Finite Group Databasebeta

← C37×#9113 #22630366

Subgroups — C37×#9113 #22630366

Order 9472.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C37C211yesmaximal, characteristic, complemented
2C37×#2847C211yesmaximal, characteristic
3C2×C37×#327C212yesmaximal, complemented
4C37×C22⋊#95C211yesmaximal, characteristic, complemented
5C37×#1294C212yesmaximal, complemented
6C24×C4×C37C2211yescharacteristic
7C23×C8×C37—21no—
8C2×#121×C37C411yescharacteristic, complemented
9C2×#121×C37C411yescharacteristic, complemented
10C2×#121×C37C2211yescharacteristic
11C2×#120×C37—21no—
12C22×C22⋊C4×C37—21no—
13C2×C22⋊C8×C37—21no—
14C2×C22⋊C8×C37—24no—
15C2×C22⋊C8×C37C2212yes—
16C37×#386—21no—
17C37×#386—21no—
18C37×#386—21no—
19C37×#380C411yescharacteristic, complemented
20C37×#380C411yescharacteristic, complemented
21C37×#380C2211yescharacteristic
22C2×#95×C37—21no—
23C2×#95×C37C2212yes—
24C37×#327—24no—
25C25×C37D411yescharacteristic
26C22×D4×C37—21no—
27C22×D4×C37—21no—
28C22×D4×C37—21no—
29C22×D4×C37C2×C411yescharacteristic
30C23×C4×C37—22no—
31C23×C4×C37—22no—
32C23×C4×C37—22no—
33C23×C4×C37—42no—
34C23×C4×C37—42no—
35C23×C4×C37C2×C411yescharacteristic
36C23×C4×C37C2×C411yescharacteristic
37C23×C4×C37D411yescharacteristic
38C23×C4×C37D411yescharacteristic
39C23×C4×C37D411yescharacteristic
40C23×C4×C37C2311yescharacteristic
41C22×C8×C37—24no—
42C22×C8×C37—22no—
43C22×C8×C37—42no—
44C22×C8×C37—42no—
45#121×C37—22no—
46#121×C37—22no—
47#121×C37—42no—
48#121×C37—42no—
49#120×C37—42no—
50#120×C37—42no—
51C2×C4⋊C4×C37C2×C411yescharacteristic
52C2×C4⋊C4×C37C2×C411yescharacteristic
53C2×C4⋊C4×C37C2×C411yescharacteristic
54C2×C22⋊C4×C37—24no—
55C2×C22⋊C4×C37—21no—
56C2×C22⋊C4×C37—21no—
57C2×C22⋊C4×C37—21no—
58C2×C22⋊C4×C37—21no—
59C2×C22⋊C4×C37—21no—
60C2×C22⋊C4×C37—21no—
61C2×C22⋊C4×C37—42no—
62C2×C22⋊C4×C37—42no—
63C22⋊C8×C37—24no—
64C22⋊C8×C37—22no—
65C22⋊C8×C37D414yescomplemented
66#95×C37—21no—
67#95×C37—21no—
68#95×C37—21no—
69#95×C37—22no—
70#95×C37—22no—
71#95×C37—42no—
72C24×C37—22no—
73C24×C37—22no—
74C24×C37—22no—
75C24×C37—22no—
76C24×C37—21no—
77C24×C37—41no—
78C24×C37—41no—
79C24×C37C22⋊C411yescharacteristic
80C24×C37C22⋊C411yescharacteristic
81C24×C37D812yes—
82C24×C37SD1612yes—
83C24×C37C2×D411yescharacteristic
84C2×D4×C37—22no—
85C2×D4×C37—41no—
86C2×D4×C37—41no—
87C2×D4×C37—42no—
88C2×D4×C37—42no—
89C2×D4×C37—42no—
90C2×D4×C37—42no—
91C2×D4×C37—42no—
92C2×D4×C37—42no—
93C2×D4×C37—42no—
94C2×D4×C37—41no—
95C2×D4×C37—41no—
96C2×D4×C37—42no—
97C22×C4×C37—22no—
98C22×C4×C37—22no—
99C22×C4×C37—21no—
100C22×C4×C37—21no—
101C22×C4×C37—22no—
102C22×C4×C37—22no—
103C22×C4×C37—22no—
104C22×C4×C37—22no—
105C22×C4×C37—22no—
106C22×C4×C37—22no—
107C22×C4×C37—21no—
108C22×C4×C37—21no—
109C22×C4×C37—24no—
110C22×C4×C37—21no—
111C22×C4×C37—21no—
