Finite Group Databasebeta

← C37×#25858 #22647111

Subgroups — C37×#25858 #22647111

Order 9472.

1346 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#532C211yesmaximal, characteristic
2C2×C37×#488C212yesmaximal, complemented
3C37×#2851C211yesmaximal, characteristic, complemented
4C37×#2043C212yesmaximal, complemented
5C37×#2041C212yesmaximal, complemented
6C37×#1958C212yesmaximal, complemented
7C37×#1788C214yesmaximal, complemented
8C4×C22⋊C8×C37C211yesmaximal, characteristic, complemented
9C22×#41×C37C2212yes—
10C37×#532—28no—
11C2×C4⋊Q8×C37C2211yescharacteristic
12C2×#127×C37C2211yescharacteristic
13C2×#125×C37C2211yescharacteristic
14C2×#124×C37C2212yes—
15C2×#121×C37—22no—
16C2×C4×D4×C37—22no—
17C22×C42×C37C2211yescharacteristic
18C37×#488—28no—
19C2×#103×C37C2214yes—
20C2×#103×C37C2214yes—
21C2×#102×C37C2214yes—
22C2×#102×C37C2214yes—
23C2×C22⋊C8×C37C2212yes—
24C2×C4×C8×C37C2212yes—
25C37×#389C2212yes—
26C37×#387—22no—
27C37×#385—22no—
28C37×#382C2211yescharacteristic
29C37×#380C2212yes—
30C37×#336C2212yes—
31C2×#41×C37—24no—
32C2×#41×C37—24no—
33C2×#41×C37—28no—
34C2×#41×C37—44no—
35C22×Q8×C37C2312yes—
36C22×D4×C37—22no—
37C22×D4×C37—22no—
38C22×D4×C37C2312yes—
39C23×C4×C37—22no—
40C23×C4×C37D412yes—
41C23×C4×C37C2311yescharacteristic
42C22×C8×C37C2314yes—
43C4⋊Q8×C37—24no—
44#127×C37—24no—
45#125×C37—24no—
46#124×C37—24no—
47#124×C37D418yes—
48#121×C37—216no—
49C4×D4×C37—216no—
50C2×C4⋊C4×C37—22no—
51C2×C4⋊C4×C37—22no—
52C2×C4⋊C4×C37—22no—
53C2×C4⋊C4×C37C2312yes—
54C2×C4⋊C4×C37C2312yes—
55C2×C22⋊C4×C37—24no—
56C2×C22⋊C4×C37—22no—
57C2×C42×C37—24no—
58C2×C42×C37D412yes—
59C2×C42×C37C2311yescharacteristic
60C2×C42×C37C2311yescharacteristic
61#103×C37—28no—
62#103×C37—44no—
63#102×C37—28no—
64#102×C37—44no—
65C22⋊C8×C37—24no—
66C4×C8×C37—24no—
67#95×C37—22no—
68#95×C37—22no—
69#95×C37—22no—
70C24×C37—22no—
71C24×C37C2×D411yescharacteristic
72#41×C37—416no—
73#41×C37—416no—
74C2×Q8×C37—22no—
75C2×Q8×C37—24no—
76C2×Q8×C37—24no—
77C2×Q8×C37C2×D414yes—
78C2×D4×C37—28no—
79C2×D4×C37—28no—
80C2×D4×C37—22no—
81C2×D4×C37—24no—
82C2×D4×C37—24no—
83C2×D4×C37—44no—
84C2×D4×C37—44no—
85C2×D4×C37—44no—
86C2×D4×C37—44no—
87C2×D4×C37C2×D414yes—
88C22×C4×C37—22no—
89C22×C4×C37—22no—
90C22×C4×C37—28no—
91C22×C4×C37—22no—
92C22×C4×C37—24no—
93C22×C4×C37—24no—
94C22×C4×C37—22no—
95C22×C4×C37—22no—
96C22×C4×C37—42no—
97C22×C4×C37—44no—
98C22×C4×C37—44no—
99C22×C4×C37C2×D412yes—
100C22×C4×C37C2×D411yescharacteristic
101C22×C4×C37C2×D412yes—
102C22×C4×C37#4114yes—
103C22×C4×C37C2411yescharacteristic
104C2×C8×C37—24no—
105C2×C8×C37—24no—
106C2×C8×C37—24no—
107C4⋊C4×C37—28no—
108C4⋊C4×C37—24no—
109C4⋊C4×C37—22no—
110C4⋊C4×C37—22no—
111C4⋊C4×C37—44no—
112C4⋊C4×C37—44no—
113C22⋊C4×C37—216no—
114C22⋊C4×C37—44no—
115C42×C37—24no—
116C42×C37—22no—
117C42×C37C2×D414yes—
