Finite Group Databasebeta

← #26119100

Subgroups — #26119100

Order 12032.

554 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×#15689526C211yesmaximal, characteristic
2C2×#15689474C211yesmaximal, characteristic
3C2×#15689473C211yesmaximal, characteristic
4#20244348C211yesmaximal, characteristic
5#20244189C211yesmaximal, characteristic
6C47⋊#1273C211yesmaximal, characteristic
7C47×#1990C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×#13094024C2211yescharacteristic
10#15689526—22no—
11#15689526—22no—
12#15689474—22no—
13#15689474—22no—
14#15689473—22no—
15#15689473—22no—
16C2×#13093957—22no—
17C2×#13093949—22no—
18C2×#13093948—22no—
19C2×#13093947—22no—
20C2×C4×C47⋊C8C2211yescharacteristic
21C2×C4×C47⋊C8C2211yescharacteristic
22#15688885—22no—
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×C4×C8×C47C2211yescharacteristic
25C47×#384C2211yescharacteristic
26C47×#340—22no—
27C22×Dic94—21no—
28C22×Dic94—21no—
29C22×C47⋊C8D412yes—
30C22×C47⋊C8D412yes—
31#13094024—21no—
32#13094024—21no—
33#13094024—21no—
34#13094024—21no—
35#13094024—21no—
36#13094024—21no—
37#13094024D412yes—
38#13094024D412yes—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47—21no—
43#13093957—28no—
44#13093949—28no—
45#13093948—28no—
46#13093947—44no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C4×C47⋊C8—21no—
51C22×Q8×C47—21no—
52C22×C8×C47D412yes—
53C4⋊Q8×C47—21no—
54C4⋊Q8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47D412yes—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C42×C47C2311yescharacteristic
63C4×C8×C47—21no—
64C4×C8×C47—21no—
65C2×Q8×C47—22no—
66C2×Q8×C47—41no—
67C2×Q8×C47—42no—
68C2×Q8×C47—42no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—41no—
75C22×Dic47—41no—
76C2×Dic94—22no—
77C2×Dic94—22no—
78C2×Dic94—42no—
79C2×Dic94—42no—
80C2×Dic94—42no—
81C2×Dic94—42no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84C2×C8×C47—22no—
85C2×C8×C47—22no—
86C2×C8×C47—22no—
87C4⋊C4×C47—22no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—42no—
92C4⋊C4×C47—42no—
93C4⋊C4×C47—42no—
94C42×C47C2×D411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47C2×D411yescharacteristic
97C42×C47#4111yescharacteristic
98C4⋊Dic47—22no—
99C4⋊Dic47—22no—
100C4⋊Dic47—22no—
101C4⋊Dic47—22no—
102C4⋊Dic47—41no—
103C4⋊Dic47—41no—
104C4⋊Dic47—41no—
105C4⋊Dic47—41no—
106C2×C47⋊C8—22no—
107C2×C47⋊C8—22no—
108C2×C47⋊C8—22no—
109C2×C47⋊C8—22no—
110C2×C47⋊C8—22no—
111C2×C47⋊C8Q1614yes—
112C23×C47#12711yescharacteristic
113Q8×C47—44no—
114Q8×C47—82no—
115C2×C4×C47—42no—
116C2×C4×C47—81no—
117C2×C4×C47—81no—
118C2×C4×C47—81no—
119C2×C4×C47—81no—
120C2×C4×C47—81no—
121C2×C4×C47#12011yescharacteristic
122C2×C4×C47#12011yescharacteristic
123C2×C4×C47#12011yescharacteristic
124C2×C4×C47#12111yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47#12111yescharacteristic
127C2×C4×C47C2×Q1612yes—
128C2×C4×C47#13512yes—
129C2×C4×C47#13512yes—
130C2×C4×C47AGL(1,ℤ/8)12yes—
131C2×C4×C47#13712yes—
132C2×C4×C47#13712yes—
133C2×Dic47—42no—
134C2×Dic47—42no—
135C2×Dic47—81no—
136C2×Dic47—81no—
137C2×Dic47—81no—
138C2×Dic47—81no—
139Dic94—44no—
140Dic94—44no—
141Dic94—82no—
142Dic94—82no—
143C8×C47—42no—
144C47⋊C8—24no—
145C47⋊C8—42no—
146#10313—471nomaximal, Sylow
147C22×C47#39211yescharacteristic
148C22×C47#49411yescharacteristic
149C22×C47#49511yescharacteristic
150C22×C47#49511yescharacteristic
151C22×C47#49611yescharacteristic
152C22×C47#49711yescharacteristic
153C22×C47#49711yescharacteristic
154C4×C47—82no—
155C4×C47—161no—
156C4×C47#44912yes—
157C4×C47#45112yes—
158C4×C47#45212yes—
159C4×C47#46212yes—
160C4×C47#46312yes—
161C4×C47#46412yes—
162Dic47—82no—
163Dic47—82no—
164C2×#500—471no—
165C2×#487—471no—
166C2×#487—471no—
167#1990—471no—
168#1990D4711yescharacteristic
169#1956—471no—
170#1273—471no—
