Finite Group Databasebeta

← #26134103

Subgroups — #26134103

Order 12032.

324 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×#15688952C211yesmaximal, characteristic, complemented
2C2×#15688929C211yesmaximal, characteristic
3#20245093C211yesmaximal, characteristic
4#20244276C211yesmaximal, characteristic
5#20241483C211yesmaximal, characteristic, complemented
6#20241466C211yesmaximal, characteristic, complemented
7C47×#1772C211yesmaximal, characteristic, complemented
8C2×#13094046C2211yescharacteristic
9C22×C47⋊C16C2211yescharacteristic
10C22×C47⋊C16C2211yescharacteristic
11C2×#13093960C2211yescharacteristic
12C2×#13093952—21no—
13#15689089—21no—
14#15688952—22no—
15#15688929—22no—
16#15688926C411yescharacteristic, complemented
17#15688926C411yescharacteristic, complemented
18#15688923C411yescharacteristic, complemented
19#15688923C411yescharacteristic, complemented
20C2×#108×C47C2211yescharacteristic
21C47×#427C2211yescharacteristic
22C47×#405—21no—
23C2×C4×C8×C47C2211yescharacteristic
24C47×#339—21no—
25C2×#10625350—21no—
26#13094046—21no—
27#13094046—21no—
28#13094046—21no—
29#13094046—21no—
30C2×Dic188C2×C411yescharacteristic
31C2×#10625325—21no—
32C2×D376C2×C411yescharacteristic
33C2×#10625329—21no—
34C2×C47⋊C16—21no—
35C2×C47⋊C16—21no—
36C2×C47⋊C16—21no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16C2×C411yescharacteristic
40C2×C47⋊C16C2×C411yescharacteristic
41#13093960—21no—
42#13093960—21no—
43#13093952—42no—
44(C2×D47)⋊C8—41no—
45(C2×D47)⋊C8—41no—
46C2×M16×C47—21no—
47C22×C8×C47D411yescharacteristic
48C22×C8×C47C2311yescharacteristic
49#117×C47—21no—
50C2×C42×C47D411yescharacteristic
51#108×C47—21no—
52#108×C47D412yes—
53#107×C47C2×C411yescharacteristic
54#107×C47C2×C411yescharacteristic
55#106×C47—21no—
56#97×C47—41no—
57C4×C8×C47—21no—
58C4×C8×C47—21no—
59C4×C8×C47—41no—
60C22×C4×C47—21no—
61C22×C4×C47C2×D411yescharacteristic
62C2×C22⋊D47—41no—
63#10625350—41no—
64#10625350—41no—
65#10625350—41no—
66#10625350—41no—
67C2×D188—21no—
68C2×C4×D47—41no—
69C2×Dic94—21no—
70M16×C47—22no—
71M16×C47—41no—
72C2×C8×C47—21no—
73C2×C8×C47—21no—
74C2×C8×C47—41no—
75C2×C8×C47D811yescharacteristic
76C2×C8×C47D811yescharacteristic
77C2×C8×C47C22×C411yescharacteristic
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47#4111yescharacteristic
80C2×C8×C47#4111yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C22⋊C4×C47—41no—
86C42×C47—21no—
87C42×C47—21no—
88C42×C47—41no—
89#10625329—41no—
90#10625329—41no—
91C2×C47⋊C8—41no—
92Dic188—21no—
93Dic188—21no—
94D376—21no—
95D376—21no—
96#10625325—41no—
97#10625325—41no—
98C47⋊C16—21no—
99C47⋊C16—21no—
100C47⋊C16—41no—
101C23×C47#13511yescharacteristic
102C22×D47—41no—
103C2×C4×C47—22no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47C4×D411yescharacteristic
109C2×C4×C47#12111yescharacteristic
110C2×C4×C47#12311yescharacteristic
111C2×C4×C47C2×D811yescharacteristic
112C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C47#13711yescharacteristic
114C22⋊D47—81no—
115C22⋊D47—81no—
116C2×Dic47—41no—
117D188—41no—
118D188—41no—
119C4×D47—81no—
120C4×D47—81no—
121Dic94—41no—
122Dic94—41no—
123C8×C47—21no—
124C8×C47—21no—
125C8×C47—42no—
126C8×C47#11711yescharacteristic
127C8×C47C4×D411yescharacteristic
128C8×C47#12411yescharacteristic
129C8×C47#12611yescharacteristic
130C47⋊C8—81no—
131#13134—471nomaximal, Sylow
132C22×C47—21no—
133C22×C47—21no—
134C22×C47C4×D811yescharacteristic
135C22×C47#46411yescharacteristic
136C22×C47#48211yescharacteristic
137C2×D47—81no—
138C2×D47—81no—
139C2×D47—81no—
140C4×C47—42no—
141C4×C47—81no—
142C4×C47—81no—
143C4×C47#38811yescharacteristic
144C4×C47#44011yescharacteristic
145C4×C47#45911yescharacteristic
146C4×C47#48011yescharacteristic
147Dic47—81no—
148C2×#368—471no—
149C2×#359—471no—
150#2138—471no—
151#1974—471no—
152#1772D4711yescharacteristic, complemented
153#1382—471no—
154#1374—471no—
155C2×C47—21no—
156C2×C47—21no—
