Finite Group Databasebeta

← C37×#12753 #22634006

Subgroups — C37×#12753 #22634006

Order 9472.

936 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3532C211yesmaximal, characteristic
2C37×#2127C211yesmaximal, characteristic, complemented
3C37×#2121C211yesmaximal, characteristic, complemented
4C2×C37×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C37×#1913C211yesmaximal, characteristic, complemented
6C37×#1911C211yesmaximal, characteristic, complemented
7C37×#1889C211yesmaximal, characteristic, complemented
8C37×H(3,𝔽4)C411yescharacteristic, complemented
9C37×#560—21no—
10C37×#560C411yescharacteristic, complemented
11C37×#551—21no—
12C37×#551C411yescharacteristic, complemented
13C37×#546—21no—
14C37×#546—21no—
15C37×#546—21no—
16D42×C37—21no—
17D42×C37C411yescharacteristic, complemented
18C37×#538—21no—
19C37×#538—21no—
20C37×#538—21no—
21C37×#535—21no—
22C37×#535C2211yescharacteristic
23C37×#534—21no—
24C37×#534C2211yescharacteristic
25C2×#120×C37—21no—
26C2×#120×C37C2211yescharacteristic
27C37×#518C2211yescharacteristic, complemented
28C37×#421—21no—
29C2×#100×C37C2211yescharacteristic, complemented
30C2×#99×C37—21no—
31C2×#99×C37C2211yescharacteristic, complemented
32C2×#99×C37C2211yescharacteristic, complemented
33C37×#379—21no—
34C37×#354—21no—
35C37×#353—21no—
36C37×#352—21no—
37C37×AΣL(1,𝔽16)—21no—
38C37×AΣL(1,𝔽16)—21no—
39C37×AΣL(1,𝔽16)—21no—
40C37×#342—21no—
41C37×#342—21no—
42C37×H(3,ℤ/4)—21no—
43C25×C37D411yescharacteristic
44C2×#41×C37—21no—
45C2×#41×C37D411yescharacteristic
46C22×D4×C37—21no—
47C22×D4×C37—21no—
48C22×D4×C37—21no—
49C22×D4×C37—21no—
50C22×D4×C37—21no—
51C22×D4×C37D411yescharacteristic
52C22×D4×C37C2311yescharacteristic
53C2×M16×C37—21no—
54#127×C37—21no—
55#127×C37C2×C411yescharacteristic
56#127×C37D411yescharacteristic
57#126×C37—21no—
58#126×C37—21no—
59#126×C37—21no—
60#126×C37—21no—
61#124×C37—21no—
62#124×C37—21no—
63#124×C37—21no—
64#124×C37—21no—
65#124×C37—21no—
66#124×C37C2×C411yescharacteristic
67#124×C37D411yescharacteristic
68#123×C37—21no—
69#123×C37—21no—
70#123×C37—21no—
71#123×C37—21no—
72#123×C37—21no—
73#123×C37—21no—
74#123×C37—21no—
75#123×C37—21no—
76#123×C37C2×C411yescharacteristic
77#123×C37D411yescharacteristic
78C22⋊Q8×C37—21no—
79C22⋊Q8×C37—21no—
80C22⋊Q8×C37—21no—
81#121×C37—21no—
82#121×C37—21no—
83#121×C37—21no—
84#121×C37—21no—
85#121×C37—21no—
86#121×C37—21no—
87#121×C37—21no—
88#121×C37—21no—
89#121×C37—21no—
90#121×C37—21no—
91#121×C37—21no—
92#121×C37—21no—
93#121×C37—21no—
94#121×C37—21no—
95#121×C37—21no—
96#120×C37—21no—
97#120×C37—21no—
98#120×C37—21no—
99#120×C37—21no—
100#120×C37—21no—
101#120×C37—21no—
102#120×C37—21no—
103#120×C37—21no—
104#120×C37—21no—
105#120×C37—21no—
106#120×C37—21no—
107#120×C37—21no—
108#120×C37—21no—
109#120×C37—21no—
110#120×C37C2×C411yescharacteristic
111#120×C37C2×C411yescharacteristic
