Finite Group Databasebeta

← C37×#29790 #22651043

Subgroups — C37×#29790 #22651043

Order 9472.

726 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3095C211yesmaximal, characteristic, complemented
2C37×#3094C211yesmaximal, characteristic
3C2×C37×#465C211yesmaximal, characteristic
4C2×C37×#424C211yesmaximal, characteristic, complemented
5C37×#2090C212yesmaximal, complemented
6C37×#2064C212yesmaximal, complemented
7C37×#2063C212yesmaximal, complemented
8C37×#2046C212yesmaximal, complemented
9C37×#1901C211yesmaximal, characteristic, complemented
10C37×#1900C211yesmaximal, characteristic
11C37×#1810C211yesmaximal, characteristic, complemented
12C22×SD16×C37C2211yescharacteristic
13C22×M16×C37C2211yescharacteristic
14C23×C8×C37C2211yescharacteristic
15C2×C22⋊Q8×C37C2211yescharacteristic
16C2×#121×C37C2211yescharacteristic
17C2×#117×C37C2211yescharacteristic
18C37×#485—22no—
19C37×#484—21no—
20C37×#483—21no—
21C37×#482—22no—
22C37×#481—21no—
23C37×#480—21no—
24C37×#465—22no—
25C37×#465—22no—
26C2×#108×C37C2212yes—
27C37×#428C2212yes—
28C37×#428C2212yes—
29C2×#106×C37C2211yescharacteristic
30C37×#424—22no—
31C37×#424C2212yes—
32C37×#424C2212yes—
33C2×C4⋊C8×C37—22no—
34C37×#419C2212yes—
35C37×#418C2212yes—
36C2×#103×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#101×C37C2212yes—
39C2×#100×C37C2212yes—
40C37×#407C2211yescharacteristic
41C37×#407C2211yescharacteristic
42C37×#343C2212yes—
43C37×#343C2212yes—
44C37×#341C2212yes—
45C22×Q8×C37C2311yescharacteristic
46C22×D4×C37—21no—
47C22×D4×C37C2311yescharacteristic
48C23×C4×C37C2311yescharacteristic
49C2×SD16×C37—22no—
50C2×SD16×C37—42no—
51C2×M16×C37—21no—
52C2×M16×C37—42no—
53C2×M16×C37C2312yes—
54C2×M16×C37C2312yes—
55C2×M16×C37C2312yes—
56C22×C8×C37—21no—
57C22×C8×C37—42no—
58C22×C8×C37D412yes—
59C22×C8×C37D412yes—
60C22×C8×C37C2311yescharacteristic
61C22×C8×C37C2311yescharacteristic
62C22⋊Q8×C37—21no—
63C22⋊Q8×C37—21no—
64C22⋊Q8×C37—21no—
65C22⋊Q8×C37—21no—
66#121×C37—21no—
67#121×C37—21no—
68#121×C37—21no—
69#121×C37—21no—
70#117×C37—21no—
71#117×C37—21no—
72#117×C37D412yes—
73#117×C37C2312yes—
74C2×C4⋊C4×C37—21no—
75C2×C4⋊C4×C37D411yescharacteristic
76C2×C4⋊C4×C37D411yescharacteristic
77C2×C4⋊C4×C37C2311yescharacteristic
78C2×C4⋊C4×C37C2311yescharacteristic
79C2×C22⋊C4×C37—21no—
80C2×C22⋊C4×C37—21no—
81C2×C22⋊C4×C37—21no—
82C2×C42×C37—21no—
83#108×C37—42no—
84#107×C37—22no—
85#107×C37—22no—
86#106×C37—22no—
87#106×C37—22no—
88#106×C37—22no—
89C4⋊C8×C37—24no—
90C4⋊C8×C37—24no—
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#101×C37—42no—
98#100×C37—42no—
99C22⋊C8×C37—21no—
100C22⋊C8×C37—21no—
101C22⋊C8×C37—21no—
102C22⋊C8×C37—21no—
103C24×C37—21no—
104C24×C37#4111yescharacteristic
105C2×Q8×C37—21no—
106C2×Q8×C37—21no—
107C2×Q8×C37—22no—
108C2×Q8×C37—22no—
109C2×D4×C37—21no—
110C2×D4×C37—21no—
111C2×D4×C37—22no—
112C2×D4×C37—22no—
113C2×D4×C37—41no—
114C2×D4×C37—41no—
115C2×D4×C37—82no—
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×C37C2×D411yescharacteristic
124C22×C4×C37C2×D411yescharacteristic
125C22×C4×C37C2×D411yescharacteristic
126C22×C4×C37C2×D411yescharacteristic
127C22×C4×C37#4111yescharacteristic
128C22×C4×C37C2411yescharacteristic
129SD16×C37—44no—
130M16×C37—22no—
131M16×C37—22no—
132M16×C37—22no—
133M16×C37—22no—
134M16×C37—22no—
135M16×C37—22no—
136M16×C37—42no—
137C2×C8×C37—22no—
138C2×C8×C37—22no—
139C2×C8×C37—22no—
140C2×C8×C37—22no—
141C2×C8×C37—22no—
142C2×C8×C37—42no—
143C2×C8×C37—42no—
144C2×C8×C37—42no—