112C22×C4×C37—21no—
113C22×C4×C37—41no—
114C22×C4×C37—41no—
115C22×C4×C37—41no—
116C22×C4×C37—41no—
117C22×C4×C37—41no—
118C22×C4×C37—41no—
119C22×C4×C37—41no—
120C22×C4×C37—48no—
121C22×C4×C37—48no—
122C22×C4×C37—42no—
123C22×C4×C37—42no—
124C22×C4×C37—42no—
125C22×C4×C37—42no—
126C22×C4×C37—42no—
127C22×C4×C37—42no—
128C22×C4×C37C22⋊C411yescharacteristic
129C22×C4×C37C22⋊C411yescharacteristic
130C22×C4×C37C22×C411yescharacteristic
131C22×C4×C37C2×D411yescharacteristic
132C22×C4×C37C2×D412yes—
133C22×C4×C37#4112yes—
134C2×C8×C37—24no—
135C2×C8×C37—48no—
136C2×C8×C37—42no—
137C2×C8×C37—42no—
138C4⋊C4×C37—22no—
139C4⋊C4×C37—41no—
140C4⋊C4×C37—41no—
141C22⋊C4×C37—42no—
142C22⋊C4×C37—48no—
143C22⋊C4×C37—42no—
144C22⋊C4×C37—42no—
145C22⋊C4×C37—41no—
146C22⋊C4×C37—41no—
147C22⋊C4×C37—42no—
148C22⋊C4×C37—41no—
149C22⋊C4×C37—41no—
150C23×C37—21no—
151C23×C37—21no—
152C23×C37—21no—
153C23×C37—21no—
154C23×C37—21no—
155C23×C37—21no—
156C23×C37—21no—
157C23×C37—21no—
158C23×C37—24no—
159C23×C37—24no—
160C23×C37—21no—
161C23×C37—21no—
162C23×C37—21no—
163C23×C37—21no—
164C23×C37—21no—
165C23×C37—21no—
166C23×C37—24no—
167C23×C37—24no—
168C23×C37—42no—
169C23×C37—42no—
170C23×C37—44no—
171C23×C37—44no—
172C23×C37—44no—
173C23×C37—44no—
174C23×C37—41no—
175C23×C37—41no—
176C23×C37—41no—
177C23×C37—41no—
178C23×C37—41no—
179C23×C37—41no—
180C23×C37—41no—
181C23×C37#9912yes—
182C23×C37#10212yes—
183C23×C37#10212yes—
184C23×C37#10412yes—
185C23×C37C2×C22⋊C411yescharacteristic
186C23×C37#12112yes—
187C23×C37C2×D811yescharacteristic
188C23×C37C2×SD1611yescharacteristic
189C23×C37#13512yes—
190D4×C37—82no—
191D4×C37—84no—
192D4×C37—84no—
193D4×C37—82no—
194D4×C37—82no—
195C2×C4×C37—24no—
196C2×C4×C37—24no—
197C2×C4×C37—21no—
198C2×C4×C37—21no—
199C2×C4×C37—21no—
200C2×C4×C37—21no—
201C2×C4×C37—21no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—21no—
205C2×C4×C37—21no—
206C2×C4×C37—42no—
207C2×C4×C37—42no—
208C2×C4×C37—44no—
209C2×C4×C37—44no—
210C2×C4×C37—44no—
211C2×C4×C37—42no—
212C2×C4×C37—42no—
213C2×C4×C37—44no—
214C2×C4×C37—44no—
215C2×C4×C37—44no—
216C2×C4×C37—41no—
217C2×C4×C37—41no—
218C2×C4×C37—41no—
219C2×C4×C37—41no—
220C2×C4×C37—41no—
221C2×C4×C37—41no—
222C2×C4×C37—41no—
223C2×C4×C37—41no—
224C2×C4×C37—41no—
225C2×C4×C37—82no—
226C2×C4×C37—82no—
227C2×C4×C37—82no—
228C2×C4×C37—82no—
229C2×C4×C37#9912yes—
230C2×C4×C37C4×D412yes—
231C2×C4×C37#12011yescharacteristic
232C2×C4×C37#12311yescharacteristic
233C8×C37—44no—
234#9113C3711yesmaximal, characteristic, direct product factor, Sylow
235C22×C37—22no—
236C22×C37—22no—
237C22×C37—22no—
238C22×C37—22no—
239C22×C37—22no—
240C22×C37—21no—
241C22×C37—21no—
242C22×C37—22no—
243C22×C37—22no—
244C22×C37—22no—
245C22×C37—22no—
246C22×C37—21no—
247C22×C37—22no—
248C22×C37—21no—
