Finite Group Databasebeta

← C37×#25554 #22646807

Subgroups — C37×#25554 #22646807

Order 9472.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#555C211yesmaximal, characteristic, complemented
2C2×C37×#482C211yesmaximal, characteristic, complemented
3C2×C37×#469C211yesmaximal, characteristic, complemented
4C37×#2416C211yesmaximal, characteristic, complemented
5C37×#2058C211yesmaximal, characteristic, complemented
6C37×#2034C211yesmaximal, characteristic, complemented
7C37×#2023C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1879C211yesmaximal, characteristic, complemented
10C37×#1875C211yesmaximal, characteristic, complemented
11C37×#1874C211yesmaximal, characteristic, complemented
12C37×#1870C211yesmaximal, characteristic, complemented
13C37×#1862C211yesmaximal, characteristic, complemented
14C37×#1854C211yesmaximal, characteristic, complemented
15C37×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C37×#555—24no—
19C37×#555—24no—
20C2×C4⋊Q8×C37C2211yescharacteristic
21C2×#124×C37—21no—
22C2×#124×C37—21no—
23C2×#121×C37—21no—
24C2×#121×C37—21no—
25C2×#121×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×C4×D4×C37C2211yescharacteristic
30C2×C4×D4×C37C2211yescharacteristic
31C2×#117×C37—21no—
32C2×#117×C37C2211yescharacteristic
33C2×#117×C37C2211yescharacteristic
34C22×C4⋊C4×C37C2211yescharacteristic
35C37×#482—24no—
36C37×#469—24no—
37C2×#107×C37C2211yescharacteristic
38C2×#106×C37C2211yescharacteristic
39C2×#106×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C37×#396—21no—
50C37×#394—21no—
51C37×#390C2211yescharacteristic
52C37×#389C2211yescharacteristic
53C37×#386—21no—
54C37×#380C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C22×Q8×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37—21no—
68C22×D4×C37D411yescharacteristic
69C22×D4×C37C2311yescharacteristic
70C22×D4×C37C2311yescharacteristic
71C23×C4×C37—21no—
72C23×C4×C37—21no—
73C23×C4×C37C2311yescharacteristic
74C23×C4×C37C2311yescharacteristic
75C2×D8×C37—22no—
76C2×D8×C37—22no—
77C2×D8×C37—41no—
78C2×M16×C37—22no—
79C2×M16×C37—22no—
80C2×M16×C37—41no—
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85C4⋊Q8×C37—22no—
86C4⋊Q8×C37—22no—
87#124×C37—28no—
88#124×C37—28no—
89#121×C37—28no—
90#121×C37—22no—
91#121×C37—22no—
92#121×C37—22no—
93#121×C37—22no—
94#121×C37—22no—
95#121×C37—22no—
96#121×C37—41no—
97#121×C37—44no—
98#121×C37D414yescomplemented
99C4×D4×C37—22no—
100C4×D4×C37—22no—
101C4×D4×C37—22no—
102C4×D4×C37—22no—
103#117×C37—28no—
104#117×C37—22no—
105#117×C37—22no—
106#117×C37—22no—
107#117×C37D414yescomplemented
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—22no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—41no—
113C2×C4⋊C4×C37D411yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C4⋊C4×C37C2311yescharacteristic
118C2×C4⋊C4×C37C2311yescharacteristic
119C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37D411yescharacteristic
131C2×C22⋊C4×C37D411yescharacteristic
132C2×C42×C37—21no—
133C2×C42×C37—21no—
134C2×C42×C37C2311yescharacteristic
135#107×C37—22no—
136#106×C37—22no—
137#106×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—41no—
144C22⋊C8×C37—22no—
145C22⋊C8×C37—22no—
146C22⋊C8×C37—41no—
147#95×C37—21no—
148#95×C37—21no—
149C24×C37—21no—
150C24×C37—21no—
151C24×C37C2×D411yescharacteristic
152C24×C37C2×D411yescharacteristic
153C2×Q8×C37—24no—
154C2×Q8×C37—81no—
155C2×Q8×C37—81no—
156C2×D4×C37—22no—
157C2×D4×C37—24no—
158C2×D4×C37—24no—
159C2×D4×C37—22no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—21no—
