Finite Group Databasebeta

← C37×#24245 #22645498

Subgroups — C37×#24245 #22645498

Order 9472.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#546C211yesmaximal, characteristic, complemented
2C2×C37×#463C211yesmaximal, characteristic, complemented
3C2×C37×#449C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C2×C4×D8×C37C211yesmaximal, characteristic, complemented
6C37×#2535C211yesmaximal, characteristic, complemented
7C37×#2036C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2000C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1958C211yesmaximal, characteristic, complemented
12C37×#1954C211yesmaximal, characteristic, complemented
13C37×#1804C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic, complemented
19C22×D8×C37C2211yescharacteristic
20C22×D8×C37C2211yescharacteristic
21C37×#546—24no—
22C37×#546—24no—
23C2×#124×C37C2211yescharacteristic
24C2×#123×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×#121×C37—21no—
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic, complemented
30C2×#120×C37—21no—
31C2×C4×D4×C37C2211yescharacteristic
32C2×C4×D4×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic, complemented
34C22×C22⋊C4×C37—21no—
35C37×#463—24no—
36C37×#449—24no—
37C37×#447—24no—
38C4×D8×C37—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C2×C4⋊C8×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C2×#102×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic, complemented
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C2×C4×C8×C37C2211yescharacteristic, complemented
56C37×#397—21no—
57C37×#392—21no—
58C37×#386—21no—
59C37×#386—21no—
60C37×#382C2211yescharacteristic, complemented
61C37×#380C2211yescharacteristic
62C37×#380C2211yescharacteristic, complemented
63C37×#340C2211yescharacteristic, complemented
64C37×#340C2211yescharacteristic, complemented
65C25×C37—21no—
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—41no—
71C2×#41×C37—41no—
72C22×Q8×C37C2311yescharacteristic
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—22no—
76C22×D4×C37—22no—
77C22×D4×C37—22no—
78C22×D4×C37—22no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37—41no—
83C22×D4×C37—41no—
84C22×D4×C37D411yescharacteristic
85C22×D4×C37C2311yescharacteristic
86C22×D4×C37C2311yescharacteristic
87C22×D4×C37C2311yescharacteristic
88C23×C4×C37—21no—
89C23×C4×C37—21no—
90C23×C4×C37—21no—
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C2×SD16×C37—22no—
94C2×SD16×C37—22no—
95C2×SD16×C37—41no—
96C2×D8×C37—22no—
97C2×D8×C37—22no—
98C2×D8×C37—22no—
99C2×D8×C37—22no—
100C2×D8×C37—41no—
101C2×D8×C37D414yescomplemented
102C22×C8×C37C2311yescharacteristic
103C22×C8×C37C2311yescharacteristic
104C22×C8×C37C2311yescharacteristic
105C22×C8×C37C2311yescharacteristic
106#124×C37—22no—
107#124×C37D414yescomplemented
108#123×C37—28no—
109C22⋊Q8×C37—22no—
110C22⋊Q8×C37—22no—
111#121×C37—28no—
112#121×C37—22no—
113#121×C37—22no—
114#121×C37—22no—
115#121×C37—22no—
116#121×C37—41no—
117#121×C37—41no—
118#120×C37—28no—
119C4×D4×C37—22no—
120C4×D4×C37—22no—
121C4×D4×C37—22no—
122C4×D4×C37—22no—
123C4×D4×C37—22no—
124C4×D4×C37D414yescomplemented
125C2×C4⋊C4×C37—21no—
126C2×C4⋊C4×C37D411yescharacteristic
127C2×C4⋊C4×C37C2311yescharacteristic
128C2×C4⋊C4×C37C2311yescharacteristic
129C2×C4⋊C4×C37C2311yescharacteristic
130C2×C4⋊C4×C37C2311yescharacteristic
131C2×C22⋊C4×C37—28no—
132C2×C22⋊C4×C37—21no—
133C2×C22⋊C4×C37—21no—
134C2×C22⋊C4×C37—21no—
135C2×C22⋊C4×C37—21no—
136C2×C22⋊C4×C37—21no—
137C2×C22⋊C4×C37—21no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—21no—
