Finite Group Databasebeta

← #26105752

Subgroups — #26105752

Order 12032.

674 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
1C2×#15689174C211yesmaximal, characteristic
2C2×#15689145C211yesmaximal, characteristic
3C2×C4⋊C8×D47C211yesmaximal, characteristic
4#20241223C211yesmaximal, characteristic, complemented
5#20241222C211yesmaximal, characteristic, complemented
6#20241222C211yesmaximal, characteristic, complemented
7C47×#1277C211yesmaximal, characteristic, complemented
8C22×#10625324—21no—
9C22×C8×D47—21no—
10C2×C42×D47C2211yescharacteristic
11#15689174—22no—
12#15689174—22no—
13#15689145—22no—
14#15689145C414yes—
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×C4⋊(C47⋊C8)C2211yescharacteristic
17C2×Dic47⋊C8—21no—
18C2×Dic47⋊C8—21no—
19C2×Dic47⋊C8C412yes—
20C4⋊C8×D47—22no—
21C4⋊C8×D47C414yes—
22C2×(C2×D47)⋊C8C412yes—
23C2×C4×C47⋊C8C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C4×C8×C47C2211yescharacteristic
27C22×C4×D47C2×C411yescharacteristic
28C22×C4×D47D411yescharacteristic
29C22×C4×D47Q811yescharacteristic
30C2×#10625324—24no—
31C2×#10625324—42no—
32C2×#10625324—42no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8C2×C412yes—
36C2×C8×D47—24no—
37C2×C8×D47—42no—
38C2×C8×D47—42no—
39C2×C4×Dic47C2×C411yescharacteristic
40C2×C4×Dic47D411yescharacteristic
41C2×C4×Dic47Q811yescharacteristic
42C42×D47C2×C412yes—
43C42×D47C2×C412yes—
44C42×D47D412yes—
45C42×D47D412yes—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)C2×C412yes—
49C4⋊(C47⋊C8)C2×C412yes—
50Dic47⋊C8—24no—
51Dic47⋊C8—24no—
52Dic47⋊C8—24no—
53(C2×D47)⋊C8—24no—
54C4×C47⋊C8—21no—
55C4×C47⋊C8—21no—
56C22×C8×C47—21no—
57C22×C8×C47—21no—
58C22×C8×C47C2×C412yes—
59C2×C42×C47C2311yescharacteristic
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47C2×C412yes—
63C4⋊C8×C47C2×C412yes—
64C4×C8×C47—21no—
65C4×C8×C47—21no—
66C23×D47C4⋊C411yescharacteristic
67C22×C4×C47C22×C411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47C2×Q811yescharacteristic
70C22×Dic47C4⋊C411yescharacteristic
71C22×Dic47C4⋊C411yescharacteristic
72C22×Dic47C4⋊C411yescharacteristic
73C2×C4×D47—22no—
74C2×C4×D47—22no—
75C2×C4×D47—42no—
76C2×C4×D47C4212yes—
77C2×C4×D47C22⋊C412yes—
78C2×C4×D47C22⋊C412yes—
79C2×C4×D47C22⋊C412yes—
80C2×C4×D47C4⋊C412yes—
81C2×C4×D47C4⋊C412yes—
82C2×C4×D47D812yes—
83C2×C4×D47SD1612yes—
84C2×C4×D47SD1612yes—
85C2×C4×D47Q1612yes—
86C2×C8×C47—22no—
87C2×C8×C47—22no—
88C2×C8×C47—22no—
89C2×C8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47—41no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C42×C47C22×C411yescharacteristic
96C42×C47C22×C411yescharacteristic
97C42×C47C2×D411yescharacteristic
98C42×C47C2×D411yescharacteristic
99C4×Dic47C4212yes—
100C4×Dic47C22⋊C412yes—
101C4×Dic47C22⋊C412yes—
102C4×Dic47C22⋊C412yes—
103C4×Dic47C4⋊C412yes—
104C4×Dic47C4⋊C412yes—
105C2×C47⋊C8—22no—
106C2×C47⋊C8—22no—
107C2×C47⋊C8—22no—
108C2×C47⋊C8—22no—
109C2×C47⋊C8—22no—
110C2×C47⋊C8—41no—
111C2×C47⋊C8—41no—
112C2×C47⋊C8—41no—
113C2×C47⋊C8—41no—
114#10625324—48no—
