Finite Group Databasebeta

← C37×#24440 #22645693

Subgroups — C37×#24440 #22645693

Order 9472.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C37C211yesmaximal, characteristic, complemented
2C2×C37×#469C211yesmaximal, characteristic, complemented
3C2×C37×#447C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C2×C37×#418C211yesmaximal, characteristic, complemented
6C37×#2414C211yesmaximal, characteristic, complemented
7C37×#2041C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#2011C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1879C211yesmaximal, characteristic, complemented
12C37×#1875C211yesmaximal, characteristic, complemented
13C37×#1870C211yesmaximal, characteristic, complemented
14C37×#1864C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C37—21no—
17C23×D4×C37C2211yescharacteristic
18C23×D4×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic
20C22×D8×C37C2211yescharacteristic, complemented
21C22×D8×C37C2211yescharacteristic, complemented
22C22×M16×C37C2211yescharacteristic, complemented
23D42×C37—24no—
24D42×C37—24no—
25C2×#127×C37C2211yescharacteristic
26C2×#121×C37—21no—
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic, complemented
30C2×#121×C37C2211yescharacteristic, complemented
31C2×#120×C37—21no—
32C2×#120×C37—21no—
33C2×C4×D4×C37C2211yescharacteristic
34C2×C4×D4×C37C2211yescharacteristic
35C2×#117×C37C2211yescharacteristic, complemented
36C37×#469—24no—
37C37×#447—24no—
38C37×#447—24no—
39C2×#106×C37C2211yescharacteristic, complemented
40C37×#418—24no—
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×#102×C37C2211yescharacteristic, complemented
48C2×#102×C37C2211yescharacteristic, complemented
49C2×#102×C37C2211yescharacteristic, complemented
50C2×#102×C37C2211yescharacteristic, complemented
51C2×C22⋊C8×C37C2211yescharacteristic, complemented
52C2×C22⋊C8×C37C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#394—21no—
55C37×#392—21no—
56C37×#390—21no—
57C37×#390C2211yescharacteristic, complemented
58C37×#389C2211yescharacteristic, complemented
59C37×#388—21no—
60C37×#380C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#336C2211yescharacteristic, complemented
64C37×#336C2211yescharacteristic, complemented
65C25×C37—21no—
66C25×C37—21no—
67C22×D4×C37—22no—
68C22×D4×C37—22no—
69C22×D4×C37—28no—
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—22no—
73C22×D4×C37—22no—
74C22×D4×C37—22no—
75C22×D4×C37—22no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—22no—
82C22×D4×C37—21no—
83C22×D4×C37—41no—
84C22×D4×C37—41no—
85C22×D4×C37—41no—
86C22×D4×C37—41no—
87C22×D4×C37—44no—
88C22×D4×C37—44no—
89C22×D4×C37D411yescharacteristic
90C22×D4×C37D414yescomplemented
91C22×D4×C37C2311yescharacteristic
92C22×D4×C37C2311yescharacteristic
93C22×D4×C37C2311yescharacteristic
94C22×D4×C37C2311yescharacteristic
95C23×C4×C37—21no—
96C23×C4×C37C2311yescharacteristic
97C23×C4×C37C2311yescharacteristic
98C2×D8×C37—22no—
99C2×D8×C37—22no—
100C2×D8×C37—22no—
101C2×D8×C37—22no—
102C2×D8×C37—22no—
103C2×D8×C37—22no—
104C2×D8×C37—41no—
105C2×D8×C37—41no—
106C2×D8×C37—41no—
107C2×M16×C37—22no—
108C2×M16×C37—22no—
109C2×M16×C37—41no—
110C22×C8×C37C2311yescharacteristic
