Finite Group Databasebeta

← C37×#29601 #22650854

Subgroups — C37×#29601 #22650854

Order 9472.

1462 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#525C211yesmaximal, characteristic
2C2×C37×#485C211yesmaximal, characteristic, complemented
3C2×C37×#452C211yesmaximal, characteristic, complemented
4C37×#2848C211yesmaximal, characteristic, complemented
5C37×#2036C211yesmaximal, characteristic, complemented
6C37×#2035C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2001C211yesmaximal, characteristic, complemented
10C37×#2001C211yesmaximal, characteristic, complemented
11C37×#2000C211yesmaximal, characteristic, complemented
12C37×#2000C211yesmaximal, characteristic, complemented
13C37×#1825C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C37×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C24×C4×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic, complemented
19C22×SD16×C37C2211yescharacteristic, complemented
20C37×#525—24no—
21C37×#525—24no—
22C2×#123×C37—21no—
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×C22⋊Q8×C37C2211yescharacteristic
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×C22⋊Q8×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#120×C37—21no—
31C2×C4×D4×C37—21no—
32C2×C4×D4×C37—21no—
33C2×#117×C37C2211yescharacteristic
34C37×#485—24no—
35C37×#452—24no—
36C2×#107×C37C2211yescharacteristic, complemented
37C2×#106×C37C2211yescharacteristic, complemented
38C2×#103×C37C2211yescharacteristic, complemented
39C2×#103×C37C2211yescharacteristic, complemented
40C2×#103×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C2×C22⋊C8×C37C2211yescharacteristic
50C2×C22⋊C8×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C37×#385—21no—
53C37×#385—21no—
54C37×#385—21no—
55C37×#380C2211yescharacteristic
56C37×#380C2211yescharacteristic
57C37×#380C2211yescharacteristic
58C37×#379—21no—
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C25×C37D411yescharacteristic
64C2×#41×C37—22no—
65C2×#41×C37—41no—
66C2×#41×C37—41no—
67C2×#41×C37—41no—
68C2×#41×C37—41no—
69C2×#41×C37D414yes—
70C22×Q8×C37C2311yescharacteristic
71C22×Q8×C37C2311yescharacteristic
72C22×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37C2311yescharacteristic
76C23×C4×C37—22no—
77C23×C4×C37—22no—
78C23×C4×C37—21no—
79C23×C4×C37—41no—
80C23×C4×C37—41no—
81C23×C4×C37—41no—
82C23×C4×C37—41no—
83C23×C4×C37D411yescharacteristic
84C23×C4×C37D411yescharacteristic
85C23×C4×C37D411yescharacteristic
86C23×C4×C37C2311yescharacteristic
87C23×C4×C37C2311yescharacteristic
88C23×C4×C37C2311yescharacteristic
89C2×Q16×C37—22no—
90C2×Q16×C37—41no—
91C2×Q16×C37—41no—
92C2×SD16×C37—22no—
93C2×SD16×C37—41no—
94C2×SD16×C37—41no—
95C22×C8×C37C2311yescharacteristic
96C22×C8×C37C2311yescharacteristic
97C22×C8×C37C2311yescharacteristic
98C22×C8×C37C2311yescharacteristic
99#123×C37—28no—
100C22⋊Q8×C37—22no—
101C22⋊Q8×C37—22no—
102C22⋊Q8×C37—22no—
103C22⋊Q8×C37—22no—
104C22⋊Q8×C37—22no—
105C22⋊Q8×C37—22no—
106C22⋊Q8×C37—41no—
107C22⋊Q8×C37—41no—
108C22⋊Q8×C37—41no—
109C22⋊Q8×C37—41no—
110#121×C37—22no—
111#121×C37—22no—
112#121×C37—22no—
113#121×C37—22no—
114#120×C37—28no—
115C4×D4×C37—28no—
116C4×D4×C37—28no—
117#117×C37—22no—
118#117×C37D414yes—
119C2×C4⋊C4×C37—21no—
120C2×C4⋊C4×C37—21no—
121C2×C4⋊C4×C37—21no—
122C2×C4⋊C4×C37—21no—
123C2×C4⋊C4×C37—21no—
124C2×C4⋊C4×C37C2311yescharacteristic
125C2×C4⋊C4×C37C2311yescharacteristic
