Finite Group Databasebeta

← C37×#10991 #22632244

Subgroups — C37×#10991 #22632244

Order 9472.

3122 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C37C211yesmaximal, characteristic
2C22×#99×C37C211yesmaximal, characteristic, complemented
3C37×#2308C211yesmaximal, characteristic, complemented
4C2×C37×#379C212yesmaximal, complemented
5C2×C37×#342C212yesmaximal, complemented
6C26×C37C2211yescharacteristic
7C23×D4×C37—21no—
8C23×D4×C37C2211yescharacteristic
9C2×#120×C37—24no—
10C2×#120×C37—22no—
11C2×#120×C37—24no—
12C2×#120×C37C414yescomplemented
13C22×C22⋊C4×C37—21no—
14C22×C22⋊C4×C37—24no—
15C22×C22⋊C4×C37C2212yes—
16C22×C22⋊C4×C37C2212yes—
17C22×C22⋊C4×C37C2211yescharacteristic
18C2×#99×C37—22no—
19C2×#99×C37—24no—
20C37×#386—24no—
21C37×#381—21no—
22C37×#379—24no—
23C37×#379—21no—
24C37×#379—24no—
25C37×#342—24no—
26C25×C37—21no—
27C25×C37—22no—
28C25×C37—21no—
29C25×C37—22no—
30C25×C37—22no—
31C25×C37—22no—
32C25×C37—22no—
33C25×C37—48no—
34C25×C37C2×C412yes—
35C25×C37D414yes—
36C25×C37D411yescharacteristic
37C25×C37C2311yescharacteristic
38C22×D4×C37—28no—
39C22×D4×C37—24no—
40C22×D4×C37—22no—
41C22×D4×C37—22no—
42C22×D4×C37—22no—
43C22×D4×C37—22no—
44C22×D4×C37—22no—
45C22×D4×C37—22no—
46C22×D4×C37—48no—
47C22×D4×C37C2×C412yes—
48C22×D4×C37D412yes—
49C23×C4×C37—21no—
50C23×C4×C37—22no—
51C23×C4×C37D411yescharacteristic
52C23×C4×C37D414yescomplemented
53#120×C37—216no—
54#120×C37—28no—
55#120×C37—28no—
56C2×C22⋊C4×C37—28no—
57C2×C22⋊C4×C37—22no—
58C2×C22⋊C4×C37—21no—
59C2×C22⋊C4×C37—24no—
60C2×C22⋊C4×C37—22no—
61C2×C22⋊C4×C37—22no—
62C2×C22⋊C4×C37—22no—
63C2×C22⋊C4×C37—22no—
64C2×C22⋊C4×C37—216no—
65C2×C22⋊C4×C37—22no—
66C2×C22⋊C4×C37—22no—
67C2×C22⋊C4×C37—22no—
68C2×C22⋊C4×C37—22no—
69C2×C22⋊C4×C37—22no—
70C2×C22⋊C4×C37—22no—
71C2×C22⋊C4×C37—22no—
72C2×C22⋊C4×C37—24no—
73C2×C22⋊C4×C37—416no—
74C2×C22⋊C4×C37C2×C412yes—
75C2×C22⋊C4×C37D414yes—
76C2×C22⋊C4×C37D414yescomplemented
77#99×C37—28no—
78#95×C37—24no—
79C24×C37—216no—
80C24×C37—28no—
81C24×C37—22no—
82C24×C37—24no—
83C24×C37—24no—
84C24×C37—24no—
85C24×C37—24no—
86C24×C37—22no—
87C24×C37—24no—
88C24×C37—24no—
89C24×C37—22no—
90C24×C37—21no—
91C24×C37—24no—
92C24×C37—24no—
93C24×C37—22no—
94C24×C37—21no—
95C24×C37—48no—
96C24×C37—416no—
97C24×C37—44no—
98C24×C37—48no—
99C24×C37—44no—
100C24×C37—416no—
101C24×C37—48no—
102C24×C37—416no—
103C24×C37—416no—
104C24×C37—416no—
105C24×C37—44no—
106C24×C37—41no—
107C24×C37—41no—
108C24×C37—42no—
109C24×C37—42no—
110C24×C37—42no—
111C24×C37—42no—
112C24×C37—41no—
113C24×C37—41no—
114C24×C37—42no—
115C24×C37—42no—
116C24×C37C22⋊C414yescomplemented
117C24×C37C22⋊C412yescomplemented
118C24×C37C22×C411yescharacteristic
119C24×C37C2×D411yescharacteristic
120C24×C37C2×D412yes—
121C24×C37C2×D412yes—
122C24×C37C2×D411yescharacteristic
123C24×C37C2×D412yes—
124C24×C37C2×D412yes—
125C24×C37#4112yes—
126C24×C37#4112yes—
127C2×D4×C37—216no—
128C2×D4×C37—22no—
129C2×D4×C37—22no—
130C2×D4×C37—24no—
131C2×D4×C37—24no—
132C2×D4×C37—22no—
133C2×D4×C37—24no—
134C2×D4×C37—24no—
135C2×D4×C37—22no—
136C2×D4×C37—416no—
137C2×D4×C37—432no—
138C2×D4×C37—42no—
139C2×D4×C37—42no—
140C2×D4×C37—42no—
