Finite Group Databasebeta

← #26233983

Subgroups — #26233983

Order 12032.

810 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
1C2×#107×D47C211yesmaximal, characteristic
2#20246264C212yesmaximal
3#20244127C211yesmaximal, characteristic, complemented
4#20243962C212yesmaximal, complemented
5#20243956C212yesmaximal, complemented
6#20243477C212yesmaximal
7#20243410C211yesmaximal, characteristic
8#20243288C211yesmaximal, characteristic, complemented
9#20243285C211yesmaximal, characteristic, complemented
10#20243165C211yesmaximal, characteristic
11C47×#1943C211yesmaximal, characteristic, complemented
12C22×C8×D47C2211yescharacteristic
13C2×C4⋊C4×D47C2212yes—
14C2×#13093958C2211yescharacteristic
15C2×#13093957C2212yes—
16#107×D47C418yescomplemented
17C2×#13093956C2211yescharacteristic
18C2×(C2×D47)⋊C8C2211yescharacteristic
19C2×#13093934C2211yescharacteristic
20#15689022C2212yes—
21#15689010—22no—
22#15689004—22no—
23#15688980—22no—
24#15688980C2212yes—
25C4⋊C4×Dic47C2212yes—
26C4×C4⋊Dic47C2212yes—
27C4×(C2×D47)⋊C4C2211yescharacteristic
28#15688970—22no—
29#15688886C2212yes—
30#15688885C2212yes—
31#15688885C2212yes—
32#15688885C2212yes—
33#15688878C2211yescharacteristic
34#15688877C2211yescharacteristic
35C2×#107×C47C2211yescharacteristic
36C2×#106×C47C2211yescharacteristic
37C2×#97×C47C2211yescharacteristic
38C47×#389C2212yes—
39C47×#340C2212yes—
40C22×C4×D47—22no—
41C22×C4×D47C2311yescharacteristic
42C22×C47⋊C8C2311yescharacteristic
43C22×C47⋊C8C2311yescharacteristic
44C2×C8×D47—22no—
45C2×C8×D47—22no—
46C2×C8×D47C2×C414yes—
47C2×C4⋊Dic47—22no—
48C2×C4⋊Dic47C2312yes—
49C2×C4⋊Dic47C2312yes—
50C2×Dic47⋊C4—22no—
51C4⋊C4×D47—24no—
52C4⋊C4×D47C2×C418yes—
53C2×(C2×D47)⋊C4—22no—
54C2×(C2×D47)⋊C4D412yes—
55C2×C4×Dic47—22no—
56C2×C4×Dic47—22no—
57C2×C4×Dic47C2311yescharacteristic
58#13093958C2×C414yes—
59#13093957C2×C418yes—
60#13093956—22no—
61(C2×D47)⋊C8—22no—
62#13093934—22no—
63C47⋊#95—22no—
64C47⋊#95—22no—
65C47⋊#95—22no—
66C47⋊#95—22no—
67C47⋊#95D412yes—
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C2×C4⋊C4×C47—22no—
71C2×C4⋊C4×C47C2312yes—
72C2×C4⋊C4×C47C2312yes—
73C2×C42×C47C2311yescharacteristic
74#107×C47C2×C414yes—
75#106×C47—22no—
76#97×C47—22no—
77#95×C47—22no—
78C23×D47C2×D411yescharacteristic
79C22×C4×C47—22no—
80C22×C4×C47—22no—
81C22×C4×C47C2×D412yes—
82C22×C4×C47C2411yescharacteristic
83C22×Dic47—22no—
84C22×Dic47—22no—
85C22×Dic47C2×D412yes—
86C22×Dic47C2×D411yescharacteristic
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47—21no—
90C2×C4×D47—21no—
91C2×C4×D47—28no—
92C2×C4×D47—82no—
93C2×C4×D47—82no—
94C2×C4×D47C22×C412yes—
95C2×C4×D47#4112yes—
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47C22×C412yes—
100C2×C8×C47#4112yes—
101C2×C8×C47#4112yes—
102C4⋊C4×C47—22no—
103C4⋊C4×C47—22no—
104C4⋊C4×C47—22no—
105C4⋊C4×C47—82no—
106C4⋊C4×C47C22×C414yes—
107C42×C47—21no—
108C42×C47—21no—
109(C2×D47)⋊C4—24no—
110(C2×D47)⋊C4—44no—
111C4⋊Dic47—22no—
112C4⋊Dic47—22no—
113C4⋊Dic47—22no—
114C4⋊Dic47—82no—
115C4⋊Dic47C22×C414yes—
116Dic47⋊C4—28no—
