Finite Group Databasebeta

← C37×#24044 #22645297

Subgroups — C37×#24044 #22645297

Order 9472.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C37C211yesmaximal, characteristic
2C2×C37×#482C211yesmaximal, characteristic, complemented
3C2×C37×#418C211yesmaximal, characteristic, complemented
4C37×#2485C211yesmaximal, characteristic, complemented
5C37×#2041C211yesmaximal, characteristic, complemented
6C37×#2041C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#1895C211yesmaximal, characteristic, complemented
10C37×#1870C211yesmaximal, characteristic, complemented
11C37×#1864C211yesmaximal, characteristic, complemented
12C37×#1862C211yesmaximal, characteristic, complemented
13C37×#1786C211yesmaximal, characteristic, complemented
14C37×#1786C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C37—21no—
17C23×D4×C37C2211yescharacteristic
18C23×D4×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic, complemented
20D42×C37—24no—
21D42×C37—24no—
22C2×#127×C37C2211yescharacteristic
23C2×#121×C37—21no—
24C2×#121×C37C2211yescharacteristic
25C2×#121×C37C2211yescharacteristic
26C2×#120×C37—21no—
27C2×#120×C37—21no—
28C2×C4×D4×C37C2211yescharacteristic
29C2×C4×D4×C37C2211yescharacteristic
30C2×#117×C37C2211yescharacteristic, complemented
31C37×#482—24no—
32C2×#107×C37C2211yescharacteristic, complemented
33C2×#106×C37C2211yescharacteristic, complemented
34C37×#418—24no—
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic, complemented
40C2×#102×C37C2211yescharacteristic, complemented
41C2×#102×C37C2211yescharacteristic, complemented
42C2×#102×C37C2211yescharacteristic, complemented
43C2×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×C22⋊C8×C37C2211yescharacteristic, complemented
48C2×C22⋊C8×C37C2211yescharacteristic, complemented
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, complemented
57C37×#380C2211yescharacteristic, complemented
58C37×#380C2211yescharacteristic, complemented
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#336C2211yescharacteristic, complemented
62C37×#336C2211yescharacteristic, complemented
63C25×C37—21no—
64C25×C37—21no—
65C22×D4×C37—22no—
66C22×D4×C37—22no—
67C22×D4×C37—28no—
68C22×D4×C37—21no—
69C22×D4×C37—21no—
70C22×D4×C37—22no—
71C22×D4×C37—22no—
72C22×D4×C37—22no—
73C22×D4×C37—22no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—22no—
78C22×D4×C37—21no—
79C22×D4×C37—41no—
80C22×D4×C37—41no—
81C22×D4×C37—41no—
82C22×D4×C37—41no—
83C22×D4×C37—44no—
84C22×D4×C37—44no—
85C22×D4×C37D411yescharacteristic
86C22×D4×C37D414yes—
87C22×D4×C37C2311yescharacteristic
88C22×D4×C37C2311yescharacteristic
89C22×D4×C37C2311yescharacteristic
90C23×C4×C37—21no—
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C2×M16×C37—22no—
94C2×M16×C37—41no—
95C2×M16×C37—41no—
96C22×C8×C37C2311yescharacteristic
97C22×C8×C37C2311yescharacteristic
98C22×C8×C37C2311yescharacteristic
99C22×C8×C37C2311yescharacteristic
100#127×C37—22no—
101#127×C37—22no—
102#121×C37—28no—
103#121×C37—22no—
104#121×C37—22no—
105#121×C37—22no—
106#121×C37D414yes—
107#120×C37—28no—
108#120×C37—28no—
109C4×D4×C37—22no—
110C4×D4×C37—22no—
111C4×D4×C37—22no—
112C4×D4×C37—22no—
113#117×C37—22no—
114#117×C37—22no—
115C2×C4⋊C4×C37—21no—
116C2×C4⋊C4×C37—21no—
117C2×C4⋊C4×C37D411yescharacteristic
118C2×C4⋊C4×C37C2311yescharacteristic
119C2×C4⋊C4×C37C2311yescharacteristic
120C2×C4⋊C4×C37C2311yescharacteristic
121C2×C4⋊C4×C37C2311yescharacteristic
122C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37D411yescharacteristic
