Finite Group Databasebeta

← C37×#29002 #22650255

Subgroups — C37×#29002 #22650255

Order 9472.

708 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2489C211yesmaximal, characteristic
2C37×#2421C211yesmaximal, characteristic
3C37×#2076C211yesmaximal, characteristic
4C37×#2074C211yesmaximal, characteristic, complemented
5C37×#2026C211yesmaximal, characteristic, complemented
6C37×#2001C211yesmaximal, characteristic
7C37×#1991C211yesmaximal, characteristic, complemented
8C37×#1969C211yesmaximal, characteristic, complemented
9C37×#1935C211yesmaximal, characteristic, complemented
10C37×#1921C211yesmaximal, characteristic, complemented
11C37×#1894C211yesmaximal, characteristic
12C37×#1894C211yesmaximal, characteristic
13C37×#1878C211yesmaximal, characteristic, complemented
14C37×#1763C211yesmaximal, characteristic, complemented
15C37×#1753C211yesmaximal, characteristic
16C22×Q16×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C2×#125×C37C2211yescharacteristic
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×C22⋊Q8×C37C2211yescharacteristic
21C2×C4×Q8×C37C2211yescharacteristic
22C2×#107×C37C2211yescharacteristic
23C2×#103×C37C2211yescharacteristic
24C2×#103×C37C2211yescharacteristic
25C2×#103×C37C2211yescharacteristic
26C2×#103×C37C2211yescharacteristic
27C2×#103×C37C2211yescharacteristic
28C2×#103×C37C2211yescharacteristic
29C2×C22⋊C8×C37C2211yescharacteristic
30C2×#97×C37C2211yescharacteristic
31C2×C4×C8×C37C2211yescharacteristic
32C37×#400—21no—
33C37×#400—21no—
34C37×#397—21no—
35C37×#397—21no—
36C37×#391C2211yescharacteristic
37C37×#391C2211yescharacteristic
38C37×#391C2211yescharacteristic
39C37×#389C2211yescharacteristic
40C37×#388—21no—
41C37×#388—21no—
42C37×#387—21no—
43C37×#382—21no—
44C37×#382C2211yescharacteristic
45C37×#380C2211yescharacteristic
46C37×#380C2211yescharacteristic
47C4×C4⋊C4×C37C2211yescharacteristic
48C4×C22⋊C4×C37C2211yescharacteristic
49C37×#340C2211yescharacteristic
50C37×#340C2211yescharacteristic
51C37×#340C2211yescharacteristic
52C37×#340C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C22×Q8×C37C2311yescharacteristic
60C22×Q8×C37C2311yescharacteristic
61C23×C4×C37C2311yescharacteristic
62C2×Q16×C37—22no—
63C2×Q16×C37—22no—
64C2×Q16×C37—41no—
65C2×M16×C37—22no—
66C2×M16×C37—41no—
67C2×M16×C37—41no—
68C22×C8×C37C2311yescharacteristic
69C22×C8×C37C2311yescharacteristic
70C22×C8×C37C2311yescharacteristic
71C22×C8×C37C2311yescharacteristic
72#125×C37—22no—
73#125×C37—41no—
74C22⋊Q8×C37—22no—
75C22⋊Q8×C37—22no—
76C22⋊Q8×C37—41no—
77C22⋊Q8×C37—41no—
78C4×Q8×C37—22no—
79C4×Q8×C37—41no—
80C2×C4⋊C4×C37—21no—
81C2×C4⋊C4×C37—21no—
82C2×C4⋊C4×C37—21no—
83C2×C4⋊C4×C37—21no—
84C2×C4⋊C4×C37—21no—
85C2×C4⋊C4×C37—21no—
86C2×C4⋊C4×C37C2311yescharacteristic
87C2×C4⋊C4×C37C2311yescharacteristic
88C2×C4⋊C4×C37C2311yescharacteristic
89C2×C4⋊C4×C37C2311yescharacteristic
90C2×C4⋊C4×C37C2311yescharacteristic
91C2×C4⋊C4×C37C2311yescharacteristic
92C2×C22⋊C4×C37—21no—
93C2×C22⋊C4×C37—21no—
94C2×C22⋊C4×C37—21no—
95C2×C22⋊C4×C37—21no—
96C2×C22⋊C4×C37D411yescharacteristic
