Finite Group Databasebeta

← #26133407

Subgroups — #26133407

Order 12032.

494 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252264C211yesmaximal, characteristic, complemented
2C2×#15688930C211yesmaximal, characteristic, complemented
3C2×#15688924C211yesmaximal, characteristic, complemented
4#20244299C211yesmaximal, characteristic, complemented
5#20241497C211yesmaximal, characteristic, complemented
6#20241478C211yesmaximal, characteristic, complemented
7C2×C47×#509C211yesmaximal, characteristic
8#15689606—21no—
9C22×C47⋊C16C2211yescharacteristic
10#15689224—22no—
11Q16×Dic47—21no—
12D8×Dic47—21no—
13C2×#13093960C2211yescharacteristic
14C2×#13093958C2211yescharacteristic
15#15689128—21no—
16#15689124—21no—
17C2×#13093941—21no—
18#15689078C2211yescharacteristic
19#15688930—22no—
20#15688924—22no—
21C2×#135×C47C2211yescharacteristic
22C22×D8×C47C2211yescharacteristic
23C47×#509—22no—
24C47×#509C414yescomplemented
25C2×SD32×C47—21no—
26C2×D16×C47—21no—
27C2×M32×C47C2211yescharacteristic
28C2×#10625329—21no—
29C2×#10625329D411yescharacteristic
30Q8×Dic47—22no—
31D4×Dic47—22no—
32D4×Dic47—42no—
33#13093983—41no—
34#13093983D411yescharacteristic
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—41no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40#13093960—21no—
41#13093960—21no—
42#13093958—21no—
43#13093958D412yes—
44#13093948—22no—
45#13093945—22no—
46#13093945—41no—
47#13093945—41no—
48#13093941—42no—
49#13093934—21no—
50C8×Dic47—21no—
51C2×#41×C47—21no—
52C22×D4×C47—21no—
53#135×C47—21no—
54#135×C47—21no—
55#135×C47C2×C412yes—
56#135×C47D412yes—
57C2×Q16×C47D411yescharacteristic
58C2×SD16×C47—21no—
59C2×D8×C47—21no—
60C2×D8×C47—21no—
61C2×D8×C47—21no—
62C2×D8×C47—21no—
63C2×D8×C47—21no—
64C2×D8×C47C2×C412yescomplemented
65C2×D8×C47D411yescharacteristic
66C22×C8×C47C2311yescharacteristic
67SD32×C47—24no—
68D16×C47—24no—
69M32×C47—21no—
70M32×C47C2×C412yescomplemented
71C2×C16×C47—21no—
72C24×C47—41no—
73#41×C47—22no—
74#41×C47—22no—
75#41×C47—41no—
76#41×C47—41no—
77C2×Q8×C47—21no—
78C2×D4×C47—22no—
79C2×D4×C47—21no—
80C2×D4×C47—41no—
81C2×D4×C47—41no—
82C2×D4×C47—41no—
83C2×D4×C47—41no—
84C2×D4×C47—41no—
85C2×D4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47C2×D411yescharacteristic
88C22×Dic47—42no—
89C22×Dic47—41no—
90Q16×C47—21no—
91Q16×C47C22⋊C412yes—
92SD16×C47—22no—
93SD16×C47—22no—
94D8×C47—22no—
95D8×C47—22no—
96D8×C47—21no—
97D8×C47—41no—
98D8×C47—41no—
99D8×C47C22⋊C412yes—
100C2×C8×C47C22×C411yescharacteristic
101C2×C8×C47C2×D411yescharacteristic
102C2×C8×C47C2×D411yescharacteristic
103C2×C8×C47C2×D411yescharacteristic
104C2×C8×C47#4111yescharacteristic
105C2×C8×C47#4111yescharacteristic
106C22⋊Dic47—21no—
107C22⋊Dic47—42no—
108C4⋊Dic47—22no—
109C4⋊Dic47—42no—
110C4⋊Dic47—41no—
111C4⋊Dic47D811yescharacteristic
112C4⋊Dic47D811yescharacteristic
113C4×Dic47—21no—
