Finite Group Databasebeta

← #26186112

Subgroups — #26186112

Order 12032.

662 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252471C211yesmaximal, characteristic, complemented
2C2×C4×#10625335C211yesmaximal, characteristic
3#20242290C214yesmaximal, complemented
4#20242276C214yesmaximal, complemented
5#20242134C211yesmaximal, characteristic, complemented
6#20241782C211yesmaximal, characteristic, complemented
7#20241779C211yesmaximal, characteristic
8#20241672C211yesmaximal, characteristic, complemented
9C47×#2975C211yesmaximal, characteristic
10C22×#10625335C411yescharacteristic
11C2×C4×Dic94C2211yescharacteristic
12#15689253C2214yescomplemented
13#15689250—22no—
14C4×#10625335C412yes—
15C4×#10625335C412yes—
16C4×#10625335C2212yes—
17C4×#10625335C2212yes—
18#15689177—22no—
19#15689176C2211yescharacteristic
20#15689176C2211yescharacteristic
21C2×#13093955C411yescharacteristic
22C2×#13093947C411yescharacteristic
23C2×#13093945C411yescharacteristic
24C2×C4×C47⋊C8C2211yescharacteristic
25#15688875C2212yescomplemented
26#15688873C2212yescomplemented
27#15688853C2214yescomplemented
28D4⋊(C47⋊C8)C2214yes—
29#15688845C2212yescomplemented
30C8×C47⋊C8C2212yescomplemented
31C2×C4×D4×C47C2211yescharacteristic
32C47×#436—22no—
33C47×#436C2214yes—
34C47×#431C2211yescharacteristic
35C47×#431C2211yescharacteristic
36C47×#407—22no—
37C22×Dic94C2×C411yescharacteristic
38C2×#10625335—24no—
39C2×#10625335C2×C412yes—
40C2×#10625335C2×C412yes—
41C22×C47⋊C8C2×C411yescharacteristic
42C22×C47⋊C8C2×C411yescharacteristic
43C4×Dic94—21no—
44C4×Dic94—21no—
45C4×Dic94C2×C412yes—
46C4×Dic94C2312yes—
47C2×C4⋊Dic47C2×C411yescharacteristic
48C2×Dic47⋊C4—21no—
49C2×C4×Dic47—21no—
50#13093955C2×C412yes—
51#13093955C2×C412yes—
52C4⋊(C47⋊C8)—21no—
53C4⋊(C47⋊C8)C2312yes—
54Dic47⋊C8—24no—
55#13093947C2×C412yes—
56#13093947C2×C412yes—
57#13093945C2×C412yes—
58#13093945C2×C412yes—
59C22⋊(C47⋊C8)—21no—
60C22⋊(C47⋊C8)—21no—
61#13093934—24no—
62C4×C47⋊C8—21no—
63C4×C47⋊C8C2×C411yescharacteristic
64C4×C47⋊C8C2×C411yescharacteristic
65C4×C47⋊C8C2312yes—
66C4×C47⋊C8C2311yescharacteristic
67C4×C47⋊C8C2311yescharacteristic
68C22×D4×C47C2×C411yescharacteristic
69C23×C4×C47—21no—
70C2×M16×C47—24no—
71C4×D4×C47—21no—
72C4×D4×C47—21no—
73C4×D4×C47C2×C412yes—
74C4×D4×C47C2312yes—
75C2×C4⋊C4×C47C2×C411yescharacteristic
76C2×C22⋊C4×C47—21no—
77C2×C42×C47C2311yescharacteristic
78C4⋊C8×C47D412yes—
79C4⋊C8×C47C2312yes—
80C22⋊C8×C47—21no—
81C22⋊C8×C47—24no—
82C22⋊C8×C47D412yes—
83C4×C8×C47—21no—
84C4×C8×C47C2312yes—
85C24×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47—22no—
88C2×D4×C47—22no—
89C2×D4×C47C22×C412yes—
90C22×C4×C47—21no—
91C22×C4×C47—22no—
92C22×C4×C47—22no—
93C22×C4×C47—82no—
94C22×C4×C47C22×C411yescharacteristic
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47#4111yescharacteristic
97C22×Dic47—21no—
98C22×Dic47—21no—
99C2×Dic94—22no—
100C2×Dic94—22no—
101C2×Dic94—21no—
102C2×Dic94C22×C412yes—
103M16×C47—84no—
104C2×C8×C47—22no—
105C2×C8×C47C2×D414yes—
106C4⋊C4×C47—21no—
107C4⋊C4×C47C22×C412yes—
108C22⋊C4×C47—22no—
109C22⋊C4×C47—22no—
110C42×C47C22×C411yescharacteristic
111C42×C47C2×D411yescharacteristic