126C2×C4⋊C4×C37C2311yescharacteristic
127C2×C4⋊C4×C37C2311yescharacteristic
128C2×C4⋊C4×C37C2311yescharacteristic
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37—21no—
133C2×C22⋊C4×C37—21no—
134C2×C22⋊C4×C37—21no—
135C2×C22⋊C4×C37—21no—
136C2×C22⋊C4×C37—21no—
137C2×C22⋊C4×C37—21no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—21no—
140C2×C42×C37—21no—
141#107×C37—22no—
142#106×C37—22no—
143#103×C37—22no—
144#103×C37—22no—
145#103×C37—22no—
146#103×C37—41no—
147#103×C37—41no—
148#102×C37—22no—
149#102×C37—41no—
150#102×C37—41no—
151C22⋊C8×C37—22no—
152C22⋊C8×C37—22no—
153C22⋊C8×C37—41no—
154C22⋊C8×C37—41no—
155C22⋊C8×C37—41no—
156C22⋊C8×C37—41no—
157#95×C37—21no—
158#95×C37—21no—
159#95×C37—21no—
160C24×C37—22no—
161C24×C37—22no—
162C24×C37—22no—
163C24×C37—21no—
164C24×C37—41no—
165C24×C37—41no—
166C24×C37—41no—
167C24×C37—41no—
168C24×C37C2×D411yescharacteristic
169C24×C37C2×D411yescharacteristic
170C24×C37C2×D411yescharacteristic
171#41×C37—44no—
172#41×C37—44no—
173#41×C37—44no—
174#41×C37—44no—
175C2×Q8×C37—21no—
176C2×Q8×C37—21no—
177C2×Q8×C37—21no—
178C2×Q8×C37—21no—
179C2×Q8×C37—21no—
180C2×Q8×C37—21no—
181C2×Q8×C37—21no—
182C2×Q8×C37—21no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37C2×D412yes—
187C2×D4×C37—24no—
188C2×D4×C37—24no—
189C2×D4×C37—24no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—21no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—42no—
196C2×D4×C37—42no—
197C2×D4×C37—42no—
198C2×D4×C37—42no—
199C2×D4×C37—42no—
200C2×D4×C37—42no—
201C2×D4×C37C2×D412yes—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—22no—
207C22×C4×C37—21no—
208C22×C4×C37—21no—
209C22×C4×C37—21no—
210C22×C4×C37—22no—
211C22×C4×C37—22no—
212C22×C4×C37—24no—
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—21no—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
229C22×C4×C37—41no—
230C22×C4×C37—41no—
231C22×C4×C37—41no—
232C22×C4×C37—41no—
233C22×C4×C37—41no—
234C22×C4×C37—41no—
235C22×C4×C37—44no—
236C22×C4×C37—44no—
237C22×C4×C37—44no—
238C22×C4×C37—44no—
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×C37C2411yescharacteristic
247Q16×C37—44no—
248SD16×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—24no—
262C4⋊C4×C37—24no—
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—42no—
273C4⋊C4×C37—42no—
274C4⋊C4×C37C2×D412yes—
275C4⋊C4×C37C2×D412yes—
276C22⋊C4×C37—24no—
277C22⋊C4×C37—24no—
278C22⋊C4×C37—24no—
279C22⋊C4×C37—24no—
280C22⋊C4×C37—24no—
281C22⋊C4×C37—42no—
282C22⋊C4×C37—42no—
283C22⋊C4×C37—42no—
284C22⋊C4×C37—42no—
285C22⋊C4×C37—42no—
286C22⋊C4×C37—42no—
287C42×C37—24no—
288C23×C37—21no—
289C23×C37—21no—
290C23×C37—21no—
291C23×C37—21no—
292C23×C37—21no—
293C23×C37—21no—
294C23×C37—21no—
295C23×C37—21no—
296C23×C37—21no—
297C23×C37—21no—
298C23×C37—21no—
299C23×C37—21no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—21no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—22no—
307C23×C37—44no—
308C23×C37—44no—
309C23×C37—44no—
310C23×C37—44no—
311C23×C37—44no—
312C23×C37—44no—
313C23×C37—44no—
314C23×C37—41no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37—41no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37#12012yes—
321C23×C37#13512yes—
322C23×C37#13712yes—
323C23×C37C22×D411yescharacteristic
324Q8×C37—22no—
325Q8×C37—22no—
326Q8×C37—41no—
327Q8×C37—41no—
328Q8×C37—41no—
329Q8×C37—41no—
330Q8×C37—41no—
331Q8×C37—41no—
332D4×C37—22no—
