Finite Group Databasebeta

← C37×#14826 #22636079

Subgroups — C37×#14826 #22636079

Order 9472.

1794 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#400C211yesmaximal, characteristic, complemented
2C2×C37×#385C211yesmaximal, characteristic
3C2×C37×#380C211yesmaximal, characteristic
4C22×#95×C37C211yesmaximal, characteristic
5C37×#1445C211yesmaximal, characteristic, complemented
6C37×#1443C212yesmaximal, complemented
7C37×#1442C212yesmaximal, complemented
8C37×#1442C211yesmaximal, characteristic, complemented
9C37×#1441C211yesmaximal, characteristic, complemented
10C37×C22⋊#95C212yesmaximal
11C37×C22⋊#95C212yesmaximal
12C24×C4×C37C2212yes—
13C24×C4×C37C2211yescharacteristic
14C22×C4⋊C4×C37C2211yescharacteristic
15C22×C4⋊C4×C37C2211yescharacteristic
16C22×C4⋊C4×C37C2211yescharacteristic
17C22×C4⋊C4×C37C2211yescharacteristic
18C22×C22⋊C4×C37C2212yes—
19C22×C22⋊C4×C37C2211yescharacteristic
20C22×C22⋊C4×C37C2211yescharacteristic
21C37×#400—24no—
22C37×#385—24no—
23C37×#380—24no—
24C2×#95×C37—24no—
25C2×#95×C37C2212yes—
26C2×#95×C37C2212yes—
27C2×#95×C37C2212yes—
28C2×#95×C37C2212yes—
29C2×#95×C37C2211yescharacteristic
30C2×#95×C37C2212yes—
31C2×#95×C37C2212yes—
32C2×#95×C37C2211yescharacteristic
33C2×#95×C37C2211yescharacteristic
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C2×#95×C37C2212yes—
37C2×#95×C37C2212yes—
38C2×#95×C37C2211yescharacteristic
39C25×C37C2311yescharacteristic
40C23×C4×C37—24no—
41C23×C4×C37—24no—
42C23×C4×C37—24no—
43C23×C4×C37—22no—
44C23×C4×C37—24no—
45C23×C4×C37—22no—
46C23×C4×C37—24no—
47C23×C4×C37—24no—
48C23×C4×C37—42no—
49C23×C4×C37—42no—
50C23×C4×C37—42no—
51C23×C4×C37D414yes—
52C23×C4×C37C2311yescharacteristic
53C23×C4×C37C2312yes—
54C23×C4×C37C2312yes—
55C23×C4×C37C2311yescharacteristic
56C23×C4×C37C2312yes—
57C23×C4×C37C2311yescharacteristic
58C23×C4×C37C2311yescharacteristic
59C23×C4×C37C2311yescharacteristic
60C23×C4×C37C2312yes—
61C23×C4×C37C2311yescharacteristic
62C2×C4⋊C4×C37—22no—
63C2×C4⋊C4×C37—22no—
64C2×C4⋊C4×C37—22no—
65C2×C4⋊C4×C37—22no—
66C2×C4⋊C4×C37—22no—
67C2×C4⋊C4×C37—22no—
68C2×C4⋊C4×C37—22no—
69C2×C4⋊C4×C37—22no—
70C2×C4⋊C4×C37—42no—
71C2×C4⋊C4×C37—42no—
72C2×C22⋊C4×C37—22no—
73C2×C22⋊C4×C37—22no—
74C2×C22⋊C4×C37—24no—
75C2×C22⋊C4×C37—22no—
76C2×C22⋊C4×C37—24no—
77C2×C22⋊C4×C37—24no—
78C2×C22⋊C4×C37—24no—
79C2×C22⋊C4×C37Q814yes—
80#95×C37—24no—
81#95×C37—22no—
82#95×C37—24no—
83#95×C37—22no—
84#95×C37—22no—
85#95×C37—24no—
86#95×C37—24no—
87#95×C37—24no—
88#95×C37—24no—
89#95×C37—42no—
90#95×C37—42no—
91#95×C37—42no—
92#95×C37—42no—
93#95×C37D414yes—
94C24×C37—21no—
95C24×C37—21no—
96C24×C37—22no—
97C24×C37—22no—
98C24×C37—21no—
99C24×C37—21no—
100C24×C37C2×D412yes—
101C24×C37C2×Q812yes—
102C24×C37#4112yes—
103C24×C37#4114yes—
104C24×C37#4114yes—
105C24×C37C2411yescharacteristic
106C22×C4×C37—22no—
107C22×C4×C37—22no—
108C22×C4×C37—216no—
109C22×C4×C37—28no—
110C22×C4×C37—21no—
111C22×C4×C37—21no—
112C22×C4×C37—22no—
113C22×C4×C37—21no—
114C22×C4×C37—21no—
115C22×C4×C37—22no—
116C22×C4×C37—21no—
117C22×C4×C37—21no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—22no—
121C22×C4×C37—22no—
122C22×C4×C37—22no—
123C22×C4×C37—22no—
124C22×C4×C37—22no—
125C22×C4×C37—22no—
126C22×C4×C37—22no—
127C22×C4×C37—22no—
128C22×C4×C37—21no—
