Finite Group Databasebeta

← C37×#18121 #22639374

Subgroups — C37×#18121 #22639374

Order 9472.

990 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3460C211yesmaximal, characteristic
2C37×#3091C212yesmaximal, complemented
3C37×#2395C211yesmaximal, characteristic, complemented
4C37×#1618C212yesmaximal, complemented
5C37×#1617C211yesmaximal, characteristic, complemented
6C37×#1616C211yesmaximal, characteristic, complemented
7C37×#1612C212yesmaximal, complemented
8C37×#1611C211yesmaximal, characteristic, complemented
9C37×#1610C211yesmaximal, characteristic, complemented
10C37×#1501C212yesmaximal, complemented
11C37×#1459C211yesmaximal, characteristic, complemented
12C37×#544C2211yescharacteristic
13C37×#542—22no—
14C37×#540—22no—
15C37×#538—21no—
16C37×#538C2212yes—
17C37×#537C2211yescharacteristic
18C37×#535—21no—
19C37×#532—22no—
20C37×#529—22no—
21C37×#525—21no—
22C37×#525C2212yes—
23C4×#41×C37—21no—
24C2×C4×D4×C37C2211yescharacteristic
25C2×#117×C37C2211yescharacteristic
26C37×#485—22no—
27C37×#484C2212yes—
28C37×#483C2212yes—
29C37×#482—22no—
30C37×#481C2212yes—
31C37×#480C2212yes—
32C37×#427—22no—
33C37×#416—22no—
34C2×C22⋊C8×C37C2212yes—
35C37×#400C2211yescharacteristic
36C37×#399C2211yescharacteristic
37C37×#398C2211yescharacteristic
38C37×#397—21no—
39C37×#397C2211yescharacteristic
40C37×#394—21no—
41C4×C4⋊C4×C37—21no—
42C4×C22⋊C4×C37—21no—
43C4×C22⋊C4×C37C2211yescharacteristic
44C37×#328C2212yes—
45C37×#328C2212yes—
46C37×#327C2212yes—
47C37×#327C2212yes—
48C37×#324C2211yescharacteristic
49C37×#324C2211yescharacteristic
50C37×#323C2212yes—
51C2×#41×C37—21no—
52C2×#41×C37—21no—
53C2×#41×C37D412yes—
54C22×D4×C37D411yescharacteristic
55C23×C4×C37D411yescharacteristic
56C23×C4×C37C2311yescharacteristic
57C22×C8×C37—22no—
58C4⋊Q8×C37—22no—
59#127×C37—22no—
60#126×C37—22no—
61#126×C37—22no—
62#125×C37—22no—
63#124×C37—22no—
64#124×C37—22no—
65#124×C37—22no—
66#123×C37—22no—
67#123×C37—22no—
68#123×C37—22no—
69#123×C37—22no—
70C22⋊Q8×C37—21no—
71C22⋊Q8×C37—21no—
72C22⋊Q8×C37—22no—
73C22⋊Q8×C37D412yes—
74C22⋊Q8×C37C2312yes—
75#121×C37—21no—
76#121×C37—22no—
77#121×C37—22no—
78#121×C37—22no—
79#121×C37—22no—
80#121×C37—22no—
81#121×C37—21no—
82#121×C37D412yes—
83#121×C37C2312yes—
84#120×C37—22no—
85#120×C37—22no—
86C4×Q8×C37—21no—
87C4×Q8×C37—21no—
88C4×D4×C37—22no—
89C4×D4×C37—21no—
90C4×D4×C37—21no—
91C4×D4×C37—22no—
92C4×D4×C37—22no—
93C4×D4×C37—22no—
94C4×D4×C37—22no—
95C4×D4×C37—22no—
96#117×C37—21no—
97#117×C37—22no—
98#117×C37—21no—
99#117×C37—22no—
100#117×C37—22no—
101#117×C37D412yes—
102C2×C4⋊C4×C37—21no—
103C2×C4⋊C4×C37—21no—
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C4⋊C4×C37C2311yescharacteristic
106C2×C4⋊C4×C37C2311yescharacteristic
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—21no—
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37D411yescharacteristic
112C2×C22⋊C4×C37C2311yescharacteristic
113C2×C42×C37—22no—
114C2×C42×C37—21no—
115C2×C42×C37—21no—
116C2×C42×C37D411yescharacteristic
117#107×C37—22no—
118#107×C37—22no—
119#106×C37—22no—
120#106×C37—22no—
121#103×C37—22no—
122#103×C37—22no—
123#102×C37—22no—
124#102×C37—22no—
125C22⋊C8×C37—22no—
