Finite Group Databasebeta

← C37×#19490 #22640743

Subgroups — C37×#19490 #22640743

Order 9472.

624 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3230C211yesmaximal, characteristic, complemented
2C37×#3107C211yesmaximal, characteristic
3C37×#3039C211yesmaximal, characteristic
4C37×#2990C211yesmaximal, characteristic
5C37×#1700C212yesmaximal, complemented
6C37×#1694C212yesmaximal, complemented
7C37×#1679C212yesmaximal, complemented
8C37×#1673C212yesmaximal, complemented
9C37×#1574C211yesmaximal, characteristic, complemented
10C37×#1561C211yesmaximal, characteristic, complemented
11C37×#1549C211yesmaximal, characteristic, complemented
12C2×#137×C37—21no—
13C37×#533C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C4×#41×C37C2211yescharacteristic
16C37×#500C2212yes—
17C37×#487C2212yes—
18C37×#485—21no—
19C37×#484—22no—
20C37×#477—21no—
21C37×#477—21no—
22C37×#475C2211yescharacteristic
23C37×#474C2211yescharacteristic
24C37×#462—21no—
25C37×#462C2211yescharacteristic
26C37×#462C2212yes—
27C37×#461—21no—
28C37×#461C2211yescharacteristic
29C37×#461C2212yes—
30C37×#452—21no—
31C37×#446C2212yes—
32C4×Q16×C37—21no—
33C4×SD16×C37—21no—
34C37×#435—22no—
35C8×D4×C37C2212yes—
36C37×#432—21no—
37C37×#431C2211yescharacteristic
38C37×#431C2211yescharacteristic
39C37×#423C2211yescharacteristic
40C37×#423C2211yescharacteristic
41C2×C4⋊C8×C37—21no—
42C37×#419—21no—
43C37×#335C2212yes—
44C37×#334C2212yes—
45C37×#332C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#332C2212yes—
49C2×#41×C37D411yescharacteristic
50C22×Q8×C37—21no—
51#137×C37—44no—
52C2×Q16×C37—22no—
53C2×Q16×C37—21no—
54C2×SD16×C37—22no—
55C2×SD16×C37—21no—
56C2×M16×C37—21no—
57C2×M16×C37—21no—
58C22×C8×C37—22no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37—21no—
61C4⋊Q8×C37—21no—
62C4⋊Q8×C37C2312yes—
63C4⋊Q8×C37C2311yescharacteristic
64C4⋊Q8×C37C2311yescharacteristic
65#125×C37—21no—
66C22⋊Q8×C37—21no—
67C22⋊Q8×C37—21no—
68C4×Q8×C37—21no—
69C4×Q8×C37—21no—
70C4×Q8×C37D411yescharacteristic
71C4×Q8×C37C2311yescharacteristic
72C4×D4×C37—21no—
73C4×D4×C37—21no—
74C4×D4×C37D411yescharacteristic
75C4×D4×C37C2311yescharacteristic
76#117×C37—21no—
77#117×C37—21no—
78#117×C37D411yescharacteristic
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37—21no—
81C2×C42×C37—21no—
82C2×C42×C37C2311yescharacteristic
83#107×C37—22no—
84#107×C37—22no—
85#107×C37—21no—
86#106×C37—21no—
87C4⋊C8×C37—22no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37D411yescharacteristic
91C4⋊C8×C37D411yescharacteristic
92C4⋊C8×C37C2312yes—
93C4⋊C8×C37C2311yescharacteristic
94C4⋊C8×C37C2312yes—
95C4⋊C8×C37C2311yescharacteristic
96#103×C37—21no—
97#103×C37—22no—
98#103×C37—22no—
99#103×C37—22no—
100#103×C37—22no—
101#103×C37—21no—
102#103×C37—21no—
103#102×C37—21no—
104C22⋊C8×C37—21no—
105C22⋊C8×C37—22no—
106C22⋊C8×C37D412yes—
107#97×C37—22no—
108C4×C8×C37—21no—
109C4×C8×C37C2312yes—
110#41×C37—22no—
111#41×C37—41no—
112C2×Q8×C37—21no—
113C2×Q8×C37—21no—
114C2×Q8×C37—22no—
115C2×Q8×C37—42no—
116C2×Q8×C37—42no—
117C2×Q8×C37—41no—
118C2×Q8×C37C2×D411yescharacteristic
119C2×D4×C37—21no—
120C2×D4×C37C2×D411yescharacteristic
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—21no—
124C22×C4×C37—41no—
125C22×C4×C37C2×D411yescharacteristic
126C22×C4×C37C2×D411yescharacteristic
127C22×C4×C37#4111yescharacteristic
128Q16×C37—42no—
129Q16×C37—44no—
130SD16×C37—42no—
131SD16×C37—44no—
132M16×C37—42no—
133M16×C37—81no—
