Finite Group Databasebeta

← #26143536

Subgroups — #26143536

Order 12032.

2070 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688982C213yesmaximal
2C2×#15688980C213yesmaximal
3C2×#95×D47C211yesmaximal, characteristic
4#20241653C211yesmaximal, characteristic, complemented
5#20241652C213yesmaximal, complemented
6#20241651C213yesmaximal, complemented
7C47×#1444C211yesmaximal, characteristic, complemented
8C23×C4×D47C2213yes—
9C22×C4⋊Dic47C2213yes—
10C22×Dic47⋊C4C2213yes—
11C22×Dic47⋊C4C2213yes—
12C22×(C2×D47)⋊C4C2211yescharacteristic
13C22×(C2×D47)⋊C4C2213yes—
14#15688982—212no—
15#15688980—212no—
16C2×C47⋊#95C2213yes—
17C2×C47⋊#95C2216yes—
18C2×C47⋊#95C2213yes—
19#95×D47C418yescomplemented
20C22×C4⋊C4×C47C2213yes—
21C2×#95×C47C2213yes—
22C2×#95×C47C2211yescharacteristic
23C24×D47C2311yescharacteristic
24C23×Dic47C2311yescharacteristic
25C23×Dic47C2313yes—
26C23×Dic47C2313yes—
27C22×C4×D47—46no—
28C22×C4×D47—46no—
29C22×C4×D47C2×C4112yes—
30C22×C4×D47D4112yes—
31C22×C4×D47Q8112yes—
32C2×C4⋊Dic47—26no—
33C2×C4⋊Dic47—46no—
34C2×Dic47⋊C4—26no—
35C2×Dic47⋊C4—26no—
36C2×Dic47⋊C4—46no—
37C2×Dic47⋊C4—46no—
38C2×(C2×D47)⋊C4—212no—
39C2×(C2×D47)⋊C4—26no—
40C2×(C2×D47)⋊C4—26no—
41C47⋊#95—26no—
42C47⋊#95—212no—
43C47⋊#95C2×C4112yes—
44C23×C4×C47C2313yes—
45C23×C4×C47C2311yescharacteristic
46C23×C4×C47C2313yes—
47C2×C4⋊C4×C47—26no—
48C2×C4⋊C4×C47—46no—
49#95×C47—26no—
50#95×C47C2×C414yes—
51C24×C47C2411yescharacteristic
52C23×D47—23no—
53C23×D47—23no—
54C23×D47—21no—
55C23×D47—21no—
56C23×D47C22×C412yes—
57C23×D47C2×D416yes—
58C23×D47C2×Q816yes—
59C22×C4×C47—26no—
60C22×C4×C47—26no—
61C22×C4×C47—26no—
62C22×C4×C47—23no—
63C22×C4×C47—23no—
64C22×C4×C47—23no—
65C22×C4×C47—26no—
66C22×C4×C47—23no—
67C22×C4×C47—23no—
68C22×C4×C47—21no—
69C22×C4×C47C22×C416yes—
70C22×C4×C47C2×D416yes—
71C22×C4×C47C2×Q816yes—
72C22×Dic47—26no—
73C22×Dic47—26no—
74C22×Dic47—23no—
75C22×Dic47—23no—
76C22×Dic47—26no—
77C22×Dic47—23no—
78C22×Dic47—26no—
79C22×Dic47—23no—
80C22×Dic47—21no—
81C22×Dic47—23no—
82C22×Dic47C22×C416yes—
83C22×Dic47C2×D416yes—
84C22×Dic47C2×Q816yes—
85C2×C4×D47—424no—
86C2×C4×D47—412no—
87C2×C4×D47—412no—
88C2×C4×D47—424no—
89C2×C4×D47C4⋊C4148yescomplemented
90C4⋊C4×C47—412no—
91(C2×D47)⋊C4—412no—
92(C2×D47)⋊C4—44no—
93C4⋊Dic47—412no—
94Dic47⋊C4—412no—
95Dic47⋊C4—412no—
96C23×C47C23×C411yescharacteristic
97C23×C47C22×D413yes—
98C23×C47C22×Q813yes—
99C23×C47H(5,𝔽2)13yes—
100C23×C47H(5,𝔽2)13yes—
101C23×C472−1+411yescharacteristic
102C23×C472−1+411yescharacteristic
103C22×D47—26no—
104C22×D47—22no—
105C22×D47—26no—
106C22×D47—26no—
107C22×D47—26no—