117C4×Dic47—21no—
118C4×Dic47—21no—
119C4×Dic47—82no—
120C4×Dic47—82no—
121C2×C47⋊C8—21no—
122C2×C47⋊C8—21no—
123C2×C47⋊C8—21no—
124C2×C47⋊C8—21no—
125C2×C47⋊C8—21no—
126C2×C47⋊C8C22×C412yes—
127C8×D47—28no—
128C23×C47C22×D411yescharacteristic
129C22×D47—21no—
130C22×D47—21no—
131C22×D47—22no—
132C22×D47C4×D412yes—
133C22×D47#13714yes—
134C2×C4×C47—24no—
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—42no—
139C2×C4×C47—42no—
140C2×C4×C47—42no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47C23×C411yescharacteristic
144C2×C4×C47C2×#4111yescharacteristic
145C2×C4×C47C2×#4111yescharacteristic
146C2×C4×C47C2×#4111yescharacteristic
147C2×C4×C472−1+411yescharacteristic
148C2×C4×C472−1+411yescharacteristic
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—24no—
152C2×Dic47—22no—
153C2×Dic47—22no—
154C2×Dic47—22no—
155C2×Dic47—42no—
156C2×Dic47—42no—
157C2×Dic47—42no—
158C2×Dic47—42no—
159C2×Dic47—42no—
160C2×Dic47C4×D412yes—
161C4×D47—22no—
162C4×D47—22no—
163C4×D47—22no—
164C4×D47—22no—
165C4×D47—88no—
166C8×C47—41no—
167C8×C47#11714yes—
168C47⋊C8—22no—
169C47⋊C8—41no—
170#22618—471nomaximal, Sylow
171C22×C47C2×C4×D411yescharacteristic
172C22×C47#54711yescharacteristic
173C22×C47#54711yescharacteristic
174C22×C47C2×#13712yes—
175C22×C47#57612yes—
176C2×D47—24no—
177C2×D47—24no—
178C2×D47—22no—
179C2×D47—22no—
180C2×D47#44114yes—
181C4×C47—42no—
182C4×C47—44no—
183C4×C47—82no—
184C4×C47C2×#11711yescharacteristic
185C4×C47#51911yescharacteristic
186C4×C47#55211yescharacteristic
187C4×C47#55211yescharacteristic
188Dic47—22no—
189Dic47—42no—
190Dic47—44no—
191Dic47—82no—
192C22×#107—471no—
193#2345—472no—
194#1943—471no—
195#1943D4711yescharacteristic, complemented
196#1918—472no—
197#1918—472no—
198#1824—472no—
199#1807—471no—
200#1776—471no—
201#1776—471no—
202#1752—471no—
203C2×C47#234411yescharacteristic
204C2×C47C2×#44111yescharacteristic
205C2×C47#294811yescharacteristic
206C2×C47#334612yes—
207C2×C47#334612yes—
208D47—24no—
209C23×C8—471no—
210C22×C4⋊C4—472no—
211C2×#107—471no—
212C2×#107—472no—
213C2×#107—478no—
214C2×#107C2×D4711yescharacteristic
215C2×#106—471no—
216C2×#106C2×D4711yescharacteristic
217C2×C22⋊C8—471no—
218C2×#97—471no—
219C2×#97C2×D4711yescharacteristic
220#389—472no—
221#389C2×D4712yes—
222#387—942no—
223#387—942no—
224#380—472no—
225#380—942no—
226C4×C4⋊C4—472no—
227C4×C4⋊C4—472no—
228C4×C22⋊C4—471no—
229C4×C22⋊C4—942no—
230#340—472no—
231#340—472no—
232#340—472no—
233#340—472no—
234#340C2×D4712yes—
235#336—471no—
236#336—471no—
237C47#2261811yescharacteristic, complemented, Sylow
238C23×C4—471no—
239C23×C4—942no—
240C22×C8—471no—
241C22×C8—474no—
242C22×C8—471no—
243C22×C8—942no—
244C22×C8—942no—
245C22×C8C22×D4711yescharacteristic
246C22×C8C22×D4711yescharacteristic
247C2×C4⋊C4—22no—
248C2×C4⋊C4—472no—
249C2×C4⋊C4—478no—
250C2×C4⋊C4—472no—
251C2×C4⋊C4—944no—
252C2×C4⋊C4—942no—
253C2×C4⋊C4—942no—
254C2×C4⋊C4C22×D4712yes—
255C2×C4⋊C4C22×D4712yes—
256C2×C22⋊C4—472no—
257C2×C22⋊C4—942no—
258C2×C42—471no—
259C2×C42—942no—
260C2×C42—942no—
