Finite Group Databasebeta

← C37×#22423 #22643676

Subgroups — C37×#22423 #22643676

Order 9472.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C37C211yesmaximal, characteristic
2C2×C37×#435C211yesmaximal, characteristic, complemented
3C2×C37×#418C211yesmaximal, characteristic, complemented
4C22×#102×C37C211yesmaximal, characteristic, complemented
5C37×#2352C211yesmaximal, characteristic, complemented
6C37×#1982C211yesmaximal, characteristic, complemented
7C37×#1961C211yesmaximal, characteristic, complemented
8C37×#1895C211yesmaximal, characteristic, complemented
9C37×#1893C211yesmaximal, characteristic, complemented
10C37×#1875C211yesmaximal, characteristic, complemented
11C37×#1874C211yesmaximal, characteristic, complemented
12C37×#1804C211yesmaximal, characteristic, complemented
13C37×#1786C211yesmaximal, characteristic, complemented
14C37×#1786C211yesmaximal, characteristic, complemented
15C37×#1762C211yesmaximal, characteristic, complemented
16C23×D4×C37—21no—
17C23×D4×C37C2211yescharacteristic
18C23×D4×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic, complemented
20C23×C8×C37C2211yescharacteristic, complemented
21D42×C37—24no—
22D42×C37C418yescomplemented
23C2×#127×C37C2211yescharacteristic
24C2×#121×C37—21no—
25C2×#121×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×#120×C37—21no—
28C2×#120×C37—21no—
29C2×C4×D4×C37C2211yescharacteristic
30C2×C4×D4×C37C2211yescharacteristic
31C2×#117×C37C2211yescharacteristic, complemented
32C22×C4⋊C4×C37C2211yescharacteristic, complemented
33C37×#435—24no—
34C2×C4⋊C8×C37C2211yescharacteristic, complemented
35C37×#418—24no—
36C2×#102×C37—24no—
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic, complemented
42C2×#102×C37C2211yescharacteristic, complemented
43C2×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×#102×C37C2211yescharacteristic, complemented
48C2×#102×C37C2211yescharacteristic, complemented
49C2×C22⋊C8×C37C2211yescharacteristic, complemented
50C2×C22⋊C8×C37C2211yescharacteristic, complemented
51C2×#97×C37C2211yescharacteristic, complemented
52C37×#388—21no—
53C37×#387—21no—
54C37×#386—21no—
55C37×#382C2211yescharacteristic, complemented
56C37×#380C2211yescharacteristic, complemented
57C37×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C37C2211yescharacteristic, complemented
59C4×C22⋊C4×C37—21no—
60C37×#340C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#340C2211yescharacteristic, complemented
64C25×C37—21no—
65C25×C37—21no—
66C22×D4×C37—22no—
67C22×D4×C37—22no—
68C22×D4×C37—22no—
69C22×D4×C37—22no—
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—28no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—22no—
77C22×D4×C37—22no—
78C22×D4×C37—21no—
79C22×D4×C37—41no—
80C22×D4×C37—41no—
81C22×D4×C37—41no—
82C22×D4×C37—41no—
83C22×D4×C37—44no—
84C22×D4×C37—44no—
85C22×D4×C37C2×C414yes—
86C22×D4×C37C2×C414yescomplemented
87C22×D4×C37D411yescharacteristic
88C22×D4×C37C2311yescharacteristic
89C22×D4×C37C2311yescharacteristic
90C22×D4×C37C2311yescharacteristic
91C23×C4×C37—21no—
92C23×C4×C37—21no—
93C23×C4×C37C2311yescharacteristic
94C23×C4×C37C2311yescharacteristic
95C2×M16×C37—22no—
96C2×M16×C37—22no—
97C2×M16×C37—41no—
98C22×C8×C37—22no—
99C22×C8×C37—22no—
100C22×C8×C37—41no—
101C22×C8×C37C2311yescharacteristic
102C22×C8×C37C2311yescharacteristic
