Finite Group Databasebeta

← C37×#28636 #22649889

Subgroups — C37×#28636 #22649889

Order 9472.

780 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3153C211yesmaximal, characteristic
2C37×#3141C211yesmaximal, characteristic, complemented
3C2×C37×#489C211yesmaximal, characteristic, complemented
4C37×#2932C211yesmaximal, characteristic, complemented
5C37×#2052C212yesmaximal, complemented
6C37×#2051C212yesmaximal, complemented
7C37×#1997C211yesmaximal, characteristic, complemented
8C37×#1967C211yesmaximal, characteristic, complemented
9C37×#1908C212yesmaximal, complemented
10C37×#1907C212yesmaximal, complemented
11C37×#1778C211yesmaximal, characteristic, complemented
12C2×#137×C37C2212yes—
13C2×AGL(1,ℤ/8)×C37C2212yes—
14C2×#131×C37C2212yes—
15C37×#532C2211yescharacteristic
16C2×C4⋊Q8×C37C2211yescharacteristic
17C2×#124×C37C2211yescharacteristic
18C37×#497—21no—
19C37×#496—21no—
20C37×#495—22no—
21C37×#489—22no—
22C37×#489—22no—
23C37×#489—22no—
24C37×#487—21no—
25C37×#486—21no—
26C37×#435—22no—
27C37×#435—22no—
28C2×#108×C37C2212yes—
29C37×#423C2211yescharacteristic
30C37×#417C2212yes—
31C37×#417C2212yes—
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#101×C37C2212yes—
37C2×#100×C37C2212yes—
38C37×#408C2212yes—
39C4×M16×C37C2211yescharacteristic
40C4×M16×C37C2211yescharacteristic
41C2×#97×C37C2211yescharacteristic
42C37×#343C2212yes—
43C37×#343C2212yes—
44C37×#341C2212yes—
45C2×#41×C37C2312yes—
46C22×Q8×C37—21no—
47C22×Q8×C37C2311yescharacteristic
48C22×D4×C37C2311yescharacteristic
49#137×C37—24no—
50#137×C37—42no—
51AGL(1,ℤ/8)×C37—24no—
52AGL(1,ℤ/8)×C37—42no—
53C2×Q16×C37—22no—
54C2×SD16×C37—22no—
55C2×SD16×C37—22no—
56C2×D8×C37—22no—
57#131×C37—42no—
58#131×C37—42no—
59C2×M16×C37—22no—
60C2×M16×C37C2312yes—
61C2×M16×C37C2312yes—
62C2×M16×C37C2312yes—
63C22×C8×C37—22no—
64C22×C8×C37C2311yescharacteristic
65C22×C8×C37C2311yescharacteristic
66C4⋊Q8×C37—21no—
67C4⋊Q8×C37—21no—
68C4⋊Q8×C37—21no—
69C4⋊Q8×C37—21no—
70C4⋊Q8×C37D411yescharacteristic
71#127×C37D411yescharacteristic
72#124×C37—21no—
73#124×C37—21no—
74#124×C37—21no—
75#124×C37—21no—
76#124×C37D412yes—
77#121×C37—21no—
78#121×C37—21no—
79C4×D4×C37—21no—
80C4×D4×C37—21no—
81C2×C4⋊C4×C37—21no—
82C2×C4⋊C4×C37C2311yescharacteristic
83C2×C4⋊C4×C37C2311yescharacteristic
84C2×C22⋊C4×C37—21no—
85C2×C22⋊C4×C37—21no—
86C2×C42×C37C2311yescharacteristic
87#108×C37—24no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37—21no—
90#103×C37—22no—
91#103×C37—22no—
92#103×C37—22no—
93#103×C37—22no—
94#102×C37—22no—
95#102×C37—22no—
96#102×C37—22no—
97#102×C37—22no—
98#101×C37—42no—
99#100×C37—42no—
100C22⋊C8×C37—24no—
101#97×C37—21no—
102#97×C37—21no—
103#97×C37D412yes—
104#97×C37D412yes—
105C4×C8×C37—21no—
106C4×C8×C37—21no—
107C24×C37—21no—
108#41×C37—22no—
109#41×C37—22no—
110#41×C37—22no—
111#41×C37—22no—
112C2×Q8×C37—21no—
113C2×Q8×C37—21no—
114C2×Q8×C37—22no—
115C2×Q8×C37—22no—
116C2×Q8×C37—41no—
117C2×Q8×C37—41no—
118C2×Q8×C37—82no—
119C2×Q8×C37C2×D412yes—
120C2×D4×C37—22no—
121C2×D4×C37—21no—
122C2×D4×C37—21no—
123C2×D4×C37—21no—
124C2×D4×C37—21no—
125C2×D4×C37—22no—
126C2×D4×C37—22no—
127C2×D4×C37C2×D412yes—
128C22×C4×C37—22no—
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37#4111yescharacteristic
133C22×C4×C37#4111yescharacteristic
134C22×C4×C37C2411yescharacteristic
135Q16×C37—44no—
136SD16×C37—44no—
137SD16×C37—44no—
138D8×C37—44no—
139M16×C37—22no—
140M16×C37—22no—
141M16×C37—22no—
142M16×C37—22no—
143M16×C37—22no—
144M16×C37—44no—
145M16×C37#4114yes—
146C2×C8×C37—22no—
147C2×C8×C37—22no—
148C2×C8×C37—22no—
149C2×C8×C37—22no—
150C2×C8×C37—22no—
151C2×C8×C37—44no—
152C2×C8×C37C2×D412yes—
