Finite Group Databasebeta

← #26135434

Subgroups — #26135434

Order 12032.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689359C211yesmaximal, characteristic
2C2×#15688949C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic, complemented
4C2×#15688925C211yesmaximal, characteristic, complemented
5#20243417C211yesmaximal, characteristic, complemented
6#20241480C211yesmaximal, characteristic, complemented
7C2×C47×C22⋊C16C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13093998—21no—
10#15689359—22no—
11#15689359—22no—
12C2×#13093958C2211yescharacteristic
13C2×#13093958C2211yescharacteristic
14C2×#13093958C2211yescharacteristic
15C2×#13093946—21no—
16#15688983—21no—
17#15688949—22no—
18#15688925—22no—
19#15688925—22no—
20#15688886—21no—
21C23×C8×C47C2211yescharacteristic
22C22×C16×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C47×C22⋊C16—22no—
25C22×D188—21no—
26C22×C22⋊D47—41no—
27C2×D376—21no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376D412yes—
33#13093998—24no—
34#13093998—42no—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—21no—
38C2×C22⋊Dic47—41no—
39C2×(C2×D47)⋊C4—41no—
40#13093958—21no—
41#13093958—21no—
42#13093958—21no—
43#13093958—21no—
44#13093958—21no—
45#13093958D412yes—
46#13093946—24no—
47C47⋊#95—41no—
48C23×C4×C47D411yescharacteristic
49C22×C8×C47—21no—
50C22×C8×C47—21no—
51C22×C8×C47—21no—
52C22×C8×C47—21no—
53C22×C8×C47—21no—
54C22×C8×C47—21no—
55C22×C8×C47D411yescharacteristic
56C22×C8×C47C2311yescharacteristic
57C2×C16×C47—21no—
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47D412yescomplemented
63C24×C47D811yescharacteristic
64C23×D47—41no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47D811yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C2×C22⋊D47—44no—
74C2×C22⋊D47—82no—
75C2×C22⋊D47—82no—
76C22×Dic47—41no—
77C22×Dic47—41no—
78C22×Dic47—41no—
79C2×D188—22no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×C8×C47—21no—
86C2×C8×C47—21no—
87C2×C8×C47—21no—
88C2×C8×C47—41no—
89C2×C8×C47—41no—
90C2×C8×C47—41no—
91C2×C8×C47—41no—
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C2×C8×C47#4111yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C22⋊Dic47—82no—
99(C2×D47)⋊C4—44no—
100C4⋊Dic47—22no—
101C4⋊Dic47—41no—
102C4⋊Dic47—41no—
103C4⋊Dic47—41no—
104C4⋊Dic47—41no—
105C4⋊Dic47—41no—
106D376—22no—
107D376—22no—
108D376—41no—
109D376—41no—
110C16×C47—22no—
111C16×C47—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47D1612yes—
119C23×C47C2×D811yescharacteristic
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123C22×D47—81no—
124C22×D47—81no—
125C22×D47—81no—
126C22×D47—81no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47#12011yescharacteristic
135C2×C4×C47#12111yescharacteristic
136C2×C4×C47#12311yescharacteristic
137C2×C4×C47#13511yescharacteristic
138C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C47#13711yescharacteristic
140C22⋊D47—88no—
141C2×Dic47—42no—
142C2×Dic47—81no—
143C2×Dic47—81no—
144C2×Dic47—81no—
145C2×Dic47—81no—
146C2×Dic47—81no—
147C2×Dic47—81no—
148C2×Dic47—81no—
149C2×Dic47—81no—
150D188—42no—
151D188—42no—
152D188—81no—
153D188—81no—
154C8×C47—41no—
155C8×C47#12111yescharacteristic
156C8×C47#12111yescharacteristic
157C8×C47#12311yescharacteristic
158C8×C47#12411yescharacteristic
159#13380—471nomaximal, Sylow
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47#44711yescharacteristic
168C22×C47#46611yescharacteristic
169C22×C47#48011yescharacteristic
170C22×C47C2×D1611yescharacteristic
171C22×C47#50811yescharacteristic
172C22×C47#50911yescharacteristic
173C22×C47#51011yescharacteristic
174C2×D47—82no—
175C2×D47—82no—
176C2×D47—82no—
177C2×D47—161no—
178C2×D47—161no—
179C2×D47—161no—
180C2×D47—161no—
181C4×C47—41no—
182C4×C47#39411yescharacteristic
183C4×C47#45211yescharacteristic
184C4×C47#46811yescharacteristic
185C4×C47#48211yescharacteristic
186Dic47—82no—
187Dic47—161no—
188Dic47—161no—
189C2×#466—471no—
190C2×#366—471no—
191C2×#357—471no—
192C2×#357—471no—
193C2×C22⋊C16D4711yescharacteristic, complemented
194#1808—471no—
195#1380—471no—
196C2×C47—42no—
197C2×C47#203311yescharacteristic
198C2×C47#218411yescharacteristic
199C2×C47#218911yescharacteristic
200C2×C47#221511yescharacteristic
201C2×C47#222011yescharacteristic
