Finite Group Databasebeta

← C37×#18793 #22640046

Subgroups — C37×#18793 #22640046

Order 9472.

948 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3475C211yesmaximal, characteristic
2C37×#3209C211yesmaximal, characteristic, complemented
3C37×#3079C211yesmaximal, characteristic, complemented
4C2×C37×#476C211yesmaximal, characteristic, complemented
5C37×#1638C212yesmaximal, complemented
6C37×#1635C212yesmaximal, complemented
7C37×#1634C212yesmaximal, complemented
8C37×#1632C212yesmaximal, complemented
9C37×#1550C211yesmaximal, characteristic, complemented
10C37×#1486C211yesmaximal, characteristic, complemented
11C37×#1477C211yesmaximal, characteristic, complemented
12C37×#556C2211yescharacteristic
13C37×#555C2211yescharacteristic
14C37×#554C2211yescharacteristic
15C37×#553—21no—
16C37×#552—21no—
17C37×#552—21no—
18C37×#551—22no—
19C37×#547C2211yescharacteristic
20C37×#546—21no—
21C37×#533C2211yescharacteristic
22C2×C4⋊Q8×C37C2211yescharacteristic
23C37×#529—22no—
24C37×#529—21no—
25C37×#525—21no—
26C4×#41×C37—21no—
27C4×#41×C37C2211yescharacteristic
28C2×C4×D4×C37C2211yescharacteristic
29C2×#117×C37—21no—
30C37×#494C2212yescomplemented
31C37×#487C2212yescomplemented
32C37×#477C2212yescomplemented
33C37×#476—21no—
34C37×#476—21no—
35C37×#476C2212yes—
36C37×#476C2212yes—
37C37×#476C2212yescomplemented
38C37×#475—21no—
39C37×#474—21no—
40C37×#462—22no—
41C37×#451—22no—
42C37×#431C2211yescharacteristic
43C37×#428—21no—
44C2×#106×C37—21no—
45C37×#423C2211yescharacteristic
46C2×C4⋊C8×C37C2211yescharacteristic
47C37×#417—21no—
48C2×#102×C37—21no—
49C37×#333C2212yescomplemented
50C37×#332C2212yescomplemented
51C37×Q8⋊C8C2212yescomplemented
52C37×D4⋊C8C2212yes—
53C37×D4⋊C8C2212yes—
54C37×D4⋊C8C2212yescomplemented
55C2×#41×C37—21no—
56C2×#41×C37D411yescharacteristic
57C22×Q8×C37—21no—
58C22×D4×C37D411yescharacteristic
59C23×C4×C37—21no—
60C2×Q16×C37—24no—
61C2×M16×C37—21no—
62C22×C8×C37—21no—
63C4⋊Q8×C37—21no—
64C4⋊Q8×C37—21no—
65C4⋊Q8×C37—21no—
66C4⋊Q8×C37C2312yes—
67C4⋊Q8×C37C2311yescharacteristic
68C4⋊Q8×C37C2311yescharacteristic
69#126×C37—22no—
70#126×C37—22no—
71#126×C37—22no—
72#125×C37—22no—
73#125×C37—21no—
74#125×C37—21no—
75#124×C37—22no—
76#124×C37—21no—
77#123×C37—22no—
78#123×C37—22no—
79#123×C37—22no—
80#123×C37—22no—
81C22⋊Q8×C37—21no—
82C22⋊Q8×C37—21no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—21no—
85C22⋊Q8×C37—21no—
86C22⋊Q8×C37D412yes—
87#121×C37—22no—
88#121×C37—21no—
89#121×C37—21no—
90#121×C37—21no—
91#120×C37—22no—
92C4×Q8×C37—21no—
93C4×Q8×C37—21no—
94C4×Q8×C37D412yes—
95C4×Q8×C37D411yescharacteristic
96C4×Q8×C37C2311yescharacteristic
97C4×D4×C37—22no—
98C4×D4×C37—22no—
99C4×D4×C37—22no—
100C4×D4×C37—21no—
101C4×D4×C37—21no—
102C4×D4×C37—21no—
103C4×D4×C37—21no—
104C4×D4×C37—21no—
105C4×D4×C37D411yescharacteristic
106C4×D4×C37D411yescharacteristic
107C4×D4×C37D411yescharacteristic