140C2×C22⋊C4×C37—21no—
141C2×C22⋊C4×C37—21no—
142C2×C22⋊C4×C37D411yescharacteristic
143C2×C22⋊C4×C37D411yescharacteristic
144C2×C42×C37C2311yescharacteristic
145#107×C37—22no—
146C4⋊C8×C37—22no—
147#103×C37—22no—
148#103×C37—22no—
149#103×C37—41no—
150#102×C37—22no—
151#102×C37—22no—
152#102×C37—22no—
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—41no—
157C22⋊C8×C37—22no—
158C22⋊C8×C37—22no—
159C22⋊C8×C37—41no—
160C22⋊C8×C37—41no—
161C4×C8×C37—22no—
162#95×C37—21no—
163#95×C37—21no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—21no—
167C24×C37—24no—
168C24×C37—21no—
169C24×C37—21no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—42no—
174C24×C37—81no—
175C24×C37—81no—
176C24×C37C2×D411yescharacteristic
177C24×C37C2×D411yescharacteristic
178#41×C37—44no—
179#41×C37—44no—
180#41×C37—44no—
181#41×C37—44no—
182C2×Q8×C37—21no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37C2×D412yes—
188C2×D4×C37—24no—
189C2×D4×C37—24no—
190C2×D4×C37—22no—
191C2×D4×C37—24no—
192C2×D4×C37—22no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—41no—
207C2×D4×C37—42no—
208C2×D4×C37—42no—
209C2×D4×C37—44no—
210C2×D4×C37—44no—
211C2×D4×C37—44no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—44no—
215C2×D4×C37—42no—
216C2×D4×C37—42no—
217C2×D4×C37—42no—
218C2×D4×C37—42no—
219C2×D4×C37—81no—
220C2×D4×C37—81no—
221C2×D4×C37—81no—
222C2×D4×C37—81no—
223C2×D4×C37C2×D412yes—
224C2×D4×C37C2×D412yes—
225C2×D4×C37C2×D412yes—
226C2×D4×C37C2×D412yes—
227C2×D4×C37#4112yes—
228C22×C4×C37—24no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—21no—
233C22×C4×C37—21no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—21no—
237C22×C4×C37—21no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—24no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—42no—
248C22×C4×C37—42no—
249C22×C4×C37—42no—
250C22×C4×C37—81no—
251C22×C4×C37—81no—
252C22×C4×C37—81no—
253C22×C4×C37—81no—
254C22×C4×C37C2×D411yescharacteristic
255C22×C4×C37C2×D411yescharacteristic
256C22×C4×C37C2×D411yescharacteristic
257C22×C4×C37C2×D411yescharacteristic
258C22×C4×C37C2411yescharacteristic
259SD16×C37—44no—
260D8×C37—28no—
261D8×C37—44no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37—21no—
272C2×C8×C37—21no—
273C2×C8×C37C2×D412yes—
274C4⋊C4×C37—24no—
275C4⋊C4×C37—22no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37C2×D412yes—
284C22⋊C4×C37—24no—
285C22⋊C4×C37—24no—
286C22⋊C4×C37—22no—
287C22⋊C4×C37—24no—
288C22⋊C4×C37—24no—
289C22⋊C4×C37—24no—
290C22⋊C4×C37—22no—
291C22⋊C4×C37—42no—
292C22⋊C4×C37—42no—
293C22⋊C4×C37—42no—
294C22⋊C4×C37—81no—
295C22⋊C4×C37—81no—
296C42×C37C2×D412yes—
297C42×C37C2×D412yes—
298C23×C37—21no—
299C23×C37—22no—
300C23×C37—21no—
301C23×C37—22no—
302C23×C37—21no—
303C23×C37—22no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—22no—
308C23×C37—21no—
309C23×C37—22no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—48no—
317C23×C37—48no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37—41no—
321C23×C37—41no—
322C23×C37—41no—
323C23×C37—41no—
324C23×C37—41no—
325C23×C37—41no—
326C23×C37—41no—
327C23×C37—41no—
328C23×C37—41no—
329C23×C37—41no—
330C23×C37—41no—
331C23×C37—41no—
332C23×C37—41no—
333C23×C37—41no—
334C23×C37—84no—
335C23×C37—84no—
336C23×C37—84no—
337C23×C37—84no—
338C23×C37—84no—
339C23×C37#13512yes—
340C23×C37C22×D411yescharacteristic
341Q8×C37—22no—
342Q8×C37—22no—
343Q8×C37—41no—
344Q8×C37—41no—
345D4×C37—22no—
346D4×C37—22no—
347D4×C37—22no—
348D4×C37—22no—
349D4×C37—22no—
350D4×C37—22no—
351D4×C37—22no—
352D4×C37—44no—
