Finite Group Databasebeta

← #26112370

Subgroups — #26112370

Order 12032.

532 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C47⋊C8C211yesmaximal, characteristic, complemented
2#20243408C211yesmaximal, characteristic, complemented
3#20241883C211yesmaximal, characteristic, complemented
4#20241839C211yesmaximal, characteristic, complemented
5#20241285C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C47×#3035C211yesmaximal, characteristic
8Q8×C47⋊C8—21no—
9D4×C47⋊C8—22no—
10D4×C47⋊C8—21no—
11#15689176—21no—
12#15689176C2211yescharacteristic
13#15689147C2211yescharacteristic
14C2×#13093951—21no—
15C2×C4×C47⋊C8—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17C4×C4⋊Dic47C2211yescharacteristic
18#15688882—21no—
19#15688857—22no—
20D4⋊(C47⋊C8)—21no—
21D4⋊(C47⋊C8)—21no—
22C2×#135×C47—21no—
23C47×#532C2211yescharacteristic
24C4×#41×C47C2211yescharacteristic
25C47×#464—21no—
26C47×#463—21no—
27C47×#462C411yescharacteristic, complemented
28C47×#461C411yescharacteristic, complemented
29C47×#460C411yescharacteristic, complemented
30C47×#459C411yescharacteristic, complemented
31C2×C4⋊C8×C47C2211yescharacteristic
32C47×#416—21no—
33C2×#10625329—21no—
34C22×C47⋊C8—22no—
35C22×C47⋊C8—21no—
36C2×C4⋊Dic47—21no—
37C2×C4×Dic47—21no—
38C4⋊(C47⋊C8)—22no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42#13093951—42no—
43C22⋊(C47⋊C8)—22no—
44C22⋊(C47⋊C8)D412yes—
45C4×C47⋊C8—22no—
46C4×C47⋊C8—21no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8D411yescharacteristic
49C4×C47⋊C8D411yescharacteristic
50C47⋊#95—21no—
51C2×#41×C47—21no—
52C2×#41×C47D411yescharacteristic
53#135×C47—42no—
54#135×C47—42no—
55C2×Q16×C47—21no—
56C2×SD16×C47—21no—
57C2×SD16×C47—21no—
58C2×D8×C47—21no—
59C22×C8×C47—21no—
60C4⋊Q8×C47C2×C411yescharacteristic
61#127×C47C2×C411yescharacteristic
62#124×C47—21no—
63#121×C47—21no—
64#121×C47—21no—
65C4×Q8×C47C2×C411yescharacteristic
66C4×Q8×C47D411yescharacteristic
67C4×D4×C47—21no—
68C4×D4×C47—21no—
69C4×D4×C47—21no—
70C4×D4×C47—21no—
71C4×D4×C47C2×C411yescharacteristic
72C4×D4×C47D411yescharacteristic
73#117×C47—21no—
74#117×C47D411yescharacteristic
75C2×C42×C47—21no—
76C2×C42×C47C2311yescharacteristic
77C4⋊C8×C47—21no—
78C4⋊C8×C47C2×C411yescharacteristic
79C4⋊C8×C47C2×C411yescharacteristic
80#103×C47—21no—
81#103×C47—21no—
82#102×C47—21no—
83#102×C47—21no—
84#41×C47—21no—
85#41×C47—21no—
86#41×C47—41no—
87#41×C47—41no—
88#41×C47—41no—
89#41×C47—41no—
90#41×C47D812yes—
91#41×C47SD1612yes—
92C2×Q8×C47—21no—
93C2×Q8×C47C22⋊C411yescharacteristic
94C2×D4×C47—21no—
95C2×D4×C47—21no—
96C2×D4×C47—21no—
97C2×D4×C47—21no—
98C2×D4×C47—41no—
99C2×D4×C47C22⋊C411yescharacteristic
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—41no—
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×Dic47—41no—
108Q16×C47—42no—
109SD16×C47—42no—
110SD16×C47—42no—
111D8×C47—42no—
112C2×C8×C47—21no—
113C2×C8×C47—21no—
114C2×C8×C47—41no—
115C2×C8×C47—41no—
116C4⋊C4×C47—21no—
117C4⋊C4×C47—21no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47—21no—
120C4⋊C4×C47C22⋊C411yescharacteristic
121C4⋊C4×C47C22⋊C411yescharacteristic
122C22⋊C4×C47—21no—
123C22⋊C4×C47—21no—
124C22⋊C4×C47—21no—
125C22⋊C4×C47—41no—
126C22⋊C4×C47—41no—
127C42×C47—21no—
128C42×C47—21no—
129C42×C47—21no—
130C42×C47C22×C411yescharacteristic
131C42×C47C2×D411yescharacteristic
132C42×C47C2×D411yescharacteristic
133C42×C47#4111yescharacteristic
134C4⋊Dic47—22no—
135C4⋊Dic47—41no—
136C4×Dic47—41no—
137C4×Dic47—41no—