134C2×C8×C37—21no—
135C2×C8×C37—21no—
136C2×C8×C37—22no—
137C2×C8×C37—22no—
138C2×C8×C37—82no—
139C2×C8×C37C2×D412yes—
140C2×C8×C37C2×D412yes—
141C4⋊C4×C37—21no—
142C4⋊C4×C37—21no—
143C4⋊C4×C37—21no—
144C4⋊C4×C37—22no—
145C4⋊C4×C37—21no—
146C4⋊C4×C37—22no—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—41no—
150C4⋊C4×C37—41no—
151C4⋊C4×C37—41no—
152C4⋊C4×C37—41no—
153C4⋊C4×C37C2×D411yescharacteristic
154C4⋊C4×C37C2×D411yescharacteristic
155C22⋊C4×C37—21no—
156C22⋊C4×C37—21no—
157C22⋊C4×C37—21no—
158C22⋊C4×C37—41no—
159C42×C37—21no—
160C42×C37—21no—
161C42×C37—21no—
162C42×C37—41no—
163C42×C37C2×D411yescharacteristic
164C42×C37C2×D411yescharacteristic
165C42×C37#4111yescharacteristic
166C42×C37C2411yescharacteristic
167C23×C37—21no—
168C23×C37#12111yescharacteristic
169Q8×C37—21no—
170Q8×C37—21no—
171Q8×C37—42no—
172Q8×C37—41no—
173Q8×C37—41no—
174Q8×C37—42no—
175Q8×C37—41no—
176Q8×C37—41no—
177Q8×C37—82no—
178D4×C37—21no—
179D4×C37—42no—
180D4×C37AGL(1,ℤ/8)12yes—
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—41no—
195C2×C4×C37—42no—
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—42no—
206C8×C37—41no—
207C8×C37—41no—
208C8×C37—42no—
209#19490C3711yesmaximal, characteristic, direct product factor, Sylow
210C22×C37—21no—
211C22×C37—21no—
212C22×C37—22no—
213C22×C37—21no—
214C22×C37—41no—
215C22×C37—41no—
216C22×C37C2×#12111yescharacteristic
217C4×C37—21no—
218C4×C37—21no—
219C4×C37—21no—
220C4×C37—41no—
221C4×C37—41no—
222C4×C37—41no—
223C4×C37—81no—
224C4×C37—82no—
225C4×C37—81no—
226C4×C37#47312yes—
227C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C37#57511yescharacteristic
229C4×C37#57711yescharacteristic
230C4×C37#57811yescharacteristic
231#3230C2×C3711yescharacteristic, complemented
232#3107C2×C3711yescharacteristic
233#3039C2×C3711yescharacteristic
234#2990C2×C3711yescharacteristic
235#1700C2×C3712yescomplemented
236#1694C2×C3712yescomplemented
237#1679C2×C3712yescomplemented
238#1673C2×C3712yescomplemented
239#1574C2×C3711yescharacteristic, complemented
240#1561C2×C3711yescharacteristic, complemented
241#1549C2×C3711yescharacteristic, complemented
242C2×C37—41no—
243C2×C37—42no—
244C2×C37#304611yescharacteristic
245C2×C37#305511yescharacteristic
246C2×C37C2×#47311yescharacteristic
247C2×#137—21no—
248#533C22×C3711yescharacteristic
249C2×C4⋊Q8C22×C3711yescharacteristic
250C4×#41C22×C3711yescharacteristic
251#500C22×C3712yes—
252#487C22×C3712yes—
253#485—21no—
254#484—22no—
255#477—21no—
256#477—21no—
257#475C22×C3711yescharacteristic
258#474C22×C3711yescharacteristic
259#462—21no—
260#462C22×C3711yescharacteristic
261#462C22×C3712yes—
262#461—21no—
263#461C22×C3711yescharacteristic
264#461C22×C3712yes—
265#452—21no—
266#446C22×C3712yes—
267C4×Q16—21no—
268C4×SD16—21no—
269#435—22no—
270C8×D4C22×C3712yes—
271#432—21no—
272#431C22×C3711yescharacteristic
273#431C22×C3711yescharacteristic
274#423C22×C3711yescharacteristic
275#423C22×C3711yescharacteristic
276C2×C4⋊C8—21no—
277#419—21no—
278#335C22×C3712yes—
279#334C22×C3712yes—
280#332C22×C3712yes—
281#332C22×C3712yes—
282#332C22×C3712yes—
283#332C22×C3712yes—
284C37#1949011yescharacteristic, direct product factor, Sylow
285C2×#41D4×C3711yescharacteristic
286C22×Q8—21no—
287#137—44no—
288C2×Q16—22no—
289C2×Q16—21no—
290C2×SD16—22no—
291C2×SD16—21no—
292C2×M16—21no—
293C2×M16—21no—
294C22×C8—22no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8C23×C3712yes—
