Finite Group Databasebeta

← #26133642

Subgroups — #26133642

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×#15689361C211yesmaximal, characteristic
3C2×#15688927C211yesmaximal, characteristic, complemented
4#20243414C211yesmaximal, characteristic
5#20241480C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C2×C47×#358C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13094000—21no—
10C22×C47⋊C16C2211yescharacteristic
11C2×C16×D47—22no—
12C2×C16×D47—22no—
13C2×C16×D47—22no—
14#15689361—22no—
15#15689361C414yescomplemented
16C2×#13093958C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093948—21no—
19#15688980—21no—
20#15688927—22no—
21#15688885—21no—
22C22×Q16×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#358—22no—
26C22×C4×D47D411yescharacteristic
27C22×C47⋊C8D411yescharacteristic
28C2×C8×D47—21no—
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47C2×C412yes—
33C2×C8×D47D412yes—
34#13094000—24no—
35#13094000—42no—
36C2×C4⋊Dic47—21no—
37C2×C4⋊Dic47—21no—
38C2×Dic47⋊C4—41no—
39C2×(C2×D47)⋊C4—41no—
40C2×(C2×D47)⋊C4—41no—
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43C2×C47⋊C16D412yes—
44C16×D47—28no—
45#13093958—21no—
46#13093958—21no—
47#13093958—21no—
48#13093958C2×C412yes—
49#13093948—24no—
50C47⋊#95—41no—
51C22×Q8×C47—21no—
52C2×Q16×C47—21no—
53C2×Q16×C47—21no—
54C2×Q16×C47—21no—
55C2×Q16×C47—21no—
56C2×Q16×C47—21no—
57C2×Q16×C47C2×C412yes—
58C22×C8×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47D412yes—
63#107×C47—21no—
64#107×C47—21no—
65C23×D47D811yescharacteristic
66C2×Q8×C47—22no—
67C2×Q8×C47—41no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C2×Q8×C47—41no—
71C2×Q8×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47C2×D411yescharacteristic
75C22×Dic47—41no—
76C22×Dic47—41no—
77C22×Dic47D811yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47C22⋊C412yes—
83C2×C4×D47SD1612yes—
84Q16×C47—22no—
85Q16×C47—22no—
86Q16×C47—41no—
87Q16×C47—41no—
88C2×C8×C47C22×C411yescharacteristic
89C2×C8×C47C2×D411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47C2×D411yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C2×C8×C47#4111yescharacteristic
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96(C2×D47)⋊C4—44no—
97(C2×D47)⋊C4—82no—
98C4⋊Dic47—22no—
99C4⋊Dic47—41no—
100C4⋊Dic47—41no—
101C4⋊Dic47—41no—
102Dic47⋊C4—44no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8C22⋊C412yes—
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—
120Q8×C47—42no—
121Q8×C47—42no—
122Q8×C47—81no—
123Q8×C47—81no—
124C2×C4×C47—42no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47—81no—
129C2×C4×C47—81no—
130C2×C4×C47C2×C22⋊C411yescharacteristic
131C2×C4×C47#12111yescharacteristic
132C2×C4×C47#12111yescharacteristic
133C2×C4×C47C2×SD1611yescharacteristic
134C2×C4×C47#13511yescharacteristic
135C2×C4×C47#13511yescharacteristic
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139C2×Dic47—81no—
140C2×Dic47—81no—
141C2×Dic47—81no—
142C2×Dic47—81no—
143C2×Dic47—81no—
144C2×Dic47#10212yes—
145C4×D47—22no—
146C4×D47—22no—
147C4×D47—22no—
148C4×D47—22no—
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×#358D4711yescharacteristic, complemented
182#1808—471no—
183#1380—471no—
184#1380—471no—
185C2×C47#189311yescharacteristic
186C2×C47C2×#35811yescharacteristic
187C2×C47#213811yescharacteristic
188C2×C47#221611yescharacteristic
189C2×C47#221611yescharacteristic
190C2×C47#221711yescharacteristic
191C2×C47#221711yescharacteristic
192D47—24no—
193C22×Q16C2×D4711yescharacteristic
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×#107—471no—
205C2×#107C2×D4711yescharacteristic
206C2×#103—941no—
207#380—941no—
208#358—22no—
209#358—942no—
210#340—941no—
211C47#1306011yescharacteristic, complemented, Sylow
212C22×Q8—21no—
213C23×C4—471no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16C4×D4712yes—
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—941no—
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×C16C22⋊D4712yes—
243#107—21no—
244#107—21no—
245#107—472no—
246#107—941no—
247#107—941no—
248#107—941no—
249#103—944no—
250#95—1881no—
251C24—471no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
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—22no—
271Q16—22no—
272Q16—41no—
273Q16—41no—
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×C8#1062535011yescharacteristic
283C2×C8D4×D4711yescharacteristic
284C2×C8D4×D4711yescharacteristic
285C2×C8#1062535211yescharacteristic
286C2×C8C2×C22⋊D4711yescharacteristic
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—942no—
290C4⋊C4—1884no—
291C4⋊C4—1881no—
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—42no—
307Q8—42no—
308Q8—81no—
309Q8—81no—
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#1309399511yescharacteristic
331C2×C4#1309399711yescharacteristic
332C2×C4SD16×D4711yescharacteristic
333C2×C4#1309404311yescharacteristic
334C2×C4#1309404511yescharacteristic
335C8—942no—
336C8(C22⋊D47)⋊C411yescharacteristic
337C8C4×C22⋊D4711yescharacteristic
338C8#1309399211yescharacteristic
339C8#1309400611yescharacteristic
340C22—474no—
341C22—942no—
342C22—942no—
343C22—942no—
344C22—942no—
345C22—942no—
346C22—942no—
347C22#102×D4711yescharacteristic
348C22#1568935611yescharacteristic
349C22#1568935811yescharacteristic
350C22SD32×D4711yescharacteristic
351C22Q32×D4711yescharacteristic
352C22#1568955411yescharacteristic
353C22#1568955611yescharacteristic
354C4—82no—
355C4—161no—
356C4—942no—
357C4—3762no—
358C4—7521no—
359C4#1568899911yescharacteristic
360C4#1568911611yescharacteristic
361C4#1568934911yescharacteristic
362C4#1568935111yescharacteristic
363C2—944no—
364C2#2024381311yescharacteristic
365C2#358×D4711yescharacteristic
366C2#2024509411yescharacteristic
367C2#2024547611yescharacteristic
368C2#2024547811yescharacteristic
369C2#2024548111yescharacteristic
370C2#2024548711yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#358C2
socleC23×C47C2×D8
prime radicalC23×D47D8
cosocleC22×C8×C47C23
hypercenterC2×#358D47
hypocenterC47#13060
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
3. C2×#15688927C2semidirect
5. #20241480C2semidirect
6. #20241479C2semidirect
7. C2×C47×#358C2semidirect
15. #15689361C4semidirect
168. C2×D47#358semidirect
181. C2×#358D47semidirect
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×#156893612
C2×#156889272
#202434142
#202414802
#202414792
C2×C47×#3582
#1306047