Finite Group Databasebeta

← #26185764

Subgroups — #26185764

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252498C212yesmaximal, complemented
2C4×#13094047C211yesmaximal, characteristic
3#20242213C211yesmaximal, characteristic, complemented
4#20242211C211yesmaximal, characteristic, complemented
5#20242207C211yesmaximal, characteristic, complemented
6C8×#10625336C212yesmaximal, complemented
7#20242185C212yesmaximal, complemented
8#334×D47C211yesmaximal, characteristic, complemented
9#20241774C212yesmaximal, complemented
10#20241673C211yesmaximal, 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#15689174—22no—
25#15689174C2211yescharacteristic
26#15689174C2211yescharacteristic
27#15689160C411yescharacteristic
28C4⋊C8×D47—22no—
29C4⋊C8×D47C2212yes—
30#15689118C412yes—
31C4×C8×D47C2211yescharacteristic
32#15688874C2211yescharacteristic
33#15688873C2212yes—
34Q8⋊(C47⋊C8)C2212yes—
35#15688852C2212yes—
36#15688850C2212yes—
37#15688844C2211yescharacteristic
38C8×C47⋊C8C2211yescharacteristic
39C8×C47⋊C8C2211yescharacteristic
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—22no—
50C2×C8×D47—22no—
51C2×C8×D47—22no—
52C2×C8×D47C2×C411yescharacteristic
53C2×C8×D47C2×C411yescharacteristic
54Q8×Dic47C2×C412yes—
55C4×D188—22no—
56C4×D188C2312yes—
57#13093986—22no—
58#13093986C2×C412yes—
59#13093982—22no—
60#13093982C2×C412yes—
61C42×D47—22no—
62C42×D47C2311yescharacteristic
63#13093958C2×C411yescharacteristic
64#13093955C2×C412yes—
65C4⋊(C47⋊C8)—22no—
66C4⋊(C47⋊C8)C2312yes—
67Dic47⋊C8—22no—
68Dic47⋊C8—21no—
69Dic47⋊C8D412yes—
70#13093948C2×C412yes—
71#13093946C2×C412yes—
72#13093944C2×C412yes—
73(C2×D47)⋊C8—21no—
74(C2×D47)⋊C8—22no—
75(C2×D47)⋊C8—22no—
76(C2×D47)⋊C8D412yes—
77C4×C47⋊C8—22no—
78C4×C47⋊C8C2311yescharacteristic
79C4×C47⋊C8C2311yescharacteristic
80C4×C47⋊C8C2311yescharacteristic
81C8×Dic47C2×C411yescharacteristic
82C8×Dic47C2×C411yescharacteristic
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—82no—
133C8×D47—82no—
134C8×D47—82no—
135C8×D47C2×C814yescomplemented
136C22×D47—22no—
137C22×D47C4×D411yescharacteristic
138Q8×C47—22no—
139Q8×C47C22×C814yes—
140C2×C4×C47—22no—
141C2×C4×C47—22no—
142C2×C4×C47C23×C411yescharacteristic
143C2×C4×C47C22×D411yescharacteristic
144C2×C4×C47C2×#4111yescharacteristic
145C2×Dic47—22no—
146C2×Dic47C4×D411yescharacteristic
147C2×Dic47C4×D411yescharacteristic
148C2×Dic47C4×D411yescharacteristic
149D188—28no—
150D188—22no—
151D188C22×C814yes—
152C4×D47—22no—
153C4×D47—28no—
154C4×D47—41no—
155C4×D47—42no—
156C4×D47—42no—
157C4×D47—82no—
158C4×D47C22×C812yes—
159C4×D47#13112yes—
160C8×C47—21no—
161C8×C47—22no—
162C8×C47—41no—
163C8×C47—42no—
164C8×C47C22×C812yes—
165C47⋊C8—21no—
166C47⋊C8—22no—
167C47⋊C8—41no—
168C47⋊C8—42no—
169C47⋊C8C22×C812yes—
170#17858—471nomaximal, Sylow
171C22×C47C2×C4×D411yescharacteristic
172C2×D47—21no—
173C2×D47—21no—
174C2×D47—24no—
175C2×D47—42no—
176C2×D47—42no—
177C2×D47C8×D412yes—
178C4×C47—24no—
179C4×C47—21no—
180C4×C47—42no—
181C4×C47C23×C811yescharacteristic
182C4×C47C2×#13111yescharacteristic
183C4×C47#57712yes—
184Dic47—21no—
185Dic47—21no—
186Dic47—42no—
187Dic47C8×D412yes—
188#2988—472no—
189C4×#135—471no—
190#1580—471no—
191#1580—471no—
192#1579—471no—
193#1579D4711yescharacteristic, complemented
194C8×SD16—472no—
195C8×SD16—472no—
196C2×#334—471no—
197#1477—472no—
198#1450—471no—
199C2×C47C2×C8×D411yescharacteristic
200C2×C47#295211yescharacteristic
201C2×C47#295711yescharacteristic
202D47—22no—
203D47—44no—
204C2×#135—471no—
205C4×#41—472no—
206C8×Q8—472no—
207C8×Q8C2×D4712yes—
208C4×Q16—471no—
209C4×Q16C2×D4711yescharacteristic
210C4×SD16—472no—
211C4×SD16—472no—
212C4×D8—471no—
213C4×D8—471no—
214C8×D4—472no—
215C8×D4—472no—
216C8×D4—942no—
217C8×D4—942no—
218#431—471no—
219#431—471no—
220#431—942no—
221#427—471no—
222C2×C4⋊C8—472no—