171C2×C47#171011yescharacteristic
172C2×C47#171811yescharacteristic
173C2×C47#171911yescharacteristic
174C2×C47#172311yescharacteristic
175C2×C47#201211yescharacteristic
176C2×C47#201511yescharacteristic
177C2×C47#201611yescharacteristic
178C2×C4⋊Q8—471no—
179C2×C4⋊Q8—471no—
180C2×C4⋊Q8C2×D4711yescharacteristic
181#500—942no—
182#500—942no—
183#487—942no—
184#487—942no—
185#487—942no—
186#487—942no—
187C2×#107—942no—
188C2×#103—942no—
189C2×#103—942no—
190C2×#103—942no—
191C2×C4×C8—471no—
192C2×C4×C8—471no—
193C2×C4×C8C2×D4711yescharacteristic
194#384C2×D4711yescharacteristic
195#340—22no—
196#340—942no—
197C47#1031311yescharacteristic, complemented, Sylow
198C22×Q8—21no—
199C22×Q8—941no—
200C22×Q8—941no—
201C22×C8—472no—
202C22×C8—472no—
203C22×C8C22⋊D4712yes—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—472no—
208C4⋊Q8—472no—
209C4⋊Q8—941no—
210C4⋊Q8—941no—
211C4⋊Q8—941no—
212C4⋊Q8—941no—
213C4⋊Q8—941no—
214C4⋊Q8—941no—
215C4⋊Q8D18812yes—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—941no—
222C2×C4⋊C4—941no—
223C2×C4⋊C4—941no—
224C2×C4⋊C4—941no—
225C2×C42C22×D4711yescharacteristic
226#107—948no—
227#103—948no—
228#103—948no—
229#103—1884no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—941no—
233C4×C8—941no—
234C4×C8—941no—
235C4×C8—941no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—942no—
241C2×Q8—942no—
242C2×Q8—1882no—
243C2×Q8—1882no—
244C2×Q8—1882no—
245C2×Q8—1882no—
246C2×Q8—1881no—
247C2×Q8—1881no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—1881no—
251C22×C4—1881no—
252C22×C4D4×D4711yescharacteristic
253C22×C4D4×D4711yescharacteristic
254C22×C4C2×C22⋊D4711yescharacteristic
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—474no—
259C2×C8—942no—
260C2×C8—942no—
261C2×C8—942no—
262C2×C8—942no—
263C2×C8—942no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—942no—
272C4⋊C4—942no—
273C4⋊C4—942no—
274C4⋊C4—942no—
275C4⋊C4—1881no—
276C4⋊C4—1881no—
277C4⋊C4—1881no—
278C4⋊C4—1881no—
279C42C2×D18811yescharacteristic
280C42#1062535011yescharacteristic
281C42D4×D4711yescharacteristic
282C42D4×D4711yescharacteristic
283C23#1309402011yescharacteristic
284Q8—44no—
285Q8—82no—
286Q8—3762no—
287Q8—3762no—
288Q8—1884no—
289Q8—1884no—
290C2×C4—42no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4#1309399211yescharacteristic
303C2×C4#1309399411yescharacteristic
304C2×C4#1309399411yescharacteristic
305C2×C4#1309399711yescharacteristic
306C2×C4#1309399711yescharacteristic
307C2×C4#1309399811yescharacteristic
308C2×C4Q16×D4712yes—
309C2×C4#1309404412yes—
310C2×C4#1309404512yes—
311C2×C4#1309404812yes—
312C2×C4#1309405312yes—
313C2×C4#1309405512yes—
314C8—42no—
315C8—944no—
316C8—1882no—
317C22#1568903211yescharacteristic
318C22#1568950111yescharacteristic
319C22#1568950411yescharacteristic
320C22#1568950511yescharacteristic
321C22#1568951111yescharacteristic
322C22#1568951411yescharacteristic
323C22#1568951511yescharacteristic
324C4—82no—
325C4—161no—
326C4—3762no—
327C4—3762no—
328C4#1568926912yes—
329C4#1568928012yes—
330C4#1568928312yes—
331C4#1568933212yes—
332C4#1568933712yes—
333C4#1568934512yes—
334C2#2024299611yescharacteristic
335C2#2024303211yescharacteristic
336C2#2024303811yescharacteristic
337C2#2024306411yescharacteristic
338C2#2024446711yescharacteristic
339C2#2024448111yescharacteristic
340C2#2024448911yescharacteristic
subgroupG/H
centerC23#13094020
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1990C2
socle, prime radicalC23×C47#127
hypercenter#1990D47
hypocenterC47#10313
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
197. C47#10313semidirect

Maximal subgroups

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

subgroupindex
C2×#156895262
C2×#156894742
C2×#156894732
#202443482
#202441892
C47⋊#12732
C47×#19902
#1031347