353D4×C37—48no—
354D4×C37—48no—
355D4×C37—41no—
356D4×C37—41no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—84no—
360D4×C37—84no—
361D4×C37—84no—
362D4×C37#12114yes—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
367C2×C4×C37—22no—
368C2×C4×C37—21no—
369C2×C4×C37—22no—
370C2×C4×C37—21no—
371C2×C4×C37—21no—
372C2×C4×C37—21no—
373C2×C4×C37—21no—
374C2×C4×C37—21no—
375C2×C4×C37—48no—
376C2×C4×C37—41no—
377C2×C4×C37—41no—
378C2×C4×C37—41no—
379C2×C4×C37—41no—
380C2×C4×C37—41no—
381C2×C4×C37—41no—
382C2×C4×C37—41no—
383C2×C4×C37—41no—
384C2×C4×C37—41no—
385C2×C4×C37—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—41no—
393C2×C4×C37—41no—
394C2×C4×C37—41no—
395C2×C4×C37—41no—
396C2×C4×C37—41no—
397C2×C4×C37—84no—
398C2×C4×C37—84no—
399C2×C4×C37#12012yes—
400C2×C4×C37#12012yes—
401C2×C4×C37C22×D411yescharacteristic
402C2×C4×C37C22×D411yescharacteristic
403C2×C4×C37C22×D411yescharacteristic
404C2×C4×C37C2×#4111yescharacteristic
405C2×C4×C37H(5,𝔽2)11yescharacteristic
406C2×C4×C37H(5,𝔽2)11yescharacteristic
407C8×C37—22no—
408C8×C37—41no—
409C8×C37—41no—
410C8×C37—41no—
411#24245C3711yesmaximal, characteristic, direct product factor, Sylow
412C22×C37—24no—
413C22×C37—22no—
414C22×C37—22no—
415C22×C37—22no—
416C22×C37—41no—
417C22×C37—42no—
418C22×C37—42no—
419C22×C37—41no—
420C22×C37—41no—
421C22×C37—42no—
422C22×C37—42no—
423C22×C37—42no—
424C22×C37—41no—
425C22×C37—42no—
426C22×C37—41no—
427C22×C37—42no—
428C22×C37—42no—
429C22×C37—41no—
430C22×C37—42no—
431C22×C37—41no—
432C22×C37—42no—
433C22×C37—41no—
434C22×C37—42no—
435C22×C37—42no—
436C22×C37—41no—
437C22×C37—41no—
438C22×C37—41no—
439C22×C37—816no—
440C22×C37—81no—
441C22×C37—81no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37C2×#12011yescharacteristic
449C22×C37D4211yescharacteristic
450C22×C37#54611yescharacteristic
451C22×C37C2×#13511yescharacteristic
452C22×C37#57511yescharacteristic
453C22×C37#57611yescharacteristic
454C22×C37#57611yescharacteristic
455C4×C37—22no—
456C4×C37—22no—
457C4×C37—41no—
458C4×C37—41no—
459C4×C37—42no—
460C4×C37—42no—
461C4×C37—81no—
462C4×C37—81no—
463C4×C37—81no—
464C4×C37C2×#12111yescharacteristic
465C4×C37#53511yescharacteristic
466C4×C37D4211yescharacteristic
467C4×C37#54611yescharacteristic
468C2×#546C2×C3711yescharacteristic, complemented
469C2×#463C2×C3711yescharacteristic, complemented
470C2×#449C2×C3711yescharacteristic, complemented
471C2×#447C2×C3711yescharacteristic, complemented
472C2×C4×D8C2×C3711yescharacteristic, complemented
473#2535C2×C3711yescharacteristic, complemented
474#2036C2×C3711yescharacteristic, complemented
475#2033C2×C3711yescharacteristic, complemented
476#2000C2×C3711yescharacteristic, complemented
477#1999C2×C3711yescharacteristic, complemented
478#1958C2×C3711yescharacteristic, complemented
479#1954C2×C3711yescharacteristic, complemented
480#1804C2×C3711yescharacteristic, complemented
481#1788C2×C3711yescharacteristic, complemented
482#1786C2×C3711yescharacteristic, complemented
483C2×C37—42no—
484C2×C37—44no—
485C2×C37—81no—
486C2×C37—82no—
487C2×C37—82no—
488C2×C37#240811yescharacteristic
489C2×C37#300211yescharacteristic
490C2×C37#300811yescharacteristic
491C2×C37#327311yescharacteristic
492C2×C37#328011yescharacteristic
493C2×C37#329711yescharacteristic
494C2×C37#332211yescharacteristic
495C22×#41C22×C3711yescharacteristic
496C23×D4C22×C3711yescharacteristic
497C22×SD16C22×C3711yescharacteristic, complemented
498C22×D8C22×C3711yescharacteristic
499C22×D8C22×C3711yescharacteristic
500#546—24no—
501#546—24no—
