Finite Group Databasebeta

← C37×#25141 #22646394

Subgroups — C37×#25141 #22646394

Order 9472.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#472C211yesmaximal, characteristic, complemented
2C37×#3055C211yesmaximal, characteristic, complemented
3C37×#3005C211yesmaximal, characteristic, complemented
4C2×C37×#449C211yesmaximal, characteristic, complemented
5C37×#2933C211yesmaximal, characteristic, complemented
6C2×C37×#413C211yesmaximal, characteristic, complemented
7C37×#2064C211yesmaximal, characteristic, complemented
8C37×#2051C211yesmaximal, characteristic, complemented
9C37×#2045C211yesmaximal, characteristic, complemented
10C37×#2019C211yesmaximal, characteristic, complemented
11C37×#1977C211yesmaximal, characteristic, complemented
12C37×#1931C211yesmaximal, characteristic, complemented
13C37×#1908C211yesmaximal, characteristic, complemented
14C37×#1900C211yesmaximal, characteristic, complemented
15C37×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C2×#137×C37C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C22×D8×C37C2211yescharacteristic
22C2×#131×C37C2211yescharacteristic
23C22×M16×C37C2211yescharacteristic
24C22×M16×C37C2211yescharacteristic
25C37×#525C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C37×#472—24no—
28C37×#469—21no—
29C37×#468—21no—
30C37×#466—21no—
31C37×#465—21no—
32C37×#452—21no—
33C37×#452—21no—
34C37×#449—21no—
35C37×#449—21no—
36C37×#449—21no—
37C37×#449—21no—
38C37×#449—21no—
39C37×#449—21no—
40C37×#436—21no—
41C37×#435—21no—
42C37×#435—21no—
43C8×D4×C37—21no—
44C2×#108×C37C2211yescharacteristic
45C2×#108×C37C2211yescharacteristic
46C37×#428C2211yescharacteristic
47C37×#424C2211yescharacteristic
48C37×#419C2211yescharacteristic
49C37×#418C2211yescharacteristic
50C37×#418C2211yescharacteristic
51C37×#417C2211yescharacteristic
52C2×#103×C37C2211yescharacteristic
53C2×#102×C37C2211yescharacteristic
54C37×#413—24no—
55C2×#101×C37C2211yescharacteristic
56C2×#101×C37C2211yescharacteristic
57C2×#100×C37C2211yescharacteristic
58C2×#100×C37C2211yescharacteristic
59C2×#100×C37C2211yescharacteristic
60C2×#100×C37C2211yescharacteristic
61C37×#408C2211yescharacteristic
62C37×#407C2211yescharacteristic
63C2×C22⋊C8×C37C2211yescharacteristic
64C37×#405C2211yescharacteristic
65C37×#343C2211yescharacteristic
66C37×#343C2211yescharacteristic
67C37×#341C2211yescharacteristic
68C37×#341C2211yescharacteristic
69C2×#41×C37—22no—
70C2×#41×C37—22no—
71C2×#41×C37—21no—
72C2×#41×C37—21no—
73C2×#41×C37—21no—
74C2×#41×C37—21no—
75C2×#41×C37—41no—
76C2×#41×C37—41no—
77C2×#41×C37C2311yescharacteristic
78C22×Q8×C37C2311yescharacteristic
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37C2311yescharacteristic
82C22×D4×C37C2311yescharacteristic
83C23×C4×C37—21no—
84C23×C4×C37C2311yescharacteristic
85#137×C37—22no—
86#137×C37—41no—
87AGL(1,ℤ/8)×C37—22no—
88AGL(1,ℤ/8)×C37—22no—
89AGL(1,ℤ/8)×C37—41no—
90AGL(1,ℤ/8)×C37—41no—
91C2×Q16×C37—21no—
92C2×SD16×C37—21no—
93C2×SD16×C37—21no—
94C2×SD16×C37—22no—
95C2×SD16×C37—21no—
96C2×SD16×C37—21no—
97C2×SD16×C37—21no—
98C2×SD16×C37—41no—
99C2×D8×C37—22no—
100C2×D8×C37—21no—
101C2×D8×C37—21no—
102C2×D8×C37—21no—
103C2×D8×C37—21no—
104C2×D8×C37—41no—
105#131×C37—22no—
106#131×C37—41no—
107C2×M16×C37—21no—
