Finite Group Databasebeta

← C37×#18228 #22639481

Subgroups — C37×#18228 #22639481

Order 9472.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3537C211yesmaximal, characteristic, complemented
2C37×#3006C211yesmaximal, characteristic, complemented
3C37×#3002C211yesmaximal, characteristic, complemented
4C37×#2615C211yesmaximal, characteristic, complemented
5C37×#1606C212yesmaximal, complemented
6C37×#1601C212yesmaximal, complemented
7C37×#1600C212yesmaximal, complemented
8C37×#1595C212yesmaximal, complemented
9C37×#1519C211yesmaximal, characteristic, complemented
10C37×#1513C211yesmaximal, characteristic, complemented
11C37×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C37C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C37—21no—
14C2×#135×C37—21no—
15C37×#560—22no—
16C37×#553—21no—
17C37×#553—21no—
18D42×C37—22no—
19D42×C37—21no—
20D42×C37—21no—
21C37×#540—21no—
22C37×#538—21no—
23C37×#538C2212yes—
24C37×#535—21no—
25C37×#534—21no—
26C37×#534C2212yes—
27C37×#525C2211yescharacteristic
28C2×#121×C37—21no—
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C37×#452—21no—
32C37×#451C2211yescharacteristic, complemented
33C37×#450C2211yescharacteristic, complemented
34C37×#449—21no—
35C37×#449—22no—
36C37×#448C2211yescharacteristic, complemented
37C37×#448C2212yescomplemented
38C37×#447C2211yescharacteristic, complemented
39C37×#447C2212yescomplemented
40C37×#417—21no—
41C37×#416—21no—
42C37×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C37C2211yescharacteristic, complemented
44C37×#393C2212yescomplemented
45C37×#392—22no—
46C37×#392C2212yescomplemented
47C37×#380—21no—
48C37×#380C2211yescharacteristic, complemented
49C37×#328C2212yescomplemented
50C37×#327C2212yescomplemented
51C37×#327C2212yescomplemented
52C37×#327C2212yescomplemented
53C37×#323C2212yescomplemented
54C37×#323C2212yescomplemented
55C2×#41×C37—21no—
56C2×#41×C37—21no—
57C2×#41×C37—21no—
58C2×#41×C37—21no—
59C2×#41×C37—44no—
60C2×#41×C37D411yescharacteristic, complemented
61C22×Q8×C37C2311yescharacteristic
62C22×D4×C37—22no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—22no—
66C22×D4×C37—21no—
67C22×D4×C37—22no—
68C22×D4×C37D411yescharacteristic
69C22×D4×C37D412yes—
70C22×D4×C37D411yescharacteristic, complemented
71C22×D4×C37C2311yescharacteristic
72C23×C4×C37—21no—
73C23×C4×C37C2311yescharacteristic
74AGL(1,ℤ/8)×C37—44no—
75#135×C37—44no—
76C2×Q16×C37—21no—
77C2×SD16×C37—21no—
78C2×SD16×C37—21no—
79C2×SD16×C37—22no—
80C2×D8×C37—21no—
81C2×D8×C37—22no—
82C2×M16×C37—21no—
83C22×C8×C37—21no—
84#127×C37—22no—
85#127×C37—21no—
86#126×C37—22no—
87#126×C37—22no—
88#125×C37—21no—
89#124×C37—22no—
90#123×C37—22no—
91#123×C37—21no—
92#123×C37—22no—
93#123×C37—22no—
94#123×C37—22no—
95C22⋊Q8×C37D411yescharacteristic, complemented
96C22⋊Q8×C37C2311yescharacteristic
97#121×C37—22no—
98#121×C37—21no—
99#121×C37—21no—
100#121×C37—22no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—22no—
104#121×C37—21no—
105#121×C37—21no—
106#121×C37—21no—
107#121×C37—21no—
108#121×C37—21no—
