Finite Group Databasebeta

← C37×#26977 #22648230

Subgroups — C37×#26977 #22648230

Order 9472.

1028 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×#466C211yesmaximal, characteristic, complemented
2C2×C37×#442C211yesmaximal, characteristic, complemented
3C37×#2428C211yesmaximal, characteristic, complemented
4C37×#2420C211yesmaximal, characteristic, complemented
5C37×#2085C211yesmaximal, characteristic, complemented
6C37×#2034C211yesmaximal, characteristic, complemented
7C37×#2011C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1961C211yesmaximal, characteristic, complemented
10C37×#1936C211yesmaximal, characteristic, complemented
11C37×#1936C211yesmaximal, characteristic, complemented
12C37×#1893C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1862C211yesmaximal, characteristic, complemented
15C37×#1752C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C23×C8×C37C2211yescharacteristic
19C2×#127×C37C2211yescharacteristic
20C2×#121×C37—21no—
21C2×#121×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×C4×D4×C37C2211yescharacteristic
25C2×C4×D4×C37C2211yescharacteristic
26C37×#466—24no—
27C37×#442—24no—
28C2×#107×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×#102×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×#97×C37C2211yescharacteristic
40C2×#97×C37C2211yescharacteristic
41C37×#397—21no—
42C37×#394—21no—
43C37×#394—21no—
44C37×#392—21no—
45C37×#390C2211yescharacteristic
46C37×#390C2211yescharacteristic
47C37×#389C2211yescharacteristic
48C37×#389C2211yescharacteristic
49C37×#386—21no—
50C37×#386—21no—
51C37×#382C2211yescharacteristic
52C37×#381—21no—
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—
78C22×C8×C37—22no—
79C22×C8×C37—22no—
80C22×C8×C37—41no—
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85#127×C37—22no—
86#127×C37—41no—
87#121×C37—22no—
88#121×C37—22no—
89#121×C37—22no—
90#121×C37—44no—
91#121×C37—41no—
92#121×C37—41no—
93#121×C37—41no—
94C4×D4×C37—22no—
95C4×D4×C37—22no—
96C4×D4×C37—41no—
97C4×D4×C37—41no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C4⋊C4×C37C2311yescharacteristic
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37—21no—
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×C37D411yescharacteristic
116C2×C22⋊C4×C37D411yescharacteristic
117C2×C42×C37C2311yescharacteristic
118C2×C42×C37C2311yescharacteristic
119#107×C37—22no—
120#106×C37—22no—
121#102×C37—22no—
122#102×C37—22no—
123#102×C37—22no—
124#102×C37—22no—
125#102×C37—41no—
126#102×C37—41no—
127#102×C37—41no—
128#102×C37D414yescomplemented
129C22⋊C8×C37—22no—
130#97×C37—22no—
131#97×C37—41no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37D411yescharacteristic
138#95×C37D411yescharacteristic
139C24×C37—21no—
140C24×C37—21no—
141C24×C37—21no—
142C24×C37C2×D411yescharacteristic
143C2×D4×C37—21no—
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—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—42no—
167C2×D4×C37—42no—
168C2×D4×C37—42no—
169C2×D4×C37—81no—
170C2×D4×C37—81no—
171C2×D4×C37—81no—
172C2×D4×C37—81no—
173C2×D4×C37—81no—
174C2×D4×C37C2×D412yes—
175C2×D4×C37#4112yes—
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—21no—
187C22×C4×C37—42no—
188C22×C4×C37—42no—
189C22×C4×C37—42no—
190C22×C4×C37—42no—
191C22×C4×C37—81no—
192C22×C4×C37—81no—
193C22×C4×C37C2×D411yescharacteristic
194C22×C4×C37C2×D411yescharacteristic
195C22×C4×C37C2×D411yescharacteristic
196C22×C4×C37C2×D411yescharacteristic
197C22×C4×C37C2×D411yescharacteristic
198C22×C4×C37C2411yescharacteristic
199D8×C37—28no—
200D8×C37—44no—
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×C37—21no—
210C2×C8×C37—44no—
211C2×C8×C37C2×D412yes—
212C2×C8×C37#4112yes—
213C2×C8×C37#4112yes—
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—21no—
223C4⋊C4×C37—42no—
224C4⋊C4×C37—81no—
225C4⋊C4×C37C2×D412yes—
226C22⋊C4×C37—22no—
227C22⋊C4×C37—41no—
228C22⋊C4×C37—42no—
229C22⋊C4×C37—42no—
230C22⋊C4×C37—42no—
231C22⋊C4×C37—42no—
232C22⋊C4×C37—42no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—81no—
235C22⋊C4×C37—81no—
236C22⋊C4×C37—81no—
237C22⋊C4×C37—81no—
238C42×C37—21no—
239C42×C37—21no—
240C42×C37—21no—
241C42×C37—21no—
242C23×C37—21no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—21no—
247C23×C37—21no—
248C23×C37—22no—
249C23×C37—22no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37—41no—
