Finite Group Databasebeta

← C37×#19482 #22640735

Subgroups — C37×#19482 #22640735

Order 9472.

626 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3206C211yesmaximal, characteristic, complemented
2C37×#3106C211yesmaximal, characteristic
3C37×#3079C211yesmaximal, characteristic, complemented
4C37×#2990C211yesmaximal, characteristic, complemented
5C37×#1704C212yesmaximal, complemented
6C37×#1686C212yesmaximal, complemented
7C37×#1683C212yesmaximal, complemented
8C37×#1665C212yesmaximal, complemented
9C37×#1574C211yesmaximal, characteristic, complemented
10C37×#1560C211yesmaximal, characteristic, complemented
11C37×#1546C211yesmaximal, characteristic, complemented
12C37×#532C2211yescharacteristic
13C2×C4⋊Q8×C37C2211yescharacteristic
14C4×#41×C37C2211yescharacteristic
15C37×#492C2212yes—
16C37×#487C2212yes—
17C37×#482—21no—
18C37×#477—21no—
19C37×#477C2211yescharacteristic
20C37×#476—21no—
21C37×#476C2211yescharacteristic
22C37×#475C2212yes—
23C37×#474C2212yes—
24C37×#461—21no—
25C37×#461—21no—
26C37×#460C2211yescharacteristic
27C37×#459C2211yescharacteristic
28C37×#449—21no—
29C37×#448—22no—
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×#332C2212yes—
47C37×#332C2212yes—
48C37×#331C2212yes—
49C2×#41×C37—21no—
50C2×#41×C37D411yescharacteristic
51C22×Q8×C37—21no—
52C2×SD16×C37—21no—
53C2×SD16×C37—22no—
54C2×SD16×C37—22no—
55C2×D8×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
64#127×C37C2311yescharacteristic
65#124×C37—21no—
66#121×C37—21no—
67#121×C37—21no—
68C4×Q8×C37D411yescharacteristic
69C4×Q8×C37C2311yescharacteristic
70C4×D4×C37—21no—
71C4×D4×C37—21no—
72C4×D4×C37—21no—
73C4×D4×C37—21no—
74C4×D4×C37D411yescharacteristic
75C4×D4×C37C2311yescharacteristic
76#117×C37—21no—
77#117×C37D411yescharacteristic
78C2×C4⋊C4×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C42×C37—21no—
81C2×C42×C37C2311yescharacteristic
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#103×C37—22no—
98#103×C37—22no—
99#102×C37—22no—
100#102×C37—21no—
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—22no—
113C2×Q8×C37—21no—
114C2×Q8×C37—41no—
115C2×Q8×C37—81no—
116C2×Q8×C37—81no—
117C2×Q8×C37C2×D411yescharacteristic
118C2×D4×C37—21no—
119C2×D4×C37—21no—
120C2×D4×C37—21no—
121C2×D4×C37—21no—
122C2×D4×C37—41no—
123C2×D4×C37C2×D411yescharacteristic
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—21no—
127C22×C4×C37—41no—
128C22×C4×C37—41no—
129C22×C4×C37C2×D411yescharacteristic
130C22×C4×C37C2×D411yescharacteristic
131C22×C4×C37#4111yescharacteristic
132SD16×C37—42no—
133SD16×C37—82no—
134SD16×C37—82no—
135D8×C37—42no—
136M16×C37—42no—
137M16×C37—81no—
138C2×C8×C37—21no—
139C2×C8×C37—21no—
140C2×C8×C37—22no—
141C2×C8×C37—22no—
142C2×C8×C37—82no—
143C2×C8×C37C2×D412yes—
144C2×C8×C37C2×D412yes—
145C4⋊C4×C37—21no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—22no—
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—
159C22⋊C4×C37—41no—
160C42×C37—21no—
161C42×C37—21no—
162C42×C37—21no—
163C42×C37C2×D411yescharacteristic
164C42×C37C2×D411yescharacteristic
165C42×C37#4111yescharacteristic
166C42×C37C2411yescharacteristic
167C23×C37—21no—
168C23×C37—41no—
169C23×C37#12111yescharacteristic
170Q8×C37—21no—
171Q8×C37—21no—
172Q8×C37—42no—
173Q8×C37—42no—
174Q8×C37—81no—
175Q8×C37—82no—
176D4×C37—21no—
177D4×C37—42no—
178D4×C37—41no—
179D4×C37—41no—
