Finite Group Databasebeta

← C37×#19468 #22640721

Subgroups — C37×#19468 #22640721

Order 9472.

672 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3208C211yesmaximal, characteristic
2C37×#3113C211yesmaximal, characteristic, complemented
3C2×C37×#460C211yesmaximal, characteristic
4C37×#2984C211yesmaximal, characteristic, complemented
5C37×#1702C212yesmaximal, complemented
6C37×#1686C212yesmaximal, complemented
7C37×#1682C212yesmaximal, complemented
8C37×#1666C212yesmaximal, complemented
9C37×#1573C211yesmaximal, characteristic, complemented
10C37×#1555C211yesmaximal, characteristic
11C37×#1552C211yesmaximal, characteristic, complemented
12C22×SD16×C37—21no—
13C37×#533C2211yescharacteristic
14C2×#127×C37C2211yescharacteristic
15C2×C4×Q8×C37C2211yescharacteristic
16C37×#492C2212yes—
17C37×#486C2212yes—
18C37×#483—21no—
19C37×#475C2211yescharacteristic, complemented
20C37×#475C2211yescharacteristic, complemented
21C37×#462C2211yescharacteristic, complemented
22C37×#462C2211yescharacteristic, complemented
23C37×#460—21no—
24C37×#460—21no—
25C37×#460—22no—
26C37×#460C2212yes—
27C37×#460C2212yes—
28C37×#451—21no—
29C37×#450—21no—
30C37×#450—21no—
31C37×#446—22no—
32C37×#446C2212yescomplemented
33C8×Q8×C37C2212yescomplemented
34C37×#441—21no—
35C37×#441—21no—
36C37×#432—21no—
37C37×#432C2211yescharacteristic
38C37×#432C2211yescharacteristic
39C37×#431—21no—
40C37×#431C2211yescharacteristic
41C2×C4⋊C8×C37C2211yescharacteristic
42C2×#102×C37—21no—
43C37×#335C2212yescomplemented
44C37×#334C2212yescomplemented
45C37×#332C2212yescomplemented
46C37×#332C2212yescomplemented
47C37×#331C2212yes—
48C37×#331C2212yes—
49C22×Q8×C37D411yescharacteristic
50C22×D4×C37—21no—
51C22×D4×C37—21no—
52C22×D4×C37—21no—
53C2×Q16×C37—21no—
54C2×Q16×C37—21no—
55C2×SD16×C37—22no—
56C2×SD16×C37—22no—
57C2×SD16×C37—22no—
58C2×SD16×C37—22no—
59C2×SD16×C37—44no—
60C22×C8×C37—21no—
61C4⋊Q8×C37C2311yescharacteristic
62C4⋊Q8×C37C2311yescharacteristic
63#127×C37—21no—
64#127×C37—21no—
65#127×C37—21no—
66#127×C37C2312yes—
67#125×C37—21no—
68C22⋊Q8×C37—21no—
69C22⋊Q8×C37—21no—
70C4×Q8×C37—21no—
71C4×Q8×C37—21no—
72C4×Q8×C37—21no—
73C4×Q8×C37—21no—
74C4×Q8×C37D411yescharacteristic
75C4×Q8×C37D411yescharacteristic
76C4×Q8×C37C2311yescharacteristic
77C4×Q8×C37C2311yescharacteristic
78#117×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37D411yescharacteristic
81C2×C42×C37—21no—
82C2×C42×C37C2311yescharacteristic
83#106×C37—21no—
84#106×C37—21no—
85C4⋊C8×C37—22no—
86C4⋊C8×C37—22no—
87C4⋊C8×C37—21no—
88C4⋊C8×C37D412yes—
89C4⋊C8×C37C2312yes—
90C4⋊C8×C37C2311yescharacteristic
91C4⋊C8×C37C2311yescharacteristic
92C4⋊C8×C37C2312yes—
93#103×C37—21no—
94#103×C37—21no—
95#103×C37—21no—
96#103×C37—21no—
97#102×C37—22no—
98#102×C37—22no—
99#102×C37—22no—
100#102×C37—22no—
101C22⋊C8×C37—21no—
102C22⋊C8×C37—21no—
103C22⋊C8×C37D411yescharacteristic
104C22⋊C8×C37D411yescharacteristic
105#97×C37—22no—
106#97×C37—21no—
107#97×C37—21no—
