Finite Group Databasebeta

← C37×#18229 #22639482

Subgroups — C37×#18229 #22639482

Order 9472.

1232 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3536C211yesmaximal, characteristic, complemented
2C37×#3007C211yesmaximal, characteristic, complemented
3C37×#3002C211yesmaximal, characteristic, complemented
4C37×#2615C211yesmaximal, characteristic, complemented
5C37×#1606C212yesmaximal, complemented
6C37×#1602C212yesmaximal, complemented
7C37×#1600C212yesmaximal, complemented
8C37×#1596C212yesmaximal, complemented
9C37×#1520C211yesmaximal, characteristic, complemented
10C37×#1513C211yesmaximal, characteristic, complemented
11C37×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C37C2211yescharacteristic
13C2×#137×C37—21no—
14C2×#135×C37—21no—
15C37×#562—22no—
16C37×#554—21no—
17C37×#548—21no—
18C37×#547—21no—
19C37×#546—22no—
20C37×#546—21no—
21C37×#543C2212yes—
22C37×#542—21no—
23C37×#539—21no—
24C37×#538C2212yes—
25C37×#537—21no—
26C37×#537—21no—
27C37×#525C2211yescharacteristic
28C2×C22⋊Q8×C37C2211yescharacteristic
29C2×#121×C37—21no—
30C2×#121×C37C2211yescharacteristic
31C37×#452—21no—
32C37×#452—22no—
33C37×#451C2211yescharacteristic
34C37×#451C2212yes—
35C37×#450C2211yescharacteristic
36C37×#450C2212yes—
37C37×#449—21no—
38C37×#448C2211yescharacteristic
39C37×#447C2211yescharacteristic
40C37×#417—21no—
41C37×#416—21no—
42C37×#407C2211yescharacteristic
43C2×C22⋊C8×C37C2211yescharacteristic
44C37×#393C2212yes—
45C37×#392—22no—
46C37×#392C2212yes—
47C37×#380—21no—
48C37×#380C2211yescharacteristic
49C37×#328C2212yes—
50C37×#328C2212yes—
51C37×#328C2212yes—
52C37×#327C2212yes—
53C37×#323C2212yes—
54C37×#323C2212yes—
55C2×#41×C37—22no—
56C2×#41×C37—21no—
57C2×#41×C37—21no—
58C2×#41×C37—21no—
59C2×#41×C37—21no—
60C2×#41×C37—21no—
61C2×#41×C37—44no—
62C2×#41×C37D411yescharacteristic, complemented
63C22×Q8×C37D411yescharacteristic, complemented
64C22×Q8×C37C2311yescharacteristic
65C22×D4×C37—21no—
66C22×D4×C37—22no—
67C22×D4×C37D411yescharacteristic
68C22×D4×C37D412yes—
69C22×D4×C37C2311yescharacteristic
70C23×C4×C37—21no—
71C23×C4×C37C2311yescharacteristic
72#137×C37—44no—
73#135×C37—44no—
74C2×Q16×C37—21no—
75C2×Q16×C37—22no—
76C2×SD16×C37—21no—
77C2×SD16×C37—22no—
78C2×SD16×C37—21no—
79C2×D8×C37—21no—
80C2×M16×C37—21no—
81C22×C8×C37—21no—
82C4⋊Q8×C37—21no—
83#126×C37—22no—
84#125×C37—22no—
85#124×C37—21no—
86#124×C37—22no—
87#124×C37—22no—
88#123×C37—22no—
89#123×C37—22no—
90#123×C37—22no—
91#123×C37—21no—
92#123×C37—22no—
93C22⋊Q8×C37—21no—
94C22⋊Q8×C37—22no—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37—22no—
100C22⋊Q8×C37—22no—
101C22⋊Q8×C37—22no—
102C22⋊Q8×C37D412yescomplemented
103C22⋊Q8×C37D411yescharacteristic, complemented
104C22⋊Q8×C37C2312yes—
105C22⋊Q8×C37C2311yescharacteristic
106#121×C37—21no—
107#121×C37—22no—
108#121×C37—22no—
109#121×C37—22no—
110#121×C37—22no—
111#121×C37—22no—
112#121×C37—21no—
113#121×C37—21no—
114#121×C37—21no—
115#121×C37—21no—
116#121×C37—44no—
117#121×C37D411yescharacteristic, complemented
