Finite Group Databasebeta

← #20243325

Subgroups — #20243325

Order 6016.

612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625352C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic, complemented
3C2×#13093947C211yesmaximal, characteristic, complemented
4C2×#13093945C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
6#15688980C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C2×#10625352—22no—
9C2×#10625352—22no—
10C2×#10625352—22no—
11C2×#10625352—22no—
12C2×#10625352—22no—
13C2×#10625352C414yescomplemented
14C22×Dic94C2211yescharacteristic
15C22×C22⋊D47—21no—
16C23×Dic47—21no—
17C22×C4×D47C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C4—21no—
21#13093949—22no—
22#13093947—22no—
23#13093945—22no—
24(C2×D47)⋊C8—22no—
25C47⋊#95—21no—
26C22×D4×C47C2211yescharacteristic
27C22×C8×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29#102×C47—22no—
30C24×C47—21no—
31C23×D47D411yescharacteristic
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47C2×C412yes—
36C2×D4×C47D412yes—
37C2×D4×C47D412yes—
38C22×C4×C47—21no—
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—24no—
41C2×C22⋊D47—24no—
42C2×C22⋊D47—24no—
43C22×Dic47—24no—
44C22×Dic47—24no—
45C22×Dic47—21no—
46C22×Dic47—24no—
47C22×Dic47—21no—
48C22×Dic47D411yescharacteristic
49#10625352—28no—
50#10625352—28no—
51#10625352—28no—
52#10625352—28no—
53C2×C4×D47—21no—
54C2×C4×D47—21no—
55C2×C4×D47—21no—
56C2×C4×D47—21no—
57C2×C4×D47C2×C412yes—
58C2×C4×D47D412yes—
59C2×Dic94—21no—
60C2×Dic94—21no—
61C2×Dic94—21no—
62C2×Dic94C2×C412yes—
63C2×Dic94D412yes—
64C2×Dic94D412yes—
65C2×C8×C47—21no—
66C2×C8×C47—21no—
67C2×C8×C47—21no—
68C4⋊C4×C47—21no—
69C4⋊C4×C47—21no—
70(C2×D47)⋊C4—42no—
71C4⋊Dic47—21no—
72C4⋊Dic47—21no—
73C2×C47⋊C8—21no—
74C2×C47⋊C8—21no—
75C2×C47⋊C8—21no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—41no—
80C23×C47—41no—
81C23×C47—41no—
82C23×C47—41no—
83C23×C47C2×D411yescharacteristic
84C22×D47—21no—
85C22×D47—21no—
86C22×D47—21no—
87C22×D47—21no—
88C22×D47—21no—
89C22×D47—21no—
90C22×D47C22⋊C412yes—
91D4×C47—22no—
92D4×C47—22no—
93D4×C47—22no—
94D4×C47C22⋊C414yescomplemented
95C2×C4×C47—41no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47C22×C411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2×D411yescharacteristic
104C22⋊D47—216no—
105C2×Dic47—216no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—21no—
110C2×Dic47—21no—
111C2×Dic47—41no—
112C2×Dic47—41no—
113C2×Dic47—41no—
114C2×Dic47C22⋊C412yes—
115C4×D47—22no—
116C4×D47—22no—
117C4×D47—22no—
118C4×D47—22no—
119Dic94—22no—
120Dic94—22no—
121Dic94—22no—
122Dic94C22⋊C414yescomplemented
123C8×C47—41no—
124C47⋊C8—41no—
125C22×C47—24no—
126C22×C47—42no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47—42no—
131C22×C47—42no—
132C22×C47C2×C22⋊C411yescharacteristic
133C22×C47#12011yescharacteristic
134C22×C47#12011yescharacteristic
135C22×C47#13511yescharacteristic
136C22×C47#13511yescharacteristic
137C22×C47AGL(1,ℤ/8)11yescharacteristic
138C22×C47#13711yescharacteristic
139C2×D47—22no—
140C2×D47—22no—
141C2×D47—22no—
142C2×D47—41no—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47—41no—
146C4×C47—81no—
147C4×C47C2×C22⋊C411yescharacteristic
148C4×C47C2×C22⋊C411yescharacteristic
149C4×C47#12011yescharacteristic
150C4×C47#12011yescharacteristic
151Dic47—24no—
152Dic47—22no—
153Dic47—81no—
154#1788—471nomaximal, Sylow
155C2×C47—44no—
156C2×C47#37911yescharacteristic
157C2×C47#41611yescharacteristic
158C2×C47#41711yescharacteristic
159C2×C47#44911yescharacteristic
160C2×C47#44911yescharacteristic
