Finite Group Databasebeta

← C2×C37×#2008 #22644663

Subgroups — C2×C37×#2008 #22644663

Order 9472.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#575C211yesmaximal, characteristic, complemented
2C22×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
3C2×C37×#535C211yesmaximal, characteristic, complemented
4C2×C37×#421C211yesmaximal, characteristic, complemented
5C2×C37×#418C211yesmaximal, characteristic, complemented
6C2×C37×#410C211yesmaximal, characteristic, complemented
7C37×#2008C218yesmaximal, direct product factor
8C2×C37×#344C211yesmaximal, characteristic, complemented
9C22×#41×C37C2211yescharacteristic
10C22×#41×C37C2211yescharacteristic
11C23×D4×C37C2211yescharacteristic
12C37×#575—22no—
13C37×#575—22no—
14C37×#575—22no—
15C37×#575C2214yescomplemented
16C2×#137×C37—21no—
17C2×#137×C37—21no—
18C2×AGL(1,ℤ/8)×C37—22no—
19C2×AGL(1,ℤ/8)×C37—22no—
20C2×AGL(1,ℤ/8)×C37—22no—
21C2×AGL(1,ℤ/8)×C37—21no—
22C2×AGL(1,ℤ/8)×C37—21no—
23C2×AGL(1,ℤ/8)×C37—22no—
24C2×AGL(1,ℤ/8)×C37—22no—
25C2×AGL(1,ℤ/8)×C37C2214yescomplemented
26C2×#135×C37—22no—
27C22×SD16×C37—21no—
28C22×D8×C37—21no—
29C22×M16×C37C2211yescharacteristic
30C22×M16×C37C2211yescharacteristic
31C37×#535—22no—
32C37×#535—22no—
33C37×#535—22no—
34C37×#535C2214yescomplemented
35C2×#127×C37—21no—
36C2×#124×C37—21no—
37C2×#121×C37—22no—
38C2×#120×C37—22no—
39C2×#117×C37C2211yescharacteristic
40C2×#117×C37C2211yescharacteristic
41C37×#421—22no—
42C37×#421C2214yescomplemented
43C2×#104×C37—22no—
44C37×#418—22no—
45C37×#418C2214yescomplemented
46C2×#102×C37—22no—
47C37×#410—22no—
48C37×#410C2214yescomplemented
49C2×#99×C37—22no—
50C37×#344C2214yescomplemented
51C25×C37—21no—
52C2×#41×C37—21no—
53C2×#41×C37—21no—
54C2×#41×C37—21no—
55C2×#41×C37—21no—
56C2×#41×C37—21no—
57C2×#41×C37—21no—
58C2×#41×C37—21no—
59C2×#41×C37—21no—
60C2×#41×C37—21no—
61C2×#41×C37—21no—
62C2×#41×C37—21no—
63C2×#41×C37—21no—
64C2×#41×C37—21no—
65C2×#41×C37—21no—
66C2×#41×C37—21no—
67C2×#41×C37—21no—
68C2×#41×C37—21no—
69C2×#41×C37—21no—
70C2×#41×C37—21no—
71C2×#41×C37—21no—
72C2×#41×C37D412yes—
73C2×#41×C37D412yescomplemented
74C2×#41×C37C2312yes—
75C2×#41×C37C2312yes—
76C22×Q8×C37D411yescharacteristic
77C22×Q8×C37D411yescharacteristic, complemented
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—24no—
81C22×D4×C37—21no—
82C22×D4×C37—21no—
83C22×D4×C37—21no—
84C22×D4×C37—21no—
85C22×D4×C37—21no—
86C22×D4×C37—21no—
87C22×D4×C37—21no—
88C22×D4×C37—21no—
89C22×D4×C37—21no—
90C22×D4×C37—21no—
91C22×D4×C37—21no—
92C22×D4×C37D412yes—
93C22×D4×C37D411yescharacteristic
94C22×D4×C37D412yes—
95C22×D4×C37D411yescharacteristic, complemented
96C22×D4×C37C2312yes—
97C23×C4×C37—21no—
98C23×C4×C37—21no—
99C23×C4×C37C2311yescharacteristic
100#137×C37—24no—
101#137×C37—24no—
102#137×C37—24no—
103#137×C37—24no—
