Finite Group Databasebeta

← C37×#10322 #22631575

Subgroups — C37×#10322 #22631575

Order 9472.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3187C211yesmaximal, characteristic, complemented
2C37×#2848C211yesmaximal, characteristic, complemented
3C37×#2847C211yesmaximal, characteristic
4C37×#1779C211yesmaximal, characteristic, complemented
5C37×#1520C211yesmaximal, characteristic, complemented
6C37×#1519C211yesmaximal, characteristic, complemented
7C37×#1289C211yesmaximal, characteristic, complemented
8C24×C4×C37C2211yescharacteristic
9C2×C22⋊Q8×C37—21no—
10C2×C22⋊Q8×C37C2211yescharacteristic
11C2×#121×C37—21no—
12C2×#121×C37C2211yescharacteristic
13C2×#120×C37—21no—
14C37×#483—21no—
15C37×#481—21no—
16C37×#465—22no—
17C37×#450—21no—
18C37×#448—21no—
19C2×C22⋊C8×C37—22no—
20C2×C22⋊C8×C37C2211yescharacteristic
21C2×C22⋊C8×C37C2211yescharacteristic
22C37×#386—21no—
23C37×#386—22no—
24C37×#385—21no—
25C37×#385—22no—
26C37×#380—21no—
27C37×#380—21no—
28C37×#380C2211yescharacteristic
29C37×#380C2211yescharacteristic
30C37×#379—21no—
31C37×#328—22no—
32C37×#327—22no—
33C25×C37D411yescharacteristic
34C22×Q8×C37D411yescharacteristic, complemented
35C22×D4×C37—22no—
36C22×D4×C37—21no—
37C22×D4×C37D411yescharacteristic
38C23×C4×C37—21no—
39C23×C4×C37—21no—
40C23×C4×C37—21no—
41C23×C4×C37—21no—
42C23×C4×C37—21no—
43C23×C4×C37—21no—
44C23×C4×C37—44no—
45C23×C4×C37D411yescharacteristic
46C23×C4×C37C2311yescharacteristic
47C2×SD16×C37—22no—
48C22×C8×C37—21no—
49C22×C8×C37D412yescomplemented
50C22⋊Q8×C37—21no—
51C22⋊Q8×C37—21no—
52C22⋊Q8×C37—21no—
53C22⋊Q8×C37—21no—
54C22⋊Q8×C37—44no—
55#121×C37—21no—
56#121×C37—21no—
57#121×C37—21no—
58#121×C37—21no—
59#121×C37—44no—
60#120×C37—42no—
61#120×C37—42no—
62C2×C4⋊C4×C37—22no—
63C2×C4⋊C4×C37—21no—
64C2×C4⋊C4×C37—21no—
65C2×C4⋊C4×C37—21no—
66C2×C4⋊C4×C37D411yescharacteristic
67C2×C4⋊C4×C37D411yescharacteristic, complemented
68C2×C22⋊C4×C37—22no—
69C2×C22⋊C4×C37—22no—
70C2×C22⋊C4×C37—22no—
71C2×C22⋊C4×C37—22no—
72C2×C22⋊C4×C37—21no—
73C2×C22⋊C4×C37—21no—
74C2×C22⋊C4×C37—21no—
75C2×C22⋊C4×C37—21no—
76#106×C37—22no—
77#103×C37—22no—
78#102×C37—22no—
79C22⋊C8×C37—21no—
80C22⋊C8×C37—21no—
81C22⋊C8×C37—21no—
82C22⋊C8×C37—21no—
83C22⋊C8×C37—44no—
84#95×C37—22no—
85#95×C37—22no—
86#95×C37D412yes—
87#95×C37D412yescomplemented
88C24×C37—21no—
89C24×C37—21no—
90C24×C37—21no—
91C24×C37—21no—
92C24×C37—21no—
93C24×C37—21no—
94C24×C37—21no—
95C24×C37—42no—
96C24×C37—42no—
97C24×C37SD1612yescomplemented
98C24×C37C2×D411yescharacteristic
99C2×Q8×C37—21no—
100C2×Q8×C37—21no—
101C2×Q8×C37—42no—
102C2×D4×C37—21no—
103C2×D4×C37—21no—
104C2×D4×C37—42no—
105C2×D4×C37—44no—
106C2×D4×C37—44no—
107C2×D4×C37—44no—
108C2×D4×C37—41no—
109C2×D4×C37—41no—
110C2×D4×C37—41no—
111C2×D4×C37—41no—
112C2×D4×C37—41no—
113C2×D4×C37—41no—
114C22×C4×C37—24no—
115C22×C4×C37—24no—
116C22×C4×C37—24no—
117C22×C4×C37—21no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—22no—
123C22×C4×C37—22no—
124C22×C4×C37—21no—
125C22×C4×C37—42no—
126C22×C4×C37—42no—
127C22×C4×C37—42no—
128C22×C4×C37—42no—
129C22×C4×C37—42no—
130C22×C4×C37—42no—
131C22×C4×C37—42no—
132C22×C4×C37—42no—
133C22×C4×C37—42no—
134C22×C4×C37—42no—
135C22×C4×C37—42no—
136C22×C4×C37—41no—
137C22×C4×C37—41no—
138C22×C4×C37—41no—
139C22×C4×C37—41no—
140C22×C4×C37C2×D411yescharacteristic
141C22×C4×C37C2×D411yescharacteristic
142C22×C4×C37C2×D411yescharacteristic
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37#4111yescharacteristic
