Finite Group Databasebeta

← C2×C47×#2204 #26073263

Subgroups — C2×C47×#2204 #26073263

Order 12032.

1200 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 222 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×C47×#555C211yesmaximal, characteristic, complemented
2C2×C47×#456C211yesmaximal, characteristic, complemented
3C2×C47×#454C212yesmaximal, complemented
4C47×#2204C218yesmaximal, direct product factor
5C2×C47×#356C211yesmaximal, characteristic, complemented
6C2×C47×#355C212yesmaximal, complemented
7C2×2−1+4×C47C2211yescharacteristic
8C2×#137×C47—21no—
9C2×AGL(1,ℤ/8)×C47—22no—
10C47×#555—22no—
11C47×#555—24no—
12C47×#555C2214yescomplemented
13C2×C4⋊Q8×C47C2211yescharacteristic
14C2×#124×C47—21no—
15C2×#124×C47C2212yes—
16C2×#121×C47—22no—
17C2×C4×D4×C47—21no—
18C2×#117×C47—22no—
19C47×#456—22no—
20C47×#456C2214yescomplemented
21C47×#454—24no—
22C47×#454C2218yescomplemented
23C2×#104×C47—22no—
24C2×#104×C47—21no—
25C2×#101×C47C2211yescharacteristic
26C2×#101×C47C2212yes—
27C47×#356C2214yescomplemented
28C47×#355C2218yescomplemented
292−1+4×C47—22no—
302−1+4×C47—21no—
312−1+4×C47—42no—
322−1+4×C47C2312yes—
33C2×#41×C47—22no—
34C2×#41×C47—21no—
35C2×#41×C47—41no—
36C22×Q8×C47—41no—
37C22×Q8×C47D411yescharacteristic
38C22×Q8×C47C2311yescharacteristic
39C22×D4×C47—21no—
40C22×D4×C47—21no—
41C22×D4×C47D412yes—
42C23×C4×C47—22no—
43#137×C47—24no—
44#137×C47—42no—
45AGL(1,ℤ/8)×C47—28no—
46AGL(1,ℤ/8)×C47—44no—
47C2×Q16×C47—41no—
48C2×SD16×C47—41no—
49C2×SD16×C47—42no—
50C2×D8×C47—42no—
51C2×M16×C47—22no—
52C2×M16×C47—21no—
53C4⋊Q8×C47—22no—
54C4⋊Q8×C47D412yes—
55C4⋊Q8×C47C2312yes—
56#124×C47—24no—
57#124×C47—24no—
58#124×C47—22no—
59#124×C47—22no—
60#124×C47D414yes—
61#124×C47C2314yes—
62#121×C47—28no—
63#121×C47—28no—
64C4×D4×C47—24no—
65C4×D4×C47—24no—
66#117×C47—28no—
67#117×C47—28no—
68C2×C4⋊C4×C47—21no—
69C2×C4⋊C4×C47—22no—
70C2×C22⋊C4×C47—22no—
71C2×C22⋊C4×C47—22no—
72C2×C22⋊C4×C47—22no—
73C2×C42×C47—21no—
74C2×C42×C47D412yes—
75C2×C42×C47D411yescharacteristic
76#104×C47—28no—
77#104×C47—24no—
78#101×C47—22no—
79#101×C47—21no—
80#101×C47C2314yes—
81#101×C47C2312yes—
82C24×C47—22no—
83#41×C47—24no—
84#41×C47—22no—
85#41×C47—24no—
86#41×C47—22no—
87#41×C47—42no—
88#41×C47—41no—
89#41×C47—42no—
90#41×C47—44no—
91#41×C47—42no—
92#41×C47—41no—
93#41×C47—42no—
94C2×Q8×C47—21no—
95C2×Q8×C47—22no—
96C2×Q8×C47—21no—
97C2×Q8×C47—41no—
98C2×Q8×C47—41no—
99C2×Q8×C47—41no—
100C2×Q8×C47—41no—
101C2×Q8×C47—42no—
102C2×Q8×C47—44no—
103C2×Q8×C47—42no—
104C2×Q8×C47C2×D412yes—
105C2×Q8×C47C2×D411yescharacteristic
106C2×Q8×C47C2×D412yes—
107C2×Q8×C47C2411yescharacteristic
108C2×D4×C47—22no—
109C2×D4×C47—21no—
110C2×D4×C47—24no—
111C2×D4×C47—24no—
112C2×D4×C47—22no—
113C2×D4×C47—44no—
114C2×D4×C47—42no—
115C2×D4×C47—42no—
116C2×D4×C47—41no—
117C2×D4×C47—81no—
118C2×D4×C47—81no—
119C2×D4×C47C2×D414yes—
120C22×C4×C47—21no—
121C22×C4×C47—28no—
122C22×C4×C47—22no—
123C22×C4×C47—21no—
124C22×C4×C47—48no—
125C22×C4×C47—42no—
126C22×C4×C47—41no—
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D412yes—
129Q16×C47—44no—
130SD16×C47—44no—
131SD16×C47—48no—
132D8×C47—48no—
133M16×C47—24no—
134M16×C47—22no—
135M16×C47—42no—
136M16×C47—41no—
137C2×C8×C47—42no—
138C2×C8×C47—41no—
139C4⋊C4×C47—24no—
140C4⋊C4×C47—24no—
141C4⋊C4×C47—24no—
142C22⋊C4×C47—28no—
143C22⋊C4×C47—24no—
