Finite Group Databasebeta

← #20243357

Subgroups — #20243357

Order 6016.

588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#13094070C211yesmaximal, characteristic
2#15689140C211yesmaximal, characteristic, complemented
3#15689129C211yesmaximal, characteristic, complemented
4#15689127C211yesmaximal, characteristic, complemented
5#15689105C211yesmaximal, characteristic, complemented
6#15689096C211yesmaximal, characteristic, complemented
7C47×#421C211yesmaximal, characteristic, complemented
8#13094070—22no—
9#13094070—22no—
10#13094070—22no—
11#13094070—22no—
12C2×#10625354C412yescomplemented
13C2×#10625350—21no—
14C2×#10625350C2211yescharacteristic
15C22×D188—21no—
16C22×D188C2211yescharacteristic
17C2×D4×D47—22no—
18C2×D4×D47C412yescomplemented
19C2×#10625329C2211yescharacteristic, complemented
20#13093983C2211yescharacteristic, complemented
21#13093951—22no—
22#13093946—22no—
23#13093944—22no—
24#13093942—21no—
25#13093940—21no—
26#13093938—22no—
27C2×#41×C47C2211yescharacteristic
28C2×M16×C47C2211yescharacteristic, complemented
29#117×C47C2211yescharacteristic, complemented
30#104×C47—22no—
31C23×D47—21no—
32C23×D47—22no—
33#41×C47—21no—
34#41×C47—21no—
35#41×C47D412yes—
36#41×C47D412yes—
37C2×Q8×C47C2×C411yescharacteristic
38C2×D4×C47—21no—
39C2×D4×C47C2×C411yescharacteristic
40C22×C4×C47—21no—
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—22no—
43C2×C22⋊D47D412yes—
44#10625354—24no—
45#10625354—24no—
46D4×D47—28no—
47D4×D47—28no—
48D4×D47—24no—
49D4×D47—24no—
50#10625350—24no—
51#10625350—24no—
52#10625350—21no—
53#10625350—21no—
54#10625350—21no—
55#10625350—21no—
56C2×D188—24no—
57C2×D188—24no—
58C2×D188—22no—
59C2×D188—21no—
60C2×D188—21no—
61C2×D188—21no—
62C2×D188C2×C412yes—
63C2×D188D411yescharacteristic
64C2×D188D412yes—
65C2×D188D412yes—
66C2×C4×D47—22no—
67C2×C4×D47C2×C412yes—
68C2×Dic94D411yescharacteristic
69M16×C47—21no—
70M16×C47—21no—
71C2×C8×C47—21no—
72C4⋊C4×C47—21no—
73C22⋊C4×C47—21no—
74C42×C47—21no—
75C22⋊Dic47—21no—
76C4⋊Dic47—21no—
77C4×Dic47—21no—
78#10625329—21no—
79#10625329—21no—
80C2×C47⋊C8—21no—
81C23×C47—21no—
82C23×C47C2×D411yescharacteristic
83C22×D47—22no—
84C22×D47—28no—
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—82no—
88C22×D47—84no—
89C22×D47C22⋊C412yes—
90Q8×C47—21no—
91Q8×C47C22⋊C412yes—
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—21no—
95D4×C47C22⋊C412yes—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—41no—
100C2×C4×C47C22×C411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47C2×D411yescharacteristic
106C22⋊D47—28no—
107C22⋊D47—22no—
108C22⋊D47—22no—
109C2×Dic47—41no—
110C2×Dic47C22⋊C412yes—
111D188—28no—
112D188—22no—
113D188—21no—
114D188—22no—
115D188—21no—
116D188—22no—
117D188C22⋊C414yes—
118C4×D47—28no—
119C4×D47—22no—
120C4×D47—22no—
121Dic94—21no—
122Dic94—21no—
123C8×C47—41no—
124C47⋊C8—41no—
125C22×C47—22no—
126C22×C47—41no—
127C22×C47—42no—
128C22×C47C2×C22⋊C411yescharacteristic
129C22×C47#12011yescharacteristic
130C22×C47#12011yescharacteristic
131C2×D47—22no—
132C2×D47—24no—
133C2×D47—44no—
134C2×D47—42no—
135C2×D47—82no—
136C2×D47—82no—
137C2×D47—88no—
138C4×C47—22no—
139C4×C47—81no—
140C4×C47C2×C22⋊C411yescharacteristic
141C4×C47C2×C22⋊C411yescharacteristic
142C4×C47#12011yescharacteristic
143C4×C47#12011yescharacteristic
144Dic47—22no—
145Dic47—81no—
146#1795—471nomaximal, Sylow
147C2×C47—21no—
148C2×C47—21no—
149C2×C47—21no—
150C2×C47—42no—
151C2×C47#37911yescharacteristic
