Finite Group Databasebeta

← #26132328

Subgroups — #26132328

Order 12032.

494 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×Dic47⋊C16C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic
4C2×#15688923C211yesmaximal, characteristic
5#20243551C211yesmaximal, 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×#13093955—21no—
15C2×#13093944—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15688988—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×(C2×D47)⋊C4—41no—
37C2×C4×Dic47D411yescharacteristic
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41#13093958—21no—
42#13093958—21no—
43#13093955—42no—
44#13093944—24no—
45C8×Dic47C2×C412yes—
46C8×Dic47D412yes—
47C47⋊#95—41no—
48C47⋊#95—41no—
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—
88C4×Dic47C22⋊C412yes—
89C4×Dic47SD1612yes—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8C22⋊C412yes—
93D376—22no—
94D376—22no—
95D376—22no—
96D376C4⋊C414yes—
97C16×C47—41no—
98C47⋊C16—41no—
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—81no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47C2×C22⋊C411yescharacteristic
114C2×C4×C47#12111yescharacteristic
115C2×C4×C47C22⋊Q811yescharacteristic
116C2×C4×C47C2×SD1611yescharacteristic
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—81no—
124C2×Dic47—81no—
125C2×Dic47—81no—
126C2×Dic47#10212yes—
127C2×Dic47#10212yes—
128D188—24no—
129D188—42no—
130D188—42no—
131D188—42no—
132C4×D47—88no—
133C8×C47C2×C4⋊C411yescharacteristic
134C8×C47#11711yescharacteristic
135C8×C47#12111yescharacteristic
136C8×C47C22⋊Q811yescharacteristic
137C47⋊C8—22no—
138#12813—471nomaximal, Sylow
139C22×C47C2×#10211yescharacteristic
140C22×C47#45911yescharacteristic
141C22×C47#47411yescharacteristic
142C22×C47#50811yescharacteristic
143C22×C47#50811yescharacteristic
144C22×C47#50911yescharacteristic
145C22×C47#50911yescharacteristic
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—161no—
155C4×C47#38011yescharacteristic
156C4×C47#41711yescharacteristic
157C4×C47#46111yescharacteristic
158C4×C47#47611yescharacteristic
159Dic47—22no—
160Dic47—22no—
161Dic47—161no—
162C2×C4×D8—471no—
163C2×C4⋊C16—471no—
164C2×#357—471no—
165C2×#357—471no—
166#1846—471no—
167#1380—471no—
168#1380D4711yescharacteristic, complemented
169C2×C47#180211yescharacteristic
170C2×C47#213811yescharacteristic
171C2×C47#214011yescharacteristic
172C2×C47#221011yescharacteristic
173C2×C47#221011yescharacteristic
174C2×C47#222811yescharacteristic
175C2×C47#222811yescharacteristic
176D47—84no—
177C22×D8—471no—
178C2×C4×D4—941no—
179C22×C16—471no—
180C22×C16C2×D4711yescharacteristic
181C4×D8—474no—
182C4×D8—942no—
183C2×#107—471no—
184C2×#107C2×D4711yescharacteristic
185C2×#107C2×D4711yescharacteristic
186C2×#106—941no—
187C2×#102—941no—
188C2×C4×C8—471no—
189#382—941no—
190C4⋊C16—942no—
191#357—942no—
192#357—942no—
193C47#1281311yescharacteristic, 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×C22⋊C4—1881no—
210C2×C42—471no—
211C2×C16—21no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—941no—
215C2×C16—941no—
216C2×C16—941no—
217#107—21no—
218#107—21no—
219#107—21no—
220#107—941no—
221#107—941no—
222#107C4×D4712yes—
223#106—1882no—
224#102—944no—
225C4×C8—472no—
226C4×C8—472no—
227#95—1881no—
228#95—1881no—
229C24—1881no—
230C2×D4—942no—
231C2×D4—942no—
232C2×D4—942no—
233C2×D4—1881no—
234C2×D4—1881no—
235C2×D4—1881no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—3762no—
241C22×C4—3762no—
242C22×C4—1884no—
243C22×C4—1881no—
244C22×C4D4×D4711yescharacteristic
245D8—474no—
246D8—942no—
247D8—942no—
248D8—942no—
249C2×C8—472no—
250C2×C8—941no—
251C2×C8—941no—
252C2×C8C2×C4×D4711yescharacteristic
253C2×C8#1062535011yescharacteristic
254C2×C8#1062535011yescharacteristic
255C2×C8D4×D4711yescharacteristic
256C2×C8D4×D4711yescharacteristic
257C2×C8Q8×D4711yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C22⋊C4—1884no—
265C42—472no—
266C42—472no—
267C16—41no—
268C16—1881no—
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—81no—
283C2×C4—81no—
284C2×C4—81no—
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—3768no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4C22⋊C4×D4711yescharacteristic
298C2×C4#1309399711yescharacteristic
299C2×C4#1309400211yescharacteristic
300C2×C4SD16×D4711yescharacteristic
301C2×C4#1309405111yescharacteristic
302C2×C4#1309405611yescharacteristic
303C8—942no—
304C8C4⋊C4×D4711yescharacteristic
305C8#1309398111yescharacteristic
306C8#1309399711yescharacteristic
307C8#1309400211yescharacteristic
308C22—3762no—
309C22—3762no—
310C22—3762no—
311C22—3762no—
312C22—3762no—
313C22—3762no—
314C22—1884no—
315C22#102×D4711yescharacteristic
316C22#1568931711yescharacteristic
317C22#1568940211yescharacteristic
318C22#1568955411yescharacteristic
319C22#1568955611yescharacteristic
320C22#1568955711yescharacteristic
321C22#1568956011yescharacteristic
322C4—82no—
323C4—161no—
324C4—942no—
325C4—942no—
326C4—7521no—
327C4#1568898211yescharacteristic
328C4#1568912311yescharacteristic
329C4#1568932711yescharacteristic
330C4#1568941211yescharacteristic
331C2—3764no—
332C2#2024338711yescharacteristic
333C2#2024509411yescharacteristic
334C2#2024510211yescharacteristic
335C2#2024544211yescharacteristic
336C2#2024544611yescharacteristic
337C2#2024554411yescharacteristic
338C2#2024554811yescharacteristic
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#12813
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. #20243551C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
12. #15689205C4semidirect
168. #1380D47semidirect
193. C47#12813semidirect

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
#202435512
#202414792
C47×#13802
#1281347