Finite Group Databasebeta

← C37×#23894 #22645147

Subgroups — C37×#23894 #22645147

Order 9472.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3586C211yesmaximal, characteristic, complemented
2C37×#3585C211yesmaximal, characteristic, complemented
3C37×#3020C211yesmaximal, characteristic, complemented
4C37×#3019C211yesmaximal, characteristic, complemented
5C37×#3010C211yesmaximal, characteristic, complemented
6C37×#3009C211yesmaximal, characteristic, complemented
7C37×#2019C211yesmaximal, characteristic, complemented
8C37×#2017C211yesmaximal, characteristic, complemented
9C37×#2009C211yesmaximal, characteristic, complemented
10C37×#2008C211yesmaximal, characteristic, complemented
11C37×#1903C211yesmaximal, characteristic, complemented
12C37×#1902C211yesmaximal, characteristic, complemented
13C37×#1881C211yesmaximal, characteristic, complemented
14C37×#1881C211yesmaximal, characteristic, complemented
15C37×#1794C211yesmaximal, characteristic, complemented
16C37×#585C2211yescharacteristic
17C2×2−1+4×C37C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C37C2211yescharacteristic
19C37×#578—22no—
20C37×#578—22no—
21C37×#577—22no—
22C37×#577—22no—
23C37×#577—22no—
24C37×#577—22no—
25C37×#576—22no—
26C37×#576—22no—
27C37×#575—22no—
28C37×#575—22no—
29C37×#575C2211yescharacteristic
30C37×#575C2211yescharacteristic
31C37×#575C2211yescharacteristic
32C37×#575C2211yescharacteristic, complemented
33C37×#575C2211yescharacteristic, complemented
34C2×#137×C37—22no—
35C2×#137×C37C2211yescharacteristic
36C2×#137×C37C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C37—22no—
38C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
40C22×SD16×C37C2211yescharacteristic, complemented
41C37×#568C2211yescharacteristic
42C37×#568C2211yescharacteristic, complemented
43C37×#536C2211yescharacteristic, complemented
44C37×#535C2211yescharacteristic, complemented
45C37×#456—22no—
46C37×#455—22no—
47C37×#454—22no—
48C37×#453—22no—
49C37×#452—22no—
50C37×#450—22no—
51C37×#449—22no—
52C37×#448—22no—
53C37×#421C2211yescharacteristic
54C37×#421C2211yescharacteristic, complemented
55C37×#421C2211yescharacteristic, complemented
56C37×#421C2211yescharacteristic, complemented
57C37×#419C2211yescharacteristic, complemented
58C37×#418C2211yescharacteristic, complemented
59C37×#416C2211yescharacteristic
60C37×#416C2211yescharacteristic, complemented
61C2×#101×C37C2211yescharacteristic, complemented
62C2×#100×C37C2211yescharacteristic, complemented
63C37×#410C2211yescharacteristic, complemented
64C37×#408C2211yescharacteristic, complemented
65C37×#408C2211yescharacteristic, complemented
66C37×#408C2211yescharacteristic, complemented
67C37×#344C2211yescharacteristic, complemented
68C37×#344C2211yescharacteristic, complemented
69C37×#341C2211yescharacteristic, complemented
70C37×#338C2211yescharacteristic, complemented
712−1+4×C37—22no—
