Finite Group Databasebeta

← #26126464

Subgroups — #26126464

Order 12032.

568 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 107 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#20249138C211yesmaximal, characteristic
2#20243121C211yesmaximal, characteristic, complemented
3#20241386C214yesmaximal, complemented
4C47×#1458C211yesmaximal, characteristic, complemented
5C2×#13094021C411yescharacteristic, complemented
6C2×#13093998—21no—
7C2×#13093983—21no—
8#15689040—21no—
9#15689040C412yescomplemented
10#15689032—21no—
11#15689032C2212yes—
12#15689025—21no—
13#15688989C411yescharacteristic, complemented
14#15688890—21no—
15#15688890C2212yes—
16C2×#117×C47C2211yescharacteristic
17C47×#431—21no—
18C47×#324—21no—
19C47×#323C2212yes—
20C22×D188—21no—
21C22×D188—21no—
22C22×D188C2×C412yes—
23C22×C22⋊D47—22no—
24#13094021—41no—
25#13094021—41no—
26#13093998—42no—
27#13093998—42no—
28#13093983—24no—
29#13093983—42no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—41no—
32C2×C22⋊Dic47—22no—
33C2×(C2×D47)⋊C4—22no—
34C2×(C2×D47)⋊C4—22no—
35C2×(C2×D47)⋊C4—22no—
36C2×C4×Dic47—41no—
37C47⋊#95—21no—
38C47⋊#95C2×C412yes—
39C23×C4×C47D411yescharacteristic
40#117×C47—41no—
41#117×C47—41no—
42C2×C4⋊C4×C47C2×C411yescharacteristic
43C2×C4⋊C4×C47D411yescharacteristic
44C2×C22⋊C4×C47D411yescharacteristic
45C2×C22⋊C4×C47C2311yescharacteristic
46C2×C42×C47C2×C411yescharacteristic
47C2×C42×C47D411yescharacteristic
48C4⋊C8×C47—41no—
49C22⋊C8×C47—22no—
50C4×C8×C47—41no—
51C24×C47C2×D411yescharacteristic
52C23×D47—22no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—22no—
56C22×C4×C47C22⋊C411yescharacteristic
57C22×C4×C47C22⋊C411yescharacteristic
58C22×C4×C47C22⋊C411yescharacteristic
59C22×C4×C47C22⋊C411yescharacteristic
60C22×C4×C47D812yes—
61C22×C4×C47SD1612yes—
62C22×C4×C47C22×C411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C2×C22⋊D47—42no—
65C2×C22⋊D47—42no—
66C2×C22⋊D47—82no—
67C2×C22⋊D47—82no—
68C22×Dic47—22no—
69C22×Dic47—42no—
70C2×D188—42no—
71C2×D188—42no—
72C2×D188—41no—
73C2×D188—41no—
74C2×D188—42no—
75C2×D188—42no—
76C2×D188—82no—
77C2×D188—82no—
78C2×C8×C47—42no—
79C4⋊C4×C47—41no—
80C4⋊C4×C47—41no—
81C22⋊C4×C47—41no—
82C22⋊C4×C47—41no—
83C42×C47—21no—
84C42×C47—21no—
85C42×C47—21no—
86C42×C47—21no—
87C22⋊Dic47—24no—
88C22⋊Dic47—42no—
89(C2×D47)⋊C4—44no—
90(C2×D47)⋊C4—82no—
91(C2×D47)⋊C4—82no—
92C4⋊Dic47—44no—
93C4⋊Dic47—42no—
94C4×Dic47—44no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—41no—
98C23×C47—41no—
99C23×C47C2×C22⋊C411yescharacteristic
100C23×C47C2×D811yescharacteristic
101C23×C47C2×SD1611yescharacteristic
102C22×D47—42no—
103C22×D47—42no—
104C22×D47—42no—
105C22×D47—42no—
106C22×D47—42no—
107C22×D47—42no—
108C22×D47—42no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47—22no—
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×C47#10212yes—
126C2×C4×C47#10212yes—
127C2×C4×C47#10412yes—
128C22⋊D47—84no—
129C22⋊D47—84no—
130C2×Dic47—44no—
131C2×Dic47—42no—
132C2×Dic47—42no—
133C2×Dic47—42no—
134C2×Dic47—82no—
135C2×Dic47—82no—
136D188—84no—
137D188—84no—
138D188—82no—
139D188—82no—
140C8×C47—82no—
141#11693—471nomaximal, Sylow
142C22×C47—21no—
143C22×C47—21no—
144C22×C47—21no—
145C22×C47—21no—
146C22×C47—41no—
147C22×C47—41no—
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—81no—
151C22×C47C2×#9911yescharacteristic
152C22×C47C2×#10211yescharacteristic
153C22×C47C2×#10411yescharacteristic
154C2×D47—82no—
155C2×D47—82no—
156C2×D47—82no—
157C2×D47—82no—
158C2×D47—82no—
159C2×D47—82no—
160C2×D47—82no—
161C4×C47—22no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47#32712yes—
167C4×C47#32712yes—
168Dic47—82no—
169Dic47—84no—
170#2619—471no—
171#1740—471no—
172#1458D4711yescharacteristic, complemented
173#1343—474no—
174C2×C47—21no—
175C2×C47—21no—
