Finite Group Databasebeta

← C37×#18262 #22639515

Subgroups — C37×#18262 #22639515

Order 9472.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3534C211yesmaximal, characteristic
2C37×#3094C211yesmaximal, characteristic, complemented
3C37×#3091C211yesmaximal, characteristic, complemented
4C37×#2498C211yesmaximal, characteristic, complemented
5C37×#1618C211yesmaximal, characteristic, complemented
6C37×#1616C211yesmaximal, characteristic, complemented
7C37×#1615C211yesmaximal, characteristic, complemented
8C37×#1613C211yesmaximal, characteristic, complemented
9C37×#1612C211yesmaximal, characteristic, complemented
10C37×#1610C211yesmaximal, characteristic, complemented
11C37×#1609C211yesmaximal, characteristic, complemented
12C37×#1607C211yesmaximal, characteristic, complemented
13C37×#1504C211yesmaximal, characteristic, complemented
14C2×C37×#327C211yesmaximal, characteristic, complemented
15C37×#1468C211yesmaximal, characteristic, complemented
16C37×#562—21no—
17C37×#560—21no—
18C37×#553—21no—
19C37×#551—21no—
20C37×#546—21no—
21C37×#546—21no—
22C37×#546—21no—
23D42×C37—21no—
24C37×#540—21no—
25C37×#539—21no—
26C37×#539C2211yescharacteristic
27C37×#538—21no—
28C37×#538C2211yescharacteristic
29C37×#537C2211yescharacteristic
30C37×#534—21no—
31C37×#534C2211yescharacteristic
32C37×#525C2211yescharacteristic
33C2×#123×C37C2211yescharacteristic
34C2×#121×C37C2211yescharacteristic
35C2×#117×C37C2211yescharacteristic, complemented
36C37×#485—21no—
37C37×#484C2211yescharacteristic, complemented
38C37×#483C2211yescharacteristic, complemented
39C37×#482—21no—
40C37×#482—21no—
41C37×#482—21no—
42C37×#481C2211yescharacteristic
43C37×#481C2211yescharacteristic, complemented
44C37×#481C2211yescharacteristic, complemented
45C37×#480C2211yescharacteristic
46C37×#480C2211yescharacteristic, complemented
47C37×#480C2211yescharacteristic, complemented
48C37×#428—21no—
49C37×#427—21no—
50C37×#418—21no—
51C37×#416—21no—
52C37×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#400C2211yescharacteristic, complemented
55C37×#399C2211yescharacteristic, complemented
56C37×#398C2211yescharacteristic, complemented
57C37×#397C2211yescharacteristic, complemented
58C37×#388—21no—
59C37×#387—21no—
60C37×#386—21no—
61C37×#380—21no—
62C2×#95×C37C2211yescharacteristic, complemented
63C37×#328C2211yescharacteristic, complemented
64C37×#328C2211yescharacteristic, complemented
65C37×#327C2211yescharacteristic
66C37×#327C2211yescharacteristic
67C37×#327C2211yescharacteristic, complemented
68C37×#327C2211yescharacteristic, complemented
69C37×#327C2211yescharacteristic, complemented
70C37×#327C2211yescharacteristic, complemented
71C37×#324C2211yescharacteristic, complemented
72C37×#324C2211yescharacteristic, complemented
73C37×#323C2211yescharacteristic, complemented
74C37×#323C2211yescharacteristic, complemented
75C2×#41×C37—21no—
76C2×#41×C37D411yescharacteristic
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37D411yescharacteristic
81C22×D4×C37D411yescharacteristic
82C23×C4×C37—21no—
