Finite Group Databasebeta

← #26112685

Subgroups — #26112685

Order 12032.

612 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
1D4×#10625329C211yesmaximal, characteristic, complemented
2#20244229C211yesmaximal, characteristic, complemented
3#20242056C211yesmaximal, characteristic, complemented
4#20241813C211yesmaximal, characteristic, complemented
5#20241263C211yesmaximal, characteristic, complemented
6#20241238C211yesmaximal, characteristic, complemented
7C2×C47×#459C211yesmaximal, characteristic
8C22×#10625329—21no—
9#15689201—21no—
10#15689195—22no—
11D4×C47⋊C8—21no—
12#15689176C2211yescharacteristic
13#15689147C2211yescharacteristic
14#15689147C2211yescharacteristic
15C2×#13093941—21no—
16C2×#13093941—21no—
17#15689087—21no—
18C4×#10625329C2211yescharacteristic
19#15688867—22no—
20D4⋊(C47⋊C8)—21no—
21D4⋊(C47⋊C8)—21no—
22C22×D8×C47C412yes—
23C2×#127×C47C2211yescharacteristic
24C2×C4×D4×C47C2211yescharacteristic
25C47×#459—21no—
26C47×#459—21no—
27C47×#459—21no—
28C47×#459—21no—
29C2×C4⋊C8×C47C2211yescharacteristic
30C2×#102×C47C412yes—
31C2×#10625329—22no—
32C2×#10625329—21no—
33C2×#10625329—21no—
34C2×#10625329—42no—
35C2×#10625329—42no—
36C2×#10625329D411yescharacteristic
37C2×#10625329D411yescharacteristic
38C22×C47⋊C8—22no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)D412yes—
44#13093941—42no—
45#13093941—42no—
46C22⋊(C47⋊C8)—22no—
47C22⋊(C47⋊C8)—22no—
48C22⋊(C47⋊C8)—21no—
49#13093935—21no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C22×D4×C47—21no—
53C22×D4×C47—21no—
54C22×D4×C47C2×C411yescharacteristic
55C22×D4×C47C2×C412yes—
56C23×C4×C47—21no—
57C2×D8×C47—22no—
58C2×D8×C47—22no—
59C2×D8×C47—44no—
60C22×C8×C47C2×C412yes—
61#127×C47—21no—
62#127×C47—21no—
63#127×C47—21no—
64#127×C47—21no—
65C4×D4×C47—21no—
66C4×D4×C47—21no—
67C4×D4×C47D411yescharacteristic
68C4×D4×C47D411yescharacteristic
69C4×D4×C47D411yescharacteristic
70C4×D4×C47D411yescharacteristic
71C2×C4⋊C4×C47C2×C411yescharacteristic
72C2×C22⋊C4×C47—21no—
73C2×C42×C47C2311yescharacteristic
74C4⋊C8×C47—21no—
75C4⋊C8×C47—21no—
76#102×C47—22no—
77#102×C47—22no—
78C24×C47—21no—
79C24×C47—22no—
80C2×D4×C47—22no—
81C2×D4×C47—22no—
82C2×D4×C47—21no—
83C2×D4×C47—22no—
84C2×D4×C47—41no—
85C2×D4×C47—42no—
86C2×D4×C47—42no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C2×D4×C47—41no—
90C2×D4×C47—41no—
91C2×D4×C47—41no—
92C2×D4×C47—41no—
93C2×D4×C47—41no—
94C2×D4×C47—41no—
95C2×D4×C47—82no—
96C2×D4×C47C22⋊C411yescharacteristic
97C2×D4×C47C22⋊C411yescharacteristic
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—41no—
104C22×C4×C47—41no—
105C22×C4×C47—41no—
106C22×C4×C47—41no—
107C22×C4×C47C22×C411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47#4111yescharacteristic
110D8×C47—44no—
111D8×C47—44no—
112C2×C8×C47—22no—
113C2×C8×C47—42no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47C22⋊C411yescharacteristic
116C4⋊C4×C47C22⋊C411yescharacteristic
117C22⋊C4×C47—21no—
118C22⋊C4×C47—21no—
119C22⋊C4×C47—21no—
120C22⋊C4×C47—21no—
121C42×C47C2×D411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47C2×D411yescharacteristic
124C42×C47#4111yescharacteristic
125#10625329—21no—
126#10625329—21no—
127#10625329—21no—
128#10625329—44no—
129#10625329—41no—
130#10625329—41no—
131#10625329—41no—
132#10625329—41no—
