Finite Group Databasebeta

← C37×#25080 #22646333

Subgroups — C37×#25080 #22646333

Order 9472.

1356 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#465C211yesmaximal, characteristic, complemented
2C2×C37×#460C211yesmaximal, characteristic, complemented
3C2×C37×#450C211yesmaximal, characteristic, complemented
4C22×#102×C37C211yesmaximal, characteristic, complemented
5C37×#2433C211yesmaximal, characteristic
6C37×#2360C211yesmaximal, characteristic, complemented
7C37×#2065C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#2041C211yesmaximal, characteristic, complemented
10C37×#2014C211yesmaximal, characteristic, complemented
11C37×#1982C211yesmaximal, characteristic, complemented
12C37×#1926C211yesmaximal, characteristic, complemented
13C37×#1880C211yesmaximal, characteristic, complemented
14C37×#1874C211yesmaximal, characteristic, complemented
15C37×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic, complemented
20C23×C8×C37C2211yescharacteristic
21C2×#127×C37C2211yescharacteristic
22C2×#127×C37C2211yescharacteristic
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#120×C37—21no—
26C2×#120×C37—21no—
27C2×C4×Q8×C37C2211yescharacteristic, complemented
28C22×C4⋊C4×C37C2211yescharacteristic
29C37×#465—24no—
30C37×#460—24no—
31C37×#450—24no—
32C2×#106×C37C2211yescharacteristic, complemented
33C2×C4⋊C8×C37C2211yescharacteristic, complemented
34C2×C4⋊C8×C37C2211yescharacteristic, complemented
35C2×#103×C37C2211yescharacteristic, complemented
36C2×#102×C37—24no—
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic, complemented
45C2×#102×C37C2211yescharacteristic, complemented
46C2×C22⋊C8×C37C2211yescharacteristic
47C37×#392—21no—
48C37×#392—21no—
49C37×#391C2211yescharacteristic, complemented
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic
52C37×#389—21no—
53C37×#389C2211yescharacteristic, complemented
54C37×#387—21no—
55C37×#385—21no—
56C4×C4⋊C4×C37C2211yescharacteristic, complemented
57C4×C22⋊C4×C37—21no—
58C4×C22⋊C4×C37C2211yescharacteristic
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#336C2211yescharacteristic, complemented
62C37×#336C2211yescharacteristic, complemented
63C25×C37—21no—
64C22×Q8×C37C2311yescharacteristic
65C22×D4×C37—22no—
66C22×D4×C37—22no—
67C22×D4×C37—21no—
68C22×D4×C37—22no—
69C22×D4×C37—21no—
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37—22no—
75C22×D4×C37—41no—
76C22×D4×C37—41no—
77C22×D4×C37C2311yescharacteristic
78C22×D4×C37C2311yescharacteristic
79C22×D4×C37C2311yescharacteristic
80C23×C4×C37—21no—
81C23×C4×C37C2311yescharacteristic
82C2×SD16×C37—22no—
83C2×SD16×C37—22no—
84C2×SD16×C37—22no—
85C2×SD16×C37—22no—
86C2×SD16×C37—22no—
87C2×SD16×C37—22no—
88C2×SD16×C37—41no—
89C2×SD16×C37—41no—
90C2×SD16×C37—41no—
91C22×C8×C37—22no—
92C22×C8×C37—22no—
93C22×C8×C37—41no—
94C22×C8×C37C2311yescharacteristic
95C22×C8×C37C2311yescharacteristic
96C22×C8×C37C2311yescharacteristic
97C22×C8×C37C2311yescharacteristic
98#127×C37—22no—
99#127×C37—22no—
100#127×C37—41no—
