Finite Group Databasebeta

← C37×#24140 #22645393

Subgroups — C37×#24140 #22645393

Order 9472.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3505C211yesmaximal, characteristic, complemented
2C37×#2848C211yesmaximal, characteristic, complemented
3C37×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C37C211yesmaximal, characteristic, complemented
5C37×#2044C212yesmaximal, complemented
6C37×#2021C212yesmaximal, complemented
7C37×#1996C211yesmaximal, characteristic, complemented
8C37×#1964C211yesmaximal, characteristic, complemented
9C37×#1889C212yesmaximal, complemented
10C37×#1867C212yesmaximal, complemented
11C37×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C37C2211yescharacteristic
13C37×#553—21no—
14C37×#553—22no—
15C37×#552—21no—
16C37×#551—22no—
17C37×#548—21no—
18C37×#546—21no—
19C37×#539—21no—
20C37×#538—21no—
21C37×#534C2212yes—
22C37×#529—21no—
23C37×#525—21no—
24C2×C22⋊Q8×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×#121×C37—21no—
27C2×#121×C37C2211yescharacteristic
28C2×#120×C37C2211yescharacteristic
29C2×#120×C37C2212yes—
30C37×#518C2212yes—
31C2×C4×D4×C37—21no—
32C2×C4×D4×C37C2211yescharacteristic
33C2×#99×C37C2212yes—
34C2×#99×C37C2212yes—
35C2×#99×C37C2212yes—
36C37×#386—21no—
37C37×#386—22no—
38C37×#386C2212yes—
39C37×#386C2211yescharacteristic
40C37×#385—21no—
41C37×#385—22no—
42C37×#385C2211yescharacteristic
43C37×#385C2212yes—
44C37×#380—21no—
45C37×#380—21no—
46C37×#380C2211yescharacteristic
47C37×#380C2211yescharacteristic
48C37×#379C2211yescharacteristic
49C37×#379C2212yes—
50C4×C22⋊C4×C37—21no—
51C4×C22⋊C4×C37C2211yescharacteristic
52C37×#342C2212yes—
53C37×#342C2212yes—
54C37×#342C2212yes—
55C25×C37C2311yescharacteristic
56C2×#41×C37—21no—
57C22×Q8×C37D411yescharacteristic, complemented
58C22×D4×C37—21no—
59C22×D4×C37—22no—
60C22×D4×C37D411yescharacteristic, complemented
61C22×D4×C37C2312yes—
62C22×D4×C37C2311yescharacteristic
63C23×C4×C37—21no—
64C23×C4×C37—21no—
65C23×C4×C37—21no—
66C23×C4×C37—21no—
67C23×C4×C37—21no—
68C23×C4×C37—21no—
69C23×C4×C37—44no—
70C23×C4×C37D411yescharacteristic, complemented
71C23×C4×C37C2311yescharacteristic
72C23×C4×C37C2311yescharacteristic
73#126×C37—22no—
74#126×C37—22no—
75#126×C37—22no—
76#125×C37—21no—
77#125×C37—22no—
78#124×C37—21no—
79#124×C37—22no—
80#123×C37—22no—
81#123×C37—22no—
82#123×C37—22no—
83#123×C37—22no—
84#123×C37—22no—
85C22⋊Q8×C37—21no—
86C22⋊Q8×C37—22no—
87C22⋊Q8×C37—21no—
88C22⋊Q8×C37—21no—
89C22⋊Q8×C37—21no—
90C22⋊Q8×C37—21no—
91C22⋊Q8×C37—44no—
92#121×C37—21no—
93#121×C37—22no—
94#121×C37—21no—
95#121×C37—21no—
96#121×C37—21no—
97#121×C37—21no—
98#121×C37—22no—
99#121×C37—22no—
100#121×C37—44no—
101#120×C37—22no—
102#120×C37—22no—
103#120×C37—22no—
104#120×C37—22no—
105#120×C37—24no—
106#120×C37—42no—
107C4×Q8×C37—21no—
108C4×D4×C37—22no—
109C4×D4×C37—21no—
110C4×D4×C37—22no—
111C4×D4×C37—22no—
112C4×D4×C37—21no—
113C4×D4×C37—21no—
114C4×D4×C37—22no—
115C4×D4×C37—21no—
116C4×D4×C37—21no—
117C4×D4×C37—22no—
118C4×D4×C37—44no—
119#117×C37—21no—
120#117×C37—22no—
121#117×C37—22no—
122C2×C4⋊C4×C37—21no—
123C2×C4⋊C4×C37—21no—
124C2×C4⋊C4×C37—22no—
125C2×C4⋊C4×C37—21no—
