Finite Group Databasebeta

← #26133463

Subgroups — #26133463

Order 12032.

476 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252272C211yesmaximal, characteristic, complemented
2#20245124C211yesmaximal, characteristic, complemented
3C2×#15688933C211yesmaximal, characteristic, complemented
4#20244287C211yesmaximal, characteristic, complemented
5#20241494C211yesmaximal, characteristic, complemented
6#20241475C211yesmaximal, characteristic, complemented
7C47×#3414C211yesmaximal, characteristic
8#15689606—21no—
9C2×#13093964C2211yescharacteristic
10#15689235—21no—
11#15689230—21no—
12SD16×Dic47—22no—
13#15689161C2211yescharacteristic
14C2×#13093956C2211yescharacteristic
15#15689140—21no—
16#15689124—21no—
17#15689097—21no—
18#15689078C2211yescharacteristic
19#15688933—22no—
20#15688933—22no—
21C2×#135×C47C2211yescharacteristic
22C2×#135×C47C2211yescharacteristic
23C47×#510—21no—
24C47×#510C412yescomplemented
25C47×#509—21no—
26C47×#509C412yescomplemented
27C47×#508—22no—
28C2×M32×C47C2211yescharacteristic
29C2×#10625329D411yescharacteristic
30Q8×Dic47—22no—
31D4×Dic47—22no—
32D4×Dic47—42no—
33#13093983—21no—
34#13093983—41no—
35#13093983D411yescharacteristic
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—41no—
38#13093964—21no—
39#13093964—21no—
40C2×C47⋊C16—21no—
41#13093958—21no—
42#13093956—21no—
43#13093956—21no—
44#13093956D412yes—
45#13093951—42no—
46#13093948—22no—
47#13093945—22no—
48#13093939—42no—
49#13093934—21no—
50C8×Dic47—21no—
51C2×#41×C47—21no—
52C2×#41×C47—21no—
53#135×C47—21no—
54#135×C47—21no—
55#135×C47—21no—
56#135×C47—21no—
57#135×C47—21no—
58#135×C47—21no—
59#135×C47C2×C412yes—
60#135×C47D412yes—
61C2×Q16×C47C2×C411yescharacteristic, complemented
62C2×Q16×C47D411yescharacteristic
63C2×SD16×C47—21no—
64C2×SD16×C47—21no—
65C2×D8×C47C2×C411yescharacteristic, complemented
66C2×D8×C47D411yescharacteristic
67C22×C8×C47C2311yescharacteristic
68Q32×C47—22no—
69SD32×C47—22no—
70SD32×C47—22no—
71D16×C47—22no—
72M32×C47—21no—
73M32×C47C2×C412yescomplemented
74C2×C16×C47—21no—
75#41×C47—22no—
76#41×C47—22no—
77#41×C47—41no—
78#41×C47—41no—
79#41×C47—41no—
80#41×C47—41no—
81#41×C47—41no—
82#41×C47—41no—
83C2×Q8×C47—21no—
84C2×Q8×C47—21no—
85C2×D4×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C22×C4×C47—41no—
90C22×C4×C47—41no—
91C22×C4×C47C2×D411yescharacteristic
92C22×Dic47—42no—
93C22×Dic47—41no—
94Q16×C47—21no—
95Q16×C47—21no—
96Q16×C47—21no—
97Q16×C47C22⋊C412yes—
98SD16×C47—22no—
99SD16×C47—22no—
100SD16×C47—41no—
101SD16×C47—41no—
102D8×C47—21no—
103D8×C47—21no—
104D8×C47—21no—
105D8×C47C22⋊C412yes—
106C2×C8×C47C22×C411yescharacteristic
107C2×C8×C47C2×D411yescharacteristic
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47C2×D411yescharacteristic
110C2×C8×C47#4111yescharacteristic
111C2×C8×C47#4111yescharacteristic
112C22⋊Dic47—42no—
113C22⋊Dic47—41no—
114C22⋊Dic47D812yes—
