Finite Group Databasebeta

← C37×#19591 #22640844

Subgroups — C37×#19591 #22640844

Order 9472.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3247C211yesmaximal, characteristic
2C37×#3238C211yesmaximal, characteristic, complemented
3C37×#3226C211yesmaximal, characteristic, complemented
4C37×#2994C211yesmaximal, characteristic, complemented
5C37×#1698C211yesmaximal, characteristic, complemented
6C37×#1697C211yesmaximal, characteristic, complemented
7C37×#1696C211yesmaximal, characteristic, complemented
8C37×#1695C211yesmaximal, characteristic, complemented
9C37×#1678C211yesmaximal, characteristic, complemented
10C37×#1677C211yesmaximal, characteristic, complemented
11C37×#1676C211yesmaximal, characteristic, complemented
12C37×#1675C211yesmaximal, characteristic, complemented
13C37×#1573C211yesmaximal, characteristic, complemented
14C37×#1551C211yesmaximal, characteristic, complemented
15C2×C37×#333C211yesmaximal, characteristic, complemented
16C37×#532C2211yescharacteristic
17C2×C4⋊Q8×C37C2211yescharacteristic
18C37×#529C2211yescharacteristic
19C37×#501—21no—
20C37×#500C2211yescharacteristic
21C37×#500C2211yescharacteristic
22C37×#489—21no—
23C37×#486C2211yescharacteristic
24C37×#486C2211yescharacteristic
25C37×#483—21no—
26C37×#480—21no—
27C37×#480—21no—
28C37×#480—21no—
29C37×#478—21no—
30C37×#477C2211yescharacteristic
31C37×#477C2211yescharacteristic
32C37×#477C2211yescharacteristic
33C37×#476C2211yescharacteristic
34C37×#476C2211yescharacteristic
35C37×#476C2211yescharacteristic
36C37×#474—21no—
37C37×#474—21no—
38C37×#466—21no—
39C37×#465—21no—
40C37×#463—21no—
41C37×#460C2211yescharacteristic
42C37×#459C2211yescharacteristic
43C37×#446C2211yescharacteristic
44C8×Q8×C37C2211yescharacteristic
45C37×#436C2211yescharacteristic
46C37×#435—21no—
47C8×D4×C37—21no—
48C8×D4×C37C2211yescharacteristic
49C37×#433—21no—
50C37×#432C2211yescharacteristic
51C37×#431C2211yescharacteristic
52C37×#424—21no—
53C2×C4⋊C8×C37C2211yescharacteristic
54C2×C4⋊C8×C37C2211yescharacteristic
55C37×#335C2211yescharacteristic
56C37×#335C2211yescharacteristic
57C37×#334C2211yescharacteristic
58C37×#334C2211yescharacteristic
59C37×#333C2211yescharacteristic
60C37×#333C2211yescharacteristic
61C37×#333C2211yescharacteristic
62C37×#333C2211yescharacteristic
63C37×#333C2211yescharacteristic
64C37×#333C2211yescharacteristic
65C37×#331C2211yescharacteristic
66C37×#331C2211yescharacteristic
67C2×#41×C37—21no—
68C22×Q8×C37—21no—
69C2×SD16×C37—21no—
70C2×D8×C37—21no—
71C2×M16×C37—21no—
72C22×C8×C37—21no—
73C22×C8×C37—21no—
74C22×C8×C37—21no—
75C4⋊Q8×C37—21no—
76C4⋊Q8×C37—21no—
77C4⋊Q8×C37—21no—
78C4⋊Q8×C37C2311yescharacteristic
79C4⋊Q8×C37C2311yescharacteristic
80C4⋊Q8×C37C2311yescharacteristic
81#127×C37C2311yescharacteristic
82#126×C37—21no—
83#125×C37D411yescharacteristic
84#124×C37—21no—
85#124×C37D411yescharacteristic
86#123×C37—21no—
87C22⋊Q8×C37D411yescharacteristic
88#121×C37—21no—
89#121×C37—21no—
90#121×C37D411yescharacteristic
91C4×Q8×C37C2311yescharacteristic
92C4×D4×C37—21no—
93C4×D4×C37—21no—
94C4×D4×C37—21no—
95C4×D4×C37C2311yescharacteristic
96#117×C37—21no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C42×C37C2311yescharacteristic
100#107×C37—21no—
101#107×C37—21no—
102#107×C37—21no—
103#107×C37—21no—
104#107×C37—21no—
105#107×C37—21no—
106#107×C37—21no—
107#106×C37—21no—
