Finite Group Databasebeta

← C37×#24668 #22645921

Subgroups — C37×#24668 #22645921

Order 9472.

914 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#460C211yesmaximal, characteristic, complemented
2C2×C37×#433C211yesmaximal, characteristic, complemented
3C37×#2619C211yesmaximal, characteristic
4C37×#2323C211yesmaximal, characteristic, complemented
5C37×#2034C211yesmaximal, characteristic, complemented
6C37×#2033C211yesmaximal, characteristic, complemented
7C37×#2000C211yesmaximal, characteristic, complemented
8C37×#2000C211yesmaximal, characteristic, complemented
9C37×#1982C211yesmaximal, characteristic, complemented
10C37×#1973C211yesmaximal, characteristic, complemented
11C37×#1968C211yesmaximal, characteristic, complemented
12C37×#1949C211yesmaximal, characteristic, complemented
13C37×#1936C211yesmaximal, characteristic, complemented
14C37×#1934C211yesmaximal, characteristic, complemented
15C37×#1805C211yesmaximal, characteristic, complemented
16C22×SD16×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C2×#127×C37C2211yescharacteristic
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×#121×C37C2211yescharacteristic
21C2×#121×C37C2211yescharacteristic
22C2×C4×Q8×C37C2211yescharacteristic
23C2×#117×C37C2211yescharacteristic
24C37×#460—24no—
25C37×#433—24no—
26C2×#107×C37C2211yescharacteristic
27C2×#106×C37C2211yescharacteristic
28C2×C4⋊C8×C37C2211yescharacteristic
29C2×C4⋊C8×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C2×#97×C37C2211yescharacteristic
41C2×C4×C8×C37C2211yescharacteristic
42C37×#394—21no—
43C37×#394—21no—
44C37×#392—21no—
45C37×#392—21no—
46C37×#391C2211yescharacteristic
47C37×#390C2211yescharacteristic
48C37×#390C2211yescharacteristic
49C37×#389—21no—
50C37×#389C2211yescharacteristic
51C37×#388—21no—
52C37×#388—21no—
53C37×#387—21no—
54C37×#382C2211yescharacteristic
55C37×#380C2211yescharacteristic
56C4×C4⋊C4×C37C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37C2311yescharacteristic
67C22×D4×C37C2311yescharacteristic
68C23×C4×C37C2311yescharacteristic
69C2×SD16×C37—22no—
70C2×SD16×C37—22no—
71C2×SD16×C37—22no—
72C2×SD16×C37—22no—
73C2×SD16×C37—41no—
74C2×SD16×C37—41no—
75C22×C8×C37C2311yescharacteristic
76C22×C8×C37C2311yescharacteristic
77C22×C8×C37C2311yescharacteristic
78C22×C8×C37C2311yescharacteristic
79#127×C37—22no—
80#127×C37—22no—
81C22⋊Q8×C37—22no—
82C22⋊Q8×C37—22no—
83#121×C37—41no—
84#121×C37—41no—
85#121×C37—41no—
86#121×C37—41no—
87C4×Q8×C37—22no—
88C4×Q8×C37—22no—
89#117×C37—22no—
90#117×C37—22no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37D411yescharacteristic
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×C22⋊C4×C37—21no—
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×C37—21no—
109C2×C22⋊C4×C37D411yescharacteristic
110C2×C22⋊C4×C37D411yescharacteristic
111C2×C42×C37—21no—
112C2×C42×C37—21no—
113C2×C42×C37C2311yescharacteristic
114C2×C42×C37C2311yescharacteristic
115#107×C37—41no—
116#106×C37—41no—
117C4⋊C8×C37—22no—
118C4⋊C8×C37D414yescomplemented
119#103×C37—41no—
120#103×C37—41no—
121#102×C37—22no—
122#102×C37—22no—
123#102×C37—22no—
124#102×C37—22no—
125#102×C37—41no—
126#102×C37—41no—
127C22⋊C8×C37—22no—
128C22⋊C8×C37—22no—
129#97×C37—22no—
130C4×C8×C37—22no—
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×C37—21no—
140C24×C37C2×D411yescharacteristic
141C2×Q8×C37—21no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37#4112yes—
147C2×D4×C37—21no—
148C2×D4×C37—21no—
149C2×D4×C37—21no—
150C2×D4×C37—21no—
151C2×D4×C37—21no—
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—21no—
159C2×D4×C37—42no—
