Finite Group Databasebeta

← #26132780

Subgroups — #26132780

Order 12032.

486 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×#107×D47C211yesmaximal, characteristic
2C2×#15688950C211yesmaximal, characteristic, complemented
3C2×(C2×D47)⋊C16C211yesmaximal, characteristic
4#20243414C211yesmaximal, characteristic
5#20241480C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C2×C47×#367C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×C4⋊C4×D47—21no—
10C22×C47⋊C16C2211yescharacteristic
11C2×#13093958C2211yescharacteristic
12C2×#13093958C2211yescharacteristic
13C2×#13093957—21no—
14#107×D47—22no—
15#107×D47—22no—
16#15688980—21no—
17#15688950—22no—
18(C2×D47)⋊C16C414yescomplemented
19#15688885—21no—
20C22×C16×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C47×#367—22no—
24C22×C4×D47—41no—
25C22×C4×D47D411yescharacteristic
26C22×C47⋊C8D411yescharacteristic
27C2×C8×D47—21no—
28C2×C8×D47—21no—
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47C2×C412yes—
32C2×C8×D47Q812yes—
33C2×C4⋊Dic47—21no—
34C2×C4⋊Dic47—21no—
35C2×Dic47⋊C4—41no—
36C4⋊C4×D47—24no—
37C4⋊C4×D47—42no—
38C2×(C2×D47)⋊C4—41no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16C2×C412yescomplemented
42#13093958—21no—
43#13093958—21no—
44#13093958—21no—
45#13093958D412yes—
46#13093957—24no—
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×C47C2×C412yescomplemented
54#107×C47—21no—
55#107×C47—21no—
56#107×C47—21no—
57#107×C47D412yes—
58C23×D47D811yescharacteristic
59C22×C4×C47—41no—
60C22×C4×C47—41no—
61C22×C4×C47C2×D411yescharacteristic
62C22×Dic47—41no—
63C22×Dic47—41no—
64C22×Dic47D811yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—44no—
70C2×C4×D47—82no—
71C2×C4×D47—82no—
72C2×C4×D47C4⋊C412yes—
73C2×C4×D47Q1612yes—
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—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84(C2×D47)⋊C4—82no—
85C4⋊Dic47—22no—
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89Dic47⋊C4—44no—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8C4⋊C412yes—
93C8×D47—22no—
94C8×D47—22no—
95C8×D47—22no—
96C8×D47—22no—
97C16×C47—22no—
98C47⋊C16—22no—
99C23×C47C2×D811yescharacteristic
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47#10712yes—
105C22×D47SD3212yes—
106C22×D47SD3212yes—
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×C4⋊C411yescharacteristic
114C2×C4×C47#12011yescharacteristic
115C2×C4×C47#12311yescharacteristic
116C2×C4×C47C2×Q1611yescharacteristic
117C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—42no—
122C2×Dic47—81no—
123C2×Dic47—81no—
124C2×Dic47—81no—
125C2×Dic47—81no—
126C2×Dic47—81no—
127C2×Dic47#10712yes—
128C4×D47—22no—
129C4×D47—22no—
130C4×D47—22no—
131C4×D47—22no—
132C4×D47—88no—
133C8×C47C4×D411yescharacteristic
134C8×C47C4×D411yescharacteristic
135C8×C47C22⋊Q811yescharacteristic
136C8×C47C22⋊Q811yescharacteristic
137C47⋊C8—22no—
138#12920—471nomaximal, Sylow
139C22×C47C2×#10711yescharacteristic
140C22×C47#44711yescharacteristic
141C22×C47#48011yescharacteristic
142C22×C47C2×SD3211yescharacteristic
143C22×C47C2×SD3211yescharacteristic
144C22×C47#50911yescharacteristic
145C22×C47#51011yescharacteristic
146C2×D47—22no—
147C2×D47—22no—
148C2×D47—22no—
149C2×D47—22no—
150C2×D47—22no—
151C2×D47—22no—
152C2×D47#36714yescomplemented
153C4×C47—82no—
154C4×C47—161no—
155C4×C47#38511yescharacteristic
156C4×C47#42811yescharacteristic
157C4×C47#45111yescharacteristic
158C4×C47#48411yescharacteristic
159Dic47—22no—
160Dic47—82no—
161Dic47—161no—
162C22×#107—471no—
163C2×#367—471no—
164C2×#367D4711yescharacteristic, complemented
165C2×C22⋊C16—471no—
166#1808—471no—
167#1380—471no—
168#1380—471no—
169C2×C47#185211yescharacteristic
170C2×C47C2×#36711yescharacteristic
171C2×C47#215911yescharacteristic
172C2×C47#218511yescharacteristic
173C2×C47#218711yescharacteristic
174C2×C47#223311yescharacteristic
175C2×C47#223511yescharacteristic
176D47—24no—
177C23×C8—471no—
178C22×C4⋊C4—941no—
