Finite Group Databasebeta

← #26119430

Subgroups — #26119430

Order 12032.

466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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#20244373C211yesmaximal, characteristic
2#20241959C211yesmaximal, characteristic
3C2×#15688859C211yesmaximal, characteristic
4#20241267C211yesmaximal, characteristic
5#20241255C211yesmaximal, characteristic
6#20241236C211yesmaximal, characteristic
7C47×#2549C211yesmaximal, characteristic
8C2×#13094003C2211yescharacteristic
9C2×C22⋊(C47⋊C8)C2211yescharacteristic
10C2×C22⋊(C47⋊C8)C2211yescharacteristic
11#15688983C2211yescharacteristic
12#15688889—21no—
13#15688889—21no—
14#15688859—21no—
15#15688859—21no—
16#15688859—21no—
17#15688859—21no—
18C2×C22⋊Q8×C47—21no—
19C47×#398—21no—
20C47×#395—21no—
21C47×#391—21no—
22C47×#389—21no—
23C47×#385—21no—
24C47×#380C2211yescharacteristic
25C4×C22⋊C4×C47C2211yescharacteristic
26C2×#95×C47C2211yescharacteristic
27C22×Dic94Q811yescharacteristic, complemented
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30#13094003—21no—
31#13094003—21no—
32#13094003—21no—
33#13094003—21no—
34C2×C4⋊Dic47—21no—
35C2×C4⋊Dic47Q811yescharacteristic, complemented
36C2×Dic47⋊C4—21no—
37C2×C22⋊Dic47—21no—
38C2×C22⋊Dic47—21no—
39C22⋊(C47⋊C8)—21no—
40C22⋊(C47⋊C8)—21no—
41C22⋊(C47⋊C8)—21no—
42C22⋊(C47⋊C8)—21no—
43C47⋊#95—21no—
44C22×Q8×C47—21no—
45C23×C4×C47—21no—
46C23×C4×C47C2311yescharacteristic
47C22⋊Q8×C47—42no—
48C22⋊Q8×C47—42no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C22⋊C4×C47—21no—
56C2×C22⋊C4×C47D411yescharacteristic
57C2×C22⋊C4×C47D411yescharacteristic
58C2×C42×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
68C2×Q8×C47—42no—
69C2×Q8×C47—42no—
70C2×Q8×C47—81no—
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—42no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—81no—
81C22×C4×C47—81no—
82C22×C4×C47C2×D411yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2×Q811yescharacteristic
85C22×C4×C47#4111yescharacteristic
86C22×C4×C47#4111yescharacteristic
87C22×C4×C47#4111yescharacteristic
88C22×Dic47—21no—
89C22×Dic47—21no—
90C22×Dic47—41no—
91C2×Dic94—21no—
92C2×Dic94—21no—
93C2×Dic94—81no—
94C4⋊C4×C47—42no—
95C4⋊C4×C47—42no—
96C4⋊C4×C47—42no—
97C4⋊C4×C47—42no—
98C4⋊C4×C47—81no—
99C4⋊C4×C47—81no—
100C22⋊C4×C47—21no—
101C22⋊C4×C47—21no—
102C22⋊C4×C47—41no—
103C22⋊C4×C47—41no—
104C22⋊C4×C47SD1612yes—
105C22⋊C4×C47Q1612yes—
106C42×C47—81no—
107C22⋊Dic47—41no—
108C22⋊Dic47—41no—
109C22⋊Dic47—41no—
110C22⋊Dic47—41no—
111C4⋊Dic47—21no—
112C4⋊Dic47—21no—
113C4⋊Dic47—81no—
114Dic47⋊C4—41no—
115Dic47⋊C4—41no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C2×C47⋊C8—81no—
119C2×C47⋊C8—81no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47#12011yescharacteristic
123C23×C47C22⋊Q811yescharacteristic
124C23×C47#12411yescharacteristic
125C23×C47C2×SD1611yescharacteristic
126C23×C47C2×Q1611yescharacteristic
127C23×C47AGL(1,ℤ/8)11yescharacteristic
128C23×C47#13711yescharacteristic
129Q8×C47—84no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
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×C47—41no—
154C2×C4×C47—82no—
155C2×C4×C47—82no—
156C2×C4×C47C22⋊Q811yescharacteristic
157C2×C4×C47C22⋊Q811yescharacteristic
158C2×C4×C47#12411yescharacteristic
159C2×C4×C47#12411yescharacteristic
160C2×Dic47—41no—
161C2×Dic47—41no—
162C2×Dic47—81no—
163C2×Dic47—81no—
164C2×Dic47—81no—
165C2×Dic47—81no—
166C2×Dic47—81no—
167Dic94—81no—
168Dic94—81no—
169C47⋊C8—81no—
170C47⋊C8—81no—
171#10375—471nomaximal, Sylow
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—21no—
177C22×C47—21no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47#39311yescharacteristic
183C22×C47#45011yescharacteristic
184C22×C47#45111yescharacteristic
185C22×C47#47511yescharacteristic
186C22×C47#47711yescharacteristic
187C22×C47#48711yescharacteristic
188C22×C47#48911yescharacteristic
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—21no—
192C4×C47—21no—
193C4×C47—42no—
194C4×C47—42no—
195C4×C47—42no—
196C4×C47—81no—
197C4×C47—81no—
198C4×C47—81no—
199Dic47—81no—
200Dic47—81no—
201Dic47—161no—
202#2549D4711yescharacteristic
203#1996—471no—
204#1520—471no—
205C2×#328—471no—
206#1294—471no—
