Finite Group Databasebeta

← C37×#24448 #22645701

Subgroups — C37×#24448 #22645701

Order 9472.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C37C211yesmaximal, characteristic
2C2×C37×#468C211yesmaximal, characteristic, complemented
3C2×C37×#450C211yesmaximal, characteristic, complemented
4C2×C37×#450C211yesmaximal, characteristic, complemented
5C2×C37×#418C211yesmaximal, characteristic, complemented
6C37×#2415C211yesmaximal, characteristic, complemented
7C37×#2041C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2014C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1877C211yesmaximal, characteristic, complemented
12C37×#1875C211yesmaximal, characteristic, complemented
13C37×#1870C211yesmaximal, characteristic, complemented
14C37×#1862C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C37—21no—
17C23×D4×C37C2211yescharacteristic
18C23×D4×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic, complemented
21C22×SD16×C37C2211yescharacteristic, complemented
22C22×M16×C37C2211yescharacteristic, complemented
23D42×C37—24no—
24D42×C37—24no—
25C2×#127×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic, complemented
27C2×C22⋊Q8×C37C2211yescharacteristic, complemented
28C2×#121×C37—21no—
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C2×#120×C37—21no—
32C2×#120×C37—21no—
33C2×C4×D4×C37C2211yescharacteristic
34C2×C4×D4×C37C2211yescharacteristic
35C2×#117×C37C2211yescharacteristic, complemented
36C37×#468—24no—
37C37×#450—24no—
38C37×#450—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C37×#418—24no—
41C2×#103×C37C2211yescharacteristic, complemented
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×C22⋊C8×C37C2211yescharacteristic, complemented
52C2×C22⋊C8×C37C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#397—21no—
55C37×#394—21no—
56C37×#391C2211yescharacteristic, complemented
57C37×#389—21no—
58C37×#389C2211yescharacteristic, complemented
59C37×#388—21no—
60C37×#380C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#336C2211yescharacteristic, complemented
64C37×#336C2211yescharacteristic, complemented
65C25×C37—21no—
66C25×C37—21no—
67C22×Q8×C37C2311yescharacteristic
68C22×D4×C37—22no—
69C22×D4×C37—22no—
70C22×D4×C37—28no—
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—22no—
74C22×D4×C37—22no—
75C22×D4×C37—22no—
76C22×D4×C37—22no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—22no—
81C22×D4×C37—21no—
82C22×D4×C37—41no—
83C22×D4×C37—41no—
84C22×D4×C37—41no—
85C22×D4×C37—41no—
86C22×D4×C37—44no—
87C22×D4×C37—44no—
88C22×D4×C37D411yescharacteristic
89C22×D4×C37D414yes—
90C22×D4×C37C2311yescharacteristic
91C22×D4×C37C2311yescharacteristic
92C22×D4×C37C2311yescharacteristic
93C23×C4×C37—21no—
94C23×C4×C37C2311yescharacteristic
95C23×C4×C37C2311yescharacteristic
96C2×SD16×C37—22no—
97C2×SD16×C37—22no—
98C2×SD16×C37—22no—
99C2×SD16×C37—22no—
100C2×SD16×C37—22no—
101C2×SD16×C37—22no—
102C2×SD16×C37—41no—
103C2×SD16×C37—41no—
104C2×SD16×C37—41no—
105C2×M16×C37—22no—
106C2×M16×C37—22no—
107C2×M16×C37—41no—
108C22×C8×C37C2311yescharacteristic
109C22×C8×C37C2311yescharacteristic
110C22×C8×C37C2311yescharacteristic
111C22×C8×C37C2311yescharacteristic
112#127×C37—22no—
