Finite Group Databasebeta

← C37×#28576 #22649829

Subgroups — C37×#28576 #22649829

Order 9472.

942 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#467C211yesmaximal, characteristic, complemented
2C2×C37×#465C211yesmaximal, characteristic
3C37×#2850C211yesmaximal, characteristic
4C4×C22⋊Q8×C37C211yesmaximal, characteristic, complemented
5C37×#2085C211yesmaximal, characteristic, complemented
6C37×#2074C211yesmaximal, characteristic, complemented
7C37×#2042C211yesmaximal, characteristic, complemented
8C37×#2015C211yesmaximal, characteristic, complemented
9C37×#1927C211yesmaximal, characteristic, complemented
10C37×#1925C211yesmaximal, characteristic, complemented
11C37×#1893C211yesmaximal, characteristic
12C37×#1892C211yesmaximal, characteristic, complemented
13C37×#1880C211yesmaximal, characteristic, complemented
14C37×#1878C211yesmaximal, characteristic, complemented
15C2×C37×#336C211yesmaximal, characteristic, complemented
16C22×Q16×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C23×C8×C37C2211yescharacteristic
19C23×C8×C37C2211yescharacteristic
20C2×#124×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×C4×Q8×C37C2211yescharacteristic
25C22×C42×C37C2211yescharacteristic
26C37×#467—24no—
27C37×#465—24no—
28C2×#107×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#103×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C37×#391C2211yescharacteristic
39C37×#391C2211yescharacteristic
40C37×#390C2211yescharacteristic
41C37×#389C2211yescharacteristic
42C37×#388—21no—
43C37×#388—21no—
44C37×#387—21no—
45C37×#386—21no—
46C37×#386—21no—
47C37×#385—21no—
48C37×#382C2211yescharacteristic
49C37×#380C2211yescharacteristic
50C4×C4⋊C4×C37—21no—
51C4×C4⋊C4×C37C2211yescharacteristic
52C4×C22⋊C4×C37—21no—
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×Q8×C37C2311yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37C2311yescharacteristic
65C23×C4×C37D411yescharacteristic
66C23×C4×C37D411yescharacteristic
67C23×C4×C37C2311yescharacteristic
68C2×Q16×C37—22no—
69C2×Q16×C37—22no—
70C2×Q16×C37—41no—
71C2×SD16×C37—22no—
72C2×SD16×C37—22no—
73C2×SD16×C37—41no—
74C22×C8×C37—22no—
75C22×C8×C37—22no—
76C22×C8×C37—22no—
77C22×C8×C37—22no—
78C22×C8×C37—41no—
79C22×C8×C37—41no—
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84#124×C37—41no—
85#124×C37—41no—
86C22⋊Q8×C37—22no—
87C22⋊Q8×C37—22no—
88C22⋊Q8×C37—22no—
89C22⋊Q8×C37D414yes—
90#121×C37—22no—
91#121×C37—22no—
92C4×Q8×C37—41no—
93C4×Q8×C37—41no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37—21no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37—21no—
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—21no—
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C42×C37—21no—
112C2×C42×C37—21no—
113C2×C42×C37—41no—
114C2×C42×C37—41no—
115C2×C42×C37D411yescharacteristic
116C2×C42×C37D411yescharacteristic
117C2×C42×C37C2311yescharacteristic
118C2×C42×C37C2311yescharacteristic
119#107×C37—22no—
120#106×C37—22no—
121#103×C37—22no—
122#103×C37—22no—
123#103×C37—22no—
124#103×C37—22no—
125#103×C37—41no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—41no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138C24×C37—21no—
139C24×C37C2×D411yescharacteristic
140C2×Q8×C37—21no—
141C2×Q8×C37—21no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37—21no—
151C2×Q8×C37C2×D412yes—
152C2×D4×C37—21no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—42no—
159C2×D4×C37—42no—
