Finite Group Databasebeta

← C37×#24405 #22645658

Subgroups — C37×#24405 #22645658

Order 9472.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3484C211yesmaximal, characteristic
2C2×C37×#458C211yesmaximal, characteristic, complemented
3C22×#99×C37C211yesmaximal, characteristic, complemented
4C37×#2412C212yesmaximal, complemented
5C37×#2405C211yesmaximal, characteristic, complemented
6C37×#2044C212yesmaximal, complemented
7C37×#2022C212yesmaximal, complemented
8C37×#1898C212yesmaximal, complemented
9C37×#1890C211yesmaximal, characteristic, complemented
10C37×#1867C211yesmaximal, characteristic, complemented
11C37×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C37C2211yescharacteristic
13C23×D4×C37C2211yescharacteristic
14C37×#546—22no—
15C37×#546—22no—
16D42×C37—22no—
17D42×C37—22no—
18C37×#535—21no—
19C37×#534—21no—
20C37×#534C2212yes—
21C37×#525—21no—
22C2×#123×C37C2211yescharacteristic
23C2×#123×C37C2212yescomplemented
24C2×#123×C37C2211yescharacteristic, complemented
25C2×#120×C37—21no—
26C2×#120×C37C2212yes—
27C37×#518C2211yescharacteristic
28C22×C22⋊C4×C37C2211yescharacteristic, complemented
29C22×C22⋊C4×C37C2212yescomplemented
30C37×#458—24no—
31C2×#99×C37—24no—
32C2×#99×C37C2211yescharacteristic
33C2×#99×C37C2211yescharacteristic
34C2×#99×C37C2212yescomplemented
35C2×#99×C37C2212yescomplemented
36C2×#99×C37C2212yescomplemented
37C37×#397—22no—
38C37×#394—21no—
39C37×#394—21no—
40C37×#394—22no—
41C37×#386—22no—
42C37×#386C2211yescharacteristic
43C37×#386C2211yescharacteristic, complemented
44C37×#386C2212yescomplemented
45C37×#385—21no—
46C37×#385C2212yescomplemented
47C37×#381C2212yescomplemented
48C37×#380—22no—
49C37×#379—21no—
50C37×#379C2211yescharacteristic, complemented
51C37×#342C2212yescomplemented
52C37×#342C2212yescomplemented
53C25×C37D411yescharacteristic
54C25×C37C2311yescharacteristic
55H(5,𝔽2)×C37—22no—
56H(5,𝔽2)×C37—22no—
57H(5,𝔽2)×C37—42no—
58C2×#41×C37—21no—
59C2×#41×C37—22no—
60C22×D4×C37—21no—
61C22×D4×C37—22no—
62C22×D4×C37—22no—
63C22×D4×C37—22no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—22no—
67C22×D4×C37—22no—
68C22×D4×C37—42no—
69C22×D4×C37D411yescharacteristic
70C22×D4×C37D411yescharacteristic
71C22×D4×C37D412yes—
72C22×D4×C37D412yes—
73C22×D4×C37C2312yes—
74C22×D4×C37C2311yescharacteristic
75C22×D4×C37C2311yescharacteristic
76C23×C4×C37—22no—
77C23×C4×C37D411yescharacteristic
78C23×C4×C37C2311yescharacteristic
79C23×C4×C37C2311yescharacteristic
80#127×C37—22no—
81#124×C37—22no—
82#123×C37—22no—
83#123×C37—22no—
84#123×C37—22no—
85#123×C37—22no—
86#123×C37—22no—
87#123×C37—24no—
88#123×C37—42no—
89#123×C37—42no—
90C22⋊Q8×C37—21no—
91C22⋊Q8×C37—21no—
92#121×C37—21no—
93#121×C37—21no—
94#121×C37—22no—
95#121×C37—22no—
96#121×C37—22no—
97#121×C37—22no—
98#121×C37—22no—
99#121×C37—22no—
100#120×C37—22no—
101#120×C37—22no—
102#120×C37—22no—
103#120×C37—22no—
104#120×C37—22no—
105#120×C37—22no—
106#120×C37—22no—
107#120×C37—22no—
108#120×C37—22no—
109C4×D4×C37—22no—
110C4×D4×C37—22no—
111C4×D4×C37—22no—
112C4×D4×C37—22no—
113#117×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—22no—
116C2×C4⋊C4×C37—21no—