722−1+4×C37—21no—
732−1+4×C37—22no—
742−1+4×C37—21no—
752−1+4×C37—22no—
762−1+4×C37—41no—
772−1+4×C37D412yescomplemented
78H(5,𝔽2)×C37—22no—
79H(5,𝔽2)×C37—21no—
80H(5,𝔽2)×C37—22no—
81H(5,𝔽2)×C37—21no—
82H(5,𝔽2)×C37—22no—
83H(5,𝔽2)×C37—41no—
84H(5,𝔽2)×C37—41no—
85H(5,𝔽2)×C37D412yescomplemented
86C2×#41×C37—22no—
87C2×#41×C37—22no—
88C2×#41×C37—21no—
89C2×#41×C37—21no—
90C2×#41×C37—21no—
91C2×#41×C37—21no—
92C2×#41×C37—41no—
93C2×#41×C37—41no—
94C2×#41×C37C2311yescharacteristic
95C2×#41×C37C2311yescharacteristic
96C2×#41×C37C2311yescharacteristic
97C2×#41×C37C2311yescharacteristic
98C2×#41×C37C2311yescharacteristic
99C22×Q8×C37—21no—
100C22×Q8×C37—21no—
101C22×Q8×C37C2311yescharacteristic
102C22×D4×C37—21no—
103C22×D4×C37—21no—
104C22×D4×C37—41no—
105C22×D4×C37C2311yescharacteristic
106#137×C37—24no—
107#137×C37—24no—
108#137×C37—24no—
109#137×C37—24no—
110#137×C37—22no—
111#137×C37—22no—
112#137×C37—21no—
113#137×C37—22no—
114#137×C37—21no—
115#137×C37—21no—
116#137×C37—21no—
117#137×C37—21no—
118#137×C37—21no—
119#137×C37—21no—
120#137×C37—21no—
121#137×C37—22no—
122#137×C37D412yes—
123#137×C37D412yescomplemented
124AGL(1,ℤ/8)×C37—24no—
125AGL(1,ℤ/8)×C37—24no—
126AGL(1,ℤ/8)×C37—24no—
127AGL(1,ℤ/8)×C37—24no—
128AGL(1,ℤ/8)×C37—22no—
129AGL(1,ℤ/8)×C37—22no—
130AGL(1,ℤ/8)×C37—21no—
131AGL(1,ℤ/8)×C37—22no—
132AGL(1,ℤ/8)×C37—21no—
133AGL(1,ℤ/8)×C37—21no—
134AGL(1,ℤ/8)×C37—21no—
135AGL(1,ℤ/8)×C37—21no—
136AGL(1,ℤ/8)×C37—21no—
137AGL(1,ℤ/8)×C37—21no—
138AGL(1,ℤ/8)×C37—21no—
139AGL(1,ℤ/8)×C37—22no—
140AGL(1,ℤ/8)×C37D412yes—
141AGL(1,ℤ/8)×C37D412yescomplemented
142#135×C37—24no—
143#135×C37—24no—
144#135×C37—24no—
145#135×C37—24no—
146#135×C37—22no—
147#135×C37—22no—
148#135×C37—22no—
149#135×C37—22no—
150#135×C37—41no—
151C2×Q16×C37—24no—
152C2×Q16×C37—21no—
153C2×Q16×C37D412yescomplemented
154C2×SD16×C37—24no—
155C2×SD16×C37—24no—
156C2×SD16×C37—21no—
157C2×SD16×C37—21no—
158C2×SD16×C37—22no—
159C2×SD16×C37—22no—
160C2×SD16×C37—41no—
161C2×SD16×C37D412yes—
162C2×SD16×C37D412yescomplemented
163C2×D8×C37—24no—
164C2×D8×C37—21no—
165C2×D8×C37D412yes—
166#131×C37—22no—
167#131×C37—22no—
168#131×C37—22no—
169#131×C37—22no—
170C2×M16×C37—22no—
171C2×M16×C37—22no—
172C2×M16×C37C2311yescharacteristic
173C2×M16×C37C2311yescharacteristic
174C2×M16×C37C2311yescharacteristic
175C2×M16×C37C2311yescharacteristic
176C2×M16×C37C2311yescharacteristic
177C22×C8×C37C2311yescharacteristic
178C4⋊Q8×C37—21no—
179#127×C37—21no—
180#124×C37—21no—
181#124×C37—21no—
182#123×C37—41no—
183C22⋊Q8×C37—22no—
184#121×C37—22no—
185#120×C37—41no—
186#117×C37C2311yescharacteristic
187#117×C37C2311yescharacteristic
188#104×C37—22no—
189#104×C37—22no—
190#104×C37—22no—
191#104×C37—22no—
192#103×C37—21no—
193#103×C37—21no—
194#103×C37—22no—
195#102×C37—21no—
196#102×C37—21no—
197#102×C37—22no—
198#101×C37—22no—
199#100×C37—22no—
