Finite Group Databasebeta

← C37×#22045 #22643298

Subgroups — C37×#22045 #22643298

Order 9472.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#449C211yesmaximal, characteristic
2C4×#121×C37C211yesmaximal, characteristic, complemented
3C37×#2297C211yesmaximal, characteristic, complemented
4C37×#1970C211yesmaximal, characteristic, complemented
5C37×#1968C211yesmaximal, characteristic, complemented
6C37×#1934C211yesmaximal, characteristic, complemented
7C37×#1933C211yesmaximal, characteristic, complemented
8C37×#1928C211yesmaximal, characteristic, complemented
9C37×#1926C211yesmaximal, characteristic, complemented
10C37×#1879C211yesmaximal, characteristic, complemented
11C37×#1877C211yesmaximal, characteristic, complemented
12C37×#1875C211yesmaximal, characteristic, complemented
13C37×#1854C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C37C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×C4×D4×C37—21no—
21C2×C4×D4×C37C2211yescharacteristic
22C2×#117×C37C2211yescharacteristic
23C22×C42×C37C2211yescharacteristic
24C37×#449C418yescomplemented
25C2×#107×C37C2211yescharacteristic
26C2×#106×C37C2211yescharacteristic
27C2×#103×C37C2211yescharacteristic
28C2×#103×C37C2211yescharacteristic
29C2×#103×C37C2211yescharacteristic
30C2×#102×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×C22⋊C8×C37C2211yescharacteristic
36C2×C22⋊C8×C37C2211yescharacteristic
37C2×C4×C8×C37C2211yescharacteristic
38C2×C4×C8×C37C2211yescharacteristic
39C37×#391C2211yescharacteristic
40C37×#391C2211yescharacteristic
41C37×#390C2211yescharacteristic
42C37×#390C2211yescharacteristic
43C37×#390C2211yescharacteristic
44C37×#389C2211yescharacteristic
45C37×#388—21no—
46C37×#386—21no—
47C37×#386—21no—
48C37×#386—21no—
49C37×#380C2211yescharacteristic
50C4×C4⋊C4×C37C2211yescharacteristic
51C4×C22⋊C4×C37—21no—
52C4×C22⋊C4×C37—21no—
53C4×C22⋊C4×C37—21no—
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C2×#41×C37—22no—
61C2×#41×C37—41no—
62C2×#41×C37—41no—
63C2×#41×C37—41no—
64C2×#41×C37—41no—
65C2×#41×C37C2×C414yescomplemented
66C22×Q8×C37C2311yescharacteristic
67C22×D4×C37—21no—
68C22×D4×C37—21no—
69C22×D4×C37C2311yescharacteristic
70C22×D4×C37C2311yescharacteristic
71C23×C4×C37—21no—
72C23×C4×C37—21no—
73C23×C4×C37D411yescharacteristic
74C23×C4×C37D411yescharacteristic
75C23×C4×C37C2311yescharacteristic
76C2×SD16×C37—41no—
77C2×SD16×C37—41no—
78C2×SD16×C37C2×C414yescomplemented
79C2×D8×C37—41no—
80C2×D8×C37—41no—
81C2×D8×C37C2×C414yescomplemented
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85C22×C8×C37C2311yescharacteristic
86#121×C37—22no—
87#121×C37C2×C414yes—
88C4×D4×C37—41no—
89C4×D4×C37—41no—
90C4×D4×C37—44no—
91#117×C37—41no—
92#117×C37—41no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37C2311yescharacteristic
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C22⋊C4×C37—21no—
100C2×C22⋊C4×C37—21no—
101C2×C22⋊C4×C37—21no—
102C2×C22⋊C4×C37—21no—
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37—21no—
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—21no—
109C2×C42×C37—21no—
110C2×C42×C37—21no—
111C2×C42×C37—41no—
112C2×C42×C37—41no—