131C2×C22⋊C4×C37D411yescharacteristic
132C2×C42×C37—21no—
133C2×C42×C37C2311yescharacteristic
134#107×C37—22no—
135#106×C37—22no—
136#102×C37—22no—
137#102×C37—22no—
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—
146#102×C37—41no—
147#102×C37—41no—
148C22⋊C8×C37—22no—
149C22⋊C8×C37—41no—
150C22⋊C8×C37—41no—
151#95×C37—21no—
152#95×C37—21no—
153#95×C37—21no—
154#95×C37—21no—
155#95×C37—21no—
156C24×C37—21no—
157C24×C37—24no—
158C24×C37—21no—
159C24×C37—21no—
160C24×C37—24no—
161C24×C37—42no—
162C24×C37—42no—
163C24×C37—42no—
164C24×C37—42no—
165C24×C37—42no—
166C24×C37—42no—
167C24×C37—42no—
168C24×C37—42no—
169C24×C37—81no—
170C24×C37—81no—
171C24×C37—81no—
172C24×C37—81no—
173C24×C37C2×D411yescharacteristic
174C24×C37C2×D411yescharacteristic
175C2×D4×C37—22no—
176C2×D4×C37—22no—
177C2×D4×C37—28no—
178C2×D4×C37—24no—
179C2×D4×C37—24no—
180C2×D4×C37—24no—
181C2×D4×C37—24no—
182C2×D4×C37—24no—
183C2×D4×C37—24no—
184C2×D4×C37—22no—
185C2×D4×C37—21no—
186C2×D4×C37—21no—
187C2×D4×C37—21no—
188C2×D4×C37—21no—
189C2×D4×C37—21no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—21no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—44no—
199C2×D4×C37—44no—
200C2×D4×C37—44no—
201C2×D4×C37—42no—
202C2×D4×C37—42no—
203C2×D4×C37—42no—
204C2×D4×C37—42no—
205C2×D4×C37—42no—
206C2×D4×C37—44no—
207C2×D4×C37—44no—
208C2×D4×C37—432no—
209C2×D4×C37—44no—
210C2×D4×C37—42no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—44no—
215C2×D4×C37—42no—
216C2×D4×C37—81no—
217C2×D4×C37—81no—
218C2×D4×C37C2×D412yes—
219C2×D4×C37C2×D412yes—
220C2×D4×C37C2×D412yes—
221C2×D4×C37#4112yes—
222C2×D4×C37#4112yes—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—24no—
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—42no—
240C22×C4×C37—42no—
241C22×C4×C37C2×D411yescharacteristic
242C22×C4×C37C2×D411yescharacteristic
243C22×C4×C37C2×D411yescharacteristic
244C22×C4×C37C2×D412yes—
245C22×C4×C37C2×D412yes—
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2411yescharacteristic
248M16×C37—44no—
249C2×C8×C37—21no—
250C2×C8×C37—21no—
251C2×C8×C37—21no—
252C2×C8×C37—21no—
253C2×C8×C37—21no—
254C2×C8×C37—21no—
255C2×C8×C37—21no—
256C2×C8×C37—21no—
257C2×C8×C37—21no—
258C2×C8×C37—21no—
259C2×C8×C37—21no—
260C2×C8×C37—21no—
261C4⋊C4×C37—22no—
262C4⋊C4×C37—21no—
263C4⋊C4×C37—21no—
264C4⋊C4×C37—21no—
265C4⋊C4×C37—21no—
266C4⋊C4×C37—21no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37—42no—
272C4⋊C4×C37—81no—
273C4⋊C4×C37C2×D412yes—
274C22⋊C4×C37—24no—
275C22⋊C4×C37—24no—
276C22⋊C4×C37—22no—
277C22⋊C4×C37—24no—
278C22⋊C4×C37—22no—
279C22⋊C4×C37—42no—
280C22⋊C4×C37—42no—
281C22⋊C4×C37—81no—
282C22⋊C4×C37—81no—
283C42×C37—21no—
284C42×C37—21no—
285C42×C37—42no—
286C23×C37—21no—
287C23×C37—22no—
288C23×C37—21no—
289C23×C37—21no—
290C23×C37—21no—
291C23×C37—21no—
292C23×C37—22no—
293C23×C37—22no—
294C23×C37—21no—
295C23×C37—21no—
296C23×C37—21no—
297C23×C37—21no—
298C23×C37—21no—
299C23×C37—21no—
300C23×C37—21no—
301C23×C37—22no—
302C23×C37—22no—
303C23×C37—48no—
304C23×C37—48no—
305C23×C37—48no—
306C23×C37—48no—
307C23×C37—41no—
308C23×C37—41no—
309C23×C37—41no—
310C23×C37—41no—
311C23×C37—41no—
312C23×C37—41no—
313C23×C37—41no—
314C23×C37—41no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37—41no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37—41no—
321C23×C37—41no—
322C23×C37—41no—
323C23×C37—84no—
324C23×C37—84no—
325C23×C37—84no—
326C23×C37—84no—
327C23×C37—84no—
328C23×C37—84no—
329C23×C37—84no—
330C23×C37—84no—
