Finite Group Databasebeta

← C37×#24277 #22645530

Subgroups — C37×#24277 #22645530

Order 9472.

1608 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
2C2×C37×#469C211yesmaximal, characteristic, complemented
3C2×C37×#468C211yesmaximal, characteristic, complemented
4C2×C37×#436C211yesmaximal, characteristic, complemented
5C37×#2408C211yesmaximal, characteristic, complemented
6C37×#2407C211yesmaximal, characteristic, complemented
7C37×#2055C211yesmaximal, characteristic, complemented
8C37×#2054C211yesmaximal, characteristic, complemented
9C37×#2000C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1970C211yesmaximal, characteristic, complemented
12C37×#1968C211yesmaximal, characteristic, complemented
13C37×#1809C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C37—24no—
19C2×AGL(1,ℤ/8)×C37—24no—
20C2×AGL(1,ℤ/8)×C37—24no—
21C22×SD16×C37C2211yescharacteristic
22C22×SD16×C37C2211yescharacteristic
23C22×D8×C37C2211yescharacteristic
24C22×D8×C37C2211yescharacteristic
25C22×M16×C37C2211yescharacteristic
26C22×M16×C37C2211yescharacteristic, complemented
27C2×C22⋊Q8×C37C2211yescharacteristic, complemented
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic, complemented
31C2×#120×C37—21no—
32C2×C4×D4×C37C2211yescharacteristic
33C37×#469—24no—
34C37×#468—24no—
35C37×#436—24no—
36C2×#107×C37C2211yescharacteristic, complemented
37C2×#106×C37C2211yescharacteristic, complemented
38C2×C4⋊C8×C37C2211yescharacteristic, complemented
39C2×#103×C37C2211yescharacteristic, complemented
40C2×#103×C37C2211yescharacteristic, complemented
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic, complemented
49C2×C4×C8×C37C2211yescharacteristic, complemented
50C37×#394—21no—
51C37×#394—21no—
52C37×#392—21no—
53C37×#392—21no—
54C37×#391C2211yescharacteristic, complemented
55C37×#390C2211yescharacteristic
56C37×#390C2211yescharacteristic
57C37×#390C2211yescharacteristic, complemented
58C37×#386—21no—
59C37×#385—21no—
60C37×#380C2211yescharacteristic
61C37×#380C2211yescharacteristic
62C37×#379—21no—
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—22no—
74C22×D4×C37—22no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—22no—
80C22×D4×C37—21no—
81C22×D4×C37—22no—
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×C37C2311yescharacteristic
90C23×C4×C37C2311yescharacteristic
91AGL(1,ℤ/8)×C37—232no—
92C2×SD16×C37—22no—
93C2×SD16×C37—22no—
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—22no—
97C2×SD16×C37D414yescomplemented
98C2×D8×C37—22no—
99C2×D8×C37—22no—
100C2×D8×C37—22no—
101C2×D8×C37—22no—
102C2×D8×C37—22no—
103C2×D8×C37D414yescomplemented
104C2×M16×C37—22no—
105C2×M16×C37—22no—
106C2×M16×C37—22no—
107C2×M16×C37—22no—
108C2×M16×C37—22no—
109C2×M16×C37D414yescomplemented
110C22×C8×C37C2311yescharacteristic
111C22×C8×C37C2311yescharacteristic
112C22×C8×C37C2311yescharacteristic
113C22×C8×C37C2311yescharacteristic
114C22⋊Q8×C37—22no—
115C22⋊Q8×C37—41no—
116#121×C37—22no—
117#121×C37—22no—
118#121×C37—22no—
119#121×C37—41no—
120#121×C37—41no—
121#121×C37—41no—
122#120×C37—44no—
123C4×D4×C37—22no—
124C4×D4×C37—22no—
125C2×C4⋊C4×C37—21no—
126C2×C4⋊C4×C37D411yescharacteristic
127C2×C4⋊C4×C37C2311yescharacteristic
128C2×C4⋊C4×C37C2311yescharacteristic
129C2×C4⋊C4×C37C2311yescharacteristic
130C2×C4⋊C4×C37C2311yescharacteristic
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×C22⋊C4×C37—21no—
142C2×C22⋊C4×C37—21no—
143C2×C22⋊C4×C37D411yescharacteristic
144C2×C22⋊C4×C37D411yescharacteristic
145C2×C42×C37C2311yescharacteristic
146#107×C37—22no—
147#106×C37—22no—
148C4⋊C8×C37—22no—
149#103×C37—22no—
150#103×C37—41no—
151#102×C37—22no—
