Finite Group Databasebeta

← #26104613

Subgroups — #26104613

Order 12032.

518 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251727C211yesmaximal, characteristic
2#20243456C211yesmaximal, characteristic
3#20241213C212yesmaximal, complemented
4#20241210C212yesmaximal, complemented
5C2×C47×#336C211yesmaximal, characteristic
6C2×#13094003C411yescharacteristic
7C2×C22⋊(C47⋊C8)—21no—
8#15689029C411yescharacteristic
9#15689029C2211yescharacteristic
10#15689021C411yescharacteristic
11#15689021C2211yescharacteristic
12#15689007—21no—
13#15689007—21no—
14#15688996—21no—
15#15688986—21no—
16#15688983C411yescharacteristic
17#15688878—21no—
18#15688878C2212yes—
19C23×C8×C47—21no—
20C22×C42×C47C2211yescharacteristic
21C47×#336—21no—
22C47×#336C2212yes—
23C22×Dic94C2×C411yescharacteristic
24C22×C47⋊C8—22no—
25#13094003—42no—
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×C22⋊Dic47—21no—
33C2×C22⋊Dic47—21no—
34C22⋊(C47⋊C8)—42no—
35C47⋊#95—21no—
36C47⋊#95—21no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C23×C4×C47C2×C411yescharacteristic
43C23×C4×C47D411yescharacteristic
44C23×C4×C47D411yescharacteristic
45C22×C8×C47—24no—
46C22×C8×C47—22no—
47C22×C8×C47—42no—
48C22×C8×C47—42no—
49C2×C42×C47—42no—
50C2×C42×C47C2×C411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47C2311yescharacteristic
54C24×C47C22⋊C411yescharacteristic
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—41no—
62C22×C4×C47—41no—
63C22×C4×C47C22⋊C411yescharacteristic
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47SD1612yes—
67C22×C4×C47Q1612yes—
68C22×C4×C47C22×C411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75C2×Dic94—22no—
76C2×Dic94—41no—
77C2×Dic94—41no—
78C2×C8×C47—24no—
79C2×C8×C47—48no—
80C2×C8×C47—42no—
81C2×C8×C47—42no—
82C42×C47—41no—
83C42×C47—41no—
84C42×C47—41no—
85C42×C47—41no—
86C22⋊Dic47—42no—
87C22⋊Dic47—42no—
88C4⋊Dic47—22no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91Dic47⋊C4—42no—
92Dic47⋊C4—42no—
93Dic47⋊C4—42no—
94C2×C47⋊C8—42no—
95C2×C47⋊C8—42no—
96C2×C47⋊C8—42no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47#9912yes—
102C23×C47#10312yes—
103C23×C47#10412yes—
104C23×C47C2×C22⋊C411yescharacteristic
105C2×C4×C47—24no—
106C2×C4×C47—24no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
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—44no—
122C2×C4×C47—44no—
123C2×C4×C47#10312yes—
124C2×C4×C47#13112yes—
125C2×C4×C47C2×SD1611yescharacteristic
126C2×C4×C47C2×Q1611yescharacteristic
127C2×C4×C47#13512yes—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140Dic94—82no—
141C8×C47—44no—
142C47⋊C8—82no—
143#7655—471nomaximal, Sylow
144C22×C47—22no—
145C22×C47—22no—
146C22×C47—22no—
147C22×C47—22no—
148C22×C47—22no—
149C22×C47—22no—
150C22×C47#32814yes—
151C22×C47#40811yescharacteristic
152C22×C47C2×#9911yescharacteristic
153C22×C47#41311yescharacteristic
154C22×C47C2×#10311yescharacteristic
155C22×C47#41611yescharacteristic
156C22×C47C2×#10411yescharacteristic
157C22×C47#42111yescharacteristic
158C4×C47—22no—
159C4×C47—21no—
160C4×C47—22no—
161C4×C47—21no—
162C4×C47—22no—
163C4×C47—41no—
164C4×C47—41no—
165Dic47—81no—
166Dic47—81no—
167Dic47—81no—
168Dic47—81no—
169#2855—471no—
170#1817—471no—
171C2×#336D4711yescharacteristic
172#1272—472no—
173#1271—472no—
174C2×C47—24no—
175C2×C47#146811yescharacteristic
176C2×C47#148111yescharacteristic
177C2×C47#149411yescharacteristic
178C2×C47C2×#32811yescharacteristic
