Finite Group Databasebeta

← C37×#24388 #22645641

Subgroups — C37×#24388 #22645641

Order 9472.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#525C211yesmaximal, characteristic, complemented
2C2×C37×#469C211yesmaximal, characteristic, complemented
3C2×C37×#468C211yesmaximal, characteristic, complemented
4C2×C37×#449C211yesmaximal, characteristic, complemented
5C2×C37×#407C211yesmaximal, characteristic, complemented
6C37×#2847C211yesmaximal, characteristic, complemented
7C37×#2035C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2000C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1894C211yesmaximal, characteristic, complemented
13C37×#1875C211yesmaximal, characteristic, complemented
14C37×#1854C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C24×C4×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic, complemented
19C22×D8×C37C2211yescharacteristic, complemented
20C22×M16×C37C2211yescharacteristic
21C22×M16×C37C2211yescharacteristic
22C37×#525—24no—
23C37×#525—24no—
24C2×#123×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C2×#121×C37C2211yescharacteristic
32C2×#120×C37—21no—
33C2×#120×C37—21no—
34C2×C4×D4×C37—21no—
35C2×C4×D4×C37—21no—
36C2×#117×C37C2211yescharacteristic
37C37×#469—24no—
38C37×#468—24no—
39C37×#449—24no—
40C2×#107×C37C2211yescharacteristic, complemented
41C2×#106×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#103×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×#102×C37C2211yescharacteristic, complemented
48C2×#102×C37C2211yescharacteristic, complemented
49C2×#102×C37C2211yescharacteristic, complemented
50C37×#407—24no—
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C2×C22⋊C8×C37C2211yescharacteristic
55C37×#386—21no—
56C37×#386—21no—
57C37×#386—21no—
58C37×#380C2211yescharacteristic
59C37×#380C2211yescharacteristic
60C37×#380C2211yescharacteristic
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#340C2211yescharacteristic, complemented
64C37×#340C2211yescharacteristic, complemented
65C25×C37D411yescharacteristic
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—41no—
71C2×#41×C37—41no—
72C22×Q8×C37C2311yescharacteristic
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37C2311yescharacteristic
80C22×D4×C37C2311yescharacteristic
81C23×C4×C37—22no—
82C23×C4×C37—22no—
83C23×C4×C37—22no—
84C23×C4×C37—21no—
85C23×C4×C37—22no—
86C23×C4×C37—41no—
87C23×C4×C37—41no—
88C23×C4×C37D411yescharacteristic
89C23×C4×C37D411yescharacteristic
90C23×C4×C37D411yescharacteristic
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C23×C4×C37C2311yescharacteristic
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—41no—
97C2×D8×C37—22no—
98C2×D8×C37—22no—
99C2×D8×C37—41no—
100C2×M16×C37—22no—
101C2×M16×C37—22no—
102C2×M16×C37—22no—
103C2×M16×C37—22no—
104C2×M16×C37—41no—
105C2×M16×C37—41no—
106C22×C8×C37C2311yescharacteristic
107C22×C8×C37C2311yescharacteristic
108C22×C8×C37C2311yescharacteristic
109C22×C8×C37C2311yescharacteristic
110#123×C37—28no—
111C22⋊Q8×C37—22no—
112C22⋊Q8×C37—22no—
113C22⋊Q8×C37—22no—
114C22⋊Q8×C37D414yescomplemented
115#121×C37—22no—
116#121×C37—22no—
117#121×C37—22no—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37—41no—
123#121×C37—41no—
124#121×C37D414yescomplemented
125#120×C37—28no—
126#120×C37—44no—
127C4×D4×C37—28no—
128C4×D4×C37—28no—
129#117×C37—22no—
130#117×C37—22no—
131C2×C4⋊C4×C37—21no—
132C2×C4⋊C4×C37—21no—
133C2×C4⋊C4×C37C2311yescharacteristic
