Finite Group Databasebeta

← #20248796

Subgroups — #20248796

Order 6016.

412 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
1#15689057C211yesmaximal, characteristic
2#15689044C211yesmaximal, characteristic
3#15689044C211yesmaximal, characteristic
4#15689043C211yesmaximal, characteristic
5#15689027C211yesmaximal, characteristic
6#15689027C211yesmaximal, characteristic
7#15689027C211yesmaximal, characteristic
8#15689021C211yesmaximal, characteristic
9#15689019C211yesmaximal, characteristic
10#15689010C211yesmaximal, characteristic
11#15689010C211yesmaximal, characteristic
12#15689009C211yesmaximal, characteristic
13C4⋊C4×Dic47C211yesmaximal, characteristic
14C4×Dic47⋊C4C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C2×C4⋊Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
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×C4×Dic47C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C2×C4⋊C4×C47C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C42×C47C2211yescharacteristic
47#95×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×Dic47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C2×Dic94—22no—
67C2×Dic94—22no—
68C2×Dic94—22no—
69C2×Dic94—41no—
70C2×Dic94—41no—
71C2×Dic94—41no—
72C4⋊C4×C47—41no—
73C4⋊C4×C47Q814yescomplemented
74C42×C47—41no—
75C4⋊Dic47—22no—
76C4⋊Dic47—22no—
77C4⋊Dic47—22no—
78C4⋊Dic47—41no—
79Dic47⋊C4—22no—
80Dic47⋊C4—41no—
81Dic47⋊C4—41no—
82Dic47⋊C4—41no—
83Dic47⋊C4—41no—
84Dic47⋊C4Q814yescomplemented
85C4×Dic47—22no—
86C4×Dic47—22no—
87C4×Dic47—41no—
88C4×Dic47—41no—
89C23×C47C2411yescharacteristic
90C2×C4×C47—21no—
91C2×C4×C47—21no—
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×C47C2×Q812yes—
108C2×C4×C47C2×Q812yes—
109C2×C4×C47C2×Q812yes—
110C2×C4×C47C2×Q812yes—
111C2×Dic47—21no—
112C2×Dic47—21no—
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×Dic47C2×Q812yes—
131C2×Dic47C2×Q812yes—
132C2×Dic47#4112yes—
133C2×Dic47#4112yes—
134C2×Dic47#4112yes—
135Dic94—44no—
136Dic94—44no—
137C22×C47C22×Q811yescharacteristic
138C22×C47C22×Q811yescharacteristic
139C22×C47C2×#4111yescharacteristic
140C22×C47C2×#4111yescharacteristic
141C22×C47C2×#4111yescharacteristic
142C22×C47H(5,𝔽2)11yescharacteristic
143C22×C47H(5,𝔽2)11yescharacteristic
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—22no—
155Dic47—22no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159#2586—471nomaximal, Sylow
160C2×C47#53311yescharacteristic
161C2×C47#53311yescharacteristic
162C2×C47#53811yescharacteristic
163C2×C47#55111yescharacteristic
164C2×C47#55411yescharacteristic
165C2×C47#55411yescharacteristic
166C2×C47Q8211yescharacteristic
167#398—471no—
168#395—471no—
169#395—471no—
170#395—471no—
171#391—471no—
172#391—471no—
173#391—471no—
174#389—471no—
175#389—471no—
176#387—471no—
177#387—471no—
178#387—471no—
179#387D4711yescharacteristic
180C4×C4⋊C4—471no—
181C4×C4⋊C4—471no—
182C47#258611yescharacteristic, complemented, Sylow
183C22×Q8—471no—
184C22×Q8—471no—
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⋊C4C2×D4711yescharacteristic
196C2×C4⋊C4C2×D4711yescharacteristic
197C2×C42—471no—
198C2×C42—471no—
199C2×C42—471no—
200C2×C42—471no—
201C2×C42C2×D4711yescharacteristic
202#95—471no—
203#95—471no—
204#95—471no—
205#95—471no—
206#95—471no—
207#95—471no—
208#95—471no—
209#95—471no—
210#95—471no—
211#95—471no—
212#95—471no—
213#95—471no—
214#95C2×D4711yescharacteristic
215#95C2×D4711yescharacteristic
216#95C2×D4711yescharacteristic
217#95C2×D4711yescharacteristic
218C2×Q8—942no—
219C2×Q8—942no—
220C2×Q8—942no—
221C2×Q8—1881no—
222C2×Q8—1881no—
223C2×Q8—1881no—
224C22×C4—471no—
225C22×C4—471no—
226C22×C4—471no—
227C22×C4—471no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4C22×D4711yescharacteristic
233C22×C4C22×D4711yescharacteristic
234C22×C4C22×D4711yescharacteristic
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237C22×C4C22×D4711yescharacteristic
238C22×C4C22×D4711yescharacteristic
239C4⋊C4—41no—
240C4⋊C4—474no—
241C4⋊C4—942no—
242C4⋊C4—942no—
243C4⋊C4—942no—
244C4⋊C4—942no—
245C4⋊C4—1881no—
246C4⋊C4—1881no—
247C4⋊C4—1881no—
248C4⋊C4—1881no—
249C4⋊C4—1881no—
250C4⋊C4Dic9414yescomplemented
251C42—41no—
252C42—942no—
253C42—942no—
254C42—1881no—
255C42—1881no—
256C23C23×D4711yescharacteristic
257Q8—1884no—
258Q8—1884no—
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—472no—
280C2×C4—472no—
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×C4Q8×D4712yes—
304C22C2×Q8×D4711yescharacteristic
305C22C22×Dic9411yescharacteristic
306C22#41×D4711yescharacteristic
307C22#41×D4711yescharacteristic
308C22#41×D4711yescharacteristic
309C22#1309406911yescharacteristic
310C22#1309407011yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—942no—
319C4—942no—
320C4—942no—
321C4—942no—
322C4—942no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C2#1568967611yescharacteristic
327C2#1568967911yescharacteristic
328C2#1568970911yescharacteristic
329C2#1568979811yescharacteristic
330C2#1568982711yescharacteristic
331C2#1568983211yescharacteristic
332C2Q8×Dic9411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#387C2
hypercenter#387D47
hypocenterC47#2586
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
73. C4⋊C4×C47Q8semidirect
84. Dic47⋊C4Q8semidirect
182. C47#2586semidirect
250. C4⋊C4Dic94semidirect