83C23×C4×C37C2311yescharacteristic
84C2×M16×C37—21no—
85C22×C8×C37—21no—
86#127×C37—21no—
87#126×C37—21no—
88#126×C37—21no—
89#126×C37—21no—
90#126×C37—21no—
91#125×C37—21no—
92#125×C37—21no—
93#124×C37—21no—
94#124×C37—21no—
95#124×C37—21no—
96#123×C37—21no—
97#123×C37—21no—
98#123×C37—21no—
99#123×C37—21no—
100#123×C37—21no—
101#123×C37—21no—
102#123×C37—21no—
103#123×C37—21no—
104#123×C37—21no—
105#123×C37—21no—
106#123×C37—21no—
107#123×C37—21no—
108#123×C37—21no—
109#123×C37—21no—
110C22⋊Q8×C37—21no—
111C22⋊Q8×C37—21no—
112C22⋊Q8×C37—21no—
113C22⋊Q8×C37—21no—
114C22⋊Q8×C37—21no—
115C22⋊Q8×C37D411yescharacteristic
116C22⋊Q8×C37C2311yescharacteristic
117#121×C37—21no—
118#121×C37—21no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37—21no—
125#121×C37—21no—
126#121×C37—21no—
127#121×C37—21no—
128#121×C37—21no—
129#121×C37—21no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37D411yescharacteristic
133#121×C37D411yescharacteristic
134#121×C37D411yescharacteristic
135#121×C37C2311yescharacteristic
136#121×C37C2311yescharacteristic
137#121×C37C2311yescharacteristic
138#120×C37—21no—
139#120×C37—21no—
140#120×C37—21no—
141#120×C37—21no—
142#120×C37—21no—
143#120×C37—21no—
144#120×C37—21no—
145#120×C37—21no—
146C4×D4×C37—21no—
147C4×D4×C37—21no—
148C4×D4×C37—21no—
149C4×D4×C37—21no—
150C4×D4×C37—21no—
151C4×D4×C37—21no—
152C4×D4×C37—21no—
153C4×D4×C37—21no—
154#117×C37—21no—
155#117×C37—21no—
156#117×C37—21no—
157#117×C37—21no—
158#117×C37—21no—
159#117×C37D411yescharacteristic
160C2×C4⋊C4×C37—21no—
161C2×C4⋊C4×C37—21no—
162C2×C4⋊C4×C37D411yescharacteristic
163C2×C4⋊C4×C37D411yescharacteristic
164C2×C4⋊C4×C37C2311yescharacteristic
165C2×C4⋊C4×C37C2311yescharacteristic
166C2×C4⋊C4×C37C2311yescharacteristic
167C2×C22⋊C4×C37—21no—
168C2×C22⋊C4×C37—21no—
169C2×C22⋊C4×C37—21no—
170C2×C22⋊C4×C37—21no—
171C2×C22⋊C4×C37—21no—
172C2×C22⋊C4×C37—21no—
173C2×C22⋊C4×C37D411yescharacteristic
174C2×C22⋊C4×C37D411yescharacteristic
175C2×C22⋊C4×C37C2311yescharacteristic
176C2×C42×C37—21no—
177#107×C37—21no—
178#107×C37—21no—
179#107×C37—21no—
180#107×C37—21no—
181#106×C37—21no—
182#106×C37—21no—
183#106×C37—21no—
184#106×C37—21no—
185#103×C37—21no—
186#103×C37—21no—
187#102×C37—21no—
188#102×C37—21no—
189#102×C37—21no—
190#102×C37—21no—
191#102×C37—21no—
192#102×C37—21no—
193C22⋊C8×C37—21no—
194C22⋊C8×C37—21no—
195C22⋊C8×C37C2311yescharacteristic
196C22⋊C8×C37C2311yescharacteristic
197C22⋊C8×C37C2311yescharacteristic
198C22⋊C8×C37C2311yescharacteristic
199#95×C37—21no—
200#95×C37—21no—
201#95×C37—21no—
202#95×C37—21no—
203#95×C37—21no—
204#95×C37C2311yescharacteristic
205#95×C37C2311yescharacteristic
206C24×C37—21no—
207C24×C37—21no—
208C24×C37C2×D411yescharacteristic
209C24×C37C2×D411yescharacteristic
210#41×C37—42no—
211#41×C37—81no—
212#41×C37—81no—
213C2×Q8×C37—21no—
214C2×Q8×C37C2×D411yescharacteristic
215C2×D4×C37—21no—
216C2×D4×C37—21no—
217C2×D4×C37—21no—
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—21no—
228C2×D4×C37—21no—
229C2×D4×C37—21no—
230C2×D4×C37—21no—
