Finite Group Databasebeta

← C47×#9177 #26048875

Subgroups — C47×#9177 #26048875

Order 12032.

494 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3077C211yesmaximal, characteristic
2C47×#2357C211yesmaximal, characteristic
3C47×#1518C211yesmaximal, characteristic, complemented
4C47×#1503C211yesmaximal, characteristic, complemented
5C47×#1478C211yesmaximal, characteristic
6C47×#1303C211yesmaximal, characteristic, complemented
7C47×#1286C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C2×C4×D4×C47C2211yescharacteristic
10C47×#478—22no—
11C47×#476C412yescomplemented
12C47×#474C412yescomplemented
13C47×#431C2211yescharacteristic
14C47×#431C2211yescharacteristic
15C47×#428—21no—
16C47×#423C2211yescharacteristic
17C47×#418—21no—
18C47×#390—21no—
19C47×#388—22no—
20C47×#382C2211yescharacteristic
21C47×#381—21no—
22C4×C4⋊C4×C47—21no—
23C4×C4⋊C4×C47C2211yescharacteristic
24C4×C22⋊C4×C47—21no—
25C47×#328—21no—
26C47×#328—21no—
27C47×#328—22no—
28C47×D4⋊C8—22no—
29C22×D4×C47D411yescharacteristic
30C23×C4×C47—21no—
31C2×M16×C47—21no—
32C4⋊Q8×C47C2×C411yescharacteristic
33C4⋊Q8×C47C2×C411yescharacteristic
34#125×C47—21no—
35C22⋊Q8×C47—21no—
36C22⋊Q8×C47—21no—
37C4×Q8×C47—21no—
38C4×Q8×C47—21no—
39C4×D4×C47—21no—
40C4×D4×C47—21no—
41C4×D4×C47C2×C412yes—
42C4×D4×C47D412yes—
43#117×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47—21no—
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C22⋊C4×C47—21no—
48C2×C22⋊C4×C47—22no—
49C2×C22⋊C4×C47—22no—
50C2×C42×C47—21no—
51C2×C42×C47—22no—
52C2×C42×C47C2311yescharacteristic
53#107×C47—22no—
54#106×C47—22no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47—21no—
58C4⋊C8×C47C2×C412yes—
59#102×C47—22no—
60#102×C47—22no—
61C22⋊C8×C47—21no—
62C22⋊C8×C47—21no—
63C4×C8×C47—21no—
64C4×C8×C47—21no—
65#95×C47—22no—
66#95×C47—21no—
67#95×C47D411yescharacteristic
68#95×C47D411yescharacteristic
69#95×C47D412yes—
70C24×C47—21no—
71C2×Q8×C47—21no—
72C2×Q8×C47—21no—
73C2×D4×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47C22⋊C412yes—
79C22×C4×C47—21no—
80C22×C4×C47—21no—
81C22×C4×C47—22no—
82C22×C4×C47—22no—
83C22×C4×C47—22no—
84C22×C4×C47—21no—
85C22×C4×C47—82no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89M16×C47—41no—
90M16×C47—41no—
91C2×C8×C47—22no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—21no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—42no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47C22⋊C412yes—
105C22⋊C4×C47—22no—
106C22⋊C4×C47—22no—
107C22⋊C4×C47—44no—
108C22⋊C4×C47—41no—
109C22⋊C4×C47—82no—
110C42×C47—41no—
111C42×C47—41no—
112C42×C47—41no—
113C42×C47—82no—
114C42×C47C22×C411yescharacteristic
115C42×C47C2×D411yescharacteristic
116C42×C47#4111yescharacteristic
117C42×C47#4111yescharacteristic
118C23×C47—22no—
119C23×C47—42no—
120C23×C47—42no—
121C23×C47—41no—
122C23×C47—41no—
123C23×C47#12011yescharacteristic
124Q8×C47—81no—
125Q8×C47—81no—
126D4×C47—22no—
127D4×C47—22no—
128D4×C47—41no—
129D4×C47—41no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—42no—
136C2×C4×C47—41no—
137C2×C4×C47—42no—
138C2×C4×C47—42no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—42no—
145C2×C4×C47—82no—
146C2×C4×C47—82no—
147C2×C4×C47C2×C22⋊C411yescharacteristic
148C2×C4×C47C4×D411yescharacteristic
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47#12111yescharacteristic
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47#12311yescharacteristic
153C2×C4×C47#13511yescharacteristic
154C2×C4×C47#13511yescharacteristic
155C2×C4×C47#13711yescharacteristic
156C2×C4×C47#13711yescharacteristic
157C8×C47—42no—
158C8×C47—81no—
159C8×C47—81no—
160#9177C4711yesmaximal, characteristic, direct product factor, Sylow
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—42no—
164C22×C47—42no—
165C22×C47—42no—
166C22×C47—82no—
167C22×C47—82no—
168C22×C47#38611yescharacteristic
169C22×C47#45211yescharacteristic
170C22×C47#45211yescharacteristic
171C4×C47—21no—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—42no—
176C4×C47—42no—
177C4×C47—81no—
178C4×C47—82no—
179C4×C47—81no—
180C4×C47—81no—