179C2×C47#151611yescharacteristic
180C2×C47#153211yescharacteristic
181C2×C47#154211yescharacteristic
182C23×C8—21no—
183C2×C22⋊Q8—471no—
184C22×C42C2×D4711yescharacteristic
185C2×C22⋊C8—941no—
186#391—471no—
187#391—471no—
188#389—471no—
189#389—471no—
190#387—941no—
191#387—941no—
192#385—941no—
193#381—941no—
194#380—471no—
195#336—21no—
196#336—472no—
197#336—941no—
198#336C2×D4712yes—
199C47#765511yescharacteristic, complemented, Sylow
200C22×Q8—471no—
201C23×C4C4×D4711yescharacteristic
202C23×C4D18811yescharacteristic
203C23×C4C22⋊D4711yescharacteristic
204C22×C8—24no—
205C22×C8—22no—
206C22×C8—42no—
207C22×C8—42no—
208C22×C8—942no—
209C22⋊Q8—1882no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—941no—
214C2×C4⋊C4—941no—
215C2×C4⋊C4—941no—
216C2×C22⋊C4—941no—
217C2×C22⋊C4—941no—
218C2×C42—42no—
219C2×C42C4×D4711yescharacteristic
220C2×C42D18811yescharacteristic
221C2×C42C22⋊D4711yescharacteristic
222C2×C42C22×D4711yescharacteristic
223C22⋊C8—1882no—
224#95—941no—
225#95—941no—
226#95—941no—
227#95—941no—
228#95—941no—
229#95—941no—
230#95—941no—
231C24(C2×D47)⋊C411yescharacteristic
232C2×Q8—942no—
233C2×Q8—1881no—
234C2×Q8—1881no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4(C2×D47)⋊C411yescharacteristic
248C22×C4(C2×D47)⋊C411yescharacteristic
249C22×C4(C2×D47)⋊C411yescharacteristic
250C22×C4#1062533512yes—
251C22×C4#1062533712yes—
252C22×C4C2×C4×D4711yescharacteristic
253C22×C4C2×D18811yescharacteristic
254C22×C4C2×C22⋊D4711yescharacteristic
255C2×C8—24no—
256C2×C8—42no—
257C2×C8—48no—
258C2×C8—42no—
259C2×C8—1882no—
260C2×C8—1882no—
261C2×C8—1882no—
262C4⋊C4—942no—
263C4⋊C4—1881no—
264C4⋊C4—1881no—
265C4⋊C4—1882no—
266C4⋊C4—1882no—
267C4⋊C4—1882no—
268C22⋊C4—1882no—
269C22⋊C4—1882no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—41no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#1309393812yes—
279C23#1309394712yes—
280C23#1309395212yes—
281C23C2×(C2×D47)⋊C411yescharacteristic
282Q8—3762no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—1881no—
302C2×C4—1881no—
303C2×C4—1881no—
304C2×C4—1881no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4—1881no—
308C2×C4—1881no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4#1309394712yes—
314C2×C4#1309403012yes—
315C2×C4C2×#1062533511yescharacteristic
316C2×C4C2×#1062533711yescharacteristic
317C2×C4#1309404612yes—
318C8—44no—
319C8—3762no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#1568885914yes—
327C22#1568908911yescharacteristic
328C22C2×#1309393811yescharacteristic
329C22#1568910511yescharacteristic
330C22C2×#1309394711yescharacteristic
331C22#1568912011yescharacteristic
332C22C2×#1309395211yescharacteristic
333C22#1568913911yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—3761no—
342C4—3761no—
343C4—3761no—
344C4—3761no—
345C2—24no—
346C2#2024173411yescharacteristic
347C2#2024179011yescharacteristic
348C2#2024184911yescharacteristic
349C2C2×#1568885911yescharacteristic
350C2#2024194511yescharacteristic
351C2#2024200611yescharacteristic
352C2#2024204611yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#336C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#336D47
hypocenterC47#7655
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #20241213C2semidirect
4. #20241210C2semidirect
199. C47#7655semidirect

Maximal subgroups

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

subgroupindex
#202517272
#202434562
#202412132
#202412102
C2×C47×#3362
#765547