115C8×D47—48no—
116C23×C47C2×C4⋊C411yescharacteristic
117C22×D47—22no—
118C22×D47—22no—
119C22×D47#9512yes—
120C22×D47#10612yes—
121C22×D47#10712yes—
122C2×C4×C47—22no—
123C2×C4×C47C2×C4211yescharacteristic
124C2×C4×C47C2×C22⋊C411yescharacteristic
125C2×C4×C47C2×C22⋊C411yescharacteristic
126C2×C4×C47C2×C22⋊C411yescharacteristic
127C2×C4×C47C2×C4⋊C411yescharacteristic
128C2×C4×C47C2×C4⋊C411yescharacteristic
129C2×C4×C47#13112yes—
130C2×C4×C47#13112yes—
131C2×C4×C47C2×D811yescharacteristic
132C2×C4×C47C2×SD1611yescharacteristic
133C2×C4×C47C2×SD1611yescharacteristic
134C2×C4×C47C2×Q1611yescharacteristic
135C2×Dic47—22no—
136C2×Dic47—22no—
137C2×Dic47#9512yes—
138C2×Dic47#9512yes—
139C2×Dic47#9512yes—
140C2×Dic47#10612yes—
141C2×Dic47#10712yes—
142C4×D47—22no—
143C4×D47—22no—
144C4×D47—24no—
145C4×D47—42no—
146C4×D47—42no—
147C4×D47#10214yes—
148C4×D47#10214yes—
149C4×D47#10314yes—
150C4×D47#10314yes—
151C8×C47—42no—
152C8×C47—42no—
153C8×C47—42no—
154C47⋊C8—42no—
155C47⋊C8—42no—
156C47⋊C8—42no—
157#7877—471nomaximal, Sylow
158C22×C47C2×#9511yescharacteristic
159C22×C47#42412yes—
160C22×C47C2×#10611yescharacteristic
161C22×C47C2×#10711yescharacteristic
162C22×C47#43012yes—
163C2×D47—24no—
164C2×D47—24no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47#34014yes—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47#40511yescharacteristic
171C4×C47#40511yescharacteristic
172C4×C47#40812yes—
173C4×C47C2×#10211yescharacteristic
174C4×C47C2×#10211yescharacteristic
175C4×C47C2×#10311yescharacteristic
176C4×C47C2×#10311yescharacteristic
177Dic47—22no—
178Dic47—22no—
179Dic47#34014yes—
180C2×#431—471no—
181C2×#423—471no—
182C22×C4⋊C8—471no—
183#1277—471no—
184#1277—471no—
185#1277—471no—
186#1277D4711yescharacteristic, complemented
187C2×C47#157012yes—
188C2×C47#157112yes—
189C2×C47#172911yescharacteristic
190C2×C47C2×#34011yescharacteristic
191C2×C47#173811yescharacteristic
192D47—24no—
193C22×M16—941no—
194C23×C8—941no—
195C22×C42—471no—
196#431—942no—
197#431—942no—
198#423—474no—
199#423—942no—
200C2×C4⋊C8—471no—
201C2×C4⋊C8—471no—
202C2×C4⋊C8—474no—
203C2×C4⋊C8—472no—
204C2×C4⋊C8—942no—
205C2×C4⋊C8—941no—
206C2×C4⋊C8—941no—
207C2×C4⋊C8C2×D4711yescharacteristic
208C2×C4⋊C8C2×D4711yescharacteristic
209C2×C22⋊C8—472no—
210C2×C4×C8—471no—
211C2×C4×C8C2×D4711yescharacteristic
212C47#787711yescharacteristic, complemented, Sylow
213C23×C4—471no—
214C23×C4—471no—
215C23×C4—471no—
216C2×M16—944no—
217C2×M16—1882no—
218C2×M16—1882no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—472no—
222C22×C8—944no—
223C22×C8—941no—
224C22×C8—941no—
225C22×C8—1882no—
226C22×C8—1882no—
227C22×C8C4×D4712yes—
228C2×C42—471no—
229C2×C42—471no—
230C2×C42—471no—
231C2×C42—472no—
232C2×C42—472no—
233C2×C42—472no—
234C2×C42—472no—
235C2×C42C22×D4711yescharacteristic
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—472no—
239C4⋊C8—472no—
240C4⋊C8—944no—
241C4⋊C8—944no—
242C4⋊C8—944no—
243C4⋊C8—941no—
244C4⋊C8—941no—
245C4⋊C8C4×D4712yes—
246C4⋊C8C4×D4712yes—