104AGL(1,ℤ/8)×C37—28no—
105AGL(1,ℤ/8)×C37—28no—
106AGL(1,ℤ/8)×C37—24no—
107AGL(1,ℤ/8)×C37—24no—
108AGL(1,ℤ/8)×C37—28no—
109AGL(1,ℤ/8)×C37—24no—
110AGL(1,ℤ/8)×C37—24no—
111AGL(1,ℤ/8)×C37—28no—
112#135×C37—28no—
113#135×C37—28no—
114C2×Q16×C37—22no—
115C2×SD16×C37—24no—
116C2×SD16×C37—24no—
117C2×SD16×C37—22no—
118C2×SD16×C37—22no—
119C2×SD16×C37—24no—
120C2×D8×C37—24no—
121C2×D8×C37—24no—
122C2×D8×C37—22no—
123C2×D8×C37—24no—
124C2×M16×C37—21no—
125C2×M16×C37—21no—
126C2×M16×C37—21no—
127C2×M16×C37—21no—
128C2×M16×C37—21no—
129C2×M16×C37—21no—
130C2×M16×C37—21no—
131C2×M16×C37D412yescomplemented
132C2×M16×C37D412yescomplemented
133C2×M16×C37D412yescomplemented
134C2×M16×C37C2312yes—
135C2×M16×C37C2312yes—
136C22×C8×C37—21no—
137C22×C8×C37D412yescomplemented
138#127×C37—24no—
139#127×C37—24no—
140#124×C37—24no—
141#124×C37—24no—
142#121×C37—28no—
143#121×C37—28no—
144#120×C37—28no—
145#120×C37—28no—
146#117×C37—21no—
147#117×C37—21no—
148#117×C37—21no—
149#117×C37—21no—
150#117×C37—21no—
151#117×C37D412yes—
152#117×C37C2312yes—
153#117×C37C2312yes—
154C2×C4⋊C4×C37—21no—
155C2×C4⋊C4×C37—21no—
156C2×C22⋊C4×C37—24no—
157C2×C22⋊C4×C37—21no—
158C2×C22⋊C4×C37D412yes—
159C2×C42×C37—21no—
160C2×C42×C37—21no—
161#104×C37—28no—
162#102×C37—28no—
163#99×C37—28no—
164C24×C37—22no—
165C24×C37—21no—
166C24×C37—22no—
167C24×C37—21no—
168C24×C37—22no—
169C24×C37—41no—
170C24×C37—41no—
171C24×C37—41no—
172C24×C37—41no—
173C24×C37—84no—
174C24×C37C2×D411yescharacteristic
175#41×C37—22no—
176#41×C37—22no—
177#41×C37—22no—
178#41×C37—22no—
179#41×C37—22no—
180#41×C37—22no—
181#41×C37—22no—
182#41×C37—22no—
183#41×C37—22no—
184#41×C37—22no—
185#41×C37—22no—
186#41×C37—22no—
187#41×C37—22no—
188#41×C37—22no—
189#41×C37—22no—
190#41×C37—22no—
191#41×C37—41no—
192#41×C37—41no—
193#41×C37—41no—
194#41×C37—41no—
195#41×C37—41no—
196#41×C37—41no—
197#41×C37—41no—
198#41×C37—41no—
199#41×C37—41no—
200#41×C37—41no—
201#41×C37—41no—
202#41×C37—41no—
203#41×C37—41no—
204#41×C37—41no—
205#41×C37—41no—
206#41×C37—41no—
207C2×Q8×C37—21no—
208C2×Q8×C37—21no—
209C2×Q8×C37—21no—
210C2×Q8×C37—21no—
211C2×Q8×C37—21no—
212C2×Q8×C37—21no—
213C2×Q8×C37—21no—
214C2×Q8×C37—21no—
215C2×Q8×C37—21no—
216C2×Q8×C37—21no—
217C2×Q8×C37C2×D412yes—
218C2×Q8×C37C2×D412yescomplemented
219C2×D4×C37—22no—
220C2×D4×C37—22no—
221C2×D4×C37—22no—
222C2×D4×C37—22no—
223C2×D4×C37—216no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—22no—
227C2×D4×C37—22no—
228C2×D4×C37—21no—
229C2×D4×C37—21no—
230C2×D4×C37—22no—
231C2×D4×C37—22no—
232C2×D4×C37—21no—
233C2×D4×C37—21no—
234C2×D4×C37—22no—
235C2×D4×C37—22no—
236C2×D4×C37—21no—
237C2×D4×C37—22no—
238C2×D4×C37—22no—
239C2×D4×C37—22no—
240C2×D4×C37—22no—
241C2×D4×C37—21no—
242C2×D4×C37—21no—
243C2×D4×C37—21no—
244C2×D4×C37—22no—
245C2×D4×C37—22no—
246C2×D4×C37—22no—
