Finite Group Databasebeta

← #26133644

Subgroups — #26133644

Order 12032.

526 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C16×D47C211yesmaximal, characteristic
2C2×#15689365C211yesmaximal, characteristic
3C2×#15688928C211yesmaximal, characteristic, complemented
4C2×#15688926C211yesmaximal, characteristic, complemented
5#20243414C211yesmaximal, characteristic
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×Dic188C2211yescharacteristic
9C22×C8×D47C2211yescharacteristic
10C2×#13094004—21no—
11C22×C47⋊C16C2211yescharacteristic
12C2×C16×D47—22no—
13C2×C16×D47—22no—
14C2×C16×D47—22no—
15#15689365—22no—
16#15689365C414yescomplemented
17C2×#13093958C2211yescharacteristic
18C2×#13093947—21no—
19#15688980—21no—
20#15688928—22no—
21#15688926—22no—
22#15688885—21no—
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C22×Dic94—21no—
27C22×C4×D47D411yescharacteristic
28C2×Dic188—21no—
29C2×Dic188—21no—
30C2×Dic188—21no—
31C2×Dic188—21no—
32C2×Dic188—21no—
33C2×Dic188C2×C412yes—
34C22×C47⋊C8D411yescharacteristic
35C2×C8×D47—21no—
36C2×C8×D47—21no—
37C2×C8×D47—21no—
38C2×C8×D47—21no—
39C2×C8×D47C2×C412yes—
40C2×C8×D47D412yes—
41#13094004—24no—
42#13094004—42no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—41no—
45C2×(C2×D47)⋊C4—41no—
46C2×(C2×D47)⋊C4—41no—
47C2×C47⋊C16—21no—
48C2×C47⋊C16—21no—
49C2×C47⋊C16D412yes—
50C16×D47—28no—
51#13093958—21no—
52#13093958—21no—
53#13093947—24no—
54C47⋊#95—41no—
55C22×C8×C47C2311yescharacteristic
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47D412yes—
61#107×C47—21no—
62#107×C47—21no—
63#107×C47—21no—
64#107×C47C2×C412yes—
65C23×D47D811yescharacteristic
66C22×C4×C47—41no—
67C22×C4×C47—41no—
68C22×C4×C47C2×D411yescharacteristic
69C22×Dic47—41no—
70C22×Dic47—41no—
71C22×Dic47D811yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47C22⋊C412yes—
77C2×C4×D47SD1612yes—
78C2×Dic94—22no—
79C2×Dic94—41no—
80C2×Dic94—41no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84C2×C8×C47C22×C411yescharacteristic
85C2×C8×C47C2×D411yescharacteristic
86C2×C8×C47C2×D411yescharacteristic
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47#4111yescharacteristic
89C2×C8×C47#4111yescharacteristic
90C4⋊C4×C47—22no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94(C2×D47)⋊C4—44no—
95(C2×D47)⋊C4—82no—
96C4⋊Dic47—44no—
97C4⋊Dic47—41no—
98C4⋊Dic47—41no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8C22⋊C412yes—
102Dic188—22no—
103Dic188—22no—
104Dic188—41no—
105Dic188—41no—
106C8×D47—22no—
107C8×D47—22no—
108C8×D47—22no—
109C8×D47—22no—
110C16×C47—22no—
111C47⋊C16—22no—
112C23×C47C2×D811yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47#10212yes—
118C22×D47SD3212yes—
119C22×D47Q3212yes—
120C2×C4×C47—42no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47—81no—
125C2×C4×C47—81no—
126C2×C4×C47C2×C22⋊C411yescharacteristic
127C2×C4×C47#12111yescharacteristic
128C2×C4×C47#12111yescharacteristic
129C2×C4×C47C2×SD1611yescharacteristic
130C2×C4×C47#13511yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135C2×Dic47—81no—
136C2×Dic47—81no—
137C2×Dic47—81no—
138C2×Dic47—81no—
139C2×Dic47—81no—
140C2×Dic47#10212yes—
141C4×D47—22no—
142C4×D47—22no—
143C4×D47—22no—
144C4×D47—22no—
145Dic94—42no—
146Dic94—42no—
147Dic94—81no—
148Dic94—81no—
149C8×C47C4×D411yescharacteristic
150C8×C47C4×D411yescharacteristic
151C8×C47#12011yescharacteristic
152C8×C47#12311yescharacteristic
153C47⋊C8—22no—
154#13060—471nomaximal, Sylow
155C22×C47C2×#10211yescharacteristic
156C22×C47#46611yescharacteristic
157C22×C47#46611yescharacteristic
158C22×C47C2×SD3211yescharacteristic
159C22×C47C2×Q3211yescharacteristic
160C22×C47#50811yescharacteristic
161C22×C47#50811yescharacteristic
162C2×D47—22no—
163C2×D47—22no—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—22no—
168C2×D47#35814yescomplemented
169C4×C47—82no—
170C4×C47—161no—
171C4×C47#38611yescharacteristic
172C4×C47#41611yescharacteristic
173C4×C47#46511yescharacteristic
174C4×C47#46511yescharacteristic
175Dic47—22no—
176Dic47—82no—
177Dic47—161no—
178C23×C16—471no—
179C2×#467—471no—
180C2×#358—471no—
181C2×#358—471no—
182#1808—471no—
183#1380—471no—
184#1380D4711yescharacteristic, complemented
185C2×C47#189311yescharacteristic
186C2×C47C2×#35811yescharacteristic
