Finite Group Databasebeta

← #26134815

Subgroups — #26134815

Order 12032.

350 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689251C211yesmaximal, characteristic
2#20245143C211yesmaximal, characteristic
3M32×Dic47C211yesmaximal, characteristic
4#20241472C211yesmaximal, characteristic
5#20241471C211yesmaximal, characteristic
6#20241471C211yesmaximal, characteristic
7C47×#1377C211yesmaximal, characteristic
8C2×C4×Dic94C411yescharacteristic
9C2×#13093964C2211yescharacteristic
10C2×#13093964C2211yescharacteristic
11#15689251—21no—
12#15689251—21no—
13#15689251—21no—
14#15689251—21no—
15C2×C4⋊(C47⋊C8)C411yescharacteristic
16C2×Dic47⋊C8C411yescharacteristic
17C2×Dic47⋊C8C411yescharacteristic
18C2×#13093934C2211yescharacteristic
19C2×C8×Dic47C2211yescharacteristic
20Dic47⋊C16—21no—
21Dic47⋊C16—21no—
22#15688898—21no—
23C16×Dic47—21no—
24C2×M32×C47C2211yescharacteristic
25C2×M32×C47C2211yescharacteristic
26C2×#97×C47C2211yescharacteristic
27C22×Dic94C811yescharacteristic
28C22×C47⋊C8C2×C411yescharacteristic
29C22×C47⋊C8C2×C411yescharacteristic
30C4×Dic94—21no—
31C4×Dic94—21no—
32C4×Dic94—21no—
33C4×Dic94—21no—
34C2×C4⋊Dic47C811yescharacteristic
35C2×Dic47⋊C4C811yescharacteristic
36C2×Dic47⋊C4C811yescharacteristic
37C2×C4×Dic47C2×C411yescharacteristic
38C2×C4×Dic47C2×C411yescharacteristic
39#13093964—21no—
40#13093964—21no—
41#13093964—21no—
42#13093964Q812yescomplemented
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47Dic47⋊C8—21no—
48Dic47⋊C8—21no—
49Dic47⋊C8—21no—
50Dic47⋊C8—21no—
51#13093934—21no—
52#13093934—21no—
53C8×Dic47D411yescharacteristic
54C8×Dic47D411yescharacteristic
55C8×Dic47D411yescharacteristic
56C8×Dic47D411yescharacteristic
57C22×C8×C47C2×C411yescharacteristic
58C22×C8×C47C2311yescharacteristic
59C2×C42×C47C2×C411yescharacteristic
60M32×C47—21no—
61M32×C47—21no—
62M32×C47—21no—
63M32×C47Q812yescomplemented
64C2×C16×C47—21no—
65C2×C16×C47—21no—
66#97×C47—21no—
67#97×C47—21no—
68C22×C4×C47C2×C811yescharacteristic
69C22×C4×C47C2×C811yescharacteristic
70C22×C4×C47C22×C411yescharacteristic
71C22×Dic47C2×C811yescharacteristic
72C22×Dic47C2×C811yescharacteristic
73C22×Dic47C2×C811yescharacteristic
74C22×Dic47C2×C811yescharacteristic
75C2×Dic94—21no—
76C2×Dic94—21no—
77C2×Dic94—42no—
78C2×C8×C47—21no—
79C2×C8×C47—21no—
80C2×C8×C47—21no—
81C2×C8×C47C2×D411yescharacteristic
82C2×C8×C47C2×D411yescharacteristic
83C2×C8×C47C2×Q811yescharacteristic
84C2×C8×C47C2×Q811yescharacteristic
85C2×C8×C47#4111yescharacteristic
86C2×C8×C47#4111yescharacteristic
87C42×C47—21no—
88C42×C47—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47C22⋊C411yescharacteristic
98C4×Dic47C22⋊C411yescharacteristic
99C4×Dic47M1611yescharacteristic
100C4×Dic47M1611yescharacteristic
101C2×C47⋊C8—21no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8C22⋊C411yescharacteristic
107C2×C47⋊C8C22⋊C411yescharacteristic
108C16×C47—22no—
109C16×C47—41no—
110C47⋊C16—22no—
111C47⋊C16—41no—
112C23×C47C22×C811yescharacteristic
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47C2×C22⋊C411yescharacteristic
118C2×C4×C47C4×Q811yescharacteristic
119C2×C4×C47C4×Q811yescharacteristic
120C2×C4×C47C2×M1611yescharacteristic
121C2×C4×C47#13111yescharacteristic
122C2×C4×C47#13111yescharacteristic
123C2×Dic47—22no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47C22⋊C811yescharacteristic
130C2×Dic47C22⋊C811yescharacteristic
131C2×Dic47C22⋊C811yescharacteristic
132C2×Dic47C22⋊C811yescharacteristic
133Dic94—42no—
134Dic94—42no—
135C8×C47—41no—
136C8×C47C22⋊Q811yescharacteristic
137C8×C47C22⋊Q811yescharacteristic
138C8×C47#12411yescharacteristic
139C8×C47C4⋊Q811yescharacteristic
140C47⋊C8—21no—
141C47⋊C8—21no—
142C47⋊C8—41no—
143#13268—471nomaximal, Sylow
144C22×C47—21no—
145C22×C47—21no—
146C22×C47C2×C22⋊C811yescharacteristic
147C22×C47C8×Q811yescharacteristic
148C22×C47C8×Q811yescharacteristic
149C4×C47—41no—
150C4×C47—41no—
151C4×C47#39111yescharacteristic
152C4×C47#40811yescharacteristic
153C4×C47#44611yescharacteristic
154C4×C47#44611yescharacteristic
155Dic47—21no—
156Dic47—21no—
157Dic47—21no—