144C22⋊C4×C47—24no—
145C22⋊C4×C47—24no—
146C22⋊C4×C47—24no—
147C42×C47—24no—
148C42×C47—22no—
149C42×C47—21no—
150C42×C47C2×D414yes—
151C42×C47C2×D412yes—
152C23×C47—24no—
153C23×C47—44no—
154C23×C47—44no—
155C23×C47—42no—
156C23×C47—41no—
157C23×C47—42no—
158C23×C47#12011yescharacteristic
159Q8×C47—24no—
160Q8×C47—22no—
161Q8×C47—42no—
162Q8×C47—41no—
163Q8×C47—41no—
164Q8×C47—42no—
165Q8×C47—42no—
166Q8×C47—41no—
167Q8×C47—81no—
168D4×C47—24no—
169D4×C47—22no—
170D4×C47—44no—
171D4×C47—48no—
172D4×C47—42no—
173D4×C47—41no—
174D4×C47—42no—
175D4×C47—42no—
176D4×C47—82no—
177D4×C47—84no—
178C2×C4×C47—24no—
179C2×C4×C47—22no—
180C2×C4×C47—22no—
181C2×C4×C47—21no—
182C2×C4×C47—22no—
183C2×C4×C47—21no—
184C2×C4×C47—24no—
185C2×C4×C47—22no—
186C2×C4×C47—416no—
187C2×C4×C47—44no—
188C2×C4×C47—42no—
189C2×C4×C47—44no—
190C2×C4×C47—42no—
191C2×C4×C47—44no—
192C2×C4×C47—41no—
193C2×C4×C47—41no—
194C2×C4×C47—41no—
195C2×C4×C47#12011yescharacteristic
196C2×C4×C47#12012yes—
197C2×C4×C47C22×D411yescharacteristic
198C2×C4×C47C22×D412yes—
199C8×C47—44no—
200C8×C47—42no—
201C2×#2204C4711yesmaximal, characteristic, direct product factor, Sylow
202C22×C47—22no—
203C22×C47—44no—
204C22×C47—44no—
205C22×C47—42no—
206C22×C47—44no—
207C22×C47—84no—
208C22×C47—82no—
209C22×C47—84no—
210C22×C47B(4,𝔽2)11yescharacteristic
211C22×C47B(4,𝔽2)11yescharacteristic
212C22×C47C2×#12011yescharacteristic
213C4×C47—24no—
214C4×C47—22no—
215C4×C47—21no—
216C4×C47—22no—
217C4×C47—21no—
218C4×C47—44no—
219C4×C47—42no—
220C4×C47—42no—
221C2×#555C2×C4711yescharacteristic, complemented
222C2×#456C2×C4711yescharacteristic, complemented
223C2×#454C2×C4712yescomplemented
224#2204C2×C4718yesdirect product factor
225C2×#356C2×C4711yescharacteristic, complemented
226C2×#355C2×C4712yescomplemented
227C2×C47—21no—
228C2×C47—21no—
229C2×C47—84no—
230C2×C47—82no—
231C2×C47#220412yesdirect product factor
232C2×C47C2×B(4,𝔽2)11yescharacteristic
233C2×2−1+4C22×C4711yescharacteristic
234C2×#137—21no—
235C2×AGL(1,ℤ/8)—22no—
236#555—22no—
237#555—24no—
238#555C22×C4714yescomplemented
239C2×C4⋊Q8C22×C4711yescharacteristic
240C2×#124—21no—
241C2×#124C22×C4712yes—
242C2×#121—22no—
243C2×C4×D4—21no—
244C2×#117—22no—
245#456—22no—
246#456C22×C4714yescomplemented
247#454—24no—
248#454C22×C4718yescomplemented
249C2×#104—22no—
250C2×#104—21no—
251C2×#101C22×C4711yescharacteristic
252C2×#101C22×C4712yes—
253#356C22×C4714yescomplemented
254#355C22×C4718yescomplemented
255C47C2×#220411yescharacteristic, direct product factor, Sylow
2562−1+4—22no—
2572−1+4—21no—
2582−1+4—42no—
2592−1+4C23×C4712yes—
260C2×#41—22no—
261C2×#41—21no—
262C2×#41—41no—
263C22×Q8—41no—
264C22×Q8D4×C4711yescharacteristic
265C22×Q8C23×C4711yescharacteristic
266C22×D4—21no—
267C22×D4—21no—
268C22×D4D4×C4712yes—
269C23×C4—22no—
270#137—24no—
271#137—42no—
272AGL(1,ℤ/8)—28no—
273AGL(1,ℤ/8)—44no—
274C2×Q16—41no—
275C2×SD16—41no—
276C2×SD16—42no—
277C2×D8—42no—
278C2×M16—22no—
279C2×M16—21no—
280C4⋊Q8—22no—
281C4⋊Q8D4×C4712yes—
282C4⋊Q8C23×C4712yes—
283#124—24no—
284#124—24no—
285#124—22no—
286#124—22no—
287#124D4×C4714yes—
288#124C23×C4714yes—
289#121—28no—
290#121—28no—
291C4×D4—24no—
292C4×D4—24no—
293#117—28no—
294#117—28no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C42—21no—
301C2×C42D4×C4712yes—
302C2×C42D4×C4711yescharacteristic
303#104—28no—