160C2×D4×C37—42no—
161C2×D4×C37—42no—
162C2×D4×C37—42no—
163C2×D4×C37—81no—
164C2×D4×C37—81no—
165C2×D4×C37—81no—
166C2×D4×C37—81no—
167C2×D4×C37—81no—
168C2×D4×C37—81no—
169C2×D4×C37—81no—
170C2×D4×C37—81no—
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—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37C2×D411yescharacteristic
184C22×C4×C37C2×D411yescharacteristic
185C22×C4×C37C2×D411yescharacteristic
186C22×C4×C37C2×D411yescharacteristic
187C22×C4×C37C2×D411yescharacteristic
188C22×C4×C37C2411yescharacteristic
189SD16×C37—44no—
190SD16×C37—44no—
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—21no—
199C2×C8×C37—21no—
200C2×C8×C37—21no—
201C2×C8×C37C2×D412yes—
202C2×C8×C37C2×D412yes—
203C4⋊C4×C37—24no—
204C4⋊C4×C37—22no—
205C4⋊C4×C37—22no—
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—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—42no—
216C4⋊C4×C37—81no—
217C4⋊C4×C37#4112yes—
218C22⋊C4×C37—24no—
219C22⋊C4×C37—22no—
220C22⋊C4×C37—22no—
221C22⋊C4×C37—42no—
222C22⋊C4×C37—42no—
223C22⋊C4×C37—81no—
224C22⋊C4×C37—81no—
225C22⋊C4×C37—81no—
226C22⋊C4×C37—81no—
227C22⋊C4×C37—81no—
228C42×C37—21no—
229C42×C37—21no—
230C42×C37—42no—
231C42×C37—81no—
232C42×C37C2×D412yes—
233C42×C37#4112yes—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—21no—
238C23×C37—21no—
239C23×C37—21no—
240C23×C37—21no—
241C23×C37—41no—
242C23×C37—41no—
243C23×C37—41no—
244C23×C37—41no—
245C23×C37—41no—
246C23×C37—41no—
247C23×C37—41no—
248C23×C37—41no—
249C23×C37—41no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37—41no—
254C23×C37—41no—
255C23×C37C22×D411yescharacteristic
256Q8×C37—22no—
257Q8×C37—22no—
258Q8×C37—41no—
259Q8×C37—41no—
260D4×C37—41no—
261D4×C37—41no—
262D4×C37—41no—
263D4×C37—41no—
264D4×C37—41no—
265D4×C37—41no—
266D4×C37—41no—
267D4×C37—41no—
268D4×C37—84no—
269D4×C37—84no—
270D4×C37—84no—
271D4×C37—84no—
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—22no—
280C2×C4×C37—22no—
281C2×C4×C37—21no—
282C2×C4×C37—21no—
283C2×C4×C37—21no—
284C2×C4×C37—21no—
285C2×C4×C37—21no—
286C2×C4×C37—21no—
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—41no—
304C2×C4×C37—41no—
305C2×C4×C37—41no—
306C2×C4×C37—41no—
307C2×C4×C37#12112yes—
308C2×C4×C37#12112yes—
309C2×C4×C37C22×D411yescharacteristic
310C2×C4×C37C2×#4111yescharacteristic
311C2×C4×C37C2×#4111yescharacteristic
312C2×C4×C37C2×#4111yescharacteristic
313C2×C4×C37H(5,𝔽2)11yescharacteristic
314C2×C4×C37H(5,𝔽2)11yescharacteristic
315C8×C37—22no—
316C8×C37—22no—
317C8×C37—41no—
318C8×C37—41no—
319#24668C3711yesmaximal, characteristic, direct product factor, Sylow
320C22×C37—41no—
321C22×C37—41no—
322C22×C37—41no—
323C22×C37—41no—
324C22×C37—41no—
325C22×C37—41no—
326C22×C37—41no—
327C22×C37—81no—
328C22×C37—81no—
329C22×C37—81no—
330C22×C37—81no—
331C22×C37—81no—
332C22×C37—81no—
333C22×C37—81no—
334C22×C37—81no—
335C22×C37—81no—
336C22×C37—81no—
337C22×C37—81no—
338C22×C37—81no—
339C22×C37—81no—
340C22×C37—81no—
341C22×C37C2×#12111yescharacteristic
342C22×C37#52511yescharacteristic
343C22×C37#53511yescharacteristic
344C22×C37#57611yescharacteristic
345C22×C37#57711yescharacteristic
346C22×C37#57711yescharacteristic
347C22×C37#57711yescharacteristic
348C4×C37—22no—
349C4×C37—22no—
350C4×C37—42no—
351C4×C37—41no—
352C4×C37—42no—
353C4×C37—41no—
354C4×C37—41no—
355C4×C37—81no—
356C4×C37—81no—
357C4×C37—81no—
358C4×C37—81no—
359C4×C37#54611yescharacteristic
360C4×C37#55011yescharacteristic
361C4×C37#55311yescharacteristic
362C4×C37#55511yescharacteristic
363C2×#460C2×C3711yescharacteristic, complemented
364C2×#433C2×C3711yescharacteristic, complemented
