Finite Group Databasebeta

← C37×#26633 #22647886

Subgroups — C37×#26633 #22647886

Order 9472.

1084 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#481C211yesmaximal, characteristic, complemented
2C2×C37×#442C211yesmaximal, characteristic, complemented
3C37×#2428C211yesmaximal, characteristic, complemented
4C37×#2361C211yesmaximal, characteristic, complemented
5C37×#2065C211yesmaximal, characteristic, complemented
6C37×#2011C211yesmaximal, characteristic, complemented
7C37×#1999C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1982C211yesmaximal, characteristic, complemented
10C37×#1936C211yesmaximal, characteristic, complemented
11C37×#1924C211yesmaximal, characteristic, complemented
12C37×#1920C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1874C211yesmaximal, characteristic, complemented
15C37×#1864C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C2×#127×C37C2211yescharacteristic
19C2×#121×C37—21no—
20C2×#121×C37C2211yescharacteristic
21C2×#121×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×C4×D4×C37—21no—
24C2×C4×D4×C37C2211yescharacteristic
25C2×C4×D4×C37C2211yescharacteristic
26C22×C4⋊C4×C37C2211yescharacteristic
27C37×#481—24no—
28C37×#442—24no—
29C2×#106×C37C2211yescharacteristic
30C2×#106×C37C2211yescharacteristic
31C2×C4⋊C8×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×C22⋊C8×C37C2211yescharacteristic
41C2×C22⋊C8×C37C2211yescharacteristic
42C2×#97×C37C2211yescharacteristic
43C37×#394—21no—
44C37×#392—21no—
45C37×#390C2211yescharacteristic
46C37×#390C2211yescharacteristic
47C37×#389C2211yescharacteristic
48C37×#389C2211yescharacteristic
49C37×#388—21no—
50C37×#386—21no—
51C37×#386—21no—
52C37×#385—21no—
53C4×C4⋊C4×C37C2211yescharacteristic
54C4×C22⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×D4×C37—21no—
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37C2311yescharacteristic
67C22×D4×C37C2311yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C23×C4×C37—21no—
70C23×C4×C37—21no—
71C23×C4×C37—21no—
72C23×C4×C37C2311yescharacteristic
73C2×D8×C37—22no—
74C2×D8×C37—22no—
75C2×D8×C37—22no—
76C2×D8×C37—22no—
77C2×D8×C37—41no—
78C2×D8×C37—41no—
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83#127×C37—22no—
84#127×C37—41no—
85#121×C37—22no—
86#121×C37—22no—
87#121×C37—22no—
88#121×C37—22no—
89#121×C37—44no—
90#121×C37—41no—
91#121×C37—41no—
92C4×D4×C37—22no—
93C4×D4×C37—22no—
94C4×D4×C37—41no—
95C4×D4×C37—41no—
96C4×D4×C37—44no—
97C2×C4⋊C4×C37—22no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37—21no—
101C2×C4⋊C4×C37—41no—
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C4⋊C4×C37C2311yescharacteristic
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C4⋊C4×C37C2311yescharacteristic
106C2×C4⋊C4×C37C2311yescharacteristic
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—21no—
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37—21no—
112C2×C22⋊C4×C37—21no—
113C2×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37D411yescharacteristic
117C2×C22⋊C4×C37D411yescharacteristic
118C2×C42×C37—21no—
119C2×C42×C37C2311yescharacteristic
120C2×C42×C37C2311yescharacteristic
121#106×C37—22no—
122#106×C37D414yescomplemented
123C4⋊C8×C37—41no—
124#102×C37—22no—
125#102×C37—22no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—22no—
129#102×C37—22no—
130#102×C37—41no—
131#102×C37—41no—
132C22⋊C8×C37—22no—
133C22⋊C8×C37—41no—
134#97×C37—22no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37D411yescharacteristic
139#95×C37D411yescharacteristic
140C24×C37—21no—
141C24×C37—21no—
142C24×C37—21no—
143C24×C37C2×D411yescharacteristic
144C2×D4×C37—24no—
145C2×D4×C37—21no—
146C2×D4×C37—21no—