141C2×D4×C37—42no—
142C2×D4×C37—42no—
143C2×D4×C37—42no—
144C2×D4×C37—42no—
145C2×D4×C37—42no—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—24no—
149C22×C4×C37—21no—
150C22×C4×C37—22no—
151C22×C4×C37—21no—
152C22×C4×C37—24no—
153C22×C4×C37—24no—
154C22×C4×C37—24no—
155C22×C4×C37—24no—
156C22×C4×C37—44no—
157C22×C4×C37—48no—
158C22×C4×C37—48no—
159C22×C4×C37—42no—
160C22×C4×C37—42no—
161C22×C4×C37C22⋊C412yescomplemented
162C22⋊C4×C37—216no—
163C22⋊C4×C37—22no—
164C22⋊C4×C37—24no—
165C22⋊C4×C37—24no—
166C22⋊C4×C37—24no—
167C22⋊C4×C37—432no—
168C22⋊C4×C37—42no—
169C22⋊C4×C37—42no—
170C22⋊C4×C37—42no—
171C22⋊C4×C37—42no—
172C22⋊C4×C37—42no—
173C22⋊C4×C37—42no—
174C22⋊C4×C37—84no—
175C22⋊C4×C37C22⋊C414yescomplemented
176C23×C37—28no—
177C23×C37—24no—
178C23×C37—216no—
179C23×C37—28no—
180C23×C37—216no—
181C23×C37—216no—
182C23×C37—216no—
183C23×C37—24no—
184C23×C37—28no—
185C23×C37—22no—
186C23×C37—22no—
187C23×C37—22no—
188C23×C37—48no—
189C23×C37—42no—
190C23×C37—42no—
191C23×C37—44no—
192C23×C37—44no—
193C23×C37—44no—
194C23×C37—44no—
195C23×C37—44no—
196C23×C37—44no—
197C23×C37—416no—
198C23×C37—48no—
199C23×C37—48no—
200C23×C37—48no—
201C23×C37—48no—
202C23×C37—416no—
203C23×C37—416no—
204C23×C37—48no—
205C23×C37—416no—
206C23×C37—48no—
207C23×C37—416no—
208C23×C37—416no—
209C23×C37—416no—
210C23×C37—416no—
211C23×C37—44no—
212C23×C37—48no—
213C23×C37—48no—
214C23×C37—416no—
215C23×C37—48no—
216C23×C37—416no—
217C23×C37—42no—
218C23×C37—42no—
219C23×C37—44no—
220C23×C37—44no—
221C23×C37—44no—
222C23×C37—44no—
223C23×C37—44no—
224C23×C37—48no—
225C23×C37—42no—
226C23×C37—42no—
227C23×C37—44no—
228C23×C37—82no—
229C23×C37—84no—
230C23×C37C2×C22⋊C411yescharacteristic
231C23×C37C2×C22⋊C411yescharacteristic
232C23×C37C2×C22⋊C411yescharacteristic
233C23×C37C4×D412yes—
234C23×C37C4×D412yes—
235C23×C37#12012yes—
236C23×C37#12012yes—
237C23×C37#12012yes—
238C23×C37#12011yescharacteristic
239C23×C37#12011yescharacteristic
240C23×C37#12112yes—
241C23×C37#12112yes—
242C23×C37#12112yes—
243C23×C37#12112yes—
244C23×C37#12112yes—
245C23×C37#12112yes—
246C23×C37#12311yescharacteristic
247C23×C37#12311yescharacteristic
248C23×C37#12312yes—
249C23×C37#12412yes—
250C23×C37#12712yes—
251D4×C37—432no—
252D4×C37—44no—
253D4×C37—44no—
254D4×C37—44no—
255D4×C37—44no—
256C2×C4×C37—22no—
257C2×C4×C37—24no—
258C2×C4×C37—22no—
259C2×C4×C37—22no—
260C2×C4×C37—44no—
261C2×C4×C37—48no—
262C2×C4×C37—42no—
263C2×C4×C37—42no—
264C2×C4×C37—48no—
265C2×C4×C37—48no—
266C2×C4×C37—44no—
267C2×C4×C37—44no—
268C2×C4×C37—48no—
269C2×C4×C37—84no—
270C2×C4×C37—84no—
271C2×C4×C37—84no—
272#10991C3711yesmaximal, characteristic, direct product factor, Sylow
273C22×C37—22no—
274C22×C37—24no—
275C22×C37—24no—
276C22×C37—22no—
277C22×C37—24no—
278C22×C37—24no—
279C22×C37—24no—
280C22×C37—24no—
281C22×C37—24no—
282C22×C37—24no—
283C22×C37—28no—
284C22×C37—216no—
285C22×C37—41no—
286C22×C37—41no—
287C22×C37—42no—
288C22×C37—42no—
289C22×C37—41no—
290C22×C37—42no—
291C22×C37—42no—
292C22×C37—42no—
293C22×C37—41no—
294C22×C37—42no—
295C22×C37—44no—
296C22×C37—416no—
297C22×C37—48no—
298C22×C37—48no—
299C22×C37—416no—
300C22×C37—416no—
