Finite Group Databasebeta

← #26132789

Subgroups — #26132789

Order 12032.

442 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689160C211yesmaximal, characteristic
2C2×#15688951C211yesmaximal, characteristic, complemented
3C2×#15688948C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C16C211yesmaximal, characteristic
5#20243414C211yesmaximal, characteristic
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13093982—21no—
10C22×C47⋊C16C2211yescharacteristic
11#15689160—22no—
12#15689160—22no—
13C2×#13093958C2211yescharacteristic
14C2×#13093958C2211yescharacteristic
15C2×#13093955—21no—
16#15688980—21no—
17#15688951—22no—
18#15688948—22no—
19(C2×D47)⋊C16C414yescomplemented
20#15688885—21no—
21C22×C16×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C22×C4×D47D411yescharacteristic
25C22×C47⋊C8D411yescharacteristic
26C2×C8×D47—21no—
27C2×C8×D47—21no—
28C2×C8×D47—21no—
29C2×C8×D47—21no—
30C2×C8×D47C2×C412yes—
31C2×C8×D47Q812yes—
32#13093982—24no—
33#13093982—42no—
34C2×C4⋊Dic47—21no—
35C2×C4⋊Dic47—21no—
36C2×(C2×D47)⋊C4—41no—
37C2×(C2×D47)⋊C4—41no—
38C2×C4×Dic47—41no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16C2×C412yes—
42#13093958—21no—
43#13093958—21no—
44#13093958—21no—
45#13093958D412yes—
46#13093955—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×C412yes—
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×D47C4⋊C412yes—
70C2×C4×D47Q1612yes—
71C2×C8×C47C22×C411yescharacteristic
72C2×C8×C47C2×D411yescharacteristic
73C2×C8×C47C2×D411yescharacteristic
74C2×C8×C47C2×Q811yescharacteristic
75C2×C8×C47#4111yescharacteristic
76C2×C8×C47#4111yescharacteristic
77C4⋊C4×C47—22no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81(C2×D47)⋊C4—44no—
82(C2×D47)⋊C4—82no—
83C4⋊Dic47—22no—
84C4⋊Dic47—41no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87C4×Dic47—44no—
88C2×C47⋊C8—21no—
89C2×C47⋊C8—21no—
90C2×C47⋊C8C4⋊C412yes—
91C8×D47—22no—
92C8×D47—22no—
93C8×D47—22no—
94C8×D47—22no—
95C16×C47—22no—
96C47⋊C16—22no—
97C23×C47C2×D811yescharacteristic
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47#10712yes—
105C2×C4×C47—42no—
106C2×C4×C47—81no—
107C2×C4×C47—81no—
108C2×C4×C47—81no—
109C2×C4×C47—81no—
110C2×C4×C47—81no—
111C2×C4×C47C2×C4⋊C411yescharacteristic
112C2×C4×C47#12011yescharacteristic
113C2×C4×C47#12311yescharacteristic
114C2×C4×C47C2×Q1611yescharacteristic
115C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C47#13711yescharacteristic
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—42no—
120C2×Dic47—81no—
121C2×Dic47—81no—
122C2×Dic47—81no—
123C2×Dic47—81no—
124C2×Dic47—81no—
125C2×Dic47#10712yes—
126C4×D47—22no—
127C4×D47—22no—
128C4×D47—22no—
129C4×D47—22no—
130C8×C47C4×D411yescharacteristic
131C8×C47C4×D411yescharacteristic
132C8×C47C22⋊Q811yescharacteristic
133C8×C47C22⋊Q811yescharacteristic
134C47⋊C8—22no—
135#12921—471nomaximal, Sylow
136C22×C47C2×#10711yescharacteristic
137C22×C47#44711yescharacteristic
138C22×C47#48011yescharacteristic
139C22×C47#50811yescharacteristic
140C22×C47#50811yescharacteristic
141C22×C47#50911yescharacteristic
142C22×C47#51011yescharacteristic
143C2×D47—22no—
144C2×D47—22no—
145C2×D47—22no—
146C2×D47—41no—
147C2×D47—41no—
148C2×D47—41no—
149C2×D47—41no—
150C4×C47—82no—
151C4×C47—161no—
152C4×C47#38511yescharacteristic
153C4×C47#42811yescharacteristic
154C4×C47#45111yescharacteristic
155C4×C47#48411yescharacteristic
156Dic47—22no—
157Dic47—82no—
158Dic47—161no—
159C2×#427—471no—
160C2×#367—471no—
161C2×#366—471no—
162C2×C22⋊C16—471no—
163#1808—471no—
164#1380—471no—
165#1380D4711yescharacteristic, complemented
166C2×C47#185211yescharacteristic
167C2×C47#215811yescharacteristic
168C2×C47#215911yescharacteristic
169C2×C47#218611yescharacteristic
170C2×C47#218911yescharacteristic
171C2×C47#223411yescharacteristic