111C22×C8×C37C2311yescharacteristic
112C22×C8×C37C2311yescharacteristic
113C22×C8×C37C2311yescharacteristic
114#127×C37—22no—
115#127×C37—22no—
116#121×C37—28no—
117#121×C37—22no—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37—22no—
123#121×C37—41no—
124#121×C37D414yescomplemented
125#120×C37—28no—
126#120×C37—28no—
127C4×D4×C37—22no—
128C4×D4×C37—22no—
129C4×D4×C37—22no—
130C4×D4×C37—22no—
131#117×C37—22no—
132#117×C37—41no—
133C2×C4⋊C4×C37—21no—
134C2×C4⋊C4×C37D411yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C4⋊C4×C37C2311yescharacteristic
137C2×C4⋊C4×C37C2311yescharacteristic
138C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
146C2×C22⋊C4×C37—21no—
147C2×C22⋊C4×C37—21no—
148C2×C22⋊C4×C37D411yescharacteristic
149C2×C22⋊C4×C37D411yescharacteristic
150C2×C42×C37—21no—
151C2×C42×C37C2311yescharacteristic
152#106×C37—22no—
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—22no—
160#102×C37—22no—
161#102×C37—41no—
162#102×C37D414yescomplemented
163C22⋊C8×C37—22no—
164C22⋊C8×C37—22no—
165C22⋊C8×C37—41no—
166#95×C37—21no—
167#95×C37—21no—
168C24×C37—21no—
169C24×C37—24no—
170C24×C37—21no—
171C24×C37—21no—
172C24×C37—24no—
173C24×C37—21no—
174C24×C37—42no—
175C24×C37—42no—
176C24×C37—42no—
177C24×C37—42no—
178C24×C37—42no—
179C24×C37—42no—
180C24×C37—42no—
181C24×C37—42no—
182C24×C37—81no—
183C24×C37—81no—
184C24×C37—81no—
185C24×C37—81no—
186C24×C37C2×D411yescharacteristic
187C24×C37C2×D411yescharacteristic
188C2×D4×C37—22no—
189C2×D4×C37—22no—
190C2×D4×C37—28no—
191C2×D4×C37—24no—
192C2×D4×C37—24no—
193C2×D4×C37—24no—
194C2×D4×C37—24no—
195C2×D4×C37—24no—
196C2×D4×C37—24no—
197C2×D4×C37—22no—
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—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—21no—
213C2×D4×C37—21no—
214C2×D4×C37—21no—
215C2×D4×C37—21no—
216C2×D4×C37—21no—
217C2×D4×C37—44no—
218C2×D4×C37—44no—
219C2×D4×C37—44no—
220C2×D4×C37—42no—
221C2×D4×C37—42no—
222C2×D4×C37—42no—
223C2×D4×C37—42no—
224C2×D4×C37—42no—
225C2×D4×C37—42no—
226C2×D4×C37—44no—
227C2×D4×C37—44no—
228C2×D4×C37—432no—
229C2×D4×C37—44no—
230C2×D4×C37—42no—
231C2×D4×C37—42no—
232C2×D4×C37—42no—
233C2×D4×C37—42no—
234C2×D4×C37—44no—
235C2×D4×C37—42no—
236C2×D4×C37—42no—
237C2×D4×C37—42no—
238C2×D4×C37—81no—
239C2×D4×C37—81no—
240C2×D4×C37—81no—
241C2×D4×C37—81no—
242C2×D4×C37—81no—
243C2×D4×C37C2×D412yes—
244C2×D4×C37C2×D412yes—
245C2×D4×C37C2×D412yes—
246C2×D4×C37C2×D412yes—
247C2×D4×C37#4112yes—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—24no—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—21no—
259C22×C4×C37—21no—
260C22×C4×C37—21no—
261C22×C4×C37—21no—
262C22×C4×C37—21no—
263C22×C4×C37—42no—
264C22×C4×C37—42no—
265C22×C4×C37C2×D411yescharacteristic
266C22×C4×C37C2×D411yescharacteristic
267C22×C4×C37C2×D411yescharacteristic
268C22×C4×C37C2×D412yes—
269C22×C4×C37C2×D412yes—
270C22×C4×C37C2×D411yescharacteristic
271C22×C4×C37C2411yescharacteristic
272D8×C37—44no—
273D8×C37—44no—
274D8×C37—44no—
275M16×C37—44no—
276C2×C8×C37—21no—
277C2×C8×C37—21no—
278C2×C8×C37—21no—
279C2×C8×C37—21no—
280C2×C8×C37—21no—
281C2×C8×C37—21no—
282C2×C8×C37—21no—
