Finite Group Databasebeta

← C37×#25124 #22646377

Subgroups — C37×#25124 #22646377

Order 9472.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#469C211yesmaximal, characteristic, complemented
2C2×C37×#447C211yesmaximal, characteristic, complemented
3C2×C37×#435C211yesmaximal, characteristic, complemented
4C22×#102×C37C211yesmaximal, characteristic, complemented
5C37×#2416C211yesmaximal, characteristic, complemented
6C37×#2408C211yesmaximal, characteristic, complemented
7C37×#2065C211yesmaximal, characteristic, complemented
8C37×#2054C211yesmaximal, characteristic, complemented
9C37×#2034C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1972C211yesmaximal, characteristic, complemented
12C37×#1936C211yesmaximal, characteristic, complemented
13C37×#1895C211yesmaximal, characteristic, complemented
14C37×#1893C211yesmaximal, characteristic, complemented
15C37×#1853C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C22×M16×C37C2211yescharacteristic, complemented
20C23×C8×C37C2211yescharacteristic
21C2×#121×C37—21no—
22C2×#121×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#121×C37C2211yescharacteristic, complemented
26C2×#120×C37—21no—
27C2×C4×D4×C37C2211yescharacteristic
28C22×C4⋊C4×C37C2211yescharacteristic
29C37×#469—24no—
30C37×#447—24no—
31C37×#435—24no—
32C2×#106×C37C2211yescharacteristic, complemented
33C2×#106×C37C2211yescharacteristic, complemented
34C2×C4⋊C8×C37C2211yescharacteristic, complemented
35C2×#102×C37—24no—
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic, complemented
43C2×#102×C37C2211yescharacteristic, complemented
44C2×C22⋊C8×C37C2211yescharacteristic
45C2×C22⋊C8×C37C2211yescharacteristic, complemented
46C2×#97×C37C2211yescharacteristic, complemented
47C37×#396—21no—
48C37×#394—21no—
49C37×#394—21no—
50C37×#392—21no—
51C37×#390C2211yescharacteristic
52C37×#390C2211yescharacteristic
53C37×#390C2211yescharacteristic, complemented
54C37×#389C2211yescharacteristic, complemented
55C37×#386—21no—
56C37×#380C2211yescharacteristic
57C37×#380C2211yescharacteristic, complemented
58C37×#379—21no—
59C37×#340C2211yescharacteristic, complemented
60C37×#340C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C25×C37—21no—
64C22×D4×C37—22no—
65C22×D4×C37—22no—
66C22×D4×C37—21no—
67C22×D4×C37—21no—
68C22×D4×C37—21no—
69C22×D4×C37—21no—
70C22×D4×C37—22no—
71C22×D4×C37—21no—
72C22×D4×C37—22no—
73C22×D4×C37—41no—
74C22×D4×C37—41no—
75C22×D4×C37D411yescharacteristic
76C22×D4×C37C2311yescharacteristic
77C22×D4×C37C2311yescharacteristic
78C22×D4×C37C2311yescharacteristic
79C23×C4×C37—21no—
80C23×C4×C37C2311yescharacteristic
81C23×C4×C37C2311yescharacteristic
82C2×D8×C37—22no—
83C2×D8×C37—22no—
84C2×D8×C37—22no—
85C2×D8×C37—22no—
86C2×D8×C37—41no—
87C2×D8×C37—41no—
88C2×M16×C37—22no—
89C2×M16×C37—22no—
90C2×M16×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#121×C37—22no—
99#121×C37—22no—
100#121×C37—22no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—41no—
104#121×C37—41no—
105#121×C37—41no—
106#121×C37—44no—
107#120×C37—44no—
108C4×D4×C37—22no—
109C4×D4×C37—22no—
110C2×C4⋊C4×C37—22no—
111C2×C4⋊C4×C37—21no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37—41no—
114C2×C4⋊C4×C37D411yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37D411yescharacteristic
133C2×C22⋊C4×C37D411yescharacteristic
134C2×C42×C37C2311yescharacteristic