101#127×C37—41no—
102C22⋊Q8×C37—22no—
103C22⋊Q8×C37D414yescomplemented
104#121×C37—22no—
105#121×C37—22no—
106#120×C37—44no—
107#120×C37—44no—
108C4×Q8×C37—22no—
109C4×Q8×C37—41no—
110C2×C4⋊C4×C37—21no—
111C2×C4⋊C4×C37—22no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—41no—
116C2×C4⋊C4×C37C2311yescharacteristic
117C2×C4⋊C4×C37C2311yescharacteristic
118C2×C4⋊C4×C37C2311yescharacteristic
119C2×C4⋊C4×C37C2311yescharacteristic
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37D411yescharacteristic
127C2×C22⋊C4×C37D411yescharacteristic
128C2×C42×C37—21no—
129C2×C42×C37—21no—
130C2×C42×C37C2311yescharacteristic
131C2×C42×C37C2311yescharacteristic
132#106×C37—22no—
133C4⋊C8×C37—22no—
134C4⋊C8×C37—41no—
135#103×C37—22no—
136#102×C37—22no—
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—22no—
143#102×C37—41no—
144#102×C37D414yescomplemented
145C22⋊C8×C37—22no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37—21no—
150#95×C37D411yescharacteristic
151#95×C37D411yescharacteristic
152C24×C37—21no—
153C24×C37—21no—
154C24×C37—21no—
155C24×C37—42no—
156C24×C37—42no—
157C24×C37—42no—
158C24×C37—42no—
159C24×C37—42no—
160C24×C37—81no—
161C24×C37—81no—
162C24×C37C2×D411yescharacteristic
163C2×Q8×C37—21no—
164C2×Q8×C37—21no—
165C2×Q8×C37—21no—
166C2×Q8×C37—21no—
167C2×Q8×C37—21no—
168C2×Q8×C37C2×D412yes—
169C2×D4×C37—28no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—21no—
174C2×D4×C37—21no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—21no—
181C2×D4×C37—21no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—21no—
186C2×D4×C37—44no—
187C2×D4×C37—44no—
188C2×D4×C37—42no—
189C2×D4×C37—42no—
190C2×D4×C37—44no—
191C2×D4×C37—42no—
192C2×D4×C37—42no—
193C2×D4×C37—42no—
194C2×D4×C37—42no—
195C2×D4×C37—42no—
196C2×D4×C37—42no—
197C2×D4×C37—42no—
198C2×D4×C37—42no—
199C2×D4×C37—42no—
200C2×D4×C37—42no—
201C2×D4×C37—42no—
202C2×D4×C37—42no—
203C2×D4×C37—81no—
204C2×D4×C37—81no—
205C2×D4×C37—81no—
206C2×D4×C37—81no—
207C2×D4×C37C2×D412yes—
208C2×D4×C37#4112yes—
209C22×C4×C37—21no—
210C22×C4×C37—21no—
211C22×C4×C37—21no—
212C22×C4×C37—21no—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—21no—
217C22×C4×C37—21no—
218C22×C4×C37—42no—
219C22×C4×C37—42no—
220C22×C4×C37—81no—
221C22×C4×C37C2×D411yescharacteristic
222C22×C4×C37C2×D411yescharacteristic
223C22×C4×C37C2×D411yescharacteristic
224C22×C4×C37C2×D412yes—
225C22×C4×C37C2×D411yescharacteristic
226C22×C4×C37C2×D411yescharacteristic
227C22×C4×C37#4112yes—
228C22×C4×C37C2411yescharacteristic
229SD16×C37—44no—
230SD16×C37—44no—
231SD16×C37—44no—
232C2×C8×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—21no—
235C2×C8×C37—21no—
236C2×C8×C37—21no—
237C2×C8×C37—21no—
238C2×C8×C37—21no—
239C2×C8×C37—21no—
240C2×C8×C37—21no—
241C2×C8×C37—21no—
242C2×C8×C37—21no—
243C2×C8×C37—44no—
244C2×C8×C37C2×D412yes—
245C4⋊C4×C37—24no—
246C4⋊C4×C37—21no—
247C4⋊C4×C37—21no—
248C4⋊C4×C37—21no—
249C4⋊C4×C37—21no—
250C4⋊C4×C37—21no—
251C4⋊C4×C37—21no—
252C4⋊C4×C37—42no—
