Finite Group Databasebeta

← C37×#28567 #22649820

Subgroups — C37×#28567 #22649820

Order 9472.

1012 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#469C211yesmaximal, characteristic, complemented
2C2×C37×#436C211yesmaximal, characteristic, complemented
3C37×#2416C211yesmaximal, characteristic, complemented
4C37×#2414C211yesmaximal, characteristic, complemented
5C37×#2088C211yesmaximal, characteristic, complemented
6C37×#2077C211yesmaximal, characteristic, complemented
7C37×#2054C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1934C211yesmaximal, characteristic, complemented
10C37×#1934C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1895C211yesmaximal, characteristic, complemented
13C37×#1875C211yesmaximal, characteristic, complemented
14C37×#1874C211yesmaximal, characteristic, complemented
15C37×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C2×#121×C37—21no—
20C2×#121×C37C2211yescharacteristic
21C2×#121×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×C4×D4×C37C2211yescharacteristic
25C2×#117×C37C2211yescharacteristic
26C22×C4⋊C4×C37C2211yescharacteristic
27C37×#469—24no—
28C37×#436—24no—
29C2×#106×C37C2211yescharacteristic
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C4×C8×C37C2211yescharacteristic
40C37×#396—21no—
41C37×#394—21no—
42C37×#394—21no—
43C37×#392—21no—
44C37×#390—21no—
45C37×#390C2211yescharacteristic
46C37×#390C2211yescharacteristic
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×D4×C37—21no—
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37D411yescharacteristic
66C22×D4×C37C2311yescharacteristic
67C22×D4×C37C2311yescharacteristic
68C23×C4×C37—21no—
69C23×C4×C37C2311yescharacteristic
70C23×C4×C37C2311yescharacteristic
71C2×D8×C37—22no—
72C2×D8×C37—41no—
73C2×D8×C37—41no—
74C2×M16×C37—22no—
75C2×M16×C37—41no—
76C2×M16×C37—41no—
77C2×M16×C37—41no—
78C2×M16×C37—41no—
79C2×M16×C37D414yescomplemented
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84#121×C37—22no—
85#121×C37—22no—
86#121×C37—22no—
87#121×C37—22no—
88#121×C37—22no—
89#121×C37—22no—
90#121×C37—41no—
91#121×C37—41no—
92#121×C37—44no—
93C4×D4×C37—22no—
94C4×D4×C37—22no—
95#117×C37—22no—
96#117×C37—41no—
97C2×C4⋊C4×C37—22no—
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×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37D411yescharacteristic
121C2×C22⋊C4×C37D411yescharacteristic
122C2×C42×C37—21no—
123C2×C42×C37C2311yescharacteristic
124#106×C37—22no—
125C4⋊C8×C37—22no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—22no—
129#102×C37—22no—
130#102×C37—41no—
131#102×C37—41no—
132C22⋊C8×C37—22no—
133C22⋊C8×C37—22no—
134C4×C8×C37—22no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37—21no—
139C24×C37—21no—
140C24×C37—21no—
141C24×C37C2×D411yescharacteristic
142C24×C37C2×D411yescharacteristic
143C2×D4×C37—22no—
144C2×D4×C37—22no—
145C2×D4×C37—21no—
146C2×D4×C37—21no—
147C2×D4×C37—21no—
148C2×D4×C37—21no—
149C2×D4×C37—21no—
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—21no—
157C2×D4×C37—41no—
158C2×D4×C37—42no—
159C2×D4×C37—42no—
160C2×D4×C37—42no—
161C2×D4×C37—42no—
162C2×D4×C37—42no—
163C2×D4×C37—42no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—81no—
167C2×D4×C37—81no—
168C2×D4×C37—81no—
169C2×D4×C37—81no—
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—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—42no—
187C22×C4×C37—42no—
188C22×C4×C37—81no—
189C22×C4×C37C2×D411yescharacteristic
