Finite Group Databasebeta

← C37×#25526 #22646779

Subgroups — C37×#25526 #22646779

Order 9472.

1098 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3495C211yesmaximal, characteristic, complemented
2C37×#3094C211yesmaximal, characteristic, complemented
3C37×#3055C211yesmaximal, characteristic
4C37×#2850C211yesmaximal, characteristic, complemented
5C37×#2061C211yesmaximal, characteristic, complemented
6C37×#2038C211yesmaximal, characteristic, complemented
7C37×#2027C211yesmaximal, characteristic, complemented
8C37×#2003C211yesmaximal, characteristic, complemented
9C37×#1901C211yesmaximal, characteristic, complemented
10C37×#1896C211yesmaximal, characteristic, complemented
11C37×#1888C211yesmaximal, characteristic, complemented
12C37×#1883C211yesmaximal, characteristic, complemented
13C37×#1860C211yesmaximal, characteristic, complemented
14C37×#1857C211yesmaximal, characteristic, complemented
15C2×C37×#339C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C37×#556—21no—
19C37×#554—21no—
20C37×#552—21no—
21C37×#552—22no—
22C37×#552—21no—
23C37×#551—22no—
24C37×#544C2211yescharacteristic
25C37×#542—21no—
26C37×#541—21no—
27C37×#536C2211yescharacteristic
28C37×#533—21no—
29C37×#529—21no—
30C2×#124×C37C2211yescharacteristic
31C37×#525C2211yescharacteristic
32C2×C22⋊Q8×C37C2211yescharacteristic
33C2×#121×C37C2211yescharacteristic
34C37×#520C2211yescharacteristic
35C37×#519C2211yescharacteristic
36C2×#117×C37C2211yescharacteristic
37C22×C42×C37C2211yescharacteristic
38C37×#482—21no—
39C37×#482—21no—
40C37×#481—21no—
41C37×#480—21no—
42C37×#469—21no—
43C37×#468—21no—
44C37×#466—21no—
45C37×#465—21no—
46C37×#428C2211yescharacteristic
47C37×#428C2211yescharacteristic
48C37×#428C2211yescharacteristic
49C2×#104×C37C2211yescharacteristic
50C2×#104×C37C2211yescharacteristic
51C37×#418C2211yescharacteristic
52C37×#418C2211yescharacteristic
53C37×#418C2211yescharacteristic
54C37×#417C2211yescharacteristic
55C2×#101×C37C2211yescharacteristic
56C2×#101×C37C2211yescharacteristic
57C37×#407C2211yescharacteristic
58C37×#391C2211yescharacteristic
59C37×#390C2211yescharacteristic
60C37×#388—22no—
61C37×#386—22no—
62C37×#382C2211yescharacteristic
63C37×#343C2211yescharacteristic
64C37×#343C2211yescharacteristic
65C37×#339C2211yescharacteristic
66C37×#339C2211yescharacteristic
67C37×#339C2211yescharacteristic
68C37×#339C2211yescharacteristic
69C37×#339C2211yescharacteristic
70C37×#339C2211yescharacteristic
71C2×#41×C37C2311yescharacteristic
72C22×Q8×C37C2311yescharacteristic
73C22×D4×C37—21no—
74C22×D4×C37C2311yescharacteristic
75C23×C4×C37—21no—
76C23×C4×C37C2311yescharacteristic
77AGL(1,ℤ/8)×C37—22no—
78AGL(1,ℤ/8)×C37—41no—
79C2×SD16×C37—21no—
80C2×D8×C37—21no—
81C2×M16×C37—21no—
82C2×M16×C37—22no—
83C2×M16×C37—41no—
84C2×M16×C37C2311yescharacteristic
85C2×M16×C37C2311yescharacteristic
86C2×M16×C37C2311yescharacteristic
87C2×M16×C37C2311yescharacteristic
88C22×C8×C37—21no—
89C4⋊Q8×C37—21no—
90C4⋊Q8×C37—21no—
91C4⋊Q8×C37—21no—
92#126×C37—22no—
93#126×C37—22no—
94#126×C37—22no—
95#126×C37—22no—
