Finite Group Databasebeta

← #26134018

Subgroups — #26134018

Order 12032.

326 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688908C211yesmaximal, characteristic
2#20245003C211yesmaximal, characteristic
3#20244987C211yesmaximal, characteristic, complemented
4#20243225C211yesmaximal, characteristic
5#20241478C211yesmaximal, characteristic, complemented
6#20241466C211yesmaximal, characteristic, complemented
7C2×C47×#364C211yesmaximal, characteristic, complemented
8C2×#13094030C2211yescharacteristic
9C22×C47⋊C16C2211yescharacteristic
10C22×C47⋊C16C2211yescharacteristic
11C2×#13093952C411yescharacteristic
12#15689120C411yescharacteristic
13#15689078C2211yescharacteristic
14#15688908—22no—
15(C2×D47)⋊C16—21no—
16(C2×D47)⋊C16—21no—
17#15688898—21no—
18C16×Dic47—21no—
19#15688888C411yescharacteristic
20#15688883C411yescharacteristic
21C2×M32×C47C2211yescharacteristic
22C2×M32×C47C2211yescharacteristic
23C2×C4×C8×C47C2211yescharacteristic
24C47×#364—22no—
25C2×#10625350C2×C411yescharacteristic
26#13094030—21no—
27#13094030—21no—
28#13094030—21no—
29#13094030—21no—
30C2×#10625329C2×C411yescharacteristic
31C2×#10625329C2×C411yescharacteristic
32C2×#10625324—21no—
33C2×C8×D47—21no—
34#13093983C2×C411yescharacteristic
35C2×C47⋊C16—21no—
36C2×C47⋊C16—21no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16D411yescharacteristic
41C2×C47⋊C16D411yescharacteristic
42#13093952—22no—
43#13093949C811yescharacteristic
44#13093949C811yescharacteristic
45#13093946C811yescharacteristic
46#13093946C811yescharacteristic
47#13093934—21no—
48C8×Dic47—21no—
49C22×C8×C47C2×C411yescharacteristic
50C22×C8×C47C2311yescharacteristic
51C2×C42×C47C2×C411yescharacteristic
52M32×C47—21no—
53M32×C47—21no—
54M32×C47—21no—
55M32×C47D412yes—
56C2×C16×C47—21no—
57C2×C16×C47—21no—
58C4×C8×C47—21no—
59C4×C8×C47—21no—
60C22×C4×C47—21no—
61C22×C4×C47C22×C411yescharacteristic
62C2×C22⋊D47—21no—
63#10625350—21no—
64#10625350—21no—
65#10625350—21no—
66#10625350—21no—
67C2×D188C2×C811yescharacteristic
68C2×C4×D47—21no—
69C2×Dic94C2×C811yescharacteristic
70C2×C8×C47—21no—
71C2×C8×C47—21no—
72C2×C8×C47C2×C811yescharacteristic
73C2×C8×C47C2×C811yescharacteristic
74C2×C8×C47C2×D411yescharacteristic
75C2×C8×C47C2×D411yescharacteristic
76C2×C8×C47#4111yescharacteristic
77C2×C8×C47#4111yescharacteristic
78C2×C8×C47#4111yescharacteristic
79C2×C8×C47#4111yescharacteristic
80C42×C47—21no—
81C42×C47—21no—
82C22⋊Dic47—21no—
83C4⋊Dic47C2×C811yescharacteristic
84C4⋊Dic47C2×C811yescharacteristic
85C4×Dic47—21no—
86#10625329—21no—
87#10625329—21no—
88#10625329—21no—
89#10625329M1612yes—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—21no—
92#10625324—41no—
93#10625324—41no—
94C8×D47—41no—
95C8×D47—41no—
96C16×C47—22no—
97C16×C47—41no—
98C47⋊C16—21no—
99C47⋊C16—21no—
100C47⋊C16—41no—
101C23×C47#13111yescharacteristic
102C22×D47—21no—
103C2×C4×C47—22no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47#11711yescharacteristic
107C2×C4×C47C4×D411yescharacteristic
108C2×C4×C47C4×D411yescharacteristic
109C2×C4×C47C22×C811yescharacteristic
110C2×C4×C47C2×M1611yescharacteristic
111C2×C4×C47#13111yescharacteristic
112C22⋊D47—41no—
113C22⋊D47—41no—
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117D188—21no—
118D188—21no—
119C4×D47—41no—
120C4×D47—41no—
121Dic94—21no—
122Dic94—21no—
123C8×C47—21no—
124C8×C47—21no—
125C8×C47#12111yescharacteristic
126C8×C47#12311yescharacteristic
127C8×C47#12411yescharacteristic
128C8×C47#12611yescharacteristic
129C47⋊C8—22no—
130C47⋊C8—41no—
131#13122—471nomaximal, Sylow
132C22×C47—21no—
133C22×C47—21no—
134C22×C47#43311yescharacteristic
135C22×C47C8×D411yescharacteristic
136C22×C47#43611yescharacteristic
137C2×D47—41no—
138C2×D47—41no—
139C2×D47—41no—
140C4×C47—42no—
141C4×C47#38811yescharacteristic
142C4×C47#43111yescharacteristic
143C4×C47C8×D411yescharacteristic
144C4×C47#43511yescharacteristic
145Dic47—41no—
146Dic47—41no—
147Dic47—41no—