108C2×M16×C37—21no—
109C2×M16×C37—21no—
110C2×M16×C37—22no—
111C2×M16×C37—22no—
112C2×M16×C37—41no—
113C2×M16×C37—41no—
114C2×M16×C37C2311yescharacteristic
115C2×M16×C37C2311yescharacteristic
116C2×M16×C37C2311yescharacteristic
117C2×M16×C37C2311yescharacteristic
118C2×M16×C37C2311yescharacteristic
119C2×M16×C37C2311yescharacteristic
120C22×C8×C37—21no—
121C22×C8×C37—21no—
122C22×C8×C37—21no—
123C22×C8×C37C2311yescharacteristic
124C22×C8×C37C2311yescharacteristic
125#123×C37—21no—
126C22⋊Q8×C37D411yescharacteristic
127C22⋊Q8×C37D411yescharacteristic
128#121×C37—21no—
129#121×C37—21no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37D411yescharacteristic
133#121×C37D411yescharacteristic
134#120×C37—21no—
135C4×D4×C37—21no—
136C4×D4×C37—21no—
137#117×C37C2311yescharacteristic
138C2×C4⋊C4×C37C2311yescharacteristic
139C2×C22⋊C4×C37—21no—
140#108×C37—22no—
141#108×C37—41no—
142#107×C37—21no—
143#106×C37—21no—
144C4⋊C8×C37—21no—
145C4⋊C8×C37—21no—
146#103×C37—21no—
147#103×C37—21no—
148#103×C37—21no—
149#103×C37—21no—
150#103×C37—21no—
151#102×C37—21no—
152#102×C37—21no—
153#102×C37—21no—
154#102×C37—21no—
155#102×C37—21no—
156#102×C37—21no—
157#102×C37—21no—
158#101×C37—22no—
159#101×C37—22no—
160#100×C37—22no—
161#100×C37—22no—
162#100×C37—41no—
163#100×C37D414yescomplemented
164C22⋊C8×C37—21no—
165C22⋊C8×C37—21no—
166C22⋊C8×C37—21no—
167C22⋊C8×C37—21no—
168C22⋊C8×C37D411yescharacteristic
169C22⋊C8×C37D411yescharacteristic
170C22⋊C8×C37D411yescharacteristic
171C22⋊C8×C37D411yescharacteristic
172#97×C37—21no—
173C4×C8×C37—21no—
174C24×C37—21no—
175C24×C37—21no—
176C24×C37#4111yescharacteristic
177#41×C37—21no—
178#41×C37—21no—
179#41×C37—21no—
180#41×C37—21no—
181#41×C37—42no—
182#41×C37—42no—
183#41×C37—42no—
184#41×C37—42no—
185#41×C37—42no—
186#41×C37—42no—
187#41×C37—42no—
188#41×C37—42no—
189C2×Q8×C37—21no—
190C2×Q8×C37—21no—
191C2×Q8×C37—21no—
192C2×Q8×C37—21no—
193C2×Q8×C37—21no—
194C2×Q8×C37C2×D411yescharacteristic
195C2×Q8×C37#4112yes—
196C2×D4×C37—24no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—42no—
212C2×D4×C37—41no—
213C2×D4×C37—41no—
214C2×D4×C37—41no—
215C2×D4×C37—41no—
216C2×D4×C37—82no—
217C2×D4×C37C2×D412yes—
218C2×D4×C37C2×D411yescharacteristic
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—21no—
223C22×C4×C37—24no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—42no—
228C22×C4×C37—41no—
229C22×C4×C37—41no—
230C22×C4×C37C2×D411yescharacteristic
231C22×C4×C37C2×D411yescharacteristic
232C22×C4×C37C2×D411yescharacteristic
233C22×C4×C37C2×D411yescharacteristic
234C22×C4×C37#4111yescharacteristic
235C22×C4×C37C2411yescharacteristic
236Q16×C37—42no—
237SD16×C37—42no—
238SD16×C37—42no—
239SD16×C37—42no—
240SD16×C37—42no—
241SD16×C37—42no—
242D8×C37—42no—
243D8×C37—42no—
244D8×C37—42no—
245D8×C37—42no—
246M16×C37—21no—
247M16×C37—21no—
248M16×C37—21no—
249M16×C37—21no—
250M16×C37—21no—
251M16×C37—21no—
252M16×C37—21no—
253M16×C37—21no—
254M16×C37—21no—
255M16×C37—21no—
256M16×C37—42no—
257M16×C37—42no—
258M16×C37—42no—
259M16×C37C2×D412yes—
260M16×C37C2×D412yes—
261C2×C8×C37—21no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37—42no—
272C2×C8×C37—42no—
273C2×C8×C37—42no—
274C2×C8×C37C2×D411yescharacteristic