146SD16×C37—82no—
147C2×C8×C37—22no—
148C2×C8×C37—42no—
149C2×C8×C37—42no—
150C2×C8×C37—41no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—42no—
156C4⋊C4×C37—42no—
157C4⋊C4×C37—44no—
158C4⋊C4×C37—41no—
159C4⋊C4×C37—41no—
160C22⋊C4×C37—44no—
161C22⋊C4×C37—44no—
162C22⋊C4×C37—44no—
163C22⋊C4×C37—44no—
164C22⋊C4×C37—41no—
165C22⋊C4×C37—41no—
166C22⋊C4×C37—41no—
167C22⋊C4×C37—41no—
168C22⋊C4×C37—41no—
169C22⋊C4×C37—41no—
170C22⋊C4×C37—41no—
171C22⋊C4×C37—41no—
172C23×C37—22no—
173C23×C37—22no—
174C23×C37—22no—
175C23×C37—22no—
176C23×C37—22no—
177C23×C37—22no—
178C23×C37—22no—
179C23×C37—22no—
180C23×C37—22no—
181C23×C37—41no—
182C23×C37—44no—
183C23×C37—41no—
184C23×C37—41no—
185C23×C37—41no—
186C23×C37—41no—
187C23×C37—41no—
188C23×C37—41no—
189C23×C37—41no—
190C23×C37—44no—
191C23×C37—44no—
192C23×C37—44no—
193C23×C37—42no—
194C23×C37—42no—
195C23×C37—41no—
196C23×C37—41no—
197C23×C37—41no—
198C23×C37—41no—
199C23×C37—41no—
200C23×C37—41no—
201C23×C37—41no—
202C23×C37#12011yescharacteristic
203C23×C37#12011yescharacteristic
204C23×C37#12111yescharacteristic
205C23×C37C2×SD1611yescharacteristic
206C23×C37#13511yescharacteristic
207C23×C37AGL(1,ℤ/8)11yescharacteristic
208C23×C37#13711yescharacteristic
209Q8×C37—42no—
210Q8×C37—81no—
211D4×C37—42no—
212D4×C37—81no—
213D4×C37—88no—
214D4×C37—81no—
215D4×C37—81no—
216D4×C37—81no—
217D4×C37—81no—
218C2×C4×C37—22no—
219C2×C4×C37—22no—
220C2×C4×C37—22no—
221C2×C4×C37—22no—
222C2×C4×C37—22no—
223C2×C4×C37—22no—
224C2×C4×C37—41no—
225C2×C4×C37—41no—
226C2×C4×C37—41no—
227C2×C4×C37—44no—
228C2×C4×C37—44no—
229C2×C4×C37—44no—
230C2×C4×C37—41no—
231C2×C4×C37—41no—
232C2×C4×C37—41no—
233C2×C4×C37—41no—
234C2×C4×C37—44no—
235C2×C4×C37—42no—
236C2×C4×C37—42no—
237C2×C4×C37—42no—
238C2×C4×C37—42no—
239C2×C4×C37—42no—
240C2×C4×C37—42no—
241C2×C4×C37—41no—
242C2×C4×C37—41no—
243C2×C4×C37—41no—
244C2×C4×C37—42no—
245C2×C4×C37—42no—
246C2×C4×C37—41no—
247C2×C4×C37—41no—
248C2×C4×C37#12011yescharacteristic
249C2×C4×C37#12111yescharacteristic
250C2×C4×C37#12111yescharacteristic
251C2×C4×C37#12711yescharacteristic
252C8×C37—42no—
253C8×C37—81no—
254#10322C3711yesmaximal, characteristic, direct product factor, Sylow
255C22×C37—21no—
256C22×C37—21no—
257C22×C37—21no—
258C22×C37—21no—
259C22×C37—21no—
260C22×C37—21no—
261C22×C37—24no—
262C22×C37—24no—
263C22×C37—24no—
264C22×C37—41no—
265C22×C37—41no—
266C22×C37—41no—
267C22×C37—41no—
268C22×C37—42no—
269C22×C37—42no—
270C22×C37—42no—
271C22×C37—42no—
272C22×C37—42no—
273C22×C37—42no—
274C22×C37—42no—
275C22×C37—42no—
276C22×C37—42no—
277C22×C37—42no—
278C22×C37—42no—
279C22×C37—42no—
280C22×C37—82no—
281C22×C37—82no—
282C22×C37—81no—
283C22×C37—81no—
284C22×C37—81no—
285C22×C37#39211yescharacteristic
286C22×C37#44811yescharacteristic
287C22×C37#44911yescharacteristic
288C22×C37#45011yescharacteristic
289C22×C37#45211yescharacteristic
290C22×C37#46511yescharacteristic
291C22×C37#46811yescharacteristic
292C4×C37—21no—
293C4×C37—21no—
294C4×C37—21no—
295C4×C37—42no—
296C4×C37—82no—
297C4×C37—82no—
298C4×C37—81no—
299C4×C37—81no—
300C4×C37—81no—
301C4×C37B(4,𝔽2)12yes—
302#3187C2×C3711yescharacteristic, complemented
303#2848C2×C3711yescharacteristic, complemented
304#2847C2×C3711yescharacteristic
305#1779C2×C3711yescharacteristic, complemented
306#1520C2×C3711yescharacteristic, complemented
307#1519C2×C3711yescharacteristic, complemented
308#1289C2×C3711yescharacteristic, complemented
309C2×C37—21no—