118C23×C37—21no—
119C23×C37—21no—
120C23×C37—22no—
121C23×C37—22no—
122C23×C37—24no—
123C23×C37—42no—
124C23×C37—42no—
125C23×C37—44no—
126C23×C37—44no—
127C23×C37#12412yes—
128C23×C37C22×D411yescharacteristic
129Q8×C37—28no—
130Q8×C37—44no—
131D4×C37—28no—
132D4×C37—416no—
133D4×C37—416no—
134D4×C37—44no—
135C2×C4×C37—22no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—22no—
139C2×C4×C37—22no—
140C2×C4×C37—22no—
141C2×C4×C37—28no—
142C2×C4×C37—24no—
143C2×C4×C37—48no—
144C2×C4×C37—416no—
145C2×C4×C37—42no—
146C2×C4×C37—42no—
147C2×C4×C37—42no—
148C2×C4×C37—42no—
149C2×C4×C37—42no—
150C2×C4×C37—42no—
151C2×C4×C37—42no—
152C2×C4×C37—42no—
153C2×C4×C37#12014yes—
154C2×C4×C37#12412yes—
155C2×C4×C37#13514yes—
156C2×C4×C37C22×D412yes—
157C2×C4×C37C2×#4112yes—
158C2×C4×C37H(5,𝔽2)12yes—
159C8×C37—44no—
160#25858C3711yesmaximal, characteristic, direct product factor, Sylow
161C22×C37—22no—
162C22×C37—22no—
163C22×C37—22no—
164C22×C37—42no—
165C22×C37—42no—
166C22×C37—44no—
167C22×C37—48no—
168C22×C37—82no—
169C22×C37—82no—
170C22×C37—84no—
171C22×C37C2×#12011yescharacteristic
172C22×C37C2×#12411yescharacteristic
173C22×C37#53511yescharacteristic
174C22×C37C2×#13512yes—
175C22×C37#57512yes—
176C4×C37—22no—
177C4×C37—24no—
178C4×C37—24no—
179C4×C37—44no—
180C4×C37—82no—
181C4×C37—82no—
182C4×C37#54614yes—
183C2×#532C2×C3711yescharacteristic
184C2×#488C2×C3712yescomplemented
185#2851C2×C3711yescharacteristic, complemented
186#2043C2×C3712yescomplemented
187#2041C2×C3712yescomplemented
188#1958C2×C3712yescomplemented
189#1788C2×C3714yescomplemented
190C4×C22⋊C8C2×C3711yescharacteristic, complemented
191C2×C37—42no—
192C2×C37—84no—
193C2×C37#243511yescharacteristic
194C2×C37#300212yes—
195C2×C37#313111yescharacteristic
196C2×C37#314211yescharacteristic
197C2×C37#321212yes—
198C22×#41C22×C3712yes—
199#532—28no—
200C2×C4⋊Q8C22×C3711yescharacteristic
201C2×#127C22×C3711yescharacteristic
202C2×#125C22×C3711yescharacteristic
203C2×#124C22×C3712yes—
204C2×#121—22no—
205C2×C4×D4—22no—
206C22×C42C22×C3711yescharacteristic
207#488—28no—
208C2×#103C22×C3714yes—
209C2×#103C22×C3714yes—
210C2×#102C22×C3714yes—
211C2×#102C22×C3714yes—
212C2×C22⋊C8C22×C3712yes—
213C2×C4×C8C22×C3712yes—
214#389C22×C3712yes—
215#387—22no—
216#385—22no—
217#382C22×C3711yescharacteristic
218#380C22×C3712yes—
219#336C22×C3712yes—
220C37#2585811yescharacteristic, direct product factor, Sylow
221C2×#41—24no—
222C2×#41—24no—
223C2×#41—28no—
224C2×#41—44no—
225C22×Q8C23×C3712yes—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4C23×C3712yes—
229C23×C4—22no—
230C23×C4D4×C3712yes—
231C23×C4C23×C3711yescharacteristic
232C22×C8C23×C3714yes—
233C4⋊Q8—24no—
234#127—24no—
235#125—24no—
236#124—24no—
237#124D4×C3718yes—
238#121—216no—
239C4×D4—216no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4C23×C3712yes—