190C22×C4×C37C2×D411yescharacteristic
191C22×C4×C37C2×D411yescharacteristic
192C22×C4×C37C2×D412yes—
193C22×C4×C37C2×D411yescharacteristic
194C22×C4×C37#4112yes—
195C22×C4×C37C2411yescharacteristic
196D8×C37—44no—
197M16×C37—44no—
198M16×C37—44no—
199C2×C8×C37—21no—
200C2×C8×C37—21no—
201C2×C8×C37—21no—
202C2×C8×C37—21no—
203C2×C8×C37—21no—
204C2×C8×C37—21no—
205C2×C8×C37—21no—
206C2×C8×C37—21no—
207C2×C8×C37—21no—
208C2×C8×C37—21no—
209C2×C8×C37C2×D412yes—
210C2×C8×C37C2×D412yes—
211C4⋊C4×C37—22no—
212C4⋊C4×C37—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—42no—
223C4⋊C4×C37—42no—
224C4⋊C4×C37—81no—
225C4⋊C4×C37#4112yes—
226C4⋊C4×C37#4112yes—
227C22⋊C4×C37—22no—
228C22⋊C4×C37—22no—
229C22⋊C4×C37—42no—
230C22⋊C4×C37—42no—
231C22⋊C4×C37—42no—
232C22⋊C4×C37—42no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—42no—
235C22⋊C4×C37—42no—
236C22⋊C4×C37—42no—
237C22⋊C4×C37—81no—
238C22⋊C4×C37—81no—
239C22⋊C4×C37—81no—
240C42×C37—21no—
241C42×C37—21no—
242C42×C37—42no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—21no—
247C23×C37—21no—
248C23×C37—21no—
249C23×C37—21no—
250C23×C37—21no—
251C23×C37—21no—
252C23×C37—21no—
253C23×C37—21no—
254C23×C37—21no—
255C23×C37—21no—
256C23×C37—41no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—41no—
260C23×C37—41no—
261C23×C37—41no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37#12112yes—
271C23×C37C22×D411yescharacteristic
272D4×C37—44no—
273D4×C37—41no—
274D4×C37—41no—
275D4×C37—41no—
276D4×C37—41no—
277D4×C37—41no—
278D4×C37—41no—
279D4×C37—41no—
280D4×C37—41no—
281D4×C37—84no—
282D4×C37—84no—
283D4×C37—84no—
284D4×C37—84no—
285C2×C4×C37—21no—
286C2×C4×C37—21no—
287C2×C4×C37—21no—
288C2×C4×C37—21no—
289C2×C4×C37—22no—
290C2×C4×C37—22no—
291C2×C4×C37—22no—
292C2×C4×C37—22no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—22no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—22no—
299C2×C4×C37—21no—
300C2×C4×C37—21no—
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—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—84no—
322C2×C4×C37#12112yes—
323C2×C4×C37AGL(1,ℤ/8)12yes—
324C2×C4×C37C22×D411yescharacteristic
325C2×C4×C37C2×#4111yescharacteristic
326C2×C4×C37C2×#4111yescharacteristic
327C2×C4×C37C2×#4111yescharacteristic
328C2×C4×C37H(5,𝔽2)11yescharacteristic
329C2×C4×C37H(5,𝔽2)11yescharacteristic
330C8×C37—22no—
331C8×C37—22no—
332C8×C37—41no—
333C8×C37—41no—
334#28567C3711yesmaximal, characteristic, direct product factor, Sylow
335C22×C37—22no—
336C22×C37—22no—
337C22×C37—22no—
338C22×C37—41no—
339C22×C37—41no—
340C22×C37—41no—
341C22×C37—41no—
342C22×C37—41no—
343C22×C37—41no—
344C22×C37—41no—
345C22×C37—41no—
346C22×C37—41no—
347C22×C37—41no—
348C22×C37—41no—
349C22×C37—81no—
350C22×C37—81no—
351C22×C37—81no—
352C22×C37—81no—
353C22×C37—81no—
354C22×C37—81no—
355C22×C37—81no—
356C22×C37—81no—
357C22×C37—81no—
358C22×C37—81no—
359C22×C37—81no—
360C22×C37—81no—
361C22×C37—81no—
362C22×C37—81no—
363C22×C37C2×#12111yescharacteristic
364C22×C37#54611yescharacteristic
365C22×C37#54611yescharacteristic
366C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C37#57511yescharacteristic
368C22×C37#57611yescharacteristic
369C22×C37#57711yescharacteristic
370C4×C37—22no—
371C4×C37—22no—
372C4×C37—41no—
373C4×C37—41no—
374C4×C37—42no—
375C4×C37—42no—
376C4×C37—81no—
377C4×C37—81no—
378C4×C37—81no—
379C4×C37—81no—
380C4×C37#53211yescharacteristic
381C4×C37#53411yescharacteristic
382C4×C37#55311yescharacteristic