180D4×C37—41no—
181D4×C37—41no—
182D4×C37—81no—
183D4×C37—82no—
184D4×C37#13712yes—
185C2×C4×C37—21no—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—21no—
189C2×C4×C37—22no—
190C2×C4×C37—21no—
191C2×C4×C37—21no—
192C2×C4×C37—21no—
193C2×C4×C37—42no—
194C2×C4×C37—41no—
195C2×C4×C37—41no—
196C2×C4×C37—42no—
197C2×C4×C37—41no—
198C2×C4×C37—42no—
199C2×C4×C37—82no—
200C2×C4×C37—82no—
201C2×C4×C37#12111yescharacteristic
202C2×C4×C37#12111yescharacteristic
203C2×C4×C37#12111yescharacteristic
204C2×C4×C37C22×D411yescharacteristic
205C2×C4×C37C22×D411yescharacteristic
206C2×C4×C37C2×#4111yescharacteristic
207C8×C37—22no—
208C8×C37—22no—
209C8×C37—41no—
210C8×C37—42no—
211C8×C37—41no—
212C8×C37—42no—
213#19482C3711yesmaximal, characteristic, direct product factor, Sylow
214C22×C37—21no—
215C22×C37—21no—
216C22×C37—22no—
217C22×C37—21no—
218C22×C37—41no—
219C22×C37—41no—
220C22×C37—81no—
221C22×C37—81no—
222C22×C37—81no—
223C22×C37C2×#12111yescharacteristic
224C4×C37—21no—
225C4×C37—21no—
226C4×C37—21no—
227C4×C37—41no—
228C4×C37—41no—
229C4×C37—41no—
230C4×C37—82no—
231C4×C37—81no—
232C4×C37#47112yes—
233C4×C37C2×#13711yescharacteristic
234C4×C37#57511yescharacteristic
235C4×C37#57611yescharacteristic
236C4×C37#57711yescharacteristic
237#3206C2×C3711yescharacteristic, complemented
238#3106C2×C3711yescharacteristic
239#3079C2×C3711yescharacteristic, complemented
240#2990C2×C3711yescharacteristic, complemented
241#1704C2×C3712yescomplemented
242#1686C2×C3712yescomplemented
243#1683C2×C3712yescomplemented
244#1665C2×C3712yescomplemented
245#1574C2×C3711yescharacteristic, complemented
246#1560C2×C3711yescharacteristic, complemented
247#1546C2×C3711yescharacteristic, complemented
248C2×C37—41no—
249C2×C37—42no—
250C2×C37—161no—
251C2×C37#304511yescharacteristic
252C2×C37#305611yescharacteristic
253C2×C37C2×#47111yescharacteristic
254#532C22×C3711yescharacteristic
255C2×C4⋊Q8C22×C3711yescharacteristic
256C4×#41C22×C3711yescharacteristic
257#492C22×C3712yes—
258#487C22×C3712yes—
259#482—21no—
260#477—21no—
261#477C22×C3711yescharacteristic
262#476—21no—
263#476C22×C3711yescharacteristic
264#475C22×C3712yes—
265#474C22×C3712yes—
266#461—21no—
267#461—21no—
268#460C22×C3711yescharacteristic
269#459C22×C3711yescharacteristic
270#449—21no—
271#448—22no—
272#446C22×C3712yes—
273C4×SD16—21no—
274C4×D8—21no—
275#435—22no—
276C8×D4C22×C3712yes—
277#432—21no—
278#431C22×C3711yescharacteristic
279#431C22×C3711yescharacteristic
280#428—21no—
281#423C22×C3711yescharacteristic
282#423C22×C3711yescharacteristic
283C2×C4⋊C8—21no—
284#417—21no—
285#335C22×C3712yes—
286#334C22×C3712yes—
287#333C22×C3712yes—
288#332C22×C3712yes—
289#332C22×C3712yes—
290#331C22×C3712yes—
291C37#1948211yescharacteristic, direct product factor, Sylow
292C2×#41—21no—
293C2×#41D4×C3711yescharacteristic
294C22×Q8—21no—
295C2×SD16—21no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×D8—21no—
299C2×M16—21no—
300C2×M16—21no—
301C22×C8—22no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C23×C3712yes—
306C4⋊Q8C23×C3711yescharacteristic
307#127C23×C3711yescharacteristic
308#124—21no—
309#121—21no—
310#121—21no—
311C4×Q8D4×C3711yescharacteristic
312C4×Q8C23×C3711yescharacteristic
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4D4×C3711yescharacteristic
318C4×D4C23×C3711yescharacteristic
319#117—21no—