304#104—24no—
305#101—22no—
306#101—21no—
307#101C23×C4712yes—
308#101C23×C4714yes—
309C24—22no—
310#41—24no—
311#41—22no—
312#41—24no—
313#41—22no—
314#41—42no—
315#41—41no—
316#41—42no—
317#41—44no—
318#41—42no—
319#41—41no—
320#41—42no—
321C2×Q8—21no—
322C2×Q8—22no—
323C2×Q8—21no—
324C2×Q8—41no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—41no—
328C2×Q8—42no—
329C2×Q8—44no—
330C2×Q8—42no—
331C2×Q8C2×D4×C4712yes—
332C2×Q8C2×D4×C4711yescharacteristic
333C2×Q8C2×D4×C4712yes—
334C2×Q8C24×C4711yescharacteristic
335C2×D4—22no—
336C2×D4—21no—
337C2×D4—24no—
338C2×D4—24no—
339C2×D4—22no—
340C2×D4—44no—
341C2×D4—42no—
342C2×D4—42no—
343C2×D4—41no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4C2×D4×C4714yes—
347C22×C4—21no—
348C22×C4—28no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—48no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4C2×D4×C4711yescharacteristic
355C22×C4C2×D4×C4712yes—
356Q16—44no—
357SD16—44no—
358SD16—48no—
359D8—48no—
360M16—24no—
361M16—22no—
362M16—42no—
363M16—41no—
364C2×C8—42no—
365C2×C8—41no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—24no—
369C22⋊C4—28no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C42—24no—
375C42—22no—
376C42—21no—
377C42C2×D4×C4714yes—
378C42C2×D4×C4712yes—
379C23—24no—
380C23—44no—
381C23—44no—
382C23—41no—
383C23—42no—
384C23—42no—
385C23#120×C4711yescharacteristic
386Q8—24no—
387Q8—22no—
388Q8—42no—
389Q8—41no—
390Q8—41no—
391Q8—42no—
392Q8—42no—
393Q8—41no—
394Q8—81no—
395D4—24no—
396D4—22no—
397D4—44no—
398D4—48no—
399D4—42no—
400D4—41no—
401D4—42no—
402D4—42no—
403D4—82no—
404D4—84no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—416no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4#120×C4711yescharacteristic
423C2×C4#120×C4712yes—
424C2×C4C22×D4×C4711yescharacteristic
425C2×C4C22×D4×C4712yes—
426C8—44no—
427C8—42no—
428C22—22no—
429C22—44no—
430C22—44no—
431C22—42no—
432C22—44no—
433C22—84no—
434C22—84no—
435C22—82no—
436C22C47×B(4,𝔽2)11yescharacteristic
437C22C47×B(4,𝔽2)11yescharacteristic
438C22C2×#120×C4711yescharacteristic
439C4—24no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—44no—
445C4—42no—
446C4—42no—
447C2—21no—
448C2—21no—
449C2—84no—
450C2—82no—
451C2C47×#220412yesdirect product factor
452C2C2×C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C47B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C47
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C47 ◁ C22×Q8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#555C2semidirect
2. C2×C47×#456C2semidirect
3. C2×C47×#454C2semidirect
4. C47×#2204C2direct (N × H)
5. C2×C47×#356C2semidirect
6. C2×C47×#355C2semidirect
12. C47×#555C22semidirect
20. C47×#456C22semidirect
22. C47×#454C22semidirect
27. C47×#356C22semidirect
28. C47×#355C22semidirect
201. C2×#2204C47direct (N × H)
221. C2×#555C2×C47semidirect
222. C2×#456C2×C47semidirect
223. C2×#454C2×C47semidirect
224. #2204C2×C47direct (N × H)
225. C2×#356C2×C47semidirect
226. C2×#355C2×C47semidirect
231. C2×C47#2204direct (N × H)
238. #555C22×C47semidirect
246. #456C22×C47semidirect
248. #454C22×C47semidirect
253. #356C22×C47semidirect
254. #355C22×C47semidirect
255. C47C2×#2204direct (N × H)
451. C2C47×#2204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5552
C2×C47×#4562
C2×C47×#4542
C47×#22042
C2×C47×#3562
C2×C47×#3552
C2×#220447