Finite Group Databasebeta

← C37×#3311 #17992129

Subgroups — C37×#3311 #17992129

Order 4736.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#556C211yesmaximal, characteristic, complemented
2C37×#546C211yesmaximal, characteristic
3C37×#489C211yesmaximal, characteristic, complemented
4C37×#485C211yesmaximal, characteristic, complemented
5C37×#482C211yesmaximal, characteristic, complemented
6C37×#476C211yesmaximal, characteristic, complemented
7C37×#470C211yesmaximal, characteristic, complemented
8C37×#465C211yesmaximal, characteristic, complemented
9C37×#464C211yesmaximal, characteristic, complemented
10C37×#452C211yesmaximal, characteristic, complemented
11C37×#450C211yesmaximal, characteristic, complemented
12C37×#440C211yesmaximal, characteristic, complemented
13C37×#435C211yesmaximal, characteristic, complemented
14C37×#418C211yesmaximal, characteristic, complemented
15C37×#416C211yesmaximal, characteristic, complemented
16C2×#41×C37C2211yescharacteristic
17C22×D4×C37C2211yescharacteristic
18C2×Q16×C37C2211yescharacteristic, complemented
19C2×SD16×C37C2211yescharacteristic
20C2×SD16×C37C2211yescharacteristic
21C2×M16×C37C2211yescharacteristic
22C22×C8×C37C2211yescharacteristic, complemented
23C4⋊Q8×C37C2211yescharacteristic, complemented
24#126×C37—21no—
25#126×C37—21no—
26#124×C37—21no—
27#124×C37C2211yescharacteristic
28#123×C37—21no—
29C22⋊Q8×C37C2211yescharacteristic
30C22⋊Q8×C37C2211yescharacteristic
31C22⋊Q8×C37C2211yescharacteristic, complemented
32#121×C37—21no—
33#121×C37C2211yescharacteristic
34#120×C37—21no—
35C4×Q8×C37—21no—
36C4×Q8×C37C2211yescharacteristic, complemented
37C4×D4×C37C2211yescharacteristic
38C4×D4×C37C2211yescharacteristic
39#117×C37C2211yescharacteristic
40#117×C37C2211yescharacteristic, complemented
41C2×C22⋊C4×C37—21no—
42#107×C37C2211yescharacteristic, complemented
43#106×C37C2211yescharacteristic, complemented
44#106×C37C2211yescharacteristic, complemented
45C4⋊C8×C37C2211yescharacteristic, complemented
46#103×C37C2211yescharacteristic, complemented
47#103×C37C2211yescharacteristic, complemented
48#103×C37C2211yescharacteristic, complemented
49#103×C37C2211yescharacteristic, complemented
50#102×C37C2211yescharacteristic
51#102×C37C2211yescharacteristic
52#102×C37C2211yescharacteristic
53#102×C37C2211yescharacteristic
54#102×C37C2211yescharacteristic
55#102×C37C2211yescharacteristic
56C22⋊C8×C37C2211yescharacteristic
57C22⋊C8×C37C2211yescharacteristic, complemented
58#97×C37C2211yescharacteristic, complemented
59C24×C37—21no—
60#41×C37—22no—
61#41×C37—41no—
62C2×Q8×C37—21no—
63C2×Q8×C37C2311yescharacteristic
64C2×Q8×C37C2311yescharacteristic
65C2×D4×C37—22no—
66C2×D4×C37—21no—
67C2×D4×C37—21no—
68C2×D4×C37—21no—
69C2×D4×C37—41no—
70C2×D4×C37D411yescharacteristic
71C2×D4×C37C2311yescharacteristic
72C2×D4×C37C2311yescharacteristic
73C22×C4×C37—21no—
74C22×C4×C37—21no—
75C22×C4×C37C2311yescharacteristic
76C22×C4×C37C2311yescharacteristic
77Q16×C37—41no—
78SD16×C37—22no—
79SD16×C37—41no—
80M16×C37—41no—
81C2×C8×C37—41no—
82C2×C8×C37C2311yescharacteristic
83C2×C8×C37C2311yescharacteristic
84C2×C8×C37C2311yescharacteristic
85C2×C8×C37C2311yescharacteristic
86C4⋊C4×C37—21no—
87C4⋊C4×C37—21no—
88C4⋊C4×C37—21no—
89C4⋊C4×C37—21no—
90C4⋊C4×C37—21no—
91C4⋊C4×C37D411yescharacteristic
92C4⋊C4×C37C2311yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C4⋊C4×C37C2311yescharacteristic
95C4⋊C4×C37C2311yescharacteristic
96C22⋊C4×C37—21no—
97C22⋊C4×C37—21no—
98C22⋊C4×C37—21no—
99C22⋊C4×C37—21no—
100C22⋊C4×C37—21no—
101C22⋊C4×C37—21no—
102C22⋊C4×C37—21no—
103C22⋊C4×C37—21no—
104C22⋊C4×C37—21no—
105C22⋊C4×C37D411yescharacteristic
106C22⋊C4×C37D411yescharacteristic
107C42×C37—21no—
108C42×C37—21no—
109C42×C37—21no—