333D4×C37—22no—
334D4×C37—48no—
335D4×C37—48no—
336D4×C37—48no—
337D4×C37—41no—
338D4×C37—41no—
339C2×C4×C37—21no—
340C2×C4×C37—21no—
341C2×C4×C37—22no—
342C2×C4×C37—22no—
343C2×C4×C37—22no—
344C2×C4×C37—22no—
345C2×C4×C37—22no—
346C2×C4×C37—22no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—22no—
350C2×C4×C37—21no—
351C2×C4×C37—21no—
352C2×C4×C37—21no—
353C2×C4×C37—21no—
354C2×C4×C37—44no—
355C2×C4×C37—44no—
356C2×C4×C37—48no—
357C2×C4×C37—44no—
358C2×C4×C37—41no—
359C2×C4×C37—41no—
360C2×C4×C37—41no—
361C2×C4×C37—41no—
362C2×C4×C37—41no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—41no—
367C2×C4×C37—41no—
368C2×C4×C37—41no—
369C2×C4×C37—41no—
370C2×C4×C37—41no—
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#12012yes—
385C2×C4×C37C22×D411yescharacteristic
386C2×C4×C37C22×D411yescharacteristic
387C2×C4×C37H(5,𝔽2)11yescharacteristic
388C2×C4×C37H(5,𝔽2)11yescharacteristic
389C2×C4×C37H(5,𝔽2)11yescharacteristic
390C2×C4×C37H(5,𝔽2)11yescharacteristic
391C8×C37—41no—
392C8×C37—41no—
393C8×C37—41no—
394C8×C37—41no—
395#29601C3711yesmaximal, characteristic, direct product factor, Sylow
396C22×C37—22no—
397C22×C37—22no—
398C22×C37—22no—
399C22×C37—22no—
400C22×C37—22no—
401C22×C37—22no—
402C22×C37—22no—
403C22×C37—22no—
404C22×C37—22no—
405C22×C37—416no—
406C22×C37—41no—
407C22×C37—41no—
408C22×C37—41no—
409C22×C37—41no—
410C22×C37—41no—
411C22×C37—41no—
412C22×C37—41no—
413C22×C37—41no—
414C22×C37—41no—
415C22×C37—41no—
416C22×C37—41no—
417C22×C37—41no—
418C22×C37—42no—
419C22×C37—42no—
420C22×C37—42no—
421C22×C37—81no—
422C22×C37—81no—
423C22×C37—81no—
424C22×C37—81no—
425C22×C37C2×#12011yescharacteristic
426C22×C37#53411yescharacteristic
427C22×C37#53411yescharacteristic
428C22×C37C2×#13511yescharacteristic
429C22×C37C2×#13711yescharacteristic
430C22×C37#57511yescharacteristic
431C22×C37#57511yescharacteristic
432C4×C37—22no—
433C4×C37—41no—
434C4×C37—41no—
435C4×C37—42no—
436C4×C37—42no—
437C4×C37—42no—
438C4×C37—81no—
439C4×C37—81no—
440C4×C37—81no—
441C4×C37—81no—
442C4×C37#53411yescharacteristic
443C4×C37#53411yescharacteristic
444C4×C37#53511yescharacteristic
445C4×C37#53511yescharacteristic
446C2×#525C2×C3711yescharacteristic
447C2×#485C2×C3711yescharacteristic, complemented
448C2×#452C2×C3711yescharacteristic, complemented
449#2848C2×C3711yescharacteristic, complemented
450#2036C2×C3711yescharacteristic, complemented
451#2035C2×C3711yescharacteristic, complemented
452#2034C2×C3711yescharacteristic, complemented
453#2033C2×C3711yescharacteristic, complemented
454#2001C2×C3711yescharacteristic, complemented
455#2001C2×C3711yescharacteristic, complemented
456#2000C2×C3711yescharacteristic, complemented
457#2000C2×C3711yescharacteristic, complemented
458#1825C2×C3711yescharacteristic, complemented
459#1788C2×C3711yescharacteristic, complemented
460#1779C2×C3711yescharacteristic, complemented
461C2×C37—42no—
462C2×C37—42no—
463C2×C37—42no—
464C2×C37—82no—
465C2×C37#261311yescharacteristic
466C2×C37#300211yescharacteristic
467C2×C37#300711yescharacteristic
468C2×C37#319011yescharacteristic
469C2×C37#319111yescharacteristic
470C2×C37#319611yescharacteristic
471C2×C37#319711yescharacteristic
472C22×#41C22×C3711yescharacteristic
473C24×C4C22×C3711yescharacteristic
474C22×Q16C22×C3711yescharacteristic, complemented
475C22×SD16C22×C3711yescharacteristic, complemented
476#525—24no—
477#525—24no—