97C2×C22⋊C4×C37D411yescharacteristic
98C2×C42×C37—21no—
99C2×C42×C37—21no—
100C2×C42×C37C2311yescharacteristic
101C2×C42×C37C2311yescharacteristic
102#107×C37—22no—
103#103×C37—22no—
104#103×C37—22no—
105#103×C37—22no—
106#103×C37—41no—
107#103×C37—41no—
108#103×C37—41no—
109C22⋊C8×C37—22no—
110#97×C37—41no—
111C4×C8×C37—41no—
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×C37C2×D411yescharacteristic
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—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—21no—
142C22×C4×C37—21no—
143C22×C4×C37—21no—
144C22×C4×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×C37—21no—
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—
160M16×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—21no—
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—21no—
184C4⋊C4×C37—42no—
185C4⋊C4×C37—42no—
186C4⋊C4×C37—42no—
187C4⋊C4×C37—42no—
188C4⋊C4×C37—42no—
189C4⋊C4×C37—42no—
190C4⋊C4×C37#4112yes—
191C22⋊C4×C37—41no—
192C22⋊C4×C37—41no—
193C22⋊C4×C37—42no—
194C22⋊C4×C37—42no—
195C22⋊C4×C37—42no—
196C22⋊C4×C37—42no—
197C42×C37—21no—
198C42×C37—21no—
199C42×C37—21no—
200C42×C37—21no—
201C42×C37—42no—
202C42×C37—42no—
203C23×C37—21no—
204C23×C37—21no—
205C23×C37—21no—
206C23×C37—21no—
207C23×C37—21no—
208C23×C37—21no—
209C23×C37—21no—
210C23×C37C22×D411yescharacteristic
211Q8×C37—22no—
212Q8×C37—22no—
213Q8×C37—41no—
214Q8×C37—41no—
215Q8×C37—41no—
216Q8×C37—41no—
217Q8×C37—41no—
218Q8×C37—41no—
219C2×C4×C37—21no—
220C2×C4×C37—21no—
221C2×C4×C37—21no—
222C2×C4×C37—21no—
223C2×C4×C37—21no—
224C2×C4×C37—22no—
225C2×C4×C37—22no—
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—21no—
234C2×C4×C37—21no—
235C2×C4×C37—21no—
236C2×C4×C37—41no—
237C2×C4×C37—41no—
238C2×C4×C37—41no—
239C2×C4×C37—41no—
240C2×C4×C37—41no—
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×C37—41no—
262C2×C4×C37C2×#4111yescharacteristic
263C2×C4×C37C2×#4111yescharacteristic
264C2×C4×C37C2×#4111yescharacteristic
265C2×C4×C37C2×#4111yescharacteristic
266C2×C4×C37H(5,𝔽2)11yescharacteristic
267C2×C4×C37H(5,𝔽2)11yescharacteristic
268C8×C37—22no—
269C8×C37—22no—
270C8×C37—41no—
271C8×C37—41no—
272#29002C3711yesmaximal, characteristic, direct product factor, Sylow
273C22×C37—41no—
274C22×C37—41no—
275C22×C37—41no—
276C22×C37—41no—
277C22×C37—41no—
278C22×C37—41no—
279C22×C37—41no—
280C22×C37#53211yescharacteristic
281C22×C37#54611yescharacteristic
282C22×C37#54611yescharacteristic
283C22×C37#57511yescharacteristic
284C22×C37#57511yescharacteristic
285C22×C37#57811yescharacteristic
286C22×C37#57811yescharacteristic
287C4×C37—41no—
288C4×C37—41no—
289C4×C37—42no—
290C4×C37—41no—
291C4×C37—42no—
292C4×C37—41no—
293C4×C37—41no—
294C4×C37—81no—
295C4×C37—81no—
296C4×C37—81no—
297C4×C37—81no—
298C4×C37—81no—
299C4×C37—81no—
300C4×C37#52911yescharacteristic
301C4×C37#53811yescharacteristic
302C4×C37#55111yescharacteristic
303C4×C37#55911yescharacteristic
304#2489C2×C3711yescharacteristic
305#2421C2×C3711yescharacteristic
306#2076C2×C3711yescharacteristic
307#2074C2×C3711yescharacteristic, complemented
