Finite Group Databasebeta

← C37×#29747 #22651000

Subgroups — C37×#29747 #22651000

Order 9472.

1024 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#468C211yesmaximal, characteristic, complemented
2C2×C37×#408C211yesmaximal, characteristic, complemented
3C37×#2616C211yesmaximal, characteristic, complemented
4C37×#2615C211yesmaximal, characteristic
5C37×#2076C211yesmaximal, characteristic, complemented
6C37×#2075C211yesmaximal, characteristic, complemented
7C37×#2036C211yesmaximal, characteristic, complemented
8C37×#2035C211yesmaximal, characteristic, complemented
9C37×#2034C211yesmaximal, characteristic, complemented
10C37×#2033C211yesmaximal, characteristic, complemented
11C37×#2000C211yesmaximal, characteristic, complemented
12C37×#2000C211yesmaximal, characteristic, complemented
13C37×#1893C211yesmaximal, characteristic, complemented
14C37×#1892C211yesmaximal, characteristic, complemented
15C37×#1809C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C23×C8×C37C2211yescharacteristic
20C2×C22⋊Q8×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#121×C37C2211yescharacteristic
26C37×#468—24no—
27C2×#107×C37C2211yescharacteristic
28C2×#107×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C37×#408—24no—
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C2×C22⋊C8×C37C2211yescharacteristic
41C37×#395—21no—
42C37×#394—21no—
43C37×#394—21no—
44C37×#394—21no—
45C37×#393—21no—
46C37×#392—21no—
47C37×#392—21no—
48C37×#392—21no—
49C37×#380C2211yescharacteristic
50C37×#380C2211yescharacteristic
51C37×#380C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C37×#380C2211yescharacteristic
54C37×#380C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C2×#41×C37—22no—
62C2×#41×C37—22no—
63C2×#41×C37—41no—
64C2×#41×C37—41no—
65C2×#41×C37—41no—
66C2×#41×C37—41no—
67C22×Q8×C37D411yescharacteristic
68C22×Q8×C37C2311yescharacteristic
69C22×D4×C37—21no—
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37D411yescharacteristic
73C22×D4×C37D411yescharacteristic
74C22×D4×C37D411yescharacteristic
75C22×D4×C37C2311yescharacteristic
76C23×C4×C37C2311yescharacteristic
77C23×C4×C37C2311yescharacteristic
78C23×C4×C37C2311yescharacteristic
79C2×SD16×C37—22no—
80C2×SD16×C37—41no—
81C2×SD16×C37—41no—
82C2×M16×C37—41no—
83C2×M16×C37—41no—
84C2×M16×C37D414yescomplemented
85C22×C8×C37—22no—
86C22×C8×C37—41no—
87C22×C8×C37—41no—
88C22×C8×C37C2311yescharacteristic
89C22×C8×C37C2311yescharacteristic
90C22×C8×C37C2311yescharacteristic
91C22×C8×C37C2311yescharacteristic
92C22⋊Q8×C37—22no—
93C22⋊Q8×C37—22no—
94C22⋊Q8×C37—41no—
95C22⋊Q8×C37—41no—
96C22⋊Q8×C37—41no—
97C22⋊Q8×C37—41no—
98#121×C37—22no—
99#121×C37—22no—
100#121×C37—41no—
101#121×C37—41no—
102#121×C37—41no—
103#121×C37—41no—
104C2×C4⋊C4×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37C2311yescharacteristic
108C2×C4⋊C4×C37C2311yescharacteristic
109C2×C4⋊C4×C37C2311yescharacteristic
110C2×C4⋊C4×C37C2311yescharacteristic
111C2×C4⋊C4×C37C2311yescharacteristic
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
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—
125#107×C37—22no—
126#107×C37—41no—
127#106×C37—41no—
128#103×C37—22no—
129#103×C37—41no—
130#103×C37—41no—
131#102×C37—22no—
132#102×C37—41no—
133#102×C37—41no—
134C22⋊C8×C37—22no—
135C22⋊C8×C37—22no—
136C22⋊C8×C37—22no—
137C22⋊C8×C37—22no—
138#95×C37—21no—
139#95×C37—21no—
140#95×C37—21no—
141#95×C37—21no—
142#95×C37—21no—
143#95×C37—21no—
144C24×C37—21no—
145C24×C37C2×D411yescharacteristic
146C24×C37C2×D411yescharacteristic
