Finite Group Databasebeta

← C37×#24462 #22645715

Subgroups — C37×#24462 #22645715

Order 9472.

1302 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#578C211yesmaximal, characteristic
2C2×C37×#473C211yesmaximal, characteristic, complemented
3C37×#3046C211yesmaximal, characteristic, complemented
4C2×C37×#456C211yesmaximal, characteristic, complemented
5C37×#3011C211yesmaximal, characteristic, complemented
6C37×#2898C211yesmaximal, characteristic, complemented
7C37×#2052C211yesmaximal, characteristic, complemented
8C37×#2047C211yesmaximal, characteristic, complemented
9C37×#2016C211yesmaximal, characteristic, complemented
10C37×#2005C211yesmaximal, characteristic, complemented
11C37×#1908C211yesmaximal, characteristic, complemented
12C37×#1882C211yesmaximal, characteristic, complemented
13C37×#1876C211yesmaximal, characteristic, complemented
14C37×#1866C211yesmaximal, characteristic, complemented
15C37×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C37C2211yescharacteristic
17C2×2−1+4×C37C2211yescharacteristic
18C37×#578—24no—
19C37×#578—24no—
20C2×#137×C37—21no—
21C2×#137×C37—21no—
22C2×#137×C37C2211yescharacteristic
23C2×#137×C37C2211yescharacteristic
24C2×#137×C37C2211yescharacteristic
25C2×#137×C37C2211yescharacteristic
26C2×#135×C37—21no—
27C2×#135×C37C2211yescharacteristic
28C22×Q16×C37—21no—
29C22×Q16×C37C2211yescharacteristic
30C22×Q16×C37C2211yescharacteristic
31C2×#131×C37C2211yescharacteristic
32C2×#131×C37C2211yescharacteristic
33C37×#536C2211yescharacteristic
34C2×C4⋊Q8×C37C2211yescharacteristic
35C37×#520C2211yescharacteristic
36C37×#473—24no—
37C37×#464—21no—
38C37×#463—21no—
39C37×#462—21no—
40C37×#461—21no—
41C37×#456—24no—
42C37×#452—21no—
43C37×#452—21no—
44C37×#451—21no—
45C37×#451—21no—
46C2×#108×C37C2211yescharacteristic
47C37×#424C2211yescharacteristic
48C2×#104×C37C2211yescharacteristic
49C2×#104×C37C2211yescharacteristic
50C2×#104×C37C2211yescharacteristic
51C37×#419—21no—
52C37×#419C2211yescharacteristic
53C37×#419C2211yescharacteristic
54C37×#417—21no—
55C37×#417C2211yescharacteristic
56C37×#417C2211yescharacteristic
57C37×#416—21no—
58C37×#416C2211yescharacteristic
59C2×#103×C37—21no—
60C2×#103×C37C2211yescharacteristic
61C2×#103×C37C2211yescharacteristic
62C2×#101×C37C2211yescharacteristic
63C2×#101×C37C2211yescharacteristic
64C2×#101×C37C2211yescharacteristic
65C37×#408C2211yescharacteristic
66C37×#391C2211yescharacteristic
67C37×#343C2211yescharacteristic
68C37×#341C2211yescharacteristic
69C37×#339C2211yescharacteristic
70C37×#336C2211yescharacteristic
712−1+4×C37—22no—
722−1+4×C37—22no—
732−1+4×C37—22no—
742−1+4×C37—22no—
752−1+4×C37—22no—
762−1+4×C37—41no—
772−1+4×C37—41no—
782−1+4×C37D414yes—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—21no—
82C2×#41×C37—21no—
83C2×#41×C37—41no—
84C2×#41×C37—41no—
85C2×#41×C37C2311yescharacteristic
86C2×#41×C37C2311yescharacteristic
87C2×#41×C37C2311yescharacteristic
88C22×Q8×C37—21no—
89C22×Q8×C37—21no—
90C22×Q8×C37—21no—
91C22×Q8×C37—21no—
92C22×Q8×C37C2311yescharacteristic
93C22×Q8×C37C2311yescharacteristic
94C22×Q8×C37C2311yescharacteristic
95#137×C37—28no—
96#137×C37—28no—
97#137×C37—22no—
98#137×C37—22no—
