Finite Group Databasebeta

← C37×#25140 #22646393

Subgroups — C37×#25140 #22646393

Order 9472.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 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×#3003C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C37×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C37C211yesmaximal, characteristic, complemented
7C37×#2063C211yesmaximal, characteristic, complemented
8C37×#2051C211yesmaximal, characteristic, complemented
9C37×#2045C211yesmaximal, characteristic, complemented
10C37×#2018C211yesmaximal, characteristic, complemented
11C37×#1978C211yesmaximal, characteristic, complemented
12C37×#1931C211yesmaximal, characteristic, complemented
13C37×#1907C211yesmaximal, characteristic, complemented
14C37×#1900C211yesmaximal, characteristic, complemented
15C37×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
20C22×D8×C37C2211yescharacteristic
21C22×D8×C37C2211yescharacteristic
22C2×#131×C37C2211yescharacteristic, complemented
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×#450—21no—
33C37×#450—21no—
34C37×#447—21no—
35C37×#447—21no—
36C37×#447—21no—
37C37×#447—21no—
38C37×#447—21no—
39C37×#447—21no—
40C37×#436—21no—
41C37×#435—21no—
42C37×#435—21no—
43C8×D4×C37—21no—
44C2×#108×C37C2211yescharacteristic, complemented
45C2×#108×C37C2211yescharacteristic, complemented
46C37×#428C2211yescharacteristic, complemented
47C37×#424C2211yescharacteristic, complemented
48C37×#418C2211yescharacteristic
49C37×#418C2211yescharacteristic
50C37×#418C2211yescharacteristic, complemented
51C37×#417C2211yescharacteristic, complemented
52C2×#102×C37C2211yescharacteristic
53C2×#102×C37C2211yescharacteristic
54C2×#100×C37—24no—
55C2×#100×C37C2211yescharacteristic
56C2×#100×C37C2211yescharacteristic
57C2×#100×C37C2211yescharacteristic
58C2×#100×C37C2211yescharacteristic
59C2×#100×C37C2211yescharacteristic, complemented
60C2×#100×C37C2211yescharacteristic, complemented
61C37×#408C2211yescharacteristic, complemented
62C37×#407C2211yescharacteristic
63C2×C22⋊C8×C37C2211yescharacteristic
64C37×#405C2211yescharacteristic, complemented
65C37×#343C2211yescharacteristic, complemented
66C37×#343C2211yescharacteristic, complemented
67C37×#341C2211yescharacteristic, complemented
68C37×#341C2211yescharacteristic, complemented
69C25×C37—21no—
70C2×#41×C37C2311yescharacteristic
71C22×D4×C37—22no—
72C22×D4×C37—22no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—41no—
80C22×D4×C37—41no—
81C22×D4×C37C2311yescharacteristic
82C22×D4×C37C2311yescharacteristic
83C22×D4×C37C2311yescharacteristic
84C23×C4×C37C2311yescharacteristic
85AGL(1,ℤ/8)×C37—22no—
86AGL(1,ℤ/8)×C37—22no—
87AGL(1,ℤ/8)×C37—22no—
88AGL(1,ℤ/8)×C37—41no—
89AGL(1,ℤ/8)×C37—41no—
90AGL(1,ℤ/8)×C37—41no—
91C2×SD16×C37—21no—
92C2×SD16×C37—21no—
93C2×SD16×C37—21no—
94C2×D8×C37—22no—
95C2×D8×C37—21no—
96C2×D8×C37—21no—
97C2×D8×C37—21no—
98C2×D8×C37—22no—
99C2×D8×C37—21no—
100C2×D8×C37—21no—
101C2×D8×C37—21no—
102C2×D8×C37—21no—
103C2×D8×C37—41no—
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#102×C37—21no—
148#102×C37—21no—
149#102×C37—21no—
150#102×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#100×C37—22no—
159#100×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—24no—
175C24×C37—21no—
176C24×C37—21no—
177C24×C37—21no—
178C24×C37—42no—
179C24×C37—41no—
180C24×C37—41no—
181C24×C37—82no—
182C24×C37—82no—
183C24×C37#4111yescharacteristic
184#41×C37—21no—
185#41×C37—21no—
186#41×C37—21no—
187#41×C37—21no—
188C2×Q8×C37C2×D411yescharacteristic
189C2×D4×C37—24no—
190C2×D4×C37—21no—
191C2×D4×C37—21no—
