Finite Group Databasebeta

← C37×#32709 #22653962

Subgroups — C37×#32709 #22653962

Order 9472.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2848C211yesmaximal, characteristic, complemented
2C37×#2847C211yesmaximal, characteristic
3C37×#2077C211yesmaximal, characteristic, complemented
4C37×#2076C211yesmaximal, characteristic, complemented
5C37×#2075C211yesmaximal, characteristic, complemented
6C37×#2036C211yesmaximal, characteristic, complemented
7C37×#2036C211yesmaximal, characteristic, complemented
8C37×#2035C211yesmaximal, characteristic, complemented
9C37×#2034C211yesmaximal, characteristic, complemented
10C37×#2033C211yesmaximal, characteristic, complemented
11C37×#2033C211yesmaximal, characteristic, complemented
12C37×#2000C211yesmaximal, characteristic, complemented
13C37×#2000C211yesmaximal, characteristic, complemented
14C37×#2000C211yesmaximal, characteristic, complemented
15C37×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic, complemented
18C2×C22⋊Q8×C37C2211yescharacteristic
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×C22⋊Q8×C37C2211yescharacteristic
21C2×#121×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#120×C37—21no—
25C2×#107×C37C2211yescharacteristic, complemented
26C2×#107×C37C2211yescharacteristic, complemented
27C2×#106×C37C2211yescharacteristic, complemented
28C2×#103×C37C2211yescharacteristic, complemented
29C2×#103×C37C2211yescharacteristic, complemented
30C2×#103×C37C2211yescharacteristic, complemented
31C2×#102×C37C2211yescharacteristic, complemented
32C2×#102×C37C2211yescharacteristic, complemented
33C2×#102×C37C2211yescharacteristic, complemented
34C2×C22⋊C8×C37C2211yescharacteristic
35C2×C22⋊C8×C37C2211yescharacteristic
36C2×C22⋊C8×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C37×#386—21no—
41C37×#386—21no—
42C37×#386—21no—
43C37×#385—21no—
44C37×#385—21no—
45C37×#385—21no—
46C37×#380C2211yescharacteristic
47C37×#380C2211yescharacteristic
48C37×#380C2211yescharacteristic
49C37×#380C2211yescharacteristic
50C37×#380C2211yescharacteristic
51C37×#380C2211yescharacteristic
52C37×#379—21no—
53C37×#340C2211yescharacteristic, complemented
54C37×#340C2211yescharacteristic, complemented
55C37×#340C2211yescharacteristic, complemented
56C37×#340C2211yescharacteristic, complemented
57C37×#340C2211yescharacteristic, complemented
58C37×#340C2211yescharacteristic, complemented
59C25×C37D411yescharacteristic
60C22×Q8×C37C2311yescharacteristic
61C22×D4×C37—21no—
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37C2311yescharacteristic
65C23×C4×C37—41no—
66C23×C4×C37—41no—
67C23×C4×C37—41no—
68C23×C4×C37—41no—
69C23×C4×C37—41no—
70C23×C4×C37—41no—
71C23×C4×C37D411yescharacteristic
72C23×C4×C37D411yescharacteristic
73C23×C4×C37D411yescharacteristic
74C23×C4×C37C2311yescharacteristic
75C23×C4×C37C2311yescharacteristic
76C23×C4×C37C2311yescharacteristic
77C2×SD16×C37—41no—
78C2×SD16×C37—41no—
79C2×SD16×C37—41no—
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C22⋊Q8×C37—41no—
85C22⋊Q8×C37—41no—
86C22⋊Q8×C37—41no—
87C22⋊Q8×C37—41no—
88C22⋊Q8×C37—41no—
89C22⋊Q8×C37—41no—
90#121×C37—41no—
91#121×C37—41no—
92#121×C37—41no—
93#121×C37—41no—
94#121×C37—41no—
95#121×C37—41no—
96#120×C37—44no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C4⋊C4×C37C2311yescharacteristic
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C4⋊C4×C37C2311yescharacteristic
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—21no—
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37—21no—
112C2×C22⋊C4×C37—21no—
113C2×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118#107×C37—41no—
119#107×C37—41no—
120#106×C37—41no—
121#103×C37—41no—
122#103×C37—41no—
123#103×C37—41no—
124#102×C37—41no—
125#102×C37—41no—
