Finite Group Databasebeta

← C2×C37×#2009 #22644664

Subgroups — C2×C37×#2009 #22644664

Order 9472.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#575C211yesmaximal, characteristic
2C22×#137×C37C211yesmaximal, characteristic, complemented
3C2×C37×#536C211yesmaximal, characteristic, complemented
4C2×C37×#421C211yesmaximal, characteristic, complemented
5C2×C37×#419C211yesmaximal, characteristic, complemented
6C2×C37×#410C211yesmaximal, characteristic, complemented
7C37×#2009C218yesmaximal, direct product factor
8C2×C37×#344C211yesmaximal, characteristic, complemented
9C22×#41×C37C2211yescharacteristic
10C22×#41×C37C2211yescharacteristic
11C23×Q8×C37C2211yescharacteristic
12C37×#575—22no—
13C37×#575—22no—
14C37×#575—22no—
15C37×#575C2214yes—
16C2×#137×C37—22no—
17C2×#137×C37—22no—
18C2×#137×C37—22no—
19C2×#137×C37—21no—
20C2×#137×C37—21no—
21C2×#137×C37—22no—
22C2×#137×C37—22no—
23C2×#137×C37C2214yescomplemented
24C2×AGL(1,ℤ/8)×C37—21no—
25C2×AGL(1,ℤ/8)×C37—21no—
26C2×#135×C37—22no—
27C22×Q16×C37—21no—
28C22×SD16×C37—21no—
29C22×M16×C37C2211yescharacteristic
30C22×M16×C37C2211yescharacteristic
31C37×#536—22no—
32C37×#536—22no—
33C37×#536—22no—
34C37×#536C2214yescomplemented
35C2×C4⋊Q8×C37—21no—
36C2×#124×C37—21no—
37C2×#123×C37—22no—
38C2×C22⋊Q8×C37—22no—
39C2×#117×C37C2211yescharacteristic
40C2×#117×C37C2211yescharacteristic
41C37×#421—22no—
42C37×#421C2214yescomplemented
43C2×#104×C37—22no—
44C37×#419—22no—
45C37×#419C2214yescomplemented
46C2×#103×C37—22no—
47C37×#410—22no—
48C37×#410C2214yescomplemented
49C2×#99×C37—22no—
50C37×#344C2214yescomplemented
51C2×#41×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×C37D412yes—
72C2×#41×C37D412yes—
73C2×#41×C37C2312yes—
74C2×#41×C37C2312yes—
75C22×Q8×C37—21no—
76C22×Q8×C37—21no—
77C22×Q8×C37—21no—
78C22×Q8×C37—21no—
79C22×Q8×C37—21no—
80C22×Q8×C37—21no—
81C22×Q8×C37—21no—
82C22×Q8×C37—21no—
83C22×Q8×C37—21no—
84C22×Q8×C37—21no—
85C22×Q8×C37—21no—
86C22×Q8×C37D412yes—
87C22×Q8×C37D411yescharacteristic
88C22×Q8×C37D412yes—
89C22×Q8×C37D411yescharacteristic
90C22×Q8×C37C2312yes—
91C22×D4×C37—21no—
92C22×D4×C37—21no—
93C22×D4×C37D411yescharacteristic
94C22×D4×C37D411yescharacteristic
95C23×C4×C37—21no—
96C23×C4×C37—21no—
97C23×C4×C37—21no—
98C23×C4×C37C2311yescharacteristic
99#137×C37—28no—
100#137×C37—28no—
101#137×C37—24no—
102#137×C37—24no—
103#137×C37—28no—
104#137×C37—24no—
105#137×C37—24no—
106#137×C37—28no—
107AGL(1,ℤ/8)×C37—24no—
108AGL(1,ℤ/8)×C37—24no—
109AGL(1,ℤ/8)×C37—24no—
110AGL(1,ℤ/8)×C37—24no—
111#135×C37—28no—
112#135×C37—28no—
113C2×Q16×C37—24no—
114C2×Q16×C37—24no—
115C2×Q16×C37—22no—
116C2×Q16×C37—24no—
117C2×SD16×C37—24no—
118C2×SD16×C37—24no—
119C2×SD16×C37—22no—
120C2×SD16×C37—22no—
121C2×SD16×C37—24no—
122C2×D8×C37—22no—
123C2×M16×C37—21no—
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×C37D412yes—
131C2×M16×C37D412yes—
132C2×M16×C37D412yes—
133C2×M16×C37C2312yes—
134C2×M16×C37C2312yes—
135C22×C8×C37—21no—
136C22×C8×C37D412yes—
