Finite Group Databasebeta

← C37×#19041 #22640294

Subgroups — C37×#19041 #22640294

Order 9472.

838 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3567C211yesmaximal, characteristic
2C37×#3240C211yesmaximal, characteristic, complemented
3C37×#3181C211yesmaximal, characteristic, complemented
4C37×#3172C211yesmaximal, characteristic, complemented
5C37×#1663C211yesmaximal, characteristic, complemented
6C37×#1663C211yesmaximal, characteristic, complemented
7C37×#1662C211yesmaximal, characteristic, complemented
8C37×#1662C211yesmaximal, characteristic, complemented
9C37×#1661C211yesmaximal, characteristic, complemented
10C37×#1661C211yesmaximal, characteristic, complemented
11C37×#1661C211yesmaximal, characteristic, complemented
12C37×#1661C211yesmaximal, characteristic, complemented
13C37×#1532C211yesmaximal, characteristic, complemented
14C37×#1529C211yesmaximal, characteristic, complemented
15C37×#1524C211yesmaximal, characteristic, complemented
16C37×#564C2211yescharacteristic
17C37×#562C2211yescharacteristic
18C37×#562C2211yescharacteristic
19C37×#562C2211yescharacteristic
20C37×#553—21no—
21C37×#553—21no—
22C37×#553—21no—
23C37×#552—21no—
24C37×#552—21no—
25C37×#552—21no—
26C37×#540—21no—
27C37×#540—21no—
28C37×#540—21no—
29C37×#539—21no—
30C37×#539—21no—
31C37×#539—21no—
32C37×#533C2211yescharacteristic
33C37×#529C2211yescharacteristic
34C37×#529C2211yescharacteristic
35C37×#529C2211yescharacteristic
36C37×#501C2211yescharacteristic
37C37×#501C2211yescharacteristic
38C37×#501C2211yescharacteristic
39C37×#501C2211yescharacteristic
40C37×#497C2211yescharacteristic
41C37×#497C2211yescharacteristic
42C37×#491C2211yescharacteristic
43C37×#491C2211yescharacteristic
44C37×#489C2211yescharacteristic
45C37×#489C2211yescharacteristic
46C37×#489C2211yescharacteristic
47C37×#489C2211yescharacteristic
48C37×#485—21no—
49C37×#482—21no—
50C37×#479—21no—
51C37×#478—21no—
52C37×#470—21no—
53C37×#468—21no—
54C37×#467—21no—
55C37×#465—21no—
56C37×#441—21no—
57C37×#440—21no—
58C4×Q16×C37—21no—
59C4×SD16×C37—21no—
60C37×#432C2211yescharacteristic
61C4×M16×C37C2211yescharacteristic
62C2×#97×C37C2211yescharacteristic
63C37×#330C2211yescharacteristic
64C37×#330C2211yescharacteristic
65C37×#330C2211yescharacteristic
66C37×#330C2211yescharacteristic
67C37×#330C2211yescharacteristic
68C37×#330C2211yescharacteristic
69C37×#329C2211yescharacteristic
70C37×#329C2211yescharacteristic
71C37×#329C2211yescharacteristic
72C37×#329C2211yescharacteristic
73C37×#329C2211yescharacteristic
74C37×#329C2211yescharacteristic
75C2×Q16×C37—21no—
76C2×Q16×C37—21no—
77C2×SD16×C37—21no—
78C2×SD16×C37—21no—
79C2×M16×C37—21no—
80C22×C8×C37—21no—
81C4⋊Q8×C37C2311yescharacteristic
82C4⋊Q8×C37C2311yescharacteristic
83#127×C37—21no—
84#126×C37—21no—
85#126×C37—21no—
86#126×C37—21no—
87#126×C37—21no—
88#126×C37—21no—
89#126×C37—21no—
90#126×C37—21no—
91#125×C37—21no—
92#125×C37—21no—
93#125×C37—21no—
94#125×C37—21no—
95#125×C37—21no—
96#125×C37—21no—
97#125×C37—21no—
98#125×C37—21no—
99#125×C37—21no—
100#125×C37—21no—
101#125×C37C2311yescharacteristic
102#125×C37C2311yescharacteristic
103#125×C37C2311yescharacteristic
104#124×C37C2311yescharacteristic
105#124×C37C2311yescharacteristic
106#124×C37C2311yescharacteristic
107#123×C37—21no—
108#123×C37—21no—
109#123×C37—21no—
