Finite Group Databasebeta

← C37×#18224 #22639477

Subgroups — C37×#18224 #22639477

Order 9472.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3534C211yesmaximal, characteristic, complemented
2C37×#3003C211yesmaximal, characteristic, complemented
3C2×C37×#447C211yesmaximal, characteristic, complemented
4C37×#2613C211yesmaximal, characteristic, complemented
5C37×#1600C212yesmaximal, complemented
6C37×#1598C212yesmaximal, complemented
7C37×#1597C212yesmaximal, complemented
8C37×#1595C212yesmaximal, complemented
9C37×#1516C211yesmaximal, characteristic, complemented
10C37×#1510C211yesmaximal, characteristic, complemented
11C37×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C37C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C37—21no—
14C22×D8×C37—21no—
15C37×#562—21no—
16C37×#560—21no—
17C37×#553—21no—
18C37×#551—21no—
19C37×#546—21no—
20C37×#546—21no—
21C37×#546—21no—
22D42×C37—21no—
23C37×#540—21no—
24C37×#539—21no—
25C37×#539C2211yescharacteristic, complemented
26C37×#538—21no—
27C37×#538C2211yescharacteristic, complemented
28C37×#537C2211yescharacteristic, complemented
29C37×#534—21no—
30C37×#534C2211yescharacteristic, complemented
31C37×#525C2211yescharacteristic
32C2×#123×C37C2211yescharacteristic
33C2×#121×C37C2211yescharacteristic
34C2×#120×C37—21no—
35C37×#450—21no—
36C37×#450C2212yescomplemented
37C37×#447—21no—
38C37×#447—21no—
39C37×#447—21no—
40C37×#447C2212yes—
41C37×#447C2212yescomplemented
42C37×#447C2212yescomplemented
43C37×#418—21no—
44C2×#102×C37—21no—
45C37×#407C2211yescharacteristic, complemented
46C2×C22⋊C8×C37C2211yescharacteristic, complemented
47C37×#394—21no—
48C37×#394C2212yescomplemented
49C37×#392—21no—
50C37×#392C2212yescomplemented
51C37×#381C2211yescharacteristic, complemented
52C37×#379—21no—
53C37×#328C2212yescomplemented
54C37×#327C2212yescomplemented
55C37×#327C2212yescomplemented
56C37×#327C2212yescomplemented
57C37×#324C2212yescomplemented
58C37×#323C2212yescomplemented
59C25×C37—21no—
60C2×#41×C37—21no—
61C2×#41×C37D411yescharacteristic, complemented
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—22no—
66C22×D4×C37—21no—
67C22×D4×C37—21no—
68C22×D4×C37—21no—
69C22×D4×C37—21no—
70C22×D4×C37—21no—
71C22×D4×C37—44no—
72C22×D4×C37D411yescharacteristic
73C22×D4×C37D411yescharacteristic, complemented
74C22×D4×C37C2312yes—
75C23×C4×C37C2311yescharacteristic
76AGL(1,ℤ/8)×C37—44no—
77C2×SD16×C37—22no—
78C2×D8×C37—22no—
79C2×D8×C37—22no—
80C2×D8×C37—22no—
81C2×D8×C37—44no—
82C2×M16×C37—21no—
83C22×C8×C37—21no—
84#127×C37—21no—
85#126×C37—21no—
86#126×C37—21no—
87#126×C37—21no—
88#126×C37—21no—
89#125×C37—21no—
90#125×C37—21no—
91#124×C37—21no—
92#124×C37—21no—
93#124×C37—21no—
94#123×C37—21no—
95#123×C37—21no—
96#123×C37—21no—
97#123×C37—21no—
98#123×C37—21no—
99#123×C37—21no—
100#123×C37—21no—
101#123×C37—21no—
102#123×C37—21no—
103#123×C37—21no—
104#123×C37—21no—
105#123×C37—21no—
106#123×C37—21no—
107#123×C37—21no—
108C22⋊Q8×C37—21no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37—21no—
111C22⋊Q8×C37—21no—
112C22⋊Q8×C37—21no—
113C22⋊Q8×C37D411yescharacteristic, complemented
114C22⋊Q8×C37C2311yescharacteristic
115#121×C37—21no—
116#121×C37—21no—
117#121×C37—21no—
118#121×C37—21no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37—21no—
125#121×C37—21no—
