Finite Group Databasebeta

← #20250421

Subgroups — #20250421

Order 6016.

456 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094024C211yesmaximal, characteristic
2C2×#13094023C211yesmaximal, characteristic
3#15689057C211yesmaximal, characteristic
4#15689055C211yesmaximal, characteristic
5#15689044C211yesmaximal, characteristic
6#15689044C211yesmaximal, characteristic
7#15689044C211yesmaximal, characteristic
8#15689043C211yesmaximal, characteristic
9#15689027C211yesmaximal, characteristic
10#15689022C211yesmaximal, characteristic
11#15689020C211yesmaximal, characteristic
12#15689010C211yesmaximal, characteristic
13#15689009C211yesmaximal, characteristic
14#15689007C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C22×Dic94C2211yescharacteristic
19#13094024—24no—
20#13094023—24no—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26C2×C4⋊Dic47C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
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×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
68C2×Dic94—22no—
69C2×Dic94—22no—
70C2×Dic94—41no—
71C2×Dic94—41no—
72C2×Dic94—41no—
73C2×Dic94—41no—
74C2×Dic94—41no—
75C2×Dic94—41no—
76C2×Dic94D414yes—
77C4⋊C4×C47—22no—
78C4⋊C4×C47Q814yescomplemented
79C42×C47—22no—
80C4⋊Dic47—22no—
81C4⋊Dic47—22no—
82C4⋊Dic47—22no—
83C4⋊Dic47—22no—
84C4⋊Dic47—22no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89Dic47⋊C4—41no—
90Dic47⋊C4—41no—
91Dic47⋊C4—41no—
92Dic47⋊C4Q814yescomplemented
93C4×Dic47—22no—
94C4×Dic47—41no—
95C23×C47C2411yescharacteristic
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×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D412yes—
113C2×C4×C47C2×Q812yes—
114C2×C4×C47C2×Q812yes—
115C2×C4×C47C2×Q812yes—
116C2×C4×C47C2×Q812yes—
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×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47C2×D412yes—
138C2×Dic47C2×D412yes—
139C2×Dic47C2×Q812yes—
140C2×Dic47C2×Q812yes—
141Dic94—44no—
142Dic94—44no—
143Dic94—44no—
144C22×C47C22×D411yescharacteristic
145C22×C47C22×Q811yescharacteristic
146C22×C47C22×Q811yescharacteristic
147C22×C47H(5,𝔽2)11yescharacteristic
148C22×C47H(5,𝔽2)11yescharacteristic
149C22×C472−1+411yescharacteristic
150C22×C472−1+411yescharacteristic
151C4×C47—22no—
152C4×C47—22no—
153C4×C47—22no—
154C4×C47—22no—
155C4×C47—22no—
156C4×C47—41no—
157C4×C47—41no—
158Dic47—22no—
159Dic47—22no—
160Dic47—22no—
161Dic47—22no—
162Dic47—41no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#2734—471nomaximal, Sylow
167C2×C47#53411yescharacteristic
168C2×C47#54411yescharacteristic
169C2×C47#54411yescharacteristic
170C2×C47D4×Q811yescharacteristic
171C2×C47D4×Q811yescharacteristic
172C2×C47Q8211yescharacteristic
173C2×C47#56311yescharacteristic
174C2×C4⋊Q8—471no—
175C2×C4⋊Q8—471no—
176#398—471no—
177#398—471no—
178#395—471no—
179#395—471no—
180#395—471no—
181#395—471no—
182#391—471no—
183#389—471no—
184#389—471no—
185#387—471no—
186#387—471no—
187#387—471no—
188#387D4711yescharacteristic
189C47#273411yescharacteristic, complemented, Sylow
190C22×Q8—471no—
191C22×Q8—471no—
192C22×Q8—471no—
193C4⋊Q8—944no—
194C4⋊Q8—944no—
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⋊C4—471no—
204C2×C4⋊C4—471no—
205C2×C4⋊C4—471no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4C2×D4711yescharacteristic
209C2×C4⋊C4C2×D4711yescharacteristic
210C2×C42—471no—
211C2×C42—471no—
212C2×C42C2×D4711yescharacteristic
213#95—471no—
214#95—471no—
215#95—471no—
216#95—471no—
217#95—471no—
218#95—471no—
219#95—471no—
220#95—471no—
221#95—471no—
222#95—471no—
223#95C2×D4711yescharacteristic
224#95C2×D4711yescharacteristic
225#95C2×D4711yescharacteristic
226#95C2×D4711yescharacteristic
227C2×Q8—474no—
228C2×Q8—942no—
229C2×Q8—942no—
230C2×Q8—1881no—
231C2×Q8—1881no—
232C2×Q8—1881no—
233C2×Q8—1881no—
234C2×Q8—1881no—
235C2×Q8—1881no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4C22×D4711yescharacteristic
245C22×C4C22×D4711yescharacteristic
246C22×C4C22×D4711yescharacteristic
247C22×C4C22×D4711yescharacteristic
248C22×C4C22×D4711yescharacteristic
249C22×C4C22×D4711yescharacteristic
250C22×C4C22×D4711yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—474no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C4⋊C4—942no—
257C4⋊C4—942no—
258C4⋊C4—942no—
259C4⋊C4—942no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C4⋊C4Dic9414yescomplemented
266C42—22no—
267C42—942no—
268C42—1881no—
269C23C23×D4711yescharacteristic
270Q8—1884no—
271Q8—1884no—
272Q8—1884no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—472no—
290C2×C4—472no—
291C2×C4—472no—
292C2×C4—472no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
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—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4C2×Dic9412yes—
314C2×C4C2×Dic9412yes—
315C2×C4C2×Dic9412yes—
316C2×C4D4×D4712yes—
317C2×C4Q8×D4712yes—
318C22C2×D4×D4711yescharacteristic
319C22C2×Q8×D4711yescharacteristic
320C22C22×Dic9411yescharacteristic
321C22#1309407011yescharacteristic
322C22#1309407011yescharacteristic
323C22#1309407111yescharacteristic
324C22#1309407111yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—41no—
331C4—41no—
332C4—942no—
333C4—942no—
334C4—942no—
335C4—942no—
336C4—1881no—
337C4—1881no—
338C4—1881no—
339C4—1881no—
340C2#1568968411yescharacteristic
341C2#1568975111yescharacteristic
342C2#1568975311yescharacteristic
343C2#1568978611yescharacteristic
344C2D4×Dic9411yescharacteristic
345C2Q8×Dic9411yescharacteristic
346C2#1568987511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#387C2
hypercenter#387D47
hypocenterC47#2734
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
78. C4⋊C4×C47Q8semidirect
92. Dic47⋊C4Q8semidirect
189. C47#2734semidirect
265. C4⋊C4Dic94semidirect