Finite Group Databasebeta

← #26109599

Subgroups — #26109599

Order 12032.

1158 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C47⋊#95C211yesmaximal, characteristic
2#20243298C211yesmaximal, characteristic
3#20241230C214yesmaximal, complemented
4C47×#1779C211yesmaximal, characteristic
5C24×Dic47C411yescharacteristic
6C24×Dic47C411yescharacteristic
7C2×C22⋊(C47⋊C8)—21no—
8C2×C22⋊(C47⋊C8)—21no—
9C2×C22⋊(C47⋊C8)C2212yes—
10C2×C47⋊#95—21no—
11C2×C47⋊#95—21no—
12C2×C47⋊#95—21no—
13C2×C47⋊#95—21no—
14C2×C47⋊#95C412yes—
15C2×C47⋊#95C2212yes—
16C24×C4×C47C2211yescharacteristic
17C2×C22⋊C8×C47—21no—
18C2×C22⋊C8×C47—21no—
19C2×C22⋊C8×C47C2212yes—
20C23×Dic47—21no—
21C23×Dic47—21no—
22C23×Dic47—21no—
23C23×Dic47—21no—
24C23×Dic47—22no—
25C23×Dic47—24no—
26C23×Dic47—42no—
27C23×Dic47—42no—
28C23×Dic47—42no—
29C23×Dic47—42no—
30C23×Dic47C814yescomplemented
31C23×Dic47C2×C412yes—
32C23×Dic47C2×C412yes—
33C22×C47⋊C8—22no—
34C22⋊(C47⋊C8)—24no—
35C22⋊(C47⋊C8)—42no—
36C22⋊(C47⋊C8)—42no—
37C47⋊#95—22no—
38C47⋊#95—22no—
39C47⋊#95—22no—
40C47⋊#95—22no—
41C25×C47C2×C411yescharacteristic
42C23×C4×C47—24no—
43C23×C4×C47—42no—
44C23×C4×C47—42no—
45C23×C4×C47C2×C411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C23×C4×C47D411yescharacteristic
48C23×C4×C47D411yescharacteristic
49C23×C4×C47D411yescharacteristic
50C23×C4×C47C2311yescharacteristic
51C22×C8×C47—22no—
52C22⋊C8×C47—24no—
53C22⋊C8×C47—42no—
54C22⋊C8×C47—42no—
55C24×C47—22no—
56C24×C47—22no—
57C24×C47—22no—
58C24×C47—22no—
59C24×C47—22no—
60C24×C47—22no—
61C24×C47C22⋊C411yescharacteristic
62C24×C47C22⋊C411yescharacteristic
63C24×C47C2×C812yes—
64C24×C47M1612yes—
65C24×C47C22×C411yescharacteristic
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—22no—
71C22×C4×C47—22no—
72C22×C4×C47—22no—
73C22×C4×C47—22no—
74C22×C4×C47—22no—
75C22×C4×C47—41no—
76C22×C4×C47—41no—
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×C47—416no—
84C22×C4×C47C22⋊C411yescharacteristic
85C22×C4×C47C22⋊C411yescharacteristic
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47#4114yes—
89C22×Dic47—24no—
90C22×Dic47—24no—
91C22×Dic47—24no—
92C22×Dic47—24no—
93C22×Dic47—22no—
94C22×Dic47—22no—
95C22×Dic47—22no—
96C22×Dic47—22no—
97C22×Dic47—416no—
98C22×Dic47—48no—
99C22×Dic47—42no—
100C22×Dic47—42no—
101C22×Dic47—42no—
102C22×Dic47—42no—
103C22×Dic47—42no—
104C22×Dic47—42no—
105C22×Dic47—42no—
106C22×Dic47—42no—
107C22×Dic47—48no—
108C22×Dic47—42no—
109C22×Dic47—42no—
110C22×Dic47—42no—
111C22×Dic47—42no—
112C22×Dic47C2×C814yes—
113C22×Dic47M1614yes—
114C2×C8×C47—42no—
115C2×C8×C47—42no—
116C2×C8×C47—42no—
117C2×C47⋊C8—42no—
118C2×C47⋊C8—42no—
119C2×C47⋊C8—42no—
120C23×C47—28no—
121C23×C47—28no—
122C23×C47—28no—
123C23×C47—28no—
124C23×C47—24no—
125C23×C47—24no—
126C23×C47—24no—
127C23×C47—24no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47—21no—
140C23×C47—24no—
141C23×C47—24no—
142C23×C47C22⋊C812yes—
143C23×C47C22⋊C812yes—
144C23×C47#9912yes—
145C23×C47#9912yes—
146C23×C47#10012yes—
147C23×C47#10112yes—
148C23×C47C2×C22⋊C411yescharacteristic
149C23×C47#11712yes—