135#106×C37—22no—
136#106×C37—41no—
137C4⋊C8×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—22no—
144#102×C37—41no—
145#102×C37D414yescomplemented
146C22⋊C8×C37—22no—
147C22⋊C8×C37D414yescomplemented
148#97×C37—22no—
149#95×C37—21no—
150#95×C37—21no—
151#95×C37—21no—
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
163C24×C37C2×D411yescharacteristic
164C2×D4×C37—28no—
165C2×D4×C37—22no—
166C2×D4×C37—22no—
167C2×D4×C37—22no—
168C2×D4×C37—21no—
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—21no—
184C2×D4×C37—44no—
185C2×D4×C37—44no—
186C2×D4×C37—42no—
187C2×D4×C37—42no—
188C2×D4×C37—44no—
189C2×D4×C37—42no—
190C2×D4×C37—42no—
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—81no—
200C2×D4×C37—81no—
201C2×D4×C37—81no—
202C2×D4×C37C2×D412yes—
203C2×D4×C37#4112yes—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—21no—
207C22×C4×C37—21no—
208C22×C4×C37—21no—
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—21no—
219C22×C4×C37—42no—
220C22×C4×C37—42no—
221C22×C4×C37—81no—
222C22×C4×C37C2×D411yescharacteristic
223C22×C4×C37C2×D411yescharacteristic
224C22×C4×C37C2×D411yescharacteristic
225C22×C4×C37C2×D411yescharacteristic
226C22×C4×C37C2×D412yes—
227C22×C4×C37#4112yes—
228C22×C4×C37C2411yescharacteristic
229D8×C37—44no—
230D8×C37—44no—
231M16×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—44no—
242C2×C8×C37C2×D412yes—
243C2×C8×C37C2×D412yes—
244C2×C8×C37C2×D412yes—
245C4⋊C4×C37—22no—
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—21no—
253C4⋊C4×C37—21no—
254C4⋊C4×C37—21no—
255C4⋊C4×C37—42no—
256C4⋊C4×C37—42no—
257C4⋊C4×C37C2×D412yes—
258C22⋊C4×C37—22no—
259C22⋊C4×C37—22no—
260C22⋊C4×C37—42no—
261C22⋊C4×C37—42no—
262C22⋊C4×C37—42no—
263C22⋊C4×C37—42no—
264C22⋊C4×C37—42no—
265C22⋊C4×C37—42no—
266C22⋊C4×C37—42no—
267C22⋊C4×C37—42no—
268C22⋊C4×C37—42no—
269C22⋊C4×C37—81no—
270C22⋊C4×C37—81no—
271C22⋊C4×C37—81no—
272C42×C37—21no—
273C42×C37—21no—
274C23×C37—21no—
275C23×C37—21no—
276C23×C37—21no—
277C23×C37—21no—
278C23×C37—21no—
279C23×C37—22no—
280C23×C37—21no—
281C23×C37—22no—
282C23×C37—21no—
283C23×C37—21no—
284C23×C37—21no—
285C23×C37—21no—
286C23×C37—21no—
287C23×C37—48no—
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—41no—
298C23×C37—41no—
299C23×C37—41no—
300C23×C37—41no—
301C23×C37—41no—
302C23×C37—41no—
303C23×C37—41no—
304C23×C37—41no—
305C23×C37—41no—
306C23×C37—41no—
307C23×C37—84no—
308C23×C37—84no—
309C23×C37—84no—
310C23×C37—84no—
311C23×C37—84no—
312C23×C37—84no—
313C23×C37#12112yes—
314C23×C37AGL(1,ℤ/8)12yes—
315C23×C37AGL(1,ℤ/8)12yes—
316C23×C37C22×D411yescharacteristic
317D4×C37—22no—
318D4×C37—22no—
319D4×C37—22no—
320D4×C37—22no—
321D4×C37—48no—
322D4×C37—44no—
323D4×C37—41no—
324D4×C37—41no—
325D4×C37—41no—
326D4×C37—41no—
327D4×C37—41no—
328D4×C37—41no—
329D4×C37—41no—
330D4×C37—41no—
331D4×C37—84no—
332D4×C37—84no—
333D4×C37—84no—
334D4×C37—84no—
335C2×C4×C37—21no—
336C2×C4×C37—21no—
337C2×C4×C37—22no—
338C2×C4×C37—22no—
339C2×C4×C37—22no—
340C2×C4×C37—22no—
341C2×C4×C37—21no—
342C2×C4×C37—21no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—22no—
346C2×C4×C37—21no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—21no—
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—41no—
361C2×C4×C37—41no—
362C2×C4×C37—41no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—41no—