112C42×C47#4111yescharacteristic
113C42×C47C2411yescharacteristic
114#10625335—24no—
115#10625335—24no—
116C4⋊Dic47—21no—
117C4⋊Dic47C22×C412yes—
118Dic47⋊C4—22no—
119Dic47⋊C4—22no—
120C4×Dic47—22no—
121C4×Dic47—22no—
122C2×C47⋊C8—22no—
123C2×C47⋊C8—22no—
124C2×C47⋊C8—22no—
125C2×C47⋊C8M1614yescomplemented
126C2×C47⋊C8C22×C411yescharacteristic
127C2×C47⋊C8C22×C411yescharacteristic
128C2×C47⋊C8C22×C411yescharacteristic
129C2×C47⋊C8C22×C411yescharacteristic
130C23×C47—22no—
131C23×C47—42no—
132C23×C47—81no—
133C23×C47—81no—
134C23×C47C4×D411yescharacteristic
135D4×C47—22no—
136D4×C47—22no—
137D4×C47—42no—
138C2×C4×C47—22no—
139C2×C4×C47—22no—
140C2×C4×C47—41no—
141C2×C4×C47—44no—
142C2×C4×C47—82no—
143C2×C4×C47—81no—
144C2×C4×C47C4×D411yescharacteristic
145C2×C4×C47C4×D411yescharacteristic
146C2×C4×C47C4×D411yescharacteristic
147C2×C4×C47C2×M1612yes—
148C2×C4×C47#13112yes—
149C2×C4×C47C23×C411yescharacteristic
150C2×C4×C47C22×D411yescharacteristic
151C2×C4×C47C2×#4111yescharacteristic
152C2×Dic47—22no—
153C2×Dic47—22no—
154C2×Dic47—42no—
155C2×Dic47—81no—
156Dic94—22no—
157Dic94—22no—
158Dic94—42no—
159C8×C47—24no—
160C8×C47—42no—
161C47⋊C8—21no—
162C47⋊C8—21no—
163C47⋊C8—42no—
164C47⋊C8—42no—
165C47⋊C8C2×M1612yes—
166C47⋊C8C2×M1612yes—
167#17896—471nomaximal, Sylow
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—42no—
171C22×C47—42no—
172C22×C47—42no—
173C22×C47—84no—
174C22×C47#43612yes—
175C22×C47C2×C4×D411yescharacteristic
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—42no—
180C4×C47#43612yes—
181C4×C47C22×M1611yescharacteristic
182C4×C47C2×#13111yescharacteristic
183C4×C47#57712yes—
184Dic47—42no—
185Dic47—42no—
186#2983—471no—
187#2975D4711yescharacteristic
188C2×C4×SD16—471no—
189#1592—474no—
190#1590—474no—
191#1564—471no—
192#1479—471no—
193#1478—471no—
194#1450—471no—
195C2×C47—22no—
196C2×C47—82no—
197C2×C47C2×#43611yescharacteristic
198C2×C47#294911yescharacteristic
199C2×C47#295711yescharacteristic
200C22×SD16—471no—
201C2×C4×Q8—471no—
202C2×C4×D4C2×D4711yescharacteristic
203#446—474no—
204#446—942no—
205C4×SD16—472no—
206C4×SD16—472no—
207C4×SD16—472no—
208C4×SD16—472no—
209#436—22no—
210#436C2×D4714yes—
211#432—942no—
212#431—471no—
213#431—471no—
214#431C2×D4711yescharacteristic
215#431C2×D4711yescharacteristic
216C2×#106—471no—
217C2×#103—471no—
218C2×#102—471no—
219#407—22no—
220C2×C4×C8—471no—
221#335—472no—
222#334—472no—
223Q8⋊C8—474no—
224D4⋊C8—474no—
225#322—472no—
226C82—472no—
227C47#1789611yescharacteristic, complemented, Sylow
228C22×Q8—471no—
229C22×D4C4×D4711yescharacteristic
230C23×C4—21no—
231C2×SD16—472no—
232C2×SD16—472no—
233C2×SD16—944no—
234C2×M16—24no—
235C22×C8—471no—
236C22×C8—471no—
237C4×Q8—472no—
238C4×Q8—472no—
239C4×Q8—941no—
240C4×Q8—941no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4C4×D4712yes—
244C4×D4C22×D4712yes—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—941no—
247C2×C4⋊C4C4×D4711yescharacteristic
248C2×C22⋊C4—21no—
249C2×C42—941no—
250C2×C42C22×D4711yescharacteristic
251#106—472no—
252#106—472no—
253C4⋊C8—472no—
254C4⋊C8—944no—
255C4⋊C8—941no—
256C4⋊C8C22⋊D4712yes—
