Finite Group Databasebeta

← #26134638

Subgroups — #26134638

Order 12032.

432 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 99 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#20253043C211yesmaximal, characteristic
2#20245082C212yesmaximal
3#20245041C212yesmaximal
4#20243438C211yesmaximal, characteristic
5C47×#1757C211yesmaximal, characteristic
6C22×Dic188C411yescharacteristic, complemented
7#15689694C2212yes—
8#15689381—21no—
9#15689381—21no—
10#15689364—21no—
11#15689364—21no—
12C2×#13093960—21no—
13#15689161C411yescharacteristic, complemented
14#15689133C412yescomplemented
15#15689107C2212yes—
16#15688921—24no—
17#15688912—24no—
18C47⋊#338—21no—
19C2×#131×C47C2211yescharacteristic
20C47×#413C2211yescharacteristic
21C47×#410C2211yescharacteristic
22C47×#405—21no—
23C47×#344—21no—
24C22×Dic94C2×C412yes—
25C2×Dic188—21no—
26C2×Dic188—21no—
27C2×Dic188—41no—
28C2×Dic188—41no—
29C2×#10625329—22no—
30#13094022—22no—
31#13094011—22no—
32#13094005—22no—
33#13094005—22no—
34#13094003—22no—
35#13094003—22no—
36#13093983C2×C412yes—
37#13093960—41no—
38#13093960—41no—
39#13093958—21no—
40#13093956—21no—
41#13093949—22no—
42#13093949—22no—
43#13093943—22no—
44#13093941—22no—
45C2×#41×C47C2311yescharacteristic
46#131×C47—41no—
47#131×C47—41no—
48C2×M16×C47—21no—
49C2×M16×C47C2×C411yescharacteristic
50C2×M16×C47D411yescharacteristic
51C2×M16×C47D411yescharacteristic
52C22×C8×C47C2×C411yescharacteristic
53C22×C8×C47D411yescharacteristic
54C22×C8×C47D411yescharacteristic
55#117×C47—21no—
56#101×C47D412yes—
57#100×C47—21no—
58#99×C47—21no—
59#99×C47D412yes—
60#97×C47—41no—
61C4×C8×C47—41no—
62#41×C47—41no—
63#41×C47—41no—
64C2×Q8×C47C2×D411yescharacteristic
65C2×D4×C47C2×D411yescharacteristic
66C2×D4×C47#4111yescharacteristic
67C2×D4×C47#4111yescharacteristic
68C22×C4×C47C22×C411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×Dic47—22no—
72C2×Dic94—22no—
73C2×Dic94—22no—
74C2×Dic94—42no—
75C2×Dic94—42no—
76M16×C47—22no—
77M16×C47—41no—
78M16×C47—41no—
79M16×C47—41no—
80M16×C47—41no—
81C2×C8×C47—21no—
82C2×C8×C47—21no—
83C2×C8×C47—21no—
84C2×C8×C47—21no—
85C2×C8×C47—21no—
86C2×C8×C47—21no—
87C2×C8×C47—41no—
88C2×C8×C47C22⋊C411yescharacteristic
89C2×C8×C47C22⋊C411yescharacteristic
90C2×C8×C47C22⋊C411yescharacteristic
91C2×C8×C47C22⋊C411yescharacteristic
92C4⋊C4×C47—41no—
93C22⋊C4×C47—22no—
94C42×C47—41no—
95C22⋊Dic47—22no—
96C22⋊Dic47—42no—
97C22⋊Dic47—42no—
98C4⋊Dic47—22no—
99Dic47⋊C4—42no—
100Dic47⋊C4—42no—
101C4×Dic47—22no—
102#10625329—42no—
103#10625329—42no—
104C2×C47⋊C8—42no—
105Dic188—42no—
106Dic188—41no—
107Dic188—41no—
108C23×C47C4×D411yescharacteristic
109C23×C47#12111yescharacteristic
110C23×C47#12411yescharacteristic
111Q8×C47—41no—
112D4×C47—41no—
113D4×C47—41no—
114D4×C47—41no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—42no—
122C2×C4×C47C2×C22⋊C411yescharacteristic
123C2×C4×C47C4×D411yescharacteristic
124C2×C4×C47#12111yescharacteristic
125C2×C4×C47#12711yescharacteristic
126C2×Dic47—42no—
127C2×Dic47—42no—
128C2×Dic47—82no—
129Dic94—42no—
130Dic94—42no—
131Dic94—82no—
132C8×C47—21no—
133C8×C47—21no—
134C8×C47—21no—
135C8×C47—42no—
136C8×C47#9911yescharacteristic
137C8×C47#9911yescharacteristic
138C47⋊C8—82no—
139#13233—471nomaximal, Sylow
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47#39011yescharacteristic
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—82no—
151C4×C47C2×#9911yescharacteristic
152C4×C47#41011yescharacteristic
153Dic47—82no—
154Dic47—82no—
155#3059—471no—
156#2135—472no—
157#2123—472no—
158#1813—471no—