115C4⋊Dic47—21no—
116C4⋊Dic47—22no—
117C4⋊Dic47—42no—
118C4⋊Dic47—41no—
119C4⋊Dic47—41no—
120C4×Dic47—21no—
121C4×Dic47—42no—
122C4×Dic47—41no—
123#10625329—21no—
124#10625329—21no—
125C2×C47⋊C8—21no—
126C16×C47—22no—
127C47⋊C16—41no—
128C23×C47—41no—
129C23×C47—41no—
130C23×C47C2×D811yescharacteristic
131Q8×C47—22no—
132Q8×C47—41no—
133Q8×C47—41no—
134Q8×C47—41no—
135D4×C47—22no—
136D4×C47—42no—
137D4×C47—42no—
138D4×C47—41no—
139D4×C47—41no—
140D4×C47—41no—
141D4×C47—81no—
142D4×C47—81no—
143C2×C4×C47—41no—
144C2×C4×C47—42no—
145C2×C4×C47—42no—
146C2×C4×C47—41no—
147C2×C4×C47—81no—
148C2×C4×C47—81no—
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47#12011yescharacteristic
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47#13511yescharacteristic
153C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C2×Dic47—22no—
156C2×Dic47—42no—
157C2×Dic47—81no—
158C2×Dic47—162no—
159C2×Dic47—161no—
160C8×C47C2×C22⋊C411yescharacteristic
161C8×C47C4×D411yescharacteristic
162C8×C47#12111yescharacteristic
163C8×C47#12311yescharacteristic
164C47⋊C8—41no—
165#13030—471nomaximal, Sylow
166C22×C47—41no—
167C22×C47—42no—
168C22×C47—81no—
169C22×C47—81no—
170C22×C47—81no—
171C22×C47—161no—
172C22×C47C4×D811yescharacteristic
173C22×C47#44711yescharacteristic
174C22×C47#45911yescharacteristic
175C4×C47—42no—
176C4×C47—81no—
177C4×C47#38611yescharacteristic
178C4×C47#44211yescharacteristic
179C4×C47#44911yescharacteristic
180C4×C47#46311yescharacteristic
181Dic47—42no—
182Dic47—82no—
183Dic47—161no—
184#3414D4711yescharacteristic
185#2952—471no—
186#2145—471no—
187C2×#360—471no—
188#1976—471no—
189#1386—471no—
190#1378—471no—
191C2×C47—21no—
192C2×C47—21no—
193C2×C47—21no—
194C2×C47—82no—
195C2×C47—161no—
196C2×C47#187911yescharacteristic
197C2×#135C2×D4711yescharacteristic
198C2×#135C2×D4711yescharacteristic
199#520—941no—
200#510—21no—
201#510Dic4712yescomplemented
202#509—21no—
203#509Dic4712yescomplemented
204#508—22no—
205C2×M32—471no—
206C2×M32C2×D4711yescharacteristic
207#442—941no—
208#441—941no—
209C4×SD16—942no—
210#427—471no—
211C2×#106—471no—
212#421—941no—
213#417—941no—
214#410—941no—
215#405—471no—
216#360—942no—
217#360—942no—
218C47#1303011yescharacteristic, complemented, Sylow
219C2×#41—21no—
220C2×#41—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135C2×Dic4712yes—
228#135C22⋊D4712yes—
229C2×Q16C2×Dic4711yescharacteristic, complemented
230C2×Q16C22⋊D4711yescharacteristic
231C2×SD16—21no—
232C2×SD16—21no—
233C2×D8C2×Dic4711yescharacteristic, complemented
234C2×D8C22⋊D4711yescharacteristic
235C2×M16—471no—
236C22×C8C22×D4711yescharacteristic
237C4×Q8—942no—
238C4×D4—942no—
239C4×D4—1882no—
240#117—471no—
241#117—941no—
242#117—1881no—
243C2×C4⋊C4—941no—
244C2×C4⋊C4—1881no—
245Q32—22no—
246SD32—22no—
247SD32—22no—
248D16—22no—
249M32—21no—
250M32—941no—
251M32—941no—
252M32C2×Dic4712yescomplemented
253C2×C16—21no—