126#102×C37—41no—
127C22⋊C8×C37—41no—
128C22⋊C8×C37—41no—
129C22⋊C8×C37—41no—
130C22⋊C8×C37—41no—
131C22⋊C8×C37—41no—
132C22⋊C8×C37—41no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37—21no—
139C24×C37—22no—
140C24×C37—22no—
141C24×C37—22no—
142C24×C37—21no—
143C24×C37—41no—
144C24×C37—41no—
145C24×C37—41no—
146C24×C37—41no—
147C24×C37C2×D411yescharacteristic
148C24×C37C2×D411yescharacteristic
149C24×C37C2×D411yescharacteristic
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×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—42no—
163C2×D4×C37—42no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—42no—
167C2×D4×C37—42no—
168C2×D4×C37—42no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—41no—
197C22×C4×C37—41no—
198C22×C4×C37—41no—
199C22×C4×C37—41no—
200C22×C4×C37—41no—
201C22×C4×C37—41no—
202C22×C4×C37—41no—
203C22×C4×C37—41no—
204C22×C4×C37—41no—
205C22×C4×C37—44no—
206C22×C4×C37—44no—
207C22×C4×C37—44no—
208C22×C4×C37—44no—
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D411yescharacteristic
211C22×C4×C37C2×D411yescharacteristic
212C22×C4×C37C2411yescharacteristic
213SD16×C37—44no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—42no—
239C4⋊C4×C37—42no—
240C4⋊C4×C37—42no—
241C22⋊C4×C37—42no—
242C22⋊C4×C37—42no—
243C22⋊C4×C37—42no—
244C22⋊C4×C37—42no—
245C22⋊C4×C37—42no—
246C22⋊C4×C37—42no—
247C22⋊C4×C37—42no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—42no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—42no—
253C23×C37—21no—
254C23×C37—21no—
255C23×C37—21no—
256C23×C37—21no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—21no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—44no—
272C23×C37—44no—
273C23×C37—44no—
274C23×C37—44no—
275C23×C37—44no—
276C23×C37—44no—
277C23×C37—44no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37#13512yes—
286C23×C37AGL(1,ℤ/8)12yes—
287C23×C37#13712yes—
288C23×C37C22×D411yescharacteristic
289Q8×C37—41no—
290Q8×C37—41no—
291Q8×C37—41no—
292Q8×C37—41no—
293D4×C37—41no—
294D4×C37—41no—
295D4×C37—41no—
296D4×C37—41no—
297D4×C37—84no—
298D4×C37—84no—
299D4×C37—84no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—21no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—44no—
310C2×C4×C37—44no—
311C2×C4×C37—44no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
331C2×C4×C37—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—41no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37H(5,𝔽2)11yescharacteristic
346C2×C4×C37H(5,𝔽2)11yescharacteristic
347C2×C4×C37H(5,𝔽2)11yescharacteristic
348C2×C4×C37H(5,𝔽2)11yescharacteristic
349C2×C4×C37H(5,𝔽2)11yescharacteristic
350C2×C4×C37H(5,𝔽2)11yescharacteristic
351C8×C37—41no—
352C8×C37—41no—
353C8×C37—41no—
354C8×C37—41no—
355#32709C3711yesmaximal, characteristic, direct product factor, Sylow
356C22×C37—22no—
357C22×C37—22no—
358C22×C37—22no—
359C22×C37—22no—
360C22×C37—22no—
361C22×C37—22no—
362C22×C37—22no—
363C22×C37—22no—
364C22×C37—22no—
365C22×C37—416no—
366C22×C37—41no—
367C22×C37—41no—
368C22×C37—41no—
369C22×C37—41no—
370C22×C37—41no—
371C22×C37—41no—
372C22×C37—41no—
373C22×C37—41no—
374C22×C37—41no—
375C22×C37—41no—
376C22×C37—41no—
377C22×C37—41no—
378C22×C37—81no—
379C22×C37—81no—
380C22×C37—81no—
381C22×C37—81no—
382C22×C37—81no—
383C22×C37—81no—
384C22×C37—81no—
385C22×C37#53411yescharacteristic
386C22×C37#53411yescharacteristic
387C22×C37#53411yescharacteristic
388C22×C37C2×#13511yescharacteristic
389C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C37C2×#13711yescharacteristic
391C22×C37#57511yescharacteristic
392C4×C37—41no—
393C4×C37—41no—
394C4×C37—41no—
395C4×C37—81no—
396C4×C37—81no—
397C4×C37—81no—
398C4×C37—81no—
399C4×C37—81no—
400C4×C37—81no—
401C4×C37—81no—
402C4×C37#56011yescharacteristic
