Finite Group Databasebeta

← C37×#24366 #22645619

Subgroups — C37×#24366 #22645619

Order 9472.

1662 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
2C2×C37×#463C211yesmaximal, characteristic, complemented
3C2×C37×#459C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C37×#2431C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
7C37×#2055C211yesmaximal, characteristic, complemented
8C37×#2054C211yesmaximal, characteristic, complemented
9C37×#2012C211yesmaximal, characteristic, complemented
10C37×#2011C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1879C211yesmaximal, characteristic, complemented
13C37×#1877C211yesmaximal, characteristic, complemented
14C37×#1851C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, 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×D8×C37C2211yescharacteristic
26C22×D8×C37C2211yescharacteristic
27C22×M16×C37C2211yescharacteristic
28C2×#127×C37C2211yescharacteristic, complemented
29C2×#124×C37C2211yescharacteristic, complemented
30C2×#121×C37C2211yescharacteristic
31C2×C4×D4×C37C2211yescharacteristic
32C2×C4×D4×C37C2211yescharacteristic
33C22×C22⋊C4×C37—21no—
34C37×#463—24no—
35C37×#459—24no—
36C37×#447—24no—
37C2×C4⋊C8×C37C2211yescharacteristic, complemented
38C2×C4⋊C8×C37C2211yescharacteristic, complemented
39C2×#103×C37C2211yescharacteristic, complemented
40C2×#103×C37C2211yescharacteristic, complemented
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×C22⋊C8×C37C2211yescharacteristic
48C37×#392—21no—
49C37×#392—21no—
50C37×#391C2211yescharacteristic, complemented
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic
53C37×#390C2211yescharacteristic, complemented
54C37×#386—21no—
55C37×#386—21no—
56C37×#386—21no—
57C37×#386—21no—
58C37×#380C2211yescharacteristic
59C37×#379—21no—
60C4×C22⋊C4×C37C2211yescharacteristic
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—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—21no—
80C22×D4×C37—22no—
81C22×D4×C37—41no—
82C22×D4×C37—41no—
83C22×D4×C37D414yescomplemented
84C22×D4×C37C2311yescharacteristic
85C22×D4×C37C2311yescharacteristic
86C22×D4×C37C2311yescharacteristic
87C22×D4×C37C2311yescharacteristic
88C23×C4×C37—21no—
89C23×C4×C37—21no—
90C23×C4×C37—21no—
91C23×C4×C37C2311yescharacteristic
92AGL(1,ℤ/8)×C37—232no—
93C2×SD16×C37—22no—
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—22no—
97C2×SD16×C37—22no—
98C2×SD16×C37D414yescomplemented
99C2×D8×C37—22no—
100C2×D8×C37—22no—
101C2×D8×C37—22no—
102C2×D8×C37—22no—
103C2×D8×C37—22no—
104C2×D8×C37—22no—
105C2×D8×C37—22no—
106C2×D8×C37—22no—
107C2×D8×C37—22no—
108C2×D8×C37—41no—
109C2×D8×C37—41no—
110C2×D8×C37D414yescomplemented
111C2×M16×C37—22no—
112C2×M16×C37—22no—
113C2×M16×C37—22no—
114C22×C8×C37C2311yescharacteristic
115C22×C8×C37C2311yescharacteristic
116C22×C8×C37C2311yescharacteristic
117C22×C8×C37C2311yescharacteristic
118#127×C37—22no—
119#127×C37—41no—
120#124×C37—22no—
121#124×C37—41no—
122#121×C37—22no—
123#121×C37—22no—
124C4×D4×C37—22no—
125C4×D4×C37—22no—
126C4×D4×C37—41no—
127C4×D4×C37—41no—
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×C37—44no—
144C2×C22⋊C4×C37D411yescharacteristic
145C2×C22⋊C4×C37D411yescharacteristic
146C2×C42×C37C2311yescharacteristic
147C2×C42×C37C2311yescharacteristic
148C4⋊C8×C37—22no—
149C4⋊C8×C37—22no—
150#103×C37—22no—
151#103×C37—41no—
152#102×C37—22no—
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—41no—
158C22⋊C8×C37—22no—
159#95×C37—21no—
160#95×C37—21no—
