Finite Group Databasebeta

← #26132872

Subgroups — #26132872

Order 12032.

490 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic47C211yesmaximal, characteristic
2C2×#15688949C211yesmaximal, characteristic, complemented
3C2×#15688924C211yesmaximal, characteristic
4#20244122C211yesmaximal, characteristic, complemented
5#20241479C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic
8C2×D4×Dic47—21no—
9C22×C47⋊C16C2211yescharacteristic
10D8×Dic47—22no—
11D8×Dic47—22no—
12C2×#13093958C2211yescharacteristic
13C2×#13093958C2211yescharacteristic
14C2×#13093945—21no—
15C2×C8×Dic47C2211yescharacteristic
16#15689022—21no—
17#15688949—22no—
18#15688924—22no—
19#15688885—21no—
20C22×D8×C47C2211yescharacteristic
21C22×C16×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C47×#357C414yescomplemented
24C23×Dic47—41no—
25C22×C47⋊C8D411yescharacteristic
26D4×Dic47—24no—
27D4×Dic47—42no—
28C2×C4⋊Dic47—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊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#13093945—24no—
41C8×Dic47—21no—
42C8×Dic47—21no—
43C47⋊#95—41no—
44C22×D4×C47—21no—
45C2×D8×C47—21no—
46C2×D8×C47—21no—
47C2×D8×C47—21no—
48C2×D8×C47C2×C412yes—
49C2×D8×C47D412yes—
50C2×D8×C47Q812yes—
51C22×C8×C47C2311yescharacteristic
52C2×C4⋊C4×C47—21no—
53C2×C16×C47—21no—
54C2×C16×C47—21no—
55C2×C16×C47C2×C412yescomplemented
56#107×C47—21no—
57#107×C47C2×C412yescomplemented
58C24×C47—41no—
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47—22no—
62C2×D4×C47—41no—
63C2×D4×C47—41no—
64C2×D4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47C2×D411yescharacteristic
67C22×Dic47—44no—
68C22×Dic47—41no—
69C22×Dic47—41no—
70C22×Dic47—82no—
71C22×Dic47—82no—
72C22×Dic47D811yescharacteristic
73C22×Dic47D811yescharacteristic
74D8×C47—22no—
75D8×C47—22no—
76D8×C47—22no—
77D8×C47C4⋊C414yescomplemented
78C2×C8×C47C22×C411yescharacteristic
79C2×C8×C47C2×D411yescharacteristic
80C2×C8×C47C2×D411yescharacteristic
81C2×C8×C47C2×Q811yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C2×C8×C47#4111yescharacteristic
84C4⋊C4×C47—22no—
85C4⋊C4×C47—41no—
86C22⋊Dic47—44no—
87C4⋊Dic47—22no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47—82no—
92C4×Dic47—21no—
93C4×Dic47—21no—
94C2×C47⋊C8—21no—
95C2×C47⋊C8—21no—
96C2×C47⋊C8—21no—
97C16×C47—22no—
98C47⋊C16—41no—
99C23×C47—42no—
100C23×C47—42no—
101C23×C47—42no—
102C23×C47—81no—
103C23×C47—81no—
104C23×C47—81no—
105C23×C47—81no—
106C23×C47C2×D811yescharacteristic
107D4×C47—24no—
108D4×C47—42no—
109D4×C47—42no—
110D4×C47—42no—
111C2×C4×C47—42no—
112C2×C4×C47—81no—
113C2×C4×C47—81no—
114C2×C4×C47C4×D411yescharacteristic
115C2×C4×C47#12011yescharacteristic
116C2×C4×C47C22⋊Q811yescharacteristic
117C2×C4×C47#13511yescharacteristic
118C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C47#13711yescharacteristic
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—42no—
126C2×Dic47—88no—
127C2×Dic47—81no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130C2×Dic47—81no—
131C2×Dic47—81no—
132C2×Dic47D1612yes—
133C8×C47C2×C4⋊C411yescharacteristic
134C8×C47C4×D411yescharacteristic
135C8×C47C22⋊Q811yescharacteristic
136C8×C47#12311yescharacteristic
137C47⋊C8—41no—
138#12935—471nomaximal, Sylow
139C22×C47—44no—
140C22×C47—82no—
141C22×C47—82no—
142C22×C47—82no—
143C22×C47—82no—
144C22×C47—82no—
145C22×C47—82no—
146C22×C47C4×D811yescharacteristic
147C22×C47#44711yescharacteristic
148C22×C47#47411yescharacteristic
149C22×C47C2×D1611yescharacteristic
150C22×C47#50811yescharacteristic
151C22×C47#50911yescharacteristic
152C22×C47#51011yescharacteristic
153C4×C47—82no—
154C4×C47#38511yescharacteristic
155C4×C47#44011yescharacteristic
156C4×C47#45211yescharacteristic
157C4×C47#47811yescharacteristic
158Dic47—22no—
159Dic47—41no—
160Dic47—82no—
161Dic47—161no—
162C2×C4×D8—471no—
163C2×#366—471no—
164C2×#357—471no—
165C2×#357D4711yescharacteristic
166#1942—471no—
167#1380—471no—
168#1374—471no—
169C2×C47—84no—
170C2×C47#186211yescharacteristic
