Finite Group Databasebeta

← #26133333

Subgroups — #26133333

Order 12032.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093965C211yesmaximal, characteristic
2C2×D8×Dic47C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic, complemented
4#20244252C211yesmaximal, characteristic, complemented
5#20241479C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×D4×Dic47—21no—
10C2×#13093965—22no—
11C2×#13093965—22no—
12C2×#13093965C414yescomplemented
13C22×C47⋊C16C2211yescharacteristic
14D8×Dic47—22no—
15D8×Dic47—22no—
16C2×#13093958C2211yescharacteristic
17C2×#13093945—21no—
18C2×#13093944—21no—
19C2×C8×Dic47C2211yescharacteristic
20#15689024—21no—
21#15688925—22no—
22C22×D8×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#357—22no—
26C22×D188—21no—
27C23×Dic47—41no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376C2×C412yescomplemented
34C22×C47⋊C8D411yescharacteristic
35D4×Dic47—24no—
36D4×Dic47—42no—
37C2×C4⋊Dic47—21no—
38C2×C22⋊Dic47—41no—
39C2×(C2×D47)⋊C4—41no—
40C2×(C2×D47)⋊C4—41no—
41C2×C4×Dic47D411yescharacteristic
42#13093965—28no—
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16C2×C412yescomplemented
46#13093958—21no—
47#13093958D412yes—
48#13093945—24no—
49#13093944—42no—
50C8×Dic47—21no—
51C8×Dic47—21no—
52C22×D4×C47—21no—
53C2×D8×C47—21no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C2×D8×C47C2×C412yes—
57C2×D8×C47D412yes—
58C2×D8×C47D412yes—
59C22×C8×C47C2311yescharacteristic
60C2×C4⋊C4×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47—21no—
63C2×C16×C47—21no—
64#107×C47—21no—
65#107×C47—21no—
66C24×C47—41no—
67C23×D47—41no—
68C2×D4×C47—22no—
69C2×D4×C47—22no—
70C2×D4×C47—22no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C2×D4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47C2×D411yescharacteristic
76C22×Dic47—44no—
77C22×Dic47—41no—
78C22×Dic47—82no—
79C22×Dic47—82no—
80C22×Dic47D811yescharacteristic
81C22×Dic47D811yescharacteristic
82C2×D188—22no—
83C2×D188—41no—
84C2×D188—41no—
85C2×D188—41no—
86C2×D188—41no—
87C2×D188—41no—
88D8×C47—22no—
89D8×C47—22no—
90D8×C47—22no—
91D8×C47C22⋊C414yescomplemented
92C2×C8×C47C22×C411yescharacteristic
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47#4111yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C22⋊Dic47—44no—
101(C2×D47)⋊C4—82no—
102(C2×D47)⋊C4—82no—
103C4⋊Dic47—22no—
104C4⋊Dic47—41no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110D376—22no—
111D376—22no—
112D376—41no—
113D376—41no—
114C16×C47—41no—
115C47⋊C16—22no—
116C23×C47—42no—
117C23×C47—42no—
118C23×C47—42no—
119C23×C47—81no—
120C23×C47—81no—
121C23×C47—81no—
122C23×C47—81no—
123C23×C47C2×D811yescharacteristic
124C22×D47—42no—
125C22×D47—81no—
126C22×D47—81no—
127C22×D47—81no—
128C22×D47—81no—
129C22×D47—81no—
130C22×D47—81no—
131D4×C47—24no—
132D4×C47—42no—
133D4×C47—42no—
134D4×C47—42no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47#13511yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—42no—
150C2×Dic47—88no—
151C2×Dic47—81no—
152C2×Dic47—81no—
153C2×Dic47D1612yescomplemented
154D188—42no—
155D188—42no—
156D188—81no—
157D188—81no—
158C8×C47C2×C22⋊C411yescharacteristic
159C8×C47C4×D411yescharacteristic
160C8×C47#12111yescharacteristic
161C8×C47#12311yescharacteristic
162C47⋊C8—41no—
163#13012—471nomaximal, Sylow
164C22×C47—44no—
165C22×C47—82no—
166C22×C47—82no—
167C22×C47—82no—
168C22×C47—82no—
169C22×C47—82no—
170C22×C47—82no—
171C22×C47C4×D811yescharacteristic
172C22×C47#44711yescharacteristic
173C22×C47#45911yescharacteristic
174C22×C47C2×D1611yescharacteristic
175C22×C47#50811yescharacteristic
176C22×C47#50911yescharacteristic
177C22×C47#50911yescharacteristic
178C2×D47—82no—
179C2×D47—82no—
180C2×D47—82no—
181C2×D47—161no—
182C2×D47—161no—
183C2×D47—161no—
184C2×D47—161no—
185C4×C47—161no—
186C4×C47#38611yescharacteristic
187C4×C47#44211yescharacteristic
188C4×C47#44911yescharacteristic
189C4×C47#46311yescharacteristic
190Dic47—22no—
191Dic47—41no—
192Dic47—82no—
193C22×D16—471no—
194C2×C4×D8—471no—
195C2×#357—471no—
196C2×#357D4711yescharacteristic, complemented
197#1970—471no—
198#1380—471no—
199#1374—471no—
200C2×C47—84no—
201C2×C47#187911yescharacteristic
202C2×C47C4×D1611yescharacteristic
203C2×C47#217711yescharacteristic
204C2×C47#218411yescharacteristic
205C2×C47#218611yescharacteristic
206C2×C47#220611yescharacteristic
207C2×C47#221011yescharacteristic
208D47—162no—
