Finite Group Databasebeta

← #26120060

Subgroups — #26120060

Order 12032.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#20253189C211yesmaximal, characteristic
2#20243400C211yesmaximal, characteristic
3#20242163C211yesmaximal, characteristic
4#20242045C211yesmaximal, characteristic
5#20241711C211yesmaximal, characteristic
6#20241246C211yesmaximal, characteristic
7C47×#1518C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9#15689427—22no—
10#15689415—21no—
11#15689405—21no—
12#15689176C2211yescharacteristic
13#15689166—21no—
14#15689147C2211yescharacteristic
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16#15689131—21no—
17C2×#13093947—21no—
18#15688885—21no—
19#15688876—22no—
20#15688872—21no—
21#15688869—21no—
22#15688848—22no—
23C47×#533C2211yescharacteristic
24C47×#431C2211yescharacteristic
25C47×#382C2211yescharacteristic
26C47×#328—22no—
27C22×Dic94D411yescharacteristic
28C2×#10625329—21no—
29C22×C47⋊C8—21no—
30C4×Dic94—21no—
31C4×Dic94—21no—
32C4×Dic94—21no—
33C4×Dic94—21no—
34C2×C4⋊Dic47D411yescharacteristic
35C2×Dic47⋊C4—21no—
36C2×C4×Dic47—21no—
37#13093957—22no—
38#13093955—22no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)D412yes—
44#13093947—22no—
45#13093947—22no—
46#13093947—42no—
47C22⋊(C47⋊C8)—21no—
48C4×C47⋊C8—21no—
49C4⋊Q8×C47D411yescharacteristic
50C4⋊Q8×C47D411yescharacteristic
51#125×C47—21no—
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47—21no—
54C4×Q8×C47—21no—
55C4×Q8×C47—21no—
56#117×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C42×C47C2311yescharacteristic
59C4⋊C8×C47—21no—
60C22⋊C8×C47D412yes—
61C4×C8×C47—21no—
62#95×C47—21no—
63#95×C47—21no—
64C2×Q8×C47—21no—
65C2×Q8×C47—21no—
66C22×C4×C47—41no—
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47#4111yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—21no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94—21no—
75C2×Dic94—21no—
76C2×Dic94—21no—
77C2×Dic94Q1612yes—
78C2×C8×C47—22no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—41no—
86C4⋊C4×C47—41no—
87C22⋊C4×C47—41no—
88C42×C47—41no—
89C42×C47C2×D411yescharacteristic
90C42×C47C2×D411yescharacteristic
91C42×C47#4111yescharacteristic
92C42×C47#4111yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97C4×Dic47—41no—
98C4×Dic47—41no—
99#10625329—41no—
100#10625329—41no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C2×C47⋊C8—41no—
106C23×C47#12111yescharacteristic
107Q8×C47—81no—
108Q8×C47—81no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—81no—
114C2×C4×C47—81no—
115C2×C4×C47—81no—
116C2×C4×C47#12011yescharacteristic
117C2×C4×C47#12111yescharacteristic
118C2×C4×C47#12111yescharacteristic
119C2×C4×C47#12311yescharacteristic
120C2×C4×C47#12311yescharacteristic
121C2×C4×C47#12411yescharacteristic
122C2×C4×C47C2×Q1611yescharacteristic
123C2×C4×C47#13511yescharacteristic
124C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C47#13711yescharacteristic
126C2×Dic47—22no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—81no—
131Dic94—22no—
132Dic94—22no—
133Dic94—41no—
134Dic94—41no—
135C8×C47—42no—
136C47⋊C8—42no—
137C47⋊C8—81no—
138C47⋊C8—81no—
139#10471—471nomaximal, Sylow
140C22×C47—21no—
141C22×C47—21no—
142C22×C47#39411yescharacteristic
143C22×C47#46711yescharacteristic
144C22×C47#46811yescharacteristic
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—81no—
150C4×C47—81no—
151C4×C47—161no—
152C4×C47#44911yescharacteristic
153C4×C47#45111yescharacteristic
154C4×C47#48411yescharacteristic
155C4×C47#48511yescharacteristic
156Dic47—42no—
157Dic47—81no—
158#3078—471no—
