Finite Group Databasebeta

← C37×#16391 #22637644

Subgroups — C37×#16391 #22637644

Order 9472.

2702 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#397C211yesmaximal, characteristic, complemented
2C2×C37×#379C212yesmaximal
3C2×C37×#379C211yesmaximal, characteristic
4C37×#1440C212yesmaximal, complemented
5C37×#1440C212yesmaximal, complemented
6C37×#1440C212yesmaximal, complemented
7C37×#1439C212yesmaximal, complemented
8C37×#1439C212yesmaximal, complemented
9C37×#1439C211yesmaximal, characteristic, complemented
10C26×C37C2211yescharacteristic
11C22×C4⋊C4×C37C2211yescharacteristic, complemented
12C22×C4⋊C4×C37C2211yescharacteristic, complemented
13C22×C22⋊C4×C37C2212yes—
14C22×C22⋊C4×C37C2212yes—
15C22×C22⋊C4×C37C2212yes—
16C22×C22⋊C4×C37C2212yes—
17C22×C22⋊C4×C37C2212yes—
18C22×C22⋊C4×C37C2212yes—
19C22×C22⋊C4×C37C2212yes—
20C22×C22⋊C4×C37C2212yes—
21C22×C22⋊C4×C37C2211yescharacteristic
22C22×C22⋊C4×C37C2211yescharacteristic
23C37×#397—24no—
24C37×#379—28no—
25C37×#379—24no—
26C2×#95×C37C2212yescomplemented
27C2×#95×C37C2211yescharacteristic, complemented
28C2×#95×C37C2212yescomplemented
29C2×#95×C37C2212yescomplemented
30C2×#95×C37C2212yescomplemented
31C2×#95×C37C2212yescomplemented
32C2×#95×C37C2211yescharacteristic, complemented
33C2×#95×C37C2212yescomplemented
34C25×C37—22no—
35C25×C37—22no—
36C25×C37—24no—
37C25×C37—24no—
38C25×C37—41no—
39C25×C37—42no—
40C25×C37—42no—
41C25×C37—41no—
42C25×C37—41no—
43C25×C37—41no—
44C25×C37D414yes—
45C25×C37C2311yescharacteristic
46C25×C37C2312yes—
47C23×C4×C37C2312yes—
48C23×C4×C37C2312yes—
49C23×C4×C37C2312yes—
50C23×C4×C37C2312yes—
51C23×C4×C37C2312yes—
52C23×C4×C37C2311yescharacteristic
53C23×C4×C37C2311yescharacteristic
54C2×C4⋊C4×C37—22no—
55C2×C4⋊C4×C37—41no—
56C2×C4⋊C4×C37—41no—
57C2×C4⋊C4×C37—41no—
58C2×C4⋊C4×C37—42no—
59C2×C22⋊C4×C37—24no—
60C2×C22⋊C4×C37—22no—
61C2×C22⋊C4×C37—24no—
62C2×C22⋊C4×C37—24no—
63C2×C22⋊C4×C37—24no—
64C2×C22⋊C4×C37—24no—
65C2×C22⋊C4×C37—24no—
66C2×C22⋊C4×C37—24no—
67C2×C22⋊C4×C37—24no—
68C2×C22⋊C4×C37—24no—
69C2×C22⋊C4×C37—24no—
70C2×C22⋊C4×C37—24no—
71C2×C22⋊C4×C37—24no—
72C2×C22⋊C4×C37—24no—
73C2×C22⋊C4×C37—24no—
74C2×C22⋊C4×C37—41no—
75C2×C22⋊C4×C37—41no—
76C2×C22⋊C4×C37—42no—
77C2×C22⋊C4×C37—42no—
78C2×C22⋊C4×C37—42no—
79C2×C22⋊C4×C37—42no—
80C2×C22⋊C4×C37—42no—
81C2×C22⋊C4×C37—42no—
82C2×C22⋊C4×C37—41no—
83C2×C22⋊C4×C37—41no—
84C2×C22⋊C4×C37—42no—
85C2×C22⋊C4×C37—42no—
86C2×C22⋊C4×C37—42no—
87C2×C22⋊C4×C37—42no—
88C2×C22⋊C4×C37D414yes—
89#95×C37—22no—
90#95×C37—24no—
91#95×C37—42no—
92#95×C37—41no—
93#95×C37—42no—
94#95×C37—42no—
95#95×C37—42no—
96#95×C37—42no—
97C24×C37—22no—
98C24×C37—22no—
99C24×C37—22no—
100C24×C37—22no—
101C24×C37—22no—
102C24×C37—22no—
103C24×C37—21no—
104C24×C37—21no—
105C24×C37—22no—
106C24×C37—22no—
107C24×C37—22no—
108C24×C37—22no—
109C24×C37—22no—
110C24×C37—22no—
111C24×C37—22no—
112C24×C37—22no—
113C24×C37—21no—
114C24×C37—21no—
115C24×C37—22no—
116C24×C37—22no—