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×C37AGL(1,ℤ/8)12yes—
270C23×C37C22×D411yescharacteristic
271D4×C37—22no—
272D4×C37—22no—
273D4×C37—22no—
274D4×C37—22no—
275D4×C37—41no—
276D4×C37—41no—
277D4×C37—41no—
278D4×C37—41no—
279D4×C37—41no—
280D4×C37—41no—
281D4×C37—41no—
282D4×C37—41no—
283D4×C37—84no—
284D4×C37—84no—
285D4×C37—84no—
286D4×C37—84no—
287D4×C37—84no—
288C2×C4×C37—21no—
289C2×C4×C37—21no—
290C2×C4×C37—21no—
291C2×C4×C37—21no—
292C2×C4×C37—22no—
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—21no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
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—41no—
322C2×C4×C37—84no—
323C2×C4×C37—84no—
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—22no—
333C8×C37—41no—
334#26977C3711yesmaximal, 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—42no—
343C22×C37—42no—
344C22×C37—42no—
345C22×C37—42no—
346C22×C37—42no—
347C22×C37—42no—
348C22×C37—81no—
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×C37#53211yescharacteristic
364C22×C37D4211yescharacteristic
365C22×C37#54611yescharacteristic
366C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C37#57511yescharacteristic
368C22×C37#57611yescharacteristic
369C22×C37#57611yescharacteristic
370C4×C37—41no—
371C4×C37—41no—
372C4×C37—42no—
373C4×C37—41no—
374C4×C37—41no—
375C4×C37—41no—
376C4×C37—81no—
377C4×C37—81no—
378C4×C37—81no—
379C4×C37—81no—
380C4×C37#52511yescharacteristic
381C4×C37#54011yescharacteristic
382C4×C37#54611yescharacteristic
383C4×C37#55311yescharacteristic
384C2×#466C2×C3711yescharacteristic, complemented
385C2×#442C2×C3711yescharacteristic, complemented
386#2428C2×C3711yescharacteristic, complemented
387#2420C2×C3711yescharacteristic, complemented
388#2085C2×C3711yescharacteristic, complemented
389#2034C2×C3711yescharacteristic, complemented
390#2011C2×C3711yescharacteristic, complemented
391#1999C2×C3711yescharacteristic, complemented
392#1961C2×C3711yescharacteristic, complemented
393#1936C2×C3711yescharacteristic, complemented
394#1936C2×C3711yescharacteristic, complemented
395#1893C2×C3711yescharacteristic, complemented
396#1879C2×C3711yescharacteristic, complemented
397#1862C2×C3711yescharacteristic, complemented
398#1752C2×C3711yescharacteristic, complemented
399C2×C37—42no—
400C2×C37—82no—
401C2×C37—82no—
402C2×C37—161no—
403C2×C37#246411yescharacteristic
404C2×C37#317611yescharacteristic
405C2×C37#318011yescharacteristic
406C2×C37#326411yescharacteristic
407C2×C37#326811yescharacteristic
408C2×C37#331811yescharacteristic
409C2×C37#331911yescharacteristic
410C22×D8C22×C3711yescharacteristic
411C22×D8C22×C3711yescharacteristic
412C23×C8C22×C3711yescharacteristic
413C2×#127C22×C3711yescharacteristic
414C2×#121—21no—
415C2×#121C22×C3711yescharacteristic
416C2×#121C22×C3711yescharacteristic
417C2×#121C22×C3711yescharacteristic
418C2×C4×D4C22×C3711yescharacteristic
419C2×C4×D4C22×C3711yescharacteristic
420#466—24no—
421#442—24no—
422C2×#107C22×C3711yescharacteristic
423C2×#106C22×C3711yescharacteristic
424C2×#102C22×C3711yescharacteristic
425C2×#102C22×C3711yescharacteristic
426C2×#102C22×C3711yescharacteristic
427C2×#102C22×C3711yescharacteristic
428C2×#102C22×C3711yescharacteristic
429C2×#102C22×C3711yescharacteristic
430C2×#102C22×C3711yescharacteristic
431C2×#102C22×C3711yescharacteristic
432C2×C22⋊C8C22×C3711yescharacteristic
433C2×#97C22×C3711yescharacteristic
434C2×#97C22×C3711yescharacteristic
435#397—21no—
436#394—21no—
437#394—21no—
438#392—21no—
439#390C22×C3711yescharacteristic
440#390C22×C3711yescharacteristic
441#389C22×C3711yescharacteristic
442#389C22×C3711yescharacteristic
443#386—21no—
444#386—21no—
445#382C22×C3711yescharacteristic
446#381—21no—
447#380C22×C3711yescharacteristic
448C4×C22⋊C4C22×C3711yescharacteristic
449#340C22×C3711yescharacteristic
450#340C22×C3711yescharacteristic
451#340C22×C3711yescharacteristic
452#340C22×C3711yescharacteristic
453#336C22×C3711yescharacteristic
454#336C22×C3711yescharacteristic
455C37#2697711yescharacteristic, direct product factor, Sylow
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C23×C3711yescharacteristic
462C22×D4C23×C3711yescharacteristic
463C22×D4C23×C3711yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4C23×C3711yescharacteristic
467C2×D8—22no—
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C22×C8—22no—
474C22×C8—22no—
475C22×C8—41no—