150C23×C47C22×C811yescharacteristic
151C23×C47C2×M1612yes—
152C23×C47C2×M1611yescharacteristic
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—44no—
164C2×C4×C47—44no—
165C2×C4×C47—44no—
166C2×C4×C47—44no—
167C2×C4×C47—44no—
168C2×C4×C47—44no—
169C2×C4×C47#12312yes—
170C2×C4×C47#12312yes—
171C2×Dic47—24no—
172C2×Dic47—24no—
173C2×Dic47—48no—
174C2×Dic47—44no—
175C2×Dic47—48no—
176C2×Dic47—48no—
177C2×Dic47—44no—
178C2×Dic47—48no—
179C2×Dic47—42no—
180C2×Dic47—42no—
181C2×Dic47—42no—
182C2×Dic47—42no—
183C2×Dic47—44no—
184C2×Dic47—44no—
185C8×C47—82no—
186C47⋊C8—82no—
187#8698—471nomaximal, Sylow
188C22×C47—216no—
189C22×C47—216no—
190C22×C47—22no—
191C22×C47—22no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—22no—
195C22×C47—22no—
196C22×C47—22no—
197C22×C47—22no—
198C22×C47—22no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—22no—
202C22×C47—21no—
203C22×C47—21no—
204C22×C47—22no—
205C22×C47—22no—
206C22×C47—22no—
207C22×C47—22no—
208C22×C47—22no—
209C22×C47—22no—
210C22×C47#32314yes—
211C22×C47#32414yes—
212C22×C47#38111yescharacteristic
213C22×C47C2×C22⋊C811yescharacteristic
214C22×C47#40711yescharacteristic
215C22×C47C2×#9911yescharacteristic
216C22×C47C2×#9911yescharacteristic
217C22×C47C2×#10011yescharacteristic
218C22×C47C2×#10111yescharacteristic
219C22×C47#43112yes—
220C22×C47#43212yes—
221C4×C47—22no—
222C4×C47—22no—
223C4×C47—41no—
224C4×C47—41no—
225Dic47—44no—
226Dic47—44no—
227C22×#95—471no—
228#1779—471no—
229#1779D4711yescharacteristic
230#1280—474no—
231C2×C47—24no—
232C2×C47—24no—
233C2×C47—22no—
234C2×C47—22no—
235C2×C47C2×#32311yescharacteristic
236C2×C47C2×#32411yescharacteristic
237C2×C47#146211yescharacteristic
238C2×C47#146311yescharacteristic
239C2×C47#181711yescharacteristic
240C2×C47#181911yescharacteristic
241C2×C47#182111yescharacteristic
242C24×C4—471no—
243C24×C4—471no—
244C24×C4C2×D4711yescharacteristic
245C2×C22⋊C8—21no—
246C2×C22⋊C8—21no—
247C2×C22⋊C8—472no—
248C2×C22⋊C8—941no—
249C2×C22⋊C8—941no—
250C2×C22⋊C8C2×D4712yes—
251C2×#95—472no—
252C2×#95—472no—
253C2×#95—941no—
254C2×#95—941no—
255C2×#95—941no—
256C2×#95—941no—
257C47#869811yescharacteristic, complemented, Sylow
258C25C4×D4711yescharacteristic
259C23×C4—24no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—474no—
263C23×C4—472no—
264C23×C4—472no—
265C23×C4—944no—
266C23×C4—942no—
267C23×C4—941no—
268C23×C4—941no—
269C23×C4—941no—
270C23×C4—941no—
271C23×C4—1882no—
272C23×C4—1882no—
273C23×C4—1882no—
274C23×C4—1882no—
275C23×C4C4×D4711yescharacteristic
276C23×C4D18811yescharacteristic
277C23×C4D18811yescharacteristic
278C23×C4C22⋊D4711yescharacteristic
279C23×C4C22⋊D4711yescharacteristic
280C23×C4C22×D4711yescharacteristic
281C22×C8—22no—
282C22×C8—942no—
283C22⋊C8—24no—
284C22⋊C8—42no—
285C22⋊C8—42no—
286C22⋊C8—944no—
287C22⋊C8—1882no—
288C22⋊C8—1882no—
289#95—942no—
290#95—942no—
291#95—942no—
292#95—942no—
293C24—22no—
294C24—22no—
295C24—22no—
296C24—22no—
297C24—22no—
298C24—22no—
299C24C8×D4712yes—
300C24#1062532412yes—
301C24(C2×D47)⋊C411yescharacteristic