331C23×C37—84no—
332C23×C37—84no—
333C23×C37#12012yes—
334C23×C37AGL(1,ℤ/8)12yes—
335C23×C37C22×D411yescharacteristic
336D4×C37—28no—
337D4×C37—22no—
338D4×C37—22no—
339D4×C37—22no—
340D4×C37—22no—
341D4×C37—22no—
342D4×C37—22no—
343D4×C37—22no—
344D4×C37—48no—
345D4×C37—48no—
346D4×C37—48no—
347D4×C37—48no—
348D4×C37—48no—
349D4×C37—41no—
350D4×C37—41no—
351D4×C37—41no—
352D4×C37—41no—
353D4×C37—84no—
354D4×C37#12314yes—
355C2×C4×C37—21no—
356C2×C4×C37—21no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—22no—
360C2×C4×C37—22no—
361C2×C4×C37—22no—
362C2×C4×C37—22no—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—22no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—21no—
370C2×C4×C37—48no—
371C2×C4×C37—41no—
372C2×C4×C37—41no—
373C2×C4×C37—41no—
374C2×C4×C37—41no—
375C2×C4×C37—41no—
376C2×C4×C37—41no—
377C2×C4×C37—41no—
378C2×C4×C37—41no—
379C2×C4×C37—41no—
380C2×C4×C37—41no—
381C2×C4×C37—41no—
382C2×C4×C37—41no—
383C2×C4×C37—41no—
384C2×C4×C37—41no—
385C2×C4×C37—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37#12012yes—
390C2×C4×C37AGL(1,ℤ/8)12yes—
391C2×C4×C37C22×D411yescharacteristic
392C2×C4×C37C22×D411yescharacteristic
393C2×C4×C37C2×#4111yescharacteristic
394C2×C4×C37C2×#4111yescharacteristic
395C2×C4×C37H(5,𝔽2)11yescharacteristic
396C2×C4×C37H(5,𝔽2)11yescharacteristic
397C8×C37—41no—
398C8×C37—41no—
399C8×C37—41no—
400C8×C37—41no—
401#24044C3711yesmaximal, characteristic, direct product factor, Sylow
402C22×C37—22no—
403C22×C37—24no—
404C22×C37—22no—
405C22×C37—22no—
406C22×C37—22no—
407C22×C37—22no—
408C22×C37—22no—
409C22×C37—41no—
410C22×C37—42no—
411C22×C37—41no—
412C22×C37—42no—
413C22×C37—41no—
414C22×C37—42no—
415C22×C37—41no—
416C22×C37—42no—
417C22×C37—41no—
418C22×C37—41no—
419C22×C37—42no—
420C22×C37—41no—
421C22×C37—41no—
422C22×C37—42no—
423C22×C37—42no—
424C22×C37—42no—
425C22×C37—42no—
426C22×C37—42no—
427C22×C37—42no—
428C22×C37—42no—
429C22×C37—816no—
430C22×C37—816no—
431C22×C37—81no—
432C22×C37—81no—
433C22×C37—81no—
434C22×C37—81no—
435C22×C37—81no—
436C22×C37—81no—
437C22×C37—81no—
438C22×C37—81no—
439C22×C37C2×#12011yescharacteristic
440C22×C37#54611yescharacteristic
441C22×C37#54611yescharacteristic
442C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C37#57611yescharacteristic
445C22×C37#57711yescharacteristic
446C4×C37—22no—
447C4×C37—22no—
448C4×C37—41no—
449C4×C37—42no—
450C4×C37—41no—
451C4×C37—81no—
452C4×C37—81no—
453C4×C37—81no—
454C4×C37—81no—
455C4×C37C2×#12311yescharacteristic
456C4×C37#53411yescharacteristic
457C4×C37#54611yescharacteristic
458C4×C37#54611yescharacteristic
459C2×D42C2×C3711yescharacteristic
460C2×#482C2×C3711yescharacteristic, complemented
461C2×#418C2×C3711yescharacteristic, complemented
462#2485C2×C3711yescharacteristic, complemented
463#2041C2×C3711yescharacteristic, complemented
464#2041C2×C3711yescharacteristic, complemented
465#2034C2×C3711yescharacteristic, complemented
466#2033C2×C3711yescharacteristic, complemented
467#1895C2×C3711yescharacteristic, complemented
468#1870C2×C3711yescharacteristic, complemented
469#1864C2×C3711yescharacteristic, complemented
470#1862C2×C3711yescharacteristic, complemented
471#1786C2×C3711yescharacteristic, complemented
472#1786C2×C3711yescharacteristic, complemented
473#1786C2×C3711yescharacteristic, complemented
474C2×C37—42no—
475C2×C37—42no—
476C2×C37—44no—
477C2×C37—82no—
478C2×C37—82no—
479C2×C37#240511yescharacteristic
480C2×C37#300311yescharacteristic
481C2×C37#301211yescharacteristic
