Finite Group Databasebeta

← C37×#24404 #22645657

Subgroups — C37×#24404 #22645657

Order 9472.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3484C211yesmaximal, characteristic, complemented
2C2×C37×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×#99×C37C211yesmaximal, characteristic, complemented
4C37×#2410C212yesmaximal, complemented
5C37×#2403C211yesmaximal, characteristic, complemented
6C37×#2044C212yesmaximal, complemented
7C37×#2021C212yesmaximal, complemented
8C37×#1898C212yesmaximal, complemented
9C37×#1889C211yesmaximal, characteristic, complemented
10C37×#1867C211yesmaximal, characteristic, complemented
11C37×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C37C2211yescharacteristic
13C23×D4×C37C2211yescharacteristic
14C23×D4×C37C2211yescharacteristic, complemented
15C37×#546—22no—
16C37×#546—22no—
17D42×C37—22no—
18D42×C37—22no—
19C37×#535—21no—
20C37×#534—21no—
21C37×#534C2212yes—
22C37×#525—21no—
23C2×#121×C37—22no—
24C2×#120×C37—21no—
25C2×#120×C37—21no—
26C2×#120×C37C2211yescharacteristic
27C2×#120×C37C2212yes—
28C2×#120×C37C2212yescomplemented
29C2×#120×C37C2211yescharacteristic, complemented
30C37×#518C2211yescharacteristic
31C22×C22⋊C4×C37C2212yescomplemented
32C37×B(4,𝔽2)—24no—
33C2×#99×C37—24no—
34C2×#99×C37C2211yescharacteristic
35C2×#99×C37C2211yescharacteristic
36C2×#99×C37C2212yescomplemented
37C2×#99×C37C2212yescomplemented
38C2×#99×C37C2212yescomplemented
39C37×#394—22no—
40C37×#392—21no—
41C37×#392—21no—
42C37×#392—22no—
43C37×#386—21no—
44C37×#386—22no—
45C37×#386C2211yescharacteristic
46C37×#386C2211yescharacteristic, complemented
47C37×#386C2212yescomplemented
48C37×#385C2212yescomplemented
49C37×#379C2212yescomplemented
50C37×#379C2211yescharacteristic, complemented
51C37×#342C2212yescomplemented
52C37×#342C2212yescomplemented
53C25×C37D411yescharacteristic, complemented
54C25×C37C2311yescharacteristic
55C25×C37C2311yescharacteristic
56H(5,𝔽2)×C37—22no—
57H(5,𝔽2)×C37—22no—
58H(5,𝔽2)×C37—42no—
59C2×#41×C37—21no—
60C2×#41×C37—22no—
61C22×D4×C37—21no—
62C22×D4×C37—21no—
63C22×D4×C37—22no—
64C22×D4×C37—22no—
65C22×D4×C37—22no—
66C22×D4×C37—22no—
67C22×D4×C37—21no—
68C22×D4×C37—21no—
69C22×D4×C37—22no—
70C22×D4×C37—22no—
71C22×D4×C37—21no—
72C22×D4×C37—22no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—22no—
76C22×D4×C37—44no—
77C22×D4×C37—42no—
78C22×D4×C37D411yescharacteristic, complemented
79C22×D4×C37D411yescharacteristic, complemented
80C22×D4×C37D412yescomplemented
81C22×D4×C37D412yescomplemented
82C22×D4×C37C2312yes—
83C22×D4×C37C2311yescharacteristic
84C22×D4×C37C2311yescharacteristic
85C23×C4×C37—22no—
86C23×C4×C37D411yescharacteristic, complemented
87C23×C4×C37C2311yescharacteristic
88#127×C37—22no—
89#124×C37—22no—
90#123×C37—22no—
91#123×C37—22no—
92#123×C37—22no—
93C22⋊Q8×C37—21no—
94C22⋊Q8×C37—21no—
95#121×C37—21no—
96#121×C37—21no—
97#121×C37—22no—
98#121×C37—22no—
