Finite Group Databasebeta

← C37×#24884 #22646137

Subgroups — C37×#24884 #22646137

Order 9472.

972 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#483C211yesmaximal, characteristic, complemented
2C2×C37×#419C211yesmaximal, characteristic, complemented
3C37×#2409C211yesmaximal, characteristic
4C37×#2352C211yesmaximal, characteristic
5C37×#2097C211yesmaximal, characteristic, complemented
6C37×#2074C211yesmaximal, characteristic, complemented
7C37×#2036C211yesmaximal, characteristic, complemented
8C37×#2036C211yesmaximal, characteristic, complemented
9C37×#1928C211yesmaximal, characteristic, complemented
10C37×#1927C211yesmaximal, characteristic, complemented
11C37×#1872C211yesmaximal, characteristic, complemented
12C37×#1870C211yesmaximal, characteristic
13C37×#1854C211yesmaximal, characteristic, complemented
14C37×#1809C211yesmaximal, characteristic, complemented
15C37×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C2×C22⋊Q8×C37C2211yescharacteristic
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×C4×D4×C37C2211yescharacteristic
21C2×#117×C37C2211yescharacteristic
22C22×C4⋊C4×C37C2211yescharacteristic
23C37×#483—24no—
24C2×#107×C37C2211yescharacteristic
25C2×#107×C37C2211yescharacteristic
26C2×#106×C37C2211yescharacteristic
27C2×#106×C37C2211yescharacteristic
28C37×#419—24no—
29C2×#103×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#103×C37C2211yescharacteristic
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C37×#395—21no—
41C37×#393—21no—
42C37×#391C2211yescharacteristic
43C37×#391C2211yescharacteristic
44C37×#388—21no—
45C37×#387—21no—
46C37×#386—21no—
47C37×#386—21no—
48C37×#385—21no—
49C37×#382C2211yescharacteristic
50C37×#380C2211yescharacteristic
51C37×#380C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C4×C4⋊C4×C37C2211yescharacteristic
54C4×C22⋊C4×C37—21no—
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37—21no—
62C22×Q8×C37—22no—
63C22×Q8×C37—22no—
64C22×Q8×C37—22no—
65C22×Q8×C37—22no—
66C22×Q8×C37—41no—
67C22×Q8×C37—41no—
68C22×Q8×C37C2311yescharacteristic
69C22×Q8×C37C2311yescharacteristic
70C22×D4×C37D411yescharacteristic
71C23×C4×C37—21no—
72C23×C4×C37—21no—
73C23×C4×C37C2311yescharacteristic
74C23×C4×C37C2311yescharacteristic
75C2×M16×C37—22no—
76C2×M16×C37—22no—
77C2×M16×C37—41no—
78C22×C8×C37C2311yescharacteristic
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—41no—
85C22⋊Q8×C37—41no—
86C4×D4×C37—22no—
87C4×D4×C37—22no—
88#117×C37—22no—
89#117×C37—41no—
90C2×C4⋊C4×C37—22no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—41no—
95C2×C4⋊C4×C37D411yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C22⋊C4×C37—21no—
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×C37D411yescharacteristic
109C2×C22⋊C4×C37D411yescharacteristic
110C2×C42×C37—21no—
111C2×C42×C37—21no—
112C2×C42×C37C2311yescharacteristic
113#107×C37—41no—
114#107×C37—41no—
115#106×C37—22no—
116#106×C37—22no—
117#103×C37—22no—
118#103×C37—22no—
119#103×C37—22no—
120#103×C37—22no—
121#103×C37—22no—
122#103×C37—41no—
123#103×C37—41no—
124#103×C37D414yescomplemented
125C22⋊C8×C37—22no—
126C22⋊C8×C37—22no—
127C22⋊C8×C37—41no—
128#95×C37—21no—
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×C37C2×D411yescharacteristic
139C24×C37C2×D411yescharacteristic
140C2×Q8×C37—21no—
141C2×Q8×C37—21no—
142C2×Q8×C37—28no—
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×C37—42no—
152C2×Q8×C37—42no—
153C2×Q8×C37—44no—
154C2×Q8×C37—44no—
155C2×Q8×C37—44no—
156C2×Q8×C37—42no—