138#10625329—41no—
139#10625329—41no—
140C2×C47⋊C8—21no—
141C2×C47⋊C8—22no—
142C2×C47⋊C8—21no—
143C2×C47⋊C8—42no—
144C2×C47⋊C8—44no—
145C2×C47⋊C8—41no—
146C23×C47—21no—
147C23×C47—41no—
148C23×C47#12111yescharacteristic
149Q8×C47—21no—
150Q8×C47—41no—
151Q8×C47—41no—
152Q8×C47#10212yes—
153D4×C47—22no—
154D4×C47—22no—
155D4×C47—21no—
156D4×C47—41no—
157D4×C47—41no—
158D4×C47—41no—
159D4×C47—41no—
160D4×C47—81no—
161D4×C47—81no—
162D4×C47—81no—
163D4×C47#10212yes—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—22no—
168C2×C4×C47—22no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—41no—
172C2×C4×C47—42no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47—81no—
177C2×C4×C47—81no—
178C2×C4×C47C2×C22⋊C411yescharacteristic
179C2×C4×C47C4×D411yescharacteristic
180C2×C4×C47C4×D411yescharacteristic
181C2×C4×C47#12011yescharacteristic
182C2×C4×C47#12111yescharacteristic
183C2×C4×C47#12311yescharacteristic
184C2×C4×C47C2×D811yescharacteristic
185C2×C4×C47C2×SD1611yescharacteristic
186C2×C4×C47#13511yescharacteristic
187C2×C4×C47#13511yescharacteristic
188C2×Dic47—42no—
189C2×Dic47—81no—
190C2×Dic47—81no—
191C8×C47—41no—
192C8×C47—41no—
193C47⋊C8—22no—
194C47⋊C8—42no—
195C47⋊C8—41no—
196C47⋊C8—81no—
197#9208—471nomaximal, Sylow
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—22no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—81no—
204C22×C47—81no—
205C22×C47—81no—
206C22×C47#38611yescharacteristic
207C22×C47#46511yescharacteristic
208C22×C47#46611yescharacteristic
209C4×C47—21no—
210C4×C47—22no—
211C4×C47—21no—
212C4×C47—21no—
213C4×C47—41no—
214C4×C47—41no—
215C4×C47—81no—
216C4×C47C2×#10211yescharacteristic
217C4×C47#41611yescharacteristic
218C4×C47#44311yescharacteristic
219C4×C47#44411yescharacteristic
220C4×C47#46511yescharacteristic
221C4×C47#46611yescharacteristic
222Dic47—82no—
223#3035D4711yescharacteristic
224C8×#41—471no—
225#1806—471no—
226#1502—471no—
227#1492—471no—
228#1301—471no—
229#1279—471no—
230C2×C47—21no—
231C2×C47—21no—
232C2×C47—42no—
233C2×C47—161no—
234C2×C47#187611yescharacteristic
235C2×C47#189311yescharacteristic
236C2×C47#190611yescharacteristic
237C2×#135—21no—
238#532C2×D4711yescharacteristic
239C4×#41C2×D4711yescharacteristic
240#464—21no—
241#463—21no—
242#462Dic4711yescharacteristic, complemented
243#461Dic4711yescharacteristic, complemented
244#460Dic4711yescharacteristic, complemented
245#459Dic4711yescharacteristic, complemented
246C8×Q8—941no—
247C8×D4—942no—
248C8×D4—941no—
249#431—471no—
250#431—941no—
251#423—471no—
252C2×C4⋊C8C2×D4711yescharacteristic
253C2×#104—941no—
254#416—21no—
255C2×C4×C8—471no—
256C2×C4×C8—941no—
257C4×C4⋊C4—471no—
258#339—941no—
259#327—942no—
260D4⋊C8—941no—
261D4⋊C8—941no—
262C47#920811yescharacteristic, complemented, Sylow
263C2×#41—21no—
264C2×#41C22⋊D4711yescharacteristic
265#135—42no—
266#135—42no—
267C2×Q16—21no—
268C2×SD16—21no—
269C2×SD16—21no—
270C2×D8—21no—
271C2×M16—941no—
272C22×C8—21no—
273C22×C8—942no—
274C22×C8—941no—
275C4⋊Q8C2×Dic4711yescharacteristic
276#127C2×Dic4711yescharacteristic
277#124—21no—
278#121—21no—
279#121—21no—
280C4×Q8C2×Dic4711yescharacteristic
281C4×Q8C22⋊D4711yescharacteristic
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4C2×Dic4711yescharacteristic
287C4×D4C22⋊D4711yescharacteristic
288#117—21no—
289#117C22⋊D4711yescharacteristic
290C2×C4⋊C4—941no—
291C2×C42—21no—
292C2×C42—941no—
293C2×C42C22×D4711yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—942no—
