Finite Group Databasebeta

← C37×#24257 #22645510

Subgroups — C37×#24257 #22645510

Order 9472.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 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×C37×#442C211yesmaximal, characteristic, complemented
6C37×#2537C211yesmaximal, characteristic, complemented
7C37×#2035C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#2000C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1959C211yesmaximal, characteristic, complemented
12C37×#1955C211yesmaximal, characteristic, complemented
13C37×#1802C211yesmaximal, 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×C37—21no—
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic, complemented
31C2×#120×C37—21no—
32C2×C4×D4×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic
34C2×C4×D4×C37C2211yescharacteristic, complemented
35C22×C22⋊C4×C37—21no—
36C37×#463—24no—
37C37×#449—24no—
38C37×#447—24no—
39C37×#442—24no—
40C2×#106×C37C2211yescharacteristic, complemented
41C2×C4⋊C8×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#103×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C2×#102×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic
51C2×#102×C37C2211yescharacteristic, complemented
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C2×C22⋊C8×C37C2211yescharacteristic, complemented
56C2×#97×C37C2211yescharacteristic, complemented
57C37×#394—21no—
58C37×#394—21no—
59C37×#384C2211yescharacteristic, complemented
60C37×#380—21no—
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#121×C37—44no—
119#120×C37—28no—
120C4×D4×C37—22no—
121C4×D4×C37—22no—
122C4×D4×C37—22no—
123C4×D4×C37—22no—
124C4×D4×C37—22no—
125C4×D4×C37D414yescomplemented
126C2×C4⋊C4×C37—21no—
127C2×C4⋊C4×C37—21no—
128C2×C4⋊C4×C37—21no—
129C2×C4⋊C4×C37D411yescharacteristic
130C2×C4⋊C4×C37C2311yescharacteristic
131C2×C4⋊C4×C37C2311yescharacteristic
132C2×C4⋊C4×C37C2311yescharacteristic
133C2×C4⋊C4×C37C2311yescharacteristic
134C2×C22⋊C4×C37—28no—
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×C37—21no—
143C2×C22⋊C4×C37—21no—
144C2×C22⋊C4×C37—21no—
145C2×C22⋊C4×C37D411yescharacteristic
146C2×C22⋊C4×C37D411yescharacteristic
147C2×C42×C37C2311yescharacteristic
148#106×C37—22no—
149C4⋊C8×C37—22no—
150#103×C37—22no—
151#103×C37—22no—
152#103×C37—41no—
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—22no—
158#102×C37—22no—
159#102×C37—41no—
160C22⋊C8×C37—22no—
161C22⋊C8×C37—22no—
162C22⋊C8×C37—41no—
163C22⋊C8×C37—41no—
164#97×C37—22no—
165#95×C37—21no—
166#95×C37—21no—
167C24×C37—21no—
168C24×C37—24no—
169C24×C37—21no—
170C24×C37—21no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—42no—
174C24×C37—42no—
175C24×C37—81no—
176C24×C37—81no—
177C24×C37C2×D411yescharacteristic
178C24×C37C2×D411yescharacteristic
179#41×C37—44no—
180#41×C37—44no—
181#41×C37—44no—
182#41×C37—44no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37—21no—
188C2×Q8×C37C2×D412yes—
189C2×D4×C37—24no—
190C2×D4×C37—24no—
191C2×D4×C37—22no—
192C2×D4×C37—24no—
193C2×D4×C37—22no—
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—21no—
207C2×D4×C37—41no—
208C2×D4×C37—42no—
209C2×D4×C37—42no—
210C2×D4×C37—44no—
211C2×D4×C37—44no—
212C2×D4×C37—44no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
215C2×D4×C37—44no—
216C2×D4×C37—42no—
217C2×D4×C37—42no—
218C2×D4×C37—42no—
219C2×D4×C37—42no—
220C2×D4×C37—81no—
221C2×D4×C37—81no—
222C2×D4×C37—81no—
223C2×D4×C37—81no—
224C2×D4×C37C2×D412yes—
225C2×D4×C37C2×D412yes—
226C2×D4×C37C2×D412yes—
227C2×D4×C37C2×D412yes—
228C2×D4×C37#4112yes—
229C22×C4×C37—24no—
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—21no—
244C22×C4×C37—24no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—42no—
249C22×C4×C37—42no—
250C22×C4×C37—42no—
251C22×C4×C37—42no—
252C22×C4×C37—42no—
253C22×C4×C37—81no—
254C22×C4×C37—81no—
255C22×C4×C37C2×D411yescharacteristic
256C22×C4×C37C2×D411yescharacteristic
