Finite Group Databasebeta

← C37×#24426 #22645679

Subgroups — C37×#24426 #22645679

Order 9472.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#546C211yesmaximal, characteristic
2C2×C37×#467C211yesmaximal, characteristic, complemented
3C2×C37×#452C211yesmaximal, characteristic, complemented
4C2×C37×#450C211yesmaximal, characteristic, complemented
5C22×#102×C37C211yesmaximal, characteristic, complemented
6C37×#2417C211yesmaximal, characteristic, complemented
7C37×#2042C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2015C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1877C211yesmaximal, characteristic, complemented
12C37×#1872C211yesmaximal, characteristic, complemented
13C37×#1869C211yesmaximal, characteristic, complemented
14C37×#1862C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic, complemented
19C22×SD16×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C23×C8×C37C2211yescharacteristic
22C37×#546—24no—
23C37×#546—24no—
24C2×#124×C37C2211yescharacteristic
25C2×#123×C37—21no—
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×C22⋊Q8×C37C2211yescharacteristic
28C2×C22⋊Q8×C37C2211yescharacteristic, complemented
29C2×#121×C37—21no—
30C2×#121×C37C2211yescharacteristic
31C2×#120×C37—21no—
32C2×C4×D4×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic
34C22×C4⋊C4×C37C2211yescharacteristic
35C22×C22⋊C4×C37—21no—
36C37×#467—24no—
37C37×#452—24no—
38C37×#450—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C2×#103×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#102×C37—24no—
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, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#398—21no—
55C37×#396—21no—
56C37×#391C2211yescharacteristic, complemented
57C37×#389C2211yescharacteristic, complemented
58C37×#386—21no—
59C37×#380—21no—
60C37×#380C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#336C2211yescharacteristic, complemented
64C37×#336C2211yescharacteristic, 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—22no—
75C22×D4×C37—22no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—22no—
80C22×D4×C37—41no—
81C22×D4×C37—41no—
82C22×D4×C37D411yescharacteristic
83C22×D4×C37D414yes—
84C22×D4×C37C2311yescharacteristic
85C22×D4×C37C2311yescharacteristic
86C23×C4×C37—21no—
87C23×C4×C37—21no—
88C23×C4×C37—21no—
89C23×C4×C37C2311yescharacteristic
90C23×C4×C37C2311yescharacteristic
91C2×Q16×C37—22no—
92C2×Q16×C37—22no—
93C2×Q16×C37—41no—
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—22no—
97C2×SD16×C37—22no—
98C2×SD16×C37—41no—
99C2×SD16×C37—41no—
100C22×C8×C37—22no—
101C22×C8×C37—22no—
102C22×C8×C37—41no—
103C22×C8×C37C2311yescharacteristic
104C22×C8×C37C2311yescharacteristic
105C22×C8×C37C2311yescharacteristic
106C22×C8×C37C2311yescharacteristic
107#124×C37—22no—
108#124×C37—22no—
109#123×C37—28no—
110C22⋊Q8×C37—22no—
111C22⋊Q8×C37—22no—
112C22⋊Q8×C37—22no—
113C22⋊Q8×C37—22no—
114C22⋊Q8×C37—41no—
115C22⋊Q8×C37D414yes—
116#121×C37—28no—
117#121×C37—22no—
118#121×C37—22no—
119#120×C37—28no—
120C4×D4×C37—22no—
121C4×D4×C37—22no—
122C4×D4×C37—22no—
123C4×D4×C37—22no—
124C2×C4⋊C4×C37—21no—
125C2×C4⋊C4×C37—22no—
126C2×C4⋊C4×C37—21no—
127C2×C4⋊C4×C37—21no—
128C2×C4⋊C4×C37—21no—
129C2×C4⋊C4×C37—21no—
130C2×C4⋊C4×C37—41no—
131C2×C4⋊C4×C37D411yescharacteristic
132C2×C4⋊C4×C37C2311yescharacteristic
133C2×C4⋊C4×C37C2311yescharacteristic