159#1757D4711yescharacteristic
160C2×C47—21no—
161C2×C47—41no—
162C2×C47—41no—
163C2×C47—41no—
164C2×C47#196411yescharacteristic
165C22×Q16—471no—
166C2×#131C2×D4711yescharacteristic
167#536—472no—
168#470—941no—
169#470—941no—
170#467—941no—
171#467—941no—
172C2×#108—941no—
173#427—471no—
174#419—472no—
175#413—472no—
176#413C2×D4711yescharacteristic
177#410C2×D4711yescharacteristic
178#405—21no—
179#356—944no—
180#352—944no—
181#344—21no—
182#338—941no—
183C47#1323311yescharacteristic, complemented, Sylow
184C2×#41C22×D4711yescharacteristic
185C22×Q8—472no—
186C2×Q16—941no—
187C2×Q16—941no—
188C2×Q16—1881no—
189C2×Q16—1881no—
190#131—41no—
191#131—41no—
192C2×M16—21no—
193C2×M16—942no—
194C2×M16C4×D4711yescharacteristic
195C2×M16D18811yescharacteristic
196C2×M16C22⋊D4711yescharacteristic
197C22×C8C4×D4711yescharacteristic
198C22×C8D18811yescharacteristic
199C22×C8C22⋊D4711yescharacteristic
200C4⋊Q8—942no—
201#124—942no—
202#123—942no—
203#123—942no—
204C22⋊Q8—942no—
205C22⋊Q8—942no—
206#117—21no—
207#117—472no—
208#108—1881no—
209#108—1881no—
210#107—941no—
211#106—941no—
212#103—942no—
213#103—942no—
214#101—942no—
215#101D18812yes—
216#100—21no—
217#100—942no—
218#99—21no—
219#99D18812yes—
220#97—41no—
221C4×C8—41no—
222#41—41no—
223#41—41no—
224C2×Q8—942no—
225C2×Q8—942no—
226C2×Q8—1882no—
227C2×Q8—1882no—
228C2×Q8C2×D18811yescharacteristic
229C2×D4C2×D18811yescharacteristic
230C2×D4#1062535011yescharacteristic
231C2×D4#1062535011yescharacteristic
232C22×C4—942no—
233C22×C4C2×C4×D4711yescharacteristic
234C22×C4C2×D18811yescharacteristic
235C22×C4C2×C22⋊D4711yescharacteristic
236Q16—1882no—
237Q16—1881no—
238Q16—1881no—
239M16—22no—
240M16—41no—
241M16—41no—
242M16—41no—
243M16—41no—
244M16—1882no—
245M16—1882no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—1882no—
254C2×C8(C2×D47)⋊C411yescharacteristic
255C2×C8(C2×D47)⋊C411yescharacteristic
256C2×C8(C2×D47)⋊C411yescharacteristic
257C2×C8(C2×D47)⋊C411yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—942no—
260C4⋊C4—1882no—
261C4⋊C4—1882no—
262C22⋊C4—22no—
263C22⋊C4—942no—
264C22⋊C4—1882no—
265C22⋊C4—1882no—
266C42—41no—
267C42—942no—
268C23C4×D18811yescharacteristic
269C23#1309399811yescharacteristic
270C23#1309401211yescharacteristic
271Q8—41no—
272Q8—3762no—
273Q8—1882no—
274Q8—1882no—
275D4—41no—
276D4—41no—
277D4—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—3762no—
286C2×C4—1882no—
287C2×C4—1882no—
288C2×C4C2×(C2×D47)⋊C411yescharacteristic
289C2×C4C4×D18811yescharacteristic
290C2×C4#1309399811yescharacteristic
291C2×C4#1309402111yescharacteristic
292C8—21no—
293C8—21no—
294C8—21no—
295C8—42no—
296C8—3762no—
297C8#1309393811yescharacteristic
298C8#1309393811yescharacteristic
299C22—21no—
300C22—21no—
301C22—21no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22#1568902511yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—82no—
310C4—3762no—
311C4—3762no—
312C4C2×#1309393811yescharacteristic
313C4#1568909611yescharacteristic
314C2—21no—
315C2—41no—
316C2—41no—
317C2—41no—
318C2#2024422411yescharacteristic
subgroupG/H
centerC2#20244224
commutatorC22×C4×C47C22×C4
FrattiniC2×#41C22×D47
FittingC47×#1757C2
socleC2×C47#1964
prime radical, cosocleC2×#41×C47C23
hypercenter#1757D47
hypocenterC47#13233
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
6. C22×Dic188C4semidirect
13. #15689161C4semidirect
14. #15689133C4semidirect
183. C47#13233semidirect

Maximal subgroups

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

subgroupindex
#202530432
#202450822
#202450412
#202434382
C47×#17572
#1323347