Finite Group Databasebeta

← #26119704

Subgroups — #26119704

Order 12032.

488 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248377C211yesmaximal, characteristic
2#20244149C211yesmaximal, characteristic
3#20243390C211yesmaximal, characteristic
4C2×#15688869C211yesmaximal, characteristic
5C2×#15688855C211yesmaximal, characteristic
6#20241228C211yesmaximal, characteristic
7C47×#1990C211yesmaximal, characteristic
8C2×#13094022—21no—
9C2×C4×Dic94C2211yescharacteristic
10C2×#13093955—21no—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093947—21no—
14#15689054—22no—
15#15689030—21no—
16#15689019—21no—
17#15689019—21no—
18C4×C4⋊Dic47C2211yescharacteristic
19#15688885—21no—
20#15688885—21no—
21#15688869—22no—
22#15688855—22no—
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×C4×C8×C47C2211yescharacteristic
25C47×#384C2211yescharacteristic
26C47×#340—22no—
27C22×Dic94D411yescharacteristic
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30#13094022—42no—
31#13094022—42no—
32C4×Dic94—21no—
33C4×Dic94—21no—
34C4×Dic94—21no—
35C4×Dic94—21no—
36C2×C4⋊Dic47D411yescharacteristic
37C2×C4⋊Dic47D411yescharacteristic
38C2×C4⋊Dic47D411yescharacteristic
39C2×Dic47⋊C4—22no—
40C2×Dic47⋊C4—22no—
41C2×Dic47⋊C4—21no—
42C2×C4×Dic47—21no—
43C2×C4×Dic47—21no—
44#13093955—42no—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)D412yes—
49#13093947—42no—
50C47⋊#95—22no—
51C47⋊#95—22no—
52C47⋊#95—21no—
53C22×Q8×C47—21no—
54C22×C8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47D412yes—
64C2×C42×C47C2311yescharacteristic
65C4×C8×C47—21no—
66C4×C8×C47—21no—
67C2×Q8×C47—41no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C2×Q8×C47—41no—
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C22×C4×C47—22no—
74C22×C4×C47—41no—
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C22×Dic47—21no—
79C22×Dic47—21no—
80C22×Dic47—21no—
81C22×Dic47—21no—
82C2×Dic94—21no—
83C2×Dic94—21no—
84C2×Dic94—21no—
85C2×Dic94—21no—
86C2×Dic94—21no—
87C2×Dic94SD1612yes—
88C2×C8×C47—22no—
89C2×C8×C47—41no—
90C2×C8×C47—41no—
91C4⋊C4×C47—22no—
92C4⋊C4×C47—22no—
93C4⋊C4×C47—42no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C42×C47C2×D411yescharacteristic
101C42×C47#4111yescharacteristic
102C42×C47#4111yescharacteristic
103C42×C47#4111yescharacteristic
104C4⋊Dic47—21no—
105C4⋊Dic47—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47SD1612yes—
109C4⋊Dic47Q1612yes—
110Dic47⋊C4—44no—
111Dic47⋊C4—44no—
112Dic47⋊C4—41no—
113Dic47⋊C4—41no—
114C4×Dic47—41no—
115C4×Dic47—41no—
116C4×Dic47—41no—
117C4×Dic47—41no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8—41no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C23×C47#12011yescharacteristic
125Q8×C47—81no—
126Q8×C47—81no—
127Q8×C47—81no—
128Q8×C47—81no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47—42no—
134C2×C4×C47—81no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47#12111yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47#12111yescharacteristic
140C2×C4×C47#12311yescharacteristic
141C2×C4×C47#12311yescharacteristic
142C2×C4×C47#12411yescharacteristic
143C2×C4×C47C2×SD1611yescharacteristic
144C2×C4×C47C2×SD1611yescharacteristic
145C2×C4×C47C2×Q1611yescharacteristic
146C2×C4×C47#13511yescharacteristic
147C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C47#13711yescharacteristic
150C2×C4×C47#13711yescharacteristic
151C2×Dic47—22no—
152C2×Dic47—22no—
153C2×Dic47—22no—
154C2×Dic47—41no—
155C2×Dic47—41no—
156C2×Dic47—41no—
157C2×Dic47—41no—
158C2×Dic47—41no—
159C2×Dic47—41no—
160C2×Dic47—41no—
161C2×Dic47—41no—
162C2×Dic47—41no—
163Dic94—22no—
164Dic94—22no—
165Dic94—41no—
166Dic94—41no—
167C8×C47—42no—
168C47⋊C8—42no—
169C47⋊C8—81no—
170#10418—471nomaximal, Sylow
171C22×C47#39411yescharacteristic
172C22×C47#44811yescharacteristic
173C22×C47#44911yescharacteristic
174C22×C47#45011yescharacteristic
175C22×C47#45111yescharacteristic
176C22×C47#45411yescharacteristic
177C22×C47#45611yescharacteristic
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—82no—
181C4×C47—161no—
182C4×C47#46111yescharacteristic
183C4×C47#46211yescharacteristic
184C4×C47#46511yescharacteristic
185C4×C47#46911yescharacteristic
186C4×C47#48111yescharacteristic
187C4×C47#48211yescharacteristic
188C4×C47#48711yescharacteristic
189C4×C47#49111yescharacteristic
190Dic47—42no—
191Dic47—42no—
192Dic47—42no—
193Dic47—81no—
194#2546—471no—
195#1990D4711yescharacteristic
196#1948—471no—