103C22×C8×C37C2311yescharacteristic
104C22×C8×C37C2311yescharacteristic
105#127×C37—22no—
106#127×C37C2×C414yescomplemented
107#121×C37—22no—
108#121×C37—22no—
109#121×C37—28no—
110#121×C37C2×C414yes—
111#121×C37C2×C414yescomplemented
112#120×C37—28no—
113#120×C37—28no—
114C4×D4×C37—22no—
115C4×D4×C37C2×C414yes—
116C4×D4×C37C2×C414yescomplemented
117C4×D4×C37D414yes—
118#117×C37—22no—
119#117×C37—41no—
120C2×C4⋊C4×C37—22no—
121C2×C4⋊C4×C37—21no—
122C2×C4⋊C4×C37—41no—
123C2×C4⋊C4×C37D411yescharacteristic
124C2×C4⋊C4×C37C2311yescharacteristic
125C2×C4⋊C4×C37C2311yescharacteristic
126C2×C4⋊C4×C37C2311yescharacteristic
127C2×C4⋊C4×C37C2311yescharacteristic
128C2×C4⋊C4×C37C2311yescharacteristic
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37—21no—
133C2×C22⋊C4×C37—21no—
134C2×C22⋊C4×C37—21no—
135C2×C22⋊C4×C37D411yescharacteristic
136C2×C22⋊C4×C37D411yescharacteristic
137C2×C42×C37—21no—
138C2×C42×C37—21no—
139C2×C42×C37C2311yescharacteristic
140C4⋊C8×C37—22no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—22no—
144#102×C37—22no—
145#102×C37—22no—
146#102×C37—22no—
147#102×C37—22no—
148#102×C37—41no—
149#102×C37—41no—
150#102×C37—41no—
151#102×C37—41no—
152#102×C37D414yescomplemented
153C22⋊C8×C37—22no—
154C22⋊C8×C37—22no—
155#97×C37—22no—
156#95×C37—21no—
157#95×C37—21no—
158#95×C37—21no—
159#95×C37—21no—
160#95×C37—21no—
161C24×C37—21no—
162C24×C37—21no—
163C24×C37—21no—
164C24×C37—24no—
165C24×C37—24no—
166C24×C37—42no—
167C24×C37—42no—
168C24×C37—42no—
169C24×C37—42no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—42no—
174C24×C37—81no—
175C24×C37—81no—
176C24×C37—81no—
177C24×C37—81no—
178C24×C37C2×D411yescharacteristic
179C24×C37C2×D411yescharacteristic
180C2×D4×C37—22no—
181C2×D4×C37—22no—
182C2×D4×C37—28no—
183C2×D4×C37—28no—
184C2×D4×C37—24no—
185C2×D4×C37—24no—
186C2×D4×C37—24no—
187C2×D4×C37—24no—
188C2×D4×C37—24no—
189C2×D4×C37—24no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—21no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—44no—
204C2×D4×C37—44no—
205C2×D4×C37—44no—
206C2×D4×C37—44no—
207C2×D4×C37—44no—
208C2×D4×C37—44no—
209C2×D4×C37—42no—
210C2×D4×C37—42no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
215C2×D4×C37—432no—
216C2×D4×C37—42no—
217C2×D4×C37—42no—
218C2×D4×C37—42no—
219C2×D4×C37—42no—
220C2×D4×C37—81no—
221C2×D4×C37—81no—
222C2×D4×C37C22⋊C414yes—
223C2×D4×C37C22×C412yes—
224C2×D4×C37C22×C412yes—
225C2×D4×C37C22×C412yes—
226C2×D4×C37C2×D412yes—
227C2×D4×C37#4112yes—
228C22×C4×C37—21no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—21no—
233C22×C4×C37—21no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—21no—
237C22×C4×C37—21no—
238C22×C4×C37—24no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—42no—
243C22×C4×C37—42no—
244C22×C4×C37—42no—
245C22×C4×C37—42no—
246C22×C4×C37—81no—
247C22×C4×C37C22×C412yes—
248C22×C4×C37C22×C412yes—
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D411yescharacteristic
251C22×C4×C37C2×D411yescharacteristic
252C22×C4×C37C2×D411yescharacteristic
253C22×C4×C37C2×D412yes—
254C22×C4×C37C2×D412yes—
255C22×C4×C37C2411yescharacteristic
256M16×C37—44no—
257C2×C8×C37—21no—
258C2×C8×C37—21no—
259C2×C8×C37—21no—
260C2×C8×C37—21no—
261C2×C8×C37—21no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—44no—
269C2×C8×C37C2×D412yescomplemented