365#2619C2×C3711yescharacteristic
366#2323C2×C3711yescharacteristic, complemented
367#2034C2×C3711yescharacteristic, complemented
368#2033C2×C3711yescharacteristic, complemented
369#2000C2×C3711yescharacteristic, complemented
370#2000C2×C3711yescharacteristic, complemented
371#1982C2×C3711yescharacteristic, complemented
372#1973C2×C3711yescharacteristic, complemented
373#1968C2×C3711yescharacteristic, complemented
374#1949C2×C3711yescharacteristic, complemented
375#1936C2×C3711yescharacteristic, complemented
376#1934C2×C3711yescharacteristic, complemented
377#1805C2×C3711yescharacteristic, complemented
378C2×C37—81no—
379C2×C37—161no—
380C2×C37—161no—
381C2×C37#241411yescharacteristic
382C2×C37#305711yescharacteristic
383C2×C37#306211yescharacteristic
384C2×C37#311911yescharacteristic
385C2×C37#312611yescharacteristic
386C2×C37#322211yescharacteristic
387C2×C37#322411yescharacteristic
388C22×SD16C22×C3711yescharacteristic
389C22×SD16C22×C3711yescharacteristic
390C2×#127C22×C3711yescharacteristic
391C2×C22⋊Q8C22×C3711yescharacteristic
392C2×#121C22×C3711yescharacteristic
393C2×#121C22×C3711yescharacteristic
394C2×C4×Q8C22×C3711yescharacteristic
395C2×#117C22×C3711yescharacteristic
396#460—24no—
397#433—24no—
398C2×#107C22×C3711yescharacteristic
399C2×#106C22×C3711yescharacteristic
400C2×C4⋊C8C22×C3711yescharacteristic
401C2×C4⋊C8C22×C3711yescharacteristic
402C2×#103C22×C3711yescharacteristic
403C2×#103C22×C3711yescharacteristic
404C2×#102C22×C3711yescharacteristic
405C2×#102C22×C3711yescharacteristic
406C2×#102C22×C3711yescharacteristic
407C2×#102C22×C3711yescharacteristic
408C2×#102C22×C3711yescharacteristic
409C2×#102C22×C3711yescharacteristic
410C2×C22⋊C8C22×C3711yescharacteristic
411C2×C22⋊C8C22×C3711yescharacteristic
412C2×#97C22×C3711yescharacteristic
413C2×C4×C8C22×C3711yescharacteristic
414#394—21no—
415#394—21no—
416#392—21no—
417#392—21no—
418#391C22×C3711yescharacteristic
419#390C22×C3711yescharacteristic
420#390C22×C3711yescharacteristic
421#389—21no—
422#389C22×C3711yescharacteristic
423#388—21no—
424#388—21no—
425#387—21no—
426#382C22×C3711yescharacteristic
427#380C22×C3711yescharacteristic
428C4×C4⋊C4C22×C3711yescharacteristic
429#340C22×C3711yescharacteristic
430#340C22×C3711yescharacteristic
431#340C22×C3711yescharacteristic
432#340C22×C3711yescharacteristic
433C37#2466811yescharacteristic, direct product factor, Sylow
434C22×Q8C23×C3711yescharacteristic
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4C23×C3711yescharacteristic
440C22×D4C23×C3711yescharacteristic
441C23×C4C23×C3711yescharacteristic
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—41no—
447C2×SD16—41no—
448C22×C8C23×C3711yescharacteristic
449C22×C8C23×C3711yescharacteristic
450C22×C8C23×C3711yescharacteristic
451C22×C8C23×C3711yescharacteristic
452#127—22no—
453#127—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456#121—41no—
457#121—41no—
458#121—41no—
459#121—41no—
460C4×Q8—22no—
461C4×Q8—22no—
462#117—22no—
463#117—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4D4×C3711yescharacteristic
468C2×C4⋊C4D4×C3711yescharacteristic
469C2×C4⋊C4C23×C3711yescharacteristic
470C2×C4⋊C4C23×C3711yescharacteristic
471C2×C4⋊C4C23×C3711yescharacteristic
472C2×C4⋊C4C23×C3711yescharacteristic
473C2×C4⋊C4C23×C3711yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4D4×C3711yescharacteristic
483C2×C22⋊C4D4×C3711yescharacteristic
484C2×C42—21no—
485C2×C42—21no—
486C2×C42C23×C3711yescharacteristic
487C2×C42C23×C3711yescharacteristic
488#107—41no—
489#106—41no—
490C4⋊C8—22no—
491C4⋊C8D4×C3714yescomplemented