202C2×C47#223211yescharacteristic
203C2×C47#223411yescharacteristic
204D47—162no—
205C22×D8—471no—
206C23×C8C2×D4711yescharacteristic
207C2×#121—941no—
208C22×C16C2×D4711yescharacteristic
209C22×C16C2×D4711yescharacteristic
210#466—942no—
211#466—942no—
212C2×#107—471no—
213C2×#107—471no—
214C2×#107—471no—
215C2×#102—941no—
216#380—941no—
217#366—942no—
218#357—942no—
219#357—942no—
220C22⋊C16—22no—
221#340—941no—
222C47#1338011yescharacteristic, complemented, Sylow
223C22×D4—941no—
224C22×D4—1881no—
225C23×C4D18811yescharacteristic
226C2×D8—472no—
227C2×D8—941no—
228C2×D8—941no—
229C2×D8—941no—
230C2×D8—941no—
231C2×D8—941no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8D18811yescharacteristic
239C22×C8C22×D4711yescharacteristic
240#121—944no—
241#121—1882no—
242C2×C4⋊C4—941no—
243C2×C4⋊C4—941no—
244C2×C4⋊C4—941no—
245C2×C22⋊C4—1881no—
246C2×C22⋊C4—1881no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16C22⋊D4712yescomplemented
253#107—472no—
254#107—941no—
255#107—941no—
256#107—941no—
257#107—941no—
258#107—941no—
259#102—944no—
260#95—1881no—
261C24—1881no—
262C24D37611yescharacteristic
263C2×D4—942no—
264C2×D4—3762no—
265C2×D4—3762no—
266C2×D4—1884no—
267C2×D4—1881no—
268C2×D4—1881no—
269C2×D4—1881no—
270C2×D4—1881no—
271C2×D4—1881no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1881no—
279C22×C4—1881no—
280C22×C4—1881no—
281C22×C4D37611yescharacteristic
282C22×C4C2×D18811yescharacteristic
283D8—942no—
284D8—942no—
285D8—1881no—
286D8—1881no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8#1062535011yescharacteristic
295C2×C8D4×D4711yescharacteristic
296C2×C8D4×D4711yescharacteristic
297C2×C8#1062535211yescharacteristic
298C2×C8#1062535211yescharacteristic
299C2×C8C2×C22⋊D4711yescharacteristic
300C4⋊C4—942no—
301C4⋊C4—1881no—
302C4⋊C4—1881no—
303C4⋊C4—1881no—
304C4⋊C4—1881no—
305C4⋊C4—1881no—
306C22⋊C4—3762no—
307C22⋊C4—1884no—
308C16—22no—
309C16—41no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—3761no—
317C23—3761no—
318C23—3761no—
319C23—3761no—
320C23—3761no—
321C23—3761no—
322C23—1882no—
323C23D75212yes—
324C23C2×D37611yescharacteristic
325D4—3768no—
326D4—3761no—
327D4—3761no—
328D4—1882no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—3761no—
338C2×C4—3761no—
339C2×C4—3761no—
340C2×C4—3761no—
341C2×C4—3761no—
342C2×C4—3761no—
343C2×C4—3761no—
344C2×C4—3761no—
345C2×C4—1882no—
346C2×C4#1309399411yescharacteristic
347C2×C4#1309399811yescharacteristic
348C2×C4#1309400811yescharacteristic
349C2×C4#1309404611yescharacteristic
350C2×C4#1309405211yescharacteristic
351C2×C4#1309405711yescharacteristic
352C8—41no—
353C8#1309399511yescharacteristic
354C8#1309399611yescharacteristic
355C8#1309400611yescharacteristic
356C8#1309401011yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—3762no—
365C22—3762no—
366C22—3762no—
367C22—7521no—
368C22—7521no—
369C22—7521no—
370C22—7521no—
371C22#1568925911yescharacteristic
372C22#1568935911yescharacteristic
373C22#1568943711yescharacteristic
374C22C2×D75211yescharacteristic
375C22#1568955511yescharacteristic
376C22#1568956111yescharacteristic
377C22#1568956611yescharacteristic
378C4—41no—
379C4—3762no—
380C4—7521no—
381C4—7521no—
382C4#1568903911yescharacteristic
383C4#1568928711yescharacteristic
384C4#1568936911yescharacteristic
385C4#1568944811yescharacteristic
386C2—42no—
387C2—7522no—
388C2#2024457111yescharacteristic
389C2#2024530211yescharacteristic
390C2#2024533011yescharacteristic
391C2#2024547411yescharacteristic
392C2#2024550111yescharacteristic
393C2#2024556911yescharacteristic
394C2#2024558011yescharacteristic
subgroupG/H
centerC23C2×D376
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC2×C47×C22⋊C16C2
socleC23×C47C2×D8
prime radicalC2×#15689359C2
hypercenterC2×C22⋊C16D47
hypocenterC47#13380
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#15688949C2semidirect
3. C2×#15688925C2semidirect
4. C2×#15688925C2semidirect
5. #20243417C2semidirect
6. #20241480C2semidirect
7. C2×C47×C22⋊C16C2semidirect
62. C2×C16×C47D4semidirect
193. C2×C22⋊C16D47semidirect
222. C47#13380semidirect
252. C2×C16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156893592
C2×#156889492
C2×#156889252
#202434172
#202414802
C2×C47×C22⋊C162
#1338047