Finite Group Databasebeta

← #26115334

Subgroups — #26115334

Order 12032.

498 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251765C211yesmaximal, characteristic
2#20243539C211yesmaximal, characteristic
3C4⋊C8×Dic47C211yesmaximal, characteristic
4C2×#15688871C211yesmaximal, characteristic
5C2×#15688871C211yesmaximal, characteristic
6C2×#15688869C211yesmaximal, characteristic
7C2×C47×#332C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×Dic47⋊C8—22no—
12C2×C8×Dic47—21no—
13#15689030—21no—
14#15689030—21no—
15#15689028C414yes—
16#15688988—22no—
17C42×Dic47C2211yescharacteristic
18#15688877—21no—
19#15688871—22no—
20#15688871—22no—
21#15688869—22no—
22C2×C4⋊Q8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C47×#332—22no—
26C22×Dic94C2×C412yes—
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29#13094024—21no—
30#13094024—21no—
31#13094024—21no—
32#13094024—21no—
33C2×C4⋊Dic47—21no—
34C2×C4⋊Dic47—21no—
35C2×C4×Dic47C2×C412yes—
36C2×C4×Dic47D411yescharacteristic
37C2×C4×Dic47D411yescharacteristic
38C2×C4×Dic47D412yes—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)D412yes—
43Dic47⋊C8—44no—
44C8×Dic47—42no—
45C47⋊#95—24no—
46C47⋊#95—24no—
47C22×Q8×C47—21no—
48C22×C8×C47—21no—
49C22×C8×C47—21no—
50C4⋊Q8×C47—21no—
51C4⋊Q8×C47—21no—
52C4⋊Q8×C47—21no—
53C4⋊Q8×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47C2×C412yes—
56C2×C42×C47C2311yescharacteristic
57C4⋊C8×C47—21no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47D412yes—
61C2×Q8×C47—41no—
62C2×Q8×C47—41no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47—41no—
66C2×Q8×C47—41no—
67C22×C4×C47—22no—
68C22×C4×C47C22×C411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×Dic47—22no—
72C22×Dic47C22⋊C412yes—
73C22×Dic47C22⋊C412yes—
74C2×Dic94—22no—
75C2×Dic94—22no—
76C2×Dic94—44no—
77C2×C8×C47—22no—
78C2×C8×C47—41no—
79C2×C8×C47—41no—
80C2×C8×C47—41no—
81C2×C8×C47—42no—
82C4⋊C4×C47—22no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C42×C47C2×D411yescharacteristic
87C42×C47C2×D411yescharacteristic
88C42×C47#4111yescharacteristic
89C42×C47#4111yescharacteristic
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47—41no—
93C4⋊Dic47—41no—
94C4×Dic47—21no—
95C4×Dic47—21no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—42no—
99C4×Dic47SD1614yes—
100C4×Dic47Q1614yes—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C2×C47⋊C8—42no—
106C23×C47C2×C22⋊C411yescharacteristic
107Q8×C47—81no—
108Q8×C47—81no—
109Q8×C47—81no—
110Q8×C47—81no—
111C2×C4×C47—22no—
112C2×C4×C47—42no—
113C2×C4×C47—42no—
114C2×C4×C47—42no—
115C2×C4×C47C4×D411yescharacteristic
116C2×C4×C47C4×D411yescharacteristic
117C2×C4×C47#12111yescharacteristic
118C2×C4×C47#12111yescharacteristic
119C2×C4×C47#12411yescharacteristic
120C2×C4×C47#12711yescharacteristic
121C2×C4×C47C2×SD1612yes—
122C2×C4×C47C2×Q1612yes—
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47#13511yescharacteristic
125C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C47#13711yescharacteristic
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—42no—
132C2×Dic47—44no—
133C2×Dic47#10314yes—
134C2×Dic47#10314yes—
135Dic94—82no—
136Dic94—82no—
137C8×C47—42no—
138C8×C47—81no—
139C47⋊C8—42no—
140C47⋊C8—81no—
141#9697—471nomaximal, Sylow
142C22×C47#39011yescharacteristic
143C22×C47#41312yes—
144C22×C47C2×#10312yes—
145C22×C47#41611yescharacteristic
146C22×C47#41711yescharacteristic
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—82no—
150C4×C47#46311yescharacteristic
151C4×C47#46311yescharacteristic
152C4×C47#46411yescharacteristic
153C4×C47#46411yescharacteristic
154C4×C47#48712yes—
155C4×C47#49211yescharacteristic
156C4×C47#49411yescharacteristic
157Dic47—24no—
158Dic47—24no—
159Dic47—82no—
160#2862—471no—
161#1842—471no—
