Finite Group Databasebeta

← #26105370

Subgroups — #26105370

Order 12032.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#20244916C211yesmaximal, characteristic, complemented
2#20244796C211yesmaximal, characteristic, complemented
3#20244791C211yesmaximal, characteristic, complemented
4#20241214C211yesmaximal, characteristic, complemented
5#20241209C211yesmaximal, characteristic, complemented
6#20241209C211yesmaximal, characteristic, complemented
7C47×#2733C211yesmaximal, characteristic
8C2×#13093957—21no—
9C2×#13093948—21no—
10C2×#13093945—21no—
11C2×#13093945—21no—
12#15688993C2211yescharacteristic
13#15688885—21no—
14#15688885—21no—
15#15688878C2211yescharacteristic
16#15688878C2211yescharacteristic
17#15688878C2211yescharacteristic
18C2×#124×C47—21no—
19C47×#394—21no—
20C47×#392—21no—
21C47×#392—21no—
22C47×#391C2211yescharacteristic
23C47×#390C2211yescharacteristic
24C47×#390C2211yescharacteristic
25C47×#388—21no—
26C47×#388—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33#13093957—42no—
34#13093948—42no—
35#13093945—42no—
36#13093945—42no—
37C22×Q8×C47D411yescharacteristic
38C22×D4×C47—21no—
39C22×D4×C47—21no—
40C22×D4×C47D411yescharacteristic
41C22×D4×C47D411yescharacteristic
42#124×C47—42no—
43#124×C47—42no—
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C4⋊C4×C47D411yescharacteristic
47C2×C22⋊C4×C47—21no—
48C2×C22⋊C4×C47—21no—
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47—21no—
51C2×C22⋊C4×C47—21no—
52C2×C22⋊C4×C47—21no—
53C2×C22⋊C4×C47—21no—
54C2×C22⋊C4×C47—21no—
55C2×C42×C47—21no—
56C2×C42×C47C2311yescharacteristic
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60C24×C47—21no—
61C24×C47—21no—
62C2×Q8×C47—21no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47D812yes—
66C2×D4×C47—21no—
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47—41no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C2×D4×C47—41no—
74C2×D4×C47—42no—
75C2×D4×C47—81no—
76C2×D4×C47—81no—
77C2×D4×C47—81no—
78C2×D4×C47—81no—
79C2×D4×C47—81no—
80C22×C4×C47—21no—
81C22×C4×C47—21no—
82C22×C4×C47—21no—
83C22×C4×C47—21no—
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47C2×D411yescharacteristic
87C22×Dic47—41no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C22⋊C4×C47—42no—
92C22⋊C4×C47—42no—
93C22⋊C4×C47—41no—
94C22⋊C4×C47—41no—
95C22⋊C4×C47—41no—
96C22⋊C4×C47—41no—
97C22⋊C4×C47—41no—
98C22⋊C4×C47—41no—
99C22⋊C4×C47—41no—
100C22⋊C4×C47—41no—
101C22⋊C4×C47—81no—
102C22⋊C4×C47—81no—
103C42×C47—41no—
104C42×C47—42no—
105C4⋊Dic47—41no—
106C4⋊Dic47—41no—
107C4⋊Dic47—41no—
108C4⋊Dic47—41no—
109C4⋊Dic47—41no—
110C4⋊Dic47—41no—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—41no—
113C2×C47⋊C8—41no—
114C2×C47⋊C8—41no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8—41no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47—41no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47—41no—
126C23×C47—41no—
127C23×C47—41no—
128C23×C47—41no—
129C23×C47—41no—
130C23×C47—41no—
131C23×C47—41no—
132C23×C47—41no—
133C23×C47—41no—
134C23×C47#12011yescharacteristic
135Q8×C47—42no—
136Q8×C47—81no—
137D4×C47—42no—
138D4×C47—42no—
139D4×C47—81no—
140D4×C47—81no—
141D4×C47—84no—
142D4×C47—84no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—22no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—41no—
159C2×C4×C47—41no—
160C2×C4×C47—41no—
161C2×C4×C47C2×D811yescharacteristic
162C2×C4×C47#13511yescharacteristic
163C2×C4×C47#13511yescharacteristic
164C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C47#13711yescharacteristic
167C2×Dic47—81no—
168C2×Dic47—81no—
169C2×Dic47—81no—
170C47⋊C8—42no—
171C47⋊C8—81no—
172C47⋊C8—81no—
173#7796—471nomaximal, Sylow
174C22×C47—81no—
175C22×C47—81no—
176C22×C47—81no—
177C22×C47—81no—
178C22×C47—81no—
179C22×C47—81no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47—81no—
183C22×C47—81no—
184C22×C47—81no—
185C22×C47—81no—
186C22×C47—81no—
187C22×C47—81no—
188C22×C47#44711yescharacteristic
189C22×C47#44911yescharacteristic
190C22×C47#45211yescharacteristic
191C22×C47#45311yescharacteristic