478C2×#123—21no—
479C2×C22⋊Q8C22×C3711yescharacteristic
480C2×C22⋊Q8C22×C3711yescharacteristic
481C2×C22⋊Q8C22×C3711yescharacteristic
482C2×C22⋊Q8C22×C3711yescharacteristic
483C2×C22⋊Q8C22×C3711yescharacteristic
484C2×#121C22×C3711yescharacteristic
485C2×#121C22×C3711yescharacteristic
486C2×#120—21no—
487C2×C4×D4—21no—
488C2×C4×D4—21no—
489C2×#117C22×C3711yescharacteristic
490#485—24no—
491#452—24no—
492C2×#107C22×C3711yescharacteristic, complemented
493C2×#106C22×C3711yescharacteristic, complemented
494C2×#103C22×C3711yescharacteristic, complemented
495C2×#103C22×C3711yescharacteristic, complemented
496C2×#103C22×C3711yescharacteristic, complemented
497C2×#103C22×C3711yescharacteristic, complemented
498C2×#103C22×C3711yescharacteristic, complemented
499C2×#102C22×C3711yescharacteristic, complemented
500C2×#102C22×C3711yescharacteristic, complemented
501C2×#102C22×C3711yescharacteristic, complemented
502C2×C22⋊C8C22×C3711yescharacteristic
503C2×C22⋊C8C22×C3711yescharacteristic
504C2×C22⋊C8C22×C3711yescharacteristic
505C2×C22⋊C8C22×C3711yescharacteristic
506C2×C22⋊C8C22×C3711yescharacteristic
507C2×C22⋊C8C22×C3711yescharacteristic
508#385—21no—
509#385—21no—
510#385—21no—
511#380C22×C3711yescharacteristic
512#380C22×C3711yescharacteristic
513#380C22×C3711yescharacteristic
514#379—21no—
515#340C22×C3711yescharacteristic, complemented
516#340C22×C3711yescharacteristic, complemented
517#340C22×C3711yescharacteristic, complemented
518#340C22×C3711yescharacteristic, complemented
519C37#2960111yescharacteristic, direct product factor, Sylow
520C25D4×C3711yescharacteristic
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41D4×C3714yes—
527C22×Q8C23×C3711yescharacteristic
528C22×Q8C23×C3711yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C23×C3711yescharacteristic
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4D4×C3711yescharacteristic
541C23×C4D4×C3711yescharacteristic
542C23×C4D4×C3711yescharacteristic
543C23×C4C23×C3711yescharacteristic
544C23×C4C23×C3711yescharacteristic
545C23×C4C23×C3711yescharacteristic
546C2×Q16—22no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C22×C8C23×C3711yescharacteristic
553C22×C8C23×C3711yescharacteristic
554C22×C8C23×C3711yescharacteristic
555C22×C8C23×C3711yescharacteristic
556#123—28no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#120—28no—
572C4×D4—28no—
573C4×D4—28no—
574#117—22no—
575#117D4×C3714yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4C23×C3711yescharacteristic
582C2×C4⋊C4C23×C3711yescharacteristic
583C2×C4⋊C4C23×C3711yescharacteristic
584C2×C4⋊C4C23×C3711yescharacteristic
585C2×C4⋊C4C23×C3711yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C42—21no—
598#107—22no—
599#106—22no—
600#103—22no—
601#103—22no—
602#103—22no—
603#103—41no—
604#103—41no—
605#102—22no—
606#102—41no—
607#102—41no—
608C22⋊C8—22no—
609C22⋊C8—22no—
610C22⋊C8—41no—
611C22⋊C8—41no—
612C22⋊C8—41no—
613C22⋊C8—41no—
614#95—21no—
615#95—21no—
616#95—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—41no—
622C24—41no—
623C24—41no—
624C24—41no—
625C24C2×D4×C3711yescharacteristic
626C24C2×D4×C3711yescharacteristic
627C24C2×D4×C3711yescharacteristic
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C3712yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4C2×D4×C3712yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4C2×D4×C3711yescharacteristic
699C22×C4C2×D4×C3711yescharacteristic
