Finite Group Databasebeta

← C37×#23580 #22644833

Subgroups — C37×#23580 #22644833

Order 9472.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#540C211yesmaximal, characteristic, complemented
2C2×C37×#442C211yesmaximal, characteristic, complemented
3C2×C4×D8×C37C211yesmaximal, characteristic, complemented
4C37×#2324C211yesmaximal, characteristic, complemented
5C37×#2059C211yesmaximal, characteristic, complemented
6C37×#2041C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2025C211yesmaximal, characteristic, complemented
10C37×#2011C211yesmaximal, characteristic, complemented
11C37×#1999C211yesmaximal, characteristic, complemented
12C37×#1999C211yesmaximal, characteristic, complemented
13C37×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C37C211yesmaximal, characteristic, complemented
15C37×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C37×#540—24no—
19C37×#540—24no—
20C2×#127×C37C2211yescharacteristic
21C2×#125×C37C2211yescharacteristic
22C2×#123×C37—21no—
23C2×#123×C37—21no—
24C2×#121×C37—21no—
25C2×#121×C37—21no—
26C2×#121×C37C2211yescharacteristic
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×C4×D4×C37C2211yescharacteristic
30C2×C4×D4×C37C2211yescharacteristic
31C2×C4×D4×C37C2211yescharacteristic
32C2×#117×C37C2211yescharacteristic
33C37×#442—24no—
34C4×D8×C37—24no—
35C2×#107×C37C2211yescharacteristic
36C2×#106×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×C22⋊C8×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×#97×C37C2211yescharacteristic
48C2×C4×C8×C37C2211yescharacteristic
49C37×#390—21no—
50C37×#390C2211yescharacteristic
51C37×#389C2211yescharacteristic
52C37×#388—21no—
53C37×#386—21no—
54C37×#385—21no—
55C37×#380C2211yescharacteristic
56C4×C4⋊C4×C37C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37—21no—
68C22×D4×C37C2311yescharacteristic
69C22×D4×C37C2311yescharacteristic
70C22×D4×C37C2311yescharacteristic
71C23×C4×C37—21no—
72C23×C4×C37—21no—
73C23×C4×C37—21no—
74C23×C4×C37C2311yescharacteristic
75C2×D8×C37—22no—
76C2×D8×C37—22no—
77C2×D8×C37—22no—
78C2×D8×C37—22no—
79C2×D8×C37—22no—
80C2×D8×C37—22no—
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85#127×C37—22no—
86#127×C37—22no—
87#125×C37—22no—
88#125×C37—22no—
89#123×C37—28no—
90#123×C37—28no—
91#121×C37—28no—
92#121×C37—28no—
93#121×C37—22no—
94#121×C37—22no—
95#121×C37—22no—
96#121×C37—22no—
97#121×C37—22no—
98#121×C37—22no—
99C4×D4×C37—22no—
100C4×D4×C37—22no—
101C4×D4×C37—22no—
102C4×D4×C37—22no—
103C4×D4×C37D414yescomplemented
104C4×D4×C37D414yescomplemented
105#117×C37—22no—
106#117×C37—22no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37D411yescharacteristic
111C2×C4⋊C4×C37D411yescharacteristic
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37D411yescharacteristic
127C2×C22⋊C4×C37D411yescharacteristic
128C2×C42×C37—21no—
129C2×C42×C37C2311yescharacteristic
130C2×C42×C37C2311yescharacteristic
131#107×C37—22no—
132#106×C37—22no—
133#102×C37—22no—
134#102×C37—22no—
135#102×C37—22no—
136#102×C37—22no—
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141C22⋊C8×C37—22no—
142C22⋊C8×C37—22no—
143#97×C37—22no—
144C4×C8×C37—22no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148C24×C37—21no—
149C24×C37—21no—
150C24×C37—21no—
151C24×C37C2×D411yescharacteristic
152C2×D4×C37—24no—
153C2×D4×C37—24no—
154C2×D4×C37—24no—
155C2×D4×C37—24no—
156C2×D4×C37—24no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—21no—