192C22×C47#45511yescharacteristic
193C22×C47#45511yescharacteristic
194C22×C47#45811yescharacteristic
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—42no—
202C4×C47—81no—
203C4×C47—81no—
204C4×C47—81no—
205Dic47—161no—
206#2733D4711yescharacteristic
207#2093—471no—
208#2072—471no—
209#2071—471no—
210#1272—471no—
211#1270—471no—
212#1270—471no—
213C2×C47—161no—
214C2×C47—161no—
215C2×C47#160711yescharacteristic
216C2×C47#161211yescharacteristic
217C2×C47#161811yescharacteristic
218C2×C47#162111yescharacteristic
219C2×C47#164111yescharacteristic
220C2×C47#164611yescharacteristic
221C2×C47#165911yescharacteristic
222C2×#124—21no—
223C2×#107—941no—
224C2×#103—941no—
225C2×#102—941no—
226C2×#102—941no—
227#394—21no—
228#392—21no—
229#392—21no—
230#391C2×D4711yescharacteristic
231#390C2×D4711yescharacteristic
232#390C2×D4711yescharacteristic
233#388—21no—
234#388—21no—
235#384—471no—
236#340—941no—
237#340—941no—
238#336—471no—
239#336—471no—
240#336—471no—
241C47#779611yescharacteristic, complemented, Sylow
242C22×Q8C22⋊D4711yescharacteristic
243C22×D4—21no—
244C22×D4—21no—
245C22×D4C22⋊D4711yescharacteristic
246C22×D4C22⋊D4711yescharacteristic
247C22×C8—941no—
248C22×C8—941no—
249C22×C8—941no—
250#124—42no—
251#124—42no—
252C2×C4⋊C4—941no—
253C2×C4⋊C4—941no—
254C2×C4⋊C4—941no—
255C2×C4⋊C4C22⋊D4711yescharacteristic
256C2×C4⋊C4C22⋊D4711yescharacteristic
257C2×C4⋊C4C22⋊D4711yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42—21no—
267C2×C42C22×D4711yescharacteristic
268#107—1882no—
269#103—1882no—
270#102—1882no—
271#102—1882no—
272#95—21no—
273#95—21no—
274#95—21no—
275C24—21no—
276C24—21no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8#1062533412yes—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—81no—
291C2×D4—81no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—81no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—1881no—
300C22×C4C2×C22⋊D4711yescharacteristic
301C22×C4C2×C22⋊D4711yescharacteristic
302C22×C4C2×C22⋊D4711yescharacteristic
303C2×C8—942no—
304C2×C8—1881no—
305C2×C8—1881no—
306C2×C8—1881no—
307C2×C8—1881no—
308C2×C8—1881no—
309C2×C8—1881no—
310C2×C8—1881no—
311C2×C8—1881no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—1881no—
316C4⋊C4—1881no—
317C4⋊C4—1881no—
318C4⋊C4—1881no—
319C4⋊C4—1881no—
320C4⋊C4—1881no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C42—41no—
334C42—42no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23#1309399311yescharacteristic
350Q8—42no—
351Q8—81no—
352D4—42no—
353D4—42no—
354D4—81no—
355D4—81no—
356D4—84no—
357D4—84no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—3761no—
377C2×C4—3761no—
378C2×C4—3761no—
379C2×C4C2×#1062533411yescharacteristic
380C2×C4#1309404411yescharacteristic
381C2×C4#1309404411yescharacteristic
382C2×C4#1309404911yescharacteristic
383C2×C4#1309405011yescharacteristic
384C2×C4#1309405411yescharacteristic
385C8—3761no—
386C8—3761no—
387C8—1882no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22#1568925711yescharacteristic
403C22#1568926811yescharacteristic
404C22#1568928511yescharacteristic
405C22#1568929111yescharacteristic
406C22#1568930111yescharacteristic
407C22#1568930111yescharacteristic
408C22#1568931311yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4—7521no—
420C2—161no—
421C2—161no—
422C2#2024237411yescharacteristic
423C2#2024240211yescharacteristic
424C2#2024243611yescharacteristic
425C2#2024245311yescharacteristic
426C2#2024258111yescharacteristic
427C2#2024261611yescharacteristic
428C2#2024269411yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#2733C2
socleC23×C47#120
hypercenter#2733D47
hypocenterC47#7796
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #20244916C2semidirect
2. #20244796C2semidirect
3. #20244791C2semidirect
4. #20241214C2semidirect
5. #20241209C2semidirect
6. #20241209C2semidirect
241. C47#7796semidirect

Maximal subgroups

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

subgroupindex
#202449162
#202447962
#202447912
#202412142
#202412092
C47×#27332
#779647