Finite Group Databasebeta

← C37×#24247 #22645500

Subgroups — C37×#24247 #22645500

Order 9472.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#546C211yesmaximal, characteristic
2C2×C37×#464C211yesmaximal, characteristic, complemented
3C2×C37×#452C211yesmaximal, characteristic, complemented
4C2×C37×#450C211yesmaximal, characteristic, complemented
5C2×C4×SD16×C37C211yesmaximal, characteristic, complemented
6C37×#2536C211yesmaximal, characteristic, complemented
7C37×#2035C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#2001C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1958C211yesmaximal, characteristic, complemented
12C37×#1954C211yesmaximal, characteristic, complemented
13C37×#1804C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic, complemented
19C22×SD16×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C37×#546—24no—
22C37×#546—24no—
23C2×#124×C37C2211yescharacteristic
24C2×#123×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×C22⋊Q8×C37C2211yescharacteristic, complemented
28C2×#121×C37—21no—
29C2×#121×C37C2211yescharacteristic
30C2×#120×C37—21no—
31C2×C4×Q8×C37C2211yescharacteristic, complemented
32C2×C4×D4×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic
34C22×C22⋊C4×C37—21no—
35C37×#464—24no—
36C37×#452—24no—
37C37×#450—24no—
38C4×SD16×C37—24no—
39C2×#106×C37C2211yescharacteristic, complemented
40C2×C4⋊C8×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#103×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C2×#102×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C2×C4×C8×C37C2211yescharacteristic, complemented
56C37×#398—21no—
57C37×#394—21no—
58C37×#388—21no—
59C37×#388—21no—
60C37×#382C2211yescharacteristic, complemented
61C37×#380C2211yescharacteristic
62C37×#380C2211yescharacteristic, complemented
63C37×#340C2211yescharacteristic, complemented
64C37×#340C2211yescharacteristic, complemented
65C25×C37—21no—
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—41no—
71C2×#41×C37—41no—
72C22×Q8×C37C2311yescharacteristic
73C22×Q8×C37C2311yescharacteristic
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—22no—
77C22×D4×C37—22no—
78C22×D4×C37—22no—
79C22×D4×C37—22no—
80C22×D4×C37—21no—
81C22×D4×C37—41no—
82C22×D4×C37—41no—
83C22×D4×C37D411yescharacteristic
84C22×D4×C37C2311yescharacteristic
85C22×D4×C37C2311yescharacteristic
86C23×C4×C37—21no—
87C23×C4×C37—21no—
88C23×C4×C37C2311yescharacteristic
89C23×C4×C37C2311yescharacteristic
90C2×Q16×C37—22no—
91C2×Q16×C37—22no—
92C2×Q16×C37—41no—
93C2×SD16×C37—22no—
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—22no—
97C2×SD16×C37—41no—
98C2×SD16×C37D414yescomplemented
99C22×C8×C37C2311yescharacteristic
100C22×C8×C37C2311yescharacteristic
101C22×C8×C37C2311yescharacteristic
102C22×C8×C37C2311yescharacteristic
103#124×C37—22no—
104#124×C37D414yes—
105#123×C37—28no—
106C22⋊Q8×C37—22no—
107C22⋊Q8×C37—22no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37—22no—
110C22⋊Q8×C37—41no—
111C22⋊Q8×C37—41no—
112#121×C37—28no—
113#121×C37—22no—
114#121×C37—22no—
115#120×C37—28no—
116C4×Q8×C37—22no—
117C4×Q8×C37—22no—
118C4×D4×C37—22no—
119C4×D4×C37—22no—
120C4×D4×C37—22no—
121C4×D4×C37D414yes—
122C2×C4⋊C4×C37—21no—
123C2×C4⋊C4×C37—21no—
124C2×C4⋊C4×C37—21no—
125C2×C4⋊C4×C37—21no—
126C2×C4⋊C4×C37D411yescharacteristic
127C2×C4⋊C4×C37C2311yescharacteristic
128C2×C4⋊C4×C37C2311yescharacteristic
129C2×C4⋊C4×C37C2311yescharacteristic
130C2×C4⋊C4×C37C2311yescharacteristic
131C2×C22⋊C4×C37—28no—
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×C22⋊C4×C37—21no—