283C2×C8×C37—21no—
284C2×C8×C37—21no—
285C2×C8×C37—21no—
286C2×C8×C37—21no—
287C2×C8×C37C2×D412yescomplemented
288C4⋊C4×C37—22no—
289C4⋊C4×C37—21no—
290C4⋊C4×C37—21no—
291C4⋊C4×C37—21no—
292C4⋊C4×C37—21no—
293C4⋊C4×C37—21no—
294C4⋊C4×C37—21no—
295C4⋊C4×C37—81no—
296C4⋊C4×C37C2×D412yes—
297C4⋊C4×C37C2×D412yescomplemented
298C22⋊C4×C37—24no—
299C22⋊C4×C37—24no—
300C22⋊C4×C37—22no—
301C22⋊C4×C37—24no—
302C22⋊C4×C37—22no—
303C22⋊C4×C37—42no—
304C22⋊C4×C37—42no—
305C22⋊C4×C37—42no—
306C22⋊C4×C37—42no—
307C22⋊C4×C37—81no—
308C22⋊C4×C37—81no—
309C42×C37—21no—
310C42×C37—21no—
311C42×C37—42no—
312C23×C37—21no—
313C23×C37—22no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—22no—
317C23×C37—21no—
318C23×C37—21no—
319C23×C37—22no—
320C23×C37—21no—
321C23×C37—21no—
322C23×C37—21no—
323C23×C37—21no—
324C23×C37—21no—
325C23×C37—21no—
326C23×C37—21no—
327C23×C37—22no—
328C23×C37—22no—
329C23×C37—48no—
330C23×C37—48no—
331C23×C37—48no—
332C23×C37—48no—
333C23×C37—41no—
334C23×C37—41no—
335C23×C37—41no—
336C23×C37—41no—
337C23×C37—41no—
338C23×C37—41no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—41no—
348C23×C37—41no—
349C23×C37—41no—
350C23×C37—41no—
351C23×C37—41no—
352C23×C37—41no—
353C23×C37—41no—
354C23×C37—41no—
355C23×C37—41no—
356C23×C37—84no—
357C23×C37—84no—
358C23×C37—84no—
359C23×C37—84no—
360C23×C37—84no—
361C23×C37—84no—
362C23×C37—84no—
363C23×C37—84no—
364C23×C37—84no—
365C23×C37—84no—
366C23×C37#12012yes—
367C23×C37AGL(1,ℤ/8)12yes—
368C23×C37C22×D411yescharacteristic
369D4×C37—28no—
370D4×C37—22no—
371D4×C37—22no—
372D4×C37—22no—
373D4×C37—22no—
374D4×C37—22no—
375D4×C37—22no—
376D4×C37—22no—
377D4×C37—48no—
378D4×C37—48no—
379D4×C37—48no—
380D4×C37—48no—
381D4×C37—48no—
382D4×C37—41no—
383D4×C37—41no—
384D4×C37—41no—
385D4×C37—41no—
386D4×C37—41no—
387D4×C37—41no—
388D4×C37—41no—
389D4×C37—41no—
390D4×C37—84no—
391D4×C37—84no—
392D4×C37—84no—
393D4×C37#12114yes—
394C2×C4×C37—21no—
395C2×C4×C37—21no—
396C2×C4×C37—21no—
397C2×C4×C37—21no—
398C2×C4×C37—22no—
399C2×C4×C37—22no—
400C2×C4×C37—22no—
401C2×C4×C37—22no—
402C2×C4×C37—21no—
403C2×C4×C37—21no—
404C2×C4×C37—22no—
405C2×C4×C37—22no—
406C2×C4×C37—21no—
407C2×C4×C37—21no—
408C2×C4×C37—21no—
409C2×C4×C37—21no—
410C2×C4×C37—48no—
411C2×C4×C37—41no—
412C2×C4×C37—41no—
413C2×C4×C37—41no—
414C2×C4×C37—41no—
415C2×C4×C37—41no—
416C2×C4×C37—41no—
417C2×C4×C37—41no—
418C2×C4×C37—41no—
419C2×C4×C37—41no—
420C2×C4×C37—41no—
421C2×C4×C37—41no—
422C2×C4×C37—41no—
423C2×C4×C37—41no—
424C2×C4×C37—41no—
425C2×C4×C37#12012yes—
426C2×C4×C37AGL(1,ℤ/8)12yes—
427C2×C4×C37C22×D411yescharacteristic
428C2×C4×C37C22×D411yescharacteristic
429C2×C4×C37C22×D411yescharacteristic
430C2×C4×C37C2×#4111yescharacteristic
431C2×C4×C37H(5,𝔽2)11yescharacteristic
432C2×C4×C37H(5,𝔽2)11yescharacteristic
433C8×C37—22no—
434C8×C37—41no—
435C8×C37—41no—
436C8×C37—41no—
437#24440C3711yesmaximal, characteristic, direct product factor, Sylow
438C22×C37—22no—
439C22×C37—24no—
440C22×C37—22no—
441C22×C37—22no—
442C22×C37—22no—
443C22×C37—22no—
444C22×C37—22no—
445C22×C37—41no—
446C22×C37—42no—
447C22×C37—41no—
448C22×C37—42no—
449C22×C37—41no—
450C22×C37—42no—
451C22×C37—41no—