482C2×C37#331011yescharacteristic
483C2×C37#331811yescharacteristic
484C2×C37#332411yescharacteristic
485C2×C37#332511yescharacteristic
486C23×D4—21no—
487C23×D4C22×C3711yescharacteristic
488C23×D4C22×C3711yescharacteristic
489C22×M16C22×C3711yescharacteristic, complemented
490D42—24no—
491D42—24no—
492C2×#127C22×C3711yescharacteristic
493C2×#121—21no—
494C2×#121C22×C3711yescharacteristic
495C2×#121C22×C3711yescharacteristic
496C2×#120—21no—
497C2×#120—21no—
498C2×C4×D4C22×C3711yescharacteristic
499C2×C4×D4C22×C3711yescharacteristic
500C2×#117C22×C3711yescharacteristic, complemented
501#482—24no—
502C2×#107C22×C3711yescharacteristic, complemented
503C2×#106C22×C3711yescharacteristic, complemented
504#418—24no—
505C2×#102C22×C3711yescharacteristic
506C2×#102C22×C3711yescharacteristic
507C2×#102C22×C3711yescharacteristic
508C2×#102C22×C3711yescharacteristic
509C2×#102C22×C3711yescharacteristic, complemented
510C2×#102C22×C3711yescharacteristic, complemented
511C2×#102C22×C3711yescharacteristic, complemented
512C2×#102C22×C3711yescharacteristic, complemented
513C2×#102C22×C3711yescharacteristic, complemented
514C2×#102C22×C3711yescharacteristic, complemented
515C2×#102C22×C3711yescharacteristic, complemented
516C2×#102C22×C3711yescharacteristic, complemented
517C2×C22⋊C8C22×C3711yescharacteristic, complemented
518C2×C22⋊C8C22×C3711yescharacteristic, complemented
519C2×C22⋊C8C22×C3711yescharacteristic, complemented
520#397—21no—
521#394—21no—
522#389C22×C3711yescharacteristic, complemented
523#389C22×C3711yescharacteristic, complemented
524#388—21no—
525#387—21no—
526#380C22×C3711yescharacteristic, complemented
527#380C22×C3711yescharacteristic, complemented
528#380C22×C3711yescharacteristic, complemented
529#340C22×C3711yescharacteristic, complemented
530#340C22×C3711yescharacteristic, complemented
531#336C22×C3711yescharacteristic, complemented
532#336C22×C3711yescharacteristic, complemented
533C37#2404411yescharacteristic, direct product factor, Sylow
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C3711yescharacteristic
557C22×D4D4×C3714yes—
558C22×D4C23×C3711yescharacteristic
559C22×D4C23×C3711yescharacteristic
560C22×D4C23×C3711yescharacteristic
561C23×C4—21no—
562C23×C4C23×C3711yescharacteristic
563C23×C4C23×C3711yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C3711yescharacteristic
568C22×C8C23×C3711yescharacteristic
569C22×C8C23×C3711yescharacteristic
570C22×C8C23×C3711yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C3714yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C3711yescharacteristic
589C2×C4⋊C4C23×C3711yescharacteristic
590C2×C4⋊C4C23×C3711yescharacteristic
591C2×C4⋊C4C23×C3711yescharacteristic
592C2×C4⋊C4C23×C3711yescharacteristic
593C2×C4⋊C4C23×C3711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C3711yescharacteristic
602C2×C22⋊C4D4×C3711yescharacteristic
603C2×C42—21no—
604C2×C42C23×C3711yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C3711yescharacteristic
645C24C2×D4×C3711yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C3712yes—
690C2×D4C2×D4×C3712yes—
691C2×D4C2×D4×C3712yes—
692C2×D4#41×C3712yes—
693C2×D4#41×C3712yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C3711yescharacteristic
713C22×C4C2×D4×C3711yescharacteristic
714C22×C4C2×D4×C3711yescharacteristic
715C22×C4C2×D4×C3712yes—
716C22×C4C2×D4×C3712yes—
717C22×C4C2×D4×C3711yescharacteristic
718C22×C4C24×C3711yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C3712yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C3712yes—