247C2×D4×C37—22no—
248C2×D4×C37—22no—
249C2×D4×C37—41no—
250C2×D4×C37—41no—
251C2×D4×C37—41no—
252C2×D4×C37—41no—
253C2×D4×C37—41no—
254C2×D4×C37—41no—
255C2×D4×C37—41no—
256C2×D4×C37—41no—
257C2×D4×C37—41no—
258C2×D4×C37—41no—
259C2×D4×C37—41no—
260C2×D4×C37—41no—
261C2×D4×C37—41no—
262C2×D4×C37—41no—
263C2×D4×C37—41no—
264C2×D4×C37—41no—
265C2×D4×C37—41no—
266C2×D4×C37—41no—
267C2×D4×C37—41no—
268C2×D4×C37—41no—
269C2×D4×C37—88no—
270C2×D4×C37C2×D414yes—
271C2×D4×C37C2×D412yes—
272C2×D4×C37C2×D412yescomplemented
273C22×C4×C37—22no—
274C22×C4×C37—21no—
275C22×C4×C37—21no—
276C22×C4×C37—22no—
277C22×C4×C37—22no—
278C22×C4×C37—22no—
279C22×C4×C37—22no—
280C22×C4×C37—41no—
281C22×C4×C37—41no—
282C22×C4×C37—41no—
283C22×C4×C37—41no—
284C22×C4×C37—41no—
285C22×C4×C37—41no—
286C22×C4×C37—41no—
287C22×C4×C37—41no—
288C22×C4×C37—41no—
289C22×C4×C37C2×D411yescharacteristic
290C22×C4×C37C2×D411yescharacteristic
291C22×C4×C37C2×D411yescharacteristic
292C22×C4×C37C2×D411yescharacteristic
293C22×C4×C37C2×D411yescharacteristic
294C22×C4×C37C2×D411yescharacteristic
295C22×C4×C37C2×D411yescharacteristic
296C22×C4×C37C2×D411yescharacteristic
297C22×C4×C37C2×D411yescharacteristic
298C22×C4×C37C2×D411yescharacteristic
299C22×C4×C37C2×D411yescharacteristic
300C22×C4×C37#4111yescharacteristic
301C22×C4×C37#4111yescharacteristic
302C22×C4×C37C2411yescharacteristic
303Q16×C37—28no—
304SD16×C37—216no—
305SD16×C37—28no—
306SD16×C37—28no—
307D8×C37—216no—
308D8×C37—28no—
309M16×C37—22no—
310M16×C37—22no—
311M16×C37—22no—
312M16×C37—22no—
313M16×C37—22no—
314M16×C37—22no—
315M16×C37—22no—
316M16×C37C2×D414yescomplemented
317C2×C8×C37—22no—
318C2×C8×C37—22no—
319C2×C8×C37—22no—
320C2×C8×C37—22no—
321C2×C8×C37—22no—
322C2×C8×C37C2×D414yescomplemented
323C4⋊C4×C37—22no—
324C4⋊C4×C37—22no—
325C4⋊C4×C37—22no—
326C4⋊C4×C37—41no—
327C22⋊C4×C37—216no—
328C22⋊C4×C37—22no—
329C22⋊C4×C37—22no—
330C22⋊C4×C37—41no—
331C22⋊C4×C37C2×D414yes—
332C42×C37—22no—
333C42×C37—22no—
334C42×C37—22no—
335C42×C37—41no—
336C23×C37—24no—
337C23×C37—22no—
338C23×C37—22no—
339C23×C37—42no—
340C23×C37—44no—
341C23×C37—48no—
342C23×C37—42no—
343C23×C37—42no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—42no—
347C23×C37—42no—
348C23×C37—42no—
349C23×C37—41no—
350C23×C37—41no—
351C23×C37—42no—
352C23×C37—82no—
353C23×C37—84no—
354C23×C37—84no—
355C23×C37—84no—
356C23×C37—84no—
357C23×C37—84no—
358C23×C37—84no—
359C23×C37#12011yescharacteristic
360C23×C37#12011yescharacteristic
361C23×C37#12111yescharacteristic
362C23×C37#12111yescharacteristic
363C23×C37#12711yescharacteristic
364C23×C37#12711yescharacteristic
365C23×C37C22×D411yescharacteristic
366Q8×C37—22no—
367Q8×C37—22no—
368Q8×C37—22no—
369Q8×C37—22no—
370Q8×C37—41no—
371Q8×C37—41no—
372Q8×C37—41no—
373Q8×C37—41no—
374D4×C37—22no—