452C22×C37—41no—
453C22×C37—42no—
454C22×C37—41no—
455C22×C37—42no—
456C22×C37—41no—
457C22×C37—41no—
458C22×C37—42no—
459C22×C37—42no—
460C22×C37—42no—
461C22×C37—42no—
462C22×C37—42no—
463C22×C37—42no—
464C22×C37—42no—
465C22×C37—816no—
466C22×C37—816no—
467C22×C37—81no—
468C22×C37—81no—
469C22×C37—81no—
470C22×C37—81no—
471C22×C37—81no—
472C22×C37—81no—
473C22×C37—81no—
474C22×C37—81no—
475C22×C37—81no—
476C22×C37—81no—
477C22×C37—81no—
478C22×C37—81no—
479C22×C37—81no—
480C22×C37—81no—
481C22×C37—81no—
482C22×C37C2×#12011yescharacteristic
483C22×C37D4211yescharacteristic
484C22×C37#54611yescharacteristic
485C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
487C22×C37#57611yescharacteristic
488C22×C37#57611yescharacteristic
489C4×C37—22no—
490C4×C37—22no—
491C4×C37—41no—
492C4×C37—42no—
493C4×C37—41no—
494C4×C37—42no—
495C4×C37—81no—
496C4×C37—81no—
497C4×C37C2×#12111yescharacteristic
498C4×C37#53411yescharacteristic
499C4×C37D4211yescharacteristic
500C4×C37#54611yescharacteristic
501C2×D42C2×C3711yescharacteristic, complemented
502C2×#469C2×C3711yescharacteristic, complemented
503C2×#447C2×C3711yescharacteristic, complemented
504C2×#447C2×C3711yescharacteristic, complemented
505C2×#418C2×C3711yescharacteristic, complemented
506#2414C2×C3711yescharacteristic, complemented
507#2041C2×C3711yescharacteristic, complemented
508#2034C2×C3711yescharacteristic, complemented
509#2011C2×C3711yescharacteristic, complemented
510#1999C2×C3711yescharacteristic, complemented
511#1879C2×C3711yescharacteristic, complemented
512#1875C2×C3711yescharacteristic, complemented
513#1870C2×C3711yescharacteristic, complemented
514#1864C2×C3711yescharacteristic, complemented
515#1786C2×C3711yescharacteristic, complemented
516C2×C37—42no—
517C2×C37—42no—
518C2×C37—44no—
519C2×C37—82no—
520C2×C37—82no—
521C2×C37—161no—
522C2×C37#241011yescharacteristic
523C2×C37#300311yescharacteristic
524C2×C37#300811yescharacteristic
525C2×C37#326411yescharacteristic
526C2×C37#327411yescharacteristic
527C2×C37#331811yescharacteristic
528C2×C37#332511yescharacteristic
529C23×D4—21no—
530C23×D4C22×C3711yescharacteristic
531C23×D4C22×C3711yescharacteristic
532C22×D8C22×C3711yescharacteristic
533C22×D8C22×C3711yescharacteristic, complemented
534C22×D8C22×C3711yescharacteristic, complemented
535C22×M16C22×C3711yescharacteristic, complemented
536D42—24no—
537D42—24no—
538C2×#127C22×C3711yescharacteristic
539C2×#121—21no—
540C2×#121C22×C3711yescharacteristic
541C2×#121C22×C3711yescharacteristic
542C2×#121C22×C3711yescharacteristic, complemented
543C2×#121C22×C3711yescharacteristic, complemented
544C2×#120—21no—
545C2×#120—21no—
546C2×C4×D4C22×C3711yescharacteristic
547C2×C4×D4C22×C3711yescharacteristic
548C2×#117C22×C3711yescharacteristic, complemented
549#469—24no—
550#447—24no—
551#447—24no—
552C2×#106C22×C3711yescharacteristic, complemented
553#418—24no—
554C2×#102C22×C3711yescharacteristic
555C2×#102C22×C3711yescharacteristic
556C2×#102C22×C3711yescharacteristic
557C2×#102C22×C3711yescharacteristic, complemented
558C2×#102C22×C3711yescharacteristic, complemented
559C2×#102C22×C3711yescharacteristic, complemented