118#121×C37C2311yescharacteristic
119#120×C37—21no—
120#120×C37—22no—
121C4×Q8×C37—21no—
122C4×D4×C37—22no—
123C4×D4×C37—21no—
124C4×D4×C37—21no—
125C4×D4×C37—21no—
126C4×D4×C37—22no—
127#117×C37D411yescharacteristic, complemented
128C2×C4⋊C4×C37—21no—
129C2×C4⋊C4×C37—21no—
130C2×C4⋊C4×C37—21no—
131C2×C4⋊C4×C37D411yescharacteristic
132C2×C4⋊C4×C37D411yescharacteristic, complemented
133C2×C22⋊C4×C37—21no—
134C2×C22⋊C4×C37—22no—
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×C37C2312yes—
148C22⋊C8×C37C2311yescharacteristic
149C22⋊C8×C37C2311yescharacteristic
150#95×C37—22no—
151#95×C37C2312yes—
152C24×C37—21no—
153C24×C37C2×D412yes—
154C24×C37C2×D411yescharacteristic
155#41×C37—24no—
156#41×C37—24no—
157#41×C37—42no—
158#41×C37—42no—
159#41×C37—42no—
160#41×C37—42no—
161#41×C37—42no—
162#41×C37—42no—
163#41×C37—42no—
164#41×C37—84no—
165#41×C37—82no—
166C2×Q8×C37—22no—
167C2×Q8×C37—21no—
168C2×Q8×C37—21no—
169C2×Q8×C37—21no—
170C2×Q8×C37—42no—
171C2×Q8×C37—42no—
172C2×Q8×C37C2×D411yescharacteristic
173C2×Q8×C37C2×D412yes—
174C2×D4×C37—21no—
175C2×D4×C37—22no—
176C2×D4×C37—21no—
177C2×D4×C37—22no—
178C2×D4×C37—22no—
179C2×D4×C37—21no—
180C2×D4×C37—22no—
181C2×D4×C37—21no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—21no—
185C2×D4×C37—42no—
186C2×D4×C37—42no—
187C2×D4×C37—42no—
188C2×D4×C37—42no—
189C2×D4×C37—41no—
190C2×D4×C37—41no—
191C2×D4×C37—44no—
192C2×D4×C37—82no—
193C2×D4×C37—82no—
194C2×D4×C37—82no—
195C2×D4×C37C2×D411yescharacteristic
196C22×C4×C37—24no—
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—22no—
200C22×C4×C37—22no—
201C22×C4×C37—22no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—22no—
205C22×C4×C37—42no—
206C22×C4×C37—42no—
207C22×C4×C37—41no—
208C22×C4×C37—41no—
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D411yescharacteristic
211C22×C4×C37C2×D411yescharacteristic
212C22×C4×C37C2×D412yes—
213C22×C4×C37C2×D411yescharacteristic
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2411yescharacteristic
216Q16×C37—42no—
217Q16×C37—44no—
218SD16×C37—42no—
219SD16×C37—44no—
220SD16×C37—42no—
221D8×C37—42no—
222M16×C37—42no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—22no—
226C2×C8×C37—42no—
227C4⋊C4×C37—22no—
228C4⋊C4×C37—22no—
229C4⋊C4×C37—22no—
230C4⋊C4×C37—22no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—22no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—22no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—42no—
239C4⋊C4×C37C2×D412yes—
240C4⋊C4×C37C2×D411yescharacteristic
241C4⋊C4×C37C2×D411yescharacteristic
242C22⋊C4×C37—22no—
243C22⋊C4×C37—22no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—22no—
248C22⋊C4×C37—21no—
249C22⋊C4×C37—21no—
250C22⋊C4×C37—22no—
251C22⋊C4×C37—21no—
252C22⋊C4×C37—21no—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—22no—
255C22⋊C4×C37—21no—
256C22⋊C4×C37—44no—
257C22⋊C4×C37—81no—
258C22⋊C4×C37—82no—
259C42×C37—22no—
260C42×C37—21no—
261C23×C37—21no—
262C23×C37—21no—
263C23×C37—22no—
264C23×C37—22no—
265C23×C37—21no—