113#127×C37—22no—
114C22⋊Q8×C37—22no—
115C22⋊Q8×C37—22no—
116C22⋊Q8×C37—22no—
117C22⋊Q8×C37—41no—
118#121×C37—28no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37D414yes—
123#120×C37—28no—
124#120×C37—28no—
125C4×D4×C37—22no—
126C4×D4×C37—22no—
127C4×D4×C37—22no—
128C4×D4×C37—22no—
129#117×C37—22no—
130#117×C37—41no—
131C2×C4⋊C4×C37—21no—
132C2×C4⋊C4×C37—21no—
133C2×C4⋊C4×C37—21no—
134C2×C4⋊C4×C37D411yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C4⋊C4×C37C2311yescharacteristic
137C2×C4⋊C4×C37C2311yescharacteristic
138C2×C4⋊C4×C37C2311yescharacteristic
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×C37D411yescharacteristic
147C2×C22⋊C4×C37D411yescharacteristic
148C2×C42×C37—21no—
149C2×C42×C37C2311yescharacteristic
150#107×C37—22no—
151#103×C37—22no—
152#102×C37—22no—
153#102×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—41no—
160#102×C37D414yescomplemented
161C22⋊C8×C37—22no—
162C22⋊C8×C37—22no—
163C22⋊C8×C37—41no—
164#95×C37—21no—
165#95×C37—21no—
166#95×C37—21no—
167#95×C37—21no—
168C24×C37—21no—
169C24×C37—24no—
170C24×C37—21no—
171C24×C37—21no—
172C24×C37—24no—
173C24×C37—42no—
174C24×C37—42no—
175C24×C37—42no—
176C24×C37—42no—
177C24×C37—42no—
178C24×C37—42no—
179C24×C37—42no—
180C24×C37—42no—
181C24×C37—81no—
182C24×C37—81no—
183C24×C37—81no—
184C24×C37—81no—
185C24×C37C2×D411yescharacteristic
186C24×C37C2×D411yescharacteristic
187C2×Q8×C37—21no—
188C2×Q8×C37—21no—
189C2×Q8×C37—21no—
190C2×Q8×C37—21no—
191C2×Q8×C37—21no—
192C2×Q8×C37—21no—
193C2×D4×C37—22no—
194C2×D4×C37—22no—
195C2×D4×C37—28no—
196C2×D4×C37—24no—
197C2×D4×C37—24no—
198C2×D4×C37—24no—
199C2×D4×C37—24no—
200C2×D4×C37—24no—
201C2×D4×C37—24no—
202C2×D4×C37—22no—
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—44no—
217C2×D4×C37—44no—
218C2×D4×C37—44no—
219C2×D4×C37—42no—
220C2×D4×C37—42no—
221C2×D4×C37—42no—
222C2×D4×C37—42no—
223C2×D4×C37—42no—
224C2×D4×C37—44no—
225C2×D4×C37—44no—
226C2×D4×C37—432no—
227C2×D4×C37—44no—
228C2×D4×C37—42no—
229C2×D4×C37—42no—
230C2×D4×C37—42no—
231C2×D4×C37—42no—
232C2×D4×C37—44no—
233C2×D4×C37—42no—
234C2×D4×C37—81no—
235C2×D4×C37—81no—
236C2×D4×C37C2×D412yes—
237C2×D4×C37C2×D412yes—
238C2×D4×C37C2×D412yes—
239C2×D4×C37C2×D412yes—
240C2×D4×C37#4112yes—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—24no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—42no—
258C22×C4×C37—42no—
259C22×C4×C37C2×D411yescharacteristic
260C22×C4×C37C2×D411yescharacteristic
261C22×C4×C37C2×D411yescharacteristic
262C22×C4×C37C2×D412yes—
263C22×C4×C37C2×D412yes—
264C22×C4×C37C2×D411yescharacteristic
265C22×C4×C37C2411yescharacteristic
266SD16×C37—44no—
267SD16×C37—44no—
268SD16×C37—44no—
269M16×C37—44no—
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×C37—21no—
278C2×C8×C37—21no—
279C2×C8×C37—21no—
280C2×C8×C37—21no—
281C2×C8×C37C2×D412yescomplemented
282C4⋊C4×C37—22no—
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×C37—42no—
290C4⋊C4×C37—42no—
291C4⋊C4×C37—42no—
292C4⋊C4×C37C2×D412yes—
293C4⋊C4×C37C2×D412yescomplemented
294C22⋊C4×C37—24no—
295C22⋊C4×C37—24no—
296C22⋊C4×C37—22no—
297C22⋊C4×C37—24no—
298C22⋊C4×C37—22no—
299C22⋊C4×C37—42no—
300C22⋊C4×C37—42no—
301C22⋊C4×C37—42no—