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—21no—
160C2×D4×C37—21no—
161C2×D4×C37—42no—
162C2×D4×C37—42no—
163C2×D4×C37—42no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—42no—
167C2×D4×C37—42no—
168C2×D4×C37—42no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C2×D4×C37—81no—
172C2×D4×C37—81no—
173C2×D4×C37—81no—
174C2×D4×C37—81no—
175C2×D4×C37#4112yes—
176C2×D4×C37#4112yes—
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×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—42no—
189C22×C4×C37—42no—
190C22×C4×C37—42no—
191C22×C4×C37—42no—
192C22×C4×C37—42no—
193C22×C4×C37—42no—
194C22×C4×C37—81no—
195C22×C4×C37—81no—
196C22×C4×C37—81no—
197C22×C4×C37C2×D411yescharacteristic
198C22×C4×C37C2×D411yescharacteristic
199C22×C4×C37C2×D411yescharacteristic
200C22×C4×C37C2×D411yescharacteristic
201C22×C4×C37C2×D411yescharacteristic
202C22×C4×C37C2411yescharacteristic
203D8×C37—28no—
204D8×C37—44no—
205C2×C8×C37—21no—
206C2×C8×C37—21no—
207C2×C8×C37—21no—
208C2×C8×C37—21no—
209C2×C8×C37—21no—
210C2×C8×C37—21no—
211C2×C8×C37—21no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37C2×D412yes—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—42no—
225C4⋊C4×C37—42no—
226C4⋊C4×C37—42no—
227C4⋊C4×C37C2×D412yes—
228C4⋊C4×C37C2×D412yes—
229C4⋊C4×C37#4112yes—
230C22⋊C4×C37—24no—
231C22⋊C4×C37—22no—
232C22⋊C4×C37—22no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—42no—
235C22⋊C4×C37—42no—
236C22⋊C4×C37—42no—
237C22⋊C4×C37—42no—
238C22⋊C4×C37—42no—
239C22⋊C4×C37—81no—
240C22⋊C4×C37—81no—
241C42×C37—21no—
242C42×C37—21no—
243C42×C37—21no—
244C42×C37—21no—
245C42×C37—42no—
246C23×C37—21no—
247C23×C37—21no—
248C23×C37—21no—
249C23×C37—21no—
250C23×C37—21no—
251C23×C37—21no—
252C23×C37—22no—
253C23×C37—22no—
254C23×C37—41no—
255C23×C37—41no—
256C23×C37—41no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—41no—
260C23×C37—41no—
261C23×C37—41no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37AGL(1,ℤ/8)12yes—
274C23×C37C22×D411yescharacteristic
275D4×C37—22no—
276D4×C37—22no—
277D4×C37—22no—
278D4×C37—22no—
279D4×C37—48no—
280D4×C37—41no—
281D4×C37—41no—
282D4×C37—41no—
283D4×C37—41no—
284D4×C37—41no—
285D4×C37—41no—
286D4×C37—41no—
287D4×C37—41no—
288D4×C37—84no—
289D4×C37—84no—
290D4×C37—84no—
291D4×C37—84no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—22no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—22no—
299C2×C4×C37—21no—
300C2×C4×C37—22no—
301C2×C4×C37—21no—
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—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
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—84no—
326C2×C4×C37—84no—
327C2×C4×C37—84no—
328C2×C4×C37AGL(1,ℤ/8)12yes—
329C2×C4×C37C22×D411yescharacteristic
330C2×C4×C37C2×#4111yescharacteristic
331C2×C4×C37C2×#4111yescharacteristic
332C2×C4×C37C2×#4111yescharacteristic
333C2×C4×C37H(5,𝔽2)11yescharacteristic
334C2×C4×C37H(5,𝔽2)11yescharacteristic
335C8×C37—22no—
336C8×C37—41no—
337C8×C37—41no—
338C8×C37—41no—
339#26633C3711yesmaximal, characteristic, direct product factor, Sylow
340C22×C37—22no—
341C22×C37—22no—
342C22×C37—22no—
343C22×C37—41no—
344C22×C37—41no—
345C22×C37—41no—
346C22×C37—41no—
347C22×C37—42no—
348C22×C37—42no—
349C22×C37—42no—
350C22×C37—42no—
351C22×C37—42no—
352C22×C37—42no—
353C22×C37—81no—
354C22×C37—81no—
355C22×C37—81no—
356C22×C37—81no—
357C22×C37—81no—
358C22×C37—81no—
359C22×C37—81no—
360C22×C37—81no—
361C22×C37—81no—
362C22×C37—81no—
363C22×C37—81no—
364C22×C37—81no—
365C22×C37—81no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37#52511yescharacteristic
369C22×C37D4211yescharacteristic
370C22×C37#54611yescharacteristic