161C2×C47#45211yescharacteristic
162C2×C47#45211yescharacteristic
163D47—42no—
164C22×#41—471no—
165C2×#103—471no—
166C2×#103—471no—
167C2×#102—471no—
168C2×#102D4711yescharacteristic, complemented
169C2×C22⋊C8—471no—
170#380—471no—
171C47#178811yescharacteristic, complemented, Sylow
172C2×#41—474no—
173C2×#41—942no—
174C2×#41—942no—
175C2×#41—942no—
176C2×#41—942no—
177C2×#41—942no—
178C22×Q8—471no—
179C22×D4—941no—
180C22×D4C2×D4711yescharacteristic
181C23×C4—471no—
182C23×C4—941no—
183C22×C8—471no—
184C22×C8C2×D4711yescharacteristic
185C2×C4⋊C4—471no—
186C2×C4⋊C4C2×D4711yescharacteristic
187C2×C22⋊C4—941no—
188#103—942no—
189#103—942no—
190#102—22no—
191#102—942no—
192C22⋊C8—942no—
193#95—941no—
194C24—21no—
195C24—471no—
196#41—948no—
197#41—948no—
198#41—948no—
199#41—948no—
200C2×Q8—472no—
201C2×Q8—472no—
202C2×Q8—472no—
203C2×Q8—941no—
204C2×Q8—941no—
205C2×Q8—941no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—944no—
210C2×D4—944no—
211C2×D4—944no—
212C2×D4C4×D4712yes—
213C2×D4D18812yes—
214C2×D4C22⋊D4712yes—
215C22×C4—21no—
216C22×C4—471no—
217C22×C4—472no—
218C22×C4—472no—
219C22×C4—944no—
220C22×C4—944no—
221C22×C4—944no—
222C22×C4—941no—
223C22×C4—941no—
224C22×C4—941no—
225C22×C4—941no—
226C22×C4—941no—
227C22×C4—941no—
228C22×C4C22×D4711yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—941no—
233C2×C8—941no—
234C2×C8—941no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C22⋊C4—1882no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23—472no—
248C23—941no—
249C23—941no—
250C23—941no—
251C23—941no—
252C23—941no—
253C23—941no—
254C23D4×D4711yescharacteristic
255Q8—474no—
256Q8—942no—
257Q8—942no—
258Q8—942no—
259D4—22no—
260D4—22no—
261D4—22no—
262D4—9416no—
263D4(C2×D47)⋊C414yescomplemented
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—472no—
268C2×C4—9416no—
269C2×C4—942no—
270C2×C4—941no—
271C2×C4—942no—
272C2×C4—941no—
273C2×C4—942no—
274C2×C4—942no—
275C2×C4—942no—
276C2×C4—942no—
277C2×C4—942no—
278C2×C4—1881no—
279C2×C4—1881no—
280C2×C4—1881no—
281C2×C4C2×C4×D4711yescharacteristic
282C2×C4C2×D18811yescharacteristic
283C2×C4D4×D4711yescharacteristic
284C2×C4D4×D4711yescharacteristic
285C2×C4D4×D4711yescharacteristic
286C2×C4C2×C22⋊D4711yescharacteristic
287C8—41no—
288C8—1881no—
289C22—24no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—942no—
297C22—942no—
298C22—942no—
299C22—1881no—
300C22—1881no—
301C22—1881no—
302C22—1881no—
303C22C22⋊C4×D4711yescharacteristic
304C22#1309399211yescharacteristic
305C22#1309399411yescharacteristic
306C22#1309404311yescharacteristic
307C22#1309404511yescharacteristic
308C22#1309404811yescharacteristic
309C22#1309405311yescharacteristic
310C4—81no—
311C4—942no—
312C4—944no—
313C4—3761no—
314C4C22⋊C4×D4711yescharacteristic
315C4C2×(C2×D47)⋊C411yescharacteristic
316C4#1309399211yescharacteristic
317C4#1309399411yescharacteristic
318C2—44no—
319C2—1882no—
320C2#1568897811yescharacteristic
321C2#1568911611yescharacteristic
322C2#1568912111yescharacteristic
323C2#1568926511yescharacteristic
324C2#1568926911yescharacteristic
325C2#1568928211yescharacteristic
326C2#1568928611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#1788
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#13093949C2semidirect
3. C2×#13093947C2semidirect
4. C2×#13093945C2semidirect
5. C2×(C2×D47)⋊C8C2semidirect
6. #15688980C2semidirect
7. C2×#102×C47C2semidirect
13. C2×#10625352C4semidirect
94. D4×C47C22⋊C4semidirect
122. Dic94C22⋊C4semidirect
168. C2×#102D47semidirect
171. C47#1788semidirect
263. D4(C2×D47)⋊C4semidirect