Finite Group Databasebeta

← #26135341

Subgroups — #26135341

Order 12032.

450 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689527C211yesmaximal, characteristic, complemented
2C2×#15688925C211yesmaximal, characteristic
3C2×#15688923C211yesmaximal, characteristic
4#20244252C211yesmaximal, characteristic
5#20241479C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13094023—21no—
10C22×C47⋊C16C2211yescharacteristic
11#15689527—22no—
12#15689527—22no—
13C2×#13093958C2211yescharacteristic
14C2×#13093957—21no—
15C2×#13093944—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15689024—21no—
18#15688925—22no—
19#15688923—22no—
20C22×C16×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C22×Dic94—41no—
24C22×D188—21no—
25C2×D376—21no—
26C2×D376—21no—
27C2×D376—21no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376Q812yescomplemented
31C22×C47⋊C8D411yescharacteristic
32#13094023—24no—
33#13094023—42no—
34C2×C4⋊Dic47—21no—
35C2×Dic47⋊C4—41no—
36C2×(C2×D47)⋊C4—41no—
37C2×(C2×D47)⋊C4—41no—
38C2×C4×Dic47D411yescharacteristic
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16—21no—
42#13093958—21no—
43#13093958D412yes—
44#13093957—24no—
45#13093944—42no—
46C8×Dic47—21no—
47C8×Dic47—21no—
48C22×C8×C47C2311yescharacteristic
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C16×C47—21no—
52C2×C16×C47—21no—
53C2×C16×C47—21no—
54#107×C47—21no—
55#107×C47—21no—
56#107×C47—21no—
57#107×C47D412yes—
58C23×D47—41no—
59C22×C4×C47—41no—
60C22×C4×C47—41no—
61C22×C4×C47C2×D411yescharacteristic
62C22×Dic47—41no—
63C22×Dic47D811yescharacteristic
64C22×Dic47D811yescharacteristic
65C2×D188—22no—
66C2×D188—41no—
67C2×D188—41no—
68C2×D188—41no—
69C2×D188—41no—
70C2×D188—41no—
71C2×Dic94—44no—
72C2×Dic94—82no—
73C2×Dic94—82no—
74C2×C8×C47C2×D411yescharacteristic
75C2×C8×C47C2×D411yescharacteristic
76C2×C8×C47C2×Q811yescharacteristic
77C2×C8×C47#4111yescharacteristic
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—
85(C2×D47)⋊C4—82no—
86C4⋊Dic47—22no—
87C4⋊Dic47—41no—
88Dic47⋊C4—44no—
89C4×Dic47—21no—
90C4×Dic47—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8—21no—
93C2×C47⋊C8SD1612yes—
94D376—22no—
95D376—22no—
96D376—41no—
97D376—41no—
98C16×C47—41no—
99C47⋊C16—41no—
100C23×C47C2×D811yescharacteristic
101C22×D47—42no—
102C22×D47—81no—
103C22×D47—81no—
104C22×D47—81no—
105C22×D47—81no—
106C22×D47—81no—
107C22×D47—81no—
108C2×C4×C47—42no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47—81no—
114C2×C4×C47#12011yescharacteristic
115C2×C4×C47C22⋊Q811yescharacteristic
116C2×C4×C47#12411yescharacteristic
117C2×C4×C47C2×SD1611yescharacteristic
118C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C47#13711yescharacteristic
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—42no—
125C2×Dic47—81no—
126C2×Dic47—81no—
127C2×Dic47D1612yes—
128C2×Dic47SD3212yes—
129D188—42no—
130D188—42no—
131D188—81no—
132D188—81no—
133Dic94—88no—
134C8×C47C22⋊Q811yescharacteristic
135C8×C47C22⋊Q811yescharacteristic
136C8×C47#12411yescharacteristic
137C8×C47#12411yescharacteristic
138C47⋊C8—22no—
139#13363—471nomaximal, Sylow
140C22×C47#44711yescharacteristic
141C22×C47#47411yescharacteristic
142C22×C47#48611yescharacteristic
143C22×C47C2×D1611yescharacteristic
144C22×C47C2×SD3211yescharacteristic
145C22×C47#50911yescharacteristic
146C22×C47#51011yescharacteristic
147C2×D47—82no—
148C2×D47—82no—
149C2×D47—82no—
150C2×D47—161no—
151C2×D47—161no—
152C2×D47—161no—
153C2×D47—161no—
154C4×C47—82no—
155C4×C47—161no—
156C4×C47#39311yescharacteristic
157C4×C47#44811yescharacteristic
158C4×C47#47611yescharacteristic
159C4×C47#48911yescharacteristic
160Dic47—22no—
161Dic47—22no—
162Dic47—82no—
163C2×#500—471no—
164C2×#357—471no—
165C2×#357—471no—
166#1970—471no—
167#1380—471no—
168#1380D4711yescharacteristic, complemented
169#1374—471no—
170C2×C47#202311yescharacteristic
171C2×C47#218411yescharacteristic
172C2×C47#218511yescharacteristic
173C2×C47#222411yescharacteristic
