Finite Group Databasebeta

← C37×#28569 #22649822

Subgroups — C37×#28569 #22649822

Order 9472.

962 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#468C211yesmaximal, characteristic, complemented
2C2×C37×#436C211yesmaximal, characteristic, complemented
3C37×#2416C211yesmaximal, characteristic
4C37×#2415C211yesmaximal, characteristic, complemented
5C37×#2086C211yesmaximal, characteristic, complemented
6C37×#2076C211yesmaximal, characteristic, complemented
7C37×#2055C211yesmaximal, characteristic, complemented
8C37×#2000C211yesmaximal, characteristic, complemented
9C37×#1934C211yesmaximal, characteristic, complemented
10C37×#1933C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1894C211yesmaximal, characteristic, complemented
13C37×#1875C211yesmaximal, characteristic, complemented
14C37×#1872C211yesmaximal, characteristic, complemented
15C37×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×C22⋊Q8×C37C2211yescharacteristic
21C2×#121×C37—21no—
22C2×#121×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×C4×D4×C37C2211yescharacteristic
25C2×#117×C37C2211yescharacteristic
26C22×C4⋊C4×C37C2211yescharacteristic
27C37×#468—24no—
28C37×#436—24no—
29C2×#107×C37C2211yescharacteristic
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C4×C8×C37C2211yescharacteristic
40C37×#397—21no—
41C37×#396—21no—
42C37×#394—21no—
43C37×#394—21no—
44C37×#391C2211yescharacteristic
45C37×#390C2211yescharacteristic
46C37×#389—21no—
47C37×#389C2211yescharacteristic
48C37×#389C2211yescharacteristic
49C37×#388—21no—
50C37×#386—21no—
51C37×#380C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37D411yescharacteristic
65C22×D4×C37C2311yescharacteristic
66C23×C4×C37—21no—
67C23×C4×C37C2311yescharacteristic
68C23×C4×C37C2311yescharacteristic
69C2×SD16×C37—22no—
70C2×SD16×C37—41no—
71C2×SD16×C37—41no—
72C2×M16×C37—22no—
73C2×M16×C37—41no—
74C2×M16×C37—41no—
75C2×M16×C37—41no—
76C2×M16×C37—41no—
77C2×M16×C37D414yescomplemented
78C22×C8×C37C2311yescharacteristic
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—22no—
85C22⋊Q8×C37—41no—
86#121×C37—22no—
87#121×C37—22no—
88#121×C37—22no—
89#121×C37—41no—
90#121×C37—44no—
91C4×D4×C37—22no—
92C4×D4×C37—22no—
93#117×C37—22no—
94#117×C37—41no—
95C2×C4⋊C4×C37—22no—
96C2×C4⋊C4×C37—21no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37—21no—
101C2×C4⋊C4×C37—41no—
102C2×C4⋊C4×C37D411yescharacteristic
103C2×C4⋊C4×C37C2311yescharacteristic
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C4⋊C4×C37C2311yescharacteristic
106C2×C4⋊C4×C37C2311yescharacteristic
107C2×C4⋊C4×C37C2311yescharacteristic
108C2×C4⋊C4×C37C2311yescharacteristic
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37—21no—
112C2×C22⋊C4×C37—21no—
113C2×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37D411yescharacteristic
119C2×C22⋊C4×C37D411yescharacteristic
120C2×C42×C37—21no—
121C2×C42×C37C2311yescharacteristic
122#107×C37—22no—
123C4⋊C8×C37—22no—
124#103×C37—22no—
125#103×C37—22no—
126#103×C37—41no—
127#102×C37—22no—
128#102×C37—22no—
129#102×C37—41no—
130C22⋊C8×C37—22no—
131C22⋊C8×C37—22no—
132C4×C8×C37—22no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37—21no—
139C24×C37—21no—
140C24×C37C2×D411yescharacteristic
141C24×C37C2×D411yescharacteristic
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×D4×C37—22no—
149C2×D4×C37—22no—
150C2×D4×C37—21no—
151C2×D4×C37—21no—
152C2×D4×C37—21no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—41no—
157C2×D4×C37—42no—
158C2×D4×C37—42no—
159C2×D4×C37—42no—
160C2×D4×C37—42no—
161C2×D4×C37—42no—
162C2×D4×C37—81no—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—42no—
181C22×C4×C37—42no—