161#95×C37—21no—
162#95×C37D411yescharacteristic
163#95×C37D411yescharacteristic
164C24×C37—21no—
165C24×C37—21no—
166C24×C37—21no—
167C24×C37—24no—
168C24×C37—21no—
169C24×C37—42no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—81no—
174C24×C37—81no—
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—24no—
188C2×D4×C37—21no—
189C2×D4×C37—21no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—21no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—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—44no—
208C2×D4×C37—44no—
209C2×D4×C37—44no—
210C2×D4×C37—42no—
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×C37—81no—
224C2×D4×C37C2×D412yes—
225C2×D4×C37C2×D412yes—
226C2×D4×C37C2×D412yes—
227C2×D4×C37C2×D412yes—
228C2×D4×C37C2×D412yes—
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—42no—
238C22×C4×C37—42no—
239C22×C4×C37—42no—
240C22×C4×C37—42no—
241C22×C4×C37—42no—
242C22×C4×C37—42no—
243C22×C4×C37—42no—
244C22×C4×C37—81no—
245C22×C4×C37—81no—
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D411yescharacteristic
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D412yes—
251C22×C4×C37C2×D411yescharacteristic
252C22×C4×C37#4112yes—
253C22×C4×C37C2411yescharacteristic
254SD16×C37—28no—
255SD16×C37—28no—
256D8×C37—28no—
257D8×C37—28no—
258D8×C37—44no—
259D8×C37—44no—
260M16×C37—28no—
261C2×C8×C37—21no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37C2×D412yes—
272C2×C8×C37C2×D412yes—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C22⋊C4×C37—22no—
280C22⋊C4×C37—41no—
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—
295C42×C37—21no—
296C42×C37—21no—
297C23×C37—22no—
298C23×C37—22no—
299C23×C37—22no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—21no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—22no—
307C23×C37—22no—
308C23×C37—48no—
309C23×C37—48no—
310C23×C37—41no—
311C23×C37—41no—
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—41no—
331C23×C37—41no—
332C23×C37—41no—
333C23×C37—84no—
334C23×C37—84no—
335C23×C37—84no—
336C23×C37—84no—
337C23×C37—84no—
338C23×C37#12112yes—
339C23×C37C22×D411yescharacteristic
340Q8×C37—22no—
341Q8×C37—22no—
342Q8×C37—41no—
343Q8×C37—41no—
344D4×C37—22no—
345D4×C37—22no—
346D4×C37—22no—
347D4×C37—22no—
348D4×C37—22no—
349D4×C37—22no—
350D4×C37—22no—
351D4×C37—48no—
352D4×C37—48no—
353D4×C37—41no—
354D4×C37—41no—
355D4×C37—41no—
356D4×C37—41no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—41no—
361D4×C37—84no—
362D4×C37—84no—
363D4×C37—84no—
364D4×C37#12014yes—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
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—21no—
376C2×C4×C37—22no—
377C2×C4×C37—21no—
378C2×C4×C37—21no—
379C2×C4×C37—21no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—48no—
384C2×C4×C37—41no—
385C2×C4×C37—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—41no—
393C2×C4×C37—41no—
394C2×C4×C37—41no—
395C2×C4×C37—84no—
396C2×C4×C37—84no—
397C2×C4×C37#12112yes—
398C2×C4×C37AGL(1,ℤ/8)12yescomplemented
399C2×C4×C37C22×D411yescharacteristic
400C2×C4×C37C22×D411yescharacteristic
401C2×C4×C37C22×D411yescharacteristic
402C2×C4×C37C2×#4111yescharacteristic
403C2×C4×C37H(5,𝔽2)11yescharacteristic
404C2×C4×C37H(5,𝔽2)11yescharacteristic
405C8×C37—22no—
406C8×C37—22no—
407C8×C37—41no—
408C8×C37—41no—
409#24366C3711yesmaximal, characteristic, direct product factor, Sylow
410C22×C37—22no—
411C22×C37—24no—
412C22×C37—22no—
413C22×C37—22no—
414C22×C37—42no—
