Finite Group Databasebeta

← C37×#28899 #22650152

Subgroups — C37×#28899 #22650152

Order 9472.

696 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2514C211yesmaximal, characteristic, complemented
2C37×#2448C211yesmaximal, characteristic
3C37×#2085C211yesmaximal, characteristic, complemented
4C37×#2068C211yesmaximal, characteristic, complemented
5C37×#2055C211yesmaximal, characteristic
6C37×#2015C211yesmaximal, characteristic
7C37×#1973C211yesmaximal, characteristic
8C37×#1971C211yesmaximal, characteristic, complemented
9C37×#1958C211yesmaximal, characteristic
10C37×#1936C211yesmaximal, characteristic
11C37×#1933C211yesmaximal, characteristic, complemented
12C37×#1926C211yesmaximal, characteristic
13C37×#1878C211yesmaximal, characteristic, complemented
14C37×#1771C211yesmaximal, characteristic, complemented
15C37×#1763C211yesmaximal, characteristic, complemented
16C22×Q16×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C2×#124×C37C2211yescharacteristic
19C2×C4×Q8×C37C2211yescharacteristic
20C2×#107×C37C2211yescharacteristic
21C2×#106×C37C2211yescharacteristic
22C2×C4⋊C8×C37C2211yescharacteristic
23C2×#103×C37C2211yescharacteristic
24C2×#103×C37C2211yescharacteristic
25C2×#103×C37C2211yescharacteristic
26C2×#103×C37C2211yescharacteristic
27C2×#103×C37C2211yescharacteristic
28C2×#102×C37C2211yescharacteristic
29C2×#102×C37C2211yescharacteristic
30C2×#102×C37C2211yescharacteristic
31C2×#97×C37C2211yescharacteristic
32C2×#97×C37C2211yescharacteristic
33C2×C4×C8×C37C2211yescharacteristic
34C37×#401—21no—
35C37×#400—21no—
36C37×#399—21no—
37C37×#397—21no—
38C37×#391C2211yescharacteristic
39C37×#391C2211yescharacteristic
40C37×#391C2211yescharacteristic
41C37×#391C2211yescharacteristic
42C37×#390C2211yescharacteristic
43C37×#390C2211yescharacteristic
44C37×#389C2211yescharacteristic
45C37×#389C2211yescharacteristic
46C37×#388—21no—
47C37×#388—21no—
48C37×#387—21no—
49C37×#383—21no—
50C37×#382C2211yescharacteristic
51C4×C4⋊C4×C37C2211yescharacteristic
52C4×C4⋊C4×C37C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C22×Q8×C37C2311yescharacteristic
60C22×Q8×C37C2311yescharacteristic
61C22×D4×C37C2311yescharacteristic
62C2×Q16×C37—22no—
63C2×Q16×C37—22no—
64C2×Q16×C37—41no—
65C2×SD16×C37—22no—
66C2×SD16×C37—41no—
67C2×SD16×C37—41no—
68C22×C8×C37C2311yescharacteristic
69C22×C8×C37C2311yescharacteristic
70C22×C8×C37C2311yescharacteristic
71C22×C8×C37C2311yescharacteristic
72#124×C37—22no—
73#124×C37—41no—
74C4×Q8×C37—22no—
75C4×Q8×C37—41no—
76C2×C4⋊C4×C37—21no—
77C2×C4⋊C4×C37—21no—
78C2×C4⋊C4×C37—21no—
79C2×C4⋊C4×C37D411yescharacteristic
80C2×C4⋊C4×C37D411yescharacteristic
81C2×C4⋊C4×C37C2311yescharacteristic
82C2×C4⋊C4×C37C2311yescharacteristic
83C2×C4⋊C4×C37C2311yescharacteristic
84C2×C4⋊C4×C37C2311yescharacteristic
85C2×C4⋊C4×C37C2311yescharacteristic
86C2×C22⋊C4×C37—21no—
87C2×C22⋊C4×C37—21no—
88C2×C22⋊C4×C37—21no—
89C2×C22⋊C4×C37—21no—
90C2×C22⋊C4×C37—21no—
91C2×C22⋊C4×C37—21no—
92C2×C42×C37—21no—
93C2×C42×C37—21no—
94C2×C42×C37C2311yescharacteristic
95C2×C42×C37C2311yescharacteristic
96C2×C42×C37C2311yescharacteristic
97#107×C37—41no—
98#106×C37—41no—
99C4⋊C8×C37—22no—
100#103×C37—22no—
101#103×C37—22no—
102#103×C37—22no—
103#103×C37—41no—
104#103×C37—41no—
105#102×C37—22no—
106#102×C37—22no—
107#102×C37—41no—
108#97×C37—22no—
109#97×C37—41no—
110C4×C8×C37—41no—
