Finite Group Databasebeta

← #20246396

Subgroups — #20246396

Order 6016.

620 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×C4×Dic94C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D47C211yesmaximal, characteristic
4#15689027C211yesmaximal, characteristic, complemented
5#15689022C211yesmaximal, characteristic, complemented
6#15689020C211yesmaximal, characteristic, complemented
7#15689018C211yesmaximal, characteristic, complemented
8#15689010C211yesmaximal, characteristic, complemented
9#15688997C211yesmaximal, characteristic
10#15688997C211yesmaximal, characteristic
11#15688974C211yesmaximal, characteristic, complemented
12C4×(C2×D47)⋊C4C211yesmaximal, characteristic
13#15688970C211yesmaximal, characteristic
14#15688970C211yesmaximal, characteristic
15C47×#387C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C4×D47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094002C418yescomplemented
21C4×Dic94—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
31C4⋊C4×D47—24no—
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C42×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54C23×D47C2311yescharacteristic
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
69C2×C4×D47—22no—
70C2×C4×D47—22no—
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×D47C2×C414yes—
78C2×Dic94—22no—
79C2×Dic94—22no—
80C2×Dic94C2×C414yescomplemented
81C4⋊C4×C47—22no—
82C4⋊C4×C47C2×C414yescomplemented
83C42×C47—22no—
84(C2×D47)⋊C4—22no—
85(C2×D47)⋊C4C2×C414yes—
86(C2×D47)⋊C4C2×C414yes—
87(C2×D47)⋊C4Q814yescomplemented
88C4⋊Dic47—22no—
89C4⋊Dic47—22no—
90C4⋊Dic47—41no—
91Dic47⋊C4—22no—
92Dic47⋊C4—22no—
93Dic47⋊C4—41no—
94Dic47⋊C4C2×C414yescomplemented
95Dic47⋊C4C2×C414yescomplemented
96Dic47⋊C4D414yes—
97C4×Dic47—22no—
98C4×Dic47—22no—
99C4×Dic47—22no—
100C4×Dic47—41no—
101C4×Dic47—41no—
102C23×C47C2411yescharacteristic
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47C22×C412yes—
108C22×D47C2×Q812yes—
109C22×D47#4112yes—
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×C47C22×C412yes—
127C2×C4×C47C22×C412yes—
128C2×C4×C47C22×C412yes—
129C2×C4×C47C2×D412yes—
130C2×C4×C47C2×Q812yes—
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×Dic47C22×C412yes—
146C2×Dic47C22×C412yes—
147C2×Dic47C22×C412yes—
148C2×Dic47C2×D412yes—
149C2×Dic47C2×D412yes—
150C2×Dic47C2×Q812yes—
151C2×Dic47#4112yes—
152C4×D47—28no—
153C4×D47—44no—
154C4×D47—44no—
155Dic94—28no—
156C22×C47C23×C411yescharacteristic
157C22×C47C22×D411yescharacteristic
158C22×C47C22×Q811yescharacteristic
159C22×C47C2×#4111yescharacteristic
160C22×C47C2×#4111yescharacteristic
161C22×C47H(5,𝔽2)11yescharacteristic
162C22×C472−1+411yescharacteristic
163C2×D47—22no—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—22no—
168C2×D47—22no—
169C2×D47C4×Q814yescomplemented
170C4×C47—22no—
171C4×C47—22no—
172C4×C47—22no—
173C4×C47—22no—
174C4×C47—22no—
175C4×C47—41no—
176C4×C47—41no—
177Dic47—22no—
178Dic47—22no—
179Dic47—22no—
180Dic47—22no—
181Dic47—41no—
182Dic47—41no—
183Dic47C4×D414yes—
184#2360—471nomaximal, Sylow
185C2×C47C2×C4×D411yescharacteristic
186C2×C47C2×C4×Q811yescharacteristic
187C2×C47#52011yescharacteristic
188C2×C47#54611yescharacteristic
189C2×C47D4×Q811yescharacteristic
190C2×C47#55211yescharacteristic
191C2×C47#55411yescharacteristic
192D47—24no—
193C2×C22⋊Q8—471no—
194C2×C4×Q8—471no—
195C22×C4⋊C4—471no—
196#391—471no—
197#389—471no—
198#389—471no—
199#389—471no—
200#387—471no—
201#387D4711yescharacteristic, complemented
202#385—471no—
203#385—471no—
