Finite Group Databasebeta

← #26111481

Subgroups — #26111481

Order 12032.

476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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#20253396C211yesmaximal, characteristic
2#20252328C211yesmaximal, characteristic, complemented
3#20242046C211yesmaximal, characteristic, complemented
4#20241813C211yesmaximal, characteristic
5#20241285C211yesmaximal, characteristic, complemented
6#20241233C211yesmaximal, characteristic, complemented
7C47×#1955C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689453C412yes—
10#15689413—21no—
11#15689328—21no—
12#15689274C412yes—
13#15689251—22no—
14#15689251—22no—
15C4×#10625335—22no—
16#15689176C2211yescharacteristic
17#15689176C2211yescharacteristic
18#15689149—21no—
19#15689147C2211yescharacteristic
20#15689078—21no—
21#15688871—21no—
22#15688868—21no—
23D4⋊(C47⋊C8)—22no—
24C2×C4×D4×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C22⋊C8×C47—21no—
27C2×C22⋊C8×C47—21no—
28C2×#97×C47C2211yescharacteristic
29C2×#10625335—22no—
30C2×#10625329—21no—
31#13094024D411yescharacteristic
32#13094024D411yescharacteristic
33#13094016—21no—
34#13094003—21no—
35#13094003C2×C412yes—
36C4×Dic94—21no—
37C4×Dic94D412yes—
38#13093983—21no—
39#13093955—22no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)D412yes—
44Dic47⋊C8—24no—
45#13093947—22no—
46#13093945—22no—
47C22⋊(C47⋊C8)—21no—
48C22⋊(C47⋊C8)C2×C412yes—
49#13093934—22no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C8×Dic47—22no—
53C22×D4×C47C2×C411yescharacteristic
54C23×C4×C47—21no—
55C22×C8×C47—21no—
56C22×C8×C47D411yescharacteristic
57C22×C8×C47D411yescharacteristic
58C4×D4×C47—21no—
59C4×D4×C47—21no—
60C4×D4×C47—21no—
61C4×D4×C47—21no—
62C2×C4⋊C4×C47C2×C411yescharacteristic
63C2×C22⋊C4×C47—21no—
64C2×C42×C47C2311yescharacteristic
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67C22⋊C8×C47—42no—
68C22⋊C8×C47—42no—
69#97×C47—21no—
70#97×C47—21no—
71C24×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47—21no—
74C2×D4×C47—42no—
75C22×C4×C47—21no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47C22×C411yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47#4111yescharacteristic
85C2×Dic94—21no—
86C2×Dic94C22⋊C412yes—
87C2×C8×C47—21no—
88C2×C8×C47—21no—
89C2×C8×C47—21no—
90C2×C8×C47—21no—
91C2×C8×C47—21no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C2×C8×C47SD1612yescomplemented
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C22⋊C4×C47—41no—
99C22⋊C4×C47—41no—
100C42×C47C2×D411yescharacteristic
101C42×C47C2×D411yescharacteristic
102C42×C47C2×D411yescharacteristic
103C42×C47#4111yescharacteristic
104C22⋊Dic47—22no—
105#10625335—44no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47—21no—
109C4⋊Dic47C22⋊C412yes—
110Dic47⋊C4—22no—
111Dic47⋊C4—22no—
112C4×Dic47—22no—
113#10625329—41no—
114#10625329—41no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—22no—
117C2×C47⋊C8—41no—
118C23×C47—22no—
119C23×C47—41no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47—41no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47C4×D411yescharacteristic
126D4×C47—22no—
127D4×C47—22no—
128D4×C47—41no—
129D4×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—81no—
136C2×C4×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47—81no—
139C2×C4×C47C2×C22⋊C411yescharacteristic
140C2×C4×C47C4×D411yescharacteristic
141C2×C4×C47#12011yescharacteristic
142C2×C4×C47#12111yescharacteristic
143C2×C4×C47#12111yescharacteristic
144C2×C4×C47#12311yescharacteristic
145C2×C4×C47C2×SD1611yescharacteristic
146C2×C4×C47#13511yescharacteristic
147C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C47#13711yescharacteristic
149C2×Dic47—22no—
150C2×Dic47—22no—
151Dic94—42no—
152Dic94—81no—
153C8×C47—22no—
154C8×C47—41no—
155C8×C47—81no—
156C47⋊C8—42no—
157C47⋊C8—42no—
158C47⋊C8—81no—
159#9050—471nomaximal, Sylow
160C22×C47—21no—
161C22×C47—21no—
162C22×C47—42no—
163C22×C47—42no—
164C22×C47—42no—
165C22×C47—81no—
166C22×C47—81no—
167C22×C47—81no—
168C22×C47—81no—
169C22×C47#38611yescharacteristic
170C22×C47C4×SD1611yescharacteristic
171C22×C47#44011yescharacteristic
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—21no—
175C4×C47—21no—