320#117D4×C3711yescharacteristic
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C42—21no—
324C2×C42C23×C3711yescharacteristic
325#107—22no—
326#107—21no—
327#106—22no—
328#106—21no—
329C4⋊C8—22no—
330C4⋊C8—21no—
331C4⋊C8—21no—
332C4⋊C8D4×C3711yescharacteristic
333C4⋊C8D4×C3711yescharacteristic
334C4⋊C8C23×C3712yes—
335C4⋊C8C23×C3712yes—
336C4⋊C8C23×C3711yescharacteristic
337C4⋊C8C23×C3711yescharacteristic
338#103—22no—
339#103—21no—
340#103—22no—
341#103—22no—
342#102—22no—
343#102—21no—
344#102—21no—
345#102—21no—
346C22⋊C8—21no—
347C22⋊C8—22no—
348C22⋊C8D4×C3712yes—
349#97—22no—
350C4×C8—21no—
351C4×C8C23×C3712yes—
352#41—22no—
353#41—41no—
354#41—82no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—41no—
358C2×Q8—81no—
359C2×Q8—81no—
360C2×Q8C2×D4×C3711yescharacteristic
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4C2×D4×C3711yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4C2×D4×C3711yescharacteristic
373C22×C4C2×D4×C3711yescharacteristic
374C22×C4#41×C3711yescharacteristic
375SD16—42no—
376SD16—82no—
377SD16—82no—
378D8—42no—
379M16—42no—
380M16—81no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—82no—
386C2×C8C2×D4×C3712yes—
387C2×C8C2×D4×C3712yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C3711yescharacteristic
397C4⋊C4C2×D4×C3711yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42C2×D4×C3711yescharacteristic
407C42C2×D4×C3711yescharacteristic
408C42#41×C3711yescharacteristic
409C42C24×C3711yescharacteristic
410C23—21no—
411C23—41no—
412C23#121×C3711yescharacteristic
413Q8—21no—
414Q8—21no—
415Q8—42no—
416Q8—42no—
417Q8—81no—
418Q8—82no—
419D4—21no—
420D4—42no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—81no—
426D4—82no—
427D4#137×C3712yes—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4#121×C3711yescharacteristic
445C2×C4#121×C3711yescharacteristic
446C2×C4#121×C3711yescharacteristic
447C2×C4C22×D4×C3711yescharacteristic
448C2×C4C22×D4×C3711yescharacteristic
449C2×C4C2×#41×C3711yescharacteristic
450C8—22no—
451C8—22no—
452C8—41no—
453C8—42no—
454C8—41no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—21no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22C2×#121×C3711yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—82no—
473C4—81no—
474C4C37×#47112yes—
475C4C2×#137×C3711yescharacteristic
476C4C37×#57511yescharacteristic
477C4C37×#57611yescharacteristic
478C4C37×#57711yescharacteristic
479C2—41no—
480C2—42no—
481C2—161no—
482C2C37×#304511yescharacteristic
483C2C37×#305611yescharacteristic
484C2C2×C37×#47111yescharacteristic
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×#3206C2semidirect
3. C37×#3079C2semidirect
4. C37×#2990C2semidirect
5. C37×#1704C2semidirect
6. C37×#1686C2semidirect
7. C37×#1683C2semidirect
8. C37×#1665C2semidirect
9. C37×#1574C2semidirect
10. C37×#1560C2semidirect
11. C37×#1546C2semidirect
213. #19482C37direct (N × H)
237. #3206C2×C37semidirect
239. #3079C2×C37semidirect
240. #2990C2×C37semidirect
241. #1704C2×C37semidirect
242. #1686C2×C37semidirect
243. #1683C2×C37semidirect
244. #1665C2×C37semidirect
245. #1574C2×C37semidirect
246. #1560C2×C37semidirect
247. #1546C2×C37semidirect
291. C37#19482direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32062
C37×#31062
C37×#30792
C37×#29902
C37×#17042
C37×#16862
C37×#16832
C37×#16652
C37×#15742
C37×#15602
C37×#15462
#1948237