Finite Group Databasebeta

← C37×#18237 #22639490

Subgroups — C37×#18237 #22639490

Order 9472.

976 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3536C211yesmaximal, characteristic
2C37×#3095C211yesmaximal, characteristic, complemented
3C37×#3091C211yesmaximal, characteristic, complemented
4C37×#2624C211yesmaximal, characteristic, complemented
5C37×#1618C212yesmaximal, complemented
6C37×#1614C212yesmaximal, complemented
7C37×#1612C212yesmaximal, complemented
8C37×#1608C212yesmaximal, complemented
9C37×#1520C211yesmaximal, characteristic, complemented
10C37×#1513C211yesmaximal, characteristic, complemented
11C37×#1471C211yesmaximal, characteristic, complemented
12C37×#562—22no—
13C37×#554—21no—
14C37×#548—21no—
15C37×#547—21no—
16C37×#546—22no—
17C37×#546—21no—
18C37×#543C2212yes—
19C37×#542—21no—
20C37×#539—21no—
21C37×#538C2212yes—
22C37×#537—21no—
23C37×#537—21no—
24C37×#525C2211yescharacteristic
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×#117×C37C2211yescharacteristic
28C37×#485—21no—
29C37×#485—22no—
30C37×#484C2211yescharacteristic
31C37×#484C2212yes—
32C37×#483C2211yescharacteristic
33C37×#483C2212yes—
34C37×#482—21no—
35C37×#481C2211yescharacteristic
36C37×#480C2211yescharacteristic
37C37×#428—21no—
38C37×#427—21no—
39C37×#419—21no—
40C37×#416—21no—
41C37×#407C2211yescharacteristic
42C2×C22⋊C8×C37C2211yescharacteristic
43C37×#399C2212yes—
44C37×#397C2212yes—
45C37×#394—22no—
46C37×#390—21no—
47C37×#389—21no—
48C37×#380C2211yescharacteristic
49C37×#328C2212yes—
50C37×#328C2212yes—
51C37×#328C2212yes—
52C37×#327C2212yes—
53C37×#323C2212yes—
54C37×#323C2212yes—
55C2×#41×C37—22no—
56C2×#41×C37—21no—
57C2×#41×C37D411yescharacteristic
58C22×Q8×C37D411yescharacteristic
59C22×D4×C37D411yescharacteristic
60C22×D4×C37D412yes—
61C23×C4×C37C2311yescharacteristic
62C2×M16×C37—21no—
63C22×C8×C37—21no—
64C4⋊Q8×C37—21no—
65#126×C37—22no—
66#125×C37—22no—
67#124×C37—21no—
68#124×C37—22no—
69#124×C37—22no—
70#123×C37—22no—
71#123×C37—22no—
72#123×C37—22no—
73#123×C37—21no—
74#123×C37—22no—
75C22⋊Q8×C37—21no—
76C22⋊Q8×C37—22no—
77C22⋊Q8×C37—22no—
78C22⋊Q8×C37—22no—
79C22⋊Q8×C37—21no—
80C22⋊Q8×C37—21no—
81C22⋊Q8×C37—22no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37D412yes—
85C22⋊Q8×C37D411yescharacteristic
86C22⋊Q8×C37C2312yes—
87C22⋊Q8×C37C2311yescharacteristic
88#121×C37—21no—
89#121×C37—22no—
90#121×C37—22no—
91#121×C37—22no—
92#121×C37—22no—
93#121×C37—22no—
94#121×C37—21no—
95#121×C37—21no—
96#121×C37—21no—
97#121×C37—21no—
98#121×C37D411yescharacteristic
99#121×C37C2311yescharacteristic
100#120×C37—21no—
101#120×C37—22no—
102C4×Q8×C37—21no—
103C4×D4×C37—22no—
104C4×D4×C37—21no—
105C4×D4×C37—21no—
106C4×D4×C37—21no—
107C4×D4×C37—22no—
108#117×C37—21no—
109#117×C37—21no—
110#117×C37—21no—
111#117×C37—21no—
112#117×C37D411yescharacteristic
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—21no—
116C2×C4⋊C4×C37—22no—
117C2×C4⋊C4×C37D411yescharacteristic
118C2×C4⋊C4×C37D411yescharacteristic
119C2×C4⋊C4×C37C2311yescharacteristic
120C2×C4⋊C4×C37C2311yescharacteristic
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—22no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—22no—
126C2×C22⋊C4×C37—22no—
127C2×C22⋊C4×C37C2312yes—
128C2×C42×C37—21no—
129#107×C37—21no—
130#107×C37—21no—
131#107×C37—22no—
132#106×C37—21no—
133#106×C37—21no—
134#106×C37—22no—
135#103×C37—21no—
136#103×C37—21no—
137#103×C37—22no—
138#103×C37—22no—
139#102×C37—21no—