253C4⋊C4×C37—42no—
254C4⋊C4×C37—81no—
255C4⋊C4×C37C2×D412yes—
256C4⋊C4×C37C2×D412yes—
257C22⋊C4×C37—24no—
258C22⋊C4×C37—22no—
259C22⋊C4×C37—42no—
260C22⋊C4×C37—42no—
261C22⋊C4×C37—42no—
262C22⋊C4×C37—42no—
263C22⋊C4×C37—42no—
264C22⋊C4×C37SD1614yescomplemented
265C42×C37—21no—
266C42×C37—21no—
267C42×C37—21no—
268C42×C37—21no—
269C42×C37—42no—
270C42×C37—81no—
271C23×C37—21no—
272C23×C37—21no—
273C23×C37—21no—
274C23×C37—21no—
275C23×C37—22no—
276C23×C37—22no—
277C23×C37—48no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37—41no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—41no—
289C23×C37—41no—
290C23×C37—41no—
291C23×C37—41no—
292C23×C37—41no—
293C23×C37—41no—
294C23×C37—41no—
295C23×C37—41no—
296C23×C37—41no—
297C23×C37—84no—
298C23×C37—84no—
299C23×C37—84no—
300C23×C37—84no—
301C23×C37—84no—
302C23×C37—84no—
303C23×C37#12112yes—
304C23×C37C2×SD1612yes—
305C23×C37AGL(1,ℤ/8)12yes—
306C23×C37C22×D411yescharacteristic
307Q8×C37—22no—
308Q8×C37—22no—
309Q8×C37—41no—
310Q8×C37—41no—
311D4×C37—22no—
312D4×C37—22no—
313D4×C37—22no—
314D4×C37—22no—
315D4×C37—48no—
316D4×C37—41no—
317D4×C37—41no—
318D4×C37—41no—
319D4×C37—41no—
320D4×C37—41no—
321D4×C37—41no—
322D4×C37—41no—
323D4×C37—41no—
324D4×C37—84no—
325D4×C37—84no—
326D4×C37—84no—
327D4×C37—84no—
328D4×C37—84no—
329C2×C4×C37—21no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—21no—
335C2×C4×C37—22no—
336C2×C4×C37—22no—
337C2×C4×C37—22no—
338C2×C4×C37—22no—
339C2×C4×C37—22no—
340C2×C4×C37—22no—
341C2×C4×C37—21no—
342C2×C4×C37—22no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—21no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—41no—
351C2×C4×C37—41no—
352C2×C4×C37—41no—
353C2×C4×C37—41no—
354C2×C4×C37—41no—
355C2×C4×C37—41no—
356C2×C4×C37—41no—
357C2×C4×C37—41no—
358C2×C4×C37—41no—
359C2×C4×C37—41no—
360C2×C4×C37—84no—
361C2×C4×C37#12112yes—
362C2×C4×C37C2×SD1612yes—
363C2×C4×C37C2×SD1612yes—
364C2×C4×C37C22×D411yescharacteristic
365C2×C4×C37C22×D411yescharacteristic
366C2×C4×C37C2×#4111yescharacteristic
367C2×C4×C37C2×#4111yescharacteristic
368C2×C4×C37H(5,𝔽2)11yescharacteristic
369C2×C4×C37H(5,𝔽2)11yescharacteristic
370C8×C37—22no—
371C8×C37—41no—
372C8×C37—41no—
373C8×C37—41no—
374#25080C3711yesmaximal, characteristic, direct product factor, Sylow
375C22×C37—22no—
376C22×C37—22no—
377C22×C37—22no—
378C22×C37—22no—
379C22×C37—22no—
380C22×C37—22no—
381C22×C37—42no—
382C22×C37—42no—
383C22×C37—42no—
384C22×C37—42no—
385C22×C37—42no—
386C22×C37—42no—
387C22×C37—816no—
388C22×C37—81no—
389C22×C37—81no—
390C22×C37—81no—
391C22×C37—81no—
392C22×C37—81no—
393C22×C37—81no—
394C22×C37—81no—
395C22×C37—81no—
396C22×C37—81no—
397C22×C37—81no—
398C22×C37—81no—
399C22×C37—81no—
400C22×C37—81no—
401C22×C37—81no—
402C22×C37—81no—
403C22×C37#46014yescomplemented
404C22×C37C2×#12111yescharacteristic
405C22×C37D4211yescharacteristic
406C22×C37#54611yescharacteristic
407C22×C37C22×SD1611yescharacteristic
