Finite Group Databasebeta

← C2×#14558142 #18007961

Subgroups — C2×#14558142 #18007961

Order 4736.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558142C2116yesmaximal, direct product factor
2C2×#11924535C211yesmaximal, characteristic, complemented
3C2×#11924531C211yesmaximal, characteristic
4C2×#11924531C211yesmaximal, characteristic
5C2×#11924531C211yesmaximal, characteristic
6C2×#11924530C211yesmaximal, characteristic
7C2×#11924527C211yesmaximal, characteristic, complemented
8C2×#11924526C211yesmaximal, characteristic, complemented
9C2×#11924526C211yesmaximal, characteristic, complemented
10C2×#11924526C211yesmaximal, characteristic, complemented
11C2×#11924514C211yesmaximal, characteristic
12C2×#11924514C211yesmaximal, characteristic
13C2×C4×Dic74C211yesmaximal, characteristic, complemented
14C2×#11924501C211yesmaximal, characteristic, complemented
15C2×#11924494C211yesmaximal, characteristic
16C2×#125×C37C211yesmaximal, characteristic, complemented
17C22×Dic74C2211yescharacteristic
18C22×Dic74C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20#11924535C2218yescomplemented
21#11924531C2218yes—
22#11924531C2218yes—
23#11924531C2218yes—
24#11924530C2218yes—
25#11924527C2218yescomplemented
26#11924526C2218yescomplemented
27#11924526C2218yescomplemented
28#11924526C2218yescomplemented
29#11924514C2218yes—
30#11924514C2218yes—
31C4×Dic74C2218yescomplemented
32#11924501C2218yescomplemented
33#11924494C2218yes—
34C2×C4⋊Dic37C2211yescharacteristic
35C2×C4⋊Dic37C2211yescharacteristic
36C2×C4⋊Dic37C2211yescharacteristic
37C2×C4⋊Dic37C2211yescharacteristic
38C2×#10596936C2211yescharacteristic
39C2×#10596936C2211yescharacteristic
40C2×#10596936C2211yescharacteristic
41C2×#10596936C2211yescharacteristic
42C2×#10596936C2211yescharacteristic
43C2×#10596936C2211yescharacteristic
44C2×#10596936C2211yescharacteristic
45C2×#10596936C2211yescharacteristic
46C2×#10596936C2211yescharacteristic
47C2×#10596936C2211yescharacteristic
48C2×#10596938C2211yescharacteristic
49C2×#10596938C2211yescharacteristic
50C2×#10596938C2211yescharacteristic
51C2×#10596938C2211yescharacteristic
52C2×#10596938C2211yescharacteristic
53C2×#10596938C2211yescharacteristic
54C2×C4×Dic37C2211yescharacteristic
55C2×C4×Dic37C2211yescharacteristic
56C2×C4×Dic37C2211yescharacteristic
57C2×C4×Dic37C2211yescharacteristic
58C2×C4×Dic37C2211yescharacteristic
59#125×C37C2218yescomplemented
60C2×C4⋊C4×C37C2211yescharacteristic
61C2×C4⋊C4×C37C2211yescharacteristic
62C2×C4⋊C4×C37C2211yescharacteristic
63C2×C4⋊C4×C37C2211yescharacteristic
64C2×C4⋊C4×C37C2211yescharacteristic
65C2×C4⋊C4×C37C2211yescharacteristic
66C2×C42×C37C2211yescharacteristic
67C23×D37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C22×C4×C37C2311yescharacteristic
72C22×C4×C37C2311yescharacteristic
73C22×C4×C37C2311yescharacteristic
74C22×C4×C37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C22×Dic37C2311yescharacteristic
80C22×Dic37C2311yescharacteristic
81C22×Dic37C2311yescharacteristic
82C2×C4×D37—24no—
83C2×C4×D37C2314yes—
84C2×Dic74—24no—
85C2×Dic74—24no—
86C2×Dic74C2314yes—
87C2×Dic74C2314yes—
88C4⋊C4×C37C2314yes—
89C4⋊C4×C37C2314yes—
90C4⋊C4×C37C2314yes—
91C4⋊C4×C37C2314yes—
92C4⋊C4×C37C2314yes—
