Finite Group Databasebeta

← D47×#1314 #26125335

Subgroups — D47×#1314 #26125335

Order 12032.

682 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×C22⋊C8×D47C211yesmaximal, characteristic
2C22⋊C16×D47C212yesmaximal, complemented
3#20241312C211yesmaximal, characteristic, complemented
4#20241311C212yesmaximal, complemented
5C47×#1314C211yesmaximal, characteristic, complemented
6C23×C4×D47C411yescharacteristic
7C22×C8×D47C411yescharacteristic
8C22×C8×D47C2211yescharacteristic
9C2×C16×D47—22no—
10C2×C22⋊(C47⋊C8)C411yescharacteristic
11C2×(C2×D47)⋊C8C411yescharacteristic
12C2×(C2×D47)⋊C8C2211yescharacteristic
13C22⋊C8×D47—22no—
14C22⋊C8×D47—22no—
15C22⋊(C47⋊C16)C2212yescomplemented
16(C2×D47)⋊C16—22no—
17C2×C22⋊C8×C47C2211yescharacteristic
18C47×C22⋊C16C2212yescomplemented
19C24×D47C811yescharacteristic
20C23×Dic47C811yescharacteristic
21C22×C4×D47—21no—
22C22×C4×D47—21no—
23C22×C4×D47—21no—
24C22×C4×D47—21no—
25C22×C4×D47—42no—
26C22×C4×D47—42no—
27C22×C4×D47C811yescharacteristic
28C22×C4×D47C811yescharacteristic
29C22×C4×D47C2×C411yescharacteristic
30C22×C4×D47C2×C411yescharacteristic
31C22×C47⋊C8C2×C411yescharacteristic
32C22×C47⋊C8C2×C411yescharacteristic
33C2×C8×D47—21no—
34C2×C8×D47—21no—
35C2×C8×D47—42no—
36C2×C8×D47—42no—
37C2×C8×D47D412yes—
38C2×C8×D47D412yes—
39C2×C47⋊C16—22no—
40C16×D47—44no—
41C22⋊(C47⋊C8)—22no—
42(C2×D47)⋊C8—22no—
43(C2×D47)⋊C8—22no—
44C23×C4×C47C2×C411yescharacteristic
45C22×C8×C47C2×C411yescharacteristic
46C22×C8×C47C2311yescharacteristic
47C2×C16×C47—22no—
48C22⋊C8×C47—22no—
49C24×C47C2×C811yescharacteristic
50C23×D47—21no—
51C23×D47—21no—
52C23×D47—22no—
53C23×D47—42no—
54C23×D47—42no—
55C23×D47C1614yescomplemented
56C23×D47C2×C811yescharacteristic
57C23×D47C2×C811yescharacteristic
58C22×C4×C47—21no—
59C22×C4×C47—21no—
60C22×C4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47C2×C811yescharacteristic
63C22×C4×C47C22×C411yescharacteristic
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—42no—
67C22×Dic47C2×C811yescharacteristic
68C22×Dic47C2×C811yescharacteristic
69C2×C4×D47—22no—
70C2×C4×D47—22no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—44no—
78C2×C4×D47—42no—
79C2×C4×D47—42no—
80C2×C4×D47—44no—
81C2×C4×D47—42no—
82C2×C4×D47—42no—
83C2×C4×D47—42no—
84C2×C4×D47—41no—
85C2×C4×D47—41no—
86C2×C4×D47—42no—
87C2×C4×D47C22⋊C411yescharacteristic
88C2×C4×D47C22⋊C411yescharacteristic
89C2×C4×D47M1611yescharacteristic
90C2×C4×D47M1611yescharacteristic
91C2×C8×C47—21no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47C2×D412yes—
95C2×C47⋊C8—21no—
96C2×C47⋊C8—41no—
97C2×C47⋊C8—41no—
98C2×C47⋊C8C22⋊C412yes—
99C8×D47—24no—
100C8×D47—42no—
101C8×D47—42no—
102C8×D47—42no—
103C16×C47—42no—
104C47⋊C16—42no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—41no—
108C23×C47—41no—
109C23×C47C2×C1612yescomplemented
110C23×C47C22×C811yescharacteristic
111C22×D47—22no—
112C22×D47—22no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—24no—
116C22×D47—24no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—48no—