257C4⋊C8C22×D4712yes—
258#103—472no—
259#103—472no—
260#102—472no—
261#102—472no—
262C22⋊C8—21no—
263C22⋊C8—24no—
264C22⋊C8—941no—
265C22⋊C8—941no—
266C22⋊C8C22⋊D4712yes—
267#97—944no—
268C4×C8—21no—
269C4×C8—471no—
270C4×C8—471no—
271C4×C8—471no—
272C4×C8—471no—
273C4×C8—472no—
274C4×C8—941no—
275C4×C8C22×D4712yes—
276C24—21no—
277C2×Q8—472no—
278C2×Q8—941no—
279C2×Q8—942no—
280C2×Q8—942no—
281C2×D4—21no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4C2×C4×D4712yes—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—82no—
289C22×C4—941no—
290C22×C4—941no—
291C22×C4C2×C4×D4711yescharacteristic
292C22×C4#1062535011yescharacteristic
293C22×C4C2×C22⋊D4711yescharacteristic
294SD16—944no—
295SD16—944no—
296M16—84no—
297C2×C8—22no—
298C2×C8—474no—
299C2×C8—471no—
300C2×C8—471no—
301C2×C8—471no—
302C2×C8—471no—
303C2×C8—942no—
304C2×C8—942no—
305C2×C8—942no—
306C2×C8C2×C22⋊D4714yes—
307C4⋊C4—21no—
308C4⋊C4—472no—
309C4⋊C4—942no—
310C4⋊C4—941no—
311C4⋊C4—942no—
312C4⋊C4C2×C4×D4712yes—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C42—942no—
316C42—942no—
317C42C2×C4×D4711yescharacteristic
318C42#1062535011yescharacteristic
319C42C2×C22⋊D4711yescharacteristic
320C42C23×D4711yescharacteristic
321C23—22no—
322C23—42no—
323C23—81no—
324C23—81no—
325C23C4×C22⋊D4711yescharacteristic
326Q8—942no—
327Q8—942no—
328Q8—1882no—
329D4—22no—
330D4—22no—
331D4—42no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—942no—
339C2×C4—942no—
340C2×C4—3761no—
341C2×C4—1882no—
342C2×C4C4×C22⋊D4711yescharacteristic
343C2×C4C4×C22⋊D4711yescharacteristic
344C2×C4C4×C22⋊D4711yescharacteristic
345C2×C4M16×D4712yes—
346C2×C4#1309403212yes—
347C2×C4C22×C4×D4711yescharacteristic
348C2×C4C22×C22⋊D4711yescharacteristic
349C2×C4C2×#1062535011yescharacteristic
350C8—24no—
351C8—42no—
352C8—472no—
353C8—472no—
354C8—941no—
355C8—941no—
356C8—1882no—
357C8—1882no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—84no—
364C22#1568919912yes—
365C22C2×C4×C22⋊D4711yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—1882no—
371C4—1882no—
372C4#1568919912yes—
373C4C2×M16×D4711yescharacteristic
374C4C2×#1309403211yescharacteristic
375C4#1568993412yes—
376C2—22no—
377C2—82no—
378C2C2×#1568919911yescharacteristic
379C2#2025224511yescharacteristic
380C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2975C2
socleC22×C47C2×C4×D4
prime radicalC22×D4×C47C2×C4
cosocleC42×C47C24
hypercenter#2975D47
hypocenterC47#17896
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2975

Complements

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

NH ≅ G/Ntype
1. #20252471C2semidirect
3. #20242290C2semidirect
4. #20242276C2semidirect
5. #20242134C2semidirect
6. #20241782C2semidirect
8. #20241672C2semidirect
12. #15689253C22semidirect
25. #15688875C22semidirect
26. #15688873C22semidirect
27. #15688853C22semidirect
29. #15688845C22semidirect
30. C8×C47⋊C8C22semidirect
125. C2×C47⋊C8M16semidirect
227. C47#17896semidirect

Maximal subgroups

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

subgroupindex
#202524712
C2×C4×#106253352
#202422902
#202422762
#202421342
#202417822
#202417792
#202416722
C47×#29752
#1789647