Finite Group Databasebeta

← #26109646

Subgroups — #26109646

Order 12032.

496 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#20245784C211yesmaximal, characteristic
2#20243365C211yesmaximal, characteristic
3C4×(C2×D47)⋊C8C211yesmaximal, characteristic
4#20241229C211yesmaximal, characteristic, complemented
5#20241228C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C47×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D47C2211yescharacteristic
9C2×C4⋊(C47⋊C8)C2211yescharacteristic
10C2×(C2×D47)⋊C8—21no—
11C2×(C2×D47)⋊C8—21no—
12C2×C4×C47⋊C8C2211yescharacteristic
13#15688990—21no—
14#15688988C411yescharacteristic
15#15688988C411yescharacteristic
16#15688985—21no—
17#15688980C411yescharacteristic
18#15688980C411yescharacteristic
19C4×C4⋊Dic47C2211yescharacteristic
20C4×(C2×D47)⋊C4—21no—
21#15688969—21no—
22#15688877—21no—
23#15688877—21no—
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C4×C4⋊C4×C47C2211yescharacteristic
27C22×C4×D47C2×C411yescharacteristic
28C22×C4×D47D411yescharacteristic
29C22×C4×D47D411yescharacteristic
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32C2×C4⋊Dic47C2×C411yescharacteristic
33C2×C4⋊Dic47C2×C411yescharacteristic
34C2×(C2×D47)⋊C4—21no—
35C2×(C2×D47)⋊C4—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47C2×C411yescharacteristic
38C2×C4×Dic47D411yescharacteristic
39C2×C4×Dic47D411yescharacteristic
40C42×D47—21no—
41C42×D47—21no—
42C42×D47—21no—
43C42×D47—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)—21no—
46(C2×D47)⋊C8—24no—
47(C2×D47)⋊C8—42no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C47⋊#95—21no—
51C47⋊#95—21no—
52C47⋊#95—21no—
53C47⋊#95—21no—
54C47⋊#95—21no—
55C47⋊#95—21no—
56C47⋊#95—21no—
57C22×C8×C47—21no—
58C22×C8×C47—21no—
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C4⋊C4×C47C2×C411yescharacteristic
61C2×C42×C47—21no—
62C2×C42×C47C2311yescharacteristic
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4×C8×C47—21no—
66C4×C8×C47—21no—
67#95×C47—21no—
68C23×D47C22⋊C411yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47C22⋊C411yescharacteristic
77C22×Dic47C22⋊C411yescharacteristic
78C22×Dic47C22⋊C411yescharacteristic
79C2×C4×D47—22no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47—21no—
88C2×C4×D47—21no—
89C2×C4×D47—21no—
90C2×C4×D47—21no—
91C2×C4×D47—21no—
92C2×C4×D47—21no—
93C2×C4×D47—21no—
94C2×C4×D47—41no—
95C2×C8×C47—22no—
96C2×C8×C47—41no—
97C2×C8×C47—41no—
98C2×C8×C47—41no—
99C2×C8×C47—41no—
100C2×C8×C47—41no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C42×C47—41no—
106C42×C47—41no—
107C42×C47#4111yescharacteristic
108C42×C47#4111yescharacteristic
109C42×C47#4111yescharacteristic
110C42×C47#4111yescharacteristic
111(C2×D47)⋊C4—42no—
112(C2×D47)⋊C4—42no—
113C4⋊Dic47—21no—
114C4⋊Dic47—21no—
115C4⋊Dic47—21no—
116C4⋊Dic47—21no—
117C4×Dic47—21no—
118C4×Dic47—21no—
119C4×Dic47—21no—
120C4×Dic47—21no—
121C4×Dic47—21no—
122C4×Dic47—21no—
123C4×Dic47—41no—
124C4×Dic47—41no—
125C2×C47⋊C8—22no—
126C2×C47⋊C8—41no—
127C2×C47⋊C8—41no—
128C2×C47⋊C8—41no—
129C2×C47⋊C8—41no—
130C2×C47⋊C8—41no—
131C23×C47C2×C22⋊C411yescharacteristic
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—21no—
138C22×D47#10412yes—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47#11711yescharacteristic
148C2×C4×C47#11711yescharacteristic
149C2×C4×C47#12311yescharacteristic
