2037C211yesmaximal, characteristic, complemented
9C37×#2006C211yesmaximal, characteristic, complemented
10C37×#2002C211yesmaximal, characteristic, complemented
11C37×#1900C211yesmaximal, characteristic, complemented
12C37×#1896C211yesmaximal, characteristic, complemented
13C37×#1883C211yesmaximal, characteristic, complemented
14C37×#1859C211yesmaximal, characteristic, complemented
15C37×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
21C22×M16×C37C2211yescharacteristic, complemented
22C37×#550—21no—
23C37×#548—21no—
24C37×#546—21no—
25C37×#546—22no—
26D42×C37—22no—
27D42×C37—21no—
28C37×#537—21no—
29C37×#537C2211yescharacteristic
30C37×#535—21no—
31C37×#535C2211yescharacteristic
32C2×#127×C37C2211yescharacteristic, complemented
33C37×#525—21no—
34C37×#525C2211yescharacteristic
35C2×#121×C37—21no—
36C2×#121×C37—22no—
37C2×#121×C37C2211yescharacteristic
38C2×#121×C37C2211yescharacteristic, complemented
39C37×#520C2211yescharacteristic
40C22×C42×C37C2211yescharacteristic, complemented
41C37×#469—21no—
42C37×#468—21no—
43C37×#466—21no—
44C37×#465—21no—
45C37×#453—24no—
46C37×#449—21no—
47C37×#449—21no—
48C37×#448—21no—
49C37×#447—21no—
50C37×#428C2211yescharacteristic, complemented
51C2×#104×C37—24no—
52C2×#104×C37C2211yescharacteristic
53C2×#104×C37C2211yescharacteristic
54C2×#104×C37C2211yescharacteristic, complemented
55C2×#104×C37C2211yescharacteristic, complemented
56C2×#104×C37C2211yescharacteristic, complemented
57C2×#104×C37C2211yescharacteristic, complemented
58C37×#418C2211yescharacteristic, complemented
59C37×#417C2211yescharacteristic
60C37×#417C2211yescharacteristic, complemented
61C37×#417C2211yescharacteristic, complemented
62C2×#100×C37C2211yescharacteristic, complemented
63C2×#100×C37C2211yescharacteristic, complemented
64C37×#407C2211yescharacteristic, complemented
65C37×#390—22no—
66C37×#390C2211yescharacteristic, complemented
67C37×#390C2211yescharacteristic, complemented
68C37×#384C2211yescharacteristic, complemented
69C37×#343C2211yescharacteristic, complemented
70C37×#343C2211yescharacteristic, complemented
71C37×#339C2211yescharacteristic, complemented
72C37×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C37—22no—
74H(5,𝔽2)×C37—22no—
75H(5,𝔽2)×C37—41no—
76H(5,𝔽2)×C37—41no—
77C2×#41×C37—21no—
78C2×#41×C37—21no—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—22no—
82C2×#41×C37—22no—
83C2×#41×C37—41no—
84C2×#41×C37—41no—
85C2×#41×C37D411yescharacteristic, complemented
86C2×#41×C37D411yescharacteristic, complemented
87C2×#41×C37C2311yescharacteristic
88C2×#41×C37C2311yescharacteristic
89C2×#41×C37C2311yescharacteristic
90C22×Q8×C37D411yescharacteristic, complemented
91C22×D4×C37—21no—
92C22×D4×C37—22no—
93C22×D4×C37—22no—
94C22×D4×C37—21no—
95C22×D4×C37—21no—
96C22×D4×C37—21no—
97C22×D4×C37—22no—
98C22×D4×C37D412yes—
99C22×D4×C37D411yescharacteristic, complemented
100C22×D4×C37C2311yescharacteristic
101C22×D4×C37C2311yescharacteristic
102C23×C4×C37—21no—
103C23×C4×C37—21no—
104C23×C4×C37C2311yescharacteristic
105AGL(1,ℤ/8)×C37—22no—
106AGL(1,ℤ/8)×C37—22no—
107AGL(1,ℤ/8)×C37—22no—
108AGL(1,ℤ/8)×C37—41no—
