Finite Group Databasebeta

← C37×#24037 #22645290

Subgroups — C37×#24037 #22645290

Order 9472.

1462 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
1C2×C37×#546C211yesmaximal, characteristic
2C2×C37×#482C211yesmaximal, characteristic, complemented
3C2×C37×#416C211yesmaximal, characteristic, complemented
4C37×#2485C211yesmaximal, characteristic, complemented
5C37×#2042C211yesmaximal, characteristic, complemented
6C37×#2042C211yesmaximal, characteristic, complemented
7C37×#2036C211yesmaximal, characteristic, complemented
8C37×#2035C211yesmaximal, characteristic, complemented
9C37×#1893C211yesmaximal, characteristic, complemented
10C37×#1869C211yesmaximal, characteristic, complemented
11C37×#1864C211yesmaximal, characteristic, complemented
12C37×#1862C211yesmaximal, characteristic, complemented
13C37×#1788C211yesmaximal, characteristic, complemented
14C37×#1786C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C23×C8×C37C2211yescharacteristic, complemented
19C37×#546—24no—
20C37×#546—24no—
21C2×#124×C37C2211yescharacteristic
22C2×#123×C37—21no—
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×#121×C37—21no—
25C2×#121×C37C2211yescharacteristic
26C2×#120×C37—21no—
27C2×C4×D4×C37C2211yescharacteristic
28C2×C4×D4×C37C2211yescharacteristic
29C2×#117×C37C2211yescharacteristic, complemented
30C22×C22⋊C4×C37—21no—
31C37×#482—24no—
32C2×#107×C37C2211yescharacteristic, complemented
33C2×#106×C37C2211yescharacteristic, complemented
34C37×#416—24no—
35C2×#103×C37C2211yescharacteristic, complemented
36C2×#103×C37C2211yescharacteristic, complemented
37C2×#103×C37C2211yescharacteristic, complemented
38C2×#103×C37C2211yescharacteristic, complemented
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C2×C22⋊C8×C37C2211yescharacteristic, complemented
50C37×#397—21no—
51C37×#394—21no—
52C37×#389C2211yescharacteristic, complemented
53C37×#389C2211yescharacteristic, complemented
54C37×#388—21no—
55C37×#387—21no—
56C37×#380C2211yescharacteristic
57C37×#380C2211yescharacteristic
58C37×#380C2211yescharacteristic, complemented
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#336C2211yescharacteristic, complemented
62C37×#336C2211yescharacteristic, complemented
63C25×C37—21no—
64C2×#41×C37—22no—
65C2×#41×C37—22no—
66C2×#41×C37—22no—
67C2×#41×C37—41no—
68C2×#41×C37—41no—
69C2×#41×C37D414yes—
70C22×Q8×C37C2311yescharacteristic
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—22no—
74C22×D4×C37—22no—
75C22×D4×C37—22no—
76C22×D4×C37—22no—
77C22×D4×C37—21no—
78C22×D4×C37—41no—
79C22×D4×C37—41no—
80C22×D4×C37D411yescharacteristic
81C22×D4×C37C2311yescharacteristic
82C22×D4×C37C2311yescharacteristic
83C23×C4×C37—21no—
84C23×C4×C37—21no—
85C23×C4×C37C2311yescharacteristic
86C23×C4×C37C2311yescharacteristic
87C22×C8×C37—22no—
88C22×C8×C37—41no—
89C22×C8×C37—41no—
90C22×C8×C37C2311yescharacteristic
91C22×C8×C37C2311yescharacteristic
92C22×C8×C37C2311yescharacteristic
93C22×C8×C37C2311yescharacteristic
94#124×C37—22no—
95#124×C37—22no—
96#123×C37—28no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—22no—
99#121×C37—28no—
100#121×C37—22no—
101#121×C37D414yes—
102#120×C37—28no—
103C4×D4×C37—22no—
104C4×D4×C37—22no—
105C4×D4×C37—22no—
106C4×D4×C37—22no—
107#117×C37—22no—
108#117×C37—22no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37D411yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C4⋊C4×C37C2311yescharacteristic
118C2×C22⋊C4×C37—28no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37D411yescharacteristic