197#1803—471no—
198C2×#332—471no—
199C2×Q8⋊C8—471no—
200#1279—471no—
201C2×C47#162611yescharacteristic
202C2×C47#163711yescharacteristic
203C2×C47#164811yescharacteristic
204C2×C47#165111yescharacteristic
205C2×C47#203411yescharacteristic
206C2×C47#203811yescharacteristic
207C2×C47#204311yescharacteristic
208C2×C4⋊Q8—941no—
209C2×C4⋊Q8C2×D4711yescharacteristic
210C2×C4×Q8—471no—
211C2×#106—941no—
212C2×C4⋊C8—471no—
213C2×C4⋊C8—471no—
214C2×#103—941no—
215C2×C4×C8C2×D4711yescharacteristic
216#398—942no—
217#391—941no—
218#389—941no—
219#389—941no—
220#384C2×D4711yescharacteristic
221C4×C4⋊C4—471no—
222#340—22no—
223#340—941no—
224#340—941no—
225#332—942no—
226Q8⋊C8—942no—
227C47#1041811yescharacteristic, complemented, Sylow
228C22×Q8—21no—
229C22×Q8—471no—
230C22×C8—21no—
231C22×C8—941no—
232C22×C8—941no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—1882no—
238C4⋊Q8—1882no—
239C4×Q8—941no—
240C4×Q8—941no—
241C4×Q8—941no—
242C4×Q8—941no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—471no—
248C2×C4⋊C4—471no—
249C2×C4⋊C4—471no—
250C2×C4⋊C4—942no—
251C2×C4⋊C4—942no—
252C2×C4⋊C4—941no—
253C2×C4⋊C4C22⋊D4712yes—
254C2×C42—941no—
255C2×C42—941no—
256C2×C42C22×D4711yescharacteristic
257#106—1882no—
258C4⋊C8—472no—
259C4⋊C8—941no—
260C4⋊C8—941no—
261C4⋊C8—941no—
262#103—1882no—
263C4×C8—21no—
264C4×C8—21no—
265#95—942no—
266#95—942no—
267#95—941no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—472no—
275C2×Q8—941no—
276C2×Q8—941no—
277C2×Q8—941no—
278C2×Q8—941no—
279C2×Q8—941no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4D4×D4711yescharacteristic
287C22×C4D4×D4711yescharacteristic
288C22×C4C2×C22⋊D4711yescharacteristic
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—942no—
293C2×C8—1881no—
294C2×C8—1881no—
295C2×C8—1881no—
296C2×C8—1881no—
297C2×C8—1881no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—472no—
308C4⋊C4—472no—
309C4⋊C4—941no—
310C4⋊C4—941no—
311C4⋊C4—941no—
312C4⋊C4—941no—
313C4⋊C4—1884no—
314C4⋊C4—1884no—
315C4⋊C4—1881no—
316C4⋊C4—1881no—
317C42—1881no—
318C42—1881no—
319C42—1881no—
320C42—1881no—
321C42#1062535011yescharacteristic
322C42#1062535011yescharacteristic
323C42D4×D4711yescharacteristic
324C42#1062535211yescharacteristic
325C23#1309399211yescharacteristic
326Q8—81no—
327Q8—81no—
328Q8—81no—
329Q8—81no—
330Q8—942no—
331Q8—942no—
332Q8—1881no—
333Q8—1881no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—942no—
343C2×C4—942no—
344C2×C4—942no—
345C2×C4—1881no—
346C2×C4—1881no—
347C2×C4—1881no—
348C2×C4—1881no—
349C2×C4—1881no—
350C2×C4—1881no—
351C2×C4—1881no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4#1309399611yescharacteristic
355C2×C4#1309399711yescharacteristic
356C2×C4#1309399711yescharacteristic
357C2×C4#1309400611yescharacteristic
358C2×C4#1309400711yescharacteristic
359C2×C4#1309401011yescharacteristic
360C2×C4SD16×D4711yescharacteristic
361C2×C4SD16×D4711yescharacteristic
362C2×C4Q16×D4711yescharacteristic
363C2×C4#1309404311yescharacteristic
364C2×C4#1309404811yescharacteristic
365C2×C4#1309405111yescharacteristic
366C2×C4#1309405311yescharacteristic
367C2×C4#1309405611yescharacteristic
368C8—42no—
369C8—3761no—
370C8—1882no—
371C22#1568903811yescharacteristic
372C22#1568926011yescharacteristic
373C22#1568926511yescharacteristic
374C22#1568927211yescharacteristic
375C22#1568927711yescharacteristic
376C22#1568929511yescharacteristic
377C22#1568930511yescharacteristic
378C4—21no—
379C4—21no—
380C4—82no—
381C4—161no—
382C4—3761no—
383C4—1882no—
384C4—1882no—
385C4—1882no—
386C4#1568932711yescharacteristic
387C4#1568933211yescharacteristic
388C4#1568935111yescharacteristic
389C4#1568937511yescharacteristic
390C4#1568944011yescharacteristic
391C4#1568944511yescharacteristic
392C4#1568947211yescharacteristic
393C4#1568949011yescharacteristic
394C2#2024248111yescharacteristic
395C2#2024255011yescharacteristic
396C2#2024262711yescharacteristic
397C2#2024264811yescharacteristic
398C2#2024457511yescharacteristic
399C2#2024460511yescharacteristic
400C2#2024463211yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1990C2
socle, prime radicalC23×C47#120
hypercenter#1990D47
hypocenterC47#10418
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
227. C47#10418semidirect

Maximal subgroups

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

subgroupindex
#202483772
#202441492
#202433902
C2×#156888692
C2×#156888552
#202412282
C47×#19902
#1041847