192C2×D4×C37—21no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
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—42no—
210C2×D4×C37—42no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
215C2×D4×C37—42no—
216C2×D4×C37—42no—
217C2×D4×C37—42no—
218C2×D4×C37—41no—
219C2×D4×C37—41no—
220C2×D4×C37—41no—
221C2×D4×C37—41no—
222C2×D4×C37—82no—
223C2×D4×C37C2×D412yes—
224C2×D4×C37C2×D411yescharacteristic
225C2×D4×C37#4112yes—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37C2×D411yescharacteristic
233C22×C4×C37C2×D411yescharacteristic
234C22×C4×C37C2×D411yescharacteristic
235C22×C4×C37C2×D411yescharacteristic
236C22×C4×C37#4111yescharacteristic
237C22×C4×C37C2411yescharacteristic
238SD16×C37—42no—
239SD16×C37—42no—
240SD16×C37—42no—
241D8×C37—42no—
242D8×C37—42no—
243D8×C37—42no—
244D8×C37—42no—
245D8×C37—42no—
246D8×C37—42no—
247D8×C37—42no—
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—21no—
257M16×C37—21no—
258M16×C37—42no—
259M16×C37—42no—
260M16×C37—42no—
261M16×C37C2×D412yes—
262M16×C37C2×D412yes—
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—21no—
272C2×C8×C37—21no—
273C2×C8×C37—42no—
274C2×C8×C37—42no—
275C2×C8×C37—42no—
276C2×C8×C37C2×D411yescharacteristic
277C2×C8×C37C2×D411yescharacteristic
278C2×C8×C37C2×D411yescharacteristic
279C2×C8×C37C2×D411yescharacteristic
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37C2×D411yescharacteristic
285C4⋊C4×C37C2×D411yescharacteristic
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—21no—
291C22⋊C4×C37—41no—
292C22⋊C4×C37—41no—
293C42×C37—21no—
294C23×C37—21no—
295C23×C37—21no—
296C23×C37—22no—
297C23×C37—21no—
298C23×C37—22no—
299C23×C37—22no—
300C23×C37—41no—
301C23×C37—44no—
302C23×C37—44no—
303C23×C37—41no—
304C23×C37—41no—
305C23×C37—41no—
306C23×C37—41no—
307C23×C37—41no—
308C23×C37—41no—
309C23×C37—41no—
310C23×C37—81no—
311C23×C37—81no—
312C23×C37—81no—
313C23×C37—81no—
314C23×C37—82no—
315C23×C37—82no—
316C23×C37—82no—
317C23×C37—81no—
318C23×C37—81no—
319C23×C37—88no—
320C23×C37—88no—
321C23×C37—82no—
322C23×C37#12111yescharacteristic
323C23×C37#12111yescharacteristic
324C23×C37C2×#4111yescharacteristic
325Q8×C37—21no—
326Q8×C37—21no—
327D4×C37—21no—
328D4×C37—22no—
329D4×C37—22no—
330D4×C37—22no—
331D4×C37—21no—
332D4×C37—22no—
333D4×C37—44no—
334D4×C37—44no—
335D4×C37—41no—
336D4×C37—41no—
337D4×C37—42no—
338D4×C37—41no—
339D4×C37—41no—
340D4×C37—41no—
341D4×C37—41no—
342D4×C37—41no—
343D4×C37—41no—
344D4×C37—41no—
345D4×C37—41no—
346D4×C37—81no—
347D4×C37—82no—
348D4×C37—82no—
349C2×C4×C37—21no—
350C2×C4×C37—21no—
351C2×C4×C37—21no—
352C2×C4×C37—21no—
353C2×C4×C37—21no—
354C2×C4×C37—21no—
355C2×C4×C37—21no—
356C2×C4×C37—21no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—21no—
360C2×C4×C37—21no—
361C2×C4×C37—21no—
362C2×C4×C37—41no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—81no—
366C2×C4×C37#12111yescharacteristic
367C2×C4×C37#12111yescharacteristic
368C2×C4×C37C22×D411yescharacteristic
369C2×C4×C37C22×D411yescharacteristic
370C2×C4×C37C22×D411yescharacteristic
371C2×C4×C37C2×#4111yescharacteristic
372C2×C4×C37H(5,𝔽2)11yescharacteristic
373C2×C4×C37H(5,𝔽2)11yescharacteristic
374C8×C37—21no—
375C8×C37—21no—
376C8×C37—22no—
377C8×C37—22no—
378C8×C37—21no—
379C8×C37—21no—
380C8×C37—41no—
381C8×C37—41no—
382C8×C37—41no—
383C8×C37—41no—
384#25140C3711yesmaximal, characteristic, direct product factor, Sylow
385C22×C37—21no—
386C22×C37—21no—
387C22×C37—21no—
388C22×C37—21no—
389C22×C37—21no—
390C22×C37—21no—
391C22×C37—21no—
392C22×C37—42no—
393C22×C37—42no—
394C22×C37—41no—
395C22×C37—42no—