302C22⋊C4×C37—42no—
303C42×C37—21no—
304C42×C37—21no—
305C42×C37—42no—
306C23×C37—21no—
307C23×C37—22no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—22no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—22no—
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—22no—
323C23×C37—48no—
324C23×C37—48no—
325C23×C37—48no—
326C23×C37—48no—
327C23×C37—41no—
328C23×C37—41no—
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—41no—
343C23×C37—84no—
344C23×C37—84no—
345C23×C37—84no—
346C23×C37—84no—
347C23×C37—84no—
348C23×C37—84no—
349C23×C37—84no—
350C23×C37—84no—
351C23×C37—84no—
352C23×C37—84no—
353C23×C37#12012yes—
354C23×C37AGL(1,ℤ/8)12yes—
355C23×C37C22×D411yescharacteristic
356Q8×C37—41no—
357Q8×C37—41no—
358Q8×C37—41no—
359Q8×C37—41no—
360D4×C37—28no—
361D4×C37—22no—
362D4×C37—22no—
363D4×C37—22no—
364D4×C37—22no—
365D4×C37—22no—
366D4×C37—22no—
367D4×C37—22no—
368D4×C37—48no—
369D4×C37—48no—
370D4×C37—48no—
371D4×C37—48no—
372D4×C37—48no—
373D4×C37—41no—
374D4×C37—41no—
375D4×C37—41no—
376D4×C37—41no—
377D4×C37—84no—
378D4×C37#12114yes—
379C2×C4×C37—21no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—22no—
384C2×C4×C37—22no—
385C2×C4×C37—22no—
386C2×C4×C37—22no—
387C2×C4×C37—21no—
388C2×C4×C37—21no—
389C2×C4×C37—22no—
390C2×C4×C37—22no—
391C2×C4×C37—21no—
392C2×C4×C37—21no—
393C2×C4×C37—21no—
394C2×C4×C37—21no—
395C2×C4×C37—48no—
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—41no—
406C2×C4×C37—41no—
407C2×C4×C37—41no—
408C2×C4×C37—41no—
409C2×C4×C37—41no—
410C2×C4×C37—41no—
411C2×C4×C37—41no—
412C2×C4×C37—41no—
413C2×C4×C37#12012yes—
414C2×C4×C37AGL(1,ℤ/8)12yes—
415C2×C4×C37C22×D411yescharacteristic
416C2×C4×C37C22×D411yescharacteristic
417C2×C4×C37C22×D411yescharacteristic
418C2×C4×C37C2×#4111yescharacteristic
419C2×C4×C37H(5,𝔽2)11yescharacteristic
420C2×C4×C37H(5,𝔽2)11yescharacteristic
421C8×C37—22no—
422C8×C37—41no—
423C8×C37—41no—
424C8×C37—41no—
425#24448C3711yesmaximal, characteristic, direct product factor, Sylow
426C22×C37—22no—
427C22×C37—24no—
428C22×C37—22no—
429C22×C37—22no—
430C22×C37—22no—
431C22×C37—22no—
432C22×C37—22no—
433C22×C37—41no—
434C22×C37—42no—
435C22×C37—41no—
436C22×C37—42no—
437C22×C37—41no—
438C22×C37—42no—
439C22×C37—41no—
440C22×C37—41no—
441C22×C37—42no—
442C22×C37—41no—
443C22×C37—42no—
444C22×C37—41no—
445C22×C37—41no—
446C22×C37—42no—
447C22×C37—42no—
448C22×C37—42no—
449C22×C37—42no—
450C22×C37—42no—
451C22×C37—42no—
452C22×C37—42no—
453C22×C37—816no—
454C22×C37—816no—
455C22×C37—81no—
456C22×C37—81no—
457C22×C37—81no—
458C22×C37—81no—
459C22×C37—81no—
460C22×C37—81no—
461C22×C37—81no—
462C22×C37—81no—
463C22×C37C2×#12011yescharacteristic
464C22×C37D4211yescharacteristic
465C22×C37#54611yescharacteristic
466C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C37#57711yescharacteristic
469C22×C37#57711yescharacteristic
470C4×C37—22no—
471C4×C37—22no—
472C4×C37—41no—
473C4×C37—42no—
474C4×C37—41no—
475C4×C37—42no—
476C4×C37—81no—
477C4×C37—81no—
478C4×C37—81no—
479C4×C37C2×#12111yescharacteristic
480C4×C37#53411yescharacteristic
481C4×C37D4211yescharacteristic
482C4×C37#54611yescharacteristic
483C2×D42C2×C3711yescharacteristic
