Finite Group Databasebeta

← C37×#25587 #22646840

Subgroups — C37×#25587 #22646840

Order 9472.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3505C211yesmaximal, characteristic, complemented
2C37×#2561C211yesmaximal, characteristic, complemented
3C37×#2539C211yesmaximal, characteristic, complemented
4C37×#2534C211yesmaximal, characteristic, complemented
5C37×#2022C212yesmaximal, complemented
6C37×#2021C212yesmaximal, complemented
7C37×#1996C211yesmaximal, characteristic, complemented
8C37×#1964C211yesmaximal, characteristic, complemented
9C37×#1890C212yesmaximal, complemented
10C37×#1889C212yesmaximal, complemented
11C4×#99×C37C211yesmaximal, characteristic, complemented
12C37×#553—22no—
13C37×#553—21no—
14C37×#552—21no—
15C37×#551—22no—
16C37×#548—21no—
17C37×#546—21no—
18C37×#539—21no—
19C37×#538—21no—
20C37×#534C2212yes—
21C37×#529—21no—
22C37×#525—21no—
23C2×#123×C37C2212yes—
24C2×#123×C37C2211yescharacteristic
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×#120×C37C2212yes—
28C2×#120×C37C2211yescharacteristic
29C37×#518C2212yes—
30C2×C4×D4×C37C2211yescharacteristic
31C22×C22⋊C4×C37C2211yescharacteristic
32C2×#99×C37C2212yes—
33C2×#99×C37C2212yes—
34C2×#99×C37C2212yes—
35C37×#399—21no—
36C37×#397—21no—
37C37×#396—21no—
38C37×#394—21no—
39C37×#393—21no—
40C37×#392—21no—
41C37×#390—22no—
42C37×#388—22no—
43C37×#388—21no—
44C37×#386—21no—
45C37×#381C2211yescharacteristic
46C37×#381C2212yes—
47C37×#380C2211yescharacteristic
48C37×#379C2211yescharacteristic
49C37×#379C2212yes—
50C4×C22⋊C4×C37C2211yescharacteristic
51C4×C22⋊C4×C37C2211yescharacteristic
52C37×#342C2212yes—
53C37×#342C2212yes—
54C37×#342C2212yes—
55C25×C37C2311yescharacteristic
56C2×#41×C37—21no—
57C22×Q8×C37D411yescharacteristic, complemented
58C22×D4×C37—21no—
59C22×D4×C37—22no—
60C22×D4×C37D411yescharacteristic, complemented
61C22×D4×C37C2312yes—
62C22×D4×C37C2311yescharacteristic
63C23×C4×C37D411yescharacteristic, complemented
64C23×C4×C37C2311yescharacteristic
65C23×C4×C37C2311yescharacteristic
66#126×C37—22no—
67#126×C37—22no—
68#126×C37—22no—
69#125×C37—21no—
70#125×C37—22no—
71#124×C37—21no—
72#124×C37—22no—
73#123×C37—22no—
74#123×C37—22no—
75#123×C37—22no—
76#123×C37—22no—
77#123×C37—22no—
78#123×C37—24no—
79#123×C37—42no—
80#123×C37—42no—
81C22⋊Q8×C37—21no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—21no—
84C22⋊Q8×C37—21no—
85C22⋊Q8×C37—21no—
86C22⋊Q8×C37—21no—
87#121×C37—21no—
88#121×C37—22no—
89#121×C37—21no—
90#121×C37—21no—
91#121×C37—21no—
92#121×C37—21no—
93#121×C37—22no—
94#121×C37—22no—
95#120×C37—22no—
96#120×C37—22no—
97#120×C37—24no—
98#120×C37—42no—
99#120×C37—42no—
100C4×Q8×C37—21no—
101C4×D4×C37—22no—
102C4×D4×C37—21no—
103C4×D4×C37—22no—
104C4×D4×C37—22no—
105C4×D4×C37—21no—
106C4×D4×C37—21no—
107C4×D4×C37—22no—
108C4×D4×C37—21no—
109C4×D4×C37—21no—
110C4×D4×C37—22no—
111#117×C37—21no—
112#117×C37—22no—