371C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C37#57611yescharacteristic
374C22×C37#57711yescharacteristic
375C4×C37—22no—
376C4×C37—42no—
377C4×C37—41no—
378C4×C37—41no—
379C4×C37—42no—
380C4×C37—41no—
381C4×C37—42no—
382C4×C37—41no—
383C4×C37—81no—
384C4×C37—81no—
385C4×C37#52511yescharacteristic
386C4×C37#53811yescharacteristic
387C4×C37#55011yescharacteristic
388C4×C37#55311yescharacteristic
389C2×#481C2×C3711yescharacteristic, complemented
390C2×#442C2×C3711yescharacteristic, complemented
391#2428C2×C3711yescharacteristic, complemented
392#2361C2×C3711yescharacteristic, complemented
393#2065C2×C3711yescharacteristic, complemented
394#2011C2×C3711yescharacteristic, complemented
395#1999C2×C3711yescharacteristic, complemented
396#1999C2×C3711yescharacteristic, complemented
397#1982C2×C3711yescharacteristic, complemented
398#1936C2×C3711yescharacteristic, complemented
399#1924C2×C3711yescharacteristic, complemented
400#1920C2×C3711yescharacteristic, complemented
401#1879C2×C3711yescharacteristic, complemented
402#1874C2×C3711yescharacteristic, complemented
403#1864C2×C3711yescharacteristic, complemented
404C2×C37—42no—
405C2×C37—82no—
406C2×C37—82no—
407C2×C37—161no—
408C2×C37#245611yescharacteristic
409C2×C37#310911yescharacteristic
410C2×C37#311911yescharacteristic
411C2×C37#326511yescharacteristic
412C2×C37#327411yescharacteristic
413C2×C37#330611yescharacteristic
414C2×C37#331811yescharacteristic
415C22×D8C22×C3711yescharacteristic
416C22×D8C22×C3711yescharacteristic
417C2×#127C22×C3711yescharacteristic
418C2×#121—21no—
419C2×#121C22×C3711yescharacteristic
420C2×#121C22×C3711yescharacteristic
421C2×#121C22×C3711yescharacteristic
422C2×C4×D4—21no—
423C2×C4×D4C22×C3711yescharacteristic
424C2×C4×D4C22×C3711yescharacteristic
425C22×C4⋊C4C22×C3711yescharacteristic
426#481—24no—
427#442—24no—
428C2×#106C22×C3711yescharacteristic
429C2×#106C22×C3711yescharacteristic
430C2×C4⋊C8C22×C3711yescharacteristic
431C2×#102C22×C3711yescharacteristic
432C2×#102C22×C3711yescharacteristic
433C2×#102C22×C3711yescharacteristic
434C2×#102C22×C3711yescharacteristic
435C2×#102C22×C3711yescharacteristic
436C2×#102C22×C3711yescharacteristic
437C2×#102C22×C3711yescharacteristic
438C2×#102C22×C3711yescharacteristic
439C2×C22⋊C8C22×C3711yescharacteristic
440C2×C22⋊C8C22×C3711yescharacteristic
441C2×#97C22×C3711yescharacteristic
442#394—21no—
443#392—21no—
444#390C22×C3711yescharacteristic
445#390C22×C3711yescharacteristic
446#389C22×C3711yescharacteristic
447#389C22×C3711yescharacteristic
448#388—21no—
449#386—21no—
450#386—21no—
451#385—21no—
452C4×C4⋊C4C22×C3711yescharacteristic
453C4×C22⋊C4C22×C3711yescharacteristic
454#340C22×C3711yescharacteristic
455#340C22×C3711yescharacteristic
456#340C22×C3711yescharacteristic
457#340C22×C3711yescharacteristic
458#336C22×C3711yescharacteristic
459#336C22×C3711yescharacteristic
460C37#2663311yescharacteristic, direct product factor, Sylow
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C3711yescharacteristic
467C22×D4C23×C3711yescharacteristic
468C22×D4C23×C3711yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4C23×C3711yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C22×C8C23×C3711yescharacteristic
480C22×C8C23×C3711yescharacteristic
481C22×C8C23×C3711yescharacteristic
482C22×C8C23×C3711yescharacteristic
483#127—22no—
484#127—41no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—44no—
490#121—41no—
491#121—41no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C4×D4—44no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C3711yescharacteristic
503C2×C4⋊C4C23×C3711yescharacteristic
504C2×C4⋊C4C23×C3711yescharacteristic
505C2×C4⋊C4C23×C3711yescharacteristic
