Finite Group Databasebeta

← #26113601

Subgroups — #26113601

Order 12032.

548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#20252417C211yesmaximal, characteristic
2#20248564C211yesmaximal, characteristic
3#20241959C212yesmaximal, complemented
4#20241266C212yesmaximal, complemented
5C47×#1799C211yesmaximal, characteristic
6C2×#13094003C2211yescharacteristic
7#15689195—24no—
8#15689180—21no—
9#15689087—21no—
10C2×C22⋊(C47⋊C8)C2212yes—
11#15689062C411yescharacteristic, complemented
12#15689059C411yescharacteristic, complemented
13#15689043C411yescharacteristic, complemented
14#15689035C411yescharacteristic, complemented
15#15689007—21no—
16#15689003—21no—
17#15688996—21no—
18#15688981—21no—
19C2×C47⋊#95C2211yescharacteristic
20#15688859—24no—
21C2×C4×D4×C47C2211yescharacteristic
22C2×#99×C47—21no—
23C47×#380C2212yes—
24C47×#342—21no—
25C22×Dic94C2×C411yescharacteristic
26C23×Dic47—21no—
27C2×#10625329—22no—
28C22×C47⋊C8—22no—
29#13094003—22no—
30#13094003—22no—
31C2×C4⋊Dic47C2×C411yescharacteristic
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37C2×C22⋊Dic47—21no—
38C4⋊(C47⋊C8)—22no—
39C22⋊(C47⋊C8)—22no—
40C22⋊(C47⋊C8)—22no—
41C22⋊(C47⋊C8)D414yes—
42#13093935—22no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95C2×C411yescharacteristic
49C47⋊#95C2×C411yescharacteristic
50C22×D4×C47D411yescharacteristic
51C23×C4×C47D411yescharacteristic
52C23×C4×C47C2311yescharacteristic
53C4×D4×C47—22no—
54C4×D4×C47—22no—
55C2×C4⋊C4×C47—22no—
56C2×C4⋊C4×C47C2×C411yescharacteristic
57C2×C22⋊C4×C47—22no—
58C2×C22⋊C4×C47C2×C411yescharacteristic
59C2×C22⋊C4×C47D411yescharacteristic
60C2×C42×C47D411yescharacteristic
61#99×C47—42no—
62#95×C47—22no—
63C24×C47C22⋊C411yescharacteristic
64C24×C47C2×D411yescharacteristic
65C2×D4×C47—22no—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—22no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—42no—
72C22×C4×C47—81no—
73C22×C4×C47—81no—
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47C22×C411yescharacteristic
78C22×C4×C47C2×D412yes—
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4112yes—
81C22×Dic47—21no—
82C22×Dic47—21no—
83C22×Dic47—21no—
84C22×Dic47—21no—
85C22×Dic47—42no—
86C22×Dic47—41no—
87C22×Dic47—41no—
88C22×Dic47—81no—
89C2×Dic94—22no—
90C2×Dic94—81no—
91C4⋊C4×C47—22no—
92C4⋊C4×C47—82no—
93C22⋊C4×C47—22no—
94C22⋊C4×C47—22no—
95C22⋊C4×C47—42no—
96C22⋊C4×C47—42no—
97C42×C47—21no—
98C42×C47—21no—
99C22⋊Dic47—42no—
100C22⋊Dic47—42no—
101C22⋊Dic47—81no—
102C4⋊Dic47—22no—
103Dic47⋊C4—42no—
104Dic47⋊C4—41no—
105Dic47⋊C4—41no—
106Dic47⋊C4—81no—
107#10625329—82no—
108C2×C47⋊C8—24no—
109C2×C47⋊C8—82no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—41no—
114C23×C47—41no—
115C23×C47—41no—
116C23×C47—41no—
117C23×C47C2×C22⋊C411yescharacteristic
118C23×C47#12112yes—
119C23×C47AGL(1,ℤ/8)11yescharacteristic
120C23×C47#13712yes—
121C23×C47#13711yescharacteristic
122D4×C47—42no—
123D4×C47—42no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—42no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—81no—
137C2×C4×C47—82no—
138C2×C4×C47—82no—
139C2×C4×C47—82no—
140C2×C4×C47C4×D412yes—
141C2×C4×C47#12011yescharacteristic
142C2×C4×C47#12311yescharacteristic
143C2×Dic47—22no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—41no—
148C2×Dic47—41no—
149C2×Dic47—41no—
150C2×Dic47—41no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—41no—
155C2×Dic47—82no—
156C2×Dic47—82no—
157Dic94—82no—
158C47⋊C8—44no—
159#9385—471nomaximal, Sylow
160C22×C47—21no—
161C22×C47—22no—
162C22×C47—21no—
163C22×C47—22no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—42no—
167C22×C47—42no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—81no—
172C22×C47#38611yescharacteristic
173C22×C47#41711yescharacteristic
174C22×C47#41911yescharacteristic
175C22×C47#46812yes—
176C22×C47#47012yes—
177C4×C47—21no—
178C4×C47—22no—
179C4×C47—21no—
180C4×C47—41no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—162no—
184Dic47—42no—