182C22×C4×C37—81no—
183C22×C4×C37C2×D411yescharacteristic
184C22×C4×C37C2×D411yescharacteristic
185C22×C4×C37C2×D411yescharacteristic
186C22×C4×C37C2×D412yes—
187C22×C4×C37C2×D411yescharacteristic
188C22×C4×C37#4112yes—
189C22×C4×C37C2411yescharacteristic
190SD16×C37—44no—
191M16×C37—44no—
192M16×C37—44no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37—21no—
198C2×C8×C37—21no—
199C2×C8×C37—21no—
200C2×C8×C37—21no—
201C2×C8×C37—21no—
202C2×C8×C37—21no—
203C2×C8×C37C2×D412yes—
204C2×C8×C37C2×D412yes—
205C4⋊C4×C37—22no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—21no—
212C4⋊C4×C37—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—42no—
217C4⋊C4×C37—42no—
218C4⋊C4×C37—42no—
219C4⋊C4×C37—42no—
220C4⋊C4×C37—42no—
221C4⋊C4×C37#4112yes—
222C4⋊C4×C37#4112yes—
223C22⋊C4×C37—22no—
224C22⋊C4×C37—22no—
225C22⋊C4×C37—42no—
226C22⋊C4×C37—42no—
227C22⋊C4×C37—42no—
228C22⋊C4×C37—42no—
229C22⋊C4×C37—42no—
230C22⋊C4×C37—42no—
231C22⋊C4×C37—42no—
232C22⋊C4×C37—42no—
233C22⋊C4×C37—81no—
234C42×C37—21no—
235C42×C37—21no—
236C42×C37—42no—
237C23×C37—21no—
238C23×C37—21no—
239C23×C37—21no—
240C23×C37—21no—
241C23×C37—21no—
242C23×C37—21no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—21no—
247C23×C37—21no—
248C23×C37—21no—
249C23×C37—21no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37—41no—
254C23×C37—41no—
255C23×C37—41no—
256C23×C37—41no—
257C23×C37#12112yes—
258C23×C37C22×D411yescharacteristic
259Q8×C37—41no—
260Q8×C37—41no—
261Q8×C37—41no—
262Q8×C37—41no—
263D4×C37—44no—
264D4×C37—41no—
265D4×C37—41no—
266D4×C37—41no—
267D4×C37—41no—
268D4×C37—84no—
269D4×C37—84no—
270C2×C4×C37—21no—
271C2×C4×C37—21no—
272C2×C4×C37—21no—
273C2×C4×C37—21no—
274C2×C4×C37—22no—
275C2×C4×C37—22no—
276C2×C4×C37—22no—
277C2×C4×C37—22no—
278C2×C4×C37—21no—
279C2×C4×C37—21no—
280C2×C4×C37—22no—
281C2×C4×C37—21no—
282C2×C4×C37—22no—
283C2×C4×C37—21no—
284C2×C4×C37—21no—
285C2×C4×C37—21no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37—41no—
292C2×C4×C37—41no—
293C2×C4×C37—41no—
294C2×C4×C37—41no—
295C2×C4×C37—41no—
296C2×C4×C37—41no—
297C2×C4×C37—41no—
298C2×C4×C37—41no—
299C2×C4×C37—41no—
300C2×C4×C37—41no—
301C2×C4×C37—41no—
302C2×C4×C37—41no—
303C2×C4×C37—41no—
304C2×C4×C37—41no—
305C2×C4×C37—41no—
306C2×C4×C37—41no—
307C2×C4×C37—41no—
308C2×C4×C37—41no—
309C2×C4×C37—84no—
310C2×C4×C37#12112yes—
311C2×C4×C37AGL(1,ℤ/8)12yes—
312C2×C4×C37C22×D411yescharacteristic
313C2×C4×C37C2×#4111yescharacteristic
314C2×C4×C37C2×#4111yescharacteristic
315C2×C4×C37C2×#4111yescharacteristic
316C2×C4×C37H(5,𝔽2)11yescharacteristic
317C2×C4×C37H(5,𝔽2)11yescharacteristic
318C8×C37—22no—
319C8×C37—22no—
320C8×C37—41no—
321C8×C37—41no—
322#28569C3711yesmaximal, characteristic, direct product factor, Sylow
323C22×C37—22no—
324C22×C37—22no—
325C22×C37—22no—
326C22×C37—41no—
327C22×C37—41no—
328C22×C37—41no—
329C22×C37—41no—
330C22×C37—41no—
331C22×C37—41no—
332C22×C37—41no—
333C22×C37—41no—
334C22×C37—41no—
335C22×C37—41no—
336C22×C37—41no—
337C22×C37—81no—
338C22×C37—81no—
339C22×C37—81no—
340C22×C37—81no—
341C22×C37—81no—
342C22×C37—81no—
343C22×C37—81no—
344C22×C37C2×#12111yescharacteristic
345C22×C37#54611yescharacteristic
346C22×C37#54611yescharacteristic
347C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C37#57511yescharacteristic
349C22×C37#57711yescharacteristic
350C22×C37#57811yescharacteristic
351C4×C37—22no—
352C4×C37—22no—
353C4×C37—42no—
354C4×C37—41no—
355C4×C37—41no—
356C4×C37—42no—
357C4×C37—81no—
358C4×C37—81no—
359C4×C37—81no—
360C4×C37—81no—
361C4×C37—81no—
362C4×C37#53211yescharacteristic
363C4×C37#53411yescharacteristic
364C4×C37#55311yescharacteristic
