Finite Group Databasebeta

← C37×#24709 #22645962

Subgroups — C37×#24709 #22645962

Order 9472.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#474C211yesmaximal, characteristic, complemented
2C2×C37×#432C211yesmaximal, characteristic, complemented
3C37×#2857C211yesmaximal, characteristic, complemented
4C4×#121×C37C211yesmaximal, characteristic
5C37×#2076C212yesmaximal, complemented
6C37×#2034C212yesmaximal
7C37×#1988C211yesmaximal, characteristic, complemented
8C37×#1948C211yesmaximal, characteristic, complemented
9C37×#1944C212yesmaximal, complemented
10C37×#1936C212yesmaximal, complemented
11C37×#1802C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C37C2211yescharacteristic
13C2×C22⋊Q8×C37—21no—
14C2×#121×C37C2211yescharacteristic
15C2×C4×D4×C37—21no—
16C2×C4×D4×C37C2211yescharacteristic
17C22×C42×C37C2211yescharacteristic
18C37×#474—24no—
19C37×#432—24no—
20C2×#107×C37C2212yes—
21C2×#106×C37C2212yes—
22C2×C4⋊C8×C37C2211yescharacteristic
23C2×C4⋊C8×C37C2211yescharacteristic
24C2×#102×C37C2212yes—
25C2×#102×C37C2212yes—
26C2×C22⋊C8×C37C2212yes—
27C2×#97×C37C2212yes—
28C37×#391—21no—
29C37×#390C2211yescharacteristic
30C37×#389—21no—
31C37×#389C2212yes—
32C37×#389C2211yescharacteristic
33C37×#388—21no—
34C37×#386—21no—
35C37×#384C2211yescharacteristic
36C37×#380—21no—
37C37×#380C2212yes—
38C37×#380C2211yescharacteristic
39C4×C4⋊C4×C37C2211yescharacteristic
40C4×C22⋊C4×C37—21no—
41C37×#340C2212yes—
42C37×#340C2212yes—
43C37×#340C2212yes—
44C37×#340C2212yes—
45C22×Q8×C37—21no—
46C22×D4×C37—21no—
47C22×D4×C37C2311yescharacteristic
48C23×C4×C37—21no—
49C23×C4×C37D411yescharacteristic
50C23×C4×C37D411yescharacteristic
51C23×C4×C37C2311yescharacteristic
52C22×C8×C37C2312yes—
53C22×C8×C37C2312yes—
54C4⋊Q8×C37—22no—
55C4⋊Q8×C37—22no—
56C22⋊Q8×C37—44no—
57#121×C37—22no—
58#121×C37—22no—
59C4×D4×C37—22no—
60C4×D4×C37—22no—
61C4×D4×C37—44no—
62C2×C4⋊C4×C37—21no—
63C2×C4⋊C4×C37—22no—
64C2×C4⋊C4×C37—21no—
65C2×C4⋊C4×C37—21no—
66C2×C4⋊C4×C37—21no—
67C2×C4⋊C4×C37C2312yes—
68C2×C4⋊C4×C37C2311yescharacteristic
69C2×C4⋊C4×C37C2312yes—
70C2×C4⋊C4×C37C2311yescharacteristic
71C2×C4⋊C4×C37C2311yescharacteristic
72C2×C22⋊C4×C37—21no—
73C2×C22⋊C4×C37—22no—
74C2×C22⋊C4×C37—21no—
75C2×C22⋊C4×C37—21no—
76C2×C22⋊C4×C37—21no—
77C2×C22⋊C4×C37—21no—
78C2×C42×C37—22no—
79C2×C42×C37—22no—
80C2×C42×C37—21no—
81C2×C42×C37D411yescharacteristic
82C2×C42×C37D411yescharacteristic
83C2×C42×C37C2311yescharacteristic
84C2×C42×C37C2311yescharacteristic
85#107×C37—24no—
86#106×C37—24no—
87C4⋊C8×C37—22no—
88C4⋊C8×C37D414yescomplemented
89#102×C37—24no—
90#102×C37—24no—
91C22⋊C8×C37—24no—
92#97×C37—24no—
93#95×C37—21no—
94#95×C37—21no—
95#95×C37—21no—
96#95×C37—22no—
97#95×C37—22no—
98C24×C37—21no—
99C24×C37C2×D411yescharacteristic
100C2×Q8×C37—42no—
101C2×Q8×C37—42no—
102C2×Q8×C37—42no—
103C2×D4×C37—24no—
104C2×D4×C37—21no—
105C2×D4×C37—21no—
106C2×D4×C37—21no—
107C2×D4×C37—21no—
108C2×D4×C37—21no—
109C2×D4×C37—42no—
110C2×D4×C37—42no—
111C2×D4×C37#4112yes—
112C22×C4×C37—22no—
113C22×C4×C37—21no—