367C2×C4×C37—41no—
368C2×C4×C37—41no—
369C2×C4×C37—84no—
370C2×C4×C37#12112yes—
371C2×C4×C37C22×D411yescharacteristic
372C2×C4×C37C22×D411yescharacteristic
373C2×C4×C37C2×#4111yescharacteristic
374C2×C4×C37C2×#4111yescharacteristic
375C2×C4×C37H(5,𝔽2)11yescharacteristic
376C2×C4×C37H(5,𝔽2)11yescharacteristic
377C8×C37—22no—
378C8×C37—22no—
379C8×C37—22no—
380C8×C37—41no—
381#25124C3711yesmaximal, characteristic, direct product factor, Sylow
382C22×C37—22no—
383C22×C37—22no—
384C22×C37—22no—
385C22×C37—22no—
386C22×C37—22no—
387C22×C37—22no—
388C22×C37—41no—
389C22×C37—42no—
390C22×C37—42no—
391C22×C37—41no—
392C22×C37—42no—
393C22×C37—41no—
394C22×C37—42no—
395C22×C37—41no—
396C22×C37—42no—
397C22×C37—41no—
398C22×C37—41no—
399C22×C37—41no—
400C22×C37—42no—
401C22×C37—816no—
402C22×C37—81no—
403C22×C37—81no—
404C22×C37—81no—
405C22×C37—81no—
406C22×C37—81no—
407C22×C37—81no—
408C22×C37—81no—
409C22×C37—81no—
410C22×C37—81no—
411C22×C37—81no—
412C22×C37—81no—
413C22×C37—81no—
414C22×C37—81no—
415C22×C37—81no—
416C22×C37—81no—
417C22×C37#46914yescomplemented
418C22×C37C2×#12111yescharacteristic
419C22×C37D4211yescharacteristic
420C22×C37#54611yescharacteristic
421C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
422C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C37#57611yescharacteristic
424C22×C37#57711yescharacteristic
425C4×C37—22no—
426C4×C37—41no—
427C4×C37—42no—
428C4×C37—41no—
429C4×C37—41no—
430C4×C37—81no—
431C4×C37—81no—
432C4×C37—81no—
433C4×C37—81no—
434C4×C37#52511yescharacteristic
435C4×C37#53811yescharacteristic
436C4×C37D4211yescharacteristic
437C4×C37#54611yescharacteristic
438C2×#469C2×C3711yescharacteristic, complemented
439C2×#447C2×C3711yescharacteristic, complemented
440C2×#435C2×C3711yescharacteristic, complemented
441C22×#102C2×C3711yescharacteristic, complemented
442#2416C2×C3711yescharacteristic, complemented
443#2408C2×C3711yescharacteristic, complemented
444#2065C2×C3711yescharacteristic, complemented
445#2054C2×C3711yescharacteristic, complemented
446#2034C2×C3711yescharacteristic, complemented
447#1999C2×C3711yescharacteristic, complemented
448#1972C2×C3711yescharacteristic, complemented
449#1936C2×C3711yescharacteristic, complemented
450#1895C2×C3711yescharacteristic, complemented
451#1893C2×C3711yescharacteristic, complemented
452#1853C2×C3711yescharacteristic, complemented
453C2×C37—24no—
454C2×C37—81no—
455C2×C37—82no—
456C2×C37—82no—
457C2×C37—161no—
458C2×C37#242411yescharacteristic
459C2×C37C2×#46911yescharacteristic
460C2×C37#306211yescharacteristic
461C2×C37#326411yescharacteristic
462C2×C37#326511yescharacteristic
463C2×C37#330611yescharacteristic
464C2×C37#331811yescharacteristic
465C23×D4C22×C3711yescharacteristic
466C22×D8C22×C3711yescharacteristic
467C22×D8C22×C3711yescharacteristic
468C22×M16C22×C3711yescharacteristic, complemented
469C23×C8C22×C3711yescharacteristic
470C2×#121—21no—
471C2×#121C22×C3711yescharacteristic
472C2×#121C22×C3711yescharacteristic
473C2×#121C22×C3711yescharacteristic
474C2×#121C22×C3711yescharacteristic, complemented
475C2×#120—21no—
476C2×C4×D4C22×C3711yescharacteristic
477C22×C4⋊C4C22×C3711yescharacteristic
478#469—24no—
479#447—24no—
480#435—24no—
481C2×#106C22×C3711yescharacteristic, complemented
482C2×#106C22×C3711yescharacteristic, complemented
