Finite Group Databasebeta

← C37×#9520 #22630773

Subgroups — C37×#9520 #22630773

Order 9472.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3003C211yesmaximal, characteristic
2C37×#2976C211yesmaximal, characteristic, complemented
3C37×#1786C211yesmaximal, characteristic, complemented
4C37×#1783C211yesmaximal, characteristic, complemented
5C37×#1513C211yesmaximal, characteristic, complemented
6C37×#1305C211yesmaximal, characteristic, complemented
7C37×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C37C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C37—21no—
10C37×#525C2211yescharacteristic
11C37×#450—21no—
12C37×#450C412yescomplemented
13C37×#447—21no—
14C37×#447C412yescomplemented
15C37×#436—21no—
16C37×#435—21no—
17C37×#435—21no—
18C8×D4×C37—21no—
19C37×#433—21no—
20C37×#418—21no—
21C2×#102×C37—21no—
22C2×#102×C37—21no—
23C2×#100×C37—21no—
24C2×#100×C37—21no—
25C37×#408—21no—
26C37×#407C2211yescharacteristic
27C37×#407C2211yescharacteristic
28C37×#407C2211yescharacteristic
29C2×C22⋊C8×C37C2211yescharacteristic
30C37×#380C2211yescharacteristic
31C37×#328—21no—
32C37×#327—21no—
33C25×C37—21no—
34C2×#41×C37D411yescharacteristic
35C22×D4×C37—21no—
36C22×D4×C37—21no—
37C22×D4×C37—21no—
38C22×D4×C37—21no—
39C22×D4×C37—21no—
40C22×D4×C37—42no—
41C22×D4×C37—42no—
42C22×D4×C37C2×C412yes—
43C23×C4×C37C2311yescharacteristic
44AGL(1,ℤ/8)×C37—42no—
45AGL(1,ℤ/8)×C37—42no—
46C2×SD16×C37—22no—
47C2×D8×C37—22no—
48C2×M16×C37—21no—
49C2×M16×C37—21no—
50C2×M16×C37—21no—
51C2×M16×C37D411yescharacteristic
52C2×M16×C37D411yescharacteristic
53C22×C8×C37—21no—
54C22×C8×C37D411yescharacteristic
55C22×C8×C37D411yescharacteristic
56#123×C37—21no—
57C22⋊Q8×C37C2×C411yescharacteristic
58C22⋊Q8×C37D411yescharacteristic
59#121×C37C2×C411yescharacteristic
60#121×C37D411yescharacteristic
61#120×C37—21no—
62C4×D4×C37—21no—
63C4×D4×C37—21no—
64#117×C37D411yescharacteristic
65C2×C4⋊C4×C37—21no—
66C2×C22⋊C4×C37—21no—
67C4⋊C8×C37—21no—
68C4⋊C8×C37—21no—
69#102×C37—22no—
70#102×C37—22no—
71#102×C37—42no—
72#102×C37—42no—
73#100×C37—42no—
74#100×C37—42no—
75C22⋊C8×C37—21no—
76C22⋊C8×C37—21no—
77C22⋊C8×C37—21no—
78C22⋊C8×C37—21no—
79C22⋊C8×C37—21no—
80C22⋊C8×C37—21no—
81C22⋊C8×C37—21no—
82C22⋊C8×C37—21no—
83C22⋊C8×C37—21no—
84C22⋊C8×C37C2×C412yes—
85#97×C37—21no—
86C4×C8×C37—21no—
87#95×C37—21no—
88C24×C37—22no—
89C24×C37—44no—
90C24×C37—41no—
91C24×C37—41no—
92C24×C37—81no—
93C24×C37—81no—
94C24×C37—82no—
95C24×C37#4111yescharacteristic
96#41×C37—41no—
97#41×C37—41no—
98C2×Q8×C37C22⋊C411yescharacteristic
99C2×D4×C37—22no—
100C2×D4×C37—22no—
101C2×D4×C37—22no—
102C2×D4×C37—22no—
103C2×D4×C37—22no—
104C2×D4×C37—22no—
105C2×D4×C37—21no—
106C2×D4×C37—21no—
107C2×D4×C37—21no—
108C2×D4×C37—22no—
109C2×D4×C37—22no—
110C2×D4×C37—41no—
111C2×D4×C37—41no—
112C2×D4×C37—41no—
113C2×D4×C37—41no—
114C2×D4×C37—41no—
115C2×D4×C37—41no—
116C2×D4×C37—44no—
117C2×D4×C37—44no—
118C2×D4×C37—44no—
119C2×D4×C37—41no—
120C2×D4×C37—41no—
121C2×D4×C37C22⋊C411yescharacteristic
122C22×C4×C37—21no—
123C22×C4×C37—41no—
124C22×C4×C37—41no—
125C22×C4×C37—41no—
126C22×C4×C37C22×C411yescharacteristic
127C22×C4×C37C2×D411yescharacteristic
128C22×C4×C37C2×D411yescharacteristic
