Finite Group Databasebeta

← #20256113

Subgroups — #20256113

Order 6016.

382 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#15689851C211yesmaximal, characteristic, complemented
2#15689487C212yesmaximal, complemented
3#15689469C211yesmaximal, characteristic, complemented
4#15689423C212yesmaximal, complemented
5#15689403C211yesmaximal, characteristic, complemented
6#15689320C212yesmaximal, complemented
7#15689320C211yesmaximal, characteristic, complemented
8#15689254C211yesmaximal, characteristic, complemented
9#15689223C212yesmaximal, complemented
10C4×#10625335C211yesmaximal, characteristic, complemented
11C47×#550C211yesmaximal, characteristic
12C2×#10625335C2212yes—
13C2×#10625335C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094022—21no—
16#13094016C2212yes—
17#13094014—22no—
18C4×Dic94C2212yes—
19C4×Dic94C2211yescharacteristic
20#13093989—21no—
21#13093957C2212yes—
22#13093955C2211yescharacteristic
23C4⋊(C47⋊C8)C2211yescharacteristic
24C4⋊(C47⋊C8)C2212yes—
25#13093947C2211yescharacteristic
26#13093945C2212yes—
27#13093945C2211yescharacteristic
28#13093945C2212yes—
29#13093945C2212yes—
30#13093945C2212yes—
31#13093935C2212yes—
32C4×C47⋊C8C2211yescharacteristic
33C2×#41×C47—21no—
34#127×C47C2212yes—
35#127×C47C2211yescharacteristic
36#121×C47—21no—
37#121×C47—22no—
38C4×Q8×C47C2211yescharacteristic
39C4×D4×C47C2212yes—
40C4×D4×C47C2211yescharacteristic
41#41×C47—44no—
42C2×Q8×C47D411yescharacteristic
43C2×D4×C47—22no—
44C2×D4×C47—21no—
45C2×D4×C47—22no—
46C2×D4×C47—21no—
47C2×D4×C47C2312yes—
48C2×D4×C47C2311yescharacteristic
49C22×C4×C47—22no—
50C22×C4×C47—21no—
51C2×Dic94—21no—
52C2×Dic94C2311yescharacteristic
53C4⋊C4×C47D411yescharacteristic
54C4⋊C4×C47D412yes—
55C4⋊C4×C47C2311yescharacteristic
56C22⋊C4×C47—22no—
57C22⋊C4×C47—21no—
58C42×C47C2311yescharacteristic
59C42×C47C2312yes—
60#10625335—24no—
61#10625335—22no—
62C4⋊Dic47—21no—
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2312yes—
65Dic47⋊C4—22no—
66Dic47⋊C4—21no—
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69C4×Dic47—22no—
70C4×Dic47—21no—
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73C2×C47⋊C8C2312yes—
74C23×C47—22no—
75C23×C47—21no—
76Q8×C47—22no—
77D4×C47—22no—
78D4×C47—21no—
79D4×C47—22no—
80D4×C47—21no—
81D4×C47—44no—
82D4×C47—42no—
83D4×C47—82no—
84D4×C47—81no—
85C2×C4×C47—21no—
86C2×C4×C47—44no—
87C2×C4×C47—42no—
88C2×C4×C47C2×D412yes—
89C2×C4×C47C2×D412yes—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2411yescharacteristic
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96Dic94—21no—
97Dic94—42no—
98Dic94#4112yescomplemented
99C47⋊C8—21no—
100C47⋊C8—22no—
101C47⋊C8—21no—
102C22×C47—42no—
103C22×C47—41no—
104C22×C47—42no—
105C22×C47—41no—
106C22×C47—42no—
107C22×C47—41no—
108C22×C47C22×D411yescharacteristic
109C4×C47—22no—
110C4×C47—22no—
111C4×C47—21no—
112C4×C47—41no—
113C4×C47AGL(1,ℤ/8)12yes—
114C4×C47C2×#4111yescharacteristic
115C4×C472−1+411yescharacteristic