117C24×C37—28no—
118C24×C37—216no—
119C24×C37—48no—
120C24×C37—44no—
121C24×C37—44no—
122C24×C37—48no—
123C24×C37—48no—
124C24×C37—48no—
125C24×C37—48no—
126C24×C37—44no—
127C24×C37—48no—
128C24×C37—44no—
129C24×C37—44no—
130C24×C37—44no—
131C24×C37—44no—
132C24×C37—44no—
133C24×C37—48no—
134C24×C37—48no—
135C24×C37—48no—
136C24×C37—48no—
137C24×C37—48no—
138C24×C37—44no—
139C24×C37—44no—
140C24×C37C2×D412yes—
141C24×C37C2×D412yes—
142C24×C37C2×D414yes—
143C24×C37#4112yes—
144C24×C37#4114yes—
145C24×C37#4114yes—
146C24×C37C2411yescharacteristic
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—21no—
150C22×C4×C37—22no—
151C22×C4×C37—21no—
152C22×C4×C37—21no—
153C22×C4×C37—21no—
154C22×C4×C37—22no—
155C22×C4×C37—22no—
156C22×C4×C37—22no—
157C22×C4×C37—22no—
158C22×C4×C37—22no—
159C22×C4×C37—22no—
160C22×C4×C37—22no—
161C22×C4×C37—22no—
162C22×C4×C37—22no—
163C22×C4×C37—22no—
164C22×C4×C37—22no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—22no—
168C22×C4×C37—22no—
169C22×C4×C37—22no—
170C22×C4×C37—22no—
171C22×C4×C37—22no—
172C22×C4×C37—22no—
173C22×C4×C37—22no—
174C22×C4×C37—22no—
175C22×C4×C37—22no—
176C22×C4×C37—22no—
177C22×C4×C37—22no—
178C22×C4×C37—22no—
179C22×C4×C37—22no—
180C22×C4×C37—22no—
181C22×C4×C37—22no—
182C22×C4×C37—22no—
183C22×C4×C37—22no—
184C22×C4×C37—22no—
185C22×C4×C37—22no—
186C22×C4×C37—22no—
187C22×C4×C37—22no—
188C22×C4×C37—22no—
189C22×C4×C37—22no—
190C22×C4×C37C2×D412yes—
191C22×C4×C37C2×D412yes—
192C4⋊C4×C37—44no—
193C4⋊C4×C37—44no—
194C22⋊C4×C37—44no—
195C22⋊C4×C37—48no—
196C22⋊C4×C37—48no—
197C22⋊C4×C37—48no—
198C22⋊C4×C37—48no—
199C22⋊C4×C37—48no—
200C22⋊C4×C37—48no—
201C22⋊C4×C37—44no—
202C22⋊C4×C37—48no—
203C22⋊C4×C37—48no—
204C23×C37—24no—
205C23×C37—24no—
206C23×C37—24no—
207C23×C37—22no—
208C23×C37—24no—
209C23×C37—24no—
210C23×C37—24no—
211C23×C37—24no—
212C23×C37—22no—
213C23×C37—22no—
214C23×C37—24no—
215C23×C37—22no—
216C23×C37—22no—
217C23×C37—22no—
218C23×C37—24no—
219C23×C37—24no—
220C23×C37—24no—
221C23×C37—24no—
222C23×C37—24no—
223C23×C37—24no—
224C23×C37—24no—
225C23×C37—24no—
226C23×C37—24no—
227C23×C37—24no—
228C23×C37—24no—
229C23×C37—24no—
230C23×C37—24no—
231C23×C37—24no—
232C23×C37—24no—
233C23×C37—24no—
234C23×C37—432no—
235C23×C37—416no—
236C23×C37—416no—
237C23×C37—432no—
238C23×C37—416no—
239C23×C37—432no—
240C23×C37—416no—
241C23×C37—432no—
242C23×C37—416no—
243C23×C37—416no—
244C23×C37—416no—
245C23×C37—42no—
246C23×C37—42no—
247C23×C37—42no—
248C23×C37—42no—
249C23×C37—42no—
250C23×C37—42no—
251C23×C37—42no—
252C23×C37—42no—
253C23×C37—42no—
254C23×C37—42no—
255C23×C37—42no—
256C23×C37—42no—
257C23×C37—42no—
258C23×C37—42no—
259C23×C37—42no—
260C23×C37—42no—
261C23×C37—41no—
262C23×C37—42no—
263C23×C37—41no—
264C23×C37—42no—
265C23×C37—42no—
266C23×C37—42no—
267C23×C37—41no—
268C23×C37—42no—
269C23×C37—41no—
270C23×C37—42no—
271C23×C37#12114yes—
272C23×C37#12318yes—
273C23×C37C22×D411yescharacteristic