129C22×C4×C37—22no—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—21no—
136C22×C4×C37—28no—
137C22×C4×C37—21no—
138C22×C4×C37—22no—
139C22×C4×C37—21no—
140C22×C4×C37—22no—
141C22×C4×C37—22no—
142C22×C4×C37—21no—
143C22×C4×C37—22no—
144C22×C4×C37—22no—
145C22×C4×C37—22no—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—22no—
151C22×C4×C37—22no—
152C22×C4×C37—22no—
153C22×C4×C37—21no—
154C22×C4×C37—22no—
155C22×C4×C37—21no—
156C22×C4×C37—22no—
157C22×C4×C37—22no—
158C22×C4×C37—22no—
159C22×C4×C37—22no—
160C22×C4×C37—21no—
161C22×C4×C37—44no—
162C22×C4×C37—48no—
163C22×C4×C37—48no—
164C22×C4×C37—48no—
165C22×C4×C37—48no—
166C22×C4×C37—48no—
167C22×C4×C37—48no—
168C22×C4×C37—48no—
169C22×C4×C37—48no—
170C22×C4×C37C2×D414yes—
171C22×C4×C37C2×D412yes—
172C22×C4×C37C2×D412yes—
173C22×C4×C37C2×D412yes—
174C22×C4×C37C2×Q812yes—
175C22×C4×C37C2×Q812yes—
176C22×C4×C37#4114yes—
177C22×C4×C37#4112yes—
178C4⋊C4×C37—44no—
179C4⋊C4×C37—44no—
180C4⋊C4×C37—44no—
181C4⋊C4×C37—44no—
182C22⋊C4×C37—28no—
183C22⋊C4×C37—44no—
184C22⋊C4×C37—48no—
185C23×C37—22no—
186C23×C37—24no—
187C23×C37—24no—
188C23×C37—22no—
189C23×C37—22no—
190C23×C37—22no—
191C23×C37—24no—
192C23×C37—24no—
193C23×C37—24no—
194C23×C37—22no—
195C23×C37—22no—
196C23×C37—24no—
197C23×C37—24no—
198C23×C37—24no—
199C23×C37—22no—
200C23×C37—24no—
201C23×C37—24no—
202C23×C37—22no—
203C23×C37C22⋊Q814yes—
204C23×C37#12314yes—
205C23×C37#12414yes—
206C23×C37#12518yes—
207C23×C37#12618yes—
208C23×C37C22×D411yescharacteristic
209C23×C37C22×D411yescharacteristic
210C23×C37C22×Q811yescharacteristic
211C23×C37C2×#4111yescharacteristic
212C23×C37C2×#4111yescharacteristic
213C23×C37C2×#4112yes—
214C23×C37C2×#4112yes—
215C23×C37C2×#4112yes—
216C23×C37H(5,𝔽2)12yes—
217C23×C37H(5,𝔽2)11yescharacteristic
218C23×C372−1+411yescharacteristic
219C2×C4×C37—22no—
220C2×C4×C37—22no—
221C2×C4×C37—24no—
222C2×C4×C37—24no—
223C2×C4×C37—22no—
224C2×C4×C37—22no—
225C2×C4×C37—22no—
226C2×C4×C37—22no—
227C2×C4×C37—24no—
228C2×C4×C37—24no—
229C2×C4×C37—22no—
230C2×C4×C37—24no—
231C2×C4×C37—24no—
232C2×C4×C37—22no—
233C2×C4×C37—24no—
234C2×C4×C37—24no—
235C2×C4×C37—24no—
236C2×C4×C37—22no—
237C2×C4×C37—416no—
238C2×C4×C37—432no—
239C2×C4×C37—41no—
240C2×C4×C37—42no—
241C2×C4×C37—42no—
242C2×C4×C37—41no—
243C2×C4×C37—41no—
244C2×C4×C37—41no—
245C2×C4×C37—42no—
246C2×C4×C37—42no—
247C2×C4×C37—41no—
248C2×C4×C37—42no—
249C2×C4×C37—42no—
250C2×C4×C37—42no—
251C2×C4×C37—42no—
252C2×C4×C37—42no—
253C2×C4×C37—42no—
254C2×C4×C37—42no—
255C2×C4×C37—41no—
256C2×C4×C37—42no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—41no—
260C2×C4×C37—42no—
261C2×C4×C37—42no—
262C2×C4×C37—42no—
263C2×C4×C37—42no—
264C2×C4×C37—42no—
265C2×C4×C37—42no—
266C2×C4×C37—42no—
267C2×C4×C37—41no—
268C2×C4×C37—42no—
269C2×C4×C37—41no—
270C2×C4×C37—42no—
271C2×C4×C37—41no—
272C2×C4×C37—42no—
273C2×C4×C37—42no—
274C2×C4×C37—42no—
275C2×C4×C37—42no—
276C2×C4×C37—42no—
277C2×C4×C37—42no—
278C2×C4×C37—42no—
279C2×C4×C37—42no—
280C2×C4×C37#12114yes—
281#14826C3711yesmaximal, characteristic, direct product factor, Sylow
282C22×C37—24no—
283C22×C37—24no—
284C22×C37—24no—
285C22×C37—24no—
286C22×C37—24no—
287C22×C37—28no—
288C22×C37—28no—
289C22×C37—28no—
290C22×C37—24no—
291C22×C37—28no—
292C22×C37#40018yescomplemented