126C2×C4⋊C4×C37D411yescharacteristic, complemented
127C2×C4⋊C4×C37D411yescharacteristic, complemented
128C2×C4⋊C4×C37D412yescomplemented
129C2×C4⋊C4×C37D411yescharacteristic, complemented
130C2×C22⋊C4×C37—22no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37—22no—
133C2×C22⋊C4×C37—21no—
134C2×C22⋊C4×C37—22no—
135C2×C22⋊C4×C37—22no—
136C2×C22⋊C4×C37—21no—
137C2×C22⋊C4×C37—22no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37D412yescomplemented
140C2×C22⋊C4×C37D411yescharacteristic, complemented
141C2×C22⋊C4×C37C2312yes—
142C2×C22⋊C4×C37C2311yescharacteristic
143C2×C22⋊C4×C37C2312yes—
144C2×C22⋊C4×C37C2312yes—
145C2×C22⋊C4×C37C2311yescharacteristic
146C2×C22⋊C4×C37C2311yescharacteristic
147C2×C42×C37—21no—
148C2×C42×C37D411yescharacteristic, complemented
149#99×C37—24no—
150#99×C37—42no—
151#99×C37—42no—
152#95×C37—21no—
153#95×C37—21no—
154#95×C37—21no—
155#95×C37—22no—
156#95×C37—22no—
157#95×C37—21no—
158#95×C37—21no—
159C24×C37—21no—
160C24×C37—21no—
161C24×C37—21no—
162C24×C37—21no—
163C24×C37—21no—
164C24×C37—21no—
165C24×C37—42no—
166C24×C37—42no—
167C24×C37C2×D412yes—
168C24×C37C2×D411yescharacteristic
169C24×C37#4112yescomplemented
170C24×C37C2411yescharacteristic
171#41×C37—82no—
172C2×Q8×C37—21no—
173C2×Q8×C37—21no—
174C2×Q8×C37—42no—
175C2×D4×C37—24no—
176C2×D4×C37—21no—
177C2×D4×C37—22no—
178C2×D4×C37—21no—
179C2×D4×C37—22no—
180C2×D4×C37—22no—
181C2×D4×C37—21no—
182C2×D4×C37—21no—
183C2×D4×C37—22no—
184C2×D4×C37—21no—
185C2×D4×C37—22no—
186C2×D4×C37—21no—
187C2×D4×C37—22no—
188C2×D4×C37—22no—
189C2×D4×C37—22no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—42no—
193C2×D4×C37—42no—
194C2×D4×C37—42no—
195C2×D4×C37—44no—
196C2×D4×C37—44no—
197C2×D4×C37—44no—
198C22×C4×C37—24no—
199C22×C4×C37—24no—
200C22×C4×C37—24no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—22no—
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—42no—
213C22×C4×C37—42no—
214C22×C4×C37—42no—
215C22×C4×C37—42no—
216C22×C4×C37—42no—
217C22×C4×C37—42no—
218C22×C4×C37—42no—
219C22×C4×C37—42no—
220C22×C4×C37—42no—
221C22×C4×C37—42no—
222C22×C4×C37—42no—
223C22×C4×C37—42no—
224C22×C4×C37—41no—
225C22×C4×C37—41no—
226C22×C4×C37—41no—
227C22×C4×C37—41no—
228C22×C4×C37C2×D411yescharacteristic
229C22×C4×C37C2×D412yes—
230C22×C4×C37C2×D411yescharacteristic
231C22×C4×C37C2×D411yescharacteristic
232C22×C4×C37C2×D411yescharacteristic
233C22×C4×C37C2×D411yescharacteristic
234C22×C4×C37C2×D412yes—
235C22×C4×C37C2×D411yescharacteristic
236C22×C4×C37C2×D412yes—
237C22×C4×C37C2×D411yescharacteristic
238C22×C4×C37C2×D411yescharacteristic
239C22×C4×C37C2×D411yescharacteristic
240C4⋊C4×C37—22no—
241C4⋊C4×C37—22no—
242C4⋊C4×C37—22no—
243C4⋊C4×C37—22no—
244C4⋊C4×C37—21no—
245C4⋊C4×C37—22no—
246C4⋊C4×C37—21no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—22no—
251C4⋊C4×C37—21no—
252C4⋊C4×C37—42no—
253C4⋊C4×C37—42no—
254C4⋊C4×C37—42no—
255C4⋊C4×C37—44no—
256C22⋊C4×C37—22no—
257C22⋊C4×C37—22no—
258C22⋊C4×C37—24no—
259C22⋊C4×C37—22no—
260C22⋊C4×C37—22no—
261C22⋊C4×C37—22no—
262C22⋊C4×C37—22no—
263C22⋊C4×C37—21no—
264C22⋊C4×C37—22no—
265C22⋊C4×C37—21no—
266C22⋊C4×C37—22no—
267C22⋊C4×C37—21no—
268C22⋊C4×C37—22no—
