Finite Group Databasebeta

← C37×#19491 #22640744

Subgroups — C37×#19491 #22640744

Order 9472.

614 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3226C211yesmaximal, characteristic, complemented
2C37×#3106C211yesmaximal, characteristic
3C37×#3079C211yesmaximal, characteristic, complemented
4C37×#2990C211yesmaximal, characteristic, complemented
5C37×#1698C212yesmaximal, complemented
6C37×#1696C212yesmaximal, complemented
7C37×#1677C212yesmaximal, complemented
8C37×#1675C212yesmaximal, complemented
9C37×#1574C211yesmaximal, characteristic, complemented
10C37×#1560C211yesmaximal, characteristic, complemented
11C37×#1548C211yesmaximal, characteristic, complemented
12C37×#532C2211yescharacteristic
13C2×C4⋊Q8×C37C2211yescharacteristic
14C4×#41×C37C2211yescharacteristic
15C37×#500C2212yes—
16C37×#486C2212yes—
17C37×#482—21no—
18C37×#480—22no—
19C37×#477C2211yescharacteristic
20C37×#477C2212yes—
21C37×#476C2211yescharacteristic
22C37×#476C2212yes—
23C37×#475—21no—
24C37×#474—21no—
25C37×#474—21no—
26C37×#474—21no—
27C37×#460C2211yescharacteristic
28C37×#459C2211yescharacteristic
29C37×#449—21no—
30C37×#446C2212yes—
31C4×SD16×C37—21no—
32C4×D8×C37—21no—
33C37×#435—22no—
34C8×D4×C37C2212yes—
35C37×#432—21no—
36C37×#431C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C37×#428—21no—
39C37×#423C2211yescharacteristic
40C37×#423C2211yescharacteristic
41C2×C4⋊C8×C37—21no—
42C37×#417—21no—
43C37×#335C2212yes—
44C37×#334C2212yes—
45C37×#333C2212yes—
46C37×#333C2212yes—
47C37×#333C2212yes—
48C37×#331C2212yes—
49C2×#41×C37—21no—
50C2×#41×C37D411yescharacteristic
51C22×Q8×C37—21no—
52C2×SD16×C37—21no—
53C2×D8×C37—21no—
54C2×M16×C37—21no—
55C2×M16×C37—21no—
56C22×C8×C37—22no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37C2312yes—
61C4⋊Q8×C37C2311yescharacteristic
62#127×C37C2311yescharacteristic
63#124×C37—21no—
64#121×C37—21no—
65#121×C37—21no—
66C4×Q8×C37D411yescharacteristic
67C4×Q8×C37C2311yescharacteristic
68C4×D4×C37—21no—
69C4×D4×C37—21no—
70C4×D4×C37—21no—
71C4×D4×C37—21no—
72C4×D4×C37D411yescharacteristic
73C4×D4×C37C2311yescharacteristic
74#117×C37—21no—
75#117×C37D411yescharacteristic
76C2×C4⋊C4×C37—21no—
77C2×C4⋊C4×C37—21no—
78C2×C42×C37—21no—
79C2×C42×C37C2311yescharacteristic
80#107×C37—22no—
81#107×C37—22no—
82#107×C37—22no—
83#107×C37—21no—
84#106×C37—22no—
85#106×C37—21no—
86C4⋊C8×C37—22no—
87C4⋊C8×C37—21no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37D411yescharacteristic
90C4⋊C8×C37D411yescharacteristic
91C4⋊C8×C37C2312yes—
92C4⋊C8×C37C2312yes—
93C4⋊C8×C37C2311yescharacteristic
94C4⋊C8×C37C2311yescharacteristic
95#103×C37—22no—
96#103×C37—21no—
97#102×C37—22no—
98#102×C37—21no—
99#102×C37—22no—
100#102×C37—22no—
101#102×C37—21no—
102#102×C37—21no—
103C22⋊C8×C37—21no—
104C22⋊C8×C37—22no—
105C22⋊C8×C37D412yes—
106#97×C37—22no—
107C4×C8×C37—21no—
108C4×C8×C37C2312yes—
109#41×C37—22no—
110#41×C37—41no—
111#41×C37—82no—
112C2×Q8×C37—21no—
113C2×Q8×C37—22no—
114C2×Q8×C37—41no—
115C2×Q8×C37—82no—
116C2×Q8×C37C2×D411yescharacteristic
117C2×D4×C37—21no—
118C2×D4×C37—21no—
119C2×D4×C37—21no—
120C2×D4×C37—21no—
121C2×D4×C37—41no—
122C2×D4×C37C2×D411yescharacteristic
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—41no—
127C22×C4×C37—41no—
128C22×C4×C37C2×D411yescharacteristic
129C22×C4×C37C2×D411yescharacteristic
130C22×C4×C37#4111yescharacteristic
131SD16×C37—42no—
132D8×C37—42no—
133M16×C37—42no—
134M16×C37—81no—
135C2×C8×C37—21no—
136C2×C8×C37—21no—
137C2×C8×C37—22no—
138C2×C8×C37—22no—
139C2×C8×C37—82no—
140C2×C8×C37C2×D412yes—
141C2×C8×C37C2×D412yes—
142C4⋊C4×C37—21no—
143C4⋊C4×C37—21no—
144C4⋊C4×C37—22no—