126#121×C37—21no—
127#121×C37—21no—
128#121×C37—21no—
129#121×C37—21no—
130#121×C37D411yescharacteristic, complemented
131#121×C37D411yescharacteristic, complemented
132#121×C37D411yescharacteristic, complemented
133#121×C37C2311yescharacteristic
134#121×C37C2311yescharacteristic
135#121×C37C2311yescharacteristic
136#120×C37—21no—
137#120×C37—21no—
138#120×C37—21no—
139#120×C37—21no—
140#120×C37—21no—
141#120×C37—21no—
142#120×C37—21no—
143#120×C37—21no—
144#120×C37—44no—
145C4×D4×C37—21no—
146C4×D4×C37—21no—
147C4×D4×C37—21no—
148C4×D4×C37—21no—
149C4×D4×C37—21no—
150C4×D4×C37—21no—
151C4×D4×C37—21no—
152C4×D4×C37—21no—
153#117×C37—21no—
154#117×C37D411yescharacteristic, complemented
155C2×C4⋊C4×C37D411yescharacteristic
156C2×C4⋊C4×C37D411yescharacteristic, complemented
157C2×C4⋊C4×C37C2311yescharacteristic
158C2×C22⋊C4×C37—21no—
159C2×C22⋊C4×C37—21no—
160C2×C22⋊C4×C37—21no—
161C2×C22⋊C4×C37—21no—
162C2×C22⋊C4×C37—22no—
163C2×C22⋊C4×C37—22no—
164C2×C22⋊C4×C37—22no—
165C2×C22⋊C4×C37D411yescharacteristic
166C2×C22⋊C4×C37D411yescharacteristic
167C2×C22⋊C4×C37C2311yescharacteristic
168#102×C37—22no—
169#102×C37—22no—
170#102×C37—22no—
171#102×C37—22no—
172C22⋊C8×C37—21no—
173C22⋊C8×C37—21no—
174C22⋊C8×C37C2312yes—
175C22⋊C8×C37C2312yes—
176#95×C37—21no—
177#95×C37C2312yes—
178C24×C37—24no—
179C24×C37—21no—
180C24×C37—22no—
181C24×C37—21no—
182C24×C37—42no—
183C24×C37—41no—
184C24×C37—41no—
185C24×C37—82no—
186C24×C37—82no—
187C24×C37C2×D411yescharacteristic
188C24×C37C2×D411yescharacteristic
189#41×C37—42no—
190#41×C37—82no—
191C2×Q8×C37—21no—
192C2×Q8×C37C2×D411yescharacteristic
193C2×D4×C37—24no—
194C2×D4×C37—24no—
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—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—22no—
213C2×D4×C37—22no—
214C2×D4×C37—42no—
215C2×D4×C37—42no—
216C2×D4×C37—42no—
217C2×D4×C37—44no—
218C2×D4×C37—44no—
219C2×D4×C37—44no—
220C2×D4×C37—44no—
221C2×D4×C37—42no—
222C2×D4×C37—44no—
223C2×D4×C37—41no—
224C2×D4×C37—41no—
225C2×D4×C37—82no—
226C2×D4×C37—82no—
227C2×D4×C37—82no—
228C2×D4×C37—82no—
229C2×D4×C37—82no—
230C2×D4×C37C2×D411yescharacteristic
231C2×D4×C37C2×D411yescharacteristic
232C2×D4×C37C2×D411yescharacteristic
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—22no—
241C22×C4×C37—42no—
242C22×C4×C37C2×D411yescharacteristic
243C22×C4×C37C2×D411yescharacteristic
244C22×C4×C37C2×D411yescharacteristic
245C22×C4×C37C2×D411yescharacteristic
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D411yescharacteristic
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2411yescharacteristic
251SD16×C37—44no—
252D8×C37—44no—
253D8×C37—44no—
254D8×C37—44no—
255M16×C37—42no—
256C2×C8×C37—22no—
257C2×C8×C37—22no—
258C2×C8×C37—42no—
259C4⋊C4×C37—21no—
260C4⋊C4×C37—21no—
261C4⋊C4×C37—21no—
262C4⋊C4×C37—21no—
263C4⋊C4×C37—21no—
264C4⋊C4×C37—21no—
265C4⋊C4×C37—21no—
266C4⋊C4×C37—21no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37C2×D411yescharacteristic
273C4⋊C4×C37C2×D411yescharacteristic
274C4⋊C4×C37C2×D411yescharacteristic
275C4⋊C4×C37C2×D411yescharacteristic
276C22⋊C4×C37—21no—
277C22⋊C4×C37—21no—
278C22⋊C4×C37—21no—
279C22⋊C4×C37—21no—
280C22⋊C4×C37—21no—
281C22⋊C4×C37—21no—
282C22⋊C4×C37—21no—
283C22⋊C4×C37—21no—
284C22⋊C4×C37—21no—
285C22⋊C4×C37—21no—