408C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C37#57611yescharacteristic
410C22×C37#57711yescharacteristic
411C4×C37—22no—
412C4×C37—22no—
413C4×C37—22no—
414C4×C37—42no—
415C4×C37—41no—
416C4×C37—42no—
417C4×C37—42no—
418C4×C37—41no—
419C4×C37—81no—
420C4×C37—81no—
421C4×C37#52511yescharacteristic
422C4×C37#53811yescharacteristic
423C4×C37D4211yescharacteristic
424C4×C37#54611yescharacteristic
425C2×#465C2×C3711yescharacteristic, complemented
426C2×#460C2×C3711yescharacteristic, complemented
427C2×#450C2×C3711yescharacteristic, complemented
428C22×#102C2×C3711yescharacteristic, complemented
429#2433C2×C3711yescharacteristic
430#2360C2×C3711yescharacteristic, complemented
431#2065C2×C3711yescharacteristic, complemented
432#2055C2×C3711yescharacteristic, complemented
433#2041C2×C3711yescharacteristic, complemented
434#2014C2×C3711yescharacteristic, complemented
435#1982C2×C3711yescharacteristic, complemented
436#1926C2×C3711yescharacteristic, complemented
437#1880C2×C3711yescharacteristic, complemented
438#1874C2×C3711yescharacteristic, complemented
439#1850C2×C3711yescharacteristic, complemented
440C2×C37—24no—
441C2×C37—82no—
442C2×C37—82no—
443C2×C37—161no—
444C2×C37#242411yescharacteristic
445C2×C37C2×#46011yescharacteristic
446C2×C37#304511yescharacteristic
447C2×C37#326411yescharacteristic
448C2×C37D4×SD1611yescharacteristic
449C2×C37#329511yescharacteristic
450C2×C37#331011yescharacteristic
451C23×D4C22×C3711yescharacteristic
452C22×SD16C22×C3711yescharacteristic
453C22×SD16C22×C3711yescharacteristic
454C22×SD16C22×C3711yescharacteristic, complemented
455C23×C8C22×C3711yescharacteristic
456C2×#127C22×C3711yescharacteristic
457C2×#127C22×C3711yescharacteristic
458C2×C22⋊Q8C22×C3711yescharacteristic
459C2×#121C22×C3711yescharacteristic
460C2×#120—21no—
461C2×#120—21no—
462C2×C4×Q8C22×C3711yescharacteristic, complemented
463C22×C4⋊C4C22×C3711yescharacteristic
464#465—24no—
465#460—24no—
466#450—24no—
467C2×#106C22×C3711yescharacteristic, complemented
468C2×C4⋊C8C22×C3711yescharacteristic, complemented
469C2×C4⋊C8C22×C3711yescharacteristic, complemented
470C2×#103C22×C3711yescharacteristic, complemented
471C2×#102—24no—
472C2×#102C22×C3711yescharacteristic
473C2×#102C22×C3711yescharacteristic
474C2×#102C22×C3711yescharacteristic
475C2×#102C22×C3711yescharacteristic
476C2×#102C22×C3711yescharacteristic
477C2×#102C22×C3711yescharacteristic
478C2×#102C22×C3711yescharacteristic, complemented
479C2×#102C22×C3711yescharacteristic, complemented
480C2×#102C22×C3711yescharacteristic, complemented
481C2×C22⋊C8C22×C3711yescharacteristic
482#392—21no—
483#392—21no—
484#391C22×C3711yescharacteristic, complemented
485#390C22×C3711yescharacteristic
486#390C22×C3711yescharacteristic
487#389—21no—
488#389C22×C3711yescharacteristic, complemented
489#387—21no—
490#385—21no—
491C4×C4⋊C4C22×C3711yescharacteristic, complemented
492C4×C22⋊C4—21no—
493C4×C22⋊C4C22×C3711yescharacteristic
494#340C22×C3711yescharacteristic, complemented
495#340C22×C3711yescharacteristic, complemented
