Finite Group Databasebeta

← #26133442

Subgroups — #26133442

Order 12032.

484 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#135×Dic47C211yesmaximal, characteristic, complemented
2#20245124C211yesmaximal, characteristic, complemented
3#20245116C211yesmaximal, characteristic, complemented
4#20244277C211yesmaximal, characteristic, complemented
5#20241503C211yesmaximal, characteristic, complemented
6#20241469C211yesmaximal, characteristic, complemented
7C47×#3414C211yesmaximal, characteristic
8#41×Dic47—21no—
9C2×#13093964C2211yescharacteristic
10Q16×Dic47—21no—
11SD16×Dic47—22no—
12D8×Dic47—21no—
13C2×#13093960C2211yescharacteristic
14#15689161C2211yescharacteristic
15C2×#13093951—21no—
16#15689119—21no—
17#15689090—21no—
18C2×C8×Dic47C2211yescharacteristic
19#15688933—22no—
20#15688930—22no—
21C2×#135×C47C2211yescharacteristic
22C2×#135×C47C2211yescharacteristic
23C47×#510—21no—
24C47×#510C412yescomplemented
25C47×#509—21no—
26C47×#509C412yescomplemented
27C47×#508—22no—
28C2×M32×C47C2211yescharacteristic
29C2×#10625329—21no—
30C22×C47⋊C8D411yescharacteristic
31Q8×Dic47—22no—
32D4×Dic47—22no—
33D4×Dic47—42no—
34#13093983—21no—
35#13093983—41no—
36C2×C4×Dic47—41no—
37C2×C4×Dic47D411yescharacteristic
38#13093964—21no—
39#13093964—21no—
40C2×C47⋊C16—21no—
41#13093960—21no—
42#13093960—21no—
43#13093958—21no—
44#13093956D412yes—
45#13093951—41no—
46#13093951—41no—
47#13093948—22no—
48#13093945—22no—
49C22⋊(C47⋊C8)—42no—
50C8×Dic47—21no—
51C8×Dic47—21no—
52C2×#41×C47—21no—
53C2×#41×C47—21no—
54#135×C47—21no—
55#135×C47—21no—
56#135×C47—21no—
57#135×C47—21no—
58#135×C47—21no—
59#135×C47—21no—
60#135×C47C2×C412yes—
61#135×C47D412yes—
62C2×Q16×C47C2×C411yescharacteristic, complemented
63C2×Q16×C47D411yescharacteristic
64C2×SD16×C47—21no—
65C2×SD16×C47—21no—
66C2×D8×C47C2×C411yescharacteristic, complemented
67C2×D8×C47D411yescharacteristic
68C22×C8×C47C2311yescharacteristic
69Q32×C47—22no—
70SD32×C47—22no—
71SD32×C47—22no—
72D16×C47—22no—
73M32×C47—21no—
74M32×C47C2×C412yescomplemented
75C2×C16×C47—21no—
76#41×C47—22no—
77#41×C47—22no—
78#41×C47—41no—
79#41×C47—41no—
80#41×C47—41no—
81#41×C47—41no—
82#41×C47—41no—
83#41×C47—41no—
84C2×Q8×C47—21no—
85C2×Q8×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47—21no—
88C2×D4×C47—41no—
89C2×D4×C47—41no—
90C22×C4×C47—41no—
91C22×C4×C47—41no—
92C22×C4×C47C2×D411yescharacteristic
93C22×Dic47—21no—
94C22×Dic47—42no—
95Q16×C47—21no—
96Q16×C47—21no—
97Q16×C47—21no—
98Q16×C47C22⋊C412yes—
99SD16×C47—22no—
100SD16×C47—22no—
101SD16×C47—41no—
102SD16×C47—41no—
103D8×C47—21no—
104D8×C47—21no—
105D8×C47—21no—
106D8×C47C22⋊C412yes—
107C2×C8×C47C22×C411yescharacteristic
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47C2×D411yescharacteristic
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47#4111yescharacteristic
112C2×C8×C47#4111yescharacteristic
113C22⋊Dic47—42no—
114C22⋊Dic47—41no—
115C4⋊Dic47—22no—
116C4⋊Dic47—42no—
