Finite Group Databasebeta

← C37×#14631 #22635884

Subgroups — C37×#14631 #22635884

Order 9472.

1130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#398C211yesmaximal, characteristic
2C2×C37×#389C211yesmaximal, characteristic
3C2×C37×#387C211yesmaximal, characteristic
4C37×#1445C211yesmaximal, characteristic
5C37×#1445C212yesmaximal
6C37×#1442C212yesmaximal
7C37×#1442C211yesmaximal, characteristic
8C37×#1442C212yesmaximal
9C37×#1441C211yesmaximal, characteristic
10C37×#1441C212yesmaximal
11C37×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C37C2211yescharacteristic
13C22×C4⋊C4×C37C2211yescharacteristic
14C22×C4⋊C4×C37C2211yescharacteristic
15C22×C4⋊C4×C37C2212yes—
16C22×C4⋊C4×C37C2211yescharacteristic
17C22×C4⋊C4×C37C2212yes—
18C22×C42×C37C2211yescharacteristic
19C37×#398C418yescomplemented
20C37×#389—24no—
21C37×#387—24no—
22C2×#95×C37C2211yescharacteristic
23C2×#95×C37C2211yescharacteristic
24C2×#95×C37C2211yescharacteristic
25C2×#95×C37C2211yescharacteristic
26C2×#95×C37C2212yes—
27C2×#95×C37C2211yescharacteristic
28C2×#95×C37C2212yes—
29C2×#95×C37C2212yes—
30C2×#95×C37C2212yes—
31C2×#95×C37C2212yes—
32C2×#95×C37C2212yes—
33C2×#95×C37C2212yes—
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C2×#95×C37C2211yescharacteristic
37C2×#95×C37C2212yes—
38C23×C4×C37C2311yescharacteristic
39C23×C4×C37C2312yes—
40C23×C4×C37C2311yescharacteristic
41C23×C4×C37C2312yes—
42C23×C4×C37C2312yes—
43C23×C4×C37C2311yescharacteristic
44C23×C4×C37C2311yescharacteristic
45C23×C4×C37C2312yes—
46C23×C4×C37C2311yescharacteristic
47C23×C4×C37C2311yescharacteristic
48C23×C4×C37C2311yescharacteristic
49C2×C4⋊C4×C37—22no—
50C2×C4⋊C4×C37—22no—
51C2×C4⋊C4×C37—22no—
52C2×C4⋊C4×C37—22no—
53C2×C4⋊C4×C37—22no—
54C2×C4⋊C4×C37—24no—
55C2×C4⋊C4×C37—22no—
56C2×C4⋊C4×C37—42no—
57C2×C4⋊C4×C37—42no—
58C2×C4⋊C4×C37—42no—
59C2×C4⋊C4×C37—42no—
60C2×C4⋊C4×C37—42no—
61C2×C4⋊C4×C37—42no—
62C2×C4⋊C4×C37C2×C414yes—
63C2×C4⋊C4×C37C2×C414yes—
64C2×C4⋊C4×C37C2×C418yes—
65C2×C42×C37—42no—
66C2×C42×C37D414yes—
67#95×C37—22no—
68#95×C37—22no—
69#95×C37—22no—
70#95×C37—22no—
71#95×C37—24no—
72#95×C37—22no—
73#95×C37—42no—
74#95×C37—42no—
75#95×C37—42no—
76#95×C37—42no—
77#95×C37—42no—
78#95×C37—42no—
79#95×C37—42no—
80#95×C37—42no—
81#95×C37C2×C418yes—
82#95×C37C2×C414yes—
83C24×C37C2411yescharacteristic
84C22×C4×C37—22no—
85C22×C4×C37—22no—
86C22×C4×C37—21no—
87C22×C4×C37—21no—
88C22×C4×C37—22no—
89C22×C4×C37—21no—
90C22×C4×C37—21no—
91C22×C4×C37—22no—
92C22×C4×C37—21no—
93C22×C4×C37—22no—
94C22×C4×C37—21no—
95C22×C4×C37—22no—
96C22×C4×C37—22no—
97C22×C4×C37—22no—
98C22×C4×C37—22no—
99C22×C4×C37—22no—
100C22×C4×C37—22no—
