Finite Group Databasebeta

← #26136590

Subgroups — #26136590

Order 12032.

416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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#20245053C212yesmaximal, complemented
2#20241553C212yesmaximal, complemented
3#20241551C212yesmaximal, complemented
4C47×#3147C211yesmaximal, characteristic
5#15689097—22no—
6#15688918—22no—
7#15688916C2214yes—
8C2×#135×C47—22no—
9C47×#532C411yescharacteristic, complemented
10C47×#532C2211yescharacteristic
11C47×#495—22no—
12C47×#494C411yescharacteristic, complemented
13C47×#493C2211yescharacteristic
14C47×#492C411yescharacteristic, complemented
15C47×#492C2211yescharacteristic
16C2×C4×C8×C47C411yescharacteristic, complemented
17#13093983—42no—
18#13093939—24no—
19#13093939—42no—
20C2×#41×C47—21no—
21C2×#41×C47D412yes—
22#135×C47—44no—
23#135×C47—44no—
24C2×Q16×C47—22no—
25C2×SD16×C47—22no—
26C2×SD16×C47—22no—
27C2×D8×C47—22no—
28C22×C8×C47—21no—
29C4⋊Q8×C47C2×C411yescharacteristic
30C4⋊Q8×C47C2×C411yescharacteristic
31#127×C47C2×C411yescharacteristic
32#127×C47C2311yescharacteristic
33#124×C47—21no—
34#124×C47D412yes—
35#121×C47—41no—
36#121×C47—41no—
37C4×D4×C47—41no—
38C4×D4×C47—41no—
39C2×C42×C47C2×C411yescharacteristic
40C4×C8×C47—21no—
41C4×C8×C47C2×C411yescharacteristic
42C4×C8×C47C2×C411yescharacteristic
43#41×C47—42no—
44#41×C47—42no—
45#41×C47—42no—
46#41×C47—42no—
47C2×Q8×C47—21no—
48C2×Q8×C47C22⋊C412yes—
49C2×D4×C47—22no—
50C2×D4×C47—21no—
51C2×D4×C47—41no—
52C2×D4×C47—41no—
53C2×D4×C47—41no—
54C2×D4×C47C2×D412yes—
55C22×C4×C47—21no—
56C22×C4×C47—22no—
57C22×C4×C47—41no—
58C22×C4×C47C22⋊C411yescharacteristic
59Q16×C47—44no—
60SD16×C47—44no—
61SD16×C47—44no—
62D8×C47—44no—
63C2×C8×C47—22no—
64C2×C8×C47—22no—
65C2×C8×C47—21no—
66C2×C8×C47—21no—
67C4⋊C4×C47—41no—
68C4⋊C4×C47—41no—
69C22⋊C4×C47—42no—
70C22⋊C4×C47—42no—
71C42×C47—21no—
72C42×C47C22⋊C411yescharacteristic
73C42×C47C22×C411yescharacteristic
74C22⋊Dic47—44no—
75C4⋊Dic47—82no—
76C4×Dic47—82no—
77C23×C47—22no—
78C23×C47—41no—
79C23×C47#9911yescharacteristic
80Q8×C47—42no—
81Q8×C47—42no—
82D4×C47—42no—
83D4×C47—42no—
84D4×C47—82no—
85D4×C47—82no—
86D4×C47—82no—
87D4×C47—82no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—42no—
94C2×C4×C47—42no—
95C2×C4×C47—42no—
96C2×C4×C47—41no—
97C2×C4×C47—81no—
98C2×C4×C47—81no—
99C2×C4×C47#9911yescharacteristic
100C2×C4×C47C2×C22⋊C411yescharacteristic
101C2×Dic47—84no—
102C8×C47—22no—
103C8×C47—22no—
104#13583—471nomaximal, Sylow
105C22×C47—21no—
106C22×C47—41no—
107C22×C47—42no—
108C22×C47—82no—
109C22×C47—82no—
110C22×C47—81no—
111C22×C47C2×#9911yescharacteristic
112C4×C47—22no—
113C4×C47—21no—
114C4×C47—41no—
115C4×C47—42no—
116C4×C47—81no—
117C4×C47#35311yescharacteristic
118C4×C47#35311yescharacteristic
119Dic47—164no—
120#3147D4711yescharacteristic
121#2126—472no—
122#1409—472no—
123#1408—472no—
124C2×C47—21no—
125C2×C47—41no—
126C2×C47—82no—
127C2×C47—161no—
