Finite Group Databasebeta

← C37×#10761 #22632014

Subgroups — C37×#10761 #22632014

Order 9472.

1866 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C37C211yesmaximal, characteristic
2C22×#99×C37C212yesmaximal
3C2×C37×#342C212yesmaximal, complemented
4C37×C22⋊#95C212yesmaximal, complemented
5C23×D4×C37C2211yescharacteristic
6C24×C4×C37C411yescharacteristic, complemented
7C24×C4×C37C2211yescharacteristic
8C2×C4×D4×C37—24no—
9C2×C4×D4×C37—24no—
10C2×C4×D4×C37—24no—
11C22×C4⋊C4×C37C411yescharacteristic, complemented
12C22×C22⋊C4×C37C411yescharacteristic, complemented
13C22×C22⋊C4×C37C2214yes—
14C22×C22⋊C4×C37C2211yescharacteristic
15C22×C42×C37C411yescharacteristic, complemented
16C2×#99×C37—24no—
17C2×#99×C37—24no—
18C2×#99×C37C418yescomplemented
19C2×#95×C37—24no—
20C37×#342—24no—
21C25×C37C2×C411yescharacteristic
22C25×C37C2311yescharacteristic
23C22×D4×C37—22no—
24C22×D4×C37—22no—
25C22×D4×C37—22no—
26C22×D4×C37—22no—
27C22×D4×C37C2×C414yes—
28C22×D4×C37D414yes—
29C22×D4×C37D412yes—
30C22×D4×C37Q812yes—
31C23×C4×C37—22no—
32C23×C4×C37—22no—
33C23×C4×C37—22no—
34C23×C4×C37—22no—
35C23×C4×C37—22no—
36C23×C4×C37—24no—
37C23×C4×C37—44no—
38C23×C4×C37—44no—
39C23×C4×C37C2×C411yescharacteristic
40C23×C4×C37C2×C411yescharacteristic
41C23×C4×C37C2×C411yescharacteristic
42C23×C4×C37C2×C411yescharacteristic
43C23×C4×C37C2×C411yescharacteristic
44C23×C4×C37D414yes—
45C4×D4×C37—232no—
46C2×C4⋊C4×C37—22no—
47C2×C4⋊C4×C37—22no—
48C2×C4⋊C4×C37—22no—
49C2×C22⋊C4×C37—22no—
50C2×C22⋊C4×C37—22no—
51C2×C22⋊C4×C37—22no—
52C2×C22⋊C4×C37—22no—
53C2×C22⋊C4×C37—22no—
54C2×C22⋊C4×C37—24no—
55C2×C22⋊C4×C37—24no—
56C2×C22⋊C4×C37—24no—
57C2×C22⋊C4×C37—24no—
58C2×C22⋊C4×C37—24no—
59C2×C22⋊C4×C37C2×C418yescomplemented
60C2×C22⋊C4×C37D414yes—
61C2×C42×C37—22no—
62C2×C42×C37—22no—
63C2×C42×C37—22no—
64#99×C37—216no—
65#95×C37—48no—
66C24×C37—21no—
67C24×C37—21no—
68C24×C37—21no—
69C24×C37—21no—
70C24×C37—42no—
71C24×C37—42no—
72C24×C37—42no—
73C24×C37—42no—
74C24×C37C4212yes—
75C24×C37C22⋊C412yes—
76C24×C37C4⋊C412yes—
77C24×C37C22×C411yescharacteristic
78C24×C37C22×C412yes—
79C24×C37C2×D412yes—
80C24×C37C2×D412yes—
81C24×C37C2×D411yescharacteristic
82C24×C37C2×D412yes—
83C24×C37C2×Q811yescharacteristic
84C24×C37#4112yes—
85C24×C37#4112yes—
86C2×D4×C37—28no—
87C2×D4×C37—28no—
88C2×D4×C37—28no—
89C2×D4×C37—24no—
90C2×D4×C37—24no—
91C2×D4×C37—24no—
92C2×D4×C37—24no—
93C2×D4×C37—28no—
94C2×D4×C37C22⋊C418yes—
95C2×D4×C37C4⋊C418yes—
96C22×C4×C37—21no—
97C22×C4×C37—21no—
98C22×C4×C37—21no—
99C22×C4×C37—21no—
100C22×C4×C37—21no—
101C22×C4×C37—21no—
102C22×C4×C37—24no—
103C22×C4×C37—28no—
104C22×C4×C37—21no—
105C22×C4×C37—21no—
106C22×C4×C37—21no—
107C22×C4×C37—21no—
108C22×C4×C37—21no—
109C22×C4×C37—21no—
110C22×C4×C37—28no—
111C22×C4×C37—28no—
112C22×C4×C37—28no—
113C22×C4×C37—42no—
114C22×C4×C37—44no—
115C22×C4×C37—48no—
116C22×C4×C37—48no—
117C22×C4×C37—48no—
118C22×C4×C37—48no—
119C22×C4×C37—44no—
120C22×C4×C37—44no—
121C22×C4×C37—42no—
122C22×C4×C37—42no—
123C22×C4×C37—48no—
124C22×C4×C37—48no—
125C22×C4×C37—44no—