365C4×C37#55311yescharacteristic
366C2×#468C2×C3711yescharacteristic, complemented
367C2×#436C2×C3711yescharacteristic, complemented
368#2416C2×C3711yescharacteristic
369#2415C2×C3711yescharacteristic, complemented
370#2086C2×C3711yescharacteristic, complemented
371#2076C2×C3711yescharacteristic, complemented
372#2055C2×C3711yescharacteristic, complemented
373#2000C2×C3711yescharacteristic, complemented
374#1934C2×C3711yescharacteristic, complemented
375#1933C2×C3711yescharacteristic, complemented
376#1895C2×C3711yescharacteristic, complemented
377#1894C2×C3711yescharacteristic, complemented
378#1875C2×C3711yescharacteristic, complemented
379#1872C2×C3711yescharacteristic, complemented
380#1736C2×C3711yescharacteristic, complemented
381C2×C37—42no—
382C2×C37—81no—
383C2×C37—161no—
384C2×C37#254311yescharacteristic
385C2×C37#305511yescharacteristic
386C2×C37#306311yescharacteristic
387C2×C37#332411yescharacteristic
388C2×C37#332611yescharacteristic
389C2×C37#332711yescharacteristic
390C2×C37#333011yescharacteristic
391C22×SD16C22×C3711yescharacteristic
392C22×M16C22×C3711yescharacteristic
393C22×M16C22×C3711yescharacteristic
394C2×C22⋊Q8C22×C3711yescharacteristic
395C2×C22⋊Q8C22×C3711yescharacteristic
396C2×#121—21no—
397C2×#121C22×C3711yescharacteristic
398C2×#121C22×C3711yescharacteristic
399C2×C4×D4C22×C3711yescharacteristic
400C2×#117C22×C3711yescharacteristic
401C22×C4⋊C4C22×C3711yescharacteristic
402#468—24no—
403#436—24no—
404C2×#107C22×C3711yescharacteristic
405C2×C4⋊C8C22×C3711yescharacteristic
406C2×#103C22×C3711yescharacteristic
407C2×#103C22×C3711yescharacteristic
408C2×#103C22×C3711yescharacteristic
409C2×#102C22×C3711yescharacteristic
410C2×#102C22×C3711yescharacteristic
411C2×#102C22×C3711yescharacteristic
412C2×C22⋊C8C22×C3711yescharacteristic
413C2×C22⋊C8C22×C3711yescharacteristic
414C2×C4×C8C22×C3711yescharacteristic
415#397—21no—
416#396—21no—
417#394—21no—
418#394—21no—
419#391C22×C3711yescharacteristic
420#390C22×C3711yescharacteristic
421#389—21no—
422#389C22×C3711yescharacteristic
423#389C22×C3711yescharacteristic
424#388—21no—
425#386—21no—
426#380C22×C3711yescharacteristic
427#380C22×C3711yescharacteristic
428#340C22×C3711yescharacteristic
429#340C22×C3711yescharacteristic
430#340C22×C3711yescharacteristic
431#340C22×C3711yescharacteristic
432#340C22×C3711yescharacteristic
433#340C22×C3711yescharacteristic
434#340C22×C3711yescharacteristic
435#340C22×C3711yescharacteristic
436C37#2856911yescharacteristic, direct product factor, Sylow
437C22×Q8C23×C3711yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4D4×C3711yescharacteristic
441C22×D4C23×C3711yescharacteristic
442C23×C4—21no—
443C23×C4C23×C3711yescharacteristic
444C23×C4C23×C3711yescharacteristic
445C2×SD16—22no—
446C2×SD16—41no—
447C2×SD16—41no—
448C2×M16—22no—
449C2×M16—41no—
450C2×M16—41no—
451C2×M16—41no—
452C2×M16—41no—
453C2×M16D4×C3714yescomplemented
454C22×C8C23×C3711yescharacteristic
455C22×C8C23×C3711yescharacteristic
456C22×C8C23×C3711yescharacteristic
457C22×C8C23×C3711yescharacteristic
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—41no—
462#121—22no—
463#121—22no—
464#121—22no—
465#121—41no—
466#121—44no—
467C4×D4—22no—
468C4×D4—22no—
469#117—22no—
470#117—41no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4D4×C3711yescharacteristic
479C2×C4⋊C4C23×C3711yescharacteristic
480C2×C4⋊C4C23×C3711yescharacteristic
481C2×C4⋊C4C23×C3711yescharacteristic
482C2×C4⋊C4C23×C3711yescharacteristic
483C2×C4⋊C4C23×C3711yescharacteristic
484C2×C4⋊C4C23×C3711yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4D4×C3711yescharacteristic