141C2×C22⋊C4×C37D411yescharacteristic
142C2×C22⋊C4×C37D411yescharacteristic
143C2×C42×C37—21no—
144C2×C42×C37C2311yescharacteristic
145#106×C37—22no—
146C4⋊C8×C37—22no—
147#103×C37—22no—
148#103×C37—22no—
149#103×C37—22no—
150#103×C37—41no—
151#102×C37—22no—
152#102×C37—22no—
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—41no—
157C22⋊C8×C37—22no—
158C22⋊C8×C37—22no—
159C22⋊C8×C37—41no—
160C22⋊C8×C37—41no—
161C4×C8×C37—22no—
162#95×C37—21no—
163#95×C37—21no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—21no—
167C24×C37—24no—
168C24×C37—21no—
169C24×C37—42no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—81no—
174C24×C37—81no—
175C24×C37C2×D411yescharacteristic
176C24×C37C2×D411yescharacteristic
177#41×C37—44no—
178#41×C37—44no—
179#41×C37—44no—
180#41×C37—44no—
181C2×Q8×C37—21no—
182C2×Q8×C37—21no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37—21no—
188C2×Q8×C37—21no—
189C2×Q8×C37—21no—
190C2×Q8×C37—21no—
191C2×Q8×C37C2×D412yes—
192C2×Q8×C37C2×D412yes—
193C2×D4×C37—24no—
194C2×D4×C37—24no—
195C2×D4×C37—22no—
196C2×D4×C37—24no—
197C2×D4×C37—22no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—41no—
207C2×D4×C37—42no—
208C2×D4×C37—42no—
209C2×D4×C37—44no—
210C2×D4×C37—44no—
211C2×D4×C37—44no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—44no—
215C2×D4×C37—81no—
216C2×D4×C37—81no—
217C2×D4×C37C2×D412yes—
218C2×D4×C37C2×D412yes—
219C2×D4×C37C2×D412yes—
220C2×D4×C37#4112yes—
221C22×C4×C37—24no—
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—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—24no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—42no—
242C22×C4×C37—42no—
243C22×C4×C37—81no—
244C22×C4×C37—81no—
245C22×C4×C37C2×D411yescharacteristic
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D411yescharacteristic
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2411yescharacteristic
250Q16×C37—44no—
251SD16×C37—28no—
252SD16×C37—44no—
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—
261C2×C8×C37—21no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37C2×D412yes—
265C4⋊C4×C37—24no—
266C4⋊C4×C37—22no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—42no—
275C4⋊C4×C37—42no—
276C4⋊C4×C37—42no—
277C4⋊C4×C37C2×D412yes—
278C22⋊C4×C37—24no—
279C22⋊C4×C37—24no—
280C22⋊C4×C37—22no—
281C22⋊C4×C37—24no—
282C22⋊C4×C37—24no—
283C22⋊C4×C37—24no—
284C22⋊C4×C37—22no—
285C22⋊C4×C37—42no—
286C22⋊C4×C37—42no—
287C22⋊C4×C37—42no—
288C22⋊C4×C37—42no—
289C42×C37—42no—
290C42×C37C2×D412yes—
291C42×C37C2×D412yes—
292C23×C37—21no—
293C23×C37—22no—
294C23×C37—21no—
295C23×C37—22no—
296C23×C37—21no—
297C23×C37—22no—
298C23×C37—21no—
299C23×C37—21no—
300C23×C37—21no—
301C23×C37—22no—
302C23×C37—21no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—48no—
310C23×C37—48no—
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—84no—
322C23×C37—84no—
323C23×C37—84no—
324C23×C37—84no—
325C23×C37—84no—
326C23×C37#13512yes—
327C23×C37C22×D411yescharacteristic
328Q8×C37—22no—
329Q8×C37—22no—
330Q8×C37—22no—
331Q8×C37—22no—
332Q8×C37—41no—
333Q8×C37—41no—
334Q8×C37—41no—
335Q8×C37—41no—
336D4×C37—22no—
337D4×C37—22no—
338D4×C37—22no—
339D4×C37—22no—
340D4×C37—22no—
341D4×C37—44no—
342D4×C37—48no—
343D4×C37—48no—
344D4×C37—41no—
345D4×C37—41no—
346D4×C37—84no—
347D4×C37#12114yes—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—21no—
351C2×C4×C37—21no—
352C2×C4×C37—22no—
353C2×C4×C37—21no—
354C2×C4×C37—22no—
355C2×C4×C37—21no—
356C2×C4×C37—22no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—21no—
