Finite Group Databasebeta

← C47×#9169 #26048867

Subgroups — C47×#9169 #26048867

Order 12032.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3079C211yesmaximal, characteristic
2C47×#2906C211yesmaximal, characteristic
3C47×#1549C211yesmaximal, characteristic, complemented
4C2×C47×#333C211yesmaximal, characteristic, complemented
5C47×#1477C211yesmaximal, characteristic
6C47×#1301C211yesmaximal, characteristic, complemented
7C47×#1292C211yesmaximal, characteristic, complemented
8C2×#131×C47—21no—
9C2×C4⋊Q8×C47C2211yescharacteristic
10C4×#41×C47C2211yescharacteristic
11C47×#477—21no—
12C47×#476—21no—
13C47×#475C412yes—
14C47×#474C412yes—
15C47×#431C2211yescharacteristic
16C47×#428—21no—
17C47×#424—21no—
18C47×#424—22no—
19C47×#423—21no—
20C47×#423C2211yescharacteristic
21C47×#423C2211yescharacteristic
22C2×C4⋊C8×C47—21no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C47×#417—21no—
26C47×#333—21no—
27C47×#333—21no—
28C47×#332—22no—
29C47×Q8⋊C8—21no—
30C47×D4⋊C8—21no—
31C2×#41×C47D411yescharacteristic
32C22×Q8×C47—21no—
33#131×C47—42no—
34#131×C47—42no—
35C2×M16×C47—22no—
36C2×M16×C47—21no—
37C2×M16×C47—21no—
38C22×C8×C47—22no—
39C22×C8×C47—21no—
40C22×C8×C47—21no—
41C4⋊Q8×C47—21no—
42C4⋊Q8×C47—21no—
43C4⋊Q8×C47—21no—
44C4⋊Q8×C47C2×C412yes—
45C4×Q8×C47C2×C411yescharacteristic
46C4×Q8×C47D411yescharacteristic
47C4×D4×C47—21no—
48C4×D4×C47—21no—
49C4×D4×C47C2×C411yescharacteristic
50C4×D4×C47D411yescharacteristic
51#117×C47—21no—
52#117×C47D411yescharacteristic
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C42×C47—21no—
56C2×C42×C47C2311yescharacteristic
57#107×C47—22no—
58#106×C47—22no—
59C4⋊C8×C47—22no—
60C4⋊C8×C47—22no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67C4⋊C8×C47C2×C412yes—
68C4⋊C8×C47D412yes—
69C4⋊C8×C47D411yescharacteristic
70C4⋊C8×C47D411yescharacteristic
71#103×C47—22no—
72#102×C47—22no—
73C22⋊C8×C47—21no—
74C4×C8×C47—21no—
75#41×C47—21no—
76#41×C47—21no—
77#41×C47SD1612yes—
78#41×C47Q1612yes—
79C2×Q8×C47—22no—
80C2×Q8×C47—41no—
81C2×Q8×C47—82no—
82C2×Q8×C47C22⋊C411yescharacteristic
83C2×D4×C47—21no—
84C2×D4×C47C22⋊C411yescharacteristic
85C22×C4×C47—21no—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—41no—
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47#4111yescharacteristic
91C22×C4×C47#4111yescharacteristic
92M16×C47—44no—
93M16×C47—41no—
94M16×C47—41no—
95M16×C47—41no—
96M16×C47—41no—
97C2×C8×C47—22no—
98C2×C8×C47—21no—
99C2×C8×C47—22no—
100C2×C8×C47—21no—
101C2×C8×C47—44no—
102C2×C8×C47—41no—
103C2×C8×C47—41no—
104C2×C8×C47—41no—
105C2×C8×C47—41no—
106C2×C8×C47—81no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—22no—
110C4⋊C4×C47—22no—
111C4⋊C4×C47—41no—
112C4⋊C4×C47—41no—
113C4⋊C4×C47C22⋊C411yescharacteristic
114C4⋊C4×C47C22⋊C411yescharacteristic
115C22⋊C4×C47—21no—
116C22⋊C4×C47—21no—
117C22⋊C4×C47—21no—
118C42×C47—21no—
119C42×C47—21no—
120C42×C47—21no—
121C42×C47C22×C411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47C2×D411yescharacteristic
124C42×C47C2×D411yescharacteristic
125C23×C47—21no—
126C23×C47#12311yescharacteristic
127Q8×C47—21no—
128Q8×C47—82no—
129Q8×C47—82no—
130Q8×C47#10312yes—
131D4×C47—22no—
132D4×C47—22no—
133D4×C47—21no—
134D4×C47#10312yes—
135C2×C4×C47—21no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—42no—
146C2×C4×C47—81no—
147C2×C4×C47—82no—
148C2×C4×C47C2×C22⋊C411yescharacteristic
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47C4×D411yescharacteristic
151C2×C4×C47#12011yescharacteristic
152C2×C4×C47#12111yescharacteristic
153C2×C4×C47#12111yescharacteristic
154C2×C4×C47C2×SD1611yescharacteristic
155C2×C4×C47C2×Q1611yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C47#13711yescharacteristic
158C8×C47—42no—
159C8×C47—41no—
160C8×C47—42no—
161C8×C47—41no—
162C8×C47—81no—
163C8×C47—81no—
164#9169C4711yesmaximal, characteristic, direct product factor, Sylow
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—22no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47#38611yescharacteristic
171C22×C47#48311yescharacteristic
172C22×C47#48411yescharacteristic
173C4×C47—22no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—82no—
180C4×C47C2×#10311yescharacteristic
181C4×C47#41711yescharacteristic
182C4×C47#45011yescharacteristic
183C4×C47#45111yescharacteristic
184C4×C47#47111yescharacteristic
185C4×C47#47311yescharacteristic
186#3079C2×C4711yescharacteristic