502C2×#124C22×C3711yescharacteristic
503C2×#123—21no—
504C2×C22⋊Q8C22×C3711yescharacteristic
505C2×#121—21no—
506C2×#121C22×C3711yescharacteristic
507C2×#121C22×C3711yescharacteristic
508C2×#121C22×C3711yescharacteristic, complemented
509C2×#120—21no—
510C2×C4×D4C22×C3711yescharacteristic
511C2×C4×D4C22×C3711yescharacteristic
512C2×C4×D4C22×C3711yescharacteristic, complemented
513C22×C22⋊C4—21no—
514#463—24no—
515#449—24no—
516#447—24no—
517C4×D8—24no—
518C2×#107C22×C3711yescharacteristic, complemented
519C2×C4⋊C8C22×C3711yescharacteristic, complemented
520C2×#103C22×C3711yescharacteristic, complemented
521C2×#103C22×C3711yescharacteristic, complemented
522C2×#103C22×C3711yescharacteristic, complemented
523C2×#102C22×C3711yescharacteristic
524C2×#102C22×C3711yescharacteristic
525C2×#102C22×C3711yescharacteristic
526C2×#102C22×C3711yescharacteristic
527C2×#102C22×C3711yescharacteristic
528C2×#102C22×C3711yescharacteristic
529C2×#102C22×C3711yescharacteristic, complemented
530C2×C22⋊C8C22×C3711yescharacteristic
531C2×C22⋊C8C22×C3711yescharacteristic
532C2×C22⋊C8C22×C3711yescharacteristic, complemented
533C2×C22⋊C8C22×C3711yescharacteristic, complemented
534C2×C4×C8C22×C3711yescharacteristic, complemented
535#397—21no—
536#392—21no—
537#386—21no—
538#386—21no—
539#382C22×C3711yescharacteristic, complemented
540#380C22×C3711yescharacteristic
541#380C22×C3711yescharacteristic, complemented
542#340C22×C3711yescharacteristic, complemented
543#340C22×C3711yescharacteristic, complemented
544C37#2424511yescharacteristic, direct product factor, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C3711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C3711yescharacteristic
565C22×D4C23×C3711yescharacteristic
566C22×D4C23×C3711yescharacteristic
567C22×D4C23×C3711yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C3711yescharacteristic
572C23×C4C23×C3711yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8D4×C3714yescomplemented
582C22×C8C23×C3711yescharacteristic
583C22×C8C23×C3711yescharacteristic
584C22×C8C23×C3711yescharacteristic
585C22×C8C23×C3711yescharacteristic
586#124—22no—
587#124D4×C3714yescomplemented
588#123—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591#121—28no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#120—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4D4×C3714yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C3711yescharacteristic
607C2×C4⋊C4C23×C3711yescharacteristic
608C2×C4⋊C4C23×C3711yescharacteristic
609C2×C4⋊C4C23×C3711yescharacteristic
610C2×C4⋊C4C23×C3711yescharacteristic
611C2×C22⋊C4—28no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C3711yescharacteristic
623C2×C22⋊C4D4×C3711yescharacteristic
624C2×C42C23×C3711yescharacteristic
625#107—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—41no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—41no—
640C22⋊C8—41no—
641C4×C8—22no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C3711yescharacteristic
657C24C2×D4×C3711yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C3712yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C3712yes—
704C2×D4C2×D4×C3712yes—
705C2×D4C2×D4×C3712yes—
706C2×D4C2×D4×C3712yes—
707C2×D4#41×C3712yes—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4C2×D4×C3711yescharacteristic
735C22×C4C2×D4×C3711yescharacteristic
736C22×C4C2×D4×C3711yescharacteristic
737C22×C4C2×D4×C3711yescharacteristic
738C22×C4C24×C3711yescharacteristic
739SD16—44no—
740D8—28no—