383C4×C37#55311yescharacteristic
384C2×#469C2×C3711yescharacteristic, complemented
385C2×#436C2×C3711yescharacteristic, complemented
386#2416C2×C3711yescharacteristic, complemented
387#2414C2×C3711yescharacteristic, complemented
388#2088C2×C3711yescharacteristic, complemented
389#2077C2×C3711yescharacteristic, complemented
390#2054C2×C3711yescharacteristic, complemented
391#1999C2×C3711yescharacteristic, complemented
392#1934C2×C3711yescharacteristic, complemented
393#1934C2×C3711yescharacteristic, complemented
394#1895C2×C3711yescharacteristic, complemented
395#1895C2×C3711yescharacteristic, complemented
396#1875C2×C3711yescharacteristic, complemented
397#1874C2×C3711yescharacteristic, complemented
398#1736C2×C3711yescharacteristic, complemented
399C2×C37—42no—
400C2×C37—81no—
401C2×C37—161no—
402C2×C37—161no—
403C2×C37#254311yescharacteristic
404C2×C37#305511yescharacteristic
405C2×C37#306211yescharacteristic
406C2×C37#332211yescharacteristic
407C2×C37#332511yescharacteristic
408C2×C37#332611yescharacteristic
409C2×C37#333211yescharacteristic
410C22×D8C22×C3711yescharacteristic
411C22×M16C22×C3711yescharacteristic
412C22×M16C22×C3711yescharacteristic
413C2×#121—21no—
414C2×#121C22×C3711yescharacteristic
415C2×#121C22×C3711yescharacteristic
416C2×#121C22×C3711yescharacteristic
417C2×#121C22×C3711yescharacteristic
418C2×C4×D4C22×C3711yescharacteristic
419C2×#117C22×C3711yescharacteristic
420C22×C4⋊C4C22×C3711yescharacteristic
421#469—24no—
422#436—24no—
423C2×#106C22×C3711yescharacteristic
424C2×C4⋊C8C22×C3711yescharacteristic
425C2×#102C22×C3711yescharacteristic
426C2×#102C22×C3711yescharacteristic
427C2×#102C22×C3711yescharacteristic
428C2×#102C22×C3711yescharacteristic
429C2×#102C22×C3711yescharacteristic
430C2×#102C22×C3711yescharacteristic
431C2×C22⋊C8C22×C3711yescharacteristic
432C2×C22⋊C8C22×C3711yescharacteristic
433C2×C4×C8C22×C3711yescharacteristic
434#396—21no—
435#394—21no—
436#394—21no—
437#392—21no—
438#390—21no—
439#390C22×C3711yescharacteristic
440#390C22×C3711yescharacteristic
441#389C22×C3711yescharacteristic
442#389C22×C3711yescharacteristic
443#388—21no—
444#386—21no—
445#380C22×C3711yescharacteristic
446#380C22×C3711yescharacteristic
447#340C22×C3711yescharacteristic
448#340C22×C3711yescharacteristic
449#340C22×C3711yescharacteristic
450#340C22×C3711yescharacteristic
451#340C22×C3711yescharacteristic
452#340C22×C3711yescharacteristic
453#340C22×C3711yescharacteristic
454#340C22×C3711yescharacteristic
455C37#2856711yescharacteristic, direct product factor, Sylow
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4D4×C3711yescharacteristic
461C22×D4C23×C3711yescharacteristic
462C22×D4C23×C3711yescharacteristic
463C23×C4—21no—
464C23×C4C23×C3711yescharacteristic
465C23×C4C23×C3711yescharacteristic
466C2×D8—22no—
467C2×D8—41no—
468C2×D8—41no—
469C2×M16—22no—
470C2×M16—41no—
471C2×M16—41no—
472C2×M16—41no—
473C2×M16—41no—
474C2×M16D4×C3714yescomplemented
475C22×C8C23×C3711yescharacteristic
476C22×C8C23×C3711yescharacteristic
477C22×C8C23×C3711yescharacteristic
478C22×C8C23×C3711yescharacteristic
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—41no—
486#121—41no—
487#121—44no—
488C4×D4—22no—
489C4×D4—22no—
490#117—22no—
491#117—41no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4D4×C3711yescharacteristic
498C2×C4⋊C4C23×C3711yescharacteristic
499C2×C4⋊C4C23×C3711yescharacteristic
500C2×C4⋊C4C23×C3711yescharacteristic
501C2×C4⋊C4C23×C3711yescharacteristic