145C4⋊C4×C37—22no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—41no—
149C4⋊C4×C37—41no—
150C4⋊C4×C37C2×D411yescharacteristic
151C4⋊C4×C37C2×D411yescharacteristic
152C22⋊C4×C37—21no—
153C22⋊C4×C37—21no—
154C22⋊C4×C37—21no—
155C22⋊C4×C37—41no—
156C22⋊C4×C37—41no—
157C42×C37—21no—
158C42×C37—21no—
159C42×C37—21no—
160C42×C37C2×D411yescharacteristic
161C42×C37C2×D411yescharacteristic
162C42×C37#4111yescharacteristic
163C42×C37C2411yescharacteristic
164C23×C37—21no—
165C23×C37—41no—
166C23×C37#12111yescharacteristic
167Q8×C37—21no—
168Q8×C37—21no—
169Q8×C37—82no—
170Q8×C37—81no—
171Q8×C37—82no—
172D4×C37—21no—
173D4×C37—42no—
174D4×C37—41no—
175D4×C37—41no—
176D4×C37—41no—
177D4×C37—41no—
178D4×C37—81no—
179D4×C37—82no—
180D4×C37#13712yes—
181C2×C4×C37—21no—
182C2×C4×C37—21no—
183C2×C4×C37—21no—
184C2×C4×C37—21no—
185C2×C4×C37—22no—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—21no—
189C2×C4×C37—42no—
190C2×C4×C37—41no—
191C2×C4×C37—41no—
192C2×C4×C37—42no—
193C2×C4×C37—41no—
194C2×C4×C37—42no—
195C2×C4×C37—82no—
196C2×C4×C37—82no—
197C2×C4×C37#12111yescharacteristic
198C2×C4×C37#12111yescharacteristic
199C2×C4×C37#12111yescharacteristic
200C2×C4×C37C22×D411yescharacteristic
201C2×C4×C37C22×D411yescharacteristic
202C2×C4×C37C2×#4111yescharacteristic
203C8×C37—22no—
204C8×C37—22no—
205C8×C37—41no—
206C8×C37—42no—
207C8×C37—41no—
208C8×C37—42no—
209#19491C3711yesmaximal, characteristic, direct product factor, Sylow
210C22×C37—21no—
211C22×C37—21no—
212C22×C37—22no—
213C22×C37—21no—
214C22×C37—41no—
215C22×C37—41no—
216C22×C37—81no—
217C22×C37—81no—
218C22×C37—81no—
219C22×C37C2×#12111yescharacteristic
220C4×C37—21no—
221C4×C37—21no—
222C4×C37—21no—
223C4×C37—41no—
224C4×C37—41no—
225C4×C37—41no—
226C4×C37—81no—
227C4×C37—82no—
228C4×C37#47212yes—
229C4×C37C2×#13711yescharacteristic
230C4×C37#57511yescharacteristic
231C4×C37#57711yescharacteristic
232C4×C37#57811yescharacteristic
233#3226C2×C3711yescharacteristic, complemented
234#3106C2×C3711yescharacteristic
235#3079C2×C3711yescharacteristic, complemented
236#2990C2×C3711yescharacteristic, complemented
237#1698C2×C3712yescomplemented
238#1696C2×C3712yescomplemented
239#1677C2×C3712yescomplemented
240#1675C2×C3712yescomplemented
241#1574C2×C3711yescharacteristic, complemented
242#1560C2×C3711yescharacteristic, complemented
243#1548C2×C3711yescharacteristic, complemented
244C2×C37—41no—
245C2×C37—42no—
246C2×C37—161no—
247C2×C37#304611yescharacteristic
248C2×C37#305611yescharacteristic
249C2×C37C2×#47211yescharacteristic
250#532C22×C3711yescharacteristic
251C2×C4⋊Q8C22×C3711yescharacteristic
252C4×#41C22×C3711yescharacteristic
253#500C22×C3712yes—
254#486C22×C3712yes—
255#482—21no—
256#480—22no—
257#477C22×C3712yes—
258#477C22×C3711yescharacteristic
259#476C22×C3712yes—
260#476C22×C3711yescharacteristic
261#475—21no—
262#474—21no—
263#474—21no—
264#474—21no—
265#460C22×C3711yescharacteristic
266#459C22×C3711yescharacteristic
267#449—21no—
268#446C22×C3712yes—
269C4×SD16—21no—
270C4×D8—21no—
271#435—22no—
272C8×D4C22×C3712yes—
273#432—21no—
274#431C22×C3711yescharacteristic
275#431C22×C3711yescharacteristic
276#428—21no—
277#423C22×C3711yescharacteristic
278#423C22×C3711yescharacteristic
279C2×C4⋊C8—21no—
280#417—21no—
281#335C22×C3712yes—
282#334C22×C3712yes—
283#333C22×C3712yes—
284#333C22×C3712yes—
285#333C22×C3712yes—
286#331C22×C3712yes—
287C37#1949111yescharacteristic, direct product factor, Sylow
288C2×#41—21no—
289C2×#41D4×C3711yescharacteristic
290C22×Q8—21no—
291C2×SD16—21no—
292C2×D8—21no—
293C2×M16—21no—
294C2×M16—21no—
295C22×C8—22no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8C23×C3712yes—
