Finite Group Databasebeta

← C47×#8739 #26048437

Subgroups — C47×#8739 #26048437

Order 12032.

656 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C47×#2297C211yesmaximal, characteristic
2C47×#1785C211yesmaximal, characteristic
3C47×#1782C211yesmaximal, characteristic
4C47×#1284C214yesmaximal, complemented
5C22×#41×C47C2211yescharacteristic
6C2×#117×C47C411yescharacteristic, complemented
7C22×C42×C47C411yescharacteristic, complemented
8C2×#101×C47—21no—
9C2×#100×C47—21no—
10C2×#99×C47—21no—
11C2×#99×C47—21no—
12C47×#407C2212yes—
13C47×#391—21no—
14C47×#390—21no—
15C47×#386—21no—
16C47×#386—21no—
17C47×#381C2212yes—
18C4×C22⋊C4×C47C412yescomplemented
19C4×C22⋊C4×C47C2212yes—
20C2×#41×C47—24no—
21C2×#41×C47—42no—
22C2×#41×C47—42no—
23C22×Q8×C47D411yescharacteristic
24C22×D4×C47D411yescharacteristic
25C22×D4×C47D411yescharacteristic
26C22×D4×C47D411yescharacteristic
27C23×C4×C47—21no—
28C23×C4×C47C2×C411yescharacteristic
29C23×C4×C47C2×C411yescharacteristic
30C23×C4×C47C2311yescharacteristic
31C2×M16×C47—22no—
32#117×C47—42no—
33C2×C4⋊C4×C47—21no—
34C2×C22⋊C4×C47—21no—
35C2×C22⋊C4×C47—22no—
36C2×C22⋊C4×C47—22no—
37C2×C22⋊C4×C47—22no—
38C2×C42×C47—21no—
39C2×C42×C47—42no—
40C2×C42×C47C2×C412yes—
41C2×C42×C47C2×C412yes—
42#101×C47—42no—
43#100×C47—42no—
44#99×C47—42no—
45#99×C47—42no—
46C22⋊C8×C47—24no—
47#95×C47—22no—
48#95×C47—22no—
49#95×C47—24no—
50C24×C47C22⋊C411yescharacteristic
51C24×C47C22⋊C411yescharacteristic
52C24×C47C2×D411yescharacteristic
53#41×C47—416no—
54C2×Q8×C47—22no—
55C2×Q8×C47—22no—
56C2×Q8×C47—41no—
57C2×D4×C47—22no—
58C2×D4×C47—22no—
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—41no—
64C2×D4×C47—41no—
65C2×D4×C47—41no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47—44no—
77C22×C4×C47—42no—
78C22×C4×C47—42no—
79C22×C4×C47C22⋊C411yescharacteristic
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22×C411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C22×C4×C47#4114yes—
84M16×C47—42no—
85M16×C47—42no—
86C2×C8×C47—42no—
87C4⋊C4×C47—42no—
88C22⋊C4×C47—44no—
89C22⋊C4×C47—44no—
90C22⋊C4×C47—42no—
91C22⋊C4×C47—42no—
92C22⋊C4×C47—42no—
93C42×C47—42no—
94C42×C47—42no—
95C42×C47—42no—
96C23×C47—21no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—42no—
104C23×C47—42no—
105C23×C47—42no—
106C23×C47#9912yes—
107C23×C47C2×C22⋊C411yescharacteristic
108C23×C47#12312yes—
109Q8×C47—44no—
110D4×C47—44no—
111D4×C47—44no—
112D4×C47—44no—
113C2×C4×C47—28no—
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—24no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—44no—
125C2×C4×C47—44no—
126C2×C4×C47—42no—
127C2×C4×C47—48no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47—82no—
133C2×C4×C47—84no—
134C2×C4×C47#9912yes—
135C2×C4×C47#11712yes—
136C2×C4×C47#12312yes—
137C8×C47—82no—
138#8739C4711yesmaximal, characteristic, direct product factor, Sylow
139C22×C47—22no—
140C22×C47—22no—
141C22×C47—22no—
142C22×C47—24no—
143C22×C47—42no—
144C22×C47—42no—
145C22×C47—42no—
146C22×C47—41no—
147C22×C47—42no—
148C22×C47—81no—
149C22×C47—81no—
150C22×C47—81no—
151C22×C47—81no—
152C22×C47#38111yescharacteristic
153C22×C47C2×#9911yescharacteristic
154C22×C47C2×#9911yescharacteristic
155C4×C47—22no—
156C4×C47—22no—
157C4×C47—22no—
158C4×C47—44no—
159C4×C47—41no—
160C4×C47—82no—
161C4×C47—162no—
162#2297C2×C4711yescharacteristic
163#1785C2×C4711yescharacteristic