99#137×C37—22no—
100#137×C37—22no—
101#137×C37—22no—
102#137×C37—22no—
103#137×C37—22no—
104#137×C37D414yes—
105#135×C37—28no—
106#135×C37—22no—
107#135×C37—22no—
108C2×Q16×C37—28no—
109C2×Q16×C37—21no—
110C2×Q16×C37—21no—
111C2×Q16×C37—22no—
112C2×Q16×C37—22no—
113C2×Q16×C37—22no—
114C2×Q16×C37—21no—
115C2×Q16×C37—21no—
116C2×Q16×C37—21no—
117C2×Q16×C37—21no—
118C2×Q16×C37—21no—
119C2×Q16×C37—21no—
120C2×Q16×C37—41no—
121C2×Q16×C37D411yescharacteristic
122C2×SD16×C37—21no—
123C2×SD16×C37—21no—
124C2×SD16×C37—21no—
125C2×SD16×C37—21no—
126C2×SD16×C37D411yescharacteristic
127C2×SD16×C37D411yescharacteristic
128C2×D8×C37D411yescharacteristic
129#131×C37—22no—
130#131×C37—22no—
131#131×C37—22no—
132#131×C37—41no—
133C2×M16×C37—21no—
134C2×M16×C37—21no—
135C2×M16×C37C2311yescharacteristic
136C2×M16×C37C2311yescharacteristic
137C2×M16×C37C2311yescharacteristic
138C2×M16×C37C2311yescharacteristic
139C22×C8×C37—21no—
140C22×C8×C37—21no—
141C22×C8×C37C2311yescharacteristic
142C22×C8×C37C2311yescharacteristic
143C4⋊Q8×C37—22no—
144C4⋊Q8×C37—21no—
145C4⋊Q8×C37—41no—
146#124×C37—21no—
147#123×C37—41no—
148C22⋊Q8×C37—21no—
149C22⋊Q8×C37—21no—
150C4×Q8×C37—21no—
151C4×D4×C37—21no—
152C4×D4×C37—41no—
153#117×C37—21no—
154#117×C37C2311yescharacteristic
155C2×C4⋊C4×C37—21no—
156C2×C4⋊C4×C37—41no—
157C2×C4⋊C4×C37C2311yescharacteristic
158C2×C42×C37C2311yescharacteristic
159#108×C37—22no—
160C4⋊C8×C37—21no—
161C4⋊C8×C37—21no—
162#104×C37—22no—
163#104×C37—22no—
164#104×C37—41no—
165#103×C37—21no—
166#103×C37—21no—
167#103×C37—21no—
168#103×C37—21no—
169#103×C37—21no—
170#103×C37—21no—
171#103×C37—21no—
172#103×C37—21no—
173#103×C37—21no—
174#103×C37—21no—
175#103×C37D411yescharacteristic
176#103×C37D411yescharacteristic
177#102×C37—21no—
178#102×C37—21no—
179#102×C37D411yescharacteristic
180#102×C37D411yescharacteristic
181#101×C37—22no—
182#101×C37—22no—
183#101×C37—22no—
184C22⋊C8×C37—21no—
185C22⋊C8×C37—21no—
186#95×C37—41no—
187#41×C37—21no—
188#41×C37—21no—
189#41×C37—21no—
190#41×C37—21no—
191#41×C37—24no—
192#41×C37—24no—
193#41×C37—24no—
194#41×C37—21no—
195#41×C37—21no—
196#41×C37—21no—
197#41×C37—21no—
198#41×C37—44no—
199#41×C37—42no—
200#41×C37—42no—
201#41×C37—42no—
202#41×C37—44no—
203#41×C37—44no—
204#41×C37—42no—
205#41×C37—44no—
206#41×C37—42no—
207#41×C37C2×D412yes—
208#41×C37C2×D412yes—
209#41×C37C2×D412yes—
210#41×C37#4112yes—
211C2×Q8×C37—21no—
212C2×Q8×C37—21no—
213C2×Q8×C37—24no—
214C2×Q8×C37—24no—
215C2×Q8×C37—24no—
216C2×Q8×C37—21no—
217C2×Q8×C37—21no—
218C2×Q8×C37—21no—
219C2×Q8×C37—21no—
220C2×Q8×C37—21no—
221C2×Q8×C37—21no—
222C2×Q8×C37—21no—
223C2×Q8×C37—21no—
224C2×Q8×C37—21no—
225C2×Q8×C37—21no—
226C2×Q8×C37—21no—
227C2×Q8×C37—21no—
228C2×Q8×C37—21no—
229C2×Q8×C37—21no—
230C2×Q8×C37—41no—
231C2×Q8×C37—41no—
232C2×Q8×C37—42no—
233C2×Q8×C37—42no—
234C2×Q8×C37—42no—
235C2×Q8×C37—42no—
236C2×Q8×C37—42no—
237C2×Q8×C37C2×D412yes—
238C2×Q8×C37C2×D412yes—
239C2×Q8×C37C2×D411yescharacteristic
240C2×Q8×C37C2×D411yescharacteristic
241C2×Q8×C37C2×D411yescharacteristic
242C2×D4×C37—21no—
243C2×D4×C37—21no—
244C2×D4×C37—21no—
245C2×D4×C37—41no—
246C2×D4×C37—41no—
247C2×D4×C37C2×D411yescharacteristic