110C42×C37C2311yescharacteristic
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—42no—
114C23×C37—42no—
115C23×C37—81no—
116C23×C37C2×D411yescharacteristic
117C23×C37C2×D411yescharacteristic
118Q8×C37—21no—
119Q8×C37—21no—
120Q8×C37—21no—
121Q8×C37—21no—
122Q8×C37—42no—
123D4×C37—21no—
124D4×C37—21no—
125D4×C37—21no—
126D4×C37—41no—
127D4×C37—42no—
128D4×C37—42no—
129D4×C37—81no—
130D4×C37#4112yes—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—42no—
142C2×C4×C37—81no—
143C2×C4×C37C2×D411yescharacteristic
144C2×C4×C37C2×D411yescharacteristic
145C2×C4×C37C2×D411yescharacteristic
146C2×C4×C37C2×D411yescharacteristic
147C2×C4×C37C2411yescharacteristic
148C8×C37—21no—
149C8×C37—21no—
150C8×C37—21no—
151C8×C37—21no—
152C22×C37—21no—
153C22×C37—21no—
154C22×C37—22no—
155C22×C37—21no—
156C22×C37—21no—
157C22×C37—21no—
158C22×C37—21no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—84no—
165C22×C37C22×D411yescharacteristic
166C4×C37—21no—
167C4×C37—21no—
168C4×C37—21no—
169C4×C37—21no—
170C4×C37—41no—
171C4×C37—41no—
172C4×C37—41no—
173C4×C37—41no—
174C4×C37—41no—
175C4×C37—41no—
176C4×C37C2×#4111yescharacteristic
177C4×C37H(5,𝔽2)11yescharacteristic
178#3311C3711yesmaximal, characteristic, direct product factor, Sylow
179C2×C37—41no—
180C2×C37—41no—
181C2×C37—42no—
182C2×C37—81no—
183C2×C37#54611yescharacteristic
184C2×C37#57511yescharacteristic
185C2×C37#57711yescharacteristic
186#556C2×C3711yescharacteristic, complemented
187#546C2×C3711yescharacteristic
188#489C2×C3711yescharacteristic, complemented
189#485C2×C3711yescharacteristic, complemented
190#482C2×C3711yescharacteristic, complemented
191#476C2×C3711yescharacteristic, complemented
192#470C2×C3711yescharacteristic, complemented
193#465C2×C3711yescharacteristic, complemented
194#464C2×C3711yescharacteristic, complemented
195#452C2×C3711yescharacteristic, complemented
196#450C2×C3711yescharacteristic, complemented
197#440C2×C3711yescharacteristic, complemented
198#435C2×C3711yescharacteristic, complemented
199#418C2×C3711yescharacteristic, complemented
200#416C2×C3711yescharacteristic, complemented
201C37#331111yescharacteristic, direct product factor, Sylow
202C2×#41C22×C3711yescharacteristic
203C22×D4C22×C3711yescharacteristic
204C2×Q16C22×C3711yescharacteristic, complemented
205C2×SD16C22×C3711yescharacteristic
206C2×SD16C22×C3711yescharacteristic
207C2×M16C22×C3711yescharacteristic
208C22×C8C22×C3711yescharacteristic, complemented
209C4⋊Q8C22×C3711yescharacteristic, complemented
210#126—21no—
211#126—21no—
212#124—21no—
213#124C22×C3711yescharacteristic
214#123—21no—
215C22⋊Q8C22×C3711yescharacteristic
216C22⋊Q8C22×C3711yescharacteristic
217C22⋊Q8C22×C3711yescharacteristic, complemented
218#121—21no—
219#121C22×C3711yescharacteristic
220#120—21no—
221C4×Q8—21no—
222C4×Q8C22×C3711yescharacteristic, complemented
223C4×D4C22×C3711yescharacteristic
224C4×D4C22×C3711yescharacteristic
225#117C22×C3711yescharacteristic
226#117C22×C3711yescharacteristic, complemented
227C2×C22⋊C4—21no—
228#107C22×C3711yescharacteristic, complemented
229#106C22×C3711yescharacteristic, complemented
230#106C22×C3711yescharacteristic, complemented
231C4⋊C8C22×C3711yescharacteristic, complemented
232#103C22×C3711yescharacteristic, complemented
233#103C22×C3711yescharacteristic, complemented
234#103C22×C3711yescharacteristic, complemented
235#103C22×C3711yescharacteristic, complemented
236#102C22×C3711yescharacteristic
237#102C22×C3711yescharacteristic
238#102C22×C3711yescharacteristic
239#102C22×C3711yescharacteristic
240#102C22×C3711yescharacteristic
241#102C22×C3711yescharacteristic
242C22⋊C8C22×C3711yescharacteristic
243C22⋊C8C22×C3711yescharacteristic, complemented