506C2×C4⋊C4C23×C3711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C3711yescharacteristic
517C2×C22⋊C4D4×C3711yescharacteristic
518C2×C42—21no—
519C2×C42C23×C3711yescharacteristic
520C2×C42C23×C3711yescharacteristic
521#106—22no—
522#106D4×C3714yescomplemented
523C4⋊C8—41no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—41no—
531#102—41no—
532C22⋊C8—22no—
533C22⋊C8—41no—
534#97—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95D4×C3711yescharacteristic
539#95D4×C3711yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24C2×D4×C3711yescharacteristic
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#41×C3712yes—
576C2×D4#41×C3712yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C3711yescharacteristic
598C22×C4C2×D4×C3711yescharacteristic
599C22×C4C2×D4×C3711yescharacteristic
600C22×C4C2×D4×C3711yescharacteristic
601C22×C4C2×D4×C3711yescharacteristic
602C22×C4C24×C3711yescharacteristic
603D8—28no—
604D8—44no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8C2×D4×C3712yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4C2×D4×C3712yes—
628C4⋊C4C2×D4×C3712yes—
629C4⋊C4#41×C3712yes—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23AGL(1,ℤ/8)×C3712yes—
674C23C22×D4×C3711yescharacteristic
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—48no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4AGL(1,ℤ/8)×C3712yes—
729C2×C4C22×D4×C3711yescharacteristic
730C2×C4C2×#41×C3711yescharacteristic
731C2×C4C2×#41×C3711yescharacteristic
732C2×C4C2×#41×C3711yescharacteristic
733C2×C4H(5,𝔽2)×C3711yescharacteristic
734C2×C4H(5,𝔽2)×C3711yescharacteristic
735C8—22no—
736C8—41no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C37×#52511yescharacteristic
768C22D42×C3711yescharacteristic
769C22C37×#54611yescharacteristic
770C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
771C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
772C22C37×#57611yescharacteristic
773C22C37×#57711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—42no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4C37×#52511yescharacteristic
785C4C37×#53811yescharacteristic
786C4C37×#55011yescharacteristic
787C4C37×#55311yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C37×#245611yescharacteristic
793C2C37×#310911yescharacteristic
794C2C37×#311911yescharacteristic
795C2C37×#326511yescharacteristic
796C2C37×#327411yescharacteristic
797C2C37×#330611yescharacteristic
798C2C37×#331811yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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
1. C2×C37×#481C2semidirect
2. C2×C37×#442C2semidirect
3. C37×#2428C2semidirect
4. C37×#2361C2semidirect
5. C37×#2065C2semidirect
6. C37×#2011C2semidirect
7. C37×#1999C2semidirect
8. C37×#1999C2semidirect
9. C37×#1982C2semidirect
10. C37×#1936C2semidirect
11. C37×#1924C2semidirect
12. C37×#1920C2semidirect
13. C37×#1879C2semidirect
14. C37×#1874C2semidirect
15. C37×#1864C2semidirect
122. #106×C37D4semidirect
339. #26633C37direct (N × H)
389. C2×#481C2×C37semidirect
390. C2×#442C2×C37semidirect
391. #2428C2×C37semidirect
392. #2361C2×C37semidirect
393. #2065C2×C37semidirect
394. #2011C2×C37semidirect
395. #1999C2×C37semidirect
396. #1999C2×C37semidirect
397. #1982C2×C37semidirect
398. #1936C2×C37semidirect
399. #1924C2×C37semidirect
400. #1920C2×C37semidirect
401. #1879C2×C37semidirect
402. #1874C2×C37semidirect
403. #1864C2×C37semidirect
460. C37#26633direct (N × H)
522. #106D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4812
C2×C37×#4422
C37×#24282
C37×#23612
C37×#20652
C37×#20112
C37×#19992
C37×#19822
C37×#19362
C37×#19242
C37×#19202
C37×#18792
C37×#18742
C37×#18642
#2663337