134C2×C4⋊C4×C37C2311yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C22⋊C4×C37—28no—
137C2×C22⋊C4×C37—21no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—21no—
140C2×C22⋊C4×C37—21no—
141C2×C22⋊C4×C37—21no—
142C2×C22⋊C4×C37—21no—
143C2×C22⋊C4×C37—21no—
144C2×C22⋊C4×C37—21no—
145C2×C22⋊C4×C37D411yescharacteristic
146C2×C22⋊C4×C37D411yescharacteristic
147C2×C42×C37C2311yescharacteristic
148#107×C37—22no—
149#103×C37—22no—
150#103×C37—22no—
151#103×C37—22no—
152#103×C37—41no—
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—22no—
158#102×C37D414yescomplemented
159C22⋊C8×C37—22no—
160C22⋊C8×C37—22no—
161C22⋊C8×C37—41no—
162#95×C37—21no—
163#95×C37—21no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—21no—
167C24×C37—21no—
168C24×C37—24no—
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×C37—21no—
192C2×Q8×C37C2×D412yes—
193C2×D4×C37—28no—
194C2×D4×C37—24no—
195C2×D4×C37—22no—
196C2×D4×C37—22no—
197C2×D4×C37—22no—
198C2×D4×C37—24no—
199C2×D4×C37—24no—
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—21no—
207C2×D4×C37—21no—
208C2×D4×C37—44no—
209C2×D4×C37—44no—
210C2×D4×C37—44no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
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—21no—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—24no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
229C22×C4×C37—24no—
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×C37—42no—
242C22×C4×C37—42no—
243C22×C4×C37—81no—
244C22×C4×C37—81no—
245C22×C4×C37—81no—
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D411yescharacteristic
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D412yes—
251C22×C4×C37C2×D412yes—
252C22×C4×C37C2411yescharacteristic
253Q16×C37—44no—
254SD16×C37—44no—
255SD16×C37—44no—
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×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—44no—
268C2×C8×C37C2×D412yes—
269C4⋊C4×C37—24no—
270C4⋊C4×C37—22no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—42no—
278C4⋊C4×C37—42no—
279C4⋊C4×C37—42no—
280C4⋊C4×C37—81no—
281C4⋊C4×C37C2×D412yes—
282C4⋊C4×C37C2×D412yes—
283C22⋊C4×C37—24no—
284C22⋊C4×C37—24no—
285C22⋊C4×C37—24no—
286C22⋊C4×C37—24no—
287C22⋊C4×C37—22no—
288C22⋊C4×C37—24no—
289C22⋊C4×C37—22no—
290C22⋊C4×C37—42no—
291C22⋊C4×C37—42no—
292C22⋊C4×C37—81no—
293C42×C37—21no—
294C42×C37—21no—
295C23×C37—21no—
296C23×C37—21no—
297C23×C37—21no—
298C23×C37—21no—
299C23×C37—22no—
300C23×C37—22no—
301C23×C37—22no—
302C23×C37—22no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
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—48no—
322C23×C37—84no—
323C23×C37—84no—
324C23×C37—84no—
325C23×C37—84no—
326C23×C37—84no—
327C23×C37#12012yes—
328C23×C37#13512yes—
329C23×C37#13712yes—
330C23×C37C22×D411yescharacteristic
331Q8×C37—22no—
332Q8×C37—22no—
333Q8×C37—41no—
334Q8×C37—41no—
335Q8×C37—41no—
336Q8×C37—41no—
337Q8×C37—41no—
338Q8×C37—41no—
339D4×C37—22no—
340D4×C37—22no—
341D4×C37—22no—
342D4×C37—22no—
343D4×C37—22no—
344D4×C37—48no—
345D4×C37—48no—
346D4×C37—44no—
347D4×C37—41no—
348D4×C37—41no—
349D4×C37—84no—
350D4×C37#12114yes—
351C2×C4×C37—21no—
352C2×C4×C37—21no—
353C2×C4×C37—22no—
354C2×C4×C37—22no—
355C2×C4×C37—22no—
356C2×C4×C37—22no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—22no—
360C2×C4×C37—21no—
361C2×C4×C37—22no—
