Finite Group Databasebeta

← C37×#29600 #22650853

Subgroups — C37×#29600 #22650853

Order 9472.

1540 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#525C211yesmaximal, characteristic, complemented
2C2×C37×#482C211yesmaximal, characteristic, complemented
3C2×C37×#449C211yesmaximal, characteristic, complemented
4C37×#2847C211yesmaximal, characteristic, complemented
5C37×#2036C211yesmaximal, characteristic, complemented
6C37×#2035C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2000C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1999C211yesmaximal, characteristic, complemented
12C37×#1999C211yesmaximal, characteristic, complemented
13C37×#1825C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C37×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C24×C4×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic, complemented
19C22×D8×C37C2211yescharacteristic, complemented
20C37×#525—24no—
21C37×#525—24no—
22C2×#123×C37—21no—
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×C22⋊Q8×C37C2211yescharacteristic
25C2×#121×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#120×C37—21no—
31C2×#120×C37—21no—
32C2×C4×D4×C37—21no—
33C2×C4×D4×C37—21no—
34C2×#117×C37C2211yescharacteristic
35C37×#482—24no—
36C37×#449—24no—
37C2×#107×C37C2211yescharacteristic, complemented
38C2×#106×C37C2211yescharacteristic, complemented
39C2×#103×C37C2211yescharacteristic, complemented
40C2×#103×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#102×C37C2211yescharacteristic, complemented
43C2×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C2×C22⋊C8×C37C2211yescharacteristic
50C2×C22⋊C8×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic
53C37×#386—21no—
54C37×#386—21no—
55C37×#386—21no—
56C37×#380C2211yescharacteristic
57C37×#380C2211yescharacteristic
58C37×#380C2211yescharacteristic
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C25×C37D411yescharacteristic
64C2×#41×C37—22no—
65C2×#41×C37—41no—
66C2×#41×C37—41no—
67C2×#41×C37—41no—
68C2×#41×C37—41no—
69C2×#41×C37D414yescomplemented
70C22×Q8×C37C2311yescharacteristic
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37C2311yescharacteristic
78C22×D4×C37C2311yescharacteristic
79C23×C4×C37—22no—
80C23×C4×C37—22no—
81C23×C4×C37—21no—
82C23×C4×C37—41no—
83C23×C4×C37—41no—
84C23×C4×C37—41no—
85C23×C4×C37—41no—
86C23×C4×C37D411yescharacteristic
87C23×C4×C37D411yescharacteristic
88C23×C4×C37D411yescharacteristic
89C23×C4×C37C2311yescharacteristic
90C23×C4×C37C2311yescharacteristic
91C23×C4×C37C2311yescharacteristic
92C2×SD16×C37—22no—
93C2×SD16×C37—41no—
94C2×SD16×C37—41no—
95C2×D8×C37—22no—
96C2×D8×C37—41no—
97C2×D8×C37—41no—
98C22×C8×C37C2311yescharacteristic
99C22×C8×C37C2311yescharacteristic
100C22×C8×C37C2311yescharacteristic
101C22×C8×C37C2311yescharacteristic
102#123×C37—28no—
103C22⋊Q8×C37—22no—
104C22⋊Q8×C37—22no—
105C22⋊Q8×C37—22no—
106C22⋊Q8×C37—22no—
107#121×C37—22no—
108#121×C37—22no—
109#121×C37—22no—
110#121×C37—22no—
111#121×C37—22no—
112#121×C37—22no—
113#121×C37—41no—
114#121×C37—41no—
115#121×C37—41no—
116#121×C37—41no—
117#120×C37—28no—
118#120×C37—44no—
119C4×D4×C37—28no—
120C4×D4×C37—28no—
121#117×C37—22no—
122#117×C37D414yescomplemented
123C2×C4⋊C4×C37—21no—
124C2×C4⋊C4×C37—21no—
125C2×C4⋊C4×C37C2311yescharacteristic
126C2×C4⋊C4×C37C2311yescharacteristic
127C2×C4⋊C4×C37C2311yescharacteristic
128C2×C4⋊C4×C37C2311yescharacteristic
129C2×C4⋊C4×C37C2311yescharacteristic
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37—21no—
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×C42×C37—21no—
