Finite Group Databasebeta

← #26199703

Subgroups — #26199703

Order 12032.

630 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
1#20254360C212yesmaximal, complemented
2#20253967C211yesmaximal, characteristic, complemented
3#20242906C211yesmaximal, characteristic, complemented
4#20242901C211yesmaximal, characteristic, complemented
5#20242872C211yesmaximal, characteristic, complemented
6#20242867C211yesmaximal, characteristic, complemented
7#20242832C212yesmaximal, complemented
8#20242825C212yesmaximal, complemented
9#20242136C211yesmaximal, characteristic, complemented
10#20242094C212yesmaximal, complemented
11C47×#2966C211yesmaximal, characteristic, complemented
12#15689673C2212yes—
13#15689528C2211yescharacteristic
14#15689505—22no—
15#15689500C2211yescharacteristic
16#15689480—22no—
17#15689470C2212yes—
18#15689359—21no—
19#15689359—21no—
20#15689333C2212yes—
21#15689328C2212yes—
22#15689323C2212yes—
23#15689318C2212yes—
24#15689283—22no—
25#15689266—22no—
26C4×D376—21no—
27C4×D376—21no—
28#15689176C2212yes—
29#15688876C2212yes—
30#15688874C2211yescharacteristic
31#15688874C2211yescharacteristic
32#15688868C2212yes—
33#15688868C2212yes—
34#15688866C2212yes—
35#15688866C2212yes—
36C47×#529C2211yescharacteristic
37C47×#446C2211yescharacteristic
38C8×Q8×C47C2211yescharacteristic
39C47×#436C2211yescharacteristic
40C47×#435—21no—
41C8×D4×C47—21no—
42C8×D4×C47C2211yescharacteristic
43C47×#433—21no—
44C47×#432C2211yescharacteristic
45C47×#405—21no—
46C2×C4×C8×C47C2211yescharacteristic
47C2×#10625350—22no—
48C2×#10625337—22no—
49C2×#10625335—22no—
50C2×#10625336—22no—
51C2×D376—21no—
52C2×D376—21no—
53C2×#10625334—22no—
54#13094024C2312yes—
55#13094021C2312yes—
56#13094012—22no—
57#13093998—22no—
58#13093998—22no—
59C4×D188—22no—
60C4×D188—22no—
61#13093958—21no—
62#13093958—21no—
63C4⋊(C47⋊C8)C2312yes—
64C4⋊(C47⋊C8)C2312yes—
65#13093947—22no—
66#13093947—22no—
67#13093946—22no—
68#13093946—22no—
69#13093944—22no—
70#13093944—22no—
71C22⋊(C47⋊C8)—22no—
72C4×C47⋊C8—22no—
73C2×M16×C47—21no—
74C22×C8×C47—21no—
75C22×C8×C47D411yescharacteristic
76C22×C8×C47D411yescharacteristic
77#126×C47—21no—
78#125×C47D411yescharacteristic
79#124×C47D411yescharacteristic
80#123×C47—21no—
81C22⋊Q8×C47D411yescharacteristic
82#121×C47D411yescharacteristic
83C4×Q8×C47C2311yescharacteristic
84C4×D4×C47—21no—
85C4×D4×C47C2311yescharacteristic
86#117×C47—21no—
87C2×C42×C47C2311yescharacteristic
88C4⋊C8×C47—21no—
89C4⋊C8×C47—21no—
90C4⋊C8×C47C2311yescharacteristic
91C4⋊C8×C47C2311yescharacteristic
92C22⋊C8×C47—21no—
93C22⋊C8×C47—21no—
94C22⋊C8×C47—21no—
95#97×C47—21no—
96#97×C47—21no—
97C4×C8×C47—21no—
98C4×C8×C47D411yescharacteristic
99C4×C8×C47D411yescharacteristic
100C4×C8×C47C2311yescharacteristic
101C4×C8×C47C2311yescharacteristic
102C2×Q8×C47C2×D411yescharacteristic
103C2×D4×C47—21no—
104C2×D4×C47C2×D411yescharacteristic
105C22×C4×C47—21no—
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C2×C22⋊D47—42no—
110#10625350—82no—
111#10625350—82no—
112C2×D188—22no—
113C2×D188—22no—
114C2×D188—22no—
115C2×C4×D47—42no—
116C2×Dic94—22no—
117M16×C47—42no—
118C2×C8×C47—22no—
119C2×C8×C47—21no—
120C2×C8×C47—21no—
121C2×C8×C47—41no—
122C2×C8×C47—42no—
123C2×C8×C47C2×D411yescharacteristic
124C2×C8×C47C2×D411yescharacteristic
125C2×C8×C47C2×D411yescharacteristic
126C2×C8×C47C2×D411yescharacteristic
127C4⋊C4×C47—21no—
128C4⋊C4×C47—21no—
129C4⋊C4×C47—21no—