275C2×C8×C37C2×D411yescharacteristic
276C2×C8×C37C2×D411yescharacteristic
277C2×C8×C37C2×D411yescharacteristic
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37C2×D411yescharacteristic
283C4⋊C4×C37C2×D411yescharacteristic
284C22⋊C4×C37—21no—
285C22⋊C4×C37—21no—
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—41no—
290C22⋊C4×C37—41no—
291C42×C37—21no—
292C23×C37—21no—
293C23×C37—21no—
294C23×C37—21no—
295C23×C37—22no—
296C23×C37—41no—
297C23×C37—41no—
298C23×C37—41no—
299C23×C37—41no—
300C23×C37—41no—
301C23×C37—41no—
302C23×C37—41no—
303C23×C37—81no—
304C23×C37—81no—
305C23×C37—81no—
306C23×C37—81no—
307C23×C37#12111yescharacteristic
308C23×C37#12111yescharacteristic
309C23×C37C2×#4111yescharacteristic
310Q8×C37—21no—
311Q8×C37—22no—
312Q8×C37—22no—
313Q8×C37—21no—
314Q8×C37—41no—
315Q8×C37—41no—
316D4×C37—21no—
317D4×C37—22no—
318D4×C37—22no—
319D4×C37—21no—
320D4×C37—42no—
321D4×C37—44no—
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—81no—
332D4×C37—82no—
333D4×C37—82no—
334C2×C4×C37—21no—
335C2×C4×C37—21no—
336C2×C4×C37—21no—
337C2×C4×C37—21no—
338C2×C4×C37—21no—
339C2×C4×C37—21no—
340C2×C4×C37—21no—
341C2×C4×C37—21no—
342C2×C4×C37—21no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—22no—
348C2×C4×C37—44no—
349C2×C4×C37—44no—
350C2×C4×C37—41no—
351C2×C4×C37—41no—
352C2×C4×C37—41no—
353C2×C4×C37—41no—
354C2×C4×C37—41no—
355C2×C4×C37—81no—
356C2×C4×C37#12111yescharacteristic
357C2×C4×C37#12111yescharacteristic
358C2×C4×C37C22×D411yescharacteristic
359C2×C4×C37C22×D411yescharacteristic
360C2×C4×C37C22×D411yescharacteristic
361C2×C4×C37C2×#4111yescharacteristic
362C2×C4×C37H(5,𝔽2)11yescharacteristic
363C2×C4×C37H(5,𝔽2)11yescharacteristic
364C8×C37—21no—
365C8×C37—21no—
366C8×C37—22no—
367C8×C37—22no—
368C8×C37—21no—
369C8×C37—21no—
370C8×C37—41no—
371C8×C37—41no—
372C8×C37—41no—
373C8×C37—41no—
374#25141C3711yesmaximal, characteristic, direct product factor, Sylow
375C22×C37—21no—
376C22×C37—21no—
377C22×C37—21no—
378C22×C37—21no—
379C22×C37—21no—
380C22×C37—21no—
381C22×C37—21no—
382C22×C37—21no—
383C22×C37—42no—
384C22×C37—41no—
385C22×C37—41no—
386C22×C37—41no—
387C22×C37—81no—
388C22×C37—81no—
389C22×C37—82no—
390C22×C37—82no—
391C22×C37—81no—
392C22×C37—81no—
393C22×C37—81no—
394C22×C37—81no—
395C22×C37—81no—
396C22×C37—161no—
397C22×C37—161no—
398C22×C37C2×#12111yescharacteristic
399C22×C37#52511yescharacteristic
400C22×C37#53811yescharacteristic
401C4×C37—21no—
402C4×C37—21no—
403C4×C37—42no—
404C4×C37—41no—
405C4×C37—41no—
406C4×C37—41no—
407C4×C37—81no—
408C4×C37D4211yescharacteristic
409C4×C37D4211yescharacteristic
410C4×C37#54611yescharacteristic
411C4×C37#54611yescharacteristic
412C2×#472C2×C3711yescharacteristic, complemented
413#3055C2×C3711yescharacteristic, complemented
414#3005C2×C3711yescharacteristic, complemented
415C2×#449C2×C3711yescharacteristic, complemented
416#2933C2×C3711yescharacteristic, complemented
417C2×#413C2×C3711yescharacteristic, complemented
418#2064C2×C3711yescharacteristic, complemented
419#2051C2×C3711yescharacteristic, complemented
420#2045C2×C3711yescharacteristic, complemented
421#2019C2×C3711yescharacteristic, complemented
422#1977C2×C3711yescharacteristic, complemented
423#1931C2×C3711yescharacteristic, complemented