157C2×C47#192511yescharacteristic
158C2×C47#217811yescharacteristic
159C2×C47#217911yescharacteristic
160D47—161no—
161C2×#135—471no—
162C22×C16—471no—
163C22×C16—471no—
164C2×#108—471no—
165C2×#108C2×D4711yescharacteristic
166#427C2×D4711yescharacteristic
167C2×#104—941no—
168#408—941no—
169#405—21no—
170C2×C4×C8C2×D4711yescharacteristic
171#368—942no—
172#359—942no—
173#358—471no—
174#358—471no—
175#357—471no—
176#357—471no—
177#339—21no—
178C47#1313411yescharacteristic, complemented, Sylow
179C2×#41—941no—
180#135—941no—
181#135—941no—
182#135—941no—
183#135—941no—
184C2×Q16—471no—
185C2×SD16—941no—
186C2×D8—471no—
187C2×M16—21no—
188C2×M16—941no—
189C22×C8C22⋊D4711yescharacteristic
190C22×C8C22×D4711yescharacteristic
191#117—21no—
192C2×C42C22⋊D4711yescharacteristic
193C2×C16—471no—
194C2×C16—471no—
195C2×C16—941no—
196C2×C16—941no—
197C2×C16—941no—
198C2×C16—941no—
199C2×C16—941no—
200#108—21no—
201#108—941no—
202#108—941no—
203#108D18812yes—
204#107C4×D4711yescharacteristic
205#107C4×D4711yescharacteristic
206#106—21no—
207#104—1882no—
208C22⋊C8—1881no—
209C22⋊C8—1881no—
210#97—41no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—41no—
214#41—1881no—
215#41—1881no—
216#41—1881no—
217#41—1881no—
218C2×Q8—941no—
219C2×D4—941no—
220C2×D4—1881no—
221C22×C4—21no—
222C22×C4—1881no—
223C22×C4C2×C22⋊D4711yescharacteristic
224Q16—941no—
225Q16—941no—
226SD16—1881no—
227SD16—1881no—
228D8—941no—
229D8—941no—
230M16—22no—
231M16—41no—
232M16—1881no—
233M16—1881no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—1881no—
238C2×C8#1062533411yescharacteristic
239C2×C8#1062533411yescharacteristic
240C2×C8C2×C4×D4711yescharacteristic
241C2×C8C2×D18811yescharacteristic
242C2×C8#1062535011yescharacteristic
243C2×C8#1062535011yescharacteristic
244C2×C8#1062535011yescharacteristic
245C2×C8#1062535011yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C22⋊C4—41no—
249C42—21no—
250C42—21no—
251C42—41no—
252C16—941no—
253C16—941no—
254C16—1881no—
255C23—1881no—
256C23#1309404411yescharacteristic
257Q8—1881no—
258Q8—1881no—
259D4—3761no—
260D4—3761no—
261D4—1881no—
262D4—1881no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—3761no—
269C2×C4—3761no—
270C2×C4—1881no—
271C2×C4C4×C22⋊D4711yescharacteristic
272C2×C4#1309399811yescharacteristic
273C2×C4#1309400711yescharacteristic
274C2×C4C2×#1062533411yescharacteristic
275C2×C4#1309404911yescharacteristic
276C2×C4#1309405511yescharacteristic
277C8—21no—
278C8—21no—
279C8—42no—
280C8—3761no—
281C8#1309398111yescharacteristic
282C8C4×D18811yescharacteristic
283C8#1309401211yescharacteristic
284C8#1309401811yescharacteristic
285C22—21no—
286C22—21no—
287C22—3761no—
288C22—3761no—
289C22—3761no—
290C22C4×#1062533411yescharacteristic
291C22#1568934511yescharacteristic
292C22#1568944711yescharacteristic
293C4—42no—
294C4—81no—
295C4—81no—
296C4—3761no—
297C4#1568901411yescharacteristic
298C4#1568922111yescharacteristic
299C4#1568931811yescharacteristic
300C4#1568943611yescharacteristic
301C2—21no—
302C2—21no—
303C2—7521no—
304C2#2024400811yescharacteristic
305C2#2024526711yescharacteristic
306C2#2024527211yescharacteristic
subgroupG/H
centerC2×C4C2×#10625334
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1772C2
socleC22×C47C4×D8
prime radicalC2×#13094046C22
cosocleC22×C8×C47C23
hypercenter#1772D47
hypocenterC47#13134
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1772

Complements

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

NH ≅ G/Ntype
1. C2×#15688952C2semidirect
5. #20241483C2semidirect
6. #20241466C2semidirect
7. C47×#1772C2semidirect
16. #15688926C4semidirect
17. #15688926C4semidirect
18. #15688923C4semidirect
19. #15688923C4semidirect
152. #1772D47semidirect
178. C47#13134semidirect

Maximal subgroups

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

subgroupindex
C2×#156889522
C2×#156889292
#202450932
#202442762
#202414832
#202414662
C47×#17722
#1313447