172C2×C47#223711yescharacteristic
173D47—42no—
174C23×C8—471no—
175C2×#117—941no—
176C22×C16—471no—
177C22×C16C2×D4711yescharacteristic
178#427—942no—
179#427—942no—
180C2×#107—471no—
181C2×#107—471no—
182C2×#107C2×D4711yescharacteristic
183C2×#107C2×D4711yescharacteristic
184C2×#106—941no—
185#380—941no—
186#367—942no—
187#366—942no—
188C22⋊C16—474no—
189#340—941no—
190C47#1292111yescharacteristic, complemented, Sylow
191C23×C4—471no—
192C22×C8—471no—
193C22×C8—472no—
194C22×C8—472no—
195C22×C8—941no—
196C22×C8—941no—
197C22×C8—941no—
198C22×C8—941no—
199C22×C8C22×D4711yescharacteristic
200#117—944no—
201#117—1882no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C22⋊C4—1881no—
207C2×C22⋊C4—1881no—
208C2×C42—1881no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16—472no—
212C2×C16—941no—
213C2×C16—941no—
214C2×C16C4×D4712yes—
215#107—21no—
216#107—21no—
217#107—21no—
218#107—472no—
219#107—941no—
220#107—941no—
221#107—941no—
222#107D18812yes—
223#106—944no—
224#95—1881no—
225C24—471no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—471no—
229C22×C4—472no—
230C22×C4—472no—
231C22×C4—941no—
232C22×C4—941no—
233C22×C4—941no—
234C22×C4—941no—
235C22×C4—1881no—
236C22×C4—1881no—
237C22×C4D4×D4711yescharacteristic
238C2×C8—472no—
239C2×C8—941no—
240C2×C8—941no—
241C2×C8—942no—
242C2×C8—942no—
243C2×C8—942no—
244C2×C8—942no—
245C2×C8C2×C4×D4711yescharacteristic
246C2×C8C2×D18811yescharacteristic
247C2×C8#1062535011yescharacteristic
248C2×C8D4×D4711yescharacteristic
249C2×C8#1062535211yescharacteristic
250C2×C8Q8×D4711yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—942no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C22⋊C4—3762no—
260C22⋊C4—1884no—
261C42—1884no—
262C16—22no—
263C16—942no—
264C23—472no—
265C23—941no—
266C23—941no—
267C23—941no—
268C23—941no—
269C23—941no—
270C23—941no—
271C23D8×D4711yescharacteristic
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—472no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—942no—
282C2×C4—942no—
283C2×C4—942no—
284C2×C4—942no—
285C2×C4—3761no—
286C2×C4—3761no—
287C2×C4—3761no—
288C2×C4—3761no—
289C2×C4—3761no—
290C2×C4—1882no—
291C2×C4C4⋊C4×D4711yescharacteristic
292C2×C4#1309399411yescharacteristic
293C2×C4#1309400611yescharacteristic
294C2×C4Q16×D4711yescharacteristic
295C2×C4#1309405111yescharacteristic
296C2×C4#1309405311yescharacteristic
297C8—942no—
298C8(C22⋊D47)⋊C411yescharacteristic
299C8C4×D18811yescharacteristic
300C8#1309400211yescharacteristic
301C8#1309400411yescharacteristic
302C22—942no—
303C22—942no—
304C22—942no—
305C22—1881no—
306C22—1881no—
307C22—1881no—
308C22—1881no—
309C22#107×D4711yescharacteristic
310C22#1568925811yescharacteristic
311C22#1568943511yescharacteristic
312C22#1568955411yescharacteristic
313C22#1568955411yescharacteristic
314C22#1568955711yescharacteristic
315C22#1568956511yescharacteristic
316C4—82no—
317C4—161no—
318C4—942no—
319C4—3762no—
320C4—7521no—
321C4#1568899711yescharacteristic
322C4#1568916211yescharacteristic
323C4#1568928011yescharacteristic
324C4#1568945711yescharacteristic
325C2—1882no—
326C2#2024357711yescharacteristic
327C2#2024517111yescharacteristic
328C2#2024517311yescharacteristic
329C2#2024531211yescharacteristic
330C2#2024533111yescharacteristic
331C2#2024557811yescharacteristic
332C2#2024559411yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#12921
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×#15688951C2semidirect
3. C2×#15688948C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
19. (C2×D47)⋊C16C4semidirect
165. #1380D47semidirect
190. C47#12921semidirect

Maximal subgroups

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

subgroupindex
C2×#156891602
C2×#156889512
C2×#156889482
C2×(C2×D47)⋊C162
#202434142
#202414792
C47×#13802
#1292147