181C4×C47#41611yescharacteristic
182C4×C47#41911yescharacteristic
183C4×C47#48511yescharacteristic
184C4×C47#48511yescharacteristic
185#3077C2×C4711yescharacteristic
186#2357C2×C4711yescharacteristic
187#1518C2×C4711yescharacteristic, complemented
188#1503C2×C4711yescharacteristic, complemented
189#1478C2×C4711yescharacteristic
190#1303C2×C4711yescharacteristic, complemented
191#1286C2×C4711yescharacteristic, complemented
192C2×C47—21no—
193C2×C47—21no—
194C2×C47—82no—
195C2×C47#187311yescharacteristic
196C2×C47#190411yescharacteristic
197C2×C47#190611yescharacteristic
198#533C22×C4711yescharacteristic
199C2×C4×D4C22×C4711yescharacteristic
200#478—22no—
201#476C4×C4712yescomplemented
202#474C4×C4712yescomplemented
203#431C22×C4711yescharacteristic
204#431C22×C4711yescharacteristic
205#428—21no—
206#423C22×C4711yescharacteristic
207#418—21no—
208#390—21no—
209#388—22no—
210#382C22×C4711yescharacteristic
211#381—21no—
212C4×C4⋊C4—21no—
213C4×C4⋊C4C22×C4711yescharacteristic
214C4×C22⋊C4—21no—
215#328—21no—
216#328—21no—
217#328—22no—
218D4⋊C8—22no—
219C47#917711yescharacteristic, direct product factor, Sylow
220C22×D4D4×C4711yescharacteristic
221C23×C4—21no—
222C2×M16—21no—
223C4⋊Q8C2×C4×C4711yescharacteristic
224C4⋊Q8C2×C4×C4711yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4C2×C4×C4712yes—
233C4×D4D4×C4712yes—
234#117—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C4711yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C42—21no—
242C2×C42—22no—
243C2×C42C23×C4711yescharacteristic
244#107—22no—
245#106—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8C2×C4×C4712yes—
250#102—22no—
251#102—22no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256#95—22no—
257#95—21no—
258#95D4×C4711yescharacteristic
259#95D4×C4711yescharacteristic
260#95D4×C4712yes—
261C24—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4C22⋊C4×C4712yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—82no—
277C22×C4C2×D4×C4711yescharacteristic
278C22×C4C2×D4×C4711yescharacteristic
279C22×C4C2×D4×C4711yescharacteristic
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C22⋊C4×C4712yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—44no—
299C22⋊C4—41no—
300C22⋊C4—82no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42—82no—
305C42C22×C4×C4711yescharacteristic
306C42C2×D4×C4711yescharacteristic
307C42#41×C4711yescharacteristic
308C42#41×C4711yescharacteristic
309C23—22no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23#120×C4711yescharacteristic
315Q8—81no—
316Q8—81no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4C2×C22⋊C4×C4711yescharacteristic
339C2×C4C4×D4×C4711yescharacteristic
340C2×C4C4×D4×C4711yescharacteristic
341C2×C4#121×C4711yescharacteristic
342C2×C4#121×C4711yescharacteristic
343C2×C4#123×C4711yescharacteristic
344C2×C4#135×C4711yescharacteristic
345C2×C4#135×C4711yescharacteristic
346C2×C4#137×C4711yescharacteristic
347C2×C4#137×C4711yescharacteristic
348C8—42no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22C47×#38611yescharacteristic
359C22C47×#45211yescharacteristic
360C22C47×#45211yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—81no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4C47×#41611yescharacteristic
372C4C47×#41911yescharacteristic
373C4C47×#48511yescharacteristic
374C4C47×#48511yescharacteristic
375C2—21no—
376C2—21no—
377C2—82no—
378C2C47×#187311yescharacteristic
379C2C47×#190411yescharacteristic
380C2C47×#190611yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC22×D4×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×#1518C2semidirect
4. C47×#1503C2semidirect
6. C47×#1303C2semidirect
7. C47×#1286C2semidirect
11. C47×#476C4semidirect
12. C47×#474C4semidirect
160. #9177C47direct (N × H)
187. #1518C2×C47semidirect
188. #1503C2×C47semidirect
190. #1303C2×C47semidirect
191. #1286C2×C47semidirect
201. #476C4×C47semidirect
202. #474C4×C47semidirect
219. C47#9177direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30772
C47×#23572
C47×#15182
C47×#15032
C47×#14782
C47×#13032
C47×#12862
#917747