Finite Group Databasebeta

← C37×#13082 #22634335

Subgroups — C37×#13082 #22634335

Order 9472.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C37C211yesmaximal, characteristic, complemented
2C37×#2403C211yesmaximal, characteristic
3C2×C37×AΣL(1,𝔽16)C212yesmaximal, complemented
4C37×#1781C211yesmaximal, characteristic, complemented
5C37×#1390C212yesmaximal, complemented
6C23×D4×C37C411yescharacteristic, complemented
7C23×D4×C37C2211yescharacteristic
8C22×M16×C37—21no—
9C2×#120×C37—21no—
10C2×#120×C37C411yescharacteristic, complemented
11C2×#120×C37C2211yescharacteristic
12C2×#100×C37—21no—
13C2×#100×C37—24no—
14C2×#100×C37C2212yes—
15C2×#99×C37—21no—
16C2×#99×C37C2212yes—
17C37×#392—21no—
18C37×#392—21no—
19C37×#386—21no—
20C37×#386C411yescharacteristic, complemented
21C37×#386C2211yescharacteristic
22C37×#379—21no—
23C37×#379C411yescharacteristic, complemented
24C37×AΣL(1,𝔽16)—24no—
25C25×C37C2×C411yescharacteristic
26C25×C37C2×C411yescharacteristic
27C25×C37D411yescharacteristic
28C22×D4×C37—21no—
29C22×D4×C37—22no—
30C22×D4×C37—22no—
31C22×D4×C37—21no—
32C22×D4×C37—21no—
33C22×D4×C37—21no—
34C22×D4×C37—42no—
35C22×D4×C37—41no—
36C22×D4×C37—41no—
37C22×D4×C37—44no—
38C22×D4×C37—41no—
39C22×D4×C37—41no—
40C22×D4×C37C2×C411yescharacteristic
41C22×D4×C37D411yescharacteristic
42C22×D4×C37D411yescharacteristic
43C22×D4×C37C2311yescharacteristic
44C23×C4×C37C2×C411yescharacteristic
45C23×C4×C37D411yescharacteristic
46C2×M16×C37—24no—
47C2×M16×C37—22no—
48C2×M16×C37—41no—
49C2×M16×C37—42no—
50C22×C8×C37—41no—
51#120×C37—22no—
52#120×C37—22no—
53#120×C37—44no—
54#120×C37—42no—
55C2×C22⋊C4×C37—21no—
56C2×C22⋊C4×C37—21no—
57C2×C22⋊C4×C37—21no—
58C2×C22⋊C4×C37—21no—
59C2×C22⋊C4×C37—21no—
60C2×C22⋊C4×C37—22no—
61C2×C22⋊C4×C37—21no—
62C2×C22⋊C4×C37—41no—
63C2×C22⋊C4×C37—41no—
64C2×C22⋊C4×C37C2×C411yescharacteristic
65C2×C22⋊C4×C37C2×C411yescharacteristic
66#100×C37—24no—
67#100×C37—22no—
68#100×C37D414yescomplemented
69#99×C37—22no—
70#99×C37—22no—
71#99×C37—42no—
72#95×C37—21no—
73#95×C37—21no—
74C24×C37—21no—
75C24×C37—21no—
76C24×C37—21no—
77C24×C37—21no—
78C24×C37—21no—
79C24×C37—22no—
80C24×C37—22no—
81C24×C37—22no—
82C24×C37—41no—
83C24×C37—41no—
84C24×C37—42no—
85C24×C37—41no—
86C24×C37—42no—
87C24×C37—42no—
88C24×C37—41no—
89C24×C37—81no—
90C24×C37—81no—
91C24×C37—81no—
92C24×C37C22⋊C411yescharacteristic
93C24×C37C22⋊C411yescharacteristic
94C24×C37C22⋊C411yescharacteristic
95C24×C37C22×C411yescharacteristic
96C24×C37C2×D411yescharacteristic
97C2×D4×C37—24no—
98C2×D4×C37—22no—
99C2×D4×C37—22no—
100C2×D4×C37—22no—
101C2×D4×C37—22no—
102C2×D4×C37—21no—
103C2×D4×C37—21no—
104C2×D4×C37—41no—
105C2×D4×C37—41no—
