Finite Group Databasebeta

← #26369620

Subgroups — #26369620

Order 12032.

696 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689559C211yesmaximal, characteristic
2#20252265C211yesmaximal, characteristic, complemented
3#20245262C212yesmaximal, complemented
4#20245252C212yesmaximal, complemented
5C4×#13093968C212yesmaximal, complemented
6C4×#13093965C212yesmaximal, complemented
7#20245177C211yesmaximal, characteristic, complemented
8#20245093C211yesmaximal, characteristic, complemented
9C2×#15688924C211yesmaximal, characteristic, complemented
10#20244985C211yesmaximal, characteristic, complemented
11C47×#2948C211yesmaximal, characteristic, complemented
12C2×#13094046C2211yescharacteristic
13#15689603—21no—
14#15689559C418yescomplemented
15C2×#13093968C2212yes—
16C2×#13093965C2212yes—
17C2×#13093964C2211yescharacteristic
18C22×C47⋊C16C2211yescharacteristic
19#15689225—22no—
20C4×Dic188C2212yescomplemented
21C4×D376C2212yescomplemented
22C2×#13093958C2211yescharacteristic
23#15689125—21no—
24#15688950C2212yescomplemented
25#15688948C2212yescomplemented
26#15688926C2211yescharacteristic, complemented
27#15688926C2211yescharacteristic, complemented
28#15688924C2212yes—
29#15688924C2212yes—
30#15688923C2211yescharacteristic, complemented
31#15688923C2211yescharacteristic, complemented
32#15688899C2212yescomplemented
33C4×C47⋊C16C2212yescomplemented
34C22×D8×C47C2211yescharacteristic
35C47×#518—21no—
36C47×#442—22no—
37C4×D8×C47C2212yes—
38C4×D8×C47C2212yes—
39C47×#427C2211yescharacteristic
40C47×#418—21no—
41C47×#405C2211yescharacteristic
42C2×#10625350—21no—
43#13094046—22no—
44#13094046C2×C414yescomplemented
45C2×Dic188C2311yescharacteristic
46C2×#10625325—21no—
47C2×D376C2311yescharacteristic
48C4×Dic94—22no—
49C4×D188—22no—
50(C22⋊D47)⋊C4—42no—
51#13093982—41no—
52C2×C4⋊Dic47—21no—
53C4⋊C4×D47—41no—
54#13093968C2×C418yescomplemented
55#13093965C2×C418yescomplemented
56#13093964C2×C414yescomplemented
57C2×C47⋊C16—22no—
58C2×C47⋊C16C2311yescharacteristic
59C2×C47⋊C16C2311yescharacteristic
60C2×C47⋊C16C2312yes—
61#13093958—21no—
62#13093958C2312yes—
63#13093949—22no—
64#13093946—22no—
65C22×D4×C47—21no—
66C2×D8×C47—21no—
67C2×D8×C47—22no—
68C2×D8×C47C2×C414yescomplemented
69C2×D8×C47C2312yes—
70C2×M16×C47D411yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C4×D4×C47—22no—
73C4×D4×C47—22no—
74C4×D4×C47—41no—
75C4×D4×C47—41no—
76#117×C47—21no—
77#117×C47D411yescharacteristic
78C2×C22⋊C4×C47—42no—
79#107×C47C2311yescharacteristic
80#107×C47C2311yescharacteristic
81#106×C47—21no—
82#102×C47—22no—
83#102×C47—22no—
84#97×C47D412yes—
85C4×C8×C47C2312yes—
86C24×C47—41no—
87C2×D4×C47—24no—
88C2×D4×C47—22no—
89C2×D4×C47—41no—
90C2×D4×C47—42no—
91C22×C4×C47—42no—
92C22×C4×C47—42no—
93C22×C4×C47C2×D411yescharacteristic
94C2×C22⋊D47—41no—
95C22×Dic47—41no—
96#10625350—24no—
97#10625350—42no—
98C2×D188—21no—
99C2×C4×D47—41no—
100C2×C4×D47—42no—
101C2×Dic94—21no—
102D8×C47—24no—
103D8×C47—22no—
104D8×C47C22×C414yes—
105M16×C47—22no—
106C2×C8×C47C22×C412yes—
107C2×C8×C47C2×D412yes—
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47#4112yes—
110C2×C8×C47C2411yescharacteristic
111C4⋊C4×C47—21no—
112C4⋊C4×C47—21no—
113C4⋊C4×C47D811yescharacteristic
114C4⋊C4×C47D811yescharacteristic
115C22⋊C4×C47—41no—