117C2×C4⋊C4×C37—22no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—24no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—22no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—22no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37—22no—
130C2×C22⋊C4×C37—22no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37—21no—
133C2×C22⋊C4×C37—21no—
134C2×C22⋊C4×C37—22no—
135C2×C22⋊C4×C37—42no—
136C2×C22⋊C4×C37D412yes—
137C2×C22⋊C4×C37D412yes—
138C2×C22⋊C4×C37C2311yescharacteristic
139C2×C22⋊C4×C37C2311yescharacteristic
140C2×C22⋊C4×C37C2312yes—
141C2×C22⋊C4×C37C2312yes—
142C2×C22⋊C4×C37C2312yes—
143#99×C37—22no—
144#99×C37—24no—
145#99×C37—24no—
146#99×C37—42no—
147#99×C37D414yescomplemented
148#95×C37—22no—
149#95×C37—22no—
150#95×C37—22no—
151#95×C37—21no—
152#95×C37—21no—
153#95×C37—22no—
154C24×C37—21no—
155C24×C37—21no—
156C24×C37—22no—
157C24×C37—21no—
158C24×C37—21no—
159C24×C37—21no—
160C24×C37—22no—
161C24×C37—41no—
162C24×C37—42no—
163C24×C37—42no—
164C24×C37—81no—
165C24×C37—81no—
166C24×C37C2×D411yescharacteristic
167C24×C37C2×D412yes—
168C24×C37C2×D411yescharacteristic
169C24×C37C2×D412yes—
170C24×C37C2×D412yes—
171C24×C37C2×D411yescharacteristic
172C24×C37C2×D411yescharacteristic
173C24×C37C2411yescharacteristic
174#41×C37—44no—
175#41×C37—44no—
176#41×C37—42no—
177#41×C37—42no—
178C2×Q8×C37—21no—
179C2×D4×C37—22no—
180C2×D4×C37—22no—
181C2×D4×C37—22no—
182C2×D4×C37—21no—
183C2×D4×C37—22no—
184C2×D4×C37—22no—
185C2×D4×C37—22no—
186C2×D4×C37—22no—
187C2×D4×C37—22no—
188C2×D4×C37—21no—
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—22no—
192C2×D4×C37—22no—
193C2×D4×C37—21no—
194C2×D4×C37—22no—
195C2×D4×C37—22no—
196C2×D4×C37—22no—
197C2×D4×C37—22no—
198C2×D4×C37—22no—
199C2×D4×C37—22no—
200C2×D4×C37—22no—
201C2×D4×C37—22no—
202C2×D4×C37—22no—
203C2×D4×C37—41no—
204C2×D4×C37—41no—
205C2×D4×C37—44no—
206C2×D4×C37—44no—
207C2×D4×C37—44no—
208C2×D4×C37—44no—
209C2×D4×C37—44no—
210C2×D4×C37—44no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—44no—
214C2×D4×C37—82no—
215C2×D4×C37—82no—
216C2×D4×C37—82no—
217C2×D4×C37C2×D412yes—
218C2×D4×C37#4112yes—
219C22×C4×C37—21no—
220C22×C4×C37—22no—
221C22×C4×C37—21no—
222C22×C4×C37—21no—
223C22×C4×C37—22no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—22no—
227C22×C4×C37—22no—
228C22×C4×C37—21no—
229C22×C4×C37—22no—
230C22×C4×C37—22no—
231C22×C4×C37—21no—
232C22×C4×C37—21no—
233C22×C4×C37—21no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—22no—
237C22×C4×C37—41no—
238C22×C4×C37—44no—
239C22×C4×C37—44no—
240C22×C4×C37—81no—
241C22×C4×C37—82no—
242C22×C4×C37C2×D412yes—
243C22×C4×C37C2×D411yescharacteristic
244C22×C4×C37C2×D411yescharacteristic
245C22×C4×C37C2×D412yes—
246C22×C4×C37C2×D412yes—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—22no—
250C4⋊C4×C37—22no—
251C4⋊C4×C37—44no—
252C4⋊C4×C37—42no—
253C4⋊C4×C37—42no—
254C4⋊C4×C37—82no—
255C22⋊C4×C37—22no—
256C22⋊C4×C37—22no—
257C22⋊C4×C37—22no—
258C22⋊C4×C37—22no—
259C22⋊C4×C37—22no—
260C22⋊C4×C37—22no—
261C22⋊C4×C37—22no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—22no—
264C22⋊C4×C37—22no—
265C22⋊C4×C37—22no—
266C22⋊C4×C37—22no—
267C22⋊C4×C37—22no—
