Finite Group Databasebeta

← C37×#24424 #22645677

Subgroups — C37×#24424 #22645677

Order 9472.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C37C211yesmaximal, characteristic, complemented
2C2×C37×#466C211yesmaximal, characteristic, complemented
3C2×C37×#447C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C22×#102×C37C211yesmaximal, characteristic, complemented
6C37×#2416C211yesmaximal, characteristic, complemented
7C37×#2041C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2011C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1879C211yesmaximal, characteristic, complemented
12C37×#1874C211yesmaximal, characteristic, complemented
13C37×#1869C211yesmaximal, characteristic, complemented
14C37×#1862C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C37—21no—
17C23×D4×C37C2211yescharacteristic
18C23×D4×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic
20C22×D8×C37C2211yescharacteristic, complemented
21C22×D8×C37C2211yescharacteristic, complemented
22C23×C8×C37C2211yescharacteristic, complemented
23D42×C37—24no—
24D42×C37—24no—
25C2×#127×C37C2211yescharacteristic
26C2×#121×C37—21no—
27C2×#121×C37—21no—
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic, complemented
31C2×#121×C37C2211yescharacteristic, complemented
32C2×#120×C37—21no—
33C2×#120×C37—21no—
34C2×C4×D4×C37C2211yescharacteristic
35C2×C4×D4×C37C2211yescharacteristic
36C22×C4⋊C4×C37C2211yescharacteristic, complemented
37C37×#466—24no—
38C37×#447—24no—
39C37×#447—24no—
40C2×#107×C37C2211yescharacteristic, complemented
41C2×#102×C37—24no—
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×#102×C37C2211yescharacteristic, complemented
48C2×#102×C37C2211yescharacteristic, complemented
49C2×#102×C37C2211yescharacteristic, complemented
50C2×#102×C37C2211yescharacteristic, complemented
51C2×#102×C37C2211yescharacteristic, complemented
52C2×C22⋊C8×C37C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C37×#396—21no—
56C37×#394—21no—
57C37×#390C2211yescharacteristic, complemented
58C37×#389C2211yescharacteristic, complemented
59C37×#386—21no—
60C37×#380C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#336C2211yescharacteristic, complemented
64C37×#336C2211yescharacteristic, complemented
65C25×C37—21no—
66C25×C37—21no—
67C22×D4×C37—22no—
68C22×D4×C37—22no—
69C22×D4×C37—28no—
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—22no—
73C22×D4×C37—22no—
74C22×D4×C37—22no—
75C22×D4×C37—22no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—22no—
82C22×D4×C37—21no—
83C22×D4×C37—41no—
84C22×D4×C37—41no—
85C22×D4×C37—41no—
86C22×D4×C37—41no—
87C22×D4×C37—44no—
88C22×D4×C37—44no—
89C22×D4×C37D411yescharacteristic
90C22×D4×C37D414yescomplemented
91C22×D4×C37C2311yescharacteristic
92C22×D4×C37C2311yescharacteristic
93C22×D4×C37C2311yescharacteristic
94C22×D4×C37C2311yescharacteristic
95C23×C4×C37—21no—
96C23×C4×C37—21no—
97C23×C4×C37C2311yescharacteristic
98C23×C4×C37C2311yescharacteristic
99C2×D8×C37—22no—
100C2×D8×C37—22no—
101C2×D8×C37—22no—
102C2×D8×C37—22no—
103C2×D8×C37—22no—
104C2×D8×C37—22no—
105C2×D8×C37—41no—
106C2×D8×C37—41no—
107C2×D8×C37—41no—
108C22×C8×C37—22no—
109C22×C8×C37—22no—
110C22×C8×C37—41no—
111C22×C8×C37C2311yescharacteristic
112C22×C8×C37C2311yescharacteristic
113C22×C8×C37C2311yescharacteristic
114C22×C8×C37C2311yescharacteristic