147C24×C37C2×D411yescharacteristic
148#41×C37—44no—
149#41×C37—44no—
150#41×C37—44no—
151#41×C37—44no—
152C2×Q8×C37—22no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—21no—
156C2×Q8×C37—21no—
157C2×Q8×C37—21no—
158C2×Q8×C37—21no—
159C2×Q8×C37—41no—
160C2×Q8×C37—41no—
161C2×D4×C37—22no—
162C2×D4×C37—22no—
163C2×D4×C37—22no—
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—41no—
171C2×D4×C37—41no—
172C2×D4×C37—41no—
173C2×D4×C37—41no—
174C2×D4×C37—41no—
175C2×D4×C37—41no—
176C2×D4×C37—42no—
177C2×D4×C37—42no—
178C2×D4×C37—42no—
179C2×D4×C37—81no—
180C2×D4×C37—81no—
181C2×D4×C37—81no—
182C2×D4×C37—81no—
183C2×D4×C37—81no—
184C2×D4×C37—81no—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
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—21no—
206C22×C4×C37—21no—
207C22×C4×C37—21no—
208C22×C4×C37C2×D411yescharacteristic
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D411yescharacteristic
211C22×C4×C37C2×D412yes—
212C22×C4×C37#4112yes—
213C22×C4×C37C2411yescharacteristic
214SD16×C37—44no—
215M16×C37—44no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—44no—
227C2×C8×C37C2×D412yes—
228C2×C8×C37C2×D412yes—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—42no—
242C4⋊C4×C37—42no—
243C4⋊C4×C37—42no—
244C22⋊C4×C37—42no—
245C22⋊C4×C37—42no—
246C22⋊C4×C37—42no—
247C22⋊C4×C37—42no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—42no—
250C22⋊C4×C37—81no—
251C22⋊C4×C37—81no—
252C22⋊C4×C37—81no—
253C22⋊C4×C37—81no—
254C22⋊C4×C37—81no—
255C22⋊C4×C37—81no—
256C23×C37—21no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—21no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
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—21no—
275C23×C37—21no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37#12112yes—
284C23×C37C22×D411yescharacteristic
285Q8×C37—44no—
286Q8×C37—41no—
287Q8×C37—41no—
288Q8×C37—41no—
289Q8×C37—41no—
290D4×C37—44no—
291D4×C37—44no—
292D4×C37—44no—
293D4×C37—41no—
294D4×C37—41no—
295D4×C37—41no—
296D4×C37—41no—
297D4×C37—84no—
298D4×C37—84no—
299D4×C37—84no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—22no—
303C2×C4×C37—22no—
304C2×C4×C37—22no—
305C2×C4×C37—22no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—21no—
310C2×C4×C37—21no—
311C2×C4×C37—21no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
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—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37#12112yes—
342C2×C4×C37C22×D411yescharacteristic
343C2×C4×C37C2×#4111yescharacteristic
344C2×C4×C37H(5,𝔽2)11yescharacteristic
345C2×C4×C37H(5,𝔽2)11yescharacteristic
346C2×C4×C37H(5,𝔽2)11yescharacteristic
347C2×C4×C37H(5,𝔽2)11yescharacteristic
348C8×C37—22no—
349C8×C37—22no—
350C8×C37—41no—
351C8×C37—41no—
352#29747C3711yesmaximal, characteristic, direct product factor, Sylow
353C22×C37—22no—
354C22×C37—22no—
355C22×C37—22no—
356C22×C37—41no—
357C22×C37—41no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—41no—
361C22×C37—41no—
362C22×C37—41no—
363C22×C37—41no—
364C22×C37—41no—
365C22×C37—41no—
366C22×C37—41no—
367C22×C37—41no—
368C22×C37—41no—
369C22×C37—41no—
370C22×C37—41no—
371C22×C37—41no—
372C22×C37—41no—
373C22×C37—41no—
374C22×C37—81no—
375C22×C37—81no—
376C22×C37—81no—
377C22×C37—81no—
378C22×C37—81no—
379C22×C37—81no—
380C22×C37—81no—
381C22×C37C2×#12111yescharacteristic
382C22×C37#53411yescharacteristic
383C22×C37#53411yescharacteristic
384C22×C37#57611yescharacteristic
385C22×C37#57711yescharacteristic
386C22×C37#57711yescharacteristic
