Finite Group Databasebeta

← #26115292

Subgroups — #26115292

Order 12032.

526 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20243241C211yesmaximal, characteristic, complemented
2C4×#13093935C211yesmaximal, characteristic, complemented
3C2×#15688865C212yesmaximal, complemented
4C2×#15688863C212yesmaximal
5C47×#2861C211yesmaximal, characteristic
6C2×C4⋊(C47⋊C8)—21no—
7C2×#13093935—21no—
8C2×#13093935C2212yes—
9C2×#13093935C2212yes—
10C2×C4×C47⋊C8—21no—
11#15688878—21no—
12#15688865—24no—
13#15688863—24no—
14C2×#125×C47C2211yescharacteristic
15C2×#124×C47C2211yescharacteristic
16C47×#391C411yescharacteristic
17C47×#391C411yescharacteristic
18C47×#390C411yescharacteristic
19C47×#390C411yescharacteristic
20C47×#388—21no—
21C47×#388—21no—
22C47×#388—21no—
23C47×#388—21no—
24C43×C47C2211yescharacteristic
25C22×C47⋊C8—22no—
26C22×C47⋊C8—22no—
27C4⋊(C47⋊C8)—24no—
28#13093935—24no—
29#13093935—22no—
30#13093935—22no—
31#13093935—22no—
32#13093935D414yes—
33C4×C47⋊C8—24no—
34C22×Q8×C47C2×C411yescharacteristic
35C22×D4×C47C2×C411yescharacteristic
36#125×C47—22no—
37#125×C47—22no—
38#124×C47—22no—
39#124×C47—22no—
40C2×C4⋊C4×C47—21no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47C2×C411yescharacteristic
43C2×C4⋊C4×C47C2×C411yescharacteristic
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47—21no—
47C2×C22⋊C4×C47—21no—
48C2×C22⋊C4×C47—21no—
49C2×C22⋊C4×C47—21no—
50C2×C42×C47C2×C411yescharacteristic
51C2×C42×C47C2×C411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C2×C42×C47D411yescharacteristic
55C2×C42×C47D411yescharacteristic
56C2×C42×C47C2311yescharacteristic
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61C24×C47—21no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×D4×C47—22no—
66C2×D4×C47—41no—
67C2×D4×C47—41no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C22×C411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C4⋊C4×C47—22no—
79C4⋊C4×C47—22no—
80C4⋊C4×C47—42no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C22⋊C4×C47—42no—
84C22⋊C4×C47—42no—
85C22⋊C4×C47—42no—
86C22⋊C4×C47—42no—
87C22⋊C4×C47—42no—
88C22⋊C4×C47—41no—
89C22⋊C4×C47—41no—
90C42×C47—22no—
91C42×C47—22no—
92C42×C47—22no—
93C42×C47—41no—
94C42×C47—41no—
95C42×C47—41no—
96C42×C47C2×D412yes—
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—41no—
105C23×C47—41no—
106C23×C47—41no—
107C23×C47—41no—
108C23×C47—41no—
109C23×C47—41no—
110C23×C47—41no—
111C23×C47C2×C22⋊C411yescharacteristic
112Q8×C47—82no—
113D4×C47—82no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
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—21no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
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#10412yes—
139C2×C4×C47#10412yes—
140C2×C4×C47#10412yes—
141C2×C4×C47C4×D412yes—
142C2×C4×C47#12112yes—
143C2×C4×C47#12411yescharacteristic
144C2×C4×C47#12711yescharacteristic
145C47⋊C8—28no—
146C47⋊C8—44no—
147#9687—471nomaximal, Sylow
148C22×C47—81no—
149C22×C47—81no—
150C22×C47—81no—
151C22×C47—81no—
152C22×C47—81no—
153C22×C47—81no—
154C22×C47—81no—
155C22×C47#39011yescharacteristic
156C22×C47#41311yescharacteristic
157C22×C47#41311yescharacteristic
158C22×C47C2×#10411yescharacteristic
159C22×C47C2×#10411yescharacteristic
160C22×C47C2×#10411yescharacteristic
161C22×C47#42111yescharacteristic
162C4×C47—22no—
163C4×C47—22no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—22no—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—41no—
170C4×C47—81no—
171C4×C47—81no—
172C4×C47—81no—
173#2861D4711yescharacteristic
174#1767—471no—
175C4×#97—471no—
176C2×#330—472no—
177C2×#329—472no—
178C2×C47—161no—
179C2×C47#152411yescharacteristic
180C2×C47#152411yescharacteristic
