Finite Group Databasebeta

← #20246131

Subgroups — #20246131

Order 6016.

460 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094022C211yesmaximal, characteristic
2#15689030C211yesmaximal, characteristic
3#15689027C211yesmaximal, characteristic
4#15689027C211yesmaximal, characteristic
5#15689020C211yesmaximal, characteristic
6#15689018C211yesmaximal, characteristic
7#15689010C211yesmaximal, characteristic
8#15689007C211yesmaximal, characteristic
9#15689005C211yesmaximal, characteristic
10#15689004C211yesmaximal, characteristic
11#15688987C211yesmaximal, characteristic
12C4×Dic47⋊C4C211yesmaximal, characteristic
13#15688974C211yesmaximal, characteristic
14#15688968C211yesmaximal, characteristic
15C47×#391C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17#13094022C418yescomplemented
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×C4×Dic47C2211yescharacteristic
28C2×C4×Dic47C2211yescharacteristic
29C2×C4×Dic47C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C22×Q8×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C42×C47C2211yescharacteristic
48#95×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52C2×Q8×C47—41no—
53C2×Q8×C47—41no—
54C2×Q8×C47C2×C414yes—
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C2×Dic94—41no—
71C2×Dic94—41no—
72C2×Dic94C2×C414yes—
73C4⋊C4×C47—41no—
74C42×C47—41no—
75C4⋊Dic47—41no—
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—41no—
79Dic47⋊C4—41no—
80Dic47⋊C4C2×C414yes—
81Dic47⋊C4C2×C414yes—
82Dic47⋊C4C2×C414yes—
83Dic47⋊C4C2×C414yes—
84C4×Dic47—22no—
85C4×Dic47—41no—
86C4×Dic47—41no—
87C4×Dic47—41no—
88C4×Dic47C2×C414yes—
89C4×Dic47Q814yescomplemented
90C23×C47C2411yescharacteristic
91Q8×C47—44no—
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×C47C22×C412yes—
110C2×C4×C47C22×C412yes—
111C2×C4×C47C22×C412yes—
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×Dic47C22×C412yes—
131C2×Dic47C22×C412yes—
132C2×Dic47C22×C412yes—
133C2×Dic47C22×C412yes—
134C2×Dic47C2×Q812yes—
135C2×Dic47C2×Q812yes—
136C2×Dic47#4112yes—
137Dic94—44no—
138C22×C47C23×C411yescharacteristic
139C22×C47C22×Q811yescharacteristic
140C22×C47C2×#4111yescharacteristic
141C22×C47H(5,𝔽2)11yescharacteristic
142C22×C47H(5,𝔽2)11yescharacteristic
143C22×C472−1+411yescharacteristic
144C22×C472−1+411yescharacteristic
145C4×C47—22no—
146C4×C47—22no—
147C4×C47—22no—
148C4×C47—22no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47—41no—
152Dic47—22no—
153Dic47—22no—
154Dic47—22no—
155Dic47—22no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47C4×Q814yes—
160#2331—471nomaximal, Sylow
161C2×C47C2×C4×Q811yescharacteristic
162C2×C47#51811yescharacteristic
163C2×C47#51911yescharacteristic
164C2×C47#54211yescharacteristic
165C2×C47#54211yescharacteristic
166C2×C47#54411yescharacteristic
167C2×C47#54411yescharacteristic
168C2×C4⋊Q8—471no—
169#391—471no—
170#391—471no—
171#391—471no—
172#391D4711yescharacteristic
173#389—471no—
174#389—471no—
175#387—471no—
176#387—471no—
177#387—471no—
178#387—471no—
179#382—471no—
180C4×C4⋊C4—471no—
181C4×C4⋊C4—471no—
182#376—471no—
183C47#233111yescharacteristic, complemented, Sylow
184C22×Q8—471no—
185C22×Q8C2×D4711yescharacteristic
186C4⋊Q8—478no—
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⋊C4C2×D4711yescharacteristic
197C2×C42—471no—
198C2×C42—471no—
199C2×C42—471no—
200C2×C42—471no—
201C2×C42—471no—
202C2×C42—471no—
203C2×C42C2×D4711yescharacteristic
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#95—471no—
215#95—471no—
216#95C2×D4711yescharacteristic
217#95C2×D4711yescharacteristic
218#95C2×D4711yescharacteristic
219#95C2×D4711yescharacteristic
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8—474no—
223C2×Q8—1881no—
224C2×Q8—1881no—
225C2×Q8C4×D4714yes—
226C22×C4—471no—
227C22×C4—471no—
228C22×C4—471no—
229C22×C4—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4C22×D4711yescharacteristic
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237C22×C4C22×D4711yescharacteristic
238C22×C4C22×D4711yescharacteristic
239C22×C4C22×D4711yescharacteristic
240C22×C4C22×D4711yescharacteristic
241C4⋊C4—41no—
242C4⋊C4—474no—
243C4⋊C4—474no—
244C4⋊C4—474no—
245C4⋊C4—474no—
246C4⋊C4—942no—
247C4⋊C4—942no—
248C4⋊C4—1881no—
249C4⋊C4—1881no—
250C4⋊C4—1881no—
251C42—41no—
252C42—474no—
253C42—474no—
254C42—942no—
255C42—1881no—
256C42—1881no—
257C42—1881no—
258C23C23×D4711yescharacteristic
259Q8—44no—
260Q8—1884no—
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—21no—
277C2×C4—21no—
278C2×C4—472no—
279C2×C4—472no—
280C2×C4—472no—
281C2×C4—472no—
282C2×C4—472no—
283C2×C4—472no—
284C2×C4—472no—
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×C4—941no—
301C2×C4—941no—
302C2×C4C2×C4×D4712yes—
303C2×C4C2×C4×D4712yes—
304C2×C4C2×C4×D4712yes—
305C2×C4Q8×D4712yes—
306C22C22×C4×D4711yescharacteristic
307C22C2×Q8×D4711yescharacteristic
308C22#41×D4711yescharacteristic
309C22#1309406911yescharacteristic
310C22#1309406911yescharacteristic
311C22#1309407111yescharacteristic
312C22#1309407211yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—474no—
321C4—942no—
322C4—942no—
323C4—942no—
324C4—942no—
325C4—1881no—
326C4—1881no—
327C4—1881no—
328C2C4×Q8×D4711yescharacteristic
329C2#1568959611yescharacteristic
330C2#1568959911yescharacteristic
331C2#1568973711yescharacteristic
332C2#1568974311yescharacteristic
333C2#1568975011yescharacteristic
334C2#1568975211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#391C2
socleC23×C47C24
hypercenter#391D47
hypocenterC47#2331
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
17. #13094022C4semidirect
89. C4×Dic47Q8semidirect
183. C47#2331semidirect