152#102×C37—22no—
153#102×C37—22no—
154#102×C37—41no—
155#102×C37—41no—
156#102×C37—41no—
157C22⋊C8×C37—22no—
158C22⋊C8×C37—22no—
159C4×C8×C37—22no—
160#95×C37—21no—
161#95×C37—21no—
162#95×C37—21no—
163#95×C37—21no—
164C24×C37—21no—
165C24×C37—21no—
166C24×C37—21no—
167C24×C37—42no—
168C24×C37—42no—
169C24×C37—42no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—81no—
173C24×C37—81no—
174C24×C37C2×D411yescharacteristic
175C24×C37C2×D411yescharacteristic
176#41×C37—28no—
177#41×C37—44no—
178#41×C37—44no—
179#41×C37—44no—
180C2×Q8×C37—21no—
181C2×Q8×C37—21no—
182C2×Q8×C37—21no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37C2×D412yes—
186C2×D4×C37—28no—
187C2×D4×C37—22no—
188C2×D4×C37—22no—
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—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—44no—
205C2×D4×C37—44no—
206C2×D4×C37—41no—
207C2×D4×C37—42no—
208C2×D4×C37—42no—
209C2×D4×C37—42no—
210C2×D4×C37—44no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
215C2×D4×C37—42no—
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×C37C2×D412yes—
224C2×D4×C37C2×D412yes—
225C2×D4×C37C2×D412yes—
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—21no—
240C22×C4×C37—21no—
241C22×C4×C37—42no—
242C22×C4×C37—42no—
243C22×C4×C37—42no—
244C22×C4×C37C2×D411yescharacteristic
245C22×C4×C37C2×D411yescharacteristic
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D412yes—
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37#4112yes—
250C22×C4×C37C2411yescharacteristic
251SD16×C37—28no—
252SD16×C37—28no—
253D8×C37—28no—
254D8×C37—28no—
255M16×C37—28no—
256M16×C37—44no—
257C2×C8×C37—21no—
258C2×C8×C37—21no—
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×C37C2×D412yes—
266C2×C8×C37C2×D412yes—
267C2×C8×C37C2×D412yes—
268C2×C8×C37C2×D412yes—
269C4⋊C4×C37—22no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—42no—
279C22⋊C4×C37—22no—
280C22⋊C4×C37—22no—
281C22⋊C4×C37—42no—
282C22⋊C4×C37—42no—
283C22⋊C4×C37—42no—
284C22⋊C4×C37—42no—
285C22⋊C4×C37—42no—
286C22⋊C4×C37—42no—
287C22⋊C4×C37—42no—
288C22⋊C4×C37—42no—
289C22⋊C4×C37—81no—
290C22⋊C4×C37—81no—
291C22⋊C4×C37—81no—
292C22⋊C4×C37—81no—
293C42×C37—21no—
294C42×C37—21no—
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—22no—
304C23×C37—22no—
305C23×C37—22no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—48no—
312C23×C37—41no—
313C23×C37—41no—
314C23×C37—41no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37—41no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37—41no—
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—84no—
331C23×C37—84no—
332C23×C37—84no—
333C23×C37—84no—
334C23×C37—84no—
335C23×C37—84no—
336C23×C37#12112yes—
337C23×C37C22×D411yescharacteristic
338Q8×C37—22no—
339Q8×C37—22no—
340Q8×C37—41no—
341Q8×C37—41no—
342D4×C37—22no—
343D4×C37—22no—
344D4×C37—22no—
345D4×C37—22no—
346D4×C37—22no—
347D4×C37—22no—
348D4×C37—44no—
349D4×C37—48no—
350D4×C37—48no—
351D4×C37—41no—
352D4×C37—41no—
353D4×C37—41no—
354D4×C37—41no—
355D4×C37—41no—
356D4×C37—41no—
357D4×C37—84no—
358D4×C37—84no—
359D4×C37—84no—
360C2×C4×C37—21no—
361C2×C4×C37—21no—
362C2×C4×C37—21no—
363C2×C4×C37—21no—
364C2×C4×C37—22no—
365C2×C4×C37—22no—
366C2×C4×C37—22no—
367C2×C4×C37—22no—
368C2×C4×C37—21no—
369C2×C4×C37—21no—
370C2×C4×C37—21no—
371C2×C4×C37—21no—
372C2×C4×C37—22no—
373C2×C4×C37—21no—
374C2×C4×C37—21no—
375C2×C4×C37—48no—
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#12112yes—
395C2×C4×C37AGL(1,ℤ/8)12yescomplemented
396C2×C4×C37C22×D411yescharacteristic
397C2×C4×C37C22×D411yescharacteristic
398C2×C4×C37C22×D411yescharacteristic