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—21no—
171C2×D4×C37—41no—
172C2×D4×C37—42no—
173C2×D4×C37—42no—
174C2×D4×C37—42no—
175C2×D4×C37—42no—
176C2×D4×C37—42no—
177C2×D4×C37—81no—
178C2×D4×C37—81no—
179C2×D4×C37—81no—
180C2×D4×C37—81no—
181C2×D4×C37—81no—
182C2×D4×C37C2×D412yes—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—24no—
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—42no—
201C22×C4×C37—42no—
202C22×C4×C37—42no—
203C22×C4×C37—42no—
204C22×C4×C37—81no—
205C22×C4×C37C2×D411yescharacteristic
206C22×C4×C37C2×D411yescharacteristic
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D412yes—
209C22×C4×C37C2×D412yes—
210C22×C4×C37C2×D411yescharacteristic
211C22×C4×C37C2411yescharacteristic
212D8×C37—44no—
213M16×C37—44no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
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#4112yes—
226C4⋊C4×C37—24no—
227C4⋊C4×C37—22no—
228C4⋊C4×C37—21no—
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—42no—
237C4⋊C4×C37—42no—
238C4⋊C4×C37C2×D412yes—
239C4⋊C4×C37C2×D412yes—
240C4⋊C4×C37C2×D412yes—
241C4⋊C4×C37#4112yes—
242C22⋊C4×C37—24no—
243C22⋊C4×C37—24no—
244C22⋊C4×C37—24no—
245C22⋊C4×C37—24no—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—24no—
248C22⋊C4×C37—22no—
249C22⋊C4×C37—42no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—42no—
253C22⋊C4×C37—81no—
254C42×C37—24no—
255C42×C37—24no—
256C42×C37—21no—
257C42×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—22no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—21no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37#12012yes—
286C23×C37C22×D411yescharacteristic
287Q8×C37—84no—
288D4×C37—22no—
289D4×C37—22no—
290D4×C37—44no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—41no—
295D4×C37—41no—
296D4×C37—41no—
297D4×C37—84no—
298D4×C37—84no—
299D4×C37—84no—
300D4×C37—84no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—22no—
306C2×C4×C37—22no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—21no—
310C2×C4×C37—22no—
311C2×C4×C37—21no—
312C2×C4×C37—22no—
313C2×C4×C37—22no—
314C2×C4×C37—21no—
315C2×C4×C37—22no—
316C2×C4×C37—21no—
317C2×C4×C37—21no—
318C2×C4×C37—21no—
319C2×C4×C37—48no—
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—84no—
339C2×C4×C37#12012yes—
340C2×C4×C37AGL(1,ℤ/8)12yes—
341C2×C4×C37C22×D411yescharacteristic
342C2×C4×C37C22×D411yescharacteristic
343C2×C4×C37C2×#4111yescharacteristic
344C2×C4×C37C2×#4111yescharacteristic
345C2×C4×C37H(5,𝔽2)11yescharacteristic
346C2×C4×C372−1+411yescharacteristic
347C8×C37—22no—
348C8×C37—41no—
349C8×C37—41no—
350C8×C37—41no—
351#25554C3711yesmaximal, characteristic, direct product factor, Sylow
352C22×C37—22no—
353C22×C37—22no—
354C22×C37—22no—
355C22×C37—41no—
356C22×C37—41no—
357C22×C37—41no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—41no—
361C22×C37—41no—
362C22×C37—42no—
363C22×C37—42no—
364C22×C37—41no—
365C22×C37—41no—
366C22×C37—42no—
367C22×C37—41no—
368C22×C37—41no—
369C22×C37—81no—
370C22×C37—81no—
371C22×C37—81no—
372C22×C37—81no—
373C22×C37—81no—
374C22×C37—81no—
375C22×C37—81no—
376C22×C37—81no—
377C22×C37—81no—
378C22×C37—81no—
379C22×C37—81no—
380C22×C37C2×#12011yescharacteristic
381C22×C37#54611yescharacteristic
382C22×C37#54711yescharacteristic
383C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C37#57511yescharacteristic
385C22×C37#57611yescharacteristic
386C22×C37#57711yescharacteristic
387C4×C37—22no—
388C4×C37—22no—
389C4×C37—41no—
390C4×C37—42no—
391C4×C37—41no—
392C4×C37—42no—
393C4×C37—42no—