495C2×C22⋊C4D4×C3711yescharacteristic
496C2×C42—21no—
497C2×C42C23×C3711yescharacteristic
498#107—22no—
499C4⋊C8—22no—
500#103—22no—
501#103—22no—
502#103—41no—
503#102—22no—
504#102—22no—
505#102—41no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C4×C8—22no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C24—21no—
516C24C2×D4×C3711yescharacteristic
517C24C2×D4×C3711yescharacteristic
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—41no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4C2×D4×C3711yescharacteristic
560C22×C4C2×D4×C3711yescharacteristic
561C22×C4C2×D4×C3711yescharacteristic
562C22×C4C2×D4×C3712yes—
563C22×C4C2×D4×C3711yescharacteristic
564C22×C4#41×C3712yes—
565C22×C4C24×C3711yescharacteristic
566SD16—44no—
567M16—44no—
568M16—44no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8C2×D4×C3712yes—
580C2×C8C2×D4×C3712yes—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4#41×C3712yes—
598C4⋊C4#41×C3712yes—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C42—21no—
611C42—21no—
612C42—42no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23#121×C3712yes—
634C23C22×D4×C3711yescharacteristic
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639D4—44no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4—84no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4#121×C3712yes—
687C2×C4AGL(1,ℤ/8)×C3712yes—
688C2×C4C22×D4×C3711yescharacteristic
689C2×C4C2×#41×C3711yescharacteristic
690C2×C4C2×#41×C3711yescharacteristic
691C2×C4C2×#41×C3711yescharacteristic
692C2×C4H(5,𝔽2)×C3711yescharacteristic
693C2×C4H(5,𝔽2)×C3711yescharacteristic
694C8—22no—
695C8—22no—
696C8—41no—
697C8—41no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C2×#121×C3711yescharacteristic
720C22C37×#54611yescharacteristic
721C22C37×#54611yescharacteristic
722C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
723C22C37×#57511yescharacteristic
724C22C37×#57711yescharacteristic
725C22C37×#57811yescharacteristic
726C4—22no—
727C4—22no—
728C4—41no—
729C4—41no—
730C4—42no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4C37×#53211yescharacteristic
738C4C37×#53411yescharacteristic
739C4C37×#55311yescharacteristic
740C4C37×#55311yescharacteristic
741C2—42no—
742C2—81no—
743C2—161no—
744C2C37×#254311yescharacteristic
745C2C37×#305511yescharacteristic
746C2C37×#306311yescharacteristic
747C2C37×#332411yescharacteristic
748C2C37×#332611yescharacteristic
749C2C37×#332711yescharacteristic
750C2C37×#333011yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2416C2
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×#468C2semidirect
2. C2×C37×#436C2semidirect
4. C37×#2415C2semidirect
5. C37×#2086C2semidirect
6. C37×#2076C2semidirect
7. C37×#2055C2semidirect
8. C37×#2000C2semidirect
9. C37×#1934C2semidirect
10. C37×#1933C2semidirect
11. C37×#1895C2semidirect
12. C37×#1894C2semidirect
13. C37×#1875C2semidirect
14. C37×#1872C2semidirect
15. C37×#1736C2semidirect
77. C2×M16×C37D4semidirect
322. #28569C37direct (N × H)
366. C2×#468C2×C37semidirect
367. C2×#436C2×C37semidirect
369. #2415C2×C37semidirect
370. #2086C2×C37semidirect
371. #2076C2×C37semidirect
372. #2055C2×C37semidirect
373. #2000C2×C37semidirect
374. #1934C2×C37semidirect
375. #1933C2×C37semidirect
376. #1895C2×C37semidirect
377. #1894C2×C37semidirect
378. #1875C2×C37semidirect
379. #1872C2×C37semidirect
380. #1736C2×C37semidirect
436. C37#28569direct (N × H)
453. C2×M16D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4682
C2×C37×#4362
C37×#24162
C37×#24152
C37×#20862
C37×#20762
C37×#20552
C37×#20002
C37×#19342
C37×#19332
C37×#18952
C37×#18942
C37×#18752
C37×#18722
C37×#17362
#2856937