130C4⋊C4×C47—21no—
131C4⋊C4×C47C2×D411yescharacteristic
132C4⋊C4×C47C2×D411yescharacteristic
133C22⋊C4×C47—21no—
134C22⋊C4×C47—21no—
135C22⋊C4×C47—21no—
136C22⋊C4×C47—21no—
137C22⋊C4×C47—21no—
138C42×C47—21no—
139C42×C47C2×D411yescharacteristic
140C42×C47C2×D411yescharacteristic
141C42×C47#4111yescharacteristic
142C42×C47C2411yescharacteristic
143#10625337—82no—
144#10625336—82no—
145#10625335—82no—
146#10625334—82no—
147(C2×D47)⋊C4—42no—
148(C2×D47)⋊C4—42no—
149C4⋊Dic47—22no—
150C4⋊Dic47—22no—
151C2×C47⋊C8—22no—
152C2×C47⋊C8—22no—
153D376—42no—
154D376—42no—
155C23×C47—21no—
156C23×C47#12111yescharacteristic
157C22×D47—42no—
158Q8×C47—22no—
159D4×C47—22no—
160D4×C47—42no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—22no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47#12111yescharacteristic
171C2×C4×C47#12111yescharacteristic
172C2×C4×C47#12111yescharacteristic
173C2×C4×C47C22×D411yescharacteristic
174C2×C4×C47C22×D411yescharacteristic
175C2×C4×C47C2×#4111yescharacteristic
176C22⋊D47—84no—
177C2×Dic47—42no—
178D188—42no—
179D188—42no—
180D188—42no—
181D188—42no—
182D188—82no—
183C4×D47—84no—
184Dic94—42no—
185Dic94—42no—
186C8×C47—21no—
187C8×C47—21no—
188C8×C47—21no—
189C8×C47—41no—
190C8×C47—41no—
191C8×C47#13512yes—
192C47⋊C8—42no—
193C47⋊C8—42no—
194#19225—471nomaximal, Sylow
195C22×C47—21no—
196C22×C47—21no—
197C22×C47—21no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47—41no—
201C22×C47C2×#12111yescharacteristic
202C2×D47—82no—
203C2×D47—82no—
204C2×D47—82no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—21no—
209C4×C47—41no—
210C4×C47—41no—
211C4×C47—41no—
212C4×C47C2×#13511yescharacteristic
213C4×C47#57511yescharacteristic
214C4×C47#57612yes—
215Dic47—82no—
216#3212—472no—
217#3169—471no—
218#2966D4711yescharacteristic, complemented
219#1694—471no—
220#1693—471no—
221#1688—471no—
222#1687—471no—
223#1682—472no—
224#1681—472no—
225#1564—471no—
226#1553—472no—
227C2×C47—41no—
228C2×C47—81no—
229C2×C47#303511yescharacteristic
230C2×C47#305811yescharacteristic
231C2×C47#306711yescharacteristic
232D47—162no—
233#532—472no—
234#529C2×D4711yescharacteristic
235#500—471no—
236#495—942no—
237#493—471no—
238#488—942no—
239#486—472no—
240#466—941no—
241#466—941no—
242#462—472no—
243#461—472no—
244#460—472no—
245#459—472no—
246#452—942no—
247#449—942no—
248#446C2×D4711yescharacteristic
249C8×Q8C2×D4711yescharacteristic
250C4×D8—941no—
251C4×D8—941no—
252#436C2×D4711yescharacteristic
253#435—21no—
254C8×D4—21no—
255C8×D4C2×D4711yescharacteristic
256#433—21no—
257#432C2×D4711yescharacteristic
258#431—472no—
259#405—21no—
260C2×C4×C8C2×D4711yescharacteristic
261#335—472no—
262#334—471no—
263#334—471no—
264#332—472no—
265#332—472no—
266#331—472no—
267#331—472no—
268C47#1922511yescharacteristic, complemented, Sylow
269C2×#41—942no—
270C2×Q16—942no—
271C2×SD16—942no—
272C2×SD16—942no—
273C2×D8—942no—
274C2×D8—941no—
275C2×D8—941no—
276C2×M16—21no—
277C22×C8—21no—
278C22×C8C22⋊D4711yescharacteristic
279C22×C8C22⋊D4711yescharacteristic
280C4⋊Q8—472no—
281#127—472no—
282#126—21no—
283#125D18811yescharacteristic
284#124—942no—
285#124D18811yescharacteristic
286#123—21no—
287C22⋊Q8D18811yescharacteristic
288#121—942no—
289#121—942no—
290#121D18811yescharacteristic
291C4×Q8C22×D4711yescharacteristic
292C4×D4—21no—
293C4×D4—942no—
294C4×D4—942no—
295C4×D4C22×D4711yescharacteristic
296#117—21no—
