Finite Group Databasebeta

← C37×#19382 #22640635

Subgroups — C37×#19382 #22640635

Order 9472.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3251C211yesmaximal, characteristic
2C37×#3238C211yesmaximal, characteristic, complemented
3C37×#3141C211yesmaximal, characteristic, complemented
4C37×#2969C211yesmaximal, characteristic, complemented
5C37×#1704C211yesmaximal, characteristic, complemented
6C37×#1703C211yesmaximal, characteristic, complemented
7C37×#1698C211yesmaximal, characteristic, complemented
8C37×#1697C211yesmaximal, characteristic, complemented
9C37×#1684C211yesmaximal, characteristic, complemented
10C37×#1683C211yesmaximal, characteristic, complemented
11C37×#1678C211yesmaximal, characteristic, complemented
12C37×#1677C211yesmaximal, characteristic, complemented
13C37×#1569C211yesmaximal, characteristic, complemented
14C37×#1553C211yesmaximal, characteristic, complemented
15C37×#1548C211yesmaximal, characteristic, complemented
16C37×#532C2211yescharacteristic
17C2×C4⋊Q8×C37C2211yescharacteristic
18C37×#529C2211yescharacteristic
19C37×#501—21no—
20C37×#489—21no—
21C37×#489—21no—
22C37×#489—21no—
23C37×#487C2211yescharacteristic
24C37×#487C2211yescharacteristic
25C37×#486C2211yescharacteristic
26C37×#486C2211yescharacteristic
27C37×#483—21no—
28C37×#480—21no—
29C37×#478—21no—
30C37×#477C2211yescharacteristic
31C37×#477C2211yescharacteristic
32C37×#476C2211yescharacteristic
33C37×#476C2211yescharacteristic
34C37×#475C2211yescharacteristic
35C37×#474C2211yescharacteristic
36C37×#469—21no—
37C37×#468—21no—
38C37×#463—21no—
39C37×#460C2211yescharacteristic
40C37×#459C2211yescharacteristic
41C37×#446C2211yescharacteristic
42C8×Q8×C37C2211yescharacteristic
43C37×#436—21no—
44C37×#436C2211yescharacteristic
45C37×#435—21no—
46C8×D4×C37C2211yescharacteristic
47C37×#433—21no—
48C37×#432C2211yescharacteristic
49C37×#431C2211yescharacteristic
50C37×#423C2211yescharacteristic
51C37×#417—21no—
52C37×#417—21no—
53C37×#405—21no—
54C4×M16×C37C2211yescharacteristic
55C37×#335C2211yescharacteristic
56C37×#335C2211yescharacteristic
57C37×#334C2211yescharacteristic
58C37×#334C2211yescharacteristic
59C37×#333C2211yescharacteristic
60C37×#333C2211yescharacteristic
61C37×#333C2211yescharacteristic
62C37×#333C2211yescharacteristic
63C37×#332C2211yescharacteristic
64C37×#332C2211yescharacteristic
65C37×#331C2211yescharacteristic
66C37×#331C2211yescharacteristic
67C2×#41×C37—21no—
68C22×Q8×C37—21no—
69C2×SD16×C37—21no—
70C2×D8×C37—21no—
71C2×M16×C37—21no—
72C2×M16×C37—21no—
73C2×M16×C37D411yescharacteristic
74C2×M16×C37D411yescharacteristic
75C22×C8×C37—21no—
76C4⋊Q8×C37—21no—
77C4⋊Q8×C37—21no—
78C4⋊Q8×C37—21no—
79C4⋊Q8×C37C2311yescharacteristic
80C4⋊Q8×C37C2311yescharacteristic
81C4⋊Q8×C37C2311yescharacteristic
82#127×C37C2311yescharacteristic
83#126×C37—21no—
84#125×C37D411yescharacteristic
85#124×C37—21no—
86#124×C37D411yescharacteristic
87#123×C37—21no—
88C22⋊Q8×C37D411yescharacteristic
89#121×C37—21no—
90#121×C37—21no—
91#121×C37D411yescharacteristic
92C4×Q8×C37C2311yescharacteristic
93C4×D4×C37—21no—
94C4×D4×C37—21no—
95C4×D4×C37—21no—
96C4×D4×C37C2311yescharacteristic
97#117×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C42×C37C2311yescharacteristic
101#107×C37—21no—
102#107×C37—21no—
103#107×C37—21no—
104#106×C37—21no—
105#106×C37—21no—
106#106×C37—21no—
107C4⋊C8×C37—21no—
108C4⋊C8×C37—21no—
109C4⋊C8×C37—21no—