112#120×C37C2×C411yescharacteristic
113#120×C37D411yescharacteristic
114#120×C37D411yescharacteristic
115#120×C37D411yescharacteristic
116C4×D4×C37—21no—
117C4×D4×C37—21no—
118C4×D4×C37—21no—
119C4×D4×C37—21no—
120C4×D4×C37—21no—
121C4×D4×C37—21no—
122C4×D4×C37—42no—
123#117×C37—21no—
124#117×C37—21no—
125#117×C37D411yescharacteristic
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37—21no—
133C2×C22⋊C4×C37—21no—
134C2×C22⋊C4×C37—21no—
135C2×C22⋊C4×C37—42no—
136C2×C22⋊C4×C37D411yescharacteristic
137C2×C22⋊C4×C37D411yescharacteristic
138#104×C37—42no—
139#100×C37—21no—
140#100×C37—21no—
141#99×C37—21no—
142#99×C37—21no—
143#99×C37—21no—
144#99×C37—21no—
145#99×C37—42no—
146C24×C37—21no—
147C24×C37—21no—
148C24×C37—21no—
149C24×C37—41no—
150C24×C37—41no—
151C24×C37—82no—
152C24×C37C22⋊C411yescharacteristic
153C24×C37C22⋊C411yescharacteristic
154C24×C37C22⋊C411yescharacteristic, complemented
155C24×C37C2×D411yescharacteristic
156C24×C37C2×D411yescharacteristic
157#41×C37—41no—
158#41×C37—41no—
159#41×C37—82no—
160C2×Q8×C37—21no—
161C2×Q8×C37C22⋊C411yescharacteristic, complemented
162C2×D4×C37—21no—
163C2×D4×C37—21no—
164C2×D4×C37—21no—
165C2×D4×C37—21no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—21no—
174C2×D4×C37—21no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—21no—
181C2×D4×C37—21no—
182C2×D4×C37—41no—
183C2×D4×C37—41no—
184C2×D4×C37—41no—
185C2×D4×C37—41no—
186C2×D4×C37—82no—
187C2×D4×C37—82no—
188C2×D4×C37—82no—
189C2×D4×C37—82no—
190C2×D4×C37—81no—
191C2×D4×C37—81no—
192C2×D4×C37C22⋊C411yescharacteristic, complemented
193C2×D4×C37C22×C411yescharacteristic
194C2×D4×C37C2×D411yescharacteristic
195C2×D4×C37C2×D411yescharacteristic
196C2×D4×C37C2×D411yescharacteristic
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—22no—
206C22×C4×C37—41no—
207C22×C4×C37—41no—
208C22×C4×C37—41no—
209C22×C4×C37C22⋊C411yescharacteristic, complemented
210C22×C4×C37C2×D411yescharacteristic
211M16×C37—41no—
212M16×C37—41no—
213C2×C8×C37—41no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—41no—
224C22⋊C4×C37—21no—
225C22⋊C4×C37—21no—
226C22⋊C4×C37—21no—
227C22⋊C4×C37—21no—
228C22⋊C4×C37—21no—
229C22⋊C4×C37—21no—
230C22⋊C4×C37—21no—
231C22⋊C4×C37—21no—
232C22⋊C4×C37—21no—
233C22⋊C4×C37—21no—
234C22⋊C4×C37—21no—
235C22⋊C4×C37—21no—
236C22⋊C4×C37—21no—
237C22⋊C4×C37—21no—
238C22⋊C4×C37—21no—
239C22⋊C4×C37—21no—
240C22⋊C4×C37—21no—
241C22⋊C4×C37—21no—
242C22⋊C4×C37—21no—
243C22⋊C4×C37—21no—
244C22⋊C4×C37—21no—
245C22⋊C4×C37—21no—
246C22⋊C4×C37—21no—
247C22⋊C4×C37—21no—
248C22⋊C4×C37—21no—
249C22⋊C4×C37—22no—
250C22⋊C4×C37—41no—
251C22⋊C4×C37—41no—
252C22⋊C4×C37—41no—
253C22⋊C4×C37—41no—
254C22⋊C4×C37—41no—
255C22⋊C4×C37—41no—
256C22⋊C4×C37—84no—
257C22⋊C4×C37C22⋊C411yescharacteristic
258C22⋊C4×C37C22⋊C411yescharacteristic
259C22⋊C4×C37C22⋊C411yescharacteristic, complemented
