Finite Group Databasebeta

← C37×#25152 #22646405

Subgroups — C37×#25152 #22646405

Order 9472.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#463C211yesmaximal, characteristic, complemented
2C2×C37×#450C211yesmaximal, characteristic, complemented
3C2×C37×#447C211yesmaximal, characteristic
4C2×C4×SD16×C37C211yesmaximal, characteristic, complemented
5C37×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
7C37×#2065C211yesmaximal, characteristic, complemented
8C37×#2036C211yesmaximal, characteristic, complemented
9C37×#2034C211yesmaximal, characteristic, complemented
10C37×#2012C211yesmaximal, characteristic, complemented
11C37×#1970C211yesmaximal, characteristic, complemented
12C37×#1923C211yesmaximal, characteristic, complemented
13C37×#1880C211yesmaximal, characteristic, complemented
14C37×#1879C211yesmaximal, characteristic, complemented
15C37×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic
20C22×D8×C37C2211yescharacteristic
21C2×#124×C37C2211yescharacteristic, complemented
22C2×C22⋊Q8×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×C4×Q8×C37C2211yescharacteristic, complemented
25C2×C4×D4×C37C2211yescharacteristic
26C2×C4×D4×C37C2211yescharacteristic
27C22×C22⋊C4×C37—21no—
28C37×#463—24no—
29C37×#450—24no—
30C37×#447—24no—
31C4×SD16×C37—24no—
32C2×#107×C37C2211yescharacteristic, complemented
33C2×#106×C37C2211yescharacteristic, complemented
34C2×C4⋊C8×C37C2211yescharacteristic, complemented
35C2×#103×C37C2211yescharacteristic, complemented
36C2×#103×C37C2211yescharacteristic, complemented
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic, complemented
42C2×#102×C37C2211yescharacteristic, complemented
43C2×C22⋊C8×C37C2211yescharacteristic
44C2×C22⋊C8×C37C2211yescharacteristic
45C2×C4×C8×C37C2211yescharacteristic, complemented
46C37×#396—21no—
47C37×#394—21no—
48C37×#390—21no—
49C37×#390C2211yescharacteristic
50C37×#390C2211yescharacteristic
51C37×#390C2211yescharacteristic, complemented
52C37×#389C2211yescharacteristic, complemented
53C37×#388—21no—
54C37×#386—21no—
55C37×#386—21no—
56C37×#380C2211yescharacteristic
57C37×#379—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—22no—
68C22×D4×C37—22no—
69C22×D4×C37—21no—
70C22×D4×C37—21no—
71C22×D4×C37—41no—
72C22×D4×C37—41no—
73C22×D4×C37C2311yescharacteristic
74C22×D4×C37C2311yescharacteristic
75C22×D4×C37C2311yescharacteristic
76C23×C4×C37—21no—
77C23×C4×C37—21no—
78C23×C4×C37C2311yescharacteristic
79C2×SD16×C37—22no—
80C2×SD16×C37—22no—
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—41no—
84C2×SD16×C37D414yescomplemented
85C2×D8×C37—22no—
86C2×D8×C37—22no—
87C2×D8×C37—22no—
88C2×D8×C37—22no—
89C2×D8×C37—22no—
90C2×D8×C37—41no—
91C22×C8×C37C2311yescharacteristic
92C22×C8×C37C2311yescharacteristic
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95#124×C37—22no—
96#124×C37—41no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—41no—
99#121×C37—22no—
100#121×C37—41no—
101C4×Q8×C37—22no—
102C4×Q8×C37—41no—
103C4×D4×C37—22no—
104C4×D4×C37—22no—
105C4×D4×C37—41no—
106C4×D4×C37—41no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37C2311yescharacteristic
111C2×C4⋊C4×C37C2311yescharacteristic
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
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×C37—21no—
127C2×C22⋊C4×C37—44no—
128C2×C22⋊C4×C37D411yescharacteristic
129C2×C22⋊C4×C37D411yescharacteristic
130C2×C42×C37—21no—
131C2×C42×C37C2311yescharacteristic
132C2×C42×C37C2311yescharacteristic
133#107×C37—41no—
134#106×C37—22no—
135C4⋊C8×C37—22no—
136#103×C37—22no—
137#103×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—41no—
143#102×C37D414yes—
144C22⋊C8×C37—22no—
145C22⋊C8×C37—22no—
146C4×C8×C37—22no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37D411yescharacteristic
150#95×C37D411yescharacteristic
151C24×C37—21no—
152C24×C37—24no—
153C24×C37—21no—
154C24×C37—21no—
155C24×C37—42no—
156C24×C37—42no—
157C24×C37—42no—
158C24×C37—42no—
159C24×C37—81no—
160C24×C37—81no—
