Finite Group Databasebeta

← #26422999

Subgroups — #26422999

Order 12032.

1304 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251663C211yesmaximal, characteristic
2#20251636C214yesmaximal
3#20251634C214yesmaximal
4#20251632C214yesmaximal
5#20251455C212yesmaximal
6#20246694C214yesmaximal
7#20246692C214yesmaximal
8#20246692C214yesmaximal
9#125×Dic47C212yesmaximal
10#20245943C211yesmaximal, characteristic
11C47×#2822C211yesmaximal, characteristic
12C2×#13094016C2211yescharacteristic
13#15689065C2214yes—
14#15689065C2214yes—
15#15689065C2214yes—
16#15689064C2214yes—
17#15689064C2214yes—
18#15689063C2214yes—
19#15689063C2214yes—
20#15689062C2214yes—
21#15689062C2214yes—
22#15689061C2214yes—
23#15689061C2214yes—
24#15689057C2214yes—
25#15689057C2214yes—
26#15689056C2214yes—
27#15689056C2214yes—
28#15689056C2214yes—
29#15689055C2214yes—
30#15689055C2214yes—
31#15689054C2214yes—
32#15689053C2214yes—
33#15689053C2214yes—
34#15689022C2212yes—
35#15689022C2212yes—
36#15689019C2212yes—
37#15689009C2214yes—
38#15689009C2214yes—
39#15689005C2214yes—
40#15688989C2212yes—
41C4⋊C4×Dic47C2214yes—
42C4⋊C4×Dic47C2212yes—
43C4⋊C4×Dic47C2214yes—
44C4⋊C4×Dic47C2212yes—
45C4⋊C4×Dic47C2214yes—
46C4⋊C4×Dic47C2212yes—
47#15688974C2214yes—
48#15688974C2214yes—
49#15688974C2214yes—
50#15688968C2214yes—
51C42×Dic47C2211yescharacteristic
52C2×#125×C47C2212yes—
53C47×#400C2214yes—
54C47×#398C2214yes—
55C47×#398C2214yes—
56C47×#382C2211yescharacteristic
57#13094016—24no—
58C2×C4⋊Dic47C2312yes—
59C2×C4⋊Dic47C2312yes—
60C2×C4⋊Dic47C2312yes—
61C2×C4⋊Dic47C2314yes—
62C2×C4⋊Dic47C2314yes—
63C2×C4⋊Dic47C2314yes—
64C2×Dic47⋊C4C2314yes—
65C2×Dic47⋊C4C2314yes—
66C2×Dic47⋊C4C2314yes—
67C2×Dic47⋊C4C2314yes—
68C2×Dic47⋊C4C2314yes—
69C2×Dic47⋊C4C2314yes—
70C2×C4×Dic47C2312yes—
71C2×C4×Dic47C2311yescharacteristic
72C2×C4×Dic47C2314yes—
73C2×C4×Dic47C2314yes—
74C2×C4×Dic47C2314yes—
75C2×C4×Dic47C2312yes—
76C2×C4×Dic47C2311yescharacteristic
77C47⋊#95C2314yes—
78C47⋊#95C2314yes—
79C47⋊#95C2314yes—
80C47⋊#95C2314yes—
81C47⋊#95C2314yes—
82C47⋊#95C2314yes—
83C47⋊#95C2314yes—
84C47⋊#95C2314yes—
85C47⋊#95C2314yes—
86C47⋊#95C2314yes—
87C47⋊#95C2314yes—
88C47⋊#95C2314yes—
89C47⋊#95C2314yes—
90C47⋊#95C2314yes—
91C47⋊#95C2314yes—
92#125×C47—28no—
93C2×C4⋊C4×C47C2314yes—
94C2×C4⋊C4×C47C2314yes—
95C2×C4⋊C4×C47C2312yes—
96C2×C4⋊C4×C47C2312yes—
97C2×C4⋊C4×C47C2312yes—
98C2×C4⋊C4×C47C2314yes—
99C2×C42×C47C2311yescharacteristic
100#95×C47C2314yes—
101#95×C47C2314yes—
102#95×C47C2314yes—
103#95×C47C2314yes—
104C22×C4×C47C2414yes—
105C22×C4×C47C2414yes—
106C22×C4×C47C2414yes—
107C22×C4×C47C2411yescharacteristic
108C22×C4×C47C2412yes—
109C22×Dic47C2412yes—
110C22×Dic47C2411yescharacteristic
111C22×Dic47C2414yes—
112C22×Dic47C2414yes—
113C22×Dic47C2414yes—