231C2×D4×C37—21no—
232C2×D4×C37—42no—
233C2×D4×C37—42no—
234C2×D4×C37—81no—
235C2×D4×C37—81no—
236C2×D4×C37—81no—
237C2×D4×C37—81no—
238C2×D4×C37—82no—
239C2×D4×C37C2×D411yescharacteristic
240C2×D4×C37C2×D411yescharacteristic
241C2×D4×C37C2×D411yescharacteristic
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—42no—
254C22×C4×C37—42no—
255C22×C4×C37—42no—
256C22×C4×C37—81no—
257C22×C4×C37C2×D411yescharacteristic
258C22×C4×C37C2×D411yescharacteristic
259C22×C4×C37C2×D411yescharacteristic
260C22×C4×C37C2×D411yescharacteristic
261C22×C4×C37C2×D411yescharacteristic
262C22×C4×C37C2×D411yescharacteristic
263C22×C4×C37C2×D411yescharacteristic
264C22×C4×C37C2×D411yescharacteristic
265C22×C4×C37C2411yescharacteristic
266M16×C37—42no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37—42no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37—21no—
285C4⋊C4×C37—21no—
286C4⋊C4×C37—21no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—21no—
289C4⋊C4×C37—42no—
290C4⋊C4×C37—81no—
291C4⋊C4×C37C2×D411yescharacteristic
292C4⋊C4×C37C2×D411yescharacteristic
293C4⋊C4×C37C2×D411yescharacteristic
294C4⋊C4×C37C2×D411yescharacteristic
295C22⋊C4×C37—21no—
296C22⋊C4×C37—21no—
297C22⋊C4×C37—21no—
298C22⋊C4×C37—21no—
299C22⋊C4×C37—21no—
300C22⋊C4×C37—21no—
301C22⋊C4×C37—21no—
302C22⋊C4×C37—21no—
303C22⋊C4×C37—21no—
304C22⋊C4×C37—21no—
305C22⋊C4×C37—21no—
306C22⋊C4×C37—21no—
307C22⋊C4×C37—21no—
308C22⋊C4×C37—21no—
309C22⋊C4×C37—21no—
310C22⋊C4×C37—21no—
311C22⋊C4×C37—21no—
312C22⋊C4×C37—21no—
313C22⋊C4×C37—21no—
314C22⋊C4×C37—21no—
315C22⋊C4×C37—21no—
316C22⋊C4×C37—21no—
317C22⋊C4×C37—21no—
318C22⋊C4×C37—21no—
319C22⋊C4×C37—21no—
320C22⋊C4×C37—42no—
321C22⋊C4×C37—41no—
322C22⋊C4×C37—41no—
323C22⋊C4×C37—81no—
324C42×C37—21no—
325C42×C37—21no—
326C42×C37—21no—
327C42×C37—41no—
328C42×C37—41no—
329C23×C37—21no—
330C23×C37—21no—
331C23×C37—22no—
332C23×C37—21no—
333C23×C37—21no—
334C23×C37—21no—
335C23×C37—21no—
336C23×C37—21no—
337C23×C37—21no—
338C23×C37—41no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—42no—
342C23×C37—81no—
343C23×C37—81no—
344C23×C37—81no—
345C23×C37—81no—
346C23×C37—81no—
347C23×C37#12011yescharacteristic
348C23×C37#12011yescharacteristic
349C23×C37C22×D411yescharacteristic
350Q8×C37—41no—
351Q8×C37—81no—
352D4×C37—41no—
353D4×C37—41no—
354D4×C37—41no—
355D4×C37—41no—
356D4×C37—41no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—41no—
361D4×C37—42no—
362D4×C37—42no—
363D4×C37—81no—
364D4×C37—81no—
365D4×C37—81no—
366D4×C37—81no—
367D4×C37—81no—
368D4×C37—81no—
369D4×C37—81no—
370D4×C37—81no—
371D4×C37—81no—
372D4×C37—81no—
373D4×C37—81no—
374D4×C37—81no—
375C2×C4×C37—22no—
376C2×C4×C37—22no—
377C2×C4×C37—22no—
378C2×C4×C37—21no—
379C2×C4×C37—21no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—21no—
384C2×C4×C37—21no—
385C2×C4×C37—21no—
386C2×C4×C37—21no—
387C2×C4×C37—21no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—41no—
393C2×C4×C37—41no—
394C2×C4×C37—41no—
395C2×C4×C37—41no—
396C2×C4×C37—41no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—81no—