142#107×C37—22no—
143#106×C37—22no—
144#103×C37—22no—
145#103×C37—41no—
146#103×C37—41no—
147#102×C37—22no—
148#102×C37—22no—
149#102×C37—22no—
150#102×C37—41no—
151#102×C37—41no—
152C22⋊C8×C37—22no—
153C22⋊C8×C37—22no—
154C22⋊C8×C37—41no—
155C22⋊C8×C37—41no—
156C22⋊C8×C37—41no—
157C22⋊C8×C37—41no—
158#95×C37—21no—
159#95×C37—21no—
160#95×C37—21no—
161C24×C37—22no—
162C24×C37—22no—
163C24×C37—22no—
164C24×C37—21no—
165C24×C37—21no—
166C24×C37—41no—
167C24×C37—41no—
168C24×C37—41no—
169C24×C37—41no—
170C24×C37C2×D411yescharacteristic
171C24×C37C2×D411yescharacteristic
172C24×C37C2×D411yescharacteristic
173#41×C37—44no—
174#41×C37—44no—
175#41×C37—44no—
176#41×C37—44no—
177C2×Q8×C37—21no—
178C2×Q8×C37—21no—
179C2×Q8×C37—21no—
180C2×Q8×C37—21no—
181C2×Q8×C37—21no—
182C2×Q8×C37C2×D412yes—
183C2×D4×C37—24no—
184C2×D4×C37—24no—
185C2×D4×C37—24no—
186C2×D4×C37—21no—
187C2×D4×C37—21no—
188C2×D4×C37—21no—
189C2×D4×C37—21no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—21no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—42no—
198C2×D4×C37—42no—
199C2×D4×C37—42no—
200C2×D4×C37—42no—
201C2×D4×C37—42no—
202C2×D4×C37—42no—
203C2×D4×C37—42no—
204C2×D4×C37—42no—
205C2×D4×C37—42no—
206C2×D4×C37—42no—
207C2×D4×C37—42no—
208C2×D4×C37—42no—
209C2×D4×C37—42no—
210C2×D4×C37—42no—
211C2×D4×C37—42no—
212C2×D4×C37C2×D412yes—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—22no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—22no—
222C22×C4×C37—22no—
223C22×C4×C37—24no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
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—41no—
240C22×C4×C37—41no—
241C22×C4×C37—41no—
242C22×C4×C37—41no—
243C22×C4×C37—41no—
244C22×C4×C37—41no—
245C22×C4×C37—44no—
246C22×C4×C37—44no—
247C22×C4×C37—44no—
248C22×C4×C37—44no—
249C22×C4×C37—42no—
250C22×C4×C37—42no—
251C22×C4×C37C2×D411yescharacteristic
252C22×C4×C37C2×D411yescharacteristic
253C22×C4×C37C2×D411yescharacteristic
254C22×C4×C37C2×D412yes—
255C22×C4×C37C2×D412yes—
256C22×C4×C37C2411yescharacteristic
257SD16×C37—44no—
258D8×C37—44no—
259C2×C8×C37—21no—
260C2×C8×C37—21no—
261C2×C8×C37—21no—
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—
271C4⋊C4×C37—24no—
272C4⋊C4×C37—24no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37C2×D412yes—
282C4⋊C4×C37C2×D412yes—
283C22⋊C4×C37—24no—
284C22⋊C4×C37—24no—
285C22⋊C4×C37—24no—
286C22⋊C4×C37—24no—
287C22⋊C4×C37—24no—
288C22⋊C4×C37—42no—
289C22⋊C4×C37—42no—
290C22⋊C4×C37—42no—
291C22⋊C4×C37—42no—
292C22⋊C4×C37—42no—
293C22⋊C4×C37—42no—
294C42×C37—24no—
295C23×C37—21no—
296C23×C37—21no—
297C23×C37—21no—
298C23×C37—21no—
299C23×C37—21no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—21no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—22no—
314C23×C37—44no—
315C23×C37—44no—
316C23×C37—44no—
317C23×C37—44no—
318C23×C37—44no—
319C23×C37—44no—
320C23×C37—44no—
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#12012yes—
335C23×C37#13512yes—
336C23×C37AGL(1,ℤ/8)12yes—
337C23×C37C22×D411yescharacteristic
338Q8×C37—22no—
339Q8×C37—22no—
340Q8×C37—41no—
341Q8×C37—41no—
342D4×C37—22no—
343D4×C37—22no—
344D4×C37—48no—
345D4×C37—48no—
346D4×C37—48no—
347D4×C37—41no—
348D4×C37—41no—
349D4×C37—41no—
350D4×C37—41no—
351D4×C37—41no—
352D4×C37—41no—
353D4×C37—84no—
354D4×C37—84no—
355D4×C37—84no—
356C2×C4×C37—21no—
357C2×C4×C37—21no—
358C2×C4×C37—22no—
359C2×C4×C37—22no—
360C2×C4×C37—22no—
361C2×C4×C37—22no—
362C2×C4×C37—22no—
363C2×C4×C37—22no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—22no—
