Finite Group Databasebeta

← C37×#24444 #22645697

Subgroups — C37×#24444 #22645697

Order 9472.

1662 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#546C211yesmaximal, characteristic, complemented
2C2×C37×#469C211yesmaximal, characteristic, complemented
3C2×C37×#449C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C2×C37×#417C211yesmaximal, characteristic, complemented
6C37×#2416C211yesmaximal, characteristic, complemented
7C37×#2042C211yesmaximal, characteristic, complemented
8C37×#2035C211yesmaximal, characteristic, complemented
9C37×#2012C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1879C211yesmaximal, characteristic, complemented
12C37×#1874C211yesmaximal, characteristic, complemented
13C37×#1870C211yesmaximal, characteristic, complemented
14C37×#1864C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic, complemented
19C22×D8×C37C2211yescharacteristic
20C22×D8×C37C2211yescharacteristic
21C22×M16×C37C2211yescharacteristic, complemented
22C37×#546—24no—
23C37×#546—24no—
24C2×#124×C37C2211yescharacteristic
25C2×#123×C37—21no—
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×#121×C37—21no—
28C2×#121×C37—21no—
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C2×#121×C37C2211yescharacteristic, complemented
32C2×#120×C37—21no—
33C2×C4×D4×C37C2211yescharacteristic
34C2×C4×D4×C37C2211yescharacteristic
35C22×C4⋊C4×C37C2211yescharacteristic, complemented
36C22×C22⋊C4×C37—21no—
37C37×#469—24no—
38C37×#449—24no—
39C37×#447—24no—
40C2×#106×C37C2211yescharacteristic, complemented
41C37×#417—24no—
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#103×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C2×#102×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic
51C2×#102×C37C2211yescharacteristic, complemented
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C37×#396—21no—
56C37×#394—21no—
57C37×#390C2211yescharacteristic, complemented
58C37×#389C2211yescharacteristic, complemented
59C37×#386—21no—
60C37×#380C2211yescharacteristic
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#336C2211yescharacteristic, complemented
64C37×#336C2211yescharacteristic, complemented
65C25×C37—21no—
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—41no—
70C2×#41×C37—41no—
71C2×#41×C37D414yescomplemented
72C22×Q8×C37C2311yescharacteristic
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—22no—
76C22×D4×C37—22no—
77C22×D4×C37—22no—
78C22×D4×C37—22no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37—41no—
83C22×D4×C37—41no—
84C22×D4×C37D411yescharacteristic
85C22×D4×C37C2311yescharacteristic
86C22×D4×C37C2311yescharacteristic
87C22×D4×C37C2311yescharacteristic
88C23×C4×C37—21no—
89C23×C4×C37—21no—
90C23×C4×C37—21no—
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C2×SD16×C37—22no—
94C2×SD16×C37—41no—
95C2×SD16×C37—41no—
96C2×D8×C37—22no—
97C2×D8×C37—22no—
98C2×D8×C37—22no—
99C2×D8×C37—22no—
100C2×D8×C37—22no—
101C2×D8×C37—41no—
102C2×M16×C37—22no—
103C2×M16×C37—22no—
104C2×M16×C37—41no—
105C22×C8×C37C2311yescharacteristic
106C22×C8×C37C2311yescharacteristic
107C22×C8×C37C2311yescharacteristic
108C22×C8×C37C2311yescharacteristic
109#124×C37—22no—
110#124×C37—22no—
111#123×C37—28no—
112C22⋊Q8×C37—22no—
113C22⋊Q8×C37—22no—
114#121×C37—28no—
115#121×C37—22no—
116#121×C37—22no—
117#121×C37—22no—
118#121×C37—22no—
119#121×C37—41no—
120#121×C37—44no—
121#121×C37D414yescomplemented
122#120×C37—28no—
123C4×D4×C37—22no—
124C4×D4×C37—22no—
125C4×D4×C37—22no—
126C4×D4×C37—22no—
127C2×C4⋊C4×C37—21no—
128C2×C4⋊C4×C37—22no—
129C2×C4⋊C4×C37—21no—
130C2×C4⋊C4×C37—21no—