308#2026C2×C3711yescharacteristic, complemented
309#2001C2×C3711yescharacteristic
310#1991C2×C3711yescharacteristic, complemented
311#1969C2×C3711yescharacteristic, complemented
312#1935C2×C3711yescharacteristic, complemented
313#1921C2×C3711yescharacteristic, complemented
314#1894C2×C3711yescharacteristic
315#1894C2×C3711yescharacteristic
316#1878C2×C3711yescharacteristic, complemented
317#1763C2×C3711yescharacteristic, complemented
318#1753C2×C3711yescharacteristic
319C2×C37—81no—
320C2×C37#255711yescharacteristic
321C2×C37#317711yescharacteristic
322C2×C37#318311yescharacteristic
323C2×C37#331311yescharacteristic
324C2×C37#331511yescharacteristic
325C2×C37#332711yescharacteristic
326C2×C37#332711yescharacteristic
327C22×Q16C22×C3711yescharacteristic
328C22×M16C22×C3711yescharacteristic
329C2×#125C22×C3711yescharacteristic
330C2×C22⋊Q8C22×C3711yescharacteristic
331C2×C22⋊Q8C22×C3711yescharacteristic
332C2×C4×Q8C22×C3711yescharacteristic
333C2×#107C22×C3711yescharacteristic
334C2×#103C22×C3711yescharacteristic
335C2×#103C22×C3711yescharacteristic
336C2×#103C22×C3711yescharacteristic
337C2×#103C22×C3711yescharacteristic
338C2×#103C22×C3711yescharacteristic
339C2×#103C22×C3711yescharacteristic
340C2×C22⋊C8C22×C3711yescharacteristic
341C2×#97C22×C3711yescharacteristic
342C2×C4×C8C22×C3711yescharacteristic
343#400—21no—
344#400—21no—
345#397—21no—
346#397—21no—
347#391C22×C3711yescharacteristic
348#391C22×C3711yescharacteristic
349#391C22×C3711yescharacteristic
350#389C22×C3711yescharacteristic
351#388—21no—
352#388—21no—
353#387—21no—
354#382—21no—
355#382C22×C3711yescharacteristic
356#380C22×C3711yescharacteristic
357#380C22×C3711yescharacteristic
358C4×C4⋊C4C22×C3711yescharacteristic
359C4×C22⋊C4C22×C3711yescharacteristic
360#340C22×C3711yescharacteristic
361#340C22×C3711yescharacteristic
362#340C22×C3711yescharacteristic
363#340C22×C3711yescharacteristic
364#340C22×C3711yescharacteristic
365#340C22×C3711yescharacteristic
366#340C22×C3711yescharacteristic
367#340C22×C3711yescharacteristic
368#336C22×C3711yescharacteristic
369#336C22×C3711yescharacteristic
370C37#2900211yescharacteristic, direct product factor, Sylow
371C22×Q8C23×C3711yescharacteristic
372C22×Q8C23×C3711yescharacteristic
373C23×C4C23×C3711yescharacteristic
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—41no—
377C2×M16—22no—
378C2×M16—41no—
379C2×M16—41no—
380C22×C8C23×C3711yescharacteristic
381C22×C8C23×C3711yescharacteristic
382C22×C8C23×C3711yescharacteristic
383C22×C8C23×C3711yescharacteristic
384#125—22no—
385#125—41no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—41no—
389C22⋊Q8—41no—
390C4×Q8—22no—
391C4×Q8—41no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4C23×C3711yescharacteristic
399C2×C4⋊C4C23×C3711yescharacteristic
400C2×C4⋊C4C23×C3711yescharacteristic
401C2×C4⋊C4C23×C3711yescharacteristic
402C2×C4⋊C4C23×C3711yescharacteristic
403C2×C4⋊C4C23×C3711yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4D4×C3711yescharacteristic
409C2×C22⋊C4D4×C3711yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C23×C3711yescharacteristic