96#125×C37—22no—
97#125×C37—22no—
98#125×C37—22no—
99#125×C37—21no—
100#125×C37—21no—
101#124×C37—22no—
102#124×C37—21no—
103#124×C37—22no—
104#124×C37—41no—
105#123×C37—22no—
106#123×C37—22no—
107#123×C37—21no—
108#123×C37—22no—
109C22⋊Q8×C37—22no—
110C22⋊Q8×C37—22no—
111C22⋊Q8×C37—21no—
112C22⋊Q8×C37—21no—
113C22⋊Q8×C37—21no—
114C22⋊Q8×C37—21no—
115C22⋊Q8×C37—22no—
116C22⋊Q8×C37—21no—
117C22⋊Q8×C37—21no—
118C22⋊Q8×C37D411yescharacteristic
119C22⋊Q8×C37D411yescharacteristic
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37D411yescharacteristic
125#121×C37D411yescharacteristic
126#120×C37—21no—
127C4×Q8×C37—22no—
128C4×Q8×C37—21no—
129C4×Q8×C37—21no—
130C4×Q8×C37—21no—
131C4×Q8×C37—21no—
132C4×Q8×C37—21no—
133C4×D4×C37—22no—
134C4×D4×C37—21no—
135C4×D4×C37—22no—
136C4×D4×C37—21no—
137C4×D4×C37—21no—
138#117×C37—22no—
139#117×C37—22no—
140#117×C37—22no—
141#117×C37—21no—
142#117×C37—21no—
143#117×C37—21no—
144#117×C37D411yescharacteristic
145#117×C37D411yescharacteristic
146#117×C37C2311yescharacteristic
147#117×C37C2311yescharacteristic
148#117×C37C2311yescharacteristic
149C2×C4⋊C4×C37—21no—
150C2×C4⋊C4×C37D412yes—
151C2×C4⋊C4×C37D411yescharacteristic
152C2×C4⋊C4×C37D411yescharacteristic
153C2×C4⋊C4×C37C2311yescharacteristic
154C2×C4⋊C4×C37C2311yescharacteristic
155C2×C22⋊C4×C37—21no—
156C2×C22⋊C4×C37—21no—
157C2×C22⋊C4×C37—22no—
158C2×C22⋊C4×C37—22no—
159C2×C22⋊C4×C37D412yes—
160C2×C42×C37—21no—
161C2×C42×C37—22no—
162C2×C42×C37—21no—
163C2×C42×C37—41no—
164C2×C42×C37C2311yescharacteristic
165C2×C42×C37C2311yescharacteristic
166#107×C37—21no—
167#107×C37—21no—
168#107×C37—21no—
169#106×C37—21no—
170#106×C37—21no—
171#106×C37—21no—
172#104×C37—22no—
173#104×C37—41no—
174#103×C37—21no—
175#102×C37—21no—
176#102×C37—21no—
177#102×C37—21no—
178#102×C37—21no—
179#102×C37—21no—
180#102×C37—21no—
181#102×C37—21no—
182#101×C37—22no—
183#101×C37—41no—
184C22⋊C8×C37—21no—
185C22⋊C8×C37—21no—
186#95×C37—22no—
187#95×C37—22no—
188C24×C37—21no—
189C24×C37C2×D411yescharacteristic
190#41×C37—21no—
191#41×C37—21no—
192#41×C37—21no—
193#41×C37—21no—
194C2×Q8×C37—22no—
195C2×Q8×C37—21no—
196C2×Q8×C37—21no—
197C2×Q8×C37—21no—
198C2×Q8×C37—21no—
199C2×Q8×C37—21no—
200C2×Q8×C37—21no—
201C2×Q8×C37C2×D411yescharacteristic
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—44no—
212C2×D4×C37—41no—
213C2×D4×C37—41no—
214C2×D4×C37C2×D411yescharacteristic
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—21no—
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—22no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—42no—
227C22×C4×C37—42no—
228C22×C4×C37—42no—
229C22×C4×C37C2×D412yes—
230C22×C4×C37C2×D411yescharacteristic
231C22×C4×C37C2×D411yescharacteristic
232C22×C4×C37C2×D411yescharacteristic
233C22×C4×C37C2×D411yescharacteristic
234C22×C4×C37C2×D411yescharacteristic
235C22×C4×C37C2×D412yes—
236C22×C4×C37C2411yescharacteristic
237SD16×C37—42no—
238D8×C37—42no—
239M16×C37—21no—
240M16×C37—21no—
241M16×C37—21no—
242M16×C37—21no—
243M16×C37—21no—
244M16×C37—21no—
245M16×C37—21no—
