Finite Group Databasebeta

← #26115135

Subgroups — #26115135

Order 12032.

502 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625337C211yesmaximal, characteristic
2#20244324C211yesmaximal, characteristic
3C2×#15688875C211yesmaximal, characteristic
4C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic
5C2×#15688853C211yesmaximal, characteristic
6C2×C8×C47⋊C8C211yesmaximal, characteristic
7C47×#1984C211yesmaximal, characteristic
8C22×#10625337C411yescharacteristic
9C2×C4×Dic94C2211yescharacteristic
10C4×#10625337—22no—
11C4×#10625337—22no—
12C2×#13093957C411yescharacteristic
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×#13093948C411yescharacteristic
15C2×#13093947C411yescharacteristic
16C2×C4×C47⋊C8C2211yescharacteristic
17C2×C4×C47⋊C8C2211yescharacteristic
18#15688877—22no—
19#15688875—22no—
20Q8⋊(C47⋊C8)—22no—
21#15688853—22no—
22C8×C47⋊C8—22no—
23C2×C4×Q8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C47×#336—22no—
27C22×Dic94C2×C411yescharacteristic
28C2×#10625337—22no—
29C2×#10625337—22no—
30C2×#10625337C814yescomplemented
31C22×C47⋊C8—21no—
32C22×C47⋊C8—21no—
33C22×C47⋊C8C2×C411yescharacteristic
34C22×C47⋊C8C2×C411yescharacteristic
35C4×Dic94—21no—
36C4×Dic94—21no—
37C4×Dic94—21no—
38C4×Dic94—21no—
39C2×C4⋊Dic47C2×C411yescharacteristic
40C2×Dic47⋊C4—21no—
41C2×C4×Dic47—21no—
42#13093957—22no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45#13093948—22no—
46#13093947—22no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8D412yes—
49C4×C47⋊C8D412yes—
50C4×C47⋊C8D412yes—
51C22×Q8×C47C2×C411yescharacteristic
52C22×C8×C47—21no—
53C22×C8×C47D412yes—
54C4×Q8×C47—21no—
55C4×Q8×C47—21no—
56C4×Q8×C47—21no—
57C4×Q8×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C42×C47—21no—
61C2×C42×C47C2311yescharacteristic
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C4×C8×C47—21no—
65C4×C8×C47—21no—
66C2×Q8×C47—21no—
67C2×Q8×C47—21no—
68C2×Q8×C47—21no—
69C2×Q8×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47C2×C812yes—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C22×C411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47#4111yescharacteristic
77C22×Dic47—21no—
78C22×Dic47—21no—
79C2×Dic94—21no—
80C2×Dic94—21no—
81C2×Dic94—21no—
82C2×Dic94—21no—
83C2×Dic94—21no—
84C2×Dic94C2×C812yes—
85C2×C8×C47—22no—
86C2×C8×C47—22no—
87C2×C8×C47—41no—
88C2×C8×C47—42no—
89C2×C8×C47Q1614yescomplemented
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94C42×C47—41no—
95C42×C47—41no—
96C42×C47C2×D411yescharacteristic
97C42×C47C2×D411yescharacteristic
98C42×C47C2×D411yescharacteristic
99C42×C47#4111yescharacteristic
100#10625337—28no—
101C4⋊Dic47—21no—
102C4⋊Dic47—21no—
103Dic47⋊C4—41no—
104Dic47⋊C4—41no—
105C4×Dic47—41no—
106C4×Dic47—41no—
107C2×C47⋊C8—24no—
108C2×C47⋊C8—22no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—41no—
112C2×C47⋊C8—42no—
113C2×C47⋊C8C22⋊C412yes—
114C2×C47⋊C8C22⋊C412yes—
115C2×C47⋊C8C2×C812yes—
116C2×C47⋊C8M1612yes—
117C23×C47C4×D411yescharacteristic
118Q8×C47—22no—
119Q8×C47—22no—
120Q8×C47—41no—
121Q8×C47—41no—
122C2×C4×C47—22no—
123C2×C4×C47—22no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—42no—
128C2×C4×C47C2×C22⋊C411yescharacteristic
129C2×C4×C47C4×D411yescharacteristic
130C2×C4×C47#12111yescharacteristic
131C2×C4×C47#12111yescharacteristic
132C2×C4×C47#12411yescharacteristic
133C2×C4×C47#12711yescharacteristic
134C2×C4×C47C22×C811yescharacteristic
135C2×C4×C47C2×M1611yescharacteristic
136C2×C4×C47#13111yescharacteristic
137C2×C4×C47#13111yescharacteristic
138C2×C4×C47C2×Q1612yes—
139C2×C4×C47#13512yes—
140C2×Dic47—22no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C2×Dic47—42no—
145Dic94—22no—
146Dic94—22no—
147Dic94—41no—
148Dic94—41no—
149C8×C47—24no—
150C8×C47—81no—
151C47⋊C8—24no—
152C47⋊C8—22no—
153C47⋊C8—81no—
154C47⋊C8C22⋊C814yes—
155#9656—471nomaximal, Sylow
156C22×C47#39011yescharacteristic
157C22×C47C8×D411yescharacteristic
158C22×C47#43611yescharacteristic
159C22×C47C4×Q1612yes—
160C22×C47#44312yes—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—42no—
164C4×C47—81no—
165C4×C47C2×C22⋊C811yescharacteristic
166C4×C47#40811yescharacteristic
167C4×C47C8×D411yescharacteristic
168C4×C47#43611yescharacteristic
169C4×C47#46712yes—
170C4×C47#49411yescharacteristic