181C2×C47#152911yescharacteristic
182C2×C47#153211yescharacteristic
183C2×C47#196211yescharacteristic
184C2×C47#196711yescharacteristic
185C2×C47#198011yescharacteristic
186C2×#125C2×D4711yescharacteristic
187C2×#124C2×D4711yescharacteristic
188C2×C4⋊C8—941no—
189C2×#97—472no—
190C2×#97—472no—
191C2×#97—941no—
192C2×C4×C8—941no—
193#391Dic4711yescharacteristic
194#391Dic4711yescharacteristic
195#390Dic4711yescharacteristic
196#390Dic4711yescharacteristic
197#388—21no—
198#388—21no—
199#388—21no—
200#388—21no—
201C43C2×D4711yescharacteristic
202#336—941no—
203#330—944no—
204#329—944no—
205C47#968711yescharacteristic, complemented, Sylow
206C22×Q8C2×Dic4711yescharacteristic
207C22×D4C2×Dic4711yescharacteristic
208C22×C8—942no—
209C22×C8—942no—
210#125—22no—
211#125—22no—
212#124—22no—
213#124—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C2×Dic4711yescharacteristic
217C2×C4⋊C4C2×Dic4711yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C42C2×Dic4711yescharacteristic
225C2×C42C2×Dic4711yescharacteristic
226C2×C42C22⋊D4711yescharacteristic
227C2×C42C22⋊D4711yescharacteristic
228C2×C42C22⋊D4711yescharacteristic
229C2×C42C22⋊D4711yescharacteristic
230C2×C42C22×D4711yescharacteristic
231C4⋊C8—944no—
232#97—474no—
233#97—944no—
234#97—942no—
235#97—942no—
236#97—942no—
237C4×C8—944no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242C24—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4C22⋊Dic4711yescharacteristic
253C22×C4C22⋊Dic4711yescharacteristic
254C22×C4C22⋊Dic4711yescharacteristic
255C22×C4C22⋊Dic4711yescharacteristic
256C22×C4C22×Dic4711yescharacteristic
257C22×C4C2×C22⋊D4711yescharacteristic
258C22×C4C2×C22⋊D4711yescharacteristic
259C2×C8—944no—
260C2×C8—944no—
261C2×C8—944no—
262C2×C8—944no—
263C2×C8—1882no—
264C2×C8—1882no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—42no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—41no—
281C42—41no—
282C42—41no—
283C42D4×D4712yes—
284C42#1062535212yes—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23C2×C22⋊Dic4711yescharacteristic
293Q8—82no—
294D4—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
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—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4#1309395112yes—
320C2×C4#1309395112yes—
321C2×C4#1309395112yes—
322C2×C4D4×Dic4712yes—
323C2×C4#1309399512yes—
324C2×C4#1309401111yescharacteristic
325C2×C4#1309402011yescharacteristic
326C8—948no—
327C8—1884no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1568902611yescharacteristic
336C22#1568910711yescharacteristic
337C22#1568910711yescharacteristic
338C22C2×#1309395111yescharacteristic
339C22C2×#1309395111yescharacteristic
340C22C2×#1309395111yescharacteristic
341C22#1568914011yescharacteristic
342C4—22no—
343C4—22no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—81no—
351C4—81no—
352C4—81no—
353C2—161no—
354C2#2024197611yescharacteristic
355C2#2024197611yescharacteristic
356C2#2024199511yescharacteristic
357C2#2024200811yescharacteristic
358C2#2024421711yescharacteristic
359C2#2024423811yescharacteristic
360C2#2024430811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2861C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D4×C47C2×C4
cosocleC2×C42×C47C23
hypercenter#2861D47
hypocenterC47#9687
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #2861

Complements

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

NH ≅ G/Ntype
1. #20243241C2semidirect
2. C4×#13093935C2semidirect
3. C2×#15688865C2semidirect
205. C47#9687semidirect

Maximal subgroups

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

subgroupindex
#202432412
C4×#130939352
C2×#156888652
C2×#156888632
C47×#28612
#968747