157C2×Q8×C37C2×D412yes—
158C2×Q8×C37#4112yes—
159C2×D4×C37—22no—
160C2×D4×C37—22no—
161C2×D4×C37—41no—
162C22×C4×C37—21no—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—42no—
181C22×C4×C37—42no—
182C22×C4×C37—42no—
183C22×C4×C37—42no—
184C22×C4×C37—42no—
185C22×C4×C37—81no—
186C22×C4×C37C2×D411yescharacteristic
187C22×C4×C37C2×D411yescharacteristic
188C22×C4×C37C2×D411yescharacteristic
189C22×C4×C37C2×D411yescharacteristic
190C22×C4×C37#4112yes—
191C22×C4×C37#4112yes—
192C22×C4×C37C2411yescharacteristic
193M16×C37—44no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37—21no—
198C2×C8×C37—21no—
199C2×C8×C37—21no—
200C2×C8×C37—21no—
201C2×C8×C37—21no—
202C2×C8×C37—21no—
203C2×C8×C37—21no—
204C2×C8×C37—21no—
205C2×C8×C37C2×D412yes—
206C4⋊C4×C37—22no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—21no—
212C4⋊C4×C37—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—42no—
219C4⋊C4×C37—42no—
220C4⋊C4×C37—42no—
221C4⋊C4×C37C2×D412yes—
222C22⋊C4×C37—22no—
223C22⋊C4×C37—22no—
224C22⋊C4×C37—42no—
225C22⋊C4×C37—42no—
226C22⋊C4×C37—42no—
227C22⋊C4×C37—42no—
228C22⋊C4×C37—42no—
229C22⋊C4×C37—81no—
230C42×C37—21no—
231C42×C37—21no—
232C42×C37—42no—
233C42×C37—81no—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—21no—
238C23×C37—21no—
239C23×C37—21no—
240C23×C37—21no—
241C23×C37—21no—
242C23×C37—21no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37#12312yes—
247C23×C37#13712yes—
248C23×C37C22×D411yescharacteristic
249Q8×C37—22no—
250Q8×C37—22no—
251Q8×C37—22no—
252Q8×C37—22no—
253Q8×C37—48no—
254Q8×C37—41no—
255Q8×C37—41no—
256Q8×C37—41no—
257Q8×C37—41no—
258D4×C37—44no—
259C2×C4×C37—21no—
260C2×C4×C37—21no—
261C2×C4×C37—22no—
262C2×C4×C37—22no—
263C2×C4×C37—22no—
264C2×C4×C37—22no—
265C2×C4×C37—21no—
266C2×C4×C37—21no—
267C2×C4×C37—21no—
268C2×C4×C37—22no—
269C2×C4×C37—22no—
270C2×C4×C37—21no—
271C2×C4×C37—22no—
272C2×C4×C37—21no—
273C2×C4×C37—21no—
274C2×C4×C37—21no—
275C2×C4×C37—21no—
276C2×C4×C37—21no—
277C2×C4×C37—48no—
278C2×C4×C37—41no—
279C2×C4×C37—41no—
280C2×C4×C37—41no—
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—41no—
301C2×C4×C37—41no—
302C2×C4×C37—41no—
303C2×C4×C37—84no—
304C2×C4×C37#12312yes—
305C2×C4×C37C22×D411yescharacteristic
306C2×C4×C37C2×#4111yescharacteristic
307C2×C4×C37C2×#4111yescharacteristic
308C2×C4×C37C2×#4111yescharacteristic
309C2×C4×C37H(5,𝔽2)11yescharacteristic
310C2×C4×C37H(5,𝔽2)11yescharacteristic
311C8×C37—22no—
312C8×C37—41no—
313C8×C37—41no—
314C8×C37—41no—
315#24884C3711yesmaximal, characteristic, direct product factor, Sylow
316C22×C37—22no—
317C22×C37—22no—
318C22×C37—22no—
319C22×C37—22no—
320C22×C37—22no—
321C22×C37—22no—
322C22×C37—41no—
323C22×C37—41no—
324C22×C37—41no—
325C22×C37—41no—
326C22×C37—41no—
327C22×C37—41no—
328C22×C37—41no—
329C22×C37—41no—
330C22×C37C2×#12311yescharacteristic
331C22×C37D4211yescharacteristic
332C22×C37#54611yescharacteristic
333C22×C37C2×#13711yescharacteristic
334C22×C37#57511yescharacteristic
335C22×C37#57711yescharacteristic
336C22×C37#57811yescharacteristic
337C4×C37—22no—
338C4×C37—41no—
339C4×C37—41no—
340C4×C37—41no—
341C4×C37—42no—
342C4×C37—42no—
343C4×C37—42no—
344C4×C37—81no—
345C4×C37—81no—
346C4×C37—81no—
347C4×C37—81no—
348C4×C37—81no—
349C4×C37#52511yescharacteristic
350C4×C37#53811yescharacteristic
351C4×C37#54611yescharacteristic
352C4×C37#55111yescharacteristic
353C2×#483C2×C3711yescharacteristic, complemented
354C2×#419C2×C3711yescharacteristic, complemented
355#2409C2×C3711yescharacteristic