145C2×C8×C37C2×D412yes—
146C2×C8×C37C2×D412yes—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—41no—
154C4⋊C4×C37—41no—
155C4⋊C4×C37C2×D412yes—
156C4⋊C4×C37C2×D412yes—
157C22⋊C4×C37—22no—
158C22⋊C4×C37—22no—
159C22⋊C4×C37—41no—
160C22⋊C4×C37—41no—
161C22⋊C4×C37—41no—
162C22⋊C4×C37—41no—
163C42×C37—22no—
164C42×C37—22no—
165C23×C37—22no—
166C23×C37—22no—
167C23×C37—41no—
168C23×C37—41no—
169C23×C37—42no—
170C23×C37—81no—
171C23×C37—81no—
172C23×C37#12111yescharacteristic
173C23×C37#12111yescharacteristic
174C23×C37C2×#4111yescharacteristic
175Q8×C37—41no—
176Q8×C37—41no—
177Q8×C37—42no—
178D4×C37—41no—
179D4×C37—41no—
180D4×C37—42no—
181D4×C37—82no—
182D4×C37—82no—
183C2×C4×C37—22no—
184C2×C4×C37—21no—
185C2×C4×C37—21no—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—22no—
189C2×C4×C37—22no—
190C2×C4×C37—22no—
191C2×C4×C37—22no—
192C2×C4×C37—42no—
193C2×C4×C37—42no—
194C2×C4×C37—41no—
195C2×C4×C37—41no—
196C2×C4×C37—41no—
197C2×C4×C37—42no—
198C2×C4×C37—81no—
199C2×C4×C37—81no—
200C2×C4×C37#12111yescharacteristic
201C2×C4×C37#12111yescharacteristic
202C2×C4×C37C22×D411yescharacteristic
203C2×C4×C37C22×D411yescharacteristic
204C2×C4×C37H(5,𝔽2)12yes—
205C2×C4×C372−1+412yes—
206C8×C37—22no—
207C8×C37—22no—
208C8×C37—42no—
209C8×C37—42no—
210C8×C37—42no—
211#29790C3711yesmaximal, characteristic, direct product factor, Sylow
212C22×C37—21no—
213C22×C37—21no—
214C22×C37—21no—
215C22×C37—21no—
216C22×C37—21no—
217C22×C37—21no—
218C22×C37—21no—
219C22×C37—44no—
220C22×C37—81no—
221C22×C37—81no—
222C22×C37—81no—
223C22×C37—162no—
224C22×C37#47112yes—
225C22×C37C2×#12111yescharacteristic
226C22×C37#53912yes—
227C4×C37—21no—
228C4×C37—21no—
229C4×C37—42no—
230C4×C37—42no—
231C4×C37—81no—
232C4×C37—81no—
233C4×C37—81no—
234C4×C37#53411yescharacteristic
235C4×C37#53611yescharacteristic
236C4×C37#53712yes—
237#3095C2×C3711yescharacteristic, complemented
238#3094C2×C3711yescharacteristic
239C2×#465C2×C3711yescharacteristic
240C2×#424C2×C3711yescharacteristic, complemented
241#2090C2×C3712yescomplemented
242#2064C2×C3712yescomplemented
243#2063C2×C3712yescomplemented
244#2046C2×C3712yescomplemented
245#1901C2×C3711yescharacteristic, complemented
246#1900C2×C3711yescharacteristic
247#1810C2×C3711yescharacteristic, complemented
248C2×C37—22no—
249C2×C37—22no—
250C2×C37—41no—
251C2×C37—161no—
252C2×C37#261811yescharacteristic
253C2×C37C2×#47111yescharacteristic
254C2×C37#306711yescharacteristic
255C22×SD16C22×C3711yescharacteristic
256C22×M16C22×C3711yescharacteristic
257C23×C8C22×C3711yescharacteristic
258C2×C22⋊Q8C22×C3711yescharacteristic
259C2×#121C22×C3711yescharacteristic
260C2×#117C22×C3711yescharacteristic
261#485—22no—
262#484—21no—
263#483—21no—
264#482—22no—
265#481—21no—
266#480—21no—
267#465—22no—
268#465—22no—
269C2×#108C22×C3712yes—
270#428C22×C3712yes—
271#428C22×C3712yes—
272C2×#106C22×C3711yescharacteristic
273#424—22no—
274#424C22×C3712yes—
275#424C22×C3712yes—
276C2×C4⋊C8—22no—
277#419C22×C3712yes—
278#418C22×C3712yes—
279C2×#103C22×C3711yescharacteristic
280C2×#102C22×C3711yescharacteristic
281C2×#101C22×C3712yes—
282C2×#100C22×C3712yes—
283#407C22×C3711yescharacteristic
284#407C22×C3711yescharacteristic
285#343C22×C3712yes—
286#343C22×C3712yes—
287#341C22×C3712yes—
288C37#2979011yescharacteristic, direct product factor, Sylow
289C22×Q8C23×C3711yescharacteristic
290C22×D4—21no—
291C22×D4C23×C3711yescharacteristic
292C23×C4C23×C3711yescharacteristic
293C2×SD16—22no—
