Finite Group Databasebeta

← #26119479

Subgroups — #26119479

Order 12032.

446 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 77 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#20244223C211yesmaximal, characteristic
2#20241916C211yesmaximal, characteristic
3#20241903C211yesmaximal, characteristic
4#20241294C211yesmaximal, characteristic, complemented
5#20241274C211yesmaximal, characteristic, complemented
6#20241240C211yesmaximal, characteristic, complemented
7C47×#2665C211yesmaximal, characteristic, complemented
8C2×#13093998C2211yescharacteristic
9C2×#13093938—21no—
10C2×#13093938—21no—
11#15689087C2211yescharacteristic
12#15689087C2211yescharacteristic
13C4×C22⋊Dic47C2211yescharacteristic
14#15688856—21no—
15#15688856—21no—
16#15688856—21no—
17#15688856—21no—
18C47×#400—21no—
19C47×#396—21no—
20C47×#395—21no—
21C47×#393—21no—
22C47×#391—21no—
23C47×#387—21no—
24C47×#381C2211yescharacteristic
25C47×#380C2211yescharacteristic
26C4×C22⋊C4×C47C2211yescharacteristic
27C22×D188Q811yescharacteristic, complemented
28C22×C22⋊D47—21no—
29C2×#10625329—21no—
30C2×#10625329—21no—
31#13093998—21no—
32#13093998—21no—
33#13093998—21no—
34#13093998—21no—
35C2×C4⋊Dic47Q811yescharacteristic, complemented
36C2×C22⋊Dic47—21no—
37C2×(C2×D47)⋊C4—21no—
38C2×C4×Dic47—21no—
39#13093938—42no—
40#13093938—42no—
41C22⋊(C47⋊C8)—21no—
42C22⋊(C47⋊C8)—21no—
43C22⋊(C47⋊C8)—21no—
44C22⋊(C47⋊C8)—21no—
45C47⋊#95—21no—
46C22×Q8×C47—21no—
47C23×C4×C47C2311yescharacteristic
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C22⋊C4×C47—21no—
53C2×C22⋊C4×C47—21no—
54C2×C22⋊C4×C47D411yescharacteristic
55C2×C22⋊C4×C47D411yescharacteristic
56C2×C42×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61#95×C47—21no—
62#95×C47—21no—
63#95×C47D411yescharacteristic
64#95×C47D411yescharacteristic
65#95×C47D411yescharacteristic
66#95×C47D411yescharacteristic
67C24×C47C2×D411yescharacteristic
68C23×D47—21no—
69C2×Q8×C47—42no—
70C2×Q8×C47—81no—
71C2×Q8×C47—81no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—81no—
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×Q811yescharacteristic
82C22×C4×C47#4111yescharacteristic
83C22×C4×C47#4111yescharacteristic
84C22×C4×C47#4111yescharacteristic
85C2×C22⋊D47—41no—
86C2×C22⋊D47—41no—
87C2×C22⋊D47—41no—
88C2×C22⋊D47—41no—
89C2×C22⋊D47—41no—
90C2×C22⋊D47—41no—
91C22×Dic47—21no—
92C22×Dic47—41no—
93C2×D188—21no—
94C2×D188—21no—
95C2×D188—81no—
96C4⋊C4×C47—42no—
97C4⋊C4×C47—81no—
98C4⋊C4×C47—81no—
99C4⋊C4×C47—81no—
100C22⋊C4×C47—42no—
101C22⋊C4×C47—41no—
102C22⋊C4×C47—41no—
103C22⋊C4×C47—81no—
104C42×C47—81no—
105C22⋊Dic47—22no—
106C22⋊Dic47—41no—
107(C2×D47)⋊C4—41no—
108(C2×D47)⋊C4—41no—
109C4⋊Dic47—21no—
110C4⋊Dic47—21no—
111C4×Dic47—81no—
112#10625329—81no—
113#10625329—81no—
114C2×C47⋊C8—41no—
115C2×C47⋊C8—41no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—41no—
119C23×C47—41no—
120C23×C47#12011yescharacteristic
121C23×C47C22⋊Q811yescharacteristic
122C23×C47#12411yescharacteristic
123C22×D47—41no—
124C22×D47—41no—
125C22×D47—41no—
126C22×D47—81no—
127C22×D47—81no—
128Q8×C47—84no—
129C2×C4×C47—22no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47C22⋊Q811yescharacteristic
154C2×C4×C47C22⋊Q811yescharacteristic
155C2×C4×C47#12411yescharacteristic
156C2×C4×C47#12411yescharacteristic
157C22⋊D47—81no—
158C22⋊D47—81no—
159C22⋊D47—81no—
160C22⋊D47—81no—
161C2×Dic47—42no—
162C2×Dic47—41no—
163C2×Dic47—41no—
164C2×Dic47—41no—
165C2×Dic47—81no—
166C2×Dic47—81no—
167D188—81no—
168D188—81no—
169C47⋊C8—81no—
170C47⋊C8—81no—
171#10382—471nomaximal, Sylow
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—81no—
181C22×C47—81no—
182C22×C47#39311yescharacteristic
183C22×C47#45311yescharacteristic
184C22×C47#45411yescharacteristic
185C2×D47—81no—
186C2×D47—81no—
187C2×D47—81no—
188C2×D47—161no—
189C2×D47—161no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—42no—
195C4×C47—81no—
196C4×C47—81no—
197C4×C47—81no—
198C4×C47—81no—
199C4×C47—81no—
200Dic47—82no—
201Dic47—81no—
202#2665D4711yescharacteristic, complemented
203#1964—471no—
204#1510—471no—