126C22×C4×C37—44no—
127C22×C4×C37C4212yes—
128C22×C4×C37C22⋊C412yes—
129C22×C4×C37C22⋊C412yes—
130C22×C4×C37C22⋊C412yes—
131C22×C4×C37C22⋊C412yes—
132C22×C4×C37C22⋊C412yes—
133C22×C4×C37C4⋊C412yes—
134C4⋊C4×C37—28no—
135C22⋊C4×C37—28no—
136C22⋊C4×C37—28no—
137C22⋊C4×C37—28no—
138C22⋊C4×C37—28no—
139C22⋊C4×C37—44no—
140C22⋊C4×C37—44no—
141C42×C37—28no—
142C23×C37—24no—
143C23×C37—22no—
144C23×C37—24no—
145C23×C37—22no—
146C23×C37—22no—
147C23×C37—22no—
148C23×C37—22no—
149C23×C37—22no—
150C23×C37—22no—
151C23×C37—22no—
152C23×C37—42no—
153C23×C37—42no—
154C23×C37—44no—
155C23×C37—42no—
156C23×C37—42no—
157C23×C37—42no—
158C23×C37—42no—
159C23×C37—44no—
160C23×C37—44no—
161C23×C37—42no—
162C23×C37—44no—
163C23×C37—42no—
164C23×C37—44no—
165C23×C37—42no—
166C23×C37—44no—
167C23×C37—44no—
168C23×C37—42no—
169C23×C37—42no—
170C23×C37—42no—
171C23×C37#9514yescomplemented
172C23×C37C2×C4211yescharacteristic
173C23×C37C2×C22⋊C411yescharacteristic
174C23×C37C2×C22⋊C411yescharacteristic
175C23×C37C2×C22⋊C412yes—
176C23×C37C2×C22⋊C411yescharacteristic
177C23×C37C2×C4⋊C411yescharacteristic
178C23×C37C2×C4⋊C412yes—
179C23×C37#11711yescharacteristic
180C23×C37#11711yescharacteristic
181C23×C37C4×D414yes—
182C23×C37C4×D414yes—
183C23×C37#12014yes—
184C23×C37#12112yes—
185C23×C37#12112yes—
186C23×C37C22⋊Q812yes—
187C23×C37C22⋊Q812yes—
188C23×C37#12314yes—
189D4×C37—216no—
190D4×C37—216no—
191C2×C4×C37—24no—
192C2×C4×C37—24no—
193C2×C4×C37—22no—
194C2×C4×C37—22no—
195C2×C4×C37—22no—
196C2×C4×C37—22no—
197C2×C4×C37—22no—
198C2×C4×C37—22no—
199C2×C4×C37—22no—
200C2×C4×C37—22no—
201C2×C4×C37—22no—
202C2×C4×C37—22no—
203C2×C4×C37—22no—
204C2×C4×C37—24no—
205C2×C4×C37—416no—
206C2×C4×C37—416no—
207C2×C4×C37—42no—
208C2×C4×C37—42no—
209C2×C4×C37—42no—
210C2×C4×C37—42no—
211C2×C4×C37—42no—
212C2×C4×C37—42no—
213C2×C4×C37—42no—
214C2×C4×C37—42no—
215C2×C4×C37—416no—
216C2×C4×C37—48no—
217C2×C4×C37—88no—
218C2×C4×C37—84no—
219C2×C4×C37—84no—
220C2×C4×C37#9514yescomplemented
221C2×C4×C37#9914yescomplemented
222#10761C3711yesmaximal, characteristic, direct product factor, Sylow
223C22×C37—24no—
224C22×C37—22no—
225C22×C37—22no—
226C22×C37—24no—
227C22×C37—28no—
228C22×C37—22no—
229C22×C37—22no—
230C22×C37—21no—
231C22×C37—21no—
232C22×C37—24no—
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—24no—
236C22×C37—24no—
237C22×C37—42no—
238C22×C37—42no—
239C22×C37—44no—
240C22×C37—42no—
241C22×C37—42no—
242C22×C37—44no—
243C22×C37—44no—
244C22×C37—44no—
245C22×C37—44no—
246C22×C37—44no—
247C22×C37—44no—
248C22×C37—44no—
249C22×C37—42no—
250C22×C37—42no—
251C22×C37C2×#9511yescharacteristic
252C22×C37C4×C22⋊C411yescharacteristic
253C22×C37C4×C22⋊C411yescharacteristic
254C22×C37#37911yescharacteristic
255C22×C37#38011yescharacteristic
256C22×C37#38011yescharacteristic
257C22×C37#38111yescharacteristic
258C22×C37#38514yes—
259C22×C37#38614yes—
260C22×C37C2×#9912yes—
261C22×C37#41012yes—
262C4×C37—24no—
263C4×C37—24no—
264C4×C37—42no—
265C4×C37—42no—
266C4×C37—42no—
267C4×C37—88no—
268C22×C4×D4C2×C3711yescharacteristic