108C22×D47—26no—
109C22×D47—212no—
110C22×D47—26no—
111C22×D47—26no—
112C22×D47C2×C4⋊C4112yes—
113C22×D47#12714yes—
114C22×D47C4⋊Q8112yes—
115C2×C4×C47—212no—
116C2×C4×C47—26no—
117C2×C4×C47—26no—
118C2×C4×C47—212no—
119C2×C4×C47—43no—
120C2×C4×C47—41no—
121C2×C4×C47—43no—
122C2×C4×C47—43no—
123C2×C4×C47—46no—
124C2×C4×C47—46no—
125C2×C4×C47—43no—
126C2×C4×C47—43no—
127C2×C4×C47C2×C4⋊C4112yes—
128C2×Dic47—212no—
129C2×Dic47—26no—
130C2×Dic47—26no—
131C2×Dic47—212no—
132C2×Dic47—41no—
133C2×Dic47—43no—
134C2×Dic47—43no—
135C2×Dic47—43no—
136C2×Dic47—46no—
137C2×Dic47—43no—
138C2×Dic47—43no—
139C2×Dic47—46no—
140C2×Dic47C2×C4⋊C4112yes—
141C4×D47—448no—
142#14353—471nomaximal, Sylow
143C22×C47C22×C4⋊C413yes—
144C22×C47#51813yes—
145C22×C47#51911yescharacteristic
146C22×C47C2×#12711yescharacteristic
147C22×C47C2×C4⋊Q813yes—
148C22×C47#53413yes—
149C22×C47#53413yes—
150C22×C47#53713yes—
151C22×C47#53713yes—
152C22×C47#54316yes—
153C22×C47#54413yes—
154C22×C47#54413yes—
155C2×D47—212no—
156C2×D47—212no—
157C2×D47—24no—
158C2×D47—24no—
159C2×D47—212no—
160C2×D47—212no—
161C2×D47#38418yes—
162C4×C47—212no—
163C4×C47—83no—
164C4×C47—81no—
165Dic47—212no—
166Dic47—81no—
167Dic47—83no—
168C2×#380—473no—
169C2×#380—473no—
170C22×#95—471no—
171#1444—473no—
172#1444—471no—
173#1444—473no—
174#1444D4711yescharacteristic, complemented
175C2×C47C2×#38411yescharacteristic
176C2×C47#231513yes—
177C2×C47#231613yes—
178C2×C47#265611yescharacteristic
179C2×C47#265611yescharacteristic
180C2×C47#265913yes—
181C2×C47#265913yes—
182D47—28no—
183C24×C4—473no—
184C22×C4⋊C4—473no—
185C22×C4⋊C4—473no—
186C22×C4⋊C4—473no—
187C22×C4⋊C4C2×D4713yes—
188C22×C22⋊C4—471no—
189C22×C22⋊C4—473no—
190#380—9412no—
191#380—9412no—
192C2×#95—473no—
193C2×#95—478no—
194C2×#95—476no—
195C2×#95—473no—
196C2×#95C2×D4713yes—
197C2×#95C2×D4711yescharacteristic
198C47#1435311yescharacteristic, complemented, Sylow
199C25—471no—
200C23×C4—473no—
201C23×C4—4712no—
202C23×C4—4712no—
203C23×C4—4712no—
204C23×C4—471no—
205C23×C4—473no—
206C23×C4—1886no—
207C23×C4—1886no—
208C23×C4C22×D4711yescharacteristic
209C23×C4C22×D4713yes—
210C23×C4C22×D4713yes—
211C2×C4⋊C4—26no—
212C2×C4⋊C4—46no—
213C2×C4⋊C4—946no—
214C2×C4⋊C4—946no—
215C2×C4⋊C4—946no—
216C2×C4⋊C4—1886no—
217C2×C4⋊C4—1886no—
218C2×C4⋊C4—1886no—
219C2×C22⋊C4—946no—
220C2×C22⋊C4—946no—
221C2×C22⋊C4—9412no—
222#95—26no—
223#95—4712no—
224#95—9412no—
225#95—946no—
226#95C4×D4714yes—
227C24—472no—
228C24—476no—
229C24—476no—
230C24—943no—
231C24—943no—
232C24—941no—
233C24—941no—
234C24C23×D4711yescharacteristic
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—21no—