424#1908C2×C3711yescharacteristic, complemented
425#1900C2×C3711yescharacteristic, complemented
426#1855C2×C3711yescharacteristic, complemented
427C2×C37—21no—
428C2×C37—21no—
429C2×C37—41no—
430C2×C37—41no—
431C2×C37—81no—
432C2×C37—82no—
433C2×C37—161no—
434C2×C37#242411yescharacteristic
435C2×C37#306711yescharacteristic
436C2×C37#306811yescharacteristic
437C22×#41C22×C3711yescharacteristic
438C2×#137C22×C3711yescharacteristic
439C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
440C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
441C22×SD16C22×C3711yescharacteristic
442C22×D8C22×C3711yescharacteristic
443C2×#131C22×C3711yescharacteristic
444C22×M16C22×C3711yescharacteristic
445C22×M16C22×C3711yescharacteristic
446#525C22×C3711yescharacteristic
447C2×#121C22×C3711yescharacteristic
448#472—24no—
449#469—21no—
450#468—21no—
451#466—21no—
452#465—21no—
453#452—21no—
454#452—21no—
455#449—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#436—21no—
462#435—21no—
463#435—21no—
464C8×D4—21no—
465C2×#108C22×C3711yescharacteristic
466C2×#108C22×C3711yescharacteristic
467#428C22×C3711yescharacteristic
468#424C22×C3711yescharacteristic
469#419C22×C3711yescharacteristic
470#418C22×C3711yescharacteristic
471#418C22×C3711yescharacteristic
472#417C22×C3711yescharacteristic
473C2×#103C22×C3711yescharacteristic
474C2×#102C22×C3711yescharacteristic
475#413—24no—
476C2×#101C22×C3711yescharacteristic
477C2×#101C22×C3711yescharacteristic
478C2×#100C22×C3711yescharacteristic
479C2×#100C22×C3711yescharacteristic
480C2×#100C22×C3711yescharacteristic
481C2×#100C22×C3711yescharacteristic
482#408C22×C3711yescharacteristic
483#407C22×C3711yescharacteristic
484C2×C22⋊C8C22×C3711yescharacteristic
485#405C22×C3711yescharacteristic
486#343C22×C3711yescharacteristic
487#343C22×C3711yescharacteristic
488#341C22×C3711yescharacteristic
489#341C22×C3711yescharacteristic
490C37#2514111yescharacteristic, direct product factor, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C3711yescharacteristic
500C22×Q8C23×C3711yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C3711yescharacteristic
504C22×D4C23×C3711yescharacteristic
505C23×C4—21no—
506C23×C4C23×C3711yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×SD16—22no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—22no—
522C2×D8—21no—
523C2×D8—21no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C3711yescharacteristic
537C2×M16C23×C3711yescharacteristic
538C2×M16C23×C3711yescharacteristic
539C2×M16C23×C3711yescharacteristic
540C2×M16C23×C3711yescharacteristic
541C2×M16C23×C3711yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C3711yescharacteristic
546C22×C8C23×C3711yescharacteristic
547#123—21no—
548C22⋊Q8D4×C3711yescharacteristic
549C22⋊Q8D4×C3711yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C3711yescharacteristic
555#121D4×C3711yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C3711yescharacteristic
560C2×C4⋊C4C23×C3711yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101—22no—
582#100—22no—
583#100—22no—
584#100—41no—
585#100D4×C3714yescomplemented
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C3711yescharacteristic
591C22⋊C8D4×C3711yescharacteristic