134C2×C4⋊C4×C37C2311yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C4⋊C4×C37C2311yescharacteristic
137C2×C4⋊C4×C37C2311yescharacteristic
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—21no—
140C2×C22⋊C4×C37—21no—
141C2×C22⋊C4×C37—21no—
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×C42×C37—21no—
150#107×C37—22no—
151#106×C37—22no—
152#103×C37—22no—
153#103×C37—22no—
154#103×C37—41no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—22no—
158#102×C37—22no—
159#102×C37—41no—
160C22⋊C8×C37—22no—
161C22⋊C8×C37—22no—
162C22⋊C8×C37—22no—
163C22⋊C8×C37D414yescomplemented
164#95×C37—21no—
165#95×C37—21no—
166#95×C37—21no—
167C24×C37—22no—
168C24×C37—22no—
169C24×C37—22no—
170C24×C37—21no—
171C24×C37—21no—
172C24×C37—41no—
173C24×C37—41no—
174C24×C37—41no—
175C24×C37—41no—
176C24×C37C2×D411yescharacteristic
177C24×C37C2×D411yescharacteristic
178C24×C37C2×D411yescharacteristic
179#41×C37—44no—
180#41×C37—44no—
181#41×C37—44no—
182#41×C37—44no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37—21no—
188C2×Q8×C37C2×D412yes—
189C2×D4×C37—24no—
190C2×D4×C37—24no—
191C2×D4×C37—24no—
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—42no—
204C2×D4×C37—42no—
205C2×D4×C37—42no—
206C2×D4×C37—42no—
207C2×D4×C37—42no—
208C2×D4×C37—42no—
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—42no—
216C2×D4×C37—42no—
217C2×D4×C37—42no—
218C2×D4×C37C2×D412yes—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—24no—
228C22×C4×C37—22no—
229C22×C4×C37—22no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—21no—
233C22×C4×C37—22no—
234C22×C4×C37—22no—
235C22×C4×C37—22no—
236C22×C4×C37—22no—
237C22×C4×C37—21no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—41no—
247C22×C4×C37—41no—
248C22×C4×C37—41no—
249C22×C4×C37—44no—
250C22×C4×C37—44no—
251C22×C4×C37—44no—
252C22×C4×C37—44no—
253C22×C4×C37—42no—
254C22×C4×C37—42no—
255C22×C4×C37C2×D411yescharacteristic
256C22×C4×C37C2×D411yescharacteristic
257C22×C4×C37C2×D412yes—
258C22×C4×C37C2×D412yes—
259C22×C4×C37C2×D411yescharacteristic
260C22×C4×C37C2×D412yes—
261C22×C4×C37#4112yes—
262C22×C4×C37C2411yescharacteristic
263SD16×C37—44no—
264D8×C37—44no—
265M16×C37—44no—
266M16×C37—44no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37—21no—
272C2×C8×C37—21no—
273C2×C8×C37—21no—
274C2×C8×C37—21no—
275C2×C8×C37—21no—
276C2×C8×C37—21no—
277C2×C8×C37C2×D412yes—
278C2×C8×C37C2×D412yes—
279C4⋊C4×C37—24no—
280C4⋊C4×C37—24no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37—21no—
285C4⋊C4×C37—21no—
286C4⋊C4×C37—21no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—21no—
289C4⋊C4×C37C2×D412yes—
290C4⋊C4×C37C2×D412yes—
291C22⋊C4×C37—24no—
292C22⋊C4×C37—24no—
293C22⋊C4×C37—24no—
294C22⋊C4×C37—24no—
295C22⋊C4×C37—24no—
296C22⋊C4×C37—42no—
297C22⋊C4×C37—42no—
298C22⋊C4×C37—42no—
299C22⋊C4×C37—42no—
300C22⋊C4×C37—42no—
301C22⋊C4×C37—42no—
302C42×C37—24no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—21no—
318C23×C37—21no—
319C23×C37—21no—
320C23×C37—21no—
321C23×C37—22no—
322C23×C37—44no—
323C23×C37—44no—
324C23×C37—44no—
325C23×C37—44no—
326C23×C37—44no—
327C23×C37—44no—
328C23×C37—44no—
329C23×C37—41no—
330C23×C37—41no—
331C23×C37—41no—
332C23×C37—41no—
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#12012yes—
343C23×C37#12112yes—
344C23×C37AGL(1,ℤ/8)12yes—
345C23×C37C22×D411yescharacteristic
346Q8×C37—22no—
347Q8×C37—22no—
348Q8×C37—41no—
349Q8×C37—41no—
350D4×C37—22no—
351D4×C37—22no—
352D4×C37—48no—
353D4×C37—48no—
