Finite Group Databasebeta

← #26106540

Subgroups — #26106540

Order 12032.

524 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252016C211yesmaximal, characteristic
2C2×#15689178C211yesmaximal, characteristic
3#432×D47C211yesmaximal, characteristic
4#20241288C211yesmaximal, characteristic, complemented
5#20241287C211yesmaximal, characteristic, complemented
6#20241286C211yesmaximal, characteristic, complemented
7C47×#1302C211yesmaximal, characteristic, complemented
8C2×C42×D47C2211yescharacteristic
9#15689180C2211yescharacteristic
10#15689179—21no—
11#15689179C412yes—
12#15689178—21no—
13#15689178—21no—
14#15689178—21no—
15#15689178C412yes—
16#15689178C412yes—
17#15689177—21no—
18#15689177C412yes—
19#15689176C2211yescharacteristic
20#15689174—21no—
21#15689145—21no—
22C2×Dic47⋊C8—21no—
23C4⋊C8×D47C412yes—
24#15689085C412yes—
25C2×(C2×D47)⋊C8—21no—
26C22⋊C8×D47—21no—
27C4×#10625324—21no—
28C2×#13093935C2211yescharacteristic
29#97×D47—21no—
30C47×#432C2211yescharacteristic
31C47×#431C2211yescharacteristic
32C2×#97×C47C2211yescharacteristic
33C22×C4×D47C2×C411yescharacteristic
34C22×C4×D47D411yescharacteristic
35C22×C4×D47Q811yescharacteristic
36C2×#10625324—22no—
37C22×C47⋊C8—21no—
38C2×C8×D47—22no—
39C2×C4×Dic47C2×C411yescharacteristic
40C2×C4×Dic47D411yescharacteristic
41C2×C4×Dic47Q811yescharacteristic
42C42×D47C2×C411yescharacteristic
43C42×D47C2×C411yescharacteristic
44C42×D47C2×C411yescharacteristic
45C42×D47C2×C411yescharacteristic
46C42×D47D411yescharacteristic
47C42×D47D411yescharacteristic
48C42×D47D411yescharacteristic
49C42×D47D411yescharacteristic
50C4⋊(C47⋊C8)—21no—
51C4⋊(C47⋊C8)C2×C412yes—
52Dic47⋊C8—22no—
53Dic47⋊C8—22no—
54Dic47⋊C8—22no—
55Dic47⋊C8—22no—
56C22⋊(C47⋊C8)—21no—
57C22⋊(C47⋊C8)C2×C412yes—
58(C2×D47)⋊C8—22no—
59(C2×D47)⋊C8—22no—
60(C2×D47)⋊C8—22no—
61(C2×D47)⋊C8—22no—
62#13093935—21no—
63#13093935—21no—
64#13093935C2×C412yes—
65#13093934—22no—
66#13093934—22no—
67C4×C47⋊C8—21no—
68C22×C8×C47—21no—
69C2×C42×C47C2311yescharacteristic
70C4⋊C8×C47—21no—
71C4⋊C8×C47C2×C412yes—
72C22⋊C8×C47—21no—
73C22⋊C8×C47C2×C412yes—
74#97×C47—21no—
75#97×C47—21no—
76#97×C47C2×C412yes—
77C4×C8×C47—21no—
78C23×D47C4⋊C411yescharacteristic
79C22×C4×C47C22×C411yescharacteristic
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×Q811yescharacteristic
82C22×Dic47C4⋊C411yescharacteristic
83C22×Dic47C4⋊C411yescharacteristic
84C22×Dic47C4⋊C411yescharacteristic
85C2×C4×D47—42no—
86C2×C4×D47—42no—
87C2×C4×D47—42no—
88C2×C4×D47C4211yescharacteristic
89C2×C4×D47C4211yescharacteristic
90C2×C4×D47C22⋊C411yescharacteristic
91C2×C4×D47C22⋊C411yescharacteristic
92C2×C4×D47C22⋊C411yescharacteristic
93C2×C4×D47C22⋊C411yescharacteristic
94C2×C4×D47C22⋊C411yescharacteristic
95C2×C4×D47C22⋊C411yescharacteristic
96C2×C4×D47C4⋊C411yescharacteristic
97C2×C4×D47C4⋊C411yescharacteristic
98C2×C4×D47C4⋊C411yescharacteristic
99C2×C4×D47C4⋊C411yescharacteristic
100C2×C8×C47—22no—
101C2×C8×C47—22no—
102C2×C8×C47—22no—
103C2×C8×C47—42no—
104C42×C47C22×C411yescharacteristic
105C42×C47C22×C411yescharacteristic