115#127×C37—22no—
116#127×C37—22no—
117#121×C37—28no—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37—22no—
123#121×C37—22no—
124#121×C37—41no—
125#121×C37—44no—
126#121×C37D414yescomplemented
127#120×C37—28no—
128#120×C37—28no—
129C4×D4×C37—22no—
130C4×D4×C37—22no—
131C4×D4×C37—22no—
132C4×D4×C37—22no—
133C2×C4⋊C4×C37—22no—
134C2×C4⋊C4×C37—21no—
135C2×C4⋊C4×C37—21no—
136C2×C4⋊C4×C37—41no—
137C2×C4⋊C4×C37D411yescharacteristic
138C2×C4⋊C4×C37C2311yescharacteristic
139C2×C4⋊C4×C37C2311yescharacteristic
140C2×C4⋊C4×C37C2311yescharacteristic
141C2×C4⋊C4×C37C2311yescharacteristic
142C2×C22⋊C4×C37—21no—
143C2×C22⋊C4×C37—21no—
144C2×C22⋊C4×C37—21no—
145C2×C22⋊C4×C37—21no—
146C2×C22⋊C4×C37—21no—
147C2×C22⋊C4×C37—21no—
148C2×C22⋊C4×C37—21no—
149C2×C22⋊C4×C37—21no—
150C2×C22⋊C4×C37D411yescharacteristic
151C2×C22⋊C4×C37D411yescharacteristic
152C2×C42×C37C2311yescharacteristic
153#107×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—22no—
158#102×C37—22no—
159#102×C37—22no—
160#102×C37—22no—
161#102×C37—22no—
162#102×C37—41no—
163#102×C37D414yescomplemented
164C22⋊C8×C37—22no—
165C22⋊C8×C37—22no—
166C22⋊C8×C37—41no—
167#95×C37—21no—
168#95×C37—21no—
169C24×C37—21no—
170C24×C37—24no—
171C24×C37—21no—
172C24×C37—21no—
173C24×C37—24no—
174C24×C37—21no—
175C24×C37—42no—
176C24×C37—42no—
177C24×C37—42no—
178C24×C37—42no—
179C24×C37—42no—
180C24×C37—42no—
181C24×C37—42no—
182C24×C37—42no—
183C24×C37—81no—
184C24×C37—81no—
185C24×C37—81no—
186C24×C37—81no—
187C24×C37C2×D411yescharacteristic
188C24×C37C2×D411yescharacteristic
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—28no—
192C2×D4×C37—24no—
193C2×D4×C37—24no—
194C2×D4×C37—24no—
195C2×D4×C37—24no—
196C2×D4×C37—24no—
197C2×D4×C37—24no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—21no—
213C2×D4×C37—21no—
214C2×D4×C37—21no—
215C2×D4×C37—21no—
216C2×D4×C37—21no—
217C2×D4×C37—44no—
218C2×D4×C37—44no—
219C2×D4×C37—44no—
220C2×D4×C37—42no—
221C2×D4×C37—42no—
222C2×D4×C37—42no—
223C2×D4×C37—42no—
224C2×D4×C37—42no—
225C2×D4×C37—42no—
226C2×D4×C37—44no—
227C2×D4×C37—44no—
228C2×D4×C37—432no—
229C2×D4×C37—44no—
230C2×D4×C37—42no—
231C2×D4×C37—42no—
232C2×D4×C37—42no—
233C2×D4×C37—42no—
234C2×D4×C37—44no—
235C2×D4×C37—42no—
236C2×D4×C37—42no—
237C2×D4×C37—42no—
238C2×D4×C37—42no—
239C2×D4×C37—42no—
240C2×D4×C37—81no—
241C2×D4×C37—81no—
242C2×D4×C37—81no—
243C2×D4×C37D814yescomplemented
244C2×D4×C37C2×D412yes—
245C2×D4×C37C2×D412yes—
246C2×D4×C37C2×D412yes—
247C2×D4×C37C2×D412yes—
248C2×D4×C37#4112yes—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—24no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—21no—
259C22×C4×C37—21no—
260C22×C4×C37—21no—
261C22×C4×C37—21no—
262C22×C4×C37—21no—
263C22×C4×C37—21no—
264C22×C4×C37—42no—
265C22×C4×C37—42no—
266C22×C4×C37—42no—
267C22×C4×C37—42no—
268C22×C4×C37—81no—
269C22×C4×C37C2×D411yescharacteristic
270C22×C4×C37C2×D411yescharacteristic
271C22×C4×C37C2×D411yescharacteristic
272C22×C4×C37C2×D412yes—
273C22×C4×C37C2×D412yes—
274C22×C4×C37C2×D411yescharacteristic
275C22×C4×C37C2411yescharacteristic
276D8×C37—44no—
277D8×C37—44no—
278D8×C37—44no—
279C2×C8×C37—21no—
280C2×C8×C37—21no—
281C2×C8×C37—21no—
282C2×C8×C37—21no—
283C2×C8×C37—21no—
284C2×C8×C37—21no—
285C2×C8×C37—21no—
286C2×C8×C37—21no—
287C2×C8×C37—21no—
288C2×C8×C37—21no—