301C22×C37—416no—
302C22×C37—44no—
303C22×C37—48no—
304C22×C37—44no—
305C22×C37—416no—
306C22×C37—44no—
307C22×C37—42no—
308C22×C37—82no—
309C22×C37—84no—
310C22×C37—84no—
311C22×C37#37911yescharacteristic
312C22×C37#38611yescharacteristic
313C22×C37#38612yes—
314C22×C37#38611yescharacteristic
315C22×C37#39012yes—
316C22×C37#39212yes—
317C22×C37#39212yes—
318C22×C37#39412yes—
319C22×C37#39412yes—
320C22×C37B(4,𝔽2)14yes—
321C4×C37—44no—
322C4×C37—42no—
323C4×C37—84no—
324C4×C37—84no—
325C22×#120C2×C3711yescharacteristic
326C22×#99C2×C3711yescharacteristic, complemented
327#2308C2×C3711yescharacteristic, complemented
328C2×#379C2×C3712yescomplemented
329C2×#342C2×C3712yescomplemented
330C2×C37—21no—
331C2×C37—22no—
332C2×C37—22no—
333C2×C37—21no—
334C2×C37—22no—
335C2×C37—22no—
336C2×C37—22no—
337C2×C37—48no—
338C2×C37—82no—
339C2×C37#143811yescharacteristic
340C2×C37#188912yes—
341C2×C37#202114yes—
342C26C22×C3711yescharacteristic
343C23×D4—21no—
344C23×D4C22×C3711yescharacteristic
345C2×#120—24no—
346C2×#120—22no—
347C2×#120—24no—
348C2×#120C4×C3714yescomplemented
349C22×C22⋊C4—21no—
350C22×C22⋊C4—24no—
351C22×C22⋊C4C22×C3712yes—
352C22×C22⋊C4C22×C3712yes—
353C22×C22⋊C4C22×C3711yescharacteristic
354C2×#99—22no—
355C2×#99—24no—
356#386—24no—
357#381—21no—
358#379—21no—
359#379—24no—
360#379—24no—
361#342—24no—
362C37#1099111yescharacteristic, direct product factor, Sylow
363C25—22no—
364C25—21no—
365C25—21no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—22no—
370C25—48no—
371C25C2×C4×C3712yes—
372C25D4×C3714yes—
373C25D4×C3711yescharacteristic
374C25C23×C3711yescharacteristic
375C22×D4—28no—
376C22×D4—24no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—48no—
384C22×D4C2×C4×C3712yes—
385C22×D4D4×C3712yes—
386C23×C4—21no—
387C23×C4—22no—
388C23×C4D4×C3711yescharacteristic
389C23×C4D4×C3714yescomplemented
390#120—216no—
391#120—28no—
392#120—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—216no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—416no—
411C2×C22⋊C4C2×C4×C3712yes—
412C2×C22⋊C4D4×C3714yes—
413C2×C22⋊C4D4×C3714yescomplemented
414#99—28no—
415#95—24no—
416C24—216no—
417C24—28no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—21no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—21no—
432C24—48no—
433C24—416no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—416no—
438C24—48no—
439C24—416no—
440C24—416no—
441C24—416no—
442C24—44no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—42no—
452C24—42no—
453C24C22⋊C4×C3714yescomplemented
454C24C22⋊C4×C3712yescomplemented
455C24C22×C4×C3711yescharacteristic
456C24C2×D4×C3711yescharacteristic
457C24C2×D4×C3712yes—
458C24C2×D4×C3712yes—
459C24C2×D4×C3711yescharacteristic
460C24C2×D4×C3712yes—
461C24C2×D4×C3712yes—
462C24#41×C3712yes—
463C24#41×C3712yes—
464C2×D4—216no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4C22⋊C4×C3712yescomplemented
499C22⋊C4—216no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—432no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—84no—
512C22⋊C4C22⋊C4×C3714yescomplemented
513C23—28no—
514C23—24no—
515C23—216no—
516C23—28no—
517C23—216no—
518C23—216no—