158Dic47—41no—
159Dic47—41no—
160Dic47#34912yes—
161C2×#446—471no—
162#2150—471no—
163C4×M32—471no—
164#1377—471no—
165#1377—471no—
166#1377—471no—
167#1377D4711yescharacteristic
168C2×C47—21no—
169C2×C47—21no—
170C2×C47#198411yescharacteristic
171C2×C47C2×#34911yescharacteristic
172C2×C47#211511yescharacteristic
173C2×C4×Q8—471no—
174C2×M32—471no—
175C2×M32—471no—
176C2×M32C2×D4711yescharacteristic
177C2×M32C2×D4711yescharacteristic
178#446—941no—
179#446—941no—
180#446—941no—
181#446—941no—
182C2×C4⋊C8—471no—
183C2×C4⋊C8—471no—
184C2×C4⋊C8—471no—
185C2×#97—471no—
186C2×#97C2×D4711yescharacteristic
187C2×C4×C8—471no—
188C4⋊C16—941no—
189C4⋊C16—941no—
190#346—941no—
191C4×C16—941no—
192C47#1326811yescharacteristic, complemented, Sylow
193C22×Q8—471no—
194C22×C8—471no—
195C22×C8—471no—
196C22×C8C4×D4711yescharacteristic
197C22×C8C22×D4711yescharacteristic
198C4×Q8—941no—
199C4×Q8—941no—
200C4×Q8—941no—
201C4×Q8—941no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C42—471no—
206C2×C42—471no—
207C2×C42C4×D4711yescharacteristic
208M32—21no—
209M32—21no—
210M32—21no—
211M32—472no—
212M32—941no—
213M32—941no—
214M32—941no—
215M32Dic9412yescomplemented
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—941no—
219C2×C16—941no—
220C4⋊C8—941no—
221C4⋊C8—941no—
222C4⋊C8—941no—
223C4⋊C8—941no—
224C4⋊C8—941no—
225C4⋊C8—941no—
226#97—21no—
227#97—21no—
228#97—941no—
229#97—941no—
230C4×C8—471no—
231C4×C8—471no—
232C4×C8—471no—
233C4×C8—471no—
234C2×Q8—941no—
235C2×Q8—941no—
236C2×Q8—1882no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4C8×D4711yescharacteristic
242C22×C4C8×D4711yescharacteristic
243C22×C4C2×C4×D4711yescharacteristic
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—471no—
248C2×C8—471no—
249C2×C8—941no—
250C2×C8—941no—
251C2×C8—941no—
252C2×C8—941no—
253C2×C8—941no—
254C2×C8C2×Dic9411yescharacteristic
255C2×C8#1062535011yescharacteristic
256C2×C8D4×D4711yescharacteristic
257C2×C8D4×D4711yescharacteristic
258C2×C8#1062535211yescharacteristic
259C2×C8Q8×D4711yescharacteristic
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C42—21no—
267C42—21no—
268C42—471no—
269C42—471no—
270C42—471no—
271C42—471no—
272C42—941no—
273C42—941no—
274C16—22no—
275C16—41no—
276C16—942no—
277C16—1881no—
278C23C2×C8×D4711yescharacteristic
279Q8—1882no—
280Q8—1882no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—471no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—471no—
289C2×C4—942no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—1881no—
293C2×C4—1881no—
294C2×C4—1881no—
295C2×C4C22⋊C4×D4711yescharacteristic
296C2×C4#1309398911yescharacteristic
297C2×C4C4×Dic9411yescharacteristic
298C2×C4M16×D4711yescharacteristic
299C2×C4#1309403011yescharacteristic
300C2×C4#1309403211yescharacteristic
301C8—41no—
302C8—941no—
303C8—941no—
304C8—1881no—
305C8#1309400111yescharacteristic
306C8#1309400211yescharacteristic
307C8#1309401011yescharacteristic
308C8#1309402311yescharacteristic
309C22—21no—
310C22—21no—
311C22C22⋊C8×D4711yescharacteristic
312C22#1568924711yescharacteristic
313C22C8×Dic9411yescharacteristic
314C4—41no—
315C4—41no—
316C4—472no—
317C4—941no—
318C4—941no—
319C4—941no—
320C4—1881no—
321C4—1881no—
322C4#1568902711yescharacteristic
323C4#1568908811yescharacteristic
324C4#1568925111yescharacteristic
325C4#1568925211yescharacteristic
326C2—21no—
327C2—21no—
328C2#2024432211yescharacteristic
329C2#349×D4711yescharacteristic
330C2#2024500711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutator, prime radicalC23×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#1377C2
socleC22×C47C2×C22⋊C8
cosocleC22×C8×C47C23
hypercenter#1377D47
hypocenterC47#13268
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1377

Complements

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

NH ≅ G/Ntype
42. #13093964Q8semidirect
63. M32×C47Q8semidirect
192. C47#13268semidirect
215. M32Dic94semidirect

Maximal subgroups

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

subgroupindex
C2×#156892512
#202451432
M32×Dic472
#202414722
#202414712
C47×#13772
#1326847