484C2×#468C2×C3711yescharacteristic, complemented
485C2×#450C2×C3711yescharacteristic, complemented
486C2×#450C2×C3711yescharacteristic, complemented
487C2×#418C2×C3711yescharacteristic, complemented
488#2415C2×C3711yescharacteristic, complemented
489#2041C2×C3711yescharacteristic, complemented
490#2033C2×C3711yescharacteristic, complemented
491#2014C2×C3711yescharacteristic, complemented
492#2000C2×C3711yescharacteristic, complemented
493#1877C2×C3711yescharacteristic, complemented
494#1875C2×C3711yescharacteristic, complemented
495#1870C2×C3711yescharacteristic, complemented
496#1862C2×C3711yescharacteristic, complemented
497#1786C2×C3711yescharacteristic, complemented
498C2×C37—42no—
499C2×C37—42no—
500C2×C37—44no—
501C2×C37—82no—
502C2×C37—82no—
503C2×C37#241011yescharacteristic
504C2×C37#300311yescharacteristic
505C2×C37#300911yescharacteristic
506C2×C37#326511yescharacteristic
507C2×C37#327211yescharacteristic
508C2×C37#331011yescharacteristic
509C2×C37#332411yescharacteristic
510C23×D4—21no—
511C23×D4C22×C3711yescharacteristic
512C23×D4C22×C3711yescharacteristic
513C22×SD16C22×C3711yescharacteristic
514C22×SD16C22×C3711yescharacteristic, complemented
515C22×SD16C22×C3711yescharacteristic, complemented
516C22×M16C22×C3711yescharacteristic, complemented
517D42—24no—
518D42—24no—
519C2×#127C22×C3711yescharacteristic
520C2×C22⋊Q8C22×C3711yescharacteristic, complemented
521C2×C22⋊Q8C22×C3711yescharacteristic, complemented
522C2×#121—21no—
523C2×#121C22×C3711yescharacteristic
524C2×#121C22×C3711yescharacteristic
525C2×#120—21no—
526C2×#120—21no—
527C2×C4×D4C22×C3711yescharacteristic
528C2×C4×D4C22×C3711yescharacteristic
529C2×#117C22×C3711yescharacteristic, complemented
530#468—24no—
531#450—24no—
532#450—24no—
533C2×#107C22×C3711yescharacteristic, complemented
534#418—24no—
535C2×#103C22×C3711yescharacteristic, complemented
536C2×#102C22×C3711yescharacteristic
537C2×#102C22×C3711yescharacteristic
538C2×#102C22×C3711yescharacteristic
539C2×#102C22×C3711yescharacteristic, complemented
540C2×#102C22×C3711yescharacteristic, complemented
541C2×#102C22×C3711yescharacteristic, complemented
542C2×#102C22×C3711yescharacteristic, complemented
543C2×#102C22×C3711yescharacteristic, complemented
544C2×#102C22×C3711yescharacteristic, complemented
545C2×C22⋊C8C22×C3711yescharacteristic, complemented
546C2×C22⋊C8C22×C3711yescharacteristic, complemented
547C2×C22⋊C8C22×C3711yescharacteristic, complemented
548#397—21no—
549#394—21no—
550#391C22×C3711yescharacteristic, complemented
551#389—21no—
552#389C22×C3711yescharacteristic, complemented
553#388—21no—
554#380C22×C3711yescharacteristic, complemented
555#340C22×C3711yescharacteristic, complemented
556#340C22×C3711yescharacteristic, complemented
557#336C22×C3711yescharacteristic, complemented
558#336C22×C3711yescharacteristic, complemented
559C37#2444811yescharacteristic, direct product factor, Sylow
560C25—21no—
561C25—21no—
562C22×Q8C23×C3711yescharacteristic
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—28no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—22no—
576C22×D4—21no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—44no—
582C22×D4—44no—
583C22×D4D4×C3711yescharacteristic