160C2×D4×C37—42no—
161C22×C4×C37—21no—
162C22×C4×C37—21no—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—22no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—41no—
176C22×C4×C37—41no—
177C22×C4×C37—41no—
178C22×C4×C37C2×D411yescharacteristic
179C22×C4×C37C2×D411yescharacteristic
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D412yes—
183C22×C4×C37C2×D411yescharacteristic
184C22×C4×C37#4112yes—
185C22×C4×C37C2411yescharacteristic
186Q16×C37—44no—
187SD16×C37—44no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37—21no—
198C2×C8×C37—44no—
199C2×C8×C37—44no—
200C2×C8×C37#4112yes—
201C2×C8×C37#4112yes—
202C4⋊C4×C37—24no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—21no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—21no—
212C4⋊C4×C37—42no—
213C4⋊C4×C37—42no—
214C4⋊C4×C37—42no—
215C4⋊C4×C37C2×D412yes—
216C22⋊C4×C37—24no—
217C22⋊C4×C37—42no—
218C22⋊C4×C37—42no—
219C22⋊C4×C37—42no—
220C22⋊C4×C37—42no—
221C22⋊C4×C37—42no—
222C22⋊C4×C37—42no—
223C22⋊C4×C37—42no—
224C42×C37—21no—
225C42×C37—21no—
226C42×C37—21no—
227C42×C37—21no—
228C42×C37—41no—
229C42×C37—41no—
230C42×C37—42no—
231C42×C37—42no—
232C23×C37—21no—
233C23×C37—21no—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—41no—
237C23×C37—41no—
238C23×C37—41no—
239C23×C37—41no—
240C23×C37—41no—
241C23×C37—41no—
242C23×C37—41no—
243C23×C37#12112yes—
244C23×C37#13512yes—
245C23×C37#13712yes—
246C23×C37C22×D411yescharacteristic
247Q8×C37—22no—
248Q8×C37—22no—
249Q8×C37—41no—
250Q8×C37—41no—
251Q8×C37—41no—
252Q8×C37—41no—
253Q8×C37—41no—
254Q8×C37—41no—
255D4×C37—41no—
256D4×C37—41no—
257D4×C37—41no—
258D4×C37—41no—
259D4×C37—84no—
260C2×C4×C37—21no—
261C2×C4×C37—21no—
262C2×C4×C37—21no—
263C2×C4×C37—21no—
264C2×C4×C37—22no—
265C2×C4×C37—22no—
266C2×C4×C37—22no—
267C2×C4×C37—22no—
268C2×C4×C37—22no—
269C2×C4×C37—22no—
270C2×C4×C37—21no—
271C2×C4×C37—21no—
272C2×C4×C37—21no—
273C2×C4×C37—21no—
274C2×C4×C37—21no—
275C2×C4×C37—21no—
276C2×C4×C37—21no—
277C2×C4×C37—21no—
278C2×C4×C37—21no—
279C2×C4×C37—44no—
280C2×C4×C37—44no—
281C2×C4×C37—41no—
282C2×C4×C37—41no—
283C2×C4×C37—41no—
284C2×C4×C37—41no—
285C2×C4×C37—41no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37—41no—
292C2×C4×C37—41no—
293C2×C4×C37—41no—
294C2×C4×C37—41no—
295C2×C4×C37—41no—
296C2×C4×C37—41no—
297C2×C4×C37—41no—
298C2×C4×C37—41no—
299C2×C4×C37—41no—
300C2×C4×C37#12112yes—
301C2×C4×C37#13512yes—
302C2×C4×C37C22×D411yescharacteristic
303C2×C4×C37C2×#4111yescharacteristic
304C2×C4×C37C2×#4111yescharacteristic
305C2×C4×C37C2×#4111yescharacteristic
306C2×C4×C37H(5,𝔽2)11yescharacteristic
307C2×C4×C37H(5,𝔽2)11yescharacteristic
308C8×C37—22no—
309C8×C37—22no—
310C8×C37—41no—
311C8×C37—41no—
312#28576C3711yesmaximal, characteristic, direct product factor, Sylow
313C22×C37—22no—
314C22×C37—22no—
315C22×C37—22no—
316C22×C37—22no—
317C22×C37—22no—
318C22×C37—22no—
319C22×C37—81no—
320C22×C37—81no—
321C22×C37—81no—
322C22×C37—81no—
323C22×C37—81no—
324C22×C37—81no—
325C22×C37—81no—
326C22×C37#46414yes—
327C22×C37C2×#12111yescharacteristic
328C22×C37#53211yescharacteristic
329C22×C37#53411yescharacteristic
330C22×C37C2×#13511yescharacteristic
331C22×C37C2×#13511yescharacteristic
332C22×C37C2×#13711yescharacteristic
333C22×C37#57511yescharacteristic
334C4×C37—22no—
335C4×C37—22no—
336C4×C37—41no—
337C4×C37—41no—
338C4×C37—41no—
339C4×C37—42no—
340C4×C37—42no—
341C4×C37—81no—
342C4×C37—81no—
343C4×C37—81no—
344C4×C37—81no—
