Finite Group Databasebeta

← #26132318

Subgroups — #26132318

Order 12032.

510 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689205C211yesmaximal, characteristic
2C2×Dic47⋊C16C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic
4C2×#15688923C211yesmaximal, characteristic
5#20243546C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13093986—21no—
10C22×C47⋊C16C2211yescharacteristic
11#15689205—22no—
12#15689205C414yescomplemented
13C2×#13093958C2211yescharacteristic
14C2×#13093957—21no—
15C2×#13093944—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15688992—21no—
18Dic47⋊C16—22no—
19#15688925—22no—
20#15688923—22no—
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×Dic47⋊C4—41no—
37C2×Dic47⋊C4—41no—
38C2×(C2×D47)⋊C4—41no—
39C2×C4×Dic47D411yescharacteristic
40C2×C47⋊C16—21no—
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43#13093958—21no—
44#13093958—21no—
45#13093957—42no—
46#13093944—24no—
47C8×Dic47C2×C412yes—
48C8×Dic47D412yes—
49C22×C8×C47C2311yescharacteristic
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C16×C47—21no—
53C2×C16×C47—21no—
54C2×C16×C47—21no—
55#107×C47—21no—
56#107×C47—21no—
57#107×C47—21no—
58#107×C47C2×C412yes—
59C23×D47—41no—
60C22×C4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47C2×D411yescharacteristic
63C22×Dic47—41no—
64C22×Dic47D811yescharacteristic
65C22×Dic47D811yescharacteristic
66C2×D188—22no—
67C2×D188—22no—
68C2×D188—22no—
69C2×D188—41no—
70C2×D188—41no—
71C2×D188—41no—
72C2×C4×D47—44no—
73C2×C4×D47—82no—
74C2×C4×D47—82no—
75C2×C8×C47C22×C411yescharacteristic
76C2×C8×C47C2×D411yescharacteristic
77C2×C8×C47C2×D411yescharacteristic
78C2×C8×C47C2×Q811yescharacteristic
79C2×C8×C47#4111yescharacteristic
80C2×C8×C47#4111yescharacteristic
81C4⋊C4×C47—22no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85(C2×D47)⋊C4—44no—
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88Dic47⋊C4—82no—
89Dic47⋊C4—82no—
90C4×Dic47C22⋊C412yes—
91C4×Dic47SD1612yes—
92C2×C47⋊C8—21no—
93C2×C47⋊C8—21no—
94C2×C47⋊C8C22⋊C412yes—
95D376—22no—
96D376—22no—
97D376—22no—
98D376C4⋊C414yescomplemented
99C16×C47—41no—
100C47⋊C16—41no—
101C23×C47C2×D811yescharacteristic
102C22×D47—42no—
103C22×D47—42no—
104C22×D47—42no—
105C22×D47—81no—
106C22×D47—81no—
107C22×D47—81no—
108C22×D47—81no—
109C2×C4×C47—42no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47—81no—
114C2×C4×C47—81no—
115C2×C4×C47C2×C22⋊C411yescharacteristic
116C2×C4×C47#12111yescharacteristic
117C2×C4×C47C22⋊Q811yescharacteristic
118C2×C4×C47C2×SD1611yescharacteristic
119C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C47#13711yescharacteristic
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—81no—
124C2×Dic47—81no—
125C2×Dic47—81no—
126C2×Dic47#10212yes—
127C2×Dic47#10212yes—
128C2×Dic47D1612yes—
129C2×Dic47SD3212yes—
130D188—24no—
131D188—42no—
132D188—42no—
133D188—42no—
134C4×D47—88no—
135C8×C47C2×C4⋊C411yescharacteristic
136C8×C47#11711yescharacteristic
137C8×C47#12111yescharacteristic
138C8×C47C22⋊Q811yescharacteristic
139C47⋊C8—22no—
140#12811—471nomaximal, Sylow
141C22×C47C2×#10211yescharacteristic
142C22×C47#45911yescharacteristic
143C22×C47#47411yescharacteristic
144C22×C47C2×D1611yescharacteristic
145C22×C47C2×SD3211yescharacteristic
146C22×C47#50911yescharacteristic
147C22×C47#51011yescharacteristic
148C2×D47—44no—
149C2×D47—82no—
150C2×D47—82no—
151C2×D47—82no—
152C2×D47—82no—
153C2×D47—82no—
154C2×D47—82no—
155C4×C47—82no—
156C4×C47—161no—
157C4×C47#38011yescharacteristic
158C4×C47#41711yescharacteristic
159C4×C47#46111yescharacteristic
160C4×C47#47611yescharacteristic
161Dic47—22no—
162Dic47—161no—
163Dic47#35714yescomplemented
164C2×C4×D8—471no—
165C2×C4⋊C16—471no—
166C2×#357—471no—
167C2×#357—471no—
168#1845—471no—
169#1380—471no—
170#1380D4711yescharacteristic, complemented
171C2×C47#180211yescharacteristic
172C2×C47C2×#35711yescharacteristic
173C2×C47#213911yescharacteristic
174C2×C47#220611yescharacteristic