354D4×C37—48no—
355D4×C37—41no—
356D4×C37—41no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—41no—
361D4×C37—84no—
362D4×C37—84no—
363D4×C37—84no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—22no—
369C2×C4×C37—22no—
370C2×C4×C37—22no—
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—21no—
379C2×C4×C37—22no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—44no—
383C2×C4×C37—44no—
384C2×C4×C37—44no—
385C2×C4×C37—48no—
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—41no—
396C2×C4×C37—41no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37#12012yes—
406C2×C4×C37#12112yes—
407C2×C4×C37C22×D411yescharacteristic
408C2×C4×C37C22×D411yescharacteristic
409C2×C4×C37C22×D411yescharacteristic
410C2×C4×C37C2×#4111yescharacteristic
411C2×C4×C37H(5,𝔽2)11yescharacteristic
412C2×C4×C37H(5,𝔽2)11yescharacteristic
413C8×C37—22no—
414C8×C37—22no—
415C8×C37—41no—
416C8×C37—41no—
417#24388C3711yesmaximal, characteristic, direct product factor, Sylow
418C22×C37—22no—
419C22×C37—22no—
420C22×C37—22no—
421C22×C37—22no—
422C22×C37—22no—
423C22×C37—22no—
424C22×C37—22no—
425C22×C37—22no—
426C22×C37—22no—
427C22×C37—416no—
428C22×C37—41no—
429C22×C37—41no—
430C22×C37—41no—
431C22×C37—41no—
432C22×C37—41no—
433C22×C37—41no—
434C22×C37—41no—
435C22×C37—41no—
436C22×C37—41no—
437C22×C37—41no—
438C22×C37—41no—
439C22×C37—41no—
440C22×C37—42no—
441C22×C37—42no—
442C22×C37—42no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37—81no—
449C22×C37—81no—
450C22×C37—81no—
451C22×C37—81no—
452C22×C37—81no—
453C22×C37—81no—
454C22×C37C2×#12011yescharacteristic
455C22×C37C2×#12111yescharacteristic
456C22×C37#53411yescharacteristic
457C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
458C22×C37#57511yescharacteristic
459C22×C37#57511yescharacteristic
460C22×C37#57511yescharacteristic
461C4×C37—22no—
462C4×C37—22no—
463C4×C37—41no—
464C4×C37—42no—
465C4×C37—42no—
466C4×C37—42no—
467C4×C37—81no—
468C4×C37—81no—
469C4×C37—81no—
470C4×C37D4211yescharacteristic
471C4×C37D4211yescharacteristic
472C4×C37#54611yescharacteristic
473C4×C37#54611yescharacteristic
474C2×#525C2×C3711yescharacteristic, complemented
475C2×#469C2×C3711yescharacteristic, complemented
476C2×#468C2×C3711yescharacteristic, complemented
477C2×#449C2×C3711yescharacteristic, complemented
478C2×#407C2×C3711yescharacteristic, complemented
479#2847C2×C3711yescharacteristic, complemented
480#2035C2×C3711yescharacteristic, complemented
481#2033C2×C3711yescharacteristic, complemented
482#2000C2×C3711yescharacteristic, complemented
483#1999C2×C3711yescharacteristic, complemented
484#1895C2×C3711yescharacteristic, complemented
485#1894C2×C3711yescharacteristic, complemented
486#1875C2×C3711yescharacteristic, complemented
487#1854C2×C3711yescharacteristic, complemented
488#1788C2×C3711yescharacteristic, complemented
489C2×C37—42no—
490C2×C37—42no—
491C2×C37—42no—
492C2×C37—82no—
493C2×C37—161no—
494C2×C37#241011yescharacteristic
495C2×C37#300511yescharacteristic
496C2×C37#300611yescharacteristic
497C2×C37#305411yescharacteristic
498C2×C37#305511yescharacteristic
499C2×C37#319411yescharacteristic
500C2×C37#319711yescharacteristic
501C22×#41C22×C3711yescharacteristic
502C24×C4C22×C3711yescharacteristic
503C22×SD16C22×C3711yescharacteristic, complemented
504C22×D8C22×C3711yescharacteristic, complemented
505C22×M16C22×C3711yescharacteristic
506C22×M16C22×C3711yescharacteristic
507#525—24no—
508#525—24no—
509C2×#123—21no—