128C2×C47C2×#35311yescharacteristic
129C2×#135—22no—
130#532Dic4711yescharacteristic, complemented
131#532C2×D4711yescharacteristic
132#495—22no—
133#494Dic4711yescharacteristic, complemented
134#493C2×D4711yescharacteristic
135#492Dic4711yescharacteristic, complemented
136#492C2×D4711yescharacteristic
137#410—942no—
138C2×C4×C8Dic4711yescharacteristic, complemented
139#354—942no—
140#353—474no—
141C47#1358311yescharacteristic, complemented, Sylow
142C2×#41—21no—
143C2×#41C22⋊D4712yes—
144#135—44no—
145#135—44no—
146C2×Q16—22no—
147C2×SD16—22no—
148C2×SD16—22no—
149C2×D8—22no—
150C22×C8—21no—
151C4⋊Q8C2×Dic4711yescharacteristic
152C4⋊Q8C2×Dic4711yescharacteristic
153#127C2×Dic4711yescharacteristic
154#127C22×D4711yescharacteristic
155#124—21no—
156#124C22⋊D4712yes—
157#121—41no—
158#121—41no—
159C4×D4—41no—
160C4×D4—41no—
161#117—1882no—
162C2×C42C2×Dic4711yescharacteristic
163#99—944no—
164#99—1882no—
165C4×C8—21no—
166C4×C8C2×Dic4711yescharacteristic
167C4×C8C2×Dic4711yescharacteristic
168#41—42no—
169#41—42no—
170#41—42no—
171#41—42no—
172C2×Q8—21no—
173C2×Q8C22⋊Dic4712yes—
174C2×D4—22no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4C2×C22⋊D4712yes—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—41no—
183C22×C4C22⋊Dic4711yescharacteristic
184Q16—44no—
185SD16—44no—
186SD16—44no—
187D8—44no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—21no—
191C2×C8—21no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—3762no—
195C22⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—1884no—
198C42—21no—
199C42—3762no—
200C42C22⋊Dic4711yescharacteristic
201C42C22×Dic4711yescharacteristic
202C23—22no—
203C23—41no—
204C23#1309393911yescharacteristic
205Q8—42no—
206Q8—42no—
207D4—42no—
208D4—42no—
209D4—82no—
210D4—82no—
211D4—82no—
212D4—82no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—3764no—
225C2×C4#1309393911yescharacteristic
226C2×C4C2×C22⋊Dic4711yescharacteristic
227C8—22no—
228C8—22no—
229C22—21no—
230C22—41no—
231C22—42no—
232C22—82no—
233C22—82no—
234C22—81no—
235C22C2×#1309393911yescharacteristic
236C4—22no—
237C4—21no—
238C4—41no—
239C4—42no—
240C4—81no—
241C4—7524no—
242C4#1568891611yescharacteristic
243C4#1568891611yescharacteristic
244C2—21no—
245C2—41no—
246C2—82no—
247C2—161no—
248C2C2×#1568891611yescharacteristic
subgroupG/H
centerC4#15688916
commutatorC42×C47C22×C4
Frattini#127C22×D47
Fitting, prime radicalC47×#3147C2
socleC2×C47C2×#353
cosocle#127×C47C23
hypercenter#3147D47
hypocenterC47#13583
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #20245053C2semidirect
2. #20241553C2semidirect
3. #20241551C2semidirect
9. C47×#532C4semidirect
12. C47×#494C4semidirect
14. C47×#492C4semidirect
16. C2×C4×C8×C47C4semidirect
130. #532Dic47semidirect
133. #494Dic47semidirect
135. #492Dic47semidirect
138. C2×C4×C8Dic47semidirect
141. C47#13583semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202450532
#202415532
#202415512
C47×#31472
#1358347