394C4×C37—42no—
395C4×C37—81no—
396C4×C37—81no—
397C4×C37#53211yescharacteristic
398C4×C37#53711yescharacteristic
399C4×C37#54611yescharacteristic
400C4×C37#54711yescharacteristic
401C2×#555C2×C3711yescharacteristic, complemented
402C2×#482C2×C3711yescharacteristic, complemented
403C2×#469C2×C3711yescharacteristic, complemented
404#2416C2×C3711yescharacteristic, complemented
405#2058C2×C3711yescharacteristic, complemented
406#2034C2×C3711yescharacteristic, complemented
407#2023C2×C3711yescharacteristic, complemented
408#1999C2×C3711yescharacteristic, complemented
409#1879C2×C3711yescharacteristic, complemented
410#1875C2×C3711yescharacteristic, complemented
411#1874C2×C3711yescharacteristic, complemented
412#1870C2×C3711yescharacteristic, complemented
413#1862C2×C3711yescharacteristic, complemented
414#1854C2×C3711yescharacteristic, complemented
415#1736C2×C3711yescharacteristic, complemented
416C2×C37—42no—
417C2×C37—81no—
418C2×C37—82no—
419C2×C37—161no—
420C2×C37#243011yescharacteristic
421C2×C37#300611yescharacteristic
422C2×C37#301211yescharacteristic
423C2×C37#332111yescharacteristic
424C2×C37#332511yescharacteristic
425C2×C37#334711yescharacteristic
426C2×C37#335411yescharacteristic
427C22×D8C22×C3711yescharacteristic
428C22×M16C22×C3711yescharacteristic
429#555—24no—
430#555—24no—
431C2×C4⋊Q8C22×C3711yescharacteristic
432C2×#124—21no—
433C2×#124—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C3711yescharacteristic
437C2×#121C22×C3711yescharacteristic
438C2×#121C22×C3711yescharacteristic
439C2×#121C22×C3711yescharacteristic
440C2×C4×D4C22×C3711yescharacteristic
441C2×C4×D4C22×C3711yescharacteristic
442C2×#117—21no—
443C2×#117C22×C3711yescharacteristic
444C2×#117C22×C3711yescharacteristic
445C22×C4⋊C4C22×C3711yescharacteristic
446#482—24no—
447#469—24no—
448C2×#107C22×C3711yescharacteristic
449C2×#106C22×C3711yescharacteristic
450C2×#106C22×C3711yescharacteristic
451C2×#102C22×C3711yescharacteristic
452C2×#102C22×C3711yescharacteristic
453C2×#102C22×C3711yescharacteristic
454C2×#102C22×C3711yescharacteristic
455C2×#102C22×C3711yescharacteristic
456C2×#102C22×C3711yescharacteristic
457C2×C22⋊C8C22×C3711yescharacteristic
458C2×C22⋊C8C22×C3711yescharacteristic
459C2×C22⋊C8C22×C3711yescharacteristic
460#396—21no—
461#394—21no—
462#390C22×C3711yescharacteristic
463#389C22×C3711yescharacteristic
464#386—21no—
465#380C22×C3711yescharacteristic
466#340C22×C3711yescharacteristic
467#340C22×C3711yescharacteristic
468#340C22×C3711yescharacteristic
469#340C22×C3711yescharacteristic
470#340C22×C3711yescharacteristic
471#340C22×C3711yescharacteristic
472#336C22×C3711yescharacteristic
473#336C22×C3711yescharacteristic
474C37#2555411yescharacteristic, direct product factor, Sylow
475C22×Q8—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C3711yescharacteristic
481C22×D4C23×C3711yescharacteristic
482C22×D4C23×C3711yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C3711yescharacteristic
486C23×C4C23×C3711yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C3711yescharacteristic
494C22×C8C23×C3711yescharacteristic
495C22×C8C23×C3711yescharacteristic
496C22×C8C23×C3711yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499#124—28no—
500#124—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C3714yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117D4×C3714yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4D4×C3711yescharacteristic
526C2×C4⋊C4C23×C3711yescharacteristic
527C2×C4⋊C4C23×C3711yescharacteristic
528C2×C4⋊C4C23×C3711yescharacteristic
