Finite Group Databasebeta

← C37×#24432 #22645685

Subgroups — C37×#24432 #22645685

Order 9472.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C37C211yesmaximal, characteristic
2C2×C37×#465C211yesmaximal, characteristic, complemented
3C2×C37×#450C211yesmaximal, characteristic, complemented
4C2×C37×#450C211yesmaximal, characteristic, complemented
5C22×#102×C37C211yesmaximal, characteristic, complemented
6C37×#2417C211yesmaximal, characteristic, complemented
7C37×#2041C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#2014C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1877C211yesmaximal, characteristic, complemented
12C37×#1874C211yesmaximal, characteristic, complemented
13C37×#1869C211yesmaximal, characteristic, complemented
14C37×#1864C211yesmaximal, 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
22C23×C8×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
35C22×C4⋊C4×C37C2211yescharacteristic, complemented
36C37×#465—24no—
37C37×#450—24no—
38C37×#450—24no—
39C2×#106×C37C2211yescharacteristic, complemented
40C2×#103×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×C22⋊C8×C37C2211yescharacteristic, complemented
52C2×C22⋊C8×C37C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#398—21no—
55C37×#396—21no—
56C37×#391C2211yescharacteristic, complemented
57C37×#389C2211yescharacteristic, complemented
58C37×#386—21no—
59C37×#380—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×C37—21no—
95C23×C4×C37C2311yescharacteristic
96C23×C4×C37C2311yescharacteristic
97C2×SD16×C37—22no—
98C2×SD16×C37—22no—
99C2×SD16×C37—22no—
100C2×SD16×C37—22no—
101C2×SD16×C37—22no—
102C2×SD16×C37—22no—
103C2×SD16×C37—41no—
104C2×SD16×C37—41no—
105C2×SD16×C37—41no—
106C22×C8×C37—22no—
107C22×C8×C37—22no—
108C22×C8×C37—41no—
109C22×C8×C37C2311yescharacteristic
110C22×C8×C37C2311yescharacteristic
111C22×C8×C37C2311yescharacteristic
112C22×C8×C37C2311yescharacteristic
113#127×C37—22no—
114#127×C37—22no—
115C22⋊Q8×C37—22no—
116C22⋊Q8×C37—22no—
117C22⋊Q8×C37—22no—
118C22⋊Q8×C37—41no—
119#121×C37—28no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37—22no—
123#121×C37D414yes—
124#120×C37—28no—
125#120×C37—28no—
126C4×D4×C37—22no—
127C4×D4×C37—22no—
128C4×D4×C37—22no—
129C4×D4×C37—22no—
130C2×C4⋊C4×C37—22no—
131C2×C4⋊C4×C37—21no—
132C2×C4⋊C4×C37—21no—
133C2×C4⋊C4×C37—21no—
134C2×C4⋊C4×C37—21no—
135C2×C4⋊C4×C37—41no—
136C2×C4⋊C4×C37D411yescharacteristic
137C2×C4⋊C4×C37C2311yescharacteristic
138C2×C4⋊C4×C37C2311yescharacteristic
139C2×C4⋊C4×C37C2311yescharacteristic
140C2×C4⋊C4×C37C2311yescharacteristic
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×C37D411yescharacteristic
148C2×C22⋊C4×C37D411yescharacteristic
149C2×C42×C37C2311yescharacteristic
150#106×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—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—44no—
216C2×D4×C37—44no—
217C2×D4×C37—44no—
218C2×D4×C37—42no—
219C2×D4×C37—42no—
220C2×D4×C37—42no—
221C2×D4×C37—42no—
222C2×D4×C37—42no—
223C2×D4×C37—44no—
224C2×D4×C37—44no—
225C2×D4×C37—432no—
226C2×D4×C37—44no—
227C2×D4×C37—42no—
228C2×D4×C37—42no—
229C2×D4×C37—42no—
230C2×D4×C37—42no—
231C2×D4×C37—44no—