108C4×D4×C37C2311yescharacteristic
109C4×D4×C37C2311yescharacteristic
110C4×D4×C37C2311yescharacteristic
111#117×C37—22no—
112#117×C37—22no—
113#117×C37—22no—
114#117×C37—21no—
115#117×C37—21no—
116#117×C37—21no—
117#117×C37—21no—
118#117×C37—21no—
119#117×C37D411yescharacteristic
120C2×C4⋊C4×C37—21no—
121C2×C4⋊C4×C37—21no—
122C2×C4⋊C4×C37—21no—
123C2×C4⋊C4×C37—21no—
124C2×C4⋊C4×C37D411yescharacteristic
125C2×C22⋊C4×C37—22no—
126C2×C22⋊C4×C37—21no—
127C2×C42×C37—22no—
128C2×C42×C37—21no—
129C2×C42×C37C2311yescharacteristic
130#107×C37—22no—
131#106×C37—22no—
132#106×C37—22no—
133#106×C37—22no—
134C4⋊C8×C37—21no—
135C4⋊C8×C37—21no—
136C4⋊C8×C37—21no—
137C4⋊C8×C37C2312yes—
138C4⋊C8×C37C2312yes—
139#103×C37—22no—
140#103×C37—24no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—22no—
144C22⋊C8×C37—21no—
145C4×C8×C37C2312yes—
146C24×C37—21no—
147#41×C37—22no—
148#41×C37—22no—
149#41×C37—42no—
150#41×C37—42no—
151C2×Q8×C37—21no—
152C2×Q8×C37—22no—
153C2×Q8×C37—41no—
154C2×Q8×C37—82no—
155C2×Q8×C37C2×D411yescharacteristic
156C2×Q8×C37C2×D412yes—
157C2×D4×C37—22no—
158C2×D4×C37—22no—
159C2×D4×C37—21no—
160C2×D4×C37—22no—
161C2×D4×C37—21no—
162C2×D4×C37—41no—
163C2×D4×C37C2×D411yescharacteristic
164C2×D4×C37C2×D411yescharacteristic
165C2×D4×C37C2×D411yescharacteristic
166C22×C4×C37—22no—
167C22×C4×C37—21no—
168C22×C4×C37—22no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—42no—
177C22×C4×C37—42no—
178C22×C4×C37—41no—
179C22×C4×C37C2×D411yescharacteristic
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182Q16×C37—84no—
183M16×C37—42no—
184C2×C8×C37—22no—
185C2×C8×C37—22no—
186C2×C8×C37—22no—
187C2×C8×C37—42no—
188C4⋊C4×C37—22no—
189C4⋊C4×C37—22no—
190C4⋊C4×C37—22no—
191C4⋊C4×C37—22no—
192C4⋊C4×C37—21no—
193C4⋊C4×C37—22no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—22no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—22no—
201C4⋊C4×C37—22no—
202C4⋊C4×C37—41no—
203C4⋊C4×C37—41no—
204C4⋊C4×C37C2×D412yes—
205C4⋊C4×C37C2×D411yescharacteristic
206C4⋊C4×C37C2×D411yescharacteristic
207C4⋊C4×C37C2×D411yescharacteristic
208C4⋊C4×C37C2×D411yescharacteristic
209C22⋊C4×C37—22no—
210C22⋊C4×C37—22no—
211C22⋊C4×C37—22no—
212C22⋊C4×C37—22no—
213C22⋊C4×C37—22no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—21no—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—21no—
218C22⋊C4×C37—21no—
219C22⋊C4×C37—21no—
220C22⋊C4×C37—21no—
221C22⋊C4×C37—21no—
222C22⋊C4×C37—21no—
223C42×C37—22no—
224C42×C37—22no—
225C42×C37—21no—
226C42×C37—22no—
227C42×C37—21no—
228C42×C37—21no—
229C42×C37C2×D411yescharacteristic
230C42×C37C2×D411yescharacteristic
231C42×C37C2×D411yescharacteristic
232C42×C37C2411yescharacteristic
233C23×C37—21no—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—42no—
237C23×C37—42no—
238C23×C37—81no—
239C23×C37#12011yescharacteristic
240Q8×C37—21no—
241Q8×C37—21no—
242Q8×C37—42no—
243Q8×C37—44no—
244Q8×C37—41no—