137C4⋊Q8×C37—24no—
138C4⋊Q8×C37—24no—
139#124×C37—24no—
140#124×C37—24no—
141#123×C37—28no—
142#123×C37—28no—
143C22⋊Q8×C37—28no—
144C22⋊Q8×C37—28no—
145#117×C37—21no—
146#117×C37—21no—
147#117×C37—21no—
148#117×C37—21no—
149#117×C37—21no—
150#117×C37D412yes—
151#117×C37C2312yes—
152#117×C37C2312yes—
153C2×C4⋊C4×C37—24no—
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#103×C37—28no—
163#99×C37—28no—
164C24×C37—21no—
165C24×C37—21no—
166C24×C37C2×D411yescharacteristic
167#41×C37—22no—
168#41×C37—22no—
169#41×C37—22no—
170#41×C37—22no—
171#41×C37—22no—
172#41×C37—22no—
173#41×C37—22no—
174#41×C37—22no—
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—41no—
184#41×C37—41no—
185#41×C37—41no—
186#41×C37—41no—
187#41×C37—41no—
188#41×C37—41no—
189#41×C37—41no—
190#41×C37—41no—
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—
199C2×Q8×C37—22no—
200C2×Q8×C37—22no—
201C2×Q8×C37—21no—
202C2×Q8×C37—21no—
203C2×Q8×C37—22no—
204C2×Q8×C37—22no—
205C2×Q8×C37—22no—
206C2×Q8×C37—21no—
207C2×Q8×C37—21no—
208C2×Q8×C37—21no—
209C2×Q8×C37—21no—
210C2×Q8×C37—22no—
211C2×Q8×C37—22no—
212C2×Q8×C37—21no—
213C2×Q8×C37—21no—
214C2×Q8×C37—22no—
215C2×Q8×C37—22no—
216C2×Q8×C37—22no—
217C2×Q8×C37—22no—
218C2×Q8×C37—21no—
219C2×Q8×C37—21no—
220C2×Q8×C37—22no—
221C2×Q8×C37—22no—
222C2×Q8×C37—22no—
223C2×Q8×C37—22no—
224C2×Q8×C37—41no—
225C2×Q8×C37—41no—
226C2×Q8×C37—41no—
227C2×Q8×C37—41no—
228C2×Q8×C37—41no—
229C2×Q8×C37—41no—
230C2×Q8×C37—41no—
231C2×Q8×C37—41no—
232C2×Q8×C37—41no—
233C2×Q8×C37—41no—
234C2×Q8×C37—41no—
235C2×Q8×C37—41no—
236C2×Q8×C37C2×D414yes—
237C2×Q8×C37C2×D412yes—
238C2×Q8×C37C2×D412yes—
239C2×D4×C37—22no—
240C2×D4×C37—22no—
241C2×D4×C37—22no—
242C2×D4×C37—22no—
243C2×D4×C37—21no—
244C2×D4×C37—21no—
245C2×D4×C37—21no—
246C2×D4×C37—21no—
247C2×D4×C37—21no—
248C2×D4×C37—21no—
249C2×D4×C37—21no—
250C2×D4×C37—21no—
251C2×D4×C37—21no—
252C2×D4×C37—21no—
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×C37C2×D412yes—
262C2×D4×C37C2×D412yes—
263C22×C4×C37—22no—
264C22×C4×C37—22no—
265C22×C4×C37—21no—
266C22×C4×C37—22no—
267C22×C4×C37—21no—
268C22×C4×C37—22no—
269C22×C4×C37—22no—
270C22×C4×C37—22no—
271C22×C4×C37—22no—
272C22×C4×C37—22no—
273C22×C4×C37—41no—
274C22×C4×C37—41no—
275C22×C4×C37—41no—
276C22×C4×C37—41no—
277C22×C4×C37—41no—
278C22×C4×C37—41no—
279C22×C4×C37—41no—
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×C37C2×D411yescharacteristic
287C22×C4×C37C2×D411yescharacteristic
288C22×C4×C37C2×D411yescharacteristic
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×C37#4111yescharacteristic
298C22×C4×C37#4111yescharacteristic
299C22×C4×C37C2411yescharacteristic
300Q16×C37—216no—
301Q16×C37—28no—
302SD16×C37—216no—
303SD16×C37—28no—
304SD16×C37—28no—
305D8×C37—28no—
306M16×C37—22no—
307M16×C37—22no—
308M16×C37—22no—
309M16×C37—22no—
310M16×C37—22no—
311M16×C37—22no—
312M16×C37—22no—
313M16×C37C2×D414yes—
314C2×C8×C37—22no—
315C2×C8×C37—22no—
316C2×C8×C37—22no—
