Finite Group Databasebeta

← #26111350

Subgroups — #26111350

Order 12032.

484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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#20252473C211yesmaximal, characteristic
2#20246679C211yesmaximal, characteristic
3#20241836C212yesmaximal
4#20241282C212yesmaximal
5C4×#101×C47C211yesmaximal, characteristic
6C2×C4×Dic94C2211yescharacteristic
7#15689254—24no—
8#15689180—21no—
9#15689180C2212yes—
10#15689176—21no—
11#15689054—21no—
12#15689053C411yescharacteristic
13#15689053C411yescharacteristic
14#15689043C411yescharacteristic
15#15689043C411yescharacteristic
16#15689042—21no—
17C4×Dic47⋊C4—21no—
18C4×Dic47⋊C4—21no—
19#15688969C2211yescharacteristic
20#15688855—24no—
21C2×C4×Q8×C47C2211yescharacteristic
22C2×#101×C47—21no—
23C4×M16×C47C2212yes—
24C47×#343—21no—
25C22×Dic94C2×C411yescharacteristic
26C4×Dic94—22no—
27C4×Dic94—22no—
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×C4×Dic47—21no—
35C2×C4×Dic47—21no—
36C4⋊(C47⋊C8)—22no—
37C4⋊(C47⋊C8)—22no—
38C4⋊(C47⋊C8)D414yes—
39C22⋊(C47⋊C8)—22no—
40#13093935—22no—
41#13093935—22no—
42C4×C47⋊C8—22no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95C2×C411yescharacteristic
49C47⋊#95C2×C411yescharacteristic
50C22×Q8×C47D411yescharacteristic
51C2×M16×C47—22no—
52C4×Q8×C47—22no—
53C4×Q8×C47—22no—
54C2×C4⋊C4×C47C2×C411yescharacteristic
55C2×C4⋊C4×C47C2×C411yescharacteristic
56C2×C4⋊C4×C47D411yescharacteristic
57C2×C42×C47D411yescharacteristic
58C2×C42×C47D411yescharacteristic
59C2×C42×C47C2311yescharacteristic
60#101×C47—24no—
61#97×C47—22no—
62C4×C8×C47—22no—
63C2×Q8×C47—22no—
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C22⋊C411yescharacteristic
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C2×Dic94—22no—
78C2×Dic94—42no—
79M16×C47—24no—
80M16×C47—42no—
81C2×C8×C47—42no—
82C4⋊C4×C47—22no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—22no—
85C42×C47—21no—
86C42×C47—21no—
87C42×C47—21no—
88C42×C47—21no—
89C42×C47C2×D412yes—
90C42×C47#4112yes—
91C4⋊Dic47—22no—
92Dic47⋊C4—42no—
93Dic47⋊C4—42no—
94Dic47⋊C4—42no—
95Dic47⋊C4—42no—
96Dic47⋊C4—42no—
97C4×Dic47—24no—
98C4×Dic47—41no—
99C4×Dic47—41no—
100C2×C47⋊C8—24no—
101C23×C47C2×C22⋊C411yescharacteristic
102Q8×C47—44no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—22no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47#10412yes—
117C2×C4×C47C4×D412yes—
118C2×C4×C47#12011yescharacteristic
119C2×C4×C47#12112yes—
120C2×C4×C47#12311yescharacteristic
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—22no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133Dic94—24no—
134Dic94—42no—
135C8×C47—44no—
136C47⋊C8—44no—
137#9030—471nomaximal, Sylow
138C22×C47—21no—
139C22×C47—21no—
140C22×C47#38611yescharacteristic
141C22×C47C2×#10411yescharacteristic
142C22×C47#42111yescharacteristic
143C4×C47—22no—
144C4×C47—22no—
145C4×C47—21no—
146C4×C47—22no—
147C4×C47—41no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47#45612yes—
151Dic47—42no—
152Dic47—42no—
153Dic47—42no—
154Dic47—81no—
155#2983—471no—
156#2399—471no—
157C4×#101D4711yescharacteristic
158#1491—472no—
159#1300—472no—
160C2×C47—21no—
161C2×C47—21no—
162C2×C47#187111yescharacteristic
