Finite Group Databasebeta

← #26108980

Subgroups — #26108980

Order 12032.

568 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#20245849C211yesmaximal, characteristic
2#20243539C211yesmaximal, characteristic, complemented
3C4×Dic47⋊C8C211yesmaximal, characteristic, complemented
4C2×#15688852C211yesmaximal, characteristic
5C2×#15688850C211yesmaximal, characteristic
6#20241229C211yesmaximal, characteristic, complemented
7C47×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D188C2211yescharacteristic
9C2×#13093981—21no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×Dic47⋊C8—21no—
12C2×Dic47⋊C8—21no—
13C2×Dic47⋊C8—21no—
14C2×C4×C47⋊C8C2211yescharacteristic
15#15689024C411yescharacteristic
16#15689024C411yescharacteristic
17#15689019C411yescharacteristic
18#15689019C411yescharacteristic
19#15689012—21no—
20#15689012—21no—
21C4×(C2×D47)⋊C4—21no—
22C42×Dic47C2211yescharacteristic
23#15688877—21no—
24#15688852—22no—
25#15688850—22no—
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4×C8×C47C2211yescharacteristic
28C4×C4⋊C4×C47C2211yescharacteristic
29C22×D188C2×C411yescharacteristic
30C22×C4×D47—21no—
31C22×C47⋊C8—21no—
32C22×C47⋊C8—21no—
33C4×D188—21no—
34C4×D188—21no—
35C4×D188D412yes—
36C4×D188Q812yes—
37#13093981—42no—
38#13093981—42no—
39C2×C4⋊Dic47C2×C411yescharacteristic
40C2×Dic47⋊C4—21no—
41C2×Dic47⋊C4—21no—
42C2×(C2×D47)⋊C4—21no—
43C2×(C2×D47)⋊C4—21no—
44C2×(C2×D47)⋊C4—21no—
45C2×(C2×D47)⋊C4—21no—
46C2×(C2×D47)⋊C4—21no—
47C2×C4×Dic47C2×C411yescharacteristic
48C2×C4×Dic47C2×C411yescharacteristic
49C2×C4×Dic47D411yescharacteristic
50C2×C4×Dic47D411yescharacteristic
51C2×C4×Dic47D411yescharacteristic
52C2×C4×Dic47D411yescharacteristic
53C4⋊(C47⋊C8)—21no—
54C4⋊(C47⋊C8)—21no—
55Dic47⋊C8—24no—
56Dic47⋊C8—42no—
57Dic47⋊C8—42no—
58C4×C47⋊C8—21no—
59C4×C47⋊C8—21no—
60C47⋊#95—21no—
61C47⋊#95—21no—
62C22×C8×C47—21no—
63C22×C8×C47—21no—
64C2×C4⋊C4×C47C2×C411yescharacteristic
65C2×C4⋊C4×C47C2×C411yescharacteristic
66C2×C42×C47—21no—
67C2×C42×C47C2311yescharacteristic
68C4⋊C8×C47—21no—
69C4⋊C8×C47—21no—
70C4×C8×C47—21no—
71C4×C8×C47—21no—
72#95×C47—21no—
73C23×D47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47C22×C411yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C22×C4×C47C2×D411yescharacteristic
79C22×Dic47—21no—
80C22×Dic47C22⋊C411yescharacteristic
81C22×Dic47C22⋊C411yescharacteristic
82C22×Dic47C22⋊C411yescharacteristic
83C22×Dic47C22⋊C411yescharacteristic
84C2×D188—21no—
85C2×D188—21no—
86C2×D188—21no—
87C2×D188—21no—
88C2×D188—21no—
89C2×D188C4⋊C412yes—
90C2×C4×D47—22no—
91C2×C4×D47—22no—
92C2×C4×D47—41no—
93C2×C4×D47—41no—
94C2×C4×D47—41no—
95C2×C4×D47—41no—
96C2×C8×C47—22no—
97C2×C8×C47—41no—
98C2×C8×C47—41no—
99C2×C8×C47—41no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C42×C47—41no—
107C42×C47—41no—
108C42×C47C2×D411yescharacteristic
109C42×C47C2×Q811yescharacteristic
110C42×C47#4111yescharacteristic
111C42×C47#4111yescharacteristic
112(C2×D47)⋊C4—22no—
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—42no—
115(C2×D47)⋊C4—42no—
116(C2×D47)⋊C4—42no—
117(C2×D47)⋊C4—42no—
118C4⋊Dic47—21no—
119C4⋊Dic47C4⋊C412yes—
120Dic47⋊C4—42no—
121Dic47⋊C4—42no—
122C4×Dic47—21no—
123C4×Dic47—21no—
124C4×Dic47—21no—
125C4×Dic47—21no—
126C4×Dic47—21no—
127C4×Dic47—21no—
128C4×Dic47—22no—
129C4×Dic47—41no—
130C4×Dic47D812yes—
131C4×Dic47SD1612yes—
132C2×C47⋊C8—22no—
133C2×C47⋊C8—41no—
134C2×C47⋊C8—41no—
135C2×C47⋊C8—41no—
136C2×C47⋊C8—41no—
137C2×C47⋊C8—41no—
138C23×C47C2×C22⋊C411yescharacteristic
139C22×D47—22no—
140C22×D47—41no—
141C22×D47—41no—
142C22×D47—41no—