101C22×C4×C37—22no—
102C22×C4×C37—21no—
103C22×C4×C37—21no—
104C22×C4×C37—22no—
105C22×C4×C37—21no—
106C22×C4×C37—21no—
107C22×C4×C37—22no—
108C22×C4×C37—22no—
109C22×C4×C37—22no—
110C22×C4×C37—21no—
111C22×C4×C37—22no—
112C22×C4×C37—22no—
113C22×C4×C37—22no—
114C22×C4×C37—22no—
115C22×C4×C37—21no—
116C22×C4×C37—21no—
117C22×C4×C37—21no—
118C22×C4×C37—22no—
119C22×C4×C37—22no—
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—22no—
124C22×C4×C37—22no—
125C22×C4×C37—22no—
126C22×C4×C37—22no—
127C22×C4×C37—22no—
128C22×C4×C37—22no—
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—22no—
136C22×C4×C37—21no—
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—22no—
140C22×C4×C37C22×C412yes—
141C22×C4×C37C22×C414yes—
142C22×C4×C37C22×C414yes—
143C22×C4×C37C22×C412yes—
144C22×C4×C37C22×C412yes—
145C22×C4×C37C2×D412yes—
146C22×C4×C37C2×D412yes—
147C22×C4×C37C2×D412yes—
148C22×C4×C37#4112yes—
149C4⋊C4×C37—28no—
150C4⋊C4×C37—28no—
151C4⋊C4×C37—48no—
152C4⋊C4×C37—44no—
153C4⋊C4×C37—44no—
154C4⋊C4×C37—48no—
155C42×C37—44no—
156C23×C37C23×C411yescharacteristic
157C23×C37C22×D411yescharacteristic
158C23×C37C2×#4111yescharacteristic
159C23×C37H(5,𝔽2)11yescharacteristic
160C23×C37H(5,𝔽2)11yescharacteristic
161C23×C37H(5,𝔽2)12yes—
162C23×C37H(5,𝔽2)11yescharacteristic
163C23×C372−1+412yes—
164C23×C372−1+412yes—
165C23×C372−1+412yes—
166C23×C372−1+411yescharacteristic
167C2×C4×C37—24no—
168C2×C4×C37—22no—
169C2×C4×C37—22no—
170C2×C4×C37—24no—
171C2×C4×C37—22no—
172C2×C4×C37—22no—
173C2×C4×C37—24no—
174C2×C4×C37—22no—
175C2×C4×C37—24no—
176C2×C4×C37—24no—
177C2×C4×C37—24no—
178C2×C4×C37—24no—
179C2×C4×C37—22no—
180C2×C4×C37—24no—
181C2×C4×C37—24no—
182C2×C4×C37—22no—
183C2×C4×C37—22no—
184C2×C4×C37—22no—
185C2×C4×C37—22no—
186C2×C4×C37—22no—
187C2×C4×C37—22no—
188C2×C4×C37—41no—
189C2×C4×C37—42no—
190C2×C4×C37—41no—
191C2×C4×C37—41no—
192C2×C4×C37—41no—
193C2×C4×C37—42no—
194C2×C4×C37—42no—
195C2×C4×C37—41no—
196C2×C4×C37—42no—
197C2×C4×C37—41no—
198C2×C4×C37—42no—
199C2×C4×C37—42no—
200C2×C4×C37—42no—
201C2×C4×C37—42no—
202C2×C4×C37—42no—
203C2×C4×C37—42no—
204C2×C4×C37—42no—
205C2×C4×C37—42no—
206C2×C4×C37—42no—
207C2×C4×C37—42no—
208C2×C4×C37—41no—
209C2×C4×C37—42no—
210C2×C4×C37—41no—
211C2×C4×C37—42no—
212C2×C4×C37—41no—
213C2×C4×C37—41no—
214C2×C4×C37—41no—
215C2×C4×C37—41no—
216C2×C4×C37—42no—
217C2×C4×C37—42no—
218C2×C4×C37—42no—
219C2×C4×C37—42no—
220C2×C4×C37—42no—
221C2×C4×C37—42no—
222C2×C4×C37—42no—
223C2×C4×C37—42no—
224C2×C4×C37—42no—
225C2×C4×C37—42no—
226C2×C4×C37—42no—
227C2×C4×C37—42no—
228C2×C4×C37—42no—
229C2×C4×C37—42no—
230C2×C4×C37—42no—
231C2×C4×C37C4×D414yes—
