Finite Group Databasebeta

← #26125680

Subgroups — #26125680

Order 12032.

446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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#20245791C211yesmaximal, characteristic
2#20241722C211yesmaximal, characteristic
3#20241333C212yesmaximal, complemented
4#20241331C212yesmaximal, complemented
5C47×#1464C211yesmaximal, characteristic
6C2×#13093983C411yescharacteristic
7C22×C4×Dic47C411yescharacteristic
8#15689180—21no—
9#15688992C411yescharacteristic
10#15688992C2211yescharacteristic
11#15688988C411yescharacteristic
12#15688988C2211yescharacteristic
13#15688981—21no—
14#15688981—21no—
15C4×Dic47⋊C4—21no—
16C4×Dic47⋊C4—21no—
17#15688849C2212yes—
18#15688847—21no—
19C2×#117×C47C2211yescharacteristic
20C47×#432—21no—
21C47×#324C2212yes—
22C47×#323—21no—
23C23×Dic47—21no—
24#13093983—41no—
25#13093983—41no—
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×Dic47⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×Dic47⋊C4—21no—
32C2×C22⋊Dic47—21no—
33C2×C4×Dic47—21no—
34C2×C4×Dic47—22no—
35C2×C4×Dic47—22no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47C2×C411yescharacteristic
38C2×C4×Dic47C2×C411yescharacteristic
39C4⋊(C47⋊C8)—41no—
40C22⋊(C47⋊C8)—22no—
41#13093935—41no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C23×C4×C47C2×C411yescharacteristic
47#117×C47—41no—
48#117×C47—41no—
49C2×C4⋊C4×C47C2×C411yescharacteristic
50C2×C4⋊C4×C47C2311yescharacteristic
51C2×C22⋊C4×C47D411yescharacteristic
52C2×C22⋊C4×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C2×C42×C47D411yescharacteristic
55C4⋊C8×C47—41no—
56C22⋊C8×C47—22no—
57#97×C47—41no—
58C24×C47C22⋊C411yescharacteristic
59C22×C4×C47—22no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22×C411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—24no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—42no—
76C22×Dic47—42no—
77C2×C8×C47—42no—
78C4⋊C4×C47—41no—
79C4⋊C4×C47—41no—
80C22⋊C4×C47—41no—
81C22⋊C4×C47—41no—
82C42×C47—21no—
83C42×C47—21no—
84C42×C47—21no—
85C42×C47—21no—
86C22⋊Dic47—42no—
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89Dic47⋊C4—42no—
90Dic47⋊C4—42no—
91Dic47⋊C4—42no—
92Dic47⋊C4—42no—
93C4×Dic47—24no—
94C4×Dic47—21no—
95C4×Dic47—21no—
96C4×Dic47—41no—
97C4×Dic47—41no—
98C4×Dic47M1612yes—
99C4×Dic47M1612yes—
100C2×C47⋊C8—42no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—41no—
104C23×C47—41no—
105C23×C47#10112yes—
106C23×C47C2×C22⋊C411yescharacteristic
107C2×C4×C47—22no—
108C2×C4×C47—22no—
109C2×C4×C47—22no—
110C2×C4×C47—22no—
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—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47#9911yescharacteristic
124C2×C4×C47#9911yescharacteristic
125C2×C4×C47C2×M1611yescharacteristic
126C2×C4×C47C2×M1611yescharacteristic
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—48no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C8×C47—82no—
141C47⋊C8—82no—
142#11513—471nomaximal, Sylow
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—22no—
146C22×C47—42no—
147C22×C47—42no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47#40711yescharacteristic
151C22×C47C2×#9911yescharacteristic
152C22×C47C2×#10111yescharacteristic
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161Dic47—24no—
162Dic47—42no—
163Dic47—81no—
164Dic47—81no—
165#2285—471no—
166#1464—471no—
167#1464D4711yescharacteristic
168#1325—472no—
169#1324—472no—
170C2×C47—21no—
171C2×C47—21no—
172C2×C47—42no—
173C2×C47#146311yescharacteristic
174C2×C47#212611yescharacteristic
175C2×C47#213211yescharacteristic
176C2×#117—471no—
177C2×#117C2×D4711yescharacteristic
178C22×C42—471no—
179#432—21no—
180#432—941no—
181#384—471no—
182#384—471no—
183#382—471no—
184#382—471no—
185#380—941no—
186#380—941no—
187C4×C4⋊C4—941no—
188C4×C4⋊C4—941no—
189#324—472no—
190#324C2×D4712yes—
191#323—21no—
192#323—941no—
193C47#1151311yescharacteristic, complemented, Sylow
194C23×C4—941no—
195C23×C4C4×D4711yescharacteristic
196#117—41no—
197#117—41no—
198#117—1881no—
199#117—1881no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4C4×D4711yescharacteristic
207C2×C4⋊C4C22×D4711yescharacteristic
208C2×C22⋊C4—941no—
209C2×C22⋊C4D18811yescharacteristic
210C2×C22⋊C4C22⋊D4711yescharacteristic
211C2×C42—471no—
212C2×C42—471no—
213C2×C42—942no—
214C2×C42—942no—
215C2×C42—941no—
216C2×C42—941no—
217C2×C42D18811yescharacteristic
218C2×C42C22⋊D4711yescharacteristic
219C4⋊C8—41no—
220C4⋊C8—1881no—
221C22⋊C8—22no—
222C22⋊C8—942no—
223#97—41no—
224#97—1881no—
225#95—941no—
226#95—941no—
227#95—941no—
228#95—941no—
229C24(C2×D47)⋊C411yescharacteristic
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—941no—
236C22×C4—944no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4—1882no—
241C22×C4—1882no—
242C22×C4(C2×D47)⋊C411yescharacteristic
243C22×C4(C2×D47)⋊C411yescharacteristic
244C22×C4(C2×D47)⋊C411yescharacteristic
245C22×C4C2×C4×D4711yescharacteristic
246C22×C4C2×D18811yescharacteristic
247C22×C4C2×C22⋊D4711yescharacteristic
248C2×C8—42no—
249C2×C8—1882no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—1881no—
253C4⋊C4—1881no—
254C4⋊C4—1882no—
255C4⋊C4—1882no—
256C4⋊C4—1882no—
257C4⋊C4—1882no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—1882no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—472no—
266C42—472no—
267C42—944no—
268C42—941no—
269C42—941no—
270C42—1881no—
271C42—1881no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#1309394212yes—
277C23C2×(C2×D47)⋊C411yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—1888no—
299C2×C4—1881no—
300C2×C4—1881no—
301C2×C4—1881no—
302C2×C4—1881no—
303C2×C4—1881no—
304C2×C4—1881no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4#1309393811yescharacteristic
308C2×C4#1309393811yescharacteristic
309C2×C4M16×D4711yescharacteristic
310C2×C4M16×D4711yescharacteristic
311C8—82no—
312C8—3762no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22#1568908611yescharacteristic
321C22C2×#1309393811yescharacteristic
322C22C2×#1309394211yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—944no—
332C4—3761no—
333C4—3761no—
334C4—1882no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#2024171711yescharacteristic
339C2#2024505111yescharacteristic
340C2#2024507111yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#1464C2
socleC22×C47C2×#99
prime radicalC24×C47C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#1464D47
hypocenterC47#11513
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #20241333C2semidirect
4. #20241331C2semidirect
193. C47#11513semidirect

Maximal subgroups

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

subgroupindex
#202457912
#202417222
#202413332
#202413312
C47×#14642
#1151347