248C2×D4×C37C2×D411yescharacteristic
249C2×D4×C37C2×D411yescharacteristic
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—41no—
259C22×C4×C37—41no—
260C22×C4×C37—41no—
261C22×C4×C37—41no—
262C22×C4×C37—41no—
263C22×C4×C37C2411yescharacteristic
264Q16×C37—24no—
265Q16×C37—24no—
266Q16×C37—24no—
267Q16×C37—22no—
268Q16×C37—24no—
269Q16×C37—42no—
270Q16×C37—42no—
271Q16×C37—42no—
272Q16×C37—42no—
273SD16×C37—24no—
274SD16×C37—22no—
275SD16×C37—24no—
276SD16×C37—22no—
277SD16×C37—42no—
278SD16×C37—42no—
279D8×C37—22no—
280M16×C37—24no—
281M16×C37—21no—
282M16×C37—21no—
283M16×C37—21no—
284M16×C37—21no—
285M16×C37—21no—
286M16×C37—21no—
287M16×C37—21no—
288M16×C37—42no—
289M16×C37C2×D412yes—
290C2×C8×C37—24no—
291C2×C8×C37—21no—
292C2×C8×C37—21no—
293C2×C8×C37—21no—
294C2×C8×C37—21no—
295C2×C8×C37—21no—
296C2×C8×C37—21no—
297C2×C8×C37—21no—
298C2×C8×C37—21no—
299C2×C8×C37—42no—
300C2×C8×C37C2×D411yescharacteristic
301C2×C8×C37C2×D411yescharacteristic
302C2×C8×C37C2×D411yescharacteristic
303C2×C8×C37C2×D411yescharacteristic
304C4⋊C4×C37—21no—
305C4⋊C4×C37—21no—
306C4⋊C4×C37—41no—
307C4⋊C4×C37—41no—
308C4⋊C4×C37—41no—
309C4⋊C4×C37—44no—
310C4⋊C4×C37C2×D411yescharacteristic
311C4⋊C4×C37C2×D411yescharacteristic
312C22⋊C4×C37—21no—
313C22⋊C4×C37—41no—
314C22⋊C4×C37—41no—
315C22⋊C4×C37—41no—
316C42×C37—21no—
317C42×C37—21no—
318C42×C37—21no—
319C42×C37—41no—
320C23×C37—21no—
321C23×C37—21no—
322C23×C37—21no—
323C23×C37H(5,𝔽2)11yescharacteristic
324Q8×C37—21no—
325Q8×C37—21no—
326Q8×C37—22no—
327Q8×C37—22no—
328Q8×C37—21no—
329Q8×C37—22no—
330Q8×C37—22no—
331Q8×C37—21no—
332Q8×C37—44no—
333Q8×C37—44no—
334Q8×C37—41no—
335Q8×C37—41no—
336Q8×C37—41no—
337Q8×C37—41no—
338Q8×C37—41no—
339Q8×C37—41no—
340Q8×C37—41no—
341Q8×C37—41no—
342Q8×C37#12012yes—
343Q8×C37#12112yes—
344D4×C37—22no—
345D4×C37—22no—
346D4×C37—22no—
347D4×C37—22no—
348D4×C37—21no—
349D4×C37—21no—
350D4×C37—21no—
351D4×C37—21no—
352D4×C37—44no—
353D4×C37—44no—
354D4×C37—41no—
355D4×C37—41no—
356D4×C37#12012yes—
357D4×C37#12112yes—
358C2×C4×C37—21no—
359C2×C4×C37—21no—
360C2×C4×C37—22no—
361C2×C4×C37—22no—
362C2×C4×C37—22no—
363C2×C4×C37—22no—
364C2×C4×C37—22no—
365C2×C4×C37—22no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—22no—
370C2×C4×C37—44no—
371C2×C4×C37—44no—
372C2×C4×C37—44no—
373C2×C4×C37—41no—
374C2×C4×C37—44no—
375C2×C4×C37—41no—
376C2×C4×C37—41no—
377C2×C4×C37—41no—
378C2×C4×C37—41no—
379C2×C4×C37—41no—
380C2×C4×C37—41no—
381C2×C4×C37—41no—
382C2×C4×C37—41no—
383C2×C4×C37—41no—
384C2×C4×C37—41no—
385C2×C4×C37—41no—
386C2×C4×C37—81no—
387C2×C4×C37—161no—
388C2×C4×C37C22×D411yescharacteristic
389C2×C4×C37C22×D411yescharacteristic
390C2×C4×C37C22×D411yescharacteristic
391C2×C4×C37C22×D411yescharacteristic
392C2×C4×C37C2×#4111yescharacteristic
393C2×C4×C37H(5,𝔽2)11yescharacteristic
394C8×C37—21no—
395C8×C37—22no—
396C8×C37—21no—
397C8×C37—21no—
398C8×C37—21no—
399C8×C37—41no—
400C8×C37—41no—
401C8×C37—41no—
402#24462C3711yesmaximal, characteristic, direct product factor, Sylow
403C22×C37—21no—
404C22×C37—21no—
405C22×C37—22no—
406C22×C37—22no—
407C22×C37—41no—
408C22×C37—41no—
409C22×C37—41no—
410C22×C37—41no—