110#123×C37—21no—
111#123×C37—21no—
112#123×C37—21no—
113#123×C37—21no—
114#123×C37—21no—
115#123×C37—21no—
116#123×C37—21no—
117#123×C37—21no—
118#123×C37—21no—
119#123×C37—21no—
120#123×C37—21no—
121#123×C37—21no—
122C22⋊Q8×C37—21no—
123C22⋊Q8×C37—21no—
124C22⋊Q8×C37—21no—
125C22⋊Q8×C37—21no—
126C22⋊Q8×C37—21no—
127C22⋊Q8×C37—21no—
128C22⋊Q8×C37—21no—
129C22⋊Q8×C37—21no—
130C22⋊Q8×C37D411yescharacteristic
131C22⋊Q8×C37D411yescharacteristic
132C22⋊Q8×C37D411yescharacteristic
133#121×C37—21no—
134#121×C37—21no—
135#121×C37—21no—
136#121×C37—21no—
137#121×C37—21no—
138#121×C37—21no—
139#121×C37—21no—
140#121×C37—21no—
141#121×C37—21no—
142#121×C37—21no—
143#121×C37—21no—
144#121×C37—21no—
145#121×C37D411yescharacteristic
146#121×C37D411yescharacteristic
147#121×C37D411yescharacteristic
148C4×Q8×C37—21no—
149C4×Q8×C37—21no—
150C4×Q8×C37D411yescharacteristic
151C4×Q8×C37D411yescharacteristic
152C4×Q8×C37D411yescharacteristic
153C4×D4×C37—21no—
154C4×D4×C37—21no—
155C4×D4×C37—21no—
156C4×D4×C37—21no—
157C4×D4×C37—21no—
158C4×D4×C37—21no—
159C4×D4×C37—21no—
160C4×D4×C37—21no—
161C4×D4×C37—21no—
162C4×D4×C37D411yescharacteristic
163C4×D4×C37D411yescharacteristic
164C4×D4×C37D411yescharacteristic
165#117×C37—21no—
166#117×C37—21no—
167#117×C37—21no—
168#117×C37—21no—
169#117×C37—21no—
170#117×C37—21no—
171#117×C37—21no—
172C2×C4⋊C4×C37—21no—
173C2×C4⋊C4×C37—21no—
174C2×C4⋊C4×C37—21no—
175C2×C42×C37C2311yescharacteristic
176#107×C37—21no—
177#107×C37—21no—
178#107×C37—21no—
179#107×C37—21no—
180#106×C37—21no—
181#106×C37—21no—
182#106×C37—21no—
183#106×C37—21no—
184C4⋊C8×C37—21no—
185#103×C37—21no—
186#103×C37—21no—
187#103×C37—21no—
188#103×C37—21no—
189#103×C37—21no—
190#103×C37—21no—
191#103×C37—21no—
192#103×C37—21no—
193#102×C37—21no—
194#102×C37—21no—
195#102×C37—21no—
196#102×C37—21no—
197C22⋊C8×C37—21no—
198#97×C37—21no—
199#97×C37C2311yescharacteristic
200#97×C37C2311yescharacteristic
201#97×C37C2311yescharacteristic
202#97×C37C2311yescharacteristic
203#97×C37C2311yescharacteristic
204#97×C37C2311yescharacteristic
205C4×C8×C37—21no—
206C2×Q8×C37—21no—
207C2×Q8×C37—21no—
208C2×Q8×C37C2×D411yescharacteristic
209C2×Q8×C37C2×D411yescharacteristic
210C2×Q8×C37C2×D411yescharacteristic
211C2×D4×C37—21no—
212C2×D4×C37—21no—
213C2×D4×C37—21no—
214C2×D4×C37—21no—
215C2×D4×C37—21no—
216C2×D4×C37—21no—
217C2×D4×C37—21no—
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37C2×D411yescharacteristic
221C2×D4×C37C2×D411yescharacteristic
222C2×D4×C37C2×D411yescharacteristic
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
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×C37C2×D411yescharacteristic
233C22×C4×C37C2×D411yescharacteristic
234C22×C4×C37C2×D411yescharacteristic
235Q16×C37—42no—
236Q16×C37—42no—
237SD16×C37—42no—
238SD16×C37—42no—
239M16×C37—42no—
240C2×C8×C37—21no—
241C2×C8×C37—21no—
242C2×C8×C37—21no—
243C2×C8×C37—21no—
244C2×C8×C37—21no—
245C2×C8×C37—21no—
246C2×C8×C37—42no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—21no—
251C4⋊C4×C37—21no—
252C4⋊C4×C37—21no—
253C4⋊C4×C37—21no—
254C4⋊C4×C37—21no—
255C4⋊C4×C37—21no—
256C4⋊C4×C37—21no—
257C4⋊C4×C37—21no—
258C4⋊C4×C37—21no—
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×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—41no—
276C4⋊C4×C37—41no—