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C4×Dic47C4211yescharacteristic
109C4×Dic47C4211yescharacteristic
110C4×Dic47C22⋊C411yescharacteristic
111C4×Dic47C22⋊C411yescharacteristic
112C4×Dic47C22⋊C411yescharacteristic
113C4×Dic47C22⋊C411yescharacteristic
114C4×Dic47C22⋊C411yescharacteristic
115C4×Dic47C22⋊C411yescharacteristic
116C4×Dic47C4⋊C411yescharacteristic
117C4×Dic47C4⋊C411yescharacteristic
118C4×Dic47C4⋊C411yescharacteristic
119C4×Dic47C4⋊C411yescharacteristic
120C2×C47⋊C8—22no—
121C2×C47⋊C8—22no—
122C2×C47⋊C8—22no—
123C2×C47⋊C8—42no—
124#10625324—44no—
125C8×D47—44no—
126C23×C47C2×C4⋊C411yescharacteristic
127C22×D47—22no—
128C22×D47—22no—
129C22×D47—41no—
130C22×D47#9511yescharacteristic
131C22×D47#9511yescharacteristic
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47—41no—
135C2×C4×C47C2×C4211yescharacteristic
136C2×C4×C47C2×C22⋊C411yescharacteristic
137C2×C4×C47C2×C22⋊C411yescharacteristic
138C2×C4×C47C2×C22⋊C411yescharacteristic
139C2×C4×C47C2×C4⋊C411yescharacteristic
140C2×C4×C47C2×C4⋊C411yescharacteristic
141C2×Dic47—22no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C2×Dic47#9511yescharacteristic
145C2×Dic47#9511yescharacteristic
146C2×Dic47#9511yescharacteristic
147C2×Dic47#9511yescharacteristic
148C2×Dic47#9511yescharacteristic
149C2×Dic47#9511yescharacteristic
150C4×D47—22no—
151C4×D47—22no—
152C4×D47—22no—
153C4×D47—22no—
154C4×D47—41no—
155C4×D47—41no—
156C4×D47—41no—
157C4×D47—41no—
158C4×D47—41no—
159C4×D47—41no—
160C4×D47—41no—
161C4×D47—41no—
162C8×C47—42no—
163C8×C47—42no—
164C8×C47—42no—
165C47⋊C8—42no—
166C47⋊C8—42no—
167C47⋊C8—42no—
168#8085—471nomaximal, Sylow
169C22×C47—21no—
170C22×C47—21no—
171C22×C47C2×#9511yescharacteristic
172C22×C47#43012yes—
173C2×D47—21no—
174C2×D47—21no—
175C2×D47—21no—
176C2×D47—21no—
177C2×D47—21no—
178C2×D47—44no—
179C2×D47#34412yes—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47#42112yes—
186Dic47—21no—
187Dic47—21no—
188Dic47—21no—
189Dic47—21no—
190Dic47—21no—
191Dic47—21no—
192#2920—471no—
193C2×#432—471no—
194C2×#432—471no—
195#1302—471no—
196#1302—471no—
197#1302—471no—
198#1302D4711yescharacteristic, complemented
199C2×C47—22no—
200C2×C47#173311yescharacteristic
201C2×C47#173811yescharacteristic
202C2×C47C2×#34411yescharacteristic
203D47—22no—
204D47—41no—
205C22×C42—471no—
206#432—472no—
207#432—472no—
208#432—472no—
209#432—471no—
210#432—472no—
211#432—941no—
212#432—941no—
213#432—941no—
214#432—941no—
215#432—941no—
216#432C2×D4711yescharacteristic
217#431—471no—
218#431—941no—
219#431C2×D4711yescharacteristic
220#423—941no—
221C2×C4⋊C8—472no—
222C2×C4⋊C8—941no—
223#407—472no—
224C2×C22⋊C8—941no—
225C2×C22⋊C8—941no—
226C4×M16—941no—
227C2×#97—471no—
228C2×#97—941no—
229C2×#97C2×D4711yescharacteristic
230C47#808511yescharacteristic, complemented, Sylow
231C23×C4—471no—
232C23×C4—471no—
233C23×C4—471no—
234C2×M16—942no—
235C22×C8—21no—
236C22×C8—942no—
237C22×C8—941no—
238C2×C42—471no—
239C2×C42—471no—
240C2×C42—471no—
241C2×C42—471no—
242C2×C42—471no—
243C2×C42—471no—
244C2×C42—471no—
245C2×C42—471no—
246C2×C42—471no—
247C2×C42—471no—
248C2×C42—471no—