560C2×#102C22×C3711yescharacteristic, complemented
561C2×#102C22×C3711yescharacteristic, complemented
562C2×#102C22×C3711yescharacteristic, complemented
563C2×#102C22×C3711yescharacteristic, complemented
564C2×C22⋊C8C22×C3711yescharacteristic, complemented
565C2×C22⋊C8C22×C3711yescharacteristic, complemented
566C2×C22⋊C8C22×C3711yescharacteristic, complemented
567#394—21no—
568#392—21no—
569#390—21no—
570#390C22×C3711yescharacteristic, complemented
571#389C22×C3711yescharacteristic, complemented
572#388—21no—
573#380C22×C3711yescharacteristic, complemented
574#340C22×C3711yescharacteristic, complemented
575#340C22×C3711yescharacteristic, complemented
576#336C22×C3711yescharacteristic, complemented
577#336C22×C3711yescharacteristic, complemented
578C37#2444011yescharacteristic, direct product factor, Sylow
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C3711yescharacteristic
604C22×D4D4×C3714yescomplemented
605C22×D4C23×C3711yescharacteristic
606C22×D4C23×C3711yescharacteristic
607C22×D4C23×C3711yescharacteristic
608C22×D4C23×C3711yescharacteristic
609C23×C4—21no—
610C23×C4C23×C3711yescharacteristic
611C23×C4C23×C3711yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C3711yescharacteristic
625C22×C8C23×C3711yescharacteristic
626C22×C8C23×C3711yescharacteristic
627C22×C8C23×C3711yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C3714yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C3711yescharacteristic
649C2×C4⋊C4C23×C3711yescharacteristic
650C2×C4⋊C4C23×C3711yescharacteristic
651C2×C4⋊C4C23×C3711yescharacteristic
652C2×C4⋊C4C23×C3711yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C3711yescharacteristic
663C2×C22⋊C4D4×C3711yescharacteristic
664C2×C42—21no—
665C2×C42C23×C3711yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C3714yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C3711yescharacteristic
701C24C2×D4×C3711yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C3712yes—
758C2×D4C2×D4×C3712yes—
759C2×D4C2×D4×C3712yes—
760C2×D4C2×D4×C3712yes—
761C2×D4#41×C3712yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C3711yescharacteristic
780C22×C4C2×D4×C3711yescharacteristic
781C22×C4C2×D4×C3711yescharacteristic
782C22×C4C2×D4×C3712yes—
783C22×C4C2×D4×C3712yes—
784C22×C4C2×D4×C3711yescharacteristic
785C22×C4C24×C3711yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C3712yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C3712yes—
811C4⋊C4C2×D4×C3712yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C3712yes—
881C23AGL(1,ℤ/8)×C3712yes—
882C23C22×D4×C3711yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C3714yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C3712yes—
940C2×C4AGL(1,ℤ/8)×C3712yes—
941C2×C4C22×D4×C3711yescharacteristic
942C2×C4C22×D4×C3711yescharacteristic
943C2×C4C22×D4×C3711yescharacteristic
944C2×C4C2×#41×C3711yescharacteristic
945C2×C4H(5,𝔽2)×C3711yescharacteristic
946C2×C4H(5,𝔽2)×C3711yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C3711yescharacteristic
996C22D42×C3711yescharacteristic
997C22C37×#54611yescharacteristic
998C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
999C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
