Finite Group Databasebeta

← #26116375

Subgroups — #26116375

Order 12032.

432 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251773C211yesmaximal, characteristic
2#20243242C211yesmaximal, characteristic
3#97×Dic47C211yesmaximal, characteristic
4#20241270C211yesmaximal, characteristic
5#20241270C211yesmaximal, characteristic
6#20241269C211yesmaximal, characteristic
7C47×#1295C211yesmaximal, characteristic
8C2×Dic47⋊C8—21no—
9C2×#13093935C2211yescharacteristic
10C2×#13093935C2211yescharacteristic
11C2×#13093934—21no—
12C2×C8×Dic47—21no—
13#15689022C411yescharacteristic
14#15689022C411yescharacteristic
15#15689019C411yescharacteristic
16#15689019C411yescharacteristic
17#15689010—21no—
18#15689010—21no—
19#15689006—21no—
20#15689006—21no—
21#15688989C2211yescharacteristic
22C42×Dic47C2211yescharacteristic
23#15688877—21no—
24C2×#97×C47C2211yescharacteristic
25C2×#97×C47C2211yescharacteristic
26C47×#382C2211yescharacteristic
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47C2×C411yescharacteristic
32C2×C4⋊Dic47C2×C411yescharacteristic
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×C4×Dic47C2×C411yescharacteristic
36C2×C4×Dic47C2×C411yescharacteristic
37C2×C4×Dic47D411yescharacteristic
38C2×C4×Dic47D411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40C2×C4×Dic47D411yescharacteristic
41Dic47⋊C8—24no—
42#13093935—21no—
43#13093935—21no—
44#13093935—21no—
45#13093935Q812yes—
46#13093934—24no—
47C8×Dic47—24no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C47⋊#95—21no—
52C47⋊#95—21no—
53C47⋊#95—21no—
54C22×C8×C47—21no—
55C22×C8×C47—21no—
56C2×C4⋊C4×C47C2×C411yescharacteristic
57C2×C4⋊C4×C47C2×C411yescharacteristic
58C2×C42×C47C2311yescharacteristic
59#97×C47—21no—
60#97×C47—21no—
61#97×C47—21no—
62#97×C47Q812yes—
63#95×C47—21no—
64#95×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47C22×C411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—21no—
72C22×Dic47C22⋊C411yescharacteristic
73C22×Dic47C22⋊C411yescharacteristic
74C22×Dic47C22⋊C411yescharacteristic
75C22×Dic47C22⋊C411yescharacteristic
76C2×C8×C47—22no—
77C2×C8×C47—22no—
78C2×C8×C47—22no—
79C2×C8×C47—22no—
80C2×C8×C47—41no—
81C2×C8×C47—41no—
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84C42×C47C2×Q811yescharacteristic
85C42×C47C2×Q811yescharacteristic
86C42×C47#4111yescharacteristic
87C42×C47#4111yescharacteristic
88C4⋊Dic47—42no—
89C4⋊Dic47—42no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92Dic47⋊C4—42no—
93Dic47⋊C4—42no—
94C4×Dic47—22no—
95C4×Dic47—22no—
96C4×Dic47—22no—
97C4×Dic47—41no—
98C4×Dic47—41no—
99C4×Dic47—41no—
100C2×C47⋊C8—22no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8—22no—
104C2×C47⋊C8—41no—
105C2×C47⋊C8—41no—
106C23×C47C2×C22⋊C411yescharacteristic
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—41no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47C4×Q811yescharacteristic
120C2×C4×C47C4×Q811yescharacteristic
121C2×C4×C47C22⋊Q811yescharacteristic
122C2×C4×C47C22⋊Q811yescharacteristic
123C2×C4×C47#12411yescharacteristic
124C2×C4×C47C4⋊Q811yescharacteristic
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47#10412yes—
141C2×Dic47#10412yes—
142C2×Dic47#10412yes—
143C8×C47—24no—
144C8×C47—42no—
145C47⋊C8—24no—
146C47⋊C8—42no—
147#9892—471nomaximal, Sylow
148C22×C47#39111yescharacteristic
149C22×C47#41311yescharacteristic
150C22×C47#41311yescharacteristic
151C22×C47C2×#10411yescharacteristic
152C22×C47C2×#10411yescharacteristic
153C22×C47C2×#10411yescharacteristic
154C22×C47#42111yescharacteristic
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—81no—
162C4×C47—81no—
163Dic47—22no—
164Dic47—22no—
165Dic47—22no—