126C22⋊C8×C37C2312yes—
127C22⋊C8×C37C2312yes—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37C2311yescharacteristic
133#95×C37C2311yescharacteristic
134C24×C37C2×D411yescharacteristic
135C24×C37C2×D411yescharacteristic
136#41×C37—42no—
137#41×C37—44no—
138#41×C37—42no—
139#41×C37—82no—
140C2×Q8×C37—21no—
141C2×Q8×C37—21no—
142C2×Q8×C37C2×D412yes—
143C2×D4×C37—21no—
144C2×D4×C37—22no—
145C2×D4×C37—22no—
146C2×D4×C37—22no—
147C2×D4×C37—22no—
148C2×D4×C37—21no—
149C2×D4×C37—22no—
150C2×D4×C37—22no—
151C2×D4×C37—22no—
152C2×D4×C37—41no—
153C2×D4×C37C2×D412yes—
154C22×C4×C37—22no—
155C22×C4×C37—21no—
156C22×C4×C37—22no—
157C22×C4×C37—22no—
158C22×C4×C37—21no—
159C22×C4×C37—21no—
160C22×C4×C37—21no—
161C22×C4×C37—21no—
162C22×C4×C37—21no—
163C22×C4×C37—42no—
164C22×C4×C37—42no—
165C22×C4×C37C2×D411yescharacteristic
166C22×C4×C37C2×D412yes—
167C22×C4×C37C2×D411yescharacteristic
168C22×C4×C37C2×D411yescharacteristic
169C22×C4×C37C2×D411yescharacteristic
170C22×C4×C37C2×D412yes—
171C22×C4×C37C2411yescharacteristic
172C2×C8×C37—22no—
173C2×C8×C37—22no—
174C2×C8×C37—44no—
175C4⋊C4×C37—21no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—22no—
178C4⋊C4×C37—21no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—22no—
181C4⋊C4×C37—22no—
182C4⋊C4×C37—22no—
183C4⋊C4×C37—22no—
184C4⋊C4×C37—22no—
185C4⋊C4×C37—22no—
186C4⋊C4×C37—42no—
187C4⋊C4×C37—42no—
188C4⋊C4×C37C2×D412yes—
189C4⋊C4×C37C2×D412yes—
190C22⋊C4×C37—22no—
191C22⋊C4×C37—22no—
192C22⋊C4×C37—22no—
193C22⋊C4×C37—22no—
194C22⋊C4×C37—22no—
195C22⋊C4×C37—22no—
196C22⋊C4×C37—22no—
197C22⋊C4×C37—22no—
198C22⋊C4×C37—22no—
199C22⋊C4×C37—22no—
200C22⋊C4×C37—22no—
201C22⋊C4×C37—42no—
202C22⋊C4×C37—42no—
203C22⋊C4×C37—42no—
204C22⋊C4×C37—42no—
205C42×C37—22no—
206C42×C37—22no—
207C42×C37—21no—
208C42×C37—21no—
209C42×C37—22no—
210C42×C37—42no—
211C42×C37—41no—
212C42×C37—41no—
213C23×C37—21no—
214C23×C37—21no—
215C23×C37—21no—
216C23×C37—22no—
217C23×C37—21no—
218C23×C37—21no—
219C23×C37—41no—
220C23×C37—41no—
221C23×C37—41no—
222C23×C37—41no—
223C23×C37#12012yes—
224C23×C37C22×D411yescharacteristic
225Q8×C37—42no—
226Q8×C37—42no—
227Q8×C37—81no—
228D4×C37—44no—
229D4×C37—42no—
230D4×C37—42no—
231D4×C37—42no—
232D4×C37—42no—
233D4×C37—82no—
234D4×C37—82no—
235D4×C37—82no—
236D4×C37—81no—
237D4×C37—82no—
238C2×C4×C37—21no—
239C2×C4×C37—21no—
240C2×C4×C37—22no—
241C2×C4×C37—24no—
242C2×C4×C37—22no—
243C2×C4×C37—21no—
244C2×C4×C37—22no—
245C2×C4×C37—22no—
246C2×C4×C37—22no—
247C2×C4×C37—21no—
248C2×C4×C37—42no—
249C2×C4×C37—41no—
250C2×C4×C37—44no—
251C2×C4×C37—41no—
252C2×C4×C37—41no—
253C2×C4×C37—42no—
254C2×C4×C37—44no—
255C2×C4×C37—41no—
256C2×C4×C37—41no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—41no—
260C2×C4×C37—41no—
261C2×C4×C37—41no—
262C2×C4×C37—41no—
263C2×C4×C37—41no—
264C2×C4×C37—41no—
265C2×C4×C37—41no—
266C2×C4×C37—81no—
267C2×C4×C37—82no—
268C2×C4×C37#12011yescharacteristic
269C2×C4×C37#12011yescharacteristic
270C2×C4×C37#13512yes—
271C2×C4×C37C22×D412yes—
272C8×C37—42no—
273C8×C37—42no—
274#18121C3711yesmaximal, characteristic, direct product factor, Sylow
275C22×C37—21no—
276C22×C37—21no—
277C22×C37—22no—
278C22×C37—22no—