317C2×C8×C37—22no—
318C2×C8×C37—22no—
319C2×C8×C37C2×D414yes—
320C4⋊C4×C37—216no—
321C4⋊C4×C37—22no—
322C4⋊C4×C37—22no—
323C4⋊C4×C37—22no—
324C4⋊C4×C37—41no—
325C22⋊C4×C37—216no—
326C22⋊C4×C37—22no—
327C22⋊C4×C37—22no—
328C22⋊C4×C37—41no—
329C22⋊C4×C37C2×D414yes—
330C42×C37—22no—
331C42×C37—22no—
332C42×C37—22no—
333C42×C37—41no—
334C23×C37—22no—
335C23×C37—22no—
336C23×C37—42no—
337C23×C37—44no—
338C23×C37—41no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—41no—
342C23×C37—82no—
343C23×C37#12011yescharacteristic
344C23×C37#12011yescharacteristic
345C23×C37#12111yescharacteristic
346C23×C37#12111yescharacteristic
347C23×C37#12711yescharacteristic
348C23×C37#12711yescharacteristic
349C23×C37C22×D411yescharacteristic
350Q8×C37—24no—
351Q8×C37—22no—
352Q8×C37—22no—
353Q8×C37—22no—
354Q8×C37—24no—
355Q8×C37—22no—
356Q8×C37—42no—
357Q8×C37—42no—
358Q8×C37—42no—
359Q8×C37—42no—
360Q8×C37—42no—
361Q8×C37—42no—
362Q8×C37—41no—
363Q8×C37—41no—
364Q8×C37—41no—
365Q8×C37—41no—
366D4×C37—22no—
367D4×C37—22no—
368D4×C37—22no—
369D4×C37—22no—
370D4×C37—42no—
371D4×C37—42no—
372D4×C37—42no—
373D4×C37—42no—
374D4×C37—42no—
375D4×C37—42no—
376D4×C37—42no—
377D4×C37—42no—
378D4×C37—41no—
379D4×C37—41no—
380D4×C37—41no—
381D4×C37—41no—
382C2×C4×C37—24no—
383C2×C4×C37—24no—
384C2×C4×C37—22no—
385C2×C4×C37—22no—
386C2×C4×C37—44no—
387C2×C4×C37—42no—
388C2×C4×C37—42no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—42no—
392C2×C4×C37—42no—
393C2×C4×C37—42no—
394C2×C4×C37—41no—
395C2×C4×C37—41no—
396C2×C4×C37—42no—
397C2×C4×C37—42no—
398C2×C4×C37—42no—
399C2×C4×C37—42no—
400C2×C4×C37—42no—
401C2×C4×C37—42no—
402C2×C4×C37—42no—
403C2×C4×C37—42no—
404C2×C4×C37—42no—
405C2×C4×C37—42no—
406C2×C4×C37—82no—
407C2×C4×C37#12011yescharacteristic
408C2×C4×C37#12011yescharacteristic
409C2×C4×C37#12011yescharacteristic
410C2×C4×C37#12011yescharacteristic
411C2×C4×C37#12011yescharacteristic
412C2×C4×C37#12011yescharacteristic
413C2×C4×C37#12011yescharacteristic
414C2×C4×C37#12011yescharacteristic
415C2×C4×C37#12011yescharacteristic
416C2×C4×C37#12011yescharacteristic
417C2×C4×C37#12111yescharacteristic
418C2×C4×C37#12111yescharacteristic
419C2×C4×C37#12111yescharacteristic
420C2×C4×C37#12111yescharacteristic
421C2×C4×C37#12111yescharacteristic
422C2×C4×C37#12111yescharacteristic
423C2×C4×C37#12111yescharacteristic
424C2×C4×C37#12111yescharacteristic
425C2×C4×C37#12111yescharacteristic
426C2×C4×C37#12111yescharacteristic
427C2×C4×C37#12711yescharacteristic
428C2×C4×C37#12711yescharacteristic
429C2×C4×C37C22×D411yescharacteristic
430C2×C4×C37C22×D411yescharacteristic
431C2×C4×C37C22×D411yescharacteristic
432C2×C4×C37C22×D411yescharacteristic
433C2×C4×C37C22×D411yescharacteristic
434C2×C4×C37C2×#4111yescharacteristic
435C8×C37—24no—
436C8×C37—24no—
437C2×#2009C3711yesmaximal, characteristic, direct product factor, Sylow
438C22×C37—22no—
439C22×C37—22no—
440C22×C37—22no—
441C22×C37—41no—
442C22×C37—41no—
443C22×C37—41no—
444C22×C37—41no—