406C2×C4×C37—81no—
407C2×C4×C37—81no—
408C2×C4×C37—81no—
409C2×C4×C37—81no—
410C2×C4×C37—81no—
411C2×C4×C37—81no—
412C2×C4×C37—84no—
413C2×C4×C37#12011yescharacteristic
414C2×C4×C37#12011yescharacteristic
415C2×C4×C37C22×D411yescharacteristic
416C2×C4×C37C22×D411yescharacteristic
417C8×C37—41no—
418C8×C37—41no—
419C8×C37—41no—
420C8×C37—41no—
421#18262C3711yesmaximal, characteristic, direct product factor, Sylow
422C22×C37—21no—
423C22×C37—21no—
424C22×C37—21no—
425C22×C37—21no—
426C22×C37—21no—
427C22×C37—21no—
428C22×C37—21no—
429C22×C37—42no—
430C22×C37—42no—
431C22×C37—41no—
432C22×C37—41no—
433C22×C37—41no—
434C22×C37—41no—
435C22×C37—41no—
436C22×C37—41no—
437C22×C37—41no—
438C22×C37—41no—
439C22×C37—41no—
440C22×C37—41no—
441C22×C37—41no—
442C22×C37—41no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—162no—
446C22×C37—162no—
447C22×C37#45812yes—
448C22×C37C2×#12011yescharacteristic
449C22×C37#57611yescharacteristic
450C22×C37#57711yescharacteristic
451C4×C37—21no—
452C4×C37—21no—
453C4×C37—21no—
454C4×C37—21no—
455C4×C37—42no—
456C4×C37—41no—
457C4×C37—41no—
458C4×C37—41no—
459C4×C37—41no—
460C4×C37—41no—
461C4×C37—41no—
462C4×C37—41no—
463C4×C37—41no—
464C4×C37—81no—
465C4×C37—81no—
466C4×C37—81no—
467#3534C2×C3711yescharacteristic
468#3094C2×C3711yescharacteristic, complemented
469#3091C2×C3711yescharacteristic, complemented
470#2498C2×C3711yescharacteristic, complemented
471#1618C2×C3711yescharacteristic, complemented
472#1616C2×C3711yescharacteristic, complemented
473#1615C2×C3711yescharacteristic, complemented
474#1613C2×C3711yescharacteristic, complemented
475#1612C2×C3711yescharacteristic, complemented
476#1610C2×C3711yescharacteristic, complemented
477#1609C2×C3711yescharacteristic, complemented
478#1607C2×C3711yescharacteristic, complemented
479#1504C2×C3711yescharacteristic, complemented
480C2×#327C2×C3711yescharacteristic, complemented
481#1468C2×C3711yescharacteristic, complemented
482C2×C37—21no—
483C2×C37—21no—
484C2×C37—22no—
485C2×C37—41no—
486C2×C37—81no—
487C2×C37—81no—
488C2×C37—81no—
489C2×C37—81no—
490C2×C37#301211yescharacteristic
491C2×C37#301811yescharacteristic
492C2×C37C2×#45811yescharacteristic
493#562—21no—
494#560—21no—
495#553—21no—
496#551—21no—
497#546—21no—
498#546—21no—
499#546—21no—
500D42—21no—
501#540—21no—
502#539—21no—
503#539C22×C3711yescharacteristic
504#538—21no—
505#538C22×C3711yescharacteristic
506#537C22×C3711yescharacteristic
507#534—21no—
508#534C22×C3711yescharacteristic
509#525C22×C3711yescharacteristic
510C2×#123C22×C3711yescharacteristic
511C2×#121C22×C3711yescharacteristic
512C2×#117C22×C3711yescharacteristic, complemented
513#485—21no—
514#484C22×C3711yescharacteristic, complemented
515#483C22×C3711yescharacteristic, complemented
516#482—21no—
517#482—21no—
518#482—21no—
519#481C22×C3711yescharacteristic
520#481C22×C3711yescharacteristic, complemented
521#481C22×C3711yescharacteristic, complemented
522#480C22×C3711yescharacteristic
523#480C22×C3711yescharacteristic, complemented