289C2×C8×C37—21no—
290C2×C8×C37—44no—
291C2×C8×C37C2×D412yescomplemented
292C4⋊C4×C37—22no—
293C4⋊C4×C37—21no—
294C4⋊C4×C37—21no—
295C4⋊C4×C37—21no—
296C4⋊C4×C37—21no—
297C4⋊C4×C37—21no—
298C4⋊C4×C37—21no—
299C4⋊C4×C37—42no—
300C4⋊C4×C37—42no—
301C4⋊C4×C37C2×D412yes—
302C4⋊C4×C37C2×D412yescomplemented
303C22⋊C4×C37—24no—
304C22⋊C4×C37—24no—
305C22⋊C4×C37—22no—
306C22⋊C4×C37—24no—
307C22⋊C4×C37—22no—
308C22⋊C4×C37—42no—
309C22⋊C4×C37—42no—
310C22⋊C4×C37—42no—
311C22⋊C4×C37—42no—
312C22⋊C4×C37—81no—
313C42×C37—21no—
314C42×C37—21no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—21no—
318C23×C37—21no—
319C23×C37—21no—
320C23×C37—22no—
321C23×C37—21no—
322C23×C37—22no—
323C23×C37—21no—
324C23×C37—22no—
325C23×C37—21no—
326C23×C37—21no—
327C23×C37—21no—
328C23×C37—22no—
329C23×C37—22no—
330C23×C37—48no—
331C23×C37—48no—
332C23×C37—48no—
333C23×C37—41no—
334C23×C37—41no—
335C23×C37—41no—
336C23×C37—41no—
337C23×C37—41no—
338C23×C37—41no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—41no—
348C23×C37—41no—
349C23×C37—48no—
350C23×C37—41no—
351C23×C37—41no—
352C23×C37—41no—
353C23×C37—41no—
354C23×C37—41no—
355C23×C37—41no—
356C23×C37—41no—
357C23×C37—84no—
358C23×C37—84no—
359C23×C37—84no—
360C23×C37—84no—
361C23×C37—84no—
362C23×C37—84no—
363C23×C37—84no—
364C23×C37—84no—
365C23×C37—84no—
366C23×C37—84no—
367C23×C37#12012yes—
368C23×C37C2×D812yes—
369C23×C37C2×D812yes—
370C23×C37AGL(1,ℤ/8)12yes—
371C23×C37C22×D411yescharacteristic
372D4×C37—28no—
373D4×C37—22no—
374D4×C37—22no—
375D4×C37—22no—
376D4×C37—22no—
377D4×C37—22no—
378D4×C37—22no—
379D4×C37—22no—
380D4×C37—48no—
381D4×C37—48no—
382D4×C37—48no—
383D4×C37—48no—
384D4×C37—48no—
385D4×C37—41no—
386D4×C37—41no—
387D4×C37—41no—
388D4×C37—41no—
389D4×C37—41no—
390D4×C37—41no—
391D4×C37—41no—
392D4×C37—41no—
393D4×C37—84no—
394D4×C37—84no—
395D4×C37—84no—
396D4×C37#12114yescomplemented
397C2×C4×C37—21no—
398C2×C4×C37—21no—
399C2×C4×C37—21no—
400C2×C4×C37—21no—
401C2×C4×C37—22no—
402C2×C4×C37—22no—
403C2×C4×C37—22no—
404C2×C4×C37—22no—
405C2×C4×C37—21no—
406C2×C4×C37—21no—
407C2×C4×C37—22no—
408C2×C4×C37—21no—
409C2×C4×C37—22no—
410C2×C4×C37—21no—
411C2×C4×C37—21no—
412C2×C4×C37—21no—
413C2×C4×C37—48no—
414C2×C4×C37—41no—
415C2×C4×C37—41no—
416C2×C4×C37—41no—
417C2×C4×C37—41no—
418C2×C4×C37—41no—
419C2×C4×C37—41no—
420C2×C4×C37—41no—
421C2×C4×C37—41no—
422C2×C4×C37—41no—
423C2×C4×C37—41no—
424C2×C4×C37—41no—
425C2×C4×C37—41no—
426C2×C4×C37—41no—
427C2×C4×C37—41no—
428C2×C4×C37—84no—
429C2×C4×C37#12012yes—
430C2×C4×C37C2×D812yes—
431C2×C4×C37C22×D411yescharacteristic
432C2×C4×C37C22×D411yescharacteristic
433C2×C4×C37C22×D411yescharacteristic
434C2×C4×C37C2×#4111yescharacteristic
435C2×C4×C37H(5,𝔽2)11yescharacteristic
436C2×C4×C37H(5,𝔽2)11yescharacteristic
437C8×C37—22no—
438C8×C37—41no—
439C8×C37—41no—
440C8×C37—41no—
441#24424C3711yesmaximal, characteristic, direct product factor, Sylow
442C22×C37—22no—
443C22×C37—22no—
444C22×C37—22no—
445C22×C37—22no—
446C22×C37—22no—
447C22×C37—22no—
448C22×C37—24no—
449C22×C37—22no—
450C22×C37—22no—
451C22×C37—22no—
452C22×C37—41no—
453C22×C37—42no—
454C22×C37—41no—
455C22×C37—42no—
456C22×C37—41no—
457C22×C37—42no—
458C22×C37—42no—
459C22×C37—42no—
460C22×C37—41no—
461C22×C37—42no—
462C22×C37—42no—
463C22×C37—42no—
464C22×C37—42no—