245Q8×C37—41no—
246Q8×C37—82no—
247D4×C37—21no—
248D4×C37—21no—
249D4×C37—21no—
250D4×C37—21no—
251D4×C37—21no—
252D4×C37—42no—
253D4×C37—44no—
254D4×C37—42no—
255D4×C37—82no—
256D4×C37#13712yes—
257C2×C4×C37—21no—
258C2×C4×C37—21no—
259C2×C4×C37—21no—
260C2×C4×C37—21no—
261C2×C4×C37—21no—
262C2×C4×C37—21no—
263C2×C4×C37—22no—
264C2×C4×C37—22no—
265C2×C4×C37—21no—
266C2×C4×C37—41no—
267C2×C4×C37—44no—
268C2×C4×C37—42no—
269C2×C4×C37—41no—
270C2×C4×C37—41no—
271C2×C4×C37—41no—
272C2×C4×C37—41no—
273C2×C4×C37—41no—
274C2×C4×C37—41no—
275C2×C4×C37—42no—
276C2×C4×C37—42no—
277C2×C4×C37—42no—
278C2×C4×C37—42no—
279C2×C4×C37—81no—
280C2×C4×C37—82no—
281C2×C4×C37—82no—
282C2×C4×C37#12011yescharacteristic
283C2×C4×C37#12011yescharacteristic
284C2×C4×C37#12011yescharacteristic
285C2×C4×C37#13512yes—
286C2×C4×C37#13712yes—
287C2×C4×C37C22×D411yescharacteristic
288C2×C4×C37C22×D411yescharacteristic
289C2×C4×C37C22×D411yescharacteristic
290C8×C37—42no—
291C8×C37—42no—
292C8×C37—42no—
293#18793C3711yesmaximal, characteristic, direct product factor, Sylow
294C22×C37—21no—
295C22×C37—21no—
296C22×C37—22no—
297C22×C37—41no—
298C22×C37—41no—
299C22×C37—41no—
300C22×C37—41no—
301C22×C37—41no—
302C22×C37—41no—
303C22×C37—41no—
304C22×C37—41no—
305C22×C37—84no—
306C22×C37#45212yes—
307C22×C37C2×#12011yescharacteristic
308C4×C37—21no—
309C4×C37—21no—
310C4×C37—21no—
311C4×C37—41no—
312C4×C37—41no—
313C4×C37—41no—
314C4×C37—41no—
315C4×C37—42no—
316C4×C37—41no—
317C4×C37—42no—
318C4×C37—82no—
319C4×C37#45212yes—
320C4×C37C2×#13511yescharacteristic
321C4×C37C2×#13711yescharacteristic
322C4×C37C2×#13711yescharacteristic
323C4×C37#57511yescharacteristic
324#3475C2×C3711yescharacteristic
325#3209C2×C3711yescharacteristic, complemented
326#3079C2×C3711yescharacteristic, complemented
327C2×#476C2×C3711yescharacteristic, complemented
328#1638C2×C3712yescomplemented
329#1635C2×C3712yescomplemented
330#1634C2×C3712yescomplemented
331#1632C2×C3712yescomplemented
332#1550C2×C3711yescharacteristic, complemented
333#1486C2×C3711yescharacteristic, complemented
334#1477C2×C3711yescharacteristic, complemented
335C2×C37—22no—
336C2×C37—42no—
337C2×C37—81no—
338C2×C37—81no—
339C2×C37C2×#45211yescharacteristic
340C2×C37#300711yescharacteristic
341C2×C37#302111yescharacteristic
342#556C22×C3711yescharacteristic
343#555C22×C3711yescharacteristic
344#554C22×C3711yescharacteristic
345#553—21no—
346#552—21no—
347#552—21no—
348#551—22no—
349#547C22×C3711yescharacteristic
350#546—21no—
351#533C22×C3711yescharacteristic
352C2×C4⋊Q8C22×C3711yescharacteristic
353#529—22no—
354#529—21no—
355#525—21no—
356C4×#41—21no—
357C4×#41C22×C3711yescharacteristic
358C2×C4×D4C22×C3711yescharacteristic
359C2×#117—21no—
360#494C22×C3712yescomplemented
361#487C22×C3712yescomplemented
362#477C22×C3712yescomplemented
363#476—21no—
364#476—21no—
365#476C22×C3712yes—
366#476C22×C3712yes—