108C4×C8×C37—22no—
109C4×C8×C37C2312yes—
110C24×C37—41no—
111C2×Q8×C37—21no—
112C2×Q8×C37—22no—
113C2×Q8×C37—21no—
114C2×Q8×C37—21no—
115C2×Q8×C37—41no—
116C2×Q8×C37C2×D411yescharacteristic
117C2×Q8×C37C2×D411yescharacteristic
118C2×D4×C37—22no—
119C2×D4×C37—22no—
120C2×D4×C37—22no—
121C2×D4×C37—42no—
122C2×D4×C37—42no—
123C2×D4×C37—41no—
124C2×D4×C37—41no—
125C2×D4×C37—41no—
126C2×D4×C37—82no—
127C2×D4×C37—82no—
128C22×C4×C37—21no—
129C22×C4×C37—21no—
130C22×C4×C37C2×D411yescharacteristic
131C22×C4×C37C2×D411yescharacteristic
132C22×C4×C37#4111yescharacteristic
133Q16×C37—42no—
134Q16×C37—42no—
135SD16×C37—44no—
136SD16×C37—44no—
137SD16×C37—82no—
138SD16×C37—82no—
139C2×C8×C37—22no—
140C2×C8×C37—21no—
141C2×C8×C37—21no—
142C2×C8×C37—22no—
143C2×C8×C37—42no—
144C2×C8×C37C2×D412yes—
145C2×C8×C37C2×D412yes—
146C4⋊C4×C37—21no—
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—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—41no—
156C4⋊C4×C37—41no—
157C4⋊C4×C37C2×D411yescharacteristic
158C4⋊C4×C37C2×D411yescharacteristic
159C22⋊C4×C37—41no—
160C42×C37—21no—
161C42×C37—21no—
162C42×C37—21no—
163C42×C37—21no—
164C42×C37—41no—
165C42×C37C2×D411yescharacteristic
166C42×C37C2×D411yescharacteristic
167C42×C37#4111yescharacteristic
168C42×C37C2411yescharacteristic
169C23×C37—42no—
170C23×C37—82no—
171C23×C37—82no—
172C23×C37—82no—
173C23×C37#12111yescharacteristic
174Q8×C37—21no—
175Q8×C37—21no—
176Q8×C37—21no—
177Q8×C37—42no—
178Q8×C37—41no—
179Q8×C37—41no—
180Q8×C37—42no—
181Q8×C37AGL(1,ℤ/8)12yes—
182D4×C37—42no—
183D4×C37—42no—
184D4×C37—42no—
185D4×C37—42no—
186D4×C37—82no—
187D4×C37—82no—
188D4×C37—82no—
189D4×C37—82no—
190C2×C4×C37—21no—
191C2×C4×C37—22no—
192C2×C4×C37—21no—
193C2×C4×C37—21no—
194C2×C4×C37—22no—
195C2×C4×C37—21no—
196C2×C4×C37—21no—
197C2×C4×C37—21no—
198C2×C4×C37—42no—
199C2×C4×C37—42no—
200C2×C4×C37—41no—
201C2×C4×C37—41no—
202C2×C4×C37#12111yescharacteristic
203C2×C4×C37#12111yescharacteristic
204C2×C4×C37#12111yescharacteristic
205C2×C4×C37C22×D411yescharacteristic
206C2×C4×C37C22×D411yescharacteristic
207C2×C4×C37C2×#4111yescharacteristic
208C8×C37—22no—
209C8×C37—22no—
210C8×C37—42no—
211C8×C37—41no—
212C8×C37—41no—
213C8×C37—42no—
214#19468C3711yesmaximal, characteristic, direct product factor, Sylow
215C22×C37—21no—
216C22×C37—21no—
217C22×C37—82no—
218C22×C37—82no—
219C22×C37—82no—
220C22×C37—164no—
221C22×C37#47112yes—
222C22×C37C2×#12111yescharacteristic
223C4×C37—21no—
224C4×C37—21no—
225C4×C37—22no—
226C4×C37—21no—
227C4×C37—21no—
228C4×C37—41no—
229C4×C37—41no—
230C4×C37—41no—
231C4×C37—81no—
232C4×C37—81no—
233C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C37#57511yescharacteristic
235C4×C37#57712yes—
236#3208C2×C3711yescharacteristic
237#3113C2×C3711yescharacteristic, complemented
238C2×#460C2×C3711yescharacteristic
239#2984C2×C3711yescharacteristic, complemented
240#1702C2×C3712yescomplemented
241#1686C2×C3712yescomplemented
242#1682C2×C3712yescomplemented