99#121×C37—22no—
100#121×C37—22no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—48no—
104#120×C37—22no—
105#120×C37—22no—
106#120×C37—22no—
107#120×C37—22no—
108#120×C37—22no—
109#120×C37—22no—
110#120×C37—22no—
111#120×C37—22no—
112#120×C37—22no—
113#120×C37—22no—
114#120×C37—22no—
115#120×C37—24no—
116#120×C37—42no—
117#120×C37—42no—
118#120×C37—44no—
119C4×D4×C37—22no—
120C4×D4×C37—22no—
121C4×D4×C37—22no—
122C4×D4×C37—22no—
123#117×C37—21no—
124C2×C4⋊C4×C37—22no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—24no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37—22no—
133C2×C22⋊C4×C37—22no—
134C2×C22⋊C4×C37—21no—
135C2×C22⋊C4×C37—21no—
136C2×C22⋊C4×C37—22no—
137C2×C22⋊C4×C37—22no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—22no—
140C2×C22⋊C4×C37—42no—
141C2×C22⋊C4×C37D412yescomplemented
142C2×C22⋊C4×C37D412yescomplemented
143C2×C22⋊C4×C37C2311yescharacteristic
144C2×C22⋊C4×C37C2311yescharacteristic
145C2×C22⋊C4×C37C2312yes—
146C2×C22⋊C4×C37C2312yes—
147C2×C22⋊C4×C37C2312yes—
148#99×C37—22no—
149#99×C37—24no—
150#99×C37—24no—
151#99×C37—42no—
152#99×C37D414yescomplemented
153#95×C37—22no—
154#95×C37—21no—
155#95×C37—21no—
156#95×C37—22no—
157C24×C37—21no—
158C24×C37—21no—
159C24×C37—22no—
160C24×C37—21no—
161C24×C37—22no—
162C24×C37—21no—
163C24×C37—21no—
164C24×C37—21no—
165C24×C37—22no—
166C24×C37—21no—
167C24×C37—21no—
168C24×C37—22no—
169C24×C37—41no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—81no—
174C24×C37—81no—
175C24×C37—81no—
176C24×C37C2×D411yescharacteristic
177C24×C37C2×D412yes—
178C24×C37C2×D411yescharacteristic
179C24×C37C2×D412yes—
180C24×C37C2×D412yes—
181C24×C37C2×D411yescharacteristic
182C24×C37C2×D411yescharacteristic
183C24×C37C2411yescharacteristic
184#41×C37—44no—
185#41×C37—44no—
186#41×C37—42no—
187#41×C37—42no—
188C2×Q8×C37—21no—
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—22no—
192C2×D4×C37—24no—
193C2×D4×C37—21no—
194C2×D4×C37—28no—
195C2×D4×C37—22no—
196C2×D4×C37—22no—
197C2×D4×C37—22no—
198C2×D4×C37—22no—
199C2×D4×C37—22no—
200C2×D4×C37—21no—
201C2×D4×C37—22no—
202C2×D4×C37—22no—
203C2×D4×C37—22no—
204C2×D4×C37—22no—
205C2×D4×C37—21no—
206C2×D4×C37—22no—
207C2×D4×C37—22no—
208C2×D4×C37—22no—
209C2×D4×C37—22no—
210C2×D4×C37—22no—
211C2×D4×C37—22no—
212C2×D4×C37—22no—
213C2×D4×C37—22no—
214C2×D4×C37—22no—
215C2×D4×C37—41no—
216C2×D4×C37—41no—
217C2×D4×C37—42no—
218C2×D4×C37—44no—
219C2×D4×C37—44no—
220C2×D4×C37—44no—
221C2×D4×C37—44no—
222C2×D4×C37—44no—
223C2×D4×C37—44no—
224C2×D4×C37—44no—
225C2×D4×C37—44no—
226C2×D4×C37—44no—
227C2×D4×C37—42no—
228C2×D4×C37—42no—
229C2×D4×C37—44no—
230C2×D4×C37—42no—
231C2×D4×C37—41no—
232C2×D4×C37—42no—
233C2×D4×C37—41no—
234C2×D4×C37—42no—
235C2×D4×C37—44no—
236C2×D4×C37—42no—
237C2×D4×C37—42no—
238C2×D4×C37—42no—
239C2×D4×C37—44no—
240C2×D4×C37—42no—
241C2×D4×C37—82no—
242C2×D4×C37—82no—
243C2×D4×C37—81no—
244C2×D4×C37—81no—
