Finite Group Databasebeta

← #26112103

Subgroups — #26112103

Order 12032.

508 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252423C211yesmaximal, characteristic, complemented
2#20243213C211yesmaximal, characteristic, complemented
3#20241999C211yesmaximal, characteristic, complemented
4#20241883C211yesmaximal, characteristic, complemented
5#20241286C211yesmaximal, characteristic, complemented
6#20241245C211yesmaximal, characteristic, complemented
7C47×#3109C211yesmaximal, characteristic
8#15689201—21no—
9#15689195—22no—
10D4×C47⋊C8—21no—
11#15689180C2211yescharacteristic
12#15689176C2211yescharacteristic
13C2×#13093945—21no—
14#15689087—21no—
15C2×C22⋊(C47⋊C8)—21no—
16C2×#13093935C2211yescharacteristic
17C4×C4⋊Dic47C2211yescharacteristic
18#15688885—21no—
19#15688863—22no—
20#15688857—21no—
21#15688857—21no—
22C47×#532C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C47×#481—21no—
25C47×#476C411yescharacteristic, complemented
26C47×#476C411yescharacteristic, complemented
27C47×#459C411yescharacteristic, complemented
28C47×#459C411yescharacteristic, complemented
29C47×#447—21no—
30C47×#442—21no—
31C47×#442—21no—
32C47×#432C2211yescharacteristic
33C2×#10625329—22no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—22no—
36C2×C4⋊Dic47—21no—
37C2×C4×Dic47—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40#13093945—24no—
41C22⋊(C47⋊C8)—22no—
42C22⋊(C47⋊C8)—22no—
43C22⋊(C47⋊C8)—21no—
44C22⋊(C47⋊C8)D411yescharacteristic
45C22⋊(C47⋊C8)D411yescharacteristic
46#13093935—21no—
47#13093935—21no—
48#13093935D412yes—
49C4×C47⋊C8—21no—
50C47⋊#95—21no—
51C2×#41×C47—21no—
52C22×D4×C47D411yescharacteristic
53C23×C4×C47—21no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C4⋊Q8×C47C2×C411yescharacteristic
57#127×C47C2×C411yescharacteristic
58#124×C47—21no—
59#121×C47—21no—
60#121×C47—21no—
61C4×D4×C47—21no—
62C4×D4×C47—21no—
63C4×D4×C47—21no—
64C4×D4×C47—21no—
65C4×D4×C47C2×C411yescharacteristic
66C4×D4×C47C2×C411yescharacteristic
67C4×D4×C47D411yescharacteristic
68C4×D4×C47D411yescharacteristic
69C2×C4⋊C4×C47D411yescharacteristic
70C2×C22⋊C4×C47—21no—
71C2×C42×C47C2311yescharacteristic
72#106×C47—21no—
73#106×C47—21no—
74C4⋊C8×C47C2×C411yescharacteristic
75C4⋊C8×C47C2×C411yescharacteristic
76#102×C47—21no—
77#102×C47—21no—
78#102×C47—21no—
79#102×C47—21no—
80C22⋊C8×C47—21no—
81#97×C47—21no—
82C24×C47—21no—
83#41×C47—81no—
84#41×C47—81no—
85C2×Q8×C47—21no—
86C2×D4×C47—22no—
87C2×D4×C47—21no—
88C2×D4×C47—21no—
89C2×D4×C47—21no—
90C2×D4×C47—21no—
91C2×D4×C47—41no—
92C2×D4×C47—41no—
93C2×D4×C47C22⋊C411yescharacteristic
94C2×D4×C47C22⋊C411yescharacteristic
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—21no—
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—41no—
101C22×C4×C47—82no—
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×Dic47—41no—
106D8×C47—42no—
107D8×C47—42no—
108C2×C8×C47—21no—
109C2×C8×C47—21no—
110C4⋊C4×C47—21no—
111C4⋊C4×C47—21no—
112C4⋊C4×C47—21no—
113C4⋊C4×C47C22⋊C411yescharacteristic
114C4⋊C4×C47C22⋊C411yescharacteristic
115C22⋊C4×C47—21no—
116C22⋊C4×C47—21no—
117C22⋊C4×C47—21no—
118C22⋊C4×C47—21no—
119C22⋊C4×C47—41no—
120C22⋊C4×C47—41no—
121C42×C47C22×C411yescharacteristic
122C42×C47C2×D411yescharacteristic