269C22⋊C4×C37—21no—
270C22⋊C4×C37—21no—
271C22⋊C4×C37—22no—
272C22⋊C4×C37—22no—
273C22⋊C4×C37—22no—
274C22⋊C4×C37—21no—
275C22⋊C4×C37—22no—
276C22⋊C4×C37—22no—
277C22⋊C4×C37—21no—
278C22⋊C4×C37—44no—
279C22⋊C4×C37—42no—
280C22⋊C4×C37—44no—
281C22⋊C4×C37—44no—
282C22⋊C4×C37—42no—
283C22⋊C4×C37—42no—
284C22⋊C4×C37—44no—
285C22⋊C4×C37#4112yescomplemented
286C42×C37—22no—
287C42×C37—22no—
288C42×C37—21no—
289C42×C37—21no—
290C42×C37—42no—
291C23×C37—22no—
292C23×C37—22no—
293C23×C37—22no—
294C23×C37—22no—
295C23×C37—22no—
296C23×C37—22no—
297C23×C37—22no—
298C23×C37—22no—
299C23×C37—22no—
300C23×C37—21no—
301C23×C37—22no—
302C23×C37—21no—
303C23×C37—21no—
304C23×C37—22no—
305C23×C37—22no—
306C23×C37—41no—
307C23×C37—44no—
308C23×C37—41no—
309C23×C37—41no—
310C23×C37—41no—
311C23×C37—41no—
312C23×C37—41no—
313C23×C37—41no—
314C23×C37—41no—
315C23×C37—44no—
316C23×C37—44no—
317C23×C37—44no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37—42no—
321C23×C37—42no—
322C23×C37—41no—
323C23×C37—41no—
324C23×C37—41no—
325C23×C37—41no—
326C23×C37C22×D411yescharacteristic
327C23×C37C22×D411yescharacteristic
328C23×C37C22×D411yescharacteristic
329C23×C37C2×#4111yescharacteristic
330C23×C37C2×#4111yescharacteristic
331C23×C37H(5,𝔽2)11yescharacteristic
332C23×C372−1+411yescharacteristic
333Q8×C37—42no—
334Q8×C37—81no—
335D4×C37—48no—
336D4×C37—42no—
337D4×C37—42no—
338D4×C37—41no—
339D4×C37—41no—
340D4×C37—41no—
341D4×C37—42no—
342D4×C37—42no—
343D4×C37—41no—
344D4×C37—42no—
345D4×C37—81no—
346D4×C37—82no—
347D4×C37—82no—
348D4×C37—88no—
349C2×C4×C37—22no—
350C2×C4×C37—22no—
351C2×C4×C37—22no—
352C2×C4×C37—22no—
353C2×C4×C37—22no—
354C2×C4×C37—22no—
355C2×C4×C37—21no—
356C2×C4×C37—22no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—22no—
360C2×C4×C37—22no—
361C2×C4×C37—21no—
362C2×C4×C37—22no—
363C2×C4×C37—21no—
364C2×C4×C37—22no—
365C2×C4×C37—22no—
366C2×C4×C37—41no—
367C2×C4×C37—41no—
368C2×C4×C37—41no—
369C2×C4×C37—44no—
370C2×C4×C37—44no—
371C2×C4×C37—44no—
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—44no—
379C2×C4×C37—42no—
380C2×C4×C37—41no—
381C2×C4×C37—42no—
382C2×C4×C37—41no—
383C2×C4×C37—42no—
384C2×C4×C37—41no—
385C2×C4×C37—42no—
386C2×C4×C37—42no—
387C2×C4×C37—42no—
388C2×C4×C37—41no—
389C2×C4×C37—42no—
390C2×C4×C37—41no—
391C2×C4×C37—42no—
392C2×C4×C37—42no—
393C2×C4×C37—81no—
394C2×C4×C37—82no—
395C2×C4×C37—82no—
396C2×C4×C37#12011yescharacteristic
397C2×C4×C37#12011yescharacteristic
398C2×C4×C37#12011yescharacteristic
399C2×C4×C37#12011yescharacteristic
400#24140C3711yesmaximal, characteristic, direct product factor, Sylow
401C22×C37—21no—
402C22×C37—21no—
403C22×C37—21no—
404C22×C37—21no—
405C22×C37—21no—
406C22×C37—21no—
407C22×C37—24no—
408C22×C37—24no—
409C22×C37—24no—
410C22×C37—41no—
411C22×C37—41no—
412C22×C37—41no—
413C22×C37—41no—
414C22×C37—42no—
415C22×C37—42no—
416C22×C37—42no—
417C22×C37—42no—
418C22×C37—42no—
419C22×C37—42no—
420C22×C37—42no—
421C22×C37—42no—
422C22×C37—42no—
423C22×C37—42no—
424C22×C37—42no—
425C22×C37—42no—
426C22×C37—42no—
427C22×C37—41no—
428C22×C37—42no—
429C22×C37—41no—
430C22×C37—42no—
431C22×C37—42no—
432C22×C37—41no—