166Dic47—41no—
167Dic47—81no—
168Dic47—81no—
169#2864—471no—
170#1767—471no—
171C4×#97—471no—
172#1295—471no—
173#1295—471no—
174#1295—471no—
175#1295D4711yescharacteristic
176C2×C47#152411yescharacteristic
177C2×C47#152411yescharacteristic
178C2×C47#152911yescharacteristic
179C2×C47#153211yescharacteristic
180C2×C47#198611yescharacteristic
181C2×C47#199411yescharacteristic
182C2×C47#199811yescharacteristic
183C2×C4⋊C8—941no—
184C2×#97—471no—
185C2×#97—471no—
186C2×#97—941no—
187C2×#97C2×D4711yescharacteristic
188C2×#97C2×D4711yescharacteristic
189C2×C4×C8—941no—
190#389—471no—
191#389—471no—
192#389—471no—
193#389—471no—
194#387—941no—
195#387—941no—
196#387—941no—
197#387—941no—
198#382—471no—
199#382C2×D4711yescharacteristic
200C43—471no—
201#336—941no—
202C47#989211yescharacteristic, complemented, Sylow
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—941no—
206C22×C8—941no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—941no—
210C2×C4⋊C4—941no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4—941no—
213C2×C4⋊C4C4×D4711yescharacteristic
214C2×C4⋊C4C4×D4711yescharacteristic
215C2×C42—471no—
216C2×C42—471no—
217C2×C42—471no—
218C2×C42—471no—
219C2×C42—471no—
220C2×C42—471no—
221C2×C42C22×D4711yescharacteristic
222C4⋊C8—944no—
223#97—21no—
224#97—21no—
225#97—21no—
226#97—472no—
227#97—944no—
228#97—941no—
229#97—941no—
230#97—941no—
231#97Dic9412yes—
232C4×C8—944no—
233#95—21no—
234#95—21no—
235#95—941no—
236#95—941no—
237#95—941no—
238#95—941no—
239#95—941no—
240#95—941no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—471no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4C2×C4×D4711yescharacteristic
250C22×C4D4×D4711yescharacteristic
251C22×C4D4×D4711yescharacteristic
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—942no—
259C2×C8—942no—
260C2×C8—942no—
261C2×C8—942no—
262C2×C8—1881no—
263C2×C8—1881no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—1881no—
267C4⋊C4—1881no—
268C4⋊C4—1882no—
269C4⋊C4—1882no—
270C4⋊C4—1882no—
271C4⋊C4—1882no—
272C42—942no—
273C42—942no—
274C42—942no—
275C42—1881no—
276C42—1881no—
277C42—1881no—
278C42C2×Dic9411yescharacteristic
279C42#1062535011yescharacteristic
280C42#1062535211yescharacteristic
281C42Q8×D4711yescharacteristic
282C23C22⋊C4×D4711yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—472no—
296C2×C4—472no—
297C2×C4—472no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—1881no—
308C2×C4—1881no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4#1309398911yescharacteristic
314C2×C4C4×Dic9411yescharacteristic
315C2×C4#1309400111yescharacteristic
316C2×C4#1309400211yescharacteristic
317C2×C4#1309401011yescharacteristic
318C2×C4#1309402311yescharacteristic
319C8—24no—
320C8—42no—
321C8—944no—
322C8—1882no—
323C22#1568902711yescharacteristic
324C22#1568910411yescharacteristic
325C22#1568910611yescharacteristic
326C22#104×D4711yescharacteristic
327C22#104×D4711yescharacteristic
328C22#104×D4711yescharacteristic
329C22#1568913811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—942no—
339C4—942no—
340C4—942no—
341C4—3761no—
342C4—3761no—
343C4—1881no—
344C2#2024197311yescharacteristic
345C2#2024197511yescharacteristic
346C2#2024199411yescharacteristic
347C2#2024200511yescharacteristic
348C2#2024433011yescharacteristic
349C2#2024436311yescharacteristic
350C2#2024437911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1295D47
hypocenterC47#9892
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
202. C47#9892semidirect

Maximal subgroups

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

subgroupindex
#202517732
#202432422
#97×Dic472
#202412702
#202412692
C47×#12952
#989247