109#121×C37—21no—
110#121×C37—22no—
111#121×C37—44no—
112#121×C37D412yescomplemented
113#121×C37D411yescharacteristic, complemented
114#121×C37C2312yes—
115#121×C37C2311yescharacteristic
116#120×C37—22no—
117#120×C37—22no—
118#120×C37—22no—
119#120×C37—21no—
120#120×C37—22no—
121#120×C37—22no—
122#120×C37—22no—
123C4×D4×C37—22no—
124C4×D4×C37—21no—
125C4×D4×C37—21no—
126C4×D4×C37—21no—
127C4×D4×C37—21no—
128C4×D4×C37—22no—
129#117×C37—21no—
130#117×C37D411yescharacteristic, complemented
131C2×C4⋊C4×C37—21no—
132C2×C4⋊C4×C37D411yescharacteristic
133C2×C4⋊C4×C37D411yescharacteristic, complemented
134C2×C22⋊C4×C37—21no—
135C2×C22⋊C4×C37—22no—
136C2×C22⋊C4×C37—21no—
137C2×C22⋊C4×C37—22no—
138C2×C22⋊C4×C37C2312yes—
139#103×C37—21no—
140#103×C37—21no—
141#103×C37—22no—
142#102×C37—21no—
143#102×C37—21no—
144#102×C37—22no—
145C22⋊C8×C37—21no—
146C22⋊C8×C37—21no—
147C22⋊C8×C37C2311yescharacteristic
148C22⋊C8×C37C2311yescharacteristic
149C22⋊C8×C37C2312yes—
150#95×C37—22no—
151#95×C37C2312yes—
152C24×C37—22no—
153C24×C37—21no—
154C24×C37—21no—
155C24×C37C2×D412yes—
156C24×C37C2×D411yescharacteristic
157#41×C37—24no—
158#41×C37—24no—
159#41×C37—42no—
160#41×C37—42no—
161#41×C37—42no—
162#41×C37—42no—
163#41×C37—42no—
164#41×C37—42no—
165#41×C37—42no—
166C2×Q8×C37—21no—
167C2×Q8×C37—21no—
168C2×Q8×C37—42no—
169C2×Q8×C37C2×D411yescharacteristic
170C2×D4×C37—22no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—22no—
174C2×D4×C37—22no—
175C2×D4×C37—22no—
176C2×D4×C37—22no—
177C2×D4×C37—22no—
178C2×D4×C37—22no—
179C2×D4×C37—21no—
180C2×D4×C37—22no—
181C2×D4×C37—22no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—21no—
186C2×D4×C37—21no—
187C2×D4×C37—42no—
188C2×D4×C37—42no—
189C2×D4×C37—42no—
190C2×D4×C37—42no—
191C2×D4×C37—42no—
192C2×D4×C37—41no—
193C2×D4×C37—41no—
194C2×D4×C37—44no—
195C2×D4×C37—82no—
196C2×D4×C37—82no—
197C2×D4×C37—82no—
198C2×D4×C37—82no—
199C2×D4×C37—81no—
200C2×D4×C37—81no—
201C2×D4×C37—82no—
202C2×D4×C37—82no—
203C2×D4×C37—84no—
204C2×D4×C37C2×D411yescharacteristic
205C2×D4×C37C2×D412yes—
206C22×C4×C37—24no—
207C22×C4×C37—21no—
208C22×C4×C37—22no—
209C22×C4×C37—22no—
210C22×C4×C37—21no—
211C22×C4×C37—21no—
212C22×C4×C37—22no—
213C22×C4×C37—42no—
214C22×C4×C37—42no—
215C22×C4×C37—41no—
216C22×C4×C37—41no—
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37C2×D411yescharacteristic
220C22×C4×C37C2×D412yes—
221C22×C4×C37C2×D411yescharacteristic
222C22×C4×C37C2×D411yescharacteristic
223C22×C4×C37C2411yescharacteristic
224Q16×C37—42no—
225SD16×C37—42no—
226SD16×C37—42no—
227SD16×C37—44no—
228D8×C37—42no—
229D8×C37—44no—
230M16×C37—42no—
231C2×C8×C37—21no—
232C2×C8×C37—21no—
233C2×C8×C37—22no—
234C2×C8×C37—42no—
235C4⋊C4×C37—22no—
236C4⋊C4×C37—22no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—42no—
243C4⋊C4×C37C2×D412yes—
244C4⋊C4×C37C2×D411yescharacteristic
245C4⋊C4×C37C2×D411yescharacteristic
246C22⋊C4×C37—22no—
247C22⋊C4×C37—22no—
248C22⋊C4×C37—22no—
249C22⋊C4×C37—22no—
250C22⋊C4×C37—22no—
251C22⋊C4×C37—21no—
252C22⋊C4×C37—21no—