1000C22C37×#57611yescharacteristic
1001C22C37×#57611yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C3711yescharacteristic
1011C4C37×#53411yescharacteristic
1012C4D42×C3711yescharacteristic
1013C4C37×#54611yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C37×#241011yescharacteristic
1021C2C37×#300311yescharacteristic
1022C2C37×#300811yescharacteristic
1023C2C37×#326411yescharacteristic
1024C2C37×#327411yescharacteristic
1025C2C37×#331811yescharacteristic
1026C2C37×#332511yescharacteristic
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×D42×C37C2semidirect
2. C2×C37×#469C2semidirect
3. C2×C37×#447C2semidirect
4. C2×C37×#447C2semidirect
5. C2×C37×#418C2semidirect
6. C37×#2414C2semidirect
7. C37×#2041C2semidirect
8. C37×#2034C2semidirect
9. C37×#2011C2semidirect
10. C37×#1999C2semidirect
11. C37×#1879C2semidirect
12. C37×#1875C2semidirect
13. C37×#1870C2semidirect
14. C37×#1864C2semidirect
15. C37×#1786C2semidirect
20. C22×D8×C37C22semidirect
21. C22×D8×C37C22semidirect
22. C22×M16×C37C22semidirect
29. C2×#121×C37C22semidirect
30. C2×#121×C37C22semidirect
35. C2×#117×C37C22semidirect
39. C2×#106×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
47. C2×#102×C37C22semidirect
48. C2×#102×C37C22semidirect
49. C2×#102×C37C22semidirect
50. C2×#102×C37C22semidirect
51. C2×C22⋊C8×C37C22semidirect
52. C2×C22⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
57. C37×#390C22semidirect
58. C37×#389C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
90. C22×D4×C37D4semidirect
124. #121×C37D4semidirect
162. #102×C37D4semidirect
287. C2×C8×C37C2×D4semidirect
297. C4⋊C4×C37C2×D4semidirect
437. #24440C37direct (N × H)
501. C2×D42C2×C37semidirect
502. C2×#469C2×C37semidirect
503. C2×#447C2×C37semidirect
504. C2×#447C2×C37semidirect
505. C2×#418C2×C37semidirect
506. #2414C2×C37semidirect
507. #2041C2×C37semidirect
508. #2034C2×C37semidirect
509. #2011C2×C37semidirect
510. #1999C2×C37semidirect
511. #1879C2×C37semidirect
512. #1875C2×C37semidirect
513. #1870C2×C37semidirect
514. #1864C2×C37semidirect
515. #1786C2×C37semidirect
533. C22×D8C22×C37semidirect
534. C22×D8C22×C37semidirect
535. C22×M16C22×C37semidirect
542. C2×#121C22×C37semidirect
543. C2×#121C22×C37semidirect
548. C2×#117C22×C37semidirect
552. C2×#106C22×C37semidirect
557. C2×#102C22×C37semidirect
558. C2×#102C22×C37semidirect
559. C2×#102C22×C37semidirect
560. C2×#102C22×C37semidirect
561. C2×#102C22×C37semidirect
562. C2×#102C22×C37semidirect
563. C2×#102C22×C37semidirect
564. C2×C22⋊C8C22×C37semidirect
565. C2×C22⋊C8C22×C37semidirect
566. C2×C22⋊C8C22×C37semidirect
570. #390C22×C37semidirect
571. #389C22×C37semidirect
573. #380C22×C37semidirect
574. #340C22×C37semidirect
575. #340C22×C37semidirect
576. #336C22×C37semidirect
577. #336C22×C37semidirect
578. C37#24440direct (N × H)
604. C22×D4D4×C37semidirect
638. #121D4×C37semidirect
676. #102D4×C37semidirect
801. C2×C8C2×D4×C37semidirect
811. C4⋊C4C2×D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C372
C2×C37×#4692
C2×C37×#4472
C2×C37×#4182
C37×#24142
C37×#20412
C37×#20342
C37×#20112
C37×#19992
C37×#18792
C37×#18752
C37×#18702
C37×#18642
C37×#17862
#2444037