Finite Group Databasebeta

← #26115810

Subgroups — #26115810

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244225C212yesmaximal, complemented
2#20243413C211yesmaximal, characteristic, complemented
3#20243164C211yesmaximal, characteristic, complemented
4#20241956C212yesmaximal, complemented
5C2×C47×#466C211yesmaximal, characteristic
6C2×#13093956—21no—
7C2×#13093939—24no—
8C2×C22⋊(C47⋊C8)C2211yescharacteristic
9C2×#13093934—21no—
10#15688983C2212yes—
11C4×C22⋊Dic47C2211yescharacteristic
12#15688886—21no—
13#15688877—21no—
14#15688857—24no—
15C22×D8×C47C411yescharacteristic, complemented
16C23×C8×C47C2211yescharacteristic
17C2×#121×C47C2212yes—
18C47×#466—21no—
19C47×#466—21no—
20C47×#466—21no—
21C47×#466—21no—
22C2×#107×C47C411yescharacteristic, complemented
23C2×#102×C47C412yescomplemented
24C22×C47⋊C8—21no—
25C2×C4⋊Dic47—22no—
26C2×C22⋊Dic47—22no—
27C2×C22⋊Dic47D412yes—
28C2×C4×Dic47—21no—
29#13093956—42no—
30#13093939—48no—
31C22⋊(C47⋊C8)—21no—
32C22⋊(C47⋊C8)D412yes—
33#13093934—42no—
34C47⋊#95—21no—
35C47⋊#95—22no—
36C22×D4×C47—22no—
37C22×D4×C47C2×C412yes—
38C23×C4×C47C2311yescharacteristic
39C2×D8×C47—21no—
40C2×D8×C47—21no—
41C2×D8×C47—42no—
42C22×C8×C47—42no—
43C22×C8×C47C2×C411yescharacteristic
44C22×C8×C47C2×C411yescharacteristic
45C22×C8×C47D411yescharacteristic
46C22×C8×C47D411yescharacteristic
47C22×C8×C47D411yescharacteristic
48C22×C8×C47D411yescharacteristic
49#121×C47—22no—
50#121×C47—22no—
51#121×C47—22no—
52#121×C47—22no—
53C2×C4⋊C4×C47C2×C412yes—
54C2×C22⋊C4×C47—22no—
55#107×C47—21no—
56#107×C47—21no—
57#102×C47—22no—
58#102×C47—22no—
59C24×C47—22no—
60C24×C47C2×D411yescharacteristic
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—42no—
64C2×D4×C47—42no—
65C2×D4×C47—42no—
66C2×D4×C47—42no—
67C2×D4×C47—44no—
68C2×D4×C47—44no—
69C22×C4×C47—22no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47C22×C411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47#4111yescharacteristic
77C22×C4×C47#4111yescharacteristic
78C22×Dic47—22no—
79C22×Dic47—42no—
80D8×C47—42no—
81D8×C47—42no—
82C2×C8×C47—22no—
83C2×C8×C47—22no—
84C2×C8×C47—22no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47C22⋊C411yescharacteristic
89C2×C8×C47C22⋊C411yescharacteristic
90C2×C8×C47C22⋊C411yescharacteristic
91C2×C8×C47C22⋊C411yescharacteristic
92C4⋊C4×C47—22no—
93C4⋊C4×C47—22no—
94C22⋊C4×C47—42no—
95C22⋊C4×C47—42no—
96C22⋊Dic47—24no—
97C22⋊Dic47—44no—
98C4⋊Dic47—42no—
99C4⋊Dic47—42no—
100C4×Dic47—41no—
101C4×Dic47—41no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C23×C47—41no—
106C23×C47—41no—
107C23×C47—42no—
108C23×C47—44no—
109C23×C47—82no—
110C23×C47—82no—
111C23×C47C4×D411yescharacteristic
112C23×C47#12111yescharacteristic
113C23×C47#12711yescharacteristic
114C23×C47AGL(1,ℤ/8)14yes—
115D4×C47—42no—
116D4×C47—42no—
117D4×C47—82no—
118D4×C47—84no—
119D4×C47—82no—
120D4×C47—82no—
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—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—42no—
131C2×C4×C47—44no—
132C2×C4×C47C2×C22⋊C411yescharacteristic
133C2×C4×C47C4×D411yescharacteristic
134C2×C4×C47#12111yescharacteristic
135C2×C4×C47#12411yescharacteristic
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47—42no—
139C2×Dic47—82no—
140C2×Dic47—82no—
141C2×Dic47—82no—
142C8×C47—21no—
143C8×C47—21no—
144C8×C47—21no—
145C8×C47#9912yescomplemented
146C47⋊C8—42no—
147#9785—471nomaximal, Sylow
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—44no—
155C22×C47—82no—
156C22×C47—82no—
157C22×C47—82no—
158C22×C47—164no—
159C22×C47#39011yescharacteristic
160C22×C47#44212yes—
161C22×C47#46912yes—
162C22×C47#49612yes—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—82no—
167C4×C47C2×#9911yescharacteristic
168C4×C47#41011yescharacteristic
169Dic47—82no—
170Dic47—162no—
171C2×#466D4711yescharacteristic
172#1964—472no—
173#1807—471no—
174#1752—471no—
175#1519—472no—
176C2×C47—22no—
177C2×C47—22no—
178C2×C47—22no—
179C2×C47—162no—
180C2×C47#196411yescharacteristic
181C2×C47#197211yescharacteristic
182C2×C47#197611yescharacteristic