152D47—44no—
153D47—42no—
154C2×H(5,𝔽2)—471no—
155#421—471no—
156#421D4711yescharacteristic, complemented
157#418—471no—
158#418—471no—
159#413—471no—
160#410—471no—
161C47#179511yescharacteristic, complemented, Sylow
162H(5,𝔽2)—942no—
163H(5,𝔽2)—942no—
164H(5,𝔽2)—942no—
165H(5,𝔽2)—942no—
166C2×#41—471no—
167C2×#41—472no—
168C2×#41—941no—
169C2×#41C2×D4711yescharacteristic
170C22×D4—472no—
171C22×D4—471no—
172C22×D4—941no—
173C22×D4—942no—
174C2×M16—471no—
175C2×M16C2×D4711yescharacteristic, complemented
176#117—471no—
177#117C2×D4711yescharacteristic, complemented
178#104—22no—
179#104—942no—
180#102—942no—
181#102—942no—
182#101—941no—
183#100—941no—
184#99—942no—
185C24—942no—
186C24—941no—
187#41—21no—
188#41—21no—
189#41—944no—
190#41—944no—
191#41—944no—
192#41—944no—
193#41—941no—
194#41—941no—
195#41—941no—
196#41—941no—
197#41D18812yes—
198#41C22⋊D4712yes—
199C2×Q8—471no—
200C2×Q8C4×D4711yescharacteristic
201C2×D4—21no—
202C2×D4—472no—
203C2×D4—472no—
204C2×D4—472no—
205C2×D4—472no—
206C2×D4—471no—
207C2×D4—942no—
208C2×D4—944no—
209C2×D4—944no—
210C2×D4—942no—
211C2×D4—944no—
212C2×D4—948no—
213C2×D4—948no—
214C2×D4—944no—
215C2×D4—941no—
216C2×D4—941no—
217C2×D4—941no—
218C2×D4C4×D4711yescharacteristic
219C22×C4—21no—
220C22×C4—472no—
221C22×C4—942no—
222C22×C4C22×D4711yescharacteristic
223M16—21no—
224M16—21no—
225M16—941no—
226M16—941no—
227C2×C8—21no—
228C2×C8—941no—
229C4⋊C4—21no—
230C4⋊C4—941no—
231C22⋊C4—21no—
232C22⋊C4—941no—
233C42—21no—
234C42—941no—
235C23—21no—
236C23—472no—
237C23—948no—
238C23—942no—
239C23—942no—
240C23—942no—
241C23—3762no—
242C23—3764no—
243C23D4×D4711yescharacteristic
244Q8—21no—
245Q8—941no—
246Q8—941no—
247Q8(C2×D47)⋊C412yes—
248D4—22no—
249D4—22no—
250D4—21no—
251D4—474no—
252D4—948no—
253D4—948no—
254D4—942no—
255D4—942no—
256D4—942no—
257D4—942no—
258D4—941no—
259D4—942no—
260D4—941no—
261D4(C2×D47)⋊C412yes—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—472no—
267C2×C4—948no—
268C2×C4—942no—
269C2×C4—942no—
270C2×C4—1881no—
271C2×C4C2×C4×D4711yescharacteristic
272C2×C4C2×D18811yescharacteristic
273C2×C4D4×D4711yescharacteristic
274C2×C4D4×D4711yescharacteristic
275C2×C4D4×D4711yescharacteristic
276C2×C4C2×C22⋊D4711yescharacteristic
277C8—41no—
278C8—1881no—
279C22—22no—
280C22—41no—
281C22—42no—
282C22—944no—
283C22—942no—
284C22—3762no—
285C22—3762no—
286C22—3768no—
287C22—1882no—
288C22—1884no—
289C22C22⋊C4×D4711yescharacteristic
290C22#1309399211yescharacteristic
291C22#1309399411yescharacteristic
292C4—22no—
293C4—81no—
294C4—942no—
295C4—3761no—
296C4C22⋊C4×D4711yescharacteristic
297C4C2×(C2×D47)⋊C411yescharacteristic
298C4#1309399211yescharacteristic
299C4#1309399411yescharacteristic
300C2—21no—
301C2—21no—
302C2—21no—
303C2—42no—
304C2—1884no—
305C2—1882no—
306C2#1568897811yescharacteristic
subgroupG/H
centerC2#15688978
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#421C2
socleC2×C47#379
hypercenter#421D47
hypocenterC47#1795
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #15689140C2semidirect
3. #15689129C2semidirect
4. #15689127C2semidirect
5. #15689105C2semidirect
6. #15689096C2semidirect
7. C47×#421C2semidirect
12. C2×#10625354C4semidirect
18. C2×D4×D47C4semidirect
19. C2×#10625329C22semidirect
20. #13093983C22semidirect
28. C2×M16×C47C22semidirect
29. #117×C47C22semidirect
156. #421D47semidirect
161. C47#1795semidirect
175. C2×M16C2×D47semidirect
177. #117C2×D47semidirect