403C4×C37#56011yescharacteristic
404C4×C37#56011yescharacteristic
405C4×C37H(3,𝔽4)11yescharacteristic
406#2848C2×C3711yescharacteristic, complemented
407#2847C2×C3711yescharacteristic
408#2077C2×C3711yescharacteristic, complemented
409#2076C2×C3711yescharacteristic, complemented
410#2075C2×C3711yescharacteristic, complemented
411#2036C2×C3711yescharacteristic, complemented
412#2036C2×C3711yescharacteristic, complemented
413#2035C2×C3711yescharacteristic, complemented
414#2034C2×C3711yescharacteristic, complemented
415#2033C2×C3711yescharacteristic, complemented
416#2033C2×C3711yescharacteristic, complemented
417#2000C2×C3711yescharacteristic, complemented
418#2000C2×C3711yescharacteristic, complemented
419#2000C2×C3711yescharacteristic, complemented
420#1779C2×C3711yescharacteristic, complemented
421C2×C37—42no—
422C2×C37—42no—
423C2×C37—42no—
424C2×C37—161no—
425C2×C37#281211yescharacteristic
426C2×C37#318811yescharacteristic
427C2×C37#319011yescharacteristic
428C2×C37#319111yescharacteristic
429C2×C37#319311yescharacteristic
430C2×C37#319411yescharacteristic
431C2×C37#319611yescharacteristic
432C24×C4C22×C3711yescharacteristic
433C22×SD16C22×C3711yescharacteristic, complemented
434C2×C22⋊Q8C22×C3711yescharacteristic
435C2×C22⋊Q8C22×C3711yescharacteristic
436C2×C22⋊Q8C22×C3711yescharacteristic
437C2×#121C22×C3711yescharacteristic
438C2×#121C22×C3711yescharacteristic
439C2×#121C22×C3711yescharacteristic
440C2×#120—21no—
441C2×#107C22×C3711yescharacteristic, complemented
442C2×#107C22×C3711yescharacteristic, complemented
443C2×#106C22×C3711yescharacteristic, complemented
444C2×#103C22×C3711yescharacteristic, complemented
445C2×#103C22×C3711yescharacteristic, complemented
446C2×#103C22×C3711yescharacteristic, complemented
447C2×#102C22×C3711yescharacteristic, complemented
448C2×#102C22×C3711yescharacteristic, complemented
449C2×#102C22×C3711yescharacteristic, complemented
450C2×C22⋊C8C22×C3711yescharacteristic
451C2×C22⋊C8C22×C3711yescharacteristic
452C2×C22⋊C8C22×C3711yescharacteristic
453C2×C22⋊C8C22×C3711yescharacteristic
454C2×C22⋊C8C22×C3711yescharacteristic
455C2×C22⋊C8C22×C3711yescharacteristic
456#386—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#380C22×C3711yescharacteristic
463#380C22×C3711yescharacteristic
464#380C22×C3711yescharacteristic
465#380C22×C3711yescharacteristic
466#380C22×C3711yescharacteristic
467#380C22×C3711yescharacteristic
468#379—21no—
469#340C22×C3711yescharacteristic, complemented
470#340C22×C3711yescharacteristic, complemented
471#340C22×C3711yescharacteristic, complemented
472#340C22×C3711yescharacteristic, complemented
473#340C22×C3711yescharacteristic, complemented
474#340C22×C3711yescharacteristic, complemented
475C37#3270911yescharacteristic, direct product factor, Sylow
476C25D4×C3711yescharacteristic
477C22×Q8C23×C3711yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4C23×C3711yescharacteristic
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4D4×C3711yescharacteristic
489C23×C4D4×C3711yescharacteristic
490C23×C4D4×C3711yescharacteristic
491C23×C4C23×C3711yescharacteristic
492C23×C4C23×C3711yescharacteristic
493C23×C4C23×C3711yescharacteristic
494C2×SD16—41no—
495C2×SD16—41no—
496C2×SD16—41no—
497C22×C8C23×C3711yescharacteristic
498C22×C8C23×C3711yescharacteristic
499C22×C8C23×C3711yescharacteristic
500C22×C8C23×C3711yescharacteristic
501C22⋊Q8—41no—
502C22⋊Q8—41no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506C22⋊Q8—41no—
507#121—41no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#121—41no—
513#120—44no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4C23×C3711yescharacteristic
518C2×C4⋊C4C23×C3711yescharacteristic
519C2×C4⋊C4C23×C3711yescharacteristic
