Finite Group Databasebeta

← #26220979

Subgroups — #26220979

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245860C211yesmaximal, characteristic
2#20244322C212yesmaximal
3#20244103C212yesmaximal
4#20243946C212yesmaximal
5#20243942C212yesmaximal
6#20243246C211yesmaximal, characteristic
7#20243242C211yesmaximal, characteristic
8#20243141C211yesmaximal, characteristic
9#20243140C211yesmaximal, characteristic
10C4×C8×Dic47C211yesmaximal, characteristic
11C47×#1768C211yesmaximal, characteristic
12C2×C4×Dic94C2211yescharacteristic
13C2×Dic47⋊C8C2212yes—
14C2×Dic47⋊C8C2212yes—
15C2×#13093935C2211yescharacteristic
16C2×C4×C47⋊C8C2211yescharacteristic
17C2×C8×Dic47C2212yes—
18C2×C8×Dic47C2212yes—
19#15689027C412yes—
20#15689020C412yes—
21#15689010C412yes—
22#15689006C412yes—
23C4×Dic47⋊C4C2211yescharacteristic
24C4×Dic47⋊C4C2211yescharacteristic
25C4×C4⋊Dic47C2211yescharacteristic
26#15688969C2211yescharacteristic
27C42×Dic47C2211yescharacteristic
28#15688878C2212yes—
29#15688878C2212yes—
30#15688877C2212yes—
31#15688877C2212yes—
32#15688877C2212yes—
33#15688877C2212yes—
34C2×C4⋊C8×C47C2212yes—
35C2×#97×C47C2211yescharacteristic
36C2×C4×C8×C47C2211yescharacteristic
37C47×#376C2211yescharacteristic
38C47×#336C2212yes—
39C22×Dic94C2×C411yescharacteristic
40C22×C47⋊C8C2312yes—
41C22×C47⋊C8C2312yes—
42C4×Dic94—24no—
43C2×C4⋊Dic47C2×C412yes—
44C2×C4⋊Dic47C2×C411yescharacteristic
45C2×Dic47⋊C4C2×C412yes—
46C2×Dic47⋊C4C2×C412yes—
47C2×Dic47⋊C4C2×C411yescharacteristic
48C2×Dic47⋊C4C2×C411yescharacteristic
49C2×C4×Dic47C2×C412yes—
50C2×C4×Dic47C2×C412yes—
51C2×C4×Dic47C2311yescharacteristic
52C2×C4×Dic47C2311yescharacteristic
53C2×C4×Dic47C2311yescharacteristic
54C2×C4×Dic47C2311yescharacteristic
55Dic47⋊C8—24no—
56Dic47⋊C8—24no—
57#13093935—22no—
58C4×C47⋊C8Q814yescomplemented
59C8×Dic47—24no—
60C8×Dic47—24no—
61C47⋊#95C2×C412yes—
62C47⋊#95C2×C412yes—
63C47⋊#95C2×C412yes—
64C47⋊#95C2×C412yes—
65C47⋊#95C2×C412yes—
66C22×C8×C47C2312yes—
67C22×C8×C47C2312yes—
68C2×C42×C47C2311yescharacteristic
69C2×C42×C47C2311yescharacteristic
70C2×C42×C47C2311yescharacteristic
71C4⋊C8×C47—24no—
72#97×C47—22no—
73C4×C8×C47—22no—
74#95×C47C2×C412yes—
75#95×C47C2×C412yes—
76C22×C4×C47C22×C412yes—
77C22×C4×C47C22×C411yescharacteristic
78C22×C4×C47C22×C411yescharacteristic
79C22×C4×C47C22×C412yes—
80C22×C4×C47C2411yescharacteristic
81C22×Dic47C22×C412yes—
82C22×Dic47C22×C411yescharacteristic
83C22×Dic47C22×C411yescharacteristic
84C22×Dic47C22×C411yescharacteristic
85C22×Dic47C22×C412yes—
86C22×Dic47C22×C411yescharacteristic
87C2×Dic94—22no—
88C2×Dic94—24no—
89C2×C8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47—22no—
92C2×C8×C47—22no—
93C2×C8×C47—22no—
94C2×C8×C47#4114yes—
95C42×C47—22no—
96C42×C47—22no—
97C42×C47C2×Q812yes—
98C42×C47#4112yes—
99C4⋊Dic47—22no—
100C4⋊Dic47—24no—
101Dic47⋊C4—22no—
102Dic47⋊C4—22no—
103Dic47⋊C4—24no—
104Dic47⋊C4—24no—
105C4×Dic47—22no—
106C4×Dic47—22no—
107C4×Dic47—22no—
108C4×Dic47—24no—
109C4×Dic47—24no—
110C4×Dic47#4114yes—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—22no—
113C2×C47⋊C8—22no—
114C2×C47⋊C8—22no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8C2×Q814yes—
117C23×C47C23×C411yescharacteristic
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—22no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—22no—
126C2×C4×C47—22no—
127C2×C4×C47C4×Q814yes—
128C2×C4×C47C22×Q811yescharacteristic
129C2×C4×C47C2×#4112yes—
130C2×C4×C47C2×#4111yescharacteristic
131C2×C4×C47C2×#4112yes—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—22no—
138C2×Dic47—22no—
139C2×Dic47—22no—
140C2×Dic47—22no—
141C2×Dic47—22no—
142C2×Dic47#11712yes—
143C2×Dic47#11712yes—
144C2×Dic47#13114yes—
145C2×Dic47#13114yes—
146Dic94—44no—
147C8×C47—24no—
148C8×C47—42no—
149C47⋊C8—24no—
150C47⋊C8—42no—
151#21341—471nomaximal, Sylow
152C22×C47C2×#11711yescharacteristic
153C22×C47C2×C4×Q811yescharacteristic
154C22×C47C4×#4111yescharacteristic
155C22×C47C2×#13112yes—
156C22×C47C2×#13112yes—