209C22×D8—471no—
210C22×D8C2×D4711yescharacteristic
211C2×C4×D4—941no—
212C2×D16—474no—
213C2×D16—942no—
214C2×D16—942no—
215C22×C16—471no—
216C22×C16C2×D4711yescharacteristic
217C4×D8—942no—
218C4×D8—942no—
219C2×#107—471no—
220C2×#107C2×D4711yescharacteristic
221C2×#102—941no—
222C2×#102—941no—
223C2×C4×C8—471no—
224#390—941no—
225#357—22no—
226#357—942no—
227C47#1301211yescharacteristic, complemented, Sylow
228C22×D4—21no—
229C22×D4—941no—
230C23×C4—1881no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—472no—
235C2×D8—941no—
236C2×D8—941no—
237C2×D8—941no—
238C2×D8—941no—
239C2×D8—941no—
240C2×D8C4×D4712yes—
241C2×D8D18812yes—
242C2×D8C22⋊D4712yes—
243C22×C8—471no—
244C22×C8C22×D4711yescharacteristic
245C4×D4—944no—
246C4×D4—1882no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—941no—
249C2×C22⋊C4—1881no—
250C2×C22⋊C4—1881no—
251C2×C22⋊C4—1881no—
252C2×C42—471no—
253D16—948no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—472no—
258C2×C16—941no—
259C2×C16—941no—
260#107—21no—
261#107—21no—
262#107—472no—
263#107—941no—
264#102—944no—
265#102—1882no—
266C4×C8—941no—
267C4×C8—941no—
268C24—41no—
269C24—1881no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—942no—
277C2×D4—1881no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4—1881no—
281C2×D4—1881no—
282C22×C4—41no—
283C22×C4—471no—
284C22×C4—471no—
285C22×C4—3762no—
286C22×C4—3762no—
287C22×C4—1884no—
288C22×C4—1881no—
289C22×C4D4×D4711yescharacteristic
290D8—22no—
291D8—22no—
292D8—22no—
293D8—942no—
294D8—942no—
295D8—1881no—
296D8—1881no—
297D8(C2×D47)⋊C414yescomplemented
298C2×C8—941no—
299C2×C8—941no—
300C2×C8—941no—
301C2×C8C2×C4×D4711yescharacteristic
302C2×C8C2×D18811yescharacteristic
303C2×C8D4×D4711yescharacteristic
304C2×C8#1062535211yescharacteristic
305C2×C8#1062535211yescharacteristic
306C2×C8C2×C22⋊D4711yescharacteristic
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—942no—
310C4⋊C4—1881no—
311C22⋊C4—3762no—
312C22⋊C4—3762no—
313C22⋊C4—1884no—
314C42—941no—
315C42—941no—
316C16—41no—
317C16—942no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—3761no—
326C23—3761no—
327C23—3761no—
328C23—3761no—
329C23—3761no—
330C23—3761no—
331C23—1882no—
332C23D8×D4711yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—3761no—
338D4—3761no—
339D4—1882no—
340D4—1882no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—472no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—3768no—
351C2×C4—3761no—
352C2×C4—3761no—
353C2×C4—1882no—
354C2×C4(C22⋊D47)⋊C411yescharacteristic
355C2×C4#1309399411yescharacteristic
356C2×C4#1309399611yescharacteristic
357C2×C4#1309404511yescharacteristic
358C2×C4#1309404811yescharacteristic
359C2×C4#1309405111yescharacteristic
360C8—1881no—
361C8C2×(C2×D47)⋊C411yescharacteristic
362C8(C22⋊D47)⋊C411yescharacteristic
363C8#1309399611yescharacteristic
364C8#1309400811yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—3762no—
373C22—3762no—
374C22—3762no—
375C22—7521no—
376C22—7521no—
377C22—7521no—
378C22—7521no—
379C22#1568920311yescharacteristic
380C22#1568925811yescharacteristic
381C22#1568931611yescharacteristic
382C22D16×D4711yescharacteristic
383C22#1568955411yescharacteristic
384C22#1568955711yescharacteristic
385C22#1568956011yescharacteristic
386C4—161no—
387C4—942no—
388C4—3762no—
389C4—1881no—
390C4#1568900011yescharacteristic
391C4#1568923211yescharacteristic
392C4#1568926911yescharacteristic
393C4#1568934011yescharacteristic
394C2—84no—
395C2—7522no—
396C2#2024373411yescharacteristic
397C2#2024523211yescharacteristic
398C2#2024526111yescharacteristic
399C2#2024530111yescharacteristic
400C2#2024531211yescharacteristic
401C2#2024542111yescharacteristic
402C2#2024544511yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC22×#13093965C2
cosocleC22×C8×C47C23
hypercenterC2×#357D47
hypocenterC47#13012
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic47C2semidirect
3. C2×#15688925C2semidirect
4. #20244252C2semidirect
5. #20241479C2semidirect
6. #20241465C2semidirect
7. C2×C47×#357C2semidirect
12. C2×#13093965C4semidirect
33. C2×D376C2×C4semidirect
45. C2×C47⋊C16C2×C4semidirect
91. D8×C47C22⋊C4semidirect
153. C2×Dic47D16semidirect
196. C2×#357D47semidirect
227. C47#13012semidirect
297. D8(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130939652
C2×D8×Dic472
C2×#156889252
#202442522
#202414792
#202414652
C2×C47×#3572
#1301247