Finite Group Databasebeta

← #26126652

Subgroups — #26126652

Order 12032.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#13093941C211yesmaximal, characteristic
2#20241706C211yesmaximal, characteristic
3#20241415C212yesmaximal, complemented
4#20241394C212yesmaximal, complemented
5C47×#2395C211yesmaximal, characteristic
6C2×#13093941—21no—
7C2×C22⋊(C47⋊C8)—21no—
8C4×#10625329—21no—
9#15688892C2212yes—
10#15688849C2212yes—
11#15688847—21no—
12C2×C4×D4×C47C2211yescharacteristic
13C2×#117×C47C411yescharacteristic
14C47×#400C2211yescharacteristic
15C47×#399C411yescharacteristic
16C47×#398C2211yescharacteristic
17C47×#397—21no—
18C47×#397C411yescharacteristic
19C47×#394—21no—
20C4×C4⋊C4×C47—21no—
21C4×C22⋊C4×C47—21no—
22C4×C22⋊C4×C47C411yescharacteristic
23C2×#10625329—22no—
24C22×C47⋊C8—41no—
25#13093941—24no—
26C22⋊(C47⋊C8)—22no—
27C22⋊(C47⋊C8)—41no—
28#13093935—41no—
29C4×C47⋊C8—41no—
30C22×D4×C47D411yescharacteristic
31C23×C4×C47C2×C411yescharacteristic
32C23×C4×C47D411yescharacteristic
33C4×D4×C47—41no—
34C4×D4×C47—41no—
35#117×C47—41no—
36#117×C47—41no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—21no—
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C4⋊C4×C47C2×C411yescharacteristic
41C2×C4⋊C4×C47C2311yescharacteristic
42C2×C22⋊C4×C47—21no—
43C2×C22⋊C4×C47—21no—
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47C2×C411yescharacteristic
47C2×C22⋊C4×C47D411yescharacteristic
48C2×C42×C47—21no—
49C2×C42×C47—21no—
50C2×C42×C47D411yescharacteristic
51#95×C47—21no—
52#95×C47—21no—
53#95×C47—21no—
54#95×C47—21no—
55#95×C47C2×C411yescharacteristic
56#95×C47C2×C411yescharacteristic
57C24×C47C22⋊C411yescharacteristic
58C24×C47C22⋊C411yescharacteristic
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47—41no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—42no—
71C22×C4×C47—42no—
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22×C411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C4⋊C4×C47—41no—
78C4⋊C4×C47—42no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C4⋊C4×C47—42no—
82C22⋊C4×C47—41no—
83C22⋊C4×C47—41no—
84C22⋊C4×C47—42no—
85C22⋊C4×C47—42no—
86C22⋊C4×C47—42no—
87C22⋊C4×C47—42no—
88C42×C47—21no—
89C42×C47—21no—
90C42×C47—42no—
91C42×C47—41no—
92C42×C47—41no—
93#10625329—24no—
94#10625329—42no—
95C2×C47⋊C8—42no—
96C2×C47⋊C8—42no—
97C2×C47⋊C8—82no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—41no—
104C23×C47—41no—
105C23×C47—41no—
106C23×C47—41no—
107C23×C47#10412yes—
108C23×C47C2×C22⋊C411yescharacteristic
109D4×C47—44no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—42no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—42no—
121C2×C4×C47—42no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—81no—
135C2×C4×C47#9911yescharacteristic
136C2×C4×C47#9911yescharacteristic
137C2×C4×C47#13512yes—
138C47⋊C8—44no—
139C47⋊C8—82no—
140#11735—471nomaximal, Sylow
141C22×C47—21no—
142C22×C47—21no—
143C22×C47—22no—
144C22×C47—42no—
145C22×C47—41no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—81no—
151C22×C47—81no—
152C22×C47—81no—
153C22×C47C2×#9911yescharacteristic
154C22×C47#41611yescharacteristic
155C22×C47C2×#10411yescharacteristic
156C4×C47—21no—
157C4×C47—22no—
158C4×C47—42no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—81no—
163C4×C47—81no—
164C4×C47—81no—
165C4×C47#35212yes—
166#2395D4711yescharacteristic
167C4×#100—471no—
168#1459—471no—
169#1353—472no—
170#1346—472no—
171C2×C47—21no—
172C2×C47—21no—
173C2×C47—42no—
174C2×C47—81no—
175C2×C47#150111yescharacteristic
176C2×C47C2×#35211yescharacteristic
177C2×C47#213211yescharacteristic
178C2×C4×D4C2×D4711yescharacteristic
179C2×#117Dic4711yescharacteristic
180C2×#100—941no—
181C2×C22⋊C8—941no—
182C4×M16—941no—
183#400C2×D4711yescharacteristic
184#399Dic4711yescharacteristic
185#398C2×D4711yescharacteristic
186#397—21no—
187#397Dic4711yescharacteristic
188#394—21no—
189C4×C4⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4Dic4711yescharacteristic
192#343—472no—
193#324—472no—
194#323—941no—
195C47#1173511yescharacteristic, complemented, Sylow
196C22×D4C22⋊D4711yescharacteristic
197C23×C4C2×Dic4711yescharacteristic
198C23×C4C22⋊D4711yescharacteristic
199C2×M16—942no—
200C22×C8—1881no—
201C4×D4—41no—
202C4×D4—41no—
203#117—41no—
204#117—41no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic4711yescharacteristic
208C2×C4⋊C4C2×Dic4711yescharacteristic
209C2×C4⋊C4C22×D4711yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4C2×Dic4711yescharacteristic
215C2×C22⋊C4C22⋊D4711yescharacteristic
216C2×C42—21no—
217C2×C42—21no—
218C2×C42C22⋊D4711yescharacteristic
219#100—944no—
220C22⋊C8—942no—
221C22⋊C8—1881no—
222#97—1881no—
223C4×C8—1881no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95C2×Dic4711yescharacteristic
229#95C2×Dic4711yescharacteristic
230C24C22⋊Dic4711yescharacteristic
231C24C22⋊Dic4711yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4C22⋊Dic4711yescharacteristic
246C22×C4C22⋊Dic4711yescharacteristic
247C22×C4C22×Dic4711yescharacteristic
248C22×C4C2×C22⋊D4711yescharacteristic
249C22×C4C2×C22⋊D4711yescharacteristic
250M16—944no—
251M16—1882no—
252C2×C8—3762no—
253C2×C8—1882no—
254C2×C8—1882no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C42—42no—
269C42—41no—
270C42—41no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#1309395112yes—
281C23C2×C22⋊Dic4711yescharacteristic
282D4—44no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4#1309393911yescharacteristic
309C2×C4#1309393911yescharacteristic
310C2×C4#1309404412yes—
311C8—3762no—
312C8—1884no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C2×#1309393911yescharacteristic
326C22#1568911911yescharacteristic
327C22C2×#1309395111yescharacteristic
328C4—21no—
329C4—22no—
330C4—42no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4#1568891312yes—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2#2024187911yescharacteristic
343C2C2×#1568891311yescharacteristic
344C2#2024507311yescharacteristic
subgroupG/H
centerC2×C4#13093939
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#2395C2
socleC22×C47C2×#99
prime radicalC22×D4×C47D4
cosocleC2×C4⋊C4×C47C23
hypercenter#2395D47
hypocenterC47#11735
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2395

Complements

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

NH ≅ G/Ntype
3. #20241415C2semidirect
4. #20241394C2semidirect
195. C47#11735semidirect

Maximal subgroups

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

subgroupindex
C4×#130939412
#202417062
#202414152
#202413942
C47×#23952
#1173547