Finite Group Databasebeta

← #26423002

Subgroups — #26423002

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#20251630C214yesmaximal
3#20251628C214yesmaximal
4#20251626C214yesmaximal
5#20251456C211yesmaximal, characteristic
6#20251455C212yesmaximal
7#20246696C214yesmaximal
8#20246695C214yesmaximal
9#20246695C214yesmaximal
10C4×#13094016C212yesmaximal
11C4×#125×C47C211yesmaximal, characteristic
12C2×#13094016C2212yes—
13#15689065C2214yes—
14#15689065C2214yes—
15#15689064C2214yes—
16#15689064C2214yes—
17#15689064C2214yes—
18#15689064C2214yes—
19#15689063C2214yes—
20#15689063C2214yes—
21#15689062C2214yes—
22#15689062C2214yes—
23#15689061C2214yes—
24#15689061C2214yes—
25#15689057C2214yes—
26#15689057C2214yes—
27#15689056C2214yes—
28#15689056C2214yes—
29#15689056C2214yes—
30#15689056C2214yes—
31#15689055C2214yes—
32#15689055C2214yes—
33#15689054C2214yes—
34#15689054C2214yes—
35#15689053C2214yes—
36#15689053C2214yes—
37#15689021C2212yes—
38#15689021C2212yes—
39#15689007C2214yes—
40#15689007C2214yes—
41#15688989C2212yes—
42C4×Dic47⋊C4C2214yes—
43C4×Dic47⋊C4C2214yes—
44C4×Dic47⋊C4C2214yes—
45C4×Dic47⋊C4C2214yes—
46C4×C4⋊Dic47C2212yes—
47C4×C4⋊Dic47C2214yes—
48C4×C4⋊Dic47C2212yes—
49#15688969C2214yes—
50C2×#125×C47C2211yescharacteristic
51C47×#389C2212yes—
52C47×#387C2214yes—
53C47×#382C2211yescharacteristic
54C4×C4⋊C4×C47C2212yes—
55C4×C4⋊C4×C47C2214yes—
56C43×C47C2211yescharacteristic
57#13094016—28no—
58C2×C4⋊Dic47C2312yes—
59C2×C4⋊Dic47C2312yes—
60C2×C4⋊Dic47C2312yes—
61C2×C4⋊Dic47C2312yes—
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×Dic47⋊C4C2314yes—
71C2×Dic47⋊C4C2314yes—
72C2×C4×Dic47C2314yes—
73C2×C4×Dic47C2314yes—
74C47⋊#95C2314yes—
75C47⋊#95C2314yes—
76C47⋊#95C2314yes—
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—
90#125×C47—24no—
91C2×C4⋊C4×C47C2314yes—
92C2×C4⋊C4×C47C2312yes—
93C2×C4⋊C4×C47C2312yes—
94C2×C4⋊C4×C47C2314yes—
95C2×C42×C47C2314yes—
96C2×C42×C47C2312yes—
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99C2×C42×C47C2312yes—
100C2×C42×C47C2311yescharacteristic
101#95×C47C2314yes—
102#95×C47C2314yes—
103#95×C47C2314yes—
104C22×C4×C47C2412yes—
105C22×C4×C47C2411yescharacteristic
106C22×C4×C47C2414yes—
107C22×C4×C47C2414yes—
108C22×C4×C47C2411yescharacteristic
109C22×C4×C47C2412yes—
110C22×C4×C47C2411yescharacteristic
111C22×Dic47C2414yes—
112C22×Dic47C2414yes—
113C22×Dic47C2414yes—
114C22×Dic47C2414yes—
115C4⋊C4×C47—24no—
116C4⋊C4×C47—28no—
117C4⋊C4×C47—42no—
118C4⋊C4×C47—44no—
119C42×C47—24no—
120C42×C47—22no—
121C42×C47—28no—
122C42×C47—42no—
123C42×C47—41no—
124C42×C47#4114yes—
125C4⋊Dic47—24no—
126C4⋊Dic47—24no—
127C4⋊Dic47—42no—
128C4⋊Dic47—44no—
129C4⋊Dic47—42no—
130C4⋊Dic47—44no—
131Dic47⋊C4—28no—
132Dic47⋊C4—28no—
133Dic47⋊C4—44no—
134Dic47⋊C4—44no—
135Dic47⋊C4—44no—
136Dic47⋊C4—44no—
137Dic47⋊C4—44no—
138Dic47⋊C4—44no—
139C4×Dic47—28no—
140C4×Dic47—28no—
141C23×C47C2511yescharacteristic
142C2×C4×C47—22no—
143C2×C4×C47—21no—
144C2×C4×C47—22no—
145C2×C4×C47—21no—
146C2×C4×C47—24no—
147C2×C4×C47—24no—
148C2×C4×C47—22no—
149C2×C4×C47—24no—
150C2×C4×C47—21no—
151C2×C4×C47—22no—
152C2×C4×C47—22no—
153C2×C4×C47—24no—
154C2×C4×C47—24no—
155C2×C4×C47—24no—
156C2×C4×C47—22no—
157C2×C4×C47C2×#4112yes—
158C2×C4×C47C2×#4114yes—
159C2×C4×C472−1+414yes—
160C2×C4×C472−1+412yes—
161C2×Dic47—24no—
162C2×Dic47—24no—
163C2×Dic47—24no—
164C2×Dic47—24no—
165C2×Dic47—24no—
166C2×Dic47—24no—
167C2×Dic47—24no—
168C2×Dic47—24no—
169C2×Dic47—24no—
170C2×Dic47—24no—
171C2×Dic47—24no—
172C2×Dic47—24no—
173#36701—471nomaximal, Sylow
174C22×C47C22×#4111yescharacteristic
175C22×C47C2×2−1+412yes—
176C22×C47C2×2−1+411yescharacteristic
177C22×C47#58512yes—
178C22×C47#58511yescharacteristic
179C4×C47—24no—
180C4×C47—22no—