375D4×C37—24no—
376D4×C37—22no—
377D4×C37—22no—
378D4×C37—24no—
379D4×C37—22no—
380D4×C37—42no—
381D4×C37—42no—
382D4×C37—42no—
383D4×C37—42no—
384D4×C37—42no—
385D4×C37—42no—
386D4×C37—42no—
387D4×C37—42no—
388D4×C37—42no—
389D4×C37—42no—
390D4×C37—42no—
391D4×C37—42no—
392D4×C37—42no—
393D4×C37—42no—
394D4×C37—41no—
395D4×C37—41no—
396D4×C37—41no—
397D4×C37—41no—
398D4×C37—816no—
399C2×C4×C37—24no—
400C2×C4×C37—22no—
401C2×C4×C37—22no—
402C2×C4×C37—44no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—41no—
406C2×C4×C37—41no—
407C2×C4×C37—42no—
408C2×C4×C37—42no—
409C2×C4×C37—42no—
410C2×C4×C37—42no—
411C2×C4×C37—42no—
412C2×C4×C37—42no—
413C2×C4×C37—42no—
414C2×C4×C37—42no—
415C2×C4×C37—42no—
416C2×C4×C37—82no—
417C2×C4×C37#12011yescharacteristic
418C2×C4×C37#12011yescharacteristic
419C2×C4×C37#12011yescharacteristic
420C2×C4×C37#12011yescharacteristic
421C2×C4×C37#12011yescharacteristic
422C2×C4×C37#12011yescharacteristic
423C2×C4×C37#12011yescharacteristic
424C2×C4×C37#12011yescharacteristic
425C2×C4×C37#12011yescharacteristic
426C2×C4×C37#12011yescharacteristic
427C2×C4×C37#12111yescharacteristic
428C2×C4×C37#12111yescharacteristic
429C2×C4×C37#12111yescharacteristic
430C2×C4×C37#12111yescharacteristic
431C2×C4×C37#12111yescharacteristic
432C2×C4×C37#12111yescharacteristic
433C2×C4×C37#12111yescharacteristic
434C2×C4×C37#12111yescharacteristic
435C2×C4×C37#12111yescharacteristic
436C2×C4×C37#12111yescharacteristic
437C2×C4×C37#12711yescharacteristic
438C2×C4×C37#12711yescharacteristic
439C2×C4×C37C22×D411yescharacteristic
440C2×C4×C37C22×D411yescharacteristic
441C2×C4×C37C22×D411yescharacteristic
442C2×C4×C37C22×D411yescharacteristic
443C2×C4×C37C22×D411yescharacteristic
444C2×C4×C37C2×#4111yescharacteristic
445C8×C37—24no—
446C8×C37—24no—
447C2×#2008C3711yesmaximal, characteristic, direct product factor, Sylow
448C22×C37—22no—
449C22×C37—22no—
450C22×C37—22no—
451C22×C37—41no—
452C22×C37—41no—
453C22×C37—41no—
454C22×C37—41no—
455C22×C37—44no—
456C22×C37—48no—
457C22×C37—42no—
458C22×C37—42no—
459C22×C37—44no—
460C22×C37—82no—
461C22×C37—82no—
462C22×C37—84no—
463C22×C37—82no—
464C22×C37—84no—
465C22×C37—84no—
466C22×C37—84no—
467C22×C37—84no—
468C22×C37—82no—
469C22×C37—84no—
470C22×C37—82no—
471C22×C37#39211yescharacteristic
472C22×C37#39211yescharacteristic
473C22×C37#39211yescharacteristic
474C22×C37#39211yescharacteristic
475C22×C37C2×#12011yescharacteristic
476C22×C37C2×#12111yescharacteristic
477C22×C37C2×#12711yescharacteristic
478C4×C37—44no—
479C4×C37—42no—
480C4×C37—42no—
481C4×C37—82no—
482C4×C37#39211yescharacteristic
483C4×C37#39211yescharacteristic
484C4×C37#39211yescharacteristic
485C4×C37#39211yescharacteristic
486C4×C37C2×#12011yescharacteristic
487C4×C37C2×#12011yescharacteristic
488C4×C37C2×#12111yescharacteristic