279C22×C37—22no—
280C22×C37—42no—
281C22×C37—42no—
282C22×C37—41no—
283C22×C37—42no—
284C22×C37—41no—
285C22×C37—41no—
286C22×C37—42no—
287C22×C37—81no—
288C22×C37—81no—
289C22×C37—81no—
290C22×C37C2×#12011yescharacteristic
291C22×C37C2×#13511yescharacteristic
292C22×C37#57511yescharacteristic
293C4×C37—22no—
294C4×C37—22no—
295C4×C37—21no—
296C4×C37—42no—
297C4×C37—42no—
298C4×C37—41no—
299C4×C37—42no—
300C4×C37—41no—
301C4×C37—42no—
302C4×C37—81no—
303C4×C37—81no—
304C4×C37—81no—
305C4×C37#45812yes—
306#3460C2×C3711yescharacteristic
307#3091C2×C3712yescomplemented
308#2395C2×C3711yescharacteristic, complemented
309#1618C2×C3712yescomplemented
310#1617C2×C3711yescharacteristic, complemented
311#1616C2×C3711yescharacteristic, complemented
312#1612C2×C3712yescomplemented
313#1611C2×C3711yescharacteristic, complemented
314#1610C2×C3711yescharacteristic, complemented
315#1501C2×C3712yescomplemented
316#1459C2×C3711yescharacteristic, complemented
317C2×C37—21no—
318C2×C37—21no—
319C2×C37—42no—
320C2×C37—82no—
321C2×C37—81no—
322C2×C37#300211yescharacteristic
323C2×C37#301811yescharacteristic
324C2×C37C2×#45811yescharacteristic
325#544C22×C3711yescharacteristic
326#542—22no—
327#540—22no—
328#538—21no—
329#538C22×C3712yes—
330#537C22×C3711yescharacteristic
331#535—21no—
332#532—22no—
333#529—22no—
334#525—21no—
335#525C22×C3712yes—
336C4×#41—21no—
337C2×C4×D4C22×C3711yescharacteristic
338C2×#117C22×C3711yescharacteristic
339#485—22no—
340#484C22×C3712yes—
341#483C22×C3712yes—
342#482—22no—
343#481C22×C3712yes—
344#480C22×C3712yes—
345#427—22no—
346#416—22no—
347C2×C22⋊C8C22×C3712yes—
348#400C22×C3711yescharacteristic
349#399C22×C3711yescharacteristic
350#398C22×C3711yescharacteristic
351#397—21no—
352#397C22×C3711yescharacteristic
353#394—21no—
354C4×C4⋊C4—21no—
355C4×C22⋊C4—21no—
356C4×C22⋊C4C22×C3711yescharacteristic
357#328C22×C3712yes—
358#328C22×C3712yes—
359#327C22×C3712yes—
360#327C22×C3712yes—
361#324C22×C3711yescharacteristic
362#324C22×C3711yescharacteristic
363#323C22×C3712yes—
364C37#1812111yescharacteristic, direct product factor, Sylow
365C2×#41—21no—
366C2×#41—21no—
367C2×#41D4×C3712yes—
368C22×D4D4×C3711yescharacteristic
369C23×C4D4×C3711yescharacteristic
370C23×C4C23×C3711yescharacteristic
371C22×C8—22no—
372C4⋊Q8—22no—
373#127—22no—
374#126—22no—
375#126—22no—
376#125—22no—
377#124—22no—
378#124—22no—
379#124—22no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8D4×C3712yes—
388C22⋊Q8C23×C3712yes—
389#121—21no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121—22no—
394#121—22no—
395#121—21no—
396#121D4×C3712yes—
397#121C23×C3712yes—
398#120—22no—
399#120—22no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410#117—22no—
411#117—21no—
412#117—21no—
413#117—22no—
414#117—22no—
415#117D4×C3712yes—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4C23×C3711yescharacteristic
419C2×C4⋊C4C23×C3711yescharacteristic
420C2×C4⋊C4C23×C3711yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4D4×C3711yescharacteristic
426C2×C22⋊C4C23×C3711yescharacteristic
427C2×C42—22no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42D4×C3711yescharacteristic
431#107—22no—
432#107—22no—