200#99×C37—41no—
201C22⋊C8×C37—22no—
202C22⋊C8×C37—22no—
203C22⋊C8×C37—41no—
204C24×C37—21no—
205C24×C37—41no—
206#41×C37—21no—
207#41×C37—21no—
208#41×C37—21no—
209#41×C37—21no—
210#41×C37—24no—
211#41×C37—24no—
212#41×C37—22no—
213#41×C37—22no—
214#41×C37—22no—
215#41×C37—22no—
216#41×C37—21no—
217#41×C37—21no—
218#41×C37—21no—
219#41×C37—21no—
220#41×C37—21no—
221#41×C37—21no—
222#41×C37—21no—
223#41×C37—21no—
224#41×C37—21no—
225#41×C37—21no—
226#41×C37—21no—
227#41×C37—21no—
228#41×C37—42no—
229#41×C37—42no—
230#41×C37—42no—
231#41×C37—42no—
232#41×C37—42no—
233#41×C37—44no—
234#41×C37—42no—
235#41×C37—42no—
236#41×C37—42no—
237#41×C37—41no—
238#41×C37—41no—
239#41×C37—44no—
240#41×C37—42no—
241#41×C37—42no—
242#41×C37C2×D412yes—
243#41×C37C2×D412yes—
244#41×C37C2×D412yes—
245#41×C37C2×D412yes—
246C2×Q8×C37—21no—
247C2×Q8×C37—24no—
248C2×Q8×C37—22no—
249C2×Q8×C37—22no—
250C2×Q8×C37—21no—
251C2×Q8×C37—21no—
252C2×Q8×C37—21no—
253C2×Q8×C37—21no—
254C2×Q8×C37—41no—
255C2×Q8×C37—42no—
256C2×Q8×C37—42no—
257C2×Q8×C37—41no—
258C2×Q8×C37—42no—
259C2×Q8×C37C2×D412yes—
260C2×Q8×C37C2×D411yescharacteristic
261C2×Q8×C37C2×D411yescharacteristic
262C2×Q8×C37C2×D411yescharacteristic
263C2×Q8×C37C2×D411yescharacteristic
264C2×Q8×C37C2×D411yescharacteristic
265C2×D4×C37—21no—
266C2×D4×C37—21no—
267C2×D4×C37—24no—
268C2×D4×C37—22no—
269C2×D4×C37—22no—
270C2×D4×C37—21no—
271C2×D4×C37—21no—
272C2×D4×C37—21no—
273C2×D4×C37—21no—
274C2×D4×C37—21no—
275C2×D4×C37—21no—
276C2×D4×C37—21no—
277C2×D4×C37—21no—
278C2×D4×C37—42no—
279C2×D4×C37—41no—
280C2×D4×C37—41no—
281C2×D4×C37—42no—
282C2×D4×C37—42no—
283C2×D4×C37—41no—
284C2×D4×C37—44no—
285C2×D4×C37—42no—
286C2×D4×C37—42no—
287C2×D4×C37—44no—
288C2×D4×C37—41no—
289C2×D4×C37—42no—
290C2×D4×C37—42no—
291C2×D4×C37C2×D412yes—
292C2×D4×C37C2×D411yescharacteristic
293C2×D4×C37C2×D411yescharacteristic
294C2×D4×C37C2×D411yescharacteristic
295C2×D4×C37C2×D411yescharacteristic
296C2×D4×C37C2×D411yescharacteristic
297C22×C4×C37—21no—
298C22×C4×C37—21no—
299C22×C4×C37—21no—
300C22×C4×C37—21no—
301C22×C4×C37—21no—
302C22×C4×C37—21no—
303C22×C4×C37—41no—
304C22×C4×C37—42no—
305C22×C4×C37—41no—
306C22×C4×C37—41no—
307C22×C4×C37C2411yescharacteristic
308Q16×C37—24no—
309Q16×C37—22no—
310Q16×C37—22no—
311Q16×C37—22no—
312Q16×C37—24no—
313Q16×C37—22no—
314Q16×C37—41no—
315SD16×C37—24no—
316SD16×C37—22no—
317SD16×C37—24no—
318SD16×C37—22no—
319SD16×C37—22no—
320SD16×C37—22no—
321SD16×C37—22no—
322SD16×C37—24no—
323SD16×C37—22no—
324SD16×C37—22no—
325SD16×C37—24no—
326SD16×C37—22no—
327SD16×C37—44no—
328SD16×C37—41no—
329SD16×C37—41no—
330D8×C37—24no—
331D8×C37—22no—
332D8×C37—22no—
333D8×C37—22no—
334D8×C37—24no—
335D8×C37—22no—
336D8×C37—41no—
337M16×C37—24no—
338M16×C37—24no—
339M16×C37—21no—
340M16×C37—21no—
341M16×C37—21no—
342M16×C37—21no—
343M16×C37—21no—
344M16×C37—21no—
345M16×C37—21no—