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—21no—
291C22⋊C4×C37—21no—
292C22⋊C4×C37—21no—
293C22⋊C4×C37—21no—
294C22⋊C4×C37—21no—
295C22⋊C4×C37—21no—
296C22⋊C4×C37—21no—
297C22⋊C4×C37—21no—
298C22⋊C4×C37—21no—
299C22⋊C4×C37—21no—
300C22⋊C4×C37—21no—
301C22⋊C4×C37—44no—
302C22⋊C4×C37—42no—
303C22⋊C4×C37—82no—
304C22⋊C4×C37—82no—
305C42×C37—21no—
306C42×C37—21no—
307C42×C37—21no—
308C23×C37—22no—
309C23×C37—22no—
310C23×C37—24no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—22no—
316C23×C37—41no—
317C23×C37—42no—
318C23×C37—42no—
319C23×C37—44no—
320C23×C37—42no—
321C23×C37—41no—
322C23×C37—41no—
323C23×C37—42no—
324C23×C37—42no—
325C23×C37—42no—
326C23×C37—44no—
327C23×C37—42no—
328C23×C37—81no—
329C23×C37—81no—
330C23×C37—82no—
331C23×C37—82no—
332C23×C37—82no—
333C23×C37—82no—
334C23×C37—88no—
335C23×C37—81no—
336C23×C37—81no—
337C23×C37—81no—
338C23×C37—88no—
339C23×C37#12011yescharacteristic
340C23×C37#12011yescharacteristic
341C23×C37C22×D411yescharacteristic
342Q8×C37—41no—
343Q8×C37—81no—
344D4×C37—24no—
345D4×C37—24no—
346D4×C37—41no—
347D4×C37—41no—
348D4×C37—41no—
349D4×C37—42no—
350D4×C37—42no—
351D4×C37—44no—
352D4×C37—44no—
353D4×C37—42no—
354D4×C37—42no—
355D4×C37—42no—
356D4×C37—42no—
357D4×C37—42no—
358D4×C37—81no—
359D4×C37—81no—
360D4×C37—81no—
361D4×C37—81no—
362D4×C37—81no—
363D4×C37—81no—
364D4×C37—81no—
365D4×C37—81no—
366D4×C37—81no—
367D4×C37—81no—
368D4×C37—81no—
369D4×C37—81no—
370D4×C37—88no—
371C2×C4×C37—22no—
372C2×C4×C37—22no—
373C2×C4×C37—21no—
374C2×C4×C37—21no—
375C2×C4×C37—21no—
376C2×C4×C37—21no—
377C2×C4×C37—21no—
378C2×C4×C37—21no—
379C2×C4×C37—21no—
380C2×C4×C37—21no—
381C2×C4×C37—22no—
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—42no—
389C2×C4×C37—42no—
390C2×C4×C37—42no—
391C2×C4×C37—81no—
392C2×C4×C37—81no—
393C2×C4×C37—81no—
394C2×C4×C37—81no—
395C2×C4×C37—81no—
396C2×C4×C37—81no—
397C2×C4×C37—81no—
398C2×C4×C37#12011yescharacteristic
399C2×C4×C37#12011yescharacteristic
400C2×C4×C37C22×D411yescharacteristic
401C2×C4×C37C22×D411yescharacteristic
402C8×C37—42no—
403C8×C37—42no—
404#18224C3711yesmaximal, characteristic, direct product factor, Sylow
405C22×C37—21no—
406C22×C37—21no—
407C22×C37—21no—
408C22×C37—21no—
409C22×C37—21no—
410C22×C37—21no—
411C22×C37—21no—
412C22×C37—44no—
413C22×C37—44no—
414C22×C37—44no—
415C22×C37—41no—
416C22×C37—41no—
417C22×C37—41no—
418C22×C37—41no—
419C22×C37—41no—
420C22×C37—41no—
421C22×C37—41no—
422C22×C37—41no—
423C22×C37—41no—
424C22×C37—41no—
425C22×C37—44no—
426C22×C37—41no—
427C22×C37—41no—
428C22×C37—82no—
429C22×C37—82no—
430C22×C37—82no—
431C22×C37—88no—
432C22×C37—88no—
433C22×C37—82no—
434C22×C37—82no—
435C22×C37—162no—
436C22×C37—162no—
437C22×C37B(4,𝔽2)12yes—
438C22×C37C2×#12011yescharacteristic
439C22×C37#57612yes—
440C4×C37—21no—
441C4×C37—21no—
442C4×C37—21no—
443C4×C37—21no—
444C4×C37—41no—
445C4×C37—41no—
446C4×C37—41no—
447C4×C37—41no—
448C4×C37—41no—
449C4×C37—41no—
450C4×C37—41no—
451C4×C37—41no—
452C4×C37—82no—
453#3534C2×C3711yescharacteristic, complemented
454#3003C2×C3711yescharacteristic, complemented
455C2×#447C2×C3711yescharacteristic, complemented
456#2613C2×C3711yescharacteristic, complemented
457#1600C2×C3712yescomplemented
458#1598C2×C3712yescomplemented
459#1597C2×C3712yescomplemented
460#1595C2×C3712yescomplemented