159#1805—471no—
160#1571—471no—
161#1542—471no—
162#1518D4711yescharacteristic
163#1461—471no—
164#1286—471no—
165C2×C47—21no—
166C2×C47—21no—
167C2×C47#203611yescharacteristic
168C2×C47#204911yescharacteristic
169C2×C47#205311yescharacteristic
170#533C2×D4711yescharacteristic
171C2×C4×Q8—471no—
172#479—942no—
173#477—941no—
174#475—941no—
175#431—471no—
176#431C2×D4711yescharacteristic
177#428—941no—
178#423—471no—
179C2×C4⋊C8—471no—
180#419—941no—
181C2×#103—941no—
182#382C2×D4711yescharacteristic
183#340—941no—
184#335—942no—
185#333—941no—
186#332—941no—
187#328—22no—
188#324—942no—
189C47#1047111yescharacteristic, complemented, Sylow
190C22×Q8—471no—
191C2×M16—941no—
192C22×C8—941no—
193C4⋊Q8D18811yescharacteristic
194C4⋊Q8D18811yescharacteristic
195#125—21no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—941no—
201C4×Q8—941no—
202C4×Q8—941no—
203C4×Q8—941no—
204#117—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—941no—
208C2×C42—941no—
209C2×C42C22×D4711yescharacteristic
210#107—942no—
211#106—942no—
212C4⋊C8—21no—
213C4⋊C8—472no—
214C4⋊C8—941no—
215C4⋊C8—941no—
216C4⋊C8—941no—
217C4⋊C8—941no—
218#103—942no—
219#103—942no—
220#103—1882no—
221C22⋊C8—941no—
222C22⋊C8C22⋊D4712yes—
223C4×C8—21no—
224C4×C8—941no—
225#95—21no—
226#95—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—472no—
230C2×Q8—941no—
231C2×Q8—941no—
232C2×Q8—941no—
233C2×Q8—941no—
234C2×Q8—941no—
235C22×C4—41no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4D4×D4711yescharacteristic
239C22×C4#1062535211yescharacteristic
240C22×C4C2×C22⋊D4711yescharacteristic
241M16—1881no—
242M16—1881no—
243C2×C8—22no—
244C2×C8—942no—
245C2×C8—1881no—
246C2×C8—1881no—
247C2×C8—1881no—
248C2×C8—1881no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4—1881no—
260C4⋊C4—1881no—
261C22⋊C4—41no—
262C42—41no—
263C42—1881no—
264C42—1881no—
265C42C2×D18811yescharacteristic
266C42#1062535011yescharacteristic
267C42D4×D4711yescharacteristic
268C42#1062535211yescharacteristic
269C23#1309399511yescharacteristic
270Q8—81no—
271Q8—81no—
272Q8—942no—
273Q8—942no—
274Q8—1881no—
275Q8—1881no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—942no—
284C2×C4—3761no—
285C2×C4—1881no—
286C2×C4—1881no—
287C2×C4—1881no—
288C2×C4#1309399411yescharacteristic
289C2×C4#1309399611yescharacteristic
290C2×C4#1309399811yescharacteristic
291C2×C4#1309400611yescharacteristic
292C2×C4#1309400811yescharacteristic
293C2×C4#1309401011yescharacteristic
294C2×C4Q16×D4711yescharacteristic
295C2×C4#1309404711yescharacteristic
296C2×C4#1309405111yescharacteristic
297C2×C4#1309405311yescharacteristic
298C8—42no—
299C8—3761no—
300C8—3761no—
301C8—1882no—
302C22—21no—
303C22—21no—
304C22#1568903911yescharacteristic
305C22#1568936111yescharacteristic
306C22#1568936611yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—81no—
313C4—161no—
314C4—3761no—
315C4—1882no—
316C4#1568927111yescharacteristic
317C4#1568928011yescharacteristic
318C4#1568945711yescharacteristic
319C4#1568946311yescharacteristic
320C2—21no—
321C2—21no—
322C2#2024459011yescharacteristic
323C2#2024466911yescharacteristic
324C2#2024469311yescharacteristic
subgroupG/H
centerC22#15689039
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1518C2
socleC22×C47#394
prime radicalC23×C47#121
hypercenter#1518D47
hypocenterC47#10471
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
189. C47#10471semidirect

Maximal subgroups

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

subgroupindex
#202531892
#202434002
#202421632
#202420452
#202417112
#202412462
C47×#15182
#1047147