157C4×C47—24no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—42no—
161C4×C47#52912yes—
162C4×C47#53312yes—
163Dic47—22no—
164Dic47—24no—
165Dic47—41no—
166Dic47—41no—
167Dic47—42no—
168Dic47#43314yes—
169#2295—471no—
170#1984—472no—
171#1939—472no—
172#1916—472no—
173#1916—472no—
174#1768—471no—
175#1768D4711yescharacteristic
176#1767—471no—
177#1746—471no—
178#1746—471no—
179C42×C8—471no—
180C2×C47#229511yescharacteristic
181C2×C47C2×#43311yescharacteristic
182C2×C47#292211yescharacteristic
183C2×C47#296012yes—
184C2×C47#296612yes—
185C2×C4×Q8—471no—
186C2×C4⋊C8—472no—
187C2×C4⋊C8—472no—
188C2×C4⋊C8C2×D4712yes—
189C2×#97—471no—
190C2×#97C2×D4711yescharacteristic
191C2×C4×C8—471no—
192C2×C4×C8—472no—
193C2×C4×C8—472no—
194C2×C4×C8C2×D4711yescharacteristic
195#391—472no—
196#389—472no—
197#387—472no—
198#387—472no—
199C4×C4⋊C4—471no—
200C4×C4⋊C4—471no—
201C4×C4⋊C4—471no—
202#376—471no—
203#376C2×D4711yescharacteristic
204C43—471no—
205#336—472no—
206#336—472no—
207#336—472no—
208#336—472no—
209#336—472no—
210#336—472no—
211#336C2×D4712yes—
212C47#2134111yescharacteristic, complemented, Sylow
213C22×Q8—471no—
214C22×C8—472no—
215C22×C8—472no—
216C22×C8C22×D4712yes—
217C22×C8C22×D4712yes—
218C4×Q8—944no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—472no—
223C2×C4⋊C4—472no—
224C2×C4⋊C4—472no—
225C2×C42—471no—
226C2×C42—472no—
227C2×C42—472no—
228C2×C42—471no—
229C2×C42—471no—
230C2×C42—471no—
231C2×C42C22×D4711yescharacteristic
232C2×C42C22×D4711yescharacteristic
233C2×C42C22×D4711yescharacteristic
234C4⋊C8—24no—
235C4⋊C8—944no—
236C4⋊C8—944no—
237#97—22no—
238#97—942no—
239C4×C8—22no—
240C4×C8—474no—
241C4×C8—944no—
242C4×C8—944no—
243#95—472no—
244#95—472no—
245#95—472no—
246#95—472no—
247#95—472no—
248#95C4×D4712yes—
249#95C4×D4712yes—
250C2×Q8—942no—
251C2×Q8—944no—
252C22×C4—471no—
253C22×C4—471no—
254C22×C4—472no—
255C22×C4—472no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4C2×C4×D4712yes—
259C22×C4C2×C4×D4711yescharacteristic
260C22×C4C2×C4×D4711yescharacteristic
261C22×C4C2×C4×D4712yes—
262C22×C4C23×D4711yescharacteristic
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—474no—
269C2×C8—942no—
270C2×C8—942no—
271C2×C8—942no—
272C2×C8—942no—
273C2×C8—942no—
274C2×C8#1062535014yes—
275C4⋊C4—944no—
276C4⋊C4—944no—
277C4⋊C4—942no—
278C4⋊C4—942no—
279C4⋊C4—944no—
280C4⋊C4—942no—
281C42—22no—
282C42—22no—
283C42—474no—
284C42—944no—
285C42—944no—
286C42—942no—
287C42—942no—
288C42—942no—
289C42#1062535212yes—
290C42Q8×D4712yes—
291C23C22×C4×D4711yescharacteristic
292Q8—1884no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—472no—
303C2×C4—474no—
304C2×C4—472no—
305C2×C4—474no—
306C2×C4—942no—
307C2×C4—942no—
308C2×C4—942no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4#1309398914yes—
317C2×C4C2×Q8×D4711yescharacteristic
318C2×C4#41×D4712yes—
319C2×C4C2×#1062535211yescharacteristic
320C2×C4C2×#1062535012yes—
321C8—24no—
322C8—42no—
323C8—944no—
324C8—1882no—
325C22#117×D4711yescharacteristic
326C22C2×#1309398911yescharacteristic
327C22C4×#1062535011yescharacteristic
328C22#131×D4712yes—
329C22#131×D4712yes—
330C4—24no—
331C4—41no—
332C4—41no—
333C4—42no—
334C4—474no—
335C4—942no—
336C4—944no—
337C4—1881no—
338C4—1881no—
339C4—1882no—
340C4#1568965312yes—
341C4#1568967712yes—
342C2#2024586411yescharacteristic
343C2#433×D4711yescharacteristic
344C2#2025202911yescharacteristic
345C2#2025232112yes—
346C2#2025235912yes—
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socle, prime radicalC23×C47C23×C4
FittingC47×#1768C2
cosocleC22×C4×C47C24
hypercenter#1768D47
hypocenterC47#21341
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1768

Complements

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

NH ≅ G/Ntype
58. C4×C47⋊C8Q8semidirect
212. C47#21341semidirect

Maximal subgroups

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

subgroupindex
#202458602
#202443222
#202441032
#202439462
#202439422
#202432462
#202432422
#202431412
#202431402
C4×C8×Dic472
C47×#17682
#2134147