163C2×C47#188611yescharacteristic
164C2×C47#189111yescharacteristic
165C2×C4×Q8—471no—
166C2×C4×Q8C2×D4711yescharacteristic
167#446—944no—
168#432—472no—
169#432—941no—
170#431—941no—
171C2×#101—21no—
172C4×M16C2×D4712yes—
173#398—471no—
174#398—471no—
175#398—941no—
176#395—471no—
177#395—471no—
178#395—941no—
179C4×C4⋊C4—941no—
180C4×C4⋊C4—941no—
181#376—471no—
182#343—21no—
183Q8⋊C8—944no—
184C47#903011yescharacteristic, complemented, Sylow
185C22×Q8—471no—
186C22×Q8C22⋊D4711yescharacteristic
187C2×M16—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—942no—
191C4×Q8—942no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—941no—
194C2×C4⋊C4—941no—
195C2×C4⋊C4—941no—
196C2×C4⋊C4—941no—
197C2×C4⋊C4—941no—
198C2×C4⋊C4C4×D4711yescharacteristic
199C2×C4⋊C4C4×D4711yescharacteristic
200C2×C4⋊C4C22⋊D4711yescharacteristic
201C2×C42—941no—
202C2×C42—941no—
203C2×C42D18811yescharacteristic
204C2×C42D18811yescharacteristic
205C2×C42C22×D4711yescharacteristic
206C4⋊C8—474no—
207C4⋊C8—942no—
208C4⋊C8—942no—
209#101—24no—
210C22⋊C8—942no—
211#97—22no—
212#97—942no—
213#97—942no—
214C4×C8—22no—
215C4×C8—942no—
216#95—471no—
217#95—471no—
218#95—941no—
219#95—941no—
220#95—941no—
221#95—941no—
222#95—941no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—942no—
227C2×Q8—1882no—
228C22×C4—941no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4—941no—
232C22×C4(C2×D47)⋊C411yescharacteristic
233C22×C4(C2×D47)⋊C411yescharacteristic
234C22×C4(C2×D47)⋊C411yescharacteristic
235C22×C4(C2×D47)⋊C411yescharacteristic
236C22×C4C2×C4×D4711yescharacteristic
237C22×C4C2×D18811yescharacteristic
238C22×C4C2×C22⋊D4711yescharacteristic
239M16—24no—
240M16—42no—
241C2×C8—42no—
242C2×C8—944no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—942no—
247C4⋊C4—1882no—
248C4⋊C4—1882no—
249C4⋊C4—1882no—
250C4⋊C4—1882no—
251C4⋊C4—1882no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—944no—
257C42—1881no—
258C42—1881no—
259C42D4×D4712yes—
260C42#1062535212yes—
261C23C2×(C2×D47)⋊C411yescharacteristic
262Q8—44no—
263Q8—944no—
264Q8—1882no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—942no—
279C2×C4—942no—
280C2×C4—942no—
281C2×C4—1881no—
282C2×C4—1881no—
283C2×C4—1881no—
284C2×C4—1881no—
285C2×C4—1881no—
286C2×C4—1881no—
287C2×C4—1881no—
288C2×C4—1881no—
289C2×C4—1881no—
290C2×C4#1309395212yes—
291C2×C4(C22⋊D47)⋊C412yes—
292C2×C4#1309399411yescharacteristic
293C2×C4#1309399612yes—
294C2×C4#1309400811yescharacteristic
295C8—44no—
296C8—1884no—
297C22—21no—
298C22—21no—
299C22#1568900011yescharacteristic
300C22C2×#1309395211yescharacteristic
301C22#1568914111yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—3761no—
310C4—1882no—
311C4—1882no—
312C4—1882no—
313C4#1568930812yes—
314C2—21no—
315C2—21no—
316C2#2024368811yescharacteristic
317C2#2024377911yescharacteristic
318C2#2024380411yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC4×#101×C47C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×#101D47
hypocenterC47#9030
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
184. C47#9030semidirect

Maximal subgroups

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

subgroupindex
#202524732
#202466792
#202418362
#202412822
C4×#101×C472
#903047