Finite Group Databasebeta

← #26135340

Subgroups — #26135340

Order 12032.

450 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689527C211yesmaximal, characteristic, complemented
2C2×#15688924C211yesmaximal, characteristic
3#20244255C211yesmaximal, characteristic
4#20241480C211yesmaximal, characteristic, complemented
5#20241479C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic
8C2×#13094023—21no—
9C22×C47⋊C16C2211yescharacteristic
10#15689527—22no—
11#15689527—22no—
12C2×#13093958C2211yescharacteristic
13C2×#13093958C2211yescharacteristic
14C2×#13093957—21no—
15C2×#13093945—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15689026—21no—
18#15688924—22no—
19C22×D8×C47C2211yescharacteristic
20C22×C16×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C47×#357—22no—
23C22×Dic94—41no—
24C22×C47⋊C8D411yescharacteristic
25#13094023—24no—
26#13094023—42no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47—21no—
29C2×Dic47⋊C4—41no—
30C2×C22⋊Dic47—41no—
31C2×C22⋊Dic47—41no—
32C2×C4×Dic47D411yescharacteristic
33C2×C47⋊C16—21no—
34C2×C47⋊C16—21no—
35C2×C47⋊C16—21no—
36#13093958—21no—
37#13093958—21no—
38#13093958—21no—
39#13093958D412yes—
40#13093957—24no—
41#13093945—42no—
42C8×Dic47—21no—
43C8×Dic47—21no—
44C22×D4×C47—21no—
45C2×D8×C47—21no—
46C2×D8×C47—21no—
47C2×D8×C47—21no—
48C2×D8×C47—21no—
49C2×D8×C47—21no—
50C2×D8×C47Q812yescomplemented
51C22×C8×C47C2311yescharacteristic
52C2×C4⋊C4×C47—21no—
53C2×C16×C47—21no—
54C2×C16×C47—21no—
55C2×C16×C47—21no—
56#107×C47—21no—
57#107×C47D412yes—
58C24×C47—41no—
59C2×D4×C47—22no—
60C2×D4×C47—41no—
61C2×D4×C47—41no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47C2×D411yescharacteristic
67C22×Dic47—41no—
68C22×Dic47—41no—
69C22×Dic47D811yescharacteristic
70C22×Dic47D811yescharacteristic
71C2×Dic94—44no—
72C2×Dic94—82no—
73C2×Dic94—82no—
74D8×C47—22no—
75D8×C47—22no—
76D8×C47—41no—
77D8×C47—41no—
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47C2×D411yescharacteristic
80C2×C8×C47C2×Q811yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C4⋊C4×C47—22no—
85C4⋊C4×C47—41no—
86C22⋊Dic47—82no—
87C22⋊Dic47—82no—
88C4⋊Dic47—22no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92Dic47⋊C4—44no—
93C4×Dic47—21no—
94C4×Dic47—21no—
95C2×C47⋊C8—21no—
96C2×C47⋊C8—21no—
97C2×C47⋊C8SD1612yes—
98C16×C47—41no—
99C47⋊C16—41no—
100C23×C47—42no—
101C23×C47—81no—
102C23×C47—81no—
103C23×C47—81no—
104C23×C47—81no—
105C23×C47—81no—
106C23×C47—81no—
107C23×C47C2×D811yescharacteristic
108D4×C47—42no—
109D4×C47—42no—
110D4×C47—81no—
111D4×C47—81no—
112C2×C4×C47—42no—
113C2×C4×C47—81no—
114C2×C4×C47—81no—
115C2×C4×C47#12011yescharacteristic
116C2×C4×C47C22⋊Q811yescharacteristic
117C2×C4×C47#12411yescharacteristic
118C2×C4×C47C2×SD1611yescharacteristic
119C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C47#13711yescharacteristic
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—42no—
126C2×Dic47—81no—
127C2×Dic47—81no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130C2×Dic47—81no—
131C2×Dic47D1612yes—
132C2×Dic47SD3212yes—
133Dic94—88no—
134C8×C47C22⋊Q811yescharacteristic
135C8×C47C22⋊Q811yescharacteristic
136C8×C47#12411yescharacteristic
137C8×C47#12411yescharacteristic
138C47⋊C8—22no—
139#13363—471nomaximal, Sylow
140C22×C47—82no—
141C22×C47—82no—
142C22×C47—82no—
143C22×C47—161no—
144C22×C47—161no—
145C22×C47—161no—
146C22×C47—161no—
147C22×C47#44711yescharacteristic
148C22×C47#47411yescharacteristic
149C22×C47#48611yescharacteristic
150C22×C47C2×D1611yescharacteristic
151C22×C47C2×SD3211yescharacteristic
152C22×C47#50911yescharacteristic
153C22×C47#51011yescharacteristic
154C4×C47—82no—
155C4×C47#39311yescharacteristic
156C4×C47#44811yescharacteristic
157C4×C47#47611yescharacteristic
158C4×C47#48911yescharacteristic
159Dic47—22no—
160Dic47—22no—
161Dic47—82no—
162Dic47—161no—
163C2×#500—471no—
164C2×#357—471no—
165C2×#357D4711yescharacteristic
166#1970—471no—
167#1380—471no—
168#1380—471no—
169#1374—471no—
170C2×C47—162no—