277C4⋊C4×C37C2×D411yescharacteristic
278C4⋊C4×C37C2×D411yescharacteristic
279C4⋊C4×C37C2×D411yescharacteristic
280C4⋊C4×C37C2×D411yescharacteristic
281C4⋊C4×C37C2×D411yescharacteristic
282C4⋊C4×C37C2×D411yescharacteristic
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—21no—
302C22⋊C4×C37—21no—
303C22⋊C4×C37—21no—
304C22⋊C4×C37—41no—
305C42×C37—21no—
306C42×C37—21no—
307C42×C37—21no—
308C42×C37—21no—
309C42×C37—21no—
310C42×C37—41no—
311C42×C37C2×D411yescharacteristic
312C42×C37C2×D411yescharacteristic
313C42×C37C2×D411yescharacteristic
314C42×C37C2411yescharacteristic
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—21no—
318C23×C37#12011yescharacteristic
319Q8×C37—41no—
320Q8×C37—41no—
321Q8×C37—41no—
322Q8×C37—41no—
323Q8×C37—41no—
324Q8×C37—41no—
325Q8×C37—41no—
326D4×C37—41no—
327D4×C37—41no—
328D4×C37—41no—
329D4×C37—81no—
330D4×C37—81no—
331D4×C37—81no—
332D4×C37—81no—
333D4×C37—81no—
334D4×C37—81no—
335D4×C37—81no—
336D4×C37—81no—
337D4×C37—81no—
338C2×C4×C37—21no—
339C2×C4×C37—21no—
340C2×C4×C37—21no—
341C2×C4×C37—21no—
342C2×C4×C37—21no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—41no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—41no—
351C2×C4×C37—41no—
352C2×C4×C37—81no—
353C2×C4×C37—81no—
354C2×C4×C37—81no—
355C2×C4×C37—81no—
356C2×C4×C37—81no—
357C2×C4×C37—81no—
358C2×C4×C37—81no—
359C2×C4×C37—81no—
360C2×C4×C37—81no—
361C2×C4×C37#12011yescharacteristic
362C2×C4×C37#12011yescharacteristic
363C2×C4×C37#12011yescharacteristic
364C2×C4×C37C22×D411yescharacteristic
365C2×C4×C37C22×D411yescharacteristic
366C2×C4×C37C22×D411yescharacteristic
367C8×C37—22no—
368C8×C37—22no—
369C8×C37—41no—
370C8×C37—41no—
371C8×C37—41no—
372C8×C37—41no—
373#19041C3711yesmaximal, characteristic, direct product factor, Sylow
374C22×C37—21no—
375C22×C37—21no—
376C22×C37—21no—
377C22×C37—41no—
378C22×C37—41no—
379C22×C37—41no—
380C22×C37—41no—
381C22×C37—41no—
382C22×C37—41no—
383C22×C37—41no—
384C22×C37—41no—
385C22×C37—41no—
386C22×C37C2×#12011yescharacteristic
387C4×C37—21no—
388C4×C37—21no—
389C4×C37—21no—
390C4×C37—21no—
391C4×C37—21no—
392C4×C37—21no—
393C4×C37—41no—
394C4×C37—41no—
395C4×C37—41no—
396C4×C37—41no—
397C4×C37—41no—
398C4×C37—41no—
399C4×C37—41no—
400C4×C37—41no—
401C4×C37—41no—
402C4×C37—81no—
403C4×C37—81no—
404#3567C2×C3711yescharacteristic
405#3240C2×C3711yescharacteristic, complemented
406#3181C2×C3711yescharacteristic, complemented
407#3172C2×C3711yescharacteristic, complemented
408#1663C2×C3711yescharacteristic, complemented
409#1663C2×C3711yescharacteristic, complemented
410#1662C2×C3711yescharacteristic, complemented
411#1662C2×C3711yescharacteristic, complemented
412#1661C2×C3711yescharacteristic, complemented
413#1661C2×C3711yescharacteristic, complemented
414#1661C2×C3711yescharacteristic, complemented
415#1661C2×C3711yescharacteristic, complemented
416#1532C2×C3711yescharacteristic, complemented
417#1529C2×C3711yescharacteristic, complemented
418#1524C2×C3711yescharacteristic, complemented
419C2×C37—41no—
420C2×C37—81no—
421C2×C37—81no—
422C2×C37—81no—
423C2×C37#301811yescharacteristic
424C2×C37#301811yescharacteristic
425C2×C37#302211yescharacteristic
426#564C22×C3711yescharacteristic
427#562C22×C3711yescharacteristic
428#562C22×C3711yescharacteristic