93C4⋊C4×C37C2314yes—
94C42×C37C2314yes—
95#10596938C2314yes—
96#10596938C2314yes—
97#10596938C2314yes—
98#10596938C2314yes—
99#10596938C2314yes—
100#10596938C2314yes—
101C4⋊Dic37C2314yes—
102C4⋊Dic37C2314yes—
103C4⋊Dic37C2314yes—
104C4⋊Dic37C2314yes—
105#10596936C2314yes—
106#10596936C2314yes—
107#10596936C2314yes—
108#10596936C2314yes—
109#10596936C2314yes—
110#10596936C2314yes—
111#10596936C2314yes—
112#10596936C2314yes—
113#10596936C2314yes—
114#10596936C2314yes—
115C4×Dic37C2314yes—
116C4×Dic37C2314yes—
117C4×Dic37C2314yes—
118C4×Dic37C2314yes—
119C4×Dic37C2314yes—
120C23×C37C2411yescharacteristic
121C22×D37—22no—
122C22×D37—22no—
123C22×D37—22no—
124C22×D37C2412yes—
125C2×C4×C37—22no—
126C2×C4×C37—22no—
127C2×C4×C37—22no—
128C2×C4×C37—22no—
129C2×C4×C37—22no—
130C2×C4×C37—22no—
131C2×C4×C37—22no—
132C2×C4×C37C2412yes—
133C2×C4×C37C2412yes—
134C2×C4×C37C2412yes—
135C2×C4×C37C2412yes—
136C2×C4×C37C2412yes—
137C2×C4×C37C2412yes—
138C2×C4×C37C2412yes—
139C2×Dic37—22no—
140C2×Dic37—22no—
141C2×Dic37—22no—
142C2×Dic37—22no—
143C2×Dic37—22no—
144C2×Dic37—22no—
145C2×Dic37#4114yes—
146C2×Dic37C2412yes—
147C2×Dic37C2412yes—
148C2×Dic37C2412yes—
149C2×Dic37C2412yes—
150C2×Dic37C2412yes—
151C2×Dic37C2412yes—
152C2×Dic37C2412yes—
153C4×D37—28no—
154Dic74—28no—
155Dic74—28no—
156C22×C37C2×#4112yes—
157C22×C372−1+412yes—
158C22×C372−1+412yes—
159C22×C37C2511yescharacteristic
160C2×D37—22no—
161C2×D37—22no—
162C2×D37—22no—
163C2×D37—44no—
164C4×C37—22no—
165C4×C37—22no—
166C4×C37—22no—
167C4×C37—22no—
168C4×C37—22no—
169C4×C37—22no—
170C4×C37—22no—
171Dic37—22no—
172Dic37—22no—
173Dic37—22no—
174Dic37—22no—
175Dic37—22no—
176Dic37—22no—
177Dic37C2×#4114yes—
178C2×#541—371nomaximal, Sylow
179C2×C37#54114yescomplemented
180C2×C37C22×#4111yescharacteristic
181C2×C37C2×2−1+411yescharacteristic
182C2×C37C2×2−1+411yescharacteristic
183D37—42no—
184#541—3716no—
185C2×C4⋊Q8—371no—
186C2×#126—371no—
187C2×#126—371no—
188C2×#126—371no—
189C2×#126—371no—
190C2×#125—371no—
191C2×#125—371no—
192C2×#125—371no—
193C2×#125—371no—
194C2×#125D3711yescharacteristic, complemented
195C2×C22⋊Q8—371no—
196C2×C22⋊Q8—371no—
197C2×C4×Q8—371no—
198C2×C4×Q8—371no—
199C2×#117—371no—
200C37C2×#54111yescharacteristic, complemented, Sylow
201C22×Q8—371no—
202C22×Q8—371no—
203C23×C4—371no—
204C4⋊Q8—378no—
205#126—378no—
206#126—378no—
207#126—378no—
208#126—378no—
209#125—378no—
210#125—378no—
211#125—378no—
212#125—378no—
213#125C2×D3718yescomplemented
214C22⋊Q8—378no—
215C22⋊Q8—378no—
216C4×Q8—378no—
217C4×Q8—378no—
218#117—378no—
219C2×C4⋊C4—371no—
220C2×C4⋊C4—371no—
221C2×C4⋊C4—371no—
222C2×C4⋊C4—371no—
223C2×C4⋊C4—371no—
224C2×C4⋊C4—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—371no—
227C2×C4⋊C4—371no—
228C2×C4⋊C4—371no—
229C2×C4⋊C4—371no—
230C2×C4⋊C4—371no—
231C2×C4⋊C4—371no—
232C2×C4⋊C4—371no—
233C2×C4⋊C4C2×D3711yescharacteristic
234C2×C4⋊C4C2×D3711yescharacteristic
235C2×C4⋊C4C2×D3711yescharacteristic
236C2×C4⋊C4C2×D3711yescharacteristic
237C2×C4⋊C4C2×D3711yescharacteristic
238C2×C4⋊C4C2×D3711yescharacteristic
239C2×C22⋊C4—371no—
240C2×C22⋊C4—371no—
241C2×C22⋊C4—371no—
242C2×C22⋊C4—371no—
243C2×C22⋊C4—371no—
244C2×C22⋊C4—371no—
245C2×C42—371no—
246C2×C42—371no—