367#476C22×C3712yescomplemented
368#475—21no—
369#474—21no—
370#462—22no—
371#451—22no—
372#431C22×C3711yescharacteristic
373#428—21no—
374C2×#106—21no—
375#423C22×C3711yescharacteristic
376C2×C4⋊C8C22×C3711yescharacteristic
377#417—21no—
378C2×#102—21no—
379#333C22×C3712yescomplemented
380#332C22×C3712yescomplemented
381Q8⋊C8C22×C3712yescomplemented
382D4⋊C8C22×C3712yes—
383D4⋊C8C22×C3712yes—
384D4⋊C8C22×C3712yescomplemented
385C37#1879311yescharacteristic, direct product factor, Sylow
386C2×#41—21no—
387C2×#41D4×C3711yescharacteristic
388C22×Q8—21no—
389C22×D4D4×C3711yescharacteristic
390C23×C4—21no—
391C2×Q16—24no—
392C2×M16—21no—
393C22×C8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C3712yes—
398C4⋊Q8C23×C3711yescharacteristic
399C4⋊Q8C23×C3711yescharacteristic
400#126—22no—
401#126—22no—
402#126—22no—
403#125—22no—
404#125—21no—
405#125—21no—
406#124—22no—
407#124—21no—
408#123—22no—
409#123—22no—
410#123—22no—
411#123—22no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—22no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8D4×C3712yes—
418#121—22no—
419#121—21no—
420#121—21no—
421#121—21no—
422#120—22no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8D4×C3711yescharacteristic
426C4×Q8D4×C3712yes—
427C4×Q8C23×C3711yescharacteristic
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4D4×C3711yescharacteristic
437C4×D4D4×C3711yescharacteristic
438C4×D4D4×C3711yescharacteristic
439C4×D4C23×C3711yescharacteristic
440C4×D4C23×C3711yescharacteristic
441C4×D4C23×C3711yescharacteristic
442#117—22no—
443#117—22no—
444#117—22no—
445#117—21no—
446#117—21no—
447#117—21no—
448#117—21no—
449#117—21no—
450#117D4×C3711yescharacteristic
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4D4×C3711yescharacteristic
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C42—22no—
459C2×C42—21no—
460C2×C42C23×C3711yescharacteristic
461#107—22no—
462#106—22no—
463#106—22no—
464#106—22no—
465C4⋊C8—21no—
466C4⋊C8—21no—
467C4⋊C8—21no—
468C4⋊C8C23×C3712yes—
469C4⋊C8C23×C3712yes—
470#103—22no—
471#103—24no—
472#102—22no—
473#102—22no—
474#102—22no—
475C22⋊C8—21no—
476C4×C8C23×C3712yes—
477C24—21no—
478#41—22no—
479#41—22no—
480#41—42no—
481#41—42no—
482C2×Q8—21no—
483C2×Q8—22no—
484C2×Q8—41no—
485C2×Q8—82no—
486C2×Q8C2×D4×C3711yescharacteristic
487C2×Q8C2×D4×C3712yes—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—41no—
494C2×D4C2×D4×C3711yescharacteristic
495C2×D4C2×D4×C3711yescharacteristic
496C2×D4C2×D4×C3711yescharacteristic
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—41no—
510C22×C4C2×D4×C3711yescharacteristic
511C22×C4C2×D4×C3711yescharacteristic
512C22×C4C2×D4×C3711yescharacteristic
513Q16—84no—
514M16—42no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—42no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4C2×D4×C3712yes—
536C4⋊C4C2×D4×C3711yescharacteristic
537C4⋊C4C2×D4×C3711yescharacteristic