257C22×C4×C37C2×D411yescharacteristic
258C22×C4×C37C2×D411yescharacteristic
259C22×C4×C37C2411yescharacteristic
260SD16×C37—44no—
261D8×C37—28no—
262D8×C37—44no—
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×C37—21no—
274C2×C8×C37C2×D412yes—
275C4⋊C4×C37—24no—
276C4⋊C4×C37—22no—
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×C37—21no—
284C4⋊C4×C37—42no—
285C4⋊C4×C37—81no—
286C4⋊C4×C37C2×D412yes—
287C22⋊C4×C37—24no—
288C22⋊C4×C37—24no—
289C22⋊C4×C37—22no—
290C22⋊C4×C37—24no—
291C22⋊C4×C37—24no—
292C22⋊C4×C37—24no—
293C22⋊C4×C37—22no—
294C22⋊C4×C37—42no—
295C22⋊C4×C37—42no—
296C22⋊C4×C37—42no—
297C22⋊C4×C37—42no—
298C22⋊C4×C37—42no—
299C42×C37C2×D412yes—
300C42×C37C2×D412yes—
301C23×C37—21no—
302C23×C37—22no—
303C23×C37—21no—
304C23×C37—22no—
305C23×C37—21no—
306C23×C37—22no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—22no—
311C23×C37—21no—
312C23×C37—22no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—21no—
318C23×C37—21no—
319C23×C37—48no—
320C23×C37—48no—
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—41no—
335C23×C37—41no—
336C23×C37—41no—
337C23×C37—84no—
338C23×C37—84no—
339C23×C37—84no—
340C23×C37—84no—
341C23×C37—84no—
342C23×C37AGL(1,ℤ/8)12yes—
343C23×C37C22×D411yescharacteristic
344Q8×C37—22no—
345Q8×C37—22no—
346Q8×C37—41no—
347Q8×C37—41no—
348D4×C37—22no—
349D4×C37—22no—
350D4×C37—22no—
351D4×C37—22no—
352D4×C37—22no—
353D4×C37—22no—
354D4×C37—22no—
355D4×C37—44no—
356D4×C37—48no—
357D4×C37—48no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—41no—
361D4×C37—41no—
362D4×C37—84no—
363D4×C37—84no—
364D4×C37—84no—
365D4×C37#12114yescomplemented
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—21no—
370C2×C4×C37—22no—
371C2×C4×C37—21no—
372C2×C4×C37—22no—
373C2×C4×C37—21no—
374C2×C4×C37—21no—
375C2×C4×C37—21no—
376C2×C4×C37—21no—
377C2×C4×C37—21no—
378C2×C4×C37—48no—
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—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—84no—
401C2×C4×C37—84no—
402C2×C4×C37#12012yes—
403C2×C4×C37#12012yes—
404C2×C4×C37C22×D411yescharacteristic
405C2×C4×C37C22×D411yescharacteristic
406C2×C4×C37C22×D411yescharacteristic
407C2×C4×C37C2×#4111yescharacteristic
408C2×C4×C37H(5,𝔽2)11yescharacteristic
409C2×C4×C37H(5,𝔽2)11yescharacteristic
410C8×C37—22no—
411C8×C37—41no—
412C8×C37—41no—
413C8×C37—41no—
414#24257C3711yesmaximal, characteristic, direct product factor, Sylow
415C22×C37—24no—
416C22×C37—22no—
417C22×C37—22no—
418C22×C37—22no—
419C22×C37—41no—
420C22×C37—42no—
421C22×C37—42no—
422C22×C37—41no—
423C22×C37—42no—
424C22×C37—42no—
425C22×C37—41no—
426C22×C37—42no—
427C22×C37—41no—
428C22×C37—42no—
429C22×C37—41no—
430C22×C37—42no—
431C22×C37—42no—
432C22×C37—41no—
433C22×C37—42no—
434C22×C37—41no—
435C22×C37—42no—
436C22×C37—41no—
437C22×C37—42no—
438C22×C37—41no—
439C22×C37—42no—
440C22×C37—41no—
441C22×C37—41no—
442C22×C37—816no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37—81no—
449C22×C37—81no—
450C22×C37—81no—
451C22×C37C2×#12011yescharacteristic
452C22×C37D4211yescharacteristic
453C22×C37#54611yescharacteristic
454C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C37#57511yescharacteristic
456C22×C37#57611yescharacteristic
457C22×C37#57711yescharacteristic
458C4×C37—22no—
459C4×C37—22no—
460C4×C37—41no—
461C4×C37—41no—
462C4×C37—42no—
463C4×C37—42no—
464C4×C37—81no—
465C4×C37—81no—
466C4×C37—81no—
467C4×C37C2×#12111yescharacteristic
468C4×C37#53511yescharacteristic
469C4×C37D4211yescharacteristic
470C4×C37#54611yescharacteristic
471C2×#546C2×C3711yescharacteristic, complemented
472C2×#463C2×C3711yescharacteristic, complemented
473C2×#449C2×C3711yescharacteristic, complemented
474C2×#447C2×C3711yescharacteristic, complemented
475C2×#442C2×C3711yescharacteristic, complemented
476#2537C2×C3711yescharacteristic, complemented
477#2035C2×C3711yescharacteristic, complemented