247C22⋊C8—944no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—941no—
251C4×C8—941no—
252C24—471no—
253C22×C4—471no—
254C22×C4—472no—
255C22×C4—472no—
256C22×C4—472no—
257C22×C4—472no—
258C22×C4—472no—
259C22×C4—472no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—472no—
263C22×C4—472no—
264C22×C4—472no—
265C22×C4—472no—
266C22×C4—942no—
267C22×C4—942no—
268C22×C4—1882no—
269C22×C4C2×C4×D4711yescharacteristic
270C22×C4D4×D4711yescharacteristic
271C22×C4Q8×D4711yescharacteristic
272M16—1888no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—942no—
283C2×C8—942no—
284C2×C8—942no—
285C2×C8—942no—
286C2×C8—942no—
287C2×C8—1888no—
288C2×C8—1881no—
289C2×C8—1881no—
290C2×C8—1881no—
291C2×C8—1881no—
292C42—472no—
293C42—472no—
294C42—472no—
295C42—472no—
296C42—472no—
297C42—472no—
298C42C2×C4×D4711yescharacteristic
299C42C2×C4×D4711yescharacteristic
300C42D4×D4711yescharacteristic
301C42D4×D4711yescharacteristic
302C23—472no—
303C23—472no—
304C23—472no—
305C23—942no—
306C23—942no—
307C23C4⋊C4×D4711yescharacteristic
308C2×C4—22no—
309C2×C4—472no—
310C2×C4—472no—
311C2×C4—472no—
312C2×C4—474no—
313C2×C4—474no—
314C2×C4—474no—
315C2×C4—474no—
316C2×C4—472no—
317C2×C4—472no—
318C2×C4—942no—
319C2×C4—942no—
320C2×C4—942no—
321C2×C4—942no—
322C2×C4—944no—
323C2×C4—1882no—
324C2×C4—1882no—
325C2×C4C42×D4711yescharacteristic
326C2×C4C22⋊C4×D4711yescharacteristic
327C2×C4C22⋊C4×D4711yescharacteristic
328C2×C4C22⋊C4×D4711yescharacteristic
329C2×C4C4⋊C4×D4711yescharacteristic
330C2×C4C4⋊C4×D4711yescharacteristic
331C2×C4#1309403012yes—
332C2×C4#1309403212yes—
333C2×C4D8×D4711yescharacteristic
334C2×C4SD16×D4711yescharacteristic
335C2×C4SD16×D4711yescharacteristic
336C2×C4Q16×D4711yescharacteristic
337C8—42no—
338C8—42no—
339C8—42no—
340C8—1882no—
341C8—1882no—
342C8—1882no—
343C22—474no—
344C22—942no—
345C22—942no—
346C22—944no—
347C22—944no—
348C22#95×D4711yescharacteristic
349C22#1568914812yes—
350C22#106×D4711yescharacteristic
351C22#107×D4711yescharacteristic
352C22#1568917012yes—
353C4—21no—
354C4—21no—
355C4—474no—
356C4—942no—
357C4—942no—
358C4#1568907711yescharacteristic
359C4#1568908011yescharacteristic
360C4#1568908812yes—
361C4#102×D4711yescharacteristic
362C4#102×D4711yescharacteristic
363C4#103×D4711yescharacteristic
364C4#103×D4711yescharacteristic
365C2—944no—
366C2#2024215712yes—
367C2#2024216112yes—
368C2#2024308311yescharacteristic
369C2#340×D4711yescharacteristic
370C2#2024311311yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1277C2
socleC23×C47C2×C4⋊C4
prime radicalC23×D47C4⋊C4
cosocleC2×C42×C47C23
hypercenter#1277D47
hypocenterC47#7877
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
4. #20241223C2semidirect
5. #20241222C2semidirect
6. #20241222C2semidirect
7. C47×#1277C2semidirect
186. #1277D47semidirect
212. C47#7877semidirect

Maximal subgroups

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

subgroupindex
C2×#156891742
C2×#156891452
C2×C4⋊C8×D472
#202412232
#202412222
C47×#12772
#787747