297C2×C42C22×D4711yescharacteristic
298#107—941no—
299#107—941no—
300C4⋊C8—21no—
301C4⋊C8—21no—
302C4⋊C8—472no—
303C4⋊C8—472no—
304C4⋊C8C22×D4711yescharacteristic
305C4⋊C8C22×D4711yescharacteristic
306#103—942no—
307#103—942no—
308#102—942no—
309#102—942no—
310#102—942no—
311#102—942no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—942no—
316#97—21no—
317#97—21no—
318C4×C8—21no—
319C4×C8—942no—
320C4×C8C22⋊D4711yescharacteristic
321C4×C8C22⋊D4711yescharacteristic
322C4×C8C22×D4711yescharacteristic
323C4×C8C22×D4711yescharacteristic
324#41—3762no—
325#41—3762no—
326C2×Q8—942no—
327C2×Q8C2×D18811yescharacteristic
328C2×D4—21no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—942no—
332C2×D4—1882no—
333C2×D4C2×D18811yescharacteristic
334C22×C4—21no—
335C22×C4—1882no—
336C22×C4C2×D18811yescharacteristic
337C22×C4#1062535011yescharacteristic
338C22×C4C2×C22⋊D4711yescharacteristic
339Q16—3762no—
340SD16—3762no—
341SD16—3762no—
342D8—3762no—
343D8—1882no—
344D8—1882no—
345M16—42no—
346C2×C8—22no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—41no—
350C2×C8—42no—
351C2×C8—942no—
352C2×C8—942no—
353C2×C8C2×C22⋊D4711yescharacteristic
354C2×C8C2×C22⋊D4711yescharacteristic
355C2×C8C2×C22⋊D4711yescharacteristic
356C2×C8C2×C22⋊D4711yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—942no—
362C4⋊C4—942no—
363C4⋊C4C2×D18811yescharacteristic
364C4⋊C4C2×D18811yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—1882no—
371C22⋊C4—1882no—
372C42—21no—
373C42C2×D18811yescharacteristic
374C42#1062535011yescharacteristic
375C42C2×C22⋊D4711yescharacteristic
376C42C23×D4711yescharacteristic
377C23—21no—
378C23—1882no—
379C23#1309399811yescharacteristic
380Q8—22no—
381Q8—1882no—
382Q8—1882no—
383D4—22no—
384D4—42no—
385D4—3762no—
386D4—3764no—
387D4—1882no—
388D4—1882no—
389D4—1882no—
390D4—1882no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—3764no—
401C2×C4—1882no—
402C2×C4#1309399811yescharacteristic
403C2×C4#1309399811yescharacteristic
404C2×C4#1309399811yescharacteristic
405C2×C4C22×C22⋊D4711yescharacteristic
406C2×C4C22×D18811yescharacteristic
407C2×C4C2×#1062535011yescharacteristic
408C8—21no—
409C8—21no—
410C8—21no—
411C8—41no—
412C8—41no—
413C8—1882no—
414C8—1882no—
415C8#1309404412yes—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—3762no—
423C22—3762no—
424C22—3762no—
425C22C2×#1309399811yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—3762no—
434C4C2×#1309404411yescharacteristic
435C4#1568992111yescharacteristic
436C4#1568992812yes—
437C2—41no—
438C2—81no—
439C2—7522no—
440C2#2025284311yescharacteristic
441C2#2025303611yescharacteristic
442C2#2025310811yescharacteristic
subgroupG/H
centerC22C2×#13093998
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#2966C2
socleC22×C47C2×#121
hypercenter#2966D47
hypocenterC47#19225
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #20254360C2semidirect
2. #20253967C2semidirect
3. #20242906C2semidirect
4. #20242901C2semidirect
5. #20242872C2semidirect
6. #20242867C2semidirect
7. #20242832C2semidirect
8. #20242825C2semidirect
9. #20242136C2semidirect
10. #20242094C2semidirect
11. C47×#2966C2semidirect
218. #2966D47semidirect
268. C47#19225semidirect

Maximal subgroups

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

subgroupindex
#202543602
#202539672
#202429062
#202429012
#202428722
#202428672
#202428322
#202428252
#202421362
#202420942
C47×#29662
#1922547