465C22×C37—42no—
466C22×C37—42no—
467C22×C37—42no—
468C22×C37—816no—
469C22×C37—816no—
470C22×C37—81no—
471C22×C37—81no—
472C22×C37—81no—
473C22×C37—81no—
474C22×C37—81no—
475C22×C37—81no—
476C22×C37—81no—
477C22×C37—81no—
478C22×C37—81no—
479C22×C37—81no—
480C22×C37—81no—
481C22×C37—81no—
482C22×C37—81no—
483C22×C37—81no—
484C22×C37—81no—
485C22×C37#44714yescomplemented
486C22×C37C2×#12011yescharacteristic
487C22×C37D4211yescharacteristic
488C22×C37#54611yescharacteristic
489C22×C37C22×D811yescharacteristic
490C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
491C22×C37#57611yescharacteristic
492C22×C37#57711yescharacteristic
493C4×C37—22no—
494C4×C37—22no—
495C4×C37—41no—
496C4×C37—42no—
497C4×C37—41no—
498C4×C37—42no—
499C4×C37—81no—
500C4×C37—81no—
501C4×C37C2×#12111yescharacteristic
502C4×C37#53411yescharacteristic
503C4×C37D4211yescharacteristic
504C4×C37#54611yescharacteristic
505C2×D42C2×C3711yescharacteristic, complemented
506C2×#466C2×C3711yescharacteristic, complemented
507C2×#447C2×C3711yescharacteristic, complemented
508C2×#447C2×C3711yescharacteristic, complemented
509C22×#102C2×C3711yescharacteristic, complemented
510#2416C2×C3711yescharacteristic, complemented
511#2041C2×C3711yescharacteristic, complemented
512#2033C2×C3711yescharacteristic, complemented
513#2011C2×C3711yescharacteristic, complemented
514#1999C2×C3711yescharacteristic, complemented
515#1879C2×C3711yescharacteristic, complemented
516#1874C2×C3711yescharacteristic, complemented
517#1869C2×C3711yescharacteristic, complemented
518#1862C2×C3711yescharacteristic, complemented
519#1786C2×C3711yescharacteristic, complemented
520C2×C37—24no—
521C2×C37—42no—
522C2×C37—44no—
523C2×C37—82no—
524C2×C37—82no—
525C2×C37—161no—
526C2×C37#241011yescharacteristic
527C2×C37C2×#44711yescharacteristic
528C2×C37#301211yescharacteristic
529C2×C37#326511yescharacteristic
530C2×C37D4×D811yescharacteristic
531C2×C37#329411yescharacteristic
532C2×C37#331811yescharacteristic
533C23×D4—21no—
534C23×D4C22×C3711yescharacteristic
535C23×D4C22×C3711yescharacteristic
536C22×D8C22×C3711yescharacteristic
537C22×D8C22×C3711yescharacteristic, complemented
538C22×D8C22×C3711yescharacteristic, complemented
539C23×C8C22×C3711yescharacteristic, complemented
540D42—24no—
541D42—24no—
542C2×#127C22×C3711yescharacteristic
543C2×#121—21no—
544C2×#121—21no—
545C2×#121C22×C3711yescharacteristic
546C2×#121C22×C3711yescharacteristic
547C2×#121C22×C3711yescharacteristic, complemented
548C2×#121C22×C3711yescharacteristic, complemented
549C2×#120—21no—
550C2×#120—21no—
551C2×C4×D4C22×C3711yescharacteristic
552C2×C4×D4C22×C3711yescharacteristic
553C22×C4⋊C4C22×C3711yescharacteristic, complemented
554#466—24no—
555#447—24no—
556#447—24no—
557C2×#107C22×C3711yescharacteristic, complemented
558C2×#102—24no—
559C2×#102C22×C3711yescharacteristic
560C2×#102C22×C3711yescharacteristic
561C2×#102C22×C3711yescharacteristic
562C2×#102C22×C3711yescharacteristic, complemented
563C2×#102C22×C3711yescharacteristic, complemented
564C2×#102C22×C3711yescharacteristic, complemented
565C2×#102C22×C3711yescharacteristic, complemented
566C2×#102C22×C3711yescharacteristic, complemented
567C2×#102C22×C3711yescharacteristic, complemented
568C2×#102C22×C3711yescharacteristic, complemented
569C2×C22⋊C8C22×C3711yescharacteristic, complemented
