Finite Group Databasebeta

← #26132883

Subgroups — #26132883

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×C4×D376C211yesmaximal, characteristic
2C2×#15688950C211yesmaximal, characteristic, complemented
3C2×#15688923C211yesmaximal, characteristic
4C2×#15688923C211yesmaximal, characteristic
5#20241479C211yesmaximal, characteristic, complemented
6#20241466C211yesmaximal, characteristic, complemented
7C47×#1942C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×C4×D188—21no—
10C22×C47⋊C16C2211yescharacteristic
11C22×C47⋊C16C2211yescharacteristic
12C4×D376—22no—
13C4×D376—22no—
14C2×#13093958C2211yescharacteristic
15C2×#13093946—21no—
16#15688950—22no—
17#15688923—22no—
18#15688923C414yescomplemented
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×C4×C8×C47C2211yescharacteristic
22C47×#389—21no—
23C47×#340—21no—
24C22×D188—21no—
25C22×C4×D47—41no—
26C2×D376—21no—
27C2×D376—21no—
28C2×D376—21no—
29C2×D376C2×C412yes—
30C2×D376D412yes—
31C2×D376Q812yes—
32C4×D188—24no—
33C4×D188—42no—
34C2×C4⋊Dic47—21no—
35C2×(C2×D47)⋊C4—41no—
36C2×C47⋊C16—21no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16C2×C412yescomplemented
42#13093958—21no—
43#13093958D412yes—
44#13093946—24no—
45C22×C8×C47D411yescharacteristic
46C22×C8×C47C2311yescharacteristic
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—41no—
50C2×C42×C47D411yescharacteristic
51#107×C47—21no—
52#107×C47—21no—
53#107×C47—21no—
54#107×C47C2×C412yescomplemented
55C4×C8×C47—21no—
56C4×C8×C47—21no—
57#95×C47—41no—
58C23×D47—41no—
59C22×C4×C47—41no—
60C22×C4×C47—41no—
61C22×C4×C47D811yescharacteristic
62C22×C4×C47D811yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×Dic47—41no—
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×C47—21no—
75C2×C8×C47—21no—
76C2×C8×C47—21no—
77C2×C8×C47C22×C411yescharacteristic
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47C2×D411yescharacteristic
80C2×C8×C47C2×Q811yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C4⋊C4×C47—22no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C4⋊C4×C47—82no—
88C42×C47—21no—
89C42×C47—21no—
90(C2×D47)⋊C4—44no—
91C4⋊Dic47—22no—
92C4⋊Dic47—41no—
93D376—22no—
94D376—22no—
95D376—22no—
96D376C4⋊C414yescomplemented
97C47⋊C16—22no—
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—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—42no—
113C2×C4×C47—81no—
114C2×C4×C47—81no—
115C2×C4×C47—81no—
116C2×C4×C47—81no—
117C2×C4×C47—81no—
118C2×C4×C47SD3212yes—
119C2×C4×C47C4×D411yescharacteristic
120C2×C4×C47#12011yescharacteristic
121C2×C4×C47C22⋊Q811yescharacteristic
122C2×C4×C47#13511yescharacteristic
123C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C47#13711yescharacteristic
125C2×Dic47—42no—
126C2×Dic47—81no—
127C2×Dic47—81no—
128D188—24no—
129D188—42no—
130D188—42no—
131D188—42no—
132C4×D47—88no—
133C8×C47—41no—
134C8×C47C2×C4⋊C411yescharacteristic
135C8×C47C4×D411yescharacteristic
136C8×C47C22⋊Q811yescharacteristic
137C8×C47#12311yescharacteristic
138#12937—471nomaximal, Sylow
139C22×C47C4×D811yescharacteristic
140C22×C47#44711yescharacteristic
141C22×C47#47411yescharacteristic
142C22×C47C2×SD3211yescharacteristic
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—22no—
154C4×C47—41no—
155C4×C47—82no—
156C4×C47—161no—
157C4×C47#38511yescharacteristic
158C4×C47#44011yescharacteristic
159C4×C47#45211yescharacteristic
160C4×C47#47811yescharacteristic
161Dic47—82no—
162C2×C4×D8—471no—
163C2×#367—471no—
164C2×#357—471no—
165C2×#357—471no—
166#1942D4711yescharacteristic, complemented
167#1380—471no—
168#1374—471no—
169C2×C47#186211yescharacteristic
170C2×C47C4×SD3211yescharacteristic
171C2×C47#217711yescharacteristic
172C2×C47#218611yescharacteristic
173C2×C47#218711yescharacteristic
174C2×C47#222611yescharacteristic
175C2×C47#222811yescharacteristic