293C22×C37C2×#12111yescharacteristic
294C22×C37C2×C22⋊Q811yescharacteristic
295C22×C37C2×#12311yescharacteristic
296C22×C37#52512yes—
297C22×C37C2×#12411yescharacteristic
298C22×C37C2×#12512yes—
299C22×C37C2×#12612yes—
300C22×C37#52912yes—
301C22×C37#53211yescharacteristic
302C22×C37#53411yescharacteristic
303C22×C37#53711yescharacteristic
304C22×C37#53812yes—
305C22×C37#53912yes—
306C22×C37#54612yes—
307C22×C37#54611yescharacteristic
308C22×C37D4×Q811yescharacteristic
309C22×C37#55112yes—
310C22×C37#55112yes—
311C22×C37#55112yes—
312C22×C37#55211yescharacteristic
313C22×C37#55212yes—
314C22×C37#55412yes—
315C22×C37#55411yescharacteristic
316C4×C37—24no—
317C4×C37—42no—
318C4×C37—42no—
319C4×C37—42no—
320C4×C37—44no—
321C4×C37—44no—
322C4×C37—82no—
323C4×C37—82no—
324C4×C37—81no—
325C4×C37—81no—
326C2×#400C2×C3711yescharacteristic, complemented
327C2×#385C2×C3711yescharacteristic
328C2×#380C2×C3711yescharacteristic
329C22×#95C2×C3711yescharacteristic
330#1445C2×C3711yescharacteristic, complemented
331#1443C2×C3712yescomplemented
332#1442C2×C3711yescharacteristic, complemented
333#1442C2×C3712yescomplemented
334#1441C2×C3711yescharacteristic, complemented
335C22⋊#95C2×C3712yes—
336C22⋊#95C2×C3712yes—
337C2×C37—28no—
338C2×C37C2×#40011yescharacteristic
339C2×C37#241211yescharacteristic
340C2×C37#241711yescharacteristic
341C2×C37#247312yes—
342C2×C37#248012yes—
343C2×C37#249312yes—
344C2×C37#249811yescharacteristic
345C2×C37#250512yes—
346C2×C37#256411yescharacteristic
347C2×C37#263911yescharacteristic
348C2×C37#285011yescharacteristic
349C24×C4C22×C3712yes—
350C24×C4C22×C3711yescharacteristic
351C22×C4⋊C4C22×C3711yescharacteristic
352C22×C4⋊C4C22×C3711yescharacteristic
353C22×C4⋊C4C22×C3711yescharacteristic
354C22×C4⋊C4C22×C3711yescharacteristic
355C22×C22⋊C4C22×C3712yes—
356C22×C22⋊C4C22×C3711yescharacteristic
357C22×C22⋊C4C22×C3711yescharacteristic
358#400—24no—
359#385—24no—
360#380—24no—
361C2×#95—24no—
362C2×#95C22×C3712yes—
363C2×#95C22×C3712yes—
364C2×#95C22×C3712yes—
365C2×#95C22×C3712yes—
366C2×#95C22×C3711yescharacteristic
367C2×#95C22×C3712yes—
368C2×#95C22×C3712yes—
369C2×#95C22×C3711yescharacteristic
370C2×#95C22×C3711yescharacteristic
371C2×#95C22×C3712yes—
372C2×#95C22×C3712yes—
373C2×#95C22×C3712yes—
374C2×#95C22×C3712yes—
375C2×#95C22×C3711yescharacteristic
376C37#1482611yescharacteristic, direct product factor, Sylow
377C25C23×C3711yescharacteristic
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4D4×C3714yes—
390C23×C4C23×C3711yescharacteristic
391C23×C4C23×C3712yes—
392C23×C4C23×C3712yes—
393C23×C4C23×C3711yescharacteristic
394C23×C4C23×C3711yescharacteristic
395C23×C4C23×C3712yes—
396C23×C4C23×C3711yescharacteristic
397C23×C4C23×C3711yescharacteristic
398C23×C4C23×C3712yes—
399C23×C4C23×C3711yescharacteristic
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—42no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4Q8×C3714yes—
418#95—24no—
419#95—22no—
420#95—24no—
421#95—22no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95D4×C3714yes—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24C2×D4×C3712yes—
439C24C2×Q8×C3712yes—
440C24#41×C3712yes—
441C24#41×C3714yes—
442C24#41×C3714yes—
443C24C24×C3711yescharacteristic
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—216no—