356#2352C2×C3711yescharacteristic
357#2097C2×C3711yescharacteristic, complemented
358#2074C2×C3711yescharacteristic, complemented
359#2036C2×C3711yescharacteristic, complemented
360#2036C2×C3711yescharacteristic, complemented
361#1928C2×C3711yescharacteristic, complemented
362#1927C2×C3711yescharacteristic, complemented
363#1872C2×C3711yescharacteristic, complemented
364#1870C2×C3711yescharacteristic
365#1854C2×C3711yescharacteristic, complemented
366#1809C2×C3711yescharacteristic, complemented
367#1787C2×C3711yescharacteristic, complemented
368C2×C37—42no—
369C2×C37—42no—
370C2×C37#241811yescharacteristic
371C2×C37#309511yescharacteristic
372C2×C37#309711yescharacteristic
373C2×C37#326611yescharacteristic
374C2×C37#327711yescharacteristic
375C2×C37#331211yescharacteristic
376C2×C37#332611yescharacteristic
377C23×Q8C22×C3711yescharacteristic
378C22×M16C22×C3711yescharacteristic
379C2×C22⋊Q8C22×C3711yescharacteristic
380C2×C22⋊Q8C22×C3711yescharacteristic
381C2×C4×D4C22×C3711yescharacteristic
382C2×#117C22×C3711yescharacteristic
383C22×C4⋊C4C22×C3711yescharacteristic
384#483—24no—
385C2×#107C22×C3711yescharacteristic
386C2×#107C22×C3711yescharacteristic
387C2×#106C22×C3711yescharacteristic
388C2×#106C22×C3711yescharacteristic
389#419—24no—
390C2×#103C22×C3711yescharacteristic
391C2×#103C22×C3711yescharacteristic
392C2×#103C22×C3711yescharacteristic
393C2×#103C22×C3711yescharacteristic
394C2×#103C22×C3711yescharacteristic
395C2×#103C22×C3711yescharacteristic
396C2×#103C22×C3711yescharacteristic
397C2×#103C22×C3711yescharacteristic
398C2×C22⋊C8C22×C3711yescharacteristic
399C2×C22⋊C8C22×C3711yescharacteristic
400C2×C22⋊C8C22×C3711yescharacteristic
401#395—21no—
402#393—21no—
403#391C22×C3711yescharacteristic
404#391C22×C3711yescharacteristic
405#388—21no—
406#387—21no—
407#386—21no—
408#386—21no—
409#385—21no—
410#382C22×C3711yescharacteristic
411#380C22×C3711yescharacteristic
412#380C22×C3711yescharacteristic
413#380C22×C3711yescharacteristic
414C4×C4⋊C4C22×C3711yescharacteristic
415C4×C22⋊C4—21no—
416#340C22×C3711yescharacteristic
417#340C22×C3711yescharacteristic
418#340C22×C3711yescharacteristic
419#340C22×C3711yescharacteristic
420#336C22×C3711yescharacteristic
421#336C22×C3711yescharacteristic
422C37#2488411yescharacteristic, direct product factor, Sylow
423C22×Q8—21no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—41no—
429C22×Q8—41no—
430C22×Q8C23×C3711yescharacteristic
431C22×Q8C23×C3711yescharacteristic
432C22×D4D4×C3711yescharacteristic
433C23×C4—21no—
434C23×C4—21no—
435C23×C4C23×C3711yescharacteristic
436C23×C4C23×C3711yescharacteristic
437C2×M16—22no—
438C2×M16—22no—
439C2×M16—41no—
440C22×C8C23×C3711yescharacteristic
441C22×C8C23×C3711yescharacteristic
442C22×C8C23×C3711yescharacteristic
443C22×C8C23×C3711yescharacteristic
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—41no—
447C22⋊Q8—41no—
448C4×D4—22no—
449C4×D4—22no—
450#117—22no—
451#117—41no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4D4×C3711yescharacteristic
458C2×C4⋊C4C23×C3711yescharacteristic
459C2×C4⋊C4C23×C3711yescharacteristic
460C2×C4⋊C4C23×C3711yescharacteristic
461C2×C4⋊C4C23×C3711yescharacteristic
462C2×C4⋊C4C23×C3711yescharacteristic
463C2×C4⋊C4C23×C3711yescharacteristic
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×C22⋊C4D4×C3711yescharacteristic
471C2×C22⋊C4D4×C3711yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C3711yescharacteristic
475#107—41no—
476#107—41no—
477#106—22no—