299C4⋊Q8C23×C3711yescharacteristic
300C4⋊Q8C23×C3711yescharacteristic
301#125—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D4×C3711yescharacteristic
307C4×Q8C23×C3711yescharacteristic
308C4×D4—21no—
309C4×D4—21no—
310C4×D4D4×C3711yescharacteristic
311C4×D4C23×C3711yescharacteristic
312#117—21no—
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—21no—
322#106—21no—
323C4⋊C8—22no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8D4×C3711yescharacteristic
327C4⋊C8D4×C3711yescharacteristic
328C4⋊C8C23×C3712yes—
329C4⋊C8C23×C3711yescharacteristic
330C4⋊C8C23×C3712yes—
331C4⋊C8C23×C3711yescharacteristic
332#103—21no—
333#103—22no—
334#103—22no—
335#103—22no—
336#103—22no—
337#103—21no—
338#103—21no—
339#102—21no—
340C22⋊C8—21no—
341C22⋊C8—22no—
342C22⋊C8D4×C3712yes—
343#97—22no—
344C4×C8—21no—
345C4×C8C23×C3712yes—
346#41—22no—
347#41—41no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—42no—
352C2×Q8—42no—
353C2×Q8—41no—
354C2×Q8C2×D4×C3711yescharacteristic
355C2×D4—21no—
356C2×D4C2×D4×C3711yescharacteristic
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4C2×D4×C3711yescharacteristic
362C22×C4C2×D4×C3711yescharacteristic
363C22×C4#41×C3711yescharacteristic
364Q16—42no—
365Q16—44no—
366SD16—42no—
367SD16—44no—
368M16—42no—
369M16—81no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—82no—
375C2×C8C2×D4×C3712yes—
376C2×C8C2×D4×C3712yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
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—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—41no—
399C42C2×D4×C3711yescharacteristic
400C42C2×D4×C3711yescharacteristic
401C42#41×C3711yescharacteristic
402C42C24×C3711yescharacteristic
403C23—21no—
404C23#121×C3711yescharacteristic
405Q8—21no—
406Q8—21no—
407Q8—42no—
408Q8—41no—
409Q8—41no—
410Q8—42no—
411Q8—41no—
412Q8—41no—
413Q8—82no—
414D4—21no—
415D4—42no—
416D4AGL(1,ℤ/8)×C3712yes—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—82no—
433C2×C4#121×C3711yescharacteristic
434C2×C4#121×C3711yescharacteristic
435C2×C4#121×C3711yescharacteristic
436C2×C4C22×D4×C3711yescharacteristic
437C2×C4C22×D4×C3711yescharacteristic
438C2×C4C2×#41×C3711yescharacteristic
439C8—22no—
440C8—22no—
441C8—42no—
442C8—41no—
443C8—41no—
444C8—42no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22C2×#121×C3711yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—81no—
459C4—82no—
460C4—81no—
461C4C37×#47312yes—
462C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
463C4C37×#57511yescharacteristic
464C4C37×#57711yescharacteristic
465C4C37×#57811yescharacteristic
466C2—41no—
467C2—42no—
468C2C37×#304611yescharacteristic
469C2C37×#305511yescharacteristic
470C2C2×C37×#47311yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC2×#41×C37D4
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×#3230C2semidirect
5. C37×#1700C2semidirect
6. C37×#1694C2semidirect
7. C37×#1679C2semidirect
8. C37×#1673C2semidirect
9. C37×#1574C2semidirect
10. C37×#1561C2semidirect
11. C37×#1549C2semidirect
209. #19490C37direct (N × H)
231. #3230C2×C37semidirect
235. #1700C2×C37semidirect
236. #1694C2×C37semidirect
237. #1679C2×C37semidirect
238. #1673C2×C37semidirect
239. #1574C2×C37semidirect
240. #1561C2×C37semidirect
241. #1549C2×C37semidirect
284. C37#19490direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32302
C37×#31072
C37×#30392
C37×#29902
C37×#17002
C37×#16942
C37×#16792
C37×#16732
C37×#15742
C37×#15612
C37×#15492
#1949037