245C2×D4×C37—82no—
246C2×D4×C37—82no—
247C2×D4×C37C2×D412yes—
248C2×D4×C37#4112yes—
249C22×C4×C37—21no—
250C22×C4×C37—22no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—21no—
254C22×C4×C37—22no—
255C22×C4×C37—22no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—22no—
259C22×C4×C37—22no—
260C22×C4×C37—21no—
261C22×C4×C37—21no—
262C22×C4×C37—42no—
263C22×C4×C37—41no—
264C22×C4×C37—44no—
265C22×C4×C37—44no—
266C22×C4×C37—82no—
267C22×C4×C37C2×D412yes—
268C22×C4×C37C2×D411yescharacteristic
269C22×C4×C37C2×D411yescharacteristic
270C22×C4×C37C2×D412yes—
271C22×C4×C37C2×D412yes—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—22no—
275C4⋊C4×C37—22no—
276C4⋊C4×C37—44no—
277C22⋊C4×C37—22no—
278C22⋊C4×C37—22no—
279C22⋊C4×C37—22no—
280C22⋊C4×C37—22no—
281C22⋊C4×C37—22no—
282C22⋊C4×C37—22no—
283C22⋊C4×C37—22no—
284C22⋊C4×C37—22no—
285C22⋊C4×C37—22no—
286C22⋊C4×C37—22no—
287C22⋊C4×C37—22no—
288C22⋊C4×C37—22no—
289C22⋊C4×C37—22no—
290C22⋊C4×C37—21no—
291C22⋊C4×C37—21no—
292C22⋊C4×C37—22no—
293C22⋊C4×C37—22no—
294C22⋊C4×C37—44no—
295C22⋊C4×C37—44no—
296C22⋊C4×C37—42no—
297C22⋊C4×C37—42no—
298C22⋊C4×C37—42no—
299C22⋊C4×C37—44no—
300C22⋊C4×C37—42no—
301C22⋊C4×C37—44no—
302C22⋊C4×C37—42no—
303C22⋊C4×C37—82no—
304C22⋊C4×C37—81no—
305C22⋊C4×C37C2×D414yescomplemented
306C42×C37—22no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—22no—
311C23×C37—22no—
312C23×C37—22no—
313C23×C37—24no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—22no—
318C23×C37—22no—
319C23×C37—24no—
320C23×C37—22no—
321C23×C37—21no—
322C23×C37—22no—
323C23×C37—21no—
324C23×C37—21no—
325C23×C37—22no—
326C23×C37—22no—
327C23×C37—41no—
328C23×C37—42no—
329C23×C37—41no—
330C23×C37—41no—
331C23×C37—41no—
332C23×C37—42no—
333C23×C37—41no—
334C23×C37—42no—
335C23×C37—42no—
336C23×C37—42no—
337C23×C37—41no—
338C23×C37—41no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—42no—
342C23×C37—42no—
343C23×C37—41no—
344C23×C37—42no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—42no—
348C23×C37—42no—
349C23×C37—42no—
350C23×C37—42no—
351C23×C37—41no—
352C23×C37—41no—
353C23×C37—41no—
354C23×C37—42no—
355C23×C37—42no—
356C23×C37—42no—
357C23×C37—81no—
358C23×C37—81no—
359C23×C37—82no—
360C23×C37—82no—
361C23×C37—82no—
362C23×C37—82no—
363C23×C37—84no—
364C23×C37—84no—
365C23×C37—81no—
366C23×C37—81no—
367C23×C37—84no—
368C23×C37—84no—
369C23×C37#12011yescharacteristic
370C23×C37#12012yes—
371C23×C37#12011yescharacteristic
372C23×C37#12112yescomplemented
373C23×C37C22×D411yescharacteristic
374C23×C37C22×D412yes—
375C23×C37C22×D411yescharacteristic
376C23×C37C2×#4111yescharacteristic
377C23×C37H(5,𝔽2)12yes—
378Q8×C37—42no—
379D4×C37—24no—
380D4×C37—24no—
381D4×C37—44no—
382D4×C37—42no—
383D4×C37—44no—
384D4×C37—48no—
385D4×C37—44no—
386D4×C37—44no—
387D4×C37—44no—
388D4×C37—42no—
389D4×C37—42no—
390D4×C37—42no—
391D4×C37—42no—
392D4×C37—42no—
393D4×C37—42no—
