Finite Group Databasebeta

← #26107208

Subgroups — #26107208

Order 12032.

572 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243137C211yesmaximal, characteristic, complemented
2C4×#13093935C211yesmaximal, characteristic, complemented
3C2×#15688863C212yesmaximal
4#20241269C212yesmaximal, complemented
5C4×#124×C47C211yesmaximal, characteristic
6C2×#13093935—21no—
7C2×#13093935C2212yes—
8C2×#13093935C2212yes—
9C2×C4×C47⋊C8—21no—
10#15688878—21no—
11#15688878—21no—
12#15688863C418yescomplemented
13C2×#124×C47C2211yescharacteristic
14C2×C4×Q8×C47C411yescharacteristic
15C2×C4×D4×C47C411yescharacteristic
16C47×#391C411yescharacteristic
17C47×#390C411yescharacteristic
18C47×#388—21no—
19C47×#388—21no—
20C47×#382C2211yescharacteristic
21C4×C22⋊C4×C47—21no—
22C4×C22⋊C4×C47—21no—
23C43×C47C2211yescharacteristic
24C22×C47⋊C8—22no—
25C22×C47⋊C8—22no—
26#13093935—24no—
27#13093935—22no—
28#13093935—22no—
29#13093935C2×C414yescomplemented
30#13093935C2×C414yescomplemented
31C4×C47⋊C8—24no—
32C22×Q8×C47C2×C411yescharacteristic
33C22×D4×C47C2×C411yescharacteristic
34C23×C4×C47—21no—
35#124×C47—22no—
36#124×C47C2×C414yes—
37C4×Q8×C47—42no—
38C4×D4×C47—42no—
39C2×C4⋊C4×C47—21no—
40C2×C4⋊C4×C47C2×C411yescharacteristic
41C2×C4⋊C4×C47C2×C411yescharacteristic
42C2×C22⋊C4×C47—21no—
43C2×C22⋊C4×C47—21no—
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47—21no—
47C2×C42×C47—21no—
48C2×C42×C47C2×C411yescharacteristic
49C2×C42×C47C2×C411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C2×C42×C47C2311yescharacteristic
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59C24×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47—41no—
62C2×Q8×C47—41no—
63C2×Q8×C47C4212yes—
64C2×D4×C47—21no—
65C2×D4×C47—41no—
66C2×D4×C47—41no—
67C2×D4×C47C4212yes—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—42no—
72C22×C4×C47—42no—
73C22×C4×C47—42no—
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47C22⋊C411yescharacteristic
78C22×C4×C47C22×C411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47C2×D411yescharacteristic
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—42no—
84C22⋊C4×C47—24no—
85C22⋊C4×C47—24no—
86C22⋊C4×C47—42no—
87C22⋊C4×C47—42no—
88C22⋊C4×C47—42no—
89C42×C47—22no—
90C42×C47—22no—
91C42×C47—22no—
92C42×C47—41no—
93C42×C47—41no—
94C42×C47—41no—
95C42×C47—42no—
96C42×C47C22×C412yes—
97C42×C47#4112yes—
98C2×C47⋊C8—24no—
99C2×C47⋊C8—24no—
100C2×C47⋊C8—24no—
101C2×C47⋊C8—24no—
102C2×C47⋊C8—42no—
103C2×C47⋊C8—42no—
104C23×C47—22no—
105C23×C47—41no—
106C23×C47—41no—
107C23×C47—41no—
108C23×C47—41no—
109C23×C47—41no—
110C23×C47—41no—
111C23×C47C2×C22⋊C411yescharacteristic
112Q8×C47—42no—
113Q8×C47—42no—
114D4×C47—42no—
115D4×C47—42no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—22no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—84no—
141C2×C4×C47#10012yes—
142C2×C4×C47#10412yes—
143C2×C4×C47#10412yes—
144C2×C4×C47C2×C4211yescharacteristic
145C2×C4×C47#11711yescharacteristic
146C2×C4×C47C4×D412yes—
147C2×C4×C47C4×D412yes—
148C47⋊C8—28no—
149C47⋊C8—44no—
150#8226—471nomaximal, Sylow
151C22×C47—42no—
152C22×C47—42no—
153C22×C47—42no—
154C22×C47—81no—
155C22×C47—81no—
156C22×C47—81no—
157C22×C47—81no—
158C22×C47C4×C22⋊C411yescharacteristic
159C22×C47C2×#10011yescharacteristic
160C22×C47#41311yescharacteristic
161C22×C47C2×#10411yescharacteristic
162C22×C47C2×#10411yescharacteristic
163C22×C47#42111yescharacteristic
164C22×C47#42111yescharacteristic
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—22no—
170C4×C47—22no—
171C4×C47—22no—
172C4×C47—42no—
173C4×C47—41no—
174C4×C47—81no—
175C4×C47—81no—
176C4×#124D4711yescharacteristic
177#1745—471no—
178C4×#97—471no—
179C2×#329—472no—
180#1295—472no—
181C2×C47—82no—
182C2×C47#152711yescharacteristic
183C2×C47#152911yescharacteristic
184C2×C47#153011yescharacteristic
185C2×C47#153211yescharacteristic
