Finite Group Databasebeta

← C47×#9958 #26049656

Subgroups — C47×#9958 #26049656

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3187C211yesmaximal, characteristic
2C2×C47×#484C211yesmaximal, characteristic, complemented
3C47×#2504C211yesmaximal, characteristic
4C47×#1996C211yesmaximal, characteristic, complemented
5C47×#1824C211yesmaximal, characteristic, complemented
6C47×#1519C211yesmaximal, characteristic
7C47×#1282C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C47C2211yescharacteristic
9C2×#121×C47C2211yescharacteristic
10C22×C4⋊C4×C47C2211yescharacteristic
11C47×#484—22no—
12C47×#484—22no—
13C47×#483—21no—
14C47×#481—21no—
15C47×#465—22no—
16C47×#450—21no—
17C47×#448—21no—
18C2×#107×C47—21no—
19C2×#103×C47—21no—
20C2×C22⋊C8×C47C2211yescharacteristic
21C2×C22⋊C8×C47C2211yescharacteristic
22C47×#397—22no—
23C47×#390—21no—
24C47×#386—22no—
25C47×#382—21no—
26C47×#380C2211yescharacteristic
27C4×C22⋊C4×C47C2211yescharacteristic
28C47×#342—22no—
29C47×#340—22no—
30C47×#327—22no—
31C22×Q8×C47D411yescharacteristic
32C22×D4×C47—21no—
33C22×D4×C47D411yescharacteristic
34C23×C4×C47—21no—
35C23×C4×C47C2311yescharacteristic
36C2×SD16×C47—22no—
37C22×C8×C47—21no—
38C22×C8×C47D412yes—
39C22⋊Q8×C47—21no—
40C22⋊Q8×C47—21no—
41C22⋊Q8×C47—21no—
42C22⋊Q8×C47—21no—
43#121×C47—21no—
44#121×C47—21no—
45#121×C47—21no—
46#121×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47D411yescharacteristic
55C2×C4⋊C4×C47D411yescharacteristic
56C2×C4⋊C4×C47D412yes—
57C2×C22⋊C4×C47—21no—
58C2×C22⋊C4×C47—21no—
59C2×C22⋊C4×C47—21no—
60C2×C22⋊C4×C47—24no—
61C2×C22⋊C4×C47D412yes—
62C2×C42×C47—21no—
63#107×C47—24no—
64#106×C47—22no—
65#103×C47—22no—
66#103×C47—24no—
67#102×C47—22no—
68C22⋊C8×C47—21no—
69C22⋊C8×C47—21no—
70C22⋊C8×C47—21no—
71C22⋊C8×C47D412yes—
72#95×C47—24no—
73#95×C47—21no—
74#95×C47—21no—
75C24×C47—21no—
76C24×C47C2×D411yescharacteristic
77C2×Q8×C47—21no—
78C2×Q8×C47—21no—
79C2×Q8×C47—42no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—42no—
83C2×D4×C47—41no—
84C2×D4×C47—41no—
85C2×D4×C47—42no—
86C2×D4×C47—42no—
87C22×C4×C47—22no—
88C22×C4×C47—22no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47—21no—
92C22×C4×C47—42no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—82no—
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47#4111yescharacteristic
103SD16×C47—82no—
104C2×C8×C47—22no—
105C2×C8×C47—22no—
106C2×C8×C47—42no—
107C2×C8×C47—42no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—22no—
110C4⋊C4×C47—21no—
111C4⋊C4×C47—21no—
112C4⋊C4×C47—22no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—42no—
115C4⋊C4×C47—41no—
116C4⋊C4×C47—41no—
117C4⋊C4×C47—41no—
118C4⋊C4×C47—41no—
119C22⋊C4×C47—22no—
120C22⋊C4×C47—22no—
121C22⋊C4×C47—41no—
122C22⋊C4×C47—41no—
123C22⋊C4×C47—41no—
124C22⋊C4×C47—41no—
125C22⋊C4×C47—42no—
126C22⋊C4×C47—84no—
127C42×C47—42no—
128C23×C47—41no—
129C23×C47—41no—
130C23×C47—42no—
131C23×C47—42no—
132C23×C47—41no—
133C23×C47—42no—
134C23×C47#12011yescharacteristic
135C23×C47#12111yescharacteristic
136C23×C47#12711yescharacteristic
137C23×C47#13512yes—
138C23×C47#13712yes—
139Q8×C47—42no—
140Q8×C47—42no—
141D4×C47—42no—
142D4×C47—81no—
143D4×C47—82no—
144D4×C47—81no—
145D4×C47—81no—
146C2×C4×C47—22no—
147C2×C4×C47—22no—
148C2×C4×C47—22no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—42no—
153C2×C4×C47—42no—
154C2×C4×C47—44no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—42no—
159C2×C4×C47—42no—
160C2×C4×C47—42no—
161C2×C4×C47—82no—
162C2×C4×C47—82no—
163C2×C4×C47—81no—
164C2×C4×C47—81no—
165C2×C4×C47—81no—
166C2×C4×C47—81no—
167C2×C4×C47—81no—
168C2×C4×C47#12011yescharacteristic
169C2×C4×C47#12011yescharacteristic
170C2×C4×C47#12111yescharacteristic
171C2×C4×C47#12111yescharacteristic
172C8×C47—42no—
173C8×C47—42no—
174#9958C4711yesmaximal, characteristic, direct product factor, Sylow
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—42no—
182C22×C47—42no—
183C22×C47—84no—
184C22×C47—81no—
185C22×C47—81no—
186C22×C47—81no—
187C22×C47#39211yescharacteristic
188C22×C47#45212yes—
189C22×C47#46412yes—