129C2×C22⋊C4×C37D411yescharacteristic
130C2×C42×C37—21no—
131C2×C42×C37C2311yescharacteristic
132#107×C37—22no—
133#106×C37—22no—
134#103×C37—22no—
135#103×C37—22no—
136#103×C37—41no—
137#103×C37—41no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—22no—
144#102×C37—41no—
145#102×C37—41no—
146C22⋊C8×C37—22no—
147C22⋊C8×C37—41no—
148C22⋊C8×C37—41no—
149#95×C37—21no—
150#95×C37—21no—
151#95×C37—21no—
152#95×C37—21no—
153#95×C37—21no—
154C24×C37—21no—
155C24×C37—24no—
156C24×C37—21no—
157C24×C37—42no—
158C24×C37—42no—
159C24×C37—42no—
160C24×C37—42no—
161C24×C37—81no—
162C24×C37—81no—
163C24×C37C2×D411yescharacteristic
164C24×C37C2×D411yescharacteristic
165#41×C37—28no—
166#41×C37—44no—
167#41×C37—44no—
168#41×C37—44no—
169C2×Q8×C37—21no—
170C2×Q8×C37—21no—
171C2×Q8×C37—21no—
172C2×Q8×C37—21no—
173C2×Q8×C37—21no—
174C2×Q8×C37C2×D412yes—
175C2×D4×C37—24no—
176C2×D4×C37—22no—
177C2×D4×C37—24no—
178C2×D4×C37—22no—
179C2×D4×C37—24no—
180C2×D4×C37—21no—
181C2×D4×C37—21no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—21no—
186C2×D4×C37—21no—
187C2×D4×C37—21no—
188C2×D4×C37—41no—
189C2×D4×C37—42no—
190C2×D4×C37—42no—
191C2×D4×C37—44no—
192C2×D4×C37—44no—
193C2×D4×C37—44no—
194C2×D4×C37—42no—
195C2×D4×C37—42no—
196C2×D4×C37—44no—
197C2×D4×C37—81no—
198C2×D4×C37—81no—
199C2×D4×C37C2×D412yes—
200C2×D4×C37C2×D412yes—
201C2×D4×C37#4112yes—
202C2×D4×C37#4112yes—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—21no—
208C22×C4×C37—21no—
209C22×C4×C37—24no—
210C22×C4×C37—24no—
211C22×C4×C37—21no—
212C22×C4×C37—21no—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
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—42no—
222C22×C4×C37—42no—
223C22×C4×C37—81no—
224C22×C4×C37—81no—
225C22×C4×C37C2×D411yescharacteristic
226C22×C4×C37C2×D411yescharacteristic
227C22×C4×C37C2×D411yescharacteristic
228C22×C4×C37C2×D411yescharacteristic
229C22×C4×C37C2×D412yes—
230C22×C4×C37C2×D412yes—
231C22×C4×C37C2411yescharacteristic
232C2×C8×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—21no—
235C2×C8×C37—21no—
236C2×C8×C37—21no—
237C2×C8×C37—21no—
238C2×C8×C37—21no—
239C2×C8×C37—21no—
240C2×C8×C37—21no—
241C2×C8×C37—21no—
242C2×C8×C37—21no—
243C2×C8×C37—21no—
244C2×C8×C37—44no—
245C4⋊C4×C37—24no—
246C4⋊C4×C37—22no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—21no—
251C4⋊C4×C37—21no—
252C4⋊C4×C37—21no—
253C4⋊C4×C37—21no—
254C4⋊C4×C37—21no—
255C4⋊C4×C37—21no—
256C4⋊C4×C37—42no—
257C4⋊C4×C37—81no—
258C4⋊C4×C37C2×D412yes—
259C22⋊C4×C37—24no—
260C22⋊C4×C37—24no—
261C22⋊C4×C37—24no—
262C22⋊C4×C37—24no—
263C22⋊C4×C37—22no—
264C22⋊C4×C37—22no—
265C22⋊C4×C37—24no—
266C22⋊C4×C37—42no—
267C22⋊C4×C37—42no—
268C22⋊C4×C37—81no—
269C22⋊C4×C37—81no—
270C42×C37—21no—
271C42×C37—21no—
272C42×C37—42no—
273C23×C37—21no—
274C23×C37—22no—
275C23×C37—21no—
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—21no—
279C23×C37—22no—
280C23×C37—22no—
281C23×C37—21no—
282C23×C37—21no—
283C23×C37—21no—
284C23×C37—21no—
285C23×C37—21no—
286C23×C37—21no—
287C23×C37—21no—
288C23×C37—22no—
289C23×C37—48no—
290C23×C37—48no—
291C23×C37—41no—
292C23×C37—41no—
293C23×C37—41no—
294C23×C37—41no—
295C23×C37—41no—
296C23×C37—41no—
297C23×C37—41no—
298C23×C37—41no—
299C23×C37—41no—
300C23×C37—41no—
301C23×C37—84no—
302C23×C37—84no—
303C23×C37—84no—
304C23×C37—84no—
305C23×C37—84no—
306C23×C37#12012yes—
307C23×C37#13512yes—
308C23×C37C22×D411yescharacteristic
309Q8×C37—22no—
310Q8×C37—22no—
311Q8×C37—41no—
312Q8×C37—41no—
313D4×C37—22no—
