Finite Group Databasebeta

← #26204070

Subgroups — #26204070

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253967C211yesmaximal, characteristic, complemented
2#20253963C212yesmaximal, complemented
3#20253814C212yesmaximal, complemented
4#20243061C212yesmaximal, complemented
5#20243058C212yesmaximal, complemented
6#20243056C212yesmaximal, complemented
7#20243053C212yesmaximal, complemented
8C2×#15688845C211yesmaximal, characteristic, complemented
9C47×#3169C211yesmaximal, characteristic, complemented
10C2×#13094044—24no—
11#15689673C2212yes—
12#15689528C2211yescharacteristic
13#15689526C2212yes—
14#15689505—24no—
15#15689502C2212yes—
16#15689500C2211yescharacteristic
17#15689499C2212yes—
18#15689499C2212yes—
19#15689497C2212yes—
20#15689495C2212yes—
21#15689471C2212yes—
22#15689470C2212yes—
23#15689469C2212yes—
24#15689359—22no—
25#15689357—24no—
26C4×D376—22no—
27C4×#10625334—24no—
28C2×C4×C47⋊C8C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
30#15688845C2212yes—
31#15688845C2212yes—
32C47×#532C2212yes—
33C47×#500C2211yescharacteristic
34C47×#493C2211yescharacteristic
35C47×#486C2212yes—
36C47×#466—22no—
37C4×D8×C47—22no—
38C2×C4×C8×C47C2211yescharacteristic
39C2×#10625350—22no—
40#13094044—416no—
41C2×#10625337—24no—
42C2×#10625335—24no—
43C2×#10625336—24no—
44C2×D376—22no—
45C2×#10625334—24no—
46C2×#10625334—24no—
47C22×C47⋊C8D412yes—
48C22×C47⋊C8D412yes—
49#13094024C2312yes—
50#13094021C2312yes—
51#13094012—22no—
52#13093998—22no—
53#13093998—22no—
54C4×D188—22no—
55C4×D188—22no—
56#13093958—22no—
57#13093957—24no—
58#13093946—24no—
59#13093945—24no—
60#13093944—24no—
61C4×C47⋊C8D412yes—
62C4×C47⋊C8D412yes—
63C4×C47⋊C8C2312yes—
64C4×C47⋊C8C2312yes—
65C2×#41×C47—22no—
66C2×D8×C47—22no—
67C22×C8×C47D412yes—
68C4⋊Q8×C47C2312yes—
69#127×C47C2312yes—
70#124×C47—22no—
71#121×C47—22no—
72#121×C47—22no—
73C4×D4×C47—22no—
74C4×D4×C47—22no—
75C2×C42×C47C2311yescharacteristic
76#107×C47—22no—
77#102×C47—24no—
78C4×C8×C47D412yes—
79C4×C8×C47C2311yescharacteristic
80C4×C8×C47C2311yescharacteristic
81#41×C47—48no—
82C2×Q8×C47—22no—
83C2×D4×C47—22no—
84C2×D4×C47—22no—
85C2×D4×C47—22no—
86C2×D4×C47—42no—
87C22×C4×C47—42no—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C2×C22⋊D47—42no—
92#10625350—48no—
93C2×D188—22no—
94C2×D188—22no—
95C2×D188—22no—
96C2×C4×D47—42no—
97C2×Dic94—22no—
98D8×C47—44no—
99C2×C8×C47—42no—
100C2×C8×C47C2×D412yes—
101C2×C8×C47C2×D412yes—
102C4⋊C4×C47—22no—
103C4⋊C4×C47—22no—
104C22⋊C4×C47—42no—
105C22⋊C4×C47—42no—
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47C2411yescharacteristic
110#10625337—48no—
111#10625336—48no—
112#10625335—48no—
113#10625334—48no—
114#10625334—48no—
115(C2×D47)⋊C4—42no—
116(C2×D47)⋊C4—42no—
117C4⋊Dic47—22no—
118C4⋊Dic47—22no—
119C2×C47⋊C8—42no—
120C2×C47⋊C8D818yescomplemented
121C2×C47⋊C8C2×D414yes—
122C2×C47⋊C8C2×D414yes—
123D376—44no—
124C23×C47—42no—
125C23×C47#12711yescharacteristic
126C22×D47—42no—
127Q8×C47—44no—
128D4×C47—44no—
129D4×C47—44no—
130D4×C47—44no—
131D4×C47—84no—
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47—42no—
135C2×C4×C47—84no—
136C2×C4×C47#12711yescharacteristic
137C2×C4×C47#12711yescharacteristic
138C2×C4×C47#12711yescharacteristic
139C2×C4×C47C2×D814yes—
140C2×C4×C47C22×D411yescharacteristic
141C2×C4×C47C22×D411yescharacteristic
142C2×C4×C47C22×D411yescharacteristic
143C22⋊D47—84no—
144C2×Dic47—42no—
145D188—44no—
146D188—44no—
147D188—44no—
148C4×D47—84no—
149Dic94—44no—
150C8×C47—22no—
151C8×C47—22no—
152C47⋊C8—24no—
153C47⋊C8C2×D818yes—
154#19616—471nomaximal, Sylow
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—82no—
158C22×C47—82no—
159C22×C47—82no—
160C22×C47#49312yes—
161C22×C47C2×#12711yescharacteristic
162C2×D47—82no—
163C2×D47—82no—
164C2×D47—82no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—82no—
168C4×C47#49312yes—
169C4×C47C22×D812yes—
170C4×C47#57512yes—
171C4×C47#57512yes—
172Dic47—82no—
173#3169—471no—
174#3169—472no—
175#3169D4711yescharacteristic, complemented
176#3147—472no—
177#1722—472no—
178#1722—472no—