447C22×C4—28no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—28no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—44no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4C2×D4×C3714yes—
509C22×C4C2×D4×C3712yes—
510C22×C4C2×D4×C3712yes—
511C22×C4C2×D4×C3712yes—
512C22×C4C2×Q8×C3712yes—
513C22×C4C2×Q8×C3712yes—
514C22×C4#41×C3714yes—
515C22×C4#41×C3712yes—
516C4⋊C4—44no—
517C4⋊C4—44no—
518C4⋊C4—44no—
519C4⋊C4—44no—
520C22⋊C4—28no—
521C22⋊C4—44no—
522C22⋊C4—48no—
523C23—22no—
524C23—24no—
525C23—24no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—22no—
533C23—22no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—22no—
538C23—24no—
539C23—22no—
540C23—24no—
541C23C22⋊Q8×C3714yes—
542C23#123×C3714yes—
543C23#124×C3714yes—
544C23#125×C3718yes—
545C23#126×C3718yes—
546C23C22×D4×C3711yescharacteristic
547C23C22×D4×C3711yescharacteristic
548C23C22×Q8×C3711yescharacteristic
549C23C2×#41×C3711yescharacteristic
550C23C2×#41×C3711yescharacteristic
551C23C2×#41×C3712yes—
552C23C2×#41×C3712yes—
553C23C2×#41×C3712yes—
554C23H(5,𝔽2)×C3712yes—
555C23H(5,𝔽2)×C3711yescharacteristic
556C232−1+4×C3711yescharacteristic
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—416no—
576C2×C4—432no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4#121×C3714yes—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—28no—
623C22—28no—
624C22—28no—
625C22—24no—
626C22—28no—
627C22—24no—
628C22—24no—
629C22C37×#40018yescomplemented
630C22C2×#121×C3711yescharacteristic
631C22C2×C22⋊Q8×C3711yescharacteristic
632C22C2×#123×C3711yescharacteristic
633C22C37×#52512yes—
634C22C2×#124×C3711yescharacteristic
635C22C2×#125×C3712yes—
636C22C2×#126×C3712yes—
637C22C37×#52912yes—
638C22C37×#53211yescharacteristic
639C22C37×#53411yescharacteristic
640C22C37×#53711yescharacteristic
641C22C37×#53812yes—
642C22C37×#53912yes—
643C22C37×#54612yes—
644C22C37×#54611yescharacteristic
645C22D4×Q8×C3711yescharacteristic
646C22C37×#55112yes—
647C22C37×#55112yes—
648C22C37×#55112yes—
649C22C37×#55211yescharacteristic
650C22C37×#55212yes—
651C22C37×#55411yescharacteristic
652C22C37×#55412yes—
653C4—24no—
654C4—42no—
655C4—42no—
656C4—44no—
657C4—44no—
658C4—42no—
659C4—82no—
660C4—81no—
661C4—81no—
662C4—82no—
663C2—28no—
664C2C2×C37×#40011yescharacteristic
665C2C37×#241211yescharacteristic
666C2C37×#241711yescharacteristic
667C2C37×#247312yes—
668C2C37×#248012yes—
669C2C37×#249312yes—
670C2C37×#249811yescharacteristic
671C2C37×#250512yes—
672C2C37×#256411yescharacteristic
673C2C37×#263911yescharacteristic
674C2C37×#285011yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutator, Frattini, cosocleC24C24×C37
prime radicalC25×C37C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#400C2semidirect
5. C37×#1445C2semidirect
6. C37×#1443C2semidirect
7. C37×#1442C2semidirect
8. C37×#1442C2semidirect
9. C37×#1441C2semidirect
281. #14826C37direct (N × H)
292. C22×C37#400semidirect
326. C2×#400C2×C37semidirect
330. #1445C2×C37semidirect
331. #1443C2×C37semidirect
332. #1442C2×C37semidirect
333. #1442C2×C37semidirect
334. #1441C2×C37semidirect
376. C37#14826direct (N × H)
629. C22C37×#400semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4002
C2×C37×#3852
C2×C37×#3802
C22×#95×C372
C37×#14452
C37×#14432
C37×#14422
C37×#14412
C37×C22⋊#952
#1482637