Finite Group Databasebeta

← #26112185

Subgroups — #26112185

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253185C211yesmaximal, characteristic
2#20241951C211yesmaximal, characteristic, complemented
3#20241886C211yesmaximal, characteristic, complemented
4#20241779C211yesmaximal, characteristic
5#20241291C211yesmaximal, characteristic, complemented
6#20241246C211yesmaximal, characteristic, complemented
7C47×#2349C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689423—22no—
10#15689413C412yescomplemented
11#15689403C412yescomplemented
12#15689176C2211yescharacteristic
13#15689176C2211yescharacteristic
14#15689163—21no—
15#15689147C2211yescharacteristic
16#15689128—21no—
17#15688859—22no—
18#15688859—21no—
19#15688859—21no—
20D4⋊(C47⋊C8)—22no—
21C2×C4×D4×C47—21no—
22C2×C4×D4×C47C2211yescharacteristic
23C47×#389—21no—
24C47×#385—22no—
25C47×#382C2211yescharacteristic
26C47×#380—21no—
27C4×C4⋊C4×C47C2211yescharacteristic
28C2×#95×C47—21no—
29C2×#10625329—21no—
30#13094024C2×C411yescharacteristic, complemented
31#13094024C2×C411yescharacteristic, complemented
32#13094016—21no—
33#13094003—21no—
34#13094003—21no—
35C4×Dic94—21no—
36C4×Dic94—21no—
37#13093983—21no—
38#13093957—22no—
39#13093955—22no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)C2×C412yescomplemented
44#13093945—22no—
45#13093945—22no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C22×D4×C47D411yescharacteristic
51C23×C4×C47—21no—
52C23×C4×C47—22no—
53C4×D4×C47—21no—
54C4×D4×C47—21no—
55C4×D4×C47—42no—
56C4×D4×C47—42no—
57C4×D4×C47C2×C412yes—
58C4×D4×C47D412yes—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47D411yescharacteristic
63C2×C22⋊C4×C47—21no—
64C2×C22⋊C4×C47—22no—
65C2×C42×C47—21no—
66C2×C42×C47C2311yescharacteristic
67#95×C47—22no—
68#95×C47—21no—
69#95×C47D411yescharacteristic
70#95×C47D411yescharacteristic
71#95×C47D412yes—
72C24×C47—21no—
73C2×D4×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47—21no—
76C2×D4×C47C22⋊C412yes—
77C2×D4×C47SD1612yes—
78C2×D4×C47Q1612yes—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—22no—
82C22×C4×C47—22no—
83C22×C4×C47—21no—
84C22×C4×C47—22no—
85C22×C4×C47—44no—
86C22×C4×C47—44no—
87C22×C4×C47—82no—
88C22×C4×C47—82no—
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C2×Dic94—21no—
93C2×Dic94—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—42no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—82no—
99C4⋊C4×C47C22⋊C412yes—
100C22⋊C4×C47—22no—
101C22⋊C4×C47—22no—
102C22⋊C4×C47—44no—
103C42×C47—41no—
104C42×C47—41no—
105C42×C47C22×C411yescharacteristic
106C42×C47C2×D411yescharacteristic
107C42×C47#4111yescharacteristic
108C42×C47#4111yescharacteristic
109C22⋊Dic47—41no—
110C4⋊Dic47—21no—
111C4⋊Dic47—21no—
112C4⋊Dic47—21no—
113C4⋊Dic47—21no—
114Dic47⋊C4—41no—
115Dic47⋊C4—41no—
116C4×Dic47—41no—
117#10625329—41no—
118#10625329—41no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122C23×C47—22no—
123C23×C47—22no—
124C23×C47—22no—
125C23×C47—42no—
126C23×C47—42no—
127C23×C47#12011yescharacteristic
128D4×C47—22no—
129D4×C47—22no—
130D4×C47—22no—
131D4×C47#10314yes—
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—42no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47—41no—
144C2×C4×C47—42no—
145C2×C4×C47—82no—
146C2×C4×C47—82no—
147C2×C4×C47—88no—
148C2×C4×C47C2×C22⋊C411yescharacteristic
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47C4×D411yescharacteristic
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47#12111yescharacteristic
153C2×C4×C47#12311yescharacteristic
154C2×C4×C47C2×SD1611yescharacteristic
155C2×C4×C47C2×Q1611yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C47#13711yescharacteristic
158C2×Dic47—41no—
159C2×Dic47—41no—
160Dic94—81no—
161Dic94—81no—
162C47⋊C8—42no—
163C47⋊C8—81no—
164C47⋊C8—81no—
165#9175—471nomaximal, Sylow
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—24no—
169C22×C47—44no—
170C22×C47—44no—
171C22×C47—42no—
172C22×C47—42no—
173C22×C47#38611yescharacteristic
174C22×C47#45011yescharacteristic
175C22×C47#45111yescharacteristic
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—42no—
181C4×C47—42no—
182C4×C47—81no—
183C4×C47—82no—
184C4×C47C2×#10311yescharacteristic
185C4×C47#41711yescharacteristic
186C4×C47#48311yescharacteristic
187C4×C47#48411yescharacteristic
188Dic47—81no—