483C2×C4⋊C8C22×C3711yescharacteristic, complemented
484C2×#102—24no—
485C2×#102C22×C3711yescharacteristic
486C2×#102C22×C3711yescharacteristic
487C2×#102C22×C3711yescharacteristic
488C2×#102C22×C3711yescharacteristic
489C2×#102C22×C3711yescharacteristic
490C2×#102C22×C3711yescharacteristic
491C2×#102C22×C3711yescharacteristic, complemented
492C2×#102C22×C3711yescharacteristic, complemented
493C2×C22⋊C8C22×C3711yescharacteristic
494C2×C22⋊C8C22×C3711yescharacteristic, complemented
495C2×#97C22×C3711yescharacteristic, complemented
496#396—21no—
497#394—21no—
498#394—21no—
499#392—21no—
500#390C22×C3711yescharacteristic
501#390C22×C3711yescharacteristic
502#390C22×C3711yescharacteristic, complemented
503#389C22×C3711yescharacteristic, complemented
504#386—21no—
505#380C22×C3711yescharacteristic
506#380C22×C3711yescharacteristic, complemented
507#379—21no—
508#340C22×C3711yescharacteristic, complemented
509#340C22×C3711yescharacteristic, complemented
510#340C22×C3711yescharacteristic, complemented
511#340C22×C3711yescharacteristic, complemented
512C37#2512411yescharacteristic, direct product factor, Sylow
513C25—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4D4×C3711yescharacteristic
526C22×D4C23×C3711yescharacteristic
527C22×D4C23×C3711yescharacteristic
528C22×D4C23×C3711yescharacteristic
529C23×C4—21no—
530C23×C4C23×C3711yescharacteristic
531C23×C4C23×C3711yescharacteristic
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—41no—
544C22×C8C23×C3711yescharacteristic
545C22×C8C23×C3711yescharacteristic
546C22×C8C23×C3711yescharacteristic
547C22×C8C23×C3711yescharacteristic
548#121—22no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—44no—
557#120—44no—
558C4×D4—22no—
559C4×D4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C3711yescharacteristic
565C2×C4⋊C4C23×C3711yescharacteristic
566C2×C4⋊C4C23×C3711yescharacteristic
567C2×C4⋊C4C23×C3711yescharacteristic
568C2×C4⋊C4C23×C3711yescharacteristic
569C2×C4⋊C4C23×C3711yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4D4×C3711yescharacteristic
583C2×C22⋊C4D4×C3711yescharacteristic
584C2×C42C23×C3711yescharacteristic
585#106—22no—
586#106—41no—
587C4⋊C8—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102D4×C3714yescomplemented
596C22⋊C8—22no—
597C22⋊C8D4×C3714yescomplemented
598#97—22no—
599#95—21no—
600#95—21no—
601#95—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24C2×D4×C3711yescharacteristic
613C24C2×D4×C3711yescharacteristic
614C2×D4—28no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4C2×D4×C3712yes—
653C2×D4#41×C3712yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4C2×D4×C3711yescharacteristic
673C22×C4C2×D4×C3711yescharacteristic
674C22×C4C2×D4×C3711yescharacteristic
675C22×C4C2×D4×C3711yescharacteristic
676C22×C4C2×D4×C3712yes—
677C22×C4#41×C3712yes—
678C22×C4C24×C3711yescharacteristic
679D8—44no—
680D8—44no—
681M16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—44no—
692C2×C8C2×D4×C3712yes—
693C2×C8C2×D4×C3712yes—
694C2×C8C2×D4×C3712yes—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4C2×D4×C3712yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23#121×C3712yes—
764C23AGL(1,ℤ/8)×C3712yes—
765C23AGL(1,ℤ/8)×C3712yes—
766C23C22×D4×C3711yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—44no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—84no—
820C2×C4#121×C3712yes—
