Finite Group Databasebeta

← #26111396

Subgroups — #26111396

Order 12032.

468 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#20252436C211yesmaximal, characteristic
2#20243487C211yesmaximal, characteristic, complemented
3#20243459C211yesmaximal, characteristic, complemented
4#20241879C211yesmaximal, characteristic
5#20241276C211yesmaximal, characteristic, complemented
6#20241234C211yesmaximal, characteristic, complemented
7C47×#3091C211yesmaximal, characteristic
8#15689201—21no—
9#15689195—21no—
10#15689195—21no—
11D4×C47⋊C8—21no—
12#15689184—21no—
13#15689090—21no—
14#15689087C2211yescharacteristic
15C2×C22⋊(C47⋊C8)C2211yescharacteristic
16C2×C22⋊(C47⋊C8)C2211yescharacteristic
17C4×C22⋊Dic47C2211yescharacteristic
18#15688882—21no—
19#15688882—21no—
20#15688878—21no—
21#15688878—21no—
22#15688860—21no—
23#15688857—21no—
24C47×#525C2211yescharacteristic
25C2×#117×C47C2211yescharacteristic
26C47×#485—21no—
27C47×#484C411yescharacteristic, complemented
28C47×#483C411yescharacteristic, complemented
29C47×#482—21no—
30C47×#481C411yescharacteristic, complemented
31C47×#480C411yescharacteristic, complemented
32C47×#427—21no—
33C47×#416—21no—
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×#10625329—21no—
36C2×#10625329D411yescharacteristic
37C2×#10625329D411yescharacteristic
38C22×C47⋊C8—21no—
39C22×C47⋊C8—21no—
40C22×C47⋊C8D411yescharacteristic
41C22×C47⋊C8D411yescharacteristic
42C2×C22⋊Dic47—21no—
43C2×C4×Dic47—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)—21no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C22⋊(C47⋊C8)—21no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)—21no—
51C22⋊(C47⋊C8)—21no—
52C22⋊(C47⋊C8)—21no—
53C22⋊(C47⋊C8)—21no—
54#13093935—21no—
55C4×C47⋊C8—21no—
56C47⋊#95—21no—
57C2×#41×C47D411yescharacteristic
58C23×C4×C47C2311yescharacteristic
59C22×C8×C47—21no—
60#123×C47—21no—
61C22⋊Q8×C47C2×C411yescharacteristic
62C22⋊Q8×C47D411yescharacteristic
63#121×C47C2×C411yescharacteristic
64#121×C47D411yescharacteristic
65#120×C47—21no—
66C4×D4×C47—21no—
67C4×D4×C47—21no—
68#117×C47—21no—
69#117×C47—21no—
70#117×C47—21no—
71#117×C47—21no—
72#117×C47D411yescharacteristic
73C2×C4⋊C4×C47C2×C411yescharacteristic
74C2×C4⋊C4×C47C2×C411yescharacteristic
75C2×C22⋊C4×C47—21no—
76C2×C42×C47—21no—
77#107×C47—21no—
78#107×C47—21no—
79#106×C47—21no—
80#106×C47—21no—
81#103×C47—21no—
82#103×C47—21no—
83#102×C47—21no—
84#102×C47—21no—
85C22⋊C8×C47—21no—
86C22⋊C8×C47C2×C411yescharacteristic
87C22⋊C8×C47C2×C411yescharacteristic
88C24×C47#4111yescharacteristic
89#41×C47—41no—
90#41×C47—41no—
91C2×Q8×C47C22⋊C411yescharacteristic
92C2×D4×C47—21no—
93C2×D4×C47—21no—
94C2×D4×C47—21no—
95C2×D4×C47C22⋊C411yescharacteristic
96C22×C4×C47—21no—
97C22×C4×C47—21no—
98C22×C4×C47—21no—
99C22×C4×C47—41no—
100C22×C4×C47—41no—
101C22×C4×C47C22×C411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×Dic47—41no—
108C2×C8×C47—21no—
109C2×C8×C47—21no—
110C2×C8×C47—41no—
111C2×C8×C47—41no—
112C4⋊C4×C47—21no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—21no—
115C4⋊C4×C47—21no—
116C4⋊C4×C47—21no—
117C4⋊C4×C47—21no—
118C4⋊C4×C47C22⋊C411yescharacteristic
119C4⋊C4×C47C22⋊C411yescharacteristic
120C22⋊C4×C47—21no—
121C22⋊C4×C47—21no—
122C22⋊C4×C47—21no—
123C22⋊C4×C47—21no—
124C22⋊C4×C47—21no—