113#117×C37—22no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—22no—
116C2×C4⋊C4×C37—21no—
117C2×C4⋊C4×C37D411yescharacteristic, complemented
118C2×C4⋊C4×C37D412yescomplemented
119C2×C4⋊C4×C37D411yescharacteristic, complemented
120C2×C4⋊C4×C37D411yescharacteristic, complemented
121C2×C22⋊C4×C37—22no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—22no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—22no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—22no—
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—22no—
136C2×C22⋊C4×C37D412yescomplemented
137C2×C22⋊C4×C37D411yescharacteristic, complemented
138C2×C22⋊C4×C37C2311yescharacteristic
139C2×C22⋊C4×C37C2311yescharacteristic
140C2×C22⋊C4×C37C2312yes—
141C2×C22⋊C4×C37C2312yes—
142C2×C22⋊C4×C37C2311yescharacteristic
143C2×C22⋊C4×C37C2312yes—
144C2×C42×C37—21no—
145C2×C42×C37—21no—
146C2×C42×C37D411yescharacteristic, complemented
147#99×C37—24no—
148#99×C37—42no—
149#99×C37—42no—
150#95×C37—21no—
151#95×C37—21no—
152#95×C37—21no—
153#95×C37—21no—
154#95×C37—22no—
155#95×C37—21no—
156#95×C37—22no—
157C24×C37—21no—
158C24×C37—21no—
159C24×C37—21no—
160C24×C37—22no—
161C24×C37—22no—
162C24×C37—42no—
163C24×C37—81no—
164C24×C37C2×D412yes—
165C24×C37C2×D411yescharacteristic
166C24×C37C2411yescharacteristic
167#41×C37—82no—
168C2×Q8×C37—21no—
169C2×Q8×C37—21no—
170C2×Q8×C37—81no—
171C2×D4×C37—21no—
172C2×D4×C37—22no—
173C2×D4×C37—21no—
174C2×D4×C37—22no—
175C2×D4×C37—22no—
176C2×D4×C37—22no—
177C2×D4×C37—22no—
178C2×D4×C37—22no—
179C2×D4×C37—22no—
180C2×D4×C37—22no—
181C2×D4×C37—22no—
182C2×D4×C37—22no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—44no—
186C2×D4×C37—42no—
187C2×D4×C37—44no—
188C2×D4×C37—42no—
189C2×D4×C37—81no—
190C2×D4×C37—82no—
191C2×D4×C37—81no—
192C22×C4×C37—22no—
193C22×C4×C37—22no—
194C22×C4×C37—22no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—22no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—22no—
204C22×C4×C37—22no—
205C22×C4×C37—81no—
206C22×C4×C37—81no—
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D412yes—
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D412yes—
211C22×C4×C37C2×D411yescharacteristic
212C22×C4×C37C2×D412yes—
213C22×C4×C37C2×D411yescharacteristic
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C4⋊C4×C37—22no—
220C4⋊C4×C37—22no—
221C4⋊C4×C37—22no—
222C4⋊C4×C37—22no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—22no—
225C4⋊C4×C37—21no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—22no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—44no—
232C4⋊C4×C37—42no—
233C4⋊C4×C37—81no—
234C22⋊C4×C37—22no—
235C22⋊C4×C37—22no—
236C22⋊C4×C37—22no—
237C22⋊C4×C37—22no—
238C22⋊C4×C37—22no—
239C22⋊C4×C37—22no—
240C22⋊C4×C37—21no—
241C22⋊C4×C37—22no—
242C22⋊C4×C37—21no—
243C22⋊C4×C37—22no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—21no—
247C22⋊C4×C37—21no—
248C22⋊C4×C37—22no—
249C22⋊C4×C37—22no—