524#480C22×C3711yescharacteristic, complemented
525#428—21no—
526#427—21no—
527#418—21no—
528#416—21no—
529#407C22×C3711yescharacteristic, complemented
530C2×C22⋊C8C22×C3711yescharacteristic, complemented
531#400C22×C3711yescharacteristic, complemented
532#399C22×C3711yescharacteristic, complemented
533#398C22×C3711yescharacteristic, complemented
534#397C22×C3711yescharacteristic, complemented
535#388—21no—
536#387—21no—
537#386—21no—
538#380—21no—
539C2×#95C22×C3711yescharacteristic, complemented
540#328C22×C3711yescharacteristic, complemented
541#328C22×C3711yescharacteristic, complemented
542#327C22×C3711yescharacteristic
543#327C22×C3711yescharacteristic
544#327C22×C3711yescharacteristic, complemented
545#327C22×C3711yescharacteristic, complemented
546#327C22×C3711yescharacteristic, complemented
547#327C22×C3711yescharacteristic, complemented
548#324C22×C3711yescharacteristic, complemented
549#324C22×C3711yescharacteristic, complemented
550#323C22×C3711yescharacteristic, complemented
551#323C22×C3711yescharacteristic, complemented
552C37#1826211yescharacteristic, direct product factor, Sylow
553C2×#41—21no—
554C2×#41D4×C3711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C3711yescharacteristic
559C22×D4D4×C3711yescharacteristic
560C23×C4—21no—
561C23×C4C23×C3711yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C3711yescharacteristic
594C22⋊Q8C23×C3711yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C3711yescharacteristic
611#121D4×C3711yescharacteristic
612#121D4×C3711yescharacteristic
613#121C23×C3711yescharacteristic
614#121C23×C3711yescharacteristic
615#121C23×C3711yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C3711yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C3711yescharacteristic
641C2×C4⋊C4D4×C3711yescharacteristic
642C2×C4⋊C4C23×C3711yescharacteristic
643C2×C4⋊C4C23×C3711yescharacteristic
644C2×C4⋊C4C23×C3711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C3711yescharacteristic
652C2×C22⋊C4D4×C3711yescharacteristic
653C2×C22⋊C4C23×C3711yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C3711yescharacteristic
674C22⋊C8C23×C3711yescharacteristic
675C22⋊C8C23×C3711yescharacteristic
676C22⋊C8C23×C3711yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C3711yescharacteristic
683#95C23×C3711yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C3711yescharacteristic
687C24C2×D4×C3711yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C3711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C3711yescharacteristic
718C2×D4C2×D4×C3711yescharacteristic
719C2×D4C2×D4×C3711yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C3711yescharacteristic
736C22×C4C2×D4×C3711yescharacteristic
737C22×C4C2×D4×C3711yescharacteristic
738C22×C4C2×D4×C3711yescharacteristic
739C22×C4C2×D4×C3711yescharacteristic
740C22×C4C2×D4×C3711yescharacteristic
741C22×C4C2×D4×C3711yescharacteristic
742C22×C4C2×D4×C3711yescharacteristic
743C22×C4C24×C3711yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C3711yescharacteristic