140#102×C37—21no—
141C22⋊C8×C37—21no—
142C22⋊C8×C37—21no—
143C22⋊C8×C37C2312yes—
144C22⋊C8×C37C2311yescharacteristic
145C22⋊C8×C37C2311yescharacteristic
146#95×C37—22no—
147#95×C37C2312yes—
148C24×C37C2×D412yes—
149C24×C37C2×D411yescharacteristic
150#41×C37—42no—
151#41×C37—84no—
152#41×C37—82no—
153C2×Q8×C37—22no—
154C2×Q8×C37—21no—
155C2×Q8×C37—42no—
156C2×Q8×C37C2×D411yescharacteristic
157C2×Q8×C37C2×D412yes—
158C2×D4×C37—21no—
159C2×D4×C37—22no—
160C2×D4×C37—21no—
161C2×D4×C37—22no—
162C2×D4×C37—22no—
163C2×D4×C37—21no—
164C2×D4×C37—22no—
165C2×D4×C37—21no—
166C2×D4×C37—21no—
167C2×D4×C37—42no—
168C2×D4×C37—82no—
169C2×D4×C37C2×D411yescharacteristic
170C22×C4×C37—21no—
171C22×C4×C37—22no—
172C22×C4×C37—22no—
173C22×C4×C37—22no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—22no—
178C22×C4×C37—21no—
179C22×C4×C37—42no—
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D411yescharacteristic
183C22×C4×C37C2×D412yes—
184C22×C4×C37C2×D411yescharacteristic
185C22×C4×C37C2×D411yescharacteristic
186C22×C4×C37C2411yescharacteristic
187M16×C37—42no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—22no—
191C2×C8×C37—42no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—22no—
194C4⋊C4×C37—22no—
195C4⋊C4×C37—22no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—22no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—22no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—21no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—42no—
208C4⋊C4×C37—82no—
209C4⋊C4×C37C2×D412yes—
210C4⋊C4×C37C2×D411yescharacteristic
211C4⋊C4×C37C2×D411yescharacteristic
212C22⋊C4×C37—22no—
213C22⋊C4×C37—22no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—22no—
218C22⋊C4×C37—21no—
219C22⋊C4×C37—21no—
220C22⋊C4×C37—22no—
221C22⋊C4×C37—21no—
222C22⋊C4×C37—21no—
223C22⋊C4×C37—22no—
224C22⋊C4×C37—22no—
225C22⋊C4×C37—21no—
226C22⋊C4×C37—41no—
227C22⋊C4×C37—41no—
228C22⋊C4×C37—81no—
229C22⋊C4×C37—82no—
230C22⋊C4×C37—82no—
231C42×C37—22no—
232C42×C37—21no—
233C42×C37—41no—
234C42×C37—41no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—22no—
238C23×C37—21no—
239C23×C37—22no—
240C23×C37—22no—
241C23×C37—41no—
242C23×C37—41no—
243C23×C37—42no—
244C23×C37—42no—
245C23×C37#12011yescharacteristic
246C23×C37#12011yescharacteristic
247C23×C37C22×D411yescharacteristic
248Q8×C37—42no—
249Q8×C37—41no—
250Q8×C37—42no—
251Q8×C37—82no—
252D4×C37—41no—
253D4×C37—44no—
254D4×C37—42no—
255D4×C37—41no—
256D4×C37—41no—
257D4×C37—42no—
258D4×C37—81no—
259D4×C37—82no—
260D4×C37—81no—
261D4×C37—82no—
262D4×C37—82no—
263C2×C4×C37—22no—
264C2×C4×C37—22no—
265C2×C4×C37—22no—
266C2×C4×C37—21no—
267C2×C4×C37—22no—
268C2×C4×C37—21no—
269C2×C4×C37—22no—
270C2×C4×C37—21no—
271C2×C4×C37—22no—
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—41no—
279C2×C4×C37—42no—
280C2×C4×C37—42no—
281C2×C4×C37—41no—
282C2×C4×C37—41no—
283C2×C4×C37—41no—
284C2×C4×C37—42no—
285C2×C4×C37—41no—
286C2×C4×C37—41no—
287C2×C4×C37—81no—
288C2×C4×C37—82no—
289C2×C4×C37—82no—
290C2×C4×C37—82no—
291C2×C4×C37#12011yescharacteristic
292C2×C4×C37#12011yescharacteristic
293C2×C4×C37C22×D411yescharacteristic
294C2×C4×C37C22×D411yescharacteristic
295C8×C37—41no—
296C8×C37—41no—
297C8×C37—42no—
298#18237C3711yesmaximal, characteristic, direct product factor, Sylow
299C22×C37—21no—
300C22×C37—21no—
301C22×C37—21no—
302C22×C37—21no—
303C22×C37—21no—
304C22×C37—21no—
305C22×C37—21no—
306C22×C37—21no—
307C22×C37—41no—