268C22⋊C4×C37—21no—
269C22⋊C4×C37—21no—
270C22⋊C4×C37—22no—
271C22⋊C4×C37—22no—
272C22⋊C4×C37—44no—
273C22⋊C4×C37—44no—
274C22⋊C4×C37—42no—
275C22⋊C4×C37—42no—
276C22⋊C4×C37—41no—
277C22⋊C4×C37—42no—
278C22⋊C4×C37—41no—
279C22⋊C4×C37—42no—
280C22⋊C4×C37—81no—
281C22⋊C4×C37—81no—
282C22⋊C4×C37—81no—
283C22⋊C4×C37—82no—
284C22⋊C4×C37C2×D414yescomplemented
285C42×C37—22no—
286C23×C37—21no—
287C23×C37—21no—
288C23×C37—21no—
289C23×C37—22no—
290C23×C37—22no—
291C23×C37—22no—
292C23×C37—24no—
293C23×C37—21no—
294C23×C37—21no—
295C23×C37—21no—
296C23×C37—22no—
297C23×C37—22no—
298C23×C37—21no—
299C23×C37—22no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—22no—
303C23×C37—22no—
304C23×C37—42no—
305C23×C37—41no—
306C23×C37—41no—
307C23×C37—41no—
308C23×C37—41no—
309C23×C37—42no—
310C23×C37—42no—
311C23×C37—41no—
312C23×C37—42no—
313C23×C37—42no—
314C23×C37—41no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37—41no—
318C23×C37—42no—
319C23×C37—42no—
320C23×C37—42no—
321C23×C37—42no—
322C23×C37—42no—
323C23×C37—81no—
324C23×C37—81no—
325C23×C37—82no—
326C23×C37—82no—
327C23×C37—84no—
328C23×C37—81no—
329C23×C37—81no—
330C23×C37—84no—
331C23×C37—84no—
332C23×C37#12011yescharacteristic
333C23×C37#12012yes—
334C23×C37#12011yescharacteristic
335C23×C37#12112yes—
336C23×C37C22×D411yescharacteristic
337C23×C37C22×D412yes—
338C23×C37C22×D411yescharacteristic
339C23×C37C2×#4111yescharacteristic
340C23×C37H(5,𝔽2)12yes—
341Q8×C37—42no—
342D4×C37—24no—
343D4×C37—24no—
344D4×C37—44no—
345D4×C37—42no—
346D4×C37—44no—
347D4×C37—44no—
348D4×C37—44no—
349D4×C37—42no—
350D4×C37—42no—
351D4×C37—42no—
352D4×C37—42no—
353D4×C37—42no—
354D4×C37—42no—
355D4×C37—44no—
356D4×C37—82no—
357D4×C37—82no—
358D4×C37—82no—
359D4×C37—82no—
360C2×C4×C37—21no—
361C2×C4×C37—21no—
362C2×C4×C37—22no—
363C2×C4×C37—22no—
364C2×C4×C37—22no—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—24no—
369C2×C4×C37—22no—
370C2×C4×C37—22no—
371C2×C4×C37—42no—
372C2×C4×C37—42no—
373C2×C4×C37—44no—
374C2×C4×C37—42no—
375C2×C4×C37—42no—
376C2×C4×C37—42no—
377C2×C4×C37—42no—
378C2×C4×C37—42no—
379C2×C4×C37—41no—
380C2×C4×C37—41no—
381C2×C4×C37—41no—
382C2×C4×C37—41no—
383C2×C4×C37—42no—
384C2×C4×C37—42no—
385C2×C4×C37—41no—
386C2×C4×C37—41no—
387C2×C4×C37—42no—
388C2×C4×C37—42no—
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—42no—
396C2×C4×C37—42no—
397C2×C4×C37—42no—
398C2×C4×C37—81no—
399C2×C4×C37—81no—
400C2×C4×C37—88no—
401C2×C4×C37#12112yes—
402#24405C3711yesmaximal, characteristic, direct product factor, Sylow
403C22×C37—21no—
404C22×C37—22no—
405C22×C37—21no—
406C22×C37—22no—
407C22×C37—21no—
408C22×C37—21no—
409C22×C37—21no—
410C22×C37—22no—
411C22×C37—22no—
412C22×C37—22no—
413C22×C37—21no—
414C22×C37—21no—
415C22×C37—22no—
416C22×C37—41no—
417C22×C37—41no—
418C22×C37—42no—
419C22×C37—44no—
420C22×C37—44no—
421C22×C37—42no—
422C22×C37—42no—
423C22×C37—42no—
424C22×C37—42no—
425C22×C37—41no—
426C22×C37—41no—
427C22×C37—42no—
428C22×C37—41no—
429C22×C37—42no—
430C22×C37—41no—
431C22×C37—42no—
432C22×C37—41no—
433C22×C37—82no—
434C22×C37—81no—
435C22×C37—81no—
436C22×C37—81no—
437C22×C37—82no—
438C22×C37—84no—