360C2×C4×C37—21no—
361C2×C4×C37—48no—
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—41no—
385C2×C4×C37—84no—
386C2×C4×C37#12012yes—
387C2×C4×C37#12012yes—
388C2×C4×C37C22×D411yescharacteristic
389C2×C4×C37C22×D411yescharacteristic
390C2×C4×C37C22×D411yescharacteristic
391C2×C4×C37C2×#4111yescharacteristic
392C2×C4×C37H(5,𝔽2)11yescharacteristic
393C2×C4×C37H(5,𝔽2)11yescharacteristic
394C8×C37—22no—
395C8×C37—41no—
396C8×C37—41no—
397C8×C37—41no—
398#24247C3711yesmaximal, characteristic, direct product factor, Sylow
399C22×C37—24no—
400C22×C37—22no—
401C22×C37—22no—
402C22×C37—22no—
403C22×C37—41no—
404C22×C37—42no—
405C22×C37—42no—
406C22×C37—41no—
407C22×C37—41no—
408C22×C37—42no—
409C22×C37—42no—
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—42no—
419C22×C37—41no—
420C22×C37—41no—
421C22×C37—41no—
422C22×C37—41no—
423C22×C37—816no—
424C22×C37—81no—
425C22×C37—81no—
426C22×C37—81no—
427C22×C37—81no—
428C22×C37C2×#12011yescharacteristic
429C22×C37D4211yescharacteristic
430C22×C37#54611yescharacteristic
431C22×C37C2×#13511yescharacteristic
432C22×C37#57511yescharacteristic
433C22×C37#57711yescharacteristic
434C22×C37#57711yescharacteristic
435C4×C37—22no—
436C4×C37—22no—
437C4×C37—41no—
438C4×C37—41no—
439C4×C37—42no—
440C4×C37—42no—
441C4×C37—42no—
442C4×C37—81no—
443C4×C37—81no—
444C4×C37—81no—
445C4×C37C2×#12111yescharacteristic
446C4×C37#53511yescharacteristic
447C4×C37D4211yescharacteristic
448C4×C37#54611yescharacteristic
449C2×#546C2×C3711yescharacteristic
450C2×#464C2×C3711yescharacteristic, complemented
451C2×#452C2×C3711yescharacteristic, complemented
452C2×#450C2×C3711yescharacteristic, complemented
453C2×C4×SD16C2×C3711yescharacteristic, complemented
454#2536C2×C3711yescharacteristic, complemented
455#2035C2×C3711yescharacteristic, complemented
456#2034C2×C3711yescharacteristic, complemented
457#2001C2×C3711yescharacteristic, complemented
458#2000C2×C3711yescharacteristic, complemented
459#1958C2×C3711yescharacteristic, complemented
460#1954C2×C3711yescharacteristic, complemented
461#1804C2×C3711yescharacteristic, complemented
462#1788C2×C3711yescharacteristic, complemented
463#1786C2×C3711yescharacteristic, complemented
464C2×C37—42no—
465C2×C37—44no—
466C2×C37—81no—
467C2×C37—82no—
468C2×C37#240811yescharacteristic
469C2×C37#300211yescharacteristic
470C2×C37#300911yescharacteristic
471C2×C37#327511yescharacteristic
472C2×C37#328211yescharacteristic
473C2×C37#329611yescharacteristic
474C2×C37#332311yescharacteristic
475C22×#41C22×C3711yescharacteristic
476C23×D4C22×C3711yescharacteristic
477C22×Q16C22×C3711yescharacteristic, complemented
478C22×SD16C22×C3711yescharacteristic
479C22×SD16C22×C3711yescharacteristic
480#546—24no—
481#546—24no—
482C2×#124C22×C3711yescharacteristic
483C2×#123—21no—
484C2×C22⋊Q8C22×C3711yescharacteristic
485C2×C22⋊Q8C22×C3711yescharacteristic
486C2×C22⋊Q8C22×C3711yescharacteristic, complemented
487C2×#121—21no—
488C2×#121C22×C3711yescharacteristic
489C2×#120—21no—
490C2×C4×Q8C22×C3711yescharacteristic, complemented
491C2×C4×D4C22×C3711yescharacteristic
492C2×C4×D4C22×C3711yescharacteristic
493C22×C22⋊C4—21no—
494#464—24no—
495#452—24no—
496#450—24no—
497C4×SD16—24no—
498C2×#106C22×C3711yescharacteristic, complemented
499C2×C4⋊C8C22×C3711yescharacteristic, complemented
500C2×#103C22×C3711yescharacteristic, complemented
501C2×#103C22×C3711yescharacteristic, complemented
502C2×#103C22×C3711yescharacteristic, complemented
503C2×#103C22×C3711yescharacteristic, complemented
504C2×#102C22×C3711yescharacteristic