489C4×C37C2×#12111yescharacteristic
490C2×#575C2×C3711yescharacteristic, complemented
491C22×AGL(1,ℤ/8)C2×C3711yescharacteristic, complemented
492C2×#535C2×C3711yescharacteristic, complemented
493C2×#421C2×C3711yescharacteristic, complemented
494C2×#418C2×C3711yescharacteristic, complemented
495C2×#410C2×C3711yescharacteristic, complemented
496#2008C2×C3718yesdirect product factor
497C2×#344C2×C3711yescharacteristic, complemented
498C2×C37—21no—
499C2×C37—21no—
500C2×C37—21no—
501C2×C37—21no—
502C2×C37—21no—
503C2×C37—21no—
504C2×C37—82no—
505C2×C37—84no—
506C2×C37—82no—
507C2×C37#200812yesdirect product factor
508C2×C37C2×#39211yescharacteristic
509C22×#41C22×C3711yescharacteristic
510C22×#41C22×C3711yescharacteristic
511C23×D4C22×C3711yescharacteristic
512#575—22no—
513#575—22no—
514#575—22no—
515#575C22×C3714yescomplemented
516C2×#137—21no—
517C2×#137—21no—
518C2×AGL(1,ℤ/8)—22no—
519C2×AGL(1,ℤ/8)—22no—
520C2×AGL(1,ℤ/8)—22no—
521C2×AGL(1,ℤ/8)—21no—
522C2×AGL(1,ℤ/8)—21no—
523C2×AGL(1,ℤ/8)—22no—
524C2×AGL(1,ℤ/8)—22no—
525C2×AGL(1,ℤ/8)C22×C3714yescomplemented
526C2×#135—22no—
527C22×SD16—21no—
528C22×D8—21no—
529C22×M16C22×C3711yescharacteristic
530C22×M16C22×C3711yescharacteristic
531#535—22no—
532#535—22no—
533#535—22no—
534#535C22×C3714yescomplemented
535C2×#127—21no—
536C2×#124—21no—
537C2×#121—22no—
538C2×#120—22no—
539C2×#117C22×C3711yescharacteristic
540C2×#117C22×C3711yescharacteristic
541#421—22no—
542#421C22×C3714yescomplemented
543C2×#104—22no—
544#418—22no—
545#418C22×C3714yescomplemented
546C2×#102—22no—
547#410—22no—
548#410C22×C3714yescomplemented
549C2×#99—22no—
550#344C22×C3714yescomplemented
551C37C2×#200811yescharacteristic, direct product factor, Sylow
552C25—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41—21no—
573C2×#41D4×C3712yes—
574C2×#41D4×C3712yescomplemented
575C2×#41C23×C3712yes—
576C2×#41C23×C3712yes—
577C22×Q8D4×C3711yescharacteristic
578C22×Q8D4×C3711yescharacteristic, complemented
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—24no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4D4×C3712yes—
594C22×D4D4×C3711yescharacteristic
595C22×D4D4×C3712yes—
596C22×D4D4×C3711yescharacteristic, complemented
597C22×D4C23×C3712yes—
598C23×C4—21no—
599C23×C4—21no—
600C23×C4C23×C3711yescharacteristic
601#137—24no—
602#137—24no—
603#137—24no—
604#137—24no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—28no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—24no—
609AGL(1,ℤ/8)—28no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—24no—
612AGL(1,ℤ/8)—28no—
613#135—28no—
614#135—28no—
615C2×Q16—22no—
616C2×SD16—24no—
617C2×SD16—24no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—24no—
621C2×D8—24no—
622C2×D8—24no—
623C2×D8—22no—
624C2×D8—24no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16—21no—