415C22×C37—41no—
416C22×C37—41no—
417C22×C37—42no—
418C22×C37—41no—
419C22×C37—42no—
420C22×C37—42no—
421C22×C37—41no—
422C22×C37—42no—
423C22×C37—42no—
424C22×C37—42no—
425C22×C37—42no—
426C22×C37—42no—
427C22×C37—42no—
428C22×C37—42no—
429C22×C37—42no—
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×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37C2×#12111yescharacteristic
447C22×C37D4211yescharacteristic
448C22×C37D4211yescharacteristic
449C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C37#57511yescharacteristic
451C22×C37#57611yescharacteristic
452C22×C37#57611yescharacteristic
453C4×C37—22no—
454C4×C37—22no—
455C4×C37—42no—
456C4×C37—41no—
457C4×C37—41no—
458C4×C37—41no—
459C4×C37—81no—
460C4×C37—81no—
461C4×C37—81no—
462C4×C37C2×#12011yescharacteristic
463C4×C37#53411yescharacteristic
464C4×C37#54611yescharacteristic
465C4×C37#54611yescharacteristic
466C22×AGL(1,ℤ/8)C2×C3711yescharacteristic, complemented
467C2×#463C2×C3711yescharacteristic, complemented
468C2×#459C2×C3711yescharacteristic, complemented
469C2×#447C2×C3711yescharacteristic, complemented
470#2431C2×C3711yescharacteristic, complemented
471D4×C22⋊C4C2×C3711yescharacteristic, complemented
472#2055C2×C3711yescharacteristic, complemented
473#2054C2×C3711yescharacteristic, complemented
474#2012C2×C3711yescharacteristic, complemented
475#2011C2×C3711yescharacteristic, complemented
476#1895C2×C3711yescharacteristic, complemented
477#1879C2×C3711yescharacteristic, complemented
478#1877C2×C3711yescharacteristic, complemented
479#1851C2×C3711yescharacteristic, complemented
480#1788C2×C3711yescharacteristic, complemented
481C2×C37—42no—
482C2×C37—44no—
483C2×C37—82no—
484C2×C37—82no—
485C2×C37—161no—
486C2×C37#241011yescharacteristic
487C2×C37#303611yescharacteristic
488C2×C37#304111yescharacteristic
489C2×C37#326411yescharacteristic
490C2×C37#326811yescharacteristic
491C2×C37#327311yescharacteristic
492C2×C37#327411yescharacteristic
493C22×#41C22×C3711yescharacteristic
494C23×D4C22×C3711yescharacteristic
495C2×AGL(1,ℤ/8)—24no—
496C2×AGL(1,ℤ/8)—24no—
497C2×AGL(1,ℤ/8)—24no—
498C22×SD16C22×C3711yescharacteristic
499C22×SD16C22×C3711yescharacteristic
500C22×D8C22×C3711yescharacteristic
501C22×D8C22×C3711yescharacteristic
502C22×D8C22×C3711yescharacteristic
503C22×D8C22×C3711yescharacteristic
504C22×M16C22×C3711yescharacteristic
505C2×#127C22×C3711yescharacteristic, complemented
506C2×#124C22×C3711yescharacteristic, complemented
507C2×#121C22×C3711yescharacteristic
508C2×C4×D4C22×C3711yescharacteristic
509C2×C4×D4C22×C3711yescharacteristic
510C22×C22⋊C4—21no—
511#463—24no—
512#459—24no—
513#447—24no—
514C2×C4⋊C8C22×C3711yescharacteristic, complemented
515C2×C4⋊C8C22×C3711yescharacteristic, complemented
516C2×#103C22×C3711yescharacteristic, complemented
517C2×#103C22×C3711yescharacteristic, complemented
518C2×#102C22×C3711yescharacteristic
519C2×#102C22×C3711yescharacteristic
520C2×#102C22×C3711yescharacteristic, complemented
521C2×#102C22×C3711yescharacteristic, complemented
522C2×#102C22×C3711yescharacteristic, complemented
523C2×#102C22×C3711yescharacteristic, complemented
524C2×C22⋊C8C22×C3711yescharacteristic
525#392—21no—
526#392—21no—
527#391C22×C3711yescharacteristic, complemented
528#390C22×C3711yescharacteristic
529#390C22×C3711yescharacteristic
530#390C22×C3711yescharacteristic, complemented
531#386—21no—
532#386—21no—
533#386—21no—
534#386—21no—
535#380C22×C3711yescharacteristic
536#379—21no—