207#1289—471no—
208#1282—471no—
209C2×C47—21no—
210C2×C47—21no—
211C2×C47—21no—
212C2×C47—21no—
213C2×C47—21no—
214C2×C47—21no—
215C2×C47#202411yescharacteristic
216C2×C47#203111yescharacteristic
217C2×C47#203211yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—471no—
220C2×C22⋊C8—471no—
221C2×C22⋊C8—471no—
222#398—21no—
223#395—21no—
224#391—21no—
225#389—21no—
226#385—21no—
227#380—471no—
228#380C2×D4711yescharacteristic
229C4×C22⋊C4C2×D4711yescharacteristic
230C2×#95C2×D4711yescharacteristic
231#342—941no—
232#342—941no—
233#328—941no—
234#328—941no—
235#328—941no—
236#328—941no—
237C47#1037511yescharacteristic, complemented, Sylow
238C22×Q8—21no—
239C22×Q8—471no—
240C23×C4—21no—
241C23×C4C22×D4711yescharacteristic
242C22×C8—941no—
243C22×C8—941no—
244C22⋊Q8—42no—
245C22⋊Q8—42no—
246C22⋊Q8—941no—
247C22⋊Q8—941no—
248C22⋊Q8—941no—
249C22⋊Q8—941no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—471no—
257C2×C4⋊C4—941no—
258C2×C4⋊C4—941no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—941no—
261C2×C22⋊C4—941no—
262C2×C22⋊C4C22⋊D4711yescharacteristic
263C2×C22⋊C4C22⋊D4711yescharacteristic
264C2×C42—21no—
265C22⋊C8—941no—
266C22⋊C8—941no—
267C22⋊C8—941no—
268C22⋊C8—941no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—941no—
274#95C22⋊D4711yescharacteristic
275#95C22⋊D4711yescharacteristic
276#95C22⋊D4711yescharacteristic
277#95C22⋊D4711yescharacteristic
278C24C2×C22⋊D4711yescharacteristic
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—81no—
282C2×Q8—941no—
283C2×Q8—941no—
284C2×Q8—3761no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—941no—
297C22×C4—941no—
298C22×C4—1881no—
299C22×C4Q8×D4711yescharacteristic
300C22×C4#1062535411yescharacteristic
301C22×C4#1062535411yescharacteristic
302C22×C4#1062535411yescharacteristic
303C22×C4C2×C22⋊D4711yescharacteristic
304C22×C4C2×C22⋊D4711yescharacteristic
305C2×C8—3761no—
306C2×C8—3761no—
307C2×C8—1881no—
308C2×C8—1881no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—81no—
314C4⋊C4—81no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C4⋊C4—3761no—
318C4⋊C4—1881no—
319C4⋊C4—1881no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—1881no—
325C22⋊C4—1881no—
326C22⋊C4—1881no—
327C22⋊C4—1881no—
328C22⋊C4#1062533512yes—
329C22⋊C4#1062533712yes—
330C42—81no—
331C23—41no—
332C23—41no—
333C23#1309399311yescharacteristic
334C23#1309400011yescharacteristic
335C23#1309401311yescharacteristic
336C23C2×#1062533511yescharacteristic
337C23C2×#1062533711yescharacteristic
338C23#1309405011yescharacteristic
339C23#1309405511yescharacteristic
340Q8—84no—
341Q8—3761no—
342Q8—3761no—
343C2×C4—22no—
344C2×C4—22no—
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—82no—
368C2×C4—82no—
369C2×C4—3761no—
370C2×C4—3761no—
371C2×C4—3761no—
372C2×C4—3761no—
373C2×C4—3761no—
374C2×C4—1881no—
375C2×C4—1881no—
376C2×C4#1309400011yescharacteristic
377C2×C4#1309400011yescharacteristic
378C2×C4#1309401311yescharacteristic
379C2×C4#1309401311yescharacteristic
380C8—3761no—
381C8—3761no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#1568903411yescharacteristic
393C22#1568927411yescharacteristic
394C22#1568927911yescharacteristic
395C22#1568940511yescharacteristic
396C22#1568941511yescharacteristic
397C22#1568947511yescharacteristic
398C22#1568948511yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—42no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—3761no—
410C4—3761no—
411C4—7521no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—21no—
418C2#2024452611yescharacteristic
419C2#2024455711yescharacteristic
420C2#2024456411yescharacteristic
subgroupG/H
centerC22#15689034
commutator, cosocleC23×C4×C47C23
FrattiniC23×C4C22×D47
FittingC47×#2549C2
socleC22×C47#393
prime radicalC24×C47C2×D4
hypercenter#2549D47
hypocenterC47#10375
LCSG ▷ C23×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2549

Complements

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

NH ≅ G/Ntype
27. C22×Dic94Q8semidirect
35. C2×C4⋊Dic47Q8semidirect
237. C47#10375semidirect

Maximal subgroups

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

subgroupindex
#202443732
#202419592
C2×#156888592
#202412672
#202412552
#202412362
C47×#25492
#1037547