399C2×C4×C37C2×#4111yescharacteristic
400C2×C4×C37H(5,𝔽2)11yescharacteristic
401C2×C4×C37H(5,𝔽2)11yescharacteristic
402C8×C37—22no—
403C8×C37—41no—
404C8×C37—41no—
405C8×C37#12014yescomplemented
406#24277C3711yesmaximal, characteristic, direct product factor, Sylow
407C22×C37—22no—
408C22×C37—22no—
409C22×C37—22no—
410C22×C37—41no—
411C22×C37—41no—
412C22×C37—41no—
413C22×C37—41no—
414C22×C37—42no—
415C22×C37—41no—
416C22×C37—42no—
417C22×C37—42no—
418C22×C37—41no—
419C22×C37—42no—
420C22×C37—42no—
421C22×C37—41no—
422C22×C37—42no—
423C22×C37—42no—
424C22×C37—41no—
425C22×C37—42no—
426C22×C37—41no—
427C22×C37—42no—
428C22×C37—41no—
429C22×C37—41no—
430C22×C37—816no—
431C22×C37—81no—
432C22×C37—81no—
433C22×C37—81no—
434C22×C37—81no—
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×C37C2×#12111yescharacteristic
444C22×C37D4211yescharacteristic
445C22×C37D4211yescharacteristic
446C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
447C22×C37#57511yescharacteristic
448C22×C37#57611yescharacteristic
449C22×C37#57711yescharacteristic
450C4×C37—22no—
451C4×C37—22no—
452C4×C37—41no—
453C4×C37—42no—
454C4×C37—41no—
455C4×C37—81no—
456C4×C37—81no—
457C4×C37—81no—
458C4×C37—81no—
459C4×C37C2×#12011yescharacteristic
460C4×C37#53511yescharacteristic
461C4×C37#54611yescharacteristic
462C4×C37#54611yescharacteristic
463C22×AGL(1,ℤ/8)C2×C3711yescharacteristic, complemented
464C2×#469C2×C3711yescharacteristic, complemented
465C2×#468C2×C3711yescharacteristic, complemented
466C2×#436C2×C3711yescharacteristic, complemented
467#2408C2×C3711yescharacteristic, complemented
468#2407C2×C3711yescharacteristic, complemented
469#2055C2×C3711yescharacteristic, complemented
470#2054C2×C3711yescharacteristic, complemented
471#2000C2×C3711yescharacteristic, complemented
472#1999C2×C3711yescharacteristic, complemented
473#1970C2×C3711yescharacteristic, complemented
474#1968C2×C3711yescharacteristic, complemented
475#1809C2×C3711yescharacteristic, complemented
476#1788C2×C3711yescharacteristic, complemented
477#1786C2×C3711yescharacteristic, complemented
478C2×C37—42no—
479C2×C37—81no—
480C2×C37—82no—
481C2×C37—82no—
482C2×C37—82no—
483C2×C37#240811yescharacteristic
484C2×C37#305511yescharacteristic
485C2×C37#306211yescharacteristic
486C2×C37#327211yescharacteristic
487C2×C37#327311yescharacteristic
488C2×C37#327411yescharacteristic
489C2×C37#327511yescharacteristic
490C22×#41C22×C3711yescharacteristic
491C23×D4C22×C3711yescharacteristic
492C2×AGL(1,ℤ/8)—24no—
493C2×AGL(1,ℤ/8)—24no—
494C2×AGL(1,ℤ/8)—24no—
495C22×SD16C22×C3711yescharacteristic
496C22×SD16C22×C3711yescharacteristic
497C22×D8C22×C3711yescharacteristic
498C22×D8C22×C3711yescharacteristic
499C22×M16C22×C3711yescharacteristic
500C22×M16C22×C3711yescharacteristic, complemented
501C2×C22⋊Q8C22×C3711yescharacteristic, complemented
502C2×#121C22×C3711yescharacteristic
503C2×#121C22×C3711yescharacteristic
504C2×#121C22×C3711yescharacteristic, complemented
505C2×#120—21no—
506C2×C4×D4C22×C3711yescharacteristic
507#469—24no—
508#468—24no—
509#436—24no—
510C2×#107C22×C3711yescharacteristic, complemented
511C2×#106C22×C3711yescharacteristic, complemented
512C2×C4⋊C8C22×C3711yescharacteristic, complemented
513C2×#103C22×C3711yescharacteristic, complemented
514C2×#103C22×C3711yescharacteristic, complemented
515C2×#102C22×C3711yescharacteristic
516C2×#102C22×C3711yescharacteristic
517C2×#102C22×C3711yescharacteristic
518C2×#102C22×C3711yescharacteristic
519C2×#102C22×C3711yescharacteristic, complemented
520C2×#102C22×C3711yescharacteristic, complemented
521C2×C22⋊C8C22×C3711yescharacteristic
522C2×C22⋊C8C22×C3711yescharacteristic, complemented