270C4⋊C4×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—42no—
279C4⋊C4×C37C22⋊C414yes—
280C4⋊C4×C37C22×C412yes—
281C4⋊C4×C37C2×D412yescomplemented
282C22⋊C4×C37—24no—
283C22⋊C4×C37—24no—
284C22⋊C4×C37—24no—
285C22⋊C4×C37—42no—
286C22⋊C4×C37—42no—
287C22⋊C4×C37—81no—
288C22⋊C4×C37C22⋊C414yes—
289C22⋊C4×C37C22⋊C414yes—
290C42×C37—42no—
291C42×C37—81no—
292C42×C37C22×C412yes—
293C42×C37C2×D412yes—
294C23×C37—21no—
295C23×C37—21no—
296C23×C37—21no—
297C23×C37—21no—
298C23×C37—22no—
299C23×C37—21no—
300C23×C37—22no—
301C23×C37—21no—
302C23×C37—22no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—22no—
308C23×C37—22no—
309C23×C37—48no—
310C23×C37—48no—
311C23×C37—48no—
312C23×C37—41no—
313C23×C37—41no—
314C23×C37—41no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37—41no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37—41no—
321C23×C37—41no—
322C23×C37—41no—
323C23×C37—41no—
324C23×C37—41no—
325C23×C37—41no—
326C23×C37—41no—
327C23×C37—41no—
328C23×C37—48no—
329C23×C37—84no—
330C23×C37—84no—
331C23×C37—84no—
332C23×C37—84no—
333C23×C37—84no—
334C23×C37—84no—
335C23×C37—84no—
336C23×C37—84no—
337C23×C37—84no—
338C23×C37—84no—
339C23×C37C2×C22⋊C412yes—
340C23×C37C2×C22⋊C412yes—
341C23×C37AGL(1,ℤ/8)12yes—
342C23×C37AGL(1,ℤ/8)12yes—
343C23×C37C22×D411yescharacteristic
344D4×C37—28no—
345D4×C37—22no—
346D4×C37—22no—
347D4×C37—22no—
348D4×C37—22no—
349D4×C37—22no—
350D4×C37—22no—
351D4×C37—22no—
352D4×C37—48no—
353D4×C37—48no—
354D4×C37—48no—
355D4×C37—48no—
356D4×C37—48no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—41no—
361D4×C37—84no—
362D4×C37C4×D414yes—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—21no—
369C2×C4×C37—21no—
370C2×C4×C37—21no—
371C2×C4×C37—22no—
372C2×C4×C37—22no—
373C2×C4×C37—22no—
374C2×C4×C37—22no—
375C2×C4×C37—22no—
376C2×C4×C37—22no—
377C2×C4×C37—22no—
378C2×C4×C37—22no—
379C2×C4×C37—22no—
380C2×C4×C37—22no—
381C2×C4×C37—48no—
382C2×C4×C37—41no—
383C2×C4×C37—41no—
384C2×C4×C37—41no—
385C2×C4×C37—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—41no—
393C2×C4×C37—41no—
394C2×C4×C37—41no—
395C2×C4×C37—84no—
396C2×C4×C37C2×C22⋊C412yes—
397C2×C4×C37C2×C22⋊C412yes—
398C2×C4×C37C2×C22⋊C412yes—
399C2×C4×C37C2×C22⋊C412yes—
400C2×C4×C37C23×C411yescharacteristic
401C2×C4×C37C22×D411yescharacteristic
402C2×C4×C37C22×D411yescharacteristic
403C2×C4×C37C2×#4111yescharacteristic
404C2×C4×C37H(5,𝔽2)11yescharacteristic
405C2×C4×C37H(5,𝔽2)11yescharacteristic
406C8×C37—22no—
407C8×C37—41no—
408C8×C37—41no—
409C8×C37—41no—
410#22423C3711yesmaximal, characteristic, direct product factor, Sylow
411C22×C37—22no—
412C22×C37—22no—
413C22×C37—22no—
414C22×C37—22no—
415C22×C37—22no—
416C22×C37—22no—
417C22×C37—22no—
418C22×C37—24no—
419C22×C37—22no—
420C22×C37—22no—
421C22×C37—42no—
422C22×C37—42no—
423C22×C37—41no—
424C22×C37—42no—
425C22×C37—41no—
426C22×C37—42no—
427C22×C37—41no—
428C22×C37—42no—
429C22×C37—41no—
430C22×C37—42no—
431C22×C37—42no—
432C22×C37—42no—
433C22×C37—42no—
434C22×C37—42no—
435C22×C37—42no—
436C22×C37—42no—
437C22×C37—816no—
438C22×C37—816no—
439C22×C37—81no—
440C22×C37—81no—
441C22×C37—81no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37#41814yescomplemented
448C22×C37C22×C22⋊C411yescharacteristic
449C22×C37D4211yescharacteristic
450C22×C37#54611yescharacteristic