162C4×C4⋊C8—471no—
163C2×#333—471no—
164C2×#333—471no—
165C2×#332—471no—
166C2×#332D4711yescharacteristic
167C2×C47#154212yes—
168C2×C47#155012yes—
169C2×C47#195611yescharacteristic
170C2×C47#196711yescharacteristic
171C2×C47#198311yescharacteristic
172C2×C4⋊Q8—471no—
173C2×C4⋊Q8C2×D4711yescharacteristic
174C2×C4⋊C8—471no—
175C2×C4⋊C8—471no—
176C2×C4⋊C8—942no—
177C2×C4⋊C8C2×D4711yescharacteristic
178C2×C4⋊C8C2×D4711yescharacteristic
179C2×C4×C8—941no—
180#391—474no—
181#391—941no—
182#391—941no—
183#382—942no—
184C43—471no—
185#336—941no—
186#333—942no—
187#333—942no—
188#332—22no—
189#332—942no—
190C47#969711yescharacteristic, complemented, Sylow
191C22×Q8—21no—
192C22×Q8—472no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—941no—
196C22×C8—941no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—941no—
202C4⋊Q8—941no—
203C4⋊Q8—941no—
204C4⋊Q8—941no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—941no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4C4×D4712yes—
209C2×C42—472no—
210C2×C42—471no—
211C2×C42—471no—
212C2×C42—472no—
213C2×C42C22×D4711yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—472no—
218C4⋊C8—941no—
219C4⋊C8—941no—
220C4⋊C8—941no—
221C4⋊C8—1884no—
222C4⋊C8C22⋊D4712yes—
223C4×C8—1882no—
224#95—944no—
225#95—944no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—942no—
233C2×Q8—942no—
234C2×Q8—1884no—
235C22×C4—22no—
236C22×C4—472no—
237C22×C4—472no—
238C22×C4—942no—
239C22×C4C2×C4×D4711yescharacteristic
240C22×C4D4×D4711yescharacteristic
241C22×C4D4×D4711yescharacteristic
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—42no—
247C2×C8—942no—
248C2×C8—1881no—
249C2×C8—1882no—
250C2×C8—1881no—
251C2×C8—1881no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C4⋊C4—1881no—
259C4⋊C4—1881no—
260C42—474no—
261C42—474no—
262C42—941no—
263C42—941no—
264C42—941no—
265C42—941no—
266C42—1882no—
267C42#1062535011yescharacteristic
268C42D4×D4711yescharacteristic
269C42#1062535211yescharacteristic
270C42C2×C22⋊D4711yescharacteristic
271C23C22⋊C4×D4711yescharacteristic
272Q8—81no—
273Q8—81no—
274Q8—81no—
275Q8—81no—
276Q8—3762no—
277Q8—3762no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—474no—
283C2×C4—474no—
284C2×C4—942no—
285C2×C4—942no—
286C2×C4—942no—
287C2×C4—942no—
288C2×C4—1882no—
289C2×C4—1884no—
290C2×C4(C22⋊D47)⋊C411yescharacteristic
291C2×C4C4×C22⋊D4711yescharacteristic
292C2×C4#1309399611yescharacteristic
293C2×C4#1309399711yescharacteristic
294C2×C4#1309401011yescharacteristic
295C2×C4#1309402011yescharacteristic
296C2×C4SD16×D4712yes—
297C2×C4Q16×D4712yes—
298C2×C4#1309404311yescharacteristic
299C2×C4#1309404511yescharacteristic
300C2×C4#1309404811yescharacteristic
301C2×C4#1309405311yescharacteristic
302C8—42no—
303C8—81no—
304C8—3761no—
305C8—1882no—
306C22#1568902311yescharacteristic
307C22#1568910612yes—
308C22#103×D4712yes—
309C22#1568911611yescharacteristic
310C22#1568912111yescharacteristic
311C4—21no—
312C4—21no—
313C4—82no—
314C4—944no—
315C4—944no—
316C4—3762no—
317C4#1568933611yescharacteristic
318C4#1568933711yescharacteristic
319C4#1568934311yescharacteristic
320C4#1568934411yescharacteristic
321C4#1568947212yes—
322C4#1568949411yescharacteristic
323C4#1568950111yescharacteristic
324C2#2024204412yes—
325C2#2024207712yes—
326C2#2024418811yescharacteristic
327C2#2024423611yescharacteristic
328C2#2024431911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#332C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#332D47
hypocenterC47#9697
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
190. C47#9697semidirect

Maximal subgroups

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

subgroupindex
#202517652
#202435392
C4⋊C8×Dic472
C2×#156888712
C2×#156888692
C2×C47×#3322
#969747