274C23×C37C22×D411yescharacteristic
275C23×C37C2×#4111yescharacteristic
276C23×C37C2×#4112yes—
277C23×C37C2×#4112yes—
278C23×C37H(5,𝔽2)11yescharacteristic
279C23×C37H(5,𝔽2)11yescharacteristic
280C23×C37H(5,𝔽2)11yescharacteristic
281C23×C37H(5,𝔽2)11yescharacteristic
282C23×C37H(5,𝔽2)12yes—
283C23×C37H(5,𝔽2)12yes—
284C2×C4×C37—22no—
285C2×C4×C37—22no—
286C2×C4×C37—24no—
287C2×C4×C37—24no—
288C2×C4×C37—42no—
289C2×C4×C37—42no—
290C2×C4×C37—41no—
291C2×C4×C37—41no—
292C2×C4×C37—41no—
293C2×C4×C37—41no—
294C2×C4×C37—42no—
295C2×C4×C37—42no—
296C2×C4×C37—42no—
297C2×C4×C37—42no—
298C2×C4×C37—42no—
299C2×C4×C37—42no—
300C2×C4×C37—42no—
301C2×C4×C37—42no—
302C2×C4×C37—42no—
303C2×C4×C37—42no—
304C2×C4×C37—42no—
305C2×C4×C37—42no—
306C2×C4×C37—42no—
307C2×C4×C37—42no—
308C2×C4×C37—42no—
309C2×C4×C37—42no—
310C2×C4×C37—42no—
311C2×C4×C37—42no—
312C2×C4×C37—42no—
313C2×C4×C37—42no—
314C2×C4×C37—42no—
315C2×C4×C37—42no—
316C2×C4×C37—42no—
317C2×C4×C37—42no—
318C2×C4×C37—42no—
319C2×C4×C37—42no—
320C2×C4×C37—42no—
321C2×C4×C37—42no—
322C2×C4×C37—42no—
323C2×C4×C37—42no—
324C2×C4×C37—42no—
325C2×C4×C37—42no—
326C2×C4×C37—42no—
327C2×C4×C37—42no—
328C2×C4×C37—42no—
329#16391C3711yesmaximal, characteristic, direct product factor, Sylow
330C22×C37—24no—
331C22×C37—28no—
332C22×C37—28no—
333C22×C37—28no—
334C22×C37—28no—
335C22×C37—464no—
336C22×C37—44no—
337C22×C37—44no—
338C22×C37—44no—
339C22×C37—44no—
340C22×C37—42no—
341C22×C37—44no—
342C22×C37—44no—
343C22×C37—44no—
344C22×C37—44no—
345C22×C37—42no—
346C22×C37—44no—
347C22×C37—44no—
348C22×C37—42no—
349C22×C37—44no—
350C22×C37—44no—
351C22×C37—44no—
352C22×C37—42no—
353C22×C37—44no—
354C22×C37—42no—
355C22×C37—42no—
356C22×C37—44no—
357C22×C37C2×#12111yescharacteristic
358C22×C37C2×#12312yes—
359C22×C37#53411yescharacteristic
360C22×C37#53411yescharacteristic
361C22×C37#53411yescharacteristic
362C22×C37#53412yes—
363C22×C37#53511yescharacteristic
364C22×C37#53811yescharacteristic
365C22×C37#53811yescharacteristic
366C22×C37#53812yes—
367C22×C37#53812yes—
368C22×C37#53812yes—
369C22×C37#53812yes—
370C22×C37#54612yes—
371C22×C37#54612yes—
372C22×C37#55112yes—
373C22×C37#55112yes—
374C22×C37#55111yescharacteristic
375C22×C37#55112yes—
376C22×C37#55111yescharacteristic
377C22×C37#56012yes—
378C22×C37#56011yescharacteristic
379C22×C37H(3,𝔽4)11yescharacteristic
380C4×C37—42no—
381C4×C37—42no—
382C4×C37—82no—
383C4×C37—82no—
384C4×C37—82no—
385C4×C37—82no—
386C4×C37—82no—
387C2×#397C2×C3711yescharacteristic, complemented
388C2×#379C2×C3712yes—
389C2×#379C2×C3711yescharacteristic
390#1440C2×C3712yescomplemented
391#1440C2×C3712yescomplemented
392#1440C2×C3712yescomplemented
393#1439C2×C3712yescomplemented
394#1439C2×C3712yescomplemented
395#1439C2×C3711yescharacteristic, complemented
396C2×C37—44no—
397C2×C37—48no—
398C2×C37#241212yes—
399C2×C37#248311yescharacteristic
400C2×C37#261711yescharacteristic
401C2×C37#262212yes—
402C2×C37#268411yescharacteristic