250C22⋊C4×C37—22no—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—44no—
254C22⋊C4×C37—44no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—44no—
257C22⋊C4×C37—42no—
258C22⋊C4×C37—42no—
259C22⋊C4×C37—41no—
260C22⋊C4×C37—41no—
261C22⋊C4×C37—41no—
262C22⋊C4×C37—41no—
263C22⋊C4×C37—81no—
264C22⋊C4×C37—82no—
265C22⋊C4×C37#4114yescomplemented
266C42×C37—22no—
267C42×C37—22no—
268C42×C37—21no—
269C42×C37—21no—
270C42×C37—81no—
271C42×C37—81no—
272C23×C37—22no—
273C23×C37—22no—
274C23×C37—22no—
275C23×C37—22no—
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—21no—
279C23×C37—22no—
280C23×C37—22no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37—42no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—42no—
289C23×C37—41no—
290C23×C37—41no—
291C23×C37—41no—
292C23×C37—42no—
293C23×C37—42no—
294C23×C37—41no—
295C23×C37—41no—
296C23×C37—41no—
297C23×C37—42no—
298C23×C37—42no—
299C23×C37—84no—
300C23×C37—84no—
301C23×C37C22×D411yescharacteristic
302C23×C37C22×D411yescharacteristic
303C23×C37C22×D411yescharacteristic
304C23×C37C2×#4112yes—
305C23×C37H(5,𝔽2)12yes—
306Q8×C37—42no—
307Q8×C37—81no—
308D4×C37—42no—
309D4×C37—42no—
310D4×C37—42no—
311D4×C37—42no—
312D4×C37—42no—
313D4×C37—42no—
314D4×C37—42no—
315D4×C37—81no—
316D4×C37—82no—
317D4×C37—82no—
318D4×C37—88no—
319D4×C37—84no—
320C2×C4×C37—21no—
321C2×C4×C37—22no—
322C2×C4×C37—21no—
323C2×C4×C37—21no—
324C2×C4×C37—22no—
325C2×C4×C37—22no—
326C2×C4×C37—21no—
327C2×C4×C37—21no—
328C2×C4×C37—24no—
329C2×C4×C37—22no—
330C2×C4×C37—22no—
331C2×C4×C37—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—42no—
338C2×C4×C37—42no—
339C2×C4×C37—42no—
340C2×C4×C37—41no—
341C2×C4×C37—42no—
342C2×C4×C37—41no—
343C2×C4×C37—42no—
344C2×C4×C37—42no—
345C2×C4×C37—42no—
346C2×C4×C37—41no—
347C2×C4×C37—41no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—41no—
351C2×C4×C37—41no—
352C2×C4×C37—41no—
353C2×C4×C37—41no—
354C2×C4×C37—41no—
355C2×C4×C37—42no—
356C2×C4×C37—42no—
357C2×C4×C37—42no—
358C2×C4×C37—81no—
359C2×C4×C37—82no—
360C2×C4×C37—82no—
361C2×C4×C37#12011yescharacteristic
362C2×C4×C37#12011yescharacteristic
363C2×C4×C37#12011yescharacteristic
364C2×C4×C37#12011yescharacteristic
365#25587C3711yesmaximal, characteristic, direct product factor, Sylow
366C22×C37—21no—
367C22×C37—21no—
368C22×C37—21no—
369C22×C37—21no—
370C22×C37—21no—
371C22×C37—21no—
372C22×C37—42no—
373C22×C37—42no—
374C22×C37—42no—
375C22×C37—44no—
376C22×C37—42no—
377C22×C37—44no—
378C22×C37—42no—
379C22×C37—41no—
380C22×C37—42no—
381C22×C37—42no—
382C22×C37—41no—
383C22×C37—42no—
384C22×C37—41no—
385C22×C37—42no—
386C22×C37—82no—
387C22×C37—82no—
388C22×C37—81no—
389C22×C37—82no—
390C22×C37—81no—
391C22×C37—82no—
392C22×C37—81no—
393C22×C37—81no—
394C22×C37—81no—
395C22×C37C2×#12011yescharacteristic
396C22×C37#53211yescharacteristic
397C22×C37#53511yescharacteristic
398C22×C37#54612yes—
399C22×C37#55012yes—