232C2×D4×C37—42no—
233C2×D4×C37—81no—
234C2×D4×C37—81no—
235C2×D4×C37SD1614yescomplemented
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×C37—42no—
260C22×C4×C37—42no—
261C22×C4×C37—81no—
262C22×C4×C37C2×D411yescharacteristic
263C22×C4×C37C2×D411yescharacteristic
264C22×C4×C37C2×D411yescharacteristic
265C22×C4×C37C2×D412yes—
266C22×C4×C37C2×D412yes—
267C22×C4×C37C2×D411yescharacteristic
268C22×C4×C37C2411yescharacteristic
269SD16×C37—44no—
270SD16×C37—44no—
271SD16×C37—44no—
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×C37—21no—
282C2×C8×C37—21no—
283C2×C8×C37—44no—
284C2×C8×C37C2×D412yescomplemented
285C4⋊C4×C37—22no—
286C4⋊C4×C37—21no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—21no—
289C4⋊C4×C37—21no—
290C4⋊C4×C37—21no—
291C4⋊C4×C37—21no—
292C4⋊C4×C37—42no—
293C4⋊C4×C37—42no—
294C4⋊C4×C37—42no—
295C4⋊C4×C37—81no—
296C4⋊C4×C37C2×D412yes—
297C4⋊C4×C37C2×D412yescomplemented
298C22⋊C4×C37—24no—
299C22⋊C4×C37—24no—
300C22⋊C4×C37—22no—
301C22⋊C4×C37—24no—
302C22⋊C4×C37—22no—
303C22⋊C4×C37—42no—
304C22⋊C4×C37—42no—
305C22⋊C4×C37—81no—
306C42×C37—21no—
307C42×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—22no—
314C23×C37—21no—
315C23×C37—22no—
316C23×C37—21no—
317C23×C37—22no—
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—41no—
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—48no—
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×C37C2×SD1612yes—
355C23×C37C2×SD1612yes—
356C23×C37AGL(1,ℤ/8)12yes—
357C23×C37C22×D411yescharacteristic
358Q8×C37—41no—
359Q8×C37—41no—
360Q8×C37—41no—
361Q8×C37—41no—
362D4×C37—28no—
363D4×C37—22no—
364D4×C37—22no—
365D4×C37—22no—
366D4×C37—22no—
367D4×C37—22no—
368D4×C37—22no—
369D4×C37—22no—
370D4×C37—48no—
371D4×C37—48no—
372D4×C37—48no—
373D4×C37—48no—
374D4×C37—48no—
375D4×C37—41no—
376D4×C37—41no—
377D4×C37—41no—
378D4×C37—41no—
379D4×C37—84no—
380D4×C37#12114yes—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—21no—
384C2×C4×C37—21no—
385C2×C4×C37—22no—
386C2×C4×C37—22no—
387C2×C4×C37—22no—
388C2×C4×C37—22no—
389C2×C4×C37—21no—
390C2×C4×C37—21no—
391C2×C4×C37—22no—
392C2×C4×C37—22no—
393C2×C4×C37—21no—
394C2×C4×C37—21no—
395C2×C4×C37—21no—
396C2×C4×C37—21no—
397C2×C4×C37—48no—
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—41no—
414C2×C4×C37—41no—
415C2×C4×C37—84no—
416C2×C4×C37#12012yes—
417C2×C4×C37C2×SD1612yes—
418C2×C4×C37C22×D411yescharacteristic
419C2×C4×C37C22×D411yescharacteristic
420C2×C4×C37C22×D411yescharacteristic
421C2×C4×C37C2×#4111yescharacteristic
422C2×C4×C37H(5,𝔽2)11yescharacteristic
423C2×C4×C37H(5,𝔽2)11yescharacteristic
424C8×C37—22no—
425C8×C37—41no—
426C8×C37—41no—
427C8×C37—41no—
428#24432C3711yesmaximal, characteristic, direct product factor, Sylow
429C22×C37—22no—
430C22×C37—22no—
431C22×C37—22no—
432C22×C37—22no—
433C22×C37—22no—
434C22×C37—22no—
435C22×C37—24no—
436C22×C37—22no—
437C22×C37—22no—
438C22×C37—22no—
439C22×C37—41no—
440C22×C37—42no—
441C22×C37—41no—
442C22×C37—42no—
443C22×C37—41no—
444C22×C37—42no—
445C22×C37—42no—
446C22×C37—42no—
447C22×C37—41no—
448C22×C37—42no—
449C22×C37—42no—
450C22×C37—42no—
451C22×C37—42no—
452C22×C37—42no—
453C22×C37—42no—
454C22×C37—42no—