253C22⋊C4×C37—21no—
254C22⋊C4×C37—22no—
255C22⋊C4×C37—21no—
256C22⋊C4×C37—22no—
257C22⋊C4×C37—22no—
258C22⋊C4×C37—22no—
259C22⋊C4×C37—21no—
260C22⋊C4×C37—44no—
261C22⋊C4×C37—81no—
262C22⋊C4×C37—82no—
263C42×C37—22no—
264C42×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—22no—
268C23×C37—22no—
269C23×C37—22no—
270C23×C37—21no—
271C23×C37—22no—
272C23×C37—22no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—42no—
279C23×C37—42no—
280C23×C37—42no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—81no—
285C23×C37—81no—
286C23×C37—82no—
287C23×C37—82no—
288C23×C37—82no—
289C23×C37#12011yescharacteristic
290C23×C37#12011yescharacteristic
291C23×C37C22×D411yescharacteristic
292Q8×C37—22no—
293Q8×C37—22no—
294Q8×C37—41no—
295Q8×C37—41no—
296Q8×C37—41no—
297D4×C37—22no—
298D4×C37—22no—
299D4×C37—42no—
300D4×C37—41no—
301D4×C37—41no—
302D4×C37—41no—
303D4×C37—44no—
304D4×C37—42no—
305D4×C37—44no—
306D4×C37—44no—
307D4×C37—42no—
308D4×C37—41no—
309D4×C37—42no—
310D4×C37—41no—
311D4×C37—42no—
312D4×C37—42no—
313D4×C37—81no—
314D4×C37—82no—
315D4×C37—82no—
316D4×C37—81no—
317D4×C37—82no—
318D4×C37—82no—
319D4×C37—82no—
320D4×C37—82no—
321D4×C37—82no—
322D4×C37—88no—
323C2×C4×C37—22no—
324C2×C4×C37—22no—
325C2×C4×C37—22no—
326C2×C4×C37—22no—
327C2×C4×C37—21no—
328C2×C4×C37—22no—
329C2×C4×C37—22no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—41no—
333C2×C4×C37—41no—
334C2×C4×C37—41no—
335C2×C4×C37—44no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—44no—
339C2×C4×C37—42no—
340C2×C4×C37—42no—
341C2×C4×C37—42no—
342C2×C4×C37—42no—
343C2×C4×C37—42no—
344C2×C4×C37—81no—
345C2×C4×C37—82no—
346C2×C4×C37—82no—
347C2×C4×C37#12011yescharacteristic
348C2×C4×C37#12011yescharacteristic
349C2×C4×C37C22×D411yescharacteristic
350C2×C4×C37C22×D411yescharacteristic
351C8×C37—41no—
352C8×C37—41no—
353C8×C37—42no—
354#18228C3711yesmaximal, characteristic, direct product factor, Sylow
355C22×C37—21no—
356C22×C37—21no—
357C22×C37—21no—
358C22×C37—21no—
359C22×C37—21no—
360C22×C37—21no—
361C22×C37—21no—
362C22×C37—21no—
363C22×C37—42no—
364C22×C37—42no—
365C22×C37—42no—
366C22×C37—42no—
367C22×C37—41no—
368C22×C37—42no—
369C22×C37—42no—
370C22×C37—41no—
371C22×C37—42no—
372C22×C37—41no—
373C22×C37—42no—
374C22×C37—42no—
375C22×C37—81no—
376C22×C37—81no—
377C22×C37—82no—
378C22×C37—82no—
379C22×C37—81no—
380C22×C37—81no—
381C22×C37—81no—
382C22×C37—81no—
383C22×C37—162no—
384C22×C37—164no—
385C22×C37C2×#12011yescharacteristic
386C22×C37#57611yescharacteristic
387C22×C37#57711yescharacteristic
388C4×C37—21no—
389C4×C37—21no—
390C4×C37—21no—
391C4×C37—42no—
392C4×C37—41no—
393C4×C37—42no—
394C4×C37—41no—
395C4×C37—42no—
396C4×C37—41no—
397C4×C37—82no—
398C4×C37B(4,𝔽2)12yes—
399#3537C2×C3711yescharacteristic, complemented
400#3006C2×C3711yescharacteristic, complemented
401#3002C2×C3711yescharacteristic, complemented
402#2615C2×C3711yescharacteristic, complemented
403#1606C2×C3712yescomplemented
404#1601C2×C3712yescomplemented
405#1600C2×C3712yescomplemented
406#1595C2×C3712yescomplemented