116Dic47—22no—
117Dic47—42no—
118Dic47—41no—
119#3368—471nomaximal, Sylow
120C2×C47—82no—
121C2×C47—81no—
122C2×C47#54811yescharacteristic
123C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
124C2×C47#57711yescharacteristic
125#557—471no—
126#550D4711yescharacteristic
127#490—472no—
128#486—471no—
129#478—472no—
130#474—471no—
131#460—472no—
132#460—471no—
133#446—471no—
134#440—472no—
135C4×SD16—471no—
136C47#336811yescharacteristic, complemented, Sylow
137C2×#41—21no—
138C2×SD16—471no—
139C2×SD16—472no—
140C4⋊Q8—471no—
141C4⋊Q8—941no—
142#127C2×D4711yescharacteristic
143#127C2×D4712yes—
144#125—472no—
145#125—942no—
146#121—21no—
147#121—22no—
148C4×Q8—471no—
149C4×Q8—472no—
150C4×Q8—941no—
151C4×Q8C2×D4711yescharacteristic
152C4×D4C2×D4711yescharacteristic
153C4×D4C2×D4712yes—
154#107—472no—
155#106—471no—
156C4⋊C8—471no—
157C4⋊C8—472no—
158#103—471no—
159#102—471no—
160#102—472no—
161#102—472no—
162#102—472no—
163#102—472no—
164#97—472no—
165C4×C8—471no—
166#41—44no—
167C2×Q8—471no—
168C2×Q8—941no—
169C2×Q8C22⋊D4711yescharacteristic
170C2×D4—22no—
171C2×D4—21no—
172C2×D4—22no—
173C2×D4—21no—
174C2×D4C22×D4711yescharacteristic
175C2×D4C22×D4712yes—
176C22×C4—22no—
177C22×C4—21no—
178SD16—942no—
179SD16—944no—
180C2×C8—471no—
181C2×C8—471no—
182C2×C8—472no—
183C4⋊C4—471no—
184C4⋊C4—472no—
185C4⋊C4—941no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C4⋊C4—941no—
190C4⋊C4C22⋊D4711yescharacteristic
191C4⋊C4C22⋊D4712yes—
192C4⋊C4C22×D4711yescharacteristic
193C22⋊C4—22no—
194C22⋊C4—21no—
195C42—942no—
196C42—941no—
197C42C22×D4711yescharacteristic
198C42C22×D4712yes—
199C23—22no—
200C23—21no—
201Q8—22no—
202Q8—472no—
203Q8—941no—
204Q8—1882no—
205D4—21no—
206D4—22no—
207D4—21no—
208D4—22no—
209D4—44no—
210D4—42no—
211D4—82no—
212D4—81no—
213C2×C4—21no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—941no—
217C2×C4—941no—
218C2×C4—942no—
219C2×C4C2×C22⋊D4712yes—
220C2×C4C2×C22⋊D4711yescharacteristic
221C2×C4C2×C22⋊D4712yes—
222C2×C4C2×C22⋊D4711yescharacteristic
223C2×C4C23×D4711yescharacteristic
224C8—941no—
225C8—942no—
226C8—941no—
227C22—42no—
228C22—41no—
229C22—42no—
230C22—41no—
231C22—42no—
232C22—41no—
233C22C22×C22⋊D4711yescharacteristic
234C4—22no—
235C4—22no—
236C4—21no—
237C4—41no—
238C4—942no—
239C4—1882no—
240C4—1881no—
241C4#1309405012yes—
242C4#41×D4711yescharacteristic
243C4#1309407111yescharacteristic
244C2—82no—
245C2—81no—
246C2#1568978011yescharacteristic
247C2C2×#1309405011yescharacteristic
248C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#550C2
socleC22×C47C22×D4
hypercenter#550D47
hypocenterC47#3368
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #15689851C2semidirect
2. #15689487C2semidirect
3. #15689469C2semidirect
4. #15689423C2semidirect
5. #15689403C2semidirect
6. #15689320C2semidirect
7. #15689320C2semidirect
8. #15689254C2semidirect
9. #15689223C2semidirect
10. C4×#10625335C2semidirect
98. Dic94#41semidirect
136. C47#3368semidirect