394D4×C37—44no—
395D4×C37—44no—
396D4×C37—82no—
397D4×C37—82no—
398D4×C37—82no—
399D4×C37—82no—
400D4×C37—88no—
401D4×C37—84no—
402D4×C37—84no—
403C2×C4×C37—21no—
404C2×C4×C37—21no—
405C2×C4×C37—22no—
406C2×C4×C37—24no—
407C2×C4×C37—22no—
408C2×C4×C37—22no—
409C2×C4×C37—22no—
410C2×C4×C37—21no—
411C2×C4×C37—21no—
412C2×C4×C37—21no—
413C2×C4×C37—24no—
414C2×C4×C37—22no—
415C2×C4×C37—22no—
416C2×C4×C37—42no—
417C2×C4×C37—42no—
418C2×C4×C37—44no—
419C2×C4×C37—42no—
420C2×C4×C37—42no—
421C2×C4×C37—41no—
422C2×C4×C37—42no—
423C2×C4×C37—42no—
424C2×C4×C37—41no—
425C2×C4×C37—42no—
426C2×C4×C37—42no—
427C2×C4×C37—42no—
428C2×C4×C37—41no—
429C2×C4×C37—41no—
430C2×C4×C37—42no—
431C2×C4×C37—41no—
432C2×C4×C37—41no—
433C2×C4×C37—41no—
434C2×C4×C37—41no—
435C2×C4×C37—42no—
436C2×C4×C37—81no—
437C2×C4×C37—81no—
438C2×C4×C37—88no—
439C2×C4×C37#12112yescomplemented
440#24404C3711yesmaximal, characteristic, direct product factor, Sylow
441C22×C37—21no—
442C22×C37—22no—
443C22×C37—21no—
444C22×C37—22no—
445C22×C37—21no—
446C22×C37—21no—
447C22×C37—21no—
448C22×C37—22no—
449C22×C37—22no—
450C22×C37—22no—
451C22×C37—21no—
452C22×C37—21no—
453C22×C37—22no—
454C22×C37—41no—
455C22×C37—41no—
456C22×C37—42no—
457C22×C37—44no—
458C22×C37—44no—
459C22×C37—42no—
460C22×C37—42no—
461C22×C37—42no—
462C22×C37—44no—
463C22×C37—42no—
464C22×C37—42no—
465C22×C37—42no—
466C22×C37—44no—
467C22×C37—41no—
468C22×C37—41no—
469C22×C37—42no—
470C22×C37—41no—
471C22×C37—42no—
472C22×C37—42no—
473C22×C37—41no—
474C22×C37—42no—
475C22×C37—41no—
476C22×C37—82no—
477C22×C37—81no—
478C22×C37—81no—
479C22×C37—81no—
480C22×C37—82no—
481C22×C37—84no—
482C22×C37—82no—
483C22×C37—82no—
484C22×C37—81no—
485C22×C37—82no—
486C22×C37—81no—
487C22×C37—81no—
488C22×C37—82no—
489C22×C37—84no—
490C22×C37—81no—
491C22×C37—81no—
492C22×C37—162no—
493C22×C37B(4,𝔽2)12yescomplemented
494C22×C37C2×#12011yescharacteristic
495C22×C37C2×#12111yescharacteristic
496C22×C37#53411yescharacteristic
497C22×C37D4212yes—
498C22×C37#54612yes—
499C4×C37—22no—
500C4×C37—44no—
501C4×C37—41no—
502C4×C37—42no—
503C4×C37—42no—
504C4×C37—42no—
505C4×C37—42no—
506C4×C37—82no—
507C4×C37—81no—
508C4×C37—81no—
509#3484C2×C3711yescharacteristic, complemented
510C2×B(4,𝔽2)C2×C3711yescharacteristic, complemented
511C22×#99C2×C3711yescharacteristic, complemented
512#2410C2×C3712yescomplemented
513#2403C2×C3711yescharacteristic, complemented
514#2044C2×C3712yescomplemented
515#2021C2×C3712yescomplemented
516#1898C2×C3712yescomplemented
517#1889C2×C3711yescharacteristic, complemented
518#1867C2×C3711yescharacteristic, complemented
519#1790C2×C3711yescharacteristic, complemented
520C2×C37—22no—
521C2×C37—21no—
522C2×C37—21no—
523C2×C37—22no—
524C2×C37—22no—
525C2×C37—42no—
526C2×C37—41no—
527C2×C37—42no—
528C2×C37—82no—
529C2×C37—81no—
530C2×C37—82no—
531C2×C37#241011yescharacteristic
532C2×C37C2×B(4,𝔽2)11yescharacteristic