400C4×C37—21no—
401C4×C37—21no—
402C4×C37—21no—
403C4×C37—21no—
404C4×C37—44no—
405C4×C37—41no—
406C4×C37—42no—
407C4×C37—41no—
408C4×C37—42no—
409C4×C37—41no—
410C4×C37—42no—
411C4×C37—81no—
412C4×C37—82no—
413C4×C37—81no—
414C4×C37—81no—
415#3505C2×C3711yescharacteristic, complemented
416#2561C2×C3711yescharacteristic, complemented
417#2539C2×C3711yescharacteristic, complemented
418#2534C2×C3711yescharacteristic, complemented
419#2022C2×C3712yescomplemented
420#2021C2×C3712yescomplemented
421#1996C2×C3711yescharacteristic, complemented
422#1964C2×C3711yescharacteristic, complemented
423#1890C2×C3712yescomplemented
424#1889C2×C3712yescomplemented
425C4×#99C2×C3711yescharacteristic, complemented
426C2×C37—22no—
427C2×C37—21no—
428C2×C37—22no—
429C2×C37—21no—
430C2×C37—82no—
431C2×C37—81no—
432C2×C37—82no—
433C2×C37#243111yescharacteristic
434C2×C37#302511yescharacteristic
435C2×C37#302611yescharacteristic
436#553—22no—
437#553—21no—
438#552—21no—
439#551—22no—
440#548—21no—
441#546—21no—
442#539—21no—
443#538—21no—
444#534C22×C3712yes—
445#529—21no—
446#525—21no—
447C2×#123C22×C3712yes—
448C2×#123C22×C3711yescharacteristic
449C2×C22⋊Q8C22×C3711yescharacteristic
450C2×#121C22×C3711yescharacteristic
451C2×#120C22×C3712yes—
452C2×#120C22×C3711yescharacteristic
453#518C22×C3712yes—
454C2×C4×D4C22×C3711yescharacteristic
455C22×C22⋊C4C22×C3711yescharacteristic
456C2×#99C22×C3712yes—
457C2×#99C22×C3712yes—
458C2×#99C22×C3712yes—
459#399—21no—
460#397—21no—
461#396—21no—
462#394—21no—
463#393—21no—
464#392—21no—
465#390—22no—
466#388—22no—
467#388—21no—
468#386—21no—
469#381C22×C3712yes—
470#381C22×C3711yescharacteristic
471#380C22×C3711yescharacteristic
472#379C22×C3712yes—
473#379C22×C3711yescharacteristic
474C4×C22⋊C4C22×C3711yescharacteristic
475C4×C22⋊C4C22×C3711yescharacteristic
476#342C22×C3712yes—
477#342C22×C3712yes—
478#342C22×C3712yes—
479C37#2558711yescharacteristic, direct product factor, Sylow
480C25C23×C3711yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C3711yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C3711yescharacteristic, complemented
486C22×D4C23×C3711yescharacteristic
487C22×D4C23×C3712yes—
488C23×C4D4×C3711yescharacteristic, complemented
489C23×C4C23×C3711yescharacteristic
490C23×C4C23×C3711yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C3711yescharacteristic, complemented
543C2×C4⋊C4D4×C3711yescharacteristic, complemented
544C2×C4⋊C4D4×C3712yescomplemented
545C2×C4⋊C4D4×C3711yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
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—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C3711yescharacteristic, complemented
562C2×C22⋊C4D4×C3712yescomplemented
563C2×C22⋊C4C23×C3711yescharacteristic
564C2×C22⋊C4C23×C3711yescharacteristic
565C2×C22⋊C4C23×C3712yes—
566C2×C22⋊C4C23×C3711yescharacteristic
567C2×C22⋊C4C23×C3712yes—