362C2×C4×C37—22no—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—48no—
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—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—84no—
390C2×C4×C37—84no—
391C2×C4×C37#12012yes—
392C2×C4×C37C22×D411yescharacteristic
393C2×C4×C37C22×D411yescharacteristic
394C2×C4×C37C22×D411yescharacteristic
395C2×C4×C37C2×#4111yescharacteristic
396C2×C4×C37H(5,𝔽2)11yescharacteristic
397C2×C4×C37H(5,𝔽2)11yescharacteristic
398C8×C37—22no—
399C8×C37—41no—
400C8×C37—41no—
401C8×C37—41no—
402#24426C3711yesmaximal, characteristic, direct product factor, Sylow
403C22×C37—22no—
404C22×C37—22no—
405C22×C37—22no—
406C22×C37—22no—
407C22×C37—22no—
408C22×C37—22no—
409C22×C37—24no—
410C22×C37—42no—
411C22×C37—42no—
412C22×C37—42no—
413C22×C37—42no—
414C22×C37—42no—
415C22×C37—42no—
416C22×C37—41no—
417C22×C37—42no—
418C22×C37—41no—
419C22×C37—42no—
420C22×C37—41no—
421C22×C37—41no—
422C22×C37—42no—
423C22×C37—41no—
424C22×C37—41no—
425C22×C37—41no—
426C22×C37—816no—
427C22×C37—81no—
428C22×C37—81no—
429C22×C37—81no—
430C22×C37—81no—
431C22×C37#45214yescomplemented
432C22×C37C2×#12011yescharacteristic
433C22×C37D4211yescharacteristic
434C22×C37#54611yescharacteristic
435C22×C37C2×#13511yescharacteristic
436C22×C37C2×#13711yescharacteristic
437C22×C37#57611yescharacteristic
438C22×C37#57711yescharacteristic
439C4×C37—22no—
440C4×C37—41no—
441C4×C37—42no—
442C4×C37—41no—
443C4×C37—41no—
444C4×C37—42no—
445C4×C37—42no—
446C4×C37—81no—
447C4×C37—81no—
448C4×C37—81no—
449C4×C37C2×#12111yescharacteristic
450C4×C37#53411yescharacteristic
451C4×C37D4211yescharacteristic
452C4×C37#54611yescharacteristic
453C2×#546C2×C3711yescharacteristic
454C2×#467C2×C3711yescharacteristic, complemented
455C2×#452C2×C3711yescharacteristic, complemented
456C2×#450C2×C3711yescharacteristic, complemented
457C22×#102C2×C3711yescharacteristic, complemented
458#2417C2×C3711yescharacteristic, complemented
459#2042C2×C3711yescharacteristic, complemented
460#2033C2×C3711yescharacteristic, complemented
461#2015C2×C3711yescharacteristic, complemented
462#2000C2×C3711yescharacteristic, complemented
463#1877C2×C3711yescharacteristic, complemented
464#1872C2×C3711yescharacteristic, complemented
465#1869C2×C3711yescharacteristic, complemented
466#1862C2×C3711yescharacteristic, complemented
467#1788C2×C3711yescharacteristic, complemented
468C2×C37—24no—
469C2×C37—44no—
470C2×C37—81no—
471C2×C37—82no—
472C2×C37#241011yescharacteristic
473C2×C37C2×#45211yescharacteristic
474C2×C37#301211yescharacteristic
475C2×C37#326611yescharacteristic
476C2×C37#328011yescharacteristic
477C2×C37#329611yescharacteristic
478C2×C37#331411yescharacteristic
479C22×#41C22×C3711yescharacteristic
480C23×D4C22×C3711yescharacteristic
481C22×Q16C22×C3711yescharacteristic, complemented
482C22×SD16C22×C3711yescharacteristic
483C22×SD16C22×C3711yescharacteristic
484C23×C8C22×C3711yescharacteristic
485#546—24no—
486#546—24no—
487C2×#124C22×C3711yescharacteristic
488C2×#123—21no—
489C2×C22⋊Q8C22×C3711yescharacteristic
490C2×C22⋊Q8C22×C3711yescharacteristic
491C2×C22⋊Q8C22×C3711yescharacteristic, complemented
492C2×#121—21no—
493C2×#121C22×C3711yescharacteristic
494C2×#120—21no—
495C2×C4×D4C22×C3711yescharacteristic
496C2×C4×D4C22×C3711yescharacteristic
497C22×C4⋊C4C22×C3711yescharacteristic
498C22×C22⋊C4—21no—
499#467—24no—
500#452—24no—