109AGL(1,ℤ/8)×C37—41no—
110AGL(1,ℤ/8)×C37—41no—
111C2×SD16×C37—21no—
112C2×SD16×C37—21no—
113C2×SD16×C37—21no—
114C2×D8×C37—21no—
115C2×D8×C37—21no—
116C2×D8×C37—21no—
117C2×M16×C37—21no—
118C2×M16×C37—22no—
119C2×M16×C37—41no—
120C2×M16×C37C2311yescharacteristic
121C2×M16×C37C2311yescharacteristic
122C2×M16×C37C2311yescharacteristic
123C2×M16×C37C2311yescharacteristic
124C22×C8×C37—21no—
125#127×C37—22no—
126#127×C37—21no—
127#127×C37—22no—
128#127×C37—41no—
129#124×C37—22no—
130#124×C37—21no—
131#123×C37—22no—
132#123×C37—21no—
133C22⋊Q8×C37—22no—
134C22⋊Q8×C37—21no—
135C22⋊Q8×C37—21no—
136C22⋊Q8×C37D411yescharacteristic, complemented
137C22⋊Q8×C37D411yescharacteristic, complemented
138#121×C37—22no—
139#121×C37—22no—
140#121×C37—22no—
141#121×C37—22no—
142#121×C37—22no—
143#121×C37—21no—
144#121×C37—21no—
145#121×C37—21no—
146#121×C37—21no—
147#121×C37—21no—
148#121×C37—21no—
149#121×C37—22no—
150#121×C37—21no—
151#121×C37—21no—
152#121×C37—21no—
153#121×C37—21no—
154#121×C37—21no—
155#121×C37—21no—
156#121×C37—48no—
157#121×C37D411yescharacteristic, complemented
158#121×C37D411yescharacteristic, complemented
159#120×C37—22no—
160#120×C37—22no—
161#120×C37—22no—
162#120×C37—21no—
163#120×C37—22no—
164C4×Q8×C37—21no—
165C4×D4×C37—22no—
166C4×D4×C37—22no—
167C4×D4×C37—21no—
168C4×D4×C37—22no—
169C4×D4×C37—21no—
170C4×D4×C37—21no—
171#117×C37—21no—
172#117×C37C2311yescharacteristic
173C2×C4⋊C4×C37—21no—
174C2×C4⋊C4×C37—22no—
175C2×C4⋊C4×C37C2311yescharacteristic
176C2×C4⋊C4×C37C2311yescharacteristic
177C2×C22⋊C4×C37—22no—
178C2×C22⋊C4×C37—22no—
179C2×C22⋊C4×C37—22no—
180C2×C22⋊C4×C37—21no—
181C2×C22⋊C4×C37D412yes—
182C2×C42×C37—22no—
183C2×C42×C37—21no—
184C2×C42×C37—41no—
185C2×C42×C37C2311yescharacteristic
186C2×C42×C37C2311yescharacteristic
187#107×C37—21no—
188#106×C37—21no—
189#104×C37—22no—
190#104×C37—22no—
191#104×C37—22no—
192#104×C37—22no—
193#104×C37—41no—
194#104×C37D414yescomplemented
195#103×C37—21no—
196#103×C37—21no—
197#103×C37—21no—
198#102×C37—21no—
199#102×C37—21no—
200#102×C37—21no—
201#102×C37—21no—
202#102×C37—21no—
203#100×C37—22no—
204#100×C37—41no—
205C22⋊C8×C37—21no—
206C22⋊C8×C37—21no—
207C24×C37—22no—
208C24×C37—21no—
209C24×C37—21no—
210C24×C37C2×D411yescharacteristic
211C24×C37C2×D412yes—
212#41×C37—21no—
213#41×C37—21no—
214#41×C37—22no—
215#41×C37—22no—
216#41×C37—21no—
217#41×C37—21no—
218#41×C37—21no—
219#41×C37—21no—
220#41×C37—21no—
221#41×C37—21no—
222#41×C37—21no—
223#41×C37—21no—
224#41×C37—42no—
225#41×C37—42no—
226#41×C37—41no—
227#41×C37—41no—
228#41×C37—42no—
229#41×C37—42no—
230#41×C37—42no—
231#41×C37—42no—
232#41×C37—42no—
233#41×C37—42no—
234#41×C37C2×D412yes—
235#41×C37#4112yes—
236C2×Q8×C37—21no—
237C2×Q8×C37—22no—
238C2×Q8×C37—41no—
239C2×Q8×C37C2×D411yescharacteristic
240C2×Q8×C37C2×D411yescharacteristic
241C2×Q8×C37C2×D411yescharacteristic
242C2×D4×C37—21no—
243C2×D4×C37—22no—
244C2×D4×C37—22no—
245C2×D4×C37—22no—
246C2×D4×C37—22no—
247C2×D4×C37—21no—
248C2×D4×C37—21no—
249C2×D4×C37—21no—
250C2×D4×C37—21no—
251C2×D4×C37—21no—
252C2×D4×C37—22no—
253C2×D4×C37—22no—