429#562C22×C3711yescharacteristic
430#553—21no—
431#553—21no—
432#553—21no—
433#552—21no—
434#552—21no—
435#552—21no—
436#540—21no—
437#540—21no—
438#540—21no—
439#539—21no—
440#539—21no—
441#539—21no—
442#533C22×C3711yescharacteristic
443#529C22×C3711yescharacteristic
444#529C22×C3711yescharacteristic
445#529C22×C3711yescharacteristic
446#501C22×C3711yescharacteristic
447#501C22×C3711yescharacteristic
448#501C22×C3711yescharacteristic
449#501C22×C3711yescharacteristic
450#497C22×C3711yescharacteristic
451#497C22×C3711yescharacteristic
452#491C22×C3711yescharacteristic
453#491C22×C3711yescharacteristic
454#489C22×C3711yescharacteristic
455#489C22×C3711yescharacteristic
456#489C22×C3711yescharacteristic
457#489C22×C3711yescharacteristic
458#485—21no—
459#482—21no—
460#479—21no—
461#478—21no—
462#470—21no—
463#468—21no—
464#467—21no—
465#465—21no—
466#441—21no—
467#440—21no—
468C4×Q16—21no—
469C4×SD16—21no—
470#432C22×C3711yescharacteristic
471C4×M16C22×C3711yescharacteristic
472C2×#97C22×C3711yescharacteristic
473#330C22×C3711yescharacteristic
474#330C22×C3711yescharacteristic
475#330C22×C3711yescharacteristic
476#330C22×C3711yescharacteristic
477#330C22×C3711yescharacteristic
478#330C22×C3711yescharacteristic
479#329C22×C3711yescharacteristic
480#329C22×C3711yescharacteristic
481#329C22×C3711yescharacteristic
482#329C22×C3711yescharacteristic
483#329C22×C3711yescharacteristic
484#329C22×C3711yescharacteristic
485C37#1904111yescharacteristic, direct product factor, Sylow
486C2×Q16—21no—
487C2×Q16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×M16—21no—
491C22×C8—21no—
492C4⋊Q8C23×C3711yescharacteristic
493C4⋊Q8C23×C3711yescharacteristic
494#127—21no—
495#126—21no—
496#126—21no—
497#126—21no—
498#126—21no—
499#126—21no—
500#126—21no—
501#126—21no—
502#125—21no—
503#125—21no—
504#125—21no—
505#125—21no—
506#125—21no—
507#125—21no—
508#125—21no—
509#125—21no—
510#125—21no—
511#125—21no—
512#125C23×C3711yescharacteristic
513#125C23×C3711yescharacteristic
514#125C23×C3711yescharacteristic
515#124C23×C3711yescharacteristic
516#124C23×C3711yescharacteristic
517#124C23×C3711yescharacteristic
518#123—21no—
519#123—21no—
520#123—21no—
521#123—21no—
522#123—21no—
523#123—21no—
524#123—21no—
525#123—21no—
526#123—21no—
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8D4×C3711yescharacteristic
542C22⋊Q8D4×C3711yescharacteristic
543C22⋊Q8D4×C3711yescharacteristic
544#121—21no—
545#121—21no—
546#121—21no—
547#121—21no—
548#121—21no—
549#121—21no—
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121—21no—
555#121—21no—
556#121D4×C3711yescharacteristic
557#121D4×C3711yescharacteristic
558#121D4×C3711yescharacteristic
559C4×Q8—21no—
560C4×Q8—21no—
561C4×Q8D4×C3711yescharacteristic
562C4×Q8D4×C3711yescharacteristic
563C4×Q8D4×C3711yescharacteristic
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4D4×C3711yescharacteristic
574C4×D4D4×C3711yescharacteristic
575C4×D4D4×C3711yescharacteristic
576#117—21no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117—21no—
581#117—21no—
582#117—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C42C23×C3711yescharacteristic
587#107—21no—
588#107—21no—
589#107—21no—
590#107—21no—
591#106—21no—
592#106—21no—
593#106—21no—
594#106—21no—
595C4⋊C8—21no—
596#103—21no—