501#450—24no—
502C2×#107C22×C3711yescharacteristic, complemented
503C2×#103C22×C3711yescharacteristic, complemented
504C2×#103C22×C3711yescharacteristic, complemented
505C2×#103C22×C3711yescharacteristic, complemented
506C2×#103C22×C3711yescharacteristic, complemented
507C2×#102—24no—
508C2×#102C22×C3711yescharacteristic
509C2×#102C22×C3711yescharacteristic
510C2×#102C22×C3711yescharacteristic
511C2×#102C22×C3711yescharacteristic
512C2×#102C22×C3711yescharacteristic
513C2×#102C22×C3711yescharacteristic
514C2×C22⋊C8C22×C3711yescharacteristic
515C2×C22⋊C8C22×C3711yescharacteristic, complemented
516C2×C22⋊C8C22×C3711yescharacteristic, complemented
517#398—21no—
518#396—21no—
519#391C22×C3711yescharacteristic, complemented
520#389C22×C3711yescharacteristic, complemented
521#386—21no—
522#380—21no—
523#380C22×C3711yescharacteristic, complemented
524#340C22×C3711yescharacteristic, complemented
525#340C22×C3711yescharacteristic, complemented
526#336C22×C3711yescharacteristic, complemented
527#336C22×C3711yescharacteristic, complemented
528C37#2442611yescharacteristic, direct product factor, Sylow
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—41no—
535C2×#41—41no—
536C22×Q8C23×C3711yescharacteristic
537C22×Q8C23×C3711yescharacteristic
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4D4×C3711yescharacteristic
547C22×D4D4×C3714yes—
548C22×D4C23×C3711yescharacteristic
549C22×D4C23×C3711yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C3711yescharacteristic
554C23×C4C23×C3711yescharacteristic
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—41no—
567C22×C8C23×C3711yescharacteristic
568C22×C8C23×C3711yescharacteristic
569C22×C8C23×C3711yescharacteristic
570C22×C8C23×C3711yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579C22⋊Q8D4×C3714yes—
580#121—28no—
581#121—22no—
582#121—22no—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C3711yescharacteristic
596C2×C4⋊C4C23×C3711yescharacteristic
597C2×C4⋊C4C23×C3711yescharacteristic
598C2×C4⋊C4C23×C3711yescharacteristic
599C2×C4⋊C4C23×C3711yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C3711yescharacteristic
610C2×C22⋊C4D4×C3711yescharacteristic
611C2×C42C23×C3711yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—22no—
622#102D4×C3714yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—21no—
632C24—24no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C3711yescharacteristic
640C24C2×D4×C3711yescharacteristic
641#41—44no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C3712yes—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C3712yes—
682C2×D4C2×D4×C3712yes—
683C2×D4C2×D4×C3712yes—
684C2×D4#41×C3712yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C3711yescharacteristic
711C22×C4C2×D4×C3711yescharacteristic
712C22×C4C2×D4×C3711yescharacteristic
713C22×C4C2×D4×C3711yescharacteristic
714C22×C4C2×D4×C3712yes—
715C22×C4C2×D4×C3712yes—
716C22×C4C24×C3711yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—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—44no—
732C2×C8C2×D4×C3712yes—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C3712yes—
746C4⋊C4C2×D4×C3712yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—22no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—48no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#120×C3712yes—
792C23#135×C3712yes—