114C22×Dic47C2411yescharacteristic
115C4⋊C4×C47—28no—
116C4⋊C4×C47—24no—
117C4⋊C4×C47—24no—
118C4⋊C4×C47—28no—
119C4⋊C4×C47—42no—
120C4⋊C4×C47—44no—
121C42×C47#4114yes—
122C4⋊Dic47—24no—
123C4⋊Dic47—44no—
124C4⋊Dic47—44no—
125C4⋊Dic47—42no—
126C4⋊Dic47—42no—
127C4⋊Dic47—44no—
128Dic47⋊C4—28no—
129Dic47⋊C4—44no—
130Dic47⋊C4—44no—
131Dic47⋊C4—44no—
132Dic47⋊C4—44no—
133Dic47⋊C4—44no—
134C4×Dic47—24no—
135C4×Dic47—22no—
136C4×Dic47—28no—
137C4×Dic47—28no—
138C4×Dic47—28no—
139C4×Dic47—42no—
140C4×Dic47—41no—
141C23×C47C2511yescharacteristic
142C2×C4×C47—21no—
143C2×C4×C47—22no—
144C2×C4×C47—22no—
145C2×C4×C47—21no—
146C2×C4×C47—24no—
147C2×C4×C47—24no—
148C2×C4×C47—24no—
149C2×C4×C47—24no—
150C2×C4×C47—24no—
151C2×C4×C47—24no—
152C2×C4×C47—24no—
153C2×C4×C47—24no—
154C2×C4×C47—24no—
155C2×C4×C47C2×#4114yes—
156C2×C4×C47C2×#4112yes—
157C2×Dic47—24no—
158C2×Dic47—24no—
159C2×Dic47—22no—
160C2×Dic47—21no—
161C2×Dic47—24no—
162C2×Dic47—24no—
163C2×Dic47—22no—
164C2×Dic47—22no—
165C2×Dic47—22no—
166C2×Dic47—24no—
167C2×Dic47—24no—
168C2×Dic47—24no—
169C2×Dic47—24no—
170C2×Dic47—24no—
171C2×Dic472−1+412yes—
172C2×Dic472−1+414yes—
173#36701—471nomaximal, Sylow
174C22×C47C22×#4111yescharacteristic
175C22×C47C2×2−1+411yescharacteristic
176C22×C47C2×2−1+412yes—
177C22×C47#58511yescharacteristic
178C22×C47#58512yes—
179C4×C47—24no—
180C4×C47—22no—
181C4×C47—44no—
182C4×C47—44no—
183C4×C47—44no—
184Dic47—44no—
185Dic47—41no—
186Dic47—44no—
187Dic47—42no—
188Dic47—44no—
189Dic47#56414yes—
190#2845—471no—
191#2839—474no—
192#2839—474no—
193#2839—474no—
194#2822—472no—
195#2822D4711yescharacteristic
196#2402—474no—
197#2402—474no—
198#2402—474no—
199C4×#125—471no—
200C4×#125—472no—
201C2×C47#346112yes—
202C2×C47#346111yescharacteristic
203C2×C47C2×#56411yescharacteristic
204C2×C47#353111yescharacteristic
205C2×C47#353112yes—
206C2×#125—471no—
207C2×#125C2×D4712yes—
208#400—474no—
209#400—474no—
210#400—474no—
211#400—474no—
212#400—474no—
213#400—474no—
214#400—474no—
215#400—474no—
216#400—474no—
217#400—474no—
218#400—474no—
219#400C2×D4714yes—
220#398—474no—
221#398—474no—
222#398—474no—
223#398—474no—
224#398—474no—
225#398—474no—
226#398—474no—
227#398—474no—
228#398—474no—
229#398—474no—
230#398C2×D4714yes—
231#398C2×D4714yes—
232#389—472no—
233#389—472no—
234#389—472no—
235#387—474no—
236#387—474no—
237#387—474no—
238#382—472no—
239#382C2×D4711yescharacteristic
240C4×C4⋊C4—474no—
241C4×C4⋊C4—474no—
242C4×C4⋊C4—472no—
243C4×C4⋊C4—472no—
244C4×C4⋊C4—472no—
245C4×C4⋊C4—474no—
246C4×C4⋊C4—474no—
247C4×C4⋊C4—474no—
248C4×C4⋊C4—474no—
249#376—474no—
250C43—471no—
251C47#3670111yescharacteristic, complemented, Sylow
252#125—28no—
253#125—944no—
254C2×C4⋊C4—474no—
255C2×C4⋊C4—472no—
256C2×C4⋊C4—474no—