114C4×Dic47—42no—
115#10625329—21no—
116#10625329—21no—
117#10625329—41no—
118#10625329—41no—
119C2×C47⋊C8—21no—
120C2×C47⋊C8—41no—
121C16×C47—22no—
122C47⋊C16—41no—
123C23×C47—41no—
124C23×C47—42no—
125C23×C47—81no—
126C23×C47—81no—
127C23×C47—161no—
128C23×C47—161no—
129C23×C47AGL(1,ℤ/8)11yescharacteristic
130Q8×C47—22no—
131Q8×C47—41no—
132D4×C47—22no—
133D4×C47—42no—
134D4×C47—42no—
135D4×C47—42no—
136D4×C47—42no—
137D4×C47—41no—
138D4×C47—81no—
139D4×C47—81no—
140C2×C4×C47—41no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47C4×D411yescharacteristic
144C2×C4×C47#12011yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47C2×D811yescharacteristic
147C2×C4×C47#13511yescharacteristic
148C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—42no—
152C2×Dic47—162no—
153C2×Dic47—161no—
154C8×C47C2×C22⋊C411yescharacteristic
155C8×C47C4×D411yescharacteristic
156C8×C47#12111yescharacteristic
157C8×C47#12311yescharacteristic
158C47⋊C8—41no—
159C47⋊C8—81no—
160#13022—471nomaximal, Sylow
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—42no—
164C22×C47—81no—
165C22×C47—81no—
166C22×C47—82no—
167C22×C47—162no—
168C22×C47—162no—
169C22×C47—161no—
170C22×C47—161no—
171C22×C47#44211yescharacteristic
172C22×C47#44711yescharacteristic
173C22×C47#46311yescharacteristic
174C4×C47—42no—
175C4×C47#38611yescharacteristic
176C4×C47C4×D811yescharacteristic
177C4×C47#44911yescharacteristic
178C4×C47#45911yescharacteristic
179Dic47—41no—
180Dic47—41no—
181Dic47—82no—
182C2×#509D4711yescharacteristic
183#2951—471no—
184C2×#359—471no—
185C2×#357—471no—
186#1978—471no—
187#1387—471no—
188#1379—471no—
189C2×C47—21no—
190C2×C47—21no—
191C2×C47—82no—
192C2×C47—162no—
193C2×C47#187911yescharacteristic
194C2×C47#219211yescharacteristic
195C2×C47#219311yescharacteristic
196C2×#135C2×D4711yescharacteristic
197C22×D8C2×D4711yescharacteristic
198#520—941no—
199#509—22no—
200#509Dic4714yescomplemented
201C2×SD32—21no—
202C2×D16—21no—
203C2×M32C2×D4711yescharacteristic
204C22×C16—471no—
205#440—942no—
206C4×Q16—941no—
207C4×D8—941no—
208C2×#108—471no—
209C2×#107—471no—
210#418—941no—
211#417—941no—
212C2×#100—941no—
213#405—471no—
214#359—942no—
215#357—942no—
216C47#1302211yescharacteristic, complemented, Sylow
217C2×#41—21no—
218C22×D4—21no—
219#135—21no—
220#135—21no—
221#135C2×Dic4712yes—
222#135C22⋊D4712yes—
223C2×Q16C22⋊D4711yescharacteristic
224C2×SD16—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8C2×Dic4712yescomplemented
231C2×D8C22⋊D4711yescharacteristic
232C2×M16—471no—
233C2×M16—941no—
234C22×C8C22×D4711yescharacteristic
235C4×Q8—942no—
236C4×D4—942no—
237C4×D4—1882no—
238#117—471no—
239#117—1881no—
240C2×C4⋊C4—941no—
241C2×C4⋊C4—1881no—
242SD32—24no—
243D16—24no—
244M32—21no—
245M32C2×Dic4712yescomplemented
246C2×C16—21no—
247C2×C16—941no—
248C2×C16—941no—
249C2×C16—941no—
250#108—941no—
251#108—941no—