131C2×C4⋊C4×C37—41no—
132C2×C4⋊C4×C37D411yescharacteristic
133C2×C4⋊C4×C37C2311yescharacteristic
134C2×C4⋊C4×C37C2311yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C4⋊C4×C37C2311yescharacteristic
137C2×C22⋊C4×C37—28no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—21no—
140C2×C22⋊C4×C37—21no—
141C2×C22⋊C4×C37—21no—
142C2×C22⋊C4×C37—21no—
143C2×C22⋊C4×C37—21no—
144C2×C22⋊C4×C37—21no—
145C2×C22⋊C4×C37—21no—
146C2×C22⋊C4×C37—21no—
147C2×C22⋊C4×C37—21no—
148C2×C22⋊C4×C37D411yescharacteristic
149C2×C22⋊C4×C37D411yescharacteristic
150C2×C42×C37C2311yescharacteristic
151#106×C37—22no—
152#103×C37—22no—
153#103×C37—22no—
154#103×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—41no—
161#102×C37D414yescomplemented
162C22⋊C8×C37—22no—
163C22⋊C8×C37—22no—
164C22⋊C8×C37—41no—
165#95×C37—21no—
166#95×C37—21no—
167C24×C37—21no—
168C24×C37—24no—
169C24×C37—21no—
170C24×C37—21no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—42no—
174C24×C37—42no—
175C24×C37—81no—
176C24×C37—81no—
177C24×C37C2×D411yescharacteristic
178C24×C37C2×D411yescharacteristic
179#41×C37—28no—
180#41×C37—44no—
181#41×C37—44no—
182#41×C37—44no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37—21no—
188C2×Q8×C37C2×D412yes—
189C2×D4×C37—24no—
190C2×D4×C37—22no—
191C2×D4×C37—24no—
192C2×D4×C37—22no—
193C2×D4×C37—24no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—41no—
209C2×D4×C37—42no—
210C2×D4×C37—42no—
211C2×D4×C37—42no—
212C2×D4×C37—44no—
213C2×D4×C37—44no—
214C2×D4×C37—44no—
215C2×D4×C37—42no—
216C2×D4×C37—42no—
217C2×D4×C37—44no—
218C2×D4×C37—42no—
219C2×D4×C37—42no—
220C2×D4×C37—42no—
221C2×D4×C37—42no—
222C2×D4×C37—81no—
223C2×D4×C37—81no—
224C2×D4×C37—81no—
225C2×D4×C37C2×D412yes—
226C2×D4×C37C2×D412yes—
227C2×D4×C37C2×D412yes—
228C2×D4×C37#4112yes—
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—24no—
237C22×C4×C37—24no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—42no—
247C22×C4×C37—42no—
248C22×C4×C37—42no—
249C22×C4×C37—42no—
250C22×C4×C37—81no—
251C22×C4×C37—81no—
252C22×C4×C37—81no—
253C22×C4×C37C2×D411yescharacteristic
254C22×C4×C37C2×D411yescharacteristic
255C22×C4×C37C2×D411yescharacteristic
256C22×C4×C37C2×D411yescharacteristic
257C22×C4×C37C2×D412yes—
258C22×C4×C37C2×D412yes—
259C22×C4×C37C2411yescharacteristic
260SD16×C37—44no—
261D8×C37—44no—
262D8×C37—44no—
263M16×C37—44no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37—21no—
272C2×C8×C37—21no—
273C2×C8×C37—21no—
274C2×C8×C37—21no—
275C2×C8×C37C2×D412yes—
276C4⋊C4×C37—24no—
277C4⋊C4×C37—22no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37—42no—
285C4⋊C4×C37—42no—
286C4⋊C4×C37C2×D412yes—
287C4⋊C4×C37C2×D412yes—
288C22⋊C4×C37—24no—
289C22⋊C4×C37—24no—
290C22⋊C4×C37—24no—
291C22⋊C4×C37—24no—
292C22⋊C4×C37—22no—
293C22⋊C4×C37—22no—
294C22⋊C4×C37—24no—
295C22⋊C4×C37—42no—
296C22⋊C4×C37—42no—
297C22⋊C4×C37—42no—
298C22⋊C4×C37—42no—
299C22⋊C4×C37—81no—
300C42×C37—21no—
301C42×C37—21no—
302C23×C37—21no—
303C23×C37—22no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—22no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—22no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—22no—
318C23×C37—48no—
319C23×C37—48no—
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—41no—
331C23×C37—41no—
332C23×C37—41no—
333C23×C37—41no—
334C23×C37—41no—
335C23×C37—41no—
336C23×C37—41no—
337C23×C37—84no—
338C23×C37—84no—
339C23×C37—84no—
340C23×C37—84no—
341C23×C37—84no—
342C23×C37#12012yes—
343C23×C37AGL(1,ℤ/8)12yes—
344C23×C37C22×D411yescharacteristic
345Q8×C37—22no—
346Q8×C37—22no—
347Q8×C37—41no—
348Q8×C37—41no—
349D4×C37—22no—