249C22×C37—22no—
250C22×C37—22no—
251C22×C37—22no—
252C22×C37—48no—
253C22×C37—48no—
254C22×C37—41no—
255C22×C37—41no—
256C22×C37—41no—
257C22×C37—41no—
258C22×C37—81no—
259C22×C37—81no—
260C22×C37—81no—
261C22×C37—81no—
262C22×C37—81no—
263C22×C37—81no—
264C22×C37—81no—
265C22×C37#32714yescomplemented
266C22×C37#38611yescharacteristic
267C22×C37C2×#9911yescharacteristic
268C22×C37C2×#9911yescharacteristic
269C22×C37C2×#10211yescharacteristic
270C22×C37#41611yescharacteristic
271C22×C37C2×#10411yescharacteristic
272C22×C37#42111yescharacteristic
273C22×C37#46512yes—
274C22×C37#46612yes—
275C4×C37—21no—
276C4×C37—22no—
277C4×C37—21no—
278C4×C37—22no—
279C4×C37—41no—
280C4×C37—84no—
281C4×C37—81no—
282C4×C37—81no—
283C4×C37—81no—
284C22×C22⋊C8C2×C3711yescharacteristic, complemented
285#2847C2×C3711yescharacteristic
286C2×#327C2×C3712yescomplemented
287C22⋊#95C2×C3711yescharacteristic, complemented
288#1294C2×C3712yescomplemented
289C2×C37—22no—
290C2×C37—24no—
291C2×C37—22no—
292C2×C37—42no—
293C2×C37—161no—
294C2×C37C2×#32711yescharacteristic
295C2×C37#150111yescharacteristic
296C2×C37#151611yescharacteristic
297C2×C37#151911yescharacteristic
298C2×C37#187111yescharacteristic
299C2×C37#189311yescharacteristic
300C2×C37#189811yescharacteristic
301C24×C4C22×C3711yescharacteristic
302C23×C8—21no—
303C2×#121C4×C3711yescharacteristic, complemented
304C2×#121C4×C3711yescharacteristic, complemented
305C2×#121C22×C3711yescharacteristic
306C2×#120—21no—
307C22×C22⋊C4—21no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8—24no—
310C2×C22⋊C8C22×C3712yes—
311#386—21no—
312#386—21no—
313#386—21no—
314#380C4×C3711yescharacteristic, complemented
315#380C4×C3711yescharacteristic, complemented
316#380C22×C3711yescharacteristic
317C2×#95—21no—
318C2×#95C22×C3712yes—
319#327—24no—
320C37#911311yescharacteristic, direct product factor, Sylow
321C25D4×C3711yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C3711yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—42no—
330C23×C4—42no—
331C23×C4C2×C4×C3711yescharacteristic
332C23×C4C2×C4×C3711yescharacteristic
333C23×C4D4×C3711yescharacteristic
334C23×C4D4×C3711yescharacteristic
335C23×C4D4×C3711yescharacteristic
336C23×C4C23×C3711yescharacteristic
337C22×C8—24no—
338C22×C8—22no—
339C22×C8—42no—
340C22×C8—42no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×C4×C3711yescharacteristic
348C2×C4⋊C4C2×C4×C3711yescharacteristic
349C2×C4⋊C4C2×C4×C3711yescharacteristic
350C2×C22⋊C4—24no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C22⋊C8—24no—
360C22⋊C8—22no—
361C22⋊C8D4×C3714yescomplemented
362#95—21no—
363#95—21no—
364#95—21no—
365#95—22no—
366#95—22no—
367#95—42no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24C22⋊C4×C3711yescharacteristic
376C24C22⋊C4×C3711yescharacteristic