252#107—472no—
253#107—941no—
254#103—942no—
255#102—942no—
256#102—1881no—
257#102—1881no—
258#100—1882no—
259#97—941no—
260C4×C8—941no—
261C24—41no—
262#41—22no—
263#41—22no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—1882no—
277C22×C4—1881no—
278C22×C4D4×D4711yescharacteristic
279Q16—21no—
280Q16C22⋊Dic4712yes—
281SD16—22no—
282SD16—22no—
283D8—22no—
284D8—22no—
285D8—21no—
286D8—41no—
287D8—41no—
288D8C22⋊Dic4712yes—
289M16—941no—
290M16—941no—
291M16—1881no—
292M16—1881no—
293C2×C8—941no—
294C2×C8—1881no—
295C2×C8D4×D4711yescharacteristic
296C2×C8#1062535211yescharacteristic
297C2×C8#1062535211yescharacteristic
298C2×C8C22×Dic4711yescharacteristic
299C2×C8C2×C22⋊D4711yescharacteristic
300C2×C8C2×C22⋊D4711yescharacteristic
301C4⋊C4—471no—
302C4⋊C4—471no—
303C4⋊C4—942no—
304C4⋊C4—1882no—
305C4⋊C4—1881no—
306C22⋊C4—941no—
307C22⋊C4—1882no—
308C42—941no—
309C42—1882no—
310C16—22no—
311C16—1881no—
312C23—41no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—161no—
317C23—161no—
318C23#1309404811yescharacteristic
319Q8—22no—
320Q8—41no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—42no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—1882no—
335C2×C4—7521no—
336C2×C4—7522no—
337C2×C4D4×Dic4711yescharacteristic
338C2×C4#1309399211yescharacteristic
339C2×C4#1309399611yescharacteristic
340C2×C4D8×D4711yescharacteristic
341C2×C4#1309404311yescharacteristic
342C2×C4#1309404811yescharacteristic
343C8—3761no—
344C8—1881no—
345C8C2×C22⋊Dic4711yescharacteristic
346C8D4×Dic4711yescharacteristic
347C8#1309399611yescharacteristic
348C8#1309400511yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22—162no—
356C22—162no—
357C22—161no—
358C22—161no—
359C22#1568923511yescharacteristic
360C22#1568925511yescharacteristic
361C22#1568933611yescharacteristic
362C4—42no—
363C4—3762no—
364C4—1881no—
365C4—1881no—
366C4#1568900311yescharacteristic
367C4D8×Dic4711yescharacteristic
368C4#1568926511yescharacteristic
369C4#1568931611yescharacteristic
370C2—21no—
371C2—21no—
372C2—82no—
373C2—162no—
374C2#2024373811yescharacteristic
375C2#2024534211yescharacteristic
376C2#2024534911yescharacteristic
subgroupG/H
centerC22#15689255
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
Fitting, prime radicalC2×C47×#509C2
socleC22×C47#447
cosocleC22×C8×C47C23
hypercenterC2×#509D47
hypocenterC47#13022
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #20252264C2semidirect
2. C2×#15688930C2semidirect
3. C2×#15688924C2semidirect
4. #20244299C2semidirect
5. #20241497C2semidirect
6. #20241478C2semidirect
24. C47×#509C4semidirect
64. C2×D8×C47C2×C4semidirect
70. M32×C47C2×C4semidirect
200. #509Dic47semidirect
216. C47#13022semidirect
230. C2×D8C2×Dic47semidirect
245. M32C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202522642
C2×#156889302
C2×#156889242
#202442992
#202414972
#202414782
C2×C47×#5092
#1302247