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—21no—
370C2×C4×C37—21no—
371C2×C4×C37—44no—
372C2×C4×C37—44no—
373C2×C4×C37—48no—
374C2×C4×C37—44no—
375C2×C4×C37—41no—
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—41no—
398C2×C4×C37#12012yes—
399C2×C4×C37C22×D411yescharacteristic
400C2×C4×C37C22×D411yescharacteristic
401C2×C4×C37H(5,𝔽2)11yescharacteristic
402C2×C4×C37H(5,𝔽2)11yescharacteristic
403C2×C4×C37H(5,𝔽2)11yescharacteristic
404C2×C4×C37H(5,𝔽2)11yescharacteristic
405C8×C37—41no—
406C8×C37—41no—
407C8×C37—41no—
408C8×C37—41no—
409#29600C3711yesmaximal, characteristic, direct product factor, Sylow
410C22×C37—22no—
411C22×C37—22no—
412C22×C37—22no—
413C22×C37—22no—
414C22×C37—22no—
415C22×C37—22no—
416C22×C37—22no—
417C22×C37—22no—
418C22×C37—22no—
419C22×C37—416no—
420C22×C37—41no—
421C22×C37—41no—
422C22×C37—41no—
423C22×C37—41no—
424C22×C37—41no—
425C22×C37—41no—
426C22×C37—41no—
427C22×C37—41no—
428C22×C37—41no—
429C22×C37—41no—
430C22×C37—41no—
431C22×C37—41no—
432C22×C37—42no—
433C22×C37—42no—
434C22×C37—42no—
435C22×C37—81no—
436C22×C37—81no—
437C22×C37—81no—
438C22×C37—81no—
439C22×C37—81no—
440C22×C37—81no—
441C22×C37—81no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37C2×#12011yescharacteristic
447C22×C37#53411yescharacteristic
448C22×C37#53411yescharacteristic
449C22×C37C2×#13511yescharacteristic
450C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C37#57511yescharacteristic
452C22×C37#57511yescharacteristic
453C4×C37—22no—
454C4×C37—41no—
455C4×C37—41no—
456C4×C37—42no—
457C4×C37—42no—
458C4×C37—42no—
459C4×C37—81no—
460C4×C37—81no—
461C4×C37—81no—
462C4×C37#53411yescharacteristic
463C4×C37#53411yescharacteristic
464C4×C37#53511yescharacteristic
465C4×C37#53511yescharacteristic
466C2×#525C2×C3711yescharacteristic, complemented
467C2×#482C2×C3711yescharacteristic, complemented
468C2×#449C2×C3711yescharacteristic, complemented
469#2847C2×C3711yescharacteristic, complemented
470#2036C2×C3711yescharacteristic, complemented
471#2035C2×C3711yescharacteristic, complemented
472#2034C2×C3711yescharacteristic, complemented
473#2033C2×C3711yescharacteristic, complemented
474#2000C2×C3711yescharacteristic, complemented
475#2000C2×C3711yescharacteristic, complemented
476#1999C2×C3711yescharacteristic, complemented
477#1999C2×C3711yescharacteristic, complemented
478#1825C2×C3711yescharacteristic, complemented
479#1788C2×C3711yescharacteristic, complemented
480#1779C2×C3711yescharacteristic, complemented
481C2×C37—42no—
482C2×C37—42no—
483C2×C37—42no—
484C2×C37—82no—
485C2×C37—161no—
486C2×C37#261311yescharacteristic
487C2×C37#300211yescharacteristic
488C2×C37#300611yescharacteristic
489C2×C37#318811yescharacteristic
490C2×C37#319111yescharacteristic
491C2×C37#319411yescharacteristic
492C2×C37#319711yescharacteristic
493C22×#41C22×C3711yescharacteristic
494C24×C4C22×C3711yescharacteristic
495C22×SD16C22×C3711yescharacteristic, complemented
496C22×D8C22×C3711yescharacteristic, complemented
497#525—24no—
498#525—24no—
499C2×#123—21no—
500C2×C22⋊Q8C22×C3711yescharacteristic
501C2×C22⋊Q8C22×C3711yescharacteristic
502C2×#121C22×C3711yescharacteristic
503C2×#121C22×C3711yescharacteristic
504C2×#121C22×C3711yescharacteristic
505C2×#121C22×C3711yescharacteristic
506C2×#121C22×C3711yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4—21no—
510C2×C4×D4—21no—
511C2×#117C22×C3711yescharacteristic
512#482—24no—
513#449—24no—
514C2×#107C22×C3711yescharacteristic, complemented
515C2×#106C22×C3711yescharacteristic, complemented