183C22×D8Dic4711yescharacteristic, complemented
184C23×C8C2×D4711yescharacteristic
185C2×#121C2×D4712yes—
186#466—21no—
187#466—21no—
188#466—21no—
189#466—21no—
190C2×#107Dic4711yescharacteristic, complemented
191C2×#106—941no—
192C2×#102Dic4712yescomplemented
193C2×#99—944no—
194C2×C22⋊C8—471no—
195C2×#97—941no—
196#380—472no—
197C4×C22⋊C4—471no—
198#340—941no—
199#336—941no—
200#327—944no—
201C47#978511yescharacteristic, complemented, Sylow
202C22×D4—22no—
203C22×D4C2×Dic4712yes—
204C23×C4C22×D4711yescharacteristic
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—42no—
208C22×C8—42no—
209C22×C8—941no—
210C22×C8C2×Dic4711yescharacteristic
211C22×C8C2×Dic4711yescharacteristic
212C22×C8C22⋊D4711yescharacteristic
213C22×C8C22⋊D4711yescharacteristic
214C22×C8C22⋊D4711yescharacteristic
215C22×C8C22⋊D4711yescharacteristic
216#121—22no—
217#121—22no—
218#121—22no—
219#121—22no—
220C2×C4⋊C4—942no—
221C2×C4⋊C4C2×Dic4712yes—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—472no—
224C2×C22⋊C4—942no—
225C2×C42—941no—
226#107—21no—
227#107—21no—
228#106—1882no—
229#102—22no—
230#102—22no—
231#99—1888no—
232C22⋊C8—472no—
233C22⋊C8—941no—
234#97—1882no—
235#95—941no—
236#95—942no—
237C24—22no—
238C24D4×D4711yescharacteristic
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—44no—
246C2×D4—44no—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—942no—
251C22×C4—1882no—
252C22×C4D4×D4711yescharacteristic
253C22×C4#1062535211yescharacteristic
254C22×C4#1062535211yescharacteristic
255C22×C4C22×Dic4711yescharacteristic
256C22×C4C2×C22⋊D4711yescharacteristic
257C22×C4C2×C22⋊D4711yescharacteristic
258D8—42no—
259D8—42no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—942no—
267C2×C8—1881no—
268C2×C8—1881no—
269C2×C8C22⋊Dic4711yescharacteristic
270C2×C8C22⋊Dic4711yescharacteristic
271C2×C8C22⋊Dic4711yescharacteristic
272C2×C8C22⋊Dic4711yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—1882no—
276C4⋊C4—1882no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—944no—
280C22⋊C4—1884no—
281C42—1881no—
282C42—1881no—
283C23—41no—
284C23—41no—
285C23—42no—
286C23—44no—
287C23—82no—
288C23—82no—
289C23D4×Dic4711yescharacteristic
290C23#1309399511yescharacteristic
291C23#1309402011yescharacteristic
292C23#1309404814yes—
293D4—42no—
294D4—42no—
295D4—82no—
296D4—82no—
297D4—82no—
298D4—84no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—3762no—
311C2×C4—3762no—
312C2×C4—3762no—
313C2×C4—1882no—
314C2×C4—1882no—
315C2×C4—1882no—
316C2×C4C2×C22⋊Dic4711yescharacteristic
317C2×C4D4×Dic4711yescharacteristic
318C2×C4#1309399511yescharacteristic
319C2×C4#1309401111yescharacteristic
320C8—21no—
321C8—21no—
322C8—21no—
323C8—1882no—
324C8#1309393912yescomplemented
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—44no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22—164no—
336C22#1568902611yescharacteristic
337C22#1568923512yes—
338C22#1568937312yes—
339C22#1568951112yes—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—82no—
344C4—3762no—
345C4—7522no—
346C4C2×#1309393911yescharacteristic
347C4#1568909711yescharacteristic
348C2—22no—
349C2—22no—
350C2—22no—
351C2—162no—
352C2#2024422511yescharacteristic
353C2#2024426511yescharacteristic
354C2#2024428711yescharacteristic
subgroupG/H
centerC22#15689026
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
Fitting, prime radicalC2×C47×#466C2
socleC22×C47#390
cosocleC23×C4×C47C23
hypercenterC2×#466D47
hypocenterC47#9785
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. #20244225C2semidirect
2. #20243413C2semidirect
3. #20243164C2semidirect
4. #20241956C2semidirect
15. C22×D8×C47C4semidirect
22. C2×#107×C47C4semidirect
23. C2×#102×C47C4semidirect
145. C8×C47#99semidirect
183. C22×D8Dic47semidirect
190. C2×#107Dic47semidirect
192. C2×#102Dic47semidirect
201. C47#9785semidirect
324. C8#13093939semidirect

Maximal subgroups

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

subgroupindex
#202442252
#202434132
#202431642
#202419562
C2×C47×#4662
#978547