114C22×C4×C37—22no—
115C22×C4×C37—22no—
116C22×C4×C37—22no—
117C22×C4×C37—22no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—22no—
127C22×C4×C37—22no—
128C22×C4×C37—41no—
129C22×C4×C37—42no—
130C22×C4×C37—42no—
131C22×C4×C37—42no—
132C22×C4×C37C2×D411yescharacteristic
133C22×C4×C37C2×D411yescharacteristic
134C22×C4×C37C2×D411yescharacteristic
135C22×C4×C37C2×D411yescharacteristic
136C22×C4×C37C2×D411yescharacteristic
137C22×C4×C37C2411yescharacteristic
138C2×C8×C37—22no—
139C2×C8×C37—22no—
140C2×C8×C37—22no—
141C2×C8×C37—22no—
142C2×C8×C37—22no—
143C2×C8×C37C2×D414yes—
144C4⋊C4×C37—21no—
145C4⋊C4×C37—22no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—22no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—22no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—42no—
154C4⋊C4×C37—42no—
155C4⋊C4×C37—44no—
156C4⋊C4×C37—42no—
157C4⋊C4×C37—42no—
158C4⋊C4×C37#4112yes—
159C22⋊C4×C37—24no—
160C22⋊C4×C37—42no—
161C22⋊C4×C37—42no—
162C22⋊C4×C37—42no—
163C22⋊C4×C37—44no—
164C22⋊C4×C37—42no—
165C42×C37—22no—
166C42×C37—22no—
167C42×C37—21no—
168C42×C37—21no—
169C42×C37—42no—
170C42×C37C2×D412yes—
171C42×C37#4112yes—
172C23×C37—21no—
173C23×C37—21no—
174C23×C37—21no—
175C23×C37—21no—
176C23×C37—21no—
177C23×C37—21no—
178C23×C37—22no—
179C23×C37—41no—
180C23×C37—41no—
181C23×C37—41no—
182C23×C37—41no—
183C23×C37—41no—
184C23×C37—41no—
185C23×C37#13712yes—
186C23×C37C22×D411yescharacteristic
187Q8×C37—84no—
188D4×C37—22no—
189D4×C37—22no—
190D4×C37—48no—
191D4×C37—41no—
192D4×C37—41no—
193C2×C4×C37—21no—
194C2×C4×C37—21no—
195C2×C4×C37—21no—
196C2×C4×C37—21no—
197C2×C4×C37—21no—
198C2×C4×C37—21no—
199C2×C4×C37—22no—
200C2×C4×C37—21no—
201C2×C4×C37—21no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—21no—
205C2×C4×C37—44no—
206C2×C4×C37—41no—
207C2×C4×C37—41no—
208C2×C4×C37—41no—
209C2×C4×C37—41no—
210C2×C4×C37—41no—
211C2×C4×C37—41no—
212C2×C4×C37—44no—
213C2×C4×C37—41no—
214C2×C4×C37—42no—
215C2×C4×C37—42no—
216C2×C4×C37—41no—
217C2×C4×C37—41no—
218C2×C4×C37—42no—
219C2×C4×C37—41no—
220C2×C4×C37—42no—
221C2×C4×C37—41no—
222C2×C4×C37—42no—
223C2×C4×C37—41no—
224C2×C4×C37—42no—
225C2×C4×C37—84no—
226C2×C4×C37#12112yes—
227C2×C4×C37#12112yes—
228C2×C4×C37AGL(1,ℤ/8)12yes—
229C2×C4×C37AGL(1,ℤ/8)12yes—
230C2×C4×C37C22×D411yescharacteristic
231C2×C4×C37C2×#4111yescharacteristic
232C2×C4×C37C2×#4111yescharacteristic
233C2×C4×C37C2×#4111yescharacteristic
234C2×C4×C372−1+411yescharacteristic
235C2×C4×C372−1+411yescharacteristic
236C8×C37—24no—
237C8×C37—42no—
238#24709C3711yesmaximal, characteristic, direct product factor, Sylow
239C22×C37—22no—
240C22×C37—22no—
241C22×C37—22no—
242C22×C37—41no—
243C22×C37—41no—
244C22×C37—41no—
245C22×C37—41no—
246C22×C37—42no—
247C22×C37—42no—
248C22×C37—42no—
249C22×C37—81no—
250C22×C37—81no—
251C22×C37—81no—
252C22×C37—81no—
253C22×C37C2×#12111yescharacteristic
254C22×C37#52511yescharacteristic
255C22×C37#53611yescharacteristic
256C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C37C2×#13711yescharacteristic