164C2×D4×C37—21no—
165C2×D4×C37—21no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—81no—
173C2×D4×C37—81no—
174C2×D4×C37—81no—
175C2×D4×C37—81no—
176C2×D4×C37—81no—
177C2×D4×C37—81no—
178C2×D4×C37—81no—
179C2×D4×C37—81no—
180C2×D4×C37—81no—
181C2×D4×C37—81no—
182C2×D4×C37C2×D412yes—
183C2×D4×C37C2×D412yes—
184C2×D4×C37#4112yes—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—24no—
195C22×C4×C37—24no—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—42no—
199C22×C4×C37—81no—
200C22×C4×C37—81no—
201C22×C4×C37—81no—
202C22×C4×C37—81no—
203C22×C4×C37—81no—
204C22×C4×C37—81no—
205C22×C4×C37C2×D411yescharacteristic
206C22×C4×C37C2×D411yescharacteristic
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D411yescharacteristic
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2411yescharacteristic
211D8×C37—28no—
212D8×C37—28no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37#4112yes—
224C2×C8×C37#4112yes—
225C4⋊C4×C37—24no—
226C4⋊C4×C37—24no—
227C4⋊C4×C37—22no—
228C4⋊C4×C37—22no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—81no—
237C4⋊C4×C37C2×D412yes—
238C4⋊C4×C37C2×D412yes—
239C4⋊C4×C37#4112yes—
240C22⋊C4×C37—24no—
241C22⋊C4×C37—24no—
242C22⋊C4×C37—24no—
243C22⋊C4×C37—24no—
244C22⋊C4×C37—24no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—42no—
248C22⋊C4×C37—81no—
249C22⋊C4×C37—81no—
250C22⋊C4×C37—81no—
251C42×C37—21no—
252C42×C37—21no—
253C42×C37—81no—
254C42×C37C2×D412yes—
255C42×C37C2×D412yes—
256C23×C37—21no—
257C23×C37—22no—
258C23×C37—22no—
259C23×C37—22no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—21no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37C22×D411yescharacteristic
285D4×C37—22no—
286D4×C37—22no—
287D4×C37—22no—
288D4×C37—22no—
289D4×C37—22no—
290D4×C37—22no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—41no—
295D4×C37—41no—
296D4×C37—41no—
297D4×C37—84no—
298D4×C37—84no—
299D4×C37—84no—
300D4×C37—84no—
301D4×C37—84no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—21no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—22no—
310C2×C4×C37—22no—
311C2×C4×C37—21no—
312C2×C4×C37—22no—
313C2×C4×C37—21no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—21no—
317C2×C4×C37—21no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
331C2×C4×C37—41no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—84no—
335C2×C4×C37—84no—
336C2×C4×C37—84no—
337C2×C4×C37#12012yes—
338C2×C4×C37#12012yes—
339C2×C4×C37C22×D411yescharacteristic
340C2×C4×C37C22×D411yescharacteristic
341C2×C4×C37C2×#4111yescharacteristic
342C2×C4×C37C2×#4111yescharacteristic
343C2×C4×C37C2×#4111yescharacteristic
344C2×C4×C37C2×#4111yescharacteristic
345C8×C37—22no—
346C8×C37—22no—
347C8×C37—41no—
348C8×C37—41no—
349#23580C3711yesmaximal, characteristic, direct product factor, Sylow
350C22×C37—41no—
351C22×C37—42no—
352C22×C37—41no—
353C22×C37—42no—
354C22×C37—41no—
355C22×C37—42no—
356C22×C37—42no—
357C22×C37—42no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—42no—
361C22×C37—41no—
362C22×C37—42no—
363C22×C37—42no—
364C22×C37—41no—
365C22×C37—42no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37—81no—
369C22×C37—81no—
370C22×C37—81no—
371C22×C37—81no—
372C22×C37—81no—
373C22×C37—81no—
374C22×C37—81no—
375C22×C37—81no—
376C22×C37—81no—
377C22×C37—81no—
378C22×C37C2×#12011yescharacteristic
379C22×C37#52511yescharacteristic
380C22×C37#53211yescharacteristic
381C22×C37#57611yescharacteristic
