Finite Group Databasebeta

← #26132871

Subgroups — #26132871

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×#15689205C211yesmaximal, characteristic
2C2×#15688948C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic
4C2×#15688923C211yesmaximal, characteristic
5#20244122C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13093986—21no—
10C22×C47⋊C16C2211yescharacteristic
11#15689205—22no—
12#15689205—22no—
13C2×#13093958C2211yescharacteristic
14C2×#13093944—21no—
15C2×C8×Dic47C2211yescharacteristic
16#15689022—21no—
17#15688948—22no—
18#15688925—22no—
19#15688923C414yescomplemented
20#15688885—21no—
21C22×C16×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C22×D188—21no—
25C22×C4×D47—41no—
26C2×D376—21no—
27C2×D376—21no—
28C2×D376—21no—
29C2×D376C2×C412yes—
30C2×D376D412yes—
31C2×D376Q812yes—
32C22×C47⋊C8D411yescharacteristic
33#13093986—24no—
34#13093986—42no—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—41no—
37C2×(C2×D47)⋊C4—41no—
38C2×C4×Dic47D411yescharacteristic
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16C2×C412yescomplemented
42#13093958—21no—
43#13093958—21no—
44#13093944—24no—
45C8×Dic47—21no—
46C8×Dic47—21no—
47C47⋊#95—41no—
48C22×C8×C47C2311yescharacteristic
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C16×C47—21no—
52C2×C16×C47—21no—
53C2×C16×C47—21no—
54#107×C47—21no—
55#107×C47—21no—
56#107×C47C2×C412yescomplemented
57#107×C47D412yes—
58C23×D47—41no—
59C22×C4×C47—41no—
60C22×C4×C47—41no—
61C22×C4×C47C2×D411yescharacteristic
62C22×Dic47—41no—
63C22×Dic47D811yescharacteristic
64C22×Dic47D811yescharacteristic
65C2×D188—22no—
66C2×D188—22no—
67C2×D188—22no—
68C2×D188—41no—
69C2×D188—41no—
70C2×D188—41no—
71C2×C4×D47—44no—
72C2×C4×D47—82no—
73C2×C4×D47—82no—
74C2×C8×C47C22×C411yescharacteristic
75C2×C8×C47C2×D411yescharacteristic
76C2×C8×C47C2×D411yescharacteristic
77C2×C8×C47C2×Q811yescharacteristic
78C2×C8×C47#4111yescharacteristic
79C2×C8×C47#4111yescharacteristic
80C4⋊C4×C47—22no—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84(C2×D47)⋊C4—44no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4⋊Dic47—82no—
88C4×Dic47—21no—
89C4×Dic47—21no—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8—21no—
93D376—22no—
94D376—22no—
95D376—22no—
96D376C4⋊C414yescomplemented
97C16×C47—41no—
98C47⋊C16—22no—
99C23×C47C2×D811yescharacteristic
100C22×D47—42no—
101C22×D47—42no—
102C22×D47—42no—
103C22×D47—81no—
104C22×D47—81no—
105C22×D47—81no—
106C22×D47—81no—
107C2×C4×C47—42no—
108C2×C4×C47—42no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47C4×D411yescharacteristic
114C2×C4×C47#12011yescharacteristic
115C2×C4×C47C22⋊Q811yescharacteristic
116C2×C4×C47#13511yescharacteristic
117C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—81no—
125C2×Dic47—81no—
126C2×Dic47—81no—
127C2×Dic47D1612yes—
128D188—24no—
129D188—42no—
130D188—42no—
131D188—42no—
132C4×D47—88no—
133C8×C47C2×C4⋊C411yescharacteristic
134C8×C47C4×D411yescharacteristic
135C8×C47C22⋊Q811yescharacteristic
136C8×C47#12311yescharacteristic
137C47⋊C8—41no—
138#12935—471nomaximal, Sylow
139C22×C47C4×D811yescharacteristic
140C22×C47#44711yescharacteristic
141C22×C47#47411yescharacteristic
142C22×C47C2×D1611yescharacteristic
143C22×C47#50811yescharacteristic
144C22×C47#50911yescharacteristic
145C22×C47#51011yescharacteristic
146C2×D47—44no—
147C2×D47—82no—
148C2×D47—82no—
149C2×D47—82no—
150C2×D47—82no—
151C2×D47—82no—
152C2×D47—82no—
153C4×C47—82no—
154C4×C47—82no—
155C4×C47#38511yescharacteristic
156C4×C47#44011yescharacteristic
157C4×C47#45211yescharacteristic
158C4×C47#47811yescharacteristic
159Dic47—22no—
160Dic47—41no—
161Dic47—161no—
162C2×C4×D8—471no—
163C2×#366—471no—
164C2×#357—471no—
165C2×#357—471no—
166#1942—471no—
167#1380D4711yescharacteristic, complemented
168#1374—471no—
169C2×C47#186211yescharacteristic
170C2×C47C4×D1611yescharacteristic
171C2×C47#217511yescharacteristic