445C22×C37—44no—
446C22×C37—42no—
447C22×C37—42no—
448C22×C37—82no—
449C22×C37—82no—
450C22×C37—82no—
451C22×C37—82no—
452C22×C37—82no—
453C22×C37#39211yescharacteristic
454C22×C37#39211yescharacteristic
455C22×C37#39211yescharacteristic
456C22×C37#39211yescharacteristic
457C22×C37C2×#12011yescharacteristic
458C22×C37C2×#12111yescharacteristic
459C22×C37C2×#12711yescharacteristic
460C4×C37—44no—
461C4×C37—42no—
462C4×C37—42no—
463C4×C37—44no—
464C4×C37—82no—
465C4×C37#39211yescharacteristic
466C4×C37#39211yescharacteristic
467C4×C37#39211yescharacteristic
468C4×C37#39211yescharacteristic
469C4×C37C2×#12011yescharacteristic
470C4×C37C2×#12011yescharacteristic
471C4×C37C2×#12111yescharacteristic
472C4×C37C2×#12111yescharacteristic
473C2×#575C2×C3711yescharacteristic
474C22×#137C2×C3711yescharacteristic, complemented
475C2×#536C2×C3711yescharacteristic, complemented
476C2×#421C2×C3711yescharacteristic, complemented
477C2×#419C2×C3711yescharacteristic, complemented
478C2×#410C2×C3711yescharacteristic, complemented
479#2009C2×C3718yesdirect product factor
480C2×#344C2×C3711yescharacteristic, complemented
481C2×C37—21no—
482C2×C37—21no—
483C2×C37—21no—
484C2×C37—21no—
485C2×C37—21no—
486C2×C37—21no—
487C2×C37—82no—
488C2×C37—82no—
489C2×C37#200912yesdirect product factor
490C2×C37C2×#39211yescharacteristic
491C22×#41C22×C3711yescharacteristic
492C22×#41C22×C3711yescharacteristic
493C23×Q8C22×C3711yescharacteristic
494#575—22no—
495#575—22no—
496#575—22no—
497#575C22×C3714yes—
498C2×#137—22no—
499C2×#137—22no—
500C2×#137—22no—
501C2×#137—21no—
502C2×#137—21no—
503C2×#137—22no—
504C2×#137—22no—
505C2×#137C22×C3714yescomplemented
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)—21no—
508C2×#135—22no—
509C22×Q16—21no—
510C22×SD16—21no—
511C22×M16C22×C3711yescharacteristic
512C22×M16C22×C3711yescharacteristic
513#536—22no—
514#536—22no—
515#536—22no—
516#536C22×C3714yescomplemented
517C2×C4⋊Q8—21no—
518C2×#124—21no—
519C2×#123—22no—
520C2×C22⋊Q8—22no—
521C2×#117C22×C3711yescharacteristic
522C2×#117C22×C3711yescharacteristic
523#421—22no—
524#421C22×C3714yescomplemented
525C2×#104—22no—
526#419—22no—
527#419C22×C3714yescomplemented
528C2×#103—22no—
529#410—22no—
530#410C22×C3714yescomplemented
531C2×#99—22no—
532#344C22×C3714yescomplemented
533C37C2×#200911yescharacteristic, direct product factor, Sylow
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41D4×C3712yes—
555C2×#41D4×C3712yes—
556C2×#41C23×C3712yes—
557C2×#41C23×C3712yes—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8—21no—
569C22×Q8D4×C3712yes—
570C22×Q8D4×C3711yescharacteristic
571C22×Q8D4×C3712yes—
572C22×Q8D4×C3711yescharacteristic
573C22×Q8C23×C3712yes—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4D4×C3711yescharacteristic
577C22×D4D4×C3711yescharacteristic
578C23×C4—21no—
579C23×C4—21no—
580C23×C4—21no—
581C23×C4C23×C3711yescharacteristic
582#137—28no—
583#137—28no—
584#137—24no—
585#137—24no—
586#137—28no—
587#137—24no—