179#1721—472no—
180#1721—472no—
181C2×#322—471no—
182C2×C47—22no—
183C2×C47—162no—
184C2×C47C2×#49311yescharacteristic
185C2×C47#315011yescharacteristic
186C2×C47#315011yescharacteristic
187D47—162no—
188C2×#135—944no—
189#532—472no—
190#532C2×D4712yes—
191#500—472no—
192#500—471no—
193#500C2×D4711yescharacteristic
194#495—944no—
195#494—472no—
196#493—472no—
197#493—472no—
198#493—471no—
199#493C2×D4711yescharacteristic
200#492—472no—
201#492—472no—
202#486—472no—
203#486—472no—
204#486—472no—
205#486C2×D4712yes—
206#466—22no—
207#466—944no—
208#466—942no—
209C4×D8—22no—
210C4×D8—944no—
211C4×D8—942no—
212C2×C4×C8—471no—
213C2×C4×C8—471no—
214C2×C4×C8C2×D4711yescharacteristic
215#322—472no—
216#322—472no—
217C47#1961611yescharacteristic, complemented, Sylow
218C2×#41—22no—
219C2×#41—942no—
220#135—18816no—
221C2×Q16—944no—
222C2×SD16—944no—
223C2×SD16—944no—
224C2×D8—22no—
225C2×D8—944no—
226C2×D8—944no—
227C2×D8—942no—
228C22×C8—472no—
229C22×C8—472no—
230C22×C8C22⋊D4712yes—
231C4⋊Q8—472no—
232C4⋊Q8C22×D4712yes—
233#127—472no—
234#127C22×D4712yes—
235#124—22no—
236#124—942no—
237#121—22no—
238#121—22no—
239#121—942no—
240#121—942no—
241C4×D4—22no—
242C4×D4—22no—
243C4×D4—942no—
244C4×D4—942no—
245C2×C42C22×D4711yescharacteristic
246#107—22no—
247#107—944no—
248#107—942no—
249#102—24no—
250#102—944no—
251#102—944no—
252#102—944no—
253C4×C8—472no—
254C4×C8—472no—
255C4×C8—472no—
256C4×C8—472no—
257C4×C8C22⋊D4712yes—
258C4×C8C22×D4711yescharacteristic
259C4×C8C22×D4711yescharacteristic
260#41—48no—
261#41—1888no—
262C2×Q8—22no—
263C2×Q8—942no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—42no—
268C2×D4—942no—
269C2×D4—942no—
270C2×D4—942no—
271C2×D4—1882no—
272C22×C4—42no—
273C22×C4—1882no—
274C22×C4D4×D4711yescharacteristic
275C22×C4D4×D4711yescharacteristic
276C22×C4C2×C22⋊D4711yescharacteristic
277Q16—1888no—
278SD16—1888no—
279SD16—1888no—
280D8—44no—
281D8—1884no—
282D8—1888no—
283D8—1888no—
284C2×C8—42no—
285C2×C8—478no—
286C2×C8—474no—
287C2×C8—474no—
288C2×C8—1882no—
289C2×C8C2×C22⋊D4712yes—
290C2×C8C2×C22⋊D4712yes—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—1882no—
298C22⋊C4—1882no—
299C42D4×D4711yescharacteristic
300C42D4×D4711yescharacteristic
301C42C2×C22⋊D4711yescharacteristic
302C42C23×D4711yescharacteristic
303C23—42no—
304C23—1882no—
305C23#1309402011yescharacteristic
306Q8—44no—
307Q8—1884no—
308D4—44no—
309D4—44no—
310D4—44no—
311D4—84no—
312D4—3764no—
313D4—1884no—
314D4—1884no—
315D4—1884no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—42no—
319C2×C4—84no—
320C2×C4—3764no—
321C2×C4—1882no—
322C2×C4#1309402011yescharacteristic
323C2×C4#1309402011yescharacteristic
324C2×C4#1309402011yescharacteristic
325C2×C4D8×D4714yes—
326C2×C4C2×D4×D4711yescharacteristic
327C2×C4C2×D4×D4711yescharacteristic
328C2×C4C22×C22⋊D4711yescharacteristic
329C8—22no—
330C8—22no—
331C8—478no—
332C8—944no—
333C22—21no—
334C22—21no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—3762no—
339C22—3762no—
340C22—3762no—
341C22#1568949812yes—
342C22C2×#1309402011yescharacteristic
343C4—21no—
344C4—21no—
345C4—82no—
346C4—3762no—
347C4#1568949812yes—
348C4C2×D8×D4712yes—
349C4#1568992012yes—
350C4#1568992112yes—
351C2—22no—
352C2—162no—
353C2—7522no—
354C2C2×#1568949811yescharacteristic
355C2#2025383111yescharacteristic
356C2#2025383311yescharacteristic
subgroupG/H
centerC2×C4#13094020
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#3169C2
socleC22×C47C2×#127
hypercenter#3169D47
hypocenterC47#19616
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #20253967C2semidirect
2. #20253963C2semidirect
3. #20253814C2semidirect
4. #20243061C2semidirect
5. #20243058C2semidirect
6. #20243056C2semidirect
7. #20243053C2semidirect
8. C2×#15688845C2semidirect
9. C47×#3169C2semidirect
120. C2×C47⋊C8D8semidirect
175. #3169D47semidirect
217. C47#19616semidirect

Maximal subgroups

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

subgroupindex
#202539672
#202539632
#202538142
#202430612
#202430582
#202430562
#202430532
C2×#156888452
C47×#31692
#1961647