Finite Group Databasebeta

← #26119447

Subgroups — #26119447

Order 12032.

422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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#20248607C211yesmaximal, characteristic
2#20241960C211yesmaximal, characteristic
3C2×#15688860C211yesmaximal, characteristic
4#20241266C211yesmaximal, characteristic
5#20241255C211yesmaximal, characteristic
6#20241236C211yesmaximal, characteristic
7C47×#1996C211yesmaximal, characteristic
8C2×C22⋊(C47⋊C8)C2211yescharacteristic
9C2×C22⋊(C47⋊C8)C2211yescharacteristic
10#15689065—21no—
11#15689057—21no—
12#15689007—21no—
13#15689007—21no—
14#15688995—21no—
15#15688983C2211yescharacteristic
16#15688981—21no—
17C2×C47⋊#95C2211yescharacteristic
18#15688860—21no—
19#15688860—21no—
20#15688860—21no—
21#15688860—21no—
22C2×C22⋊Q8×C47C2211yescharacteristic
23C47×#380C2211yescharacteristic
24C4×C22⋊C4×C47C2211yescharacteristic
25C47×#342—21no—
26C47×#342—21no—
27C23×Dic47—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C2×C4⋊Dic47—21no—
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×C22⋊Dic47—21no—
36C22⋊(C47⋊C8)—21no—
37C22⋊(C47⋊C8)—21no—
38C22⋊(C47⋊C8)—21no—
39C22⋊(C47⋊C8)—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95D411yescharacteristic
46C47⋊#95D411yescharacteristic
47C47⋊#95D411yescharacteristic
48C47⋊#95D411yescharacteristic
49C22×Q8×C47Q811yescharacteristic
50C23×C4×C47C2311yescharacteristic
51C22⋊Q8×C47—21no—
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47—21no—
55C2×C4⋊C4×C47—21no—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47Q811yescharacteristic
58C2×C22⋊C4×C47—21no—
59C2×C22⋊C4×C47—21no—
60C2×C22⋊C4×C47D411yescharacteristic
61C2×C22⋊C4×C47D411yescharacteristic
62C2×C42×C47—21no—
63#95×C47—21no—
64#95×C47—21no—
65C24×C47C2×D411yescharacteristic
66C2×Q8×C47—21no—
67C2×Q8×C47—21no—
68C2×Q8×C47—81no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—41no—
74C22×C4×C47—81no—
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C22×C4×C47C2×Q811yescharacteristic
78C22×C4×C47#4111yescharacteristic
79C22×C4×C47#4111yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C22×Dic47—21no—
82C22×Dic47—21no—
83C22×Dic47—21no—
84C22×Dic47—21no—
85C22×Dic47—42no—
86C22×Dic47—41no—
87C22×Dic47—41no—
88C22×Dic47—81no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—81no—
94C22⋊C4×C47—21no—
95C22⋊C4×C47—21no—
96C22⋊C4×C47—21no—
97C22⋊C4×C47—21no—
98C22⋊C4×C47—41no—
99C22⋊C4×C47—41no—
100C22⋊C4×C47—41no—
101C22⋊C4×C47—41no—
102C42×C47—81no—
103C22⋊Dic47—41no—
104C22⋊Dic47—41no—
105C4⋊Dic47—81no—
106Dic47⋊C4—42no—
107Dic47⋊C4—42no—
108Dic47⋊C4—81no—
109Dic47⋊C4—81no—
110C2×C47⋊C8—41no—
111C2×C47⋊C8—41no—
112C2×C47⋊C8—81no—
113C2×C47⋊C8—81no—
114C23×C47—41no—
115C23×C47—41no—
116C23×C47#12011yescharacteristic
117C23×C47C22⋊Q811yescharacteristic
118C23×C47#12411yescharacteristic
119C23×C47#13511yescharacteristic
120C23×C47#13511yescharacteristic
121C23×C47#13711yescharacteristic
122C23×C47#13711yescharacteristic
123Q8×C47—81no—
124Q8×C47—81no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
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—81no—
140C2×C4×C47—81no—
141C2×C4×C47—81no—
142C2×C4×C47—81no—
143C2×C4×C47—81no—
144C2×C4×C47C22⋊Q811yescharacteristic
145C2×C4×C47C22⋊Q811yescharacteristic
146C2×C4×C47#12411yescharacteristic
147C2×C4×C47#12411yescharacteristic
148C2×Dic47—22no—
149C2×Dic47—41no—
150C2×Dic47—41no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—41no—
155C2×Dic47—41no—
156C2×Dic47—41no—
157C2×Dic47—41no—
158C2×Dic47—41no—
159C2×Dic47—41no—
160C2×Dic47—82no—
161C2×Dic47—82no—
162C47⋊C8—81no—
163C47⋊C8—81no—
164#10377—471nomaximal, Sylow
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—21no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47#39311yescharacteristic
176C22×C47#45211yescharacteristic
177C22×C47#45211yescharacteristic
178C22×C47#47911yescharacteristic
179C22×C47#47911yescharacteristic
180C22×C47#48811yescharacteristic
181C22×C47#49111yescharacteristic