411C22×C37—41no—
412C22×C37—41no—
413C22×C37—41no—
414C22×C37#53411yescharacteristic
415C22×C37D4211yescharacteristic
416C22×C37#54611yescharacteristic
417C4×C37—22no—
418C4×C37—22no—
419C4×C37—42no—
420C4×C37—42no—
421C4×C37—41no—
422C4×C37—42no—
423C4×C37—41no—
424C4×C37—41no—
425C4×C37—81no—
426C4×C37—81no—
427C4×C37C2×#12011yescharacteristic
428C4×C37C2×#12111yescharacteristic
429C4×C37D4211yescharacteristic
430C4×C37#54611yescharacteristic
431C2×#578C2×C3711yescharacteristic
432C2×#473C2×C3711yescharacteristic, complemented
433#3046C2×C3711yescharacteristic, complemented
434C2×#456C2×C3711yescharacteristic, complemented
435#3011C2×C3711yescharacteristic, complemented
436#2898C2×C3711yescharacteristic, complemented
437#2052C2×C3711yescharacteristic, complemented
438#2047C2×C3711yescharacteristic, complemented
439#2016C2×C3711yescharacteristic, complemented
440#2005C2×C3711yescharacteristic, complemented
441#1908C2×C3711yescharacteristic, complemented
442#1882C2×C3711yescharacteristic, complemented
443#1876C2×C3711yescharacteristic, complemented
444#1866C2×C3711yescharacteristic, complemented
445#1793C2×C3711yescharacteristic, complemented
446C2×C37—21no—
447C2×C37—21no—
448C2×C37—42no—
449C2×C37—42no—
450C2×C37—81no—
451C2×C37#241011yescharacteristic
452C2×C37#328911yescharacteristic
453C2×C37#329311yescharacteristic
454C2×2−1+4C22×C3711yescharacteristic
455C2×2−1+4C22×C3711yescharacteristic
456#578—24no—
457#578—24no—
458C2×#137—21no—
459C2×#137—21no—
460C2×#137C22×C3711yescharacteristic
461C2×#137C22×C3711yescharacteristic
462C2×#137C22×C3711yescharacteristic
463C2×#137C22×C3711yescharacteristic
464C2×#135—21no—
465C2×#135C22×C3711yescharacteristic
466C22×Q16—21no—
467C22×Q16C22×C3711yescharacteristic
468C22×Q16C22×C3711yescharacteristic
469C2×#131C22×C3711yescharacteristic
470C2×#131C22×C3711yescharacteristic
471#536C22×C3711yescharacteristic
472C2×C4⋊Q8C22×C3711yescharacteristic
473#520C22×C3711yescharacteristic
474#473—24no—
475#464—21no—
476#463—21no—
477#462—21no—
478#461—21no—
479#456—24no—
480#452—21no—
481#452—21no—
482#451—21no—
483#451—21no—
484C2×#108C22×C3711yescharacteristic
485#424C22×C3711yescharacteristic
486C2×#104C22×C3711yescharacteristic
487C2×#104C22×C3711yescharacteristic
488C2×#104C22×C3711yescharacteristic
489#419—21no—
490#419C22×C3711yescharacteristic
491#419C22×C3711yescharacteristic
492#417—21no—
493#417C22×C3711yescharacteristic
494#417C22×C3711yescharacteristic
495#416—21no—
496#416C22×C3711yescharacteristic
497C2×#103—21no—
498C2×#103C22×C3711yescharacteristic
499C2×#103C22×C3711yescharacteristic
500C2×#101C22×C3711yescharacteristic
501C2×#101C22×C3711yescharacteristic
502C2×#101C22×C3711yescharacteristic
503#408C22×C3711yescharacteristic
504#391C22×C3711yescharacteristic
505#343C22×C3711yescharacteristic
506#341C22×C3711yescharacteristic
507#339C22×C3711yescharacteristic
508#336C22×C3711yescharacteristic
509C37#2446211yescharacteristic, direct product factor, Sylow
5102−1+4—22no—
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—41no—
5162−1+4—41no—
5172−1+4D4×C3714yes—
518C2×#41—21no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C3711yescharacteristic