407#1519C2×C3711yescharacteristic, complemented
408#1513C2×C3711yescharacteristic, complemented
409#1471C2×C3711yescharacteristic, complemented
410C2×C37—21no—
411C2×C37—21no—
412C2×C37—41no—
413C2×C37—41no—
414C2×C37—82no—
415C2×C37—82no—
416C2×C37—82no—
417C2×C37—81no—
418C2×C37#301211yescharacteristic
419C2×C37#301911yescharacteristic
420C2×C37C2×B(4,𝔽2)11yescharacteristic
421C22×#41C22×C3711yescharacteristic, complemented
422C2×AGL(1,ℤ/8)—21no—
423C2×#135—21no—
424#560—22no—
425#553—21no—
426#553—21no—
427D42—22no—
428D42—21no—
429D42—21no—
430#540—21no—
431#538—21no—
432#538C22×C3712yes—
433#535—21no—
434#534—21no—
435#534C22×C3712yes—
436#525C22×C3711yescharacteristic
437C2×#121—21no—
438C2×#121C22×C3711yescharacteristic
439C2×#121C22×C3711yescharacteristic
440#452—21no—
441#451C22×C3711yescharacteristic, complemented
442#450C22×C3711yescharacteristic, complemented
443#449—21no—
444#449—22no—
445#448C22×C3711yescharacteristic, complemented
446#448C22×C3712yescomplemented
447#447C22×C3711yescharacteristic, complemented
448#447C22×C3712yescomplemented
449#417—21no—
450#416—21no—
451#407C22×C3711yescharacteristic, complemented
452C2×C22⋊C8C22×C3711yescharacteristic, complemented
453#393C22×C3712yescomplemented
454#392—22no—
455#392C22×C3712yescomplemented
456#380—21no—
457#380C22×C3711yescharacteristic, complemented
458#328C22×C3712yescomplemented
459#327C22×C3712yescomplemented
460#327C22×C3712yescomplemented
461#327C22×C3712yescomplemented
462#323C22×C3712yescomplemented
463#323C22×C3712yescomplemented
464C37#1822811yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C3711yescharacteristic, complemented
471C22×Q8C23×C3711yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C3711yescharacteristic
479C22×D4D4×C3712yes—
480C22×D4D4×C3711yescharacteristic, complemented
481C22×D4C23×C3711yescharacteristic
482C23×C4—21no—
483C23×C4C23×C3711yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C3711yescharacteristic, complemented
506C22⋊Q8C23×C3711yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C3712yescomplemented
523#121D4×C3711yescharacteristic, complemented
524#121C23×C3712yes—
525#121C23×C3711yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C3711yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C3711yescharacteristic
543C2×C4⋊C4D4×C3711yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C3712yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C3711yescharacteristic
558C22⋊C8C23×C3711yescharacteristic
559C22⋊C8C23×C3712yes—
560#95—22no—
561#95C23×C3712yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C3712yes—
566C24C2×D4×C3711yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C3711yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C3711yescharacteristic
615C2×D4C2×D4×C3712yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C3711yescharacteristic
628C22×C4C2×D4×C3711yescharacteristic
629C22×C4C2×D4×C3711yescharacteristic
630C22×C4C2×D4×C3712yes—
631C22×C4C2×D4×C3711yescharacteristic
632C22×C4C2×D4×C3711yescharacteristic