243#1666C2×C3712yescomplemented
244#1573C2×C3711yescharacteristic, complemented
245#1555C2×C3711yescharacteristic
246#1552C2×C3711yescharacteristic, complemented
247C2×C37—22no—
248C2×C37—162no—
249C2×C37#304311yescharacteristic
250C2×C37#305511yescharacteristic
251C2×C37C2×#47111yescharacteristic
252C22×SD16—21no—
253#533C22×C3711yescharacteristic
254C2×#127C22×C3711yescharacteristic
255C2×C4×Q8C22×C3711yescharacteristic
256#492C22×C3712yes—
257#486C22×C3712yes—
258#483—21no—
259#475C22×C3711yescharacteristic, complemented
260#475C22×C3711yescharacteristic, complemented
261#462C22×C3711yescharacteristic, complemented
262#462C22×C3711yescharacteristic, complemented
263#460—21no—
264#460—21no—
265#460—22no—
266#460C22×C3712yes—
267#460C22×C3712yes—
268#451—21no—
269#450—21no—
270#450—21no—
271#446—22no—
272#446C22×C3712yescomplemented
273C8×Q8C22×C3712yescomplemented
274#441—21no—
275#441—21no—
276#432—21no—
277#432C22×C3711yescharacteristic
278#432C22×C3711yescharacteristic
279#431—21no—
280#431C22×C3711yescharacteristic
281C2×C4⋊C8C22×C3711yescharacteristic
282C2×#102—21no—
283#335C22×C3712yescomplemented
284#334C22×C3712yescomplemented
285#332C22×C3712yescomplemented
286#332C22×C3712yescomplemented
287#331C22×C3712yes—
288#331C22×C3712yes—
289C37#1946811yescharacteristic, direct product factor, Sylow
290C22×Q8D4×C3711yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C2×Q16—21no—
295C2×Q16—21no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×SD16—22no—
299C2×SD16—22no—
300C2×SD16—44no—
301C22×C8—21no—
302C4⋊Q8C23×C3711yescharacteristic
303C4⋊Q8C23×C3711yescharacteristic
304#127—21no—
305#127—21no—
306#127—21no—
307#127C23×C3712yes—
308#125—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8D4×C3711yescharacteristic
316C4×Q8D4×C3711yescharacteristic
317C4×Q8C23×C3711yescharacteristic
318C4×Q8C23×C3711yescharacteristic
319#117—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4D4×C3711yescharacteristic
322C2×C42—21no—
323C2×C42C23×C3711yescharacteristic
324#106—21no—
325#106—21no—
326C4⋊C8—22no—
327C4⋊C8—22no—
328C4⋊C8—21no—
329C4⋊C8D4×C3712yes—
330C4⋊C8C23×C3712yes—
331C4⋊C8C23×C3711yescharacteristic
332C4⋊C8C23×C3711yescharacteristic
333C4⋊C8C23×C3712yes—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—21no—
338#102—22no—
339#102—22no—
340#102—22no—
341#102—22no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8D4×C3711yescharacteristic
345C22⋊C8D4×C3711yescharacteristic
346#97—22no—
347#97—21no—
348#97—21no—
349C4×C8—22no—
350C4×C8C23×C3712yes—
351C24—41no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—41no—
357C2×Q8C2×D4×C3711yescharacteristic
358C2×Q8C2×D4×C3711yescharacteristic
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—42no—
363C2×D4—42no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—82no—
368C2×D4—82no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4C2×D4×C3711yescharacteristic
372C22×C4C2×D4×C3711yescharacteristic