113C2×C42×C37D411yescharacteristic
114C2×C42×C37D411yescharacteristic
115C2×C42×C37C2311yescharacteristic
116C2×C42×C37C2311yescharacteristic
117#107×C37—41no—
118#106×C37—41no—
119#103×C37—41no—
120#103×C37—41no—
121#103×C37C2×C414yescomplemented
122#102×C37—41no—
123#102×C37—41no—
124#102×C37—41no—
125#102×C37—41no—
126#102×C37C2×C414yescomplemented
127C22⋊C8×C37—22no—
128C22⋊C8×C37C2×C414yescomplemented
129C4×C8×C37—41no—
130C4×C8×C37—41no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138C24×C37—21no—
139C24×C37—21no—
140C24×C37C2×D411yescharacteristic
141#41×C37—44no—
142#41×C37—44no—
143#41×C37—44no—
144#41×C37—44no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37C22×C412yes—
151C2×D4×C37—24no—
152C2×D4×C37—24no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—42no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—42no—
167C2×D4×C37C22×C412yes—
168C2×D4×C37C22×C412yes—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—24no—
176C22×C4×C37—22no—
177C22×C4×C37—22no—
178C22×C4×C37—22no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—41no—
184C22×C4×C37—41no—
185C22×C4×C37—41no—
186C22×C4×C37—42no—
187C22×C4×C37—42no—
188C22×C4×C37—42no—
189C22×C4×C37—42no—
190C22×C4×C37—42no—
191C22×C4×C37C22×C412yes—
192C22×C4×C37C2×D411yescharacteristic
193C22×C4×C37C2×D411yescharacteristic
194C22×C4×C37C2×D411yescharacteristic
195C22×C4×C37C2×D411yescharacteristic
196C22×C4×C37C2×D411yescharacteristic
197C22×C4×C37#4112yes—
198C22×C4×C37C2411yescharacteristic
199SD16×C37—44no—
200D8×C37—44no—
201C2×C8×C37—21no—
202C2×C8×C37—21no—
203C2×C8×C37—21no—
204C2×C8×C37—21no—
205C2×C8×C37—21no—
206C2×C8×C37—21no—
207C2×C8×C37—21no—
208C2×C8×C37—21no—
209C2×C8×C37—21no—
210C2×C8×C37—21no—
211C2×C8×C37C22×C412yes—
212C2×C8×C37C22×C412yes—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—42no—
223C4⋊C4×C37C22×C412yes—
224C22⋊C4×C37—24no—
225C22⋊C4×C37—42no—
226C22⋊C4×C37—42no—
227C22⋊C4×C37—42no—
228C22⋊C4×C37—42no—
229C22⋊C4×C37—42no—
230C22⋊C4×C37—42no—
231C22⋊C4×C37—42no—
232C22⋊C4×C37—42no—
233C22⋊C4×C37—42no—
234C42×C37—21no—
235C42×C37—21no—
236C42×C37—21no—
237C42×C37—21no—
238C42×C37—41no—
239C42×C37—41no—
240C42×C37—42no—
241C42×C37—42no—
242C23×C37—21no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—21no—
247C23×C37—21no—
248C23×C37—22no—
249C23×C37—22no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37—41no—
254C23×C37—41no—
255C23×C37—41no—
256C23×C37—41no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—41no—
260C23×C37—41no—
261C23×C37—41no—
262C23×C37C4×D412yes—
263C23×C37C22×D411yescharacteristic
264Q8×C37—22no—
265Q8×C37—22no—
266Q8×C37—41no—
267Q8×C37—41no—
268D4×C37—22no—
269D4×C37—22no—
270D4×C37—22no—
271D4×C37—22no—
272D4×C37—48no—
273D4×C37—48no—
274D4×C37—41no—
275D4×C37—41no—
276D4×C37—41no—
277D4×C37—41no—
278C2×C4×C37—21no—
279C2×C4×C37—21no—
280C2×C4×C37—21no—
281C2×C4×C37—21no—
282C2×C4×C37—21no—
283C2×C4×C37—21no—
284C2×C4×C37—21no—
285C2×C4×C37—21no—
286C2×C4×C37—22no—
287C2×C4×C37—22no—
288C2×C4×C37—22no—
289C2×C4×C37—22no—
290C2×C4×C37—22no—
291C2×C4×C37—22no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—44no—