439C22×C37—82no—
440C22×C37—82no—
441C22×C37—81no—
442C22×C37—84no—
443C22×C37—162no—
444C22×C37#45812yescomplemented
445C22×C37C2×#12011yescharacteristic
446C22×C37C2×#12111yescharacteristic
447C22×C37#53411yescharacteristic
448C22×C37D4212yes—
449C22×C37#54612yes—
450C4×C37—22no—
451C4×C37—44no—
452C4×C37—41no—
453C4×C37—42no—
454C4×C37—42no—
455C4×C37—42no—
456C4×C37—81no—
457C4×C37—81no—
458C4×C37—82no—
459C4×C37—81no—
460C4×C37—81no—
461#3484C2×C3711yescharacteristic
462C2×#458C2×C3711yescharacteristic, complemented
463C22×#99C2×C3711yescharacteristic, complemented
464#2412C2×C3712yescomplemented
465#2405C2×C3711yescharacteristic, complemented
466#2044C2×C3712yescomplemented
467#2022C2×C3712yescomplemented
468#1898C2×C3712yescomplemented
469#1890C2×C3711yescharacteristic, complemented
470#1867C2×C3711yescharacteristic, complemented
471#1790C2×C3711yescharacteristic, complemented
472C2×C37—22no—
473C2×C37—21no—
474C2×C37—21no—
475C2×C37—22no—
476C2×C37—22no—
477C2×C37—42no—
478C2×C37—41no—
479C2×C37—42no—
480C2×C37—81no—
481C2×C37—82no—
482C2×C37#241011yescharacteristic
483C2×C37C2×#45811yescharacteristic
484C2×C37#302611yescharacteristic
485C2×H(5,𝔽2)C22×C3711yescharacteristic
486C23×D4C22×C3711yescharacteristic
487#546—22no—
488#546—22no—
489D42—22no—
490D42—22no—
491#535—21no—
492#534—21no—
493#534C22×C3712yes—
494#525—21no—
495C2×#123C22×C3711yescharacteristic
496C2×#123C22×C3712yescomplemented
497C2×#123C22×C3711yescharacteristic, complemented
498C2×#120—21no—
499C2×#120C22×C3712yes—
500#518C22×C3711yescharacteristic
501C22×C22⋊C4C22×C3711yescharacteristic, complemented
502C22×C22⋊C4C22×C3712yescomplemented
503#458—24no—
504C2×#99—24no—
505C2×#99C22×C3711yescharacteristic
506C2×#99C22×C3711yescharacteristic
507C2×#99C22×C3712yescomplemented
508C2×#99C22×C3712yescomplemented
509C2×#99C22×C3712yescomplemented
510#397—22no—
511#394—21no—
512#394—21no—
513#394—22no—
514#386—22no—
515#386C22×C3711yescharacteristic
516#386C22×C3711yescharacteristic, complemented
517#386C22×C3712yescomplemented
518#385—21no—
519#385C22×C3712yescomplemented
520#381C22×C3712yescomplemented
521#380—22no—
522#379—21no—
523#379C22×C3711yescharacteristic, complemented
524#342C22×C3712yescomplemented
525#342C22×C3712yescomplemented
526C37#2440511yescharacteristic, direct product factor, Sylow
527C25D4×C3711yescharacteristic
528C25C23×C3711yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C3711yescharacteristic
544C22×D4D4×C3711yescharacteristic
545C22×D4D4×C3712yes—
546C22×D4D4×C3712yes—
547C22×D4C23×C3712yes—
548C22×D4C23×C3711yescharacteristic
549C22×D4C23×C3711yescharacteristic
550C23×C4—22no—
551C23×C4D4×C3711yescharacteristic
552C23×C4C23×C3711yescharacteristic
553C23×C4C23×C3711yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C3712yes—
611C2×C22⋊C4D4×C3712yes—
612C2×C22⋊C4C23×C3712yes—
613C2×C22⋊C4C23×C3711yescharacteristic
614C2×C22⋊C4C23×C3711yescharacteristic
615C2×C22⋊C4C23×C3712yes—
616C2×C22⋊C4C23×C3712yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C3714yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C3711yescharacteristic
641C24C2×D4×C3712yes—
642C24C2×D4×C3711yescharacteristic