123C42×C47C2×D411yescharacteristic
124C42×C47#4111yescharacteristic
125C4⋊Dic47—22no—
126C4⋊Dic47—41no—
127C4×Dic47—81no—
128#10625329—82no—
129C2×C47⋊C8—22no—
130C2×C47⋊C8—21no—
131C2×C47⋊C8—21no—
132C2×C47⋊C8—22no—
133C2×C47⋊C8—41no—
134C2×C47⋊C8—41no—
135C2×C47⋊C8—82no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—42no—
139C23×C47—41no—
140C23×C47—41no—
141C23×C47—41no—
142C23×C47—81no—
143C23×C47#12111yescharacteristic
144Q8×C47—81no—
145D4×C47—21no—
146D4×C47—21no—
147D4×C47—21no—
148D4×C47—42no—
149D4×C47—41no—
150D4×C47—41no—
151D4×C47—81no—
152D4×C47—81no—
153D4×C47—81no—
154D4×C47—81no—
155D4×C47#10412yes—
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—41no—
163C2×C4×C47—42no—
164C2×C4×C47—42no—
165C2×C4×C47—41no—
166C2×C4×C47—81no—
167C2×C4×C47—81no—
168C2×C4×C47—82no—
169C2×C4×C47—81no—
170C2×C4×C47C2×C22⋊C411yescharacteristic
171C2×C4×C47C4×D411yescharacteristic
172C2×C4×C47C4×D411yescharacteristic
173C2×C4×C47#12011yescharacteristic
174C2×C4×C47#12111yescharacteristic
175C2×C4×C47#12311yescharacteristic
176C2×Dic47—42no—
177C2×Dic47—81no—
178C2×Dic47—81no—
179C8×C47—41no—
180C8×C47—41no—
181C47⋊C8—42no—
182C47⋊C8—41no—
183C47⋊C8—42no—
184C47⋊C8—41no—
185#9163—471nomaximal, Sylow
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—22no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—82no—
195C22×C47—82no—
196C22×C47—81no—
197C22×C47—81no—
198C22×C47—81no—
199C22×C47#38611yescharacteristic
200C22×C47#47111yescharacteristic
201C22×C47#47211yescharacteristic
202C4×C47—21no—
203C4×C47—21no—
204C4×C47—21no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—41no—
208C4×C47—41no—
209C4×C47—81no—
210C4×C47C2×#10411yescharacteristic
211C4×C47#42111yescharacteristic
212Dic47—82no—
213#3109D4711yescharacteristic
214#2974—471no—
215#1762—471no—
216#1530—471no—
217#1502—471no—
218#1302—471no—
219#1285—471no—
220C2×C47—21no—
221C2×C47—21no—
222C2×C47—42no—
223C2×C47—81no—
224C2×C47—161no—
225C2×C47#187111yescharacteristic
226C2×C47#190411yescharacteristic
227C2×C47#190711yescharacteristic
228#532C2×D4711yescharacteristic
229C2×C4×D4C2×D4711yescharacteristic
230#481—21no—
231#476Dic4711yescharacteristic, complemented
232#476Dic4711yescharacteristic, complemented
233#459Dic4711yescharacteristic, complemented
234#459Dic4711yescharacteristic, complemented
235#447—21no—
236#442—21no—
237#442—21no—
238#436—941no—
239#435—942no—
240C8×D4—941no—
241#432—471no—
242#432C2×D4711yescharacteristic
243#431—471no—
244C2×#102—941no—
245#407—941no—
246C2×C22⋊C8—941no—
247C2×#97—471no—
248C4×C4⋊C4—471no—
249#340—941no—
250#329—942no—
251#327—941no—
252#327—941no—
253C47#916311yescharacteristic, complemented, Sylow
254C2×#41—21no—
255C22×D4C22⋊D4711yescharacteristic
256C23×C4—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×M16—942no—
260C22×C8—942no—
261C22×C8—941no—
262C4⋊Q8C2×Dic4711yescharacteristic
263#127C2×Dic4711yescharacteristic
264#124—21no—
265#121—21no—
266#121—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4C2×Dic4711yescharacteristic
272C4×D4C2×Dic4711yescharacteristic
273C4×D4C22⋊D4711yescharacteristic
274C4×D4C22⋊D4711yescharacteristic
275C2×C4⋊C4—941no—
276C2×C4⋊C4C22⋊D4711yescharacteristic
277C2×C22⋊C4—21no—