187C2×C47#213811yescharacteristic
188C2×C47#221611yescharacteristic
189C2×C47#221611yescharacteristic
190C2×C47#221711yescharacteristic
191C2×C47#221711yescharacteristic
192D47—24no—
193C22×Q16—471no—
194C23×C8—471no—
195C2×C22⋊Q8—941no—
196C22×C16—471no—
197C22×C16—942no—
198C22×C16—942no—
199C22×C16—942no—
200C22×C16C2×D4711yescharacteristic
201#467—474no—
202#467—942no—
203C2×#107—471no—
204C2×#107C2×D4711yescharacteristic
205C2×#107C2×D4711yescharacteristic
206C2×#103—941no—
207#380—941no—
208#358—942no—
209#358—942no—
210#340—941no—
211C47#1306011yescharacteristic, complemented, Sylow
212C22×Q8—941no—
213C23×C4—471no—
214C2×Q16—472no—
215C2×Q16—941no—
216C2×Q16—941no—
217C2×Q16—941no—
218C2×Q16—941no—
219C2×Q16—941no—
220C22×C8—471no—
221C22×C8—472no—
222C22×C8—472no—
223C22×C8—941no—
224C22×C8—941no—
225C22×C8—941no—
226C22×C8—941no—
227C22×C8C22×D4711yescharacteristic
228C22⋊Q8—944no—
229C22⋊Q8—1882no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—941no—
233C2×C4⋊C4—1881no—
234C2×C22⋊C4—1881no—
235C2×C22⋊C4—1881no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—472no—
239C2×C16—948no—
240C2×C16—941no—
241C2×C16—941no—
242C2×C16D18812yes—
243#107—21no—
244#107—21no—
245#107—21no—
246#107—941no—
247#107—941no—
248#107C4×D4712yes—
249#103—944no—
250#95—1881no—
251C24—471no—
252C2×Q8—942no—
253C2×Q8—1881no—
254C2×Q8—1881no—
255C2×Q8—1881no—
256C2×Q8—1881no—
257C2×Q8—1881no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—471no—
261C22×C4—472no—
262C22×C4—472no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—1881no—
268C22×C4—1881no—
269C22×C4D4×D4711yescharacteristic
270Q16—942no—
271Q16—942no—
272Q16—1881no—
273Q16—1881no—
274C2×C8—472no—
275C2×C8—941no—
276C2×C8—941no—
277C2×C8—942no—
278C2×C8—942no—
279C2×C8—942no—
280C2×C8—942no—
281C2×C8C2×C4×D4711yescharacteristic
282C2×C8C2×D18811yescharacteristic
283C2×C8#1062535011yescharacteristic
284C2×C8D4×D4711yescharacteristic
285C2×C8D4×D4711yescharacteristic
286C2×C8#1062535411yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—1884no—
292C4⋊C4—1881no—
293C4⋊C4—1881no—
294C22⋊C4—3762no—
295C22⋊C4—1884no—
296C16—22no—
297C16—942no—
298C23—472no—
299C23—472no—
300C23—472no—
301C23—941no—
302C23—941no—
303C23—941no—
304C23—941no—
305C23D8×D4711yescharacteristic
306Q8—3761no—
307Q8—3761no—
308Q8—1882no—
309Q8—1882no—
310C2×C4—42no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—472no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—942no—
320C2×C4—942no—
321C2×C4—942no—
322C2×C4—942no—
323C2×C4—3761no—
324C2×C4—3761no—
325C2×C4—3761no—
326C2×C4—3761no—
327C2×C4—3761no—
328C2×C4—1882no—
329C2×C4C22⋊C4×D4711yescharacteristic
330C2×C4#1309399711yescharacteristic
331C2×C4#1309399911yescharacteristic
332C2×C4SD16×D4711yescharacteristic
333C2×C4#1309404511yescharacteristic
334C2×C4#1309404711yescharacteristic
335C8—942no—
336C8#1309398611yescharacteristic
337C8C4×D18811yescharacteristic
338C8#1309399411yescharacteristic
339C8#1309400911yescharacteristic
340C22—474no—
341C22—942no—
342C22—942no—
343C22—942no—
344C22—942no—
345C22—942no—
346C22—942no—
347C22#102×D4711yescharacteristic
348C22#1568935811yescharacteristic
349C22#1568936011yescharacteristic
350C22SD32×D4711yescharacteristic
351C22Q32×D4711yescharacteristic
352C22#1568955211yescharacteristic
353C22#1568955411yescharacteristic
354C4—82no—
355C4—161no—
356C4—942no—
357C4—3762no—
358C4—7521no—
359C4#1568900111yescharacteristic
360C4#1568911811yescharacteristic
361C4#1568935311yescharacteristic
362C4#1568935511yescharacteristic
363C2—944no—
364C2#2024381511yescharacteristic
365C2#358×D4711yescharacteristic
366C2#2024509211yescharacteristic
367C2#2024547811yescharacteristic
368C2#2024548011yescharacteristic
369C2#2024548311yescharacteristic
370C2#2024548511yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#13060
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#15688928C2semidirect
4. C2×#15688926C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
16. #15689365C4semidirect
168. C2×D47#358semidirect
184. #1380D47semidirect
211. C47#13060semidirect

Maximal subgroups

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

subgroupindex
C22×C16×D472
C2×#156893652
C2×#156889282
C2×#156889262
#202434142
#202414792
C47×#13802
#1306047