296C2×C4×C37—44no—
297C2×C4×C37—48no—
298C2×C4×C37—41no—
299C2×C4×C37—41no—
300C2×C4×C37—41no—
301C2×C4×C37—41no—
302C2×C4×C37—41no—
303C2×C4×C37—41no—
304C2×C4×C37—41no—
305C2×C4×C37—41no—
306C2×C4×C37—41no—
307C2×C4×C37—41no—
308C2×C4×C37—41no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—84no—
315C2×C4×C37C4×D412yes—
316C2×C4×C37#13512yes—
317C2×C4×C37#13512yes—
318C2×C4×C37AGL(1,ℤ/8)12yes—
319C2×C4×C37C23×C411yescharacteristic
320C2×C4×C37C2×#4111yescharacteristic
321C2×C4×C37H(5,𝔽2)11yescharacteristic
322C2×C4×C37H(5,𝔽2)11yescharacteristic
323C2×C4×C37H(5,𝔽2)11yescharacteristic
324C2×C4×C37H(5,𝔽2)11yescharacteristic
325C8×C37—22no—
326C8×C37—22no—
327C8×C37—41no—
328C8×C37—41no—
329#22045C3711yesmaximal, characteristic, direct product factor, Sylow
330C22×C37—22no—
331C22×C37—22no—
332C22×C37—22no—
333C22×C37—41no—
334C22×C37—41no—
335C22×C37—41no—
336C22×C37—41no—
337C22×C37—42no—
338C22×C37—42no—
339C22×C37—42no—
340C22×C37—42no—
341C22×C37—42no—
342C22×C37—42no—
343C22×C37—81no—
344C22×C37—81no—
345C22×C37—81no—
346C22×C37—81no—
347C22×C37—81no—
348C22×C37—81no—
349C22×C37—81no—
350C22×C37—81no—
351C22×C37C2×C4×D411yescharacteristic
352C22×C37#53411yescharacteristic
353C22×C37#53511yescharacteristic
354C22×C37C2×#13511yescharacteristic
355C22×C37C2×#13511yescharacteristic
356C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C37#57511yescharacteristic
358C4×C37—22no—
359C4×C37—22no—
360C4×C37—22no—
361C4×C37—22no—
362C4×C37—42no—
363C4×C37—41no—
364C4×C37—42no—
365C4×C37—81no—
366C4×C37—81no—
367C4×C37—81no—
368C4×C37—81no—
369C4×C37#51811yescharacteristic
370C4×C37#51811yescharacteristic
371C4×C37#53811yescharacteristic
372C4×C37#53811yescharacteristic
373C2×#449C2×C3711yescharacteristic
374C4×#121C2×C3711yescharacteristic, complemented
375#2297C2×C3711yescharacteristic, complemented
376#1970C2×C3711yescharacteristic, complemented
377#1968C2×C3711yescharacteristic, complemented
378#1934C2×C3711yescharacteristic, complemented
379#1933C2×C3711yescharacteristic, complemented
380#1928C2×C3711yescharacteristic, complemented
381#1926C2×C3711yescharacteristic, complemented
382#1879C2×C3711yescharacteristic, complemented
383#1877C2×C3711yescharacteristic, complemented
384#1875C2×C3711yescharacteristic, complemented
385#1854C2×C3711yescharacteristic, complemented
386#1788C2×C3711yescharacteristic, complemented
387C4×C22⋊C8C2×C3711yescharacteristic, complemented
388C2×C37—42no—
389C2×C37—82no—
390C2×C37—82no—
391C2×C37#232111yescharacteristic
392C2×C37C4×#13511yescharacteristic
393C2×C37C4×AGL(1,ℤ/8)11yescharacteristic
394C2×C37#318811yescharacteristic
395C2×C37#319111yescharacteristic
396C2×C37#320711yescharacteristic
397C2×C37#321211yescharacteristic
398C22×#41C22×C3711yescharacteristic
399C22×SD16C22×C3711yescharacteristic
400C22×D8C22×C3711yescharacteristic
401C2×#121C22×C3711yescharacteristic
402C2×C4×D4—21no—
403C2×C4×D4C22×C3711yescharacteristic
404C2×#117C22×C3711yescharacteristic
405C22×C42C22×C3711yescharacteristic
406#449C4×C3718yescomplemented
407C2×#107C22×C3711yescharacteristic
408C2×#106C22×C3711yescharacteristic
409C2×#103C22×C3711yescharacteristic
