Finite Group Databasebeta

← #26133350

Subgroups — #26133350

Order 12032.

554 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
1C22×#13093969C211yesmaximal, characteristic
2C2×#15689205C211yesmaximal, characteristic
3C2×#15688926C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic
5#20244247C211yesmaximal, characteristic, complemented
6#20241465C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×Dic188C2211yescharacteristic
9C22×D376C2211yescharacteristic
10C2×#13093986—21no—
11C2×#13093969—22no—
12C2×#13093969—22no—
13C2×#13093969C414yescomplemented
14C22×C47⋊C16C2211yescharacteristic
15#15689205—22no—
16#15689205—22no—
17C2×#13093947—21no—
18C2×#13093944—21no—
19C2×C8×Dic47C2211yescharacteristic
20#15689028—21no—
21#15688926—22no—
22#15688923—22no—
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C22×Dic94—21no—
27C22×D188—21no—
28C22×C4×D47—41no—
29C2×Dic188—21no—
30C2×Dic188—21no—
31C2×Dic188—21no—
32C2×Dic188—21no—
33C2×Dic188—21no—
34C2×Dic188C2×C412yescomplemented
35C2×D376—21no—
36C2×D376—21no—
37C2×D376—21no—
38C2×D376C2×C412yes—
39C2×D376D412yes—
40C2×D376D412yes—
41C22×C47⋊C8D411yescharacteristic
42#13093986—24no—
43#13093986—42no—
44C2×(C2×D47)⋊C4—41no—
45C2×C4×Dic47D411yescharacteristic
46#13093969—28no—
47C2×C47⋊C16—21no—
48C2×C47⋊C16—21no—
49C2×C47⋊C16—21no—
50#13093947—42no—
51#13093944—24no—
52C8×Dic47—21no—
53C8×Dic47—21no—
54C47⋊#95—41no—
55C47⋊#95—41no—
56C22×C8×C47C2311yescharacteristic
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47C2×C412yescomplemented
62#107×C47—21no—
63#107×C47—21no—
64#107×C47—21no—
65#107×C47D412yes—
66C23×D47—41no—
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47—41no—
71C22×Dic47D811yescharacteristic
72C22×Dic47D811yescharacteristic
73C2×D188—22no—
74C2×D188—22no—
75C2×D188—22no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×C4×D47—44no—
80C2×C4×D47—82no—
81C2×C4×D47—82no—
82C2×Dic94—22no—
83C2×Dic94—41no—
84C2×Dic94—41no—
85C2×Dic94—41no—
86C2×Dic94—41no—
87C2×Dic94—41no—
88C2×C8×C47C22×C411yescharacteristic
89C2×C8×C47C2×D411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47C2×D411yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C2×C8×C47#4111yescharacteristic
94C4⋊C4×C47—22no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47—41no—
98(C2×D47)⋊C4—44no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C2×C47⋊C8—21no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104Dic188—22no—
105Dic188—22no—
106Dic188—41no—
107Dic188—41no—
108D376—22no—
109D376—22no—
110D376—22no—
111D376C22⋊C414yes—
112C16×C47—22no—
113C47⋊C16—41no—
114C23×C47C2×D811yescharacteristic
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47—81no—
122C2×C4×C47—42no—
123C2×C4×C47—81no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47C4×D411yescharacteristic
129C2×C4×C47#12011yescharacteristic
130C2×C4×C47#12111yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—42no—
140C2×Dic47—81no—
141C2×Dic47—81no—
142C2×Dic47SD3212yescomplemented
143D188—24no—
144D188—42no—
145D188—42no—
146D188—42no—
147C4×D47—88no—
148Dic94—42no—
149Dic94—42no—
150Dic94—81no—
151Dic94—81no—
152C8×C47C2×C22⋊C411yescharacteristic
153C8×C47C4×D411yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12311yescharacteristic
156C47⋊C8—41no—
157#13014—471nomaximal, Sylow
158C22×C47C4×D811yescharacteristic
159C22×C47#44711yescharacteristic
160C22×C47#45911yescharacteristic
161C22×C47C2×SD3211yescharacteristic
162C22×C47#50811yescharacteristic
163C22×C47#50911yescharacteristic
164C22×C47#51011yescharacteristic
165C2×D47—44no—
166C2×D47—82no—
167C2×D47—82no—
168C2×D47—82no—
169C2×D47—82no—
170C2×D47—82no—
171C2×D47—82no—
172C4×C47—82no—
173C4×C47—161no—
174C4×C47#38611yescharacteristic
175C4×C47#44211yescharacteristic
176C4×C47#44911yescharacteristic
177C4×C47#46311yescharacteristic
178Dic47—22no—
179Dic47—41no—
180Dic47—82no—
181C22×SD32—471no—
182C2×C4×D8—471no—
183C2×#358—471no—
184C2×#357—471no—
185#1969—471no—
186#1380D4711yescharacteristic, complemented
187#1374—471no—
188C2×C47#187911yescharacteristic
189C2×C47C4×SD3211yescharacteristic
190C2×C47#217511yescharacteristic
191C2×C47#218711yescharacteristic
192C2×C47#218911yescharacteristic
