Finite Group Databasebeta

← #26125684

Subgroups — #26125684

Order 12032.

434 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 87 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#20246012C211yesmaximal, characteristic
2#20241718C211yesmaximal, characteristic
3#20241333C212yesmaximal, complemented
4#20241331C212yesmaximal, complemented
5C47×#1463C211yesmaximal, characteristic
6C2×#13093983C411yescharacteristic
7C2×#13093983C411yescharacteristic
8#15689087—21no—
9#15689019—21no—
10#15689019—21no—
11#15688996—21no—
12#15688996—21no—
13#15688992C411yescharacteristic
14#15688992C2211yescharacteristic
15#15688988C411yescharacteristic
16#15688988C2211yescharacteristic
17#15688849—21no—
18#15688849C2212yes—
19C22×C4⋊C4×C47C2211yescharacteristic
20C47×#407—21no—
21C47×#324—21no—
22C47×#324C2212yes—
23C2×#10625329—41no—
24#13093983—22no—
25#13093983—22no—
26#13093983—41no—
27#13093983—41no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47C2×C411yescharacteristic
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47C2×C411yescharacteristic
39C2×C4×Dic47C2×C411yescharacteristic
40C22⋊(C47⋊C8)—22no—
41C22⋊(C47⋊C8)—41no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C23×C4×C47C2×C411yescharacteristic
47C23×C4×C47D411yescharacteristic
48C23×C4×C47D411yescharacteristic
49C2×M16×C47—41no—
50C2×C4⋊C4×C47—41no—
51C2×C4⋊C4×C47—41no—
52C2×C4⋊C4×C47C2×C411yescharacteristic
53C2×C4⋊C4×C47D411yescharacteristic
54C2×C4⋊C4×C47D411yescharacteristic
55C2×C4⋊C4×C47C2311yescharacteristic
56C22⋊C8×C47—22no—
57C22⋊C8×C47—41no—
58C24×C47C22⋊C411yescharacteristic
59C22×C4×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47—22no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—81no—
69C22×C4×C47—81no—
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×Dic47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—21no—
80M16×C47—82no—
81C2×C8×C47—42no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C22⋊Dic47—24no—
87C22⋊Dic47—41no—
88C22⋊Dic47—41no—
89C4⋊Dic47—24no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92Dic47⋊C4—81no—
93Dic47⋊C4—81no—
94Dic47⋊C4—81no—
95Dic47⋊C4—81no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—42no—
99C4×Dic47M1612yescomplemented
100C4×Dic47M1612yescomplemented
101#10625329—82no—
102C2×C47⋊C8—42no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—41no—
106C23×C47—41no—
107C23×C47#9911yescharacteristic
108C23×C47#9911yescharacteristic
109C23×C47C2×C22⋊C411yescharacteristic
110C2×C4×C47—22no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—81no—
129C2×C4×C47—81no—
130C2×C4×C47#10112yes—
131C2×C4×C47C2×M1611yescharacteristic
132C2×C4×C47C2×M1611yescharacteristic
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—42no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C8×C47—82no—
145C47⋊C8—82no—
146#11514—471nomaximal, Sylow
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—42no—
156C22×C47—42no—
157C22×C47#40711yescharacteristic
158C22×C47C2×#9911yescharacteristic
159C22×C47C2×#10111yescharacteristic
160C4×C47—22no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47—41no—
167Dic47—42no—
168Dic47—42no—
169Dic47—81no—
170Dic47—81no—
171#2317—471no—
172#1463—471no—
173#1463D4711yescharacteristic
174#1325—472no—
175#1324—472no—
176C2×C47—21no—
177C2×C47—21no—
178C2×C47—41no—
179C2×C47—41no—
180C2×C47#146311yescharacteristic
181C2×C47#212711yescharacteristic
182C2×C47#213311yescharacteristic
183C2×#117—471no—
184C2×#117—471no—
185C22×C4⋊C4C2×D4711yescharacteristic
186#407—21no—
187#407—941no—
188#389—941no—
189#389—941no—
190#385—941no—
191#385—941no—
192#384—471no—
193#384—471no—
194#382—471no—
195#382—471no—
196#324—21no—
197#324—472no—
198#324—941no—
199#324C2×D4712yes—
200C47#1151411yescharacteristic, complemented, Sylow
201C23×C4C4×D4711yescharacteristic
202C23×C4D18811yescharacteristic
203C23×C4C22⋊D4711yescharacteristic
204C2×M16—41no—
205C2×M16—1881no—
206#117—942no—
207#117—942no—
208#117—1881no—
209#117—1881no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—941no—
215C2×C4⋊C4—941no—
216C2×C4⋊C4—941no—
217C2×C4⋊C4—941no—
218C2×C4⋊C4—941no—
219C2×C4⋊C4C4×D4711yescharacteristic
220C2×C4⋊C4D18811yescharacteristic
221C2×C4⋊C4C22⋊D4711yescharacteristic
222C2×C4⋊C4C22×D4711yescharacteristic
223C2×C22⋊C4—941no—
224C2×C22⋊C4—941no—
225C2×C42—471no—
226C2×C42—471no—
227C2×C42—941no—
228C22⋊C8—22no—
229C22⋊C8—41no—
230C22⋊C8—942no—
231C22⋊C8—1881no—
232#95—941no—
233#95—941no—
234#95—941no—
235#95—941no—
236C24(C2×D47)⋊C411yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4(C2×D47)⋊C411yescharacteristic
253C22×C4(C2×D47)⋊C411yescharacteristic
254C22×C4(C2×D47)⋊C411yescharacteristic
255C22×C4C2×C4×D4711yescharacteristic
256C22×C4C2×D18811yescharacteristic
257C22×C4C2×C22⋊D4711yescharacteristic
258M16—82no—
259M16—3762no—
260C2×C8—42no—
261C2×C8—1882no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—944no—
267C4⋊C4—3761no—
268C4⋊C4—3761no—
269C4⋊C4—3761no—
270C4⋊C4—3761no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C22⋊C4—944no—
274C22⋊C4—1881no—
275C22⋊C4—1881no—
276C42—472no—
277C42—472no—
278C42—941no—
279C42—941no—
280C42—1882no—
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23#1309393811yescharacteristic
286C23#1309393811yescharacteristic
287C23C2×(C2×D47)⋊C411yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1882no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4#1309394212yes—
320C2×C4M16×D4711yescharacteristic
321C2×C4M16×D4711yescharacteristic
322C8—82no—
323C8—3762no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—42no—
333C22—42no—
334C22#1568908611yescharacteristic
335C22C2×#1309393811yescharacteristic
336C22C2×#1309394211yescharacteristic
337C4—22no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—3761no—
345C4—3761no—
346C4—1882no—
347C4—1882no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2#2024171711yescharacteristic
353C2#2024505511yescharacteristic
354C2#2024507511yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#1463C2
socleC22×C47C2×#99
prime radicalC24×C47C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#1463D47
hypocenterC47#11514
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #20241333C2semidirect
4. #20241331C2semidirect
99. C4×Dic47M16semidirect
100. C4×Dic47M16semidirect
200. C47#11514semidirect

Maximal subgroups

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

subgroupindex
#202460122
#202417182
#202413332
#202413312
C47×#14632
#1151447