133#10625329D812yescomplemented
134C2×C47⋊C8—21no—
135C2×C47⋊C8—21no—
136C2×C47⋊C8—22no—
137C2×C47⋊C8—44no—
138C2×C47⋊C8—41no—
139C2×C47⋊C8—41no—
140C23×C47—21no—
141C23×C47—21no—
142C23×C47—42no—
143C23×C47—41no—
144C23×C47—41no—
145C23×C47—42no—
146C23×C47—42no—
147C23×C47—42no—
148C23×C47—81no—
149C23×C47—82no—
150C23×C47—82no—
151C23×C47C4×D411yescharacteristic
152D4×C47—21no—
153D4×C47—21no—
154D4×C47—21no—
155D4×C47—42no—
156D4×C47—42no—
157D4×C47—42no—
158D4×C47—82no—
159D4×C47—82no—
160D4×C47—82no—
161D4×C47—81no—
162D4×C47—81no—
163D4×C47—81no—
164D4×C47—81no—
165D4×C47#10012yescomplemented
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—21no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47—41no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47—41no—
177C2×C4×C47—41no—
178C2×C4×C47—41no—
179C2×C4×C47—41no—
180C2×C4×C47—41no—
181C2×C4×C47C2×C22⋊C411yescharacteristic
182C2×C4×C47C4×D411yescharacteristic
183C2×C4×C47#12011yescharacteristic
184C2×C4×C47#12111yescharacteristic
185C2×C4×C47#12111yescharacteristic
186C2×C4×C47#12311yescharacteristic
187C2×C4×C47C2×D811yescharacteristic
188C2×C4×C47#13511yescharacteristic
189C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
191C8×C47—42no—
192C47⋊C8—22no—
193C47⋊C8—42no—
194C47⋊C8—41no—
195C47⋊C8—81no—
196C47⋊C8—81no—
197#9253—471nomaximal, Sylow
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—22no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—82no—
207C22×C47—82no—
208C22×C47—82no—
209C22×C47—82no—
210C22×C47—82no—
211C22×C47—162no—
212C22×C47—162no—
213C22×C47#38611yescharacteristic
214C22×C47C4×D811yescharacteristic
215C22×C47#44211yescharacteristic
216C4×C47—21no—
217C4×C47—21no—
218C4×C47—21no—
219C4×C47—41no—
220C4×C47—41no—
221C4×C47C2×#10011yescharacteristic
222C4×C47#41311yescharacteristic
223C4×C47#44711yescharacteristic
224C4×C47#44911yescharacteristic
225C4×C47#45911yescharacteristic
226C4×C47#46311yescharacteristic
227C2×#459D4711yescharacteristic
228D4×M16—471no—
229#1965—471no—
230#1545—471no—
231#1486—471no—
232#1292—471no—
233#1283—471no—
234C2×C47—21no—
235C2×C47—21no—
236C2×C47—42no—
237C2×C47—81no—
238C2×C47—162no—
239C2×C47#187911yescharacteristic
240C2×C47#190011yescharacteristic
241C2×C47#190311yescharacteristic
242C22×D8Dic4712yes—
243C22×M16—941no—
244C2×#127C2×D4711yescharacteristic
245C2×C4×D4C2×D4711yescharacteristic
246#459—21no—
247#459—21no—
248#459—21no—
249#459—21no—
250#436—941no—
251#435—942no—
252C8×D4—941no—
253#431—471no—
254#423—471no—
255#423—471no—
256C2×C4⋊C8C2×D4711yescharacteristic
257C2×#102Dic4712yes—
258C2×#100—941no—
259C2×#100—941no—
260#407—941no—
261C4×M16—471no—
262#331—942no—
263D4⋊C8—941no—
264D4⋊C8—941no—
265C47#925311yescharacteristic, complemented, Sylow
266C22×D4—21no—
267C22×D4—21no—
268C22×D4C2×Dic4711yescharacteristic
269C22×D4C2×Dic4712yes—
270C23×C4—21no—
271C2×D8—22no—
272C2×D8—22no—
273C2×D8—44no—
274C2×M16—471no—
275C2×M16—471no—
276C2×M16—942no—
277C2×M16—941no—
278C2×M16—941no—
279C2×M16—1882no—
280C2×M16—1882no—
281C22×C8—942no—
282C22×C8C2×Dic4712yes—
283#127—21no—
284#127—21no—
285#127—21no—
286#127—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4C22⋊D4711yescharacteristic
290C4×D4C22⋊D4711yescharacteristic
291C4×D4C22⋊D4711yescharacteristic
292C4×D4C22⋊D4711yescharacteristic