597#103—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#103—21no—
602#103—21no—
603#103—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607#102—21no—
608C22⋊C8—21no—
609#97—21no—
610#97C23×C3711yescharacteristic
611#97C23×C3711yescharacteristic
612#97C23×C3711yescharacteristic
613#97C23×C3711yescharacteristic
614#97C23×C3711yescharacteristic
615#97C23×C3711yescharacteristic
616C4×C8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8C2×D4×C3711yescharacteristic
620C2×Q8C2×D4×C3711yescharacteristic
621C2×Q8C2×D4×C3711yescharacteristic
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4C2×D4×C3711yescharacteristic
632C2×D4C2×D4×C3711yescharacteristic
633C2×D4C2×D4×C3711yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4C2×D4×C3711yescharacteristic
644C22×C4C2×D4×C3711yescharacteristic
645C22×C4C2×D4×C3711yescharacteristic
646Q16—42no—
647Q16—42no—
648SD16—42no—
649SD16—42no—
650M16—42no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—42no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—41no—
687C4⋊C4—41no—
688C4⋊C4C2×D4×C3711yescharacteristic
689C4⋊C4C2×D4×C3711yescharacteristic
690C4⋊C4C2×D4×C3711yescharacteristic
691C4⋊C4C2×D4×C3711yescharacteristic
692C4⋊C4C2×D4×C3711yescharacteristic
693C4⋊C4C2×D4×C3711yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
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—41no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—41no—
722C42C2×D4×C3711yescharacteristic
723C42C2×D4×C3711yescharacteristic
724C42C2×D4×C3711yescharacteristic
725C42C24×C3711yescharacteristic
726C23—21no—
727C23—21no—
728C23—21no—
729C23#120×C3711yescharacteristic
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4#120×C3711yescharacteristic
773C2×C4#120×C3711yescharacteristic
774C2×C4#120×C3711yescharacteristic
775C2×C4C22×D4×C3711yescharacteristic
776C2×C4C22×D4×C3711yescharacteristic
777C2×C4C22×D4×C3711yescharacteristic
778C8—22no—
779C8—22no—
780C8—41no—
781C8—41no—
782C8—41no—
783C8—41no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22C2×#120×C3711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—81no—
813C4—81no—
814C2—41no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2C37×#301811yescharacteristic
819C2C37×#301811yescharacteristic
820C2C37×#302211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3567C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3240C2semidirect
3. C37×#3181C2semidirect
4. C37×#3172C2semidirect
5. C37×#1663C2semidirect
6. C37×#1663C2semidirect
7. C37×#1662C2semidirect
8. C37×#1662C2semidirect
9. C37×#1661C2semidirect
10. C37×#1661C2semidirect
11. C37×#1661C2semidirect
12. C37×#1661C2semidirect
13. C37×#1532C2semidirect
14. C37×#1529C2semidirect
15. C37×#1524C2semidirect
373. #19041C37direct (N × H)
405. #3240C2×C37semidirect
406. #3181C2×C37semidirect
407. #3172C2×C37semidirect
408. #1663C2×C37semidirect
409. #1663C2×C37semidirect
410. #1662C2×C37semidirect
411. #1662C2×C37semidirect
412. #1661C2×C37semidirect
413. #1661C2×C37semidirect
414. #1661C2×C37semidirect
415. #1661C2×C37semidirect
416. #1532C2×C37semidirect
417. #1529C2×C37semidirect
418. #1524C2×C37semidirect
485. C37#19041direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35672
C37×#32402
C37×#31812
C37×#31722
C37×#16632
C37×#16622
C37×#16612
C37×#15322
C37×#15292
C37×#15242
#1904137