413C2×C42C23×C3711yescharacteristic
414#107—22no—
415#103—22no—
416#103—22no—
417#103—22no—
418#103—41no—
419#103—41no—
420#103—41no—
421C22⋊C8—22no—
422#97—41no—
423C4×C8—41no—
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#95—21no—
436#95D4×C3711yescharacteristic
437#95D4×C3711yescharacteristic
438C24C2×D4×C3711yescharacteristic
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—21no—
450C2×Q8#41×C3712yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C2×D4×C3711yescharacteristic
466C22×C4C2×D4×C3711yescharacteristic
467C22×C4C2×D4×C3711yescharacteristic
468C22×C4C2×D4×C3711yescharacteristic
469C22×C4C2×D4×C3711yescharacteristic
470C22×C4C24×C3711yescharacteristic
471Q16—44no—
472M16—44no—
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—21no—
482C2×C8—21no—
483C2×C8#41×C3712yes—
484C2×C8#41×C3712yes—
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—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4#41×C3712yes—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—42no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23C22×D4×C3711yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
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—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
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×C4—41no—
573C2×C4—41no—
574C2×C4C2×#41×C3711yescharacteristic
575C2×C4C2×#41×C3711yescharacteristic
576C2×C4C2×#41×C3711yescharacteristic
577C2×C4C2×#41×C3711yescharacteristic
578C2×C4H(5,𝔽2)×C3711yescharacteristic
579C2×C4H(5,𝔽2)×C3711yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C37×#53211yescharacteristic
592C22C37×#54611yescharacteristic
593C22C37×#54611yescharacteristic
594C22C37×#57511yescharacteristic
595C22C37×#57511yescharacteristic
596C22C37×#57811yescharacteristic
597C22C37×#57811yescharacteristic
598C4—41no—
599C4—41no—
600C4—42no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4C37×#52911yescharacteristic
612C4C37×#53811yescharacteristic
613C4C37×#55111yescharacteristic
614C4C37×#55911yescharacteristic
615C2—81no—
616C2C37×#255711yescharacteristic
617C2C37×#317711yescharacteristic
618C2C37×#318311yescharacteristic
619C2C37×#331311yescharacteristic
620C2C37×#331511yescharacteristic
621C2C37×#332711yescharacteristic
622C2C37×#332711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC24×C37C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#2074C2semidirect
5. C37×#2026C2semidirect
7. C37×#1991C2semidirect
8. C37×#1969C2semidirect
9. C37×#1935C2semidirect
10. C37×#1921C2semidirect
13. C37×#1878C2semidirect
14. C37×#1763C2semidirect
272. #29002C37direct (N × H)
307. #2074C2×C37semidirect
308. #2026C2×C37semidirect
310. #1991C2×C37semidirect
311. #1969C2×C37semidirect
312. #1935C2×C37semidirect
313. #1921C2×C37semidirect
316. #1878C2×C37semidirect
317. #1763C2×C37semidirect
370. C37#29002direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#24892
C37×#24212
C37×#20762
C37×#20742
C37×#20262
C37×#20012
C37×#19912
C37×#19692
C37×#19352
C37×#19212
C37×#18942
C37×#18782
C37×#17632
C37×#17532
#2900237