633C22×C4C24×C3711yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C3712yes—
654C4⋊C4C2×D4×C3711yescharacteristic
655C4⋊C4C2×D4×C3711yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C3711yescharacteristic
700C23#120×C3711yescharacteristic
701C23C22×D4×C3711yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C3711yescharacteristic
758C2×C4#120×C3711yescharacteristic
759C2×C4C22×D4×C3711yescharacteristic
760C2×C4C22×D4×C3711yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C3711yescharacteristic
795C22C37×#57611yescharacteristic
796C22C37×#57711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4C37×B(4,𝔽2)12yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C37×#301211yescharacteristic
817C2C37×#301911yescharacteristic
818C2C2×C37×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
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
1. C37×#3537C2semidirect
2. C37×#3006C2semidirect
3. C37×#3002C2semidirect
4. C37×#2615C2semidirect
5. C37×#1606C2semidirect
6. C37×#1601C2semidirect
7. C37×#1600C2semidirect
8. C37×#1595C2semidirect
9. C37×#1519C2semidirect
10. C37×#1513C2semidirect
11. C37×#1471C2semidirect
12. C22×#41×C37C22semidirect
32. C37×#451C22semidirect
33. C37×#450C22semidirect
36. C37×#448C22semidirect
37. C37×#448C22semidirect
38. C37×#447C22semidirect
39. C37×#447C22semidirect
42. C37×#407C22semidirect
43. C2×C22⋊C8×C37C22semidirect
44. C37×#393C22semidirect
46. C37×#392C22semidirect
48. C37×#380C22semidirect
49. C37×#328C22semidirect
50. C37×#327C22semidirect
51. C37×#327C22semidirect
52. C37×#327C22semidirect
53. C37×#323C22semidirect
54. C37×#323C22semidirect
60. C2×#41×C37D4semidirect
70. C22×D4×C37D4semidirect
95. C22⋊Q8×C37D4semidirect
112. #121×C37D4semidirect
113. #121×C37D4semidirect
130. #117×C37D4semidirect
133. C2×C4⋊C4×C37D4semidirect
354. #18228C37direct (N × H)
399. #3537C2×C37semidirect
400. #3006C2×C37semidirect
401. #3002C2×C37semidirect
402. #2615C2×C37semidirect
403. #1606C2×C37semidirect
404. #1601C2×C37semidirect
405. #1600C2×C37semidirect
406. #1595C2×C37semidirect
407. #1519C2×C37semidirect
408. #1513C2×C37semidirect
409. #1471C2×C37semidirect
421. C22×#41C22×C37semidirect
441. #451C22×C37semidirect
442. #450C22×C37semidirect
445. #448C22×C37semidirect
446. #448C22×C37semidirect
447. #447C22×C37semidirect
448. #447C22×C37semidirect
451. #407C22×C37semidirect
452. C2×C22⋊C8C22×C37semidirect
453. #393C22×C37semidirect
455. #392C22×C37semidirect
457. #380C22×C37semidirect
458. #328C22×C37semidirect
459. #327C22×C37semidirect
460. #327C22×C37semidirect
461. #327C22×C37semidirect
462. #323C22×C37semidirect
463. #323C22×C37semidirect
464. C37#18228direct (N × H)
470. C2×#41D4×C37semidirect
480. C22×D4D4×C37semidirect
505. C22⋊Q8D4×C37semidirect
522. #121D4×C37semidirect
523. #121D4×C37semidirect
540. #117D4×C37semidirect
543. C2×C4⋊C4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35372
C37×#30062
C37×#30022
C37×#26152
C37×#16062
C37×#16012
C37×#16002
C37×#15952
C37×#15192
C37×#15132
C37×#14712
#1822837