106C2×D4×C37—41no—
107C2×D4×C37—41no—
108C2×D4×C37—41no—
109C2×D4×C37—41no—
110C2×D4×C37—44no—
111C2×D4×C37—44no—
112C2×D4×C37—44no—
113C2×D4×C37—44no—
114C2×D4×C37—42no—
115C2×D4×C37—42no—
116C2×D4×C37—42no—
117C2×D4×C37—42no—
118C2×D4×C37—44no—
119C2×D4×C37—44no—
120C2×D4×C37—44no—
121C2×D4×C37—41no—
122C2×D4×C37—41no—
123C2×D4×C37—44no—
124C2×D4×C37—42no—
125C2×D4×C37—42no—
126C2×D4×C37—42no—
127C2×D4×C37—42no—
128C2×D4×C37—81no—
129C2×D4×C37—81no—
130C2×D4×C37C2×D412yes—
131C2×D4×C37#4112yes—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—22no—
135C22×C4×C37—21no—
136C22×C4×C37—21no—
137C22×C4×C37—21no—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—42no—
141C22×C4×C37—41no—
142C22×C4×C37—42no—
143C22×C4×C37C22⋊C411yescharacteristic
144C22×C4×C37C2×D411yescharacteristic
145M16×C37—24no—
146M16×C37—44no—
147M16×C37—42no—
148C2×C8×C37—44no—
149C2×C8×C37—42no—
150C22⋊C4×C37—22no—
151C22⋊C4×C37—42no—
152C22⋊C4×C37—42no—
153C22⋊C4×C37—42no—
154C22⋊C4×C37—42no—
155C22⋊C4×C37—41no—
156C22⋊C4×C37—41no—
157C22⋊C4×C37—41no—
158C22⋊C4×C37—42no—
159C22⋊C4×C37—42no—
160C22⋊C4×C37—81no—
161C22⋊C4×C37—82no—
162C22⋊C4×C37—82no—
163C23×C37—22no—
164C23×C37—21no—
165C23×C37—21no—
166C23×C37—21no—
167C23×C37—21no—
168C23×C37—21no—
169C23×C37—21no—
170C23×C37—22no—
171C23×C37—21no—
172C23×C37—21no—
173C23×C37—21no—
174C23×C37—21no—
175C23×C37—21no—
176C23×C37—21no—
177C23×C37—41no—
178C23×C37—42no—
179C23×C37—42no—
180C23×C37—42no—
181C23×C37—42no—
182C23×C37—41no—
183C23×C37—41no—
184C23×C37—41no—
185C23×C37—41no—
186C23×C37—41no—
187C23×C37—41no—
188C23×C37—42no—
189C23×C37—41no—
190C23×C37—42no—
191C23×C37—41no—
192C23×C37—41no—
193C23×C37—41no—
194C23×C37—41no—
195C23×C37—42no—
196C23×C37—42no—
197C23×C37—42no—
198C23×C37—42no—
199C23×C37—41no—
200C23×C37—41no—
201C23×C37—41no—
202C23×C37—81no—
203C23×C37—81no—
204C23×C37—81no—
205C23×C37—81no—
206C23×C37—82no—
207C23×C37—84no—
208C23×C37—84no—
209C23×C37—84no—
210C23×C37—84no—
211C23×C37—84no—
212C23×C37—84no—
213C23×C37—82no—
214C23×C37#9911yescharacteristic
215C23×C37#9911yescharacteristic
216C23×C37C2×C22⋊C411yescharacteristic
217C23×C37C4×D412yes—
218C23×C37#12112yes—
219D4×C37—42no—
220D4×C37—42no—
221D4×C37—44no—
222D4×C37—44no—
223D4×C37—42no—
224D4×C37—42no—
225D4×C37—44no—
226D4×C37—48no—
227D4×C37—44no—
228D4×C37—84no—
229D4×C37—84no—
230C2×C4×C37—22no—
231C2×C4×C37—22no—
232C2×C4×C37—22no—
233C2×C4×C37—22no—
234C2×C4×C37—21no—
235C2×C4×C37—21no—
236C2×C4×C37—21no—
237C2×C4×C37—21no—
238C2×C4×C37—22no—
239C2×C4×C37—41no—
240C2×C4×C37—42no—
241C2×C4×C37—41no—
242C2×C4×C37—42no—
243C2×C4×C37—41no—
244C2×C4×C37—41no—
245C2×C4×C37—41no—
246C2×C4×C37—41no—