193C2×C47#220811yescharacteristic
194C2×C47#221011yescharacteristic
195D47—84no—
196C22×Q16—471no—
197C22×D8—471no—
198C2×C4×D4—941no—
199C2×SD32—474no—
200C2×SD32—942no—
201C2×SD32—942no—
202C22×C16—471no—
203C22×C16C2×D4711yescharacteristic
204C4×D8—942no—
205C4×D8—942no—
206C2×#107C2×D4711yescharacteristic
207C2×#107C2×D4711yescharacteristic
208C2×#103—941no—
209C2×#102—941no—
210C2×C4×C8—471no—
211#391—941no—
212#358—942no—
213#357—942no—
214C47#1301411yescharacteristic, complemented, Sylow
215C22×Q8—941no—
216C22×D4—941no—
217C23×C4—1881no—
218C2×Q16—472no—
219C2×Q16—941no—
220C2×Q16—941no—
221C2×Q16—941no—
222C2×Q16—941no—
223C2×Q16—941no—
224C2×D8—472no—
225C2×D8—472no—
226C2×D8—472no—
227C2×D8—941no—
228C2×D8—941no—
229C2×D8—941no—
230C22×C8—471no—
231C22×C8C22×D4711yescharacteristic
232C4×D4—944no—
233C4×D4—1882no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C22⋊C4—1881no—
237C2×C42—471no—
238SD32—948no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—941no—
242C2×C16—941no—
243C2×C16—941no—
244C2×C16C4×D4712yescomplemented
245#107—21no—
246#107—21no—
247#107—21no—
248#107D18812yes—
249#103—1882no—
250#102—944no—
251C4×C8—941no—
252C4×C8—941no—
253#95—1881no—
254#95—1881no—
255C24—1881no—
256C2×Q8—942no—
257C2×Q8—1881no—
258C2×Q8—1881no—
259C2×Q8—1881no—
260C2×Q8—1881no—
261C2×Q8—1881no—
262C2×D4—942no—
263C2×D4—942no—
264C2×D4—942no—
265C2×D4—1881no—
266C2×D4—1881no—
267C2×D4—1881no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—3762no—
273C22×C4—3762no—
274C22×C4—1884no—
275C22×C4—1881no—
276C22×C4D4×D4711yescharacteristic
277Q16—942no—
278Q16—942no—
279Q16—1881no—
280Q16—1881no—
281D8—474no—
282D8—942no—
283D8—942no—
284D8—942no—
285C2×C8—941no—
286C2×C8—941no—
287C2×C8—941no—
288C2×C8C2×C4×D4711yescharacteristic
289C2×C8C2×D18811yescharacteristic
290C2×C8#1062535011yescharacteristic
291C2×C8D4×D4711yescharacteristic
292C2×C8D4×D4711yescharacteristic
293C2×C8#1062535411yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—1884no—
299C42—941no—
300C42—941no—
301C16—22no—
302C16—1881no—
303C23—3761no—
304C23—3761no—
305C23—3761no—
306C23—3761no—
307C23—1882no—
308C23—1882no—
309C23—1882no—
310C23D8×D4711yescharacteristic
311Q8—3761no—
312Q8—3761no—
313Q8—1882no—
314Q8—1882no—
315D4—944no—
316D4—1882no—
317D4—1882no—
318D4—1882no—
319C2×C4—42no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—472no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—3768no—
332C2×C4—3761no—
333C2×C4—3761no—
334C2×C4—1882no—
335C2×C4#1309398611yescharacteristic
336C2×C4#1309399411yescharacteristic
337C2×C4#1309399711yescharacteristic
338C2×C4#1309404711yescharacteristic
339C2×C4#1309405111yescharacteristic
340C2×C4#1309405111yescharacteristic
341C8—1881no—
342C8C22⋊C4×D4711yescharacteristic
343C8C4×D18811yescharacteristic
344C8#1309399911yescharacteristic
345C8#1309400911yescharacteristic
346C22—3762no—
347C22—3762no—
348C22—3762no—
349C22—3762no—
350C22—3762no—
351C22—3762no—
352C22—1884no—
353C22#1568920511yescharacteristic
354C22#1568925811yescharacteristic
355C22#1568931711yescharacteristic
356C22SD32×D4711yescharacteristic
357C22#1568955411yescharacteristic
358C22#1568955711yescharacteristic
359C22#1568956511yescharacteristic
360C4—82no—
361C4—161no—
362C4—942no—
363C4—3762no—
364C4—1881no—
365C4#1568900111yescharacteristic
366C4#1568923411yescharacteristic
367C4#1568927111yescharacteristic
368C4#1568934111yescharacteristic
369C2—3764no—
370C2#2024373711yescharacteristic
371C2#2024523911yescharacteristic
372C2#2024525111yescharacteristic
373C2#2024531811yescharacteristic
374C2#2024533111yescharacteristic
375C2#2024543211yescharacteristic
376C2#2024544211yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#13014
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#15688926C2semidirect
5. #20244247C2semidirect
6. #20241465C2semidirect
7. C47×#1380C2semidirect
13. C2×#13093969C4semidirect
34. C2×Dic188C2×C4semidirect
61. C2×C16×C47C2×C4semidirect
142. C2×Dic47SD32semidirect
186. #1380D47semidirect
214. C47#13014semidirect
244. C2×C16C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939692
C2×#156892052
C2×#156889262
C2×#156889232
#202442472
#202414652
C47×#13802
#1301447