111#95×C37—21no—
112#95×C37—21no—
113#95×C37—21no—
114#95×C37—21no—
115#95×C37—21no—
116#95×C37—21no—
117#95×C37—21no—
118#95×C37—21no—
119#95×C37—21no—
120#95×C37—21no—
121#95×C37—21no—
122#95×C37—21no—
123#95×C37—21no—
124#95×C37D411yescharacteristic
125#95×C37D411yescharacteristic
126C24×C37—21no—
127C2×Q8×C37—21no—
128C2×Q8×C37—21no—
129C2×Q8×C37—21no—
130C2×Q8×C37—21no—
131C2×Q8×C37—21no—
132C2×Q8×C37—21no—
133C2×Q8×C37—21no—
134C2×Q8×C37—21no—
135C2×Q8×C37—21no—
136C2×Q8×C37—21no—
137C2×Q8×C37—21no—
138C2×Q8×C37#4112yes—
139C2×D4×C37—21no—
140C2×D4×C37—21no—
141C2×D4×C37—21no—
142C2×D4×C37—21no—
143C2×D4×C37—21no—
144C2×D4×C37—21no—
145C22×C4×C37—21no—
146C22×C4×C37—21no—
147C22×C4×C37—21no—
148C22×C4×C37—21no—
149C22×C4×C37—21no—
150C22×C4×C37—21no—
151C22×C4×C37—21no—
152C22×C4×C37C2×D411yescharacteristic
153C22×C4×C37C2×D411yescharacteristic
154C22×C4×C37C2×D411yescharacteristic
155C22×C4×C37C2×D411yescharacteristic
156C22×C4×C37C2×D411yescharacteristic
157C22×C4×C37C2×D411yescharacteristic
158C22×C4×C37C2411yescharacteristic
159Q16×C37—44no—
160SD16×C37—44no—
161C2×C8×C37—21no—
162C2×C8×C37—21no—
163C2×C8×C37—21no—
164C2×C8×C37—21no—
165C2×C8×C37—21no—
166C2×C8×C37—21no—
167C2×C8×C37—21no—
168C2×C8×C37—21no—
169C2×C8×C37—21no—
170C2×C8×C37#4112yes—
171C2×C8×C37#4112yes—
172C2×C8×C37#4112yes—
173C4⋊C4×C37—21no—
174C4⋊C4×C37—21no—
175C4⋊C4×C37—21no—
176C4⋊C4×C37—21no—
177C4⋊C4×C37—21no—
178C4⋊C4×C37—21no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—21no—
181C4⋊C4×C37—21no—
182C4⋊C4×C37—21no—
183C4⋊C4×C37—41no—
184C4⋊C4×C37—41no—
185C4⋊C4×C37—42no—
186C4⋊C4×C37—42no—
187C4⋊C4×C37—81no—
188C22⋊C4×C37—42no—
189C22⋊C4×C37—42no—
190C22⋊C4×C37—42no—
191C22⋊C4×C37—42no—
192C22⋊C4×C37—81no—
193C22⋊C4×C37—81no—
194C42×C37—21no—
195C42×C37—21no—
196C42×C37—21no—
197C42×C37—21no—
198C42×C37—21no—
199C42×C37—21no—
200C42×C37—42no—
201C42×C37—42no—
202C23×C37—41no—
203C23×C37—41no—
204C23×C37—41no—
205C23×C37—41no—
206C23×C37—41no—
207C23×C37—41no—
208C23×C37—41no—
209C23×C37C22×D411yescharacteristic
210Q8×C37—22no—
211Q8×C37—22no—
212Q8×C37—41no—
213Q8×C37—41no—
214Q8×C37—41no—
215Q8×C37—41no—
216Q8×C37—41no—
217Q8×C37—41no—
218D4×C37—41no—
219D4×C37—41no—
220D4×C37—41no—
221D4×C37—41no—
222C2×C4×C37—21no—
223C2×C4×C37—21no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—21no—
227C2×C4×C37—21no—
228C2×C4×C37—22no—
229C2×C4×C37—21no—
230C2×C4×C37—21no—
231C2×C4×C37—21no—
232C2×C4×C37—21no—
233C2×C4×C37—21no—
234C2×C4×C37—21no—
235C2×C4×C37—21no—
236C2×C4×C37—21no—
237C2×C4×C37—21no—
238C2×C4×C37—21no—
239C2×C4×C37—21no—
240C2×C4×C37—21no—
241C2×C4×C37—41no—
242C2×C4×C37—41no—
243C2×C4×C37—41no—
244C2×C4×C37—41no—
245C2×C4×C37—41no—
246C2×C4×C37—41no—
247C2×C4×C37—41no—
248C2×C4×C37—41no—
249C2×C4×C37—41no—
250C2×C4×C37—41no—
251C2×C4×C37—41no—
252C2×C4×C37—41no—
253C2×C4×C37—41no—
254C2×C4×C37—41no—
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×C37C2×#4111yescharacteristic
262C2×C4×C37C2×#4111yescharacteristic
263C2×C4×C37C2×#4111yescharacteristic
264C2×C4×C37C2×#4111yescharacteristic
265C2×C4×C37H(5,𝔽2)11yescharacteristic
266C2×C4×C37H(5,𝔽2)11yescharacteristic
267C8×C37—22no—
268C8×C37—22no—
269C8×C37—22no—
270C8×C37—41no—
271#28899C3711yesmaximal, characteristic, direct product factor, Sylow
272C22×C37—81no—
273C22×C37—81no—
274C22×C37—81no—
