Finite Group Databasebeta

← #20247089

Subgroups — #20247089

Order 6016.

608 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094023C211yesmaximal, characteristic, complemented
2C2×#13094003C211yesmaximal, characteristic
3C2×#13094001C211yesmaximal, characteristic
4C22×Dic47⋊C4C211yesmaximal, characteristic
5#15689057C211yesmaximal, characteristic, complemented
6#15689056C211yesmaximal, characteristic, complemented
7#15689044C211yesmaximal, characteristic, complemented
8#15689043C211yesmaximal, characteristic, complemented
9#15689020C211yesmaximal, characteristic, complemented
10#15689020C211yesmaximal, characteristic, complemented
11#15688998C211yesmaximal, characteristic
12#15688992C211yesmaximal, characteristic, complemented
13#15688981C211yesmaximal, characteristic
14C22⋊C4×Dic47C211yesmaximal, characteristic
15C47×#385C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C22×Dic94C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20#13094023—24no—
21#13094003—24no—
22#13094001—24no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26C2×C4⋊Dic47C2211yescharacteristic
27C2×Dic47⋊C4—24no—
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×Dic47⋊C4C2211yescharacteristic
37C2×Dic47⋊C4C2211yescharacteristic
38C2×C22⋊Dic47C2211yescharacteristic
39C2×C22⋊Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C2×C4×Dic47C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C22×C4×C47—22no—
57C22×C4×C47—22no—
58C22×C4×C47—41no—
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×Dic47—22no—
66C22×Dic47—22no—
67C22×Dic47—22no—
68C22×Dic47—22no—
69C22×Dic47—41no—
70C22×Dic47Q814yescomplemented
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C2×Dic94—22no—
80C2×Dic94—22no—
81C2×Dic94—22no—
82C2×Dic94—22no—
83C2×Dic94—41no—
84C2×Dic94—41no—
85C4⋊C4×C47—22no—
86C4⋊C4×C47—41no—
87C22⋊C4×C47—22no—
88C22⋊C4×C47Q814yescomplemented
89C22⋊Dic47—22no—
90C22⋊Dic47D414yes—
91C4⋊Dic47—22no—
92C4⋊Dic47—22no—
93C4⋊Dic47—22no—
94C4⋊Dic47—41no—
95Dic47⋊C4—22no—
96Dic47⋊C4—22no—
97Dic47⋊C4—22no—
98Dic47⋊C4—22no—
99Dic47⋊C4—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—22no—
102Dic47⋊C4—22no—
103Dic47⋊C4—22no—
104Dic47⋊C4D414yes—
105C4×Dic47—22no—
106C4×Dic47—22no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47C2×D412yes—
112C23×C47C2×Q812yes—
113C23×C47C2×Q812yes—
114C23×C47C2411yescharacteristic
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×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—44no—
131C2×C4×C47C2×D412yes—
132C2×C4×C47C2×Q812yes—
133C2×C4×C47C2×Q812yes—
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—28no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—44no—
153C2×Dic47C2×D412yes—
154C2×Dic47C2×D412yes—
155C2×Dic47C2×D412yes—
156C2×Dic47C2×D412yes—
157C2×Dic47C2×Q812yes—
158C2×Dic47C2×Q812yes—
159C2×Dic47#4112yes—
160Dic94—44no—
161Dic94—44no—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—22no—
168C22×C47C4⋊Q814yescomplemented
169C22×C47C22×D411yescharacteristic
170C22×C47C22×D411yescharacteristic
171C22×C47C22×Q811yescharacteristic
172C22×C47C22×Q811yescharacteristic
173C22×C47C2×#4111yescharacteristic
174C22×C47H(5,𝔽2)11yescharacteristic
175C22×C472−1+411yescharacteristic
176C4×C47—22no—
177C4×C47—22no—
178C4×C47—22no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182Dic47—22no—
183Dic47—22no—
184Dic47—22no—
185Dic47—22no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189Dic47C22⋊Q814yescomplemented
190#2440—471nomaximal, Sylow
191C2×C47—24no—
192C2×C47C2×C22⋊Q811yescharacteristic
193C2×C47C2×C4⋊Q811yescharacteristic
194C2×C47#54411yescharacteristic
195C2×C47D4211yescharacteristic
196C2×C47#54711yescharacteristic
197C2×C47D4×Q811yescharacteristic