120C22×D47—48no—
121C22×D47—42no—
122C22×D47—42no—
123C22×D47—41no—
124C22×D47—41no—
125C22×D47C22⋊C811yescharacteristic
126C22×D47C22⋊C811yescharacteristic
127C22×D47C2×C1612yes—
128C22×D47C2×C1612yescomplemented
129C22×D47M3212yes—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—42no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47C2×C22⋊C411yescharacteristic
138C2×C4×C47C2×M1611yescharacteristic
139C2×Dic47—22no—
140C2×Dic47—21no—
141C2×Dic47—42no—
142C2×Dic47—42no—
143C2×Dic47—41no—
144C2×Dic47C22⋊C811yescharacteristic
145C2×Dic47C22⋊C811yescharacteristic
146C4×D47—22no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—22no—
150C4×D47—42no—
151C4×D47—42no—
152C4×D47—42no—
153C4×D47—42no—
154C4×D47—41no—
155C4×D47—41no—
156C4×D47—42no—
157C4×D47#9912yes—
158C4×D47#10012yes—
159C8×C47—22no—
160C8×C47—41no—
161C47⋊C8—22no—
162C47⋊C8—41no—
163C2×#1314—471nomaximal, Sylow
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—22no—
167C22×C47—42no—
168C22×C47—42no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47C2×C22⋊C811yescharacteristic
172C22×C47C22×C1611yescharacteristic
173C22×C47C2×M3211yescharacteristic
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—24no—
177C2×D47—24no—
178C2×D47—22no—
179C2×D47—48no—
180C2×D47—42no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—48no—
184C2×D47—42no—
185C2×D47#32312yes—
186C2×D47C22⋊C1612yes—
187C2×D47C22⋊C1612yes—
188C2×D47#34912yes—
189C4×C47—21no—
190C4×C47—41no—
191C4×C47C2×#9911yescharacteristic
192C4×C47C2×#10011yescharacteristic
193Dic47—21no—
194Dic47—41no—
195Dic47#32312yes—
196C22×C22⋊C8—471no—
197C2×C22⋊C16—472no—
198#1314—471no—
199#1314—472no—
200#1314D4711yescharacteristic, direct product factor
201C2×C47—21no—
202C2×C47—21no—
203C2×C47—42no—
204C2×C47C2×#32311yescharacteristic
205C2×C47C2×C22⋊C1611yescharacteristic
206C2×C47C2×#34911yescharacteristic
207D47—22no—
208D47—42no—
209D47#131414yesdirect product factor
210C24×C4—471no—
211C23×C8—471no—
212C23×C8—471no—
213C22×C16—942no—
214C2×C22⋊C8—471no—
215C2×C22⋊C8—471no—
216C2×C22⋊C8—471no—
217C2×C22⋊C8—942no—
218C2×C22⋊C8—942no—
219C2×C22⋊C8C2×D4711yescharacteristic
220C22⋊C16—472no—
221C22⋊C16—942no—
222C22⋊C16C2×D4712yescomplemented
223C47C2×#131411yescharacteristic, complemented, Sylow
224C25—471no—
225C23×C4—471no—
226C23×C4—471no—
227C23×C4—471no—
228C23×C4—471no—
229C23×C4—471no—
230C23×C4—941no—
231C23×C4—941no—
232C23×C4—941no—
233C23×C4—941no—
234C23×C4—1882no—
235C23×C4—1882no—
236C23×C4C4×D4711yescharacteristic
237C22×C8—471no—
238C22×C8—472no—
239C22×C8—472no—
240C22×C8—471no—
241C22×C8—941no—
242C22×C8—941no—
243C22×C8—1882no—
244C22×C8—1882no—
245C22×C8C4×D4711yescharacteristic
246C22×C8C22×D4711yescharacteristic
247C2×C16—22no—
248C2×C16—942no—
249C2×C16—1884no—
250C22⋊C8—22no—
251C22⋊C8—942no—
252C22⋊C8—942no—
253C22⋊C8—942no—
254C24—471no—
255C24—474no—
256C24—471no—
257C24—941no—
258C24—941no—
259C24—942no—
260C24—1882no—
261C24—1882no—
262C24C8×D4711yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—471no—