266C23×C37—22no—
267C23×C37—22no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—42no—
274C23×C37—42no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37#12011yescharacteristic
279C23×C37#12011yescharacteristic
280C23×C37C22×D411yescharacteristic
281Q8×C37—22no—
282Q8×C37—22no—
283Q8×C37—42no—
284Q8×C37—41no—
285Q8×C37—41no—
286Q8×C37—41no—
287Q8×C37—42no—
288Q8×C37—82no—
289D4×C37—22no—
290D4×C37—22no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—44no—
295D4×C37—42no—
296D4×C37—44no—
297D4×C37—44no—
298D4×C37—41no—
299D4×C37—41no—
300D4×C37—42no—
301D4×C37—81no—
302D4×C37—82no—
303D4×C37—81no—
304D4×C37—82no—
305D4×C37—82no—
306D4×C37—88no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—22no—
310C2×C4×C37—22no—
311C2×C4×C37—21no—
312C2×C4×C37—22no—
313C2×C4×C37—21no—
314C2×C4×C37—22no—
315C2×C4×C37—21no—
316C2×C4×C37—22no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—44no—
321C2×C4×C37—41no—
322C2×C4×C37—42no—
323C2×C4×C37—41no—
324C2×C4×C37—44no—
325C2×C4×C37—42no—
326C2×C4×C37—42no—
327C2×C4×C37—42no—
328C2×C4×C37—42no—
329C2×C4×C37—42no—
330C2×C4×C37—81no—
331C2×C4×C37—82no—
332C2×C4×C37—82no—
333C2×C4×C37—82no—
334C2×C4×C37#12011yescharacteristic
335C2×C4×C37#12011yescharacteristic
336C2×C4×C37C22×D411yescharacteristic
337C2×C4×C37C22×D411yescharacteristic
338C8×C37—41no—
339C8×C37—41no—
340C8×C37—42no—
341#18229C3711yesmaximal, characteristic, direct product factor, Sylow
342C22×C37—21no—
343C22×C37—21no—
344C22×C37—21no—
345C22×C37—21no—
346C22×C37—21no—
347C22×C37—21no—
348C22×C37—21no—
349C22×C37—21no—
350C22×C37—42no—
351C22×C37—42no—
352C22×C37—41no—
353C22×C37—42no—
354C22×C37—41no—
355C22×C37—42no—
356C22×C37—42no—
357C22×C37—41no—
358C22×C37—42no—
359C22×C37—81no—
360C22×C37—81no—
361C22×C37—82no—
362C22×C37—82no—
363C22×C37—81no—
364C22×C37—81no—
365C22×C37—81no—
366C22×C37—81no—
367C22×C37C2×#12011yescharacteristic
368C22×C37#57711yescharacteristic
369C22×C37#57811yescharacteristic
370C4×C37—21no—
371C4×C37—21no—
372C4×C37—21no—
373C4×C37—41no—
374C4×C37—42no—
375C4×C37—42no—
376C4×C37—41no—
377C4×C37—42no—
378C4×C37—41no—
379C4×C37—42no—
380C4×C37—82no—
381C4×C37B(4,𝔽2)12yes—
382#3536C2×C3711yescharacteristic, complemented
383#3007C2×C3711yescharacteristic, complemented
384#3002C2×C3711yescharacteristic, complemented
385#2615C2×C3711yescharacteristic, complemented
386#1606C2×C3712yescomplemented
387#1602C2×C3712yescomplemented
388#1600C2×C3712yescomplemented
389#1596C2×C3712yescomplemented
390#1520C2×C3711yescharacteristic, complemented
391#1513C2×C3711yescharacteristic, complemented
392#1471C2×C3711yescharacteristic, complemented
393C2×C37—21no—
394C2×C37—21no—
395C2×C37—41no—
396C2×C37—41no—
397C2×C37—81no—
398C2×C37—82no—
399C2×C37—82no—
400C2×C37#301311yescharacteristic
401C2×C37#301911yescharacteristic
402C2×C37C2×B(4,𝔽2)11yescharacteristic
403C22×#41C22×C3711yescharacteristic
404C2×#137—21no—
405C2×#135—21no—
406#562—22no—
407#554—21no—
408#548—21no—
409#547—21no—
410#546—22no—
411#546—21no—