350D4×C37—22no—
351D4×C37—22no—
352D4×C37—22no—
353D4×C37—22no—
354D4×C37—44no—
355D4×C37—48no—
356D4×C37—48no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—41no—
361D4×C37—41no—
362D4×C37—41no—
363D4×C37—84no—
364D4×C37—84no—
365D4×C37—84no—
366D4×C37#12114yescomplemented
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—22no—
370C2×C4×C37—22no—
371C2×C4×C37—22no—
372C2×C4×C37—22no—
373C2×C4×C37—21no—
374C2×C4×C37—21no—
375C2×C4×C37—22no—
376C2×C4×C37—22no—
377C2×C4×C37—21no—
378C2×C4×C37—21no—
379C2×C4×C37—22no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—21no—
384C2×C4×C37—21no—
385C2×C4×C37—48no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—41no—
393C2×C4×C37—41no—
394C2×C4×C37—41no—
395C2×C4×C37—41no—
396C2×C4×C37—41no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—84no—
403C2×C4×C37—84no—
404C2×C4×C37#12012yes—
405C2×C4×C37C22×D411yescharacteristic
406C2×C4×C37C22×D411yescharacteristic
407C2×C4×C37C22×D411yescharacteristic
408C2×C4×C37C2×#4111yescharacteristic
409C2×C4×C37H(5,𝔽2)11yescharacteristic
410C2×C4×C37H(5,𝔽2)11yescharacteristic
411C8×C37—22no—
412C8×C37—41no—
413C8×C37—41no—
414C8×C37—41no—
415#24444C3711yesmaximal, characteristic, direct product factor, Sylow
416C22×C37—22no—
417C22×C37—24no—
418C22×C37—22no—
419C22×C37—22no—
420C22×C37—22no—
421C22×C37—22no—
422C22×C37—22no—
423C22×C37—41no—
424C22×C37—42no—
425C22×C37—41no—
426C22×C37—42no—
427C22×C37—42no—
428C22×C37—41no—
429C22×C37—41no—
430C22×C37—41no—
431C22×C37—42no—
432C22×C37—41no—
433C22×C37—42no—
434C22×C37—41no—
435C22×C37—41no—
436C22×C37—42no—
437C22×C37—42no—
438C22×C37—42no—
439C22×C37—42no—
440C22×C37—816no—
441C22×C37—81no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37—81no—
449C22×C37—81no—
450C22×C37—81no—
451C22×C37—81no—
452C22×C37C2×#12011yescharacteristic
453C22×C37D4211yescharacteristic
454C22×C37#54611yescharacteristic
455C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C37#57511yescharacteristic
457C22×C37#57611yescharacteristic
458C22×C37#57711yescharacteristic
459C4×C37—22no—
460C4×C37—41no—
461C4×C37—42no—
462C4×C37—41no—
463C4×C37—42no—
464C4×C37—41no—
465C4×C37—42no—
466C4×C37—81no—
467C4×C37—81no—
468C4×C37C2×#12111yescharacteristic
469C4×C37#53411yescharacteristic
470C4×C37D4211yescharacteristic
471C4×C37#54611yescharacteristic
472C2×#546C2×C3711yescharacteristic, complemented
473C2×#469C2×C3711yescharacteristic, complemented
474C2×#449C2×C3711yescharacteristic, complemented
475C2×#447C2×C3711yescharacteristic, complemented
476C2×#417C2×C3711yescharacteristic, complemented
477#2416C2×C3711yescharacteristic, complemented
478#2042C2×C3711yescharacteristic, complemented
479#2035C2×C3711yescharacteristic, complemented
480#2012C2×C3711yescharacteristic, complemented
481#2000C2×C3711yescharacteristic, complemented
482#1879C2×C3711yescharacteristic, complemented
483#1874C2×C3711yescharacteristic, complemented
484#1870C2×C3711yescharacteristic, complemented
485#1864C2×C3711yescharacteristic, complemented
486#1786C2×C3711yescharacteristic, complemented
487C2×C37—42no—
488C2×C37—42no—
489C2×C37—44no—
490C2×C37—82no—
491C2×C37—161no—
492C2×C37#241011yescharacteristic
493C2×C37#300611yescharacteristic
494C2×C37#301211yescharacteristic
495C2×C37#326411yescharacteristic
496C2×C37#327511yescharacteristic
497C2×C37#330611yescharacteristic
498C2×C37#332211yescharacteristic
499C22×#41C22×C3711yescharacteristic
500C23×D4C22×C3711yescharacteristic
501C22×SD16C22×C3711yescharacteristic, complemented
502C22×D8C22×C3711yescharacteristic
503C22×D8C22×C3711yescharacteristic