175C2×C47#220811yescharacteristic
176C2×C47#222411yescharacteristic
177C2×C47#222611yescharacteristic
178D47—84no—
179C22×D8—471no—
180C2×C4×D4—941no—
181C22×C16—471no—
182C22×C16C2×D4711yescharacteristic
183C4×D8—474no—
184C4×D8—942no—
185C2×#107—471no—
186C2×#107—941no—
187C2×#107C2×D4711yescharacteristic
188C2×#107C2×D4711yescharacteristic
189C2×#102—941no—
190C2×C4×C8—471no—
191#384—941no—
192C4⋊C16—942no—
193#357—942no—
194#357—942no—
195C47#1281111yescharacteristic, complemented, Sylow
196C22×D4—941no—
197C23×C4—1881no—
198C2×D8—472no—
199C2×D8—472no—
200C2×D8—472no—
201C2×D8—941no—
202C2×D8—941no—
203C2×D8—941no—
204C22×C8—471no—
205C22×C8C22×D4711yescharacteristic
206C4×D4—944no—
207C4×D4—1882no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4—1881no—
212C2×C4⋊C4—1881no—
213C2×C22⋊C4—1881no—
214C2×C42—471no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—941no—
219C2×C16—941no—
220C2×C16—941no—
221#107—21no—
222#107—21no—
223#107—21no—
224#107—941no—
225#107—941no—
226#107—1882no—
227#107C4×D4712yes—
228#102—944no—
229C4×C8—472no—
230C4×C8—472no—
231C24—1881no—
232C2×D4—942no—
233C2×D4—942no—
234C2×D4—942no—
235C2×D4—1881no—
236C2×D4—1881no—
237C2×D4—1881no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—3762no—
243C22×C4—3762no—
244C22×C4—1884no—
245C22×C4—1881no—
246C22×C4D4×D4711yescharacteristic
247D8—474no—
248D8—942no—
249D8—942no—
250D8—942no—
251C2×C8—472no—
252C2×C8—941no—
253C2×C8—941no—
254C2×C8C2×C4×D4711yescharacteristic
255C2×C8#1062535011yescharacteristic
256C2×C8#1062535011yescharacteristic
257C2×C8D4×D4711yescharacteristic
258C2×C8D4×D4711yescharacteristic
259C2×C8Q8×D4711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—3762no—
265C4⋊C4—3762no—
266C4⋊C4—1881no—
267C4⋊C4—1881no—
268C22⋊C4—1884no—
269C42—472no—
270C42—472no—
271C16—41no—
272C16—1881no—
273C23—3761no—
274C23—3761no—
275C23—3761no—
276C23—3761no—
277C23—1882no—
278C23—1882no—
279C23—1882no—
280C23D8×D4711yescharacteristic
281D4—944no—
282D4—1882no—
283D4—1882no—
284D4—1882no—
285C2×C4—42no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—472no—
292C2×C4—472no—
293C2×C4—472no—
294C2×C4—472no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—3768no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—3761no—
301C2×C4C22⋊C4×D4711yescharacteristic
302C2×C4#1309399711yescharacteristic
303C2×C4#1309400211yescharacteristic
304C2×C4SD16×D4711yescharacteristic
305C2×C4#1309405111yescharacteristic
306C2×C4#1309405611yescharacteristic
307C8—942no—
308C8C4⋊C4×D4711yescharacteristic
309C8#1309398111yescharacteristic
310C8#1309399711yescharacteristic
311C8#1309400211yescharacteristic
312C22—3762no—
313C22—3762no—
314C22—3762no—
315C22—3762no—
316C22—3762no—
317C22—3762no—
318C22—1884no—
319C22#102×D4711yescharacteristic
320C22#1568931711yescharacteristic
321C22#1568940211yescharacteristic
322C22D16×D4711yescharacteristic
323C22SD32×D4711yescharacteristic
324C22#1568956011yescharacteristic
325C22#1568956511yescharacteristic
326C4—82no—
327C4—161no—
328C4—474no—
329C4—942no—
330C4—7521no—
331C4#1568898211yescharacteristic
332C4#1568912311yescharacteristic
333C4#1568932711yescharacteristic
334C4#1568941211yescharacteristic
335C2—3764no—
336C2#2024338711yescharacteristic
337C2#357×D4711yescharacteristic
338C2#2024509911yescharacteristic
339C2#2024542211yescharacteristic
340C2#2024543211yescharacteristic
341C2#2024552411yescharacteristic
342C2#2024553411yescharacteristic
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#12811
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×Dic47⋊C16C2semidirect
5. #20243546C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
12. #15689205C4semidirect
98. D376C4⋊C4semidirect
163. Dic47#357semidirect
170. #1380D47semidirect
195. C47#12811semidirect

Maximal subgroups

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

subgroupindex
C2×#156892052
C2×Dic47⋊C162
C2×#156889252
C2×#156889232
#202435462
#202414792
C47×#13802
#1281147