161C24×C37C2×D411yescharacteristic
162C2×Q8×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37—21no—
165C2×Q8×C37—21no—
166C2×Q8×C37—21no—
167C2×Q8×C37C2×D412yes—
168C2×D4×C37—24no—
169C2×D4×C37—21no—
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—42no—
184C2×D4×C37—42no—
185C2×D4×C37—42no—
186C2×D4×C37—44no—
187C2×D4×C37—44no—
188C2×D4×C37—44no—
189C2×D4×C37—44no—
190C2×D4×C37—42no—
191C2×D4×C37—81no—
192C2×D4×C37C2×D412yes—
193C2×D4×C37C2×D412yes—
194C2×D4×C37#4112yes—
195C2×D4×C37#4112yes—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—42no—
208C22×C4×C37—42no—
209C22×C4×C37—42no—
210C22×C4×C37—42no—
211C22×C4×C37—81no—
212C22×C4×C37—81no—
213C22×C4×C37C2×D411yescharacteristic
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2411yescharacteristic
219SD16×C37—28no—
220SD16×C37—44no—
221D8×C37—44no—
222D8×C37—44no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—21no—
227C2×C8×C37—21no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—21no—
231C2×C8×C37—21no—
232C2×C8×C37—21no—
233C2×C8×C37C2×D412yes—
234C2×C8×C37C2×D412yes—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—42no—
243C4⋊C4×C37—42no—
244C4⋊C4×C37—81no—
245C4⋊C4×C37C2×D412yes—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—22no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—42no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—42no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—42no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—42no—
257C22⋊C4×C37—42no—
258C22⋊C4×C37—81no—
259C22⋊C4×C37—81no—
260C22⋊C4×C37—81no—
261C42×C37—21no—
262C42×C37—21no—
263C42×C37—21no—
264C42×C37—21no—
265C42×C37—42no—
266C23×C37—21no—
267C23×C37—22no—
268C23×C37—21no—
269C23×C37—22no—
270C23×C37—22no—
271C23×C37—21no—
272C23×C37—21no—
273C23×C37—21no—
274C23×C37—21no—
275C23×C37—22no—
276C23×C37—48no—
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—84no—
296C23×C37—84no—
297C23×C37—84no—
298C23×C37—84no—
299C23×C37—84no—
300C23×C37#13512yes—
301C23×C37C22×D411yescharacteristic
302Q8×C37—22no—
303Q8×C37—22no—
304Q8×C37—41no—
305Q8×C37—41no—
306D4×C37—22no—
307D4×C37—22no—
308D4×C37—22no—
309D4×C37—22no—
310D4×C37—22no—
311D4×C37—48no—
312D4×C37—41no—
313D4×C37—41no—
314D4×C37—41no—
315D4×C37—41no—
316D4×C37—41no—
317D4×C37—41no—
318D4×C37—84no—
319D4×C37#12114yes—
320C2×C4×C37—21no—
321C2×C4×C37—21no—
322C2×C4×C37—21no—
323C2×C4×C37—21no—
324C2×C4×C37—21no—
325C2×C4×C37—21no—
326C2×C4×C37—22no—
327C2×C4×C37—22no—
328C2×C4×C37—21no—
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—21no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—41no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37—41no—
346C2×C4×C37—41no—
347C2×C4×C37—41no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—41no—
351C2×C4×C37—41no—
352C2×C4×C37—41no—
353C2×C4×C37—84no—
354C2×C4×C37—84no—
355C2×C4×C37AGL(1,ℤ/8)12yes—
356C2×C4×C37C22×D411yescharacteristic
357C2×C4×C37C22×D411yescharacteristic
358C2×C4×C37C2×#4111yescharacteristic
359C2×C4×C37C2×#4111yescharacteristic
360C2×C4×C37H(5,𝔽2)11yescharacteristic
361C2×C4×C37H(5,𝔽2)11yescharacteristic
362C8×C37—22no—
363C8×C37—22no—
364C8×C37—41no—
365C8×C37—41no—
366#25152C3711yesmaximal, characteristic, direct product factor, Sylow
367C22×C37—22no—
368C22×C37—24no—
369C22×C37—22no—
370C22×C37—22no—
371C22×C37—42no—
372C22×C37—41no—
373C22×C37—42no—
374C22×C37—41no—
375C22×C37—42no—
376C22×C37—41no—
377C22×C37—42no—
378C22×C37—41no—
379C22×C37—42no—
380C22×C37—42no—
381C22×C37—42no—
382C22×C37—42no—
383C22×C37—42no—
384C22×C37—816no—
385C22×C37—81no—
386C22×C37—81no—
387C22×C37—81no—
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#52511yescharacteristic
397C22×C37D4211yescharacteristic
398C22×C37D4211yescharacteristic
399C22×C37C2×#13511yescharacteristic
400C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C37#57611yescharacteristic
402C22×C37#57711yescharacteristic
403C4×C37—22no—
404C4×C37—41no—
405C4×C37—42no—
406C4×C37—41no—
407C4×C37—41no—
408C4×C37—42no—