245C22×C4—476no—
246C22×C4—476no—
247C22×C4—476no—
248C22×C4—4748no—
249C22×C4—946no—
250C22×C4—946no—
251C22×C4—943no—
252C22×C4—943no—
253C22×C4—946no—
254C22×C4—943no—
255C22×C4—946no—
256C22×C4—943no—
257C22×C4—941no—
258C22×C4—943no—
259C22×C4—18824no—
260C22×C4—18824no—
261C22×C4—18812no—
262C22×C4—18812no—
263C22×C4C2×C4×D4716yes—
264C22×C4D4×D4716yes—
265C22×C4Q8×D4716yes—
266C4⋊C4—412no—
267C4⋊C4—18812no—
268C4⋊C4—18812no—
269C4⋊C4—18812no—
270C22⋊C4—18812no—
271C22⋊C4—1884no—
272C23—4712no—
273C23—474no—
274C23—4712no—
275C23—9412no—
276C23—946no—
277C23—946no—
278C23—946no—
279C23—942no—
280C23—946no—
281C23—946no—
282C23—946no—
283C23—946no—
284C23C22×C4×D4711yescharacteristic
285C23C2×D4×D4713yes—
286C23C2×Q8×D4713yes—
287C23#1309406913yes—
288C23#1309407013yes—
289C23#1309407111yescharacteristic
290C23#1309407211yescharacteristic
291C2×C4—212no—
292C2×C4—212no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—43no—
296C2×C4—41no—
297C2×C4—46no—
298C2×C4—43no—
299C2×C4—43no—
300C2×C4—43no—
301C2×C4—46no—
302C2×C4—43no—
303C2×C4—4712no—
304C2×C4—9412no—
305C2×C4—9412no—
306C2×C4—946no—
307C2×C4—946no—
308C2×C4—18848no—
309C2×C4—1881no—
310C2×C4—1883no—
311C2×C4—1883no—
312C2×C4—1883no—
313C2×C4—1886no—
314C2×C4—1883no—
315C2×C4—1883no—
316C2×C4—1886no—
317C2×C4C4⋊C4×D47112yes—
318C22—478no—
319C22—944no—
320C22—944no—
321C22—9412no—
322C22—9412no—
323C22—9412no—
324C22—9412no—
325C22C2×C4⋊C4×D4713yes—
326C22#1568959513yes—
327C22#1568959911yescharacteristic
328C22#127×D4711yescharacteristic
329C22C4⋊Q8×D4713yes—
330C22#1568968313yes—
331C22#1568968413yes—
332C22#1568970213yes—
333C22#1568970313yes—
334C22#1568974816yes—
335C22#1568975013yes—
336C22#1568975313yes—
337C4—212no—
338C4—83no—
339C4—81no—
340C4—9412no—
341C4—3761no—
342C4—3763no—
343C2—948no—
344C2#384×D4711yescharacteristic
345C2#2024599913yes—
346C2#2024600313yes—
347C2#2024948911yescharacteristic
348C2#2024949111yescharacteristic
349C2#2024950113yes—
350C2#2024950313yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1444C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenter#1444D47
hypocenterC47#14353
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. #20241653C2semidirect
5. #20241652C2semidirect
6. #20241651C2semidirect
7. C47×#1444C2semidirect
19. #95×D47C4semidirect
89. C2×C4×D47C4⋊C4semidirect
174. #1444D47semidirect
198. C47#14353semidirect

Maximal subgroups

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

subgroupindex
C2×#156889822
C2×#156889802
C2×#95×D472
#202416532
#202416522
#202416512
C47×#14442
#1435347