476C22×C8C23×C3711yescharacteristic
477C22×C8C23×C3711yescharacteristic
478C22×C8C23×C3711yescharacteristic
479C22×C8C23×C3711yescharacteristic
480#127—22no—
481#127—41no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—44no—
486#121—41no—
487#121—41no—
488#121—41no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—41no—
492C4×D4—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C3711yescharacteristic
496C2×C4⋊C4C23×C3711yescharacteristic
497C2×C4⋊C4C23×C3711yescharacteristic
498C2×C4⋊C4C23×C3711yescharacteristic
499C2×C4⋊C4C23×C3711yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
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⋊C4D4×C3711yescharacteristic
511C2×C22⋊C4D4×C3711yescharacteristic
512C2×C42C23×C3711yescharacteristic
513C2×C42C23×C3711yescharacteristic
514#107—22no—
515#106—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102D4×C3714yescomplemented
524C22⋊C8—22no—
525#97—22no—
526#97—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95D4×C3711yescharacteristic
533#95D4×C3711yescharacteristic
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C3711yescharacteristic
538C2×D4—21no—
539C2×D4—21no—
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—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×D4×C3712yes—
570C2×D4#41×C3712yes—
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—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C2×D4×C3711yescharacteristic
589C22×C4C2×D4×C3711yescharacteristic
590C22×C4C2×D4×C3711yescharacteristic
591C22×C4C2×D4×C3711yescharacteristic
592C22×C4C2×D4×C3711yescharacteristic
593C22×C4C24×C3711yescharacteristic
594D8—28no—
595D8—44no—
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×C8—21no—
605C2×C8—44no—
606C2×C8C2×D4×C3712yes—
607C2×C8#41×C3712yes—
608C2×C8#41×C3712yes—
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—21no—
618C4⋊C4—42no—
619C4⋊C4—81no—
620C4⋊C4C2×D4×C3712yes—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
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—
664C23AGL(1,ℤ/8)×C3712yes—
665C23C22×D4×C3711yescharacteristic
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
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—21no—
698C2×C4—21no—
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—41no—
717C2×C4—84no—
718C2×C4—84no—
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—22no—
728C8—41no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—81no—
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—
757C22C37×#53211yescharacteristic
758C22D42×C3711yescharacteristic
759C22C37×#54611yescharacteristic
760C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
761C22C37×#57511yescharacteristic
762C22C37×#57611yescharacteristic
763C22C37×#57611yescharacteristic
764C4—41no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4C37×#52511yescharacteristic
775C4C37×#54011yescharacteristic
776C4C37×#54611yescharacteristic
777C4C37×#55311yescharacteristic
778C2—42no—
779C2—82no—
780C2—82no—
781C2—161no—
782C2C37×#246411yescharacteristic
783C2C37×#317611yescharacteristic
784C2C37×#318011yescharacteristic
785C2C37×#326411yescharacteristic
786C2C37×#326811yescharacteristic
787C2C37×#331811yescharacteristic
788C2C37×#331911yescharacteristic
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×#466C2semidirect
2. C2×C37×#442C2semidirect
3. C37×#2428C2semidirect
4. C37×#2420C2semidirect
5. C37×#2085C2semidirect
6. C37×#2034C2semidirect
7. C37×#2011C2semidirect
8. C37×#1999C2semidirect
9. C37×#1961C2semidirect
10. C37×#1936C2semidirect
11. C37×#1936C2semidirect
12. C37×#1893C2semidirect
13. C37×#1879C2semidirect
14. C37×#1862C2semidirect
15. C37×#1752C2semidirect
128. #102×C37D4semidirect
334. #26977C37direct (N × H)
384. C2×#466C2×C37semidirect
385. C2×#442C2×C37semidirect
386. #2428C2×C37semidirect
387. #2420C2×C37semidirect
388. #2085C2×C37semidirect
389. #2034C2×C37semidirect
390. #2011C2×C37semidirect
391. #1999C2×C37semidirect
392. #1961C2×C37semidirect
393. #1936C2×C37semidirect
394. #1936C2×C37semidirect
395. #1893C2×C37semidirect
396. #1879C2×C37semidirect
397. #1862C2×C37semidirect
398. #1752C2×C37semidirect
455. C37#26977direct (N × H)
523. #102D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4662
C2×C37×#4422
C37×#24282
C37×#24202
C37×#20852
C37×#20342
C37×#20112
C37×#19992
C37×#19612
C37×#19362
C37×#18932
C37×#18792
C37×#18622
C37×#17522
#2697737