125C22⋊C4×C47—41no—
126C22⋊C4×C47—41no—
127C42×C47—21no—
128C42×C47—41no—
129C42×C47—41no—
130C22⋊Dic47—22no—
131C22⋊Dic47—41no—
132C4×Dic47—41no—
133C4×Dic47—41no—
134#10625329—41no—
135#10625329—41no—
136#10625329—81no—
137C2×C47⋊C8—21no—
138C2×C47⋊C8—21no—
139C2×C47⋊C8—21no—
140C2×C47⋊C8—21no—
141C2×C47⋊C8—41no—
142C2×C47⋊C8—41no—
143C2×C47⋊C8—41no—
144C2×C47⋊C8—41no—
145C2×C47⋊C8—41no—
146C2×C47⋊C8—81no—
147C23×C47—21no—
148C23×C47—21no—
149C23×C47—21no—
150C23×C47—41no—
151C23×C47—41no—
152C23×C47C4×D411yescharacteristic
153C23×C47#12111yescharacteristic
154C23×C47#12311yescharacteristic
155Q8×C47—41no—
156D4×C47—41no—
157D4×C47—41no—
158D4×C47—41no—
159D4×C47—81no—
160D4×C47—81no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
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—42no—
176C2×C4×C47—41no—
177C2×C4×C47—41no—
178C2×C4×C47—41no—
179C2×C4×C47—41no—
180C2×C4×C47C2×C22⋊C411yescharacteristic
181C2×C4×C47C4×D411yescharacteristic
182C2×C4×C47#12011yescharacteristic
183C2×C4×C47#12111yescharacteristic
184C2×Dic47—42no—
185C2×Dic47—81no—
186C2×Dic47—81no—
187C8×C47—41no—
188C8×C47—41no—
189C47⋊C8—41no—
190C47⋊C8—41no—
191C47⋊C8—41no—
192C47⋊C8—41no—
193C47⋊C8—81no—
194#9038—471nomaximal, Sylow
195C22×C47—21no—
196C22×C47—21no—
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—21no—
200C22×C47—21no—
201C22×C47—21no—
202C22×C47—21no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—81no—
207C22×C47—81no—
208C22×C47#38611yescharacteristic
209C22×C47#44311yescharacteristic
210C22×C47#44411yescharacteristic
211C4×C47—21no—
212C4×C47—21no—
213C4×C47—21no—
214C4×C47—41no—
215C4×C47—41no—
216C4×C47—41no—
217C4×C47—81no—
218C4×C47—81no—
219C4×C47#45811yescharacteristic
220C4×C47#45811yescharacteristic
221Dic47—82no—
222#3091D4711yescharacteristic
223#2976—471no—
224#1826—471no—
225#1818—471no—
226#1501—471no—
227#1298—471no—
228#1282—471no—
229C2×C47—21no—
230C2×C47—21no—
231C2×C47—41no—
232C2×C47—41no—
233C2×C47—81no—
234C2×C47#187611yescharacteristic
235C2×C47#188111yescharacteristic
236C2×C47#189011yescharacteristic
237#525C2×D4711yescharacteristic
238C2×#117C2×D4711yescharacteristic
239#485—21no—
240#484Dic4711yescharacteristic, complemented
241#483Dic4711yescharacteristic, complemented
242#482—21no—
243#481Dic4711yescharacteristic, complemented
244#480Dic4711yescharacteristic, complemented
245#436—941no—
246#435—941no—
247#435—941no—
248C8×D4—941no—
249#433—941no—
250#427—21no—
251#416—21no—
252#408—941no—
253#407—471no—
254C2×C22⋊C8—471no—
255C2×C22⋊C8—471no—
256C2×C22⋊C8C2×D4711yescharacteristic
257C4×C22⋊C4—471no—
258#339—941no—
259#339—941no—
260#336—941no—
261#336—941no—
262#328—941no—
263#327—941no—
264C47#903811yescharacteristic, complemented, Sylow
265C2×#41C22⋊D4711yescharacteristic
266C23×C4C22×D4711yescharacteristic
267C2×M16—471no—
268C2×M16—471no—
269C2×M16—941no—
270C22×C8—21no—
271C22×C8—471no—
272C22×C8—471no—
273C22×C8—941no—
274C22×C8—941no—
275#123—21no—
276C22⋊Q8C2×Dic4711yescharacteristic
277C22⋊Q8C22⋊D4711yescharacteristic
278#121C2×Dic4711yescharacteristic
279#121C22⋊D4711yescharacteristic
280#120—21no—
281C4×D4—21no—
282C4×D4—21no—
283#117—21no—
284#117—21no—
285#117—21no—
286#117—21no—
287#117C22⋊D4711yescharacteristic
288C2×C4⋊C4C2×Dic4711yescharacteristic