537C4×C22⋊C4C22×C3711yescharacteristic
538#340C22×C3711yescharacteristic, complemented
539#340C22×C3711yescharacteristic, complemented
540#336C22×C3711yescharacteristic, complemented
541#336C22×C3711yescharacteristic, complemented
542C37#2436611yescharacteristic, direct product factor, Sylow
543C25—21no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—41no—
549C2×#41—41no—
550C22×Q8C23×C3711yescharacteristic
551C22×D4—22no—
552C22×D4—22no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4D4×C3714yescomplemented
562C22×D4C23×C3711yescharacteristic
563C22×D4C23×C3711yescharacteristic
564C22×D4C23×C3711yescharacteristic
565C22×D4C23×C3711yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C3711yescharacteristic
570AGL(1,ℤ/8)—232no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16D4×C3714yescomplemented
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8D4×C3714yescomplemented
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C22×C8C23×C3711yescharacteristic
593C22×C8C23×C3711yescharacteristic
594C22×C8C23×C3711yescharacteristic
595C22×C8C23×C3711yescharacteristic
596#127—22no—
597#127—41no—
598#124—22no—
599#124—41no—
600#121—22no—
601#121—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C2×C4⋊C4C23×C3711yescharacteristic
607C2×C4⋊C4C23×C3711yescharacteristic
608C2×C4⋊C4C23×C3711yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4D4×C3711yescharacteristic
623C2×C22⋊C4D4×C3711yescharacteristic
624C2×C42C23×C3711yescharacteristic
625C2×C42C23×C3711yescharacteristic
626C4⋊C8—22no—
627C4⋊C8—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95D4×C3711yescharacteristic
641#95D4×C3711yescharacteristic
642C24—21no—
643C24—21no—
644C24—21no—
645C24—24no—
646C24—21no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—81no—
652C24—81no—
653C24C2×D4×C3711yescharacteristic
654#41—28no—
655#41—44no—
656#41—44no—
657#41—44no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8C2×D4×C3712yes—
664C2×D4—28no—
665C2×D4—24no—
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—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C2×D4×C3712yes—
703C2×D4C2×D4×C3712yes—
704C2×D4C2×D4×C3712yes—
705C2×D4C2×D4×C3712yes—
706C2×D4C2×D4×C3712yes—
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—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—81no—
723C22×C4—81no—
724C22×C4C2×D4×C3711yescharacteristic
725C22×C4C2×D4×C3711yescharacteristic
726C22×C4C2×D4×C3711yescharacteristic
727C22×C4C2×D4×C3711yescharacteristic
728C22×C4C2×D4×C3712yes—
729C22×C4C2×D4×C3711yescharacteristic
730C22×C4#41×C3712yes—
731C22×C4C24×C3711yescharacteristic
732SD16—28no—
733SD16—28no—
734D8—28no—
735D8—28no—
736D8—44no—
737D8—44no—
738M16—28no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8C2×D4×C3712yes—
750C2×C8C2×D4×C3712yes—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C22⋊C4—22no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C22⋊C4—81no—
771C42—21no—
772C42—21no—
773C42—21no—
774C42—21no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—48no—
787C23—48no—
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—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23#121×C3712yes—
817C23C22×D4×C3711yescharacteristic
818Q8—22no—
819Q8—22no—
820Q8—41no—
821Q8—41no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—48no—
830D4—48no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#120×C3714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4—84no—
875C2×C4#121×C3712yes—