260C22⋊C4×C37C22⋊C411yescharacteristic, complemented
261C42×C37—21no—
262C42×C37—21no—
263C42×C37—22no—
264C42×C37C22⋊C411yescharacteristic, complemented
265C42×C37C22⋊C411yescharacteristic, complemented
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—21no—
272C23×C37—21no—
273C23×C37—21no—
274C23×C37—42no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—42no—
278C23×C37—42no—
279C23×C37—42no—
280C23×C37—41no—
281C23×C37—44no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—81no—
285C23×C37—81no—
286C23×C37—81no—
287C23×C37—81no—
288C23×C37—81no—
289C23×C37—81no—
290C23×C37—81no—
291C23×C37—81no—
292C23×C37—81no—
293C23×C37—82no—
294C23×C37—82no—
295C23×C37—82no—
296C23×C37C2×C22⋊C411yescharacteristic
297C23×C37C2×C22⋊C411yescharacteristic
298C23×C37#12011yescharacteristic
299C23×C37#12011yescharacteristic
300C23×C37#12011yescharacteristic
301Q8×C37—41no—
302Q8×C37—81no—
303D4×C37—41no—
304D4×C37—41no—
305D4×C37—41no—
306D4×C37—41no—
307D4×C37—41no—
308D4×C37—42no—
309D4×C37—42no—
310D4×C37—42no—
311D4×C37—42no—
312D4×C37—41no—
313D4×C37—41no—
314D4×C37—41no—
315D4×C37—41no—
316D4×C37—81no—
317D4×C37—81no—
318D4×C37—81no—
319D4×C37—81no—
320D4×C37—81no—
321D4×C37—81no—
322D4×C37—81no—
323D4×C37—81no—
324D4×C37—81no—
325D4×C37—81no—
326D4×C37—81no—
327D4×C37—81no—
328D4×C37—81no—
329D4×C37—81no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—21no—
335C2×C4×C37—21no—
336C2×C4×C37—21no—
337C2×C4×C37—21no—
338C2×C4×C37—21no—
339C2×C4×C37—21no—
340C2×C4×C37—42no—
341C2×C4×C37—41no—
342C2×C4×C37—42no—
343C2×C4×C37—81no—
344C2×C4×C37—81no—
345C2×C4×C37—81no—
346C2×C4×C37—81no—
347C2×C4×C37—81no—
348C2×C4×C37—81no—
349C2×C4×C37—81no—
350C2×C4×C37—82no—
351C2×C4×C37—81no—
352C2×C4×C37—81no—
353C2×C4×C37—82no—
354C2×C4×C37—161no—
355C2×C4×C37—161no—
356C2×C4×C37C2×C22⋊C411yescharacteristic
357C2×C4×C37#12011yescharacteristic
358C8×C37—81no—
359#12753C3711yesmaximal, characteristic, direct product factor, Sylow
360C22×C37—22no—
361C22×C37—21no—
362C22×C37—21no—
363C22×C37—21no—
364C22×C37—21no—
365C22×C37—41no—
366C22×C37—41no—
367C22×C37—41no—
368C22×C37—41no—
369C22×C37—41no—
370C22×C37—42no—
371C22×C37—41no—
372C22×C37—41no—
373C22×C37—41no—
374C22×C37—41no—
375C22×C37—41no—
376C22×C37—41no—
377C22×C37—41no—
378C22×C37—42no—
379C22×C37—41no—
380C22×C37—42no—
381C22×C37—41no—
382C22×C37—41no—
383C22×C37—41no—
384C22×C37—81no—
385C22×C37—81no—
386C22×C37—81no—
387C22×C37—82no—
388C22×C37—82no—
389C22×C37—81no—
390C22×C37—84no—
391C22×C37—81no—
392C22×C37—161no—
393C22×C37—162no—
394C22×C37#37911yescharacteristic
395C22×C37B(4,𝔽2)11yescharacteristic
396C22×C37#45811yescharacteristic
397C4×C37—21no—
398C4×C37—21no—
399C4×C37—41no—
400C4×C37—41no—
401C4×C37—41no—
402C4×C37—41no—
403C4×C37—41no—
404C4×C37—41no—
405C4×C37—41no—
406C4×C37—41no—
407C4×C37—82no—
408C4×C37—161no—