232#14631C3711yesmaximal, characteristic, direct product factor, Sylow
233C22×C37C2×C4×D411yescharacteristic
234C22×C37#51811yescharacteristic
235C22×C37#51912yes—
236C22×C37#52012yes—
237C22×C37#52011yescharacteristic
238C22×C37#53411yescharacteristic
239C22×C37#53511yescharacteristic
240C22×C37#53611yescharacteristic
241C22×C37#53611yescharacteristic
242C22×C37#53611yescharacteristic
243C22×C37#53711yescharacteristic
244C22×C37#53912yes—
245C22×C37#54011yescharacteristic
246C22×C37#54112yes—
247C22×C37#54211yescharacteristic
248C22×C37#56212yes—
249C22×C37#56212yes—
250C22×C37#56212yes—
251C22×C37#56312yes—
252C22×C37#56312yes—
253C22×C37#56312yes—
254C22×C37#56312yes—
255C22×C37#56412yes—
256C4×C37—24no—
257C4×C37—42no—
258C4×C37—42no—
259C4×C37—42no—
260C4×C37—44no—
261C4×C37—44no—
262C4×C37—42no—
263C4×C37—82no—
264C4×C37—81no—
265C4×C37—82no—
266C4×C37—81no—
267C2×#398C2×C3711yescharacteristic
268C2×#389C2×C3711yescharacteristic
269C2×#387C2×C3711yescharacteristic
270#1445C2×C3711yescharacteristic
271#1445C2×C3712yes—
272#1442C2×C3712yes—
273#1442C2×C3711yescharacteristic
274#1442C2×C3712yes—
275#1441C2×C3711yescharacteristic
276#1441C2×C3712yes—
277#1434C2×C3711yescharacteristic
278C2×C37#232211yescharacteristic
279C2×C37#232411yescharacteristic
280C2×C37#232711yescharacteristic
281C2×C37#237812yes—
282C2×C37#238212yes—
283C2×C37#281411yescharacteristic
284C2×C37#281611yescharacteristic
285C2×C37#282111yescharacteristic
286C2×C37#282211yescharacteristic
287C2×C37#283612yes—
288C2×C37#283912yes—
289C22×C4⋊C4C22×C3711yescharacteristic
290C22×C4⋊C4C22×C3711yescharacteristic
291C22×C4⋊C4C22×C3711yescharacteristic
292C22×C4⋊C4C22×C3712yes—
293C22×C4⋊C4C22×C3711yescharacteristic
294C22×C4⋊C4C22×C3712yes—
295C22×C42C22×C3711yescharacteristic
296#398C4×C3718yescomplemented
297#389—24no—
298#387—24no—
299C2×#95C22×C3711yescharacteristic
300C2×#95C22×C3711yescharacteristic
301C2×#95C22×C3711yescharacteristic
302C2×#95C22×C3711yescharacteristic
303C2×#95C22×C3712yes—
304C2×#95C22×C3711yescharacteristic
305C2×#95C22×C3712yes—
306C2×#95C22×C3712yes—
307C2×#95C22×C3712yes—
308C2×#95C22×C3712yes—
309C2×#95C22×C3712yes—
310C2×#95C22×C3712yes—
311C2×#95C22×C3712yes—
312C2×#95C22×C3712yes—
313C2×#95C22×C3711yescharacteristic
314C2×#95C22×C3712yes—
315C37#1463111yescharacteristic, direct product factor, Sylow
316C23×C4C23×C3712yes—
317C23×C4C23×C3711yescharacteristic
318C23×C4C23×C3711yescharacteristic
319C23×C4C23×C3712yes—
320C23×C4C23×C3711yescharacteristic
321C23×C4C23×C3712yes—
322C23×C4C23×C3711yescharacteristic
323C23×C4C23×C3712yes—
324C23×C4C23×C3711yescharacteristic
325C23×C4C23×C3711yescharacteristic