387C22×C37#57811yescharacteristic
388C4×C37—22no—
389C4×C37—41no—
390C4×C37—41no—
391C4×C37—81no—
392C4×C37—81no—
393C4×C37—81no—
394C4×C37—81no—
395C4×C37—81no—
396C4×C37—81no—
397C4×C37—81no—
398C4×C37#53411yescharacteristic
399C4×C37#53511yescharacteristic
400C4×C37#53811yescharacteristic
401C4×C37#53811yescharacteristic
402C2×#468C2×C3711yescharacteristic, complemented
403C2×#408C2×C3711yescharacteristic, complemented
404#2616C2×C3711yescharacteristic, complemented
405#2615C2×C3711yescharacteristic
406#2076C2×C3711yescharacteristic, complemented
407#2075C2×C3711yescharacteristic, complemented
408#2036C2×C3711yescharacteristic, complemented
409#2035C2×C3711yescharacteristic, complemented
410#2034C2×C3711yescharacteristic, complemented
411#2033C2×C3711yescharacteristic, complemented
412#2000C2×C3711yescharacteristic, complemented
413#2000C2×C3711yescharacteristic, complemented
414#1893C2×C3711yescharacteristic, complemented
415#1892C2×C3711yescharacteristic, complemented
416#1809C2×C3711yescharacteristic, complemented
417C2×C37—42no—
418C2×C37—81no—
419C2×C37—81no—
420C2×C37—161no—
421C2×C37#261711yescharacteristic
422C2×C37#306211yescharacteristic
423C2×C37#306311yescharacteristic
424C2×C37#319811yescharacteristic
425C2×C37#320011yescharacteristic
426C2×C37#320111yescharacteristic
427C2×C37#320311yescharacteristic
428C22×#41C22×C3711yescharacteristic
429C22×SD16C22×C3711yescharacteristic
430C22×M16C22×C3711yescharacteristic
431C23×C8C22×C3711yescharacteristic
432C2×C22⋊Q8C22×C3711yescharacteristic
433C2×C22⋊Q8C22×C3711yescharacteristic
434C2×C22⋊Q8C22×C3711yescharacteristic
435C2×#121C22×C3711yescharacteristic
436C2×#121C22×C3711yescharacteristic
437C2×#121C22×C3711yescharacteristic
438#468—24no—
439C2×#107C22×C3711yescharacteristic
440C2×#107C22×C3711yescharacteristic
441C2×#106C22×C3711yescharacteristic
442C2×#103C22×C3711yescharacteristic
443C2×#103C22×C3711yescharacteristic
444C2×#103C22×C3711yescharacteristic
445C2×#102C22×C3711yescharacteristic
446C2×#102C22×C3711yescharacteristic
447C2×#102C22×C3711yescharacteristic
448#408—24no—
449C2×C22⋊C8C22×C3711yescharacteristic
450C2×C22⋊C8C22×C3711yescharacteristic
451C2×C22⋊C8C22×C3711yescharacteristic
452C2×C22⋊C8C22×C3711yescharacteristic
453#395—21no—
454#394—21no—
455#394—21no—
456#394—21no—
457#393—21no—
458#392—21no—
459#392—21no—
460#392—21no—
461#380C22×C3711yescharacteristic
462#380C22×C3711yescharacteristic
463#380C22×C3711yescharacteristic
464#380C22×C3711yescharacteristic
465#380C22×C3711yescharacteristic
466#380C22×C3711yescharacteristic
467#340C22×C3711yescharacteristic
468#340C22×C3711yescharacteristic
469#340C22×C3711yescharacteristic
470#340C22×C3711yescharacteristic
471#340C22×C3711yescharacteristic
472#340C22×C3711yescharacteristic
473C37#2974711yescharacteristic, direct product factor, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8D4×C3711yescharacteristic
481C22×Q8C23×C3711yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C3711yescharacteristic
486C22×D4D4×C3711yescharacteristic
487C22×D4D4×C3711yescharacteristic
488C22×D4C23×C3711yescharacteristic
489C23×C4C23×C3711yescharacteristic
490C23×C4C23×C3711yescharacteristic
491C23×C4C23×C3711yescharacteristic
492C2×SD16—22no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×M16—41no—
496C2×M16—41no—
497C2×M16D4×C3714yescomplemented
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C23×C3711yescharacteristic
502C22×C8C23×C3711yescharacteristic
503C22×C8C23×C3711yescharacteristic
504C22×C8C23×C3711yescharacteristic