455C22×C37—816no—
456C22×C37—816no—
457C22×C37—81no—
458C22×C37—81no—
459C22×C37—81no—
460C22×C37—81no—
461C22×C37—81no—
462C22×C37—81no—
463C22×C37—81no—
464C22×C37—81no—
465C22×C37#45014yescomplemented
466C22×C37C2×#12011yescharacteristic
467C22×C37D4211yescharacteristic
468C22×C37#54611yescharacteristic
469C22×C37C22×SD1611yescharacteristic
470C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C37#57611yescharacteristic
472C22×C37#57711yescharacteristic
473C4×C37—22no—
474C4×C37—22no—
475C4×C37—41no—
476C4×C37—42no—
477C4×C37—42no—
478C4×C37—41no—
479C4×C37—81no—
480C4×C37—81no—
481C4×C37—81no—
482C4×C37C2×#12111yescharacteristic
483C4×C37#53411yescharacteristic
484C4×C37D4211yescharacteristic
485C4×C37#54611yescharacteristic
486C2×D42C2×C3711yescharacteristic
487C2×#465C2×C3711yescharacteristic, complemented
488C2×#450C2×C3711yescharacteristic, complemented
489C2×#450C2×C3711yescharacteristic, complemented
490C22×#102C2×C3711yescharacteristic, complemented
491#2417C2×C3711yescharacteristic, complemented
492#2041C2×C3711yescharacteristic, complemented
493#2034C2×C3711yescharacteristic, complemented
494#2014C2×C3711yescharacteristic, complemented
495#2000C2×C3711yescharacteristic, complemented
496#1877C2×C3711yescharacteristic, complemented
497#1874C2×C3711yescharacteristic, complemented
498#1869C2×C3711yescharacteristic, complemented
499#1864C2×C3711yescharacteristic, complemented
500#1786C2×C3711yescharacteristic, complemented
501C2×C37—24no—
502C2×C37—42no—
503C2×C37—44no—
504C2×C37—82no—
505C2×C37—82no—
506C2×C37#241011yescharacteristic
507C2×C37C2×#45011yescharacteristic
508C2×C37#301211yescharacteristic
509C2×C37#326411yescharacteristic
510C2×C37D4×SD1611yescharacteristic
511C2×C37#329511yescharacteristic
512C2×C37#331011yescharacteristic
513C23×D4—21no—
514C23×D4C22×C3711yescharacteristic
515C23×D4C22×C3711yescharacteristic
516C22×SD16C22×C3711yescharacteristic
517C22×SD16C22×C3711yescharacteristic, complemented
518C22×SD16C22×C3711yescharacteristic, complemented
519C23×C8C22×C3711yescharacteristic, complemented
520D42—24no—
521D42—24no—
522C2×#127C22×C3711yescharacteristic
523C2×C22⋊Q8C22×C3711yescharacteristic, complemented
524C2×C22⋊Q8C22×C3711yescharacteristic, complemented
525C2×#121—21no—
526C2×#121C22×C3711yescharacteristic
527C2×#121C22×C3711yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C22×C3711yescharacteristic
531C2×C4×D4C22×C3711yescharacteristic
532C22×C4⋊C4C22×C3711yescharacteristic, complemented
533#465—24no—
534#450—24no—
535#450—24no—
536C2×#106C22×C3711yescharacteristic, complemented
537C2×#103C22×C3711yescharacteristic, complemented
538C2×#102—24no—
539C2×#102C22×C3711yescharacteristic
540C2×#102C22×C3711yescharacteristic
541C2×#102C22×C3711yescharacteristic
542C2×#102C22×C3711yescharacteristic, complemented
543C2×#102C22×C3711yescharacteristic, complemented
544C2×#102C22×C3711yescharacteristic, complemented
545C2×#102C22×C3711yescharacteristic, complemented
546C2×#102C22×C3711yescharacteristic, complemented
547C2×#102C22×C3711yescharacteristic, complemented
548C2×C22⋊C8C22×C3711yescharacteristic, complemented
549C2×C22⋊C8C22×C3711yescharacteristic, complemented