496#336C22×C3711yescharacteristic, complemented
497#336C22×C3711yescharacteristic, complemented
498C37#2508011yescharacteristic, direct product factor, Sylow
499C25—21no—
500C22×Q8C23×C3711yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C23×C3711yescharacteristic
514C22×D4C23×C3711yescharacteristic
515C22×D4C23×C3711yescharacteristic
516C23×C4—21no—
517C23×C4C23×C3711yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8C23×C3711yescharacteristic
531C22×C8C23×C3711yescharacteristic
532C22×C8C23×C3711yescharacteristic
533C22×C8C23×C3711yescharacteristic
534#127—22no—
535#127—22no—
536#127—41no—
537#127—41no—
538C22⋊Q8—22no—
539C22⋊Q8D4×C3714yescomplemented
540#121—22no—
541#121—22no—
542#120—44no—
543#120—44no—
544C4×Q8—22no—
545C4×Q8—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4C23×C3711yescharacteristic
553C2×C4⋊C4C23×C3711yescharacteristic
554C2×C4⋊C4C23×C3711yescharacteristic
555C2×C4⋊C4C23×C3711yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4D4×C3711yescharacteristic
563C2×C22⋊C4D4×C3711yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C23×C3711yescharacteristic
567C2×C42C23×C3711yescharacteristic
568#106—22no—
569C4⋊C8—22no—
570C4⋊C8—41no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—41no—
580#102D4×C3714yescomplemented
581C22⋊C8—22no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586#95D4×C3711yescharacteristic
587#95D4×C3711yescharacteristic
588C24—21no—
589C24—21no—
590C24—21no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×D4×C3711yescharacteristic
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C2×D4×C3712yes—
605C2×D4—28no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4C2×D4×C3712yes—
644C2×D4#41×C3712yes—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4C2×D4×C3711yescharacteristic
658C22×C4C2×D4×C3711yescharacteristic
659C22×C4C2×D4×C3711yescharacteristic
660C22×C4C2×D4×C3712yes—
661C22×C4C2×D4×C3711yescharacteristic
662C22×C4C2×D4×C3711yescharacteristic
663C22×C4#41×C3712yes—
664C22×C4C24×C3711yescharacteristic
665SD16—44no—
666SD16—44no—
667SD16—44no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—44no—
680C2×C8C2×D4×C3712yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—81no—
691C4⋊C4C2×D4×C3712yes—
692C4⋊C4C2×D4×C3712yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4SD16×C3714yescomplemented
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—81no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#121×C3712yes—
740C23C2×SD16×C3712yes—
741C23AGL(1,ℤ/8)×C3712yes—
742C23C22×D4×C3711yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4#121×C3712yes—
798C2×C4C2×SD16×C3712yes—
799C2×C4C2×SD16×C3712yes—
800C2×C4C22×D4×C3711yescharacteristic
801C2×C4C22×D4×C3711yescharacteristic
802C2×C4C2×#41×C3711yescharacteristic
803C2×C4C2×#41×C3711yescharacteristic
804C2×C4H(5,𝔽2)×C3711yescharacteristic
805C2×C4H(5,𝔽2)×C3711yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22C37×#46014yescomplemented
839C22C2×#121×C3711yescharacteristic
