Finite Group Databasebeta

← #26185683

Subgroups — #26185683

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10625354C212yesmaximal, complemented
2C4×#13094047C211yesmaximal, characteristic
3#20242213C211yesmaximal, characteristic, complemented
4#20242211C211yesmaximal, characteristic, complemented
5#20242207C211yesmaximal, characteristic, complemented
6#20242203C212yesmaximal, complemented
7#20242198C212yesmaximal, complemented
8#20242133C211yesmaximal, characteristic, complemented
9#20241769C212yesmaximal, complemented
10#322×D47C211yesmaximal, characteristic, complemented
11C47×#1579C211yesmaximal, characteristic, complemented
12C2×#13094047C411yescharacteristic
13C4×#10625354C2212yes—
14Q8×C47⋊C8C2212yes—
15Q16×Dic47C411yescharacteristic
16C4×#10625336C2212yes—
17#15689208C412yes—
18C4×D376C2211yescharacteristic
19#15689205C411yescharacteristic
20C8×D188—22no—
21C8×D188C2212yes—
22#15689188—22no—
23#15689188C2212yes—
24#15689175—22no—
25#15689175C2212yes—
26#15689160C411yescharacteristic
27#15689118C412yes—
28C4×C8×D47—22no—
29C4×C8×D47C2211yescharacteristic
30C4×C8×D47C2211yescharacteristic
31C4×C8×D47C2211yescharacteristic
32#15688875C2212yes—
33#15688874C2211yescharacteristic
34Q8⋊(C47⋊C8)C2212yes—
35#15688852C2212yes—
36#15688850C2212yes—
37#15688845C2211yescharacteristic
38#15688845C2211yescharacteristic
39#15688844C2211yescharacteristic
40C8×Q8×C47C2212yes—
41C4×Q16×C47C2211yescharacteristic
42C47×#334C2211yescharacteristic
43C47×Q8⋊C8C2212yes—
44C47×#322C2211yescharacteristic
45C2×#10625354C2×C412yes—
46#13094047C818yescomplemented
47C2×#10625336C2×C412yes—
48C2×D376C2×C411yescharacteristic
49C2×C8×D47—21no—
50C2×C8×D47—22no—
51C2×C8×D47—22no—
52C2×C8×D47C2×C411yescharacteristic
53C2×C8×D47C2×C411yescharacteristic
54C2×C8×D47D412yes—
55Q8×Dic47C2×C412yes—
56C4×D188—22no—
57C4×D188C2312yes—
58#13093986—22no—
59#13093986C2×C412yes—
60#13093982—22no—
61#13093982C2×C412yes—
62C42×D47—22no—
63C42×D47C2311yescharacteristic
64#13093958C2×C411yescharacteristic
65#13093955C2×C412yes—
66C4⋊(C47⋊C8)—22no—
67C4⋊(C47⋊C8)C2312yes—
68#13093948C2×C412yes—
69#13093946C2×C412yes—
70#13093944C2×C412yes—
71(C2×D47)⋊C8—22no—
72(C2×D47)⋊C8—22no—
73(C2×D47)⋊C8—22no—
74C4×C47⋊C8—22no—
75C4×C47⋊C8C2311yescharacteristic
76C4×C47⋊C8C2311yescharacteristic
77C4×C47⋊C8C2311yescharacteristic
78C8×Dic47—22no—
79C8×Dic47—21no—
80C8×Dic47C2×C411yescharacteristic
81C8×Dic47C2×C411yescharacteristic
82C8×Dic47D412yes—
83C2×Q16×C47C2×C411yescharacteristic
84C4×Q8×C47C2312yes—
85#107×C47C2×C411yescharacteristic
86C4⋊C8×C47—22no—
87C4⋊C8×C47C2312yes—
88#103×C47C2×C412yes—
89C4×C8×C47—22no—
90C4×C8×C47C2311yescharacteristic
91C4×C8×C47C2311yescharacteristic
92C4×C8×C47C2311yescharacteristic
93C2×Q8×C47C22×C412yes—
94#10625354—24no—
95#10625354C2×C818yescomplemented
96C2×D188—22no—
97C2×D188C22×C412yes—
98C2×C4×D47—22no—
99C2×C4×D47—22no—
100C2×C4×D47—22no—
101C2×C4×D47C22×C411yescharacteristic
102C2×C4×D47C2×D411yescharacteristic
103C2×C4×D47#4111yescharacteristic
104Q16×C47C2×C814yescomplemented
105C2×C8×C47—22no—
106C2×C8×C47—21no—
107C2×C8×C47C22×C411yescharacteristic
108C2×C8×C47C22×C411yescharacteristic
109C2×C8×C47C2×D412yes—
110C4⋊C4×C47—22no—