550C2×C22⋊C8C22×C3711yescharacteristic, complemented
551#398—21no—
552#396—21no—
553#391C22×C3711yescharacteristic, complemented
554#389C22×C3711yescharacteristic, complemented
555#386—21no—
556#380—21no—
557#380C22×C3711yescharacteristic, complemented
558#340C22×C3711yescharacteristic, complemented
559#340C22×C3711yescharacteristic, complemented
560#336C22×C3711yescharacteristic, complemented
561#336C22×C3711yescharacteristic, complemented
562C37#2443211yescharacteristic, direct product factor, Sylow
563C25—21no—
564C25—21no—
565C22×Q8C23×C3711yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C3711yescharacteristic
587C22×D4D4×C3714yes—
588C22×D4C23×C3711yescharacteristic
589C22×D4C23×C3711yescharacteristic
590C22×D4C23×C3711yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C3711yescharacteristic
594C23×C4C23×C3711yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C3711yescharacteristic
608C22×C8C23×C3711yescharacteristic
609C22×C8C23×C3711yescharacteristic
610C22×C8C23×C3711yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C3714yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C3711yescharacteristic
635C2×C4⋊C4C23×C3711yescharacteristic
636C2×C4⋊C4C23×C3711yescharacteristic
637C2×C4⋊C4C23×C3711yescharacteristic
638C2×C4⋊C4C23×C3711yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C3711yescharacteristic
646C2×C22⋊C4D4×C3711yescharacteristic
647C2×C42C23×C3711yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C3714yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C3711yescharacteristic
684C24C2×D4×C3711yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
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—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C3714yescomplemented
734C2×D4C2×D4×C3712yes—
735C2×D4C2×D4×C3712yes—
736C2×D4C2×D4×C3712yes—
737C2×D4C2×D4×C3712yes—
738C2×D4#41×C3712yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
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—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C3711yescharacteristic
761C22×C4C2×D4×C3711yescharacteristic
762C22×C4C2×D4×C3711yescharacteristic
763C22×C4C2×D4×C3712yes—
764C22×C4C2×D4×C3712yes—
765C22×C4C2×D4×C3711yescharacteristic
766C22×C4C24×C3711yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C3712yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C3712yes—
795C4⋊C4C2×D4×C3712yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
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—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C3712yes—
852C23C2×SD16×C3712yes—
853C23C2×SD16×C3712yes—
854C23AGL(1,ℤ/8)×C3712yes—
855C23C22×D4×C3711yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C3714yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
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—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C3712yes—
915C2×C4C2×SD16×C3712yes—
916C2×C4C22×D4×C3711yescharacteristic
917C2×C4C22×D4×C3711yescharacteristic
918C2×C4C22×D4×C3711yescharacteristic
919C2×C4C2×#41×C3711yescharacteristic
920C2×C4H(5,𝔽2)×C3711yescharacteristic
