Finite Group Databasebeta

← #26109329

Subgroups — #26109329

Order 12032.

542 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×C8×D188C211yesmaximal, characteristic
2#20243385C212yesmaximal
3C2×#15688876C211yesmaximal, characteristic, complemented
4#20241271C212yesmaximal, complemented
5C47×#1845C211yesmaximal, characteristic, complemented
6C22×C8×D47—21no—
7C2×C4×D188C2211yescharacteristic
8C8×D188—22no—
9C8×D188C414yescomplemented
10C2×C4⋊(C47⋊C8)C2212yes—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×#13093944—22no—
13C2×(C2×D47)⋊C8—21no—
14#15688885—22no—
15#15688876—22no—
16C2×#107×C47—21no—
17C2×#107×C47—21no—
18C2×C4×C8×C47C2211yescharacteristic
19C47×#384C2212yes—
20C22×D188D411yescharacteristic
21C22×C4×D47—21no—
22C22×C47⋊C8—21no—
23C22×C47⋊C8—22no—
24C2×C8×D47—24no—
25C2×C8×D47—42no—
26C2×C8×D47—42no—
27C4×D188—21no—
28C4×D188—21no—
29C4×D188C2×C412yes—
30C4×D188Q812yes—
31C2×C4⋊Dic47D411yescharacteristic
32C2×(C2×D47)⋊C4—21no—
33C4⋊(C47⋊C8)—21no—
34C4⋊(C47⋊C8)—22no—
35C4⋊(C47⋊C8)—22no—
36C4⋊(C47⋊C8)C2×C412yes—
37#13093944—44no—
38(C2×D47)⋊C8—24no—
39C22×C8×C47D411yescharacteristic
40C22×C8×C47D411yescharacteristic
41C2×C4⋊C4×C47—22no—
42C2×C4⋊C4×C47—22no—
43C2×C4⋊C4×C47—22no—
44C2×C42×C47C2311yescharacteristic
45#107×C47—42no—
46#107×C47—42no—
47C4×C8×C47C2×C412yes—
48C4×C8×C47D412yes—
49C23×D47—21no—
50C22×C4×C47—42no—
51C22×C4×C47C2×D411yescharacteristic
52C22×C4×C47C2×D411yescharacteristic
53C22×C4×C47#4111yescharacteristic
54C22×Dic47—21no—
55C2×D188—21no—
56C2×D188—21no—
57C2×D188—21no—
58C2×D188C4⋊C412yes—
59C2×D188D812yes—
60C2×D188Q1612yes—
61C2×C4×D47—22no—
62C2×C4×D47—22no—
63C2×C4×D47—41no—
64C2×C4×D47—41no—
65C2×C4×D47—41no—
66C2×C4×D47—41no—
67C2×C8×C47—21no—
68C2×C8×C47—21no—
69C2×C8×C47C22⋊C412yes—
70C2×C8×C47C22⋊C412yes—
71C2×C8×C47D812yes—
72C2×C8×C47SD1612yes—
73C4⋊C4×C47—42no—
74C4⋊C4×C47—42no—
75C4⋊C4×C47—42no—
76C4⋊C4×C47—42no—
77C4⋊C4×C47—82no—
78C42×C47C22×C411yescharacteristic
79C42×C47C2×D411yescharacteristic
80C42×C47C2×Q811yescharacteristic
81C42×C47#4111yescharacteristic
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—22no—
84C4⋊Dic47—21no—
85C4⋊Dic47C4⋊C412yes—
86C2×C47⋊C8—22no—
87C2×C47⋊C8—41no—
88C2×C47⋊C8—41no—
89C2×C47⋊C8—42no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—42no—
92C8×D47—48no—
93C23×C47#12111yescharacteristic
94C22×D47—22no—
95C22×D47—22no—
96C22×D47—22no—
97C22×D47—41no—
98C22×D47—41no—
99C22×D47—41no—
100C22×D47—41no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—82no—
104C2×C4×C47—82no—
105C2×C4×C47—82no—
106C2×C4×C47C2×C22⋊C411yescharacteristic
107C2×C4×C47C2×C4⋊C411yescharacteristic
108C2×C4×C47#11711yescharacteristic
109C2×C4×C47#12111yescharacteristic
110C2×C4×C47C22⋊Q811yescharacteristic
111C2×C4×C47C22⋊Q811yescharacteristic
112C2×C4×C47C2×D811yescharacteristic
113C2×C4×C47C2×D811yescharacteristic
114C2×C4×C47C2×SD1611yescharacteristic
115C2×C4×C47C2×Q1611yescharacteristic
