Finite Group Databasebeta

← C37×#28387 #22649640

Subgroups — C37×#28387 #22649640

Order 9472.

1042 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#478C212yesmaximal, complemented
2C2×C37×#459C212yesmaximal, complemented
3C37×#2641C211yesmaximal, characteristic, complemented
4C37×#2328C211yesmaximal, characteristic, complemented
5C37×#2092C212yesmaximal, complemented
6C37×#2011C212yesmaximal, complemented
7C37×#1972C212yesmaximal, complemented
8C37×#1970C212yesmaximal, complemented
9C37×#1768C211yesmaximal, characteristic, complemented
10C22×D8×C37C2212yes—
11C22×D8×C37C2212yes—
12C2×#127×C37C2211yescharacteristic
13C2×#127×C37C2211yescharacteristic
14C2×#125×C37C2211yescharacteristic
15C2×C4×D4×C37C2212yes—
16C37×#478—28no—
17C37×#459—28no—
18C2×#107×C37C2212yes—
19C2×#106×C37C2212yes—
20C2×C4⋊C8×C37C2212yes—
21C2×#102×C37C2212yes—
22C2×#102×C37C2212yes—
23C2×#102×C37C2212yes—
24C2×#102×C37C2212yes—
25C2×#97×C37C2211yescharacteristic
26C2×C4×C8×C37C2211yescharacteristic
27C37×#394—24no—
28C37×#390C2212yes—
29C37×#390C2212yes—
30C37×#390C2212yes—
31C37×#386—24no—
32C37×#382C2211yescharacteristic
33C37×#376C2211yescharacteristic
34C37×#336C2212yes—
35C22×D4×C37—22no—
36C22×D4×C37—22no—
37C22×D4×C37C2312yes—
38C22×D4×C37C2312yes—
39C23×C4×C37—22no—
40C2×D8×C37—24no—
41C2×D8×C37—24no—
42C2×D8×C37—24no—
43C2×D8×C37—24no—
44C2×D8×C37—42no—
45C2×D8×C37—42no—
46C22×C8×C37C2312yes—
47C22×C8×C37C2312yes—
48#127×C37—24no—
49#127×C37—24no—
50#125×C37—24no—
51C4×D4×C37—24no—
52C4×D4×C37—24no—
53C2×C4⋊C4×C37—22no—
54C2×C4⋊C4×C37C2312yes—
55C2×C4⋊C4×C37C2312yes—
56C2×C22⋊C4×C37—22no—
57C2×C22⋊C4×C37—24no—
58C2×C22⋊C4×C37—24no—
59C2×C22⋊C4×C37—24no—
60C2×C42×C37C2311yescharacteristic
61C2×C42×C37C2311yescharacteristic
62C2×C42×C37C2311yescharacteristic
63#107×C37—24no—
64#106×C37—24no—
65C4⋊C8×C37D418yescomplemented
66#102×C37—24no—
67#102×C37—24no—
68#102×C37—24no—
69#102×C37—24no—
70#97×C37—41no—
71C4×C8×C37—41no—
72#95×C37—22no—
73#95×C37D414yes—
74C24×C37—22no—
75C24×C37—22no—
76C2×D4×C37—28no—
77C2×D4×C37—22no—
78C2×D4×C37—22no—
79C2×D4×C37—22no—
80C2×D4×C37—22no—
81C2×D4×C37—22no—
82C2×D4×C37—22no—
83C2×D4×C37—22no—
84C2×D4×C37—22no—
85C2×D4×C37—22no—
86C2×D4×C37—22no—
87C2×D4×C37—22no—
88C2×D4×C37—44no—
89C2×D4×C37—84no—
90C2×D4×C37—84no—
91C2×D4×C37#4114yes—
92C22×C4×C37—22no—
93C22×C4×C37—22no—
94C22×C4×C37—44no—
95C22×C4×C37—84no—
96C22×C4×C37C2×D412yes—
97C22×C4×C37C2×D412yes—
98C22×C4×C37C2×D412yes—
99C22×C4×C37C2411yescharacteristic
100D8×C37—48no—
101D8×C37—48no—
102C2×C8×C37—22no—
103C2×C8×C37—22no—
104C2×C8×C37—22no—
105C2×C8×C37—22no—
106C2×C8×C37C2×D414yes—
107C2×C8×C37C2×D414yes—
108C4⋊C4×C37—22no—
109C4⋊C4×C37—22no—
110C4⋊C4×C37—22no—
111C4⋊C4×C37—22no—
112C4⋊C4×C37—44no—
113C22⋊C4×C37—44no—
114C22⋊C4×C37—84no—
115C22⋊C4×C37—84no—
116C22⋊C4×C37—84no—
117C42×C37—22no—
