Finite Group Databasebeta

← #26119102

Subgroups — #26119102

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×#15689528C211yesmaximal, characteristic
2C2×#15689474C211yesmaximal, characteristic
3C2×#15689474C211yesmaximal, characteristic
4#20244349C211yesmaximal, characteristic
5#20244349C211yesmaximal, characteristic
6#20244190C211yesmaximal, characteristic
7C47×#1273C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9C2×#13094024C2211yescharacteristic
10C2×#13094024C2211yescharacteristic
11#15689528—22no—
12#15689528—22no—
13#15689474—22no—
14#15689474—22no—
15#15689474—22no—
16#15689474—22no—
17C2×#13093958—22no—
18C2×#13093949—22no—
19C2×#13093949—22no—
20C2×#13093949—22no—
21#15688993C2211yescharacteristic
22#15688886—22no—
23#15688886—22no—
24C2×C4×C8×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C2×C4×C8×C47C2211yescharacteristic
27C22×Dic94—21no—
28C22×Dic94—21no—
29C22×Dic94—21no—
30#13094024—21no—
31#13094024—21no—
32#13094024—21no—
33#13094024—21no—
34#13094024—21no—
35#13094024—21no—
36#13094024—21no—
37#13094024—21no—
38#13094024—21no—
39#13094024D412yes—
40#13094024D412yes—
41#13094024D412yes—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47—21no—
50C2×C4⋊Dic47—21no—
51#13093958—28no—
52#13093949—28no—
53#13093949—28no—
54#13093949—44no—
55C22×C8×C47D412yes—
56C22×C8×C47D412yes—
57C22×C8×C47D412yes—
58C2×C42×C47C2311yescharacteristic
59C4×C8×C47—21no—
60C4×C8×C47—21no—
61C4×C8×C47—21no—
62C4×C8×C47—21no—
63C4×C8×C47—21no—
64C4×C8×C47—21no—
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×Dic47—41no—
69C22×Dic47—41no—
70C22×Dic47—41no—
71C22×Dic47—41no—
72C2×Dic94—22no—
73C2×Dic94—22no—
74C2×Dic94—22no—
75C2×Dic94—42no—
76C2×Dic94—42no—
77C2×Dic94—42no—
78C2×Dic94—42no—
79C2×Dic94—42no—
80C2×Dic94—42no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84C2×C8×C47—22no—
85C2×C8×C47—22no—
86C2×C8×C47—22no—
87C2×C8×C47—22no—
88C2×C8×C47—22no—
89C2×C8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47—22no—
92C2×C8×C47Q1614yes—
93C42×C47C2×D411yescharacteristic
94C42×C47C2×D411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47#4111yescharacteristic
97C4⋊Dic47—22no—
98C4⋊Dic47—22no—
99C4⋊Dic47—22no—
100C4⋊Dic47—22no—
101C4⋊Dic47—22no—
102C4⋊Dic47—22no—
103C4⋊Dic47—41no—
104C4⋊Dic47—41no—
105C4⋊Dic47—41no—
106C4⋊Dic47—41no—
107C4⋊Dic47—41no—
108C4⋊Dic47—41no—
109C4⋊Dic47—42no—
110C4⋊Dic47—42no—
111C4⋊Dic47—42no—
112C23×C47#12711yescharacteristic
113C2×C4×C47#12011yescharacteristic
114C2×C4×C47#12011yescharacteristic
115C2×C4×C47#12011yescharacteristic
116C2×C4×C47#12111yescharacteristic
117C2×C4×C47#12111yescharacteristic
118C2×C4×C47#12111yescharacteristic
119C2×C4×C47C2×Q1612yes—
120C2×C4×C47#13512yes—
121C2×C4×C47#13512yes—
122C2×C4×C47AGL(1,ℤ/8)12yes—
123C2×C4×C47#13712yes—
124C2×C4×C47#13712yes—
125C2×Dic47—42no—
126C2×Dic47—42no—
127C2×Dic47—42no—
128C2×Dic47—81no—
129C2×Dic47—81no—
130C2×Dic47—81no—
131C2×Dic47—81no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135C2×Dic47—81no—
136C2×Dic47—81no—
137Dic94—44no—
138Dic94—44no—
139Dic94—44no—
140Dic94—82no—
141Dic94—82no—
142Dic94—82no—
143C8×C47—24no—
144C8×C47—42no—
145C8×C47—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#44912yes—
155C4×C47#45112yes—
156C4×C47#45212yes—
157C4×C47#46212yes—
158C4×C47#46312yes—
159C4×C47#46412yes—
160Dic47—82no—
161Dic47—82no—
162Dic47—82no—
163Dic47—161no—
164C2×#500—471no—
165C2×#487—471no—
166C2×#487—471no—
167#1990—471no—
168#1990—471no—
