Finite Group Databasebeta

← #26111383

Subgroups — #26111383

Order 12032.

566 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252026C211yesmaximal, characteristic, complemented
2#20241813C212yesmaximal, complemented
3#20241702C211yesmaximal, characteristic, complemented
4#20241291C212yesmaximal, complemented
5C47×#2392C211yesmaximal, characteristic
6#15689184—24no—
7#15689176C2212yes—
8#15689147C2212yes—
9#15689087—21no—
10C4×#10625329—21no—
11D4⋊(C47⋊C8)—24no—
12#15688849—21no—
13#15688847—21no—
14C2×C4×D4×C47—21no—
15C2×C4×D4×C47C2211yescharacteristic
16C2×#117×C47C2211yescharacteristic
17C47×#398C411yescharacteristic
18C47×#397C411yescharacteristic
19C47×#396—21no—
20C47×#394—21no—
21C47×#394C411yescharacteristic
22C47×#392C411yescharacteristic
23C4×C4⋊C4×C47C2211yescharacteristic
24C4×C22⋊C4×C47—21no—
25C2×#10625329—22no—
26C4⋊(C47⋊C8)—22no—
27C4⋊(C47⋊C8)—22no—
28C4⋊(C47⋊C8)D414yescomplemented
29C22⋊(C47⋊C8)—24no—
30C22⋊(C47⋊C8)—22no—
31#13093935—22no—
32C4×C47⋊C8—22no—
33C4×C47⋊C8—22no—
34C22×D4×C47—21no—
35C22×D4×C47C2×C411yescharacteristic
36C23×C4×C47—21no—
37C23×C4×C47D411yescharacteristic
38C4×D4×C47—22no—
39C4×D4×C47—22no—
40C4×D4×C47—44no—
41#117×C47—22no—
42#117×C47—22no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47C2×C411yescharacteristic
46C2×C4⋊C4×C47C2×C411yescharacteristic
47C2×C4⋊C4×C47D411yescharacteristic
48C2×C22⋊C4×C47—21no—
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47—21no—
51C2×C22⋊C4×C47—21no—
52C2×C22⋊C4×C47—21no—
53C2×C22⋊C4×C47C2×C411yescharacteristic
54C2×C22⋊C4×C47D411yescharacteristic
55C2×C42×C47—21no—
56C2×C42×C47D411yescharacteristic
57C2×C42×C47C2311yescharacteristic
58#95×C47—21no—
59#95×C47—21no—
60#95×C47C2×C411yescharacteristic
61#95×C47C2×C411yescharacteristic
62C24×C47—21no—
63C24×C47C22⋊C411yescharacteristic
64C2×D4×C47—22no—
65C2×D4×C47—42no—
66C2×D4×C47—42no—
67C2×D4×C47—42no—
68C2×D4×C47—42no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—22no—
73C22×C4×C47—22no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47—42no—
79C22×C4×C47—42no—
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22⋊C411yescharacteristic
82C22×C4×C47C22⋊C411yescharacteristic
83C22×C4×C47C22×C411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C4⋊C4×C47—22no—
87C4⋊C4×C47—22no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—42no—
90C4⋊C4×C47—42no—
91C22⋊C4×C47—22no—
92C22⋊C4×C47—22no—
93C22⋊C4×C47—42no—
94C22⋊C4×C47—42no—
95C22⋊C4×C47—42no—
96C22⋊C4×C47—42no—
97C22⋊C4×C47—42no—
98C42×C47—21no—
99C42×C47—21no—
100C42×C47—42no—
101C42×C47C2×D412yes—
102C42×C47#4112yes—
103#10625329—42no—
104#10625329—42no—
105C2×C47⋊C8—24no—
106C2×C47⋊C8—42no—
107C23×C47—22no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—41no—
112C23×C47—41no—
113C23×C47—41no—
114C23×C47—41no—
115C23×C47—41no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47—41no—
119C23×C47C2×C22⋊C411yescharacteristic
120D4×C47—24no—
121D4×C47—42no—
122D4×C47—48no—
123C2×C4×C47—22no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—42no—
134C2×C4×C47—42no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—82no—
144C2×C4×C47—82no—
145C2×C4×C47C4×D412yes—
146C2×C4×C47#12011yescharacteristic
147C2×C4×C47#12112yes—
148C2×C4×C47#12311yescharacteristic
149C2×C4×C47#13512yes—
150C2×C4×C47AGL(1,ℤ/8)12yes—
151C47⋊C8—44no—
152C47⋊C8—82no—
153#9036—471nomaximal, Sylow
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—42no—
157C22×C47—42no—
158C22×C47—42no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—42no—
162C22×C47—41no—
163C22×C47—81no—
164C22×C47—81no—
165C22×C47—81no—
166C22×C47—81no—
167C22×C47—81no—
168C22×C47#38611yescharacteristic
169C22×C47#41611yescharacteristic
