Finite Group Databasebeta

← C37×#26984 #22648237

Subgroups — C37×#26984 #22648237

Order 9472.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#469C211yesmaximal, characteristic, complemented
2C2×C37×#442C211yesmaximal, characteristic, complemented
3C37×#2428C211yesmaximal, characteristic, complemented
4C37×#2422C211yesmaximal, characteristic, complemented
5C37×#2084C211yesmaximal, characteristic, complemented
6C37×#2034C211yesmaximal, characteristic, complemented
7C37×#2011C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1957C211yesmaximal, characteristic, complemented
10C37×#1936C211yesmaximal, characteristic, complemented
11C37×#1934C211yesmaximal, characteristic, complemented
12C37×#1895C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1864C211yesmaximal, characteristic, complemented
15C37×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C2×#127×C37C2211yescharacteristic
20C2×#123×C37—21no—
21C2×#121×C37—21no—
22C2×#121×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×C4×D4×C37C2211yescharacteristic
26C2×C4×D4×C37C2211yescharacteristic
27C37×#469—24no—
28C37×#442—24no—
29C2×#106×C37C2211yescharacteristic
30C2×#106×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C2×#97×C37C2211yescharacteristic
41C2×C4×C8×C37C2211yescharacteristic
42C37×#397—21no—
43C37×#394—21no—
44C37×#394—21no—
45C37×#392—21no—
46C37×#390C2211yescharacteristic
47C37×#390C2211yescharacteristic
48C37×#389C2211yescharacteristic
49C37×#389C2211yescharacteristic
50C37×#386—21no—
51C37×#385—21no—
52C37×#384C2211yescharacteristic
53C37×#380C2211yescharacteristic
54C4×C22⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×D4×C37—21no—
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37C2311yescharacteristic
67C22×D4×C37C2311yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C23×C4×C37—21no—
70C23×C4×C37—21no—
71C23×C4×C37C2311yescharacteristic
72C2×D8×C37—22no—
73C2×D8×C37—22no—
74C2×D8×C37—22no—
75C2×D8×C37—22no—
76C2×D8×C37—22no—
77C2×D8×C37—41no—
78C2×M16×C37—22no—
79C2×M16×C37—22no—
80C2×M16×C37—41no—
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85#127×C37—22no—
86#127×C37—41no—
87#123×C37—44no—
88#121×C37—22no—
89#121×C37—22no—
90#121×C37—22no—
91#121×C37—44no—
92#121×C37—41no—
93#121×C37—41no—
94#121×C37—41no—
95C4×D4×C37—22no—
96C4×D4×C37—22no—
97C4×D4×C37—41no—
98C4×D4×C37—41no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37—21no—
101C2×C4⋊C4×C37—21no—
102C2×C4⋊C4×C37—21no—
103C2×C4⋊C4×C37C2311yescharacteristic
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C4⋊C4×C37C2311yescharacteristic
106C2×C4⋊C4×C37C2311yescharacteristic
107C2×C4⋊C4×C37C2311yescharacteristic
108C2×C22⋊C4×C37—21no—
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×C37C2311yescharacteristic
121C2×C42×C37C2311yescharacteristic
122#106×C37—22no—
123#106×C37—22no—
124#102×C37—22no—
125#102×C37—22no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—41no—
129#102×C37—41no—
130#102×C37—41no—
131#102×C37D414yescomplemented
132C22⋊C8×C37—22no—
133#97×C37—22no—
134C4×C8×C37—41no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37D411yescharacteristic
139#95×C37D411yescharacteristic
140C24×C37—21no—
141C24×C37—21no—
142C24×C37—21no—
143C24×C37C2×D411yescharacteristic
144C2×D4×C37—21no—
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—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
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—42no—
167C2×D4×C37—42no—