190C22×C47#49511yescharacteristic
191C22×C47#49711yescharacteristic
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—21no—
195C4×C47—82no—
196C4×C47—82no—
197C4×C47—81no—
198C4×C47—81no—
199C4×C47—81no—
200C4×C47—161no—
201C4×C47#45812yes—
202#3187C2×C4711yescharacteristic
203C2×#484C2×C4711yescharacteristic, complemented
204#2504C2×C4711yescharacteristic
205#1996C2×C4711yescharacteristic, complemented
206#1824C2×C4711yescharacteristic, complemented
207#1519C2×C4711yescharacteristic
208#1282C2×C4711yescharacteristic, complemented
209C2×C47—22no—
210C2×C47—21no—
211C2×C47—22no—
212C2×C47—21no—
213C2×C47—161no—
214C2×C47#200811yescharacteristic
215C2×C47#201511yescharacteristic
216C2×C47#202211yescharacteristic
217C2×C22⋊Q8C22×C4711yescharacteristic
218C2×#121C22×C4711yescharacteristic
219C22×C4⋊C4C22×C4711yescharacteristic
220#484—22no—
221#484—22no—
222#483—21no—
223#481—21no—
224#465—22no—
225#450—21no—
226#448—21no—
227C2×#107—21no—
228C2×#103—21no—
229C2×C22⋊C8C22×C4711yescharacteristic
230C2×C22⋊C8C22×C4711yescharacteristic
231#397—22no—
232#390—21no—
233#386—22no—
234#382—21no—
235#380C22×C4711yescharacteristic
236C4×C22⋊C4C22×C4711yescharacteristic
237#342—22no—
238#340—22no—
239#327—22no—
240C47#995811yescharacteristic, direct product factor, Sylow
241C22×Q8D4×C4711yescharacteristic
242C22×D4—21no—
243C22×D4D4×C4711yescharacteristic
244C23×C4—21no—
245C23×C4C23×C4711yescharacteristic
246C2×SD16—22no—
247C22×C8—21no—
248C22×C8D4×C4712yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#121—21no—
254#121—21no—
255#121—21no—
256#121—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4D4×C4712yes—
265C2×C4⋊C4D4×C4711yescharacteristic
266C2×C4⋊C4D4×C4711yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4D4×C4712yes—
272C2×C42—21no—
273#107—24no—
274#106—22no—
275#103—24no—
276#103—22no—
277#102—22no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8D4×C4712yes—
282#95—24no—
283#95—21no—
284#95—21no—
285C24—21no—
286C24C2×D4×C4711yescharacteristic
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—82no—
307C22×C4C2×D4×C4711yescharacteristic
308C22×C4C2×D4×C4711yescharacteristic
309C22×C4C2×D4×C4711yescharacteristic
310C22×C4C2×D4×C4711yescharacteristic
311C22×C4C2×D4×C4711yescharacteristic
312C22×C4#41×C4711yescharacteristic
313SD16—82no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—42no—
317C2×C8—42no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—42no—
336C22⋊C4—84no—
337C42—42no—
338C23—41no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—41no—
344C23#120×C4711yescharacteristic
345C23#121×C4711yescharacteristic
346C23#127×C4711yescharacteristic
347C23#135×C4712yes—
348C23#137×C4712yes—
349Q8—42no—
350Q8—42no—
351D4—42no—
352D4—81no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4#120×C4711yescharacteristic
379C2×C4#120×C4711yescharacteristic
380C2×C4#121×C4711yescharacteristic
381C2×C4#121×C4711yescharacteristic
382C8—42no—
383C8—42no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—84no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22C47×#39211yescharacteristic
397C22C47×#45212yes—
398C22C47×#46412yes—
399C22C47×#49511yescharacteristic
400C22C47×#49711yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—82no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—161no—
410C4C47×#45812yes—
411C2—22no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—161no—
416C2C47×#200811yescharacteristic
417C2C47×#201511yescharacteristic
418C2C47×#202211yescharacteristic
subgroupG/H
center, socleC22×C47#392
commutator, Frattini, cosocleC23×C4C23×C47
prime radicalC2×#121×C47C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#484C2semidirect
4. C47×#1996C2semidirect
5. C47×#1824C2semidirect
7. C47×#1282C2semidirect
174. #9958C47direct (N × H)
203. C2×#484C2×C47semidirect
205. #1996C2×C47semidirect
206. #1824C2×C47semidirect
208. #1282C2×C47semidirect
240. C47#9958direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31872
C2×C47×#4842
C47×#25042
C47×#19962
C47×#18242
C47×#15192
C47×#12822
#995847