246M16×C37—42no—
247M16×C37#4112yes—
248C2×C8×C37—21no—
249C2×C8×C37—21no—
250C2×C8×C37—21no—
251C2×C8×C37—21no—
252C2×C8×C37—42no—
253C4⋊C4×C37—22no—
254C4⋊C4×C37—22no—
255C4⋊C4×C37—22no—
256C4⋊C4×C37—22no—
257C4⋊C4×C37—22no—
258C4⋊C4×C37—22no—
259C4⋊C4×C37—22no—
260C4⋊C4×C37—22no—
261C4⋊C4×C37—21no—
262C4⋊C4×C37—21no—
263C4⋊C4×C37—22no—
264C4⋊C4×C37—22no—
265C4⋊C4×C37—21no—
266C4⋊C4×C37—21no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37C2×D411yescharacteristic
272C4⋊C4×C37C2×D411yescharacteristic
273C4⋊C4×C37C2×D411yescharacteristic
274C4⋊C4×C37C2×D411yescharacteristic
275C4⋊C4×C37C2×D411yescharacteristic
276C4⋊C4×C37C2×D411yescharacteristic
277C22⋊C4×C37—22no—
278C22⋊C4×C37—22no—
279C22⋊C4×C37—22no—
280C22⋊C4×C37—21no—
281C22⋊C4×C37—21no—
282C22⋊C4×C37—22no—
283C22⋊C4×C37—22no—
284C22⋊C4×C37—21no—
285C22⋊C4×C37—21no—
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—21no—
291C22⋊C4×C37—44no—
292C22⋊C4×C37—44no—
293C22⋊C4×C37—41no—
294C22⋊C4×C37—41no—
295C42×C37—22no—
296C42×C37—22no—
297C42×C37—22no—
298C42×C37—21no—
299C42×C37—21no—
300C42×C37—21no—
301C42×C37—21no—
302C42×C37—21no—
303C42×C37—21no—
304C42×C37—21no—
305C42×C37—21no—
306C42×C37—42no—
307C42×C37#4112yes—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—22no—
311C23×C37—21no—
312C23×C37—41no—
313C23×C37—42no—
314C23×C37—42no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37—41no—
318C23×C37#12011yescharacteristic
319C23×C37#12011yescharacteristic
320C23×C37C22×D411yescharacteristic
321Q8×C37—21no—
322Q8×C37—21no—
323Q8×C37—41no—
324Q8×C37—41no—
325Q8×C37—41no—
326Q8×C37—41no—
327Q8×C37—82no—
328D4×C37—21no—
329D4×C37—21no—
330D4×C37—41no—
331D4×C37—41no—
332D4×C37—42no—
333D4×C37—41no—
334D4×C37—41no—
335D4×C37—41no—
336D4×C37—41no—
337D4×C37—81no—
338D4×C37—82no—
339D4×C37—82no—
340C2×C4×C37—21no—
341C2×C4×C37—21no—
342C2×C4×C37—21no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—22no—
351C2×C4×C37—21no—
352C2×C4×C37—21no—
353C2×C4×C37—21no—
354C2×C4×C37—21no—
355C2×C4×C37—21no—
356C2×C4×C37—22no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—22no—
360C2×C4×C37—22no—
361C2×C4×C37—22no—
362C2×C4×C37—22no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—48no—
367C2×C4×C37—41no—
368C2×C4×C37—42no—
369C2×C4×C37—41no—
370C2×C4×C37—41no—
371C2×C4×C37—42no—
372C2×C4×C37—42no—
373C2×C4×C37—41no—
374C2×C4×C37—81no—
375C2×C4×C37—82no—
376C2×C4×C37#12011yescharacteristic
377C2×C4×C37#12011yescharacteristic
378C2×C4×C37C22×D411yescharacteristic
379C2×C4×C37C22×D411yescharacteristic
380C2×C4×C37C2×#4111yescharacteristic
381C2×C4×C37C2×#4111yescharacteristic
382C2×C4×C37H(5,𝔽2)11yescharacteristic
383C2×C4×C372−1+411yescharacteristic
384C8×C37—22no—
385C8×C37—41no—
386C8×C37—41no—
387C8×C37—41no—
388#25526C3711yesmaximal, characteristic, direct product factor, Sylow
389C22×C37—21no—
390C22×C37—21no—
391C22×C37—21no—
392C22×C37—21no—
393C22×C37—21no—
394C22×C37—21no—
395C22×C37—21no—
396C22×C37—42no—
397C22×C37—42no—
398C22×C37—41no—
399C22×C37—41no—
400C22×C37—41no—
401C22×C37—82no—