632C2×M16D4×C3712yescomplemented
633C2×M16D4×C3712yescomplemented
634C2×M16D4×C3712yescomplemented
635C2×M16C23×C3712yes—
636C2×M16C23×C3712yes—
637C22×C8—21no—
638C22×C8D4×C3712yescomplemented
639#127—24no—
640#127—24no—
641#124—24no—
642#124—24no—
643#121—28no—
644#121—28no—
645#120—28no—
646#120—28no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117—21no—
652#117D4×C3712yes—
653#117C23×C3712yes—
654#117C23×C3712yes—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4D4×C3712yes—
660C2×C42—21no—
661C2×C42—21no—
662#104—28no—
663#102—28no—
664#99—28no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C3711yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C3712yes—
719C2×Q8C2×D4×C3712yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C3714yes—
772C2×D4C2×D4×C3712yes—
773C2×D4C2×D4×C3712yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C3711yescharacteristic
791C22×C4C2×D4×C3711yescharacteristic
792C22×C4C2×D4×C3711yescharacteristic
793C22×C4C2×D4×C3711yescharacteristic
794C22×C4C2×D4×C3711yescharacteristic
795C22×C4C2×D4×C3711yescharacteristic
796C22×C4C2×D4×C3711yescharacteristic
797C22×C4C2×D4×C3711yescharacteristic
798C22×C4C2×D4×C3711yescharacteristic
799C22×C4C2×D4×C3711yescharacteristic
800C22×C4C2×D4×C3711yescharacteristic
801C22×C4#41×C3711yescharacteristic
802C22×C4#41×C3711yescharacteristic
803C22×C4C24×C3711yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C3714yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C3714yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C3714yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—42no—
844C23—42no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23#120×C3711yescharacteristic
861C23#120×C3711yescharacteristic
862C23#121×C3711yescharacteristic
863C23#121×C3711yescharacteristic
864C23#127×C3711yescharacteristic
865C23#127×C3711yescharacteristic
866C23C22×D4×C3711yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—42no—
895D4—41no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4#120×C3711yescharacteristic
919C2×C4#120×C3711yescharacteristic
920C2×C4#120×C3711yescharacteristic
921C2×C4#120×C3711yescharacteristic
922C2×C4#120×C3711yescharacteristic
923C2×C4#120×C3711yescharacteristic
924C2×C4#120×C3711yescharacteristic
925C2×C4#120×C3711yescharacteristic
926C2×C4#120×C3711yescharacteristic
927C2×C4#120×C3711yescharacteristic
928C2×C4#121×C3711yescharacteristic
929C2×C4#121×C3711yescharacteristic
930C2×C4#121×C3711yescharacteristic
931C2×C4#121×C3711yescharacteristic
932C2×C4#121×C3711yescharacteristic
933C2×C4#121×C3711yescharacteristic
934C2×C4#121×C3711yescharacteristic
935C2×C4#121×C3711yescharacteristic
936C2×C4#121×C3711yescharacteristic
937C2×C4#121×C3711yescharacteristic
938C2×C4#127×C3711yescharacteristic