244C2×C4⋊C4C23×C3712yes—
245C2×C22⋊C4—24no—
246C2×C22⋊C4—22no—
247C2×C42—24no—
248C2×C42D4×C3712yes—
249C2×C42C23×C3711yescharacteristic
250C2×C42C23×C3711yescharacteristic
251#103—28no—
252#103—44no—
253#102—28no—
254#102—44no—
255C22⋊C8—24no—
256C4×C8—24no—
257#95—22no—
258#95—22no—
259#95—22no—
260C24—22no—
261C24C2×D4×C3711yescharacteristic
262#41—416no—
263#41—416no—
264C2×Q8—22no—
265C2×Q8—24no—
266C2×Q8—24no—
267C2×Q8C2×D4×C3714yes—
268C2×D4—28no—
269C2×D4—28no—
270C2×D4—22no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4C2×D4×C3714yes—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—28no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—42no—
287C22×C4—44no—
288C22×C4—44no—
289C22×C4C2×D4×C3712yes—
290C22×C4C2×D4×C3711yescharacteristic
291C22×C4C2×D4×C3712yes—
292C22×C4#41×C3714yes—
293C22×C4C24×C3711yescharacteristic
294C2×C8—24no—
295C2×C8—24no—
296C2×C8—24no—
297C4⋊C4—28no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—44no—
302C4⋊C4—44no—
303C22⋊C4—216no—
304C22⋊C4—44no—
305C42—24no—
306C42—22no—
307C42C2×D4×C3714yes—
308C23—21no—
309C23—21no—
310C23—22no—
311C23—22no—
312C23—24no—
313C23—42no—
314C23—42no—
315C23—44no—
316C23—44no—
317C23#124×C3712yes—
318C23C22×D4×C3711yescharacteristic
319Q8—28no—
320Q8—44no—
321D4—28no—
322D4—416no—
323D4—416no—
324D4—44no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—48no—
334C2×C4—416no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4#120×C3714yes—
344C2×C4#124×C3712yes—
345C2×C4#135×C3714yes—
346C2×C4C22×D4×C3712yes—
347C2×C4C2×#41×C3712yes—
348C2×C4H(5,𝔽2)×C3712yes—
349C8—44no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—42no—
354C22—42no—
355C22—44no—
356C22—48no—
357C22—82no—
358C22—82no—
359C22—84no—
360C22C2×#120×C3711yescharacteristic
361C22C2×#124×C3711yescharacteristic
362C22C37×#53511yescharacteristic
363C22C2×#135×C3712yes—
364C22C37×#57512yes—
365C4—22no—
366C4—24no—
367C4—24no—
368C4—44no—
369C4—82no—
370C4—82no—
371C4C37×#54614yes—
372C2—42no—
373C2—84no—
374C2C37×#243511yescharacteristic
375C2C37×#300212yes—
376C2C37×#313111yescharacteristic
377C2C37×#314211yescharacteristic
378C2C37×#321212yes—
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#532C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#488C2semidirect
3. C37×#2851C2semidirect
4. C37×#2043C2semidirect
5. C37×#2041C2semidirect
6. C37×#1958C2semidirect
7. C37×#1788C2semidirect
8. C4×C22⋊C8×C37C2semidirect
160. #25858C37direct (N × H)
184. C2×#488C2×C37semidirect
185. #2851C2×C37semidirect
186. #2043C2×C37semidirect
187. #2041C2×C37semidirect
188. #1958C2×C37semidirect
189. #1788C2×C37semidirect
190. C4×C22⋊C8C2×C37semidirect
220. C37#25858direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5322
C2×C37×#4882
C37×#28512
C37×#20432
C37×#20412
C37×#19582
C37×#17882
C4×C22⋊C8×C372
#2585837