254C2×D4×C37—22no—
255C2×D4×C37—21no—
256C2×D4×C37—22no—
257C2×D4×C37—21no—
258C2×D4×C37—21no—
259C2×D4×C37—21no—
260C2×D4×C37—21no—
261C2×D4×C37—21no—
262C2×D4×C37—21no—
263C2×D4×C37—21no—
264C2×D4×C37—21no—
265C2×D4×C37—21no—
266C2×D4×C37—21no—
267C2×D4×C37—21no—
268C2×D4×C37—21no—
269C2×D4×C37—21no—
270C2×D4×C37—41no—
271C2×D4×C37—42no—
272C2×D4×C37—42no—
273C2×D4×C37—44no—
274C2×D4×C37—44no—
275C2×D4×C37—44no—
276C2×D4×C37—42no—
277C2×D4×C37—42no—
278C2×D4×C37—44no—
279C2×D4×C37—44no—
280C2×D4×C37—42no—
281C2×D4×C37—42no—
282C2×D4×C37—44no—
283C2×D4×C37—44no—
284C2×D4×C37—41no—
285C2×D4×C37—41no—
286C2×D4×C37—84no—
287C2×D4×C37C2×D411yescharacteristic
288C2×D4×C37C2×D411yescharacteristic
289C2×D4×C37C2×D411yescharacteristic
290C22×C4×C37—21no—
291C22×C4×C37—21no—
292C22×C4×C37—21no—
293C22×C4×C37—21no—
294C22×C4×C37—21no—
295C22×C4×C37—21no—
296C22×C4×C37—22no—
297C22×C4×C37—24no—
298C22×C4×C37—21no—
299C22×C4×C37—21no—
300C22×C4×C37—22no—
301C22×C4×C37—21no—
302C22×C4×C37—21no—
303C22×C4×C37—21no—
304C22×C4×C37—21no—
305C22×C4×C37—21no—
306C22×C4×C37—42no—
307C22×C4×C37—42no—
308C22×C4×C37—42no—
309C22×C4×C37—42no—
310C22×C4×C37C2×D411yescharacteristic
311C22×C4×C37C2×D411yescharacteristic
312C22×C4×C37C2×D411yescharacteristic
313C22×C4×C37C2×D411yescharacteristic
314C22×C4×C37C2×D411yescharacteristic
315C22×C4×C37C2×D412yes—
316C22×C4×C37C2411yescharacteristic
317SD16×C37—42no—
318SD16×C37—42no—
319SD16×C37—42no—
320D8×C37—42no—
321D8×C37—42no—
322D8×C37—42no—
323M16×C37—21no—
324M16×C37—21no—
325M16×C37—21no—
326M16×C37—21no—
327M16×C37—21no—
328M16×C37—21no—
329M16×C37—21no—
330M16×C37—42no—
331M16×C37C2×D412yescomplemented
332C2×C8×C37—21no—
333C2×C8×C37—21no—
334C2×C8×C37—21no—
335C2×C8×C37—21no—
336C2×C8×C37—42no—
337C4⋊C4×C37—22no—
338C4⋊C4×C37—22no—
339C4⋊C4×C37—21no—
340C4⋊C4×C37—21no—
341C4⋊C4×C37—21no—
342C4⋊C4×C37—21no—
343C4⋊C4×C37—21no—
344C4⋊C4×C37—21no—
345C4⋊C4×C37—44no—
346C4⋊C4×C37C2×D411yescharacteristic
347C4⋊C4×C37C2×D411yescharacteristic
348C22⋊C4×C37—22no—
349C22⋊C4×C37—22no—
350C22⋊C4×C37—22no—
351C22⋊C4×C37—22no—
352C22⋊C4×C37—22no—
353C22⋊C4×C37—21no—
354C22⋊C4×C37—21no—
355C22⋊C4×C37—21no—
356C22⋊C4×C37—21no—
357C22⋊C4×C37—22no—
358C22⋊C4×C37—22no—
359C22⋊C4×C37—21no—
360C22⋊C4×C37—44no—
361C22⋊C4×C37—44no—
362C22⋊C4×C37—41no—
363C22⋊C4×C37—41no—
364C42×C37—22no—
365C42×C37—21no—
366C42×C37—21no—
367C42×C37—21no—
368C42×C37—21no—
369C42×C37—42no—
370C42×C37C2×D412yescomplemented
371C23×C37—21no—
372C23×C37—21no—
373C23×C37—21no—
374C23×C37—22no—
375C23×C37—22no—
376C23×C37—21no—
377C23×C37—21no—
378C23×C37—22no—
379C23×C37—22no—
380C23×C37—41no—
381C23×C37—42no—
382C23×C37—44no—
383C23×C37—42no—
384C23×C37—42no—
385C23×C37—42no—
386C23×C37—42no—
387C23×C37—42no—
388C23×C37—41no—
389C23×C37—41no—
390C23×C37—41no—
391C23×C37—81no—
392C23×C37—82no—
393C23×C37—82no—
394C23×C37#12011yescharacteristic
395C23×C37#12011yescharacteristic
396C23×C37C22×D411yescharacteristic
397Q8×C37—21no—
398Q8×C37—21no—
399Q8×C37—21no—
400Q8×C37—21no—
401Q8×C37—21no—
402Q8×C37—42no—
403Q8×C37#12112yescomplemented
404D4×C37—22no—