169#1956—471no—
170#1273D4711yescharacteristic
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⋊Q8—471no—
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×C8C2×D4711yescharacteristic
192C2×C4×C8C2×D4711yescharacteristic
193C2×C4×C8C2×D4711yescharacteristic
194#384—471no—
195#340—942no—
196#340—942no—
197C47#1031311yescharacteristic, complemented, Sylow
198C22×Q8—941no—
199C22×Q8—941no—
200C22×Q8—941no—
201C22×C8D18812yes—
202C22×C8D18812yes—
203C22×C8D18812yes—
204C4⋊Q8—472no—
205C4⋊Q8—472no—
206C4⋊Q8—472no—
207C4⋊Q8—941no—
208C4⋊Q8—941no—
209C4⋊Q8—941no—
210C4⋊Q8—941no—
211C4⋊Q8—941no—
212C4⋊Q8—941no—
213C4⋊Q8—941no—
214C4⋊Q8—941no—
215C4⋊Q8—941no—
216C2×C4⋊C4—941no—
217C2×C4⋊C4—941no—
218C2×C4⋊C4—941no—
219C2×C4⋊C4—941no—
220C2×C4⋊C4—941no—
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—21no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—21no—
236C2×Q8—942no—
237C2×Q8—942no—
238C2×Q8—942no—
239C2×Q8—1882no—
240C2×Q8—1882no—
241C2×Q8—1882no—
242C2×Q8—1882no—
243C2×Q8—1882no—
244C2×Q8—1882no—
245C2×Q8—1881no—
246C2×Q8—1881no—
247C2×Q8—1881no—
248C22×C4—1881no—
249C22×C4—1881no—
250C22×C4—1881no—
251C22×C4—1881no—
252C22×C4C2×D18811yescharacteristic
253C22×C4C2×D18811yescharacteristic
254C22×C4C2×D18811yescharacteristic
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8Dic18814yes—
264C4⋊C4—942no—
265C4⋊C4—942no—
266C4⋊C4—942no—
267C4⋊C4—942no—
268C4⋊C4—942no—
269C4⋊C4—942no—
270C4⋊C4—1882no—
271C4⋊C4—1882no—
272C4⋊C4—1882no—
273C4⋊C4—1881no—
274C4⋊C4—1881no—
275C4⋊C4—1881no—
276C4⋊C4—1881no—
277C4⋊C4—1881no—
278C4⋊C4—1881no—
279C42D4×D4711yescharacteristic
280C42D4×D4711yescharacteristic
281C42D4×D4711yescharacteristic
282C42#1062535411yescharacteristic
283C23#1309402111yescharacteristic
284Q8—3762no—
285Q8—3762no—
286Q8—3762no—
287Q8—1884no—
288Q8—1884no—
289Q8—1884no—
290C2×C4—3761no—
291C2×C4—3761no—
292C2×C4—3761no—
293C2×C4—3761no—
294C2×C4—3761no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4—3761no—
298C2×C4—3761no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4#1309399411yescharacteristic
303C2×C4#1309399411yescharacteristic
304C2×C4#1309399411yescharacteristic
305C2×C4#1309399911yescharacteristic
306C2×C4#1309399911yescharacteristic
307C2×C4#1309399911yescharacteristic
308C2×C4C2×Dic18812yes—
309C2×C4#1309404612yes—
310C2×C4#1309404612yes—
311C2×C4#1309405212yes—
312C2×C4#1309405712yes—
313C2×C4#1309405712yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22#1568903311yescharacteristic
318C22#1568950311yescharacteristic
319C22#1568950711yescharacteristic
320C22#1568950711yescharacteristic
321C22#1568951211yescharacteristic
322C22#1568951711yescharacteristic
323C22#1568951711yescharacteristic
324C4—3762no—
325C4—3762no—
326C4—3762no—
327C4—7521no—
328C4#1568927012yes—
329C4#1568928112yes—
330C4#1568928712yes—
331C4#1568933412yes—
332C4#1568933912yes—
333C4#1568934612yes—
334C2#2024299811yescharacteristic
335C2#2024303411yescharacteristic
336C2#2024304111yescharacteristic
337C2#2024306511yescharacteristic
338C2#2024446811yescharacteristic
339C2#2024448511yescharacteristic
340C2#2024449011yescharacteristic
subgroupG/H
centerC23#13094021
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1273C2
socle, prime radicalC23×C47#127
hypercenter#1273D47
hypocenterC47#10313
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1273

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×#156895282
C2×#156894742
#202443492
#202441902
C47×#12732
#1031347