275C22×C37—81no—
276C22×C37—81no—
277C22×C37—81no—
278C22×C37—81no—
279C22×C37#53211yescharacteristic
280C22×C37#54611yescharacteristic
281C22×C37#55011yescharacteristic
282C22×C37#57511yescharacteristic
283C22×C37#57511yescharacteristic
284C22×C37#57711yescharacteristic
285C22×C37#57811yescharacteristic
286C4×C37—41no—
287C4×C37—41no—
288C4×C37—41no—
289C4×C37—41no—
290C4×C37—41no—
291C4×C37—41no—
292C4×C37—42no—
293C4×C37—81no—
294C4×C37—81no—
295C4×C37—81no—
296C4×C37—81no—
297C4×C37—81no—
298C4×C37—81no—
299C4×C37#52911yescharacteristic
300C4×C37#53811yescharacteristic
301C4×C37#55111yescharacteristic
302C4×C37#55311yescharacteristic
303#2514C2×C3711yescharacteristic, complemented
304#2448C2×C3711yescharacteristic
305#2085C2×C3711yescharacteristic, complemented
306#2068C2×C3711yescharacteristic, complemented
307#2055C2×C3711yescharacteristic
308#2015C2×C3711yescharacteristic
309#1973C2×C3711yescharacteristic
310#1971C2×C3711yescharacteristic, complemented
311#1958C2×C3711yescharacteristic
312#1936C2×C3711yescharacteristic
313#1933C2×C3711yescharacteristic, complemented
314#1926C2×C3711yescharacteristic
315#1878C2×C3711yescharacteristic, complemented
316#1771C2×C3711yescharacteristic, complemented
317#1763C2×C3711yescharacteristic, complemented
318C2×C37—161no—
319C2×C37#255411yescharacteristic
320C2×C37#317811yescharacteristic
321C2×C37#318311yescharacteristic
322C2×C37#331311yescharacteristic
323C2×C37#331711yescharacteristic
324C2×C37#340111yescharacteristic
325C2×C37#340211yescharacteristic
326C22×Q16C22×C3711yescharacteristic
327C22×SD16C22×C3711yescharacteristic
328C2×#124C22×C3711yescharacteristic
329C2×C4×Q8C22×C3711yescharacteristic
330C2×#107C22×C3711yescharacteristic
331C2×#106C22×C3711yescharacteristic
332C2×C4⋊C8C22×C3711yescharacteristic
333C2×#103C22×C3711yescharacteristic
334C2×#103C22×C3711yescharacteristic
335C2×#103C22×C3711yescharacteristic
336C2×#103C22×C3711yescharacteristic
337C2×#103C22×C3711yescharacteristic
338C2×#102C22×C3711yescharacteristic
339C2×#102C22×C3711yescharacteristic
340C2×#102C22×C3711yescharacteristic
341C2×#97C22×C3711yescharacteristic
342C2×#97C22×C3711yescharacteristic
343C2×C4×C8C22×C3711yescharacteristic
344#401—21no—
345#400—21no—
346#399—21no—
347#397—21no—
348#391C22×C3711yescharacteristic
349#391C22×C3711yescharacteristic
350#391C22×C3711yescharacteristic
351#391C22×C3711yescharacteristic
352#390C22×C3711yescharacteristic
353#390C22×C3711yescharacteristic
354#389C22×C3711yescharacteristic
355#389C22×C3711yescharacteristic
356#388—21no—
357#388—21no—
358#387—21no—
359#383—21no—
360#382C22×C3711yescharacteristic
361C4×C4⋊C4C22×C3711yescharacteristic
362C4×C4⋊C4C22×C3711yescharacteristic
363#340C22×C3711yescharacteristic
364#340C22×C3711yescharacteristic
365#340C22×C3711yescharacteristic
366#340C22×C3711yescharacteristic
367#336C22×C3711yescharacteristic
368#336C22×C3711yescharacteristic
369C37#2889911yescharacteristic, direct product factor, Sylow
370C22×Q8C23×C3711yescharacteristic
371C22×Q8C23×C3711yescharacteristic
372C22×D4C23×C3711yescharacteristic
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16—41no—
376C2×SD16—22no—
377C2×SD16—41no—
378C2×SD16—41no—
379C22×C8C23×C3711yescharacteristic
380C22×C8C23×C3711yescharacteristic
381C22×C8C23×C3711yescharacteristic
382C22×C8C23×C3711yescharacteristic
383#124—22no—