314D4×C37—22no—
315D4×C37—22no—
316D4×C37—22no—
317D4×C37—22no—
318D4×C37—44no—
319D4×C37—48no—
320D4×C37—48no—
321D4×C37—41no—
322D4×C37—41no—
323D4×C37—84no—
324D4×C37#12314yes—
325C2×C4×C37—21no—
326C2×C4×C37—21no—
327C2×C4×C37—22no—
328C2×C4×C37—22no—
329C2×C4×C37—22no—
330C2×C4×C37—22no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—22no—
334C2×C4×C37—22no—
335C2×C4×C37—21no—
336C2×C4×C37—21no—
337C2×C4×C37—21no—
338C2×C4×C37—21no—
339C2×C4×C37—21no—
340C2×C4×C37—21no—
341C2×C4×C37—21no—
342C2×C4×C37—48no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37—41no—
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—41no—
356C2×C4×C37—41no—
357C2×C4×C37—41no—
358C2×C4×C37—41no—
359C2×C4×C37—41no—
360C2×C4×C37—41no—
361C2×C4×C37—41no—
362C2×C4×C37—41no—
363C2×C4×C37—84no—
364C2×C4×C37#12012yes—
365C2×C4×C37C22×D411yescharacteristic
366C2×C4×C37C22×D411yescharacteristic
367C2×C4×C37C2×#4111yescharacteristic
368C2×C4×C37C2×#4111yescharacteristic
369C2×C4×C37H(5,𝔽2)11yescharacteristic
370C2×C4×C37H(5,𝔽2)11yescharacteristic
371C8×C37—41no—
372C8×C37—41no—
373C8×C37—41no—
374C8×C37—41no—
375#24037C3711yesmaximal, characteristic, direct product factor, Sylow
376C22×C37—22no—
377C22×C37—24no—
378C22×C37—22no—
379C22×C37—22no—
380C22×C37—22no—
381C22×C37—22no—
382C22×C37—22no—
383C22×C37—41no—
384C22×C37—42no—
385C22×C37—42no—
386C22×C37—41no—
387C22×C37—41no—
388C22×C37—42no—
389C22×C37—41no—
390C22×C37—42no—
391C22×C37—41no—
392C22×C37—41no—
393C22×C37—42no—
394C22×C37—41no—
395C22×C37—41no—
396C22×C37—42no—
397C22×C37—42no—
398C22×C37—42no—
399C22×C37—42no—
400C22×C37—816no—
401C22×C37—81no—
402C22×C37—81no—
403C22×C37—81no—
404C22×C37—81no—
405C22×C37C2×#12011yescharacteristic
406C22×C37#54611yescharacteristic
407C22×C37#54611yescharacteristic
408C22×C37C2×#13511yescharacteristic
409C22×C37#57511yescharacteristic
410C22×C37#57611yescharacteristic
411C22×C37#57711yescharacteristic
412C4×C37—22no—
413C4×C37—41no—
414C4×C37—42no—
415C4×C37—41no—
416C4×C37—41no—
417C4×C37—42no—
418C4×C37—81no—
419C4×C37—81no—
420C4×C37—81no—
421C4×C37—81no—
422C4×C37C2×#12311yescharacteristic
423C4×C37#53411yescharacteristic
424C4×C37#54611yescharacteristic
425C4×C37#54611yescharacteristic
426C2×#546C2×C3711yescharacteristic
427C2×#482C2×C3711yescharacteristic, complemented
428C2×#416C2×C3711yescharacteristic, complemented
429#2485C2×C3711yescharacteristic, complemented
430#2042C2×C3711yescharacteristic, complemented
431#2042C2×C3711yescharacteristic, complemented
432#2036C2×C3711yescharacteristic, complemented
433#2035C2×C3711yescharacteristic, complemented
434#1893C2×C3711yescharacteristic, complemented
435#1869C2×C3711yescharacteristic, complemented
436#1864C2×C3711yescharacteristic, complemented
437#1862C2×C3711yescharacteristic, complemented
438#1788C2×C3711yescharacteristic, complemented
439#1786C2×C3711yescharacteristic, complemented
440#1786C2×C3711yescharacteristic, complemented
441C2×C37—42no—
442C2×C37—42no—
443C2×C37—44no—
444C2×C37—82no—
445C2×C37#240511yescharacteristic
446C2×C37#300211yescharacteristic
447C2×C37#301211yescharacteristic
448C2×C37#329611yescharacteristic
449C2×C37#329711yescharacteristic
450C2×C37#331111yescharacteristic
451C2×C37#331911yescharacteristic
452C22×#41C22×C3711yescharacteristic
453C23×D4C22×C3711yescharacteristic
454C23×C8C22×C3711yescharacteristic, complemented
455#546—24no—
456#546—24no—
457C2×#124C22×C3711yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C22×C3711yescharacteristic
