Finite Group Databasebeta

← #26120072

Subgroups — #26120072

Order 12032.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244195C211yesmaximal, characteristic, complemented
2#20244183C211yesmaximal, characteristic, complemented
3#20243388C211yesmaximal, characteristic, complemented
4C2×#15688873C211yesmaximal, characteristic, complemented
5C2×#15688867C211yesmaximal, characteristic, complemented
6#20241272C211yesmaximal, characteristic, complemented
7C2×C47×#459C211yesmaximal, characteristic
8C2×C4⋊(C47⋊C8)C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×#13093945—21no—
11C2×#13093945—21no—
12C2×#13093945—21no—
13C2×C22⋊(C47⋊C8)—21no—
14C2×C22⋊(C47⋊C8)—21no—
15C2×C4×C47⋊C8C2211yescharacteristic
16#15688993C2211yescharacteristic
17#15688885—21no—
18#15688873—22no—
19#15688867—22no—
20C22×D8×C47—21no—
21C2×#127×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C47×#459—22no—
24C47×#459—22no—
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×#102×C47—21no—
27C22×C47⋊C8—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8D411yescharacteristic
30C22×C47⋊C8D411yescharacteristic
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47—21no—
34C4⋊(C47⋊C8)—21no—
35C4⋊(C47⋊C8)—21no—
36C4⋊(C47⋊C8)—21no—
37C4⋊(C47⋊C8)—21no—
38#13093945—42no—
39#13093945—42no—
40#13093945—42no—
41C22⋊(C47⋊C8)—42no—
42C22⋊(C47⋊C8)—42no—
43C4×C47⋊C8—21no—
44C4×C47⋊C8—21no—
45C22×D4×C47—21no—
46C22×D4×C47—21no—
47C22×D4×C47—21no—
48C22×D4×C47D411yescharacteristic
49C23×C4×C47—21no—
50C2×D8×C47—24no—
51C2×D8×C47—42no—
52C2×D8×C47—42no—
53C22×C8×C47—21no—
54#127×C47—21no—
55#127×C47—21no—
56#127×C47—21no—
57#127×C47D412yes—
58C4×D4×C47—21no—
59C4×D4×C47—21no—
60C4×D4×C47—21no—
61C4×D4×C47—21no—
62C2×C4⋊C4×C47D411yescharacteristic
63C2×C22⋊C4×C47—21no—
64C2×C42×C47C2311yescharacteristic
65C4⋊C8×C47—21no—
66C4⋊C8×C47D412yes—
67#102×C47—24no—
68C24×C47—21no—
69C24×C47—41no—
70C2×D4×C47—21no—
71C2×D4×C47—22no—
72C2×D4×C47—22no—
73C2×D4×C47—21no—
74C2×D4×C47—22no—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—41no—
79C2×D4×C47—41no—
80C2×D4×C47—41no—
81C2×D4×C47—41no—
82C2×D4×C47—41no—
83C2×D4×C47—41no—
84C2×D4×C47—41no—
85C2×D4×C47—41no—
86C2×D4×C47—41no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C2×D4×C47—81no—
90C2×D4×C47—81no—
91C2×D4×C47SD1612yes—
92C22×C4×C47—21no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47—41no—
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47#4111yescharacteristic
102C22×Dic47—41no—
103D8×C47—48no—
104C2×C8×C47—22no—
105C2×C8×C47—41no—
106C2×C8×C47—41no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C22⋊C4×C47—41no—
110C22⋊C4×C47—41no—
111C42×C47C2×D411yescharacteristic
112C42×C47C2×D411yescharacteristic
113C42×C47#4111yescharacteristic
114C42×C47#4111yescharacteristic
115C4⋊Dic47—41no—
116C4⋊Dic47—41no—
117C4⋊Dic47—41no—
118C4⋊Dic47—41no—
119C4⋊Dic47—81no—
120C2×C47⋊C8—21no—
121C2×C47⋊C8—21no—
122C2×C47⋊C8—21no—
123C2×C47⋊C8—21no—
124C2×C47⋊C8—21no—
125C2×C47⋊C8—41no—
126C2×C47⋊C8—41no—
127C2×C47⋊C8—41no—
128C2×C47⋊C8—41no—
129C2×C47⋊C8—41no—
130C2×C47⋊C8—41no—
131C2×C47⋊C8D812yescomplemented
132C23×C47—22no—
133C23×C47—41no—
134C23×C47—41no—
135C23×C47—41no—
136C23×C47—41no—
137C23×C47—41no—
138C23×C47—41no—
139C23×C47—42no—
140C23×C47—81no—
141C23×C47—81no—
142C23×C47—81no—