116C22⋊C4×C47—42no—
117C22⋊C4×C47—42no—
118C22⋊C4×C47D812yes—
119C42×C47—41no—
120C42×C47C2×D412yes—
121(C2×D47)⋊C4—42no—
122C4⋊Dic47—22no—
123C4⋊Dic47—41no—
124Dic47⋊C4—42no—
125C4×Dic47—42no—
126Dic188—21no—
127Dic188C22×C412yes—
128D376—21no—
129D376C22×C412yes—
130#10625325—24no—
131C47⋊C16—21no—
132C47⋊C16—21no—
133C47⋊C16C22×C414yes—
134C23×C47—42no—
135C23×C47—44no—
136C23×C47—161no—
137C23×C47—161no—
138C23×C47C2×D811yescharacteristic
139C22×D47—41no—
140D4×C47—24no—
141D4×C47—42no—
142D4×C47—44no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—162no—
146C2×C4×C47—162no—
147C2×C4×C47C4×D412yes—
148C2×C4×C47C2×D812yes—
149C2×C4×C47C2×D812yes—
150C2×C4×C47C2×D811yescharacteristic
151C2×C4×C47#13512yes—
152C2×C4×C47C22×D411yescharacteristic
153C22⋊D47—44no—
154C2×Dic47—41no—
155C2×Dic47—42no—
156C2×Dic47—161no—
157D188—22no—
158D188—41no—
159C4×D47—44no—
160C4×D47—162no—
161Dic94—22no—
162Dic94—41no—
163C8×C47—22no—
164C8×C47C4×D412yes—
165C8×C47C23×C411yescharacteristic
166C8×C47C2×#4111yescharacteristic
167#33454—471nomaximal, Sylow
168C22×C47—21no—
169C22×C47—21no—
170C22×C47—44no—
171C22×C47—82no—
172C22×C47—82no—
173C22×C47—164no—
174C22×C47C4×D812yes—
175C22×C47C22×D811yescharacteristic
176C2×D47—42no—
177C2×D47—81no—
178C2×D47—81no—
179C4×C47—22no—
180C4×C47—22no—
181C4×C47—81no—
182C4×C47—81no—
183C4×C47C4×D812yes—
184C4×C47C2×C4×D411yescharacteristic
185C4×C47C2×#13511yescharacteristic
186Dic47—42no—
187Dic47—82no—
188C2×#509—471no—
189#2951—471no—
190#2948D4711yescharacteristic, complemented
191#2177—472no—
192#2175—472no—
193C4×SD32—472no—
194C4×D16—472no—
195#2159—471no—
196#2138—471no—
197C2×#357—471no—
198#2108—471no—
199C2×C47—22no—
200C2×C47—84no—
201C2×C47C2×C4×D811yescharacteristic
202C2×C47#341511yescharacteristic
203C2×C47#341611yescharacteristic
204D47—82no—
205C2×#135—471no—
206C22×D8C2×D4711yescharacteristic
207#520—941no—
208#518—21no—
209#509—478no—
210C2×SD32—472no—
211C2×D16—472no—
212C2×M32—471no—
213C22×C16—471no—
214#442—22no—
215#440—942no—
216C4×Q16—472no—
217C4×D8—472no—
218C4×D8C2×D4712yes—
219C4×D8C2×D4712yes—
220#427C2×D4711yescharacteristic
221C2×#107—471no—
222#418—21no—
223#417—941no—
224#405C2×D4711yescharacteristic
225#367—472no—
226#366—472no—
227#358—471no—
228#358—471no—
229#357—472no—
230#357—472no—
231#357—471no—
232#357—471no—
233#346—472no—
234C4×C16—472no—
235C47#3345411yescharacteristic, complemented, Sylow
236C2×#41—941no—
237C22×D4—21no—
238#135—474no—
239#135—942no—
240C2×Q16—471no—
241C2×SD16—941no—
242C2×D8—22no—
243C2×D8—21no—
244C2×D8—471no—
245C2×D8C4×D4714yescomplemented
246C2×D8C22×D4712yes—
247C2×M16C22⋊D4711yescharacteristic
248C22×C8C22×D4711yescharacteristic
249C4×Q8—942no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4—41no—
253C4×D4—41no—
254C4×D4—942no—
255C4×D4—1882no—
256#117—21no—
257#117—1881no—
258#117C22⋊D4711yescharacteristic
259C2×C4⋊C4—941no—
260C2×C4⋊C4—1881no—
261C2×C22⋊C4—42no—
262SD32—478no—
263D16—478no—
264M32—474no—
265C2×C16—472no—
266C2×C16—471no—
267C2×C16—471no—
268C2×C16—942no—
269#107—472no—
270#107—941no—
271#107C22×D4711yescharacteristic
272#107C22×D4711yescharacteristic
273#106—21no—
274#103—942no—
275#102—22no—
276#102—22no—
277#102—942no—
278#97C22⋊D4712yes—
279C4×C8C22×D4712yes—