377C24D8×C3712yes—
378C24SD16×C3712yes—
379C24C2×D4×C3711yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C22⋊C4×C3711yescharacteristic
425C22×C4C22⋊C4×C3711yescharacteristic
426C22×C4C22×C4×C3711yescharacteristic
427C22×C4C2×D4×C3711yescharacteristic
428C22×C4C2×D4×C3712yes—
429C22×C4#41×C3712yes—
430C2×C8—24no—
431C2×C8—48no—
432C2×C8—42no—
433C2×C8—42no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—48no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—42no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—24no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#99×C3712yes—
478C23#102×C3712yes—
479C23#102×C3712yes—
480C23#104×C3712yes—
481C23C2×C22⋊C4×C3711yescharacteristic
482C23#121×C3712yes—
483C23C2×D8×C3711yescharacteristic
484C23C2×SD16×C3711yescharacteristic
485C23#135×C3712yes—
486D4—82no—
487D4—84no—
488D4—84no—
489D4—82no—
490D4—82no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4#99×C3712yes—
526C2×C4C4×D4×C3712yes—
527C2×C4#120×C3711yescharacteristic
528C2×C4#123×C3711yescharacteristic
529C8—44no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—21no—
536C22—21no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C37×#32714yescomplemented
561C22C37×#38611yescharacteristic
562C22C2×#99×C3711yescharacteristic
563C22C2×#99×C3711yescharacteristic
564C22C2×#102×C3711yescharacteristic
565C22C37×#41611yescharacteristic
566C22C2×#104×C3711yescharacteristic
567C22C37×#42111yescharacteristic
568C22C37×#46512yes—
569C22C37×#46612yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—84no—
576C4—81no—
577C4—81no—
578C4—81no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—42no—
583C2—161no—
584C2C2×C37×#32711yescharacteristic
585C2C37×#150111yescharacteristic
586C2C37×#151611yescharacteristic
587C2C37×#151911yescharacteristic
588C2C37×#187111yescharacteristic
589C2C37×#189311yescharacteristic
590C2C37×#189811yescharacteristic
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC37×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C24×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊C8×C37C2semidirect
3. C2×C37×#327C2semidirect
4. C37×C22⋊#95C2semidirect
5. C37×#1294C2semidirect
8. C2×#121×C37C4semidirect
9. C2×#121×C37C4semidirect
19. C37×#380C4semidirect
20. C37×#380C4semidirect
65. C22⋊C8×C37D4semidirect
234. #9113C37direct (N × H)
265. C22×C37#327semidirect
284. C22×C22⋊C8C2×C37semidirect
286. C2×#327C2×C37semidirect
287. C22⋊#95C2×C37semidirect
288. #1294C2×C37semidirect
303. C2×#121C4×C37semidirect
304. C2×#121C4×C37semidirect
314. #380C4×C37semidirect
315. #380C4×C37semidirect
320. C37#9113direct (N × H)
361. C22⋊C8D4×C37semidirect
560. C22C37×#327semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C372
C37×#28472
C2×C37×#3272
C37×C22⋊#952
C37×#12942
#911337