523C2×C4×C8C22×C3711yescharacteristic, complemented
524#394—21no—
525#394—21no—
526#392—21no—
527#392—21no—
528#391C22×C3711yescharacteristic, complemented
529#390C22×C3711yescharacteristic
530#390C22×C3711yescharacteristic
531#390C22×C3711yescharacteristic, complemented
532#386—21no—
533#385—21no—
534#380C22×C3711yescharacteristic
535#380C22×C3711yescharacteristic
536#379—21no—
537#340C22×C3711yescharacteristic, complemented
538#340C22×C3711yescharacteristic, complemented
539C37#2427711yescharacteristic, direct product factor, Sylow
540C25—21no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—41no—
546C2×#41—41no—
547C22×Q8C23×C3711yescharacteristic
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—41no—
558C22×D4—41no—
559C22×D4D4×C3711yescharacteristic
560C22×D4C23×C3711yescharacteristic
561C22×D4C23×C3711yescharacteristic
562C22×D4C23×C3711yescharacteristic
563C23×C4—21no—
564C23×C4C23×C3711yescharacteristic
565C23×C4C23×C3711yescharacteristic
566AGL(1,ℤ/8)—232no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16D4×C3714yescomplemented
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8D4×C3714yescomplemented
579C2×M16—22no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—22no—
584C2×M16D4×C3714yescomplemented
585C22×C8C23×C3711yescharacteristic
586C22×C8C23×C3711yescharacteristic
587C22×C8C23×C3711yescharacteristic
588C22×C8C23×C3711yescharacteristic
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#120—44no—
598C4×D4—22no—
599C4×D4—22no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4D4×C3711yescharacteristic
602C2×C4⋊C4C23×C3711yescharacteristic
603C2×C4⋊C4C23×C3711yescharacteristic
604C2×C4⋊C4C23×C3711yescharacteristic
605C2×C4⋊C4C23×C3711yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
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⋊C4D4×C3711yescharacteristic
619C2×C22⋊C4D4×C3711yescharacteristic
620C2×C42C23×C3711yescharacteristic
621#107—22no—
622#106—22no—
623C4⋊C8—22no—
624#103—22no—
625#103—41no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—41no—
630#102—41no—
631#102—41no—
632C22⋊C8—22no—
633C22⋊C8—22no—
634C4×C8—22no—
635#95—21no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24C2×D4×C3711yescharacteristic
650C24C2×D4×C3711yescharacteristic
651#41—28no—
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—28no—
662C2×D4—22no—
663C2×D4—22no—
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—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4C2×D4×C3712yes—
699C2×D4C2×D4×C3712yes—
700C2×D4C2×D4×C3712yes—
701C22×C4—21no—
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—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4C2×D4×C3711yescharacteristic
720C22×C4C2×D4×C3711yescharacteristic
721C22×C4C2×D4×C3711yescharacteristic
722C22×C4C2×D4×C3712yes—
723C22×C4C2×D4×C3711yescharacteristic
724C22×C4#41×C3712yes—
725C22×C4C24×C3711yescharacteristic
726SD16—28no—
727SD16—28no—
728D8—28no—
729D8—28no—
730M16—28no—
731M16—44no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8C2×D4×C3712yes—
741C2×C8C2×D4×C3712yes—
742C2×C8C2×D4×C3712yes—
743C2×C8C2×D4×C3712yes—
744C4⋊C4—22no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C42—21no—
769C42—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—48no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23—84no—
811C23#121×C3712yes—
812C23C22×D4×C3711yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—44no—
824D4—48no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—48no—
851C2×C4—41no—
852C2×C4—41no—
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#121×C3712yes—