116C2×C4×C47#13511yescharacteristic
117C2×C4×C47#13511yescharacteristic
118C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C47#13711yescharacteristic
120C2×Dic47—22no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123D188—22no—
124D188—22no—
125D188—22no—
126D188#10714yescomplemented
127C4×D47—42no—
128C4×D47—42no—
129C4×D47—42no—
130C4×D47—42no—
131C8×C47—22no—
132C8×C47#10214yescomplemented
133C47⋊C8—42no—
134C47⋊C8—82no—
135#8644—471nomaximal, Sylow
136C22×C47#38011yescharacteristic
137C22×C47#45911yescharacteristic
138C22×C47#46111yescharacteristic
139C22×C47#46611yescharacteristic
140C22×C47#46711yescharacteristic
141C22×C47#47211yescharacteristic
142C22×C47#47311yescharacteristic
143C2×D47—24no—
144C2×D47—42no—
145C2×D47—42no—
146C2×D47—42no—
147C2×D47—42no—
148C2×D47—42no—
149C2×D47—42no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—162no—
153C4×C47C2×#10211yescharacteristic
154C4×C47#41711yescharacteristic
155C4×C47C2×#10711yescharacteristic
156C4×C47#42711yescharacteristic
157C4×C47#46611yescharacteristic
158C4×C47#46711yescharacteristic
159C4×C47#47411yescharacteristic
160C4×C47#47611yescharacteristic
161Dic47—42no—
162C2×C8×D4—471no—
163#1845D4711yescharacteristic, complemented
164#1802—472no—
165C2×#335—471no—
166#1296—472no—
167C2×C47#166711yescharacteristic
168C2×C47#166911yescharacteristic
169C2×C47#167311yescharacteristic
170C2×C47#167511yescharacteristic
171C2×C47#180211yescharacteristic
172C2×C47#180811yescharacteristic
173C2×C47#181611yescharacteristic
174D47—44no—
175C23×C8—941no—
176C2×C4×D4—471no—
177C8×D4—474no—
178C8×D4—942no—
179C2×#107—21no—
180C2×#107—21no—
181C2×C4⋊C8—471no—
182C2×C4⋊C8—472no—
183C2×#102—942no—
184C2×C22⋊C8—941no—
185C2×C4×C8C2×D4711yescharacteristic
186#384C2×D4712yes—
187#340—942no—
188#335—942no—
189C47#864411yescharacteristic, complemented, Sylow
190C22×D4—471no—
191C23×C4—941no—
192C22×C8—941no—
193C22×C8—944no—
194C22×C8—942no—
195C22×C8—1882no—
196C22×C8—1882no—
197C22×C8C22⋊D4711yescharacteristic
198C22×C8C22⋊D4711yescharacteristic
199C4×D4—472no—
200C4×D4—472no—
201C4×D4—941no—
202C4×D4—941no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—471no—
207C2×C22⋊C4—941no—
208C2×C42C22×D4711yescharacteristic
209#107—42no—
210#107—42no—
211C4⋊C8—472no—
212C4⋊C8—941no—
213C4⋊C8—942no—
214C4⋊C8—942no—
215#102—1884no—
216C22⋊C8—944no—
217C4×C8C4×D4712yes—
218C4×C8D18812yes—
219C24—941no—
220C2×D4—472no—
221C2×D4—472no—
222C2×D4—472no—
223C2×D4—941no—
224C2×D4—941no—
225C2×D4—941no—
226C22×C4—42no—
227C22×C4—941no—
228C22×C4—942no—
229C22×C4—942no—
230C22×C4—1881no—
231C22×C4—1881no—
232C22×C4—1881no—
233C22×C4—1881no—
234C22×C4D4×D4711yescharacteristic
235C22×C4#1062535211yescharacteristic
236C22×C4C2×C22⋊D4711yescharacteristic
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—942no—
240C2×C8—1882no—
241C2×C8—1882no—
242C2×C8—1882no—
243C2×C8—1881no—
244C2×C8—1881no—