110C4⋊C8×C37C2311yescharacteristic
111C4⋊C8×C37C2311yescharacteristic
112C4⋊C8×C37C2311yescharacteristic
113C4⋊C8×C37C2311yescharacteristic
114C4⋊C8×C37C2311yescharacteristic
115C4⋊C8×C37C2311yescharacteristic
116#103×C37—21no—
117#103×C37—21no—
118#103×C37—21no—
119#103×C37—21no—
120#103×C37—21no—
121#103×C37—21no—
122#103×C37—21no—
123#102×C37—21no—
124#102×C37—21no—
125#102×C37—21no—
126#102×C37—21no—
127#102×C37—21no—
128#102×C37—21no—
129#102×C37—21no—
130#102×C37—21no—
131#102×C37—21no—
132C22⋊C8×C37—21no—
133C22⋊C8×C37—21no—
134C22⋊C8×C37—21no—
135C22⋊C8×C37—21no—
136#97×C37—21no—
137#97×C37—21no—
138#97×C37D411yescharacteristic
139#97×C37D411yescharacteristic
140C4×C8×C37—21no—
141C4×C8×C37—21no—
142C4×C8×C37C2311yescharacteristic
143C4×C8×C37C2311yescharacteristic
144#41×C37—42no—
145#41×C37—42no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—41no—
150C2×Q8×C37—82no—
151C2×Q8×C37C2×D411yescharacteristic
152C2×D4×C37—21no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—41no—
157C2×D4×C37C2×D411yescharacteristic
158C22×C4×C37—21no—
159C22×C4×C37—41no—
160C22×C4×C37—41no—
161C22×C4×C37C2×D411yescharacteristic
162C22×C4×C37C2×D411yescharacteristic
163C22×C4×C37#4111yescharacteristic
164SD16×C37—81no—
165D8×C37—81no—
166M16×C37—41no—
167M16×C37—41no—
168M16×C37—42no—
169M16×C37—81no—
170C2×C8×C37—21no—
171C2×C8×C37—21no—
172C2×C8×C37—21no—
173C2×C8×C37—21no—
174C2×C8×C37—21no—
175C2×C8×C37—21no—
176C2×C8×C37—42no—
177C2×C8×C37C2×D411yescharacteristic
178C2×C8×C37C2×D411yescharacteristic
179C2×C8×C37C2×D411yescharacteristic
180C2×C8×C37C2×D411yescharacteristic
181C4⋊C4×C37—21no—
182C4⋊C4×C37—21no—
183C4⋊C4×C37—21no—
184C4⋊C4×C37—21no—
185C4⋊C4×C37—21no—
186C4⋊C4×C37—21no—
187C4⋊C4×C37—21no—
188C4⋊C4×C37—21no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—21no—
191C4⋊C4×C37—41no—
192C4⋊C4×C37—41no—
193C4⋊C4×C37C2×D411yescharacteristic
194C4⋊C4×C37C2×D411yescharacteristic
195C22⋊C4×C37—21no—
196C22⋊C4×C37—21no—
197C22⋊C4×C37—21no—
198C22⋊C4×C37—21no—
199C22⋊C4×C37—21no—
200C22⋊C4×C37—41no—
201C22⋊C4×C37—41no—
202C42×C37—21no—
203C42×C37C2×D411yescharacteristic
204C42×C37C2×D411yescharacteristic
205C42×C37#4111yescharacteristic
206C42×C37C2411yescharacteristic
207C23×C37—21no—
208C23×C37—41no—
209C23×C37#12111yescharacteristic
210Q8×C37—21no—
211Q8×C37—21no—
212Q8×C37—41no—
213Q8×C37—41no—
214Q8×C37—81no—
215Q8×C37—81no—
216Q8×C37—82no—
217D4×C37—21no—
218D4×C37—21no—
219D4×C37—41no—
220D4×C37—41no—
221D4×C37—41no—
222D4×C37—41no—
223D4×C37—81no—
224D4×C37—81no—
225D4×C37—82no—
226C2×C4×C37—21no—
227C2×C4×C37—21no—
228C2×C4×C37—21no—
229C2×C4×C37—21no—
230C2×C4×C37—21no—
231C2×C4×C37—21no—
232C2×C4×C37—21no—
233C2×C4×C37—41no—
234C2×C4×C37—41no—
235C2×C4×C37—41no—
236C2×C4×C37—41no—
237C2×C4×C37—41no—
238C2×C4×C37—41no—
239C2×C4×C37—82no—
240C2×C4×C37—82no—
241C2×C4×C37#12111yescharacteristic
242C2×C4×C37#12111yescharacteristic
243C2×C4×C37#12111yescharacteristic
244C2×C4×C37C22×D411yescharacteristic
245C2×C4×C37C22×D411yescharacteristic
246C2×C4×C37C2×#4111yescharacteristic
247C8×C37—21no—
248C8×C37—21no—
249C8×C37—21no—
250C8×C37—21no—
251C8×C37—41no—
252C8×C37—41no—
253C8×C37—41no—
254C8×C37—41no—
255C8×C37—41no—
256C8×C37—41no—
257#19382C3711yesmaximal, characteristic, direct product factor, Sylow
258C22×C37—21no—
259C22×C37—21no—
260C22×C37—21no—
261C22×C37—41no—
262C22×C37—41no—