460C2×#121—21no—
461C2×#121C22×C3711yescharacteristic
462C2×#120—21no—
463C2×C4×D4C22×C3711yescharacteristic
464C2×C4×D4C22×C3711yescharacteristic
465C2×#117C22×C3711yescharacteristic, complemented
466C22×C22⋊C4—21no—
467#482—24no—
468C2×#107C22×C3711yescharacteristic, complemented
469C2×#106C22×C3711yescharacteristic, complemented
470#416—24no—
471C2×#103C22×C3711yescharacteristic, complemented
472C2×#103C22×C3711yescharacteristic, complemented
473C2×#103C22×C3711yescharacteristic, complemented
474C2×#103C22×C3711yescharacteristic, complemented
475C2×#102C22×C3711yescharacteristic
476C2×#102C22×C3711yescharacteristic
477C2×#102C22×C3711yescharacteristic
478C2×#102C22×C3711yescharacteristic
479C2×#102C22×C3711yescharacteristic
480C2×#102C22×C3711yescharacteristic
481C2×#102C22×C3711yescharacteristic
482C2×#102C22×C3711yescharacteristic
483C2×C22⋊C8C22×C3711yescharacteristic
484C2×C22⋊C8C22×C3711yescharacteristic
485C2×C22⋊C8C22×C3711yescharacteristic, complemented
486#397—21no—
487#394—21no—
488#389C22×C3711yescharacteristic, complemented
489#389C22×C3711yescharacteristic, complemented
490#388—21no—
491#387—21no—
492#380C22×C3711yescharacteristic
493#380C22×C3711yescharacteristic
494#380C22×C3711yescharacteristic, complemented
495#340C22×C3711yescharacteristic, complemented
496#340C22×C3711yescharacteristic, complemented
497#336C22×C3711yescharacteristic, complemented
498#336C22×C3711yescharacteristic, complemented
499C37#2403711yescharacteristic, direct product factor, Sylow
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C3714yes—
507C22×Q8C23×C3711yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4D4×C3711yescharacteristic
518C22×D4C23×C3711yescharacteristic
519C22×D4C23×C3711yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C3711yescharacteristic
523C23×C4C23×C3711yescharacteristic
524C22×C8—22no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8C23×C3711yescharacteristic
528C22×C8C23×C3711yescharacteristic
529C22×C8C23×C3711yescharacteristic
530C22×C8C23×C3711yescharacteristic
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536#121—28no—
537#121—22no—
538#121D4×C3714yes—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C3711yescharacteristic
550C2×C4⋊C4C23×C3711yescharacteristic
551C2×C4⋊C4C23×C3711yescharacteristic
552C2×C4⋊C4C23×C3711yescharacteristic
553C2×C4⋊C4C23×C3711yescharacteristic
554C2×C4⋊C4C23×C3711yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C3711yescharacteristic
566C2×C22⋊C4D4×C3711yescharacteristic
567C2×C42—21no—
568C2×C42C23×C3711yescharacteristic
569#107—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—41no—
585C22⋊C8—41no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—21no—
592C24—24no—
593C24—21no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C3711yescharacteristic
601C24C2×D4×C3711yescharacteristic
602#41—28no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C3712yes—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—41no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C3712yes—
637C2×D4C2×D4×C3712yes—
638C2×D4#41×C3712yes—
639C2×D4#41×C3712yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—24no—
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—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C3711yescharacteristic
663C22×C4C2×D4×C3711yescharacteristic
664C22×C4C2×D4×C3711yescharacteristic
665C22×C4C2×D4×C3711yescharacteristic
666C22×C4C2×D4×C3712yes—
667C22×C4C2×D4×C3712yes—
668C22×C4C24×C3711yescharacteristic