405D4×C37—22no—
406D4×C37—21no—
407D4×C37—21no—
408D4×C37—21no—
409D4×C37—21no—
410D4×C37—21no—
411D4×C37—42no—
412D4×C37—42no—
413D4×C37—44no—
414D4×C37—42no—
415D4×C37—44no—
416D4×C37—41no—
417D4×C37—41no—
418D4×C37—41no—
419D4×C37—41no—
420D4×C37—44no—
421D4×C37—42no—
422D4×C37—41no—
423D4×C37—41no—
424D4×C37—41no—
425D4×C37—41no—
426D4×C37—41no—
427D4×C37—41no—
428D4×C37—41no—
429D4×C37—41no—
430D4×C37—88no—
431D4×C37—81no—
432D4×C37—82no—
433D4×C37—82no—
434D4×C37—82no—
435D4×C37—82no—
436D4×C37—82no—
437D4×C37—82no—
438D4×C37#12112yescomplemented
439C2×C4×C37—22no—
440C2×C4×C37—22no—
441C2×C4×C37—21no—
442C2×C4×C37—22no—
443C2×C4×C37—21no—
444C2×C4×C37—21no—
445C2×C4×C37—21no—
446C2×C4×C37—21no—
447C2×C4×C37—21no—
448C2×C4×C37—21no—
449C2×C4×C37—21no—
450C2×C4×C37—21no—
451C2×C4×C37—22no—
452C2×C4×C37—21no—
453C2×C4×C37—21no—
454C2×C4×C37—22no—
455C2×C4×C37—22no—
456C2×C4×C37—21no—
457C2×C4×C37—22no—
458C2×C4×C37—21no—
459C2×C4×C37—21no—
460C2×C4×C37—21no—
461C2×C4×C37—42no—
462C2×C4×C37—42no—
463C2×C4×C37—42no—
464C2×C4×C37—48no—
465C2×C4×C37—44no—
466C2×C4×C37—41no—
467C2×C4×C37—41no—
468C2×C4×C37—41no—
469C2×C4×C37—41no—
470C2×C4×C37—41no—
471C2×C4×C37—41no—
472C2×C4×C37—42no—
473C2×C4×C37—42no—
474C2×C4×C37—41no—
475C2×C4×C37—82no—
476C2×C4×C37#12011yescharacteristic
477C2×C4×C37#12011yescharacteristic
478C2×C4×C37C22×D411yescharacteristic
479C2×C4×C37C22×D411yescharacteristic
480C2×C4×C37C22×D411yescharacteristic
481C2×C4×C37C2×#4111yescharacteristic
482C2×C4×C37H(5,𝔽2)11yescharacteristic
483C2×C4×C37H(5,𝔽2)11yescharacteristic
484C8×C37—22no—
485C8×C37—41no—
486C8×C37—41no—
487C8×C37—41no—
488#24464C3711yesmaximal, characteristic, direct product factor, Sylow
489C22×C37—21no—
490C22×C37—21no—
491C22×C37—21no—
492C22×C37—21no—
493C22×C37—21no—
494C22×C37—22no—
495C22×C37—21no—
496C22×C37—21no—
497C22×C37—42no—
498C22×C37—42no—
499C22×C37—41no—
500C22×C37—41no—
501C22×C37—41no—
502C22×C37—41no—
503C22×C37—42no—
504C22×C37—42no—
505C22×C37—41no—
506C22×C37—41no—
507C22×C37—41no—
508C22×C37—42no—
509C22×C37—41no—
510C22×C37—84no—
511C22×C37—82no—
512C22×C37—82no—
513C22×C37—82no—
514C22×C37—82no—
515C22×C37—81no—
516C22×C37—81no—
517C22×C37—81no—
518C22×C37—164no—
519C22×C37#45312yescomplemented
520C22×C37C2×#12011yescharacteristic
521C22×C37D4211yescharacteristic
522C22×C37#54611yescharacteristic
523C4×C37—24no—
524C4×C37—21no—
525C4×C37—21no—
526C4×C37—22no—
527C4×C37—42no—
528C4×C37—41no—
529C4×C37—41no—
530C4×C37—42no—
531C4×C37—41no—
532C4×C37—41no—
533C4×C37—81no—
534C4×C37C2×#12111yescharacteristic
535C4×C37#53411yescharacteristic
536C4×C37D4211yescharacteristic
537C4×C37#54611yescharacteristic
538#3488C2×C3711yescharacteristic, complemented
539#3055C2×C3711yescharacteristic, complemented
540C2×#453C2×C3711yescharacteristic, complemented
541#3006C2×C3711yescharacteristic, complemented
542C22×#104C2×C3711yescharacteristic, complemented
543#2856C2×C3711yescharacteristic, complemented
544#2039C2×C3711yescharacteristic, complemented
545#2037C2×C3711yescharacteristic, complemented
546#2006C2×C3711yescharacteristic, complemented