129C22×C4×C37C2×D411yescharacteristic
130C22×C4×C37C2×D411yescharacteristic
131C22×C4×C37#4111yescharacteristic
132SD16×C37—44no—
133D8×C37—44no—
134M16×C37—41no—
135M16×C37—41no—
136M16×C37—41no—
137M16×C37—41no—
138M16×C37—41no—
139M16×C37—41no—
140M16×C37—81no—
141C2×C8×C37—22no—
142C2×C8×C37—21no—
143C2×C8×C37—21no—
144C2×C8×C37—21no—
145C2×C8×C37—21no—
146C2×C8×C37—41no—
147C2×C8×C37—41no—
148C2×C8×C37—41no—
149C2×C8×C37—81no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—41no—
153C4⋊C4×C37—41no—
154C4⋊C4×C37C22⋊C411yescharacteristic
155C4⋊C4×C37C22⋊C411yescharacteristic
156C22⋊C4×C37—21no—
157C22⋊C4×C37—21no—
158C22⋊C4×C37—21no—
159C22⋊C4×C37—21no—
160C22⋊C4×C37—21no—
161C22⋊C4×C37—81no—
162C42×C37—21no—
163C23×C37—21no—
164C23×C37—21no—
165C23×C37—24no—
166C23×C37—21no—
167C23×C37—41no—
168C23×C37—41no—
169C23×C37—42no—
170C23×C37—42no—
171C23×C37—42no—
172C23×C37—42no—
173C23×C37—42no—
174C23×C37—42no—
175C23×C37—82no—
176C23×C37—82no—
177C23×C37—82no—
178C23×C37—81no—
179C23×C37—81no—
180C23×C37—82no—
181C23×C37—88no—
182C23×C37—88no—
183C23×C37—81no—
184C23×C37—81no—
185C23×C37C4×D411yescharacteristic
186C23×C37#12111yescharacteristic
187C23×C37#12311yescharacteristic
188Q8×C37—41no—
189D4×C37—24no—
190D4×C37—24no—
191D4×C37—41no—
192D4×C37—42no—
193D4×C37—42no—
194D4×C37—42no—
195D4×C37—42no—
196D4×C37—41no—
197D4×C37—41no—
198D4×C37—42no—
199D4×C37—42no—
200D4×C37—81no—
201D4×C37—81no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—21no—
205C2×C4×C37—21no—
206C2×C4×C37—21no—
207C2×C4×C37—21no—
208C2×C4×C37—21no—
209C2×C4×C37—21no—
210C2×C4×C37—21no—
211C2×C4×C37—41no—
212C2×C4×C37—41no—
213C2×C4×C37—41no—
214C2×C4×C37—41no—
215C2×C4×C37—41no—
216C2×C4×C37—81no—
217C2×C4×C37—81no—
218C2×C4×C37—81no—
219C2×C4×C37C2×C22⋊C411yescharacteristic
220C2×C4×C37C4×D411yescharacteristic
221C2×C4×C37#12011yescharacteristic
222C2×C4×C37#12111yescharacteristic
223C8×C37—42no—
224C8×C37—41no—
225C8×C37—41no—
226C8×C37—41no—
227C8×C37—41no—
228C8×C37—81no—
229#9520C3711yesmaximal, characteristic, direct product factor, Sylow
230C22×C37—21no—
231C22×C37—21no—
232C22×C37—21no—
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—21no—
236C22×C37—21no—
237C22×C37—21no—
238C22×C37—42no—
239C22×C37—42no—
240C22×C37—41no—
241C22×C37—44no—
242C22×C37—41no—
243C22×C37—41no—
244C22×C37—82no—
245C22×C37—82no—
246C22×C37—82no—
247C22×C37—82no—
248C22×C37—84no—
249C22×C37—84no—
250C22×C37—84no—
251C22×C37—84no—
252C22×C37—82no—
253C22×C37—82no—
254C22×C37#38611yescharacteristic
255C22×C37#47111yescharacteristic
256C22×C37#47211yescharacteristic
257C4×C37—21no—
258C4×C37—21no—
259C4×C37—21no—
260C4×C37—41no—
261C4×C37—41no—
262C4×C37—41no—
263C4×C37—161no—
264C4×C37B(4,𝔽2)11yescharacteristic
265C4×C37B(4,𝔽2)11yescharacteristic
266#3003C2×C3711yescharacteristic
267#2976C2×C3711yescharacteristic, complemented
268#1786C2×C3711yescharacteristic, complemented
269#1783C2×C3711yescharacteristic, complemented
270#1513C2×C3711yescharacteristic, complemented
271#1305C2×C3711yescharacteristic, complemented
272#1293C2×C3711yescharacteristic, complemented
273C2×C37—21no—
274C2×C37—21no—
275C2×C37—41no—
276C2×C37—41no—
277C2×C37—81no—
278C2×C37—84no—