108#106×C37—21no—
109#106×C37—21no—
110C4⋊C8×C37—21no—
111C4⋊C8×C37—21no—
112C4⋊C8×C37—21no—
113C4⋊C8×C37—21no—
114C4⋊C8×C37D411yescharacteristic
115C4⋊C8×C37D411yescharacteristic
116C4⋊C8×C37C2311yescharacteristic
117C4⋊C8×C37C2311yescharacteristic
118C4⋊C8×C37C2311yescharacteristic
119C4⋊C8×C37C2311yescharacteristic
120C4⋊C8×C37C2311yescharacteristic
121C4⋊C8×C37C2311yescharacteristic
122#103×C37—21no—
123#103×C37—21no—
124#103×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—
132#102×C37—21no—
133#102×C37—21no—
134C22⋊C8×C37—21no—
135C22⋊C8×C37—21no—
136C22⋊C8×C37—21no—
137C22⋊C8×C37D411yescharacteristic
138C22⋊C8×C37D411yescharacteristic
139#97×C37—21no—
140#97×C37—21no—
141C4×C8×C37—21no—
142C4×C8×C37C2311yescharacteristic
143C4×C8×C37C2311yescharacteristic
144#41×C37—82no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—41no—
149C2×Q8×C37—82no—
150C2×Q8×C37C2×D411yescharacteristic
151C2×D4×C37—21no—
152C2×D4×C37—21no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—41no—
156C2×D4×C37C2×D411yescharacteristic
157C22×C4×C37—21no—
158C22×C4×C37—41no—
159C22×C4×C37—41no—
160C22×C4×C37C2×D411yescharacteristic
161C22×C4×C37C2×D411yescharacteristic
162C22×C4×C37#4111yescharacteristic
163SD16×C37—81no—
164D8×C37—81no—
165M16×C37—81no—
166C2×C8×C37—21no—
167C2×C8×C37—21no—
168C2×C8×C37—21no—
169C2×C8×C37—21no—
170C2×C8×C37—21no—
171C2×C8×C37—21no—
172C2×C8×C37—81no—
173C2×C8×C37—81no—
174C2×C8×C37—81no—
175C2×C8×C37C2×D411yescharacteristic
176C2×C8×C37C2×D411yescharacteristic
177C2×C8×C37C2×D411yescharacteristic
178C2×C8×C37C2×D411yescharacteristic
179C4⋊C4×C37—21no—
180C4⋊C4×C37—21no—
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—41no—
190C4⋊C4×C37—41no—
191C4⋊C4×C37C2×D411yescharacteristic
192C4⋊C4×C37C2×D411yescharacteristic
193C22⋊C4×C37—21no—
194C22⋊C4×C37—21no—
195C22⋊C4×C37—21no—
196C22⋊C4×C37—21no—
197C22⋊C4×C37—21no—
198C22⋊C4×C37—41no—
199C22⋊C4×C37—41no—
200C42×C37—21no—
201C42×C37C2×D411yescharacteristic
202C42×C37C2×D411yescharacteristic
203C42×C37#4111yescharacteristic
204C42×C37C2411yescharacteristic
205C23×C37—21no—
206C23×C37—41no—
207C23×C37#12111yescharacteristic
208Q8×C37—21no—
209Q8×C37—21no—
210Q8×C37—81no—
211Q8×C37—81no—
212Q8×C37—81no—
213Q8×C37—82no—
214D4×C37—21no—
215D4×C37—21no—
216D4×C37—42no—
217D4×C37—41no—
218D4×C37—41no—
219D4×C37—41no—
220D4×C37—41no—
221D4×C37—81no—
222D4×C37—82no—
223C2×C4×C37—22no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—21no—
227C2×C4×C37—21no—
228C2×C4×C37—21no—
229C2×C4×C37—21no—
230C2×C4×C37—21no—
231C2×C4×C37—41no—
232C2×C4×C37—41no—
233C2×C4×C37—41no—
234C2×C4×C37—41no—
235C2×C4×C37—41no—
236C2×C4×C37—82no—
237C2×C4×C37—82no—
238C2×C4×C37#12111yescharacteristic
239C2×C4×C37#12111yescharacteristic
240C2×C4×C37#12111yescharacteristic
241C2×C4×C37C22×D411yescharacteristic
242C2×C4×C37C22×D411yescharacteristic
243C2×C4×C37C2×#4111yescharacteristic
244C8×C37—21no—
245C8×C37—21no—
246C8×C37—21no—
247C8×C37—21no—
248C8×C37—41no—
249C8×C37—41no—
250C8×C37—41no—
251C8×C37—41no—
252C8×C37—41no—
253C8×C37—41no—
254#19591C3711yesmaximal, characteristic, direct product factor, Sylow
255C22×C37—21no—
256C22×C37—21no—
257C22×C37—41no—
258C22×C37—41no—
259C22×C37—41no—
260C22×C37—81no—
261C22×C37—81no—
262C22×C37—81no—
263C22×C37#47212yes—
264C22×C37C2×#12111yescharacteristic
265C4×C37—21no—
266C4×C37—21no—