168C2×D4×C37—42no—
169C2×D4×C37—42no—
170C2×D4×C37—81no—
171C2×D4×C37—81no—
172C2×D4×C37—81no—
173C2×D4×C37—81no—
174C2×D4×C37—81no—
175C2×D4×C37C2×D412yes—
176C2×D4×C37#4112yes—
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—21no—
187C22×C4×C37—21no—
188C22×C4×C37—42no—
189C22×C4×C37—42no—
190C22×C4×C37—42no—
191C22×C4×C37—42no—
192C22×C4×C37—81no—
193C22×C4×C37—81no—
194C22×C4×C37C2×D411yescharacteristic
195C22×C4×C37C2×D411yescharacteristic
196C22×C4×C37C2×D411yescharacteristic
197C22×C4×C37C2×D411yescharacteristic
198C22×C4×C37C2×D411yescharacteristic
199C22×C4×C37C2411yescharacteristic
200D8×C37—28no—
201D8×C37—44no—
202M16×C37—44no—
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×C37—21no—
210C2×C8×C37—21no—
211C2×C8×C37—21no—
212C2×C8×C37C2×D412yes—
213C2×C8×C37#4112yes—
214C2×C8×C37#4112yes—
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—21no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—42no—
225C4⋊C4×C37—42no—
226C4⋊C4×C37—42no—
227C4⋊C4×C37—81no—
228C4⋊C4×C37C2×D412yes—
229C22⋊C4×C37—22no—
230C22⋊C4×C37—22no—
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—42no—
238C22⋊C4×C37—42no—
239C22⋊C4×C37—42no—
240C22⋊C4×C37—81no—
241C42×C37—21no—
242C42×C37—21no—
243C42×C37—21no—
244C42×C37—21no—
245C23×C37—21no—
246C23×C37—22no—
247C23×C37—21no—
248C23×C37—22no—
249C23×C37—21no—
250C23×C37—21no—
251C23×C37—21no—
252C23×C37—21no—
253C23×C37—21no—
254C23×C37—41no—
255C23×C37—41no—
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—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37C22×D411yescharacteristic
274D4×C37—22no—
275D4×C37—22no—
276D4×C37—22no—
277D4×C37—22no—
278D4×C37—41no—
279D4×C37—41no—
280D4×C37—41no—
281D4×C37—41no—
282D4×C37—41no—
283D4×C37—41no—
284D4×C37—41no—
285D4×C37—41no—
286D4×C37—84no—
287D4×C37—84no—
288D4×C37—84no—
289D4×C37—84no—
290D4×C37—84no—
291C2×C4×C37—21no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—21no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—22no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
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—41no—
322C2×C4×C37—41no—
323C2×C4×C37—84no—
324C2×C4×C37—84no—
325C2×C4×C37AGL(1,ℤ/8)12yes—
326C2×C4×C37AGL(1,ℤ/8)12yes—
327C2×C4×C37C22×D411yescharacteristic
328C2×C4×C37C2×#4111yescharacteristic
329C2×C4×C37C2×#4111yescharacteristic
330C2×C4×C37C2×#4111yescharacteristic
331C2×C4×C37H(5,𝔽2)11yescharacteristic
332C2×C4×C37H(5,𝔽2)11yescharacteristic
333C8×C37—22no—
334C8×C37—22no—
335C8×C37—22no—
336C8×C37—41no—
337#26984C3711yesmaximal, characteristic, direct product factor, Sylow
338C22×C37—41no—
339C22×C37—41no—
340C22×C37—41no—
341C22×C37—42no—
342C22×C37—42no—
343C22×C37—41no—
344C22×C37—42no—
345C22×C37—42no—
346C22×C37—41no—
347C22×C37—42no—
348C22×C37—41no—
349C22×C37—41no—
350C22×C37—42no—
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×C37—81no—
364C22×C37—81no—
365C22×C37—81no—
366C22×C37#53211yescharacteristic
367C22×C37D4211yescharacteristic
368C22×C37#54611yescharacteristic
369C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C37#57611yescharacteristic
372C22×C37#57711yescharacteristic
373C4×C37—22no—
374C4×C37—22no—
375C4×C37—41no—
376C4×C37—41no—
377C4×C37—42no—
378C4×C37—41no—
379C4×C37—81no—
380C4×C37—81no—
381C4×C37—81no—
382C4×C37—81no—
383C4×C37#52511yescharacteristic
384C4×C37#54011yescharacteristic
385C4×C37#54611yescharacteristic
386C4×C37#55311yescharacteristic
387C2×#469C2×C3711yescharacteristic, complemented