409C4×C37—161no—
410#3532C2×C3711yescharacteristic
411#2127C2×C3711yescharacteristic, complemented
412#2121C2×C3711yescharacteristic, complemented
413C2×AΣL(1,𝔽16)C2×C3711yescharacteristic, complemented
414#1913C2×C3711yescharacteristic, complemented
415#1911C2×C3711yescharacteristic, complemented
416#1889C2×C3711yescharacteristic, complemented
417C2×C37—21no—
418C2×C37—21no—
419C2×C37—21no—
420C2×C37—41no—
421C2×C37—41no—
422C2×C37—41no—
423C2×C37—42no—
424C2×C37—41no—
425C2×C37—81no—
426C2×C37—81no—
427C2×C37—81no—
428C2×C37#179011yescharacteristic
429H(3,𝔽4)C4×C3711yescharacteristic, complemented
430#560—21no—
431#560C4×C3711yescharacteristic, complemented
432#551—21no—
433#551C4×C3711yescharacteristic, complemented
434#546—21no—
435#546—21no—
436#546—21no—
437D42—21no—
438D42C4×C3711yescharacteristic, complemented
439#538—21no—
440#538—21no—
441#538—21no—
442#535—21no—
443#535C22×C3711yescharacteristic
444#534—21no—
445#534C22×C3711yescharacteristic
446C2×#120—21no—
447C2×#120C22×C3711yescharacteristic
448#518C22×C3711yescharacteristic, complemented
449#421—21no—
450C2×#100C22×C3711yescharacteristic, complemented
451C2×#99—21no—
452C2×#99C22×C3711yescharacteristic, complemented
453C2×#99C22×C3711yescharacteristic, complemented
454#379—21no—
455#354—21no—
456#353—21no—
457#352—21no—
458AΣL(1,𝔽16)—21no—
459AΣL(1,𝔽16)—21no—
460AΣL(1,𝔽16)—21no—
461#342—21no—
462#342—21no—
463H(3,ℤ/4)—21no—
464C37#1275311yescharacteristic, direct product factor, Sylow
465C25D4×C3711yescharacteristic
466C2×#41—21no—
467C2×#41D4×C3711yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C3711yescharacteristic
474C22×D4C23×C3711yescharacteristic
475C2×M16—21no—
476#127—21no—
477#127C2×C4×C3711yescharacteristic
478#127D4×C3711yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124C2×C4×C3711yescharacteristic
489#124D4×C3711yescharacteristic
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123C2×C4×C3711yescharacteristic
499#123D4×C3711yescharacteristic
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120—21no—
532#120C2×C4×C3711yescharacteristic
533#120C2×C4×C3711yescharacteristic
534#120C2×C4×C3711yescharacteristic
535#120D4×C3711yescharacteristic
536#120D4×C3711yescharacteristic
537#120D4×C3711yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—42no—
545#117—21no—
546#117—21no—
547#117D4×C3711yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4D4×C3711yescharacteristic
559C2×C22⋊C4D4×C3711yescharacteristic
560#104—42no—
561#100—21no—
562#100—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—21no—
567#99—42no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C3711yescharacteristic
575C24C22⋊C4×C3711yescharacteristic
576C24C22⋊C4×C3711yescharacteristic, complemented
577C24C2×D4×C3711yescharacteristic
578C24C2×D4×C3711yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C3711yescharacteristic, complemented