478#2034C2×C3711yescharacteristic, complemented
479#2000C2×C3711yescharacteristic, complemented
480#1999C2×C3711yescharacteristic, complemented
481#1959C2×C3711yescharacteristic, complemented
482#1955C2×C3711yescharacteristic, complemented
483#1802C2×C3711yescharacteristic, complemented
484#1788C2×C3711yescharacteristic, complemented
485#1786C2×C3711yescharacteristic, complemented
486C2×C37—42no—
487C2×C37—44no—
488C2×C37—81no—
489C2×C37—82no—
490C2×C37—82no—
491C2×C37#240811yescharacteristic
492C2×C37#300611yescharacteristic
493C2×C37#301211yescharacteristic
494C2×C37#326411yescharacteristic
495C2×C37#326711yescharacteristic
496C2×C37#330611yescharacteristic
497C2×C37#331911yescharacteristic
498C22×#41C22×C3711yescharacteristic
499C23×D4C22×C3711yescharacteristic
500C22×SD16C22×C3711yescharacteristic, complemented
501C22×D8C22×C3711yescharacteristic
502C22×D8C22×C3711yescharacteristic
503#546—24no—
504#546—24no—
505C2×#124C22×C3711yescharacteristic
506C2×#123—21no—
507C2×C22⋊Q8C22×C3711yescharacteristic
508C2×#121—21no—
509C2×#121—21no—
510C2×#121C22×C3711yescharacteristic
511C2×#121C22×C3711yescharacteristic
512C2×#121C22×C3711yescharacteristic, complemented
513C2×#120—21no—
514C2×C4×D4C22×C3711yescharacteristic
515C2×C4×D4C22×C3711yescharacteristic
516C2×C4×D4C22×C3711yescharacteristic, complemented
517C22×C22⋊C4—21no—
518#463—24no—
519#449—24no—
520#447—24no—
521#442—24no—
522C2×#106C22×C3711yescharacteristic, complemented
523C2×C4⋊C8C22×C3711yescharacteristic, complemented
524C2×#103C22×C3711yescharacteristic, complemented
525C2×#103C22×C3711yescharacteristic, complemented
526C2×#103C22×C3711yescharacteristic, complemented
527C2×#102C22×C3711yescharacteristic
528C2×#102C22×C3711yescharacteristic
529C2×#102C22×C3711yescharacteristic
530C2×#102C22×C3711yescharacteristic
531C2×#102C22×C3711yescharacteristic
532C2×#102C22×C3711yescharacteristic
533C2×#102C22×C3711yescharacteristic, complemented
534C2×C22⋊C8C22×C3711yescharacteristic
535C2×C22⋊C8C22×C3711yescharacteristic
536C2×C22⋊C8C22×C3711yescharacteristic, complemented
537C2×C22⋊C8C22×C3711yescharacteristic, complemented
538C2×#97C22×C3711yescharacteristic, complemented
539#394—21no—
540#394—21no—
541#384C22×C3711yescharacteristic, complemented
542#380—21no—
543#380C22×C3711yescharacteristic
544#380C22×C3711yescharacteristic, complemented
545#340C22×C3711yescharacteristic, complemented
546#340C22×C3711yescharacteristic, complemented
547C37#2425711yescharacteristic, direct product factor, Sylow
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C3711yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C3711yescharacteristic
568C22×D4C23×C3711yescharacteristic
569C22×D4C23×C3711yescharacteristic
570C22×D4C23×C3711yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C3711yescharacteristic
575C23×C4C23×C3711yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C3714yescomplemented
585C22×C8C23×C3711yescharacteristic
586C22×C8C23×C3711yescharacteristic
587C22×C8C23×C3711yescharacteristic
588C22×C8C23×C3711yescharacteristic
589#124—22no—
590#124D4×C3714yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C3714yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C3711yescharacteristic
613C2×C4⋊C4C23×C3711yescharacteristic
614C2×C4⋊C4C23×C3711yescharacteristic
615C2×C4⋊C4C23×C3711yescharacteristic
616C2×C4⋊C4C23×C3711yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C3711yescharacteristic
629C2×C22⋊C4D4×C3711yescharacteristic
630C2×C42C23×C3711yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C3711yescharacteristic
661C24C2×D4×C3711yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C3712yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
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—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C3712yes—
708C2×D4C2×D4×C3712yes—
709C2×D4C2×D4×C3712yes—
710C2×D4C2×D4×C3712yes—