382C22×C37#57611yescharacteristic
383C22×C37#57611yescharacteristic
384C22×C37#57711yescharacteristic
385C4×C37—22no—
386C4×C37—22no—
387C4×C37—42no—
388C4×C37—41no—
389C4×C37—41no—
390C4×C37—42no—
391C4×C37—41no—
392C4×C37—42no—
393C4×C37—81no—
394C4×C37—81no—
395C4×C37#52511yescharacteristic
396C4×C37#52511yescharacteristic
397C4×C37#53211yescharacteristic
398C4×C37#53211yescharacteristic
399C2×#540C2×C3711yescharacteristic, complemented
400C2×#442C2×C3711yescharacteristic, complemented
401C2×C4×D8C2×C3711yescharacteristic, complemented
402#2324C2×C3711yescharacteristic, complemented
403#2059C2×C3711yescharacteristic, complemented
404#2041C2×C3711yescharacteristic, complemented
405#2034C2×C3711yescharacteristic, complemented
406#2033C2×C3711yescharacteristic, complemented
407#2025C2×C3711yescharacteristic, complemented
408#2011C2×C3711yescharacteristic, complemented
409#1999C2×C3711yescharacteristic, complemented
410#1999C2×C3711yescharacteristic, complemented
411#1762C2×C3711yescharacteristic, complemented
412C4×#102C2×C3711yescharacteristic, complemented
413#1750C2×C3711yescharacteristic, complemented
414C2×C37—81no—
415C2×C37—82no—
416C2×C37—82no—
417C2×C37—82no—
418C2×C37#238811yescharacteristic
419C2×C37#300811yescharacteristic
420C2×C37#301211yescharacteristic
421C2×C37#311911yescharacteristic
422C2×C37#312211yescharacteristic
423C2×C37#317611yescharacteristic
424C2×C37#317911yescharacteristic
425C22×D8C22×C3711yescharacteristic
426C22×D8C22×C3711yescharacteristic
427#540—24no—
428#540—24no—
429C2×#127C22×C3711yescharacteristic
430C2×#125C22×C3711yescharacteristic
431C2×#123—21no—
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C3711yescharacteristic
436C2×#121C22×C3711yescharacteristic
437C2×#121C22×C3711yescharacteristic
438C2×C4×D4C22×C3711yescharacteristic
439C2×C4×D4C22×C3711yescharacteristic
440C2×C4×D4C22×C3711yescharacteristic
441C2×#117C22×C3711yescharacteristic
442#442—24no—
443C4×D8—24no—
444C2×#107C22×C3711yescharacteristic
445C2×#106C22×C3711yescharacteristic
446C2×#102C22×C3711yescharacteristic
447C2×#102C22×C3711yescharacteristic
448C2×#102C22×C3711yescharacteristic
449C2×#102C22×C3711yescharacteristic
450C2×#102C22×C3711yescharacteristic
451C2×#102C22×C3711yescharacteristic
452C2×#102C22×C3711yescharacteristic
453C2×#102C22×C3711yescharacteristic
454C2×C22⋊C8C22×C3711yescharacteristic
455C2×C22⋊C8C22×C3711yescharacteristic
456C2×#97C22×C3711yescharacteristic
457C2×C4×C8C22×C3711yescharacteristic
458#390—21no—
459#390C22×C3711yescharacteristic
460#389C22×C3711yescharacteristic
461#388—21no—
462#386—21no—
463#385—21no—
464#380C22×C3711yescharacteristic
465C4×C4⋊C4C22×C3711yescharacteristic
466#340C22×C3711yescharacteristic
467#340C22×C3711yescharacteristic
468#340C22×C3711yescharacteristic
469#340C22×C3711yescharacteristic
470#336C22×C3711yescharacteristic
471#336C22×C3711yescharacteristic
472C37#2358011yescharacteristic, direct product factor, Sylow
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C3711yescharacteristic
479C22×D4C23×C3711yescharacteristic
480C22×D4C23×C3711yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C3711yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C3711yescharacteristic
492C22×C8C23×C3711yescharacteristic
493C22×C8C23×C3711yescharacteristic
494C22×C8C23×C3711yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C3714yescomplemented
514C4×D4D4×C3714yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C3711yescharacteristic
