Finite Group Databasebeta

← #26370545

Subgroups — #26370545

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689553C212yesmaximal, complemented
2#20253816C211yesmaximal, characteristic, complemented
3#20245450C212yesmaximal, complemented
4#20245443C212yesmaximal, complemented
5#20245438C211yesmaximal, characteristic, complemented
6#20245433C211yesmaximal, characteristic, complemented
7#20245428C211yesmaximal, characteristic, complemented
8#20245423C211yesmaximal, characteristic, complemented
9C2×C4⋊(C47⋊C16)C211yesmaximal, characteristic, complemented
10#20245093C212yesmaximal, complemented
11C4×#135×C47C211yesmaximal, characteristic, complemented
12C2×#13094046—21no—
13C2×#13094046C2212yes—
14#15689673—21no—
15#15689553—28no—
16C2×#13093970C2212yes—
17C2×#13093968C2212yes—
18C2×#13093967C2212yes—
19C2×#13093965C2212yes—
20C22×C47⋊C16C2212yes—
21#15689507—21no—
22#15689507C2212yes—
23#15689503C2211yescharacteristic
24#15689500C2211yescharacteristic
25#15689496—21no—
26C4⋊(C47⋊C16)C2211yescharacteristic
27C4⋊(C47⋊C16)C2211yescharacteristic
28C4⋊(C47⋊C16)C2212yes—
29#15688926C2212yes—
30#15688926C2212yes—
31#15688923C2212yes—
32#15688923C2212yes—
33C2×#135×C47C2211yescharacteristic
34C4×#41×C47—21no—
35C4×Q16×C47C2211yescharacteristic
36C4×Q16×C47C2211yescharacteristic
37C4×SD16×C47—21no—
38C4×SD16×C47—21no—
39C4×D8×C47C2211yescharacteristic
40C4×D8×C47C2211yescharacteristic
41C47×#427C2211yescharacteristic
42C47×#416—21no—
43C2×C4×C8×C47C2211yescharacteristic
44C2×#10625350—22no—
45#13094046—24no—
46#13094046—24no—
47#13094046—44no—
48C2×Dic188—21no—
49C2×Dic188C2312yes—
50C2×#10625325—22no—
51C2×#10625325—22no—
52C2×D376—21no—
53C2×D376C2312yes—
54#13094024—21no—
55#13094021—21no—
56#13094012—22no—
57#13093998—41no—
58#13093998—41no—
59C4×D188—41no—
60C4×D188—41no—
61#13093970—24no—
62#13093968—24no—
63#13093967—24no—
64#13093965—24no—
65C2×C47⋊C16—24no—
66C2×C47⋊C16C2312yes—
67C2×C47⋊C16C2312yes—
68C2×#41×C47—21no—
69#135×C47—22no—
70#135×C47D414yescomplemented
71C2×Q16×C47C2311yescharacteristic
72C2×SD16×C47—21no—
73C2×D8×C47C2311yescharacteristic
74C22×C8×C47D411yescharacteristic
75C22×C8×C47C2311yescharacteristic
76C4×Q8×C47—21no—
77C4×Q8×C47—21no—
78C4×D4×C47—21no—
79C4×D4×C47—21no—
80C4×D4×C47—41no—
81C4×D4×C47—41no—
82#117×C47—21no—
83#117×C47—41no—
84C2×C42×C47—41no—
85C2×C42×C47D411yescharacteristic
86#107×C47C2311yescharacteristic
87#107×C47C2311yescharacteristic
88#106×C47—21no—
89#103×C47—21no—
90#103×C47—21no—
91#102×C47—21no—
92#102×C47—21no—
93C4×C8×C47D411yescharacteristic
94C4×C8×C47D411yescharacteristic
95C4×C8×C47C2311yescharacteristic
96C4×C8×C47C2311yescharacteristic
97#41×C47—24no—
98#41×C47—42no—
99C2×Q8×C47—21no—
100C2×D4×C47—21no—
101C2×D4×C47—41no—
102C22×C4×C47—41no—
103C22×C4×C47—41no—
104C22×C4×C47—41no—
105C22×C4×C47D811yescharacteristic
106C22×C4×C47D811yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C2×C22⋊D47—42no—
109#10625350—44no—
110#10625350—44no—
111C2×D188—22no—
112C2×D188—41no—
113C2×D188—41no—
114C2×C4×D47—42no—
115C2×Dic94—22no—
116Q16×C47—21no—
117Q16×C47C2×D412yes—
118SD16×C47—24no—
119D8×C47—21no—
120D8×C47C2×D412yes—
121C2×C8×C47—22no—
122C2×C8×C47C2×D411yescharacteristic
123C2×C8×C47C2×D411yescharacteristic
124C2×C8×C47C2×D411yescharacteristic
125C2×C8×C47C2×D412yes—
126C2×C8×C47#4112yes—
127C2×C8×C47C2411yescharacteristic
128C4⋊C4×C47—21no—
129C4⋊C4×C47—21no—
130C4⋊C4×C47—41no—
131C4⋊C4×C47—41no—
132C22⋊C4×C47—41no—
133C22⋊C4×C47—41no—
134C22⋊C4×C47—41no—
135C42×C47—41no—
136C42×C47—41no—