504C22×M16C22×C3711yescharacteristic, complemented
505#546—24no—
506#546—24no—
507C2×#124C22×C3711yescharacteristic
508C2×#123—21no—
509C2×C22⋊Q8C22×C3711yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C3711yescharacteristic
513C2×#121C22×C3711yescharacteristic
514C2×#121C22×C3711yescharacteristic, complemented
515C2×#120—21no—
516C2×C4×D4C22×C3711yescharacteristic
517C2×C4×D4C22×C3711yescharacteristic
518C22×C4⋊C4C22×C3711yescharacteristic, complemented
519C22×C22⋊C4—21no—
520#469—24no—
521#449—24no—
522#447—24no—
523C2×#106C22×C3711yescharacteristic, complemented
524#417—24no—
525C2×#103C22×C3711yescharacteristic, complemented
526C2×#103C22×C3711yescharacteristic, complemented
527C2×#103C22×C3711yescharacteristic, complemented
528C2×#102C22×C3711yescharacteristic
529C2×#102C22×C3711yescharacteristic
530C2×#102C22×C3711yescharacteristic
531C2×#102C22×C3711yescharacteristic
532C2×#102C22×C3711yescharacteristic
533C2×#102C22×C3711yescharacteristic
534C2×#102C22×C3711yescharacteristic, complemented
535C2×C22⋊C8C22×C3711yescharacteristic
536C2×C22⋊C8C22×C3711yescharacteristic
537C2×C22⋊C8C22×C3711yescharacteristic, complemented
538#396—21no—
539#394—21no—
540#390C22×C3711yescharacteristic, complemented
541#389C22×C3711yescharacteristic, complemented
542#386—21no—
543#380C22×C3711yescharacteristic
544#340C22×C3711yescharacteristic, complemented
545#340C22×C3711yescharacteristic, complemented
546#336C22×C3711yescharacteristic, complemented
547#336C22×C3711yescharacteristic, complemented
548C37#2444411yescharacteristic, direct product factor, Sylow
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C3714yescomplemented
556C22×Q8C23×C3711yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4D4×C3711yescharacteristic
569C22×D4C23×C3711yescharacteristic
570C22×D4C23×C3711yescharacteristic
571C22×D4C23×C3711yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C3711yescharacteristic
576C23×C4C23×C3711yescharacteristic
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—41no—
589C22×C8C23×C3711yescharacteristic
590C22×C8C23×C3711yescharacteristic
591C22×C8C23×C3711yescharacteristic
592C22×C8C23×C3711yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—44no—
605#121D4×C3714yescomplemented
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C3711yescharacteristic
617C2×C4⋊C4C23×C3711yescharacteristic
618C2×C4⋊C4C23×C3711yescharacteristic
619C2×C4⋊C4C23×C3711yescharacteristic
620C2×C4⋊C4C23×C3711yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C3711yescharacteristic
633C2×C22⋊C4D4×C3711yescharacteristic
634C2×C42C23×C3711yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—41no—
645#102D4×C3714yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—24no—
653C24—21no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C3711yescharacteristic
662C24C2×D4×C3711yescharacteristic
663#41—28no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C3712yes—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—44no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C3712yes—
710C2×D4C2×D4×C3712yes—
711C2×D4C2×D4×C3712yes—
712C2×D4#41×C3712yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C3711yescharacteristic
738C22×C4C2×D4×C3711yescharacteristic
739C22×C4C2×D4×C3711yescharacteristic
740C22×C4C2×D4×C3711yescharacteristic
741C22×C4C2×D4×C3712yes—
742C22×C4C2×D4×C3712yes—
743C22×C4C24×C3711yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747M16—44no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8C2×D4×C3712yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C3712yes—