300C4⋊Q8C23×C3711yescharacteristic
301#127C23×C3711yescharacteristic
302#124—21no—
303#121—21no—
304#121—21no—
305C4×Q8D4×C3711yescharacteristic
306C4×Q8C23×C3711yescharacteristic
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4D4×C3711yescharacteristic
312C4×D4C23×C3711yescharacteristic
313#117—21no—
314#117D4×C3711yescharacteristic
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C42—21no—
318C2×C42C23×C3711yescharacteristic
319#107—22no—
320#107—22no—
321#107—22no—
322#107—21no—
323#106—22no—
324#106—21no—
325C4⋊C8—22no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8D4×C3711yescharacteristic
329C4⋊C8D4×C3711yescharacteristic
330C4⋊C8C23×C3712yes—
331C4⋊C8C23×C3712yes—
332C4⋊C8C23×C3711yescharacteristic
333C4⋊C8C23×C3711yescharacteristic
334#103—22no—
335#103—21no—
336#102—22no—
337#102—21no—
338#102—22no—
339#102—22no—
340#102—21no—
341#102—21no—
342C22⋊C8—21no—
343C22⋊C8—22no—
344C22⋊C8D4×C3712yes—
345#97—22no—
346C4×C8—21no—
347C4×C8C23×C3712yes—
348#41—22no—
349#41—41no—
350#41—82no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×Q8C2×D4×C3711yescharacteristic
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4C2×D4×C3711yescharacteristic
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×D4×C3711yescharacteristic
368C22×C4C2×D4×C3711yescharacteristic
369C22×C4#41×C3711yescharacteristic
370SD16—42no—
371D8—42no—
372M16—42no—
373M16—81no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—82no—
379C2×C8C2×D4×C3712yes—
380C2×C8C2×D4×C3712yes—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4C2×D4×C3711yescharacteristic
390C4⋊C4C2×D4×C3711yescharacteristic
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42C2×D4×C3711yescharacteristic
400C42C2×D4×C3711yescharacteristic
401C42#41×C3711yescharacteristic
402C42C24×C3711yescharacteristic
403C23—21no—
404C23—41no—
405C23#121×C3711yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—82no—
409Q8—81no—
410Q8—82no—
411D4—21no—
412D4—42no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—81no—
418D4—82no—
419D4#137×C3712yes—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4#121×C3711yescharacteristic
437C2×C4#121×C3711yescharacteristic
438C2×C4#121×C3711yescharacteristic
439C2×C4C22×D4×C3711yescharacteristic
440C2×C4C22×D4×C3711yescharacteristic
441C2×C4C2×#41×C3711yescharacteristic
442C8—22no—
443C8—22no—
444C8—41no—
445C8—42no—
446C8—41no—
447C8—42no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22C2×#121×C3711yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—81no—
465C4—82no—
466C4C37×#47212yes—
467C4C2×#137×C3711yescharacteristic
468C4C37×#57511yescharacteristic
469C4C37×#57711yescharacteristic
470C4C37×#57811yescharacteristic
471C2—41no—
472C2—42no—
473C2—161no—
474C2C37×#304611yescharacteristic
475C2C37×#305611yescharacteristic
476C2C2×C37×#47211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3226C2semidirect
3. C37×#3079C2semidirect
4. C37×#2990C2semidirect
5. C37×#1698C2semidirect
6. C37×#1696C2semidirect
7. C37×#1677C2semidirect
8. C37×#1675C2semidirect
9. C37×#1574C2semidirect
10. C37×#1560C2semidirect
11. C37×#1548C2semidirect
209. #19491C37direct (N × H)
233. #3226C2×C37semidirect
235. #3079C2×C37semidirect
236. #2990C2×C37semidirect
237. #1698C2×C37semidirect
238. #1696C2×C37semidirect
239. #1677C2×C37semidirect
240. #1675C2×C37semidirect
241. #1574C2×C37semidirect
242. #1560C2×C37semidirect
243. #1548C2×C37semidirect
287. C37#19491direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32262
C37×#31062
C37×#30792
C37×#29902
C37×#16982
C37×#16962
C37×#16772
C37×#16752
C37×#15742
C37×#15602
C37×#15482
#1949137