584C22×D4D4×C3714yes—
585C22×D4C23×C3711yescharacteristic
586C22×D4C23×C3711yescharacteristic
587C22×D4C23×C3711yescharacteristic
588C23×C4—21no—
589C23×C4C23×C3711yescharacteristic
590C23×C4C23×C3711yescharacteristic
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—41no—
598C2×SD16—41no—
599C2×SD16—41no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—41no—
603C22×C8C23×C3711yescharacteristic
604C22×C8C23×C3711yescharacteristic
605C22×C8C23×C3711yescharacteristic
606C22×C8C23×C3711yescharacteristic
607#127—22no—
608#127—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—41no—
613#121—28no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121D4×C3714yes—
618#120—28no—
619#120—28no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624#117—22no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4D4×C3711yescharacteristic
630C2×C4⋊C4C23×C3711yescharacteristic
631C2×C4⋊C4C23×C3711yescharacteristic
632C2×C4⋊C4C23×C3711yescharacteristic
633C2×C4⋊C4C23×C3711yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C3711yescharacteristic
642C2×C22⋊C4D4×C3711yescharacteristic
643C2×C42—21no—
644C2×C42C23×C3711yescharacteristic
645#107—22no—
646#103—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—41no—
655#102D4×C3714yescomplemented
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663C24—21no—
664C24—24no—
665C24—21no—
666C24—21no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24—81no—
680C24C2×D4×C3711yescharacteristic
681C24C2×D4×C3711yescharacteristic
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—28no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4C2×D4×C3712yes—
732C2×D4C2×D4×C3712yes—
733C2×D4C2×D4×C3712yes—
734C2×D4C2×D4×C3712yes—
735C2×D4#41×C3712yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4C2×D4×C3711yescharacteristic
755C22×C4C2×D4×C3711yescharacteristic
756C22×C4C2×D4×C3711yescharacteristic
757C22×C4C2×D4×C3712yes—
758C22×C4C2×D4×C3712yes—
759C22×C4C2×D4×C3711yescharacteristic
760C22×C4C24×C3711yescharacteristic
761SD16—44no—
762SD16—44no—
763SD16—44no—
764M16—44no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8C2×D4×C3712yescomplemented
777C4⋊C4—22no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4C2×D4×C3712yes—
788C4⋊C4C2×D4×C3712yescomplemented
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—22no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—42no—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23#120×C3712yes—
849C23AGL(1,ℤ/8)×C3712yes—
850C23C22×D4×C3711yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4#121×C3714yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4#120×C3712yes—
909C2×C4AGL(1,ℤ/8)×C3712yes—
910C2×C4C22×D4×C3711yescharacteristic
911C2×C4C22×D4×C3711yescharacteristic
912C2×C4C22×D4×C3711yescharacteristic
913C2×C4C2×#41×C3711yescharacteristic
914C2×C4H(5,𝔽2)×C3711yescharacteristic
915C2×C4H(5,𝔽2)×C3711yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—24no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—42no—
931C22—41no—
932C22—42no—
933C22—41no—
934C22—41no—
935C22—42no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×#120×C3711yescharacteristic
958C22D42×C3711yescharacteristic