171C2×C47C4×D1611yescharacteristic
172C2×C47#217511yescharacteristic
173C2×C47#218411yescharacteristic
174C2×C47#218911yescharacteristic
175C2×C47#222411yescharacteristic
176C2×C47#222811yescharacteristic
177C22×D8C2×D4711yescharacteristic
178C2×C4×D4—941no—
179C22×C16—471no—
180C22×C16C2×D4711yescharacteristic
181C4×D8—942no—
182C4×D8—942no—
183C2×#107—471no—
184C2×#107—471no—
185C2×#107C2×D4711yescharacteristic
186C2×#102—941no—
187C2×C4×C8—471no—
188#389—941no—
189#366—942no—
190#357—942no—
191#357Dic4714yescomplemented
192#340—941no—
193C47#1293511yescharacteristic, complemented, Sylow
194C22×D4—21no—
195C23×C4—1881no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8Dic9412yes—
200C2×D8D18812yes—
201C2×D8C2×Dic4712yes—
202C22×C8—471no—
203C22×C8C22×D4711yescharacteristic
204C4×D4—944no—
205C4×D4—1882no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—1881no—
210C2×C22⋊C4—1881no—
211C2×C42—471no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—941no—
215C2×C16—941no—
216C2×C16—941no—
217C2×C16C2×Dic4712yescomplemented
218#107—21no—
219#107—472no—
220#107—941no—
221#107—941no—
222#107—941no—
223#107C2×Dic4712yescomplemented
224#102—944no—
225C4×C8—941no—
226C4×C8—941no—
227#95—1881no—
228C24—41no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—41no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—3762no—
239C22×C4—3762no—
240C22×C4—1884no—
241C22×C4—1881no—
242C22×C4—1881no—
243C22×C4D4×D4711yescharacteristic
244D8—22no—
245D8—22no—
246D8—22no—
247D8C4⋊Dic4714yescomplemented
248C2×C8—941no—
249C2×C8—941no—
250C2×C8—941no—
251C2×C8C2×Dic9411yescharacteristic
252C2×C8C2×D18811yescharacteristic
253C2×C8D4×D4711yescharacteristic
254C2×C8#1062535211yescharacteristic
255C2×C8#1062535211yescharacteristic
256C2×C8C22×Dic4711yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—942no—
260C4⋊C4—3762no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C22⋊C4—1884no—
265C42—941no—
266C42—941no—
267C16—22no—
268C16—1881no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23D8×D4711yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—472no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—3768no—
291C2×C4—3761no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—1882no—
297C2×C4D4×Dic4711yescharacteristic
298C2×C4#1309399411yescharacteristic
299C2×C4#1309400111yescharacteristic
300C2×C4#1309404311yescharacteristic
301C2×C4#1309405111yescharacteristic
302C2×C4#1309405311yescharacteristic
303C8—1881no—
304C8C2×C4⋊Dic4711yescharacteristic
305C8D4×Dic4711yescharacteristic
306C8#1309400111yescharacteristic
307C8#1309400811yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22D8×Dic4711yescharacteristic
316C22#1568925811yescharacteristic
317C22#1568940111yescharacteristic
318C22D16×D4711yescharacteristic
319C22#1568955211yescharacteristic
320C22#1568956011yescharacteristic
321C22#1568956211yescharacteristic
322C4—82no—
323C4—942no—
324C4—3762no—
325C4—1881no—
326C4—7521no—
327C4#1568899811yescharacteristic
328C4#1568922411yescharacteristic
329C4#1568928611yescharacteristic
330C4#1568942111yescharacteristic
331C2—84no—
332C2#2024363711yescharacteristic
333C2D16×Dic4711yescharacteristic
334C2#2024525311yescharacteristic
335C2#2024530111yescharacteristic
336C2#2024532911yescharacteristic
337C2#2024552311yescharacteristic
338C2#2024554311yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC22×D8×C47C22
cosocleC22×C8×C47C23
hypercenterC2×#357D47
hypocenterC47#12935
LCSG ▷ C2×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
2. C2×#15688949C2semidirect
4. #20244122C2semidirect
5. #20241479C2semidirect
6. #20241465C2semidirect
23. C47×#357C4semidirect
55. C2×C16×C47C2×C4semidirect
57. #107×C47C2×C4semidirect
77. D8×C47C4⋊C4semidirect
191. #357Dic47semidirect
193. C47#12935semidirect
217. C2×C16C2×Dic47semidirect
223. #107C2×Dic47semidirect
247. D8C4⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic472
C2×#156889492
C2×#156889242
#202441222
#202414792
#202414652
C2×C47×#3572
#1293547