771C4⋊C4C2×D4×C3712yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—24no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23—84no—
826C23#120×C3712yes—
827C23AGL(1,ℤ/8)×C3712yes—
828C23C22×D4×C3711yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C3714yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C3712yes—
889C2×C4C22×D4×C3711yescharacteristic
890C2×C4C22×D4×C3711yescharacteristic
891C2×C4C22×D4×C3711yescharacteristic
892C2×C4C2×#41×C3711yescharacteristic
893C2×C4H(5,𝔽2)×C3711yescharacteristic
894C2×C4H(5,𝔽2)×C3711yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—24no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—816no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22C2×#120×C3711yescharacteristic
936C22D42×C3711yescharacteristic
937C22C37×#54611yescharacteristic
938C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
939C22C37×#57511yescharacteristic
940C22C37×#57611yescharacteristic
941C22C37×#57711yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C3711yescharacteristic
952C4C37×#53411yescharacteristic
953C4D42×C3711yescharacteristic
954C4C37×#54611yescharacteristic
955C2—42no—
956C2—42no—
957C2—44no—
958C2—82no—
959C2—161no—
960C2C37×#241011yescharacteristic
961C2C37×#300611yescharacteristic
962C2C37×#301211yescharacteristic
963C2C37×#326411yescharacteristic
964C2C37×#327511yescharacteristic
965C2C37×#330611yescharacteristic
966C2C37×#332211yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#546C2semidirect
2. C2×C37×#469C2semidirect
3. C2×C37×#449C2semidirect
4. C2×C37×#447C2semidirect
5. C2×C37×#417C2semidirect
6. C37×#2416C2semidirect
7. C37×#2042C2semidirect
8. C37×#2035C2semidirect
9. C37×#2012C2semidirect
10. C37×#2000C2semidirect
11. C37×#1879C2semidirect
12. C37×#1874C2semidirect
13. C37×#1870C2semidirect
14. C37×#1864C2semidirect
15. C37×#1786C2semidirect
18. C22×SD16×C37C22semidirect
21. C22×M16×C37C22semidirect
31. C2×#121×C37C22semidirect
35. C22×C4⋊C4×C37C22semidirect
40. C2×#106×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
44. C2×#103×C37C22semidirect
51. C2×#102×C37C22semidirect
54. C2×C22⋊C8×C37C22semidirect
57. C37×#390C22semidirect
58. C37×#389C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
71. C2×#41×C37D4semidirect
121. #121×C37D4semidirect
161. #102×C37D4semidirect
366. D4×C37#121semidirect
415. #24444C37direct (N × H)
472. C2×#546C2×C37semidirect
473. C2×#469C2×C37semidirect
474. C2×#449C2×C37semidirect
475. C2×#447C2×C37semidirect
476. C2×#417C2×C37semidirect
477. #2416C2×C37semidirect
478. #2042C2×C37semidirect
479. #2035C2×C37semidirect
480. #2012C2×C37semidirect
481. #2000C2×C37semidirect
482. #1879C2×C37semidirect
483. #1874C2×C37semidirect
484. #1870C2×C37semidirect
485. #1864C2×C37semidirect
486. #1786C2×C37semidirect
501. C22×SD16C22×C37semidirect
504. C22×M16C22×C37semidirect
514. C2×#121C22×C37semidirect
518. C22×C4⋊C4C22×C37semidirect
523. C2×#106C22×C37semidirect
525. C2×#103C22×C37semidirect
526. C2×#103C22×C37semidirect
527. C2×#103C22×C37semidirect
534. C2×#102C22×C37semidirect
537. C2×C22⋊C8C22×C37semidirect
540. #390C22×C37semidirect
541. #389C22×C37semidirect
544. #340C22×C37semidirect
545. #340C22×C37semidirect
546. #336C22×C37semidirect
547. #336C22×C37semidirect
548. C37#24444direct (N × H)
555. C2×#41D4×C37semidirect
605. #121D4×C37semidirect
645. #102D4×C37semidirect
850. D4#121×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5462
C2×C37×#4692
C2×C37×#4492
C2×C37×#4472
C2×C37×#4172
C37×#24162
C37×#20422
C37×#20352
C37×#20122
C37×#20002
C37×#18792
C37×#18742
C37×#18702
C37×#18642
C37×#17862
#2444437