302C24(C2×D47)⋊C411yescharacteristic
303C24C2×C4×D4711yescharacteristic
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—416no—
322C22×C4—474no—
323C22×C4—474no—
324C22×C4—944no—
325C22×C4—944no—
326C22×C4—944no—
327C22×C4—944no—
328C22×C4—942no—
329C22×C4—942no—
330C22×C4—942no—
331C22×C4—942no—
332C22×C4—18816no—
333C22×C4—1882no—
334C22×C4—1882no—
335C22×C4—1882no—
336C22×C4—1882no—
337C22×C4—1888no—
338C22×C4—1882no—
339C22×C4—1882no—
340C22×C4—1882no—
341C22×C4—1882no—
342C22×C4—1882no—
343C22×C4—1882no—
344C22×C4—1882no—
345C22×C4—1882no—
346C22×C4—1888no—
347C22×C4(C2×D47)⋊C411yescharacteristic
348C22×C4(C2×D47)⋊C411yescharacteristic
349C22×C4C2×D18811yescharacteristic
350C22×C4#1062535214yes—
351C22×C4C2×C22⋊D4711yescharacteristic
352C2×C8—42no—
353C2×C8—42no—
354C2×C8—42no—
355C2×C8—1882no—
356C2×C8—1882no—
357C2×C8—1882no—
358C23—28no—
359C23—28no—
360C23—28no—
361C23—28no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—24no—
373C23—24no—
374C23—21no—
375C23—21no—
376C23—24no—
377C23—24no—
378C23—24no—
379C23—24no—
380C23(C2×D47)⋊C812yes—
381C23(C2×D47)⋊C812yes—
382C23#1309393812yes—
383C23#1309393812yes—
384C23#1309394012yes—
385C23#1309394212yes—
386C23C2×(C2×D47)⋊C411yescharacteristic
387C23#1309398012yes—
388C23C2×C8×D4711yescharacteristic
389C23M16×D4712yes—
390C23C2×#1062532411yescharacteristic
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—944no—
408C2×C4—944no—
409C2×C4—1888no—
410C2×C4—1884no—
411C2×C4—1888no—
412C2×C4—1888no—
413C2×C4—1884no—
414C2×C4—1882no—
415C2×C4—1882no—
416C2×C4—1882no—
417C2×C4—1882no—
418C2×C4—1888no—
419C2×C4—1884no—
420C2×C4—1884no—
421C2×C4#1309400512yes—
422C2×C4#1309400812yes—
423C8—82no—
424C8—3762no—
425C22—216no—
426C22—216no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—21no—
435C22—21no—
436C22—22no—
437C22—21no—
438C22—21no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22#1568884614yes—
448C22#1568884814yes—
449C22#1568898411yescharacteristic
450C22C2×(C2×D47)⋊C811yescharacteristic
451C22#1568908611yescharacteristic
452C22C2×#1309393811yescharacteristic
453C22C2×#1309393811yescharacteristic
454C22C2×#1309394011yescharacteristic
455C22C2×#1309394211yescharacteristic
456C22#1568917312yes—
457C22#1568917712yes—
458C4—22no—
459C4—22no—
460C4—41no—
461C4—41no—
462C4—1884no—
463C4—1884no—
464C2—24no—
465C2—24no—
466C2—22no—
467C2—22no—
468C2C2×#1568884611yescharacteristic
469C2C2×#1568884811yescharacteristic
470C2#2024171411yescharacteristic
471C2#2024171711yescharacteristic
472C2#2024345411yescharacteristic
473C2#2024346011yescharacteristic
474C2#2024346611yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC23×C47C22×C8
FrattiniC23×C4C22×D47
FittingC47×#1779C2
socleC23×C47C2×C22⋊C4
prime radicalC25×C47C2×C4
cosocleC23×C4×C47C23
hypercenter#1779D47
hypocenterC47#8698
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. #20241230C2semidirect
30. C23×Dic47C8semidirect
257. C47#8698semidirect

Maximal subgroups

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

subgroupindex
C22×C47⋊#952
#202432982
#202412302
C47×#17792
#869847