257C2×C4⋊C4—474no—
258C2×C4⋊C4—474no—
259C2×C4⋊C4—474no—
260C2×C4⋊C4—474no—
261C2×C4⋊C4—472no—
262C2×C4⋊C4—472no—
263C2×C4⋊C4—474no—
264C2×C4⋊C4—474no—
265C2×C4⋊C4—474no—
266C2×C4⋊C4C22×D4714yes—
267C2×C4⋊C4C22×D4714yes—
268C2×C4⋊C4C22×D4712yes—
269C2×C4⋊C4C22×D4712yes—
270C2×C4⋊C4C22×D4712yes—
271C2×C4⋊C4C22×D4714yes—
272C2×C42—471no—
273C2×C42—472no—
274C2×C42—474no—
275C2×C42—474no—
276C2×C42—474no—
277C2×C42—471no—
278C2×C42—472no—
279C2×C42C22×D4711yescharacteristic
280#95—474no—
281#95—474no—
282#95—474no—
283#95—474no—
284#95—474no—
285#95—474no—
286#95—474no—
287#95—474no—
288#95—474no—
289#95—474no—
290#95—474no—
291#95—474no—
292#95—474no—
293#95—474no—
294#95—474no—
295#95C22×D4714yes—
296#95C22×D4714yes—
297#95C22×D4714yes—
298#95C22×D4714yes—
299C22×C4—471no—
300C22×C4—472no—
301C22×C4—471no—
302C22×C4—474no—
303C22×C4—474no—
304C22×C4—474no—
305C22×C4C23×D4714yes—
306C22×C4C23×D4714yes—
307C22×C4C23×D4714yes—
308C22×C4C23×D4711yescharacteristic
309C22×C4C23×D4712yes—
310C4⋊C4—28no—
311C4⋊C4—28no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—42no—
315C4⋊C4—44no—
316C4⋊C4—948no—
317C4⋊C4—944no—
318C4⋊C4—1884no—
319C4⋊C4—1884no—
320C4⋊C4—1884no—
321C4⋊C4—1884no—
322C4⋊C4—1884no—
323C4⋊C4—1882no—
324C4⋊C4—1882no—
325C4⋊C4—1884no—
326C4⋊C4—1884no—
327C4⋊C4—1884no—
328C42—944no—
329C42—942no—
330C42—948no—
331C42—948no—
332C42—948no—
333C42—1881no—
334C42—1882no—
335C42#1062535214yes—
336C23C24×D4711yescharacteristic
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—472no—
351C2×C4—474no—
352C2×C4—944no—
353C2×C4—941no—
354C2×C4—944no—
355C2×C4—944no—
356C2×C4—942no—
357C2×C4—944no—
358C2×C4—942no—
359C2×C4—944no—
360C2×C4—942no—
361C2×C4—942no—
362C2×C4—944no—
363C2×C4—944no—
364C2×C4—944no—
365C2×C4—944no—
366C2×C4C2×#1062535214yes—
367C2×C4C2×#1062535212yes—
368C22C22×#1062535211yescharacteristic
369C222−1+4×D4711yescharacteristic
370C222−1+4×D4712yes—
371C22#1568995811yescharacteristic
372C22#1568996012yes—
373C4—24no—
374C4—22no—
375C4—44no—
376C4—44no—
377C4—44no—
378C4—474no—
379C4—1881no—
380C4—1884no—
381C4—1884no—
382C4—1882no—
383C4—1884no—
384C2#2025681212yes—
385C2#2025681611yescharacteristic
386C2#564×D4711yescharacteristic
387C2#2025753412yes—
388C2#2025753611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, prime radical, cosocleC23×C47C25
FittingC47×#2822C2
hypercenter#2822D47
hypocenterC47#36701
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2822

Complements

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

NH ≅ G/Ntype
251. C47#36701semidirect

Maximal subgroups

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

subgroupindex
#202516632
#202516362
#202516342
#202516322
#202514552
#202466942
#202466922
#125×Dic472
#202459432
C47×#28222
#3670147