267C4×C37—21no—
268C4×C37—21no—
269C4×C37—41no—
270C4×C37—41no—
271C4×C37—41no—
272C4×C37—81no—
273C4×C37—81no—
274C4×C37—81no—
275C4×C37#57711yescharacteristic
276C4×C37#57711yescharacteristic
277C4×C37#57811yescharacteristic
278C4×C37#57811yescharacteristic
279#3247C2×C3711yescharacteristic
280#3238C2×C3711yescharacteristic, complemented
281#3226C2×C3711yescharacteristic, complemented
282#2994C2×C3711yescharacteristic, complemented
283#1698C2×C3711yescharacteristic, complemented
284#1697C2×C3711yescharacteristic, complemented
285#1696C2×C3711yescharacteristic, complemented
286#1695C2×C3711yescharacteristic, complemented
287#1678C2×C3711yescharacteristic, complemented
288#1677C2×C3711yescharacteristic, complemented
289#1676C2×C3711yescharacteristic, complemented
290#1675C2×C3711yescharacteristic, complemented
291#1573C2×C3711yescharacteristic, complemented
292#1551C2×C3711yescharacteristic, complemented
293C2×#333C2×C3711yescharacteristic, complemented
294C2×C37—22no—
295C2×C37—81no—
296C2×C37—161no—
297C2×C37#304611yescharacteristic
298C2×C37#306311yescharacteristic
299C2×C37C2×#47211yescharacteristic
300#532C22×C3711yescharacteristic
301C2×C4⋊Q8C22×C3711yescharacteristic
302#529C22×C3711yescharacteristic
303#501—21no—
304#500C22×C3711yescharacteristic
305#500C22×C3711yescharacteristic
306#489—21no—
307#486C22×C3711yescharacteristic
308#486C22×C3711yescharacteristic
309#483—21no—
310#480—21no—
311#480—21no—
312#480—21no—
313#478—21no—
314#477C22×C3711yescharacteristic
315#477C22×C3711yescharacteristic
316#477C22×C3711yescharacteristic
317#476C22×C3711yescharacteristic
318#476C22×C3711yescharacteristic
319#476C22×C3711yescharacteristic
320#474—21no—
321#474—21no—
322#466—21no—
323#465—21no—
324#463—21no—
325#460C22×C3711yescharacteristic
326#459C22×C3711yescharacteristic
327#446C22×C3711yescharacteristic
328C8×Q8C22×C3711yescharacteristic
329#436C22×C3711yescharacteristic
330#435—21no—
331C8×D4—21no—
332C8×D4C22×C3711yescharacteristic
333#433—21no—
334#432C22×C3711yescharacteristic
335#431C22×C3711yescharacteristic
336#424—21no—
337C2×C4⋊C8C22×C3711yescharacteristic
338C2×C4⋊C8C22×C3711yescharacteristic
339#335C22×C3711yescharacteristic
340#335C22×C3711yescharacteristic
341#334C22×C3711yescharacteristic
342#334C22×C3711yescharacteristic
343#333C22×C3711yescharacteristic
344#333C22×C3711yescharacteristic
345#333C22×C3711yescharacteristic
346#333C22×C3711yescharacteristic
347#333C22×C3711yescharacteristic
348#333C22×C3711yescharacteristic
349#331C22×C3711yescharacteristic
350#331C22×C3711yescharacteristic
351C37#1959111yescharacteristic, direct product factor, Sylow
352C2×#41—21no—
353C22×Q8—21no—
354C2×SD16—21no—
355C2×D8—21no—
356C2×M16—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C23×C3711yescharacteristic
364C4⋊Q8C23×C3711yescharacteristic
365C4⋊Q8C23×C3711yescharacteristic
366#127C23×C3711yescharacteristic
367#126—21no—
368#125D4×C3711yescharacteristic
369#124—21no—
370#124D4×C3711yescharacteristic
371#123—21no—
372C22⋊Q8D4×C3711yescharacteristic
373#121—21no—
374#121—21no—
375#121D4×C3711yescharacteristic
376C4×Q8C23×C3711yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C23×C3711yescharacteristic
381#117—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C42C23×C3711yescharacteristic
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
