Finite Group Databasebeta

← #26125508

Subgroups — #26125508

Order 12032.

418 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689194C211yesmaximal, characteristic
2#20244999C211yesmaximal, characteristic, complemented
3#20241327C212yesmaximal, complemented
4#20241311C212yesmaximal, complemented
5C2×C47×C22⋊C16C211yesmaximal, characteristic, complemented
6C22×#10625324C411yescharacteristic
7C2×C4×C22⋊D47C411yescharacteristic
8C2×#13093964—21no—
9#15689194—21no—
10#15689194—21no—
11#15689194—21no—
12#15689194—21no—
13C2×Dic47⋊C8C2211yescharacteristic
14C2×C22⋊(C47⋊C8)C411yescharacteristic
15C2×(C2×D47)⋊C8C2211yescharacteristic
16C2×#13093934C411yescharacteristic
17C22⋊(C47⋊C16)—21no—
18C22⋊(C47⋊C16)C2212yes—
19C23×C8×C47C2211yescharacteristic
20C22×C16×C47—21no—
21C47×C22⋊C16—21no—
22C47×C22⋊C16C2212yes—
23C22×C22⋊D47C811yescharacteristic
24C22×C4×D47C2×C411yescharacteristic
25C2×#10625324—21no—
26C2×#10625324—21no—
27C2×#10625324—42no—
28C22×C47⋊C8C2×C411yescharacteristic
29C22×C47⋊C8C2×C411yescharacteristic
30C4×C22⋊D47—21no—
31C4×C22⋊D47—21no—
32C4×C22⋊D47—21no—
33C4×C22⋊D47—21no—
34C2×Dic47⋊C4C811yescharacteristic
35C2×C22⋊Dic47C811yescharacteristic
36C2×(C2×D47)⋊C4C811yescharacteristic
37C2×C4×Dic47C2×C411yescharacteristic
38#13093964—42no—
39C2×C47⋊C16—22no—
40Dic47⋊C8—21no—
41Dic47⋊C8—21no—
42C22⋊(C47⋊C8)—21no—
43C22⋊(C47⋊C8)—21no—
44(C2×D47)⋊C8—21no—
45(C2×D47)⋊C8—21no—
46#13093934—21no—
47#13093934—21no—
48C23×C4×C47C2×C411yescharacteristic
49C22×C8×C47—42no—
50C22×C8×C47C2×C411yescharacteristic
51C22×C8×C47D411yescharacteristic
52C22×C8×C47D411yescharacteristic
53C22×C8×C47D411yescharacteristic
54C22×C8×C47D411yescharacteristic
55C22×C8×C47C2311yescharacteristic
56C2×C16×C47—22no—
57C2×C16×C47—42no—
58C24×C47C2×C811yescharacteristic
59C23×D47C2×C811yescharacteristic
60C22×C4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47C22⋊C411yescharacteristic
63C22×C4×C47C22⋊C411yescharacteristic
64C22×C4×C47C2×C811yescharacteristic
65C22×C4×C47M1611yescharacteristic
66C22×C4×C47M1611yescharacteristic
67C22×C4×C47C22×C411yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—42no—
71C22×Dic47C2×C811yescharacteristic
72C22×Dic47C2×C811yescharacteristic
73C22×Dic47C2×C811yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—41no—
77C2×C4×D47—41no—
78C2×C8×C47—22no—
79C2×C8×C47—22no—
80C2×C8×C47—22no—
81C2×C8×C47—41no—
82C2×C8×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47C22⋊C411yescharacteristic
85C2×C8×C47C22⋊C411yescharacteristic
86C2×C8×C47C2×D411yescharacteristic
87C2×C8×C47C2×D411yescharacteristic
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94C4×Dic47—21no—
95C4×Dic47—21no—
96C2×C47⋊C8—21no—
97C2×C47⋊C8—21no—
98C2×C47⋊C8—41no—
99C2×C47⋊C8—41no—
100#10625324—42no—
101#10625324—42no—
102C16×C47—42no—
103C47⋊C16—42no—
104C23×C47—22no—
105C23×C47—22no—
106C23×C47—41no—
107C23×C47C22⋊C811yescharacteristic
108C23×C47C22⋊C811yescharacteristic
109C23×C47C22×C811yescharacteristic
110C22×D47—21no—
111C22×D47—22no—
112C22×D47—41no—
113C22×D47—41no—
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—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47C22⋊C811yescharacteristic
124C2×C4×C47C22⋊C811yescharacteristic
125C2×C4×C47C2×C22⋊C411yescharacteristic
126C2×C4×C47C2×M1611yescharacteristic
127C22⋊D47—42no—
128C22⋊D47—42no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—22no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C4×D47—42no—
136C4×D47—41no—
137C4×D47—41no—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47—21no—
141C8×C47#9912yes—
142C47⋊C8—41no—
143C47⋊C8—41no—
144#11467—471nomaximal, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—44no—
153C22×C47#34912yes—
154C22×C47C2×C22⋊C811yescharacteristic
155C22×C47#50412yes—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—82no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47C2×#9911yescharacteristic
164C4×C47#41311yescharacteristic