172C2×C47#218411yescharacteristic
173C2×C47#218911yescharacteristic
174C2×C47#222411yescharacteristic
175C2×C47#222811yescharacteristic
176D47—84no—
177C22×D8—471no—
178C2×C4×D4—941no—
179C22×C16—471no—
180C22×C16C2×D4711yescharacteristic
181C4×D8—942no—
182C4×D8—942no—
183C2×#107—471no—
184C2×#107C2×D4711yescharacteristic
185C2×#107C2×D4711yescharacteristic
186C2×#102—941no—
187C2×C4×C8—471no—
188#389—941no—
189#366—942no—
190#357—474no—
191#357—942no—
192#340—941no—
193C47#1293511yescharacteristic, complemented, Sylow
194C22×D4—941no—
195C23×C4—1881no—
196C2×D8—472no—
197C2×D8—472no—
198C2×D8—472no—
199C2×D8—941no—
200C2×D8—941no—
201C2×D8—941no—
202C22×C8—471no—
203C22×C8C22×D4711yescharacteristic
204C4×D4—944no—
205C4×D4—1882no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—1881no—
210C2×C22⋊C4—1881no—
211C2×C42—471no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—472no—
216C2×C16—941no—
217C2×C16—941no—
218#107—21no—
219#107—21no—
220#107—941no—
221#107—941no—
222#107C4×D4712yescomplemented
223#107D18812yes—
224#102—944no—
225C4×C8—941no—
226C4×C8—941no—
227#95—1881no—
228C24—1881no—
229C2×D4—942no—
230C2×D4—942no—
231C2×D4—942no—
232C2×D4—1881no—
233C2×D4—1881no—
234C2×D4—1881no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—3762no—
240C22×C4—3762no—
241C22×C4—1884no—
242C22×C4—1881no—
243C22×C4D4×D4711yescharacteristic
244D8—474no—
245D8—942no—
246D8—942no—
247D8—942no—
248C2×C8—941no—
249C2×C8—941no—
250C2×C8—941no—
251C2×C8C2×C4×D4711yescharacteristic
252C2×C8C2×D18811yescharacteristic
253C2×C8#1062535011yescharacteristic
254C2×C8D4×D4711yescharacteristic
255C2×C8#1062535211yescharacteristic
256C2×C8Q8×D4711yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—3762no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C22⋊C4—1884no—
265C42—941no—
266C42—941no—
267C16—41no—
268C16—942no—
269C23—3761no—
270C23—3761no—
271C23—3761no—
272C23—3761no—
273C23—1882no—
274C23—1882no—
275C23—1882no—
276C23D8×D4711yescharacteristic
277D4—944no—
278D4—1882no—
279D4—1882no—
280D4—1882no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—472no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—3768no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4(C22⋊D47)⋊C411yescharacteristic
298C2×C4#1309399411yescharacteristic
299C2×C4#1309400211yescharacteristic
300C2×C4#1309404511yescharacteristic
301C2×C4#1309405111yescharacteristic
302C2×C4#1309405611yescharacteristic
303C8—1881no—
304C8C4⋊C4×D4711yescharacteristic
305C8C4×D18811yescharacteristic
306C8#1309400411yescharacteristic
307C8#1309400611yescharacteristic
308C22—3762no—
309C22—3762no—
310C22—3762no—
311C22—3762no—
312C22—3762no—
313C22—3762no—
314C22—1884no—
315C22#1568920311yescharacteristic
316C22#1568925811yescharacteristic
317C22#1568940211yescharacteristic
318C22D16×D4711yescharacteristic
319C22#1568955411yescharacteristic
320C22#1568956011yescharacteristic
321C22#1568956511yescharacteristic
322C4—82no—
323C4—82no—
324C4—942no—
325C4—1881no—
326C4—7521no—
327C4#1568899711yescharacteristic
328C4#1568922611yescharacteristic
329C4#1568928811yescharacteristic
330C4#1568942211yescharacteristic
331C2—3764no—
332C2#2024363611yescharacteristic
333C2#2024523211yescharacteristic
334C2#2024525511yescharacteristic
335C2#2024530111yescharacteristic
336C2#2024533111yescharacteristic
337C2#2024552411yescharacteristic
338C2#2024554411yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#12935
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#15688948C2semidirect
5. #20244122C2semidirect
6. #20241465C2semidirect
7. C47×#1380C2semidirect
19. #15688923C4semidirect
41. C2×C47⋊C16C2×C4semidirect
56. #107×C47C2×C4semidirect
96. D376C4⋊C4semidirect
167. #1380D47semidirect
193. C47#12935semidirect
222. #107C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892052
C2×#156889482
C2×#156889252
C2×#156889232
#202441222
#202414652
C47×#13802
#1293547