244#97C22×C3711yescharacteristic, complemented
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—21no—
249C2×Q8C23×C3711yescharacteristic
250C2×Q8C23×C3711yescharacteristic
251C2×D4—22no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4D4×C3711yescharacteristic
257C2×D4C23×C3711yescharacteristic
258C2×D4C23×C3711yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4C23×C3711yescharacteristic
262C22×C4C23×C3711yescharacteristic
263Q16—41no—
264SD16—22no—
265SD16—41no—
266M16—41no—
267C2×C8—41no—
268C2×C8C23×C3711yescharacteristic
269C2×C8C23×C3711yescharacteristic
270C2×C8C23×C3711yescharacteristic
271C2×C8C23×C3711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4D4×C3711yescharacteristic
278C4⋊C4C23×C3711yescharacteristic
279C4⋊C4C23×C3711yescharacteristic
280C4⋊C4C23×C3711yescharacteristic
281C4⋊C4C23×C3711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4D4×C3711yescharacteristic
292C22⋊C4D4×C3711yescharacteristic
293C42—21no—
294C42—21no—
295C42—21no—
296C42C23×C3711yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×D4×C3711yescharacteristic
303C23C2×D4×C3711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—42no—
314D4—42no—
315D4—81no—
316D4#41×C3712yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—81no—
329C2×C4C2×D4×C3711yescharacteristic
330C2×C4C2×D4×C3711yescharacteristic
331C2×C4C2×D4×C3711yescharacteristic
332C2×C4C2×D4×C3711yescharacteristic
333C2×C4C24×C3711yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×D4×C3711yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4C2×#41×C3711yescharacteristic
363C4H(5,𝔽2)×C3711yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2C37×#54611yescharacteristic
369C2C37×#57511yescharacteristic
370C2C37×#57711yescharacteristic
subgroupG/H
center, socleC22×C37C22×D4
commutator, Frattini, cosocleC2×C4C24×C37
prime radicalC37×#546C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#556C2semidirect
3. C37×#489C2semidirect
4. C37×#485C2semidirect
5. C37×#482C2semidirect
6. C37×#476C2semidirect
7. C37×#470C2semidirect
8. C37×#465C2semidirect
9. C37×#464C2semidirect
10. C37×#452C2semidirect
11. C37×#450C2semidirect
12. C37×#440C2semidirect
13. C37×#435C2semidirect
14. C37×#418C2semidirect
15. C37×#416C2semidirect
18. C2×Q16×C37C22semidirect
22. C22×C8×C37C22semidirect
23. C4⋊Q8×C37C22semidirect
31. C22⋊Q8×C37C22semidirect
36. C4×Q8×C37C22semidirect
40. #117×C37C22semidirect
42. #107×C37C22semidirect
43. #106×C37C22semidirect
44. #106×C37C22semidirect
45. C4⋊C8×C37C22semidirect
46. #103×C37C22semidirect
47. #103×C37C22semidirect
48. #103×C37C22semidirect
49. #103×C37C22semidirect
57. C22⋊C8×C37C22semidirect
58. #97×C37C22semidirect
178. #3311C37direct (N × H)
186. #556C2×C37semidirect
188. #489C2×C37semidirect
189. #485C2×C37semidirect
190. #482C2×C37semidirect
191. #476C2×C37semidirect
192. #470C2×C37semidirect
193. #465C2×C37semidirect
194. #464C2×C37semidirect
195. #452C2×C37semidirect
196. #450C2×C37semidirect
197. #440C2×C37semidirect
198. #435C2×C37semidirect
199. #418C2×C37semidirect
200. #416C2×C37semidirect
201. C37#3311direct (N × H)
204. C2×Q16C22×C37semidirect
208. C22×C8C22×C37semidirect
209. C4⋊Q8C22×C37semidirect
217. C22⋊Q8C22×C37semidirect
222. C4×Q8C22×C37semidirect
226. #117C22×C37semidirect
228. #107C22×C37semidirect
229. #106C22×C37semidirect
230. #106C22×C37semidirect
231. C4⋊C8C22×C37semidirect
232. #103C22×C37semidirect
233. #103C22×C37semidirect
234. #103C22×C37semidirect
235. #103C22×C37semidirect
243. C22⋊C8C22×C37semidirect
244. #97C22×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#5562
C37×#5462
C37×#4892
C37×#4852
C37×#4822
C37×#4762
C37×#4702
C37×#4652
C37×#4642
C37×#4522
C37×#4502
C37×#4402
C37×#4352
C37×#4182
C37×#4162
#331137