310C2×C37—21no—
311C2×C37—21no—
312C2×C37—21no—
313C2×C37—21no—
314C2×C37—21no—
315C2×C37—44no—
316C2×C37—161no—
317C2×C37#200011yescharacteristic
318C2×C37#201011yescharacteristic
319C2×C37#202111yescharacteristic
320C24×C4C22×C3711yescharacteristic
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8C22×C3711yescharacteristic
323C2×#121—21no—
324C2×#121C22×C3711yescharacteristic
325C2×#120—21no—
326#483—21no—
327#481—21no—
328#465—22no—
329#450—21no—
330#448—21no—
331C2×C22⋊C8—22no—
332C2×C22⋊C8C22×C3711yescharacteristic
333C2×C22⋊C8C22×C3711yescharacteristic
334#386—21no—
335#386—22no—
336#385—21no—
337#385—22no—
338#380—21no—
339#380—21no—
340#380C22×C3711yescharacteristic
341#380C22×C3711yescharacteristic
342#379—21no—
343#328—22no—
344#327—22no—
345C37#1032211yescharacteristic, direct product factor, Sylow
346C25D4×C3711yescharacteristic
347C22×Q8D4×C3711yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C3711yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C3711yescharacteristic
359C23×C4C23×C3711yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C3712yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C3711yescharacteristic
380C2×C4⋊C4D4×C3711yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C3712yes—
400#95D4×C3712yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C3712yescomplemented
411C24C2×D4×C3711yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C3711yescharacteristic
454C22×C4C2×D4×C3711yescharacteristic
455C22×C4C2×D4×C3711yescharacteristic
456C22×C4C2×D4×C3711yescharacteristic
457C22×C4C2×D4×C3711yescharacteristic
458C22×C4#41×C3711yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C3711yescharacteristic
516C23#120×C3711yescharacteristic
517C23#121×C3711yescharacteristic
518C23C2×SD16×C3711yescharacteristic
519C23#135×C3711yescharacteristic
520C23AGL(1,ℤ/8)×C3711yescharacteristic
521C23#137×C3711yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C3711yescharacteristic
562C2×C4#121×C3711yescharacteristic
563C2×C4#121×C3711yescharacteristic
564C2×C4#127×C3711yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C37×#39211yescharacteristic
598C22C37×#44811yescharacteristic
599C22C37×#44911yescharacteristic
600C22C37×#45011yescharacteristic
601C22C37×#45211yescharacteristic
602C22C37×#46511yescharacteristic
603C22C37×#46811yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C37×B(4,𝔽2)12yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2C37×#200011yescharacteristic
623C2C37×#201011yescharacteristic
624C2C37×#202111yescharacteristic
subgroupG/H
center, socleC22×C37#392
commutator, Frattini, cosocleC23×C4C23×C37
prime radicalC37×#2847C2
LCSG ▷ C23×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×#3187C2semidirect
2. C37×#2848C2semidirect
4. C37×#1779C2semidirect
5. C37×#1520C2semidirect
6. C37×#1519C2semidirect
7. C37×#1289C2semidirect
34. C22×Q8×C37D4semidirect
49. C22×C8×C37D4semidirect
67. C2×C4⋊C4×C37D4semidirect
87. #95×C37D4semidirect
97. C24×C37SD16semidirect
254. #10322C37direct (N × H)
302. #3187C2×C37semidirect
303. #2848C2×C37semidirect
305. #1779C2×C37semidirect
306. #1520C2×C37semidirect
307. #1519C2×C37semidirect
308. #1289C2×C37semidirect
345. C37#10322direct (N × H)
347. C22×Q8D4×C37semidirect
362. C22×C8D4×C37semidirect
380. C2×C4⋊C4D4×C37semidirect
400. #95D4×C37semidirect
410. C24SD16×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#31872
C37×#28482
C37×#28472
C37×#17792
C37×#15202
C37×#15192
C37×#12892
#1032237