396C22×C37—42no—
397C22×C37—41no—
398C22×C37—41no—
399C22×C37—82no—
400C22×C37—82no—
401C22×C37—88no—
402C22×C37—82no—
403C22×C37—82no—
404C22×C37—88no—
405C22×C37—81no—
406C22×C37—81no—
407C22×C37—81no—
408C22×C37—81no—
409C22×C37—81no—
410C22×C37—81no—
411C22×C37—81no—
412C22×C37—161no—
413C22×C37—161no—
414C22×C37#47212yescomplemented
415C22×C37C2×#12111yescharacteristic
416C22×C37#52511yescharacteristic
417C22×C37#53811yescharacteristic
418C4×C37—21no—
419C4×C37—21no—
420C4×C37—41no—
421C4×C37—41no—
422C4×C37—41no—
423C4×C37—81no—
424C4×C37D4211yescharacteristic
425C4×C37D4211yescharacteristic
426C4×C37#54611yescharacteristic
427C4×C37#54611yescharacteristic
428C2×#472C2×C3711yescharacteristic, complemented
429#3055C2×C3711yescharacteristic, complemented
430#3003C2×C3711yescharacteristic, complemented
431C2×#447C2×C3711yescharacteristic, complemented
432#2933C2×C3711yescharacteristic, complemented
433C22×#100C2×C3711yescharacteristic, complemented
434#2063C2×C3711yescharacteristic, complemented
435#2051C2×C3711yescharacteristic, complemented
436#2045C2×C3711yescharacteristic, complemented
437#2018C2×C3711yescharacteristic, complemented
438#1978C2×C3711yescharacteristic, complemented
439#1931C2×C3711yescharacteristic, complemented
440#1907C2×C3711yescharacteristic, complemented
441#1900C2×C3711yescharacteristic, complemented
442#1855C2×C3711yescharacteristic, complemented
443C2×C37—21no—
444C2×C37—21no—
445C2×C37—22no—
446C2×C37—41no—
447C2×C37—81no—
448C2×C37—82no—
449C2×C37—82no—
450C2×C37—161no—
451C2×C37#242411yescharacteristic
452C2×C37C2×#47211yescharacteristic
453C2×C37#306811yescharacteristic
454C23×D4C22×C3711yescharacteristic
455C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
456C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
457C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
458C22×D8C22×C3711yescharacteristic
459C22×D8C22×C3711yescharacteristic
460C2×#131C22×C3711yescharacteristic, complemented
461C22×M16C22×C3711yescharacteristic
462C22×M16C22×C3711yescharacteristic
463#525C22×C3711yescharacteristic
464C2×#121C22×C3711yescharacteristic
465#472—24no—
466#469—21no—
467#468—21no—
468#466—21no—
469#465—21no—
470#450—21no—
471#450—21no—
472#447—21no—
473#447—21no—
474#447—21no—
475#447—21no—
476#447—21no—
477#447—21no—
478#436—21no—
479#435—21no—
480#435—21no—
481C8×D4—21no—
482C2×#108C22×C3711yescharacteristic, complemented
483C2×#108C22×C3711yescharacteristic, complemented
484#428C22×C3711yescharacteristic, complemented
485#424C22×C3711yescharacteristic, complemented
486#418C22×C3711yescharacteristic
487#418C22×C3711yescharacteristic
488#418C22×C3711yescharacteristic, complemented
489#417C22×C3711yescharacteristic, complemented
490C2×#102C22×C3711yescharacteristic
491C2×#102C22×C3711yescharacteristic
492C2×#100—24no—
493C2×#100C22×C3711yescharacteristic
494C2×#100C22×C3711yescharacteristic
495C2×#100C22×C3711yescharacteristic
496C2×#100C22×C3711yescharacteristic
497C2×#100C22×C3711yescharacteristic, complemented
498C2×#100C22×C3711yescharacteristic, complemented
499#408C22×C3711yescharacteristic, complemented
500#407C22×C3711yescharacteristic
501C2×C22⋊C8C22×C3711yescharacteristic
502#405C22×C3711yescharacteristic, complemented
503#343C22×C3711yescharacteristic, complemented
504#343C22×C3711yescharacteristic, complemented
505#341C22×C3711yescharacteristic, complemented
506#341C22×C3711yescharacteristic, complemented
507C37#2514011yescharacteristic, direct product factor, Sylow
508C25—21no—
509C2×#41C23×C3711yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C23×C3711yescharacteristic