505C2×#102C22×C3711yescharacteristic
506C2×#102C22×C3711yescharacteristic
507C2×#102C22×C3711yescharacteristic
508C2×#102C22×C3711yescharacteristic
509C2×#102C22×C3711yescharacteristic
510C2×C22⋊C8C22×C3711yescharacteristic
511C2×C22⋊C8C22×C3711yescharacteristic
512C2×C22⋊C8C22×C3711yescharacteristic, complemented
513C2×C22⋊C8C22×C3711yescharacteristic, complemented
514C2×C4×C8C22×C3711yescharacteristic, complemented
515#398—21no—
516#394—21no—
517#388—21no—
518#388—21no—
519#382C22×C3711yescharacteristic, complemented
520#380C22×C3711yescharacteristic
521#380C22×C3711yescharacteristic, complemented
522#340C22×C3711yescharacteristic, complemented
523#340C22×C3711yescharacteristic, complemented
524C37#2424711yescharacteristic, direct product factor, Sylow
525C25—21no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C22×Q8C23×C3711yescharacteristic
533C22×Q8C23×C3711yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C3711yescharacteristic
544C22×D4C23×C3711yescharacteristic
545C22×D4C23×C3711yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C3711yescharacteristic
549C23×C4C23×C3711yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16D4×C3714yescomplemented
559C22×C8C23×C3711yescharacteristic
560C22×C8C23×C3711yescharacteristic
561C22×C8C23×C3711yescharacteristic
562C22×C8C23×C3711yescharacteristic
563#124—22no—
564#124D4×C3714yes—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—28no—
573#121—22no—
574#121—22no—
575#120—28no—
576C4×Q8—22no—
577C4×Q8—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4D4×C3714yes—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4D4×C3711yescharacteristic
587C2×C4⋊C4C23×C3711yescharacteristic
588C2×C4⋊C4C23×C3711yescharacteristic
589C2×C4⋊C4C23×C3711yescharacteristic
590C2×C4⋊C4C23×C3711yescharacteristic
591C2×C22⋊C4—28no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
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#106—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—41no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8—41no—
620C22⋊C8—41no—
621C4×C8—22no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—24no—
628C24—21no—
629C24—42no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—81no—
634C24—81no—
635C24C2×D4×C3711yescharacteristic
636C24C2×D4×C3711yescharacteristic
637#41—44no—
638#41—44no—
639#41—44no—
640#41—44no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8C2×D4×C3712yes—
652C2×Q8C2×D4×C3712yes—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
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—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—44no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C3712yes—
678C2×D4C2×D4×C3712yes—
679C2×D4C2×D4×C3712yes—
680C2×D4#41×C3712yes—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—81no—
704C22×C4—81no—
705C22×C4C2×D4×C3711yescharacteristic
706C22×C4C2×D4×C3711yescharacteristic
707C22×C4C2×D4×C3711yescharacteristic
708C22×C4C2×D4×C3711yescharacteristic
709C22×C4C24×C3711yescharacteristic
710Q16—44no—
711SD16—28no—
712SD16—44no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8C2×D4×C3712yes—
725C4⋊C4—24no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4C2×D4×C3712yes—
738C22⋊C4—24no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—42no—
750C42C2×D4×C3712yes—
751C42C2×D4×C3712yes—
752C23—21no—
753C23—22no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—48no—
770C23—48no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—84no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23#135×C3712yes—