294C2×SD16—42no—
295C2×M16—21no—
296C2×M16—42no—
297C2×M16C23×C3712yes—
298C2×M16C23×C3712yes—
299C2×M16C23×C3712yes—
300C22×C8—21no—
301C22×C8—42no—
302C22×C8D4×C3712yes—
303C22×C8D4×C3712yes—
304C22×C8C23×C3711yescharacteristic
305C22×C8C23×C3711yescharacteristic
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#117—21no—
315#117—21no—
316#117D4×C3712yes—
317#117C23×C3712yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C3711yescharacteristic
320C2×C4⋊C4D4×C3711yescharacteristic
321C2×C4⋊C4C23×C3711yescharacteristic
322C2×C4⋊C4C23×C3711yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C42—21no—
327#108—42no—
328#107—22no—
329#107—22no—
330#106—22no—
331#106—22no—
332#106—22no—
333C4⋊C8—24no—
334C4⋊C8—24no—
335#103—22no—
336#103—22no—
337#103—22no—
338#102—22no—
339#102—22no—
340#102—22no—
341#101—42no—
342#100—42no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C24—21no—
348C24#41×C3711yescharacteristic
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—82no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4C2×D4×C3711yescharacteristic
368C22×C4C2×D4×C3711yescharacteristic
369C22×C4C2×D4×C3711yescharacteristic
370C22×C4C2×D4×C3711yescharacteristic
371C22×C4#41×C3711yescharacteristic
372C22×C4C24×C3711yescharacteristic
373SD16—44no—
374M16—22no—
375M16—22no—
376M16—22no—
377M16—22no—
378M16—22no—
379M16—22no—
380M16—42no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—42no—
387C2×C8—42no—
388C2×C8—42no—
389C2×C8C2×D4×C3712yes—
390C2×C8C2×D4×C3712yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C3712yes—
400C4⋊C4C2×D4×C3712yes—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C42—22no—
408C42—22no—
409C23—22no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—42no—
414C23—81no—
415C23—81no—
416C23#121×C3711yescharacteristic
417C23#121×C3711yescharacteristic
418C23C2×#41×C3711yescharacteristic
419Q8—41no—
420Q8—41no—
421Q8—42no—
422D4—41no—
423D4—41no—
424D4—42no—
425D4—82no—
426D4—82no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4#121×C3711yescharacteristic
445C2×C4#121×C3711yescharacteristic
446C2×C4C22×D4×C3711yescharacteristic
447C2×C4C22×D4×C3711yescharacteristic
448C2×C4H(5,𝔽2)×C3712yes—
449C2×C42−1+4×C3712yes—
450C8—22no—
451C8—22no—
452C8—42no—
453C8—42no—
454C8—42no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—44no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—162no—
467C22C37×#47112yes—
468C22C2×#121×C3711yescharacteristic
469C22C37×#53912yes—
470C4—21no—
471C4—21no—
472C4—42no—
473C4—42no—
474C4—81no—
475C4—81no—
476C4—81no—
477C4C37×#53411yescharacteristic
478C4C37×#53611yescharacteristic
479C4C37×#53712yes—
480C2—22no—
481C2—22no—
482C2—41no—
483C2—161no—
484C2C37×#261811yescharacteristic
485C2C2×C37×#47111yescharacteristic
486C2C37×#306711yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3095C2semidirect
4. C2×C37×#424C2semidirect
5. C37×#2090C2semidirect
6. C37×#2064C2semidirect
7. C37×#2063C2semidirect
8. C37×#2046C2semidirect
9. C37×#1901C2semidirect
11. C37×#1810C2semidirect
211. #29790C37direct (N × H)
237. #3095C2×C37semidirect
240. C2×#424C2×C37semidirect
241. #2090C2×C37semidirect
242. #2064C2×C37semidirect
243. #2063C2×C37semidirect
244. #2046C2×C37semidirect
245. #1901C2×C37semidirect
247. #1810C2×C37semidirect
288. C37#29790direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#30952
C37×#30942
C2×C37×#4652
C2×C37×#4242
C37×#20902
C37×#20642
C37×#20632
C37×#20462
C37×#19012
C37×#19002
C37×#18102
#2979037