117C4×Dic47—21no—
118C4×Dic47—42no—
119C4×Dic47—41no—
120C4×Dic47D811yescharacteristic
121C4×Dic47D811yescharacteristic
122#10625329—41no—
123#10625329—41no—
124C2×C47⋊C8—21no—
125C2×C47⋊C8—21no—
126C2×C47⋊C8—21no—
127C2×C47⋊C8—41no—
128C16×C47—22no—
129C47⋊C16—41no—
130C23×C47—41no—
131C23×C47—41no—
132C23×C47AGL(1,ℤ/8)11yescharacteristic
133Q8×C47—22no—
134Q8×C47—41no—
135Q8×C47—41no—
136Q8×C47—41no—
137D4×C47—22no—
138D4×C47—42no—
139D4×C47—42no—
140D4×C47—41no—
141D4×C47—41no—
142D4×C47—41no—
143D4×C47—81no—
144D4×C47—81no—
145C2×C4×C47—41no—
146C2×C4×C47—42no—
147C2×C4×C47—42no—
148C2×C4×C47—41no—
149C2×C4×C47—81no—
150C2×C4×C47—81no—
151C2×C4×C47C4×D411yescharacteristic
152C2×C4×C47#12011yescharacteristic
153C2×C4×C47#12111yescharacteristic
154C2×C4×C47C2×D811yescharacteristic
155C2×C4×C47#13511yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—42no—
160C2×Dic47—42no—
161C2×Dic47—84no—
162C8×C47C2×C22⋊C411yescharacteristic
163C8×C47C4×D411yescharacteristic
164C8×C47#12111yescharacteristic
165C8×C47#12311yescharacteristic
166C47⋊C8—41no—
167C47⋊C8—81no—
168#13027—471nomaximal, Sylow
169C22×C47—41no—
170C22×C47—42no—
171C22×C47—82no—
172C22×C47—82no—
173C22×C47—81no—
174C22×C47#44211yescharacteristic
175C22×C47#44711yescharacteristic
176C22×C47#46311yescharacteristic
177C4×C47—42no—
178C4×C47—81no—
179C4×C47#38611yescharacteristic
180C4×C47C4×D811yescharacteristic
181C4×C47#44911yescharacteristic
182C4×C47#45911yescharacteristic
183Dic47—22no—
184Dic47—41no—
185Dic47—82no—
186#3414D4711yescharacteristic
187C4×#135—471no—
188#2145—471no—
189#2143—471no—
190#1974—471no—
191#1389—471no—
192#1376—471no—
193C2×C47—21no—
194C2×C47—21no—
195C2×C47—21no—
196C2×C47—82no—
197C2×C47—161no—
198C2×C47#187911yescharacteristic
199C2×#135C2×D4711yescharacteristic
200C2×#135C2×D4711yescharacteristic
201C4×#41—941no—
202#510—21no—
203#510Dic4712yescomplemented
204#509—21no—
205#509Dic4712yescomplemented
206#508—22no—
207C2×M32—471no—
208C2×M32C2×D4711yescharacteristic
209C4×Q16—941no—
210C4×SD16—942no—
211C4×D8—941no—
212C2×#108—471no—
213#427—471no—
214C2×#104—941no—
215#416—941no—
216#408—941no—
217C2×C4×C8—471no—
218#360—942no—
219#359—942no—
220C47#1302711yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C2×#41—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—21no—
228#135—21no—
229#135C2×Dic4712yes—
230#135C22⋊D4712yes—
231C2×Q16C2×Dic4711yescharacteristic, complemented
232C2×Q16C22⋊D4711yescharacteristic
233C2×SD16—21no—
234C2×SD16—21no—
235C2×D8C2×Dic4711yescharacteristic, complemented
236C2×D8C22⋊D4711yescharacteristic
237C2×M16—941no—
238C22×C8—471no—
239C22×C8C22×D4711yescharacteristic
240C4×Q8—942no—
241C4×D4—942no—
242C4×D4—1882no—
243#117—941no—
244#117—1881no—
245C2×C42—471no—
246C2×C42—1881no—
247Q32—22no—
248SD32—22no—
249SD32—22no—
250D16—22no—
251M32—21no—
252M32—941no—
253M32—941no—
254M32C2×Dic4712yescomplemented
255C2×C16—21no—
256C2×C16—941no—
257#108—941no—