741D8—44no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8C2×D4×C3712yes—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4C2×D4×C3712yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42C2×D4×C3712yes—
777C42C2×D4×C3712yes—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#135×C3712yes—
820C23C22×D4×C3711yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#121×C3714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#120×C3712yes—
880C2×C4#120×C3712yes—
881C2×C4C22×D4×C3711yescharacteristic
882C2×C4C22×D4×C3711yescharacteristic
883C2×C4C22×D4×C3711yescharacteristic
884C2×C4C2×#41×C3711yescharacteristic
885C2×C4H(5,𝔽2)×C3711yescharacteristic
886C2×C4H(5,𝔽2)×C3711yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—42no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C3711yescharacteristic
928C22D42×C3711yescharacteristic
929C22C37×#54611yescharacteristic
930C22C2×#135×C3711yescharacteristic
931C22C37×#57511yescharacteristic
932C22C37×#57611yescharacteristic
933C22C37×#57611yescharacteristic
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×#121×C3711yescharacteristic
944C4C37×#53511yescharacteristic
945C4D42×C3711yescharacteristic
946C4C37×#54611yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2C37×#240811yescharacteristic
953C2C37×#300211yescharacteristic
954C2C37×#300811yescharacteristic
955C2C37×#327311yescharacteristic
956C2C37×#328011yescharacteristic
957C2C37×#329711yescharacteristic
958C2C37×#332211yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#546C2semidirect
2. C2×C37×#463C2semidirect
3. C2×C37×#449C2semidirect
4. C2×C37×#447C2semidirect
5. C2×C4×D8×C37C2semidirect
6. C37×#2535C2semidirect
7. C37×#2036C2semidirect
8. C37×#2033C2semidirect
9. C37×#2000C2semidirect
10. C37×#1999C2semidirect
11. C37×#1958C2semidirect
12. C37×#1954C2semidirect
13. C37×#1804C2semidirect
14. C37×#1788C2semidirect
15. C37×#1786C2semidirect
18. C22×SD16×C37C22semidirect
29. C2×#121×C37C22semidirect
33. C2×C4×D4×C37C22semidirect
39. C2×#107×C37C22semidirect
40. C2×C4⋊C8×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
50. C2×#102×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C2×C22⋊C8×C37C22semidirect
55. C2×C4×C8×C37C22semidirect
60. C37×#382C22semidirect
62. C37×#380C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
101. C2×D8×C37D4semidirect
107. #124×C37D4semidirect
124. C4×D4×C37D4semidirect
411. #24245C37direct (N × H)
468. C2×#546C2×C37semidirect
469. C2×#463C2×C37semidirect
470. C2×#449C2×C37semidirect
471. C2×#447C2×C37semidirect
472. C2×C4×D8C2×C37semidirect
473. #2535C2×C37semidirect
474. #2036C2×C37semidirect
475. #2033C2×C37semidirect
476. #2000C2×C37semidirect
477. #1999C2×C37semidirect
478. #1958C2×C37semidirect
479. #1954C2×C37semidirect
480. #1804C2×C37semidirect
481. #1788C2×C37semidirect
482. #1786C2×C37semidirect
497. C22×SD16C22×C37semidirect
508. C2×#121C22×C37semidirect
512. C2×C4×D4C22×C37semidirect
518. C2×#107C22×C37semidirect
519. C2×C4⋊C8C22×C37semidirect
520. C2×#103C22×C37semidirect
521. C2×#103C22×C37semidirect
522. C2×#103C22×C37semidirect
529. C2×#102C22×C37semidirect
532. C2×C22⋊C8C22×C37semidirect
533. C2×C22⋊C8C22×C37semidirect
534. C2×C4×C8C22×C37semidirect
539. #382C22×C37semidirect
541. #380C22×C37semidirect
542. #340C22×C37semidirect
543. #340C22×C37semidirect
544. C37#24245direct (N × H)
581. C2×D8D4×C37semidirect
587. #124D4×C37semidirect
604. C4×D4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5462
C2×C37×#4632
C2×C37×#4492
C2×C37×#4472
C2×C4×D8×C372
C37×#25352
C37×#20362
C37×#20332
C37×#20002
C37×#19992
C37×#19582
C37×#19542
C37×#18042
C37×#17882
C37×#17862
#2424537