179C22×C16—471no—
180C22×C16C2×D4711yescharacteristic
181C2×#107—471no—
182C2×#107—471no—
183C2×#107—942no—
184C2×#107—941no—
185C2×#107—942no—
186C2×#107C2×D4711yescharacteristic
187C2×#107C2×D4711yescharacteristic
188#380—941no—
189#367—22no—
190#367—942no—
191C22⋊C16—474no—
192#340—941no—
193C47#1292011yescharacteristic, complemented, Sylow
194C23×C4—471no—
195C23×C4—1881no—
196C22×C8—471no—
197C22×C8—472no—
198C22×C8—472no—
199C22×C8—941no—
200C22×C8—941no—
201C22×C8—941no—
202C22×C8—941no—
203C22×C8C22×D4711yescharacteristic
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—944no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—1882no—
210C2×C4⋊C4—1881no—
211C2×C22⋊C4—1881no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—472no—
215C2×C16—941no—
216C2×C16—941no—
217C2×C16C4×D4712yescomplemented
218#107—21no—
219#107—21no—
220#107—21no—
221#107—472no—
222#107—944no—
223#107—941no—
224#107—941no—
225#107—941no—
226#107C22⋊D4712yes—
227#95—1881no—
228C24—471no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—471no—
232C22×C4—472no—
233C22×C4—472no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—3762no—
239C22×C4—3762no—
240C22×C4—1884no—
241C22×C4—1881no—
242C22×C4—1881no—
243C22×C4D4×D4711yescharacteristic
244C2×C8—472no—
245C2×C8—941no—
246C2×C8—941no—
247C2×C8—942no—
248C2×C8—942no—
249C2×C8—942no—
250C2×C8—942no—
251C2×C8C2×C4×D4711yescharacteristic
252C2×C8#1062535011yescharacteristic
253C2×C8D4×D4711yescharacteristic
254C2×C8Q8×D4711yescharacteristic
255C2×C8#1062535411yescharacteristic
256C2×C8C2×C22⋊D4711yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—942no—
262C4⋊C4—1884no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C4⋊C4—1881no—
266C22⋊C4—3762no—
267C16—22no—
268C16—942no—
269C23—472no—
270C23—472no—
271C23—472no—
272C23—941no—
273C23—941no—
274C23—941no—
275C23—941no—
276C23D8×D4711yescharacteristic
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—472no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—942no—
287C2×C4—942no—
288C2×C4—942no—
289C2×C4—942no—
290C2×C4—3768no—
291C2×C4—3761no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—1882no—
297C2×C4C4⋊C4×D4711yescharacteristic
298C2×C4#1309399211yescharacteristic
299C2×C4#1309400911yescharacteristic
300C2×C4Q16×D4711yescharacteristic
301C2×C4#1309404811yescharacteristic
302C2×C4#1309405611yescharacteristic
303C8—942no—
304C8C4×C22⋊D4711yescharacteristic
305C8#1309398611yescharacteristic
306C8#1309400011yescharacteristic
307C8#1309400211yescharacteristic
308C22—474no—
309C22—942no—
310C22—942no—
311C22—942no—
312C22—942no—
313C22—942no—
314C22—942no—
315C22#107×D4711yescharacteristic
316C22#1568925511yescharacteristic
317C22#1568943811yescharacteristic
318C22SD32×D4711yescharacteristic
319C22SD32×D4711yescharacteristic
320C22#1568956011yescharacteristic
321C22#1568956211yescharacteristic
322C4—82no—
323C4—161no—
324C4—942no—
325C4—3762no—
326C4—7521no—
327C4#1568899411yescharacteristic
328C4#1568916411yescharacteristic
329C4#1568927711yescharacteristic
330C4#1568946011yescharacteristic
331C2—944no—
332C2#2024357411yescharacteristic
333C2#367×D4711yescharacteristic
334C2#2024517511yescharacteristic
335C2#2024530311yescharacteristic
336C2#2024531511yescharacteristic
337C2#2024557511yescharacteristic
338C2#2024558711yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#367C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenterC2×#367D47
hypocenterC47#12920
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
2. C2×#15688950C2semidirect
5. #20241480C2semidirect
6. #20241479C2semidirect
7. C2×C47×#367C2semidirect
18. (C2×D47)⋊C16C4semidirect
41. C2×C47⋊C16C2×C4semidirect
53. C2×C16×C47C2×C4semidirect
152. C2×D47#367semidirect
164. C2×#367D47semidirect
193. C47#12920semidirect
217. C2×C16C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
C2×#156889502
C2×(C2×D47)⋊C162
#202434142
#202414802
#202414792
C2×C47×#3672
#1292047