403C2×C37#268512yes—
404C2×C37#269711yescharacteristic
405C2×C37#273512yes—
406C2×C37#273511yescharacteristic
407C2×C37#273611yescharacteristic
408C2×C37#281211yescharacteristic
409C26C22×C3711yescharacteristic
410C22×C4⋊C4C22×C3711yescharacteristic, complemented
411C22×C4⋊C4C22×C3711yescharacteristic, complemented
412C22×C22⋊C4C22×C3712yes—
413C22×C22⋊C4C22×C3712yes—
414C22×C22⋊C4C22×C3712yes—
415C22×C22⋊C4C22×C3712yes—
416C22×C22⋊C4C22×C3712yes—
417C22×C22⋊C4C22×C3712yes—
418C22×C22⋊C4C22×C3712yes—
419C22×C22⋊C4C22×C3712yes—
420C22×C22⋊C4C22×C3711yescharacteristic
421C22×C22⋊C4C22×C3711yescharacteristic
422#397—24no—
423#379—28no—
424#379—24no—
425C2×#95C22×C3712yescomplemented
426C2×#95C22×C3711yescharacteristic, complemented
427C2×#95C22×C3712yescomplemented
428C2×#95C22×C3712yescomplemented
429C2×#95C22×C3712yescomplemented
430C2×#95C22×C3712yescomplemented
431C2×#95C22×C3711yescharacteristic, complemented
432C2×#95C22×C3712yescomplemented
433C37#1639111yescharacteristic, direct product factor, Sylow
434C25—22no—
435C25—22no—
436C25—24no—
437C25—24no—
438C25—41no—
439C25—42no—
440C25—42no—
441C25—41no—
442C25—41no—
443C25—41no—
444C25D4×C3714yes—
445C25C23×C3711yescharacteristic
446C25C23×C3712yes—
447C23×C4C23×C3712yes—
448C23×C4C23×C3712yes—
449C23×C4C23×C3712yes—
450C23×C4C23×C3712yes—
451C23×C4C23×C3712yes—
452C23×C4C23×C3711yescharacteristic
453C23×C4C23×C3711yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—42no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—41no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—41no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4D4×C3714yes—
489#95—22no—
490#95—24no—
491#95—42no—
492#95—41no—
493#95—42no—
494#95—42no—
495#95—42no—
496#95—42no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—21no—
504C24—21no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—21no—
514C24—21no—
515C24—22no—
516C24—22no—
517C24—28no—
518C24—216no—
519C24—48no—
520C24—44no—
521C24—44no—
522C24—48no—
523C24—48no—
524C24—48no—
525C24—48no—
526C24—44no—
527C24—48no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—48no—
534C24—48no—
535C24—48no—
536C24—48no—
537C24—48no—
538C24—44no—
539C24—44no—
540C24C2×D4×C3712yes—
541C24C2×D4×C3712yes—
542C24C2×D4×C3714yes—
543C24#41×C3712yes—
544C24#41×C3714yes—
545C24#41×C3714yes—
546C24C24×C3711yescharacteristic
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4C2×D4×C3712yes—
591C22×C4C2×D4×C3712yes—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—44no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—432no—
635C23—416no—
636C23—416no—
637C23—432no—
638C23—416no—
639C23—432no—
640C23—416no—
641C23—432no—
642C23—416no—
643C23—416no—
644C23—416no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—41no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23#121×C3714yes—
672C23#123×C3718yes—
673C23C22×D4×C3711yescharacteristic
674C23C22×D4×C3711yescharacteristic