388C2×#442C2×C3711yescharacteristic, complemented
389#2428C2×C3711yescharacteristic, complemented
390#2422C2×C3711yescharacteristic, complemented
391#2084C2×C3711yescharacteristic, complemented
392#2034C2×C3711yescharacteristic, complemented
393#2011C2×C3711yescharacteristic, complemented
394#1999C2×C3711yescharacteristic, complemented
395#1957C2×C3711yescharacteristic, complemented
396#1936C2×C3711yescharacteristic, complemented
397#1934C2×C3711yescharacteristic, complemented
398#1895C2×C3711yescharacteristic, complemented
399#1879C2×C3711yescharacteristic, complemented
400#1864C2×C3711yescharacteristic, complemented
401#1753C2×C3711yescharacteristic, complemented
402C2×C37—81no—
403C2×C37—82no—
404C2×C37—82no—
405C2×C37—161no—
406C2×C37#246411yescharacteristic
407C2×C37#317911yescharacteristic
408C2×C37#318411yescharacteristic
409C2×C37#327211yescharacteristic
410C2×C37#327411yescharacteristic
411C2×C37#330611yescharacteristic
412C2×C37#331811yescharacteristic
413C22×D8C22×C3711yescharacteristic
414C22×D8C22×C3711yescharacteristic
415C22×M16C22×C3711yescharacteristic
416C2×#127C22×C3711yescharacteristic
417C2×#123—21no—
418C2×#121—21no—
419C2×#121C22×C3711yescharacteristic
420C2×#121C22×C3711yescharacteristic
421C2×#121C22×C3711yescharacteristic
422C2×C4×D4C22×C3711yescharacteristic
423C2×C4×D4C22×C3711yescharacteristic
424#469—24no—
425#442—24no—
426C2×#106C22×C3711yescharacteristic
427C2×#106C22×C3711yescharacteristic
428C2×#102C22×C3711yescharacteristic
429C2×#102C22×C3711yescharacteristic
430C2×#102C22×C3711yescharacteristic
431C2×#102C22×C3711yescharacteristic
432C2×#102C22×C3711yescharacteristic
433C2×#102C22×C3711yescharacteristic
434C2×#102C22×C3711yescharacteristic
435C2×#102C22×C3711yescharacteristic
436C2×C22⋊C8C22×C3711yescharacteristic
437C2×#97C22×C3711yescharacteristic
438C2×C4×C8C22×C3711yescharacteristic
439#397—21no—
440#394—21no—
441#394—21no—
442#392—21no—
443#390C22×C3711yescharacteristic
444#390C22×C3711yescharacteristic
445#389C22×C3711yescharacteristic
446#389C22×C3711yescharacteristic
447#386—21no—
448#385—21no—
449#384C22×C3711yescharacteristic
450#380C22×C3711yescharacteristic
451C4×C22⋊C4C22×C3711yescharacteristic
452#340C22×C3711yescharacteristic
453#340C22×C3711yescharacteristic
454#340C22×C3711yescharacteristic
455#340C22×C3711yescharacteristic
456#336C22×C3711yescharacteristic
457#336C22×C3711yescharacteristic
458C37#2698411yescharacteristic, direct product factor, Sylow
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C3711yescharacteristic
465C22×D4C23×C3711yescharacteristic
466C22×D4C23×C3711yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C3711yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C3711yescharacteristic
480C22×C8C23×C3711yescharacteristic
481C22×C8C23×C3711yescharacteristic
482C22×C8C23×C3711yescharacteristic
483#127—22no—
484#127—41no—
485#123—44no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—44no—
490#121—41no—
491#121—41no—
492#121—41no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C3711yescharacteristic
502C2×C4⋊C4C23×C3711yescharacteristic
503C2×C4⋊C4C23×C3711yescharacteristic
504C2×C4⋊C4C23×C3711yescharacteristic
505C2×C4⋊C4C23×C3711yescharacteristic
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⋊C4—21no—
516C2×C22⋊C4D4×C3711yescharacteristic
517C2×C22⋊C4D4×C3711yescharacteristic
518C2×C42C23×C3711yescharacteristic
519C2×C42C23×C3711yescharacteristic
520#106—22no—