111C4⋊C4×C47C22×C412yes—
112C42×C47—22no—
113C42×C47C2411yescharacteristic
114#10625336C2×C818yescomplemented
115(C2×D47)⋊C4—22no—
116(C2×D47)⋊C4—22no—
117(C2×D47)⋊C4—22no—
118C4⋊Dic47—22no—
119C4⋊Dic47C22×C412yes—
120C4×Dic47—22no—
121C4×Dic47—22no—
122C4×Dic47C22×C411yescharacteristic
123C4×Dic47C2×D411yescharacteristic
124C4×Dic47#4111yescharacteristic
125C2×C47⋊C8—22no—
126C2×C47⋊C8—21no—
127C2×C47⋊C8C22×C411yescharacteristic
128C2×C47⋊C8C22×C411yescharacteristic
129C2×C47⋊C8C2×D412yes—
130D376C2×C814yescomplemented
131C8×D47—22no—
132C8×D47—42no—
133C8×D47—44no—
134C8×D47—44no—
135C8×D47—42no—
136C8×D47C2×C814yescomplemented
137C22×D47—22no—
138C22×D47C4×D411yescharacteristic
139Q8×C47—22no—
140Q8×C47C22×C814yes—
141C2×C4×C47—22no—
142C2×C4×C47—22no—
143C2×C4×C47C23×C411yescharacteristic
144C2×C4×C47C22×D411yescharacteristic
145C2×C4×C47C2×#4111yescharacteristic
146C2×Dic47—22no—
147C2×Dic47C4×D411yescharacteristic
148C2×Dic47C4×D411yescharacteristic
149C2×Dic47C4×D411yescharacteristic
150D188—28no—
151D188—22no—
152D188C22×C814yes—
153C4×D47—22no—
154C4×D47—28no—
155C4×D47—22no—
156C4×D47—42no—
157C4×D47—42no—
158C4×D47—44no—
159C4×D47C22×C812yes—
160C4×D47#13112yes—
161C8×C47—21no—
162C8×C47—22no—
163C8×C47—41no—
164C8×C47—42no—
165C8×C47C22×C812yes—
166C47⋊C8—21no—
167C47⋊C8—22no—
168C47⋊C8—41no—
169C47⋊C8—42no—
170C47⋊C8C22×C812yes—
171#17849—471nomaximal, Sylow
172C22×C47C2×C4×D411yescharacteristic
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—24no—
176C2×D47—42no—
177C2×D47—42no—
178C2×D47C8×D412yes—
179C4×C47—24no—
180C4×C47—21no—
181C4×C47—42no—
182C4×C47C23×C811yescharacteristic
183C4×C47C2×#13111yescharacteristic
184C4×C47#57512yes—
185Dic47—21no—
186Dic47—42no—
187Dic47C8×D412yes—
188Dic47#44412yes—
189C8×#41—472no—
190C4×#135—471no—
191#1580—471no—
192#1580—471no—
193#1579—471no—
194#1579D4711yescharacteristic, complemented
195SD16⋊C8—472no—
196SD16⋊C8—472no—
197#1564—471no—
198#1476—472no—
199C2×#322—471no—
200C2×C47C2×C8×D411yescharacteristic
201C2×C47#294311yescharacteristic
202C2×C47C2×#44411yescharacteristic
203D47—22no—
204D47—44no—
205C2×#135—471no—
206C4×#41—472no—
207C8×Q8—472no—
208C8×Q8C2×D4712yes—
209C4×Q16—471no—
210C4×Q16C2×D4711yescharacteristic
211C4×SD16—472no—
212C4×SD16—472no—
213C4×D8—471no—
214C4×D8—471no—
215C8×D4—472no—
216C8×D4—472no—
217C8×D4—942no—
218C8×D4—942no—
219#431—472no—
220#431—942no—
221#427—471no—
222#416—472no—
223C2×C4×C8—471no—
224C2×C4×C8—471no—
225C2×C4×C8—471no—
226C2×C4×C8—942no—
227#335—472no—
228#334—471no—
229#334C2×D4711yescharacteristic
230Q8⋊C8—472no—
231Q8⋊C8C2×D4712yes—
232D4⋊C8—472no—
233D4⋊C8—472no—
234#322—471no—
235#322—471no—
236#322—471no—
237#322C2×D4711yescharacteristic
238C47#1784911yescharacteristic, complemented, Sylow
239C2×#41—472no—
240#135—478no—
241C2×Q16C4×D4711yescharacteristic
242C2×SD16—472no—
243C2×D8—471no—
244C22×C8—471no—
245C22×C8—471no—
246C22×C8—472no—
247C22×C8—942no—
248C22×C8—941no—
249C22×C8—942no—
250C4×Q8—472no—
251C4×Q8C22×D4712yes—
252C4×D4—472no—
253C4×D4—472no—
254C4×D4—942no—
255C4×D4—942no—
256#117—472no—
257#117—942no—
258C2×C42—471no—
259C2×C42—942no—
260#107—471no—
261#107C4×D4711yescharacteristic
262#106—472no—
263C4⋊C8—22no—
