Finite Group Databasebeta

← #20248397

Subgroups — #20248397

Order 6016.

544 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094002C211yesmaximal, characteristic
2C2×#13094000C211yesmaximal, characteristic
3#15689057C211yesmaximal, characteristic, complemented
4#15689054C211yesmaximal, characteristic, complemented
5#15689044C211yesmaximal, characteristic, complemented
6#15689042C211yesmaximal, characteristic, complemented
7#15689027C211yesmaximal, characteristic, complemented
8#15689021C211yesmaximal, characteristic, complemented
9#15689020C211yesmaximal, characteristic, complemented
10#15688997C211yesmaximal, characteristic
11#15688997C211yesmaximal, characteristic
12#15688982C211yesmaximal, characteristic
13C4×(C2×D47)⋊C4C211yesmaximal, characteristic
14#95×D47C211yesmaximal, characteristic
15C47×#391C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094002—24no—
21#13094000—24no—
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
24C2×C4⋊Dic47C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×Q8×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C42×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C23×D47C2311yescharacteristic
54C2×Q8×C47—22no—
55C2×Q8×C47—22no—
56C2×Q8×C47—41no—
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C2×C4×D47—22no—
72C2×C4×D47—22no—
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—41no—
76C2×C4×D47—41no—
77C2×C4×D47—41no—
78C2×C4×D47—41no—
79C2×C4×D47Q814yescomplemented
80C2×Dic94—22no—
81C2×Dic94—22no—
82C2×Dic94—41no—
83C4⋊C4×C47—22no—
84C42×C47—41no—
85(C2×D47)⋊C4—22no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4D414yes—
88(C2×D47)⋊C4Q814yescomplemented
89C4⋊Dic47—22no—
90C4⋊Dic47—22no—
91C4⋊Dic47—41no—
92Dic47⋊C4—22no—
93Dic47⋊C4—22no—
94Dic47⋊C4—22no—
95Dic47⋊C4—22no—
96Dic47⋊C4—22no—
97Dic47⋊C4—41no—
98Dic47⋊C4—41no—
99Dic47⋊C4—41no—
100C4×Dic47—41no—
101C23×C47C2411yescharacteristic
102C22×D47—21no—
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47C2×D412yes—
107C22×D47C2×Q812yes—
108C22×D47C2×Q812yes—
109Q8×C47—44no—
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×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47C2×D412yes—
128C2×C4×C47C2×Q812yes—
129C2×C4×C47C2×Q812yes—
130C2×C4×C47#4112yes—
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×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47C2×D412yes—
149C2×Dic47C2×Q812yes—
150C2×Dic47C2×Q812yes—
151C2×Dic47#4112yes—
152C4×D47—44no—
153C4×D47—44no—
154C4×D47—44no—
155Dic94—44no—
156C22×C47C22×D411yescharacteristic
157C22×C47C22×Q811yescharacteristic
158C22×C47C22×Q811yescharacteristic
159C22×C47C2×#4111yescharacteristic
160C22×C47C2×#4111yescharacteristic
161C22×C47H(5,𝔽2)11yescharacteristic
162C22×C47H(5,𝔽2)11yescharacteristic
163C2×D47—22no—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—22no—
168C2×D47—22no—
169C2×D47C4⋊Q814yes—
170C4×C47—22no—
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—22no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177Dic47—22no—
178Dic47—22no—
179Dic47—22no—
180Dic47—22no—
181Dic47—41no—
182Dic47—41no—
183Dic47—41no—
184#2549—471nomaximal, Sylow
185C2×C47C2×C4⋊Q811yescharacteristic
186C2×C47#53311yescharacteristic
187C2×C47#54311yescharacteristic
188C2×C47#54611yescharacteristic
189C2×C47#54611yescharacteristic
190C2×C47#55411yescharacteristic
191C2×C47#55411yescharacteristic
192D47—24no—