198C2×C47#55411yescharacteristic
199C2×C4⋊Q8—471no—
200C2×C22⋊Q8—471no—
201C2×C22⋊Q8—471no—
202C22×C4⋊C4—471no—
203#398—471no—
204#398—471no—
205#395—471no—
206#395—471no—
207#389—471no—
208#389—471no—
209#385—471no—
210#385D4711yescharacteristic
211#384—471no—
212#380—471no—
213C4×C22⋊C4—471no—
214C47#244011yescharacteristic, complemented, Sylow
215C22×Q8—471no—
216C22×Q8—471no—
217C23×C4—471no—
218C23×C4—471no—
219C23×C4C2×D4711yescharacteristic
220C4⋊Q8—944no—
221C22⋊Q8—944no—
222C22⋊Q8—944no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C4⋊C4—471no—
230C2×C4⋊C4—471no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—944no—
238C2×C4⋊C4C2×D4711yescharacteristic
239C2×C4⋊C4C2×D4711yescharacteristic
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4C2×D4711yescharacteristic
243C2×C22⋊C4C2×D4711yescharacteristic
244C2×C42—471no—
245C2×C42—471no—
246#95—471no—
247#95—471no—
248#95—471no—
249#95—471no—
250#95—471no—
251#95—471no—
252#95C2×D4711yescharacteristic
253#95C2×D4711yescharacteristic
254C24C22×D4711yescharacteristic
255C2×Q8—942no—
256C2×Q8—942no—
257C2×Q8—942no—
258C2×Q8—942no—
259C2×Q8—1881no—
260C2×Q8—1881no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—471no—
265C22×C4—474no—
266C22×C4—471no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—942no—
274C22×C4—942no—
275C22×C4—942no—
276C22×C4—942no—
277C22×C4—1881no—
278C22×C4C22×D4711yescharacteristic
279C22×C4C22×D4711yescharacteristic
280C22×C4C22×D4711yescharacteristic
281C22×C4C22×D4711yescharacteristic
282C22×C4C22×D4711yescharacteristic
283C22×C4C22×D4711yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—474no—
287C4⋊C4—942no—
288C4⋊C4—942no—
289C4⋊C4—942no—
290C4⋊C4—942no—
291C4⋊C4—942no—
292C4⋊C4—942no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C4⋊C4—942no—
296C4⋊C4—942no—
297C4⋊C4—942no—
298C4⋊C4—942no—
299C4⋊C4—1881no—
300C22⋊C4—22no—
301C22⋊C4—474no—
302C22⋊C4—942no—
303C22⋊C4Dic9414yescomplemented
304C42—942no—
305C42—942no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23C2×Dic9412yes—
311C23D4×D4712yes—
312C23Q8×D4712yes—
313C23C23×D4711yescharacteristic
314Q8—1884no—
315Q8—1884no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—472no—
333C2×C4—472no—
334C2×C4—472no—
335C2×C4—472no—
336C2×C4—472no—
337C2×C4—472no—
338C2×C4—472no—
339C2×C4—948no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—1884no—
358C2×C4C2×Dic9412yes—
359C2×C4C2×Dic9412yes—
360C2×C4D4×D4712yes—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22#1309402314yescomplemented
368C22C2×D4×D4711yescharacteristic
369C22C2×D4×D4711yescharacteristic
370C22C2×Q8×D4711yescharacteristic
371C22C22×Dic9411yescharacteristic
372C22#41×D4711yescharacteristic
373C22#1309406911yescharacteristic
374C22#1309407111yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—474no—
382C4—942no—
383C4—942no—
384C4—942no—
385C4—942no—
386C4—1881no—
387C4—1881no—
388C4—1881no—
389C2—24no—
390C2C22⋊Q8×D4711yescharacteristic
391C2C2×#1309402311yescharacteristic
392C2#1568975211yescharacteristic
393C2#1568975511yescharacteristic
394C2#1568977111yescharacteristic
395C2D4×Dic9411yescharacteristic
396C2#1568983211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#385C2
hypercenter#385D47
hypocenterC47#2440
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#13094023C2semidirect
5. #15689057C2semidirect
6. #15689056C2semidirect
7. #15689044C2semidirect
8. #15689043C2semidirect
9. #15689020C2semidirect
10. #15689020C2semidirect
12. #15688992C2semidirect
70. C22×Dic47Q8semidirect
88. C22⋊C4×C47Q8semidirect
168. C22×C47C4⋊Q8semidirect
189. Dic47C22⋊Q8semidirect
214. C47#2440semidirect
303. C22⋊C4Dic94semidirect
367. C22#13094023semidirect