410C2×#103C22×C3711yescharacteristic
411C2×#103C22×C3711yescharacteristic
412C2×#102C22×C3711yescharacteristic
413C2×#102C22×C3711yescharacteristic
414C2×#102C22×C3711yescharacteristic
415C2×#102C22×C3711yescharacteristic
416C2×#102C22×C3711yescharacteristic
417C2×C22⋊C8C22×C3711yescharacteristic
418C2×C22⋊C8C22×C3711yescharacteristic
419C2×C4×C8C22×C3711yescharacteristic
420C2×C4×C8C22×C3711yescharacteristic
421#391C22×C3711yescharacteristic
422#391C22×C3711yescharacteristic
423#390C22×C3711yescharacteristic
424#390C22×C3711yescharacteristic
425#390C22×C3711yescharacteristic
426#389C22×C3711yescharacteristic
427#388—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#380C22×C3711yescharacteristic
432C4×C4⋊C4C22×C3711yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436#340C22×C3711yescharacteristic
437#340C22×C3711yescharacteristic
438#340C22×C3711yescharacteristic
439#340C22×C3711yescharacteristic
440#336C22×C3711yescharacteristic
441#336C22×C3711yescharacteristic
442C37#2204511yescharacteristic, direct product factor, Sylow
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41C2×C4×C3714yescomplemented
449C22×Q8C23×C3711yescharacteristic
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C23×C3711yescharacteristic
453C22×D4C23×C3711yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4D4×C3711yescharacteristic
457C23×C4D4×C3711yescharacteristic
458C23×C4C23×C3711yescharacteristic
459C2×SD16—41no—
460C2×SD16—41no—
461C2×SD16C2×C4×C3714yescomplemented
462C2×D8—41no—
463C2×D8—41no—
464C2×D8C2×C4×C3714yescomplemented
465C22×C8C23×C3711yescharacteristic
466C22×C8C23×C3711yescharacteristic
467C22×C8C23×C3711yescharacteristic
468C22×C8C23×C3711yescharacteristic
469#121—22no—
470#121C2×C4×C3714yes—
471C4×D4—41no—
472C4×D4—41no—
473C4×D4—44no—
474#117—41no—
475#117—41no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4C23×C3711yescharacteristic
478C2×C4⋊C4C23×C3711yescharacteristic
479C2×C4⋊C4C23×C3711yescharacteristic
480C2×C4⋊C4C23×C3711yescharacteristic
481C2×C4⋊C4C23×C3711yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—41no—
495C2×C42—41no—
496C2×C42D4×C3711yescharacteristic
497C2×C42D4×C3711yescharacteristic
498C2×C42C23×C3711yescharacteristic
499C2×C42C23×C3711yescharacteristic
500#107—41no—
501#106—41no—
502#103—41no—
503#103—41no—
504#103C2×C4×C3714yescomplemented
505#102—41no—
506#102—41no—
507#102—41no—
508#102—41no—
509#102C2×C4×C3714yescomplemented
510C22⋊C8—22no—
511C22⋊C8C2×C4×C3714yescomplemented
512C4×C8—41no—
513C4×C8—41no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521C24—21no—
522C24—21no—
523C24C2×D4×C3711yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C22×C4×C3712yes—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4C22×C4×C3712yes—
551C2×D4C22×C4×C3712yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4C22×C4×C3712yes—
575C22×C4C2×D4×C3711yescharacteristic
576C22×C4C2×D4×C3711yescharacteristic
577C22×C4C2×D4×C3711yescharacteristic
578C22×C4C2×D4×C3711yescharacteristic
579C22×C4C2×D4×C3711yescharacteristic
580C22×C4#41×C3712yes—
581C22×C4C24×C3711yescharacteristic