143C23×C47—81no—
144C23×C47—81no—
145C23×C47—81no—
146C23×C47#12111yescharacteristic
147D4×C47—22no—
148D4×C47—22no—
149D4×C47—41no—
150D4×C47—42no—
151D4×C47—42no—
152D4×C47—42no—
153D4×C47—42no—
154D4×C47—41no—
155D4×C47—82no—
156D4×C47—82no—
157D4×C47—81no—
158D4×C47—81no—
159D4×C47—81no—
160D4×C47—81no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—41no—
164C2×C4×C47—41no—
165C2×C4×C47—41no—
166C2×C4×C47—81no—
167C2×C4×C47—81no—
168C2×C4×C47—81no—
169C2×C4×C47—81no—
170C2×C4×C47#12011yescharacteristic
171C2×C4×C47#12111yescharacteristic
172C2×C4×C47#12111yescharacteristic
173C2×C4×C47#12311yescharacteristic
174C2×C4×C47#12311yescharacteristic
175C2×C4×C47#12411yescharacteristic
176C2×C4×C47C2×D811yescharacteristic
177C2×C4×C47C2×SD1611yescharacteristic
178C2×C4×C47#13511yescharacteristic
179C2×C4×C47#13511yescharacteristic
180C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
184C2×Dic47—81no—
185C2×Dic47—81no—
186C2×Dic47—81no—
187C8×C47—42no—
188C47⋊C8—22no—
189C47⋊C8—41no—
190C47⋊C8—81no—
191C47⋊C8—81no—
192#10473—471nomaximal, Sylow
193C22×C47—42no—
194C22×C47—42no—
195C22×C47—42no—
196C22×C47—81no—
197C22×C47—81no—
198C22×C47—81no—
199C22×C47—81no—
200C22×C47—82no—
201C22×C47—82no—
202C22×C47—82no—
203C22×C47—161no—
204C22×C47—161no—
205C22×C47—161no—
206C22×C47—161no—
207C22×C47#39411yescharacteristic
208C22×C47#45911yescharacteristic
209C22×C47#46311yescharacteristic
210C22×C47#46511yescharacteristic
211C22×C47#46911yescharacteristic
212C22×C47#47111yescharacteristic
213C22×C47#47211yescharacteristic
214C4×C47—21no—
215C4×C47—21no—
216C4×C47—81no—
217C4×C47#44911yescharacteristic
218C4×C47#45011yescharacteristic
219C4×C47#45911yescharacteristic
220C4×C47#46311yescharacteristic
221C4×C47#46611yescharacteristic
222C4×C47#46911yescharacteristic
223C4×C47#48111yescharacteristic
224C4×C47#48211yescharacteristic
225Dic47—161no—
226C2×#459D4711yescharacteristic
227#1957—471no—
228#1954—471no—
229#1802—471no—
230C2×#334—471no—
231C2×#331—471no—
232#1296—471no—
233C2×C47—82no—
234C2×C47—162no—
235C2×C47#166511yescharacteristic
236C2×C47#167711yescharacteristic
237C2×C47#168711yescharacteristic
238C2×C47#170111yescharacteristic
239C2×C47#203411yescharacteristic
240C2×C47#205111yescharacteristic
241C2×C47#205411yescharacteristic
242C22×D8—21no—
243C2×#127C2×D4711yescharacteristic
244C2×C4×D4C2×D4711yescharacteristic
245#459—22no—
246#459—22no—
247C2×C4⋊C8—471no—
248C2×C4⋊C8—471no—
249C2×C4⋊C8C2×D4711yescharacteristic
250C2×#102—21no—
251C2×#102—941no—
252C2×#102—941no—
253C2×#102—941no—
254C2×C22⋊C8—941no—
255C2×C22⋊C8—941no—
256C2×C4×C8—471no—
257#384—471no—
258#340—941no—
259#334—942no—
260#331—942no—
261C47#1047311yescharacteristic, complemented, Sylow
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4C22⋊D4711yescharacteristic
266C23×C4—21no—
267C2×D8—24no—
268C2×D8—42no—
269C2×D8—42no—
270C22×C8—21no—
271C22×C8—471no—
272C22×C8—471no—
273C22×C8—941no—
274C22×C8—941no—
275#127—21no—
276#127—21no—
277#127—21no—
278#127C22⋊D4712yes—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—941no—
284C2×C4⋊C4—941no—
285C2×C4⋊C4—941no—
286C2×C4⋊C4C22⋊D4711yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C22×D4711yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—941no—
291C4⋊C8—941no—
292C4⋊C8—941no—
293C4⋊C8—941no—