247C2×C42—371no—
248C2×C42—371no—
249C2×C42—371no—
250C2×C42C2×D3711yescharacteristic
251C24—371no—
252C2×Q8—374no—
253C2×Q8—374no—
254C2×Q8—744no—
255C2×Q8—744no—
256C22×C4—371no—
257C22×C4—371no—
258C22×C4—371no—
259C22×C4—371no—
260C22×C4—371no—
261C22×C4—371no—
262C22×C4—371no—
263C22×C4—374no—
264C22×C4—744no—
265C22×C4C22×D3711yescharacteristic
266C22×C4C22×D3711yescharacteristic
267C22×C4C22×D3711yescharacteristic
268C22×C4C22×D3711yescharacteristic
269C22×C4C22×D3711yescharacteristic
270C22×C4C22×D3711yescharacteristic
271C22×C4C22×D3711yescharacteristic
272C4⋊C4—374no—
273C4⋊C4—374no—
274C4⋊C4—374no—
275C4⋊C4—374no—
276C4⋊C4—374no—
277C4⋊C4—374no—
278C4⋊C4—374no—
279C4⋊C4—374no—
280C4⋊C4—374no—
281C4⋊C4—374no—
282C4⋊C4—374no—
283C4⋊C4—374no—
284C4⋊C4—374no—
285C4⋊C4—374no—
286C4⋊C4C22×D3714yes—
287C4⋊C4C22×D3714yes—
288C4⋊C4C22×D3714yes—
289C4⋊C4C22×D3714yes—
290C4⋊C4C22×D3714yes—
291C4⋊C4C22×D3714yes—
292C22⋊C4—374no—
293C22⋊C4—374no—
294C22⋊C4—374no—
295C22⋊C4—374no—
296C22⋊C4—374no—
297C22⋊C4—374no—
298C42—374no—
299C42—374no—
300C42—374no—
301C42—374no—
302C42—374no—
303C42C22×D3714yes—
304C23—372no—
305C23—742no—
306C23—742no—
307C23—742no—
308C23C23×D3711yescharacteristic
309Q8—748no—
310Q8—748no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—374no—
319C2×C4—372no—
320C2×C4—372no—
321C2×C4—372no—
322C2×C4—372no—
323C2×C4—372no—
324C2×C4—372no—
325C2×C4—372no—
326C2×C4—748no—
327C2×C4—742no—
328C2×C4—742no—
329C2×C4—742no—
330C2×C4—742no—
331C2×C4—742no—
332C2×C4—742no—
333C2×C4C23×D3712yes—
334C2×C4C23×D3712yes—
335C2×C4C23×D3712yes—
336C2×C4C23×D3712yes—
337C2×C4C23×D3712yes—
338C2×C4C23×D3712yes—
339C2×C4C23×D3712yes—
340C22—742no—
341C22—742no—
342C22—742no—
343C22—1484no—
344C22#41×D3712yes—
345C22#1192458312yes—
346C22#1192458412yes—
347C22C24×D3711yescharacteristic
348C4—22no—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—374no—
356C4—742no—
357C4—742no—
358C4—742no—
359C4—742no—
360C4—742no—
361C4—742no—
362C2—1482no—
363C2#1455814214yesdirect product factor
364C2C2×#41×D3711yescharacteristic
365C2C2×#1192458311yescharacteristic
366C2C2×#1192458411yescharacteristic
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC2×#125×C37C2
socleC23×C37C24
prime radicalC23×D37C23
hypercenterC2×#125D37
hypocenterC37C2×#541
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14558142C2direct (N × H)
2. C2×#11924535C2semidirect
7. C2×#11924527C2semidirect
8. C2×#11924526C2semidirect
9. C2×#11924526C2semidirect
10. C2×#11924526C2semidirect
13. C2×C4×Dic74C2semidirect
14. C2×#11924501C2semidirect
16. C2×#125×C37C2semidirect
20. #11924535C22semidirect
25. #11924527C22semidirect
26. #11924526C22semidirect
27. #11924526C22semidirect
28. #11924526C22semidirect
31. C4×Dic74C22semidirect
32. #11924501C22semidirect
59. #125×C37C22semidirect
179. C2×C37#541semidirect
194. C2×#125D37semidirect
200. C37C2×#541semidirect
213. #125C2×D37semidirect
363. C2#14558142direct (N × H)

Maximal subgroups

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

subgroupindex
#145581422
C2×#119245352
C2×#119245312
C2×#119245302
C2×#119245272
C2×#119245262
C2×#119245142
C2×C4×Dic742
C2×#119245012
C2×#119244942
C2×#125×C372
C2×#54137