582SD16—44no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8C22×C4×C3712yes—
595C2×C8C22×C4×C3712yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4C22×C4×C3712yes—
607C22⋊C4—24no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—42no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C4×D4×C3712yes—
646C23C22×D4×C3711yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—44no—
679C2×C4—48no—
680C2×C4—44no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4C4×D4×C3712yes—
699C2×C4#135×C3712yes—
700C2×C4#135×C3712yes—
701C2×C4AGL(1,ℤ/8)×C3712yes—
702C2×C4C23×C4×C3711yescharacteristic
703C2×C4C2×#41×C3711yescharacteristic
704C2×C4H(5,𝔽2)×C3711yescharacteristic
705C2×C4H(5,𝔽2)×C3711yescharacteristic
706C2×C4H(5,𝔽2)×C3711yescharacteristic
707C2×C4H(5,𝔽2)×C3711yescharacteristic
708C8—22no—
709C8—22no—
710C8—41no—
711C8—41no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×D4×C3711yescharacteristic
734C22C37×#53411yescharacteristic
735C22C37×#53511yescharacteristic
736C22C2×#135×C3711yescharacteristic
737C22C2×#135×C3711yescharacteristic
738C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
739C22C37×#57511yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4C37×#51811yescharacteristic
752C4C37×#51811yescharacteristic
753C4C37×#53811yescharacteristic
754C4C37×#53811yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2C37×#232111yescharacteristic
759C2C4×#135×C3711yescharacteristic
760C2C4×AGL(1,ℤ/8)×C3711yescharacteristic
761C2C37×#318811yescharacteristic
762C2C37×#319111yescharacteristic
763C2C37×#320711yescharacteristic
764C2C37×#321211yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutatorC2×C4C23×C4×C37
Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#121×C37C2semidirect
3. C37×#2297C2semidirect
4. C37×#1970C2semidirect
5. C37×#1968C2semidirect
6. C37×#1934C2semidirect
7. C37×#1933C2semidirect
8. C37×#1928C2semidirect
9. C37×#1926C2semidirect
10. C37×#1879C2semidirect
11. C37×#1877C2semidirect
12. C37×#1875C2semidirect
13. C37×#1854C2semidirect
14. C37×#1788C2semidirect
15. C4×C22⋊C8×C37C2semidirect
24. C37×#449C4semidirect
65. C2×#41×C37C2×C4semidirect
78. C2×SD16×C37C2×C4semidirect
81. C2×D8×C37C2×C4semidirect
121. #103×C37C2×C4semidirect
126. #102×C37C2×C4semidirect
128. C22⋊C8×C37C2×C4semidirect
329. #22045C37direct (N × H)
374. C4×#121C2×C37semidirect
375. #2297C2×C37semidirect
376. #1970C2×C37semidirect
377. #1968C2×C37semidirect
378. #1934C2×C37semidirect
379. #1933C2×C37semidirect
380. #1928C2×C37semidirect
381. #1926C2×C37semidirect
382. #1879C2×C37semidirect
383. #1877C2×C37semidirect
384. #1875C2×C37semidirect
385. #1854C2×C37semidirect
386. #1788C2×C37semidirect
387. C4×C22⋊C8C2×C37semidirect
406. #449C4×C37semidirect
442. C37#22045direct (N × H)
448. C2×#41C2×C4×C37semidirect
461. C2×SD16C2×C4×C37semidirect
464. C2×D8C2×C4×C37semidirect
504. #103C2×C4×C37semidirect
509. #102C2×C4×C37semidirect
511. C22⋊C8C2×C4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4492
C4×#121×C372
C37×#22972
C37×#19702
C37×#19682
C37×#19342
C37×#19332
C37×#19282
C37×#19262
C37×#18792
C37×#18772
C37×#18752
C37×#18542
C37×#17882
C4×C22⋊C8×C372
#2204537