959C22C37×#54611yescharacteristic
960C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
961C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
962C22C37×#57711yescharacteristic
963C22C37×#57711yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—42no—
968C4—41no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×#121×C3711yescharacteristic
974C4C37×#53411yescharacteristic
975C4D42×C3711yescharacteristic
976C4C37×#54611yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2C37×#241011yescharacteristic
983C2C37×#300311yescharacteristic
984C2C37×#300911yescharacteristic
985C2C37×#326511yescharacteristic
986C2C37×#327211yescharacteristic
987C2C37×#331011yescharacteristic
988C2C37×#332411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×D42×C37C2
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
2. C2×C37×#468C2semidirect
3. C2×C37×#450C2semidirect
4. C2×C37×#450C2semidirect
5. C2×C37×#418C2semidirect
6. C37×#2415C2semidirect
7. C37×#2041C2semidirect
8. C37×#2033C2semidirect
9. C37×#2014C2semidirect
10. C37×#2000C2semidirect
11. C37×#1877C2semidirect
12. C37×#1875C2semidirect
13. C37×#1870C2semidirect
14. C37×#1862C2semidirect
15. C37×#1786C2semidirect
20. C22×SD16×C37C22semidirect
21. C22×SD16×C37C22semidirect
22. C22×M16×C37C22semidirect
26. C2×C22⋊Q8×C37C22semidirect
27. C2×C22⋊Q8×C37C22semidirect
35. C2×#117×C37C22semidirect
39. C2×#107×C37C22semidirect
41. C2×#103×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×C22⋊C8×C37C22semidirect
52. C2×C22⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
56. C37×#391C22semidirect
58. C37×#389C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
160. #102×C37D4semidirect
281. C2×C8×C37C2×D4semidirect
293. C4⋊C4×C37C2×D4semidirect
425. #24448C37direct (N × H)
484. C2×#468C2×C37semidirect
485. C2×#450C2×C37semidirect
486. C2×#450C2×C37semidirect
487. C2×#418C2×C37semidirect
488. #2415C2×C37semidirect
489. #2041C2×C37semidirect
490. #2033C2×C37semidirect
491. #2014C2×C37semidirect
492. #2000C2×C37semidirect
493. #1877C2×C37semidirect
494. #1875C2×C37semidirect
495. #1870C2×C37semidirect
496. #1862C2×C37semidirect
497. #1786C2×C37semidirect
514. C22×SD16C22×C37semidirect
515. C22×SD16C22×C37semidirect
516. C22×M16C22×C37semidirect
520. C2×C22⋊Q8C22×C37semidirect
521. C2×C22⋊Q8C22×C37semidirect
529. C2×#117C22×C37semidirect
533. C2×#107C22×C37semidirect
535. C2×#103C22×C37semidirect
539. C2×#102C22×C37semidirect
540. C2×#102C22×C37semidirect
541. C2×#102C22×C37semidirect
542. C2×#102C22×C37semidirect
543. C2×#102C22×C37semidirect
544. C2×#102C22×C37semidirect
545. C2×C22⋊C8C22×C37semidirect
546. C2×C22⋊C8C22×C37semidirect
547. C2×C22⋊C8C22×C37semidirect
550. #391C22×C37semidirect
552. #389C22×C37semidirect
554. #380C22×C37semidirect
555. #340C22×C37semidirect
556. #340C22×C37semidirect
557. #336C22×C37semidirect
558. #336C22×C37semidirect
559. C37#24448direct (N × H)
655. #102D4×C37semidirect
776. C2×C8C2×D4×C37semidirect
788. C4⋊C4C2×D4×C37semidirect

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×#4682
C2×C37×#4502
C2×C37×#4182
C37×#24152
C37×#20412
C37×#20332
C37×#20142
C37×#20002
C37×#18772
C37×#18752
C37×#18702
C37×#18622
C37×#17862
#2444837