592C22⋊C8D4×C3711yescharacteristic
593C22⋊C8D4×C3711yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C3711yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C3711yescharacteristic
617C2×Q8#41×C3712yes—
618C2×D4—24no—
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—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C3712yes—
640C2×D4C2×D4×C3711yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C3711yescharacteristic
653C22×C4C2×D4×C3711yescharacteristic
654C22×C4C2×D4×C3711yescharacteristic
655C22×C4C2×D4×C3711yescharacteristic
656C22×C4#41×C3711yescharacteristic
657C22×C4C24×C3711yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C3712yes—
682M16C2×D4×C3712yes—
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—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C3711yescharacteristic
697C2×C8C2×D4×C3711yescharacteristic
698C2×C8C2×D4×C3711yescharacteristic
699C2×C8C2×D4×C3711yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C3711yescharacteristic
705C4⋊C4C2×D4×C3711yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C3711yescharacteristic
730C23#121×C3711yescharacteristic
731C23C2×#41×C3711yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—22no—
741D4—21no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C3711yescharacteristic
779C2×C4#121×C3711yescharacteristic
780C2×C4C22×D4×C3711yescharacteristic
781C2×C4C22×D4×C3711yescharacteristic
782C2×C4C22×D4×C3711yescharacteristic
783C2×C4C2×#41×C3711yescharacteristic
784C2×C4H(5,𝔽2)×C3711yescharacteristic
785C2×C4H(5,𝔽2)×C3711yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—42no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C3711yescharacteristic
820C22C37×#52511yescharacteristic
821C22C37×#53811yescharacteristic
822C4—21no—
823C4—21no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—81no—
829C4D42×C3711yescharacteristic
830C4D42×C3711yescharacteristic
831C4C37×#54611yescharacteristic
832C4C37×#54611yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C37×#242411yescharacteristic
841C2C37×#306711yescharacteristic
842C2C37×#306811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C37×#472C2semidirect
2. C37×#3055C2semidirect
3. C37×#3005C2semidirect
4. C2×C37×#449C2semidirect
5. C37×#2933C2semidirect
6. C2×C37×#413C2semidirect
7. C37×#2064C2semidirect
8. C37×#2051C2semidirect
9. C37×#2045C2semidirect
10. C37×#2019C2semidirect
11. C37×#1977C2semidirect
12. C37×#1931C2semidirect
13. C37×#1908C2semidirect
14. C37×#1900C2semidirect
15. C37×#1855C2semidirect
163. #100×C37D4semidirect
374. #25141C37direct (N × H)
412. C2×#472C2×C37semidirect
413. #3055C2×C37semidirect
414. #3005C2×C37semidirect
415. C2×#449C2×C37semidirect
416. #2933C2×C37semidirect
417. C2×#413C2×C37semidirect
418. #2064C2×C37semidirect
419. #2051C2×C37semidirect
420. #2045C2×C37semidirect
421. #2019C2×C37semidirect
422. #1977C2×C37semidirect
423. #1931C2×C37semidirect
424. #1908C2×C37semidirect
425. #1900C2×C37semidirect
426. #1855C2×C37semidirect
490. C37#25141direct (N × H)
585. #100D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4722
C37×#30552
C37×#30052
C2×C37×#4492
C37×#29332
C2×C37×#4132
C37×#20642
C37×#20512
C37×#20452
C37×#20192
C37×#19772
C37×#19312
C37×#19082
C37×#19002
C37×#18552
#2514137