520C2×C4⋊C4C23×C3711yescharacteristic
521C2×C4⋊C4C23×C3711yescharacteristic
522C2×C4⋊C4C23×C3711yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535#107—41no—
536#107—41no—
537#106—41no—
538#103—41no—
539#103—41no—
540#103—41no—
541#102—41no—
542#102—41no—
543#102—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24C2×D4×C3711yescharacteristic
565C24C2×D4×C3711yescharacteristic
566C24C2×D4×C3711yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×D4×C3711yescharacteristic
627C22×C4C2×D4×C3711yescharacteristic
628C22×C4C2×D4×C3711yescharacteristic
629C22×C4C24×C3711yescharacteristic
630SD16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23#135×C3712yes—
703C23AGL(1,ℤ/8)×C3712yes—
704C23#137×C3712yes—
705C23C22×D4×C3711yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4H(5,𝔽2)×C3711yescharacteristic
763C2×C4H(5,𝔽2)×C3711yescharacteristic
764C2×C4H(5,𝔽2)×C3711yescharacteristic
765C2×C4H(5,𝔽2)×C3711yescharacteristic
766C2×C4H(5,𝔽2)×C3711yescharacteristic
767C2×C4H(5,𝔽2)×C3711yescharacteristic
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C37×#53411yescharacteristic
802C22C37×#53411yescharacteristic
803C22C37×#53411yescharacteristic
804C22C2×#135×C3711yescharacteristic
805C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
806C22C2×#137×C3711yescharacteristic
807C22C37×#57511yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C37×#56011yescharacteristic
819C4C37×#56011yescharacteristic
820C4C37×#56011yescharacteristic
821C4C37×H(3,𝔽4)11yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2C37×#281211yescharacteristic
827C2C37×#318811yescharacteristic
828C2C37×#319011yescharacteristic
829C2C37×#319111yescharacteristic
830C2C37×#319311yescharacteristic
831C2C37×#319411yescharacteristic
832C2C37×#319611yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2847C2
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. C37×#2848C2semidirect
3. C37×#2077C2semidirect
4. C37×#2076C2semidirect
5. C37×#2075C2semidirect
6. C37×#2036C2semidirect
7. C37×#2036C2semidirect
8. C37×#2035C2semidirect
9. C37×#2034C2semidirect
10. C37×#2033C2semidirect
11. C37×#2033C2semidirect
12. C37×#2000C2semidirect
13. C37×#2000C2semidirect
14. C37×#2000C2semidirect
15. C37×#1779C2semidirect
17. C22×SD16×C37C22semidirect
25. C2×#107×C37C22semidirect
26. C2×#107×C37C22semidirect
27. C2×#106×C37C22semidirect
28. C2×#103×C37C22semidirect
29. C2×#103×C37C22semidirect
30. C2×#103×C37C22semidirect
31. C2×#102×C37C22semidirect
32. C2×#102×C37C22semidirect
33. C2×#102×C37C22semidirect
53. C37×#340C22semidirect
54. C37×#340C22semidirect
55. C37×#340C22semidirect
56. C37×#340C22semidirect
57. C37×#340C22semidirect
58. C37×#340C22semidirect
355. #32709C37direct (N × H)
406. #2848C2×C37semidirect
408. #2077C2×C37semidirect
409. #2076C2×C37semidirect
410. #2075C2×C37semidirect
411. #2036C2×C37semidirect
412. #2036C2×C37semidirect
413. #2035C2×C37semidirect
414. #2034C2×C37semidirect
415. #2033C2×C37semidirect
416. #2033C2×C37semidirect
417. #2000C2×C37semidirect
418. #2000C2×C37semidirect
419. #2000C2×C37semidirect
420. #1779C2×C37semidirect
433. C22×SD16C22×C37semidirect
441. C2×#107C22×C37semidirect
442. C2×#107C22×C37semidirect
443. C2×#106C22×C37semidirect
444. C2×#103C22×C37semidirect
445. C2×#103C22×C37semidirect
446. C2×#103C22×C37semidirect
447. C2×#102C22×C37semidirect
448. C2×#102C22×C37semidirect
449. C2×#102C22×C37semidirect
469. #340C22×C37semidirect
470. #340C22×C37semidirect
471. #340C22×C37semidirect
472. #340C22×C37semidirect
473. #340C22×C37semidirect
474. #340C22×C37semidirect
475. C37#32709direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#28482
C37×#28472
C37×#20772
C37×#20762
C37×#20752
C37×#20362
C37×#20352
C37×#20342
C37×#20332
C37×#20002
C37×#17792
#3270937