171C4×C47#49511yescharacteristic
172Dic47—42no—
173Dic47—81no—
174C2×C4×Q16—471no—
175#1984—471no—
176#1984D4711yescharacteristic
177C2×#335—471no—
178C2×Q8⋊C8—471no—
179C2×Q8⋊C8—471no—
180C2×C82—471no—
181C2×C47C8×Q1612yes—
182C2×C47#159112yes—
183C2×C47#195411yescharacteristic
184C2×C47#196911yescharacteristic
185C2×C47#197411yescharacteristic
186C22×Q16—471no—
187C2×C4×Q8—471no—
188C2×C4×Q8C2×D4711yescharacteristic
189C4×Q16—942no—
190C4×Q16—942no—
191C2×#107—471no—
192C2×C4⋊C8—471no—
193C2×C4⋊C8C2×D4711yescharacteristic
194C2×#103—471no—
195C2×#103—471no—
196C2×C4×C8—471no—
197C2×C4×C8—471no—
198C2×C4×C8C2×D4711yescharacteristic
199#336—22no—
200#336—942no—
201#335—942no—
202Q8⋊C8—942no—
203Q8⋊C8—942no—
204C82—942no—
205C47#965611yescharacteristic, complemented, Sylow
206C22×Q8—471no—
207C22×Q8C4×D4711yescharacteristic
208C2×Q16—474no—
209C2×Q16—942no—
210C2×Q16—942no—
211C22×C8—21no—
212C22×C8—471no—
213C22×C8—471no—
214C22×C8—941no—
215C22×C8—941no—
216C22×C8C22⋊D4712yes—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—941no—
222C4×Q8—941no—
223C4×Q8—941no—
224C4×Q8—941no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4—941no—
228C2×C4⋊C4C4×D4711yescharacteristic
229C2×C42—21no—
230C2×C42—941no—
231C2×C42C22×D4711yescharacteristic
232#107—942no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—941no—
236C4⋊C8—941no—
237#103—942no—
238#103—942no—
239C4×C8—21no—
240C4×C8—21no—
241C4×C8—472no—
242C4×C8—472no—
243C4×C8—472no—
244C4×C8—941no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—472no—
251C2×Q8—941no—
252C2×Q8—941no—
253C2×Q8—941no—
254C2×Q8—941no—
255C2×Q8—941no—
256C2×Q8C8×D4712yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4C2×C4×D4711yescharacteristic
262C22×C4#1062535011yescharacteristic
263C22×C4C2×C22⋊D4711yescharacteristic
264Q16—948no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—42no—
269C2×C8—472no—
270C2×C8—472no—
271C2×C8—472no—
272C2×C8—472no—
273C2×C8—944no—
274C2×C8—942no—
275C2×C8—941no—
276C2×C8—941no—
277C2×C8—1881no—
278C2×C8—1882no—
279C2×C8#1062533714yescomplemented
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4—1881no—
287C4⋊C4—1881no—
288C42—41no—
289C42—41no—
290C42—1881no—
291C42—1881no—
292C42D4×D4711yescharacteristic
293C42D4×D4711yescharacteristic
294C42D4×D4711yescharacteristic
295C42#1062535211yescharacteristic
296C23C4×C22⋊D4711yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—41no—
300Q8—41no—
301Q8—942no—
302Q8—942no—
303Q8—1881no—
304Q8—1881no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—942no—
312C2×C4—1882no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4C22⋊C4×D4711yescharacteristic
317C2×C4(C22⋊D47)⋊C411yescharacteristic
318C2×C4#1309399611yescharacteristic
319C2×C4#1309399711yescharacteristic
320C2×C4#1309401011yescharacteristic
321C2×C4#1309402011yescharacteristic
322C2×C4C2×C8×D4711yescharacteristic
323C2×C4M16×D4711yescharacteristic
324C2×C4#1309403011yescharacteristic
325C2×C4#1309403211yescharacteristic
326C2×C4C2×#1062533712yes—
327C2×C4#1309404412yes—
328C8—24no—
329C8—81no—
330C8—474no—
331C8—944no—
332C8—942no—
333C8—3761no—
334C22#1568902311yescharacteristic
335C22C8×C22⋊D4711yescharacteristic
336C22#1568919911yescharacteristic
337C22C4×#1062533712yes—
338C22#1568923812yes—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—3761no—
344C4—1882no—
345C4C22⋊C8×D4711yescharacteristic
346C4#1568908811yescharacteristic
347C4(C22⋊D47)⋊C811yescharacteristic
348C4#1568919811yescharacteristic
349C4#1568936212yes—
350C4#1568950211yescharacteristic
351C4#1568950511yescharacteristic
352C2C8×#1062533712yes—
353C2#2024228312yes—
354C2#2024418011yescharacteristic
355C2#2024424811yescharacteristic
356C2#2024427511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1984C2
socle, prime radicalC23×C47C4×D4
cosocleC2×C42×C47C23
hypercenter#1984D47
hypocenterC47#9656
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1984

Complements

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

NH ≅ G/Ntype
30. C2×#10625337C8semidirect
89. C2×C8×C47Q16semidirect
205. C47#9656semidirect
279. C2×C8#10625337semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253372
#202443242
C2×#156888752
C2×Q8⋊(C47⋊C8)2
C2×#156888532
C2×C8×C47⋊C82
C47×#19842
#965647