461#1516C2×C3711yescharacteristic, complemented
462#1510C2×C3711yescharacteristic, complemented
463#1468C2×C3711yescharacteristic, complemented
464C2×C37—22no—
465C2×C37—22no—
466C2×C37—41no—
467C2×C37—84no—
468C2×C37—81no—
469C2×C37—81no—
470C2×C37—81no—
471C2×C37—81no—
472C2×C37#300811yescharacteristic
473C2×C37#302111yescharacteristic
474C2×C37C2×B(4,𝔽2)11yescharacteristic
475C23×D4C22×C3711yescharacteristic, complemented
476C2×AGL(1,ℤ/8)—21no—
477C22×D8—21no—
478#562—21no—
479#560—21no—
480#553—21no—
481#551—21no—
482#546—21no—
483#546—21no—
484#546—21no—
485D42—21no—
486#540—21no—
487#539—21no—
488#539C22×C3711yescharacteristic, complemented
489#538—21no—
490#538C22×C3711yescharacteristic, complemented
491#537C22×C3711yescharacteristic, complemented
492#534—21no—
493#534C22×C3711yescharacteristic, complemented
494#525C22×C3711yescharacteristic
495C2×#123C22×C3711yescharacteristic
496C2×#121C22×C3711yescharacteristic
497C2×#120—21no—
498#450—21no—
499#450C22×C3712yescomplemented
500#447—21no—
501#447—21no—
502#447—21no—
503#447C22×C3712yes—
504#447C22×C3712yescomplemented
505#447C22×C3712yescomplemented
506#418—21no—
507C2×#102—21no—
508#407C22×C3711yescharacteristic, complemented
509C2×C22⋊C8C22×C3711yescharacteristic, complemented
510#394—21no—
511#394C22×C3712yescomplemented
512#392—21no—
513#392C22×C3712yescomplemented
514#381C22×C3711yescharacteristic, complemented
515#379—21no—
516#328C22×C3712yescomplemented
517#327C22×C3712yescomplemented
518#327C22×C3712yescomplemented
519#327C22×C3712yescomplemented
520#324C22×C3712yescomplemented
521#323C22×C3712yescomplemented
522C37#1822411yescharacteristic, direct product factor, Sylow
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C3711yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C3711yescharacteristic
537C22×D4D4×C3711yescharacteristic, complemented
538C22×D4C23×C3712yes—
539C23×C4C23×C3711yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C3711yescharacteristic, complemented
578C22⋊Q8C23×C3711yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C3711yescharacteristic, complemented
595#121D4×C3711yescharacteristic, complemented
596#121D4×C3711yescharacteristic, complemented
597#121C23×C3711yescharacteristic
598#121C23×C3711yescharacteristic
599#121C23×C3711yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C3711yescharacteristic, complemented
619C2×C4⋊C4D4×C3711yescharacteristic
620C2×C4⋊C4D4×C3711yescharacteristic, complemented
621C2×C4⋊C4C23×C3711yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C3711yescharacteristic
630C2×C22⋊C4D4×C3711yescharacteristic
631C2×C22⋊C4C23×C3711yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C3712yes—
639C22⋊C8C23×C3712yes—
640#95—21no—
641#95C23×C3712yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C3711yescharacteristic
652C24C2×D4×C3711yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C3711yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
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—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C3711yescharacteristic
695C2×D4C2×D4×C3711yescharacteristic
696C2×D4C2×D4×C3711yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C3711yescharacteristic
707C22×C4C2×D4×C3711yescharacteristic
708C22×C4C2×D4×C3711yescharacteristic