247C2×C4×C37—41no—
248C2×C4×C37—41no—
249C2×C4×C37—82no—
250C2×C4×C37—82no—
251C2×C4×C37—82no—
252C2×C4×C37#9912yes—
253C2×C4×C37#12011yescharacteristic
254C2×C4×C37#12311yescharacteristic
255C8×C37—44no—
256#13082C3711yesmaximal, characteristic, direct product factor, Sylow
257C22×C37—21no—
258C22×C37—21no—
259C22×C37—21no—
260C22×C37—21no—
261C22×C37—21no—
262C22×C37—21no—
263C22×C37—21no—
264C22×C37—22no—
265C22×C37—22no—
266C22×C37—42no—
267C22×C37—42no—
268C22×C37—42no—
269C22×C37—42no—
270C22×C37—42no—
271C22×C37—42no—
272C22×C37—42no—
273C22×C37—42no—
274C22×C37—41no—
275C22×C37—41no—
276C22×C37—41no—
277C22×C37—41no—
278C22×C37—42no—
279C22×C37—41no—
280C22×C37—41no—
281C22×C37—41no—
282C22×C37—41no—
283C22×C37—41no—
284C22×C37—41no—
285C22×C37—81no—
286C22×C37—84no—
287C22×C37—84no—
288C22×C37—81no—
289C22×C37—81no—
290C22×C37—81no—
291C22×C37—81no—
292C22×C37—81no—
293C22×C37—84no—
294C22×C37—84no—
295C22×C37—84no—
296C22×C37—84no—
297C22×C37—81no—
298C22×C37—81no—
299C22×C37AΣL(1,𝔽16)12yescomplemented
300C22×C37#38611yescharacteristic
301C22×C37C2×#9911yescharacteristic
302C22×C37C2×#9911yescharacteristic
303C4×C37—21no—
304C4×C37—22no—
305C4×C37—21no—
306C4×C37—42no—
307C4×C37—81no—
308C4×C37—81no—
309C4×C37—162no—
310C22×#100C2×C3711yescharacteristic, complemented
311#2403C2×C3711yescharacteristic
312C2×AΣL(1,𝔽16)C2×C3712yescomplemented
313#1781C2×C3711yescharacteristic, complemented
314#1390C2×C3712yescomplemented
315C2×C37—21no—
316C2×C37—21no—
317C2×C37—22no—
318C2×C37—42no—
319C2×C37—41no—
320C2×C37—42no—
321C2×C37—81no—
322C2×C37—82no—
323C2×C37—81no—
324C2×C37#189811yescharacteristic
325C2×C37C2×AΣL(1,𝔽16)11yescharacteristic
326C2×C37#212111yescharacteristic
327C23×D4C4×C3711yescharacteristic, complemented
328C23×D4C22×C3711yescharacteristic
329C22×M16—21no—
330C2×#120—21no—
331C2×#120C4×C3711yescharacteristic, complemented
332C2×#120C22×C3711yescharacteristic
333C2×#100—21no—
334C2×#100—24no—
335C2×#100C22×C3712yes—
336C2×#99—21no—
337C2×#99C22×C3712yes—
338#392—21no—
339#392—21no—
340#386—21no—
341#386C4×C3711yescharacteristic, complemented
342#386C22×C3711yescharacteristic
343#379—21no—
344#379C4×C3711yescharacteristic, complemented
345AΣL(1,𝔽16)—24no—
346C37#1308211yescharacteristic, direct product factor, Sylow
347C25C2×C4×C3711yescharacteristic
348C25C2×C4×C3711yescharacteristic
349C25D4×C3711yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—44no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C3711yescharacteristic
363C22×D4D4×C3711yescharacteristic
364C22×D4D4×C3711yescharacteristic
365C22×D4C23×C3711yescharacteristic
366C23×C4C2×C4×C3711yescharacteristic
367C23×C4D4×C3711yescharacteristic