521#106—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102D4×C3714yescomplemented
530C22⋊C8—22no—
531#97—22no—
532C4×C8—41no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C3711yescharacteristic
537#95D4×C3711yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C3711yescharacteristic
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—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C3712yes—
574C2×D4#41×C3712yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C3711yescharacteristic
593C22×C4C2×D4×C3711yescharacteristic
594C22×C4C2×D4×C3711yescharacteristic
595C22×C4C2×D4×C3711yescharacteristic
596C22×C4C2×D4×C3711yescharacteristic
597C22×C4C24×C3711yescharacteristic
598D8—28no—
599D8—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×D4×C3712yes—
611C2×C8#41×C3712yes—
612C2×C8#41×C3712yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C3712yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
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—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C3711yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
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—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4AGL(1,ℤ/8)×C3712yes—
724C2×C4AGL(1,ℤ/8)×C3712yes—
725C2×C4C22×D4×C3711yescharacteristic
726C2×C4C2×#41×C3711yescharacteristic
727C2×C4C2×#41×C3711yescharacteristic
728C2×C4C2×#41×C3711yescharacteristic
729C2×C4H(5,𝔽2)×C3711yescharacteristic
730C2×C4H(5,𝔽2)×C3711yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22C37×#53211yescharacteristic
764C22D42×C3711yescharacteristic
765C22C37×#54611yescharacteristic
766C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
767C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
768C22C37×#57611yescharacteristic
769C22C37×#57711yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4C37×#52511yescharacteristic
781C4C37×#54011yescharacteristic
782C4C37×#54611yescharacteristic
783C4C37×#55311yescharacteristic
784C2—81no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2C37×#246411yescharacteristic
789C2C37×#317911yescharacteristic
790C2C37×#318411yescharacteristic
791C2C37×#327211yescharacteristic
792C2C37×#327411yescharacteristic
793C2C37×#330611yescharacteristic
794C2C37×#331811yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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×#469C2semidirect
2. C2×C37×#442C2semidirect
3. C37×#2428C2semidirect
4. C37×#2422C2semidirect
5. C37×#2084C2semidirect
6. C37×#2034C2semidirect
7. C37×#2011C2semidirect
8. C37×#1999C2semidirect
9. C37×#1957C2semidirect
10. C37×#1936C2semidirect
11. C37×#1934C2semidirect
12. C37×#1895C2semidirect
13. C37×#1879C2semidirect
14. C37×#1864C2semidirect
15. C37×#1753C2semidirect
131. #102×C37D4semidirect
337. #26984C37direct (N × H)
387. C2×#469C2×C37semidirect
388. C2×#442C2×C37semidirect
389. #2428C2×C37semidirect
390. #2422C2×C37semidirect
391. #2084C2×C37semidirect
392. #2034C2×C37semidirect
393. #2011C2×C37semidirect
394. #1999C2×C37semidirect
395. #1957C2×C37semidirect
396. #1936C2×C37semidirect
397. #1934C2×C37semidirect
398. #1895C2×C37semidirect
399. #1879C2×C37semidirect
400. #1864C2×C37semidirect
401. #1753C2×C37semidirect
458. C37#26984direct (N × H)
529. #102D4×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×#4422
C37×#24282
C37×#24222
C37×#20842
C37×#20342
C37×#20112
C37×#19992
C37×#19572
C37×#19362
C37×#19342
C37×#18952
C37×#18792
C37×#18642
C37×#17532
#2698437