451C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
453C22×C37#57611yescharacteristic
454C22×C37#57711yescharacteristic
455C4×C37—22no—
456C4×C37—22no—
457C4×C37—22no—
458C4×C37—22no—
459C4×C37—42no—
460C4×C37—42no—
461C4×C37—81no—
462C4×C37—81no—
463C4×C37—81no—
464C4×C37C2×C4×D411yescharacteristic
465C4×C37#51811yescharacteristic
466C4×C37D4211yescharacteristic
467C4×C37#54611yescharacteristic
468C2×D42C2×C3711yescharacteristic
469C2×#435C2×C3711yescharacteristic, complemented
470C2×#418C2×C3711yescharacteristic, complemented
471C22×#102C2×C3711yescharacteristic, complemented
472#2352C2×C3711yescharacteristic, complemented
473#1982C2×C3711yescharacteristic, complemented
474#1961C2×C3711yescharacteristic, complemented
475#1895C2×C3711yescharacteristic, complemented
476#1893C2×C3711yescharacteristic, complemented
477#1875C2×C3711yescharacteristic, complemented
478#1874C2×C3711yescharacteristic, complemented
479#1804C2×C3711yescharacteristic, complemented
480#1786C2×C3711yescharacteristic, complemented
481#1786C2×C3711yescharacteristic, complemented
482#1762C2×C3711yescharacteristic, complemented
483C2×C37—24no—
484C2×C37—42no—
485C2×C37—44no—
486C2×C37—82no—
487C2×C37—82no—
488C2×C37D4×C22⋊C411yescharacteristic
489C2×C37C2×#41811yescharacteristic
490C2×C37#289711yescharacteristic
491C2×C37#326411yescharacteristic
492C2×C37#326511yescharacteristic
493C2×C37#331011yescharacteristic
494C2×C37#331811yescharacteristic
495C23×D4—21no—
496C23×D4C22×C3711yescharacteristic
497C23×D4C22×C3711yescharacteristic
498C22×M16C22×C3711yescharacteristic, complemented
499C23×C8C22×C3711yescharacteristic, complemented
500D42—24no—
501D42C4×C3718yescomplemented
502C2×#127C22×C3711yescharacteristic
503C2×#121—21no—
504C2×#121C22×C3711yescharacteristic
505C2×#121C22×C3711yescharacteristic
506C2×#120—21no—
507C2×#120—21no—
508C2×C4×D4C22×C3711yescharacteristic
509C2×C4×D4C22×C3711yescharacteristic
510C2×#117C22×C3711yescharacteristic, complemented
511C22×C4⋊C4C22×C3711yescharacteristic, complemented
512#435—24no—
513C2×C4⋊C8C22×C3711yescharacteristic, complemented
514#418—24no—
515C2×#102—24no—
516C2×#102C22×C3711yescharacteristic
517C2×#102C22×C3711yescharacteristic
518C2×#102C22×C3711yescharacteristic
519C2×#102C22×C3711yescharacteristic
520C2×#102C22×C3711yescharacteristic, complemented
521C2×#102C22×C3711yescharacteristic, complemented
522C2×#102C22×C3711yescharacteristic, complemented
523C2×#102C22×C3711yescharacteristic, complemented
524C2×#102C22×C3711yescharacteristic, complemented
525C2×#102C22×C3711yescharacteristic, complemented
526C2×#102C22×C3711yescharacteristic, complemented
527C2×#102C22×C3711yescharacteristic, complemented
528C2×C22⋊C8C22×C3711yescharacteristic, complemented
529C2×C22⋊C8C22×C3711yescharacteristic, complemented
530C2×#97C22×C3711yescharacteristic, complemented
531#388—21no—
532#387—21no—
533#386—21no—
534#382C22×C3711yescharacteristic, complemented
535#380C22×C3711yescharacteristic, complemented
536#380C22×C3711yescharacteristic, complemented
537C4×C4⋊C4C22×C3711yescharacteristic, complemented
538C4×C22⋊C4—21no—
539#340C22×C3711yescharacteristic, complemented
540#340C22×C3711yescharacteristic, complemented
541#340C22×C3711yescharacteristic, complemented
542#340C22×C3711yescharacteristic, complemented
543C37#2242311yescharacteristic, direct product factor, Sylow