675C23C2×#41×C3711yescharacteristic
676C23C2×#41×C3712yes—
677C23C2×#41×C3712yes—
678C23H(5,𝔽2)×C3711yescharacteristic
679C23H(5,𝔽2)×C3711yescharacteristic
680C23H(5,𝔽2)×C3711yescharacteristic
681C23H(5,𝔽2)×C3711yescharacteristic
682C23H(5,𝔽2)×C3712yes—
683C23H(5,𝔽2)×C3712yes—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C22—24no—
730C22—28no—
731C22—28no—
732C22—28no—
733C22—28no—
734C22—464no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—42no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—44no—
746C22—44no—
747C22—42no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—42no—
752C22—44no—
753C22—42no—
754C22—42no—
755C22—44no—
756C22C2×#121×C3711yescharacteristic
757C22C2×#123×C3712yes—
758C22C37×#53411yescharacteristic
759C22C37×#53411yescharacteristic
760C22C37×#53411yescharacteristic
761C22C37×#53412yes—
762C22C37×#53511yescharacteristic
763C22C37×#53811yescharacteristic
764C22C37×#53811yescharacteristic
765C22C37×#53812yes—
766C22C37×#53812yes—
767C22C37×#53812yes—
768C22C37×#53812yes—
769C22C37×#54612yes—
770C22C37×#54612yes—
771C22C37×#55112yes—
772C22C37×#55112yes—
773C22C37×#55111yescharacteristic
774C22C37×#55112yes—
775C22C37×#55111yescharacteristic
776C22C37×#56012yes—
777C22C37×#56011yescharacteristic
778C22C37×H(3,𝔽4)11yescharacteristic
779C4—42no—
780C4—42no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C2—44no—
787C2—48no—
788C2C37×#241212yes—
789C2C37×#248311yescharacteristic
790C2C37×#261711yescharacteristic
791C2C37×#262212yes—
792C2C37×#268411yescharacteristic
793C2C37×#268512yes—
794C2C37×#269711yescharacteristic
795C2C37×#273512yes—
796C2C37×#273511yescharacteristic
797C2C37×#273611yescharacteristic
798C2C37×#281211yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutator, Frattini, cosocleC24C24×C37
prime radicalC26×C37C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#397C2semidirect
4. C37×#1440C2semidirect
5. C37×#1440C2semidirect
6. C37×#1440C2semidirect
7. C37×#1439C2semidirect
8. C37×#1439C2semidirect
9. C37×#1439C2semidirect
11. C22×C4⋊C4×C37C22semidirect
12. C22×C4⋊C4×C37C22semidirect
26. C2×#95×C37C22semidirect
27. C2×#95×C37C22semidirect
28. C2×#95×C37C22semidirect
29. C2×#95×C37C22semidirect
30. C2×#95×C37C22semidirect
31. C2×#95×C37C22semidirect
32. C2×#95×C37C22semidirect
33. C2×#95×C37C22semidirect
329. #16391C37direct (N × H)
387. C2×#397C2×C37semidirect
390. #1440C2×C37semidirect
391. #1440C2×C37semidirect
392. #1440C2×C37semidirect
393. #1439C2×C37semidirect
394. #1439C2×C37semidirect
395. #1439C2×C37semidirect
410. C22×C4⋊C4C22×C37semidirect
411. C22×C4⋊C4C22×C37semidirect
425. C2×#95C22×C37semidirect
426. C2×#95C22×C37semidirect
427. C2×#95C22×C37semidirect
428. C2×#95C22×C37semidirect
429. C2×#95C22×C37semidirect
430. C2×#95C22×C37semidirect
431. C2×#95C22×C37semidirect
432. C2×#95C22×C37semidirect
433. C37#16391direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#3972
C2×C37×#3792
C37×#14402
C37×#14392
#1639137