143C22×D47—41no—
144C22×D47—41no—
145C22×D47—41no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—41no—
154C2×C4×C47C2×C4⋊C411yescharacteristic
155C2×C4×C47#11711yescharacteristic
156C2×C4×C47#12111yescharacteristic
157C2×C4×C47#12111yescharacteristic
158C2×C4×C47C22⋊Q811yescharacteristic
159C2×C4×C47C22⋊Q811yescharacteristic
160C2×C4×C47#13111yescharacteristic
161C2×C4×C47#13111yescharacteristic
162C2×C4×C47#13111yescharacteristic
163C2×C4×C47#13111yescharacteristic
164C2×C4×C47C2×D811yescharacteristic
165C2×C4×C47C2×SD1611yescharacteristic
166C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C47#13711yescharacteristic
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—22no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—41no—
179C2×Dic47—41no—
180C2×Dic47#10212yes—
181C2×Dic47#10212yes—
182C2×Dic47#10412yes—
183D188—22no—
184D188—22no—
185D188—41no—
186D188—41no—
187C4×D47—42no—
188C4×D47—42no—
189C4×D47—42no—
190C4×D47—42no—
191C8×C47—42no—
192C8×C47—81no—
193C47⋊C8—42no—
194C47⋊C8—81no—
195#8567—471nomaximal, Sylow
196C22×C47#38011yescharacteristic
197C22×C47#40811yescharacteristic
198C22×C47#40811yescharacteristic
199C22×C47C2×#10211yescharacteristic
200C22×C47#41711yescharacteristic
201C22×C47C2×#10411yescharacteristic
202C22×C47#42111yescharacteristic
203C2×D47—42no—
204C2×D47—42no—
205C2×D47—42no—
206C2×D47—81no—
207C2×D47—81no—
208C2×D47—81no—
209C2×D47—81no—
210C4×C47—21no—
211C4×C47—21no—
212C4×C47—81no—
213C4×C47—81no—
214C4×C47#42411yescharacteristic
215C4×C47#42411yescharacteristic
216C4×C47#43311yescharacteristic
217C4×C47#43311yescharacteristic
218C4×C47#45911yescharacteristic
219C4×C47#46111yescharacteristic
220C4×C47#47411yescharacteristic
221C4×C47#47611yescharacteristic
222Dic47—22no—
223Dic47—22no—
224Dic47—22no—
225Dic47—42no—
226Dic47—41no—
227#2293—471no—
228#1842—471no—
229C4×C4⋊C8—471no—
230C2×D4⋊C8—471no—
231C2×D4⋊C8—471no—
232#1279—471no—
233#1279D4711yescharacteristic, complemented
234C2×C47#148011yescharacteristic
235C2×C47#148311yescharacteristic
236C2×C47#149211yescharacteristic
237C2×C47#149511yescharacteristic
238C2×C47#179811yescharacteristic
239C2×C47#180211yescharacteristic
240C2×C47#180611yescharacteristic
241D47—82no—
242C2×C4×D4—471no—
243C2×#117—941no—
244C2×C4⋊C8—471no—
245C2×C4⋊C8—941no—
246C2×C4⋊C8—941no—
247C2×C4⋊C8—941no—
248C2×C4⋊C8C2×D4711yescharacteristic
249C2×C4×C8—471no—
250C2×C4×C8C2×D4711yescharacteristic
251#390—471no—
252#390—471no—
253#389—471no—
254#389—471no—
255#388—941no—
256#388—941no—
257C4×C4⋊C4C2×D4711yescharacteristic
258C4×C22⋊C4—941no—
259C43—471no—
260#336—941no—
261D4⋊C8—942no—
262D4⋊C8—942no—
263C47#856711yescharacteristic, complemented, Sylow
264C22×D4—471no—
265C23×C4—941no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—941no—
269C22×C8—941no—
270C4×D4—472no—
271C4×D4—472no—
272C4×D4—941no—
273C4×D4—941no—
274#117—1882no—
275#117—1882no—
276C2×C4⋊C4—471no—
277C2×C4⋊C4—941no—
278C2×C4⋊C4—941no—
279C2×C4⋊C4C4×D4711yescharacteristic
280C2×C4⋊C4C4×D4711yescharacteristic
281C2×C22⋊C4—941no—
282C2×C22⋊C4—941no—
283C2×C22⋊C4—941no—
284C2×C22⋊C4—941no—
285C2×C22⋊C4—941no—
286C2×C42—21no—
287C2×C42—471no—
288C2×C42—471no—
289C2×C42—471no—
290C2×C42—471no—
291C2×C42—471no—
292C2×C42—471no—
293C2×C42C22×D4711yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—944no—
297C4⋊C8—941no—
298C4⋊C8—941no—
299C4⋊C8—1882no—
300C4⋊C8—1882no—
301C4×C8—21no—
302C4×C8—21no—
303C4×C8—941no—
304C4×C8—941no—
305#95—21no—
306#95—941no—
307#95—941no—
308C24—941no—
309C2×D4—472no—
310C2×D4—941no—
311C2×D4—941no—
312C2×D4—941no—
313C2×D4—941no—