521C2×C4⋊C4D4×C3711yescharacteristic
522C2×C4⋊C4C23×C3711yescharacteristic
523C2×C4⋊C4C23×C3711yescharacteristic
524C2×C4⋊C4C23×C3711yescharacteristic
525C2×C4⋊C4C23×C3711yescharacteristic
526C2×C4⋊C4C23×C3711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C3711yescharacteristic
537C2×C22⋊C4D4×C3711yescharacteristic
538C2×C42—21no—
539C2×C42C23×C3711yescharacteristic
540C2×C42C23×C3711yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C3711yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C3712yes—
593C2×D4C2×D4×C3712yes—
594C2×D4#41×C3712yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C3711yescharacteristic
616C22×C4C2×D4×C3711yescharacteristic
617C22×C4C2×D4×C3711yescharacteristic
618C22×C4C2×D4×C3711yescharacteristic
619C22×C4C2×D4×C3711yescharacteristic
620C22×C4C24×C3711yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C3712yes—
634C2×C8#41×C3712yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C3712yes—
648C4⋊C4C2×D4×C3712yes—
649C4⋊C4#41×C3712yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C3712yes—
665C42C2×D4×C3712yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C3711yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C3712yes—
748C2×C4#120×C3712yes—
749C2×C4C22×D4×C3711yescharacteristic
750C2×C4C22×D4×C3711yescharacteristic
751C2×C4C2×#41×C3711yescharacteristic
752C2×C4C2×#41×C3711yescharacteristic
753C2×C4C2×#41×C3711yescharacteristic
754C2×C4C2×#41×C3711yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C3711yescharacteristic
788C22C37×#52511yescharacteristic
789C22C37×#53211yescharacteristic
790C22C37×#57611yescharacteristic
791C22C37×#57611yescharacteristic
792C22C37×#57611yescharacteristic
793C22C37×#57711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4C37×#52511yescharacteristic
805C4C37×#52511yescharacteristic
806C4C37×#53211yescharacteristic
807C4C37×#53211yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C37×#238811yescharacteristic
813C2C37×#300811yescharacteristic
814C2C37×#301211yescharacteristic
815C2C37×#311911yescharacteristic
816C2C37×#312211yescharacteristic
817C2C37×#317611yescharacteristic
818C2C37×#317911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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×#540C2semidirect
2. C2×C37×#442C2semidirect
3. C2×C4×D8×C37C2semidirect
4. C37×#2324C2semidirect
5. C37×#2059C2semidirect
6. C37×#2041C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#2025C2semidirect
10. C37×#2011C2semidirect
11. C37×#1999C2semidirect
12. C37×#1999C2semidirect
13. C37×#1762C2semidirect
14. C4×#102×C37C2semidirect
15. C37×#1750C2semidirect
103. C4×D4×C37D4semidirect
104. C4×D4×C37D4semidirect
349. #23580C37direct (N × H)
399. C2×#540C2×C37semidirect
400. C2×#442C2×C37semidirect
401. C2×C4×D8C2×C37semidirect
402. #2324C2×C37semidirect
403. #2059C2×C37semidirect
404. #2041C2×C37semidirect
405. #2034C2×C37semidirect
406. #2033C2×C37semidirect
407. #2025C2×C37semidirect
408. #2011C2×C37semidirect
409. #1999C2×C37semidirect
410. #1999C2×C37semidirect
411. #1762C2×C37semidirect
412. C4×#102C2×C37semidirect
413. #1750C2×C37semidirect
472. C37#23580direct (N × H)
513. C4×D4D4×C37semidirect
514. C4×D4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5402
C2×C37×#4422
C2×C4×D8×C372
C37×#23242
C37×#20592
C37×#20412
C37×#20342
C37×#20332
C37×#20252
C37×#20112
C37×#19992
C37×#17622
C4×#102×C372
C37×#17502
#2358037