193C2×C22⋊Q8—471no—
194C2×C22⋊Q8—471no—
195#398—471no—
196#398—471no—
197#395—471no—
198#395—471no—
199#391—471no—
200#391D4711yescharacteristic, complemented
201#389—471no—
202#389—471no—
203#385—471no—
204#385—471no—
205#380—471no—
206C4×C22⋊C4—471no—
207C2×#95—471no—
208C47#254911yescharacteristic, complemented, Sylow
209C22×Q8—471no—
210C22×Q8C2×D4711yescharacteristic
211C23×C4—471no—
212C23×C4—471no—
213C23×C4—471no—
214C22⋊Q8—944no—
215C22⋊Q8—944no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4C2×D4711yescharacteristic
228C2×C22⋊C4—471no—
229C2×C22⋊C4—471no—
230C2×C22⋊C4—471no—
231C2×C22⋊C4—471no—
232C2×C42—471no—
233C2×C42C2×D4711yescharacteristic
234#95—471no—
235#95—471no—
236#95—471no—
237#95—471no—
238#95—471no—
239#95—471no—
240#95—471no—
241#95—471no—
242#95C2×D4711yescharacteristic
243#95C2×D4711yescharacteristic
244#95C2×D4711yescharacteristic
245#95C2×D4711yescharacteristic
246C24—471no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—942no—
251C2×Q8—942no—
252C2×Q8—1881no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—474no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—942no—
262C22×C4—942no—
263C22×C4—942no—
264C22×C4—942no—
265C22×C4—1881no—
266C22×C4—1881no—
267C22×C4—1881no—
268C22×C4—1881no—
269C22×C4C22×D4711yescharacteristic
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C22×C4C22×D4711yescharacteristic
274C22×C4C22×D4711yescharacteristic
275C22×C4C22×D4711yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—942no—
278C4⋊C4—942no—
279C4⋊C4—942no—
280C4⋊C4—942no—
281C4⋊C4—942no—
282C4⋊C4—942no—
283C4⋊C4—942no—
284C4⋊C4—1881no—
285C4⋊C4—1881no—
286C4⋊C4—1881no—
287C4⋊C4—1881no—
288C22⋊C4—474no—
289C22⋊C4—474no—
290C22⋊C4—942no—
291C22⋊C4—942no—
292C42—41no—
293C42—1881no—
294C23—472no—
295C23—472no—
296C23—472no—
297C23—941no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23C23×D4711yescharacteristic
302Q8—44no—
303Q8—1884no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—472no—
322C2×C4—472no—
323C2×C4—472no—
324C2×C4—472no—
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—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—1884no—
343C2×C4—1884no—
344C2×C4—1884no—
345C2×C4#1062535012yes—
346C2×C4D4×D4712yes—
347C2×C4Q8×D4712yes—
348C2×C4Q8×D4712yes—
349C22—474no—
350C22—942no—
351C22—942no—
352C22—942no—
353C22—942no—
354C22—942no—
355C22—942no—
356C22C2×D4×D4711yescharacteristic
357C22C2×Q8×D4711yescharacteristic
358C22C2×Q8×D4711yescharacteristic
359C22#41×D4711yescharacteristic
360C22C2×#1062535011yescharacteristic
361C22#1309406911yescharacteristic
362C22#1309407011yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—942no—
371C4—942no—
372C4—942no—
373C4—942no—
374C4—1881no—
375C4—1881no—
376C4—1881no—
377C2—944no—
378C2C4⋊Q8×D4711yescharacteristic
379C2#1568967711yescharacteristic
380C2#1568974811yescharacteristic
381C2#1568976311yescharacteristic
382C2#1568976611yescharacteristic
383C2#1568982711yescharacteristic
384C2#1568983311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2549
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #15689057C2semidirect
4. #15689054C2semidirect
5. #15689044C2semidirect
6. #15689042C2semidirect
7. #15689027C2semidirect
8. #15689021C2semidirect
9. #15689020C2semidirect
15. C47×#391C2semidirect
79. C2×C4×D47Q8semidirect
88. (C2×D47)⋊C4Q8semidirect
200. #391D47semidirect
208. C47#2549semidirect