525C2×#41C23×C3711yescharacteristic
526C2×#41C23×C3711yescharacteristic
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8C23×C3711yescharacteristic
532C22×Q8C23×C3711yescharacteristic
533C22×Q8C23×C3711yescharacteristic
534#137—28no—
535#137—28no—
536#137—22no—
537#137—22no—
538#137—22no—
539#137—22no—
540#137—22no—
541#137—22no—
542#137—22no—
543#137D4×C3714yes—
544#135—28no—
545#135—22no—
546#135—22no—
547C2×Q16—28no—
548C2×Q16—21no—
549C2×Q16—21no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—21no—
554C2×Q16—21no—
555C2×Q16—21no—
556C2×Q16—21no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—41no—
560C2×Q16D4×C3711yescharacteristic
561C2×SD16—21no—
562C2×SD16—21no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16D4×C3711yescharacteristic
566C2×SD16D4×C3711yescharacteristic
567C2×D8D4×C3711yescharacteristic
568#131—22no—
569#131—22no—
570#131—22no—
571#131—41no—
572C2×M16—21no—
573C2×M16—21no—
574C2×M16C23×C3711yescharacteristic
575C2×M16C23×C3711yescharacteristic
576C2×M16C23×C3711yescharacteristic
577C2×M16C23×C3711yescharacteristic
578C22×C8—21no—
579C22×C8—21no—
580C22×C8C23×C3711yescharacteristic
581C22×C8C23×C3711yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—41no—
585#124—21no—
586#123—41no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C3711yescharacteristic
594C2×C4⋊C4—21no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4C23×C3711yescharacteristic
597C2×C42C23×C3711yescharacteristic
598#108—22no—
599C4⋊C8—21no—
600C4⋊C8—21no—
601#104—22no—
602#104—22no—
603#104—41no—
604#103—21no—
605#103—21no—
606#103—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#103—21no—
611#103—21no—
612#103—21no—
613#103—21no—
614#103D4×C3711yescharacteristic
615#103D4×C3711yescharacteristic
616#102—21no—
617#102—21no—
618#102D4×C3711yescharacteristic
619#102D4×C3711yescharacteristic
620#101—22no—
621#101—22no—
622#101—22no—
623C22⋊C8—21no—
624C22⋊C8—21no—
625#95—41no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—24no—
631#41—24no—
632#41—24no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—44no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—44no—
642#41—44no—
643#41—42no—
644#41—44no—
645#41—42no—
646#41C2×D4×C3712yes—
647#41C2×D4×C3712yes—
648#41C2×D4×C3712yes—
649#41#41×C3712yes—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—24no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—41no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8C2×D4×C3712yes—
677C2×Q8C2×D4×C3712yes—
678C2×Q8C2×D4×C3711yescharacteristic
679C2×Q8C2×D4×C3711yescharacteristic
680C2×Q8C2×D4×C3711yescharacteristic
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4C2×D4×C3711yescharacteristic
687C2×D4C2×D4×C3711yescharacteristic
688C2×D4C2×D4×C3711yescharacteristic
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—41no—
698C22×C4—41no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C3711yescharacteristic
703Q16—24no—
704Q16—24no—
705Q16—24no—
706Q16—22no—
707Q16—24no—
708Q16—42no—
709Q16—42no—
710Q16—42no—
711Q16—42no—
712SD16—24no—
713SD16—22no—
714SD16—24no—
715SD16—22no—
716SD16—42no—
717SD16—42no—
718D8—22no—
719M16—24no—
720M16—21no—