259C22×C37#57511yescharacteristic
260C4×C37—22no—
261C4×C37—42no—
262C4×C37—41no—
263C4×C37—41no—
264C4×C37—41no—
265C4×C37—82no—
266C4×C37—81no—
267C4×C37—81no—
268C4×C37—82no—
269C4×C37#46914yes—
270C4×C37#54711yescharacteristic
271C4×C37#54811yescharacteristic
272C4×C37#55211yescharacteristic
273C4×C37#55611yescharacteristic
274C2×#474C2×C3711yescharacteristic, complemented
275C2×#432C2×C3711yescharacteristic, complemented
276#2857C2×C3711yescharacteristic, complemented
277C4×#121C2×C3711yescharacteristic
278#2076C2×C3712yescomplemented
279#2034C2×C3712yes—
280#1988C2×C3711yescharacteristic, complemented
281#1948C2×C3711yescharacteristic, complemented
282#1944C2×C3712yescomplemented
283#1936C2×C3712yescomplemented
284#1802C2×C3711yescharacteristic, complemented
285C2×C37—42no—
286C2×C37—82no—
287C2×C37#241511yescharacteristic
288C2×C37C2×#46911yescharacteristic
289C2×C37#305611yescharacteristic
290C2×C37#311011yescharacteristic
291C2×C37#311511yescharacteristic
292C2×C37#323511yescharacteristic
293C2×C37#323911yescharacteristic
294C2×C4⋊Q8C22×C3711yescharacteristic
295C2×C22⋊Q8—21no—
296C2×#121C22×C3711yescharacteristic
297C2×C4×D4—21no—
298C2×C4×D4C22×C3711yescharacteristic
299C22×C42C22×C3711yescharacteristic
300#474—24no—
301#432—24no—
302C2×#107C22×C3712yes—
303C2×#106C22×C3712yes—
304C2×C4⋊C8C22×C3711yescharacteristic
305C2×C4⋊C8C22×C3711yescharacteristic
306C2×#102C22×C3712yes—
307C2×#102C22×C3712yes—
308C2×C22⋊C8C22×C3712yes—
309C2×#97C22×C3712yes—
310#391—21no—
311#390C22×C3711yescharacteristic
312#389—21no—
313#389C22×C3712yes—
314#389C22×C3711yescharacteristic
315#388—21no—
316#386—21no—
317#384C22×C3711yescharacteristic
318#380—21no—
319#380C22×C3711yescharacteristic
320#380C22×C3712yes—
321C4×C4⋊C4C22×C3711yescharacteristic
322C4×C22⋊C4—21no—
323#340C22×C3712yes—
324#340C22×C3712yes—
325#340C22×C3712yes—
326#340C22×C3712yes—
327C37#2470911yescharacteristic, direct product factor, Sylow
328C22×Q8—21no—
329C22×D4—21no—
330C22×D4C23×C3711yescharacteristic
331C23×C4—21no—
332C23×C4D4×C3711yescharacteristic
333C23×C4D4×C3711yescharacteristic
334C23×C4C23×C3711yescharacteristic
335C22×C8C23×C3712yes—
336C22×C8C23×C3712yes—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C22⋊Q8—44no—
340#121—22no—
341#121—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—44no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4C23×C3711yescharacteristic
351C2×C4⋊C4C23×C3712yes—
352C2×C4⋊C4C23×C3711yescharacteristic
353C2×C4⋊C4C23×C3712yes—
354C2×C4⋊C4C23×C3711yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—21no—
364C2×C42D4×C3711yescharacteristic
365C2×C42D4×C3711yescharacteristic
366C2×C42C23×C3711yescharacteristic
367C2×C42C23×C3711yescharacteristic
368#107—24no—
369#106—24no—
370C4⋊C8—22no—
371C4⋊C8D4×C3714yescomplemented
372#102—24no—
373#102—24no—
374C22⋊C8—24no—
375#97—24no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—22no—
380#95—22no—
381C24—21no—
382C24C2×D4×C3711yescharacteristic