249C2×C42C22×D4711yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—472no—
252C4⋊C8—942no—
253C4⋊C8—942no—
254C4⋊C8—942no—
255C4⋊C8—942no—
256C4⋊C8—941no—
257C4⋊C8C4×D4712yes—
258C22⋊C8—21no—
259C22⋊C8—472no—
260C22⋊C8—942no—
261C22⋊C8—942no—
262C22⋊C8—942no—
263C22⋊C8—942no—
264C22⋊C8—941no—
265C22⋊C8C4×D4712yes—
266#97—21no—
267#97—21no—
268#97—472no—
269#97—942no—
270#97—942no—
271#97—941no—
272#97—941no—
273#97C4×D4712yes—
274C4×C8—21no—
275C4×C8—941no—
276C24—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—471no—
285C22×C4—471no—
286C22×C4—471no—
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—1882no—
293C22×C4—1882no—
294C22×C4—1882no—
295C22×C4C2×C4×D4711yescharacteristic
296C22×C4D4×D4711yescharacteristic
297C22×C4Q8×D4711yescharacteristic
298M16—1884no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—942no—
304C2×C8—942no—
305C2×C8—942no—
306C2×C8—1884no—
307C2×C8—1882no—
308C42—471no—
309C42—471no—
310C42—471no—
311C42—471no—
312C42—471no—
313C42—471no—
314C42—471no—
315C42—471no—
316C42—471no—
317C42—471no—
318C42—471no—
319C42—471no—
320C42C2×C4×D4711yescharacteristic
321C42C2×C4×D4711yescharacteristic
322C42D4×D4711yescharacteristic
323C42D4×D4711yescharacteristic
324C23—471no—
325C23—471no—
326C23—942no—
327C23—942no—
328C23—1881no—
329C23C4⋊C4×D4711yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—471no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—471no—
337C2×C4—471no—
338C2×C4—471no—
339C2×C4—942no—
340C2×C4—942no—
341C2×C4—942no—
342C2×C4—942no—
343C2×C4—942no—
344C2×C4—1881no—
345C2×C4—1881no—
346C2×C4—1881no—
347C2×C4—1881no—
348C2×C4—1881no—
349C2×C4—1881no—
350C2×C4—1881no—
351C2×C4—1881no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4C42×D4711yescharacteristic
355C2×C4C22⋊C4×D4711yescharacteristic
356C2×C4C22⋊C4×D4711yescharacteristic
357C2×C4C22⋊C4×D4711yescharacteristic
358C2×C4C4⋊C4×D4711yescharacteristic
359C2×C4C4⋊C4×D4711yescharacteristic
360C8—42no—
361C8—42no—
362C8—42no—
363C8—1882no—
364C8—1882no—
365C8—1882no—
366C22—21no—
367C22—21no—
368C22—472no—
369C22—941no—
370C22—941no—
371C22—941no—
372C22—941no—
373C22—941no—
374C22—1884no—
375C22#95×D4711yescharacteristic
376C22#1568917012yes—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—941no—
383C4—941no—
384C4—941no—
385C4—941no—
386C4—941no—
387C4—941no—
388C4#1568913812yes—
389C2—22no—
390C2—942no—
391C2—1881no—
392C2#2024309611yescharacteristic
393C2#2024311311yescharacteristic
394C2#344×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1302C2
socleC22×C47C2×#95
prime radicalC23×D47C4⋊C4
cosocleC2×C42×C47C23
hypercenter#1302D47
hypocenterC47#8085
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

Complements

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

NH ≅ G/Ntype
4. #20241288C2semidirect
5. #20241287C2semidirect
6. #20241286C2semidirect
7. C47×#1302C2semidirect
198. #1302D47semidirect
230. C47#8085semidirect

Maximal subgroups

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

subgroupindex
#202520162
C2×#156891782
#432×D472
#202412882
#202412872
#202412862
C47×#13022
#808547