263C22×C37—41no—
264C22×C37—81no—
265C22×C37—81no—
266C22×C37—81no—
267C22×C37C2×#12111yescharacteristic
268C4×C37—21no—
269C4×C37—21no—
270C4×C37—21no—
271C4×C37—21no—
272C4×C37—41no—
273C4×C37—41no—
274C4×C37—41no—
275C4×C37—81no—
276C4×C37—81no—
277C4×C37—81no—
278C4×C37#57511yescharacteristic
279C4×C37#57511yescharacteristic
280C4×C37#57711yescharacteristic
281C4×C37#57811yescharacteristic
282#3251C2×C3711yescharacteristic
283#3238C2×C3711yescharacteristic, complemented
284#3141C2×C3711yescharacteristic, complemented
285#2969C2×C3711yescharacteristic, complemented
286#1704C2×C3711yescharacteristic, complemented
287#1703C2×C3711yescharacteristic, complemented
288#1698C2×C3711yescharacteristic, complemented
289#1697C2×C3711yescharacteristic, complemented
290#1684C2×C3711yescharacteristic, complemented
291#1683C2×C3711yescharacteristic, complemented
292#1678C2×C3711yescharacteristic, complemented
293#1677C2×C3711yescharacteristic, complemented
294#1569C2×C3711yescharacteristic, complemented
295#1553C2×C3711yescharacteristic, complemented
296#1548C2×C3711yescharacteristic, complemented
297C2×C37—41no—
298C2×C37—81no—
299C2×C37—161no—
300C2×C37#304011yescharacteristic
301C2×C37#306311yescharacteristic
302C2×C37#306811yescharacteristic
303#532C22×C3711yescharacteristic
304C2×C4⋊Q8C22×C3711yescharacteristic
305#529C22×C3711yescharacteristic
306#501—21no—
307#489—21no—
308#489—21no—
309#489—21no—
310#487C22×C3711yescharacteristic
311#487C22×C3711yescharacteristic
312#486C22×C3711yescharacteristic
313#486C22×C3711yescharacteristic
314#483—21no—
315#480—21no—
316#478—21no—
317#477C22×C3711yescharacteristic
318#477C22×C3711yescharacteristic
319#476C22×C3711yescharacteristic
320#476C22×C3711yescharacteristic
321#475C22×C3711yescharacteristic
322#474C22×C3711yescharacteristic
323#469—21no—
324#468—21no—
325#463—21no—
326#460C22×C3711yescharacteristic
327#459C22×C3711yescharacteristic
328#446C22×C3711yescharacteristic
329C8×Q8C22×C3711yescharacteristic
330#436—21no—
331#436C22×C3711yescharacteristic
332#435—21no—
333C8×D4C22×C3711yescharacteristic
334#433—21no—
335#432C22×C3711yescharacteristic
336#431C22×C3711yescharacteristic
337#423C22×C3711yescharacteristic
338#417—21no—
339#417—21no—
340#405—21no—
341C4×M16C22×C3711yescharacteristic
342#335C22×C3711yescharacteristic
343#335C22×C3711yescharacteristic
344#334C22×C3711yescharacteristic
345#334C22×C3711yescharacteristic
346#333C22×C3711yescharacteristic
347#333C22×C3711yescharacteristic
348#333C22×C3711yescharacteristic
349#333C22×C3711yescharacteristic
350#332C22×C3711yescharacteristic
351#332C22×C3711yescharacteristic
352#331C22×C3711yescharacteristic
353#331C22×C3711yescharacteristic
354C37#1938211yescharacteristic, direct product factor, Sylow
355C2×#41—21no—
356C22×Q8—21no—
357C2×SD16—21no—
358C2×D8—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16D4×C3711yescharacteristic
362C2×M16D4×C3711yescharacteristic
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8C23×C3711yescharacteristic
368C4⋊Q8C23×C3711yescharacteristic
369C4⋊Q8C23×C3711yescharacteristic
370#127C23×C3711yescharacteristic
371#126—21no—
372#125D4×C3711yescharacteristic
373#124—21no—
374#124D4×C3711yescharacteristic
375#123—21no—
376C22⋊Q8D4×C3711yescharacteristic
377#121—21no—
378#121—21no—
379#121D4×C3711yescharacteristic