346M16×C37—21no—
347M16×C37C2×D412yes—
348M16×C37C2×D412yes—
349C2×C8×C37—24no—
350C2×C8×C37—24no—
351C2×C8×C37—21no—
352C2×C8×C37—21no—
353C2×C8×C37—21no—
354C2×C8×C37—21no—
355C2×C8×C37—21no—
356C2×C8×C37—21no—
357C2×C8×C37C2×D412yes—
358C2×C8×C37C2×D412yes—
359C4⋊C4×C37—21no—
360C4⋊C4×C37—21no—
361C4⋊C4×C37—42no—
362C22⋊C4×C37—21no—
363C22⋊C4×C37—21no—
364C22⋊C4×C37—42no—
365C22⋊C4×C37—42no—
366C42×C37—21no—
367C42×C37—21no—
368C23×C37—21no—
369C23×C37—21no—
370C23×C37—21no—
371C23×C37—21no—
372C23×C37—21no—
373C23×C37—22no—
374C23×C37—42no—
375C23×C37—44no—
376C23×C37—41no—
377C23×C37—41no—
378C23×C37—161no—
379C23×C37—162no—
380C23×C37H(5,𝔽2)11yescharacteristic
381Q8×C37—21no—
382Q8×C37—21no—
383Q8×C37—21no—
384Q8×C37—21no—
385Q8×C37—22no—
386Q8×C37—21no—
387Q8×C37—21no—
388Q8×C37—22no—
389Q8×C37—21no—
390Q8×C37—21no—
391Q8×C37—42no—
392Q8×C37—44no—
393Q8×C37—41no—
394Q8×C37—41no—
395Q8×C37#12012yes—
396Q8×C37#12012yes—
397D4×C37—22no—
398D4×C37—22no—
399D4×C37—22no—
400D4×C37—22no—
401D4×C37—21no—
402D4×C37—21no—
403D4×C37—22no—
404D4×C37—21no—
405D4×C37—21no—
406D4×C37—21no—
407D4×C37—21no—
408D4×C37—21no—
409D4×C37—21no—
410D4×C37—22no—
411D4×C37—42no—
412D4×C37—42no—
413D4×C37—44no—
414D4×C37—42no—
415D4×C37—44no—
416D4×C37—44no—
417D4×C37—41no—
418D4×C37—41no—
419D4×C37—41no—
420D4×C37—41no—
421D4×C37—41no—
422D4×C37—41no—
423D4×C37—41no—
424D4×C37—41no—
425D4×C37—162no—
426D4×C37#12012yes—
427D4×C37#12012yes—
428C2×C4×C37—21no—
429C2×C4×C37—21no—
430C2×C4×C37—22no—
431C2×C4×C37—22no—
432C2×C4×C37—22no—
433C2×C4×C37—22no—
434C2×C4×C37—21no—
435C2×C4×C37—21no—
436C2×C4×C37—22no—
437C2×C4×C37—21no—
438C2×C4×C37—42no—
439C2×C4×C37—42no—
440C2×C4×C37—42no—
441C2×C4×C37—44no—
442C2×C4×C37—44no—
443C2×C4×C37—44no—
444C2×C4×C37—41no—
445C2×C4×C37—41no—
446C2×C4×C37—41no—
447C2×C4×C37—41no—
448C2×C4×C37—41no—
449C2×C4×C37—41no—
450C2×C4×C37—41no—
451C2×C4×C37—41no—
452C2×C4×C37—41no—
453C2×C4×C37—41no—
454C2×C4×C37C22×D411yescharacteristic
455C2×C4×C37C22×D411yescharacteristic
456C2×C4×C37C22×D411yescharacteristic
457C2×C4×C37C22×D411yescharacteristic
458C2×C4×C37C22×D411yescharacteristic
459C2×C4×C37H(5,𝔽2)11yescharacteristic
460C8×C37—22no—
461C8×C37—22no—
462C8×C37—22no—
463C8×C37—22no—
464C8×C37—41no—
465C8×C37—41no—
466#23894C3711yesmaximal, characteristic, direct product factor, Sylow
467C22×C37—22no—
468C22×C37—22no—
469C22×C37—41no—
470C22×C37—42no—
471C22×C37—42no—
472C22×C37—41no—
473C22×C37—41no—
474C22×C37—41no—
475C22×C37—42no—
476C22×C37—81no—
477C22×C37—81no—
478C22×C37—82no—
479C22×C37—81no—
480C22×C37—82no—
481C22×C37—161no—
482C22×C37—162no—
483C22×C37—164no—
484C22×C37#53411yescharacteristic
485C22×C37D4211yescharacteristic
486C22×C37D4211yescharacteristic
487C4×C37—22no—
488C4×C37—22no—
489C4×C37—41no—
490C4×C37—41no—
491C4×C37—41no—
492C4×C37—42no—
493C4×C37—81no—
494C4×C37—81no—