368C2×M16—24no—
369C2×M16—22no—
370C2×M16—41no—
371C2×M16—42no—
372C22×C8—41no—
373#120—22no—
374#120—22no—
375#120—44no—
376#120—42no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4C2×C4×C3711yescharacteristic
387C2×C22⋊C4C2×C4×C3711yescharacteristic
388#100—24no—
389#100—22no—
390#100D4×C3714yescomplemented
391#99—22no—
392#99—22no—
393#99—42no—
394#95—21no—
395#95—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—41no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C3711yescharacteristic
415C24C22⋊C4×C3711yescharacteristic
416C24C22⋊C4×C3711yescharacteristic
417C24C22×C4×C3711yescharacteristic
418C24C2×D4×C3711yescharacteristic
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C3712yes—
453C2×D4#41×C3712yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4C22⋊C4×C3711yescharacteristic
466C22×C4C2×D4×C3711yescharacteristic
467M16—24no—
468M16—44no—
469M16—42no—
470C2×C8—44no—
471C2×C8—42no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—82no—
484C22⋊C4—82no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23#99×C3711yescharacteristic
537C23#99×C3711yescharacteristic
538C23C2×C22⋊C4×C3711yescharacteristic
539C23C4×D4×C3712yes—
540C23#121×C3712yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#99×C3712yes—
575C2×C4#120×C3711yescharacteristic
576C2×C4#123×C3711yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22C37×AΣL(1,𝔽16)12yescomplemented
621C22C37×#38611yescharacteristic
622C22C2×#99×C3711yescharacteristic
623C22C2×#99×C3711yescharacteristic
624C4—21no—
625C4—22no—
626C4—21no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2C37×#189811yescharacteristic
641C2C2×C37×AΣL(1,𝔽16)11yescharacteristic
642C2C37×#212111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#99
commutatorC24C22×C4×C37
Frattini, cosocleC22×D4C23×C37
prime radicalC37×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C24×C37 ◁ C23×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#100×C37C2semidirect
3. C2×C37×AΣL(1,𝔽16)C2semidirect
4. C37×#1781C2semidirect
5. C37×#1390C2semidirect
6. C23×D4×C37C4semidirect
10. C2×#120×C37C4semidirect
20. C37×#386C4semidirect
23. C37×#379C4semidirect
68. #100×C37D4semidirect
256. #13082C37direct (N × H)
299. C22×C37AΣL(1,𝔽16)semidirect
310. C22×#100C2×C37semidirect
312. C2×AΣL(1,𝔽16)C2×C37semidirect
313. #1781C2×C37semidirect
314. #1390C2×C37semidirect
327. C23×D4C4×C37semidirect
331. C2×#120C4×C37semidirect
341. #386C4×C37semidirect
344. #379C4×C37semidirect
346. C37#13082direct (N × H)
390. #100D4×C37semidirect
620. C22C37×AΣL(1,𝔽16)semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C372
C37×#24032
C2×C37×AΣL(1,𝔽16)2
C37×#17812
C37×#13902
#1308237