Finite Group Databasebeta

← C37×#2759 #17991577

Subgroups — C37×#2759 #17991577

Order 4736.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#401C211yesmaximal, characteristic, complemented
2C37×#397C211yesmaximal, characteristic
3C37×#397C211yesmaximal, characteristic
4C37×#395C211yesmaximal, characteristic, complemented
5C37×#393C211yesmaximal, characteristic
6C37×#393C211yesmaximal, characteristic
7C37×#391C211yesmaximal, characteristic, complemented
8C37×#391C211yesmaximal, characteristic, complemented
9C37×#391C211yesmaximal, characteristic, complemented
10C37×#388C211yesmaximal, characteristic
11C37×#388C211yesmaximal, characteristic
12C37×#388C211yesmaximal, characteristic
13C37×#387C211yesmaximal, characteristic, complemented
14C37×#387C211yesmaximal, characteristic, complemented
15C37×#383C211yesmaximal, characteristic, complemented
16C22×Q8×C37C2211yescharacteristic
17C22×Q8×C37C2211yescharacteristic
18C2×C4⋊C4×C37C2211yescharacteristic
19C2×C4⋊C4×C37C2211yescharacteristic
20C2×C4⋊C4×C37C2211yescharacteristic
21C2×C4⋊C4×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23C2×C22⋊C4×C37C2211yescharacteristic
24C2×C22⋊C4×C37C2211yescharacteristic
25C2×C22⋊C4×C37C2211yescharacteristic
26C2×C22⋊C4×C37C2211yescharacteristic
27C2×C22⋊C4×C37C2211yescharacteristic
28C2×C22⋊C4×C37C2211yescharacteristic
29C2×C22⋊C4×C37C2211yescharacteristic
30C2×C42×C37C2211yescharacteristic
31C2×C42×C37C2211yescharacteristic
32C2×C42×C37C2211yescharacteristic
33#95×C37C2211yescharacteristic
34#95×C37C2211yescharacteristic
35#95×C37C2211yescharacteristic
36#95×C37C2211yescharacteristic
37#95×C37C2211yescharacteristic
38#95×C37C2211yescharacteristic
39#95×C37C2211yescharacteristic
40#95×C37C2211yescharacteristic
41#95×C37C2211yescharacteristic
42#95×C37C2211yescharacteristic
43#95×C37C2211yescharacteristic
44#95×C37C2211yescharacteristic
45#95×C37C2211yescharacteristic
46#95×C37C2211yescharacteristic
47#95×C37C2211yescharacteristic
48#95×C37C2211yescharacteristic
49#95×C37C2211yescharacteristic
50#95×C37C2211yescharacteristic
51C24×C37C2311yescharacteristic
52C2×Q8×C37—22no—
53C2×Q8×C37—22no—
54C2×Q8×C37—22no—
55C2×Q8×C37—41no—
56C2×Q8×C37—41no—
57C2×Q8×C37—41no—
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C22×C4×C37C2311yescharacteristic
72C4⋊C4×C37—22no—
73C4⋊C4×C37—22no—
74C4⋊C4×C37—41no—
75C4⋊C4×C37—41no—
76C4⋊C4×C37—41no—
77C22⋊C4×C37—22no—
78C22⋊C4×C37—22no—
79C22⋊C4×C37—22no—
80C22⋊C4×C37—41no—
81C22⋊C4×C37—41no—
82C22⋊C4×C37—41no—
83C22⋊C4×C37—41no—
84C42×C37—22no—
85C42×C37—41no—
86C42×C37—41no—
87C23×C37—21no—
88C23×C37—21no—
89C23×C37—21no—
90C23×C37—21no—
91C23×C37—21no—
92C23×C37—21no—
93C23×C37—21no—
94C23×C37C2411yescharacteristic
95Q8×C37—44no—
96Q8×C37—44no—
97C2×C4×C37—21no—
98C2×C4×C37—21no—
99C2×C4×C37—21no—
100C2×C4×C37—21no—
101C2×C4×C37—21no—
102C2×C4×C37—21no—
103C2×C4×C37—21no—
104C2×C4×C37—21no—
105C2×C4×C37—21no—
106C2×C4×C37—21no—
107C2×C4×C37—21no—
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37#4112yes—
137C2×C4×C37#4112yes—
138C2×C4×C37#4112yes—
139C22×C37—41no—
140C22×C37—41no—
141C22×C37—41no—
142C22×C37—41no—
143C22×C37—41no—
144C22×C37—41no—
145C22×C37—41no—
146C22×C37C2×#4111yescharacteristic
147C22×C37C2×#4111yescharacteristic
148C22×C37C2×#4111yescharacteristic
149C22×C37H(5,𝔽2)11yescharacteristic
150C22×C37H(5,𝔽2)11yescharacteristic
151C22×C372−1+411yescharacteristic
152C22×C372−1+411yescharacteristic
153C4×C37—22no—
154C4×C37—22no—
155C4×C37—22no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37—41no—
163C4×C37—41no—
164C4×C37—41no—
165C4×C37—41no—
166C4×C37—41no—
167#2759C3711yesmaximal, characteristic, direct product factor, Sylow
168C2×C37—81no—
169C2×C37#53811yescharacteristic
170C2×C37#54211yescharacteristic
171C2×C37#54211yescharacteristic
172C2×C37#55111yescharacteristic
173C2×C37#55611yescharacteristic
174C2×C37#55611yescharacteristic
175C2×C37#56311yescharacteristic
176#401C2×C3711yescharacteristic, complemented
177#397C2×C3711yescharacteristic
178#397C2×C3711yescharacteristic