433C22×C37—82no—
434C22×C37—81no—
435C22×C37—82no—
436C22×C37C2×#12011yescharacteristic
437C22×C37#52511yescharacteristic
438C22×C37#53711yescharacteristic
439C22×C37#54611yescharacteristic
440C22×C37#54711yescharacteristic
441C22×C37#54811yescharacteristic
442C22×C37#55011yescharacteristic
443C4×C37—21no—
444C4×C37—21no—
445C4×C37—21no—
446C4×C37—42no—
447C4×C37—41no—
448C4×C37—42no—
449C4×C37—42no—
450C4×C37—41no—
451C4×C37—42no—
452C4×C37—41no—
453C4×C37—42no—
454C4×C37—82no—
455C4×C37—81no—
456C4×C37—82no—
457C4×C37B(4,𝔽2)12yes—
458#3505C2×C3711yescharacteristic, complemented
459#2848C2×C3711yescharacteristic, complemented
460#2847C2×C3711yescharacteristic, complemented
461C4×#120C2×C3711yescharacteristic, complemented
462#2044C2×C3712yescomplemented
463#2021C2×C3712yescomplemented
464#1996C2×C3711yescharacteristic, complemented
465#1964C2×C3711yescharacteristic, complemented
466#1889C2×C3712yescomplemented
467#1867C2×C3712yescomplemented
468#1799C2×C3711yescharacteristic, complemented
469C2×C37—21no—
470C2×C37—21no—
471C2×C37—21no—
472C2×C37—21no—
473C2×C37—21no—
474C2×C37—21no—
475C2×C37—44no—
476C2×C37—81no—
477C2×C37—82no—
478C2×C37#240711yescharacteristic
479C2×C37C2×B(4,𝔽2)11yescharacteristic
480C2×C37#302511yescharacteristic
481C24×C4C22×C3711yescharacteristic
482#553—21no—
483#553—22no—
484#552—21no—
485#551—22no—
486#548—21no—
487#546—21no—
488#539—21no—
489#538—21no—
490#534C22×C3712yes—
491#529—21no—
492#525—21no—
493C2×C22⋊Q8—21no—
494C2×C22⋊Q8C22×C3711yescharacteristic
495C2×#121—21no—
496C2×#121C22×C3711yescharacteristic
497C2×#120C22×C3711yescharacteristic
498C2×#120C22×C3712yes—
499#518C22×C3712yes—
500C2×C4×D4—21no—
501C2×C4×D4C22×C3711yescharacteristic
502C2×#99C22×C3712yes—
503C2×#99C22×C3712yes—
504C2×#99C22×C3712yes—
505#386—22no—
506#386—21no—
507#386C22×C3712yes—
508#386C22×C3711yescharacteristic
509#385—22no—
510#385—21no—
511#385C22×C3712yes—
512#385C22×C3711yescharacteristic
513#380—21no—
514#380—21no—
515#380C22×C3711yescharacteristic
516#380C22×C3711yescharacteristic
517#379C22×C3712yes—
518#379C22×C3711yescharacteristic
519C4×C22⋊C4—21no—
520C4×C22⋊C4C22×C3711yescharacteristic
521#342C22×C3712yes—
522#342C22×C3712yes—
523#342C22×C3712yes—
524C37#2414011yescharacteristic, direct product factor, Sylow
525C25C23×C3711yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C3711yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C3711yescharacteristic, complemented
531C22×D4C23×C3711yescharacteristic
532C22×D4C23×C3712yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C3711yescharacteristic, complemented
541C23×C4C23×C3711yescharacteristic
542C23×C4C23×C3711yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C3711yescharacteristic, complemented
597C2×C4⋊C4D4×C3711yescharacteristic, complemented
598C2×C4⋊C4D4×C3711yescharacteristic, complemented
599C2×C4⋊C4D4×C3712yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C3711yescharacteristic, complemented
610C2×C22⋊C4D4×C3712yescomplemented
611C2×C22⋊C4C23×C3712yes—
612C2×C22⋊C4C23×C3711yescharacteristic
613C2×C22⋊C4C23×C3712yes—
614C2×C22⋊C4C23×C3711yescharacteristic
615C2×C22⋊C4C23×C3712yes—