516C2×#103C22×C3711yescharacteristic, complemented
517C2×#103C22×C3711yescharacteristic, complemented
518C2×#103C22×C3711yescharacteristic, complemented
519C2×#102C22×C3711yescharacteristic, complemented
520C2×#102C22×C3711yescharacteristic, complemented
521C2×#102C22×C3711yescharacteristic, complemented
522C2×#102C22×C3711yescharacteristic, complemented
523C2×#102C22×C3711yescharacteristic, complemented
524C2×C22⋊C8C22×C3711yescharacteristic
525C2×C22⋊C8C22×C3711yescharacteristic
526C2×C22⋊C8C22×C3711yescharacteristic
527C2×C22⋊C8C22×C3711yescharacteristic
528C2×C22⋊C8C22×C3711yescharacteristic
529C2×C22⋊C8C22×C3711yescharacteristic
530#386—21no—
531#386—21no—
532#386—21no—
533#380C22×C3711yescharacteristic
534#380C22×C3711yescharacteristic
535#380C22×C3711yescharacteristic
536#340C22×C3711yescharacteristic, complemented
537#340C22×C3711yescharacteristic, complemented
538#340C22×C3711yescharacteristic, complemented
539#340C22×C3711yescharacteristic, complemented
540C37#2960011yescharacteristic, direct product factor, Sylow
541C25D4×C3711yescharacteristic
542C2×#41—22no—
543C2×#41—41no—
544C2×#41—41no—
545C2×#41—41no—
546C2×#41—41no—
547C2×#41D4×C3714yescomplemented
548C22×Q8C23×C3711yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4C23×C3711yescharacteristic
556C22×D4C23×C3711yescharacteristic
557C23×C4—21no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4D4×C3711yescharacteristic
565C23×C4D4×C3711yescharacteristic
566C23×C4D4×C3711yescharacteristic
567C23×C4C23×C3711yescharacteristic
568C23×C4C23×C3711yescharacteristic
569C23×C4C23×C3711yescharacteristic
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C22×C8C23×C3711yescharacteristic
577C22×C8C23×C3711yescharacteristic
578C22×C8C23×C3711yescharacteristic
579C22×C8C23×C3711yescharacteristic
580#123—28no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#120—28no—
596#120—44no—
597C4×D4—28no—
598C4×D4—28no—
599#117—22no—
600#117D4×C3714yescomplemented
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4C23×C3711yescharacteristic
604C2×C4⋊C4C23×C3711yescharacteristic
605C2×C4⋊C4C23×C3711yescharacteristic
606C2×C4⋊C4C23×C3711yescharacteristic
607C2×C4⋊C4C23×C3711yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
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×C42—21no—
620#107—22no—
621#106—22no—
622#103—22no—
623#103—41no—
624#103—41no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632C22⋊C8—41no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—41no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—41no—
645C24—41no—
646C24—41no—
647C24—41no—
648C24C2×D4×C3711yescharacteristic
649C24C2×D4×C3711yescharacteristic
650C24C2×D4×C3711yescharacteristic
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C3712yes—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4C2×D4×C3712yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
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—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4C2×D4×C3711yescharacteristic
730C22×C4C2×D4×C3711yescharacteristic
731C22×C4C2×D4×C3711yescharacteristic
732C22×C4C2×D4×C3712yes—
733C22×C4C2×D4×C3712yes—
734C22×C4C24×C3711yescharacteristic
735SD16—44no—
736D8—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4C2×D4×C3712yes—
760C4⋊C4C2×D4×C3712yes—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C42—24no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—22no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
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#120×C3712yes—
