Finite Group Databasebeta

← #20247107

Subgroups — #20247107

Order 6016.

520 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094014C211yesmaximal, characteristic, complemented
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3#15689065C211yesmaximal, characteristic, complemented
4#15689062C211yesmaximal, characteristic, complemented
5#15689057C211yesmaximal, characteristic, complemented
6#15689018C211yesmaximal, characteristic, complemented
7#15689018C211yesmaximal, characteristic, complemented
8#15688994C211yesmaximal, characteristic
9#15688994C211yesmaximal, characteristic
10#15688987C211yesmaximal, characteristic, complemented
11#15688982C211yesmaximal, characteristic
12#15688982C211yesmaximal, characteristic
13#15688980C211yesmaximal, characteristic
14#15688970C211yesmaximal, characteristic
15C47×#398C211yesmaximal, characteristic, complemented
16C22×C4×D47C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19#13094014—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C4⋊C4×D47—24no—
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C2×C4×D47—22no—
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—22no—
74C2×C4×D47—41no—
75C2×C4×D47—41no—
76C2×C4×D47Q814yes—
77C4⋊C4×C47—22no—
78C4⋊C4×C47—22no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81(C2×D47)⋊C4—22no—
82(C2×D47)⋊C4—22no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4—22no—
85C4⋊Dic47—22no—
86C4⋊Dic47—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92Dic47⋊C4—41no—
93Dic47⋊C4—41no—
94Dic47⋊C4D414yes—
95C4×Dic47—22no—
96C4×Dic47—22no—
97C23×C47C2411yescharacteristic
98C22×D47—21no—
99C22×D47—21no—
100C22×D47—21no—
101C22×D47—21no—
102C22×D47C2×Q812yes—
103C22×D47#4112yes—
104C22×D47#4112yes—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
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—21no—
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×C47C2×D412yes—
125C2×C4×C47C2×Q812yes—
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—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47C2×D412yes—
144C2×Dic47C2×D412yes—
145C2×Dic47C2×Q812yes—
146C2×Dic47#4112yes—
147C4×D47—28no—
148C4×D47—44no—
149C4×D47—44no—
150C22×C47C22×D411yescharacteristic
151C22×C47C22×Q811yescharacteristic
152C22×C47C2×#4111yescharacteristic
153C22×C47C2×#4111yescharacteristic
154C22×C47C2×#4111yescharacteristic
155C22×C47H(5,𝔽2)11yescharacteristic
156C22×C472−1+411yescharacteristic
157C2×D47—22no—
158C2×D47—22no—
159C2×D47—22no—
160C2×D47—22no—
161C2×D47—22no—
162C2×D47—22no—
163C2×D47#12514yescomplemented
164C4×C47—22no—
165C4×C47—22no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47—41no—
171Dic47—22no—
172Dic47—41no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177Dic47C22⋊Q814yes—
178#2442—471nomaximal, Sylow
179C2×C47C2×C22⋊Q811yescharacteristic
180C2×C47C2×#12511yescharacteristic
181C2×C47#54411yescharacteristic
182C2×C47#54611yescharacteristic
183C2×C47#54811yescharacteristic
184C2×C47#55211yescharacteristic
185C2×C47#55311yescharacteristic
186D47—24no—
187C2×#125—471no—
188C22×C4⋊C4—471no—
189#400—471no—
190#400—471no—
191#398—471no—
192#398D4711yescharacteristic, complemented
193#389—471no—
194#389—471no—
195#385—471no—
196#385—471no—
197#382—471no—
198#380—471no—
199#380—471no—
200#380—471no—
201C4×C22⋊C4—471no—
202C47#244211yescharacteristic, complemented, Sylow
203C23×C4—471no—
204C23×C4—471no—
205C23×C4—471no—
206#125—944no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4—944no—
218C2×C4⋊C4C2×D4711yescharacteristic
219C2×C4⋊C4C2×D4711yescharacteristic
220C2×C4⋊C4C2×D4711yescharacteristic
221C2×C4⋊C4C2×D4711yescharacteristic
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C22⋊C4—471no—
225C2×C22⋊C4—471no—
226C2×C42—471no—
227C2×C42—471no—
228#95—471no—
229#95—471no—
230#95—471no—
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95—471no—
236#95—471no—
237#95C2×D4711yescharacteristic
238#95C2×D4711yescharacteristic
239#95C2×D4711yescharacteristic
240C24—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—474no—
244C22×C4—471no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—942no—
250C22×C4—942no—
251C22×C4—942no—
252C22×C4—942no—
253C22×C4—942no—
254C22×C4—942no—
255C22×C4—1881no—
256C22×C4—1881no—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259C22×C4C22×D4711yescharacteristic
260C22×C4C22×D4711yescharacteristic
261C22×C4C22×D4711yescharacteristic
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—474no—
269C4⋊C4—942no—
270C4⋊C4—942no—
271C4⋊C4—942no—
272C4⋊C4—942no—
273C4⋊C4—942no—
274C4⋊C4—942no—
275C4⋊C4—942no—
276C4⋊C4—1881no—
277C4⋊C4—1881no—
278C22⋊C4—942no—
279C22⋊C4—942no—
280C22⋊C4—942no—
281C22⋊C4—942no—
282C42—942no—
283C42—942no—
284C23—472no—
285C23—472no—
286C23—472no—
287C23—941no—
288C23—941no—
289C23—941no—
290C23—941no—
291C23C23×D4711yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
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—21no—
311C2×C4—472no—
312C2×C4—472no—
313C2×C4—472no—
314C2×C4—472no—
315C2×C4—948no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—1884no—
334C2×C4—1884no—
335C2×C4D4×D4712yes—
336C2×C4Q8×D4712yes—
337C22—474no—
338C22—942no—
339C22—942no—
340C22—942no—
341C22—942no—
342C22—942no—
343C22—942no—
344C22C2×D4×D4711yescharacteristic
345C22C2×Q8×D4711yescharacteristic
346C22#41×D4711yescharacteristic
347C22#41×D4711yescharacteristic
348C22#41×D4711yescharacteristic
349C22#1309406911yescharacteristic
350C22#1309407211yescharacteristic
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—474no—
359C4—942no—
360C4—1881no—
361C4—1881no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C2—944no—
366C2C22⋊Q8×D4711yescharacteristic
367C2#125×D4711yescharacteristic
368C2#1568975011yescharacteristic
369C2#1568976211yescharacteristic
370C2#1568978311yescharacteristic
371C2#1568980511yescharacteristic
372C2#1568981811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2442
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13094014C2semidirect
3. #15689065C2semidirect
4. #15689062C2semidirect
5. #15689057C2semidirect
6. #15689018C2semidirect
7. #15689018C2semidirect
10. #15688987C2semidirect
15. C47×#398C2semidirect
163. C2×D47#125semidirect
192. #398D47semidirect
202. C47#2442semidirect