529C2×C4⋊C4C23×C3711yescharacteristic
530C2×C4⋊C4C23×C3711yescharacteristic
531C2×C4⋊C4C23×C3711yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4D4×C3711yescharacteristic
543C2×C22⋊C4D4×C3711yescharacteristic
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C3711yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C3711yescharacteristic
564C24C2×D4×C3711yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C3712yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
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—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C3711yescharacteristic
618C22×C4C2×D4×C3711yescharacteristic
619C22×C4C2×D4×C3711yescharacteristic
620C22×C4C2×D4×C3712yes—
621C22×C4C2×D4×C3712yes—
622C22×C4C2×D4×C3711yescharacteristic
623C22×C4C24×C3711yescharacteristic
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
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#41×C3712yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C3712yes—
651C4⋊C4C2×D4×C3712yes—
652C4⋊C4C2×D4×C3712yes—
653C4⋊C4#41×C3712yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23#120×C3712yes—
698C23C22×D4×C3711yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
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—84no—
751C2×C4#120×C3712yes—
752C2×C4AGL(1,ℤ/8)×C3712yes—
753C2×C4C22×D4×C3711yescharacteristic
754C2×C4C22×D4×C3711yescharacteristic
755C2×C4C2×#41×C3711yescharacteristic
756C2×C4C2×#41×C3711yescharacteristic
757C2×C4H(5,𝔽2)×C3711yescharacteristic
758C2×C42−1+4×C3711yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C3711yescharacteristic
792C22C37×#54611yescharacteristic
793C22C37×#54711yescharacteristic
794C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
795C22C37×#57511yescharacteristic
796C22C37×#57611yescharacteristic
797C22C37×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4C37×#53211yescharacteristic
809C4C37×#53711yescharacteristic
810C4C37×#54611yescharacteristic
811C4C37×#54711yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C37×#243011yescharacteristic
817C2C37×#300611yescharacteristic
818C2C37×#301211yescharacteristic
819C2C37×#332111yescharacteristic
820C2C37×#332511yescharacteristic
821C2C37×#334711yescharacteristic
822C2C37×#335411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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
1. C2×C37×#555C2semidirect
2. C2×C37×#482C2semidirect
3. C2×C37×#469C2semidirect
4. C37×#2416C2semidirect
5. C37×#2058C2semidirect
6. C37×#2034C2semidirect
7. C37×#2023C2semidirect
8. C37×#1999C2semidirect
9. C37×#1879C2semidirect
10. C37×#1875C2semidirect
11. C37×#1874C2semidirect
12. C37×#1870C2semidirect
13. C37×#1862C2semidirect
14. C37×#1854C2semidirect
15. C37×#1736C2semidirect
98. #121×C37D4semidirect
107. #117×C37D4semidirect
351. #25554C37direct (N × H)
401. C2×#555C2×C37semidirect
402. C2×#482C2×C37semidirect
403. C2×#469C2×C37semidirect
404. #2416C2×C37semidirect
405. #2058C2×C37semidirect
406. #2034C2×C37semidirect
407. #2023C2×C37semidirect
408. #1999C2×C37semidirect
409. #1879C2×C37semidirect
410. #1875C2×C37semidirect
411. #1874C2×C37semidirect
412. #1870C2×C37semidirect
413. #1862C2×C37semidirect
414. #1854C2×C37semidirect
415. #1736C2×C37semidirect
474. C37#25554direct (N × H)
510. #121D4×C37semidirect
519. #117D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5552
C2×C37×#4822
C2×C37×#4692
C37×#24162
C37×#20582
C37×#20342
C37×#20232
C37×#19992
C37×#18792
C37×#18752
C37×#18742
C37×#18702
C37×#18622
C37×#18542
C37×#17362
#2555437