510C2×C22⋊Q8C22×C3711yescharacteristic
511C2×C22⋊Q8C22×C3711yescharacteristic
512C2×#121C22×C3711yescharacteristic
513C2×#121C22×C3711yescharacteristic
514C2×#121C22×C3711yescharacteristic
515C2×#121C22×C3711yescharacteristic
516C2×#121C22×C3711yescharacteristic
517C2×#120—21no—
518C2×#120—21no—
519C2×C4×D4—21no—
520C2×C4×D4—21no—
521C2×#117C22×C3711yescharacteristic
522#469—24no—
523#468—24no—
524#449—24no—
525C2×#107C22×C3711yescharacteristic, complemented
526C2×#106C22×C3711yescharacteristic, complemented
527C2×#103C22×C3711yescharacteristic, complemented
528C2×#103C22×C3711yescharacteristic, complemented
529C2×#103C22×C3711yescharacteristic, complemented
530C2×#102C22×C3711yescharacteristic, complemented
531C2×#102C22×C3711yescharacteristic, complemented
532C2×#102C22×C3711yescharacteristic, complemented
533C2×#102C22×C3711yescharacteristic, complemented
534C2×#102C22×C3711yescharacteristic, complemented
535#407—24no—
536C2×C22⋊C8C22×C3711yescharacteristic
537C2×C22⋊C8C22×C3711yescharacteristic
538C2×C22⋊C8C22×C3711yescharacteristic
539C2×C22⋊C8C22×C3711yescharacteristic
540#386—21no—
541#386—21no—
542#386—21no—
543#380C22×C3711yescharacteristic
544#380C22×C3711yescharacteristic
545#380C22×C3711yescharacteristic
546#340C22×C3711yescharacteristic, complemented
547#340C22×C3711yescharacteristic, complemented
548#340C22×C3711yescharacteristic, complemented
549#340C22×C3711yescharacteristic, complemented
550C37#2438811yescharacteristic, direct product factor, Sylow
551C25D4×C3711yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C23×C3711yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4C23×C3711yescharacteristic
566C22×D4C23×C3711yescharacteristic
567C23×C4—21no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4D4×C3711yescharacteristic
575C23×C4D4×C3711yescharacteristic
576C23×C4D4×C3711yescharacteristic
577C23×C4C23×C3711yescharacteristic
578C23×C4C23×C3711yescharacteristic
579C23×C4C23×C3711yescharacteristic
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—22no—
590C2×M16—41no—
591C2×M16—41no—
592C22×C8C23×C3711yescharacteristic
593C22×C8C23×C3711yescharacteristic
594C22×C8C23×C3711yescharacteristic
595C22×C8C23×C3711yescharacteristic
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8D4×C3714yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#121D4×C3714yescomplemented
611#120—28no—
612#120—44no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C3711yescharacteristic
620C2×C4⋊C4C23×C3711yescharacteristic
621C2×C4⋊C4C23×C3711yescharacteristic
622C2×C4⋊C4C23×C3711yescharacteristic
623C2×C4⋊C4C23×C3711yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636#107—22no—
637#106—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8D4×C3714yescomplemented
650#95—21no—
651#95—21no—
652#95—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24C2×D4×C3711yescharacteristic
663C24C2×D4×C3711yescharacteristic
664C24C2×D4×C3711yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C3712yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C3712yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C3711yescharacteristic
742C22×C4C2×D4×C3711yescharacteristic
743C22×C4C2×D4×C3712yes—
744C22×C4C2×D4×C3712yes—
745C22×C4C2×D4×C3711yescharacteristic
746C22×C4C2×D4×C3712yes—
747C22×C4#41×C3712yes—
748C22×C4C24×C3711yescharacteristic
749SD16—44no—
750D8—44no—
751M16—44no—
752M16—44no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8C2×D4×C3712yes—