616C2×C22⋊C4C23×C3711yescharacteristic
617C2×C42—21no—
618C2×C42D4×C3711yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C3712yes—
638C24C2×D4×C3711yescharacteristic
639C24#41×C3712yescomplemented
640C24C24×C3711yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C3711yescharacteristic
699C22×C4C2×D4×C3712yes—
700C22×C4C2×D4×C3711yescharacteristic
701C22×C4C2×D4×C3711yescharacteristic
702C22×C4C2×D4×C3711yescharacteristic
703C22×C4C2×D4×C3711yescharacteristic
704C22×C4C2×D4×C3712yes—
705C22×C4C2×D4×C3711yescharacteristic
706C22×C4C2×D4×C3712yes—
707C22×C4C2×D4×C3711yescharacteristic
708C22×C4C2×D4×C3711yescharacteristic
709C22×C4C2×D4×C3711yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4#41×C3712yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C3711yescharacteristic
797C23C22×D4×C3711yescharacteristic
798C23C22×D4×C3711yescharacteristic
799C23C2×#41×C3711yescharacteristic
800C23C2×#41×C3711yescharacteristic
801C23H(5,𝔽2)×C3711yescharacteristic
802C232−1+4×C3711yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C3711yescharacteristic
867C2×C4#120×C3711yescharacteristic
868C2×C4#120×C3711yescharacteristic
869C2×C4#120×C3711yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C3711yescharacteristic
906C22C37×#52511yescharacteristic
907C22C37×#53711yescharacteristic
908C22C37×#54611yescharacteristic
909C22C37×#54711yescharacteristic
910C22C37×#54811yescharacteristic
911C22C37×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C37×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C37×#240711yescharacteristic
937C2C2×C37×B(4,𝔽2)11yescharacteristic
938C2C37×#302511yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3505C2semidirect
2. C37×#2848C2semidirect
3. C37×#2847C2semidirect
4. C4×#120×C37C2semidirect
5. C37×#2044C2semidirect
6. C37×#2021C2semidirect
7. C37×#1996C2semidirect
8. C37×#1964C2semidirect
9. C37×#1889C2semidirect
10. C37×#1867C2semidirect
11. C37×#1799C2semidirect
57. C22×Q8×C37D4semidirect
60. C22×D4×C37D4semidirect
70. C23×C4×C37D4semidirect
126. C2×C4⋊C4×C37D4semidirect
127. C2×C4⋊C4×C37D4semidirect
128. C2×C4⋊C4×C37D4semidirect
129. C2×C4⋊C4×C37D4semidirect
139. C2×C22⋊C4×C37D4semidirect
140. C2×C22⋊C4×C37D4semidirect
148. C2×C42×C37D4semidirect
169. C24×C37#41semidirect
285. C22⋊C4×C37#41semidirect
400. #24140C37direct (N × H)
458. #3505C2×C37semidirect
459. #2848C2×C37semidirect
460. #2847C2×C37semidirect
461. C4×#120C2×C37semidirect
462. #2044C2×C37semidirect
463. #2021C2×C37semidirect
464. #1996C2×C37semidirect
465. #1964C2×C37semidirect
466. #1889C2×C37semidirect
467. #1867C2×C37semidirect
468. #1799C2×C37semidirect
524. C37#24140direct (N × H)
527. C22×Q8D4×C37semidirect
530. C22×D4D4×C37semidirect
540. C23×C4D4×C37semidirect
596. C2×C4⋊C4D4×C37semidirect
597. C2×C4⋊C4D4×C37semidirect
598. C2×C4⋊C4D4×C37semidirect
599. C2×C4⋊C4D4×C37semidirect
609. C2×C22⋊C4D4×C37semidirect
610. C2×C22⋊C4D4×C37semidirect
618. C2×C42D4×C37semidirect
639. C24#41×C37semidirect
755. C22⋊C4#41×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35052
C37×#28482
C37×#28472
C4×#120×C372
C37×#20442
C37×#20212
C37×#19962
C37×#19642
C37×#18892
C37×#18672
C37×#17992
#2414037