293C2×C4⋊C4C2×Dic4711yescharacteristic
294C2×C22⋊C4—21no—
295C2×C42C22×D4711yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—472no—
299C4⋊C8—941no—
300C4⋊C8—941no—
301C4⋊C8—941no—
302C4⋊C8—941no—
303#102—22no—
304#102—22no—
305#100—1882no—
306#100—1882no—
307C22⋊C8—942no—
308C22⋊C8—942no—
309C22⋊C8—941no—
310#97—941no—
311C4×C8—941no—
312C4×C8—941no—
313C24—21no—
314C24—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—42no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—82no—
331C2×D4C22⋊Dic4711yescharacteristic
332C2×D4C22⋊Dic4711yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4D4×D4711yescharacteristic
343C22×C4#1062535211yescharacteristic
344C22×C4C22×Dic4711yescharacteristic
345D8—44no—
346D8—44no—
347M16—472no—
348M16—941no—
349M16—941no—
350M16—941no—
351M16—1884no—
352M16—1881no—
353M16—1881no—
354M16—1881no—
355M16—1881no—
356C2×C8—22no—
357C2×C8—42no—
358C2×C8—941no—
359C2×C8—941no—
360C2×C8—942no—
361C2×C8—1884no—
362C2×C8—1881no—
363C2×C8—1881no—
364C4⋊C4—21no—
365C4⋊C4C22⋊Dic4711yescharacteristic
366C4⋊C4C22⋊Dic4711yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C42D4×D4711yescharacteristic
372C42#1062535211yescharacteristic
373C42C2×C22⋊D4711yescharacteristic
374C42C2×C22⋊D4711yescharacteristic
375C23—21no—
376C23—21no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—82no—
385C23—82no—
386C23D4×Dic4711yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—42no—
392D4—42no—
393D4—82no—
394D4—82no—
395D4—82no—
396D4—81no—
397D4—81no—
398D4—81no—
399D4—81no—
400D4#1309394112yescomplemented
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4C2×C22⋊Dic4711yescharacteristic
417C2×C4D4×Dic4711yescharacteristic
418C2×C4#1309399211yescharacteristic
419C2×C4#1309399611yescharacteristic
420C2×C4#1309399611yescharacteristic
421C2×C4#1309400511yescharacteristic
422C2×C4D8×D4711yescharacteristic
423C2×C4#1309404311yescharacteristic
424C2×C4#1309404811yescharacteristic
425C2×C4#1309404811yescharacteristic
426C8—42no—
427C8—942no—
428C8—3761no—
429C8—3761no—
430C8—1882no—
431C8—1881no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—162no—
446C22—162no—
447C22#1568900311yescharacteristic
448C22D8×Dic4711yescharacteristic
449C22#1568923511yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—41no—
455C4C2×#1309394111yescharacteristic
456C4#1568910711yescharacteristic
457C4#1568925511yescharacteristic
458C4#1568926511yescharacteristic
459C4#1568931611yescharacteristic
460C4#1568933611yescharacteristic
461C2—21no—
462C2—21no—
463C2—42no—
464C2—81no—
465C2—162no—
466C2#2024373811yescharacteristic
467C2#2024385211yescharacteristic
468C2#2024387011yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC2×C47×#459C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenterC2×#459D47
hypocenterC47#9253
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. D4×#10625329C2semidirect
2. #20244229C2semidirect
3. #20242056C2semidirect
4. #20241813C2semidirect
5. #20241263C2semidirect
6. #20241238C2semidirect
133. #10625329D8semidirect
165. D4×C47#100semidirect
265. C47#9253semidirect
400. D4#13093941semidirect

Maximal subgroups

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

subgroupindex
D4×#106253292
#202442292
#202420562
#202418132
#202412632
#202412382
C2×C47×#4592
#925347