289C2×C4⋊C4C2×Dic4711yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—941no—
292C2×C42—21no—
293C2×C42—941no—
294#107—21no—
295#107—21no—
296#106—21no—
297#106—21no—
298C4⋊C8—941no—
299C4⋊C8—941no—
300#103—21no—
301#103—21no—
302#102—21no—
303#102—21no—
304C22⋊C8—21no—
305C22⋊C8—941no—
306C22⋊C8—941no—
307C22⋊C8—941no—
308C22⋊C8—941no—
309C22⋊C8—941no—
310C22⋊C8—941no—
311C22⋊C8—941no—
312C22⋊C8—941no—
313C22⋊C8C2×Dic4711yescharacteristic
314C22⋊C8C2×Dic4711yescharacteristic
315#97—941no—
316C4×C8—941no—
317#95—941no—
318C24#1062535211yescharacteristic
319#41—41no—
320#41—41no—
321C2×Q8C22⋊Dic4711yescharacteristic
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4C22⋊Dic4711yescharacteristic
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—1881no—
332C22×C4D4×D4711yescharacteristic
333C22×C4D4×D4711yescharacteristic
334C22×C4#1062535211yescharacteristic
335C22×C4C22×Dic4711yescharacteristic
336C22×C4C2×C22⋊D4711yescharacteristic
337C22×C4C2×C22⋊D4711yescharacteristic
338M16—3761no—
339M16—1881no—
340M16—1881no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—941no—
346C2×C8—941no—
347C2×C8—941no—
348C2×C8—941no—
349C2×C8—3761no—
350C2×C8—1881no—
351C2×C8—1881no—
352C2×C8—1881no—
353C2×C8—1881no—
354C2×C8—1881no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4C22⋊Dic4711yescharacteristic
362C4⋊C4C22⋊Dic4711yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—942no—
371C22⋊C4—1881no—
372C42—21no—
373C42—41no—
374C42—41no—
375C42—1881no—
376C42—1881no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—41no—
381C23—41no—
382C23D4×Dic4711yescharacteristic
383C23#1309399611yescharacteristic
384C23#1309400511yescharacteristic
385Q8—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—81no—
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—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—3761no—
411C2×C4—3761no—
412C2×C4—1882no—
413C2×C4C2×C22⋊Dic4711yescharacteristic
414C2×C4D4×Dic4711yescharacteristic
415C2×C4#1309399211yescharacteristic
416C2×C4#1309399611yescharacteristic
417C8—41no—
418C8—41no—
419C8—3761no—
420C8—1881no—
421C8—1881no—
422C8—1881no—
423C8—1881no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22#1568900311yescharacteristic
438C22#1568924011yescharacteristic
439C22#1568924511yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—81no—
447C4—81no—
448C4—3762no—
449C4#1568931211yescharacteristic
450C4#1568931211yescharacteristic
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2#2024371711yescharacteristic
457C2#2024375211yescharacteristic
458C2#2024380211yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#3091C2
socleC22×C47#386
prime radicalC47×#525C22
cosocleC23×C4×C47C23
hypercenter#3091D47
hypocenterC47#9038
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #20243487C2semidirect
3. #20243459C2semidirect
5. #20241276C2semidirect
6. #20241234C2semidirect
27. C47×#484C4semidirect
28. C47×#483C4semidirect
30. C47×#481C4semidirect
31. C47×#480C4semidirect
240. #484Dic47semidirect
241. #483Dic47semidirect
243. #481Dic47semidirect
244. #480Dic47semidirect
264. C47#9038semidirect

Maximal subgroups

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

subgroupindex
#202524362
#202434872
#202434592
#202418792
#202412762
#202412342
C47×#30912
#903847