533C2×C37#302611yescharacteristic
534C2×H(5,𝔽2)C22×C3711yescharacteristic
535C23×D4C22×C3711yescharacteristic
536C23×D4C22×C3711yescharacteristic, complemented
537#546—22no—
538#546—22no—
539D42—22no—
540D42—22no—
541#535—21no—
542#534—21no—
543#534C22×C3712yes—
544#525—21no—
545C2×#121—22no—
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C3711yescharacteristic
549C2×#120C22×C3712yes—
550C2×#120C22×C3712yescomplemented
551C2×#120C22×C3711yescharacteristic, complemented
552#518C22×C3711yescharacteristic
553C22×C22⋊C4C22×C3712yescomplemented
554B(4,𝔽2)—24no—
555C2×#99—24no—
556C2×#99C22×C3711yescharacteristic
557C2×#99C22×C3711yescharacteristic
558C2×#99C22×C3712yescomplemented
559C2×#99C22×C3712yescomplemented
560C2×#99C22×C3712yescomplemented
561#394—22no—
562#392—21no—
563#392—21no—
564#392—22no—
565#386—21no—
566#386—22no—
567#386C22×C3711yescharacteristic
568#386C22×C3711yescharacteristic, complemented
569#386C22×C3712yescomplemented
570#385C22×C3712yescomplemented
571#379C22×C3712yescomplemented
572#379C22×C3711yescharacteristic, complemented
573#342C22×C3712yescomplemented
574#342C22×C3712yescomplemented
575C37#2440411yescharacteristic, direct product factor, Sylow
576C25D4×C3711yescharacteristic, complemented
577C25C23×C3711yescharacteristic
578C25C23×C3711yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C3711yescharacteristic, complemented
602C22×D4D4×C3711yescharacteristic, complemented
603C22×D4D4×C3712yescomplemented
604C22×D4D4×C3712yescomplemented
605C22×D4C23×C3712yes—
606C22×D4C23×C3711yescharacteristic
607C22×D4C23×C3711yescharacteristic
608C23×C4—22no—
609C23×C4D4×C3711yescharacteristic, complemented
610C23×C4C23×C3711yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C3712yescomplemented
665C2×C22⋊C4D4×C3712yescomplemented
666C2×C22⋊C4C23×C3712yes—
667C2×C22⋊C4C23×C3711yescharacteristic
668C2×C22⋊C4C23×C3711yescharacteristic
669C2×C22⋊C4C23×C3712yes—
670C2×C22⋊C4C23×C3712yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C3714yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C3711yescharacteristic
700C24C2×D4×C3712yes—
701C24C2×D4×C3711yescharacteristic
702C24C2×D4×C3712yes—
703C24C2×D4×C3712yes—
704C24C2×D4×C3711yescharacteristic
705C24C2×D4×C3711yescharacteristic
706C24C24×C3711yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C3712yes—
771C2×D4#41×C3712yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C3712yes—
791C22×C4C2×D4×C3711yescharacteristic
792C22×C4C2×D4×C3711yescharacteristic
793C22×C4C2×D4×C3712yes—
794C22×C4C2×D4×C3712yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C3714yescomplemented
829C42—22no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C3711yescharacteristic
893C23#120×C3712yes—
894C23#120×C3711yescharacteristic
895C23#121×C3712yescomplemented
896C23C22×D4×C3711yescharacteristic
897C23C22×D4×C3712yes—
898C23C22×D4×C3711yescharacteristic
899C23C2×#41×C3711yescharacteristic