721M16—21no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—42no—
728M16C2×D4×C3712yes—
729C2×C8—24no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—42no—
739C2×C8C2×D4×C3711yescharacteristic
740C2×C8C2×D4×C3711yescharacteristic
741C2×C8C2×D4×C3711yescharacteristic
742C2×C8C2×D4×C3711yescharacteristic
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—41no—
746C4⋊C4—41no—
747C4⋊C4—41no—
748C4⋊C4—44no—
749C4⋊C4C2×D4×C3711yescharacteristic
750C4⋊C4C2×D4×C3711yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—41no—
753C22⋊C4—41no—
754C22⋊C4—41no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—41no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23H(5,𝔽2)×C3711yescharacteristic
763Q8—21no—
764Q8—21no—
765Q8—22no—
766Q8—22no—
767Q8—21no—
768Q8—22no—
769Q8—22no—
770Q8—21no—
771Q8—44no—
772Q8—44no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C3712yes—
782Q8#121×C3712yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—44no—
792D4—44no—
793D4—41no—
794D4—41no—
795D4#120×C3712yes—
796D4#121×C3712yes—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—81no—
826C2×C4—161no—
827C2×C4C22×D4×C3711yescharacteristic
828C2×C4C22×D4×C3711yescharacteristic
829C2×C4C22×D4×C3711yescharacteristic
830C2×C4C22×D4×C3711yescharacteristic
831C2×C4C2×#41×C3711yescharacteristic
832C2×C4H(5,𝔽2)×C3711yescharacteristic
833C8—21no—
834C8—22no—
835C8—21no—
836C8—21no—
837C8—21no—
838C8—41no—
839C8—41no—
840C8—41no—
841C22—21no—
842C22—21no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22C37×#53411yescharacteristic
853C22D42×C3711yescharacteristic
854C22C37×#54611yescharacteristic
855C4—22no—
856C4—22no—
857C4—42no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—81no—
865C4C2×#120×C3711yescharacteristic
866C4C2×#121×C3711yescharacteristic
867C4D42×C3711yescharacteristic
868C4C37×#54611yescharacteristic
869C2—21no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—81no—
874C2C37×#241011yescharacteristic
875C2C37×#328911yescharacteristic
876C2C37×#329311yescharacteristic
subgroupG/H
center, socleC22×C37D42
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#578C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#473C2semidirect
3. C37×#3046C2semidirect
4. C2×C37×#456C2semidirect
5. C37×#3011C2semidirect
6. C37×#2898C2semidirect
7. C37×#2052C2semidirect
8. C37×#2047C2semidirect
9. C37×#2016C2semidirect
10. C37×#2005C2semidirect
11. C37×#1908C2semidirect
12. C37×#1882C2semidirect
13. C37×#1876C2semidirect
14. C37×#1866C2semidirect
15. C37×#1793C2semidirect
402. #24462C37direct (N × H)
432. C2×#473C2×C37semidirect
433. #3046C2×C37semidirect
434. C2×#456C2×C37semidirect
435. #3011C2×C37semidirect
436. #2898C2×C37semidirect
437. #2052C2×C37semidirect
438. #2047C2×C37semidirect
439. #2016C2×C37semidirect
440. #2005C2×C37semidirect
441. #1908C2×C37semidirect
442. #1882C2×C37semidirect
443. #1876C2×C37semidirect
444. #1866C2×C37semidirect
445. #1793C2×C37semidirect
509. C37#24462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5782
C2×C37×#4732
C37×#30462
C2×C37×#4562
C37×#30112
C37×#28982
C37×#20522
C37×#20472
C37×#20162
C37×#20052
C37×#19082
C37×#18822
C37×#18762
C37×#18662
C37×#17932
#2446237