412#543C22×C3712yes—
413#542—21no—
414#539—21no—
415#538C22×C3712yes—
416#537—21no—
417#537—21no—
418#525C22×C3711yescharacteristic
419C2×C22⋊Q8C22×C3711yescharacteristic
420C2×#121—21no—
421C2×#121C22×C3711yescharacteristic
422#452—21no—
423#452—22no—
424#451C22×C3711yescharacteristic
425#451C22×C3712yes—
426#450C22×C3711yescharacteristic
427#450C22×C3712yes—
428#449—21no—
429#448C22×C3711yescharacteristic
430#447C22×C3711yescharacteristic
431#417—21no—
432#416—21no—
433#407C22×C3711yescharacteristic
434C2×C22⋊C8C22×C3711yescharacteristic
435#393C22×C3712yes—
436#392—22no—
437#392C22×C3712yes—
438#380—21no—
439#380C22×C3711yescharacteristic
440#328C22×C3712yes—
441#328C22×C3712yes—
442#328C22×C3712yes—
443#327C22×C3712yes—
444#323C22×C3712yes—
445#323C22×C3712yes—
446C37#1822911yescharacteristic, direct product factor, Sylow
447C2×#41—22no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—44no—
454C2×#41D4×C3711yescharacteristic, complemented
455C22×Q8D4×C3711yescharacteristic, complemented
456C22×Q8C23×C3711yescharacteristic
457C22×D4—21no—
458C22×D4—22no—
459C22×D4D4×C3711yescharacteristic
460C22×D4D4×C3712yes—
461C22×D4C23×C3711yescharacteristic
462C23×C4—21no—
463C23×C4C23×C3711yescharacteristic
464#137—44no—
465#135—44no—
466C2×Q16—21no—
467C2×Q16—22no—
468C2×SD16—21no—
469C2×SD16—22no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×M16—21no—
473C22×C8—21no—
474C4⋊Q8—21no—
475#126—22no—
476#125—22no—
477#124—21no—
478#124—22no—
479#124—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—21no—
484#123—22no—
485C22⋊Q8—21no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8D4×C3712yescomplemented
495C22⋊Q8D4×C3711yescharacteristic, complemented
496C22⋊Q8C23×C3712yes—
497C22⋊Q8C23×C3711yescharacteristic
498#121—21no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—44no—
509#121D4×C3711yescharacteristic, complemented
510#121C23×C3711yescharacteristic
511#120—21no—
512#120—22no—
513C4×Q8—21no—
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—22no—
519#117D4×C3711yescharacteristic, complemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C3711yescharacteristic
524C2×C4⋊C4D4×C3711yescharacteristic, complemented
525C2×C22⋊C4—21no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4C23×C3712yes—
531#103—21no—
532#103—21no—
533#103—22no—
534#102—21no—
535#102—21no—
536#102—22no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8C23×C3712yes—
540C22⋊C8C23×C3711yescharacteristic
541C22⋊C8C23×C3711yescharacteristic
542#95—22no—
543#95C23×C3712yes—
544C24—21no—
545C24C2×D4×C3712yes—
546C24C2×D4×C3711yescharacteristic
547#41—24no—
548#41—24no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—84no—
557#41—82no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8C2×D4×C3711yescharacteristic
565C2×Q8C2×D4×C3712yes—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—44no—
584C2×D4—82no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4C2×D4×C3711yescharacteristic
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4C2×D4×C3711yescharacteristic