153C2×C8×C37C2×D412yes—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—21no—
159C4⋊C4×C37—21no—
160C4⋊C4×C37—41no—
161C4⋊C4×C37—41no—
162C22⋊C4×C37—22no—
163C22⋊C4×C37—22no—
164C22⋊C4×C37—41no—
165C22⋊C4×C37—41no—
166C22⋊C4×C37—41no—
167C22⋊C4×C37—41no—
168C42×C37C2×D411yescharacteristic
169C42×C37C2×D411yescharacteristic
170C42×C37C2×D411yescharacteristic
171C42×C37C2×D411yescharacteristic
172C23×C37—22no—
173C23×C37—41no—
174C23×C37—42no—
175C23×C37—81no—
176C23×C37—81no—
177C23×C37C2×#4111yescharacteristic
178Q8×C37—22no—
179Q8×C37—22no—
180Q8×C37—41no—
181Q8×C37—41no—
182Q8×C37—42no—
183Q8×C37—82no—
184Q8×C37—82no—
185D4×C37—22no—
186D4×C37—22no—
187D4×C37—42no—
188D4×C37—42no—
189D4×C37—41no—
190D4×C37—41no—
191D4×C37—42no—
192D4×C37—81no—
193D4×C37—81no—
194C2×C4×C37—22no—
195C2×C4×C37—41no—
196C2×C4×C37—41no—
197C2×C4×C37—42no—
198C2×C4×C37—42no—
199C2×C4×C37—41no—
200C2×C4×C37—41no—
201C2×C4×C37—41no—
202C2×C4×C37—42no—
203C2×C4×C37—81no—
204C2×C4×C37—81no—
205C2×C4×C37#12111yescharacteristic
206C2×C4×C37#12111yescharacteristic
207C2×C4×C37#12111yescharacteristic
208C2×C4×C37#12111yescharacteristic
209C2×C4×C37C22×D411yescharacteristic
210C2×C4×C37C22×D411yescharacteristic
211C2×C4×C37C2×#4112yes—
212C2×C4×C37H(5,𝔽2)12yes—
213C8×C37—22no—
214C8×C37—22no—
215C8×C37—24no—
216C8×C37—42no—
217C8×C37—42no—
218#28636C3711yesmaximal, characteristic, direct product factor, Sylow
219C22×C37—21no—
220C22×C37—21no—
221C22×C37—42no—
222C22×C37—42no—
223C22×C37—42no—
224C22×C37—81no—
225C22×C37—81no—
226C22×C37—81no—
227C22×C37—162no—
228C22×C37C2×#12111yescharacteristic
229C22×C37#55912yes—
230C4×C37—21no—
231C4×C37—21no—
232C4×C37—21no—
233C4×C37—21no—
234C4×C37—42no—
235C4×C37—81no—
236C4×C37—81no—
237C4×C37—81no—
238C4×C37#53211yescharacteristic
239C4×C37#53511yescharacteristic
240C4×C37#54612yes—
241#3153C2×C3711yescharacteristic
242#3141C2×C3711yescharacteristic, complemented
243C2×#489C2×C3711yescharacteristic, complemented
244#2932C2×C3711yescharacteristic, complemented
245#2052C2×C3712yescomplemented
246#2051C2×C3712yescomplemented
247#1997C2×C3711yescharacteristic, complemented
248#1967C2×C3711yescharacteristic, complemented
249#1908C2×C3712yescomplemented
250#1907C2×C3712yescomplemented
251#1778C2×C3711yescharacteristic, complemented
252C2×C37—22no—
253C2×C37—82no—
254C2×C37—161no—
255C2×C37#254411yescharacteristic
256C2×C37#306811yescharacteristic
257C2×C37#306911yescharacteristic
258C2×#137C22×C3712yes—
259C2×AGL(1,ℤ/8)C22×C3712yes—
260C2×#131C22×C3712yes—
261#532C22×C3711yescharacteristic
262C2×C4⋊Q8C22×C3711yescharacteristic
263C2×#124C22×C3711yescharacteristic
264#497—21no—
265#496—21no—
266#495—22no—
267#489—22no—
268#489—22no—
269#489—22no—
270#487—21no—
271#486—21no—
272#435—22no—
273#435—22no—
274C2×#108C22×C3712yes—
275#423C22×C3711yescharacteristic
276#417C22×C3712yes—
277#417C22×C3712yes—
278C2×#103C22×C3711yescharacteristic
279C2×#103C22×C3711yescharacteristic
280C2×#102C22×C3711yescharacteristic
281C2×#102C22×C3711yescharacteristic
282C2×#101C22×C3712yes—
283C2×#100C22×C3712yes—
284#408C22×C3712yes—
285C4×M16C22×C3711yescharacteristic
286C4×M16C22×C3711yescharacteristic
287C2×#97C22×C3711yescharacteristic
288#343C22×C3712yes—
289#343C22×C3712yes—
290#341C22×C3712yes—
291C37#2863611yescharacteristic, direct product factor, Sylow
292C2×#41C23×C3712yes—
293C22×Q8—21no—
294C22×Q8C23×C3711yescharacteristic
295C22×D4C23×C3711yescharacteristic
296#137—24no—
297#137—42no—
298AGL(1,ℤ/8)—24no—
299AGL(1,ℤ/8)—42no—
300C2×Q16—22no—
301C2×SD16—22no—
302C2×SD16—22no—
303C2×D8—22no—
304#131—42no—
305#131—42no—
306C2×M16—22no—
307C2×M16C23×C3712yes—
308C2×M16C23×C3712yes—