278C2×C42—941no—
279C2×C42C22×D4711yescharacteristic
280#106—21no—
281#106—21no—
282C4⋊C8—941no—
283C4⋊C8—941no—
284C4⋊C8C2×Dic4711yescharacteristic
285C4⋊C8C2×Dic4711yescharacteristic
286#102—21no—
287#102—21no—
288#102—21no—
289#102—21no—
290#102—944no—
291C22⋊C8—21no—
292C22⋊C8—471no—
293C22⋊C8—471no—
294C22⋊C8—942no—
295C22⋊C8—942no—
296C22⋊C8—941no—
297#97—21no—
298#97—472no—
299#97—941no—
300#97—941no—
301C4×C8—941no—
302#95—941no—
303C24—21no—
304#41—81no—
305#41—81no—
306C2×Q8—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4C22⋊Dic4711yescharacteristic
315C2×D4C22⋊Dic4711yescharacteristic
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—82no—
323C22×C4—1881no—
324C22×C4D4×D4711yescharacteristic
325C22×C4#1062535211yescharacteristic
326C22×C4C2×C22⋊D4711yescharacteristic
327D8—42no—
328D8—42no—
329M16—3762no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—942no—
333C2×C8—941no—
334C2×C8—941no—
335C2×C8—942no—
336C2×C8—3762no—
337C2×C8—1881no—
338C2×C8—1881no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—942no—
343C4⋊C4—1881no—
344C4⋊C4C22⋊Dic4711yescharacteristic
345C4⋊C4C22⋊Dic4711yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42—3761no—
353C42D4×D4711yescharacteristic
354C42#1062535211yescharacteristic
355C42C22×Dic4711yescharacteristic
356C42C2×C22⋊D4711yescharacteristic
357C23—21no—
358C23—21no—
359C23—42no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—81no—
364C23#1309399611yescharacteristic
365Q8—81no—
366D4—21no—
367D4—21no—
368D4—21no—
369D4—42no—
370D4—41no—
371D4—41no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4#1309395112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4—3761no—
392C2×C4—3761no—
393C2×C4—1882no—
394C2×C4C2×C22⋊Dic4711yescharacteristic
395C2×C4D4×Dic4711yescharacteristic
396C2×C4D4×Dic4711yescharacteristic
397C2×C4#1309399211yescharacteristic
398C2×C4#1309399611yescharacteristic
399C2×C4#1309400511yescharacteristic
400C8—41no—
401C8—41no—
402C8—1881no—
403C8—1882no—
404C8—1882no—
405C8—1881no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22#1568900311yescharacteristic
420C22#1568938411yescharacteristic
421C22#1568939111yescharacteristic
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—81no—
430C4—3762no—
431C4C2×#1309395111yescharacteristic
432C4#1568914011yescharacteristic
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—161no—
438C2#2024369111yescharacteristic
439C2#2024387711yescharacteristic
440C2#2024389811yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3109C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenter#3109D47
hypocenterC47#9163
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #20252423C2semidirect
2. #20243213C2semidirect
3. #20241999C2semidirect
4. #20241883C2semidirect
5. #20241286C2semidirect
6. #20241245C2semidirect
25. C47×#476C4semidirect
26. C47×#476C4semidirect
27. C47×#459C4semidirect
28. C47×#459C4semidirect
231. #476Dic47semidirect
232. #476Dic47semidirect
233. #459Dic47semidirect
234. #459Dic47semidirect
253. C47#9163semidirect

Maximal subgroups

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

subgroupindex
#202524232
#202432132
#202419992
#202418832
#202412862
#202412452
C47×#31092
#916347