308C22×C37—42no—
309C22×C37—41no—
310C22×C37—42no—
311C22×C37—41no—
312C22×C37—42no—
313C22×C37—81no—
314C22×C37—81no—
315C22×C37—82no—
316C22×C37—82no—
317C22×C37C2×#12011yescharacteristic
318C22×C37#57711yescharacteristic
319C22×C37#57811yescharacteristic
320C4×C37—21no—
321C4×C37—21no—
322C4×C37—21no—
323C4×C37—41no—
324C4×C37—42no—
325C4×C37—42no—
326C4×C37—41no—
327C4×C37—41no—
328C4×C37—42no—
329C4×C37—82no—
330C4×C37—81no—
331C4×C37—81no—
332C4×C37#45812yes—
333#3536C2×C3711yescharacteristic
334#3095C2×C3711yescharacteristic, complemented
335#3091C2×C3711yescharacteristic, complemented
336#2624C2×C3711yescharacteristic, complemented
337#1618C2×C3712yescomplemented
338#1614C2×C3712yescomplemented
339#1612C2×C3712yescomplemented
340#1608C2×C3712yescomplemented
341#1520C2×C3711yescharacteristic, complemented
342#1513C2×C3711yescharacteristic, complemented
343#1471C2×C3711yescharacteristic, complemented
344C2×C37—21no—
345C2×C37—21no—
346C2×C37—41no—
347C2×C37—41no—
348C2×C37—81no—
349C2×C37—82no—
350C2×C37#301311yescharacteristic
351C2×C37#301911yescharacteristic
352C2×C37C2×#45811yescharacteristic
353#562—22no—
354#554—21no—
355#548—21no—
356#547—21no—
357#546—22no—
358#546—21no—
359#543C22×C3712yes—
360#542—21no—
361#539—21no—
362#538C22×C3712yes—
363#537—21no—
364#537—21no—
365#525C22×C3711yescharacteristic
366C2×C22⋊Q8C22×C3711yescharacteristic
367C2×#121C22×C3711yescharacteristic
368C2×#117C22×C3711yescharacteristic
369#485—21no—
370#485—22no—
371#484C22×C3711yescharacteristic
372#484C22×C3712yes—
373#483C22×C3711yescharacteristic
374#483C22×C3712yes—
375#482—21no—
376#481C22×C3711yescharacteristic
377#480C22×C3711yescharacteristic
378#428—21no—
379#427—21no—
380#419—21no—
381#416—21no—
382#407C22×C3711yescharacteristic
383C2×C22⋊C8C22×C3711yescharacteristic
384#399C22×C3712yes—
385#397C22×C3712yes—
386#394—22no—
387#390—21no—
388#389—21no—
389#380C22×C3711yescharacteristic
390#328C22×C3712yes—
391#328C22×C3712yes—
392#328C22×C3712yes—
393#327C22×C3712yes—
394#323C22×C3712yes—
395#323C22×C3712yes—
396C37#1823711yescharacteristic, direct product factor, Sylow
397C2×#41—22no—
398C2×#41—21no—
399C2×#41D4×C3711yescharacteristic
400C22×Q8D4×C3711yescharacteristic
401C22×D4D4×C3711yescharacteristic
402C22×D4D4×C3712yes—
403C23×C4C23×C3711yescharacteristic
404C2×M16—21no—
405C22×C8—21no—
406C4⋊Q8—21no—
407#126—22no—
408#125—22no—
409#124—21no—
410#124—22no—
411#124—22no—
412#123—22no—
413#123—22no—
414#123—22no—
415#123—21no—
416#123—22no—
417C22⋊Q8—21no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8D4×C3712yes—
427C22⋊Q8D4×C3711yescharacteristic
428C22⋊Q8C23×C3712yes—
429C22⋊Q8C23×C3711yescharacteristic
430#121—21no—
431#121—22no—
432#121—22no—
433#121—22no—
434#121—22no—
435#121—22no—
436#121—21no—
437#121—21no—
438#121—21no—
439#121—21no—
440#121D4×C3711yescharacteristic
441#121C23×C3711yescharacteristic
442#120—21no—
443#120—22no—
444C4×Q8—21no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—22no—
450#117—21no—
451#117—21no—
452#117—21no—
453#117—21no—
454#117D4×C3711yescharacteristic
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4D4×C3711yescharacteristic
460C2×C4⋊C4D4×C3711yescharacteristic
461C2×C4⋊C4C23×C3711yescharacteristic
462C2×C4⋊C4C23×C3711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4C23×C3712yes—
470C2×C42—21no—
471#107—21no—
472#107—21no—
473#107—22no—
474#106—21no—
475#106—21no—
476#106—22no—
477#103—21no—
