Finite Group Databasebeta

← #20250342

Subgroups — #20250342

Order 6016.

416 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094016C211yesmaximal, characteristic
2C2×#13094015C211yesmaximal, characteristic
3#15689057C211yesmaximal, characteristic
4#15689057C211yesmaximal, characteristic
5#15689057C211yesmaximal, characteristic
6#15689056C211yesmaximal, characteristic
7#15689055C211yesmaximal, characteristic
8#15689055C211yesmaximal, characteristic
9#15689022C211yesmaximal, characteristic
10#15689021C211yesmaximal, characteristic
11#15689020C211yesmaximal, characteristic
12#15689020C211yesmaximal, characteristic
13#15689020C211yesmaximal, characteristic
14#15689009C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic
16#13094016—24no—
17#13094015—24no—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×Dic47⋊C4C2211yescharacteristic
35C2×Dic47⋊C4C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
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×C42×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C4⋊C4×C47—22no—
69C4⋊C4×C47Q814yes—
70C42×C47—22no—
71C4⋊Dic47—22no—
72C4⋊Dic47—22no—
73C4⋊Dic47—22no—
74C4⋊Dic47—22no—
75C4⋊Dic47—22no—
76C4⋊Dic47—22no—
77C4⋊Dic47—41no—
78C4⋊Dic47—41no—
79Dic47⋊C4—22no—
80Dic47⋊C4—22no—
81Dic47⋊C4—22no—
82Dic47⋊C4—22no—
83Dic47⋊C4—22no—
84Dic47⋊C4—22no—
85Dic47⋊C4—41no—
86Dic47⋊C4—41no—
87Dic47⋊C4—41no—
88Dic47⋊C4D414yes—
89C4×Dic47—22no—
90C4×Dic47—41no—
91C23×C47C2411yescharacteristic
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47C2×D412yes—
110C2×C4×C47C2×Q812yes—
111C2×C4×C47C2×Q812yes—
112C2×C4×C47C2×Q812yes—
113C2×Dic47—21no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
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×Dic47C2×D412yes—
135C2×Dic47C2×D412yes—
136C2×Dic47#4112yes—
137C22×C47C22×D411yescharacteristic
138C22×C47C22×Q811yescharacteristic
139C22×C47C2×#4111yescharacteristic
140C22×C47H(5,𝔽2)11yescharacteristic
141C22×C472−1+411yescharacteristic
142C22×C472−1+411yescharacteristic
143C22×C472−1+411yescharacteristic
144C4×C47—22no—
145C4×C47—22no—
146C4×C47—22no—
147C4×C47—22no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151Dic47—22no—
152Dic47—22no—
153Dic47—22no—
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#2726—471nomaximal, Sylow
160C2×C47#53711yescharacteristic
161C2×C47#53911yescharacteristic
162C2×C47#54411yescharacteristic
163C2×C47#54711yescharacteristic
164C2×C47D4×Q811yescharacteristic
165C2×C47#55711yescharacteristic
166C2×C47#56411yescharacteristic
167C2×#125—471no—
168C2×#125—471no—
169#398—471no—
170#398—471no—
171#398—471no—
172#398—471no—
173#398—471no—
174#398—471no—
175#389—471no—
176#389—471no—
177#389—471no—
178#389—471no—
179#389—471no—
180#387—471no—
181#387D4711yescharacteristic
182C47#272611yescharacteristic, complemented, Sylow
183#125—944no—
184#125—944no—
185C2×C4⋊C4—471no—
186C2×C4⋊C4—471no—
187C2×C4⋊C4—471no—
188C2×C4⋊C4—471no—
189C2×C4⋊C4—471no—
190C2×C4⋊C4—471no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—471no—
193C2×C4⋊C4—471no—
194C2×C4⋊C4—471no—
195C2×C4⋊C4—471no—
196C2×C4⋊C4—471no—
197C2×C4⋊C4—471no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4C2×D4711yescharacteristic
204C2×C4⋊C4C2×D4711yescharacteristic
205C2×C42—471no—
206C2×C42—471no—
207C2×C42C2×D4711yescharacteristic
208#95—471no—
209#95—471no—
210#95—471no—
211#95—471no—
212#95—471no—
213#95—471no—
214#95—471no—
215#95—471no—
216#95C2×D4711yescharacteristic
217#95C2×D4711yescharacteristic
218#95C2×D4711yescharacteristic
219#95C2×D4711yescharacteristic
220C22×C4—471no—
221C22×C4—471no—
222C22×C4—471no—
223C22×C4—471no—
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—471no—
228C22×C4C22×D4711yescharacteristic
229C22×C4C22×D4711yescharacteristic
230C22×C4C22×D4711yescharacteristic
231C22×C4C22×D4711yescharacteristic
232C22×C4C22×D4711yescharacteristic
233C22×C4C22×D4711yescharacteristic
234C22×C4C22×D4711yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—474no—
237C4⋊C4—942no—
238C4⋊C4—942no—
239C4⋊C4—942no—
240C4⋊C4—942no—
241C4⋊C4—942no—
242C4⋊C4—942no—
243C4⋊C4—942no—
244C4⋊C4—942no—
245C4⋊C4—942no—
246C4⋊C4—942no—
247C4⋊C4—942no—
248C4⋊C4—942no—
249C4⋊C4—1881no—
250C4⋊C4—1881no—
251C4⋊C4—1881no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C4⋊C4Dic9414yes—
255C42—22no—
256C42—942no—
257C42—1881no—
258C23C23×D4711yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—472no—
277C2×C4—472no—
278C2×C4—472no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4C2×Dic9412yes—
301C2×C4C2×Dic9412yes—
302C2×C4C2×Dic9412yes—
303C2×C4D4×D4712yes—
304C22C2×D4×D4711yescharacteristic
305C22C22×Dic9411yescharacteristic
306C22#41×D4711yescharacteristic
307C22#1309407011yescharacteristic
308C22#1309407111yescharacteristic
309C22#1309407111yescharacteristic
310C22#1309407211yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—942no—
319C4—942no—
320C4—942no—
321C4—1881no—
322C4—1881no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C2#1568970311yescharacteristic
327C2#1568971411yescharacteristic
328C2#1568975111yescharacteristic
329C2#1568977111yescharacteristic
330C2D4×Dic9411yescharacteristic
331C2#1568984911yescharacteristic
332C2C47⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#387C2
hypercenter#387D47
hypocenterC47#2726
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
182. C47#2726semidirect