547#2002C2×C3711yescharacteristic, complemented
548#1900C2×C3711yescharacteristic, complemented
549#1896C2×C3711yescharacteristic, complemented
550#1883C2×C3711yescharacteristic, complemented
551#1859C2×C3711yescharacteristic, complemented
552#1792C2×C3711yescharacteristic, complemented
553C2×C37—21no—
554C2×C37—21no—
555C2×C37—22no—
556C2×C37—41no—
557C2×C37—42no—
558C2×C37—81no—
559C2×C37—82no—
560C2×C37—81no—
561C2×C37—161no—
562C2×C37#241011yescharacteristic
563C2×C37C2×#45311yescharacteristic
564C2×C37#301811yescharacteristic
565C2×H(5,𝔽2)C22×C3711yescharacteristic
566C22×#41C22×C3711yescharacteristic
567C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
568C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
569C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
570C22×M16C22×C3711yescharacteristic, complemented
571#550—21no—
572#548—21no—
573#546—21no—
574#546—22no—
575D42—22no—
576D42—21no—
577#537—21no—
578#537C22×C3711yescharacteristic
579#535—21no—
580#535C22×C3711yescharacteristic
581C2×#127C22×C3711yescharacteristic, complemented
582#525—21no—
583#525C22×C3711yescharacteristic
584C2×#121—21no—
585C2×#121—22no—
586C2×#121C22×C3711yescharacteristic
587C2×#121C22×C3711yescharacteristic, complemented
588#520C22×C3711yescharacteristic
589C22×C42C22×C3711yescharacteristic, complemented
590#469—21no—
591#468—21no—
592#466—21no—
593#465—21no—
594#453—24no—
595#449—21no—
596#449—21no—
597#448—21no—
598#447—21no—
599#428C22×C3711yescharacteristic, complemented
600C2×#104—24no—
601C2×#104C22×C3711yescharacteristic
602C2×#104C22×C3711yescharacteristic
603C2×#104C22×C3711yescharacteristic, complemented
604C2×#104C22×C3711yescharacteristic, complemented
605C2×#104C22×C3711yescharacteristic, complemented
606C2×#104C22×C3711yescharacteristic, complemented
607#418C22×C3711yescharacteristic, complemented
608#417C22×C3711yescharacteristic
609#417C22×C3711yescharacteristic, complemented
610#417C22×C3711yescharacteristic, complemented
611C2×#100C22×C3711yescharacteristic, complemented
612C2×#100C22×C3711yescharacteristic, complemented
613#407C22×C3711yescharacteristic, complemented
614#390—22no—
615#390C22×C3711yescharacteristic, complemented
616#390C22×C3711yescharacteristic, complemented
617#384C22×C3711yescharacteristic, complemented
618#343C22×C3711yescharacteristic, complemented
619#343C22×C3711yescharacteristic, complemented
620#339C22×C3711yescharacteristic, complemented
621#339C22×C3711yescharacteristic, complemented
622C37#2446411yescharacteristic, direct product factor, Sylow
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C3711yescharacteristic, complemented
636C2×#41D4×C3711yescharacteristic, complemented
637C2×#41C23×C3711yescharacteristic
638C2×#41C23×C3711yescharacteristic
639C2×#41C23×C3711yescharacteristic
640C22×Q8D4×C3711yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C3712yes—
649C22×D4D4×C3711yescharacteristic, complemented
650C22×D4C23×C3711yescharacteristic
651C22×D4C23×C3711yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C3711yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C3711yescharacteristic