495C4×C37C2×#12011yescharacteristic
496C4×C37C2×#12011yescharacteristic
497C4×C37D4211yescharacteristic
498C4×C37D4211yescharacteristic
499#3586C2×C3711yescharacteristic, complemented
500#3585C2×C3711yescharacteristic, complemented
501#3020C2×C3711yescharacteristic, complemented
502#3019C2×C3711yescharacteristic, complemented
503#3010C2×C3711yescharacteristic, complemented
504#3009C2×C3711yescharacteristic, complemented
505#2019C2×C3711yescharacteristic, complemented
506#2017C2×C3711yescharacteristic, complemented
507#2009C2×C3711yescharacteristic, complemented
508#2008C2×C3711yescharacteristic, complemented
509#1903C2×C3711yescharacteristic, complemented
510#1902C2×C3711yescharacteristic, complemented
511#1881C2×C3711yescharacteristic, complemented
512#1881C2×C3711yescharacteristic, complemented
513#1794C2×C3711yescharacteristic, complemented
514C2×C37—21no—
515C2×C37—21no—
516C2×C37—21no—
517C2×C37—42no—
518C2×C37—42no—
519C2×C37—81no—
520C2×C37—81no—
521C2×C37—82no—
522C2×C37—81no—
523C2×C37#240311yescharacteristic
524#585C22×C3711yescharacteristic
525C2×2−1+4C22×C3711yescharacteristic, complemented
526C2×H(5,𝔽2)C22×C3711yescharacteristic
527#578—22no—
528#578—22no—
529#577—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#576—22no—
534#576—22no—
535#575—22no—
536#575—22no—
537#575C22×C3711yescharacteristic
538#575C22×C3711yescharacteristic
539#575C22×C3711yescharacteristic
540#575C22×C3711yescharacteristic, complemented
541#575C22×C3711yescharacteristic, complemented
542C2×#137—22no—
543C2×#137C22×C3711yescharacteristic
544C2×#137C22×C3711yescharacteristic, complemented
545C2×AGL(1,ℤ/8)—22no—
546C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
547C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
548C22×SD16C22×C3711yescharacteristic, complemented
549#568C22×C3711yescharacteristic
550#568C22×C3711yescharacteristic, complemented
551#536C22×C3711yescharacteristic, complemented
552#535C22×C3711yescharacteristic, complemented
553#456—22no—
554#455—22no—
555#454—22no—
556#453—22no—
557#452—22no—
558#450—22no—
559#449—22no—
560#448—22no—
561#421C22×C3711yescharacteristic
562#421C22×C3711yescharacteristic, complemented
563#421C22×C3711yescharacteristic, complemented
564#421C22×C3711yescharacteristic, complemented
565#419C22×C3711yescharacteristic, complemented
566#418C22×C3711yescharacteristic, complemented
567#416C22×C3711yescharacteristic
568#416C22×C3711yescharacteristic, complemented
569C2×#101C22×C3711yescharacteristic, complemented
570C2×#100C22×C3711yescharacteristic, complemented
571#410C22×C3711yescharacteristic, complemented
572#408C22×C3711yescharacteristic, complemented
573#408C22×C3711yescharacteristic, complemented
574#408C22×C3711yescharacteristic, complemented
575#344C22×C3711yescharacteristic, complemented
576#344C22×C3711yescharacteristic, complemented