279C2×C37#188911yescharacteristic
280C2×C37#190311yescharacteristic
281C2×C37#190711yescharacteristic
282C23×D4C22×C3711yescharacteristic
283C2×AGL(1,ℤ/8)—21no—
284#525C22×C3711yescharacteristic
285#450—21no—
286#450C4×C3712yescomplemented
287#447—21no—
288#447C4×C3712yescomplemented
289#436—21no—
290#435—21no—
291#435—21no—
292C8×D4—21no—
293#433—21no—
294#418—21no—
295C2×#102—21no—
296C2×#102—21no—
297C2×#100—21no—
298C2×#100—21no—
299#408—21no—
300#407C22×C3711yescharacteristic
301#407C22×C3711yescharacteristic
302#407C22×C3711yescharacteristic
303C2×C22⋊C8C22×C3711yescharacteristic
304#380C22×C3711yescharacteristic
305#328—21no—
306#327—21no—
307C37#952011yescharacteristic, direct product factor, Sylow
308C25—21no—
309C2×#41D4×C3711yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C3712yes—
318C23×C4C23×C3711yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C3711yescharacteristic
327C2×M16D4×C3711yescharacteristic
328C22×C8—21no—
329C22×C8D4×C3711yescharacteristic
330C22×C8D4×C3711yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C3711yescharacteristic
333C22⋊Q8D4×C3711yescharacteristic
334#121C2×C4×C3711yescharacteristic
335#121D4×C3711yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C3711yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C3712yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C3711yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C3711yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C3711yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C3711yescharacteristic
402C22×C4C2×D4×C3711yescharacteristic
403C22×C4C2×D4×C3711yescharacteristic
404C22×C4C2×D4×C3711yescharacteristic
405C22×C4C2×D4×C3711yescharacteristic
406C22×C4#41×C3711yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C3711yescharacteristic
430C4⋊C4C22⋊C4×C3711yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C3711yescharacteristic
461C23#121×C3711yescharacteristic
462C23#123×C3711yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C3711yescharacteristic
495C2×C4C4×D4×C3711yescharacteristic
496C2×C4#120×C3711yescharacteristic
497C2×C4#121×C3711yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C37×#38611yescharacteristic
529C22C37×#47111yescharacteristic
530C22C37×#47211yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4C37×B(4,𝔽2)11yescharacteristic
539C4C37×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C37×#188911yescharacteristic
547C2C37×#190311yescharacteristic
548C2C37×#190711yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC37×#3003C2
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
2. C37×#2976C2semidirect
3. C37×#1786C2semidirect
4. C37×#1783C2semidirect
5. C37×#1513C2semidirect
6. C37×#1305C2semidirect
7. C37×#1293C2semidirect
12. C37×#450C4semidirect
14. C37×#447C4semidirect
229. #9520C37direct (N × H)
267. #2976C2×C37semidirect
268. #1786C2×C37semidirect
269. #1783C2×C37semidirect
270. #1513C2×C37semidirect
271. #1305C2×C37semidirect
272. #1293C2×C37semidirect
286. #450C4×C37semidirect
288. #447C4×C37semidirect
307. C37#9520direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#30032
C37×#29762
C37×#17862
C37×#17832
C37×#15132
C37×#13052
C37×#12932
#952037