187#2906C2×C4711yescharacteristic
188#1549C2×C4711yescharacteristic, complemented
189C2×#333C2×C4711yescharacteristic, complemented
190#1477C2×C4711yescharacteristic
191#1301C2×C4711yescharacteristic, complemented
192#1292C2×C4711yescharacteristic, complemented
193C2×C47—21no—
194C2×C47—21no—
195C2×C47—42no—
196C2×C47#187211yescharacteristic
197C2×C47#190311yescharacteristic
198C2×C47#190811yescharacteristic
199C2×#131—21no—
200C2×C4⋊Q8C22×C4711yescharacteristic
201C4×#41C22×C4711yescharacteristic
202#477—21no—
203#476—21no—
204#475C4×C4712yes—
205#474C4×C4712yes—
206#431C22×C4711yescharacteristic
207#428—21no—
208#424—21no—
209#424—22no—
210#423—21no—
211#423C22×C4711yescharacteristic
212#423C22×C4711yescharacteristic
213C2×C4⋊C8—21no—
214C2×C4⋊C8C22×C4711yescharacteristic
215C2×C4⋊C8C22×C4711yescharacteristic
216#417—21no—
217#333—21no—
218#333—21no—
219#332—22no—
220Q8⋊C8—21no—
221D4⋊C8—21no—
222C47#916911yescharacteristic, direct product factor, Sylow
223C2×#41D4×C4711yescharacteristic
224C22×Q8—21no—
225#131—42no—
226#131—42no—
227C2×M16—22no—
228C2×M16—21no—
229C2×M16—21no—
230C22×C8—22no—
231C22×C8—21no—
232C22×C8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8C2×C4×C4712yes—
237C4×Q8C2×C4×C4711yescharacteristic
238C4×Q8D4×C4711yescharacteristic
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C2×C4×C4711yescharacteristic
242C4×D4D4×C4711yescharacteristic
243#117—21no—
244#117D4×C4711yescharacteristic
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42C23×C4711yescharacteristic
249#107—22no—
250#106—22no—
251C4⋊C8—22no—
252C4⋊C8—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8C2×C4×C4712yes—
260C4⋊C8D4×C4712yes—
261C4⋊C8D4×C4711yescharacteristic
262C4⋊C8D4×C4711yescharacteristic
263#103—22no—
264#102—22no—
265C22⋊C8—21no—
266C4×C8—21no—
267#41—21no—
268#41—21no—
269#41SD16×C4712yes—
270#41Q16×C4712yes—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8C22⋊C4×C4711yescharacteristic
275C2×D4—21no—
276C2×D4C22⋊C4×C4711yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4C2×D4×C4711yescharacteristic
282C22×C4#41×C4711yescharacteristic
283C22×C4#41×C4711yescharacteristic
284M16—44no—
285M16—41no—
286M16—41no—
287M16—41no—
288M16—41no—
289C2×C8—22no—
290C2×C8—21no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—44no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—81no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4C22⋊C4×C4711yescharacteristic
306C4⋊C4C22⋊C4×C4711yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C42—21no—
311C42—21no—
312C42—21no—
313C42C22×C4×C4711yescharacteristic
314C42C2×D4×C4711yescharacteristic
315C42C2×D4×C4711yescharacteristic
316C42C2×D4×C4711yescharacteristic
317C23—21no—
318C23#123×C4711yescharacteristic
319Q8—21no—
320Q8—82no—
321Q8—82no—
322Q8#103×C4712yes—
323D4—22no—
324D4—22no—
325D4—21no—
326D4#103×C4712yes—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4C2×C22⋊C4×C4711yescharacteristic
341C2×C4C4×D4×C4711yescharacteristic
342C2×C4C4×D4×C4711yescharacteristic
343C2×C4#120×C4711yescharacteristic
344C2×C4#121×C4711yescharacteristic
345C2×C4#121×C4711yescharacteristic
346C2×C4C2×SD16×C4711yescharacteristic
347C2×C4C2×Q16×C4711yescharacteristic
348C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
349C2×C4#137×C4711yescharacteristic
350C8—41no—
351C8—42no—
352C8—41no—
353C8—42no—
354C8—81no—
355C8—81no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22C47×#38611yescharacteristic
362C22C47×#48311yescharacteristic
363C22C47×#48411yescharacteristic
364C4—22no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—82no—
371C4C2×#103×C4711yescharacteristic
372C4C47×#41711yescharacteristic
373C4C47×#45011yescharacteristic
374C4C47×#45111yescharacteristic
375C4C47×#47111yescharacteristic
376C4C47×#47311yescharacteristic
377C2—21no—
378C2—21no—
379C2—42no—
380C2C47×#187211yescharacteristic
381C2C47×#190311yescharacteristic
382C2C47×#190811yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC2×#41×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1549C2semidirect
4. C2×C47×#333C2semidirect
6. C47×#1301C2semidirect
7. C47×#1292C2semidirect
164. #9169C47direct (N × H)
188. #1549C2×C47semidirect
189. C2×#333C2×C47semidirect
191. #1301C2×C47semidirect
192. #1292C2×C47semidirect
222. C47#9169direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30792
C47×#29062
C47×#15492
C2×C47×#3332
C47×#14772
C47×#13012
C47×#12922
#916947