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×C4×C3714yes—
566C22×D4C2×C4×C3714yescomplemented
567C22×D4D4×C3711yescharacteristic
568C22×D4C23×C3711yescharacteristic
569C22×D4C23×C3711yescharacteristic
570C22×D4C23×C3711yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C3711yescharacteristic
574C23×C4C23×C3711yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C3711yescharacteristic
582C22×C8C23×C3711yescharacteristic
583C22×C8C23×C3711yescharacteristic
584C22×C8C23×C3711yescharacteristic
585#127—22no—
586#127C2×C4×C3714yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×C4×C3714yes—
591#121C2×C4×C3714yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×C4×C3714yes—
596C4×D4C2×C4×C3714yescomplemented
597C4×D4D4×C3714yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C3711yescharacteristic
604C2×C4⋊C4C23×C3711yescharacteristic
605C2×C4⋊C4C23×C3711yescharacteristic
606C2×C4⋊C4C23×C3711yescharacteristic
607C2×C4⋊C4C23×C3711yescharacteristic
608C2×C4⋊C4C23×C3711yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C3711yescharacteristic
616C2×C22⋊C4D4×C3711yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C23×C3711yescharacteristic
620C4⋊C8—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102—41no—
632#102D4×C3714yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C3711yescharacteristic
659C24C2×D4×C3711yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C3714yes—
703C2×D4C22×C4×C3712yes—
704C2×D4C22×C4×C3712yes—
705C2×D4C22×C4×C3712yes—
706C2×D4C2×D4×C3712yes—
707C2×D4#41×C3712yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C3712yes—
728C22×C4C22×C4×C3712yes—
729C22×C4C2×D4×C3711yescharacteristic
730C22×C4C2×D4×C3711yescharacteristic
731C22×C4C2×D4×C3711yescharacteristic
732C22×C4C2×D4×C3711yescharacteristic
733C22×C4C2×D4×C3712yes—
734C22×C4C2×D4×C3712yes—
735C22×C4C24×C3711yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C3712yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C3714yes—
760C4⋊C4C22×C4×C3712yes—
761C4⋊C4C2×D4×C3712yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C3714yes—
769C22⋊C4C22⋊C4×C3714yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C3712yes—
773C42C2×D4×C3712yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—48no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C3712yes—
820C23C2×C22⋊C4×C3712yes—
821C23AGL(1,ℤ/8)×C3712yes—
822C23AGL(1,ℤ/8)×C3712yes—
823C23C22×D4×C3711yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C3714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C3712yes—
877C2×C4C2×C22⋊C4×C3712yes—
878C2×C4C2×C22⋊C4×C3712yes—
879C2×C4C2×C22⋊C4×C3712yes—
880C2×C4C23×C4×C3711yescharacteristic
881C2×C4C22×D4×C3711yescharacteristic
882C2×C4C22×D4×C3711yescharacteristic
883C2×C4C2×#41×C3711yescharacteristic
884C2×C4H(5,𝔽2)×C3711yescharacteristic
885C2×C4H(5,𝔽2)×C3711yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22C37×#41814yescomplemented
927C22C22×C22⋊C4×C3711yescharacteristic
928C22D42×C3711yescharacteristic
929C22C37×#54611yescharacteristic
930C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
931C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
932C22C37×#57611yescharacteristic
933C22C37×#57711yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C3711yescharacteristic
944C4C37×#51811yescharacteristic
945C4D42×C3711yescharacteristic
