Finite Group Databasebeta

← #26120076

Subgroups — #26120076

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
1C2×#15689318C211yesmaximal, characteristic
2#20244194C211yesmaximal, characteristic, complemented
3#20243388C211yesmaximal, characteristic, complemented
4C2×#15688874C211yesmaximal, characteristic, complemented
5C2×#15688866C211yesmaximal, characteristic, complemented
6#20241272C211yesmaximal, characteristic, complemented
7C47×#1954C211yesmaximal, characteristic, complemented
8C22×#10625334—21no—
9C2×#13094021C2211yescharacteristic
10#15689318—22no—
11#15689318—22no—
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×#13093946—21no—
15C2×#13093946—21no—
16C2×#13093945—21no—
17C2×#13093944—21no—
18#15688993C2211yescharacteristic
19#15688885—21no—
20#15688874—22no—
21#15688866—22no—
22C2×C4×D4×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C22⋊C8×C47—21no—
25C2×C22⋊C8×C47—21no—
26C2×C4×C8×C47C2211yescharacteristic
27C22×D188—21no—
28C22×D188—21no—
29C22×D188—21no—
30C2×#10625334—24no—
31C2×#10625334—42no—
32C2×#10625334—42no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35#13094021—21no—
36#13094021—21no—
37#13094021—21no—
38#13094021D412yes—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D412yes—
46#13093946—42no—
47#13093946—42no—
48#13093945—42no—
49#13093944—24no—
50C22×D4×C47D411yescharacteristic
51C23×C4×C47—21no—
52C22×C8×C47—21no—
53C22×C8×C47D411yescharacteristic
54C22×C8×C47D411yescharacteristic
55C4×D4×C47—21no—
56C4×D4×C47—21no—
57C4×D4×C47—21no—
58C4×D4×C47—21no—
59C2×C4⋊C4×C47D411yescharacteristic
60C2×C22⋊C4×C47—21no—
61C2×C42×C47C2311yescharacteristic
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C22⋊C8×C47—42no—
65C22⋊C8×C47—42no—
66C4×C8×C47—21no—
67C4×C8×C47—21no—
68C24×C47—21no—
69C23×D47—41no—
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47SD1612yes—
76C22×C4×C47—21no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C22×C4×C47#4111yescharacteristic
86C22×Dic47—41no—
87C2×D188—22no—
88C2×D188—22no—
89C2×D188—22no—
90C2×D188—41no—
91C2×D188—41no—
92C2×D188—41no—
93C2×D188—41no—
94C2×D188—41no—
95C2×D188—41no—
96C2×D188—41no—
97C2×D188—41no—
98C2×D188—41no—
99C2×D188—41no—
100C2×D188—41no—
101C2×D188—81no—
102C2×D188—81no—
103C2×C8×C47—21no—
104C2×C8×C47—21no—
105C2×C8×C47—21no—
106C2×C8×C47—21no—
107C2×C8×C47—21no—
108C2×C8×C47—41no—
109C2×C8×C47—41no—
110C2×C8×C47—41no—
111C2×C8×C47D812yescomplemented
112C4⋊C4×C47—21no—
113C4⋊C4×C47—21no—
114C22⋊C4×C47—41no—
115C22⋊C4×C47—41no—
116C42×C47C2×D411yescharacteristic
117C42×C47C2×D411yescharacteristic
118C42×C47#4111yescharacteristic
119C42×C47#4111yescharacteristic
120#10625334—48no—
121C4⋊Dic47—41no—
122C4⋊Dic47—41no—
123C4⋊Dic47—41no—
124C4⋊Dic47—41no—
125C4⋊Dic47—81no—
126C2×C47⋊C8—22no—
127C2×C47⋊C8—41no—
128C2×C47⋊C8—41no—
129C2×C47⋊C8—41no—
130C2×C47⋊C8—41no—
131C2×C47⋊C8—41no—
132C23×C47—22no—
133C23×C47—41no—
134C23×C47—41no—
135C23×C47—41no—
136C23×C47—41no—
137C23×C47—41no—
138C23×C47—41no—
139C23×C47#12111yescharacteristic
140C22×D47—42no—
141C22×D47—81no—
142C22×D47—81no—
143C22×D47—81no—
144C22×D47—81no—
145C22×D47—81no—
146C22×D47—81no—
147D4×C47—22no—
148D4×C47—22no—
149D4×C47—41no—