326C23×C4C23×C3711yescharacteristic
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4C2×C4×C3714yes—
341C2×C4⋊C4C2×C4×C3714yes—
342C2×C4⋊C4C2×C4×C3718yes—
343C2×C42—42no—
344C2×C42D4×C3714yes—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—24no—
350#95—22no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95C2×C4×C3718yes—
360#95C2×C4×C3714yes—
361C24C24×C3711yescharacteristic
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4C22×C4×C3714yes—
419C22×C4C22×C4×C3712yes—
420C22×C4C22×C4×C3714yes—
421C22×C4C22×C4×C3712yes—
422C22×C4C22×C4×C3712yes—
423C22×C4C2×D4×C3712yes—
424C22×C4C2×D4×C3712yes—
425C22×C4C2×D4×C3712yes—
426C22×C4#41×C3712yes—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—48no—
430C4⋊C4—44no—
431C4⋊C4—44no—
432C4⋊C4—48no—
433C42—44no—
434C23C23×C4×C3711yescharacteristic
435C23C22×D4×C3711yescharacteristic
436C23C2×#41×C3711yescharacteristic
437C23H(5,𝔽2)×C3712yes—
438C23H(5,𝔽2)×C3711yescharacteristic
439C23H(5,𝔽2)×C3711yescharacteristic
440C23H(5,𝔽2)×C3711yescharacteristic
441C232−1+4×C3712yes—
442C232−1+4×C3712yes—
443C232−1+4×C3712yes—
444C232−1+4×C3711yescharacteristic
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4C4×D4×C3714yes—
510C22C2×C4×D4×C3711yescharacteristic
511C22C37×#51811yescharacteristic
512C22C37×#51912yes—
513C22C37×#52012yes—
514C22C37×#52011yescharacteristic
515C22C37×#53411yescharacteristic
516C22C37×#53511yescharacteristic
517C22C37×#53611yescharacteristic
518C22C37×#53611yescharacteristic
519C22C37×#53611yescharacteristic
520C22C37×#53711yescharacteristic
521C22C37×#53912yes—
522C22C37×#54011yescharacteristic
523C22C37×#54112yes—
524C22C37×#54211yescharacteristic
525C22C37×#56212yes—
526C22C37×#56212yes—
527C22C37×#56212yes—
528C22C37×#56312yes—
529C22C37×#56312yes—
530C22C37×#56312yes—
531C22C37×#56312yes—
532C22C37×#56412yes—
533C4—24no—
534C4—44no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—42no—
539C4—44no—
540C4—81no—
541C4—82no—
542C4—81no—
543C4—82no—
544C2C37×#232211yescharacteristic
545C2C37×#232411yescharacteristic
546C2C37×#232711yescharacteristic
547C2C37×#237812yes—
548C2C37×#238212yes—
549C2C37×#281411yescharacteristic
550C2C37×#281611yescharacteristic
551C2C37×#282111yescharacteristic
552C2C37×#282211yescharacteristic
553C2C37×#283612yes—
554C2C37×#283912yes—
subgroupG/H
center, socle, prime radicalC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
19. C37×#398C4semidirect
232. #14631C37direct (N × H)
296. #398C4×C37semidirect
315. C37#14631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#3982
C2×C37×#3892
C2×C37×#3872
C37×#14452
C37×#14422
C37×#14412
C37×#14342
#1463137