189Dic47—81no—
190#3077—471no—
191#2349D4711yescharacteristic
192#1518—471no—
193#1503—471no—
194#1478—471no—
195#1303—471no—
196#1286—471no—
197C2×C47—21no—
198C2×C47—21no—
199C2×C47—44no—
200C2×C47#187211yescharacteristic
201C2×C47#190411yescharacteristic
202C2×C47#190611yescharacteristic
203#533—471no—
204C2×C4×D4—21no—
205C2×C4×D4C2×D4711yescharacteristic
206#478—942no—
207#476—472no—
208#474—472no—
209#431—471no—
210#431—471no—
211#428—941no—
212#423—471no—
213#418—941no—
214#389—21no—
215#385—22no—
216#382C2×D4711yescharacteristic
217#380—21no—
218C4×C4⋊C4C2×D4711yescharacteristic
219C2×#95—21no—
220#328—941no—
221#328—941no—
222#328—942no—
223D4⋊C8—942no—
224C47#917511yescharacteristic, complemented, Sylow
225C22×D4C22⋊D4711yescharacteristic
226C23×C4—21no—
227C23×C4—22no—
228C2×M16—941no—
229C4⋊Q8—471no—
230C4⋊Q8—471no—
231#125—941no—
232C22⋊Q8—941no—
233C22⋊Q8—941no—
234C4×Q8—941no—
235C4×Q8—941no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—42no—
239C4×D4—42no—
240C4×D4C4×D4712yes—
241C4×D4D18812yes—
242#117—941no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4C22⋊D4711yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—22no—
249C2×C42—21no—
250C2×C42C22×D4711yescharacteristic
251#107—942no—
252#106—942no—
253C4⋊C8—472no—
254C4⋊C8—941no—
255C4⋊C8—941no—
256C4⋊C8—941no—
257#102—942no—
258#102—942no—
259C22⋊C8—941no—
260C22⋊C8—941no—
261C4×C8—941no—
262C4×C8—941no—
263#95—22no—
264#95—21no—
265#95C22⋊D4711yescharacteristic
266#95C22⋊D4711yescharacteristic
267#95C22⋊D4712yes—
268C24—21no—
269C2×Q8—941no—
270C2×Q8—941no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4(C2×D47)⋊C412yes—
275C2×D4#1062533512yes—
276C2×D4#1062533712yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4C2×C22⋊D4711yescharacteristic
288C22×C4C2×C22⋊D4711yescharacteristic
289C22×C4C2×C22⋊D4711yescharacteristic
290M16—1881no—
291M16—1881no—
292C2×C8—942no—
293C2×C8—1881no—
294C2×C8—1881no—
295C4⋊C4—21no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—82no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4—941no—
303C4⋊C4—941no—
304C4⋊C4—1881no—
305C4⋊C4—1881no—
306C4⋊C4(C2×D47)⋊C412yes—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—44no—
310C22⋊C4—1881no—
311C42—41no—
312C42—41no—
313C42—1881no—
314C42C2×C4×D4711yescharacteristic
315C42C2×D18811yescharacteristic
316C42#1062535011yescharacteristic
317C42#1062535011yescharacteristic
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23#1309399311yescharacteristic
324Q8—3761no—
325Q8—3761no—
326D4—22no—
327D4—22no—
328D4—22no—
329D4#1309394714yes—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—88no—
346C2×C4—1881no—
347C2×C4—1881no—
348C2×C4C2×(C2×D47)⋊C411yescharacteristic
349C2×C4C4×C22⋊D4711yescharacteristic
350C2×C4C4×C22⋊D4711yescharacteristic
351C2×C4#1309399811yescharacteristic
352C2×C4#1309399811yescharacteristic
353C2×C4#1309400711yescharacteristic
354C2×C4C2×#1062533511yescharacteristic
355C2×C4C2×#1062533711yescharacteristic
356C2×C4#1309405011yescharacteristic
357C2×C4#1309405511yescharacteristic
358C8—3761no—
359C8—3761no—
360C8—1882no—
361C22—21no—
362C22—21no—
363C22—24no—
364C22—44no—
365C22—44no—
366C22—42no—
367C22—42no—
368C22#1568900211yescharacteristic
369C22#1568927411yescharacteristic
370C22#1568927911yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—82no—
378C4—81no—
379C4—3761no—
380C4—3761no—
381C4C2×#1309394711yescharacteristic
382C4#1568912211yescharacteristic
383C4#1568945311yescharacteristic
384C4#1568945811yescharacteristic
385C2—21no—
386C2—21no—
387C2—44no—
388C2#2024369511yescharacteristic
389C2#2024387511yescharacteristic
390C2#2024388911yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2349C2
socleC22×C47#386
prime radicalC22×D4×C47D4
cosocleC2×C42×C47C23
hypercenter#2349D47
hypocenterC47#9175
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #20241951C2semidirect
3. #20241886C2semidirect
5. #20241291C2semidirect
6. #20241246C2semidirect
10. #15689413C4semidirect
11. #15689403C4semidirect
30. #13094024C2×C4semidirect
31. #13094024C2×C4semidirect
43. C4⋊(C47⋊C8)C2×C4semidirect
224. C47#9175semidirect

Maximal subgroups

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

subgroupindex
#202531852
#202419512
#202418862
#202417792
#202412912
#202412462
C47×#23492
#917547