502C2×C4⋊C4C23×C3711yescharacteristic
503C2×C4⋊C4C23×C3711yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4D4×C3711yescharacteristic
516C2×C22⋊C4D4×C3711yescharacteristic
517C2×C42—21no—
518C2×C42C23×C3711yescharacteristic
519#106—22no—
520C4⋊C8—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C4×C8—22no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534C24—21no—
535C24—21no—
536C24C2×D4×C3711yescharacteristic
537C24C2×D4×C3711yescharacteristic
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4C2×D4×C3711yescharacteristic
585C22×C4C2×D4×C3711yescharacteristic
586C22×C4C2×D4×C3711yescharacteristic
587C22×C4C2×D4×C3712yes—
588C22×C4C2×D4×C3711yescharacteristic
589C22×C4#41×C3712yes—
590C22×C4C24×C3711yescharacteristic
591D8—44no—
592M16—44no—
593M16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8C2×D4×C3712yes—
605C2×C8C2×D4×C3712yes—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—81no—
620C4⋊C4#41×C3712yes—
621C4⋊C4#41×C3712yes—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C42—21no—
636C42—21no—
637C42—42no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23#121×C3712yes—
666C23C22×D4×C3711yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4#121×C3712yes—
718C2×C4AGL(1,ℤ/8)×C3712yes—
719C2×C4C22×D4×C3711yescharacteristic
720C2×C4C2×#41×C3711yescharacteristic
721C2×C4C2×#41×C3711yescharacteristic
722C2×C4C2×#41×C3711yescharacteristic
723C2×C4H(5,𝔽2)×C3711yescharacteristic
724C2×C4H(5,𝔽2)×C3711yescharacteristic
725C8—22no—
726C8—22no—
727C8—41no—
728C8—41no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×#121×C3711yescharacteristic
758C22C37×#54611yescharacteristic
759C22C37×#54611yescharacteristic
760C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
761C22C37×#57511yescharacteristic
762C22C37×#57611yescharacteristic
763C22C37×#57711yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—42no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4C37×#53211yescharacteristic
775C4C37×#53411yescharacteristic
776C4C37×#55311yescharacteristic
777C4C37×#55311yescharacteristic
778C2—42no—
779C2—81no—
780C2—161no—
781C2—161no—
782C2C37×#254311yescharacteristic
783C2C37×#305511yescharacteristic
784C2C37×#306211yescharacteristic
785C2C37×#332211yescharacteristic
786C2C37×#332511yescharacteristic
787C2C37×#332611yescharacteristic
788C2C37×#333211yescharacteristic
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×#436C2semidirect
3. C37×#2416C2semidirect
4. C37×#2414C2semidirect
5. C37×#2088C2semidirect
6. C37×#2077C2semidirect
7. C37×#2054C2semidirect
8. C37×#1999C2semidirect
9. C37×#1934C2semidirect
10. C37×#1934C2semidirect
11. C37×#1895C2semidirect
12. C37×#1895C2semidirect
13. C37×#1875C2semidirect
14. C37×#1874C2semidirect
15. C37×#1736C2semidirect
79. C2×M16×C37D4semidirect
334. #28567C37direct (N × H)
384. C2×#469C2×C37semidirect
385. C2×#436C2×C37semidirect
386. #2416C2×C37semidirect
387. #2414C2×C37semidirect
388. #2088C2×C37semidirect
389. #2077C2×C37semidirect
390. #2054C2×C37semidirect
391. #1999C2×C37semidirect
392. #1934C2×C37semidirect
393. #1934C2×C37semidirect
394. #1895C2×C37semidirect
395. #1895C2×C37semidirect
396. #1875C2×C37semidirect
397. #1874C2×C37semidirect
398. #1736C2×C37semidirect
455. C37#28567direct (N × H)
474. 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×#4692
C2×C37×#4362
C37×#24162
C37×#24142
C37×#20882
C37×#20772
C37×#20542
C37×#19992
C37×#19342
C37×#18952
C37×#18752
C37×#18742
C37×#17362
#2856737