264C4⋊C8—472no—
265C4⋊C8—942no—
266C4⋊C8C22×D4712yes—
267#103—472no—
268#103C4×D4712yes—
269#102—472no—
270#102—472no—
271C22⋊C8—942no—
272C22⋊C8—942no—
273C22⋊C8—942no—
274C4×C8—22no—
275C4×C8—471no—
276C4×C8—471no—
277C4×C8—472no—
278C4×C8—471no—
279C4×C8—471no—
280C4×C8—471no—
281C4×C8—942no—
282C4×C8—941no—
283C4×C8—942no—
284C4×C8C22×D4711yescharacteristic
285C4×C8C22×D4711yescharacteristic
286C4×C8C22×D4711yescharacteristic
287#41—478no—
288#41—944no—
289C2×Q8C2×C4×D4712yes—
290C2×D4—472no—
291C2×D4—942no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—471no—
295C22×C4—942no—
296C22×C4—942no—
297C22×C4—942no—
298Q16C8×D4714yescomplemented
299SD16—478no—
300D8—474no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—471no—
304C2×C8—474no—
305C2×C8—471no—
306C2×C8—472no—
307C2×C8—942no—
308C2×C8—942no—
309C2×C8—941no—
310C2×C8—1882no—
311C2×C8—1884no—
312C2×C8—1884no—
313C2×C8—1882no—
314C2×C8C2×C4×D4711yescharacteristic
315C2×C8C2×C4×D4711yescharacteristic
316C2×C8D4×D4712yes—
317C4⋊C4—22no—
318C4⋊C4—472no—
319C4⋊C4—942no—
320C4⋊C4C2×C4×D4712yes—
321C22⋊C4—942no—
322C22⋊C4—942no—
323C22⋊C4—942no—
324C42—22no—
325C42—471no—
326C42—471no—
327C42—471no—
328C42—942no—
329C42—942no—
330C42C23×D4711yescharacteristic
331C23—471no—
332C23—942no—
333Q8—22no—
334Q8C2×C8×D4714yes—
335D4—474no—
336D4—948no—
337D4—942no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—471no—
341C2×C4—471no—
342C2×C4—472no—
343C2×C4—472no—
344C2×C4—471no—
345C2×C4—942no—
346C2×C4—948no—
347C2×C4—942no—
348C2×C4—942no—
349C2×C4—1884no—
350C2×C4—1882no—
351C2×C4—1882no—
352C2×C4C22×C4×D4711yescharacteristic
353C2×C4C2×D4×D4711yescharacteristic
354C2×C4#41×D4711yescharacteristic
355C8—21no—
356C8—22no—
357C8—41no—
358C8—42no—
359C8—472no—
360C8—941no—
361C8—942no—
362C8—1881no—
363C8—1882no—
364C8C2×C8×D4712yes—
365C22—472no—
366C22—941no—
367C22—941no—
368C22—944no—
369C22—1882no—
370C22—1882no—
371C22C4×D4×D4711yescharacteristic
372C4—21no—
373C4—24no—
374C4—42no—
375C4—472no—
376C4—472no—
377C4—941no—
378C4—1882no—
379C4C22×C8×D4711yescharacteristic
380C4#131×D4711yescharacteristic
381C4#1568992212yes—
382C2—942no—
383C2—1884no—
384C2C8×D4×D4711yescharacteristic
385C2#2025218711yescharacteristic
386C2#444×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC47×#1579C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094047C4
cosocleC42×C47C24
hypercenter#1579D47
hypocenterC47#17849
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
1. C8×#10625354C2semidirect
3. #20242213C2semidirect
4. #20242211C2semidirect
5. #20242207C2semidirect
6. #20242203C2semidirect
7. #20242198C2semidirect
8. #20242133C2semidirect
9. #20241769C2semidirect
10. #322×D47C2semidirect
11. C47×#1579C2semidirect
46. #13094047C8semidirect
95. #10625354C2×C8semidirect
104. Q16×C47C2×C8semidirect
114. #10625336C2×C8semidirect
130. D376C2×C8semidirect
136. C8×D47C2×C8semidirect
194. #1579D47semidirect
238. C47#17849semidirect
298. Q16C8×D47semidirect

Maximal subgroups

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

subgroupindex
C8×#106253542
C4×#130940472
#202422132
#202422112
#202422072
#202422032
#202421982
#202421332
#202417692
#322×D472
C47×#15792
#1784947