150D4×C47—41no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—41no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—81no—
157C2×C4×C47—81no—
158C2×C4×C47—81no—
159C2×C4×C47—81no—
160C2×C4×C47#12011yescharacteristic
161C2×C4×C47#12111yescharacteristic
162C2×C4×C47#12111yescharacteristic
163C2×C4×C47#12311yescharacteristic
164C2×C4×C47#12311yescharacteristic
165C2×C4×C47#12411yescharacteristic
166C2×C4×C47C2×D811yescharacteristic
167C2×C4×C47C2×SD1611yescharacteristic
168C2×C4×C47#13511yescharacteristic
169C2×C4×C47#13511yescharacteristic
170C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
174C2×Dic47—81no—
175C2×Dic47—81no—
176C2×Dic47—81no—
177D188—42no—
178D188—42no—
179D188—42no—
180D188—42no—
181D188—82no—
182D188—82no—
183D188—81no—
184D188—81no—
185D188—81no—
186D188—81no—
187C8×C47—22no—
188C8×C47—41no—
189C8×C47—81no—
190C47⋊C8—42no—
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#39411yescharacteristic
201C22×C47#45911yescharacteristic
202C22×C47#46311yescharacteristic
203C22×C47#46511yescharacteristic
204C22×C47#46911yescharacteristic
205C22×C47#47111yescharacteristic
206C22×C47#47211yescharacteristic
207C2×D47—82no—
208C2×D47—82no—
209C2×D47—82no—
210C2×D47—161no—
211C2×D47—161no—
212C2×D47—161no—
213C2×D47—161no—
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×#459—471no—
227#1957—471no—
228#1954D4711yescharacteristic, complemented
229#1802—471no—
230C2×#334—471no—
231C2×#331—471no—
232#1296—471no—
233C2×C47—82no—
234C2×C47#166511yescharacteristic
235C2×C47#167711yescharacteristic
236C2×C47#168711yescharacteristic
237C2×C47#170111yescharacteristic
238C2×C47#203411yescharacteristic
239C2×C47#205111yescharacteristic
240C2×C47#205411yescharacteristic
241D47—162no—
242C22×D8—941no—
243C2×#127—471no—
244C2×C4×D4C2×D4711yescharacteristic
245#459—942no—
246#459—942no—
247C2×C4⋊C8—471no—
248C2×C4⋊C8—471no—
249C2×C4⋊C8C2×D4711yescharacteristic
250C2×#102—941no—
251C2×#102—941no—
252C2×#102—941no—
253C2×#102—941no—
254C2×C22⋊C8—21no—
255C2×C22⋊C8—21no—
256C2×C4×C8C2×D4711yescharacteristic
257#384—471no—
258#340—941no—
259#334—942no—
260#331—942no—
261C47#1047311yescharacteristic, complemented, Sylow
262C22×D4—941no—
263C22×D4—941no—
264C22×D4—941no—
265C22×D4D18811yescharacteristic
266C23×C4—21no—
267C2×D8—944no—
268C2×D8—1882no—
269C2×D8—1882no—
270C22×C8—21no—
271C22×C8—941no—
272C22×C8—941no—
273C22×C8C22⋊D4711yescharacteristic
274C22×C8C22⋊D4711yescharacteristic
275#127—472no—
276#127—941no—
277#127—941no—
278#127—941no—
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⋊C4D18811yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C22×D4711yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—472no—
292C4⋊C8—941no—
293C4⋊C8—941no—
294C4⋊C8—941no—
295#102—944no—
296#102—1882no—
297#102—1882no—
298#102—1882no—
299C22⋊C8—42no—
300C22⋊C8—42no—
301C4×C8—21no—
302C4×C8—21no—
303C24—21no—
304C24—1881no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—942no—
311C2×D4—942no—
312C2×D4—942no—
313C2×D4—3761no—
314C2×D4—3761no—
315C2×D4—1881no—
316C2×D4—1881no—
317C2×D4—1881no—
318C2×D4—1881no—
319C2×D4—1881no—
320C2×D4—1881no—
321C2×D4—1881no—
322C2×D4—1881no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4—1881no—