137C42×C47—41no—
138C42×C47D811yescharacteristic
139C42×C47D811yescharacteristic
140C42×C47C2×D411yescharacteristic
141C42×C47C2×D411yescharacteristic
142(C2×D47)⋊C4—42no—
143(C2×D47)⋊C4—42no—
144C4⋊Dic47—41no—
145C4⋊Dic47—41no—
146Dic188—22no—
147Dic188—22no—
148Dic188—42no—
149D376—22no—
150D376—22no—
151D376—42no—
152#10625325—44no—
153#10625325—44no—
154C47⋊C16—22no—
155C47⋊C16—22no—
156C23×C47—41no—
157C23×C47C2×D811yescharacteristic
158C22×D47—42no—
159Q8×C47—22no—
160Q8×C47—41no—
161D4×C47—22no—
162D4×C47—44no—
163D4×C47—41no—
164C2×C4×C47—22no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47—44no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—82no—
171C2×C4×C47—82no—
172C2×C4×C47#12112yes—
173C2×C4×C47C2×D811yescharacteristic
174C2×C4×C47C2×D811yescharacteristic
175C2×C4×C47C2×D811yescharacteristic
176C2×C4×C47C2×D811yescharacteristic
177C2×C4×C47C2×D811yescharacteristic
178C2×C4×C47AGL(1,ℤ/8)12yes—
179C2×C4×C47C22×D411yescharacteristic
180C22⋊D47—84no—
181C2×Dic47—42no—
182D188—42no—
183D188—42no—
184D188—82no—
185D188—82no—
186C4×D47—84no—
187Dic94—42no—
188Dic94—42no—
189C8×C47—21no—
190C8×C47—21no—
191C8×C47#12112yes—
192C8×C47C22×D411yescharacteristic
193C8×C47C2×#4111yescharacteristic
194#33579—471nomaximal, Sylow
195C22×C47—21no—
196C22×C47—21no—
197C22×C47—42no—
198C22×C47—81no—
199C22×C47—81no—
200C22×C47#45912yes—
201C22×C47C22×D811yescharacteristic
202C2×D47—82no—
203C2×D47—82no—
204C2×D47—82no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—42no—
209C4×C47—81no—
210C4×C47—81no—
211C4×C47#45912yes—
212C4×C47#50812yescomplemented
213C4×C47C2×#12111yescharacteristic
214C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
215Dic47—82no—
216C2×#508—472no—
217#3147—471no—
218C4×#135D4711yescharacteristic, complemented
219#2211—472no—
220#2210—472no—
221#2209—471no—
222#2208—471no—
223#2207—471no—
224#2206—471no—
225C2×C4⋊C16—471no—
226#2138—472no—
227C2×C47—22no—
228C2×C47—82no—
229C2×C47C2×#45911yescharacteristic
230C2×C47C2×#50811yescharacteristic
231C2×C47#341411yescharacteristic
232D47—162no—
233C2×#135—472no—
234C2×#135—941no—
235C2×#135C2×D4711yescharacteristic
236#532—941no—
237C4×#41—21no—
238#508—948no—
239C2×Q32—472no—
240C2×SD32—472no—
241C2×SD32—472no—
242C2×D16—472no—
243C22×C16—472no—
244#495—472no—
245#495—941no—
246#494—471no—
247#493—471no—
248#492—941no—
249C4×Q16C2×D4711yescharacteristic
250C4×Q16C2×D4711yescharacteristic
251C4×SD16—21no—
252C4×SD16—21no—
253C4×D8C2×D4711yescharacteristic
254C4×D8C2×D4711yescharacteristic
255#427C2×D4711yescharacteristic
256#416—21no—
257C2×C4×C8C2×D4711yescharacteristic
258C4⋊C16—471no—
259C4⋊C16—471no—
260C4⋊C16—472no—
261#358—472no—
262#358—472no—
263#357—472no—
264#357—472no—
265C47#3357911yescharacteristic, complemented, Sylow
266C2×#41—21no—
267C2×#41—942no—
268#135—22no—
269#135—944no—
270#135—944no—
271#135—1884no—
272#135D18814yescomplemented
273C2×Q16—472no—
274C2×Q16—941no—
275C2×Q16C22×D4711yescharacteristic
276C2×SD16—21no—
277C2×SD16—942no—
278C2×SD16—942no—
279C2×D8—472no—
280C2×D8—941no—
281C2×D8C22×D4711yescharacteristic
282C22×C8C22⋊D4711yescharacteristic
283C22×C8C22×D4711yescharacteristic
284C4⋊Q8—941no—
285#127—941no—
286#124—942no—
287#121—1881no—
288#121—1881no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—41no—
294C4×D4—41no—
295C4×D4—1881no—
296C4×D4—1881no—
297#117—21no—
298#117—41no—
299C2×C42—41no—
300C2×C42C22⋊D4711yescharacteristic
301Q32—944no—
302SD32—944no—
303SD32—944no—
304D16—944no—
305C2×C16—472no—
306C2×C16—472no—