269C22×#99C2×C3712yes—
270C2×#342C2×C3712yescomplemented
271C22⋊#95C2×C3712yescomplemented
272C2×C37—24no—
273C2×C37—21no—
274C2×C37—21no—
275C2×C37—21no—
276C2×C37—21no—
277C2×C37—24no—
278C2×C37—44no—
279C2×C37C22⋊#9511yescharacteristic
280C2×C37C4×#9912yes—
281C2×C37#178111yescharacteristic
282C2×C37#178211yescharacteristic
283C2×C37#179912yes—
284C23×D4C22×C3711yescharacteristic
285C24×C4C4×C3711yescharacteristic, complemented
286C24×C4C22×C3711yescharacteristic
287C2×C4×D4—24no—
288C2×C4×D4—24no—
289C2×C4×D4—24no—
290C22×C4⋊C4C4×C3711yescharacteristic, complemented
291C22×C22⋊C4C4×C3711yescharacteristic, complemented
292C22×C22⋊C4C22×C3714yes—
293C22×C22⋊C4C22×C3711yescharacteristic
294C22×C42C4×C3711yescharacteristic, complemented
295C2×#99—24no—
296C2×#99—24no—
297C2×#99C4×C3718yescomplemented
298C2×#95—24no—
299#342—24no—
300C37#1076111yescharacteristic, direct product factor, Sylow
301C25C2×C4×C3711yescharacteristic
302C25C23×C3711yescharacteristic
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4C2×C4×C3714yes—
308C22×D4D4×C3714yes—
309C22×D4D4×C3712yes—
310C22×D4Q8×C3712yes—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—24no—
317C23×C4—44no—
318C23×C4—44no—
319C23×C4C2×C4×C3711yescharacteristic
320C23×C4C2×C4×C3711yescharacteristic
321C23×C4C2×C4×C3711yescharacteristic
322C23×C4C2×C4×C3711yescharacteristic
323C23×C4C2×C4×C3711yescharacteristic
324C23×C4D4×C3714yes—
325C4×D4—232no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4C2×C4×C3718yescomplemented
340C2×C22⋊C4D4×C3714yes—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344#99—216no—
345#95—48no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—42no—
351C24—42no—
352C24—42no—
353C24—42no—
354C24C42×C3712yes—
355C24C22⋊C4×C3712yes—
356C24C4⋊C4×C3712yes—
357C24C22×C4×C3711yescharacteristic
358C24C22×C4×C3712yes—
359C24C2×D4×C3712yes—
360C24C2×D4×C3712yes—
361C24C2×D4×C3711yescharacteristic
362C24C2×D4×C3712yes—
363C24C2×Q8×C3711yescharacteristic
364C24#41×C3712yes—
365C24#41×C3712yes—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—28no—
369C2×D4—24no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—24no—
373C2×D4—28no—
374C2×D4C22⋊C4×C3718yes—
375C2×D4C4⋊C4×C3718yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—28no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—28no—
391C22×C4—28no—
392C22×C4—28no—
393C22×C4—42no—
394C22×C4—44no—
395C22×C4—48no—
396C22×C4—48no—
397C22×C4—48no—
398C22×C4—48no—
399C22×C4—44no—
400C22×C4—44no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—48no—
404C22×C4—48no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4C42×C3712yes—
408C22×C4C22⋊C4×C3712yes—
409C22×C4C22⋊C4×C3712yes—
410C22×C4C22⋊C4×C3712yes—
411C22×C4C22⋊C4×C3712yes—
412C22×C4C22⋊C4×C3712yes—
413C22×C4C4⋊C4×C3712yes—
414C4⋊C4—28no—
415C22⋊C4—28no—
416C22⋊C4—28no—
417C22⋊C4—28no—
418C22⋊C4—28no—
419C22⋊C4—44no—
420C22⋊C4—44no—
421C42—28no—
422C23—24no—
423C23—22no—
424C23—24no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—42no—
433C23—42no—