787C23C22×D4×C3711yescharacteristic
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—44no—
802D4—48no—
803D4—48no—
804D4—41no—
805D4—41no—
806D4—84no—
807D4#121×C3714yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—48no—
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—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—84no—
846C2×C4#120×C3712yes—
847C2×C4#120×C3712yes—
848C2×C4C22×D4×C3711yescharacteristic
849C2×C4C22×D4×C3711yescharacteristic
850C2×C4C22×D4×C3711yescharacteristic
851C2×C4C2×#41×C3711yescharacteristic
852C2×C4H(5,𝔽2)×C3711yescharacteristic
853C2×C4H(5,𝔽2)×C3711yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—816no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22C2×#120×C3711yescharacteristic
888C22D42×C3711yescharacteristic
889C22C37×#54611yescharacteristic
890C22C2×#135×C3711yescharacteristic
891C22C37×#57511yescharacteristic
892C22C37×#57711yescharacteristic
893C22C37×#57711yescharacteristic
894C4—22no—
895C4—22no—
896C4—41no—
897C4—41no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4C2×#121×C3711yescharacteristic
905C4C37×#53511yescharacteristic
906C4D42×C3711yescharacteristic
907C4C37×#54611yescharacteristic
908C2—42no—
909C2—44no—
910C2—81no—
911C2—82no—
912C2C37×#240811yescharacteristic
913C2C37×#300211yescharacteristic
914C2C37×#300911yescharacteristic
915C2C37×#327511yescharacteristic
916C2C37×#328211yescharacteristic
917C2C37×#329611yescharacteristic
918C2C37×#332311yescharacteristic
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×#464C2semidirect
3. C2×C37×#452C2semidirect
4. C2×C37×#450C2semidirect
5. C2×C4×SD16×C37C2semidirect
6. C37×#2536C2semidirect
7. C37×#2035C2semidirect
8. C37×#2034C2semidirect
9. C37×#2001C2semidirect
10. C37×#2000C2semidirect
11. C37×#1958C2semidirect
12. C37×#1954C2semidirect
13. C37×#1804C2semidirect
14. C37×#1788C2semidirect
15. C37×#1786C2semidirect
18. C22×Q16×C37C22semidirect
27. C2×C22⋊Q8×C37C22semidirect
31. C2×C4×Q8×C37C22semidirect
39. C2×#106×C37C22semidirect
40. C2×C4⋊C8×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
44. C2×#103×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C2×C22⋊C8×C37C22semidirect
55. C2×C4×C8×C37C22semidirect
60. C37×#382C22semidirect
62. C37×#380C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
98. C2×SD16×C37D4semidirect
398. #24247C37direct (N × H)
450. C2×#464C2×C37semidirect
451. C2×#452C2×C37semidirect
452. C2×#450C2×C37semidirect
453. C2×C4×SD16C2×C37semidirect
454. #2536C2×C37semidirect
455. #2035C2×C37semidirect
456. #2034C2×C37semidirect
457. #2001C2×C37semidirect
458. #2000C2×C37semidirect
459. #1958C2×C37semidirect
460. #1954C2×C37semidirect
461. #1804C2×C37semidirect
462. #1788C2×C37semidirect
463. #1786C2×C37semidirect
477. C22×Q16C22×C37semidirect
486. C2×C22⋊Q8C22×C37semidirect
490. C2×C4×Q8C22×C37semidirect
498. C2×#106C22×C37semidirect
499. C2×C4⋊C8C22×C37semidirect
500. C2×#103C22×C37semidirect
501. C2×#103C22×C37semidirect
502. C2×#103C22×C37semidirect
503. C2×#103C22×C37semidirect
512. C2×C22⋊C8C22×C37semidirect
513. C2×C22⋊C8C22×C37semidirect
514. C2×C4×C8C22×C37semidirect
519. #382C22×C37semidirect
521. #380C22×C37semidirect
522. #340C22×C37semidirect
523. #340C22×C37semidirect
524. C37#24247direct (N × H)
558. C2×SD16D4×C37semidirect

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×#4642
C2×C37×#4522
C2×C37×#4502
C2×C4×SD16×C372
C37×#25362
C37×#20352
C37×#20342
C37×#20012
C37×#20002
C37×#19582
C37×#19542
C37×#18042
C37×#17882
C37×#17862
#2424737