326C2×D4#1062532512yes—
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×C4C2×D18811yescharacteristic
336C22×C4#1062535011yescharacteristic
337C22×C4C2×C22⋊D4711yescharacteristic
338D8—1888no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—942no—
348C2×C8—1881no—
349C2×C8—1881no—
350C2×C8—1881no—
351C2×C8—1881no—
352C2×C8—1881no—
353C2×C8#1062533412yescomplemented
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—
363C42D4×D4711yescharacteristic
364C42D4×D4711yescharacteristic
365C42#1062535211yescharacteristic
366C42#1062535211yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—3761no—
375C23—3761no—
376C23—3761no—
377C23—3761no—
378C23—3761no—
379C23—3761no—
380C23—1882no—
381C23#1309399811yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—41no—
386D4—3762no—
387D4—3762no—
388D4—3761no—
389D4—3761no—
390D4—3761no—
391D4—3761no—
392D4—1882no—
393D4—1882no—
394D4—1882no—
395D4—1882no—
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#1309399411yescharacteristic
409C2×C4#1309399511yescharacteristic
410C2×C4#1309399611yescharacteristic
411C2×C4#1309400611yescharacteristic
412C2×C4#1309400811yescharacteristic
413C2×C4#1309401011yescharacteristic
414C2×C4C2×#1062533411yescharacteristic
415C2×C4C2×#1062532511yescharacteristic
416C2×C4#1309404411yescharacteristic
417C2×C4#1309404611yescharacteristic
418C2×C4#1309404911yescharacteristic
419C2×C4#1309405011yescharacteristic
420C2×C4#1309405211yescharacteristic
421C2×C4#1309405211yescharacteristic
422C8—22no—
423C8—41no—
424C8—81no—
425C8—3761no—
426C8—1882no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—3762no—
435C22—3762no—
436C22—3762no—
437C22—7521no—
438C22—7521no—
439C22—7521no—
440C22—7521no—
441C22#1568903911yescharacteristic
442C22#1568931811yescharacteristic
443C22#1568933811yescharacteristic
444C22#1568935211yescharacteristic
445C22#1568937611yescharacteristic
446C22#1568938611yescharacteristic
447C22#1568939311yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—7521no—
452C4#1568927011yescharacteristic
453C4#1568927611yescharacteristic
454C4#1568931511yescharacteristic
455C4#1568933511yescharacteristic
456C4#1568935711yescharacteristic
457C4#1568937411yescharacteristic
458C4#1568944211yescharacteristic
459C4#1568944811yescharacteristic
460C2—82no—
461C2—7522no—
462C2#2024272911yescharacteristic
463C2#2024279711yescharacteristic
464C2#2024286711yescharacteristic
465C2#2024294911yescharacteristic
466C2#2024457811yescharacteristic
467C2#2024467911yescharacteristic
468C2#2024469811yescharacteristic
subgroupG/H
centerC23#13093998
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1954C2
socleC23×C47#121
prime radicalC2×#15689318C2
hypercenter#1954D47
hypocenterC47#10473
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #20244194C2semidirect
3. #20243388C2semidirect
4. C2×#15688874C2semidirect
5. C2×#15688866C2semidirect
6. #20241272C2semidirect
7. C47×#1954C2semidirect
111. C2×C8×C47D8semidirect
228. #1954D47semidirect
261. C47#10473semidirect
353. C2×C8#10625334semidirect

Maximal subgroups

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

subgroupindex
C2×#156893182
#202441942
#202433882
C2×#156888742
C2×#156888662
#202412722
C47×#19542
#1047347