179#395C2×C3711yescharacteristic, complemented
180#393C2×C3711yescharacteristic
181#393C2×C3711yescharacteristic
182#391C2×C3711yescharacteristic, complemented
183#391C2×C3711yescharacteristic, complemented
184#391C2×C3711yescharacteristic, complemented
185#388C2×C3711yescharacteristic
186#388C2×C3711yescharacteristic
187#388C2×C3711yescharacteristic
188#387C2×C3711yescharacteristic, complemented
189#387C2×C3711yescharacteristic, complemented
190#383C2×C3711yescharacteristic, complemented
191C37#275911yescharacteristic, direct product factor, Sylow
192C22×Q8C22×C3711yescharacteristic
193C22×Q8C22×C3711yescharacteristic
194C2×C4⋊C4C22×C3711yescharacteristic
195C2×C4⋊C4C22×C3711yescharacteristic
196C2×C4⋊C4C22×C3711yescharacteristic
197C2×C4⋊C4C22×C3711yescharacteristic
198C2×C4⋊C4C22×C3711yescharacteristic
199C2×C22⋊C4C22×C3711yescharacteristic
200C2×C22⋊C4C22×C3711yescharacteristic
201C2×C22⋊C4C22×C3711yescharacteristic
202C2×C22⋊C4C22×C3711yescharacteristic
203C2×C22⋊C4C22×C3711yescharacteristic
204C2×C22⋊C4C22×C3711yescharacteristic
205C2×C22⋊C4C22×C3711yescharacteristic
206C2×C42C22×C3711yescharacteristic
207C2×C42C22×C3711yescharacteristic
208C2×C42C22×C3711yescharacteristic
209#95C22×C3711yescharacteristic
210#95C22×C3711yescharacteristic
211#95C22×C3711yescharacteristic
212#95C22×C3711yescharacteristic
213#95C22×C3711yescharacteristic
214#95C22×C3711yescharacteristic
215#95C22×C3711yescharacteristic
216#95C22×C3711yescharacteristic
217#95C22×C3711yescharacteristic
218#95C22×C3711yescharacteristic
219#95C22×C3711yescharacteristic
220#95C22×C3711yescharacteristic
221#95C22×C3711yescharacteristic
222#95C22×C3711yescharacteristic
223#95C22×C3711yescharacteristic
224#95C22×C3711yescharacteristic
225#95C22×C3711yescharacteristic
226#95C22×C3711yescharacteristic
227C24C23×C3711yescharacteristic
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4C23×C3711yescharacteristic
235C22×C4C23×C3711yescharacteristic
236C22×C4C23×C3711yescharacteristic
237C22×C4C23×C3711yescharacteristic
238C22×C4C23×C3711yescharacteristic
239C22×C4C23×C3711yescharacteristic
240C22×C4C23×C3711yescharacteristic
241C22×C4C23×C3711yescharacteristic
242C22×C4C23×C3711yescharacteristic
243C22×C4C23×C3711yescharacteristic
244C22×C4C23×C3711yescharacteristic
245C22×C4C23×C3711yescharacteristic
246C22×C4C23×C3711yescharacteristic
247C22×C4C23×C3711yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—22no—
261C42—41no—
262C42—41no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23C24×C3711yescharacteristic
271Q8—44no—
272Q8—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4#41×C3712yes—
313C2×C4#41×C3712yes—
314C2×C4#41×C3712yes—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22C2×#41×C3711yescharacteristic
323C22C2×#41×C3711yescharacteristic
324C22C2×#41×C3711yescharacteristic
325C22H(5,𝔽2)×C3711yescharacteristic
326C22H(5,𝔽2)×C3711yescharacteristic
327C222−1+4×C3711yescharacteristic
328C222−1+4×C3711yescharacteristic
329C4—22no—
330C4—22no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C2—81no—
344C2C37×#53811yescharacteristic
345C2C37×#54211yescharacteristic
346C2C37×#54211yescharacteristic
347C2C37×#55111yescharacteristic
348C2C37×#55611yescharacteristic
349C2C37×#55611yescharacteristic
350C2C37×#56311yescharacteristic
subgroupG/H
center, socleC23×C37C24
commutator, Frattini, cosocleC23C24×C37
prime radicalC24×C37C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#401C2semidirect
4. C37×#395C2semidirect
7. C37×#391C2semidirect
8. C37×#391C2semidirect
9. C37×#391C2semidirect
13. C37×#387C2semidirect
14. C37×#387C2semidirect
15. C37×#383C2semidirect
167. #2759C37direct (N × H)
176. #401C2×C37semidirect
179. #395C2×C37semidirect
182. #391C2×C37semidirect
183. #391C2×C37semidirect
184. #391C2×C37semidirect
188. #387C2×C37semidirect
189. #387C2×C37semidirect
190. #383C2×C37semidirect
191. C37#2759direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#4012
C37×#3972
C37×#3952
C37×#3932
C37×#3912
C37×#3882
C37×#3872
C37×#3832
#275937