577#341C22×C3711yescharacteristic, complemented
578#338C22×C3711yescharacteristic, complemented
579C37#2389411yescharacteristic, direct product factor, Sylow
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C3712yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C3712yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C3711yescharacteristic
604C2×#41C23×C3711yescharacteristic
605C2×#41C23×C3711yescharacteristic
606C2×#41C23×C3711yescharacteristic
607C2×#41C23×C3711yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C3711yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C3711yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C3712yes—
632#137D4×C3712yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C3712yes—
650AGL(1,ℤ/8)D4×C3712yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C3712yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C3712yes—
671C2×SD16D4×C3712yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C3712yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C3711yescharacteristic
682C2×M16C23×C3711yescharacteristic
683C2×M16C23×C3711yescharacteristic
684C2×M16C23×C3711yescharacteristic
685C2×M16C23×C3711yescharacteristic
686C22×C8C23×C3711yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C3711yescharacteristic
696#117C23×C3711yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C3712yes—
752#41C2×D4×C3712yes—
753#41C2×D4×C3712yes—
754#41C2×D4×C3712yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C3712yes—
769C2×Q8C2×D4×C3711yescharacteristic
770C2×Q8C2×D4×C3711yescharacteristic
771C2×Q8C2×D4×C3711yescharacteristic
772C2×Q8C2×D4×C3711yescharacteristic
773C2×Q8C2×D4×C3711yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C3712yes—
801C2×D4C2×D4×C3711yescharacteristic
802C2×D4C2×D4×C3711yescharacteristic
803C2×D4C2×D4×C3711yescharacteristic
804C2×D4C2×D4×C3711yescharacteristic
805C2×D4C2×D4×C3711yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C3711yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C3712yes—
857M16C2×D4×C3712yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C3712yes—
867C2×C8C2×D4×C3712yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C3711yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C3712yes—
905Q8#120×C3712yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C3712yes—
936D4#120×C3712yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C3711yescharacteristic
964C2×C4C22×D4×C3711yescharacteristic
965C2×C4C22×D4×C3711yescharacteristic
966C2×C4C22×D4×C3711yescharacteristic
967C2×C4C22×D4×C3711yescharacteristic
968C2×C4H(5,𝔽2)×C3711yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C37×#53411yescharacteristic
993C22D42×C3711yescharacteristic
994C22D42×C3711yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C3711yescharacteristic
1004C4C2×#120×C3711yescharacteristic
1005C4D42×C3711yescharacteristic