118C42×C37—21no—
119C42×C37—21no—
120C42×C37C2×D414yes—
121C23×C37—24no—
122C23×C37—42no—
123C23×C37—42no—
124C23×C37—44no—
125C23×C37—44no—
126C23×C37—42no—
127C23×C37—42no—
128C23×C37—42no—
129C23×C37—44no—
130C23×C37—44no—
131C23×C37C22×D411yescharacteristic
132D4×C37—24no—
133D4×C37—24no—
134D4×C37—42no—
135D4×C37—42no—
136D4×C37—42no—
137D4×C37—42no—
138D4×C37—42no—
139D4×C37—42no—
140D4×C37—88no—
141D4×C37—88no—
142C2×C4×C37—24no—
143C2×C4×C37—22no—
144C2×C4×C37—22no—
145C2×C4×C37—24no—
146C2×C4×C37—24no—
147C2×C4×C37—42no—
148C2×C4×C37—42no—
149C2×C4×C37—44no—
150C2×C4×C37—44no—
151C2×C4×C37—88no—
152C2×C4×C37#12714yes—
153C2×C4×C37C22×D412yes—
154C2×C4×C37C2×#4112yes—
155C2×C4×C37H(5,𝔽2)11yescharacteristic
156C2×C4×C372−1+411yescharacteristic
157C8×C37—24no—
158C8×C37—24no—
159#28387C3711yesmaximal, characteristic, direct product factor, Sylow
160C22×C37—48no—
161C22×C37—44no—
162C22×C37—82no—
163C22×C37—82no—
164C22×C37—84no—
165C22×C37—84no—
166C22×C37—82no—
167C22×C37—82no—
168C22×C37—84no—
169C22×C37—82no—
170C22×C37#52511yescharacteristic
171C22×C37C2×#12711yescharacteristic
172C22×C37#53711yescharacteristic
173C22×C37#57614yes—
174C4×C37—24no—
175C4×C37—42no—
176C4×C37—42no—
177C4×C37—82no—
178C4×C37—82no—
179C4×C37#54612yes—
180C4×C37#54812yes—
181C2×#478C2×C3712yescomplemented
182C2×#459C2×C3712yescomplemented
183#2641C2×C3711yescharacteristic, complemented
184#2328C2×C3711yescharacteristic, complemented
185#2092C2×C3712yescomplemented
186#2011C2×C3712yescomplemented
187#1972C2×C3712yescomplemented
188#1970C2×C3712yescomplemented
189#1768C2×C3711yescharacteristic, complemented
190C2×C37—84no—
191C2×C37—162no—
192C2×C37#254011yescharacteristic
193C2×C37#312212yes—
194C2×C37#315512yes—
195C2×C37#325912yes—
196C22×D8C22×C3712yes—
197C22×D8C22×C3712yes—
198C2×#127C22×C3711yescharacteristic
199C2×#127C22×C3711yescharacteristic
200C2×#125C22×C3711yescharacteristic
201C2×C4×D4C22×C3712yes—
202#478—28no—
203#459—28no—
204C2×#107C22×C3712yes—
205C2×#106C22×C3712yes—
206C2×C4⋊C8C22×C3712yes—
207C2×#102C22×C3712yes—
208C2×#102C22×C3712yes—
209C2×#102C22×C3712yes—
210C2×#102C22×C3712yes—
211C2×#97C22×C3711yescharacteristic
212C2×C4×C8C22×C3711yescharacteristic
213#394—24no—
214#390C22×C3712yes—
215#390C22×C3712yes—
216#390C22×C3712yes—
217#386—24no—
218#382C22×C3711yescharacteristic
219#376C22×C3711yescharacteristic
220#336C22×C3712yes—
221C37#2838711yescharacteristic, direct product factor, Sylow
222C22×D4—22no—
223C22×D4—22no—
224C22×D4C23×C3712yes—
225C22×D4C23×C3712yes—
226C23×C4—22no—
227C2×D8—24no—
228C2×D8—24no—
229C2×D8—24no—
230C2×D8—24no—
231C2×D8—42no—
232C2×D8—42no—
233C22×C8C23×C3712yes—
234C22×C8C23×C3712yes—
235#127—24no—
236#127—24no—
237#125—24no—
238C4×D4—24no—
239C4×D4—24no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4C23×C3712yes—