150C2×C4×C47#12311yescharacteristic
151C2×C4×C47#12311yescharacteristic
152C2×C4×C47#12311yescharacteristic
153C2×C4×C47#13111yescharacteristic
154C2×C4×C47#13111yescharacteristic
155C2×C4×C47#13111yescharacteristic
156C2×C4×C47#13111yescharacteristic
157C2×C4×C47#13511yescharacteristic
158C2×C4×C47#13511yescharacteristic
159C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C47#13711yescharacteristic
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47—41no—
173C2×Dic47—41no—
174C2×Dic47—41no—
175C2×Dic47—41no—
176C4×D47—42no—
177C4×D47—42no—
178C4×D47—41no—
179C4×D47—41no—
180C4×D47—41no—
181C4×D47—41no—
182C4×D47—41no—
183C4×D47—41no—
184C4×D47—41no—
185C4×D47—41no—
186C8×C47—42no—
187C8×C47—81no—
188C47⋊C8—42no—
189C47⋊C8—81no—
190#8711—471nomaximal, Sylow
191C22×C47#38111yescharacteristic
192C22×C47#40811yescharacteristic
193C22×C47#40811yescharacteristic
194C22×C47#41611yescharacteristic
195C22×C47#41711yescharacteristic
196C22×C47C2×#10411yescharacteristic
197C22×C47#42111yescharacteristic
198C2×D47—22no—
199C2×D47—22no—
200C2×D47—22no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47—41no—
204C2×D47—41no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—81no—
208C4×C47—81no—
209C4×C47#43311yescharacteristic
210C4×C47#43311yescharacteristic
211C4×C47#43311yescharacteristic
212C4×C47#43311yescharacteristic
213C4×C47#48211yescharacteristic
214C4×C47#48211yescharacteristic
215C4×C47#48511yescharacteristic
216C4×C47#48511yescharacteristic
217Dic47—41no—
218Dic47—41no—
219Dic47—41no—
220Dic47—81no—
221Dic47—81no—
222#2283—471no—
223#1797—471no—
224C4×C22⋊C8—471no—
225#1279—471no—
226#1279—471no—
227#1279—471no—
228#1279D4711yescharacteristic, complemented
229C2×C47#148211yescharacteristic
230C2×C47#148311yescharacteristic
231C2×C47#149411yescharacteristic
232C2×C47#149511yescharacteristic
233C2×C47#181811yescharacteristic
234C2×C47#182511yescharacteristic
235C2×C47#182611yescharacteristic
236D47—42no—
237C22×C42—471no—
238C2×C4⋊C8—471no—
239C2×C4⋊C8C2×D4711yescharacteristic
240C2×C22⋊C8—941no—
241C2×C22⋊C8—941no—
242C2×C4×C8—471no—
243C2×C4×C8C2×D4711yescharacteristic
244#383—941no—
245#382—471no—
246#382—471no—
247#381—941no—
248#380—471no—
249#380—471no—
250C4×C4⋊C4—471no—
251C4×C4⋊C4C2×D4711yescharacteristic
252C4×C22⋊C4—941no—
253#376—941no—
254#336—941no—
255#336—941no—
256C47#871111yescharacteristic, complemented, Sylow
257C23×C4—471no—
258C23×C4—471no—
259C23×C4—471no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—941no—
263C22×C8—941no—
264C2×C4⋊C4—471no—
265C2×C4⋊C4—471no—
266C2×C4⋊C4C4×D4711yescharacteristic
267C2×C4⋊C4C4×D4711yescharacteristic
268C2×C22⋊C4—941no—
269C2×C22⋊C4—941no—
270C2×C42—21no—
271C2×C42—471no—
272C2×C42—471no—
273C2×C42—471no—
274C2×C42—941no—
275C2×C42—941no—
276C2×C42—941no—
277C2×C42—941no—
278C2×C42—941no—
279C2×C42C22×D4711yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—941no—
283C4⋊C8—941no—
284C22⋊C8—944no—
285C22⋊C8—1882no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8—941no—
289C4×C8—941no—
290#95—21no—
291#95—941no—
292#95—941no—
293#95—941no—
294#95—941no—
295#95—941no—
296#95—941no—
297#95—941no—
298C24—471no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—471no—
302C22×C4—471no—
303C22×C4—471no—
304C22×C4—942no—
305C22×C4—941no—
306C22×C4—941no—
307C22×C4—941no—
308C22×C4—941no—