254C2×C16—941no—
255#107—941no—
256#106—472no—
257#106—941no—
258#106—941no—
259#104—1882no—
260#103—942no—
261#102—942no—
262#99—1882no—
263#97—941no—
264C4×C8—941no—
265#41—22no—
266#41—22no—
267#41—41no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—1882no—
282C22×C4—1881no—
283C22×C4D4×D4711yescharacteristic
284Q16—21no—
285Q16—21no—
286Q16—21no—
287Q16C22⋊Dic4712yes—
288SD16—22no—
289SD16—22no—
290SD16—41no—
291SD16—41no—
292D8—21no—
293D8—21no—
294D8—21no—
295D8C22⋊Dic4712yes—
296M16—941no—
297M16—941no—
298C2×C8—941no—
299C2×C8D4×D4711yescharacteristic
300C2×C8#1062535211yescharacteristic
301C2×C8#1062535211yescharacteristic
302C2×C8C22×Dic4711yescharacteristic
303C2×C8C2×C22⋊D4711yescharacteristic
304C2×C8C2×C22⋊D4711yescharacteristic
305C4⋊C4—941no—
306C4⋊C4—942no—
307C4⋊C4—1882no—
308C4⋊C4—1881no—
309C4⋊C4—1881no—
310C22⋊C4—472no—
311C22⋊C4—1882no—
312C22⋊C4—1881no—
313C42—941no—
314C42—1882no—
315C42—1881no—
316C16—22no—
317C16—1881no—
318C23—41no—
319C23—41no—
320C23D8×D4711yescharacteristic
321Q8—22no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325D4—22no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—942no—
340C2×C4—3761no—
341C2×C4—1882no—
342C2×C4—7521no—
343C2×C4—7522no—
344C2×C4D4×Dic4711yescharacteristic
345C2×C4#1309399211yescharacteristic
346C2×C4#1309399611yescharacteristic
347C2×C4#1309404311yescharacteristic
348C2×C4#1309404811yescharacteristic
349C2×C4#1309404811yescharacteristic
350C8—1881no—
351C8C2×C22⋊Dic4711yescharacteristic
352C8D4×Dic4711yescharacteristic
353C8#1309399611yescharacteristic
354C8#1309400511yescharacteristic
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—161no—
361C22D8×Dic4711yescharacteristic
362C22#1568925511yescharacteristic
363C22#1568931611yescharacteristic
364C4—42no—
365C4—81no—
366C4—3762no—
367C4—1882no—
368C4—7521no—
369C4#1568900311yescharacteristic
370C4#1568923511yescharacteristic
371C4#1568926511yescharacteristic
372C4#1568933611yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—161no—
378C2#2024373811yescharacteristic
subgroupG/H
centerC2#20243738
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
Fitting, prime radicalC47×#3414C2
socleC2×C47#1879
cosocleC22×C8×C47C23
hypercenter#3414D47
hypocenterC47#13030
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #20252272C2semidirect
2. #20245124C2semidirect
3. C2×#15688933C2semidirect
4. #20244287C2semidirect
5. #20241494C2semidirect
6. #20241475C2semidirect
24. C47×#510C4semidirect
26. C47×#509C4semidirect
61. C2×Q16×C47C2×C4semidirect
65. C2×D8×C47C2×C4semidirect
73. M32×C47C2×C4semidirect
201. #510Dic47semidirect
203. #509Dic47semidirect
218. C47#13030semidirect
229. C2×Q16C2×Dic47semidirect
233. C2×D8C2×Dic47semidirect
252. M32C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202522722
#202451242
C2×#156889332
#202442872
#202414942
#202414752
C47×#34142
#1303047