433#106—22no—
434#106—22no—
435#103—22no—
436#103—22no—
437#102—22no—
438#102—22no—
439C22⋊C8—22no—
440C22⋊C8C23×C3712yes—
441C22⋊C8C23×C3712yes—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95C23×C3711yescharacteristic
447#95C23×C3711yescharacteristic
448C24C2×D4×C3711yescharacteristic
449C24C2×D4×C3711yescharacteristic
450#41—42no—
451#41—44no—
452#41—42no—
453#41—82no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×D4×C3712yes—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—41no—
467C2×D4C2×D4×C3712yes—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4C2×D4×C3711yescharacteristic
480C22×C4C2×D4×C3712yes—
481C22×C4C2×D4×C3711yescharacteristic
482C22×C4C2×D4×C3711yescharacteristic
483C22×C4C2×D4×C3711yescharacteristic
484C22×C4C2×D4×C3712yes—
485C22×C4C24×C3711yescharacteristic
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—44no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4C2×D4×C3712yes—
503C4⋊C4C2×D4×C3712yes—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C42—22no—
520C42—22no—
521C42—21no—
522C42—22no—
523C42—21no—
524C42—42no—
525C42—41no—
526C42—41no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—22no—
531C23—21no—
532C23—21no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23#120×C3712yes—
538C23C22×D4×C3711yescharacteristic
539Q8—42no—
540Q8—42no—
541Q8—81no—
542D4—44no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—42no—
547D4—82no—
548D4—82no—
549D4—81no—
550D4—82no—
551D4—82no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—44no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—81no—
581C2×C4—82no—
582C2×C4#120×C3711yescharacteristic
583C2×C4#120×C3711yescharacteristic
584C2×C4#135×C3712yes—
585C2×C4C22×D4×C3712yes—
586C8—42no—
587C8—42no—
588C22—21no—
589C22—21no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C2×#120×C3711yescharacteristic
604C22C2×#135×C3711yescharacteristic
605C22C37×#57511yescharacteristic
606C4—22no—
607C4—22no—
608C4—21no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—42no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4C37×#45812yes—
619C2—21no—
620C2—21no—
621C2—42no—
622C2—81no—
623C2—82no—
624C2C37×#300211yescharacteristic
625C2C37×#301811yescharacteristic
626C2C2×C37×#45811yescharacteristic
subgroupG/H
centerC2×C4×C37#120
commutator, Frattini, cosocleC22×C4C24×C37
socleC22×C37C2×#120
prime radicalC37×#3460C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3091C2semidirect
3. C37×#2395C2semidirect
4. C37×#1618C2semidirect
5. C37×#1617C2semidirect
6. C37×#1616C2semidirect
7. C37×#1612C2semidirect
8. C37×#1611C2semidirect
9. C37×#1610C2semidirect
10. C37×#1501C2semidirect
11. C37×#1459C2semidirect
274. #18121C37direct (N × H)
307. #3091C2×C37semidirect
308. #2395C2×C37semidirect
309. #1618C2×C37semidirect
310. #1617C2×C37semidirect
311. #1616C2×C37semidirect
312. #1612C2×C37semidirect
313. #1611C2×C37semidirect
314. #1610C2×C37semidirect
315. #1501C2×C37semidirect
316. #1459C2×C37semidirect
364. C37#18121direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34602
C37×#30912
C37×#23952
C37×#16182
C37×#16172
C37×#16162
C37×#16122
C37×#16112
C37×#16102
C37×#15012
C37×#14592
#1812137