478#106—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—22no—
484#103—41no—
485#103—41no—
486#103D4×C3714yescomplemented
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—41no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—21no—
500C24C2×D4×C3711yescharacteristic
501C24C2×D4×C3711yescharacteristic
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—28no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—42no—
519C2×Q8C2×D4×C3712yes—
520C2×Q8#41×C3712yes—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—41no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—81no—
548C22×C4C2×D4×C3711yescharacteristic
549C22×C4C2×D4×C3711yescharacteristic
550C22×C4C2×D4×C3711yescharacteristic
551C22×C4C2×D4×C3711yescharacteristic
552C22×C4#41×C3712yes—
553C22×C4#41×C3712yes—
554C22×C4C24×C3711yescharacteristic
555M16—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8C2×D4×C3712yes—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4C2×D4×C3712yes—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C42—21no—
593C42—21no—
594C42—42no—
595C42—81no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23#123×C3712yes—
609C23#137×C3712yes—
610C23C22×D4×C3711yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—48no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—44no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—48no—
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—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4#123×C3712yes—
667C2×C4C22×D4×C3711yescharacteristic
668C2×C4C2×#41×C3711yescharacteristic
669C2×C4C2×#41×C3711yescharacteristic
670C2×C4C2×#41×C3711yescharacteristic
671C2×C4H(5,𝔽2)×C3711yescharacteristic
672C2×C4H(5,𝔽2)×C3711yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C2×#123×C3711yescharacteristic
692C22D42×C3711yescharacteristic
693C22C37×#54611yescharacteristic
694C22C2×#137×C3711yescharacteristic
695C22C37×#57511yescharacteristic
696C22C37×#57711yescharacteristic
697C22C37×#57811yescharacteristic
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C37×#52511yescharacteristic
711C4C37×#53811yescharacteristic
712C4C37×#54611yescharacteristic
713C4C37×#55111yescharacteristic
714C2—42no—
715C2—42no—
716C2C37×#241811yescharacteristic
717C2C37×#309511yescharacteristic
718C2C37×#309711yescharacteristic
719C2C37×#326611yescharacteristic
720C2C37×#327711yescharacteristic
721C2C37×#331211yescharacteristic
722C2C37×#332611yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×D4×C37D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#483C2semidirect
2. C2×C37×#419C2semidirect
5. C37×#2097C2semidirect
6. C37×#2074C2semidirect
7. C37×#2036C2semidirect
8. C37×#2036C2semidirect
9. C37×#1928C2semidirect
10. C37×#1927C2semidirect
11. C37×#1872C2semidirect
13. C37×#1854C2semidirect
14. C37×#1809C2semidirect
15. C37×#1787C2semidirect
124. #103×C37D4semidirect
315. #24884C37direct (N × H)
353. C2×#483C2×C37semidirect
354. C2×#419C2×C37semidirect
357. #2097C2×C37semidirect
358. #2074C2×C37semidirect
359. #2036C2×C37semidirect
360. #2036C2×C37semidirect
361. #1928C2×C37semidirect
362. #1927C2×C37semidirect
363. #1872C2×C37semidirect
365. #1854C2×C37semidirect
366. #1809C2×C37semidirect
367. #1787C2×C37semidirect
422. C37#24884direct (N × H)
486. #103D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4832
C2×C37×#4192
C37×#24092
C37×#23522
C37×#20972
C37×#20742
C37×#20362
C37×#19282
C37×#19272
C37×#18722
C37×#18702
C37×#18542
C37×#18092
C37×#17872
#2488437