568C2×C22⋊C4C23×C3712yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C3711yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C3712yes—
590C24C2×D4×C3711yescharacteristic
591C24C24×C3711yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C3711yescharacteristic
633C22×C4C2×D4×C3712yes—
634C22×C4C2×D4×C3711yescharacteristic
635C22×C4C2×D4×C3712yes—
636C22×C4C2×D4×C3711yescharacteristic
637C22×C4C2×D4×C3712yes—
638C22×C4C2×D4×C3711yescharacteristic
639C22×C4C2×D4×C3711yescharacteristic
640C22×C4C2×D4×C3711yescharacteristic
641C22×C4C2×D4×C3711yescharacteristic
642C22×C4C2×D4×C3711yescharacteristic
643C22×C4C2×D4×C3711yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C3714yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C3711yescharacteristic
727C23C22×D4×C3711yescharacteristic
728C23C22×D4×C3711yescharacteristic
729C23C2×#41×C3712yes—
730C23H(5,𝔽2)×C3712yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C3711yescharacteristic
787C2×C4#120×C3711yescharacteristic
788C2×C4#120×C3711yescharacteristic
789C2×C4#120×C3711yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C3711yescharacteristic
820C22C37×#53211yescharacteristic
821C22C37×#53511yescharacteristic
822C22C37×#54612yes—
823C22C37×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C37×#243111yescharacteristic
847C2C37×#302511yescharacteristic
848C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
LCSG ▷ C24 ▷ 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×#3505C2semidirect
2. C37×#2561C2semidirect
3. C37×#2539C2semidirect
4. C37×#2534C2semidirect
5. C37×#2022C2semidirect
6. C37×#2021C2semidirect
7. C37×#1996C2semidirect
8. C37×#1964C2semidirect
9. C37×#1890C2semidirect
10. C37×#1889C2semidirect
11. C4×#99×C37C2semidirect
57. C22×Q8×C37D4semidirect
60. C22×D4×C37D4semidirect
63. C23×C4×C37D4semidirect
117. C2×C4⋊C4×C37D4semidirect
118. C2×C4⋊C4×C37D4semidirect
119. C2×C4⋊C4×C37D4semidirect
120. C2×C4⋊C4×C37D4semidirect
136. C2×C22⋊C4×C37D4semidirect
137. C2×C22⋊C4×C37D4semidirect
146. C2×C42×C37D4semidirect
265. C22⋊C4×C37#41semidirect
365. #25587C37direct (N × H)
415. #3505C2×C37semidirect
416. #2561C2×C37semidirect
417. #2539C2×C37semidirect
418. #2534C2×C37semidirect
419. #2022C2×C37semidirect
420. #2021C2×C37semidirect
421. #1996C2×C37semidirect
422. #1964C2×C37semidirect
423. #1890C2×C37semidirect
424. #1889C2×C37semidirect
425. C4×#99C2×C37semidirect
479. C37#25587direct (N × H)
482. C22×Q8D4×C37semidirect
485. C22×D4D4×C37semidirect
488. C23×C4D4×C37semidirect
542. C2×C4⋊C4D4×C37semidirect
543. C2×C4⋊C4D4×C37semidirect
544. C2×C4⋊C4D4×C37semidirect
545. C2×C4⋊C4D4×C37semidirect
561. C2×C22⋊C4D4×C37semidirect
562. C2×C22⋊C4D4×C37semidirect
571. C2×C42D4×C37semidirect
690. C22⋊C4#41×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35052
C37×#25612
C37×#25392
C37×#25342
C37×#20222
C37×#20212
C37×#19962
C37×#19642
C37×#18902
C37×#18892
C4×#99×C372
#2558737