711C2×D4#41×C3712yes—
712C22×C4—24no—
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—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C3711yescharacteristic
739C22×C4C2×D4×C3711yescharacteristic
740C22×C4C2×D4×C3711yescharacteristic
741C22×C4C2×D4×C3711yescharacteristic
742C22×C4C24×C3711yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C3712yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C3712yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C3712yes—
783C42C2×D4×C3712yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C3712yes—
826C23C22×D4×C3711yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C3714yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
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—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C3712yes—
886C2×C4#120×C3712yes—
887C2×C4C22×D4×C3711yescharacteristic
888C2×C4C22×D4×C3711yescharacteristic
889C2×C4C22×D4×C3711yescharacteristic
890C2×C4C2×#41×C3711yescharacteristic
891C2×C4H(5,𝔽2)×C3711yescharacteristic
892C2×C4H(5,𝔽2)×C3711yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C3711yescharacteristic
934C22D42×C3711yescharacteristic
935C22C37×#54611yescharacteristic
936C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
937C22C37×#57511yescharacteristic
938C22C37×#57611yescharacteristic
939C22C37×#57711yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C3711yescharacteristic
950C4C37×#53511yescharacteristic
951C4D42×C3711yescharacteristic
952C4C37×#54611yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C37×#240811yescharacteristic
959C2C37×#300611yescharacteristic
960C2C37×#301211yescharacteristic
961C2C37×#326411yescharacteristic
962C2C37×#326711yescharacteristic
963C2C37×#330611yescharacteristic
964C2C37×#331911yescharacteristic
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×C37×#442C2semidirect
6. C37×#2537C2semidirect
7. C37×#2035C2semidirect
8. C37×#2034C2semidirect
9. C37×#2000C2semidirect
10. C37×#1999C2semidirect
11. C37×#1959C2semidirect
12. C37×#1955C2semidirect
13. C37×#1802C2semidirect
14. C37×#1788C2semidirect
15. C37×#1786C2semidirect
18. C22×SD16×C37C22semidirect
30. C2×#121×C37C22semidirect
34. C2×C4×D4×C37C22semidirect
40. C2×#106×C37C22semidirect
41. C2×C4⋊C8×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
44. C2×#103×C37C22semidirect
51. C2×#102×C37C22semidirect
54. C2×C22⋊C8×C37C22semidirect
55. C2×C22⋊C8×C37C22semidirect
56. C2×#97×C37C22semidirect
59. C37×#384C22semidirect
62. C37×#380C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
101. C2×D8×C37D4semidirect
107. #124×C37D4semidirect
125. C4×D4×C37D4semidirect
365. D4×C37#121semidirect
414. #24257C37direct (N × H)
471. C2×#546C2×C37semidirect
472. C2×#463C2×C37semidirect
473. C2×#449C2×C37semidirect
474. C2×#447C2×C37semidirect
475. C2×#442C2×C37semidirect
476. #2537C2×C37semidirect
477. #2035C2×C37semidirect
478. #2034C2×C37semidirect
479. #2000C2×C37semidirect
480. #1999C2×C37semidirect
481. #1959C2×C37semidirect
482. #1955C2×C37semidirect
483. #1802C2×C37semidirect
484. #1788C2×C37semidirect
485. #1786C2×C37semidirect
500. C22×SD16C22×C37semidirect
512. C2×#121C22×C37semidirect
516. C2×C4×D4C22×C37semidirect
522. C2×#106C22×C37semidirect
523. C2×C4⋊C8C22×C37semidirect
524. C2×#103C22×C37semidirect
525. C2×#103C22×C37semidirect
526. C2×#103C22×C37semidirect
533. C2×#102C22×C37semidirect
536. C2×C22⋊C8C22×C37semidirect
537. C2×C22⋊C8C22×C37semidirect
538. C2×#97C22×C37semidirect
541. #384C22×C37semidirect
544. #380C22×C37semidirect
545. #340C22×C37semidirect
546. #340C22×C37semidirect
547. C37#24257direct (N × H)
584. C2×D8D4×C37semidirect
590. #124D4×C37semidirect
608. C4×D4D4×C37semidirect
848. D4#121×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×C37×#4422
C37×#25372
C37×#20352
C37×#20342
C37×#20002
C37×#19992
C37×#19592
C37×#19552
C37×#18022
C37×#17882
C37×#17862
#2425737