588#137—24no—
589#137—28no—
590AGL(1,ℤ/8)—24no—
591AGL(1,ℤ/8)—24no—
592AGL(1,ℤ/8)—24no—
593AGL(1,ℤ/8)—24no—
594#135—28no—
595#135—28no—
596C2×Q16—24no—
597C2×Q16—24no—
598C2×Q16—22no—
599C2×Q16—24no—
600C2×SD16—24no—
601C2×SD16—24no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—24no—
605C2×D8—22no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16—21no—
611C2×M16—21no—
612C2×M16—21no—
613C2×M16D4×C3712yes—
614C2×M16D4×C3712yes—
615C2×M16D4×C3712yes—
616C2×M16C23×C3712yes—
617C2×M16C23×C3712yes—
618C22×C8—21no—
619C22×C8D4×C3712yes—
620C4⋊Q8—24no—
621C4⋊Q8—24no—
622#124—24no—
623#124—24no—
624#123—28no—
625#123—28no—
626C22⋊Q8—28no—
627C22⋊Q8—28no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117D4×C3712yes—
634#117C23×C3712yes—
635#117C23×C3712yes—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C3712yes—
642C2×C42—21no—
643C2×C42—21no—
644#104—28no—
645#103—28no—
646#99—28no—
647C24—21no—
648C24—21no—
649C24C2×D4×C3711yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—41no—
708C2×Q8—41no—
709C2×Q8—41no—
710C2×Q8—41no—
711C2×Q8—41no—
712C2×Q8—41no—
713C2×Q8—41no—
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8C2×D4×C3714yes—
720C2×Q8C2×D4×C3712yes—
721C2×Q8C2×D4×C3712yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4C2×D4×C3712yes—
745C2×D4C2×D4×C3712yes—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4C2×D4×C3711yescharacteristic
770C22×C4C2×D4×C3711yescharacteristic
771C22×C4C2×D4×C3711yescharacteristic
772C22×C4C2×D4×C3711yescharacteristic
773C22×C4C2×D4×C3711yescharacteristic
774C22×C4C2×D4×C3711yescharacteristic
775C22×C4C2×D4×C3711yescharacteristic
776C22×C4C2×D4×C3711yescharacteristic
777C22×C4C2×D4×C3711yescharacteristic
778C22×C4C2×D4×C3711yescharacteristic
779C22×C4C2×D4×C3711yescharacteristic
780C22×C4#41×C3711yescharacteristic
781C22×C4#41×C3711yescharacteristic
782C22×C4C24×C3711yescharacteristic
783Q16—216no—
784Q16—28no—
785SD16—216no—
786SD16—28no—
787SD16—28no—
788D8—28no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—22no—
793M16—22no—
794M16—22no—
795M16—22no—
796M16C2×D4×C3714yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8C2×D4×C3714yes—
803C4⋊C4—216no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—41no—
808C22⋊C4—216no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—41no—
812C22⋊C4C2×D4×C3714yes—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—41no—
817C23—22no—
818C23—22no—
819C23—42no—
820C23—44no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—82no—
826C23#120×C3711yescharacteristic
827C23#120×C3711yescharacteristic
828C23#121×C3711yescharacteristic
829C23#121×C3711yescharacteristic
830C23#127×C3711yescharacteristic
831C23#127×C3711yescharacteristic
832C23C22×D4×C3711yescharacteristic
833Q8—24no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—24no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—42no—
843Q8—42no—
844Q8—42no—
845Q8—41no—
846Q8—41no—
847Q8—41no—