570C2×C22⋊C8C22×C3711yescharacteristic, complemented
571C2×C22⋊C8C22×C3711yescharacteristic, complemented
572#396—21no—
573#394—21no—
574#390C22×C3711yescharacteristic, complemented
575#389C22×C3711yescharacteristic, complemented
576#386—21no—
577#380C22×C3711yescharacteristic, complemented
578#340C22×C3711yescharacteristic, complemented
579#340C22×C3711yescharacteristic, complemented
580#336C22×C3711yescharacteristic, complemented
581#336C22×C3711yescharacteristic, complemented
582C37#2442411yescharacteristic, direct product factor, Sylow
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C3711yescharacteristic
608C22×D4D4×C3714yescomplemented
609C22×D4C23×C3711yescharacteristic
610C22×D4C23×C3711yescharacteristic
611C22×D4C23×C3711yescharacteristic
612C22×D4C23×C3711yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C3711yescharacteristic
616C23×C4C23×C3711yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C3711yescharacteristic
630C22×C8C23×C3711yescharacteristic
631C22×C8C23×C3711yescharacteristic
632C22×C8C23×C3711yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C3714yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C3711yescharacteristic
656C2×C4⋊C4C23×C3711yescharacteristic
657C2×C4⋊C4C23×C3711yescharacteristic
658C2×C4⋊C4C23×C3711yescharacteristic
659C2×C4⋊C4C23×C3711yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C3711yescharacteristic
669C2×C22⋊C4D4×C3711yescharacteristic
670C2×C42C23×C3711yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C3714yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C3711yescharacteristic
706C24C2×D4×C3711yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C3714yescomplemented
762C2×D4C2×D4×C3712yes—
763C2×D4C2×D4×C3712yes—
764C2×D4C2×D4×C3712yes—
765C2×D4C2×D4×C3712yes—
766C2×D4#41×C3712yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C3711yescharacteristic
788C22×C4C2×D4×C3711yescharacteristic
789C22×C4C2×D4×C3711yescharacteristic
790C22×C4C2×D4×C3712yes—
791C22×C4C2×D4×C3712yes—
792C22×C4C2×D4×C3711yescharacteristic
793C22×C4C24×C3711yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C3712yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C3712yes—
820C4⋊C4C2×D4×C3712yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—48no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C3712yes—
886C23C2×D8×C3712yes—
887C23C2×D8×C3712yes—
888C23AGL(1,ℤ/8)×C3712yes—
889C23C22×D4×C3711yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C3714yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C3712yes—
948C2×C4C2×D8×C3712yes—
949C2×C4C22×D4×C3711yescharacteristic
950C2×C4C22×D4×C3711yescharacteristic
951C2×C4C22×D4×C3711yescharacteristic
952C2×C4C2×#41×C3711yescharacteristic
953C2×C4H(5,𝔽2)×C3711yescharacteristic
954C2×C4H(5,𝔽2)×C3711yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—24no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—41no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22C37×#44714yescomplemented
1003C22C2×#120×C3711yescharacteristic
1004C22D42×C3711yescharacteristic
1005C22C37×#54611yescharacteristic
1006C22C22×D8×C3711yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
1008C22C37×#57611yescharacteristic
1009C22C37×#57711yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—41no—