176C4×C47—81no—
177C4×C47#44811yescharacteristic
178C4×C47#44911yescharacteristic
179C4×C47#46011yescharacteristic
180C4×C47#46411yescharacteristic
181Dic47—42no—
182Dic47—42no—
183#3101—471no—
184#2961—471no—
185#1955D4711yescharacteristic
186#1542—471no—
187#1486—471no—
188#1301—471no—
189#1281—471no—
190C2×C47—21no—
191C2×C47—21no—
192C2×C47—82no—
193C2×C47#188011yescharacteristic
194C2×C47#188111yescharacteristic
195C2×C47#189111yescharacteristic
196#533—471no—
197C2×C4×D4C2×D4711yescharacteristic
198#483—472no—
199#476—941no—
200#461—941no—
201#450—472no—
202#446—942no—
203#446—942no—
204C4×SD16—942no—
205#431—471no—
206#431—471no—
207#424—941no—
208#423—471no—
209C2×C4⋊C8C2×D4711yescharacteristic
210C2×C22⋊C8—21no—
211C2×C22⋊C8—21no—
212#405—941no—
213C2×#97C2×D4711yescharacteristic
214#333—941no—
215#332—941no—
216D4⋊C8—942no—
217C47#905011yescharacteristic, complemented, Sylow
218C22×D4C4×D4711yescharacteristic
219C23×C4—21no—
220C2×SD16—942no—
221C2×M16—941no—
222C22×C8—21no—
223C22×C8C22⋊D4711yescharacteristic
224C22×C8C22⋊D4711yescharacteristic
225C4⋊Q8—471no—
226C4⋊Q8—471no—
227#125—941no—
228C22⋊Q8—472no—
229C22⋊Q8—941no—
230C4×Q8—472no—
231C4×Q8—941no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236#117—941no—
237C2×C4⋊C4C4×D4711yescharacteristic
238C2×C22⋊C4—21no—
239C2×C42C22×D4711yescharacteristic
240#106—942no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—472no—
244C4⋊C8—944no—
245C4⋊C8—941no—
246C4⋊C8—941no—
247C4⋊C8—941no—
248#103—942no—
249#102—942no—
250C22⋊C8—42no—
251C22⋊C8—42no—
252C22⋊C8—472no—
253C22⋊C8—941no—
254#97—21no—
255#97—21no—
256#97—942no—
257C4×C8—942no—
258C4×C8—941no—
259C4×C8—941no—
260C24—21no—
261C2×Q8—472no—
262C2×Q8—941no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—42no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4C2×C4×D4711yescharacteristic
274C22×C4#1062535011yescharacteristic
275C22×C4C2×C22⋊D4711yescharacteristic
276SD16—1884no—
277M16—1881no—
278M16—1881no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—942no—
288C2×C8—942no—
289C2×C8—1881no—
290C2×C8#1062533512yescomplemented
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—472no—
294C4⋊C4—942no—
295C4⋊C4—941no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4—942no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—942no—
302C42—942no—
303C42D4×D4711yescharacteristic
304C42D4×D4711yescharacteristic
305C42D4×D4711yescharacteristic
306C42#1062535211yescharacteristic
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23C4×C22⋊D4711yescharacteristic
315Q8—3761no—
316Q8—1882no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—942no—
331C2×C4—942no—
332C2×C4C22⋊C4×D4711yescharacteristic
333C2×C4(C22⋊D47)⋊C411yescharacteristic
334C2×C4#1309399211yescharacteristic
335C2×C4#1309399511yescharacteristic
336C2×C4#1309399711yescharacteristic
337C2×C4#1309400611yescharacteristic
338C2×C4C2×#1062533511yescharacteristic
339C2×C4#1309404411yescharacteristic
340C2×C4#1309405011yescharacteristic
341C2×C4#1309405411yescharacteristic
342C8—22no—
343C8—41no—
344C8—81no—
345C8—3761no—
346C8—1882no—
347C8—1882no—
348C22—21no—
349C22—21no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1568899911yescharacteristic
358C22C4×#1062533511yescharacteristic
359C22#1568922311yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—1882no—
366C4—1882no—
367C4#1568926111yescharacteristic
368C4#1568926611yescharacteristic
369C4#1568932011yescharacteristic
370C4#1568934211yescharacteristic
371C2—21no—
372C2—21no—
373C2—82no—
374C2#2024374611yescharacteristic
375C2#2024375311yescharacteristic
376C2#2024380311yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1955C2
socleC22×C47#386
prime radicalC22×D4×C47C2×C4
cosocleC2×C42×C47C23
hypercenter#1955D47
hypocenterC47#9050
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #20252328C2semidirect
3. #20242046C2semidirect
5. #20241285C2semidirect
6. #20241233C2semidirect
95. C2×C8×C47SD16semidirect
217. C47#9050semidirect
290. C2×C8#10625335semidirect

Maximal subgroups

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

subgroupindex
#202533962
#202523282
#202420462
#202418132
#202412852
#202412332
C47×#19552
#905047