242C2×C4⋊C4C23×C3712yes—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—24no—
245C2×C22⋊C4—24no—
246C2×C22⋊C4—24no—
247C2×C42C23×C3711yescharacteristic
248C2×C42C23×C3711yescharacteristic
249C2×C42C23×C3711yescharacteristic
250#107—24no—
251#106—24no—
252C4⋊C8D4×C3718yescomplemented
253#102—24no—
254#102—24no—
255#102—24no—
256#102—24no—
257#97—41no—
258C4×C8—41no—
259#95—22no—
260#95D4×C3714yes—
261C24—22no—
262C24—22no—
263C2×D4—28no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—44no—
276C2×D4—84no—
277C2×D4—84no—
278C2×D4#41×C3714yes—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—44no—
282C22×C4—84no—
283C22×C4C2×D4×C3712yes—
284C22×C4C2×D4×C3712yes—
285C22×C4C2×D4×C3712yes—
286C22×C4C24×C3711yescharacteristic
287D8—48no—
288D8—48no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8C2×D4×C3714yes—
294C2×C8C2×D4×C3714yes—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—44no—
300C22⋊C4—44no—
301C22⋊C4—84no—
302C22⋊C4—84no—
303C22⋊C4—84no—
304C42—22no—
305C42—21no—
306C42—21no—
307C42C2×D4×C3714yes—
308C23—24no—
309C23—42no—
310C23—42no—
311C23—44no—
312C23—44no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—44no—
317C23—44no—
318C23C22×D4×C3711yescharacteristic
319D4—24no—
320D4—24no—
321D4—42no—
322D4—42no—
323D4—42no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—88no—
328D4—88no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—88no—
339C2×C4#127×C3714yes—
340C2×C4C22×D4×C3712yes—
341C2×C4C2×#41×C3712yes—
342C2×C4H(5,𝔽2)×C3711yescharacteristic
343C2×C42−1+4×C3711yescharacteristic
344C8—24no—
345C8—24no—
346C22—48no—
347C22—44no—
348C22—82no—
349C22—82no—
350C22—84no—
351C22—84no—
352C22—82no—
353C22—82no—
354C22—84no—
355C22—82no—
356C22C37×#52511yescharacteristic
357C22C2×#127×C3711yescharacteristic
358C22C37×#53711yescharacteristic
359C22C37×#57614yes—
360C4—24no—
361C4—42no—
362C4—42no—
363C4—82no—
364C4—82no—
365C4C37×#54612yes—
366C4C37×#54812yes—
367C2—84no—
368C2—162no—
369C2C37×#254011yescharacteristic
370C2C37×#312212yes—
371C2C37×#315512yes—
372C2C37×#325912yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C37×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#478C2semidirect
2. C2×C37×#459C2semidirect
3. C37×#2641C2semidirect
4. C37×#2328C2semidirect
5. C37×#2092C2semidirect
6. C37×#2011C2semidirect
7. C37×#1972C2semidirect
8. C37×#1970C2semidirect
9. C37×#1768C2semidirect
65. C4⋊C8×C37D4semidirect
159. #28387C37direct (N × H)
181. C2×#478C2×C37semidirect
182. C2×#459C2×C37semidirect
183. #2641C2×C37semidirect
184. #2328C2×C37semidirect
185. #2092C2×C37semidirect
186. #2011C2×C37semidirect
187. #1972C2×C37semidirect
188. #1970C2×C37semidirect
189. #1768C2×C37semidirect
221. C37#28387direct (N × H)
252. C4⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4782
C2×C37×#4592
C37×#26412
C37×#23282
C37×#20922
C37×#20112
C37×#19722
C37×#19702
C37×#17682
#2838737