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—81no—
187C4×C47—81no—
188C4×C47—81no—
189C4×C47—81no—
190C4×C47—161no—
191Dic47—42no—
192Dic47—81no—
193Dic47—81no—
194Dic47—81no—
195#2569—471no—
196#1996D4711yescharacteristic
197#1520—471no—
198C2×#328—471no—
199#1294—471no—
200#1289—471no—
201#1282—471no—
202C2×C47—21no—
203C2×C47—21no—
204C2×C47—21no—
205C2×C47—21no—
206C2×C47—21no—
207C2×C47—21no—
208C2×C47#202611yescharacteristic
209C2×C47#203111yescharacteristic
210C2×C47#203211yescharacteristic
211C2×C22⋊Q8C2×D4711yescharacteristic
212C2×C22⋊C8—471no—
213C2×C22⋊C8—471no—
214#400—941no—
215#398—941no—
216#387—941no—
217#387—941no—
218#385—941no—
219#380—471no—
220#380—941no—
221#380C2×D4711yescharacteristic
222C4×C22⋊C4C2×D4711yescharacteristic
223C2×#95—471no—
224#342—21no—
225#342—21no—
226#328—941no—
227#328—941no—
228#328—941no—
229#328—941no—
230C47#1037711yescharacteristic, complemented, Sylow
231C22×Q8Dic9411yescharacteristic
232C23×C4—941no—
233C23×C4C22×D4711yescharacteristic
234C22×C8—941no—
235C22×C8—941no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—941no—
243C2×C4⋊C4—941no—
244C2×C4⋊C4—941no—
245C2×C4⋊C4—941no—
246C2×C4⋊C4—941no—
247C2×C4⋊C4Dic9411yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—941no—
251C2×C22⋊C4C22⋊D4711yescharacteristic
252C2×C22⋊C4C22⋊D4711yescharacteristic
253C2×C42—21no—
254C22⋊C8—941no—
255C22⋊C8—941no—
256C22⋊C8—941no—
257C22⋊C8—941no—
258#95—21no—
259#95—21no—
260#95—471no—
261#95—471no—
262#95—471no—
263#95—471no—
264#95—941no—
265#95—941no—
266#95—941no—
267#95—941no—
268#95—941no—
269C24C2×C22⋊D4711yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—81no—
279C22×C4—941no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—3761no—
284C22×C4—1882no—
285C22×C4—1881no—
286C22×C4—1881no—
287C22×C4C2×Dic9411yescharacteristic
288C22×C4#1062535011yescharacteristic
289C22×C4D4×D4711yescharacteristic
290C22×C4D4×D4711yescharacteristic
291C22×C4#1062535211yescharacteristic
292C22×C4#1062535211yescharacteristic
293C2×C8—3761no—
294C2×C8—3761no—
295C2×C8—1881no—
296C2×C8—1881no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—81no—
302C4⋊C4—3761no—
303C4⋊C4—3761no—
304C4⋊C4—3761no—
305C4⋊C4—1882no—
306C4⋊C4—1882no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—1881no—
316C22⋊C4—1881no—
317C42—81no—
318C23—41no—
319C23—41no—
320C23#1309399211yescharacteristic
321C23#1309400311yescharacteristic
322C23#1309401111yescharacteristic
323C23#1309404411yescharacteristic
324C23#1309404411yescharacteristic
325C23#1309405511yescharacteristic
326C23#1309405511yescharacteristic
327Q8—81no—
328Q8—81no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—942no—
349C2×C4—3762no—
350C2×C4—3762no—
351C2×C4—1881no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4—1881no—
355C2×C4—1881no—
356C2×C4—1881no—
357C2×C4—1881no—
358C2×C4—1881no—
359C2×C4—1881no—
360C2×C4—1881no—
361C2×C4—1881no—
362C2×C4#1309400111yescharacteristic
363C2×C4#1309400111yescharacteristic
364C2×C4#1309401011yescharacteristic
365C2×C4#1309401011yescharacteristic
366C8—3761no—
367C8—3761no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1568903511yescharacteristic
379C22#1568928311yescharacteristic
380C22#1568928311yescharacteristic
381C22#1568943011yescharacteristic
382C22#1568943011yescharacteristic
383C22#1568947711yescharacteristic
384C22#1568949111yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—161no—
394C4—3761no—
395C4—3761no—
396C4—3761no—
397C4—1882no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#2024453911yescharacteristic
405C2#2024456211yescharacteristic
406C2#2024456511yescharacteristic
subgroupG/H
centerC22#15689035
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#1996C2
socleC22×C47#393
prime radicalC24×C47C2×D4
hypercenter#1996D47
hypocenterC47#10377
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
230. C47#10377semidirect

Maximal subgroups

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

subgroupindex
#202486072
#202419602
C2×#156888602
#202412662
#202412552
#202412362
C47×#19962
#1037747