434C23—44no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—44no—
440C23—44no—
441C23—42no—
442C23—44no—
443C23—42no—
444C23—44no—
445C23—42no—
446C23—44no—
447C23—42no—
448C23—44no—
449C23—42no—
450C23—42no—
451C23#95×C3714yescomplemented
452C23C2×C42×C3711yescharacteristic
453C23C2×C22⋊C4×C3711yescharacteristic
454C23C2×C22⋊C4×C3711yescharacteristic
455C23C2×C22⋊C4×C3712yes—
456C23C2×C22⋊C4×C3711yescharacteristic
457C23C2×C4⋊C4×C3711yescharacteristic
458C23C2×C4⋊C4×C3712yes—
459C23#117×C3711yescharacteristic
460C23#117×C3711yescharacteristic
461C23C4×D4×C3714yes—
462C23C4×D4×C3714yes—
463C23#120×C3714yes—
464C23#121×C3712yes—
465C23#121×C3712yes—
466C23C22⋊Q8×C3712yes—
467C23C22⋊Q8×C3712yes—
468C23#123×C3714yes—
469D4—216no—
470D4—216no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—416no—
486C2×C4—416no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—416no—
496C2×C4—48no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4—88no—
500C2×C4#95×C3714yescomplemented
501C2×C4#99×C3714yescomplemented
502C22—28no—
503C22—22no—
504C22—22no—
505C22—21no—
506C22—21no—
507C22—24no—
508C22—21no—
509C22—21no—
510C22—24no—
511C22—24no—
512C22—22no—
513C22—22no—
514C22—24no—
515C22—24no—
516C22—42no—
517C22—42no—
518C22—44no—
519C22—42no—
520C22—42no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—44no—
525C22—44no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—44no—
530C22C2×#95×C3711yescharacteristic
531C22C4×C22⋊C4×C3711yescharacteristic
532C22C4×C22⋊C4×C3711yescharacteristic
533C22C37×#37911yescharacteristic
534C22C37×#38011yescharacteristic
535C22C37×#38011yescharacteristic
536C22C37×#38111yescharacteristic
537C22C37×#38514yes—
538C22C37×#38614yes—
539C22C2×#99×C3712yes—
540C22C37×#41012yes—
541C4—24no—
542C4—24no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—88no—
547C2—24no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—24no—
553C2—44no—
554C2C37×C22⋊#9511yescharacteristic
555C2C4×#99×C3712yes—
556C2C37×#178111yescharacteristic
557C2C37×#178211yescharacteristic
558C2C37×#179912yes—
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC23C2×C42×C37
Frattini, cosocleC25C23×C37
prime radicalC23×D4×C37C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C24×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C37×#342C2semidirect
4. C37×C22⋊#95C2semidirect
6. C24×C4×C37C4semidirect
11. C22×C4⋊C4×C37C4semidirect
12. C22×C22⋊C4×C37C4semidirect
15. C22×C42×C37C4semidirect
18. C2×#99×C37C4semidirect
59. C2×C22⋊C4×C37C2×C4semidirect
171. C23×C37#95semidirect
220. C2×C4×C37#95semidirect
221. C2×C4×C37#99semidirect
222. #10761C37direct (N × H)
270. C2×#342C2×C37semidirect
271. C22⋊#95C2×C37semidirect
285. C24×C4C4×C37semidirect
290. C22×C4⋊C4C4×C37semidirect
291. C22×C22⋊C4C4×C37semidirect
294. C22×C42C4×C37semidirect
297. C2×#99C4×C37semidirect
300. C37#10761direct (N × H)
339. C2×C22⋊C4C2×C4×C37semidirect
451. C23#95×C37semidirect
500. C2×C4#95×C37semidirect
501. C2×C4#99×C37semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C372
C22×#99×C372
C2×C37×#3422
C37×C22⋊#952
#1076137