538C4⋊C4C2×D4×C3711yescharacteristic
539C4⋊C4C2×D4×C3711yescharacteristic
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C42—22no—
555C42—22no—
556C42—21no—
557C42—22no—
558C42—21no—
559C42—21no—
560C42C2×D4×C3711yescharacteristic
561C42C2×D4×C3711yescharacteristic
562C42C2×D4×C3711yescharacteristic
563C42C24×C3711yescharacteristic
564C23—21no—
565C23—21no—
566C23—21no—
567C23—42no—
568C23—42no—
569C23—81no—
570C23#120×C3711yescharacteristic
571Q8—21no—
572Q8—21no—
573Q8—42no—
574Q8—44no—
575Q8—41no—
576Q8—41no—
577Q8—82no—
578D4—21no—
579D4—21no—
580D4—21no—
581D4—21no—
582D4—21no—
583D4—42no—
584D4—44no—
585D4—42no—
586D4—82no—
587D4#137×C3712yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—81no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4#120×C3711yescharacteristic
614C2×C4#120×C3711yescharacteristic
615C2×C4#120×C3711yescharacteristic
616C2×C4#135×C3712yes—
617C2×C4#137×C3712yes—
618C2×C4C22×D4×C3711yescharacteristic
619C2×C4C22×D4×C3711yescharacteristic
620C2×C4C22×D4×C3711yescharacteristic
621C8—42no—
622C8—42no—
623C8—42no—
624C22—21no—
625C22—21no—
626C22—22no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—84no—
636C22C37×#45212yes—
637C22C2×#120×C3711yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—42no—
646C4—41no—
647C4—42no—
648C4—82no—
649C4C37×#45212yes—
650C4C2×#135×C3711yescharacteristic
651C4C2×#137×C3711yescharacteristic
652C4C2×#137×C3711yescharacteristic
653C4C37×#57511yescharacteristic
654C2—22no—
655C2—42no—
656C2—81no—
657C2—81no—
658C2C2×C37×#45211yescharacteristic
659C2C37×#300711yescharacteristic
660C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3475C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3209C2semidirect
3. C37×#3079C2semidirect
4. C2×C37×#476C2semidirect
5. C37×#1638C2semidirect
6. C37×#1635C2semidirect
7. C37×#1634C2semidirect
8. C37×#1632C2semidirect
9. C37×#1550C2semidirect
10. C37×#1486C2semidirect
11. C37×#1477C2semidirect
30. C37×#494C22semidirect
31. C37×#487C22semidirect
32. C37×#477C22semidirect
37. C37×#476C22semidirect
49. C37×#333C22semidirect
50. C37×#332C22semidirect
51. C37×Q8⋊C8C22semidirect
54. C37×D4⋊C8C22semidirect
293. #18793C37direct (N × H)
325. #3209C2×C37semidirect
326. #3079C2×C37semidirect
327. C2×#476C2×C37semidirect
328. #1638C2×C37semidirect
329. #1635C2×C37semidirect
330. #1634C2×C37semidirect
331. #1632C2×C37semidirect
332. #1550C2×C37semidirect
333. #1486C2×C37semidirect
334. #1477C2×C37semidirect
360. #494C22×C37semidirect
361. #487C22×C37semidirect
362. #477C22×C37semidirect
367. #476C22×C37semidirect
379. #333C22×C37semidirect
380. #332C22×C37semidirect
381. Q8⋊C8C22×C37semidirect
384. D4⋊C8C22×C37semidirect
385. C37#18793direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34752
C37×#32092
C37×#30792
C2×C37×#4762
C37×#16382
C37×#16352
C37×#16342
C37×#16322
C37×#15502
C37×#14862
C37×#14772
#1879337