148C2×#364D4711yescharacteristic, complemented
149C2×#350—471no—
150#2113—471no—
151#2108—471no—
152#1764—471no—
153#1379—471no—
154#1374—471no—
155C2×C47—21no—
156C2×C47—21no—
157C2×C47#192311yescharacteristic
158C2×C47#217011yescharacteristic
159C2×C47#217111yescharacteristic
160D47—81no—
161C2×#131—471no—
162C2×M32C2×D4711yescharacteristic
163C2×M32C2×D4711yescharacteristic
164C22×C16—471no—
165C22×C16—471no—
166C2×#104—471no—
167#416—471no—
168#405—471no—
169C2×C4×C8C2×D4711yescharacteristic
170#364—22no—
171#350—942no—
172C22⋊C16—941no—
173C22⋊C16—941no—
174#346—941no—
175C4×C16—941no—
176#341—471no—
177#339—471no—
178C47#1312211yescharacteristic, complemented, Sylow
179C2×#41—471no—
180#131—941no—
181#131—941no—
182#131—941no—
183#131—941no—
184C2×M16—471no—
185C2×M16—471no—
186C2×M16—941no—
187C22×C8—941no—
188C22×C8C4×D4711yescharacteristic
189C22×C8C22×D4711yescharacteristic
190#117—471no—
191C2×C42C4×D4711yescharacteristic
192M32—21no—
193M32—21no—
194M32—21no—
195M32C22⋊D4712yes—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—471no—
199C2×C16—471no—
200C2×C16—941no—
201C2×C16—941no—
202C2×C16—941no—
203C2×C16—941no—
204C2×C16—941no—
205#104—942no—
206#103—471no—
207#103—471no—
208#102—471no—
209#102—471no—
210#97—941no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—941no—
214#41—941no—
215#41—941no—
216#41—941no—
217#41—941no—
218C2×Q8—471no—
219C2×D4—471no—
220C2×D4—941no—
221C22×C4—21no—
222C22×C4—941no—
223C22×C4C2×C4×D4711yescharacteristic
224M16—472no—
225M16—941no—
226M16—941no—
227M16—941no—
228M16—1881no—
229M16—1881no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—941no—
233C2×C8—941no—
234C2×C8—1881no—
235C2×C8—1881no—
236C2×C8C8×D4711yescharacteristic
237C2×C8C8×D4711yescharacteristic
238C2×C8#1062535011yescharacteristic
239C2×C8D4×D4711yescharacteristic
240C2×C8#1062535211yescharacteristic
241C2×C8#1062535411yescharacteristic
242C2×C8#1062535411yescharacteristic
243C2×C8C2×C22⋊D4711yescharacteristic
244C4⋊C4—471no—
245C4⋊C4—471no—
246C22⋊C4—941no—
247C42—21no—
248C42—21no—
249C42—941no—
250C16—22no—
251C16—41no—
252C16—941no—
253C16—941no—
254C16—1881no—
255C23—941no—
256C23#1309403211yescharacteristic
257Q8—941no—
258Q8—941no—
259D4—941no—
260D4—941no—
261D4—1881no—
262D4—1881no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—941no—
269C2×C4—1881no—
270C2×C4—1881no—
271C2×C4#1309398211yescharacteristic
272C2×C4C4×C22⋊D4711yescharacteristic
273C2×C4#1309398611yescharacteristic
274C2×C4C2×C8×D4711yescharacteristic
275C2×C4M16×D4711yescharacteristic
276C2×C4#1309403011yescharacteristic
277C8—21no—
278C8—21no—
279C8—942no—
280C8—1881no—
281C8#1309399611yescharacteristic
282C8#1309400911yescharacteristic
283C8#1309401311yescharacteristic
284C8#1309401911yescharacteristic
285C22—21no—
286C22—21no—
287C22—1881no—
288C22—1881no—
289C22—1881no—
290C22#1568918311yescharacteristic
291C22#1568918811yescharacteristic
292C22#1568919911yescharacteristic
293C4—42no—
294C4—1881no—
295C4—1881no—
296C4—1881no—
297C4#1568901311yescharacteristic
298C4#1568917511yescharacteristic
299C4C8×C22⋊D4711yescharacteristic
300C4#1568919311yescharacteristic
301C2—21no—
302C2—21no—
303C2—3761no—
304C2#2024399311yescharacteristic
305C2#2024522411yescharacteristic
306C2#2024522911yescharacteristic
subgroupG/H
centerC2×C8D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC2×C47×#364C2
socleC22×C47C8×D4
prime radicalC2×#10625350C2×C4
cosocleC22×C8×C47C23
hypercenterC2×#364D47
hypocenterC47#13122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#364

Complements

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

NH ≅ G/Ntype
3. #20244987C2semidirect
5. #20241478C2semidirect
6. #20241466C2semidirect
7. C2×C47×#364C2semidirect
148. C2×#364D47semidirect
178. C47#13122semidirect

Maximal subgroups

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

subgroupindex
C2×#156889082
#202450032
#202449872
#202432252
#202414782
#202414662
C2×C47×#3642
#1312247