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—41no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510C22⋊Q8—41no—
511#121—22no—
512#121—22no—
513#121—41no—
514#121—41no—
515#121—41no—
516#121—41no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4C23×C3711yescharacteristic
521C2×C4⋊C4C23×C3711yescharacteristic
522C2×C4⋊C4C23×C3711yescharacteristic
523C2×C4⋊C4C23×C3711yescharacteristic
524C2×C4⋊C4C23×C3711yescharacteristic
525C2×C4⋊C4C23×C3711yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538#107—22no—
539#107—41no—
540#106—41no—
541#103—22no—
542#103—41no—
543#103—41no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24C2×D4×C3711yescharacteristic
559C24C2×D4×C3711yescharacteristic
560C24C2×D4×C3711yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—41no—
573C2×Q8—41no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4C2×D4×C3711yescharacteristic
622C22×C4C2×D4×C3711yescharacteristic
623C22×C4C2×D4×C3711yescharacteristic
624C22×C4C2×D4×C3712yes—
625C22×C4#41×C3712yes—
626C22×C4C24×C3711yescharacteristic
627SD16—44no—
628M16—44no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—44no—
640C2×C8C2×D4×C3712yes—
641C2×C8C2×D4×C3712yes—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23#121×C3712yes—
697C23C22×D4×C3711yescharacteristic
698Q8—44no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703D4—44no—
704D4—44no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4#121×C3712yes—
755C2×C4C22×D4×C3711yescharacteristic
756C2×C4C2×#41×C3711yescharacteristic
757C2×C4H(5,𝔽2)×C3711yescharacteristic
758C2×C4H(5,𝔽2)×C3711yescharacteristic
759C2×C4H(5,𝔽2)×C3711yescharacteristic
760C2×C4H(5,𝔽2)×C3711yescharacteristic
761C8—22no—
762C8—22no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22C2×#121×C3711yescharacteristic
794C22C37×#53411yescharacteristic
795C22C37×#53411yescharacteristic
796C22C37×#57611yescharacteristic
797C22C37×#57711yescharacteristic
798C22C37×#57711yescharacteristic
799C22C37×#57811yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4C37×#53411yescharacteristic
811C4C37×#53511yescharacteristic
812C4C37×#53811yescharacteristic
813C4C37×#53811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—161no—
818C2C37×#261711yescharacteristic
819C2C37×#306211yescharacteristic
820C2C37×#306311yescharacteristic
821C2C37×#319811yescharacteristic
822C2C37×#320011yescharacteristic
823C2C37×#320111yescharacteristic
824C2C37×#320311yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#468C2semidirect
2. C2×C37×#408C2semidirect
3. C37×#2616C2semidirect
5. C37×#2076C2semidirect
6. C37×#2075C2semidirect
7. C37×#2036C2semidirect
8. C37×#2035C2semidirect
9. C37×#2034C2semidirect
10. C37×#2033C2semidirect
11. C37×#2000C2semidirect
12. C37×#2000C2semidirect
13. C37×#1893C2semidirect
14. C37×#1892C2semidirect
15. C37×#1809C2semidirect
84. C2×M16×C37D4semidirect
352. #29747C37direct (N × H)
402. C2×#468C2×C37semidirect
403. C2×#408C2×C37semidirect
404. #2616C2×C37semidirect
406. #2076C2×C37semidirect
407. #2075C2×C37semidirect
408. #2036C2×C37semidirect
409. #2035C2×C37semidirect
410. #2034C2×C37semidirect
411. #2033C2×C37semidirect
412. #2000C2×C37semidirect
413. #2000C2×C37semidirect
414. #1893C2×C37semidirect
415. #1892C2×C37semidirect
416. #1809C2×C37semidirect
473. C37#29747direct (N × H)
497. C2×M16D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4682
C2×C37×#4082
C37×#26162
C37×#26152
C37×#20762
C37×#20752
C37×#20362
C37×#20352
C37×#20342
C37×#20332
C37×#20002
C37×#18932
C37×#18922
C37×#18092
#2974737