402C22×C37—82no—
403C22×C37—81no—
404C22×C37—81no—
405C22×C37—81no—
406C22×C37#45412yes—
407C22×C37C2×#12011yescharacteristic
408C22×C37#54611yescharacteristic
409C22×C37#54711yescharacteristic
410C4×C37—21no—
411C4×C37—21no—
412C4×C37—42no—
413C4×C37—42no—
414C4×C37—42no—
415C4×C37—41no—
416C4×C37—41no—
417C4×C37—41no—
418C4×C37—41no—
419C4×C37—42no—
420C4×C37—41no—
421C4×C37—41no—
422C4×C37—41no—
423C4×C37—81no—
424C4×C37#53211yescharacteristic
425C4×C37#53711yescharacteristic
426C4×C37#54611yescharacteristic
427C4×C37#54711yescharacteristic
428#3495C2×C3711yescharacteristic, complemented
429#3094C2×C3711yescharacteristic, complemented
430#3055C2×C3711yescharacteristic
431#2850C2×C3711yescharacteristic, complemented
432#2061C2×C3711yescharacteristic, complemented
433#2038C2×C3711yescharacteristic, complemented
434#2027C2×C3711yescharacteristic, complemented
435#2003C2×C3711yescharacteristic, complemented
436#1901C2×C3711yescharacteristic, complemented
437#1896C2×C3711yescharacteristic, complemented
438#1888C2×C3711yescharacteristic, complemented
439#1883C2×C3711yescharacteristic, complemented
440#1860C2×C3711yescharacteristic, complemented
441#1857C2×C3711yescharacteristic, complemented
442C2×#339C2×C3711yescharacteristic, complemented
443C2×C37—21no—
444C2×C37—21no—
445C2×C37—22no—
446C2×C37—41no—
447C2×C37—81no—
448C2×C37—161no—
449C2×C37#243011yescharacteristic
450C2×C37C2×#45411yescharacteristic
451C2×C37#301811yescharacteristic
452C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
453C22×M16C22×C3711yescharacteristic
454#556—21no—
455#554—21no—
456#552—21no—
457#552—22no—
458#552—21no—
459#551—22no—
460#544C22×C3711yescharacteristic
461#542—21no—
462#541—21no—
463#536C22×C3711yescharacteristic
464#533—21no—
465#529—21no—
466C2×#124C22×C3711yescharacteristic
467#525C22×C3711yescharacteristic
468C2×C22⋊Q8C22×C3711yescharacteristic
469C2×#121C22×C3711yescharacteristic
470#520C22×C3711yescharacteristic
471#519C22×C3711yescharacteristic
472C2×#117C22×C3711yescharacteristic
473C22×C42C22×C3711yescharacteristic
474#482—21no—
475#482—21no—
476#481—21no—
477#480—21no—
478#469—21no—
479#468—21no—
480#466—21no—
481#465—21no—
482#428C22×C3711yescharacteristic
483#428C22×C3711yescharacteristic
484#428C22×C3711yescharacteristic
485C2×#104C22×C3711yescharacteristic
486C2×#104C22×C3711yescharacteristic
487#418C22×C3711yescharacteristic
488#418C22×C3711yescharacteristic
489#418C22×C3711yescharacteristic
490#417C22×C3711yescharacteristic
491C2×#101C22×C3711yescharacteristic
492C2×#101C22×C3711yescharacteristic
493#407C22×C3711yescharacteristic
494#391C22×C3711yescharacteristic
495#390C22×C3711yescharacteristic
496#388—22no—
497#386—22no—
498#382C22×C3711yescharacteristic
499#343C22×C3711yescharacteristic
500#343C22×C3711yescharacteristic
501#339C22×C3711yescharacteristic
502#339C22×C3711yescharacteristic
503#339C22×C3711yescharacteristic
504#339C22×C3711yescharacteristic
505#339C22×C3711yescharacteristic
506#339C22×C3711yescharacteristic
507C37#2552611yescharacteristic, direct product factor, Sylow