671C2×M16C23×C3711yescharacteristic
672C2×M16C23×C3711yescharacteristic
673C2×M16C23×C3711yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C3711yescharacteristic, complemented
687C22⋊Q8D4×C3711yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C3711yescharacteristic, complemented
708#121D4×C3711yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C3711yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C3711yescharacteristic
726C2×C4⋊C4C23×C3711yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C3712yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C3711yescharacteristic
736C2×C42C23×C3711yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C3714yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C3711yescharacteristic
761C24C2×D4×C3712yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C3712yes—
785#41#41×C3712yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C3711yescharacteristic
790C2×Q8C2×D4×C3711yescharacteristic
791C2×Q8C2×D4×C3711yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C3711yescharacteristic
838C2×D4C2×D4×C3711yescharacteristic
839C2×D4C2×D4×C3711yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C3711yescharacteristic
861C22×C4C2×D4×C3711yescharacteristic
862C22×C4C2×D4×C3711yescharacteristic
863C22×C4C2×D4×C3711yescharacteristic
864C22×C4C2×D4×C3711yescharacteristic
865C22×C4C2×D4×C3712yes—
866C22×C4C24×C3711yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C3712yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C3711yescharacteristic
897C4⋊C4C2×D4×C3711yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C3712yescomplemented
921C23—21no—
922C23—21no—
923C23—21no—
924C23—22no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C3711yescharacteristic
945C23#120×C3711yescharacteristic
946C23C22×D4×C3711yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C3712yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—44no—
971D4—42no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—82no—
982D4—81no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C3712yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C3711yescharacteristic
1027C2×C4#120×C3711yescharacteristic
1028C2×C4C22×D4×C3711yescharacteristic
1029C2×C4C22×D4×C3711yescharacteristic
1030C2×C4C22×D4×C3711yescharacteristic
1031C2×C4C2×#41×C3711yescharacteristic
1032C2×C4H(5,𝔽2)×C3711yescharacteristic
1033C2×C4H(5,𝔽2)×C3711yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C37×#45312yescomplemented
1069C22C2×#120×C3711yescharacteristic
1070C22D42×C3711yescharacteristic
1071C22C37×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C3711yescharacteristic
1084C4C37×#53411yescharacteristic
1085C4D42×C3711yescharacteristic
1086C4C37×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C37×#241011yescharacteristic
1097C2C2×C37×#45311yescharacteristic
1098C2C37×#301811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3488C2semidirect
2. C37×#3055C2semidirect
3. C2×C37×#453C2semidirect
4. C37×#3006C2semidirect
5. C22×#104×C37C2semidirect
6. C37×#2856C2semidirect
7. C37×#2039C2semidirect