793C23#137×C3712yes—
794C23C22×D4×C3711yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—48no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C3714yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
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—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4#120×C3712yes—
856C2×C4C22×D4×C3711yescharacteristic
857C2×C4C22×D4×C3711yescharacteristic
858C2×C4C22×D4×C3711yescharacteristic
859C2×C4C2×#41×C3711yescharacteristic
860C2×C4H(5,𝔽2)×C3711yescharacteristic
861C2×C4H(5,𝔽2)×C3711yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—816no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22C37×#45214yescomplemented
895C22C2×#120×C3711yescharacteristic
896C22D42×C3711yescharacteristic
897C22C37×#54611yescharacteristic
898C22C2×#135×C3711yescharacteristic
899C22C2×#137×C3711yescharacteristic
900C22C37×#57611yescharacteristic
901C22C37×#57711yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C3711yescharacteristic
913C4C37×#53411yescharacteristic
914C4D42×C3711yescharacteristic
915C4C37×#54611yescharacteristic
916C2—24no—
917C2—44no—
918C2—81no—
919C2—82no—
920C2C37×#241011yescharacteristic
921C2C2×C37×#45211yescharacteristic
922C2C37×#301211yescharacteristic
923C2C37×#326611yescharacteristic
924C2C37×#328011yescharacteristic
925C2C37×#329611yescharacteristic
926C2C37×#331411yescharacteristic
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×#467C2semidirect
3. C2×C37×#452C2semidirect
4. C2×C37×#450C2semidirect
5. C22×#102×C37C2semidirect
6. C37×#2417C2semidirect
7. C37×#2042C2semidirect
8. C37×#2033C2semidirect
9. C37×#2015C2semidirect
10. C37×#2000C2semidirect
11. C37×#1877C2semidirect
12. C37×#1872C2semidirect
13. C37×#1869C2semidirect
14. C37×#1862C2semidirect
15. C37×#1788C2semidirect
18. C22×Q16×C37C22semidirect
28. C2×C22⋊Q8×C37C22semidirect
39. C2×#107×C37C22semidirect
40. C2×#103×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
52. C2×C22⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
56. C37×#391C22semidirect
57. C37×#389C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
158. #102×C37D4semidirect
402. #24426C37direct (N × H)
431. C22×C37#452semidirect
454. C2×#467C2×C37semidirect
455. C2×#452C2×C37semidirect
456. C2×#450C2×C37semidirect
457. C22×#102C2×C37semidirect
458. #2417C2×C37semidirect
459. #2042C2×C37semidirect
460. #2033C2×C37semidirect
461. #2015C2×C37semidirect
462. #2000C2×C37semidirect
463. #1877C2×C37semidirect
464. #1872C2×C37semidirect
465. #1869C2×C37semidirect
466. #1862C2×C37semidirect
467. #1788C2×C37semidirect
481. C22×Q16C22×C37semidirect
491. C2×C22⋊Q8C22×C37semidirect
502. C2×#107C22×C37semidirect
503. C2×#103C22×C37semidirect
504. C2×#103C22×C37semidirect
505. C2×#103C22×C37semidirect
506. C2×#103C22×C37semidirect
515. C2×C22⋊C8C22×C37semidirect
516. C2×C22⋊C8C22×C37semidirect
519. #391C22×C37semidirect
520. #389C22×C37semidirect
523. #380C22×C37semidirect
524. #340C22×C37semidirect
525. #340C22×C37semidirect
526. #336C22×C37semidirect
527. #336C22×C37semidirect
528. C37#24426direct (N × H)
622. #102D4×C37semidirect
894. C22C37×#452semidirect

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×#4672
C2×C37×#4522
C2×C37×#4502
C22×#102×C372
C37×#24172
C37×#20422
C37×#20332
C37×#20152
C37×#20002
C37×#18772
C37×#18722
C37×#18692
C37×#18622
C37×#17882
#2442637