171C2×C47#202311yescharacteristic
172C2×C47#218411yescharacteristic
173C2×C47#218511yescharacteristic
174C2×C47#222411yescharacteristic
175C2×C47#222611yescharacteristic
176C2×C47#224011yescharacteristic
177C2×C47#224311yescharacteristic
178C22×D8C2×D4711yescharacteristic
179C2×C4⋊Q8—941no—
180C22×C16—471no—
181C22×C16C2×D4711yescharacteristic
182#500—942no—
183#500—942no—
184C2×#107—471no—
185C2×#107—471no—
186C2×#107—941no—
187C2×#107C2×D4711yescharacteristic
188C2×#102—941no—
189C2×C4×C8—471no—
190#390—941no—
191#357—22no—
192#357—942no—
193C47#1336311yescharacteristic, complemented, Sylow
194C22×Q8—1881no—
195C22×D4—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8—21no—
200C2×D8—21no—
201C2×D8Dic9412yescomplemented
202C22×C8—471no—
203C22×C8C22×D4711yescharacteristic
204C4⋊Q8—944no—
205C4⋊Q8—1882no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—1881no—
210C2×C22⋊C4—1881no—
211C2×C22⋊C4—1881no—
212C2×C42—471no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—941no—
217C2×C16—941no—
218C2×C16—941no—
219#107—21no—
220#107—472no—
221#107—944no—
222#107—941no—
223#107—941no—
224#107—941no—
225#107C22⋊D4712yes—
226#102—1882no—
227C4×C8—941no—
228C4×C8—941no—
229C24—41no—
230C2×Q8—3762no—
231C2×Q8—3762no—
232C2×Q8—1884no—
233C2×D4—22no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C22×C4—41no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—1881no—
243C22×C4—1881no—
244C22×C4D4×D4711yescharacteristic
245D8—22no—
246D8—22no—
247D8—41no—
248D8—41no—
249C2×C8—472no—
250C2×C8—941no—
251C2×C8—941no—
252C2×C8C2×Dic9411yescharacteristic
253C2×C8#1062535011yescharacteristic
254C2×C8D4×D4711yescharacteristic
255C2×C8#1062535211yescharacteristic
256C2×C8#1062535211yescharacteristic
257C2×C8C2×C22⋊D4711yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—942no—
261C4⋊C4—1884no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C22⋊C4—3762no—
266C22⋊C4—3762no—
267C42—941no—
268C42—941no—
269C16—41no—
270C16—1881no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23—81no—
277C23—81no—
278C23D8×D4711yescharacteristic
279Q8—3768no—
280D4—42no—
281D4—42no—
282D4—81no—
283D4—81no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—472no—
288C2×C4—472no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—1882no—
299C2×C4#1309399211yescharacteristic
300C2×C4#1309400111yescharacteristic
301C2×C4#1309401011yescharacteristic
302C2×C4SD16×D4711yescharacteristic
303C2×C4#1309404811yescharacteristic
304C2×C4#1309405311yescharacteristic
305C8—942no—
306C8#1309400111yescharacteristic
307C8#1309400311yescharacteristic
308C8#1309401011yescharacteristic
309C8#1309401111yescharacteristic
310C22—82no—
311C22—82no—
312C22—82no—
313C22—161no—
314C22—161no—
315C22—161no—
316C22—161no—
317C22#1568925511yescharacteristic
318C22#1568940111yescharacteristic
319C22#1568946811yescharacteristic
320C22D16×D4711yescharacteristic
321C22SD32×D4711yescharacteristic
322C22#1568955711yescharacteristic
323C22#1568956211yescharacteristic
324C4—82no—
325C4—942no—
326C4—942no—
327C4—3762no—
328C4—7521no—
329C4#1568903511yescharacteristic
330C4#1568926011yescharacteristic
331C4#1568941111yescharacteristic
332C4#1568948111yescharacteristic
333C2—162no—
334C2#2024452211yescharacteristic
335C2#2024529811yescharacteristic
336C2#2024530311yescharacteristic
337C2#2024552311yescharacteristic
338C2#2024553311yescharacteristic
339C2#2024561011yescharacteristic
340C2#2024562311yescharacteristic
subgroupG/H
centerC23D8×D47
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC22×D8×C47C22
hypercenterC2×#357D47
hypocenterC47#13363
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. C2×#15689527C2semidirect
4. #20241480C2semidirect
5. #20241479C2semidirect
6. #20241465C2semidirect
50. C2×D8×C47Q8semidirect
193. C47#13363semidirect
201. C2×D8Dic94semidirect

Maximal subgroups

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

subgroupindex
C2×#156895272
C2×#156889242
#202442552
#202414802
#202414792
#202414652
C2×C47×#3572
#1336347