8. C37×#2037C2semidirect
9. C37×#2006C2semidirect
10. C37×#2002C2semidirect
11. C37×#1900C2semidirect
12. C37×#1896C2semidirect
13. C37×#1883C2semidirect
14. C37×#1859C2semidirect
15. C37×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C37C22semidirect
20. C2×AGL(1,ℤ/8)×C37C22semidirect
21. C22×M16×C37C22semidirect
32. C2×#127×C37C22semidirect
38. C2×#121×C37C22semidirect
40. C22×C42×C37C22semidirect
50. C37×#428C22semidirect
54. C2×#104×C37C22semidirect
55. C2×#104×C37C22semidirect
56. C2×#104×C37C22semidirect
57. C2×#104×C37C22semidirect
58. C37×#418C22semidirect
60. C37×#417C22semidirect
61. C37×#417C22semidirect
62. C2×#100×C37C22semidirect
63. C2×#100×C37C22semidirect
64. C37×#407C22semidirect
66. C37×#390C22semidirect
67. C37×#390C22semidirect
68. C37×#384C22semidirect
69. C37×#343C22semidirect
70. C37×#343C22semidirect
71. C37×#339C22semidirect
72. C37×#339C22semidirect
85. C2×#41×C37D4semidirect
86. C2×#41×C37D4semidirect
90. C22×Q8×C37D4semidirect
99. C22×D4×C37D4semidirect
136. C22⋊Q8×C37D4semidirect
137. C22⋊Q8×C37D4semidirect
157. #121×C37D4semidirect
158. #121×C37D4semidirect
194. #104×C37D4semidirect
331. M16×C37C2×D4semidirect
370. C42×C37C2×D4semidirect
403. Q8×C37#121semidirect
438. D4×C37#121semidirect
488. #24464C37direct (N × H)
519. C22×C37#453semidirect
538. #3488C2×C37semidirect
539. #3055C2×C37semidirect
540. C2×#453C2×C37semidirect
541. #3006C2×C37semidirect
542. C22×#104C2×C37semidirect
543. #2856C2×C37semidirect
544. #2039C2×C37semidirect
545. #2037C2×C37semidirect
546. #2006C2×C37semidirect
547. #2002C2×C37semidirect
548. #1900C2×C37semidirect
549. #1896C2×C37semidirect
550. #1883C2×C37semidirect
551. #1859C2×C37semidirect
552. #1792C2×C37semidirect
568. C2×AGL(1,ℤ/8)C22×C37semidirect
569. C2×AGL(1,ℤ/8)C22×C37semidirect
570. C22×M16C22×C37semidirect
581. C2×#127C22×C37semidirect
587. C2×#121C22×C37semidirect
589. C22×C42C22×C37semidirect
599. #428C22×C37semidirect
603. C2×#104C22×C37semidirect
604. C2×#104C22×C37semidirect
605. C2×#104C22×C37semidirect
606. C2×#104C22×C37semidirect
607. #418C22×C37semidirect
609. #417C22×C37semidirect
610. #417C22×C37semidirect
611. C2×#100C22×C37semidirect
612. C2×#100C22×C37semidirect
613. #407C22×C37semidirect
615. #390C22×C37semidirect
616. #390C22×C37semidirect
617. #384C22×C37semidirect
618. #343C22×C37semidirect
619. #343C22×C37semidirect
620. #339C22×C37semidirect
621. #339C22×C37semidirect
622. C37#24464direct (N × H)
635. C2×#41D4×C37semidirect
636. C2×#41D4×C37semidirect
640. C22×Q8D4×C37semidirect
649. C22×D4D4×C37semidirect
686. C22⋊Q8D4×C37semidirect
687. C22⋊Q8D4×C37semidirect
707. #121D4×C37semidirect
708. #121D4×C37semidirect
744. #104D4×C37semidirect
881. M16C2×D4×C37semidirect
920. C42C2×D4×C37semidirect
953. Q8#121×C37semidirect
988. D4#121×C37semidirect
1068. C22C37×#453semidirect

Maximal subgroups

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

subgroupindex
C37×#34882
C37×#30552
C2×C37×#4532
C37×#30062
C22×#104×C372
C37×#28562
C37×#20392
C37×#20372
C37×#20062
C37×#20022
C37×#19002
C37×#18962
C37×#18832
C37×#18592
C37×#17922
#2446437