223C2×C4⋊C8—942no—
224#416—472no—
225C2×C4×C8—471no—
226#334—472no—
227#334—471no—
228#334C2×D4711yescharacteristic
229Q8⋊C8—472no—
230Q8⋊C8C2×D4712yes—
231D4⋊C8—472no—
232D4⋊C8—472no—
233#322—471no—
234#322C2×D4711yescharacteristic
235C82—471no—
236C82—471no—
237C47#1785811yescharacteristic, complemented, Sylow
238C2×#41—472no—
239#135—478no—
240C2×Q16C4×D4711yescharacteristic
241C2×SD16—472no—
242C2×D8—471no—
243C22×C8—471no—
244C22×C8—471no—
245C22×C8—942no—
246C22×C8—942no—
247C22×C8—942no—
248C4×Q8—472no—
249C4×Q8C22×D4712yes—
250C4×D4—472no—
251C4×D4—472no—
252C4×D4—942no—
253C4×D4—942no—
254#117—472no—
255#117—942no—
256C2×C42—471no—
257C2×C42—942no—
258#107—471no—
259#107C4×D4711yescharacteristic
260#106—472no—
261C4⋊C8—22no—
262C4⋊C8—472no—
263C4⋊C8—472no—
264C4⋊C8—942no—
265C4⋊C8—942no—
266C4⋊C8—941no—
267C4⋊C8C22×D4712yes—
268#103—472no—
269#103C4×D4712yes—
270#102—472no—
271#102—472no—
272C22⋊C8—472no—
273C22⋊C8—942no—
274C22⋊C8—941no—
275C22⋊C8—942no—
276C4×C8—22no—
277C4×C8—471no—
278C4×C8—471no—
279C4×C8—471no—
280C4×C8—471no—
281C4×C8—471no—
282C4×C8—942no—
283C4×C8C22×D4711yescharacteristic
284C4×C8C22×D4711yescharacteristic
285C4×C8C22×D4711yescharacteristic
286#41—478no—
287#41—944no—
288C2×Q8C2×C4×D4712yes—
289C2×D4—472no—
290C2×D4—942no—
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—942no—
295C22×C4—942no—
296C22×C4—942no—
297Q16C8×D4714yescomplemented
298SD16—478no—
299D8—474no—
300C2×C8—22no—
301C2×C8—21no—
302C2×C8—471no—
303C2×C8—474no—
304C2×C8—471no—
305C2×C8—472no—
306C2×C8—942no—
307C2×C8—942no—
308C2×C8—941no—
309C2×C8—3762no—
310C2×C8—3762no—
311C2×C8—3762no—
312C2×C8C2×C4×D4711yescharacteristic
313C2×C8C2×C4×D4711yescharacteristic
314C2×C8D4×D4712yes—
315C4⋊C4—22no—
316C4⋊C4—472no—
317C4⋊C4—942no—
318C4⋊C4C2×C4×D4712yes—
319C22⋊C4—942no—
320C22⋊C4—942no—
321C22⋊C4—942no—
322C42—22no—
323C42—471no—
324C42—471no—
325C42—471no—
326C42—942no—
327C42—942no—
328C42C23×D4711yescharacteristic
329C23—471no—
330C23—942no—
331Q8—22no—
332Q8C2×C8×D4714yes—
333D4—474no—
334D4—948no—
335D4—942no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—471no—
339C2×C4—472no—
340C2×C4—472no—
341C2×C4—471no—
342C2×C4—471no—
343C2×C4—948no—
344C2×C4—942no—
345C2×C4—942no—
346C2×C4—3762no—
347C2×C4—1881no—
348C2×C4—1882no—
349C2×C4—1882no—
350C2×C4C22×C4×D4711yescharacteristic
351C2×C4C2×D4×D4711yescharacteristic
352C2×C4#41×D4711yescharacteristic
353C8—21no—
354C8—22no—
355C8—41no—
356C8—42no—
357C8—472no—
358C8—941no—
359C8—942no—
360C8—1881no—
361C8—1882no—
362C8C2×C8×D4712yes—
363C22—472no—
364C22—941no—
365C22—941no—
366C22—944no—
367C22—1882no—
368C22—1882no—
369C22C4×D4×D4711yescharacteristic
370C4—21no—
371C4—24no—
372C4—42no—
373C4—472no—
374C4—941no—
375C4—941no—
376C4—1882no—
377C4C22×C8×D4711yescharacteristic
378C4#131×D4711yescharacteristic
379C4#1568993212yes—
380C2—942no—
381C2—1884no—
382C2C8×D4×D4711yescharacteristic
383C2#2025226811yescharacteristic
384C2#2025230211yescharacteristic
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#17858
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. #20252498C2semidirect
3. #20242213C2semidirect
4. #20242211C2semidirect
5. #20242207C2semidirect
6. C8×#10625336C2semidirect
7. #20242185C2semidirect
8. #334×D47C2semidirect
9. #20241774C2semidirect
10. #20241673C2semidirect
11. C47×#1579C2semidirect
46. #13094047C8semidirect
95. #10625354C2×C8semidirect
104. Q16×C47C2×C8semidirect
114. #10625336C2×C8semidirect
130. D376C2×C8semidirect
135. C8×D47C2×C8semidirect
193. #1579D47semidirect
237. C47#17858semidirect
297. Q16C8×D47semidirect

Maximal subgroups

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

subgroupindex
#202524982
C4×#130940472
#202422132
#202422112
#202422072
C8×#106253362
#202421852
#334×D472
#202417742
#202416732
C47×#15792
#1785847