1015C4—42no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C3711yescharacteristic
1019C4C37×#53411yescharacteristic
1020C4D42×C3711yescharacteristic
1021C4C37×#54611yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2C37×#241011yescharacteristic
1029C2C2×C37×#44711yescharacteristic
1030C2C37×#301211yescharacteristic
1031C2C37×#326511yescharacteristic
1032C2D4×D8×C3711yescharacteristic
1033C2C37×#329411yescharacteristic
1034C2C37×#331811yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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×D42×C37C2semidirect
2. C2×C37×#466C2semidirect
3. C2×C37×#447C2semidirect
4. C2×C37×#447C2semidirect
5. C22×#102×C37C2semidirect
6. C37×#2416C2semidirect
7. C37×#2041C2semidirect
8. C37×#2033C2semidirect
9. C37×#2011C2semidirect
10. C37×#1999C2semidirect
11. C37×#1879C2semidirect
12. C37×#1874C2semidirect
13. C37×#1869C2semidirect
14. C37×#1862C2semidirect
15. C37×#1786C2semidirect
20. C22×D8×C37C22semidirect
21. C22×D8×C37C22semidirect
22. C23×C8×C37C22semidirect
30. C2×#121×C37C22semidirect
31. C2×#121×C37C22semidirect
36. C22×C4⋊C4×C37C22semidirect
40. C2×#107×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
47. C2×#102×C37C22semidirect
48. C2×#102×C37C22semidirect
49. C2×#102×C37C22semidirect
50. C2×#102×C37C22semidirect
51. C2×#102×C37C22semidirect
52. C2×C22⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C2×C22⋊C8×C37C22semidirect
57. C37×#390C22semidirect
58. C37×#389C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
90. C22×D4×C37D4semidirect
126. #121×C37D4semidirect
163. #102×C37D4semidirect
243. C2×D4×C37D8semidirect
291. C2×C8×C37C2×D4semidirect
302. C4⋊C4×C37C2×D4semidirect
396. D4×C37#121semidirect
441. #24424C37direct (N × H)
485. C22×C37#447semidirect
505. C2×D42C2×C37semidirect
506. C2×#466C2×C37semidirect
507. C2×#447C2×C37semidirect
508. C2×#447C2×C37semidirect
509. C22×#102C2×C37semidirect
510. #2416C2×C37semidirect
511. #2041C2×C37semidirect
512. #2033C2×C37semidirect
513. #2011C2×C37semidirect
514. #1999C2×C37semidirect
515. #1879C2×C37semidirect
516. #1874C2×C37semidirect
517. #1869C2×C37semidirect
518. #1862C2×C37semidirect
519. #1786C2×C37semidirect
537. C22×D8C22×C37semidirect
538. C22×D8C22×C37semidirect
539. C23×C8C22×C37semidirect
547. C2×#121C22×C37semidirect
548. C2×#121C22×C37semidirect
553. C22×C4⋊C4C22×C37semidirect
557. C2×#107C22×C37semidirect
562. C2×#102C22×C37semidirect
563. C2×#102C22×C37semidirect
564. C2×#102C22×C37semidirect
565. C2×#102C22×C37semidirect
566. C2×#102C22×C37semidirect
567. C2×#102C22×C37semidirect
568. C2×#102C22×C37semidirect
569. C2×C22⋊C8C22×C37semidirect
570. C2×C22⋊C8C22×C37semidirect
571. C2×C22⋊C8C22×C37semidirect
574. #390C22×C37semidirect
575. #389C22×C37semidirect
577. #380C22×C37semidirect
578. #340C22×C37semidirect
579. #340C22×C37semidirect
580. #336C22×C37semidirect
581. #336C22×C37semidirect
582. C37#24424direct (N × H)
608. C22×D4D4×C37semidirect
644. #121D4×C37semidirect
681. #102D4×C37semidirect
761. C2×D4D8×C37semidirect
809. C2×C8C2×D4×C37semidirect
820. C4⋊C4C2×D4×C37semidirect
914. D4#121×C37semidirect
1002. C22C37×#447semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C372
C2×C37×#4662
C2×C37×#4472
C22×#102×C372
C37×#24162
C37×#20412
C37×#20332
C37×#20112
C37×#19992
C37×#18792
C37×#18742
C37×#18692
C37×#18622
C37×#17862
#2442437