521C22×D4C23×C3711yescharacteristic
522C22×D4C23×C3711yescharacteristic
523C23×C4C23×C3711yescharacteristic
524AGL(1,ℤ/8)—22no—
525AGL(1,ℤ/8)—22no—
526AGL(1,ℤ/8)—22no—
527AGL(1,ℤ/8)—41no—
528AGL(1,ℤ/8)—41no—
529AGL(1,ℤ/8)—41no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×SD16—21no—
533C2×D8—22no—
534C2×D8—21no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—22no—
538C2×D8—21no—
539C2×D8—21no—
540C2×D8—21no—
541C2×D8—21no—
542C2×D8—41no—
543C2×D8—41no—
544#131—22no—
545#131—41no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16C23×C3711yescharacteristic
554C2×M16C23×C3711yescharacteristic
555C2×M16C23×C3711yescharacteristic
556C2×M16C23×C3711yescharacteristic
557C2×M16C23×C3711yescharacteristic
558C2×M16C23×C3711yescharacteristic
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8C23×C3711yescharacteristic
563C22×C8C23×C3711yescharacteristic
564#123—21no—
565C22⋊Q8D4×C3711yescharacteristic
566C22⋊Q8D4×C3711yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121D4×C3711yescharacteristic
572#121D4×C3711yescharacteristic
573#120—21no—
574C4×D4—21no—
575C4×D4—21no—
576#117C23×C3711yescharacteristic
577C2×C4⋊C4C23×C3711yescharacteristic
578C2×C22⋊C4—21no—
579#108—22no—
580#108—41no—
581#107—21no—
582#106—21no—
583C4⋊C8—21no—
584C4⋊C8—21no—
585#103—21no—
586#102—21no—
587#102—21no—
588#102—21no—
589#102—21no—
590#102—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594#102—21no—
595#102—21no—
596#102—21no—
597#100—22no—
598#100—22no—
599#100—22no—
600#100—22no—
601#100—41no—
602#100D4×C3714yescomplemented
603C22⋊C8—21no—
604C22⋊C8—21no—
605C22⋊C8—21no—
606C22⋊C8—21no—
607C22⋊C8D4×C3711yescharacteristic
608C22⋊C8D4×C3711yescharacteristic
609C22⋊C8D4×C3711yescharacteristic
610C22⋊C8D4×C3711yescharacteristic
611#97—21no—
612C4×C8—21no—
613C24—24no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—42no—
618C24—41no—
619C24—41no—
620C24—82no—
621C24—82no—
622C24#41×C3711yescharacteristic
623#41—21no—
624#41—21no—
625#41—21no—
626#41—21no—
627C2×Q8C2×D4×C3711yescharacteristic
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—41no—
658C2×D4—41no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—82no—
662C2×D4C2×D4×C3712yes—
663C2×D4C2×D4×C3711yescharacteristic
664C2×D4#41×C3712yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4C2×D4×C3711yescharacteristic
672C22×C4C2×D4×C3711yescharacteristic
673C22×C4C2×D4×C3711yescharacteristic
674C22×C4C2×D4×C3711yescharacteristic
675C22×C4#41×C3711yescharacteristic
676C22×C4C24×C3711yescharacteristic
677SD16—42no—
678SD16—42no—
679SD16—42no—
680D8—42no—
681D8—42no—
682D8—42no—
683D8—42no—
684D8—42no—
685D8—42no—
686D8—42no—
687M16—21no—
688M16—21no—
689M16—21no—
690M16—21no—
691M16—21no—
692M16—21no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—21no—
697M16—42no—
698M16—42no—
699M16—42no—
700M16C2×D4×C3712yes—
701M16C2×D4×C3712yes—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—42no—
713C2×C8—42no—
714C2×C8—42no—
715C2×C8C2×D4×C3711yescharacteristic
716C2×C8C2×D4×C3711yescharacteristic
717C2×C8C2×D4×C3711yescharacteristic
718C2×C8C2×D4×C3711yescharacteristic
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4C2×D4×C3711yescharacteristic
724C4⋊C4C2×D4×C3711yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C42—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—44no—
741C23—44no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23—81no—
753C23—82no—
754C23—82no—
755C23—82no—
756C23—81no—
757C23—81no—
758C23—88no—
759C23—88no—
760C23—82no—
761C23#121×C3711yescharacteristic