380C4×Q8C23×C3711yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4C23×C3711yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C42C23×C3711yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C3711yescharacteristic
399C4⋊C8C23×C3711yescharacteristic
400C4⋊C8C23×C3711yescharacteristic
401C4⋊C8C23×C3711yescharacteristic
402C4⋊C8C23×C3711yescharacteristic
403C4⋊C8C23×C3711yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424#97—21no—
425#97—21no—
426#97D4×C3711yescharacteristic
427#97D4×C3711yescharacteristic
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C23×C3711yescharacteristic
431C4×C8C23×C3711yescharacteristic
432#41—42no—
433#41—42no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8—82no—
439C2×Q8C2×D4×C3711yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×D4×C3711yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4C2×D4×C3711yescharacteristic
450C22×C4C2×D4×C3711yescharacteristic
451C22×C4#41×C3711yescharacteristic
452SD16—81no—
453D8—81no—
454M16—41no—
455M16—41no—
456M16—42no—
457M16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
465C2×C8C2×D4×C3711yescharacteristic
466C2×C8C2×D4×C3711yescharacteristic
467C2×C8C2×D4×C3711yescharacteristic
468C2×C8C2×D4×C3711yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C3711yescharacteristic
482C4⋊C4C2×D4×C3711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42C2×D4×C3711yescharacteristic
492C42C2×D4×C3711yescharacteristic
493C42#41×C3711yescharacteristic
494C42C24×C3711yescharacteristic
495C23—21no—
496C23—41no—
497C23#121×C3711yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503Q8—81no—
504Q8—82no—
505D4—21no—
506D4—21no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4—81no—
513D4—82no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4#121×C3711yescharacteristic
530C2×C4#121×C3711yescharacteristic
531C2×C4#121×C3711yescharacteristic
532C2×C4C22×D4×C3711yescharacteristic
533C2×C4C22×D4×C3711yescharacteristic
534C2×C4C2×#41×C3711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×#121×C3711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C37×#57511yescharacteristic
566C4C37×#57511yescharacteristic
567C4C37×#57711yescharacteristic
568C4C37×#57811yescharacteristic
569C2—41no—
570C2—81no—
571C2—161no—
572C2C37×#304011yescharacteristic
573C2C37×#306311yescharacteristic
574C2C37×#306811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3251C2
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×#3238C2semidirect
3. C37×#3141C2semidirect
4. C37×#2969C2semidirect
5. C37×#1704C2semidirect
6. C37×#1703C2semidirect
7. C37×#1698C2semidirect
8. C37×#1697C2semidirect
9. C37×#1684C2semidirect
10. C37×#1683C2semidirect
11. C37×#1678C2semidirect
12. C37×#1677C2semidirect
13. C37×#1569C2semidirect
14. C37×#1553C2semidirect
15. C37×#1548C2semidirect
257. #19382C37direct (N × H)
283. #3238C2×C37semidirect
284. #3141C2×C37semidirect
285. #2969C2×C37semidirect
286. #1704C2×C37semidirect
287. #1703C2×C37semidirect
288. #1698C2×C37semidirect
289. #1697C2×C37semidirect
290. #1684C2×C37semidirect
291. #1683C2×C37semidirect
292. #1678C2×C37semidirect
293. #1677C2×C37semidirect
294. #1569C2×C37semidirect
295. #1553C2×C37semidirect
296. #1548C2×C37semidirect
354. C37#19382direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32512
C37×#32382
C37×#31412
C37×#29692
C37×#17042
C37×#17032
C37×#16982
C37×#16972
C37×#16842
C37×#16832
C37×#16782
C37×#16772
C37×#15692
C37×#15532
C37×#15482
#1938237