876C2×C4AGL(1,ℤ/8)×C3712yescomplemented
877C2×C4C22×D4×C3711yescharacteristic
878C2×C4C22×D4×C3711yescharacteristic
879C2×C4C22×D4×C3711yescharacteristic
880C2×C4C2×#41×C3711yescharacteristic
881C2×C4H(5,𝔽2)×C3711yescharacteristic
882C2×C4H(5,𝔽2)×C3711yescharacteristic
883C8—22no—
884C8—22no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—24no—
889C22—22no—
890C22—22no—
891C22—42no—
892C22—41no—
893C22—41no—
894C22—42no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—816no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#121×C3711yescharacteristic
924C22D42×C3711yescharacteristic
925C22D42×C3711yescharacteristic
926C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
927C22C37×#57511yescharacteristic
928C22C37×#57611yescharacteristic
929C22C37×#57611yescharacteristic
930C4—22no—
931C4—22no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4C2×#120×C3711yescharacteristic
940C4C37×#53411yescharacteristic
941C4C37×#54611yescharacteristic
942C4C37×#54611yescharacteristic
943C2—42no—
944C2—44no—
945C2—82no—
946C2—82no—
947C2—161no—
948C2C37×#241011yescharacteristic
949C2C37×#303611yescharacteristic
950C2C37×#304111yescharacteristic
951C2C37×#326411yescharacteristic
952C2C37×#326811yescharacteristic
953C2C37×#327311yescharacteristic
954C2C37×#327411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×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×#463C2semidirect
3. C2×C37×#459C2semidirect
4. C2×C37×#447C2semidirect
5. C37×#2431C2semidirect
6. D4×C22⋊C4×C37C2semidirect
7. C37×#2055C2semidirect
8. C37×#2054C2semidirect
9. C37×#2012C2semidirect
10. C37×#2011C2semidirect
11. C37×#1895C2semidirect
12. C37×#1879C2semidirect
13. C37×#1877C2semidirect
14. C37×#1851C2semidirect
15. C37×#1788C2semidirect
28. C2×#127×C37C22semidirect
29. C2×#124×C37C22semidirect
37. C2×C4⋊C8×C37C22semidirect
38. C2×C4⋊C8×C37C22semidirect
39. C2×#103×C37C22semidirect
40. C2×#103×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
50. C37×#391C22semidirect
53. C37×#390C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
83. C22×D4×C37D4semidirect
98. C2×SD16×C37D4semidirect
110. C2×D8×C37D4semidirect
398. C2×C4×C37AGL(1,ℤ/8)semidirect
409. #24366C37direct (N × H)
466. C22×AGL(1,ℤ/8)C2×C37semidirect
467. C2×#463C2×C37semidirect
468. C2×#459C2×C37semidirect
469. C2×#447C2×C37semidirect
470. #2431C2×C37semidirect
471. D4×C22⋊C4C2×C37semidirect
472. #2055C2×C37semidirect
473. #2054C2×C37semidirect
474. #2012C2×C37semidirect
475. #2011C2×C37semidirect
476. #1895C2×C37semidirect
477. #1879C2×C37semidirect
478. #1877C2×C37semidirect
479. #1851C2×C37semidirect
480. #1788C2×C37semidirect
505. C2×#127C22×C37semidirect
506. C2×#124C22×C37semidirect
514. C2×C4⋊C8C22×C37semidirect
515. C2×C4⋊C8C22×C37semidirect
516. C2×#103C22×C37semidirect
517. C2×#103C22×C37semidirect
520. C2×#102C22×C37semidirect
521. C2×#102C22×C37semidirect
522. C2×#102C22×C37semidirect
523. C2×#102C22×C37semidirect
527. #391C22×C37semidirect
530. #390C22×C37semidirect
538. #340C22×C37semidirect
539. #340C22×C37semidirect
540. #336C22×C37semidirect
541. #336C22×C37semidirect
542. C37#24366direct (N × H)
561. C22×D4D4×C37semidirect
576. C2×SD16D4×C37semidirect
588. C2×D8D4×C37semidirect
876. C2×C4AGL(1,ℤ/8)×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×#4632
C2×C37×#4592
C2×C37×#4472
C37×#24312
D4×C22⋊C4×C372
C37×#20552
C37×#20542
C37×#20122
C37×#20112
C37×#18952
C37×#18792
C37×#18772
C37×#18512
C37×#17882
#2436637