770C4⋊C4C2×D4×C3711yescharacteristic
771C4⋊C4C2×D4×C3711yescharacteristic
772C4⋊C4C2×D4×C3711yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C3711yescharacteristic
826C23#120×C3711yescharacteristic
827C23C22×D4×C3711yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C3711yescharacteristic
892C2×C4#120×C3711yescharacteristic
893C2×C4C22×D4×C3711yescharacteristic
894C2×C4C22×D4×C3711yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C37×#45812yes—
925C22C2×#120×C3711yescharacteristic
926C22C37×#57611yescharacteristic
927C22C37×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C37×#301211yescharacteristic
953C2C37×#301811yescharacteristic
954C2C2×C37×#45811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3094C2semidirect
3. C37×#3091C2semidirect
4. C37×#2498C2semidirect
5. C37×#1618C2semidirect
6. C37×#1616C2semidirect
7. C37×#1615C2semidirect
8. C37×#1613C2semidirect
9. C37×#1612C2semidirect
10. C37×#1610C2semidirect
11. C37×#1609C2semidirect
12. C37×#1607C2semidirect
13. C37×#1504C2semidirect
14. C2×C37×#327C2semidirect
15. C37×#1468C2semidirect
35. C2×#117×C37C22semidirect
37. C37×#484C22semidirect
38. C37×#483C22semidirect
43. C37×#481C22semidirect
44. C37×#481C22semidirect
46. C37×#480C22semidirect
47. C37×#480C22semidirect
52. C37×#407C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C37×#400C22semidirect
55. C37×#399C22semidirect
56. C37×#398C22semidirect
57. C37×#397C22semidirect
62. C2×#95×C37C22semidirect
63. C37×#328C22semidirect
64. C37×#328C22semidirect
67. C37×#327C22semidirect
68. C37×#327C22semidirect
69. C37×#327C22semidirect
70. C37×#327C22semidirect
71. C37×#324C22semidirect
72. C37×#324C22semidirect
73. C37×#323C22semidirect
74. C37×#323C22semidirect
421. #18262C37direct (N × H)
468. #3094C2×C37semidirect
469. #3091C2×C37semidirect
470. #2498C2×C37semidirect
471. #1618C2×C37semidirect
472. #1616C2×C37semidirect
473. #1615C2×C37semidirect
474. #1613C2×C37semidirect
475. #1612C2×C37semidirect
476. #1610C2×C37semidirect
477. #1609C2×C37semidirect
478. #1607C2×C37semidirect
479. #1504C2×C37semidirect
480. C2×#327C2×C37semidirect
481. #1468C2×C37semidirect
512. C2×#117C22×C37semidirect
514. #484C22×C37semidirect
515. #483C22×C37semidirect
520. #481C22×C37semidirect
521. #481C22×C37semidirect
523. #480C22×C37semidirect
524. #480C22×C37semidirect
529. #407C22×C37semidirect
530. C2×C22⋊C8C22×C37semidirect
531. #400C22×C37semidirect
532. #399C22×C37semidirect
533. #398C22×C37semidirect
534. #397C22×C37semidirect
539. C2×#95C22×C37semidirect
540. #328C22×C37semidirect
541. #328C22×C37semidirect
544. #327C22×C37semidirect
545. #327C22×C37semidirect
546. #327C22×C37semidirect
547. #327C22×C37semidirect
548. #324C22×C37semidirect
549. #324C22×C37semidirect
550. #323C22×C37semidirect
551. #323C22×C37semidirect
552. C37#18262direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35342
C37×#30942
C37×#30912
C37×#24982
C37×#16182
C37×#16162
C37×#16152
C37×#16132
C37×#16122
C37×#16102
C37×#16092
C37×#16072
C37×#15042
C2×C37×#3272
C37×#14682
#1826237