762C23#121×C3711yescharacteristic
763C23C2×#41×C3711yescharacteristic
764Q8—21no—
765Q8—21no—
766D4—21no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—21no—
771D4—22no—
772D4—44no—
773D4—44no—
774D4—41no—
775D4—41no—
776D4—42no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—81no—
786D4—82no—
787D4—82no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—81no—
805C2×C4#121×C3711yescharacteristic
806C2×C4#121×C3711yescharacteristic
807C2×C4C22×D4×C3711yescharacteristic
808C2×C4C22×D4×C3711yescharacteristic
809C2×C4C22×D4×C3711yescharacteristic
810C2×C4C2×#41×C3711yescharacteristic
811C2×C4H(5,𝔽2)×C3711yescharacteristic
812C2×C4H(5,𝔽2)×C3711yescharacteristic
813C8—21no—
814C8—21no—
815C8—22no—
816C8—22no—
817C8—21no—
818C8—21no—
819C8—41no—
820C8—41no—
821C8—41no—
822C8—41no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—41no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—88no—
842C22—88no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—161no—
851C22—161no—
852C22C37×#47212yescomplemented
853C22C2×#121×C3711yescharacteristic
854C22C37×#52511yescharacteristic
855C22C37×#53811yescharacteristic
856C4—21no—
857C4—21no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4D42×C3711yescharacteristic
863C4D42×C3711yescharacteristic
864C4C37×#54611yescharacteristic
865C4C37×#54611yescharacteristic
866C2—21no—
867C2—21no—
868C2—22no—
869C2—41no—
870C2—81no—
871C2—82no—
872C2—82no—
873C2—161no—
874C2C37×#242411yescharacteristic
875C2C2×C37×#47211yescharacteristic
876C2C37×#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×#3003C2semidirect
4. C2×C37×#447C2semidirect
5. C37×#2933C2semidirect
6. C22×#100×C37C2semidirect
7. C37×#2063C2semidirect
8. C37×#2051C2semidirect
9. C37×#2045C2semidirect
10. C37×#2018C2semidirect
11. C37×#1978C2semidirect
12. C37×#1931C2semidirect
13. C37×#1907C2semidirect
14. C37×#1900C2semidirect
15. C37×#1855C2semidirect
19. C2×AGL(1,ℤ/8)×C37C22semidirect
22. C2×#131×C37C22semidirect
44. C2×#108×C37C22semidirect
45. C2×#108×C37C22semidirect
46. C37×#428C22semidirect
47. C37×#424C22semidirect
50. C37×#418C22semidirect
51. C37×#417C22semidirect
59. C2×#100×C37C22semidirect
60. C2×#100×C37C22semidirect
61. C37×#408C22semidirect
64. C37×#405C22semidirect
65. C37×#343C22semidirect
66. C37×#343C22semidirect
67. C37×#341C22semidirect
68. C37×#341C22semidirect
163. #100×C37D4semidirect
384. #25140C37direct (N × H)
414. C22×C37#472semidirect
428. C2×#472C2×C37semidirect
429. #3055C2×C37semidirect
430. #3003C2×C37semidirect
431. C2×#447C2×C37semidirect
432. #2933C2×C37semidirect
433. C22×#100C2×C37semidirect
434. #2063C2×C37semidirect
435. #2051C2×C37semidirect
436. #2045C2×C37semidirect
437. #2018C2×C37semidirect
438. #1978C2×C37semidirect
439. #1931C2×C37semidirect
440. #1907C2×C37semidirect
441. #1900C2×C37semidirect
442. #1855C2×C37semidirect
457. C2×AGL(1,ℤ/8)C22×C37semidirect
460. C2×#131C22×C37semidirect
482. C2×#108C22×C37semidirect
483. C2×#108C22×C37semidirect
484. #428C22×C37semidirect
485. #424C22×C37semidirect
488. #418C22×C37semidirect
489. #417C22×C37semidirect
497. C2×#100C22×C37semidirect
498. C2×#100C22×C37semidirect
499. #408C22×C37semidirect
502. #405C22×C37semidirect
503. #343C22×C37semidirect
504. #343C22×C37semidirect
505. #341C22×C37semidirect
506. #341C22×C37semidirect
507. C37#25140direct (N × H)
602. #100D4×C37semidirect
852. C22C37×#472semidirect

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×#30032
C2×C37×#4472
C37×#29332
C22×#100×C372
C37×#20632
C37×#20512
C37×#20452
C37×#20182
C37×#19782
C37×#19312
C37×#19072
C37×#19002
C37×#18552
#2514037