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⋊C8—21no—
399C4⋊C8D4×C3711yescharacteristic
400C4⋊C8D4×C3711yescharacteristic
401C4⋊C8C23×C3711yescharacteristic
402C4⋊C8C23×C3711yescharacteristic
403C4⋊C8C23×C3711yescharacteristic
404C4⋊C8C23×C3711yescharacteristic
405C4⋊C8C23×C3711yescharacteristic
406C4⋊C8C23×C3711yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#102—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—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8D4×C3711yescharacteristic
423C22⋊C8D4×C3711yescharacteristic
424#97—21no—
425#97—21no—
426C4×C8—21no—
427C4×C8C23×C3711yescharacteristic
428C4×C8C23×C3711yescharacteristic
429#41—82no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—82no—
435C2×Q8C2×D4×C3711yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4C2×D4×C3711yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4C2×D4×C3711yescharacteristic
446C22×C4C2×D4×C3711yescharacteristic
447C22×C4#41×C3711yescharacteristic
448SD16—81no—
449D8—81no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8C2×D4×C3711yescharacteristic
461C2×C8C2×D4×C3711yescharacteristic
462C2×C8C2×D4×C3711yescharacteristic
463C2×C8C2×D4×C3711yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4C2×D4×C3711yescharacteristic
477C4⋊C4C2×D4×C3711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42C2×D4×C3711yescharacteristic
487C42C2×D4×C3711yescharacteristic
488C42#41×C3711yescharacteristic
489C42C24×C3711yescharacteristic
490C23—21no—
491C23—41no—
492C23#121×C3711yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—81no—
496Q8—81no—
497Q8—81no—
498Q8—82no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4#121×C3711yescharacteristic
524C2×C4#121×C3711yescharacteristic
525C2×C4#121×C3711yescharacteristic
526C2×C4C22×D4×C3711yescharacteristic
527C2×C4C22×D4×C3711yescharacteristic
528C2×C4C2×#41×C3711yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C37×#47212yes—
548C22C2×#121×C3711yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4C37×#57711yescharacteristic
560C4C37×#57711yescharacteristic
561C4C37×#57811yescharacteristic
562C4C37×#57811yescharacteristic
563C2—22no—
564C2—81no—
565C2—161no—
566C2C37×#304611yescharacteristic
567C2C37×#306311yescharacteristic
568C2C2×C37×#47211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3247C2
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×#3226C2semidirect
4. C37×#2994C2semidirect
5. C37×#1698C2semidirect
6. C37×#1697C2semidirect
7. C37×#1696C2semidirect
8. C37×#1695C2semidirect
9. C37×#1678C2semidirect
10. C37×#1677C2semidirect
11. C37×#1676C2semidirect
12. C37×#1675C2semidirect
13. C37×#1573C2semidirect
14. C37×#1551C2semidirect
15. C2×C37×#333C2semidirect
254. #19591C37direct (N × H)
280. #3238C2×C37semidirect
281. #3226C2×C37semidirect
282. #2994C2×C37semidirect
283. #1698C2×C37semidirect
284. #1697C2×C37semidirect
285. #1696C2×C37semidirect
286. #1695C2×C37semidirect
287. #1678C2×C37semidirect
288. #1677C2×C37semidirect
289. #1676C2×C37semidirect
290. #1675C2×C37semidirect
291. #1573C2×C37semidirect
292. #1551C2×C37semidirect
293. C2×#333C2×C37semidirect
351. C37#19591direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32472
C37×#32382
C37×#32262
C37×#29942
C37×#16982
C37×#16972
C37×#16962
C37×#16952
C37×#16782
C37×#16772
C37×#16762
C37×#16752
C37×#15732
C37×#15512
C2×C37×#3332
#1959137