764C2×C8C2×D4×C3712yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C3712yes—
776C4⋊C4C2×D4×C3712yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23#120×C3712yes—
829C23#121×C3712yes—
830C23AGL(1,ℤ/8)×C3712yes—
831C23C22×D4×C3711yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4#120×C3712yes—
892C2×C4#121×C3712yes—
893C2×C4C22×D4×C3711yescharacteristic
894C2×C4C22×D4×C3711yescharacteristic
895C2×C4C22×D4×C3711yescharacteristic
896C2×C4C2×#41×C3711yescharacteristic
897C2×C4H(5,𝔽2)×C3711yescharacteristic
898C2×C4H(5,𝔽2)×C3711yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×#120×C3711yescharacteristic
940C22C2×#121×C3711yescharacteristic
941C22C37×#53411yescharacteristic
942C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
943C22C37×#57511yescharacteristic
944C22C37×#57511yescharacteristic
945C22C37×#57511yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C3711yescharacteristic
956C4D42×C3711yescharacteristic
957C4C37×#54611yescharacteristic
958C4C37×#54611yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C37×#241011yescharacteristic
965C2C37×#300511yescharacteristic
966C2C37×#300611yescharacteristic
967C2C37×#305411yescharacteristic
968C2C37×#305511yescharacteristic
969C2C37×#319411yescharacteristic
970C2C37×#319711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C24×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#525C2semidirect
2. C2×C37×#469C2semidirect
3. C2×C37×#468C2semidirect
4. C2×C37×#449C2semidirect
5. C2×C37×#407C2semidirect
6. C37×#2847C2semidirect
7. C37×#2035C2semidirect
8. C37×#2033C2semidirect
9. C37×#2000C2semidirect
10. C37×#1999C2semidirect
11. C37×#1895C2semidirect
12. C37×#1894C2semidirect
13. C37×#1875C2semidirect
14. C37×#1854C2semidirect
15. C37×#1788C2semidirect
18. C22×SD16×C37C22semidirect
19. C22×D8×C37C22semidirect
40. C2×#107×C37C22semidirect
41. C2×#106×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
44. C2×#103×C37C22semidirect
45. C2×#102×C37C22semidirect
46. C2×#102×C37C22semidirect
47. C2×#102×C37C22semidirect
48. C2×#102×C37C22semidirect
49. C2×#102×C37C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
114. C22⋊Q8×C37D4semidirect
124. #121×C37D4semidirect
163. C22⋊C8×C37D4semidirect
417. #24388C37direct (N × H)
474. C2×#525C2×C37semidirect
475. C2×#469C2×C37semidirect
476. C2×#468C2×C37semidirect
477. C2×#449C2×C37semidirect
478. C2×#407C2×C37semidirect
479. #2847C2×C37semidirect
480. #2035C2×C37semidirect
481. #2033C2×C37semidirect
482. #2000C2×C37semidirect
483. #1999C2×C37semidirect
484. #1895C2×C37semidirect
485. #1894C2×C37semidirect
486. #1875C2×C37semidirect
487. #1854C2×C37semidirect
488. #1788C2×C37semidirect
503. C22×SD16C22×C37semidirect
504. C22×D8C22×C37semidirect
525. C2×#107C22×C37semidirect
526. C2×#106C22×C37semidirect
527. C2×#103C22×C37semidirect
528. C2×#103C22×C37semidirect
529. C2×#103C22×C37semidirect
530. C2×#102C22×C37semidirect
531. C2×#102C22×C37semidirect
532. C2×#102C22×C37semidirect
533. C2×#102C22×C37semidirect
534. C2×#102C22×C37semidirect
546. #340C22×C37semidirect
547. #340C22×C37semidirect
548. #340C22×C37semidirect
549. #340C22×C37semidirect
550. C37#24388direct (N × H)
600. C22⋊Q8D4×C37semidirect
610. #121D4×C37semidirect
649. C22⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5252
C2×C37×#4692
C2×C37×#4682
C2×C37×#4492
C2×C37×#4072
C37×#28472
C37×#20352
C37×#20332
C37×#20002
C37×#19992
C37×#18952
C37×#18942
C37×#18752
C37×#18542
C37×#17882
#2438837