345C4×C37—81no—
346C4×C37#54611yescharacteristic
347C4×C37#54611yescharacteristic
348C4×C37#55311yescharacteristic
349C4×C37#55311yescharacteristic
350C2×#467C2×C3711yescharacteristic, complemented
351C2×#465C2×C3711yescharacteristic
352#2850C2×C3711yescharacteristic
353C4×C22⋊Q8C2×C3711yescharacteristic, complemented
354#2085C2×C3711yescharacteristic, complemented
355#2074C2×C3711yescharacteristic, complemented
356#2042C2×C3711yescharacteristic, complemented
357#2015C2×C3711yescharacteristic, complemented
358#1927C2×C3711yescharacteristic, complemented
359#1925C2×C3711yescharacteristic, complemented
360#1893C2×C3711yescharacteristic
361#1892C2×C3711yescharacteristic, complemented
362#1880C2×C3711yescharacteristic, complemented
363#1878C2×C3711yescharacteristic, complemented
364C2×#336C2×C3711yescharacteristic, complemented
365C2×C37—24no—
366C2×C37—161no—
367C2×C37#254311yescharacteristic
368C2×C37C2×#46411yescharacteristic
369C2×C37#303511yescharacteristic
370C2×C37#316811yescharacteristic
371C2×C37#318111yescharacteristic
372C2×C37#319011yescharacteristic
373C2×C37#319111yescharacteristic
374C22×Q16C22×C3711yescharacteristic
375C22×SD16C22×C3711yescharacteristic
376C23×C8C22×C3711yescharacteristic
377C23×C8C22×C3711yescharacteristic
378C2×#124C22×C3711yescharacteristic
379C2×C22⋊Q8C22×C3711yescharacteristic
380C2×C22⋊Q8C22×C3711yescharacteristic
381C2×#121C22×C3711yescharacteristic
382C2×C4×Q8C22×C3711yescharacteristic
383C22×C42C22×C3711yescharacteristic
384#467—24no—
385#465—24no—
386C2×#107C22×C3711yescharacteristic
387C2×#106C22×C3711yescharacteristic
388C2×#103C22×C3711yescharacteristic
389C2×#103C22×C3711yescharacteristic
390C2×#103C22×C3711yescharacteristic
391C2×#103C22×C3711yescharacteristic
392C2×#103C22×C3711yescharacteristic
393C2×#102C22×C3711yescharacteristic
394C2×#102C22×C3711yescharacteristic
395C2×#102C22×C3711yescharacteristic
396#391C22×C3711yescharacteristic
397#391C22×C3711yescharacteristic
398#390C22×C3711yescharacteristic
399#389C22×C3711yescharacteristic
400#388—21no—
401#388—21no—
402#387—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#382C22×C3711yescharacteristic
407#380C22×C3711yescharacteristic
408C4×C4⋊C4—21no—
409C4×C4⋊C4C22×C3711yescharacteristic
410C4×C22⋊C4—21no—
411#340C22×C3711yescharacteristic
412#340C22×C3711yescharacteristic
413#340C22×C3711yescharacteristic
414#340C22×C3711yescharacteristic
415#336C22×C3711yescharacteristic
416#336C22×C3711yescharacteristic
417#336C22×C3711yescharacteristic
418#336C22×C3711yescharacteristic
419C37#2857611yescharacteristic, direct product factor, Sylow
420C22×Q8C23×C3711yescharacteristic
421C22×Q8C23×C3711yescharacteristic
422C22×D4—21no—
423C22×D4C23×C3711yescharacteristic
424C23×C4D4×C3711yescharacteristic
425C23×C4D4×C3711yescharacteristic
426C23×C4C23×C3711yescharacteristic
427C2×Q16—22no—
428C2×Q16—22no—
429C2×Q16—41no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—41no—
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8—41no—
439C22×C8C23×C3711yescharacteristic
440C22×C8C23×C3711yescharacteristic
441C22×C8C23×C3711yescharacteristic
442C22×C8C23×C3711yescharacteristic
443#124—41no—
444#124—41no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8D4×C3714yes—
449#121—22no—
450#121—22no—
451C4×Q8—41no—
452C4×Q8—41no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4C23×C3711yescharacteristic
458C2×C4⋊C4C23×C3711yescharacteristic
459C2×C4⋊C4C23×C3711yescharacteristic