840C22D42×C3711yescharacteristic
841C22C37×#54611yescharacteristic
842C22C22×SD16×C3711yescharacteristic
843C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
844C22C37×#57611yescharacteristic
845C22C37×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—42no—
853C4—41no—
854C4—81no—
855C4—81no—
856C4C37×#52511yescharacteristic
857C4C37×#53811yescharacteristic
858C4D42×C3711yescharacteristic
859C4C37×#54611yescharacteristic
860C2—24no—
861C2—82no—
862C2—82no—
863C2—161no—
864C2C37×#242411yescharacteristic
865C2C2×C37×#46011yescharacteristic
866C2C37×#304511yescharacteristic
867C2C37×#326411yescharacteristic
868C2D4×SD16×C3711yescharacteristic
869C2C37×#329511yescharacteristic
870C2C37×#331011yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2433C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#465C2semidirect
2. C2×C37×#460C2semidirect
3. C2×C37×#450C2semidirect
4. C22×#102×C37C2semidirect
6. C37×#2360C2semidirect
7. C37×#2065C2semidirect
8. C37×#2055C2semidirect
9. C37×#2041C2semidirect
10. C37×#2014C2semidirect
11. C37×#1982C2semidirect
12. C37×#1926C2semidirect
13. C37×#1880C2semidirect
14. C37×#1874C2semidirect
15. C37×#1850C2semidirect
19. C22×SD16×C37C22semidirect
27. C2×C4×Q8×C37C22semidirect
32. C2×#106×C37C22semidirect
33. C2×C4⋊C8×C37C22semidirect
34. C2×C4⋊C8×C37C22semidirect
35. C2×#103×C37C22semidirect
43. C2×#102×C37C22semidirect
44. C2×#102×C37C22semidirect
45. C2×#102×C37C22semidirect
49. C37×#391C22semidirect
53. C37×#389C22semidirect
56. C4×C4⋊C4×C37C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#336C22semidirect
62. C37×#336C22semidirect
103. C22⋊Q8×C37D4semidirect
144. #102×C37D4semidirect
264. C22⋊C4×C37SD16semidirect
374. #25080C37direct (N × H)
403. C22×C37#460semidirect
425. C2×#465C2×C37semidirect
426. C2×#460C2×C37semidirect
427. C2×#450C2×C37semidirect
428. C22×#102C2×C37semidirect
430. #2360C2×C37semidirect
431. #2065C2×C37semidirect
432. #2055C2×C37semidirect
433. #2041C2×C37semidirect
434. #2014C2×C37semidirect
435. #1982C2×C37semidirect
436. #1926C2×C37semidirect
437. #1880C2×C37semidirect
438. #1874C2×C37semidirect
439. #1850C2×C37semidirect
454. C22×SD16C22×C37semidirect
462. C2×C4×Q8C22×C37semidirect
467. C2×#106C22×C37semidirect
468. C2×C4⋊C8C22×C37semidirect
469. C2×C4⋊C8C22×C37semidirect
470. C2×#103C22×C37semidirect
478. C2×#102C22×C37semidirect
479. C2×#102C22×C37semidirect
480. C2×#102C22×C37semidirect
484. #391C22×C37semidirect
488. #389C22×C37semidirect
491. C4×C4⋊C4C22×C37semidirect
494. #340C22×C37semidirect
495. #340C22×C37semidirect
496. #336C22×C37semidirect
497. #336C22×C37semidirect
498. C37#25080direct (N × H)
539. C22⋊Q8D4×C37semidirect
580. #102D4×C37semidirect
700. C22⋊C4SD16×C37semidirect
838. C22C37×#460semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4652
C2×C37×#4602
C2×C37×#4502
C22×#102×C372
C37×#24332
C37×#23602
C37×#20652
C37×#20552
C37×#20412
C37×#20142
C37×#19822
C37×#19262
C37×#18802
C37×#18742
C37×#18502
#2508037