185Dic47—81no—
186Dic47—81no—
187Dic47—81no—
188#2973—471no—
189#2564—471no—
190#1799D4711yescharacteristic
191#1520—472no—
192#1294—472no—
193C2×C47—21no—
194C2×C47—22no—
195C2×C47—21no—
196C2×C47—22no—
197C2×C47—81no—
198C2×C47#188411yescharacteristic
199C2×C47#189411yescharacteristic
200C2×C47#191311yescharacteristic
201C2×C22⋊Q8—471no—
202C2×C4×D4C2×D4711yescharacteristic
203#435—944no—
204#432—941no—
205C2×#99—21no—
206#407—941no—
207C2×C22⋊C8—472no—
208#400—471no—
209#399—471no—
210#395—471no—
211#393—471no—
212#387—941no—
213#386—941no—
214#385—941no—
215#380—941no—
216#380C2×D4712yes—
217C2×#95—471no—
218#342—21no—
219#328—944no—
220C47#938511yescharacteristic, complemented, Sylow
221C22×Q8—471no—
222C22×D4C22⋊D4711yescharacteristic
223C23×C4—941no—
224C23×C4D18811yescharacteristic
225C23×C4C22×D4711yescharacteristic
226C2×M16—942no—
227C22×C8—942no—
228C22⋊Q8—942no—
229C22⋊Q8—942no—
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4—941no—
235C2×C4⋊C4—941no—
236C2×C4⋊C4—941no—
237C2×C4⋊C4C4×D4711yescharacteristic
238C2×C22⋊C4—22no—
239C2×C22⋊C4—941no—
240C2×C22⋊C4—941no—
241C2×C22⋊C4—941no—
242C2×C22⋊C4C4×D4711yescharacteristic
243C2×C22⋊C4C22⋊D4711yescharacteristic
244C2×C42D18811yescharacteristic
245C4⋊C8—942no—
246#99—42no—
247C22⋊C8—474no—
248C22⋊C8—942no—
249C22⋊C8—942no—
250#97—942no—
251#95—22no—
252#95—471no—
253#95—471no—
254#95—941no—
255#95—941no—
256#95—941no—
257#95—941no—
258#95—941no—
259C24(C2×D47)⋊C411yescharacteristic
260C24C2×C22⋊D4711yescharacteristic
261C2×Q8—942no—
262C2×Q8—3761no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—22no—
266C2×D4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4—3761no—
277C22×C4—1882no—
278C22×C4—1881no—
279C22×C4—1881no—
280C22×C4(C2×D47)⋊C411yescharacteristic
281C22×C4(C2×D47)⋊C411yescharacteristic
282C22×C4(C2×D47)⋊C411yescharacteristic
283C22×C4C2×C4×D4711yescharacteristic
284C22×C4C2×D18811yescharacteristic
285C22×C4D4×D4712yes—
286C22×C4#1062535212yes—
287M16—3762no—
288C2×C8—944no—
289C2×C8—3762no—
290C4⋊C4—22no—
291C4⋊C4—82no—
292C4⋊C4—942no—
293C4⋊C4—3761no—
294C4⋊C4—1882no—
295C4⋊C4—1881no—
296C4⋊C4—1881no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—3761no—
302C22⋊C4—1882no—
303C22⋊C4—1882no—
304C42—21no—
305C42—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23C2×(C2×D47)⋊C411yescharacteristic
314C23#1309399612yes—
315C23#1309405011yescharacteristic
316C23#1309405412yes—
317C23#1309405511yescharacteristic
318Q8—3762no—
319D4—42no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—942no—
338C2×C4—3762no—
339C2×C4—3762no—
340C2×C4—1881no—
341C2×C4—1881no—
342C2×C4—1881no—
343C2×C4—1881no—
344C2×C4—1881no—
345C2×C4—1881no—
346C2×C4—1881no—
347C2×C4—1881no—
348C2×C4—1881no—
349C2×C4—1881no—
350C2×C4—1881no—
351C2×C4(C22⋊D47)⋊C412yes—
352C2×C4#1309399411yescharacteristic
353C2×C4#1309400811yescharacteristic
354C8—1884no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22#1568900011yescharacteristic
368C22#1568912211yescharacteristic
369C22#1568913111yescharacteristic
370C22#1568936712yes—
371C22#1568937912yes—
372C4—21no—
373C4—21no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—162no—
379C4—3761no—
380C4—3761no—
381C4—3761no—
382C4—1882no—
383C2—22no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—81no—
388C2#2024376911yescharacteristic
389C2#2024381911yescharacteristic
390C2#2024392811yescharacteristic
subgroupG/H
centerC22#15689000
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1799C2
socleC22×C47#386
prime radicalC22×D4×C47D4
cosocleC23×C4×C47C23
hypercenter#1799D47
hypocenterC47#9385
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #20241959C2semidirect
4. #20241266C2semidirect
11. #15689062C4semidirect
12. #15689059C4semidirect
13. #15689043C4semidirect
14. #15689035C4semidirect
220. C47#9385semidirect

Maximal subgroups

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

subgroupindex
#202524172
#202485642
#202419592
#202412662
C47×#17992
#938547