174C2×C47#222611yescharacteristic
175C2×C47#224011yescharacteristic
176C2×C47#224311yescharacteristic
177D47—162no—
178C22×D8—471no—
179C2×C4⋊Q8—941no—
180C22×C16—471no—
181C22×C16C2×D4711yescharacteristic
182#500—942no—
183#500—942no—
184C2×#107—471no—
185C2×#107—941no—
186C2×#107C2×D4711yescharacteristic
187C2×#107C2×D4711yescharacteristic
188C2×#102—941no—
189C2×C4×C8—471no—
190#390—941no—
191#357—942no—
192#357—942no—
193C47#1336311yescharacteristic, complemented, Sylow
194C22×Q8—1881no—
195C22×D4—941no—
196C2×D8—472no—
197C2×D8—941no—
198C2×D8—941no—
199C2×D8—941no—
200C2×D8—941no—
201C2×D8—941no—
202C22×C8—471no—
203C22×C8C22×D4711yescharacteristic
204C4⋊Q8—944no—
205C4⋊Q8—1882no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—941no—
209C2×C4⋊C4—1881no—
210C2×C22⋊C4—1881no—
211C2×C22⋊C4—1881no—
212C2×C42—471no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—941no—
217C2×C16—941no—
218C2×C16—941no—
219#107—21no—
220#107—21no—
221#107—21no—
222#107—472no—
223#107—944no—
224#107—941no—
225#107D18812yes—
226#102—1882no—
227C4×C8—941no—
228C4×C8—941no—
229C24—1881no—
230C2×Q8—3762no—
231C2×Q8—3762no—
232C2×Q8—1884no—
233C2×D4—942no—
234C2×D4—1881no—
235C2×D4—1881no—
236C2×D4—1881no—
237C2×D4—1881no—
238C2×D4—1881no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—1881no—
244C22×C4D4×D4711yescharacteristic
245D8—942no—
246D8—942no—
247D8—1881no—
248D8—1881no—
249C2×C8—472no—
250C2×C8—941no—
251C2×C8—941no—
252C2×C8C2×D18811yescharacteristic
253C2×C8#1062535011yescharacteristic
254C2×C8#1062535011yescharacteristic
255C2×C8D4×D4711yescharacteristic
256C2×C8#1062535211yescharacteristic
257C2×C8Q8×D4711yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—942no—
263C4⋊C4—1884no—
264C4⋊C4—1881no—
265C22⋊C4—3762no—
266C22⋊C4—3762no—
267C42—941no—
268C42—941no—
269C16—41no—
270C16—1881no—
271C23—3761no—
272C23—3761no—
273C23—3761no—
274C23—3761no—
275C23—3761no—
276C23—3761no—
277C23—1882no—
278C23D8×D4711yescharacteristic
279Q8—3768no—
280D4—3761no—
281D4—3761no—
282D4—1882no—
283D4—1882no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—472no—
291C2×C4—472no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—1882no—
299C2×C4#1309399411yescharacteristic
300C2×C4#1309400211yescharacteristic
301C2×C4#1309401011yescharacteristic
302C2×C4SD16×D4711yescharacteristic
303C2×C4#1309405111yescharacteristic
304C2×C4#1309405611yescharacteristic
305C8—942no—
306C8#1309400211yescharacteristic
307C8#1309400411yescharacteristic
308C8#1309401011yescharacteristic
309C8#1309401211yescharacteristic
310C22—3762no—
311C22—3762no—
312C22—3762no—
313C22—7521no—
314C22—7521no—
315C22—7521no—
316C22—7521no—
317C22#1568925811yescharacteristic
318C22#1568940211yescharacteristic
319C22#1568946811yescharacteristic
320C22D16×D4711yescharacteristic
321C22SD32×D4711yescharacteristic
322C22#1568956011yescharacteristic
323C22#1568956511yescharacteristic
324C4—82no—
325C4—161no—
326C4—942no—
327C4—942no—
328C4—3762no—
329C4#1568903611yescharacteristic
330C4#1568926311yescharacteristic
331C4#1568941211yescharacteristic
332C4#1568948411yescharacteristic
333C2—7522no—
334C2#2024452311yescharacteristic
335C2#2024530111yescharacteristic
336C2#2024530611yescharacteristic
337C2#2024552411yescharacteristic
338C2#2024553411yescharacteristic
339C2#2024561011yescharacteristic
340C2#2024562611yescharacteristic
subgroupG/H
centerC23D8×D47
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC22×D376C22
hypercenter#1380D47
hypocenterC47#13363
LCSG ▷ C22×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
1. C2×#15689527C2semidirect
5. #20241479C2semidirect
6. #20241465C2semidirect
7. C47×#1380C2semidirect
30. C2×D376Q8semidirect
168. #1380D47semidirect
193. C47#13363semidirect

Maximal subgroups

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

subgroupindex
C2×#156895272
C2×#156889252
C2×#156889232
#202442522
#202414792
#202414652
C47×#13802
#1336347