373C22×C4#41×C3711yescharacteristic
374Q16—42no—
375Q16—42no—
376SD16—44no—
377SD16—44no—
378SD16—82no—
379SD16—82no—
380C2×C8—22no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—42no—
385C2×C8C2×D4×C3712yes—
386C2×C8C2×D4×C3712yes—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C3711yescharacteristic
399C4⋊C4C2×D4×C3711yescharacteristic
400C22⋊C4—41no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42—41no—
406C42C2×D4×C3711yescharacteristic
407C42C2×D4×C3711yescharacteristic
408C42#41×C3711yescharacteristic
409C42C24×C3711yescharacteristic
410C23—42no—
411C23—82no—
412C23—82no—
413C23—82no—
414C23#121×C3711yescharacteristic
415Q8—21no—
416Q8—21no—
417Q8—21no—
418Q8—42no—
419Q8—41no—
420Q8—41no—
421Q8—42no—
422Q8AGL(1,ℤ/8)×C3712yes—
423D4—42no—
424D4—42no—
425D4—42no—
426D4—42no—
427D4—82no—
428D4—82no—
429D4—82no—
430D4—82no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4#121×C3711yescharacteristic
444C2×C4#121×C3711yescharacteristic
445C2×C4#121×C3711yescharacteristic
446C2×C4C22×D4×C3711yescharacteristic
447C2×C4C22×D4×C3711yescharacteristic
448C2×C4C2×#41×C3711yescharacteristic
449C8—22no—
450C8—22no—
451C8—42no—
452C8—41no—
453C8—41no—
454C8—42no—
455C22—21no—
456C22—21no—
457C22—82no—
458C22—82no—
459C22—82no—
460C22—164no—
461C22C37×#47112yes—
462C22C2×#121×C3711yescharacteristic
463C4—21no—
464C4—21no—
465C4—22no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—81no—
472C4—81no—
473C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
474C4C37×#57511yescharacteristic
475C4C37×#57712yes—
476C2—22no—
477C2—162no—
478C2C37×#304311yescharacteristic
479C2C37×#305511yescharacteristic
480C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC2×#127×C37C22
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
2. C37×#3113C2semidirect
4. C37×#2984C2semidirect
5. C37×#1702C2semidirect
6. C37×#1686C2semidirect
7. C37×#1682C2semidirect
8. C37×#1666C2semidirect
9. C37×#1573C2semidirect
11. C37×#1552C2semidirect
19. C37×#475C22semidirect
20. C37×#475C22semidirect
21. C37×#462C22semidirect
22. C37×#462C22semidirect
32. C37×#446C22semidirect
33. C8×Q8×C37C22semidirect
43. C37×#335C22semidirect
44. C37×#334C22semidirect
45. C37×#332C22semidirect
46. C37×#332C22semidirect
214. #19468C37direct (N × H)
237. #3113C2×C37semidirect
239. #2984C2×C37semidirect
240. #1702C2×C37semidirect
241. #1686C2×C37semidirect
242. #1682C2×C37semidirect
243. #1666C2×C37semidirect
244. #1573C2×C37semidirect
246. #1552C2×C37semidirect
259. #475C22×C37semidirect
260. #475C22×C37semidirect
261. #462C22×C37semidirect
262. #462C22×C37semidirect
272. #446C22×C37semidirect
273. C8×Q8C22×C37semidirect
283. #335C22×C37semidirect
284. #334C22×C37semidirect
285. #332C22×C37semidirect
286. #332C22×C37semidirect
289. C37#19468direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32082
C37×#31132
C2×C37×#4602
C37×#29842
C37×#17022
C37×#16862
C37×#16822
C37×#16662
C37×#15732
C37×#15552
C37×#15522
#1946837