813C23#135×C3712yes—
814C23AGL(1,ℤ/8)×C3712yes—
815C23C22×D4×C3711yescharacteristic
816Q8—22no—
817Q8—22no—
818Q8—41no—
819Q8—41no—
820D4—22no—
821D4—22no—
822D4—48no—
823D4—48no—
824D4—48no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—84no—
832D4—84no—
833D4—84no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
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#120×C3712yes—
877C2×C4C22×D4×C3711yescharacteristic
878C2×C4C22×D4×C3711yescharacteristic
879C2×C4H(5,𝔽2)×C3711yescharacteristic
880C2×C4H(5,𝔽2)×C3711yescharacteristic
881C2×C4H(5,𝔽2)×C3711yescharacteristic
882C2×C4H(5,𝔽2)×C3711yescharacteristic
883C8—41no—
884C8—41no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—416no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#120×C3711yescharacteristic
924C22C37×#53411yescharacteristic
925C22C37×#53411yescharacteristic
926C22C2×#135×C3711yescharacteristic
927C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
928C22C37×#57511yescharacteristic
929C22C37×#57511yescharacteristic
930C4—22no—
931C4—41no—
932C4—41no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C37×#53411yescharacteristic
940C4C37×#53411yescharacteristic
941C4C37×#53511yescharacteristic
942C4C37×#53511yescharacteristic
943C2—42no—
944C2—42no—
945C2—42no—
946C2—82no—
947C2—161no—
948C2C37×#261311yescharacteristic
949C2C37×#300211yescharacteristic
950C2C37×#300611yescharacteristic
951C2C37×#318811yescharacteristic
952C2C37×#319111yescharacteristic
953C2C37×#319411yescharacteristic
954C2C37×#319711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C24×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#525C2semidirect
2. C2×C37×#482C2semidirect
3. C2×C37×#449C2semidirect
4. C37×#2847C2semidirect
5. C37×#2036C2semidirect
6. C37×#2035C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#2000C2semidirect
10. C37×#2000C2semidirect
11. C37×#1999C2semidirect
12. C37×#1999C2semidirect
13. C37×#1825C2semidirect
14. C37×#1788C2semidirect
15. C37×#1779C2semidirect
18. C22×SD16×C37C22semidirect
19. C22×D8×C37C22semidirect
37. C2×#107×C37C22semidirect
38. C2×#106×C37C22semidirect
39. C2×#103×C37C22semidirect
40. C2×#103×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#102×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
69. C2×#41×C37D4semidirect
122. #117×C37D4semidirect
409. #29600C37direct (N × H)
466. C2×#525C2×C37semidirect
467. C2×#482C2×C37semidirect
468. C2×#449C2×C37semidirect
469. #2847C2×C37semidirect
470. #2036C2×C37semidirect
471. #2035C2×C37semidirect
472. #2034C2×C37semidirect
473. #2033C2×C37semidirect
474. #2000C2×C37semidirect
475. #2000C2×C37semidirect
476. #1999C2×C37semidirect
477. #1999C2×C37semidirect
478. #1825C2×C37semidirect
479. #1788C2×C37semidirect
480. #1779C2×C37semidirect
495. C22×SD16C22×C37semidirect
496. C22×D8C22×C37semidirect
514. C2×#107C22×C37semidirect
515. C2×#106C22×C37semidirect
516. C2×#103C22×C37semidirect
517. C2×#103C22×C37semidirect
518. C2×#103C22×C37semidirect
519. C2×#102C22×C37semidirect
520. C2×#102C22×C37semidirect
521. C2×#102C22×C37semidirect
522. C2×#102C22×C37semidirect
523. C2×#102C22×C37semidirect
536. #340C22×C37semidirect
537. #340C22×C37semidirect
538. #340C22×C37semidirect
539. #340C22×C37semidirect
540. C37#29600direct (N × H)
547. C2×#41D4×C37semidirect
600. #117D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5252
C2×C37×#4822
C2×C37×#4492
C37×#28472
C37×#20362
C37×#20352
C37×#20342
C37×#20332
C37×#20002
C37×#19992
C37×#18252
C37×#17882
C37×#17792
#2960037