939C2×C4#127×C3711yescharacteristic
940C2×C4C22×D4×C3711yescharacteristic
941C2×C4C22×D4×C3711yescharacteristic
942C2×C4C22×D4×C3711yescharacteristic
943C2×C4C22×D4×C3711yescharacteristic
944C2×C4C22×D4×C3711yescharacteristic
945C2×C4C2×#41×C3711yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22C37×#39211yescharacteristic
972C22C37×#39211yescharacteristic
973C22C37×#39211yescharacteristic
974C22C37×#39211yescharacteristic
975C22C2×#120×C3711yescharacteristic
976C22C2×#121×C3711yescharacteristic
977C22C2×#127×C3711yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4C37×#39211yescharacteristic
983C4C37×#39211yescharacteristic
984C4C37×#39211yescharacteristic
985C4C37×#39211yescharacteristic
986C4C2×#120×C3711yescharacteristic
987C4C2×#120×C3711yescharacteristic
988C4C2×#121×C3711yescharacteristic
989C4C2×#121×C3711yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C37×#200812yesdirect product factor
1000C2C2×C37×#39211yescharacteristic
subgroupG/H
center, socleC22×C37#392
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#575C2semidirect
2. C22×AGL(1,ℤ/8)×C37C2semidirect
3. C2×C37×#535C2semidirect
4. C2×C37×#421C2semidirect
5. C2×C37×#418C2semidirect
6. C2×C37×#410C2semidirect
7. C37×#2008C2direct (N × H)
8. C2×C37×#344C2semidirect
15. C37×#575C22semidirect
25. C2×AGL(1,ℤ/8)×C37C22semidirect
34. C37×#535C22semidirect
42. C37×#421C22semidirect
45. C37×#418C22semidirect
48. C37×#410C22semidirect
50. C37×#344C22semidirect
73. C2×#41×C37D4semidirect
77. C22×Q8×C37D4semidirect
95. C22×D4×C37D4semidirect
131. C2×M16×C37D4semidirect
132. C2×M16×C37D4semidirect
133. C2×M16×C37D4semidirect
137. C22×C8×C37D4semidirect
218. C2×Q8×C37C2×D4semidirect
272. C2×D4×C37C2×D4semidirect
316. M16×C37C2×D4semidirect
322. C2×C8×C37C2×D4semidirect
447. C2×#2008C37direct (N × H)
490. C2×#575C2×C37semidirect
491. C22×AGL(1,ℤ/8)C2×C37semidirect
492. C2×#535C2×C37semidirect
493. C2×#421C2×C37semidirect
494. C2×#418C2×C37semidirect
495. C2×#410C2×C37semidirect
496. #2008C2×C37direct (N × H)
497. C2×#344C2×C37semidirect
507. C2×C37#2008direct (N × H)
515. #575C22×C37semidirect
525. C2×AGL(1,ℤ/8)C22×C37semidirect
534. #535C22×C37semidirect
542. #421C22×C37semidirect
545. #418C22×C37semidirect
548. #410C22×C37semidirect
550. #344C22×C37semidirect
551. C37C2×#2008direct (N × H)
574. C2×#41D4×C37semidirect
578. C22×Q8D4×C37semidirect
596. C22×D4D4×C37semidirect
632. C2×M16D4×C37semidirect
633. C2×M16D4×C37semidirect
634. C2×M16D4×C37semidirect
638. C22×C8D4×C37semidirect
719. C2×Q8C2×D4×C37semidirect
773. C2×D4C2×D4×C37semidirect
817. M16C2×D4×C37semidirect
823. C2×C8C2×D4×C37semidirect
999. C2C37×#2008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5752
C22×AGL(1,ℤ/8)×C372
C2×C37×#5352
C2×C37×#4212
C2×C37×#4182
C2×C37×#4102
C37×#20082
C2×C37×#3442
C2×#200837