519C23—216no—
520C23—24no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—48no—
526C23—42no—
527C23—42no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23—44no—
534C23—416no—
535C23—48no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—416no—
540C23—416no—
541C23—48no—
542C23—416no—
543C23—48no—
544C23—416no—
545C23—416no—
546C23—416no—
547C23—416no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—416no—
552C23—48no—
553C23—416no—
554C23—42no—
555C23—42no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—48no—
562C23—42no—
563C23—42no—
564C23—44no—
565C23—82no—
566C23—84no—
567C23C2×C22⋊C4×C3711yescharacteristic
568C23C2×C22⋊C4×C3711yescharacteristic
569C23C2×C22⋊C4×C3711yescharacteristic
570C23C4×D4×C3712yes—
571C23C4×D4×C3712yes—
572C23#120×C3712yes—
573C23#120×C3712yes—
574C23#120×C3712yes—
575C23#120×C3711yescharacteristic
576C23#120×C3711yescharacteristic
577C23#121×C3712yes—
578C23#121×C3712yes—
579C23#121×C3712yes—
580C23#121×C3712yes—
581C23#121×C3712yes—
582C23#121×C3712yes—
583C23#123×C3711yescharacteristic
584C23#123×C3711yescharacteristic
585C23#123×C3712yes—
586C23#124×C3712yes—
587C23#127×C3712yes—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592D4—44no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—48no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C22—22no—
610C22—24no—
611C22—24no—
612C22—22no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—28no—
620C22—216no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—42no—
631C22—44no—
632C22—416no—
633C22—48no—
634C22—48no—
635C22—416no—
636C22—416no—
637C22—416no—
638C22—44no—
639C22—48no—
640C22—44no—
641C22—416no—
642C22—44no—
643C22—42no—
644C22—82no—
645C22—84no—
646C22—84no—
647C22C37×#37911yescharacteristic
648C22C37×#38611yescharacteristic
649C22C37×#38612yes—
650C22C37×#38611yescharacteristic
651C22C37×#39012yes—
652C22C37×#39212yes—
653C22C37×#39212yes—
654C22C37×#39412yes—
655C22C37×#39412yes—
656C22C37×B(4,𝔽2)14yes—
657C4—44no—
658C4—42no—
659C4—84no—
660C4—84no—
661C2—21no—
662C2—22no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—48no—
669C2—82no—
670C2C37×#143811yescharacteristic
671C2C37×#188912yes—
672C2C37×#202114yes—
subgroupG/H
center, socleC23×C37#120
commutatorC24C22×C4×C37
Frattini, cosocleC25C23×C37
prime radicalC22×#120×C37C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C37C2semidirect
3. C37×#2308C2semidirect
4. C2×C37×#379C2semidirect
5. C2×C37×#342C2semidirect
12. C2×#120×C37C4semidirect
52. C23×C4×C37D4semidirect
76. C2×C22⋊C4×C37D4semidirect
116. C24×C37C22⋊C4semidirect
117. C24×C37C22⋊C4semidirect
161. C22×C4×C37C22⋊C4semidirect
175. C22⋊C4×C37C22⋊C4semidirect
272. #10991C37direct (N × H)
326. C22×#99C2×C37semidirect
327. #2308C2×C37semidirect
328. C2×#379C2×C37semidirect
329. C2×#342C2×C37semidirect
348. C2×#120C4×C37semidirect
362. C37#10991direct (N × H)
389. C23×C4D4×C37semidirect
413. C2×C22⋊C4D4×C37semidirect
453. C24C22⋊C4×C37semidirect
454. C24C22⋊C4×C37semidirect
498. C22×C4C22⋊C4×C37semidirect
512. C22⋊C4C22⋊C4×C37semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C372
C22×#99×C372
C37×#23082
C2×C37×#3792
C2×C37×#3422
#1099137