709C22×C4C2×D4×C3711yescharacteristic
710C22×C4C2×D4×C3711yescharacteristic
711C22×C4C2×D4×C3711yescharacteristic
712C22×C4C2×D4×C3711yescharacteristic
713C22×C4C2×D4×C3711yescharacteristic
714C22×C4C24×C3711yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C3711yescharacteristic
737C4⋊C4C2×D4×C3711yescharacteristic
738C4⋊C4C2×D4×C3711yescharacteristic
739C4⋊C4C2×D4×C3711yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—44no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C3711yescharacteristic
804C23#120×C3711yescharacteristic
805C23C22×D4×C3711yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C3711yescharacteristic
863C2×C4#120×C3711yescharacteristic
864C2×C4C22×D4×C3711yescharacteristic
865C2×C4C22×D4×C3711yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22C37×B(4,𝔽2)12yes—
901C22C2×#120×C3711yescharacteristic
902C22C37×#57612yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C37×#300811yescharacteristic
925C2C37×#302111yescharacteristic
926C2C2×C37×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3534C2semidirect
2. C37×#3003C2semidirect
3. C2×C37×#447C2semidirect
4. C37×#2613C2semidirect
5. C37×#1600C2semidirect
6. C37×#1598C2semidirect
7. C37×#1597C2semidirect
8. C37×#1595C2semidirect
9. C37×#1516C2semidirect
10. C37×#1510C2semidirect
11. C37×#1468C2semidirect
12. C23×D4×C37C22semidirect
25. C37×#539C22semidirect
27. C37×#538C22semidirect
28. C37×#537C22semidirect
30. C37×#534C22semidirect
36. C37×#450C22semidirect
41. C37×#447C22semidirect
42. C37×#447C22semidirect
45. C37×#407C22semidirect
46. C2×C22⋊C8×C37C22semidirect
48. C37×#394C22semidirect
50. C37×#392C22semidirect
51. C37×#381C22semidirect
53. C37×#328C22semidirect
54. C37×#327C22semidirect
55. C37×#327C22semidirect
56. C37×#327C22semidirect
57. C37×#324C22semidirect
58. C37×#323C22semidirect
61. C2×#41×C37D4semidirect
73. C22×D4×C37D4semidirect
113. C22⋊Q8×C37D4semidirect
130. #121×C37D4semidirect
131. #121×C37D4semidirect
132. #121×C37D4semidirect
154. #117×C37D4semidirect
156. C2×C4⋊C4×C37D4semidirect
404. #18224C37direct (N × H)
453. #3534C2×C37semidirect
454. #3003C2×C37semidirect
455. C2×#447C2×C37semidirect
456. #2613C2×C37semidirect
457. #1600C2×C37semidirect
458. #1598C2×C37semidirect
459. #1597C2×C37semidirect
460. #1595C2×C37semidirect
461. #1516C2×C37semidirect
462. #1510C2×C37semidirect
463. #1468C2×C37semidirect
475. C23×D4C22×C37semidirect
488. #539C22×C37semidirect
490. #538C22×C37semidirect
491. #537C22×C37semidirect
493. #534C22×C37semidirect
499. #450C22×C37semidirect
504. #447C22×C37semidirect
505. #447C22×C37semidirect
508. #407C22×C37semidirect
509. C2×C22⋊C8C22×C37semidirect
511. #394C22×C37semidirect
513. #392C22×C37semidirect
514. #381C22×C37semidirect
516. #328C22×C37semidirect
517. #327C22×C37semidirect
518. #327C22×C37semidirect
519. #327C22×C37semidirect
520. #324C22×C37semidirect
521. #323C22×C37semidirect
522. C37#18224direct (N × H)
525. C2×#41D4×C37semidirect
537. C22×D4D4×C37semidirect
577. C22⋊Q8D4×C37semidirect
594. #121D4×C37semidirect
595. #121D4×C37semidirect
596. #121D4×C37semidirect
618. #117D4×C37semidirect
620. C2×C4⋊C4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35342
C37×#30032
C2×C37×#4472
C37×#26132
C37×#16002
C37×#15982
C37×#15972
C37×#15952
C37×#15162
C37×#15102
C37×#14682
#1822437