309C22×C4—941no—
310C22×C4—941no—
311C22×C4—941no—
312C22×C4—941no—
313C22×C4—941no—
314C22×C4—941no—
315C22×C4—941no—
316C22×C4—941no—
317C22×C4—941no—
318C22×C4—941no—
319C22×C4—941no—
320C22×C4—941no—
321C22×C4—1881no—
322C22×C4C2×C4×D4711yescharacteristic
323C22×C4D4×D4711yescharacteristic
324C22×C4D4×D4711yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—942no—
332C2×C8—1881no—
333C2×C8—1881no—
334C2×C8—1881no—
335C2×C8—1881no—
336C2×C8—1881no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—941no—
342C4⋊C4—941no—
343C4⋊C4—941no—
344C4⋊C4—941no—
345C22⋊C4—1882no—
346C22⋊C4—1882no—
347C42—41no—
348C42—41no—
349C42—941no—
350C42—941no—
351C42—941no—
352C42—941no—
353C42—941no—
354C42—941no—
355C42—1881no—
356C42—1881no—
357C42#1062535011yescharacteristic
358C42#1062535011yescharacteristic
359C42#1062535211yescharacteristic
360C42#1062535411yescharacteristic
361C23—472no—
362C23—941no—
363C23—941no—
364C23—941no—
365C23—941no—
366C23—941no—
367C23—941no—
368C23C22⋊C4×D4711yescharacteristic
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—1882no—
387C2×C4—1882no—
388C2×C4—1881no—
389C2×C4—1881no—
390C2×C4—1881no—
391C2×C4—1881no—
392C2×C4—1881no—
393C2×C4—1881no—
394C2×C4—1881no—
395C2×C4—1881no—
396C2×C4—1881no—
397C2×C4—1881no—
398C2×C4—1881no—
399C2×C4—1881no—
400C2×C4—1881no—
401C2×C4—1881no—
402C2×C4#1309398111yescharacteristic
403C2×C4#1309398211yescharacteristic
404C2×C4#1309400611yescharacteristic
405C2×C4#1309400611yescharacteristic
406C2×C4#1309400911yescharacteristic
407C2×C4#1309400911yescharacteristic
408C2×C4#1309403011yescharacteristic
409C2×C4#1309403011yescharacteristic
410C2×C4#1309403211yescharacteristic
411C2×C4#1309403211yescharacteristic
412C2×C4#1309404511yescharacteristic
413C2×C4#1309404711yescharacteristic
414C2×C4#1309404811yescharacteristic
415C2×C4#1309405311yescharacteristic
416C8—42no—
417C8—81no—
418C8—3761no—
419C8—1882no—
420C22—942no—
421C22—942no—
422C22—942no—
423C22—1881no—
424C22—1881no—
425C22—1881no—
426C22—1881no—
427C22#1568898511yescharacteristic
428C22#1568908811yescharacteristic
429C22#1568908811yescharacteristic
430C22#1568911811yescharacteristic
431C22#1568912111yescharacteristic
432C22#104×D4711yescharacteristic
433C22#1568913811yescharacteristic
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—3761no—
439C4—3761no—
440C4—1881no—
441C4—1881no—
442C4—1881no—
443C4#1568918211yescharacteristic
444C4#1568918311yescharacteristic
445C4#1568918311yescharacteristic
446C4#1568918511yescharacteristic
447C4#1568944611yescharacteristic
448C4#1568945011yescharacteristic
449C4#1568946311yescharacteristic
450C4#1568946711yescharacteristic
451C2—1882no—
452C2#2024179511yescharacteristic
453C2#2024179811yescharacteristic
454C2#2024184711yescharacteristic
455C2#2024185011yescharacteristic
456C2#2024345811yescharacteristic
457C2#2024348211yescharacteristic
458C2#2024348611yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1279D47
hypocenterC47#8711
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #20241229C2semidirect
5. #20241228C2semidirect
6. #20241227C2semidirect
7. C47×#1279C2semidirect
228. #1279D47semidirect
256. C47#8711semidirect

Maximal subgroups

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

subgroupindex
#202457842
#202433652
C4×(C2×D47)⋊C82
#202412292
#202412282
#202412272
C47×#12792
#871147