176D47—84no—
177C22×D8—471no—
178C2×C4×D4—941no—
179C22×C16—471no—
180C22×C16—471no—
181C4×D8—942no—
182C4×D8—942no—
183C2×#107—471no—
184C2×#107C2×D4711yescharacteristic
185C2×#107C2×D4711yescharacteristic
186C2×#102—941no—
187C2×C4×C8C2×D4711yescharacteristic
188#389—21no—
189#367—942no—
190#357—474no—
191#357—942no—
192#340—21no—
193C47#1293711yescharacteristic, 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×C8C22⋊D4711yescharacteristic
203C22×C8C22×D4711yescharacteristic
204C4×D4—944no—
205C4×D4—1882no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—941no—
210C2×C22⋊C4—1881no—
211C2×C42C22⋊D4711yescharacteristic
212C2×C16—472no—
213C2×C16—941no—
214C2×C16—941no—
215C2×C16—941no—
216C2×C16—941no—
217C2×C16—941no—
218#107—21no—
219#107—21no—
220#107—21no—
221#107—472no—
222#107—941no—
223#107C4×D4712yescomplemented
224#102—944no—
225C4×C8—21no—
226C4×C8—21no—
227#95—41no—
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—3762no—
238C22×C4—3762no—
239C22×C4—1884no—
240C22×C4—1881no—
241C22×C4#1062533411yescharacteristic
242C22×C4#1062533411yescharacteristic
243C22×C4C2×C22⋊D4711yescharacteristic
244D8—474no—
245D8—942no—
246D8—942no—
247D8—942no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8C2×C4×D4711yescharacteristic
252C2×C8#1062535011yescharacteristic
253C2×C8D4×D4711yescharacteristic
254C2×C8D4×D4711yescharacteristic
255C2×C8Q8×D4711yescharacteristic
256C2×C8#1062535411yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—82no—
262C4⋊C4—942no—
263C4⋊C4—1881no—
264C22⋊C4—1884no—
265C42—21no—
266C42—21no—
267C16—942no—
268C16—1881no—
269C23—3761no—
270C23—3761no—
271C23—3761no—
272C23—3761no—
273C23—1882no—
274C23—1882no—
275C23—1882no—
276C23C2×#1062533411yescharacteristic
277D4—944no—
278D4—1882no—
279D4—1882no—
280D4—1882no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—3768no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4—1882no—
296C2×C4#1309396712yes—
297C2×C4C4×C22⋊D4711yescharacteristic
298C2×C4#1309399211yescharacteristic
299C2×C4#1309400011yescharacteristic
300C2×C4#1309404411yescharacteristic
301C2×C4#1309404911yescharacteristic
302C2×C4#1309405511yescharacteristic
303C8—41no—
304C8C4⋊C4×D4711yescharacteristic
305C8#1309398611yescharacteristic
306C8#1309400211yescharacteristic
307C8#1309400911yescharacteristic
308C22—3762no—
309C22—3762no—
310C22—3762no—
311C22—3762no—
312C22—3762no—
313C22—3762no—
314C22—1884no—
315C22C4×#1062533411yescharacteristic
316C22#1568925611yescharacteristic
317C22#1568940011yescharacteristic
318C22C2×#1309396711yescharacteristic
319C22#1568955311yescharacteristic
320C22#1568955811yescharacteristic
321C22#1568955911yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—161no—
326C4—3762no—
327C4#1568899411yescharacteristic
328C4#1568922111yescharacteristic
329C4#1568928311yescharacteristic
330C4#1568942011yescharacteristic
331C2—3764no—
332C2#2024363411yescharacteristic
333C2C4×#1309396711yescharacteristic
334C2#2024526211yescharacteristic
335C2#2024530911yescharacteristic
336C2#2024531611yescharacteristic
337C2#2024553211yescharacteristic
338C2#2024554211yescharacteristic
subgroupG/H
centerC23C2×#10625334
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1942C2
socleC23×C47C2×D8
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1942D47
hypocenterC47#12937
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×#15688950C2semidirect
5. #20241479C2semidirect
6. #20241466C2semidirect
7. C47×#1942C2semidirect
18. #15688923C4semidirect
41. C2×C47⋊C16C2×C4semidirect
54. #107×C47C2×C4semidirect
96. D376C4⋊C4semidirect
166. #1942D47semidirect
193. C47#12937semidirect
223. #107C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3762
C2×#156889502
C2×#156889232
#202414792
#202414662
C47×#19422
#1293747