258#108—941no—
259#107—941no—
260#106—472no—
261#104—1881no—
262#104—1881no—
263#103—942no—
264#102—942no—
265C22⋊C8—1882no—
266C4×C8—941no—
267C4×C8—941no—
268#41—22no—
269#41—22no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275#41—41no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—941no—
285C22×C4—1882no—
286C22×C4D4×D4711yescharacteristic
287Q16—21no—
288Q16—21no—
289Q16—21no—
290Q16C22⋊Dic4712yes—
291SD16—22no—
292SD16—22no—
293SD16—41no—
294SD16—41no—
295D8—21no—
296D8—21no—
297D8—21no—
298D8C22⋊Dic4712yes—
299M16—1881no—
300M16—1881no—
301C2×C8—941no—
302C2×C8—941no—
303C2×C8—941no—
304C2×C8—1881no—
305C2×C8D4×D4711yescharacteristic
306C2×C8#1062535211yescharacteristic
307C2×C8#1062535211yescharacteristic
308C2×C8C22×Dic4711yescharacteristic
309C2×C8C2×C22⋊D4711yescharacteristic
310C2×C8C2×C22⋊D4711yescharacteristic
311C4⋊C4—942no—
312C4⋊C4—1882no—
313C22⋊C4—1882no—
314C22⋊C4—1881no—
315C42—471no—
316C42—471no—
317C42—941no—
318C42—1882no—
319C42—1881no—
320C16—22no—
321C16—1881no—
322C23—41no—
323C23—41no—
324C23#1309404811yescharacteristic
325Q8—22no—
326Q8—41no—
327Q8—41no—
328Q8—41no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—81no—
336D4—81no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—3764no—
346C2×C4—1882no—
347C2×C4—1882no—
348C2×C4D4×Dic4711yescharacteristic
349C2×C4#1309399211yescharacteristic
350C2×C4#1309399611yescharacteristic
351C2×C4D8×D4711yescharacteristic
352C2×C4#1309404311yescharacteristic
353C2×C4#1309404811yescharacteristic
354C8—3761no—
355C8—1881no—
356C8C2×C22⋊Dic4711yescharacteristic
357C8D4×Dic4711yescharacteristic
358C8#1309399611yescharacteristic
359C8#1309400511yescharacteristic
360C22—41no—
361C22—42no—
362C22—82no—
363C22—82no—
364C22—81no—
365C22#1568923511yescharacteristic
366C22#1568925511yescharacteristic
367C22#1568933611yescharacteristic
368C4—42no—
369C4—81no—
370C4—942no—
371C4—3762no—
372C4—1881no—
373C4#1568900311yescharacteristic
374C4D8×Dic4711yescharacteristic
375C4#1568926511yescharacteristic
376C4#1568931611yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2#2024373811yescharacteristic
subgroupG/H
centerC4#15689316
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
Fitting, prime radicalC47×#3414C2
socleC2×C47#1879
cosocleC22×C8×C47C23
hypercenter#3414D47
hypocenterC47#13027
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #135×Dic47C2semidirect
2. #20245124C2semidirect
3. #20245116C2semidirect
4. #20244277C2semidirect
5. #20241503C2semidirect
6. #20241469C2semidirect
24. C47×#510C4semidirect
26. C47×#509C4semidirect
62. C2×Q16×C47C2×C4semidirect
66. C2×D8×C47C2×C4semidirect
74. M32×C47C2×C4semidirect
203. #510Dic47semidirect
205. #509Dic47semidirect
220. C47#13027semidirect
231. C2×Q16C2×Dic47semidirect
235. C2×D8C2×Dic47semidirect
254. M32C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#135×Dic472
#202451242
#202451162
#202442772
#202415032
#202414692
C47×#34142
#1302747