921C2×C4H(5,𝔽2)×C3711yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C37×#45014yescomplemented
963C22C2×#120×C3711yescharacteristic
964C22D42×C3711yescharacteristic
965C22C37×#54611yescharacteristic
966C22C22×SD16×C3711yescharacteristic
967C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
968C22C37×#57611yescharacteristic
969C22C37×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C3711yescharacteristic
980C4C37×#53411yescharacteristic
981C4D42×C3711yescharacteristic
982C4C37×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C37×#241011yescharacteristic
989C2C2×C37×#45011yescharacteristic
990C2C37×#301211yescharacteristic
991C2C37×#326411yescharacteristic
992C2D4×SD16×C3711yescharacteristic
993C2C37×#329511yescharacteristic
994C2C37×#331011yescharacteristic
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×#465C2semidirect
3. C2×C37×#450C2semidirect
4. C2×C37×#450C2semidirect
5. C22×#102×C37C2semidirect
6. C37×#2417C2semidirect
7. C37×#2041C2semidirect
8. C37×#2034C2semidirect
9. C37×#2014C2semidirect
10. C37×#2000C2semidirect
11. C37×#1877C2semidirect
12. C37×#1874C2semidirect
13. C37×#1869C2semidirect
14. C37×#1864C2semidirect
15. C37×#1786C2semidirect
20. C22×SD16×C37C22semidirect
21. C22×SD16×C37C22semidirect
22. C23×C8×C37C22semidirect
26. C2×C22⋊Q8×C37C22semidirect
27. C2×C22⋊Q8×C37C22semidirect
35. C22×C4⋊C4×C37C22semidirect
39. C2×#106×C37C22semidirect
40. 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
57. C37×#389C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
160. #102×C37D4semidirect
235. C2×D4×C37SD16semidirect
284. C2×C8×C37C2×D4semidirect
297. C4⋊C4×C37C2×D4semidirect
428. #24432C37direct (N × H)
465. C22×C37#450semidirect
487. C2×#465C2×C37semidirect
488. C2×#450C2×C37semidirect
489. C2×#450C2×C37semidirect
490. C22×#102C2×C37semidirect
491. #2417C2×C37semidirect
492. #2041C2×C37semidirect
493. #2034C2×C37semidirect
494. #2014C2×C37semidirect
495. #2000C2×C37semidirect
496. #1877C2×C37semidirect
497. #1874C2×C37semidirect
498. #1869C2×C37semidirect
499. #1864C2×C37semidirect
500. #1786C2×C37semidirect
517. C22×SD16C22×C37semidirect
518. C22×SD16C22×C37semidirect
519. C23×C8C22×C37semidirect
523. C2×C22⋊Q8C22×C37semidirect
524. C2×C22⋊Q8C22×C37semidirect
532. C22×C4⋊C4C22×C37semidirect
536. C2×#106C22×C37semidirect
537. C2×#103C22×C37semidirect
542. C2×#102C22×C37semidirect
543. C2×#102C22×C37semidirect
544. C2×#102C22×C37semidirect
545. C2×#102C22×C37semidirect
546. C2×#102C22×C37semidirect
547. C2×#102C22×C37semidirect
548. C2×C22⋊C8C22×C37semidirect
549. C2×C22⋊C8C22×C37semidirect
550. C2×C22⋊C8C22×C37semidirect
553. #391C22×C37semidirect
554. #389C22×C37semidirect
557. #380C22×C37semidirect
558. #340C22×C37semidirect
559. #340C22×C37semidirect
560. #336C22×C37semidirect
561. #336C22×C37semidirect
562. C37#24432direct (N × H)
658. #102D4×C37semidirect
733. C2×D4SD16×C37semidirect
782. C2×C8C2×D4×C37semidirect
795. C4⋊C4C2×D4×C37semidirect
962. C22C37×#450semidirect

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×#4652
C2×C37×#4502
C22×#102×C372
C37×#24172
C37×#20412
C37×#20342
C37×#20142
C37×#20002
C37×#18772
C37×#18742
C37×#18692
C37×#18642
C37×#17862
#2443237