478#103—21no—
479#103—22no—
480#103—22no—
481#102—21no—
482#102—21no—
483C22⋊C8—21no—
484C22⋊C8—21no—
485C22⋊C8C23×C3712yes—
486C22⋊C8C23×C3711yescharacteristic
487C22⋊C8C23×C3711yescharacteristic
488#95—22no—
489#95C23×C3712yes—
490C24C2×D4×C3712yes—
491C24C2×D4×C3711yescharacteristic
492#41—42no—
493#41—84no—
494#41—82no—
495C2×Q8—22no—
496C2×Q8—21no—
497C2×Q8—42no—
498C2×Q8C2×D4×C3711yescharacteristic
499C2×Q8C2×D4×C3712yes—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—82no—
511C2×D4C2×D4×C3711yescharacteristic
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4C2×D4×C3711yescharacteristic
523C22×C4C2×D4×C3711yescharacteristic
524C22×C4C2×D4×C3711yescharacteristic
525C22×C4C2×D4×C3712yes—
526C22×C4C2×D4×C3711yescharacteristic
527C22×C4C2×D4×C3711yescharacteristic
528C22×C4C24×C3711yescharacteristic
529M16—42no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—22no—
533C2×C8—42no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—82no—
551C4⋊C4C2×D4×C3712yes—
552C4⋊C4C2×D4×C3711yescharacteristic
553C4⋊C4C2×D4×C3711yescharacteristic
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—22no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—21no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—81no—
571C22⋊C4—82no—
572C22⋊C4—82no—
573C42—22no—
574C42—21no—
575C42—41no—
576C42—41no—
577C23—21no—
578C23—21no—
579C23—22no—
580C23—21no—
581C23—22no—
582C23—22no—
583C23—41no—
584C23—41no—
585C23—42no—
586C23—42no—
587C23#120×C3711yescharacteristic
588C23#120×C3711yescharacteristic
589C23C22×D4×C3711yescharacteristic
590Q8—42no—
591Q8—41no—
592Q8—42no—
593Q8—82no—
594D4—41no—
595D4—44no—
596D4—42no—
597D4—41no—
598D4—41no—
599D4—42no—
600D4—81no—
601D4—82no—
602D4—81no—
603D4—82no—
604D4—82no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4#120×C3711yescharacteristic
634C2×C4#120×C3711yescharacteristic
635C2×C4C22×D4×C3711yescharacteristic
636C2×C4C22×D4×C3711yescharacteristic
637C8—41no—
638C8—41no—
639C8—42no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—41no—
649C22—42no—
650C22—41no—
651C22—42no—
652C22—41no—
653C22—42no—
654C22—81no—
655C22—81no—
656C22—82no—
657C22—82no—
658C22C2×#120×C3711yescharacteristic
659C22C37×#57711yescharacteristic
660C22C37×#57811yescharacteristic
661C4—21no—
662C4—21no—
663C4—21no—
664C4—41no—
665C4—42no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—82no—
671C4—81no—
672C4—81no—
673C4C37×#45812yes—
674C2—21no—
675C2—21no—
676C2—41no—
677C2—41no—
678C2—82no—
679C2—81no—
680C2C37×#301311yescharacteristic
681C2C37×#301911yescharacteristic
682C2C2×C37×#45811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3536C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3095C2semidirect
3. C37×#3091C2semidirect
4. C37×#2624C2semidirect
5. C37×#1618C2semidirect
6. C37×#1614C2semidirect
7. C37×#1612C2semidirect
8. C37×#1608C2semidirect
9. C37×#1520C2semidirect
10. C37×#1513C2semidirect
11. C37×#1471C2semidirect
298. #18237C37direct (N × H)
334. #3095C2×C37semidirect
335. #3091C2×C37semidirect
336. #2624C2×C37semidirect
337. #1618C2×C37semidirect
338. #1614C2×C37semidirect
339. #1612C2×C37semidirect
340. #1608C2×C37semidirect
341. #1520C2×C37semidirect
342. #1513C2×C37semidirect
343. #1471C2×C37semidirect
396. C37#18237direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35362
C37×#30952
C37×#30912
C37×#26242
C37×#16182
C37×#16142
C37×#16122
C37×#16082
C37×#15202
C37×#15132
C37×#14712
#1823737