508C2×#41C23×C3711yescharacteristic
509C22×Q8C23×C3711yescharacteristic
510C22×D4—21no—
511C22×D4C23×C3711yescharacteristic
512C23×C4—21no—
513C23×C4C23×C3711yescharacteristic
514AGL(1,ℤ/8)—22no—
515AGL(1,ℤ/8)—41no—
516C2×SD16—21no—
517C2×D8—21no—
518C2×M16—21no—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16C23×C3711yescharacteristic
522C2×M16C23×C3711yescharacteristic
523C2×M16C23×C3711yescharacteristic
524C2×M16C23×C3711yescharacteristic
525C22×C8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—21no—
529#126—22no—
530#126—22no—
531#126—22no—
532#126—22no—
533#125—22no—
534#125—22no—
535#125—22no—
536#125—21no—
537#125—21no—
538#124—22no—
539#124—21no—
540#124—22no—
541#124—41no—
542#123—22no—
543#123—22no—
544#123—21no—
545#123—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—22no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8D4×C3711yescharacteristic
556C22⋊Q8D4×C3711yescharacteristic
557#121—21no—
558#121—21no—
559#121—21no—
560#121—21no—
561#121D4×C3711yescharacteristic
562#121D4×C3711yescharacteristic
563#120—21no—
564C4×Q8—22no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×D4—22no—
571C4×D4—21no—
572C4×D4—22no—
573C4×D4—21no—
574C4×D4—21no—
575#117—22no—
576#117—22no—
577#117—21no—
578#117—21no—
579#117—22no—
580#117—21no—
581#117D4×C3711yescharacteristic
582#117D4×C3711yescharacteristic
583#117C23×C3711yescharacteristic
584#117C23×C3711yescharacteristic
585#117C23×C3711yescharacteristic
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C3712yes—
588C2×C4⋊C4D4×C3711yescharacteristic
589C2×C4⋊C4D4×C3711yescharacteristic
590C2×C4⋊C4C23×C3711yescharacteristic
591C2×C4⋊C4C23×C3711yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4D4×C3712yes—
597C2×C42—21no—
598C2×C42—22no—
599C2×C42—21no—
600C2×C42—41no—
601C2×C42C23×C3711yescharacteristic
602C2×C42C23×C3711yescharacteristic
603#107—21no—
604#107—21no—
605#107—21no—
606#106—21no—
607#106—21no—
608#106—21no—
609#104—22no—
610#104—41no—
611#103—21no—
612#102—21no—
613#102—21no—
614#102—21no—
615#102—21no—
616#102—21no—
617#102—21no—
618#102—21no—
619#101—22no—
620#101—41no—
621C22⋊C8—21no—
622C22⋊C8—21no—
623#95—22no—
624#95—22no—
625C24—21no—
626C24C2×D4×C3711yescharacteristic
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631C2×Q8—22no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8C2×D4×C3711yescharacteristic
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—44no—
649C2×D4—41no—
650C2×D4—41no—
651C2×D4C2×D4×C3711yescharacteristic
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4C2×D4×C3712yes—
667C22×C4C2×D4×C3711yescharacteristic
668C22×C4C2×D4×C3711yescharacteristic
669C22×C4C2×D4×C3711yescharacteristic
670C22×C4C2×D4×C3711yescharacteristic
671C22×C4C2×D4×C3711yescharacteristic
672C22×C4C2×D4×C3712yes—
673C22×C4C24×C3711yescharacteristic
674SD16—42no—
675D8—42no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16#41×C3712yes—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4C2×D4×C3711yescharacteristic
709C4⋊C4C2×D4×C3711yescharacteristic