176C2×C47—41no—
177C2×C47—41no—
178C2×C47C2×#32711yescharacteristic
179C2×C47#212211yescharacteristic
180C2×C47#212811yescharacteristic
181D47—162no—
182C2×#127—471no—
183C2×#121—941no—
184C2×#117—941no—
185C2×#117C2×D4711yescharacteristic
186#431—21no—
187#394—472no—
188#394—941no—
189#392—472no—
190#392—941no—
191#390—941no—
192#382—471no—
193#342—472no—
194#342—941no—
195#324—21no—
196#323C2×D4712yes—
197C47#1169311yescharacteristic, complemented, Sylow
198C22×D4—472no—
199C22×D4—942no—
200C22×D4—941no—
201C22×D4—941no—
202C23×C4D18811yescharacteristic
203#127—1881no—
204#127—1881no—
205#121—1882no—
206#121—1882no—
207#117—41no—
208#117—41no—
209#117—944no—
210#117—1882no—
211C2×C4⋊C4—941no—
212C2×C4⋊C4—1881no—
213C2×C4⋊C4C4×D4711yescharacteristic
214C2×C4⋊C4C22⋊D4711yescharacteristic
215C2×C22⋊C4—942no—
216C2×C22⋊C4—942no—
217C2×C22⋊C4—942no—
218C2×C22⋊C4—942no—
219C2×C22⋊C4D18811yescharacteristic
220C2×C22⋊C4C22×D4711yescharacteristic
221C2×C42—1881no—
222C2×C42C4×D4711yescharacteristic
223C2×C42C22⋊D4711yescharacteristic
224C4⋊C8—41no—
225C22⋊C8—22no—
226C4×C8—41no—
227#95—472no—
228#95—941no—
229C24—942no—
230C24C2×D18811yescharacteristic
231C2×D4—3762no—
232C2×D4—3762no—
233C2×D4—3762no—
234C2×D4—3762no—
235C2×D4—1882no—
236C2×D4—1882no—
237C2×D4—1882no—
238C2×D4—1882no—
239C2×D4—1881no—
240C2×D4—1881no—
241C2×D4—1882no—
242C2×D4—1882no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—942no—
247C22×C4—1882no—
248C22×C4#1062532512yes—
249C22×C4D37612yes—
250C22×C4(C2×D47)⋊C411yescharacteristic
251C22×C4(C2×D47)⋊C411yescharacteristic
252C22×C4(C2×D47)⋊C411yescharacteristic
253C22×C4(C2×D47)⋊C411yescharacteristic
254C22×C4C2×C4×D4711yescharacteristic
255C22×C4C2×C22⋊D4711yescharacteristic
256C2×C8—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—1884no—
260C4⋊C4—1882no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—944no—
264C22⋊C4—3762no—
265C22⋊C4—3762no—
266C22⋊C4—1882no—
267C22⋊C4—1884no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—1884no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—1882no—
278C23—1882no—
279C23—1882no—
280C23—1882no—
281C23—1882no—
282C23—1882no—
283C23—1882no—
284C23C2×(C2×D47)⋊C411yescharacteristic
285C23C2×D37611yescharacteristic
286C23C2×#1062532511yescharacteristic
287D4—3764no—
288D4—3764no—
289D4—3764no—
290D4—3764no—
291D4—3762no—
292D4—3762no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—3762no—
308C2×C4—3762no—
309C2×C4—1884no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4#1309393811yescharacteristic
314C2×C4#1309393811yescharacteristic
315C2×C4#1309394612yes—
316C2×C4#1309394612yes—
317C2×C4#1309395012yes—
318C8—82no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—3762no—
329C22—3762no—
330C22—3762no—
331C22—3762no—
332C22—3762no—
333C22—3762no—
334C22—3762no—
335C22C2×#1309393811yescharacteristic
336C22C2×#1309394611yescharacteristic
337C22C2×#1309395011yescharacteristic
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3762no—
344C4—3764no—
345C4#1568885812yes—
346C4#1568885812yes—
347C2—21no—
348C2—21no—
349C2—41no—
350C2—41no—
351C2—7522no—
352C2C2×#1568885811yescharacteristic
353C2#2024503911yescharacteristic
354C2#2024505911yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C22⋊C4C22×D47
FittingC47×#1458C2
socleC22×C47C2×#99
prime radical#20249138C2
cosocleC2×C22⋊C4×C47C23
hypercenter#1458D47
hypocenterC47#11693
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #20243121C2semidirect
3. #20241386C2semidirect
4. C47×#1458C2semidirect
5. C2×#13094021C4semidirect
9. #15689040C4semidirect
13. #15688989C4semidirect
172. #1458D47semidirect
197. C47#11693semidirect

Maximal subgroups

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

subgroupindex
#202491382
#202431212
#202413862
C47×#14582
#1169347