409C4×C37—41no—
410C4×C37—81no—
411C4×C37—81no—
412C4×C37—81no—
413C4×C37C2×#12111yescharacteristic
414C4×C37#53811yescharacteristic
415C4×C37#54611yescharacteristic
416C4×C37#54611yescharacteristic
417C2×#463C2×C3711yescharacteristic, complemented
418C2×#450C2×C3711yescharacteristic, complemented
419C2×#447C2×C3711yescharacteristic
420C2×C4×SD16C2×C3711yescharacteristic, complemented
421#2426C2×C3711yescharacteristic, complemented
422D4×C22⋊C4C2×C3711yescharacteristic, complemented
423#2065C2×C3711yescharacteristic, complemented
424#2036C2×C3711yescharacteristic, complemented
425#2034C2×C3711yescharacteristic, complemented
426#2012C2×C3711yescharacteristic, complemented
427#1970C2×C3711yescharacteristic, complemented
428#1923C2×C3711yescharacteristic, complemented
429#1880C2×C3711yescharacteristic, complemented
430#1879C2×C3711yescharacteristic, complemented
431#1862C2×C3711yescharacteristic, complemented
432C2×C37—42no—
433C2×C37—44no—
434C2×C37—82no—
435C2×C37—161no—
436C2×C37#242411yescharacteristic
437C2×C37#310511yescharacteristic
438C2×C37#311811yescharacteristic
439C2×C37#326511yescharacteristic
440C2×C37#327411yescharacteristic
441C2×C37#328011yescharacteristic
442C2×C37#328211yescharacteristic
443C23×D4C22×C3711yescharacteristic
444C22×SD16C22×C3711yescharacteristic
445C22×SD16C22×C3711yescharacteristic
446C22×D8C22×C3711yescharacteristic
447C22×D8C22×C3711yescharacteristic
448C2×#124C22×C3711yescharacteristic, complemented
449C2×C22⋊Q8C22×C3711yescharacteristic
450C2×#121C22×C3711yescharacteristic
451C2×C4×Q8C22×C3711yescharacteristic, complemented
452C2×C4×D4C22×C3711yescharacteristic
453C2×C4×D4C22×C3711yescharacteristic
454C22×C22⋊C4—21no—
455#463—24no—
456#450—24no—
457#447—24no—
458C4×SD16—24no—
459C2×#107C22×C3711yescharacteristic, complemented
460C2×#106C22×C3711yescharacteristic, complemented
461C2×C4⋊C8C22×C3711yescharacteristic, complemented
462C2×#103C22×C3711yescharacteristic, complemented
463C2×#103C22×C3711yescharacteristic, complemented
464C2×#102C22×C3711yescharacteristic
465C2×#102C22×C3711yescharacteristic
466C2×#102C22×C3711yescharacteristic
467C2×#102C22×C3711yescharacteristic
468C2×#102C22×C3711yescharacteristic, complemented
469C2×#102C22×C3711yescharacteristic, complemented
470C2×C22⋊C8C22×C3711yescharacteristic
471C2×C22⋊C8C22×C3711yescharacteristic
472C2×C4×C8C22×C3711yescharacteristic, complemented
473#396—21no—
474#394—21no—
475#390—21no—
476#390C22×C3711yescharacteristic
477#390C22×C3711yescharacteristic
478#390C22×C3711yescharacteristic, complemented
479#389C22×C3711yescharacteristic, complemented
480#388—21no—
481#386—21no—
482#386—21no—
483#380C22×C3711yescharacteristic
484#379—21no—
485C4×C22⋊C4C22×C3711yescharacteristic
486#340C22×C3711yescharacteristic, complemented
487#340C22×C3711yescharacteristic, complemented
488#336C22×C3711yescharacteristic, complemented
489#336C22×C3711yescharacteristic, complemented
490C37#2515211yescharacteristic, direct product factor, Sylow
491C25—21no—
492C22×Q8C23×C3711yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C3711yescharacteristic
502C22×D4C23×C3711yescharacteristic
503C22×D4C23×C3711yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C3711yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C3714yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C3711yescharacteristic
520C22×C8C23×C3711yescharacteristic
521C22×C8C23×C3711yescharacteristic
522C22×C8C23×C3711yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C3711yescharacteristic
539C2×C4⋊C4C23×C3711yescharacteristic
540C2×C4⋊C4C23×C3711yescharacteristic
541C2×C4⋊C4C23×C3711yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C3711yescharacteristic
557C2×C22⋊C4D4×C3711yescharacteristic
558C2×C42—21no—
559C2×C42C23×C3711yescharacteristic
560C2×C42C23×C3711yescharacteristic
561#107—41no—
562#106—22no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C3714yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C4×C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C3711yescharacteristic