848Q8—41no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—82no—
890C2×C4#120×C3711yescharacteristic
891C2×C4#120×C3711yescharacteristic
892C2×C4#120×C3711yescharacteristic
893C2×C4#120×C3711yescharacteristic
894C2×C4#120×C3711yescharacteristic
895C2×C4#120×C3711yescharacteristic
896C2×C4#120×C3711yescharacteristic
897C2×C4#120×C3711yescharacteristic
898C2×C4#120×C3711yescharacteristic
899C2×C4#120×C3711yescharacteristic
900C2×C4#121×C3711yescharacteristic
901C2×C4#121×C3711yescharacteristic
902C2×C4#121×C3711yescharacteristic
903C2×C4#121×C3711yescharacteristic
904C2×C4#121×C3711yescharacteristic
905C2×C4#121×C3711yescharacteristic
906C2×C4#121×C3711yescharacteristic
907C2×C4#121×C3711yescharacteristic
908C2×C4#121×C3711yescharacteristic
909C2×C4#121×C3711yescharacteristic
910C2×C4#127×C3711yescharacteristic
911C2×C4#127×C3711yescharacteristic
912C2×C4C22×D4×C3711yescharacteristic
913C2×C4C22×D4×C3711yescharacteristic
914C2×C4C22×D4×C3711yescharacteristic
915C2×C4C22×D4×C3711yescharacteristic
916C2×C4C22×D4×C3711yescharacteristic
917C2×C4C2×#41×C3711yescharacteristic
918C8—24no—
919C8—24no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22C37×#39211yescharacteristic
936C22C37×#39211yescharacteristic
937C22C37×#39211yescharacteristic
938C22C37×#39211yescharacteristic
939C22C2×#120×C3711yescharacteristic
940C22C2×#121×C3711yescharacteristic
941C22C2×#127×C3711yescharacteristic
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4C37×#39211yescharacteristic
948C4C37×#39211yescharacteristic
949C4C37×#39211yescharacteristic
950C4C37×#39211yescharacteristic
951C4C2×#120×C3711yescharacteristic
952C4C2×#120×C3711yescharacteristic
953C4C2×#121×C3711yescharacteristic
954C4C2×#121×C3711yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2C37×#200912yesdirect product factor
964C2C2×C37×#39211yescharacteristic
subgroupG/H
center, socleC22×C37#392
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#575C2
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
2. C22×#137×C37C2semidirect
3. C2×C37×#536C2semidirect
4. C2×C37×#421C2semidirect
5. C2×C37×#419C2semidirect
6. C2×C37×#410C2semidirect
7. C37×#2009C2direct (N × H)
8. C2×C37×#344C2semidirect
23. C2×#137×C37C22semidirect
34. C37×#536C22semidirect
42. C37×#421C22semidirect
45. C37×#419C22semidirect
48. C37×#410C22semidirect
50. C37×#344C22semidirect
437. C2×#2009C37direct (N × H)
474. C22×#137C2×C37semidirect
475. C2×#536C2×C37semidirect
476. C2×#421C2×C37semidirect
477. C2×#419C2×C37semidirect
478. C2×#410C2×C37semidirect
479. #2009C2×C37direct (N × H)
480. C2×#344C2×C37semidirect
489. C2×C37#2009direct (N × H)
505. C2×#137C22×C37semidirect
516. #536C22×C37semidirect
524. #421C22×C37semidirect
527. #419C22×C37semidirect
530. #410C22×C37semidirect
532. #344C22×C37semidirect
533. C37C2×#2009direct (N × H)
963. C2C37×#2009direct (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×#137×C372
C2×C37×#5362
C2×C37×#4212
C2×C37×#4192
C2×C37×#4102
C37×#20092
C2×C37×#3442
C2×#200937