700C22×C4C2×D4×C3711yescharacteristic
701C22×C4C2×D4×C3712yes—
702C22×C4C2×D4×C3712yes—
703C22×C4C24×C3711yescharacteristic
704Q16—44no—
705SD16—44no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4C2×D4×C3712yes—
732C4⋊C4C2×D4×C3712yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C42—24no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C3712yes—
778C23#135×C3712yes—
779C23#137×C3712yes—
780C23C22×D4×C3711yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—44no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C3712yes—
842C2×C4C22×D4×C3711yescharacteristic
843C2×C4C22×D4×C3711yescharacteristic
844C2×C4H(5,𝔽2)×C3711yescharacteristic
845C2×C4H(5,𝔽2)×C3711yescharacteristic
846C2×C4H(5,𝔽2)×C3711yescharacteristic
847C2×C4H(5,𝔽2)×C3711yescharacteristic
848C8—41no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—416no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C3711yescharacteristic
882C22C37×#53411yescharacteristic
883C22C37×#53411yescharacteristic
884C22C2×#135×C3711yescharacteristic
885C22C2×#137×C3711yescharacteristic
886C22C37×#57511yescharacteristic
887C22C37×#57511yescharacteristic
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4C37×#53411yescharacteristic
899C4C37×#53411yescharacteristic
900C4C37×#53511yescharacteristic
901C4C37×#53511yescharacteristic
902C2—42no—
903C2—42no—
904C2—42no—
905C2—82no—
906C2C37×#261311yescharacteristic
907C2C37×#300211yescharacteristic
908C2C37×#300711yescharacteristic
909C2C37×#319011yescharacteristic
910C2C37×#319111yescharacteristic
911C2C37×#319611yescharacteristic
912C2C37×#319711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C24×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#485C2semidirect
3. C2×C37×#452C2semidirect
4. C37×#2848C2semidirect
5. C37×#2036C2semidirect
6. C37×#2035C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#2001C2semidirect
10. C37×#2001C2semidirect
11. C37×#2000C2semidirect
12. C37×#2000C2semidirect
13. C37×#1825C2semidirect
14. C37×#1788C2semidirect
15. C37×#1779C2semidirect
18. C22×Q16×C37C22semidirect
19. C22×SD16×C37C22semidirect
36. C2×#107×C37C22semidirect
37. C2×#106×C37C22semidirect
38. C2×#103×C37C22semidirect
39. C2×#103×C37C22semidirect
40. C2×#103×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
395. #29601C37direct (N × H)
447. C2×#485C2×C37semidirect
448. C2×#452C2×C37semidirect
449. #2848C2×C37semidirect
450. #2036C2×C37semidirect
451. #2035C2×C37semidirect
452. #2034C2×C37semidirect
453. #2033C2×C37semidirect
454. #2001C2×C37semidirect
455. #2001C2×C37semidirect
456. #2000C2×C37semidirect
457. #2000C2×C37semidirect
458. #1825C2×C37semidirect
459. #1788C2×C37semidirect
460. #1779C2×C37semidirect
474. C22×Q16C22×C37semidirect
475. C22×SD16C22×C37semidirect
492. C2×#107C22×C37semidirect
493. C2×#106C22×C37semidirect
494. C2×#103C22×C37semidirect
495. C2×#103C22×C37semidirect
496. C2×#103C22×C37semidirect
497. C2×#103C22×C37semidirect
498. C2×#103C22×C37semidirect
499. C2×#102C22×C37semidirect
500. C2×#102C22×C37semidirect
501. C2×#102C22×C37semidirect
515. #340C22×C37semidirect
516. #340C22×C37semidirect
517. #340C22×C37semidirect
518. #340C22×C37semidirect
519. C37#29601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5252
C2×C37×#4852
C2×C37×#4522
C37×#28482
C37×#20362
C37×#20352
C37×#20342
C37×#20332
C37×#20012
C37×#20002
C37×#18252
C37×#17882
C37×#17792
#2960137