492#103—41no—
493#103—41no—
494#102—22no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—41no—
499#102—41no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502#97—22no—
503C4×C8—22no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511C24—21no—
512C24—21no—
513C24C2×D4×C3711yescharacteristic
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8#41×C3712yes—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—81no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4—81no—
543C2×D4—81no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4C2×D4×C3711yescharacteristic
557C22×C4C2×D4×C3711yescharacteristic
558C22×C4C2×D4×C3711yescharacteristic
559C22×C4C2×D4×C3711yescharacteristic
560C22×C4C2×D4×C3711yescharacteristic
561C22×C4C24×C3711yescharacteristic
562SD16—44no—
563SD16—44no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8C2×D4×C3712yes—
575C2×C8C2×D4×C3712yes—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—81no—
590C4⋊C4#41×C3712yes—
591C22⋊C4—24no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C42—21no—
602C42—21no—
603C42—42no—
604C42—81no—
605C42C2×D4×C3712yes—
606C42#41×C3712yes—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×D4×C3711yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—84no—
642D4—84no—
643D4—84no—
644D4—84no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4#121×C3712yes—
681C2×C4#121×C3712yes—
682C2×C4C22×D4×C3711yescharacteristic
683C2×C4C2×#41×C3711yescharacteristic
684C2×C4C2×#41×C3711yescharacteristic
685C2×C4C2×#41×C3711yescharacteristic
686C2×C4H(5,𝔽2)×C3711yescharacteristic
687C2×C4H(5,𝔽2)×C3711yescharacteristic
688C8—22no—
689C8—22no—
690C8—41no—
691C8—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×#121×C3711yescharacteristic
714C22C37×#52511yescharacteristic
715C22C37×#53511yescharacteristic
716C22C37×#57611yescharacteristic
717C22C37×#57711yescharacteristic
718C22C37×#57711yescharacteristic
719C22C37×#57711yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—41no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4C37×#54611yescharacteristic
732C4C37×#55011yescharacteristic
733C4C37×#55311yescharacteristic
734C4C37×#55511yescharacteristic
735C2—81no—
736C2—161no—
737C2—161no—
738C2C37×#241411yescharacteristic
739C2C37×#305711yescharacteristic
740C2C37×#306211yescharacteristic
741C2C37×#311911yescharacteristic
742C2C37×#312611yescharacteristic
743C2C37×#322211yescharacteristic
744C2C37×#322411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2619C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#460C2semidirect
2. C2×C37×#433C2semidirect
4. C37×#2323C2semidirect
5. C37×#2034C2semidirect
6. C37×#2033C2semidirect
7. C37×#2000C2semidirect
8. C37×#2000C2semidirect
9. C37×#1982C2semidirect
10. C37×#1973C2semidirect
11. C37×#1968C2semidirect
12. C37×#1949C2semidirect
13. C37×#1936C2semidirect
14. C37×#1934C2semidirect
15. C37×#1805C2semidirect
118. C4⋊C8×C37D4semidirect
319. #24668C37direct (N × H)
363. C2×#460C2×C37semidirect
364. C2×#433C2×C37semidirect
366. #2323C2×C37semidirect
367. #2034C2×C37semidirect
368. #2033C2×C37semidirect
369. #2000C2×C37semidirect
370. #2000C2×C37semidirect
371. #1982C2×C37semidirect
372. #1973C2×C37semidirect
373. #1968C2×C37semidirect
374. #1949C2×C37semidirect
375. #1936C2×C37semidirect
376. #1934C2×C37semidirect
377. #1805C2×C37semidirect
433. C37#24668direct (N × H)
491. C4⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4602
C2×C37×#4332
C37×#26192
C37×#23232
C37×#20342
C37×#20332
C37×#20002
C37×#19822
C37×#19732
C37×#19682
C37×#19492
C37×#19362
C37×#19342
C37×#18052
#2466837