578#95D4×C3711yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C3711yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C3712yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C3712yes—
621C2×D4C2×D4×C3712yes—
622C2×D4#41×C3712yes—
623C2×D4#41×C3712yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C3711yescharacteristic
642C22×C4C2×D4×C3711yescharacteristic
643C22×C4C2×D4×C3711yescharacteristic
644C22×C4C2×D4×C3711yescharacteristic
645C22×C4C2×D4×C3711yescharacteristic
646C22×C4C24×C3711yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C3712yes—
662C2×C8C2×D4×C3712yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C3712yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23#135×C3712yes—
729C23C22×D4×C3711yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C3714yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4AGL(1,ℤ/8)×C3712yes—
784C2×C4C22×D4×C3711yescharacteristic
785C2×C4C22×D4×C3711yescharacteristic
786C2×C4C2×#41×C3711yescharacteristic
787C2×C4C2×#41×C3711yescharacteristic
788C2×C4H(5,𝔽2)×C3711yescharacteristic
789C2×C4H(5,𝔽2)×C3711yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22C37×#52511yescharacteristic
824C22D42×C3711yescharacteristic
825C22D42×C3711yescharacteristic
826C22C2×#135×C3711yescharacteristic
827C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
828C22C37×#57611yescharacteristic
829C22C37×#57711yescharacteristic
830C4—22no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C3711yescharacteristic
841C4C37×#53811yescharacteristic
842C4C37×#54611yescharacteristic
843C4C37×#54611yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C37×#242411yescharacteristic
849C2C37×#310511yescharacteristic
850C2C37×#311811yescharacteristic
851C2C37×#326511yescharacteristic
852C2C37×#327411yescharacteristic
853C2C37×#328011yescharacteristic
854C2C37×#328211yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#447C2
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×#463C2semidirect
2. C2×C37×#450C2semidirect
4. C2×C4×SD16×C37C2semidirect
5. C37×#2426C2semidirect
6. D4×C22⋊C4×C37C2semidirect
7. C37×#2065C2semidirect
8. C37×#2036C2semidirect
9. C37×#2034C2semidirect
10. C37×#2012C2semidirect
11. C37×#1970C2semidirect
12. C37×#1923C2semidirect
13. C37×#1880C2semidirect
14. C37×#1879C2semidirect
15. C37×#1862C2semidirect
21. C2×#124×C37C22semidirect
24. C2×C4×Q8×C37C22semidirect
32. C2×#107×C37C22semidirect
33. C2×#106×C37C22semidirect
34. C2×C4⋊C8×C37C22semidirect
35. C2×#103×C37C22semidirect
36. C2×#103×C37C22semidirect
41. C2×#102×C37C22semidirect
42. C2×#102×C37C22semidirect
45. C2×C4×C8×C37C22semidirect
51. C37×#390C22semidirect
52. C37×#389C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#336C22semidirect
62. C37×#336C22semidirect
84. C2×SD16×C37D4semidirect
366. #25152C37direct (N × H)
417. C2×#463C2×C37semidirect
418. C2×#450C2×C37semidirect
420. C2×C4×SD16C2×C37semidirect
421. #2426C2×C37semidirect
422. D4×C22⋊C4C2×C37semidirect
423. #2065C2×C37semidirect
424. #2036C2×C37semidirect
425. #2034C2×C37semidirect
426. #2012C2×C37semidirect
427. #1970C2×C37semidirect
428. #1923C2×C37semidirect
429. #1880C2×C37semidirect
430. #1879C2×C37semidirect
431. #1862C2×C37semidirect
448. C2×#124C22×C37semidirect
451. C2×C4×Q8C22×C37semidirect
459. C2×#107C22×C37semidirect
460. C2×#106C22×C37semidirect
461. C2×C4⋊C8C22×C37semidirect
462. C2×#103C22×C37semidirect
463. C2×#103C22×C37semidirect
468. C2×#102C22×C37semidirect
469. C2×#102C22×C37semidirect
472. C2×C4×C8C22×C37semidirect
478. #390C22×C37semidirect
479. #389C22×C37semidirect
486. #340C22×C37semidirect
487. #340C22×C37semidirect
488. #336C22×C37semidirect
489. #336C22×C37semidirect
490. C37#25152direct (N × H)
512. C2×SD16D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4632
C2×C37×#4502
C2×C37×#4472
C2×C4×SD16×C372
C37×#24262
D4×C22⋊C4×C372
C37×#20652
C37×#20362
C37×#20342
C37×#20122
C37×#19702
C37×#19232
C37×#18802
C37×#18792
C37×#18622
#2515237