261C2×C42C22×D4711yescharacteristic
262#107—474no—
263#107—478no—
264#107C4×D4714yes—
265#106—22no—
266#106—942no—
267C22⋊C8—942no—
268#97—22no—
269#97—942no—
270#95—22no—
271#95—472no—
272#95—942no—
273#95—942no—
274#95—942no—
275#95—942no—
276C24—471no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—471no—
280C22×C4—472no—
281C22×C4—472no—
282C22×C4—472no—
283C22×C4—948no—
284C22×C4—941no—
285C22×C4—941no—
286C22×C4—941no—
287C22×C4—941no—
288C22×C4—942no—
289C22×C4—942no—
290C22×C4—3762no—
291C22×C4—3762no—
292C22×C4D4×D4712yes—
293C22×C4C23×D4711yescharacteristic
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—472no—
298C2×C8—941no—
299C2×C8—941no—
300C2×C8—948no—
301C2×C8—941no—
302C2×C8—941no—
303C2×C8—941no—
304C2×C8C2×C4×D4712yes—
305C2×C8#1062535212yes—
306C2×C8#1062535412yes—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—82no—
311C4⋊C4—474no—
312C4⋊C4—948no—
313C4⋊C4—942no—
314C4⋊C4—942no—
315C4⋊C4—942no—
316C4⋊C4—3762no—
317C4⋊C4C2×C4×D4714yes—
318C22⋊C4—944no—
319C22⋊C4—1884no—
320C42—21no—
321C42—21no—
322C42—941no—
323C42—941no—
324C42—3762no—
325C42—3762no—
326C23—472no—
327C23—474no—
328C23—941no—
329C23—941no—
330C23—942no—
331C23C2×D4×D4711yescharacteristic
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—472no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—942no—
345C2×C4—942no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4—942no—
349C2×C4—944no—
350C2×C4—942no—
351C2×C4—942no—
352C2×C4—3768no—
353C2×C4—1882no—
354C2×C4—1882no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4—1882no—
358C2×C4C22×C4×D4711yescharacteristic
359C2×C4#41×D4711yescharacteristic
360C2×C4C2×#1062535211yescharacteristic
361C2×C4C2×#1062535411yescharacteristic
362C2×C4#1309407111yescharacteristic
363C2×C4#1309407211yescharacteristic
364C8—41no—
365C8—942no—
366C8—1881no—
367C8#1309398214yes—
368C22—474no—
369C22—942no—
370C22—944no—
371C22—944no—
372C22—942no—
373C22C4×D4×D4711yescharacteristic
374C22#1568977311yescharacteristic
375C22#1568977611yescharacteristic
376C22#137×D4712yes—
377C22#1568992712yes—
378C4—44no—
379C4—42no—
380C4—82no—
381C4—942no—
382C4—3762no—
383C4—1884no—
384C4—1882no—
385C4C2×#1309398211yescharacteristic
386C4#1568959911yescharacteristic
387C4#1568980711yescharacteristic
388C4#1568981111yescharacteristic
389C2—944no—
390C2#2024625611yescharacteristic
391C2#441×D4711yescharacteristic
392C2#2025223711yescharacteristic
393C2#2025586812yes—
394C2#2025587212yes—
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1943C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1943D47
hypocenterC47#22618
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
3. #20244127C2semidirect
4. #20243962C2semidirect
5. #20243956C2semidirect
8. #20243288C2semidirect
9. #20243285C2semidirect
11. C47×#1943C2semidirect
16. #107×D47C4semidirect
195. #1943D47semidirect
237. C47#22618semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
#202462642
#202441272
#202439622
#202439562
#202434772
#202434102
#202432882
#202432852
#202431652
C47×#19432
#2261847