314C2×D4—941no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—471no—
318C22×C4—471no—
319C22×C4—471no—
320C22×C4—471no—
321C22×C4—941no—
322C22×C4—942no—
323C22×C4—942no—
324C22×C4—1881no—
325C22×C4—1881no—
326C22×C4—1881no—
327C22×C4—1881no—
328C22×C4C2×C4×D4711yescharacteristic
329C22×C4D4×D4711yescharacteristic
330C22×C4D4×D4711yescharacteristic
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—942no—
338C2×C8—1881no—
339C2×C8—1881no—
340C2×C8—1881no—
341C2×C8—1881no—
342C2×C8—1881no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—472no—
348C4⋊C4—941no—
349C4⋊C4—1882no—
350C4⋊C4—1882no—
351C22⋊C4—942no—
352C22⋊C4—942no—
353C22⋊C4—1882no—
354C22⋊C4—1882no—
355C22⋊C4—1882no—
356C22⋊C4—1882no—
357C42—41no—
358C42—41no—
359C42—472no—
360C42—472no—
361C42—942no—
362C42—941no—
363C42—941no—
364C42—941no—
365C42—941no—
366C42—941no—
367C42—941no—
368C42—1881no—
369C42#1062535011yescharacteristic
370C42#1062535011yescharacteristic
371C42D4×D4711yescharacteristic
372C42Q8×D4711yescharacteristic
373C23—942no—
374C23—1881no—
375C23—1881no—
376C23—1881no—
377C23—1881no—
378C23—1881no—
379C23—1881no—
380C23C22⋊C4×D4711yescharacteristic
381D4—942no—
382D4—942no—
383D4—1881no—
384D4—1881no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—472no—
394C2×C4—472no—
395C2×C4—472no—
396C2×C4—941no—
397C2×C4—941no—
398C2×C4—941no—
399C2×C4—941no—
400C2×C4—941no—
401C2×C4—941no—
402C2×C4—942no—
403C2×C4—941no—
404C2×C4—941no—
405C2×C4—941no—
406C2×C4—1881no—
407C2×C4—1881no—
408C2×C4—1882no—
409C2×C4—1882no—
410C2×C4—1882no—
411C2×C4—1882no—
412C2×C4C4⋊C4×D4711yescharacteristic
413C2×C4#1309398111yescharacteristic
414C2×C4#1309399711yescharacteristic
415C2×C4#1309399711yescharacteristic
416C2×C4#1309400211yescharacteristic
417C2×C4#1309400211yescharacteristic
418C2×C4#1309403011yescharacteristic
419C2×C4#1309403011yescharacteristic
420C2×C4#1309403211yescharacteristic
421C2×C4#1309403211yescharacteristic
422C2×C4D8×D4711yescharacteristic
423C2×C4SD16×D4711yescharacteristic
424C2×C4#1309405111yescharacteristic
425C2×C4#1309405611yescharacteristic
426C8—42no—
427C8—81no—
428C8—3761no—
429C8—1882no—
430C22—3761no—
431C22—3761no—
432C22—3761no—
433C22—3761no—
434C22—1882no—
435C22—1882no—
436C22—1882no—
437C22#1568898211yescharacteristic
438C22#1568908811yescharacteristic
439C22#1568908811yescharacteristic
440C22#102×D4711yescharacteristic
441C22#1568912311yescharacteristic
442C22#104×D4711yescharacteristic
443C22#1568913811yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—942no—
449C4—942no—
450C4—942no—
451C4—1882no—
452C4—1881no—
453C4#1568914811yescharacteristic
454C4#1568914811yescharacteristic
455C4#1568918211yescharacteristic
456C4#1568918511yescharacteristic
457C4#1568931711yescharacteristic
458C4#1568932711yescharacteristic
459C4#1568940211yescharacteristic
460C4#1568941211yescharacteristic
461C2—3762no—
462C2#2024178511yescharacteristic
463C2#2024180011yescharacteristic
464C2#2024183711yescharacteristic
465C2#2024185211yescharacteristic
466C2#2024337111yescharacteristic
467C2#2024338711yescharacteristic
468C2#2024340711yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenter#1279D47
hypocenterC47#8567
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
2. #20243539C2semidirect
3. C4×Dic47⋊C8C2semidirect
6. #20241229C2semidirect
7. C47×#1279C2semidirect
233. #1279D47semidirect
263. C47#8567semidirect

Maximal subgroups

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

subgroupindex
#202458492
#202435392
C4×Dic47⋊C82
C2×#156888522
C2×#156888502
#202412292
C47×#12792
#856747