384#124—41no—
385C4×Q8—22no—
386C4×Q8—41no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C3711yescharacteristic
391C2×C4⋊C4D4×C3711yescharacteristic
392C2×C4⋊C4C23×C3711yescharacteristic
393C2×C4⋊C4C23×C3711yescharacteristic
394C2×C4⋊C4C23×C3711yescharacteristic
395C2×C4⋊C4C23×C3711yescharacteristic
396C2×C4⋊C4C23×C3711yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C23×C3711yescharacteristic
406C2×C42C23×C3711yescharacteristic
407C2×C42C23×C3711yescharacteristic
408#107—41no—
409#106—41no—
410C4⋊C8—22no—
411#103—22no—
412#103—22no—
413#103—22no—
414#103—41no—
415#103—41no—
416#102—22no—
417#102—22no—
418#102—41no—
419#97—22no—
420#97—41no—
421C4×C8—41no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95D4×C3711yescharacteristic
436#95D4×C3711yescharacteristic
437C24—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8#41×C3712yes—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4C2×D4×C3711yescharacteristic
464C22×C4C2×D4×C3711yescharacteristic
465C22×C4C2×D4×C3711yescharacteristic
466C22×C4C2×D4×C3711yescharacteristic
467C22×C4C2×D4×C3711yescharacteristic
468C22×C4C2×D4×C3711yescharacteristic
469C22×C4C24×C3711yescharacteristic
470Q16—44no—
471SD16—44no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8#41×C3712yes—
482C2×C8#41×C3712yes—
483C2×C8#41×C3712yes—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—81no—
504C22⋊C4—81no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23C22×D4×C3711yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4C2×#41×C3711yescharacteristic
573C2×C4C2×#41×C3711yescharacteristic
574C2×C4C2×#41×C3711yescharacteristic
575C2×C4C2×#41×C3711yescharacteristic
576C2×C4H(5,𝔽2)×C3711yescharacteristic
577C2×C4H(5,𝔽2)×C3711yescharacteristic
578C8—22no—
579C8—22no—
580C8—22no—
581C8—41no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22C37×#53211yescharacteristic
590C22C37×#54611yescharacteristic
591C22C37×#55011yescharacteristic
592C22C37×#57511yescharacteristic
593C22C37×#57511yescharacteristic
594C22C37×#57711yescharacteristic
595C22C37×#57811yescharacteristic
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4C37×#52911yescharacteristic
610C4C37×#53811yescharacteristic
611C4C37×#55111yescharacteristic
612C4C37×#55311yescharacteristic
613C2—161no—
614C2C37×#255411yescharacteristic
615C2C37×#317811yescharacteristic
616C2C37×#318311yescharacteristic
617C2C37×#331311yescharacteristic
618C2C37×#331711yescharacteristic
619C2C37×#340111yescharacteristic
620C2C37×#340211yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×D4×C37C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C4⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#2514C2semidirect
3. C37×#2085C2semidirect
4. C37×#2068C2semidirect
8. C37×#1971C2semidirect
11. C37×#1933C2semidirect
13. C37×#1878C2semidirect
14. C37×#1771C2semidirect
15. C37×#1763C2semidirect
271. #28899C37direct (N × H)
303. #2514C2×C37semidirect
305. #2085C2×C37semidirect
306. #2068C2×C37semidirect
310. #1971C2×C37semidirect
313. #1933C2×C37semidirect
315. #1878C2×C37semidirect
316. #1771C2×C37semidirect
317. #1763C2×C37semidirect
369. C37#28899direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#25142
C37×#24482
C37×#20852
C37×#20682
C37×#20552
C37×#20152
C37×#19732
C37×#19712
C37×#19582
C37×#19362
C37×#19332
C37×#19262
C37×#18782
C37×#17712
C37×#17632
#2889937