164#1782C2×C4711yescharacteristic
165#1284C2×C4714yescomplemented
166C2×C47—21no—
167C2×C47—21no—
168C2×C47—42no—
169C2×C47—42no—
170C2×C47—81no—
171C2×C47#181911yescharacteristic
172C2×C47#182712yes—
173C22×#41C22×C4711yescharacteristic
174C2×#117C4×C4711yescharacteristic, complemented
175C22×C42C4×C4711yescharacteristic, complemented
176C2×#101—21no—
177C2×#100—21no—
178C2×#99—21no—
179C2×#99—21no—
180#407C22×C4712yes—
181#391—21no—
182#390—21no—
183#386—21no—
184#386—21no—
185#381C22×C4712yes—
186C4×C22⋊C4C4×C4712yescomplemented
187C4×C22⋊C4C22×C4712yes—
188C47#873911yescharacteristic, direct product factor, Sylow
189C2×#41—24no—
190C2×#41—42no—
191C2×#41—42no—
192C22×Q8D4×C4711yescharacteristic
193C22×D4D4×C4711yescharacteristic
194C22×D4D4×C4711yescharacteristic
195C22×D4D4×C4711yescharacteristic
196C23×C4—21no—
197C23×C4C2×C4×C4711yescharacteristic
198C23×C4C2×C4×C4711yescharacteristic
199C23×C4C23×C4711yescharacteristic
200C2×M16—22no—
201#117—42no—
202C2×C4⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C42—21no—
208C2×C42—42no—
209C2×C42C2×C4×C4712yes—
210C2×C42C2×C4×C4712yes—
211#101—42no—
212#100—42no—
213#99—42no—
214#99—42no—
215C22⋊C8—24no—
216#95—22no—
217#95—22no—
218#95—24no—
219C24C22⋊C4×C4711yescharacteristic
220C24C22⋊C4×C4711yescharacteristic
221C24C2×D4×C4711yescharacteristic
222#41—416no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
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—41no—
244C22×C4—41no—
245C22×C4—44no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C22⋊C4×C4711yescharacteristic
249C22×C4C22⋊C4×C4711yescharacteristic
250C22×C4C22×C4×C4711yescharacteristic
251C22×C4C2×D4×C4711yescharacteristic
252C22×C4#41×C4714yes—
253M16—42no—
254M16—42no—
255C2×C8—42no—
256C4⋊C4—42no—
257C22⋊C4—44no—
258C22⋊C4—44no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C42—42no—
263C42—42no—
264C42—42no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23#99×C4712yes—
276C23C2×C22⋊C4×C4711yescharacteristic
277C23#123×C4712yes—
278Q8—44no—
279D4—44no—
280D4—44no—
281D4—44no—
282C2×C4—28no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—24no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—48no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—82no—
302C2×C4—84no—
303C2×C4#99×C4712yes—
304C2×C4#117×C4712yes—
305C2×C4#123×C4712yes—
306C8—82no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—24no—
311C22—42no—
312C22—42no—
313C22—42no—
314C22—41no—
315C22—42no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22C47×#38111yescharacteristic
321C22C2×#99×C4711yescharacteristic
322C22C2×#99×C4711yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—44no—
327C4—41no—
328C4—82no—
329C4—162no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2—81no—
335C2C47×#181911yescharacteristic
336C2C47×#182712yes—
subgroupG/H
center, socleC22×C47#381
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC22×#41×C47C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1284C2semidirect
6. C2×#117×C47C4semidirect
7. C22×C42×C47C4semidirect
18. C4×C22⋊C4×C47C4semidirect
138. #8739C47direct (N × H)
165. #1284C2×C47semidirect
174. C2×#117C4×C47semidirect
175. C22×C42C4×C47semidirect
186. C4×C22⋊C4C4×C47semidirect
188. C47#8739direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#22972
C47×#17852
C47×#17822
C47×#12842
#873947