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C3711yescharacteristic, complemented
615C2×D4C22×C4×C3711yescharacteristic
616C2×D4C2×D4×C3711yescharacteristic
617C2×D4C2×D4×C3711yescharacteristic
618C2×D4C2×D4×C3711yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C3711yescharacteristic, complemented
632C22×C4C2×D4×C3711yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C3711yescharacteristic
680C22⋊C4C22⋊C4×C3711yescharacteristic
681C22⋊C4C22⋊C4×C3711yescharacteristic, complemented
682C22⋊C4C22⋊C4×C3711yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C3711yescharacteristic, complemented
687C42C22⋊C4×C3711yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C3711yescharacteristic
719C23C2×C22⋊C4×C3711yescharacteristic
720C23#120×C3711yescharacteristic
721C23#120×C3711yescharacteristic
722C23#120×C3711yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C3711yescharacteristic
779C2×C4#120×C3711yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22C37×#37911yescharacteristic
816C22C37×B(4,𝔽2)11yescharacteristic
817C22C37×#45811yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C37×#179011yescharacteristic
subgroupG/H
center, socleC2×C37#1790
commutatorC2×D4C22×C4×C37
Frattini, cosocleC22×D4C23×C37
prime radicalC37×#3532C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C23×C37 ◁ C22×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2127C2semidirect
3. C37×#2121C2semidirect
4. C2×C37×AΣL(1,𝔽16)C2semidirect
5. C37×#1913C2semidirect
6. C37×#1911C2semidirect
7. C37×#1889C2semidirect
8. C37×H(3,𝔽4)C4semidirect
10. C37×#560C4semidirect
12. C37×#551C4semidirect
17. D42×C37C4semidirect
27. C37×#518C22semidirect
29. C2×#100×C37C22semidirect
31. C2×#99×C37C22semidirect
32. C2×#99×C37C22semidirect
154. C24×C37C22⋊C4semidirect
161. C2×Q8×C37C22⋊C4semidirect
192. C2×D4×C37C22⋊C4semidirect
209. C22×C4×C37C22⋊C4semidirect
259. C22⋊C4×C37C22⋊C4semidirect
260. C22⋊C4×C37C22⋊C4semidirect
264. C42×C37C22⋊C4semidirect
265. C42×C37C22⋊C4semidirect
359. #12753C37direct (N × H)
411. #2127C2×C37semidirect
412. #2121C2×C37semidirect
413. C2×AΣL(1,𝔽16)C2×C37semidirect
414. #1913C2×C37semidirect
415. #1911C2×C37semidirect
416. #1889C2×C37semidirect
429. H(3,𝔽4)C4×C37semidirect
431. #560C4×C37semidirect
433. #551C4×C37semidirect
438. D42C4×C37semidirect
448. #518C22×C37semidirect
450. C2×#100C22×C37semidirect
452. C2×#99C22×C37semidirect
453. C2×#99C22×C37semidirect
464. C37#12753direct (N × H)
576. C24C22⋊C4×C37semidirect
583. C2×Q8C22⋊C4×C37semidirect
614. C2×D4C22⋊C4×C37semidirect
631. C22×C4C22⋊C4×C37semidirect
681. C22⋊C4C22⋊C4×C37semidirect
682. C22⋊C4C22⋊C4×C37semidirect
686. C42C22⋊C4×C37semidirect
687. C42C22⋊C4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35322
C37×#21272
C37×#21212
C2×C37×AΣL(1,𝔽16)2
C37×#19132
C37×#19112
C37×#18892
#1275337