900C23H(5,𝔽2)×C3712yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—44no—
918D4—44no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C3712yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C37×B(4,𝔽2)12yescomplemented
1016C22C2×#120×C3711yescharacteristic
1017C22C2×#121×C3711yescharacteristic
1018C22C37×#53411yescharacteristic
1019C22D42×C3712yes—
1020C22C37×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C37×#241011yescharacteristic
1043C2C2×C37×B(4,𝔽2)11yescharacteristic
1044C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3484C2semidirect
2. C2×C37×B(4,𝔽2)C2semidirect
3. C22×#99×C37C2semidirect
4. C37×#2410C2semidirect
5. C37×#2403C2semidirect
6. C37×#2044C2semidirect
7. C37×#2021C2semidirect
8. C37×#1898C2semidirect
9. C37×#1889C2semidirect
10. C37×#1867C2semidirect
11. C37×#1790C2semidirect
14. C23×D4×C37C22semidirect
28. C2×#120×C37C22semidirect
29. C2×#120×C37C22semidirect
31. C22×C22⋊C4×C37C22semidirect
36. C2×#99×C37C22semidirect
37. C2×#99×C37C22semidirect
38. C2×#99×C37C22semidirect
46. C37×#386C22semidirect
47. C37×#386C22semidirect
48. C37×#385C22semidirect
49. C37×#379C22semidirect
50. C37×#379C22semidirect
51. C37×#342C22semidirect
52. C37×#342C22semidirect
53. C25×C37D4semidirect
78. C22×D4×C37D4semidirect
79. C22×D4×C37D4semidirect
80. C22×D4×C37D4semidirect
81. C22×D4×C37D4semidirect
86. C23×C4×C37D4semidirect
141. C2×C22⋊C4×C37D4semidirect
142. C2×C22⋊C4×C37D4semidirect
152. #99×C37D4semidirect
305. C22⋊C4×C37C2×D4semidirect
372. C23×C37#121semidirect
439. C2×C4×C37#121semidirect
440. #24404C37direct (N × H)
493. C22×C37B(4,𝔽2)semidirect
509. #3484C2×C37semidirect
510. C2×B(4,𝔽2)C2×C37semidirect
511. C22×#99C2×C37semidirect
512. #2410C2×C37semidirect
513. #2403C2×C37semidirect
514. #2044C2×C37semidirect
515. #2021C2×C37semidirect
516. #1898C2×C37semidirect
517. #1889C2×C37semidirect
518. #1867C2×C37semidirect
519. #1790C2×C37semidirect
536. C23×D4C22×C37semidirect
550. C2×#120C22×C37semidirect
551. C2×#120C22×C37semidirect
553. C22×C22⋊C4C22×C37semidirect
558. C2×#99C22×C37semidirect
559. C2×#99C22×C37semidirect
560. C2×#99C22×C37semidirect
568. #386C22×C37semidirect
569. #386C22×C37semidirect
570. #385C22×C37semidirect
571. #379C22×C37semidirect
572. #379C22×C37semidirect
573. #342C22×C37semidirect
574. #342C22×C37semidirect
575. C37#24404direct (N × H)
576. C25D4×C37semidirect
601. C22×D4D4×C37semidirect
602. C22×D4D4×C37semidirect
603. C22×D4D4×C37semidirect
604. C22×D4D4×C37semidirect
609. C23×C4D4×C37semidirect
664. C2×C22⋊C4D4×C37semidirect
665. C2×C22⋊C4D4×C37semidirect
675. #99D4×C37semidirect
828. C22⋊C4C2×D4×C37semidirect
895. C23#121×C37semidirect
962. C2×C4#121×C37semidirect
1015. C22C37×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C37×#34842
C2×C37×B(4,𝔽2)2
C22×#99×C372
C37×#24102
C37×#24032
C37×#20442
C37×#20212
C37×#18982
C37×#18892
C37×#18672
C37×#17902
#2440437