1006C4D42×C3711yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C37×#240311yescharacteristic
subgroupG/H
center, socleC2×C37#2403
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3586C2semidirect
2. C37×#3585C2semidirect
3. C37×#3020C2semidirect
4. C37×#3019C2semidirect
5. C37×#3010C2semidirect
6. C37×#3009C2semidirect
7. C37×#2019C2semidirect
8. C37×#2017C2semidirect
9. C37×#2009C2semidirect
10. C37×#2008C2semidirect
11. C37×#1903C2semidirect
12. C37×#1902C2semidirect
13. C37×#1881C2semidirect
14. C37×#1881C2semidirect
15. C37×#1794C2semidirect
17. C2×2−1+4×C37C22semidirect
32. C37×#575C22semidirect
33. C37×#575C22semidirect
36. C2×#137×C37C22semidirect
40. C22×SD16×C37C22semidirect
42. C37×#568C22semidirect
43. C37×#536C22semidirect
44. C37×#535C22semidirect
54. C37×#421C22semidirect
55. C37×#421C22semidirect
56. C37×#421C22semidirect
57. C37×#419C22semidirect
58. C37×#418C22semidirect
60. C37×#416C22semidirect
61. C2×#101×C37C22semidirect
62. C2×#100×C37C22semidirect
63. C37×#410C22semidirect
64. C37×#408C22semidirect
65. C37×#408C22semidirect
66. C37×#408C22semidirect
67. C37×#344C22semidirect
68. C37×#344C22semidirect
69. C37×#341C22semidirect
70. C37×#338C22semidirect
77. 2−1+4×C37D4semidirect
85. H(5,𝔽2)×C37D4semidirect
123. #137×C37D4semidirect
141. AGL(1,ℤ/8)×C37D4semidirect
153. C2×Q16×C37D4semidirect
162. C2×SD16×C37D4semidirect
466. #23894C37direct (N × H)
499. #3586C2×C37semidirect
500. #3585C2×C37semidirect
501. #3020C2×C37semidirect
502. #3019C2×C37semidirect
503. #3010C2×C37semidirect
504. #3009C2×C37semidirect
505. #2019C2×C37semidirect
506. #2017C2×C37semidirect
507. #2009C2×C37semidirect
508. #2008C2×C37semidirect
509. #1903C2×C37semidirect
510. #1902C2×C37semidirect
511. #1881C2×C37semidirect
512. #1881C2×C37semidirect
513. #1794C2×C37semidirect
525. C2×2−1+4C22×C37semidirect
540. #575C22×C37semidirect
541. #575C22×C37semidirect
544. C2×#137C22×C37semidirect
548. C22×SD16C22×C37semidirect
550. #568C22×C37semidirect
551. #536C22×C37semidirect
552. #535C22×C37semidirect
562. #421C22×C37semidirect
563. #421C22×C37semidirect
564. #421C22×C37semidirect
565. #419C22×C37semidirect
566. #418C22×C37semidirect
568. #416C22×C37semidirect
569. C2×#101C22×C37semidirect
570. C2×#100C22×C37semidirect
571. #410C22×C37semidirect
572. #408C22×C37semidirect
573. #408C22×C37semidirect
574. #408C22×C37semidirect
575. #344C22×C37semidirect
576. #344C22×C37semidirect
577. #341C22×C37semidirect
578. #338C22×C37semidirect
579. C37#23894direct (N × H)
586. 2−1+4D4×C37semidirect
594. H(5,𝔽2)D4×C37semidirect
632. #137D4×C37semidirect
650. AGL(1,ℤ/8)D4×C37semidirect
662. C2×Q16D4×C37semidirect
671. C2×SD16D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35862
C37×#35852
C37×#30202
C37×#30192
C37×#30102
C37×#30092
C37×#20192
C37×#20172
C37×#20092
C37×#20082
C37×#19032
C37×#19022
C37×#18812
C37×#17942
#2389437