170C22×C47#41811yescharacteristic
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—42no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47—81no—
178C4×C47—81no—
179C4×C47#44912yes—
180C4×C47#48212yes—
181#2921—471no—
182#2392D4711yescharacteristic
183#1486—472no—
184#1458—471no—
185#1303—472no—
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—81no—
189C2×C47—82no—
190C2×C47#187511yescharacteristic
191C2×C47#188411yescharacteristic
192C2×C47#189111yescharacteristic
193C2×C4×D4—21no—
194C2×C4×D4C2×D4711yescharacteristic
195C2×#117C2×D4711yescharacteristic
196#433—944no—
197#431—472no—
198#423—472no—
199#407—941no—
200C4×M16—941no—
201#398Dic4711yescharacteristic
202#397Dic4711yescharacteristic
203#396—21no—
204#394—21no—
205#394Dic4711yescharacteristic
206#392Dic4711yescharacteristic
207C4×C4⋊C4C2×D4711yescharacteristic
208C4×C22⋊C4—21no—
209D4⋊C8—944no—
210#324—941no—
211#323—941no—
212C47#903611yescharacteristic, complemented, Sylow
213C22×D4—21no—
214C22×D4C2×Dic4711yescharacteristic
215C23×C4—21no—
216C23×C4C22⋊D4711yescharacteristic
217C2×M16—942no—
218C4×D4—22no—
219C4×D4—22no—
220C4×D4—44no—
221#117—22no—
222#117—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C2×Dic4711yescharacteristic
226C2×C4⋊C4C2×Dic4711yescharacteristic
227C2×C4⋊C4C22⋊D4711yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4C2×Dic4711yescharacteristic
234C2×C22⋊C4C22⋊D4711yescharacteristic
235C2×C42—21no—
236C2×C42C22⋊D4711yescharacteristic
237C2×C42C22×D4711yescharacteristic
238C4⋊C8—474no—
239C4⋊C8—942no—
240C4⋊C8—942no—
241C22⋊C8—944no—
242C22⋊C8—942no—
243#97—942no—
244C4×C8—942no—
245C4×C8—942no—
246#95—21no—
247#95—21no—
248#95C2×Dic4711yescharacteristic
249#95C2×Dic4711yescharacteristic
250C24—21no—
251C24C22⋊Dic4711yescharacteristic
252C2×D4—22no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—42no—
256C2×D4—42no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4C22⋊Dic4711yescharacteristic
269C22×C4C22⋊Dic4711yescharacteristic
270C22×C4C22⋊Dic4711yescharacteristic
271C22×C4C22×Dic4711yescharacteristic
272C22×C4C2×C22⋊D4711yescharacteristic
273C22×C4C2×C22⋊D4711yescharacteristic
274M16—1882no—
275M16—1882no—
276C2×C8—944no—
277C2×C8—1882no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C42—21no—
291C42—21no—
292C42—42no—
293C42D4×D4712yes—
294C42#1062535212yes—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23C2×C22⋊Dic4711yescharacteristic
308D4—24no—
309D4—42no—
310D4—48no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4D4×Dic4712yes—
334C2×C4#1309399211yescharacteristic
335C2×C4#1309399612yes—
336C2×C4#1309400511yescharacteristic
337C2×C4#1309404412yes—
338C2×C4#1309405012yes—
339C8—3762no—
340C8—1884no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—42no—
346C22—41no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22#1568900311yescharacteristic
356C22#1568911911yescharacteristic
357C22#1568912811yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—81no—
365C4—81no—
366C4#1568926612yes—
367C4#1568944412yes—
368C2—21no—
369C2—21no—
370C2—81no—
371C2—82no—
372C2#2024371111yescharacteristic
373C2#2024377211yescharacteristic
374C2#2024380711yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2392C2
socleC22×C47#386
prime radicalC47×#392C4
cosocleC2×C42×C47C23
hypercenter#2392D47
hypocenterC47#9036
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #20252026C2semidirect
2. #20241813C2semidirect
3. #20241702C2semidirect
4. #20241291C2semidirect
28. C4⋊(C47⋊C8)D4semidirect
212. C47#9036semidirect

Maximal subgroups

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

subgroupindex
#202520262
#202418132
#202417022
#202412912
C47×#23922
#903647