204C4×C4⋊C4—471no—
205C4×C22⋊C4—471no—
206C4×C22⋊C4—471no—
207C4×C22⋊C4—471no—
208C47#236011yescharacteristic, complemented, Sylow
209C22×Q8—471no—
210C23×C4—471no—
211C23×C4—471no—
212C23×C4—471no—
213C22⋊Q8—478no—
214C4×Q8—944no—
215C2×C4⋊C4—471no—
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—944no—
225C2×C4⋊C4C2×D4711yescharacteristic
226C2×C4⋊C4C2×D4711yescharacteristic
227C2×C22⋊C4—471no—
228C2×C22⋊C4—471no—
229C2×C22⋊C4—471no—
230C2×C22⋊C4—471no—
231C2×C42—471no—
232C2×C42—471no—
233C2×C42—471no—
234C2×C42—471no—
235C2×C42—471no—
236C2×C42C2×D4711yescharacteristic
237#95—471no—
238#95—471no—
239#95—471no—
240#95—471no—
241#95—471no—
242#95—471no—
243#95C2×D4711yescharacteristic
244#95C2×D4711yescharacteristic
245#95C2×D4711yescharacteristic
246#95C2×D4711yescharacteristic
247C24—471no—
248C2×Q8—474no—
249C2×Q8—942no—
250C2×Q8—942no—
251C22×C4—471no—
252C22×C4—471no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—474no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—942no—
260C22×C4—942no—
261C22×C4—942no—
262C22×C4—942no—
263C22×C4—942no—
264C22×C4—942no—
265C22×C4—1881no—
266C22×C4—1881no—
267C22×C4C22×D4711yescharacteristic
268C22×C4C22×D4711yescharacteristic
269C22×C4C22×D4711yescharacteristic
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C22×C4C22×D4711yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—474no—
276C4⋊C4—474no—
277C4⋊C4—474no—
278C4⋊C4—942no—
279C4⋊C4—942no—
280C4⋊C4—942no—
281C4⋊C4—942no—
282C4⋊C4—1881no—
283C4⋊C4—1881no—
284C4⋊C4C4×D4714yescomplemented
285C22⋊C4—474no—
286C22⋊C4—474no—
287C22⋊C4—474no—
288C22⋊C4—942no—
289C42—22no—
290C42—942no—
291C42—942no—
292C42—942no—
293C42—1881no—
294C42—1881no—
295C23—472no—
296C23—472no—
297C23—472no—
298C23—941no—
299C23—941no—
300C23—941no—
301C23—941no—
302C23C23×D4711yescharacteristic
303Q8—948no—
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—472no—
321C2×C4—472no—
322C2×C4—472no—
323C2×C4—472no—
324C2×C4—472no—
325C2×C4—472no—
326C2×C4—472no—
327C2×C4—948no—
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×C4C2×C4×D4712yes—
345C2×C4C2×C4×D4712yes—
346C2×C4C2×C4×D4712yes—
347C2×C4D4×D4712yes—
348C2×C4Q8×D4712yes—
349C22—474no—
350C22—942no—
351C22—942no—
352C22—942no—
353C22—942no—
354C22—942no—
355C22—942no—
356C22C22×C4×D4711yescharacteristic
357C22C2×D4×D4711yescharacteristic
358C22C2×Q8×D4711yescharacteristic
359C22#41×D4711yescharacteristic
360C22#41×D4711yescharacteristic
361C22#1309407011yescharacteristic
362C22#1309407111yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—474no—
371C4—942no—
372C4—942no—
373C4—942no—
374C4—942no—
375C4—1881no—
376C4—1881no—
377C2—944no—
378C2C4×D4×D4711yescharacteristic
379C2C4×Q8×D4711yescharacteristic
380C2#1568960311yescharacteristic
381C2#1568976511yescharacteristic
382C2#1568978611yescharacteristic
383C2#1568980911yescharacteristic
384C2#1568982911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#387C2
socleC23×C47C24
hypercenter#387D47
hypocenterC47#2360
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic94C2semidirect
4. #15689027C2semidirect
5. #15689022C2semidirect
6. #15689020C2semidirect
7. #15689018C2semidirect
8. #15689010C2semidirect
11. #15688974C2semidirect
15. C47×#387C2semidirect
20. #13094002C4semidirect
80. C2×Dic94C2×C4semidirect
82. C4⋊C4×C47C2×C4semidirect
87. (C2×D47)⋊C4Q8semidirect
94. Dic47⋊C4C2×C4semidirect
95. Dic47⋊C4C2×C4semidirect
169. C2×D47C4×Q8semidirect
201. #387D47semidirect
208. C47#2360semidirect
284. C4⋊C4C4×D47semidirect