294C4⋊C8C22⋊D4712yes—
295#102—24no—
296#102—1882no—
297#102—1882no—
298#102—1882no—
299C22⋊C8—1882no—
300C22⋊C8—1882no—
301C4×C8—941no—
302C4×C8—941no—
303C24—21no—
304C24—41no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4#1062533512yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—1881no—
335C22×C4D4×D4711yescharacteristic
336C22×C4#1062535211yescharacteristic
337C22×C4C2×C22⋊D4711yescharacteristic
338D8—48no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—472no—
343C2×C8—941no—
344C2×C8—941no—
345C2×C8—941no—
346C2×C8—941no—
347C2×C8—941no—
348C2×C8—1881no—
349C2×C8—1881no—
350C2×C8—1881no—
351C2×C8—1881no—
352C2×C8—1881no—
353C2×C8—1881no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—3761no—
357C4⋊C4—1881no—
358C4⋊C4—1881no—
359C4⋊C4—1881no—
360C4⋊C4—1881no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42#1062535211yescharacteristic
364C42#1062535211yescharacteristic
365C42C2×C22⋊D4711yescharacteristic
366C42C2×C22⋊D4711yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23#1309399611yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—41no—
390D4—82no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—3761no—
406C2×C4—3761no—
407C2×C4—3761no—
408C2×C4#1309399311yescharacteristic
409C2×C4#1309399511yescharacteristic
410C2×C4#1309399611yescharacteristic
411C2×C4#1309400511yescharacteristic
412C2×C4#1309400511yescharacteristic
413C2×C4#1309401111yescharacteristic
414C2×C4D8×D4711yescharacteristic
415C2×C4C2×#1062533511yescharacteristic
416C2×C4#1309404311yescharacteristic
417C2×C4#1309404411yescharacteristic
418C2×C4#1309404811yescharacteristic
419C2×C4#1309404811yescharacteristic
420C2×C4#1309404911yescharacteristic
421C2×C4#1309405011yescharacteristic
422C8—42no—
423C8—942no—
424C8—3761no—
425C8—3761no—
426C8—1881no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22#1568903711yescharacteristic
442C22#1568931611yescharacteristic
443C22#1568933611yescharacteristic
444C22#1568935011yescharacteristic
445C22#1568937411yescharacteristic
446C22#1568938411yescharacteristic
447C22#1568939111yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—7521no—
452C4#1568926811yescharacteristic
453C4#1568927411yescharacteristic
454C4#1568931611yescharacteristic
455C4#1568933611yescharacteristic
456C4#1568935611yescharacteristic
457C4#1568937311yescharacteristic
458C4#1568943911yescharacteristic
459C4#1568944411yescharacteristic
460C2—82no—
461C2—162no—
462C2#2024272711yescharacteristic
463C2#2024279511yescharacteristic
464C2#2024286511yescharacteristic
465C2#2024294711yescharacteristic
466C2#2024457411yescharacteristic
467C2#2024467711yescharacteristic
468C2#2024469611yescharacteristic
subgroupG/H
centerC23#13093996
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
Fitting, prime radicalC2×C47×#459C2
socleC23×C47#121
hypercenterC2×#459D47
hypocenterC47#10473
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #20244195C2semidirect
2. #20244183C2semidirect
3. #20243388C2semidirect
4. C2×#15688873C2semidirect
5. C2×#15688867C2semidirect
6. #20241272C2semidirect
131. C2×C47⋊C8D8semidirect
261. C47#10473semidirect

Maximal subgroups

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

subgroupindex
#202441952
#202441832
#202433882
C2×#156888732
C2×#156888672
#202412722
C2×C47×#4592
#1047347