460C2×C4⋊C4C23×C3711yescharacteristic
461C2×C4⋊C4C23×C3711yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—41no—
473C2×C42—41no—
474C2×C42D4×C3711yescharacteristic
475C2×C42D4×C3711yescharacteristic
476C2×C42C23×C3711yescharacteristic
477C2×C42C23×C3711yescharacteristic
478#107—22no—
479#106—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—22no—
484#103—41no—
485#102—22no—
486#102—22no—
487#102—41no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—21no—
498C24C2×D4×C3711yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C2×D4×C3712yes—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4C2×D4×C3711yescharacteristic
538C22×C4C2×D4×C3711yescharacteristic
539C22×C4C2×D4×C3711yescharacteristic
540C22×C4C2×D4×C3711yescharacteristic
541C22×C4C2×D4×C3712yes—
542C22×C4C2×D4×C3711yescharacteristic
543C22×C4#41×C3712yes—
544C22×C4C24×C3711yescharacteristic
545Q16—44no—
546SD16—44no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8#41×C3712yes—
560C2×C8#41×C3712yes—
561C4⋊C4—24no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4C2×D4×C3712yes—
575C22⋊C4—24no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—41no—
588C42—41no—
589C42—42no—
590C42—42no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23#121×C3712yes—
603C23#135×C3712yes—
604C23#137×C3712yes—
605C23C22×D4×C3711yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—84no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4#121×C3712yes—
660C2×C4#135×C3712yes—
661C2×C4C22×D4×C3711yescharacteristic
662C2×C4C2×#41×C3711yescharacteristic
663C2×C4C2×#41×C3711yescharacteristic
664C2×C4C2×#41×C3711yescharacteristic
665C2×C4H(5,𝔽2)×C3711yescharacteristic
666C2×C4H(5,𝔽2)×C3711yescharacteristic
667C8—22no—
668C8—22no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22C37×#46414yes—
685C22C2×#121×C3711yescharacteristic
686C22C37×#53211yescharacteristic
687C22C37×#53411yescharacteristic
688C22C2×#135×C3711yescharacteristic
689C22C2×#135×C3711yescharacteristic
690C22C2×#137×C3711yescharacteristic
691C22C37×#57511yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C37×#54611yescharacteristic
705C4C37×#54611yescharacteristic
706C4C37×#55311yescharacteristic
707C4C37×#55311yescharacteristic
708C2—24no—
709C2—161no—
710C2C37×#254311yescharacteristic
711C2C2×C37×#46411yescharacteristic
712C2C37×#303511yescharacteristic
713C2C37×#316811yescharacteristic
714C2C37×#318111yescharacteristic
715C2C37×#319011yescharacteristic
716C2C37×#319111yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#467C2semidirect
4. C4×C22⋊Q8×C37C2semidirect
5. C37×#2085C2semidirect
6. C37×#2074C2semidirect
7. C37×#2042C2semidirect
8. C37×#2015C2semidirect
9. C37×#1927C2semidirect
10. C37×#1925C2semidirect
12. C37×#1892C2semidirect
13. C37×#1880C2semidirect
14. C37×#1878C2semidirect
15. C2×C37×#336C2semidirect
312. #28576C37direct (N × H)
350. C2×#467C2×C37semidirect
353. C4×C22⋊Q8C2×C37semidirect
354. #2085C2×C37semidirect
355. #2074C2×C37semidirect
356. #2042C2×C37semidirect
357. #2015C2×C37semidirect
358. #1927C2×C37semidirect
359. #1925C2×C37semidirect
361. #1892C2×C37semidirect
362. #1880C2×C37semidirect
363. #1878C2×C37semidirect
364. C2×#336C2×C37semidirect
419. C37#28576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4672
C2×C37×#4652
C37×#28502
C4×C22⋊Q8×C372
C37×#20852
C37×#20742
C37×#20422
C37×#20152
C37×#19272
C37×#19252
C37×#18932
C37×#18922
C37×#18802
C37×#18782
C2×C37×#3362
#2857637