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—44no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C3712yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—24no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—21no—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—48no—
727C23—48no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23#120×C3712yes—
744C23#135×C3712yes—
745C23C22×D4×C3711yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—44no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#123×C3714yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4#120×C3712yes—
802C2×C4C22×D4×C3711yescharacteristic
803C2×C4C22×D4×C3711yescharacteristic
804C2×C4C2×#41×C3711yescharacteristic
805C2×C4C2×#41×C3711yescharacteristic
806C2×C4H(5,𝔽2)×C3711yescharacteristic
807C2×C4H(5,𝔽2)×C3711yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#120×C3711yescharacteristic
842C22C37×#54611yescharacteristic
843C22C37×#54611yescharacteristic
844C22C2×#135×C3711yescharacteristic
845C22C37×#57511yescharacteristic
846C22C37×#57611yescharacteristic
847C22C37×#57711yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×#123×C3711yescharacteristic
859C4C37×#53411yescharacteristic
860C4C37×#54611yescharacteristic
861C4C37×#54611yescharacteristic
862C2—42no—
863C2—42no—
864C2—44no—
865C2—82no—
866C2C37×#240511yescharacteristic
867C2C37×#300211yescharacteristic
868C2C37×#301211yescharacteristic
869C2C37×#329611yescharacteristic
870C2C37×#329711yescharacteristic
871C2C37×#331111yescharacteristic
872C2C37×#331911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#482C2semidirect
3. C2×C37×#416C2semidirect
4. C37×#2485C2semidirect
5. C37×#2042C2semidirect
6. C37×#2042C2semidirect
7. C37×#2036C2semidirect
8. C37×#2035C2semidirect
9. C37×#1893C2semidirect
10. C37×#1869C2semidirect
11. C37×#1864C2semidirect
12. C37×#1862C2semidirect
13. C37×#1788C2semidirect
14. C37×#1786C2semidirect
15. C37×#1786C2semidirect
18. C23×C8×C37C22semidirect
29. C2×#117×C37C22semidirect
32. C2×#107×C37C22semidirect
33. C2×#106×C37C22semidirect
35. C2×#103×C37C22semidirect
36. C2×#103×C37C22semidirect
37. C2×#103×C37C22semidirect
38. C2×#103×C37C22semidirect
49. C2×C22⋊C8×C37C22semidirect
52. C37×#389C22semidirect
53. C37×#389C22semidirect
58. C37×#380C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#336C22semidirect
62. C37×#336C22semidirect
375. #24037C37direct (N × H)
427. C2×#482C2×C37semidirect
428. C2×#416C2×C37semidirect
429. #2485C2×C37semidirect
430. #2042C2×C37semidirect
431. #2042C2×C37semidirect
432. #2036C2×C37semidirect
433. #2035C2×C37semidirect
434. #1893C2×C37semidirect
435. #1869C2×C37semidirect
436. #1864C2×C37semidirect
437. #1862C2×C37semidirect
438. #1788C2×C37semidirect
439. #1786C2×C37semidirect
440. #1786C2×C37semidirect
454. C23×C8C22×C37semidirect
465. C2×#117C22×C37semidirect
468. C2×#107C22×C37semidirect
469. C2×#106C22×C37semidirect
471. C2×#103C22×C37semidirect
472. C2×#103C22×C37semidirect
473. C2×#103C22×C37semidirect
474. C2×#103C22×C37semidirect
485. C2×C22⋊C8C22×C37semidirect
488. #389C22×C37semidirect
489. #389C22×C37semidirect
494. #380C22×C37semidirect
495. #340C22×C37semidirect
496. #340C22×C37semidirect
497. #336C22×C37semidirect
498. #336C22×C37semidirect
499. C37#24037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5462
C2×C37×#4822
C2×C37×#4162
C37×#24852
C37×#20422
C37×#20362
C37×#20352
C37×#18932
C37×#18692
C37×#18642
C37×#18622
C37×#17882
C37×#17862
#2403737