821C2×C4C22×D4×C3711yescharacteristic
822C2×C4C22×D4×C3711yescharacteristic
823C2×C4C2×#41×C3711yescharacteristic
824C2×C4C2×#41×C3711yescharacteristic
825C2×C4H(5,𝔽2)×C3711yescharacteristic
826C2×C4H(5,𝔽2)×C3711yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22C37×#46914yescomplemented
867C22C2×#121×C3711yescharacteristic
868C22D42×C3711yescharacteristic
869C22C37×#54611yescharacteristic
870C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
871C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
872C22C37×#57611yescharacteristic
873C22C37×#57711yescharacteristic
874C4—22no—
875C4—41no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4C37×#52511yescharacteristic
884C4C37×#53811yescharacteristic
885C4D42×C3711yescharacteristic
886C4C37×#54611yescharacteristic
887C2—24no—
888C2—81no—
889C2—82no—
890C2—82no—
891C2—161no—
892C2C37×#242411yescharacteristic
893C2C2×C37×#46911yescharacteristic
894C2C37×#306211yescharacteristic
895C2C37×#326411yescharacteristic
896C2C37×#326511yescharacteristic
897C2C37×#330611yescharacteristic
898C2C37×#331811yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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
1. C2×C37×#469C2semidirect
2. C2×C37×#447C2semidirect
3. C2×C37×#435C2semidirect
4. C22×#102×C37C2semidirect
5. C37×#2416C2semidirect
6. C37×#2408C2semidirect
7. C37×#2065C2semidirect
8. C37×#2054C2semidirect
9. C37×#2034C2semidirect
10. C37×#1999C2semidirect
11. C37×#1972C2semidirect
12. C37×#1936C2semidirect
13. C37×#1895C2semidirect
14. C37×#1893C2semidirect
15. C37×#1853C2semidirect
19. C22×M16×C37C22semidirect
25. C2×#121×C37C22semidirect
32. C2×#106×C37C22semidirect
33. C2×#106×C37C22semidirect
34. C2×C4⋊C8×C37C22semidirect
42. C2×#102×C37C22semidirect
43. C2×#102×C37C22semidirect
45. C2×C22⋊C8×C37C22semidirect
46. C2×#97×C37C22semidirect
53. C37×#390C22semidirect
54. C37×#389C22semidirect
57. C37×#380C22semidirect
59. C37×#340C22semidirect
60. C37×#340C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
145. #102×C37D4semidirect
147. C22⋊C8×C37D4semidirect
381. #25124C37direct (N × H)
417. C22×C37#469semidirect
438. C2×#469C2×C37semidirect
439. C2×#447C2×C37semidirect
440. C2×#435C2×C37semidirect
441. C22×#102C2×C37semidirect
442. #2416C2×C37semidirect
443. #2408C2×C37semidirect
444. #2065C2×C37semidirect
445. #2054C2×C37semidirect
446. #2034C2×C37semidirect
447. #1999C2×C37semidirect
448. #1972C2×C37semidirect
449. #1936C2×C37semidirect
450. #1895C2×C37semidirect
451. #1893C2×C37semidirect
452. #1853C2×C37semidirect
468. C22×M16C22×C37semidirect
474. C2×#121C22×C37semidirect
481. C2×#106C22×C37semidirect
482. C2×#106C22×C37semidirect
483. C2×C4⋊C8C22×C37semidirect
491. C2×#102C22×C37semidirect
492. C2×#102C22×C37semidirect
494. C2×C22⋊C8C22×C37semidirect
495. C2×#97C22×C37semidirect
502. #390C22×C37semidirect
503. #389C22×C37semidirect
506. #380C22×C37semidirect
508. #340C22×C37semidirect
509. #340C22×C37semidirect
510. #340C22×C37semidirect
511. #340C22×C37semidirect
512. C37#25124direct (N × H)
595. #102D4×C37semidirect
597. C22⋊C8D4×C37semidirect
866. C22C37×#469semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4692
C2×C37×#4472
C2×C37×#4352
C22×#102×C372
C37×#24162
C37×#24082
C37×#20652
C37×#20542
C37×#20342
C37×#19992
C37×#19722
C37×#19362
C37×#18952
C37×#18932
C37×#18532
#2512437