383C2×Q8—42no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×D4—24no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4#41×C3712yes—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—41no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4C2×D4×C3711yescharacteristic
416C22×C4C2×D4×C3711yescharacteristic
417C22×C4C2×D4×C3711yescharacteristic
418C22×C4C2×D4×C3711yescharacteristic
419C22×C4C2×D4×C3711yescharacteristic
420C22×C4C24×C3711yescharacteristic
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8C2×D4×C3714yes—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—42no—
437C4⋊C4—42no—
438C4⋊C4—44no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4#41×C3712yes—
442C22⋊C4—24no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—44no—
447C22⋊C4—42no—
448C42—22no—
449C42—22no—
450C42—21no—
451C42—21no—
452C42—42no—
453C42C2×D4×C3712yes—
454C42#41×C3712yes—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23#137×C3712yes—
469C23C22×D4×C3711yescharacteristic
470Q8—84no—
471D4—22no—
472D4—22no—
473D4—48no—
474D4—41no—
475D4—41no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4#121×C3712yes—
510C2×C4#121×C3712yes—
511C2×C4AGL(1,ℤ/8)×C3712yes—
512C2×C4AGL(1,ℤ/8)×C3712yes—
513C2×C4C22×D4×C3711yescharacteristic
514C2×C4C2×#41×C3711yescharacteristic
515C2×C4C2×#41×C3711yescharacteristic
516C2×C4C2×#41×C3711yescharacteristic
517C2×C42−1+4×C3711yescharacteristic
518C2×C42−1+4×C3711yescharacteristic
519C8—24no—
520C8—42no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22C2×#121×C3711yescharacteristic
536C22C37×#52511yescharacteristic
537C22C37×#53611yescharacteristic
538C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
539C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
540C22C2×#137×C3711yescharacteristic
541C22C37×#57511yescharacteristic
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—81no—
548C4—81no—
549C4—82no—
550C4—82no—
551C4C37×#46914yes—
552C4C37×#54711yescharacteristic
553C4C37×#54811yescharacteristic
554C4C37×#55211yescharacteristic
555C4C37×#55611yescharacteristic
556C2—42no—
557C2—82no—
558C2C37×#241511yescharacteristic
559C2C2×C37×#46911yescharacteristic
560C2C37×#305611yescharacteristic
561C2C37×#311011yescharacteristic
562C2C37×#311511yescharacteristic
563C2C37×#323511yescharacteristic
564C2C37×#323911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#474C2semidirect
2. C2×C37×#432C2semidirect
3. C37×#2857C2semidirect
5. C37×#2076C2semidirect
7. C37×#1988C2semidirect
8. C37×#1948C2semidirect
9. C37×#1944C2semidirect
10. C37×#1936C2semidirect
11. C37×#1802C2semidirect
88. C4⋊C8×C37D4semidirect
238. #24709C37direct (N × H)
274. C2×#474C2×C37semidirect
275. C2×#432C2×C37semidirect
276. #2857C2×C37semidirect
278. #2076C2×C37semidirect
280. #1988C2×C37semidirect
281. #1948C2×C37semidirect
282. #1944C2×C37semidirect
283. #1936C2×C37semidirect
284. #1802C2×C37semidirect
327. C37#24709direct (N × H)
371. C4⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4742
C2×C37×#4322
C37×#28572
C4×#121×C372
C37×#20762
C37×#20342
C37×#19882
C37×#19482
C37×#19442
C37×#19362
C37×#18022
#2470937