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168C2×#435—471no—
169#2112—471no—
170C2×C22⋊C16D4711yescharacteristic, complemented
171#1322—472no—
172#1314—472no—
173C2×C47—22no—
174C2×C47—22no—
175C2×C47—41no—
176C2×C47#145911yescharacteristic
177C2×C47#211311yescharacteristic
178C2×C47C2×#34911yescharacteristic
179D47—81no—
180C22×M16—471no—
181C23×C8C2×D4711yescharacteristic
182C2×C4×D4—471no—
183C2×M32—941no—
184C22×C16—21no—
185#435—941no—
186#435—941no—
187#435—941no—
188#435—941no—
189C2×C4⋊C8—471no—
190C2×C22⋊C8—471no—
191C2×C22⋊C8—471no—
192C2×#97—471no—
193C22⋊C16—21no—
194C22⋊C16—472no—
195C22⋊C16—941no—
196C22⋊C16C2×D4712yes—
197C47#1146711yescharacteristic, complemented, Sylow
198C22×D4—471no—
199C23×C4—471no—
200C23×C4C4×D4711yescharacteristic
201C2×M16—941no—
202C2×M16—941no—
203C2×M16—1882no—
204C22×C8—42no—
205C22×C8—471no—
206C22×C8—471no—
207C22×C8C4×D4711yescharacteristic
208C22×C8D18811yescharacteristic
209C22×C8D18811yescharacteristic
210C22×C8C22⋊D4711yescharacteristic
211C22×C8C22⋊D4711yescharacteristic
212C22×C8C22×D4711yescharacteristic
213C4×D4—941no—
214C4×D4—941no—
215C4×D4—941no—
216C4×D4—941no—
217C2×C4⋊C4—471no—
218C2×C22⋊C4—471no—
219C2×C22⋊C4—471no—
220C2×C42—471no—
221M32—1882no—
222C2×C16—22no—
223C2×C16—42no—
224C2×C16—942no—
225C4⋊C8—941no—
226C4⋊C8—941no—
227C22⋊C8—941no—
228C22⋊C8—941no—
229C22⋊C8—941no—
230C22⋊C8—941no—
231#97—941no—
232#97—941no—
233C24—471no—
234C24C8×D4711yescharacteristic
235C2×D4—941no—
236C2×D4—941no—
237C2×D4—1882no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—1881no—
246C22×C4—1881no—
247C22×C4C8×D4711yescharacteristic
248C22×C4#1062532411yescharacteristic
249C22×C4#1062532411yescharacteristic
250C22×C4(C2×D47)⋊C411yescharacteristic
251C22×C4(C2×D47)⋊C411yescharacteristic
252C22×C4C2×C4×D4711yescharacteristic
253M16—1882no—
254M16—1882no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—1881no—
264C2×C8—1881no—
265C2×C8(C2×D47)⋊C411yescharacteristic
266C2×C8(C2×D47)⋊C411yescharacteristic
267C2×C8C2×D18811yescharacteristic
268C2×C8C2×C22⋊D4711yescharacteristic
269C4⋊C4—941no—
270C4⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—941no—
276C42—941no—
277C16—42no—
278C16—1882no—
279C23—22no—
280C23—22no—
281C23—41no—
282C23—942no—
283C23—941no—
284C23—1881no—
285C23—1881no—
286C23(C2×D47)⋊C811yescharacteristic
287C23(C2×D47)⋊C811yescharacteristic
288C23C2×C8×D4711yescharacteristic
289D4—1882no—
290D4—1882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—942no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—1882no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4—1881no—
308C2×C4—1881no—
309C2×C4(C2×D47)⋊C811yescharacteristic
310C2×C4(C2×D47)⋊C811yescharacteristic
311C2×C4C2×(C2×D47)⋊C411yescharacteristic
312C2×C4C2×#1062532411yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—1881no—
317C8—1881no—
318C8#1309393812yes—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—44no—
327C22—3762no—
328C22—1881no—
329C22—1881no—
330C22—1881no—
331C22#1568890412yes—
332C22C2×(C2×D47)⋊C811yescharacteristic
333C22#1568953912yes—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—1881no—
338C4—1881no—
339C4—1881no—
340C4C2×#1309393811yescharacteristic
341C4#1568910511yescharacteristic
342C2—22no—
343C2—22no—
344C2—41no—
345C2—3761no—
346C2#2024170411yescharacteristic
347C2#2024500111yescharacteristic
348C2C2×#1568890411yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC23×C47C22×C8
FrattiniC22×C8C22×D47
FittingC2×C47×C22⋊C16C2
socleC22×C47C2×C22⋊C8
prime radicalC22×C22⋊D47C8
cosocleC22×C8×C47C23
hypercenterC2×C22⋊C16D47
hypocenterC47#11467
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. #20244999C2semidirect
3. #20241327C2semidirect
4. #20241311C2semidirect
5. C2×C47×C22⋊C16C2semidirect
170. C2×C22⋊C16D47semidirect
197. C47#11467semidirect

Maximal subgroups

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

subgroupindex
C2×#156891942
#202449992
#202413272
#202413112
C2×C47×C22⋊C162
#1146747