181C4×C47—44no—
182C4×C47—42no—
183C4×C47—44no—
184C4×C47—41no—
185C4×C47#56414yes—
186Dic47—44no—
187Dic47—44no—
188Dic47—44no—
189Dic47—44no—
190#2845—471no—
191#2839—474no—
192#2839—474no—
193#2839—474no—
194#2822—471no—
195#2822—472no—
196#2402—474no—
197#2402—474no—
198#2402—474no—
199C4×#125—472no—
200C4×#125D4711yescharacteristic
201C2×C47#346112yes—
202C2×C47#346111yescharacteristic
203C2×C47C2×#56411yescharacteristic
204C2×C47#353112yes—
205C2×C47#353111yescharacteristic
206C2×#125—472no—
207C2×#125C2×D4711yescharacteristic
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#400—474no—
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#398—474no—
231#398—474no—
232#389—472no—
233#389—472no—
234#389C2×D4712yes—
235#387—474no—
236#387—474no—
237#387C2×D4714yes—
238#382—472no—
239#382C2×D4711yescharacteristic
240C4×C4⋊C4—472no—
241C4×C4⋊C4—472no—
242C4×C4⋊C4—474no—
243C4×C4⋊C4—474no—
244C4×C4⋊C4—474no—
245C4×C4⋊C4—474no—
246C4×C4⋊C4—474no—
247C4×C4⋊C4C2×D4714yes—
248C4×C4⋊C4C2×D4712yes—
249#376—474no—
250C43C2×D4711yescharacteristic
251C47#3670111yescharacteristic, complemented, Sylow
252#125—24no—
253#125—948no—
254C2×C4⋊C4—474no—
255C2×C4⋊C4—474no—
256C2×C4⋊C4—472no—
257C2×C4⋊C4—472no—
258C2×C4⋊C4—474no—
259C2×C4⋊C4—474no—
260C2×C4⋊C4—474no—
261C2×C4⋊C4—474no—
262C2×C4⋊C4—474no—
263C2×C4⋊C4—474no—
264C2×C4⋊C4—472no—
265C2×C4⋊C4—472no—
266C2×C4⋊C4—474no—
267C2×C4⋊C4—474no—
268C2×C4⋊C4C22×D4714yes—
269C2×C4⋊C4C22×D4712yes—
270C2×C4⋊C4C22×D4712yes—
271C2×C4⋊C4C22×D4714yes—
272C2×C42—474no—
273C2×C42—474no—
274C2×C42C22×D4712yes—
275C2×C42C22×D4711yescharacteristic
276C2×C42C22×D4714yes—
277C2×C42C22×D4711yescharacteristic
278C2×C42C22×D4712yes—
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#95—474no—
296#95C22×D4714yes—
297#95C22×D4714yes—
298#95C22×D4714yes—
299C22×C4—474no—
300C22×C4—474no—
301C22×C4—474no—
302C22×C4—474no—
303C22×C4C23×D4712yes—
304C22×C4C23×D4714yes—
305C22×C4C23×D4711yescharacteristic
306C22×C4C23×D4714yes—
307C22×C4C23×D4711yescharacteristic
308C22×C4C23×D4712yes—
309C22×C4C23×D4711yescharacteristic
310C4⋊C4—28no—
311C4⋊C4—24no—
312C4⋊C4—42no—
313C4⋊C4—44no—
314C4⋊C4—948no—
315C4⋊C4—948no—
316C4⋊C4—944no—
317C4⋊C4—944no—
318C4⋊C4—1884no—
319C4⋊C4—1884no—
320C4⋊C4—1884no—
321C4⋊C4—1884no—
322C4⋊C4—1884no—
323C4⋊C4—1884no—
324C4⋊C4—1882no—
325C4⋊C4—1882no—
326C4⋊C4—1884no—
327C4⋊C4—1884no—
328C42—24no—
329C42—28no—
330C42—22no—
331C42—41no—
332C42—42no—
333C42—948no—
334C42—948no—
335C42#1062535014yes—
336C23C24×D4711yescharacteristic
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—944no—
353C2×C4—944no—
354C2×C4—944no—
355C2×C4—944no—
356C2×C4—944no—
357C2×C4—944no—
358C2×C4—944no—
359C2×C4—944no—
360C2×C4—944no—
361C2×C4—944no—
362C2×C4—944no—
363C2×C4—944no—
364C2×C4C2×#1062535014yes—
365C2×C4C2×#1062535012yes—
366C2×C4#1309407114yes—
367C2×C4#1309407212yes—
368C22C22×#1062535011yescharacteristic
369C22C2×#1309407112yes—
370C22C2×#1309407211yescharacteristic
371C22#1568995912yes—
372C22#1568995911yescharacteristic
373C4—24no—
374C4—22no—
375C4—44no—
376C4—42no—
377C4—44no—
378C4—41no—
379C4—1884no—
380C4—1884no—
381C4—1884no—
382C4—1884no—
383C4C47⋊#56414yes—
384C2#2025681512yes—
385C2#2025682111yescharacteristic
386C2C2×C47⋊#56411yescharacteristic
387C2#2025753312yes—
388C2#2025753511yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, socle, prime radical, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC4×#125×C47C2
hypercenterC4×#125D47
hypocenterC47#36701
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#125

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
#202516302
#202516282
#202516262
#202514562
#202514552
#202466962
#202466952
C4×#130940162
C4×#125×C472
#3670147