309C2×M16C23×C3712yes—
310C22×C8—22no—
311C22×C8C23×C3711yescharacteristic
312C22×C8C23×C3711yescharacteristic
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8D4×C3711yescharacteristic
318#127D4×C3711yescharacteristic
319#124—21no—
320#124—21no—
321#124—21no—
322#124—21no—
323#124D4×C3712yes—
324#121—21no—
325#121—21no—
326C4×D4—21no—
327C4×D4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4C23×C3711yescharacteristic
330C2×C4⋊C4C23×C3711yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42C23×C3711yescharacteristic
334#108—24no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337#103—22no—
338#103—22no—
339#103—22no—
340#103—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345#101—42no—
346#100—42no—
347C22⋊C8—24no—
348#97—21no—
349#97—21no—
350#97D4×C3712yes—
351#97D4×C3712yes—
352C4×C8—21no—
353C4×C8—21no—
354C24—21no—
355#41—22no—
356#41—22no—
357#41—22no—
358#41—22no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—82no—
366C2×Q8C2×D4×C3712yes—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4C2×D4×C3712yes—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4#41×C3711yescharacteristic
380C22×C4#41×C3711yescharacteristic
381C22×C4C24×C3711yescharacteristic
382Q16—44no—
383SD16—44no—
384SD16—44no—
385D8—44no—
386M16—22no—
387M16—22no—
388M16—22no—
389M16—22no—
390M16—22no—
391M16—44no—
392M16#41×C3714yes—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—44no—
399C2×C8C2×D4×C3712yes—
400C2×C8C2×D4×C3712yes—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C42C2×D4×C3711yescharacteristic
416C42C2×D4×C3711yescharacteristic
417C42C2×D4×C3711yescharacteristic
418C42C2×D4×C3711yescharacteristic
419C23—22no—
420C23—41no—
421C23—42no—
422C23—81no—
423C23—81no—
424C23C2×#41×C3711yescharacteristic
425Q8—22no—
426Q8—22no—
427Q8—41no—
428Q8—41no—
429Q8—42no—
430Q8—82no—
431Q8—82no—
432D4—22no—
433D4—22no—
434D4—42no—
435D4—42no—
436D4—41no—
437D4—41no—
438D4—42no—
439D4—81no—
440D4—81no—
441C2×C4—22no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4#121×C3711yescharacteristic
453C2×C4#121×C3711yescharacteristic
454C2×C4#121×C3711yescharacteristic
455C2×C4#121×C3711yescharacteristic
456C2×C4C22×D4×C3711yescharacteristic
457C2×C4C22×D4×C3711yescharacteristic
458C2×C4C2×#41×C3712yes—
459C2×C4H(5,𝔽2)×C3712yes—
460C8—22no—
461C8—22no—
462C8—24no—
463C8—42no—
464C8—42no—
465C22—21no—
466C22—21no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—162no—
474C22C2×#121×C3711yescharacteristic
475C22C37×#55912yes—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—42no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4C37×#53211yescharacteristic
485C4C37×#53511yescharacteristic
486C4C37×#54612yes—
487C2—22no—
488C2—82no—
489C2—161no—
490C2C37×#254411yescharacteristic
491C2C37×#306811yescharacteristic
492C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3153C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3141C2semidirect
3. C2×C37×#489C2semidirect
4. C37×#2932C2semidirect
5. C37×#2052C2semidirect
6. C37×#2051C2semidirect
7. C37×#1997C2semidirect
8. C37×#1967C2semidirect
9. C37×#1908C2semidirect
10. C37×#1907C2semidirect
11. C37×#1778C2semidirect
218. #28636C37direct (N × H)
242. #3141C2×C37semidirect
243. C2×#489C2×C37semidirect
244. #2932C2×C37semidirect
245. #2052C2×C37semidirect
246. #2051C2×C37semidirect
247. #1997C2×C37semidirect
248. #1967C2×C37semidirect
249. #1908C2×C37semidirect
250. #1907C2×C37semidirect
251. #1778C2×C37semidirect
291. C37#28636direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31532
C37×#31412
C2×C37×#4892
C37×#29322
C37×#20522
C37×#20512
C37×#19972
C37×#19672
C37×#19082
C37×#19072
C37×#17782
#2863637