870C2×C4AGL(1,ℤ/8)×C3712yescomplemented
871C2×C4C22×D4×C3711yescharacteristic
872C2×C4C22×D4×C3711yescharacteristic
873C2×C4C22×D4×C3711yescharacteristic
874C2×C4C2×#41×C3711yescharacteristic
875C2×C4H(5,𝔽2)×C3711yescharacteristic
876C2×C4H(5,𝔽2)×C3711yescharacteristic
877C8—22no—
878C8—41no—
879C8—41no—
880C8#120×C3714yescomplemented
881C22—22no—
882C22—22no—
883C22—22no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—41no—
904C22—816no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#121×C3711yescharacteristic
918C22D42×C3711yescharacteristic
919C22D42×C3711yescharacteristic
920C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
921C22C37×#57511yescharacteristic
922C22C37×#57611yescharacteristic
923C22C37×#57711yescharacteristic
924C4—22no—
925C4—22no—
926C4—41no—
927C4—42no—
928C4—41no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4C2×#120×C3711yescharacteristic
934C4C37×#53511yescharacteristic
935C4C37×#54611yescharacteristic
936C4C37×#54611yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—82no—
942C2C37×#240811yescharacteristic
943C2C37×#305511yescharacteristic
944C2C37×#306211yescharacteristic
945C2C37×#327211yescharacteristic
946C2C37×#327311yescharacteristic
947C2C37×#327411yescharacteristic
948C2C37×#327511yescharacteristic
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. C22×AGL(1,ℤ/8)×C37C2semidirect
2. C2×C37×#469C2semidirect
3. C2×C37×#468C2semidirect
4. C2×C37×#436C2semidirect
5. C37×#2408C2semidirect
6. C37×#2407C2semidirect
7. C37×#2055C2semidirect
8. C37×#2054C2semidirect
9. C37×#2000C2semidirect
10. C37×#1999C2semidirect
11. C37×#1970C2semidirect
12. C37×#1968C2semidirect
13. C37×#1809C2semidirect
14. C37×#1788C2semidirect
15. C37×#1786C2semidirect
26. C22×M16×C37C22semidirect
27. C2×C22⋊Q8×C37C22semidirect
30. C2×#121×C37C22semidirect
36. C2×#107×C37C22semidirect
37. C2×#106×C37C22semidirect
38. C2×C4⋊C8×C37C22semidirect
39. C2×#103×C37C22semidirect
40. C2×#103×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
48. C2×C22⋊C8×C37C22semidirect
49. C2×C4×C8×C37C22semidirect
54. C37×#391C22semidirect
57. C37×#390C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
97. C2×SD16×C37D4semidirect
103. C2×D8×C37D4semidirect
109. C2×M16×C37D4semidirect
395. C2×C4×C37AGL(1,ℤ/8)semidirect
405. C8×C37#120semidirect
406. #24277C37direct (N × H)
463. C22×AGL(1,ℤ/8)C2×C37semidirect
464. C2×#469C2×C37semidirect
465. C2×#468C2×C37semidirect
466. C2×#436C2×C37semidirect
467. #2408C2×C37semidirect
468. #2407C2×C37semidirect
469. #2055C2×C37semidirect
470. #2054C2×C37semidirect
471. #2000C2×C37semidirect
472. #1999C2×C37semidirect
473. #1970C2×C37semidirect
474. #1968C2×C37semidirect
475. #1809C2×C37semidirect
476. #1788C2×C37semidirect
477. #1786C2×C37semidirect
500. C22×M16C22×C37semidirect
501. C2×C22⋊Q8C22×C37semidirect
504. C2×#121C22×C37semidirect
510. C2×#107C22×C37semidirect
511. C2×#106C22×C37semidirect
512. C2×C4⋊C8C22×C37semidirect
513. C2×#103C22×C37semidirect
514. C2×#103C22×C37semidirect
519. C2×#102C22×C37semidirect
520. C2×#102C22×C37semidirect
522. C2×C22⋊C8C22×C37semidirect
523. C2×C4×C8C22×C37semidirect
528. #391C22×C37semidirect
531. #390C22×C37semidirect
537. #340C22×C37semidirect
538. #340C22×C37semidirect
539. C37#24277direct (N × H)
572. C2×SD16D4×C37semidirect
578. C2×D8D4×C37semidirect
584. C2×M16D4×C37semidirect
870. C2×C4AGL(1,ℤ/8)×C37semidirect
880. C8#120×C37semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C372
C2×C37×#4692
C2×C37×#4682
C2×C37×#4362
C37×#24082
C37×#24072
C37×#20552
C37×#20542
C37×#20002
C37×#19992
C37×#19702
C37×#19682
C37×#18092
C37×#17882
C37×#17862
#2427737