280C24—41no—
281#41—944no—
282#41—1882no—
283C2×Q8—941no—
284C2×D4—24no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—42no—
288C2×D4—941no—
289C2×D4—1881no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—1881no—
293C22×C4—1881no—
294C22×C4—1882no—
295C22×C4C2×C22⋊D4711yescharacteristic
296Q16—472no—
297Q16—941no—
298SD16—944no—
299D8—24no—
300D8—22no—
301D8—472no—
302D8—941no—
303D8C2×C4×D4714yes—
304M16—22no—
305C2×C8C2×C4×D4712yes—
306C2×C8#1062535012yes—
307C2×C8C2×C22⋊D4712yes—
308C2×C8C2×C22⋊D4711yescharacteristic
309C2×C8C23×D4711yescharacteristic
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—942no—
313C4⋊C4—1882no—
314C4⋊C4—1881no—
315C4⋊C4#1062533411yescharacteristic
316C4⋊C4#1062533411yescharacteristic
317C22⋊C4—41no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—1882no—
321C22⋊C4#1062533412yes—
322C42—41no—
323C42—1882no—
324C42C2×C22⋊D4712yes—
325C16—474no—
326C16—941no—
327C16—941no—
328C23—42no—
329C23—44no—
330C23—161no—
331C23—161no—
332C23—1881no—
333C23C2×#1062533411yescharacteristic
334Q8—942no—
335Q8—1881no—
336D4—24no—
337D4—42no—
338D4—44no—
339D4—942no—
340D4—1884no—
341D4—1881no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—162no—
345C2×C4—162no—
346C2×C4—1882no—
347C2×C4—1881no—
348C2×C4—1884no—
349C2×C4—7522no—
350C2×C4—7521no—
351C2×C4C4×C22⋊D4712yes—
352C2×C4C2×#1062533412yes—
353C2×C4C2×#1062533412yes—
354C2×C4C2×#1062533411yescharacteristic
355C2×C4#1309404412yes—
356C2×C4C22×C22⋊D4711yescharacteristic
357C8—22no—
358C8C4×C22⋊D4712yes—
359C8C22×C4×D4711yescharacteristic
360C8C2×#1062535011yescharacteristic
361C22—21no—
362C22—21no—
363C22—44no—
364C22—82no—
365C22—82no—
366C22—164no—
367C22—3761no—
368C22—3761no—
369C22—1882no—
370C22C4×#1062533412yes—
371C22C22×#1062533411yescharacteristic
372C4—22no—
373C4—22no—
374C4—81no—
375C4—81no—
376C4—3762no—
377C4—1882no—
378C4C4×#1062533412yes—
379C4C2×C4×C22⋊D4711yescharacteristic
380C4C2×#1309404411yescharacteristic
381C2—22no—
382C2—84no—
383C2—3762no—
384C2C2×C4×#1062533411yescharacteristic
385C2#2025652711yescharacteristic
386C2#2025653511yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2948C2
socleC22×C47C22×D8
prime radicalC2×#15689559C2
cosocleC2×C8×C47C24
hypercenter#2948D47
hypocenterC47#33454
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
2. #20252265C2semidirect
3. #20245262C2semidirect
4. #20245252C2semidirect
5. C4×#13093968C2semidirect
6. C4×#13093965C2semidirect
7. #20245177C2semidirect
8. #20245093C2semidirect
9. C2×#15688924C2semidirect
10. #20244985C2semidirect
11. C47×#2948C2semidirect
14. #15689559C4semidirect
20. C4×Dic188C22semidirect
21. C4×D376C22semidirect
24. #15688950C22semidirect
25. #15688948C22semidirect
26. #15688926C22semidirect
27. #15688926C22semidirect
30. #15688923C22semidirect
31. #15688923C22semidirect
32. #15688899C22semidirect
33. C4×C47⋊C16C22semidirect
44. #13094046C2×C4semidirect
54. #13093968C2×C4semidirect
55. #13093965C2×C4semidirect
56. #13093964C2×C4semidirect
68. C2×D8×C47C2×C4semidirect
190. #2948D47semidirect
235. C47#33454semidirect
245. C2×D8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156895592
#202522652
#202452622
#202452522
C4×#130939682
C4×#130939652
#202451772
#202450932
C2×#156889242
#202449852
C47×#29482
#3345447