805C23AGL(1,ℤ/8)×C3712yes—
806C23C22×D4×C3711yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C3714yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C3712yes—
861C2×C4AGL(1,ℤ/8)×C3712yes—
862C2×C4C22×D4×C3711yescharacteristic
863C2×C4C22×D4×C3711yescharacteristic
864C2×C4C2×#41×C3711yescharacteristic
865C2×C4C2×#41×C3711yescharacteristic
866C2×C4H(5,𝔽2)×C3711yescharacteristic
867C2×C4H(5,𝔽2)×C3711yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C3711yescharacteristic
910C22C37×#54611yescharacteristic
911C22C37×#54611yescharacteristic
912C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
913C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
914C22C37×#57611yescharacteristic
915C22C37×#57711yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C3711yescharacteristic
926C4C37×#53411yescharacteristic
927C4C37×#54611yescharacteristic
928C4C37×#54611yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C37×#240511yescharacteristic
935C2C37×#300311yescharacteristic
936C2C37×#301211yescharacteristic
937C2C37×#331011yescharacteristic
938C2C37×#331811yescharacteristic
939C2C37×#332411yescharacteristic
940C2C37×#332511yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×D42×C37C2
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×#418C2semidirect
4. C37×#2485C2semidirect
5. C37×#2041C2semidirect
6. C37×#2041C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#1895C2semidirect
10. C37×#1870C2semidirect
11. C37×#1864C2semidirect
12. C37×#1862C2semidirect
13. C37×#1786C2semidirect
14. C37×#1786C2semidirect
15. C37×#1786C2semidirect
19. C22×M16×C37C22semidirect
30. C2×#117×C37C22semidirect
32. C2×#107×C37C22semidirect
33. C2×#106×C37C22semidirect
39. C2×#102×C37C22semidirect
40. C2×#102×C37C22semidirect
41. C2×#102×C37C22semidirect
42. C2×#102×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
47. C2×C22⋊C8×C37C22semidirect
48. C2×C22⋊C8×C37C22semidirect
49. C2×C22⋊C8×C37C22semidirect
52. C37×#389C22semidirect
53. C37×#389C22semidirect
56. C37×#380C22semidirect
57. C37×#380C22semidirect
58. C37×#380C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#336C22semidirect
62. C37×#336C22semidirect
401. #24044C37direct (N × H)
460. C2×#482C2×C37semidirect
461. C2×#418C2×C37semidirect
462. #2485C2×C37semidirect
463. #2041C2×C37semidirect
464. #2041C2×C37semidirect
465. #2034C2×C37semidirect
466. #2033C2×C37semidirect
467. #1895C2×C37semidirect
468. #1870C2×C37semidirect
469. #1864C2×C37semidirect
470. #1862C2×C37semidirect
471. #1786C2×C37semidirect
472. #1786C2×C37semidirect
473. #1786C2×C37semidirect
489. C22×M16C22×C37semidirect
500. C2×#117C22×C37semidirect
502. C2×#107C22×C37semidirect
503. C2×#106C22×C37semidirect
509. C2×#102C22×C37semidirect
510. C2×#102C22×C37semidirect
511. C2×#102C22×C37semidirect
512. C2×#102C22×C37semidirect
513. C2×#102C22×C37semidirect
514. C2×#102C22×C37semidirect
515. C2×#102C22×C37semidirect
516. C2×#102C22×C37semidirect
517. C2×C22⋊C8C22×C37semidirect
518. C2×C22⋊C8C22×C37semidirect
519. C2×C22⋊C8C22×C37semidirect
522. #389C22×C37semidirect
523. #389C22×C37semidirect
526. #380C22×C37semidirect
527. #380C22×C37semidirect
528. #380C22×C37semidirect
529. #340C22×C37semidirect
530. #340C22×C37semidirect
531. #336C22×C37semidirect
532. #336C22×C37semidirect
533. C37#24044direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C372
C2×C37×#4822
C2×C37×#4182
C37×#24852
C37×#20412
C37×#20342
C37×#20332
C37×#18952
C37×#18702
C37×#18642
C37×#18622
C37×#17862
#2404437