710C4⋊C4C2×D4×C3711yescharacteristic
711C4⋊C4C2×D4×C3711yescharacteristic
712C4⋊C4C2×D4×C3711yescharacteristic
713C4⋊C4C2×D4×C3711yescharacteristic
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C42—22no—
733C42—22no—
734C42—22no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—42no—
744C42#41×C3712yes—
745C23—21no—
746C23—21no—
747C23—22no—
748C23—21no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23#120×C3711yescharacteristic
756C23#120×C3711yescharacteristic
757C23C22×D4×C3711yescharacteristic
758Q8—21no—
759Q8—21no—
760Q8—41no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—82no—
765D4—21no—
766D4—21no—
767D4—41no—
768D4—41no—
769D4—42no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—81no—
775D4—82no—
776D4—82no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—48no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—81no—
812C2×C4—82no—
813C2×C4#120×C3711yescharacteristic
814C2×C4#120×C3711yescharacteristic
815C2×C4C22×D4×C3711yescharacteristic
816C2×C4C22×D4×C3711yescharacteristic
817C2×C4C2×#41×C3711yescharacteristic
818C2×C4C2×#41×C3711yescharacteristic
819C2×C4H(5,𝔽2)×C3711yescharacteristic
820C2×C42−1+4×C3711yescharacteristic
821C8—22no—
822C8—41no—
823C8—41no—
824C8—41no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—42no—
833C22—42no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—82no—
838C22—82no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22C37×#45412yes—
843C22C2×#120×C3711yescharacteristic
844C22C37×#54611yescharacteristic
845C22C37×#54711yescharacteristic
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—81no—
860C4C37×#53211yescharacteristic
861C4C37×#53711yescharacteristic
862C4C37×#54611yescharacteristic
863C4C37×#54711yescharacteristic
864C2—21no—
865C2—21no—
866C2—22no—
867C2—41no—
868C2—81no—
869C2—161no—
870C2C37×#243011yescharacteristic
871C2C2×C37×#45411yescharacteristic
872C2C37×#301811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3055C2
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. C37×#3495C2semidirect
2. C37×#3094C2semidirect
4. C37×#2850C2semidirect
5. C37×#2061C2semidirect
6. C37×#2038C2semidirect
7. C37×#2027C2semidirect
8. C37×#2003C2semidirect
9. C37×#1901C2semidirect
10. C37×#1896C2semidirect
11. C37×#1888C2semidirect
12. C37×#1883C2semidirect
13. C37×#1860C2semidirect
14. C37×#1857C2semidirect
15. C2×C37×#339C2semidirect
388. #25526C37direct (N × H)
428. #3495C2×C37semidirect
429. #3094C2×C37semidirect
431. #2850C2×C37semidirect
432. #2061C2×C37semidirect
433. #2038C2×C37semidirect
434. #2027C2×C37semidirect
435. #2003C2×C37semidirect
436. #1901C2×C37semidirect
437. #1896C2×C37semidirect
438. #1888C2×C37semidirect
439. #1883C2×C37semidirect
440. #1860C2×C37semidirect
441. #1857C2×C37semidirect
442. C2×#339C2×C37semidirect
507. C37#25526direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34952
C37×#30942
C37×#30552
C37×#28502
C37×#20612
C37×#20382
C37×#20272
C37×#20032
C37×#19012
C37×#18962
C37×#18882
C37×#18832
C37×#18602
C37×#18572
C2×C37×#3392
#2552637