946C4C37×#54611yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C3711yescharacteristic
953C2C2×C37×#41811yescharacteristic
954C2C37×#289711yescharacteristic
955C2C37×#326411yescharacteristic
956C2C37×#326511yescharacteristic
957C2C37×#331011yescharacteristic
958C2C37×#331811yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutatorC2×C4C23×C4×C37
Frattini, cosocleC22×C4C24×C37
prime radicalC2×D42×C37C2
LCSG ▷ C2×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
2. C2×C37×#435C2semidirect
3. C2×C37×#418C2semidirect
4. C22×#102×C37C2semidirect
5. C37×#2352C2semidirect
6. C37×#1982C2semidirect
7. C37×#1961C2semidirect
8. C37×#1895C2semidirect
9. C37×#1893C2semidirect
10. C37×#1875C2semidirect
11. C37×#1874C2semidirect
12. C37×#1804C2semidirect
13. C37×#1786C2semidirect
14. C37×#1786C2semidirect
15. C37×#1762C2semidirect
19. C22×M16×C37C22semidirect
20. C23×C8×C37C22semidirect
22. D42×C37C4semidirect
31. C2×#117×C37C22semidirect
32. C22×C4⋊C4×C37C22semidirect
34. C2×C4⋊C8×C37C22semidirect
41. C2×#102×C37C22semidirect
42. C2×#102×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
47. C2×#102×C37C22semidirect
48. C2×#102×C37C22semidirect
49. C2×C22⋊C8×C37C22semidirect
50. C2×C22⋊C8×C37C22semidirect
51. C2×#97×C37C22semidirect
55. C37×#382C22semidirect
56. C37×#380C22semidirect
57. C37×#380C22semidirect
58. C4×C4⋊C4×C37C22semidirect
60. C37×#340C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#340C22semidirect
86. C22×D4×C37C2×C4semidirect
106. #127×C37C2×C4semidirect
111. #121×C37C2×C4semidirect
116. C4×D4×C37C2×C4semidirect
152. #102×C37D4semidirect
269. C2×C8×C37C2×D4semidirect
281. C4⋊C4×C37C2×D4semidirect
410. #22423C37direct (N × H)
447. C22×C37#418semidirect
469. C2×#435C2×C37semidirect
470. C2×#418C2×C37semidirect
471. C22×#102C2×C37semidirect
472. #2352C2×C37semidirect
473. #1982C2×C37semidirect
474. #1961C2×C37semidirect
475. #1895C2×C37semidirect
476. #1893C2×C37semidirect
477. #1875C2×C37semidirect
478. #1874C2×C37semidirect
479. #1804C2×C37semidirect
480. #1786C2×C37semidirect
481. #1786C2×C37semidirect
482. #1762C2×C37semidirect
498. C22×M16C22×C37semidirect
499. C23×C8C22×C37semidirect
501. D42C4×C37semidirect
510. C2×#117C22×C37semidirect
511. C22×C4⋊C4C22×C37semidirect
513. C2×C4⋊C8C22×C37semidirect
520. C2×#102C22×C37semidirect
521. C2×#102C22×C37semidirect
522. C2×#102C22×C37semidirect
523. C2×#102C22×C37semidirect
524. C2×#102C22×C37semidirect
525. C2×#102C22×C37semidirect
526. C2×#102C22×C37semidirect
527. C2×#102C22×C37semidirect
528. C2×C22⋊C8C22×C37semidirect
529. C2×C22⋊C8C22×C37semidirect
530. C2×#97C22×C37semidirect
534. #382C22×C37semidirect
535. #380C22×C37semidirect
536. #380C22×C37semidirect
537. C4×C4⋊C4C22×C37semidirect
539. #340C22×C37semidirect
540. #340C22×C37semidirect
541. #340C22×C37semidirect
542. #340C22×C37semidirect
543. C37#22423direct (N × H)
566. C22×D4C2×C4×C37semidirect
586. #127C2×C4×C37semidirect
591. #121C2×C4×C37semidirect
596. C4×D4C2×C4×C37semidirect
632. #102D4×C37semidirect
749. C2×C8C2×D4×C37semidirect
761. C4⋊C4C2×D4×C37semidirect
926. C22C37×#418semidirect

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×#4352
C2×C37×#4182
C22×#102×C372
C37×#23522
C37×#19822
C37×#19612
C37×#18952
C37×#18932
C37×#18752
C37×#18742
C37×#18042
C37×#17862
C37×#17622
#2242337