643C24C2×D4×C3712yes—
644C24C2×D4×C3712yes—
645C24C2×D4×C3711yescharacteristic
646C24C2×D4×C3711yescharacteristic
647C24C24×C3711yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C3712yes—
692C2×D4#41×C3712yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C3712yes—
717C22×C4C2×D4×C3711yescharacteristic
718C22×C4C2×D4×C3711yescharacteristic
719C22×C4C2×D4×C3712yes—
720C22×C4C2×D4×C3712yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C3714yescomplemented
759C42—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C3711yescharacteristic
807C23#120×C3712yes—
808C23#120×C3711yescharacteristic
809C23#121×C3712yes—
810C23C22×D4×C3711yescharacteristic
811C23C22×D4×C3712yes—
812C23C22×D4×C3711yescharacteristic
813C23C2×#41×C3711yescharacteristic
814C23H(5,𝔽2)×C3712yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—44no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C3712yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22C37×#45812yescomplemented
918C22C2×#120×C3711yescharacteristic
919C22C2×#121×C3711yescharacteristic
920C22C37×#53411yescharacteristic
921C22D42×C3712yes—
922C22C37×#54612yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C37×#241011yescharacteristic
945C2C2×C37×#45811yescharacteristic
946C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
prime radicalC37×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#458C2semidirect
3. C22×#99×C37C2semidirect
4. C37×#2412C2semidirect
5. C37×#2405C2semidirect
6. C37×#2044C2semidirect
7. C37×#2022C2semidirect
8. C37×#1898C2semidirect
9. C37×#1890C2semidirect
10. C37×#1867C2semidirect
11. C37×#1790C2semidirect
23. C2×#123×C37C22semidirect
24. C2×#123×C37C22semidirect
28. C22×C22⋊C4×C37C22semidirect
29. C22×C22⋊C4×C37C22semidirect
34. C2×#99×C37C22semidirect
35. C2×#99×C37C22semidirect
36. C2×#99×C37C22semidirect
43. C37×#386C22semidirect
44. C37×#386C22semidirect
46. C37×#385C22semidirect
47. C37×#381C22semidirect
50. C37×#379C22semidirect
51. C37×#342C22semidirect
52. C37×#342C22semidirect
147. #99×C37D4semidirect
284. C22⋊C4×C37C2×D4semidirect
402. #24405C37direct (N × H)
444. C22×C37#458semidirect
462. C2×#458C2×C37semidirect
463. C22×#99C2×C37semidirect
464. #2412C2×C37semidirect
465. #2405C2×C37semidirect
466. #2044C2×C37semidirect
467. #2022C2×C37semidirect
468. #1898C2×C37semidirect
469. #1890C2×C37semidirect
470. #1867C2×C37semidirect
471. #1790C2×C37semidirect
496. C2×#123C22×C37semidirect
497. C2×#123C22×C37semidirect
501. C22×C22⋊C4C22×C37semidirect
502. C22×C22⋊C4C22×C37semidirect
507. C2×#99C22×C37semidirect
508. C2×#99C22×C37semidirect
509. C2×#99C22×C37semidirect
516. #386C22×C37semidirect
517. #386C22×C37semidirect
519. #385C22×C37semidirect
520. #381C22×C37semidirect
523. #379C22×C37semidirect
524. #342C22×C37semidirect
525. #342C22×C37semidirect
526. C37#24405direct (N × H)
621. #99D4×C37semidirect
758. C22⋊C4C2×D4×C37semidirect
917. C22C37×#458semidirect

Maximal subgroups

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

subgroupindex
C37×#34842
C2×C37×#4582
C22×#99×C372
C37×#24122
C37×#24052
C37×#20442
C37×#20222
C37×#18982
C37×#18902
C37×#18672
C37×#17902
#2440537