205#1507—471no—
206#1305—471no—
207#1297—471no—
208#1284—471no—
209C2×C47—21no—
210C2×C47—21no—
211C2×C47—41no—
212C2×C47—41no—
213C2×C47#202711yescharacteristic
214C2×C47#203111yescharacteristic
215C2×C47#203211yescharacteristic
216D47—161no—
217C2×#121—471no—
218C2×#99—941no—
219C2×#99—941no—
220#407—471no—
221#407—471no—
222#400—21no—
223#396—21no—
224#395—21no—
225#393—21no—
226#391—21no—
227#387—21no—
228#381C2×D4711yescharacteristic
229#380C2×D4711yescharacteristic
230C4×C22⋊C4—471no—
231C4×C22⋊C4C2×D4711yescharacteristic
232#327—941no—
233#327—941no—
234#327—941no—
235#327—941no—
236C47#1038211yescharacteristic, complemented, Sylow
237C22×Q8—21no—
238C22×D4—471no—
239C22×D4—941no—
240C23×C4C22×D4711yescharacteristic
241C2×M16—941no—
242C2×M16—941no—
243#121—941no—
244#121—941no—
245#121—941no—
246#121—941no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—471no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—941no—
255C2×C22⋊C4—941no—
256C2×C22⋊C4C22⋊D4711yescharacteristic
257C2×C22⋊C4C22⋊D4711yescharacteristic
258C2×C42—21no—
259C2×C42—941no—
260#99—1882no—
261#99—1882no—
262C22⋊C8—941no—
263C22⋊C8—941no—
264C22⋊C8—941no—
265C22⋊C8—941no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—941no—
273#95C22⋊D4711yescharacteristic
274#95C22⋊D4711yescharacteristic
275#95C22⋊D4711yescharacteristic
276#95C22⋊D4711yescharacteristic
277C24—941no—
278C24C2×C22⋊D4711yescharacteristic
279C2×Q8—42no—
280C2×Q8—81no—
281C2×Q8—81no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—3761no—
285C2×D4—1881no—
286C2×D4—1881no—
287C2×D4—1881no—
288C2×D4—1881no—
289C2×D4—1881no—
290C2×D4—1881no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—81no—
298C22×C4—941no—
299C22×C4—1881no—
300C22×C4Q8×D4711yescharacteristic
301C22×C4#1062535411yescharacteristic
302C22×C4#1062535411yescharacteristic
303C22×C4#1062535411yescharacteristic
304C22×C4C2×C22⋊D4711yescharacteristic
305C22×C4C2×C22⋊D4711yescharacteristic
306M16—3761no—
307M16—3761no—
308C2×C8—1881no—
309C2×C8—1881no—
310C4⋊C4—42no—
311C4⋊C4—81no—
312C4⋊C4—81no—
313C4⋊C4—81no—
314C4⋊C4—941no—
315C4⋊C4—941no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—81no—
320C22⋊C4—942no—
321C22⋊C4—1881no—
322C22⋊C4—1881no—
323C22⋊C4—1881no—
324C42—81no—
325C42—3761no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—3761no—
331C23—3761no—
332C23—1881no—
333C23—1881no—
334C23—1881no—
335C23#1309399311yescharacteristic
336C23#1309400011yescharacteristic
337C23#1309401311yescharacteristic
338Q8—84no—
339D4—3761no—
340D4—3761no—
341D4—3761no—
342D4—3761no—
343D4—3761no—
344D4—3761no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—3761no—
370C2×C4—3761no—
371C2×C4—1882no—
372C2×C4—1881no—
373C2×C4—1881no—
374C2×C4—1881no—
375C2×C4#1309400011yescharacteristic
376C2×C4#1309400011yescharacteristic
377C2×C4#1309401311yescharacteristic
378C2×C4#1309401311yescharacteristic
379C8—3761no—
380C8—3761no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—3761no—
392C22—3761no—
393C22—3761no—
394C22—7521no—
395C22—7521no—
396C22#1568903411yescharacteristic
397C22#1568929111yescharacteristic
398C22#1568929611yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—3762no—
410C4—3761no—
411C2—21no—
412C2—21no—
413C2—41no—
414C2—41no—
415C2—7521no—
416C2#2024454111yescharacteristic
417C2#2024455711yescharacteristic
418C2#2024456411yescharacteristic
subgroupG/H
centerC22#15689034
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#2665C2
socleC22×C47#393
prime radicalC2×#13093998C22
hypercenter#2665D47
hypocenterC47#10382
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2665

Complements

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

NH ≅ G/Ntype
4. #20241294C2semidirect
5. #20241274C2semidirect
6. #20241240C2semidirect
7. C47×#2665C2semidirect
27. C22×D188Q8semidirect
35. C2×C4⋊Dic47Q8semidirect
202. #2665D47semidirect
236. C47#10382semidirect

Maximal subgroups

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

subgroupindex
#202442232
#202419162
#202419032
#202412942
#202412742
#202412402
C47×#26652
#1038247