602C22×C4C2×D4×C3711yescharacteristic
603C22×C4C2×D4×C3711yescharacteristic
604C22×C4C2×D4×C3712yes—
605C22×C4C2×D4×C3711yescharacteristic
606C22×C4C2×D4×C3711yescharacteristic
607C22×C4C24×C3711yescharacteristic
608Q16—42no—
609Q16—44no—
610SD16—42no—
611SD16—44no—
612SD16—42no—
613D8—42no—
614M16—42no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—22no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C3712yes—
632C4⋊C4C2×D4×C3711yescharacteristic
633C4⋊C4C2×D4×C3711yescharacteristic
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—44no—
649C22⋊C4—81no—
650C22⋊C4—82no—
651C42—22no—
652C42—21no—
653C23—21no—
654C23—21no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23#120×C3711yescharacteristic
671C23#120×C3711yescharacteristic
672C23C22×D4×C3711yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—42no—
680Q8—82no—
681D4—22no—
682D4—22no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—42no—
693D4—81no—
694D4—82no—
695D4—81no—
696D4—82no—
697D4—82no—
698D4—88no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C3711yescharacteristic
727C2×C4#120×C3711yescharacteristic
728C2×C4C22×D4×C3711yescharacteristic
729C2×C4C22×D4×C3711yescharacteristic
730C8—41no—
731C8—41no—
732C8—42no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—82no—
753C22—82no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22C2×#120×C3711yescharacteristic
759C22C37×#57711yescharacteristic
760C22C37×#57811yescharacteristic
761C4—21no—
762C4—21no—
763C4—21no—
764C4—41no—
765C4—42no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—42no—
771C4—82no—
772C4C37×B(4,𝔽2)12yes—
773C2—21no—
774C2—21no—
775C2—41no—
776C2—41no—
777C2—82no—
778C2—82no—
779C2—81no—
780C2C37×#301311yescharacteristic
781C2C37×#301911yescharacteristic
782C2C2×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×#3536C2semidirect
2. C37×#3007C2semidirect
3. C37×#3002C2semidirect
4. C37×#2615C2semidirect
5. C37×#1606C2semidirect
6. C37×#1602C2semidirect
7. C37×#1600C2semidirect
8. C37×#1596C2semidirect
9. C37×#1520C2semidirect
10. C37×#1513C2semidirect
11. C37×#1471C2semidirect
62. C2×#41×C37D4semidirect
63. C22×Q8×C37D4semidirect
102. C22⋊Q8×C37D4semidirect
103. C22⋊Q8×C37D4semidirect
117. #121×C37D4semidirect
127. #117×C37D4semidirect
132. C2×C4⋊C4×C37D4semidirect
341. #18229C37direct (N × H)
382. #3536C2×C37semidirect
383. #3007C2×C37semidirect
384. #3002C2×C37semidirect
385. #2615C2×C37semidirect
386. #1606C2×C37semidirect
387. #1602C2×C37semidirect
388. #1600C2×C37semidirect
389. #1596C2×C37semidirect
390. #1520C2×C37semidirect
391. #1513C2×C37semidirect
392. #1471C2×C37semidirect
446. C37#18229direct (N × H)
454. C2×#41D4×C37semidirect
455. C22×Q8D4×C37semidirect
494. C22⋊Q8D4×C37semidirect
495. C22⋊Q8D4×C37semidirect
509. #121D4×C37semidirect
519. #117D4×C37semidirect
524. 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×#35362
C37×#30072
C37×#30022
C37×#26152
C37×#16062
C37×#16022
C37×#16002
C37×#15962
C37×#15202
C37×#15132
C37×#14712
#1822937