296C4⋊C8—941no—
297C4⋊C8—941no—
298C4⋊C8—941no—
299C4⋊C8C2×Dic4711yescharacteristic
300C4⋊C8C2×Dic4711yescharacteristic
301#104—1882no—
302#103—21no—
303#103—21no—
304#102—21no—
305#102—21no—
306C22⋊C8—472no—
307C22⋊C8—942no—
308C4×C8—471no—
309C4×C8—471no—
310C4×C8—942no—
311C4×C8—941no—
312C4×C8—941no—
313#95—941no—
314#41—21no—
315#41—21no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41#1062533412yes—
321#41#1062533512yes—
322C2×Q8—21no—
323C2×Q8C22⋊Dic4711yescharacteristic
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4C22⋊Dic4711yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—41no—
334C22×C4—1881no—
335C22×C4D4×D4711yescharacteristic
336C22×C4#1062535211yescharacteristic
337C22×C4C2×C22⋊D4711yescharacteristic
338Q16—42no—
339SD16—42no—
340SD16—42no—
341D8—42no—
342M16—1881no—
343M16—1881no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—941no—
349C2×C8—941no—
350C2×C8—942no—
351C2×C8—1882no—
352C2×C8—1884no—
353C2×C8—1881no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—942no—
359C4⋊C4—1881no—
360C4⋊C4C22⋊Dic4711yescharacteristic
361C4⋊C4C22⋊Dic4711yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—1881no—
371C42—1881no—
372C42D4×D4711yescharacteristic
373C42#1062535211yescharacteristic
374C42C22×Dic4711yescharacteristic
375C42C2×C22⋊D4711yescharacteristic
376C23—21no—
377C23—41no—
378C23#1309399611yescharacteristic
379Q8—21no—
380Q8—41no—
381Q8—41no—
382Q8#1309394512yes—
383D4—22no—
384D4—22no—
385D4—21no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—81no—
392D4—81no—
393D4#1309394512yes—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—3761no—
409C2×C4—3761no—
410C2×C4—1882no—
411C2×C4C2×C22⋊Dic4711yescharacteristic
412C2×C4D4×Dic4711yescharacteristic
413C2×C4D4×Dic4711yescharacteristic
414C2×C4#1309399211yescharacteristic
415C2×C4#1309399611yescharacteristic
416C2×C4#1309400511yescharacteristic
417C2×C4C2×#1062533411yescharacteristic
418C2×C4C2×#1062533511yescharacteristic
419C2×C4#1309404411yescharacteristic
420C2×C4#1309404411yescharacteristic
421C8—41no—
422C8—41no—
423C8—942no—
424C8—3761no—
425C8—1881no—
426C8—1882no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22#1568900311yescharacteristic
436C22#1568935011yescharacteristic
437C22#1568935711yescharacteristic
438C4—21no—
439C4—22no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—81no—
445C4—3762no—
446C4C2×#1309394511yescharacteristic
447C4#1568911911yescharacteristic
448C4#1568924011yescharacteristic
449C4#1568924511yescharacteristic
450C4#1568935011yescharacteristic
451C4#1568935711yescharacteristic
452C2—21no—
453C2—21no—
454C2—42no—
455C2—161no—
456C2#2024371711yescharacteristic
457C2#2024381711yescharacteristic
458C2#2024389111yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3035C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenter#3035D47
hypocenterC47#9208
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #41×C47⋊C8C2semidirect
2. #20243408C2semidirect
3. #20241883C2semidirect
4. #20241839C2semidirect
5. #20241285C2semidirect
6. #20241227C2semidirect
27. C47×#462C4semidirect
28. C47×#461C4semidirect
29. C47×#460C4semidirect
30. C47×#459C4semidirect
242. #462Dic47semidirect
243. #461Dic47semidirect
244. #460Dic47semidirect
245. #459Dic47semidirect
262. C47#9208semidirect

Maximal subgroups

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

subgroupindex
#41×C47⋊C82
#202434082
#202418832
#202418392
#202412852
#202412272
C47×#30352
#920847