273C22×C4—942no—
274C22×C4—942no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4—941no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—1881no—
284C22×C4—1881no—
285C22×C4—1882no—
286C22×C4—1882no—
287C22×C4—1884no—
288C22×C4—1884no—
289C22×C4—1882no—
290C22×C4—1882no—
291C22×C4—1882no—
292C22×C4—1882no—
293C22×C4—1882no—
294C22×C4C8×D4711yescharacteristic
295C22×C4C2×C4×D4711yescharacteristic
296C2×C8—21no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—472no—
300C2×C8—944no—
301C2×C8—941no—
302C2×C8—1882no—
303C2×C8—1882no—
304C2×C8—1882no—
305C2×C8—1881no—
306C2×C8—1881no—
307C2×C8D4×D4712yes—
308C16—42no—
309C16—1882no—
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—471no—
315C23—472no—
316C23—472no—
317C23—471no—
318C23—472no—
319C23—942no—
320C23—942no—
321C23—944no—
322C23—944no—
323C23—941no—
324C23—941no—
325C23—1881no—
326C23—1881no—
327C23—1882no—
328C23—1882no—
329C23—1888no—
330C23—1882no—
331C23—1888no—
332C23—1882no—
333C23C16×D4712yescomplemented
334C23C2×C8×D4711yescharacteristic
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—471no—
343C2×C4—472no—
344C2×C4—472no—
345C2×C4—471no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4—942no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—1882no—
353C2×C4—1882no—
354C2×C4—1882no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4—1882no—
358C2×C4—1882no—
359C2×C4—1881no—
360C2×C4—1881no—
361C2×C4—1881no—
362C2×C4C22⋊C4×D4711yescharacteristic
363C2×C4M16×D4711yescharacteristic
364C8—22no—
365C8—41no—
366C8—942no—
367C8—1881no—
368C22—21no—
369C22—21no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—472no—
376C22—472no—
377C22—472no—
378C22—472no—
379C22—944no—
380C22—944no—
381C22—941no—
382C22—941no—
383C22—942no—
384C22—1882no—
385C22—1882no—
386C22—1888no—
387C22—1888no—
388C22—1881no—
389C22—1881no—
390C22C22⋊C8×D4711yescharacteristic
391C22C2×C16×D4711yescharacteristic
392C22M32×D4711yescharacteristic
393C4—21no—
394C4—41no—
395C4—472no—
396C4—941no—
397C4—1881no—
398C4#99×D4711yescharacteristic
399C4#100×D4711yescharacteristic
400C2—21no—
401C2—21no—
402C2—42no—
403C2—474no—
404C2—942no—
405C2—1882no—
406C2#323×D4711yescharacteristic
407C2C22⋊C16×D4711yescharacteristic
408C2#349×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C22×C16
FrattiniC22×C8C22×D47
FittingC47×#1314C2
socleC22×C47C2×C22⋊C8
prime radicalC24×D47C8
cosocleC22×C8×C47C23
hypercenter#1314D47
hypocenterC47C2×#1314
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. C22⋊C16×D47C2semidirect
3. #20241312C2semidirect
4. #20241311C2semidirect
5. C47×#1314C2semidirect
15. C22⋊(C47⋊C16)C22semidirect
18. C47×C22⋊C16C22semidirect
55. C23×D47C16semidirect
109. C23×C47C2×C16semidirect
128. C22×D47C2×C16semidirect
200. #1314D47direct (N × H)
209. D47#1314direct (N × H)
222. C22⋊C16C2×D47semidirect
223. C47C2×#1314semidirect
333. C23C16×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D472
C22⋊C16×D472
#202413122
#202413112
C47×#13142
C2×#131447