307C2×C16—944no—
308#107C22×D4711yescharacteristic
309#107C22×D4711yescharacteristic
310#106—21no—
311#103—21no—
312#103—21no—
313#102—21no—
314#102—21no—
315C4×C8C22⋊D4711yescharacteristic
316C4×C8C22⋊D4711yescharacteristic
317C4×C8C22×D4711yescharacteristic
318C4×C8C22×D4711yescharacteristic
319#41—24no—
320#41—42no—
321#41—1884no—
322#41—1884no—
323C2×Q8—21no—
324C2×Q8—942no—
325C2×D4—21no—
326C2×D4—41no—
327C2×D4—942no—
328C2×D4—1882no—
329C2×D4—1881no—
330C2×D4—1881no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—1882no—
335C22×C4#1062533411yescharacteristic
336C22×C4#1062533411yescharacteristic
337C22×C4C2×C22⋊D4711yescharacteristic
338Q16—21no—
339Q16—942no—
340Q16—942no—
341Q16—1882no—
342Q16C2×D18812yes—
343SD16—24no—
344SD16—1884no—
345SD16—1884no—
346D8—21no—
347D8—942no—
348D8—942no—
349D8—1882no—
350D8C2×D18812yes—
351C2×C8—22no—
352C2×C8C2×D18812yes—
353C2×C8#1062535012yes—
354C2×C8C2×C22⋊D4711yescharacteristic
355C2×C8C2×C22⋊D4711yescharacteristic
356C2×C8C2×C22⋊D4711yescharacteristic
357C2×C8C23×D4711yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—1881no—
363C4⋊C4—1881no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—1882no—
368C22⋊C4—1882no—
369C42—41no—
370C42—41no—
371C42—41no—
372C42#1062533411yescharacteristic
373C42#1062533411yescharacteristic
374C42C2×C22⋊D4711yescharacteristic
375C42C2×C22⋊D4711yescharacteristic
376C16—942no—
377C16—942no—
378C23—41no—
379C23—1882no—
380C23C2×#1062533411yescharacteristic
381Q8—22no—
382Q8—41no—
383Q8—1882no—
384Q8—1882no—
385D4—22no—
386D4—44no—
387D4—41no—
388D4—3762no—
389D4—3764no—
390D4—3762no—
391D4—1882no—
392D4—1882no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—3764no—
402C2×C4—1882no—
403C2×C4#1309399812yes—
404C2×C4C2×#1062533411yescharacteristic
405C2×C4C2×#1062533411yescharacteristic
406C2×C4C2×#1062533411yescharacteristic
407C2×C4C2×#1062533411yescharacteristic
408C2×C4C2×#1062533411yescharacteristic
409C2×C4#1309404912yes—
410C2×C4C22×C22⋊D4711yescharacteristic
411C8—21no—
412C8—21no—
413C8#1309399812yes—
414C8C22×D18811yescharacteristic
415C8C2×#1062535011yescharacteristic
416C22—21no—
417C22—21no—
418C22—42no—
419C22—81no—
420C22—81no—
421C22—3762no—
422C22—3762no—
423C22—3762no—
424C22#1568931812yes—
425C22C22×#1062533411yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—81no—
431C4—81no—
432C4—3762no—
433C4#1568931812yes—
434C4#1568955312yescomplemented
435C4C2×#1309399811yescharacteristic
436C4C2×#1309404911yescharacteristic
437C2—22no—
438C2—82no—
439C2—7522no—
440C2C2×#1568931811yescharacteristic
441C2C2×#1568955311yescharacteristic
442C2#2025652211yescharacteristic
subgroupG/H
centerC2×C4C2×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC4×#135×C47C2
socleC22×C47C22×D8
hypercenterC4×#135D47
hypocenterC47#33579
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. C2×#15689553C2semidirect
2. #20253816C2semidirect
3. #20245450C2semidirect
4. #20245443C2semidirect
5. #20245438C2semidirect
6. #20245433C2semidirect
7. #20245428C2semidirect
8. #20245423C2semidirect
9. C2×C4⋊(C47⋊C16)C2semidirect
10. #20245093C2semidirect
11. C4×#135×C47C2semidirect
70. #135×C47D4semidirect
212. C4×C47#508semidirect
218. C4×#135D47semidirect
265. C47#33579semidirect
272. #135D188semidirect
434. C4#15689553semidirect

Maximal subgroups

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

subgroupindex
C2×#156895532
#202538162
#202454502
#202454432
#202454382
#202454332
#202454282
#202454232
C2×C4⋊(C47⋊C16)2
#202450932
C4×#135×C472
#3357947