186C2×C47C4×#10011yescharacteristic
187C2×C47C4×#10411yescharacteristic
188C2×C47#175911yescharacteristic
189C2×#124C2×D4711yescharacteristic
190C2×C4×Q8Dic4711yescharacteristic
191C2×C4×D4Dic4711yescharacteristic
192C2×#97—472no—
193C2×#97—472no—
194C2×#97—941no—
195C2×C4×C8—941no—
196#391Dic4711yescharacteristic
197#390Dic4711yescharacteristic
198#388—21no—
199#388—21no—
200#382C2×D4711yescharacteristic
201C4×C22⋊C4—21no—
202C4×C22⋊C4—21no—
203C43C2×D4711yescharacteristic
204#336—941no—
205#336—941no—
206#329—478no—
207C47#822611yescharacteristic, complemented, Sylow
208C22×Q8C2×Dic4711yescharacteristic
209C22×D4C2×Dic4711yescharacteristic
210C23×C4—21no—
211C22×C8—942no—
212C22×C8—942no—
213#124—22no—
214#124C4×D4714yes—
215C4×Q8—42no—
216C4×D4—42no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×Dic4711yescharacteristic
219C2×C4⋊C4C2×Dic4711yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C42—21no—
226C2×C42C2×Dic4711yescharacteristic
227C2×C42C2×Dic4711yescharacteristic
228C2×C42C22⋊D4711yescharacteristic
229C2×C42C22⋊D4711yescharacteristic
230C2×C42C22⋊D4711yescharacteristic
231C2×C42C22⋊D4711yescharacteristic
232C2×C42C22×D4711yescharacteristic
233#97—474no—
234#97—474no—
235#97—944no—
236#97—942no—
237#97—942no—
238C4×C8—944no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243C24—21no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8C4×Dic4712yes—
248C2×D4—21no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4C4×Dic4712yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4C22⋊Dic4711yescharacteristic
259C22×C4C22⋊Dic4711yescharacteristic
260C22×C4C22⋊Dic4711yescharacteristic
261C22×C4C22⋊Dic4711yescharacteristic
262C22×C4C22×Dic4711yescharacteristic
263C22×C4C2×C22⋊D4711yescharacteristic
264C22×C4C2×C22⋊D4711yescharacteristic
265C2×C8—944no—
266C2×C8—944no—
267C2×C8—944no—
268C2×C8—944no—
269C2×C8—1882no—
270C2×C8—1882no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C22⋊C4—24no—
275C22⋊C4—24no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C42—22no—
280C42—22no—
281C42—22no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—42no—
286C42C2×C4×D4712yes—
287C42#1062535012yes—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23C2×C22⋊Dic4711yescharacteristic
296Q8—42no—
297Q8—42no—
298D4—42no—
299D4—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—84no—
325C2×C4#1309394112yes—
326C2×C4#1309395112yes—
327C2×C4#1309395112yes—
328C2×C4C2×C4×Dic4711yescharacteristic
329C2×C4#1309398311yescharacteristic
330C2×C4C4×C22⋊D4712yes—
331C2×C4C4×C22⋊D4712yes—
332C8—948no—
333C8—1884no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C4×C22⋊Dic4711yescharacteristic
342C22C2×#1309394111yescharacteristic
343C22#1568910711yescharacteristic
344C22C2×#1309395111yescharacteristic
345C22C2×#1309395111yescharacteristic
346C22#1568914011yescharacteristic
347C22#1568914011yescharacteristic
348C4—22no—
349C4—22no—
350C4—22no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—42no—
357C4—81no—
358C4—81no—
359C2—82no—
360C2#2024198611yescharacteristic
361C2#2024199511yescharacteristic
362C2#2024199911yescharacteristic
363C2#2024200811yescharacteristic
364C2C4×#1309394111yescharacteristic
365C2C4×#1309395111yescharacteristic
366C2#2024319811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC4×#124×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D4×C47C2×C4
cosocleC2×C42×C47C23
hypercenterC4×#124D47
hypocenterC47#8226
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #20243137C2semidirect
2. C4×#13093935C2semidirect
4. #20241269C2semidirect
12. #15688863C4semidirect
29. #13093935C2×C4semidirect
30. #13093935C2×C4semidirect
207. C47#8226semidirect

Maximal subgroups

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

subgroupindex
#202431372
C4×#130939352
C2×#156888632
#202412692
C4×#124×C472
#822647