245C2×C8—1888no—
246C2×C8(C2×D47)⋊C412yes—
247C2×C8(C2×D47)⋊C412yes—
248C2×C8#1062533412yes—
249C2×C8#1062533612yes—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—82no—
255C4⋊C4—472no—
256C4⋊C4—941no—
257C22⋊C4—942no—
258C22⋊C4—942no—
259C42C2×C4×D4711yescharacteristic
260C42C2×D18811yescharacteristic
261C42Q8×D4711yescharacteristic
262C42#1062535411yescharacteristic
263C23—942no—
264C23—942no—
265C23—942no—
266C23—1881no—
267C23—1881no—
268C23—1881no—
269C23—1881no—
270C23#1309399511yescharacteristic
271D4—474no—
272D4—942no—
273D4—942no—
274D4—942no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4—942no—
281C2×C4—1881no—
282C2×C4—1881no—
283C2×C4—1882no—
284C2×C4—1882no—
285C2×C4—1882no—
286C2×C4—1882no—
287C2×C4C2×(C2×D47)⋊C411yescharacteristic
288C2×C4C4⋊C4×D4711yescharacteristic
289C2×C4#1309398211yescharacteristic
290C2×C4#1309399911yescharacteristic
291C2×C4#1309400011yescharacteristic
292C2×C4#1309400411yescharacteristic
293C2×C4D8×D4711yescharacteristic
294C2×C4C2×#1062533411yescharacteristic
295C2×C4C2×#1062533611yescharacteristic
296C2×C4Q16×D4711yescharacteristic
297C2×C4#1309404311yescharacteristic
298C2×C4#1309404711yescharacteristic
299C2×C4#1309405011yescharacteristic
300C2×C4#1309405511yescharacteristic
301C8—22no—
302C8—3762no—
303C8—1882no—
304C8#1309394414yescomplemented
305C22—944no—
306C22—1882no—
307C22—1882no—
308C22—1882no—
309C22—1882no—
310C22—1882no—
311C22—1882no—
312C22#1568898011yescharacteristic
313C22#1568931511yescharacteristic
314C22#1568932511yescharacteristic
315C22#1568935611yescharacteristic
316C22#1568936111yescharacteristic
317C22#1568939011yescharacteristic
318C22#1568939511yescharacteristic
319C4—21no—
320C4—21no—
321C4—162no—
322C4—1882no—
323C4C2×#1309394411yescharacteristic
324C4#1568912211yescharacteristic
325C4#107×D4711yescharacteristic
326C4#1568916011yescharacteristic
327C4#1568936011yescharacteristic
328C4#1568936511yescharacteristic
329C4#1568940011yescharacteristic
330C4#1568941011yescharacteristic
331C2—1884no—
332C2#2024274011yescharacteristic
333C2#2024275011yescharacteristic
334C2#2024277411yescharacteristic
335C2#2024278411yescharacteristic
336C2#2024338511yescharacteristic
337C2#2024341411yescharacteristic
338C2#2024345311yescharacteristic
subgroupG/H
centerC23#13093995
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1845C2
socleC23×C47#121
prime radicalC22×D188D4
cosocleC2×C42×C47C23
hypercenter#1845D47
hypocenterC47#8644
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1845

Complements

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

NH ≅ G/Ntype
3. C2×#15688876C2semidirect
4. #20241271C2semidirect
5. C47×#1845C2semidirect
9. C8×D188C4semidirect
126. D188#107semidirect
132. C8×C47#102semidirect
163. #1845D47semidirect
189. C47#8644semidirect
304. C8#13093944semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D1882
#202433852
C2×#156888762
#202412712
C47×#18452
#864447