Finite Group Databasebeta

← #26111174

Subgroups — #26111174

Order 12032.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252054C211yesmaximal, characteristic, complemented
2#20241839C211yesmaximal, characteristic, complemented
3#20241787C211yesmaximal, characteristic, complemented
4#20241770C211yesmaximal, characteristic, complemented
5#20241285C211yesmaximal, characteristic, complemented
6#20241222C211yesmaximal, characteristic, complemented
7C47×#3035C211yesmaximal, characteristic
8#15689184—22no—
9#15689180—21no—
10#15689176—21no—
11#15689176C2211yescharacteristic
12#15689147C2211yescharacteristic
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14#15689090—21no—
15#15689079—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17Q8⋊(C47⋊C8)—21no—
18D4⋊(C47⋊C8)—21no—
19D4⋊(C47⋊C8)—21no—
20D4⋊(C47⋊C8)—22no—
21D4⋊(C47⋊C8)—21no—
22C2×#135×C47—21no—
23C47×#532C2211yescharacteristic
24C4×#41×C47C2211yescharacteristic
25C47×#464—21no—
26C47×#463—21no—
27C47×#462C411yescharacteristic
28C47×#461C411yescharacteristic
29C47×#460C411yescharacteristic
30C47×#459C411yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C47×#416—21no—
33C2×#10625329—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C4⋊(C47⋊C8)—21no—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)D411yescharacteristic
40C4⋊(C47⋊C8)D411yescharacteristic
41C4⋊(C47⋊C8)D412yes—
42C22⋊(C47⋊C8)—22no—
43C22⋊(C47⋊C8)—22no—
44C22⋊(C47⋊C8)—21no—
45#13093935—22no—
46C4×C47⋊C8—22no—
47C4×C47⋊C8—21no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C2×#41×C47—21no—
51C2×#41×C47D411yescharacteristic
52#135×C47—42no—
53#135×C47—42no—
54C2×Q16×C47—21no—
55C2×SD16×C47—21no—
56C2×SD16×C47—21no—
57C2×D8×C47—21no—
58C22×C8×C47—21no—
59C4⋊Q8×C47C2×C411yescharacteristic
60#127×C47C2×C411yescharacteristic
61#124×C47—21no—
62#121×C47—21no—
63#121×C47—21no—
64C4×Q8×C47C2×C411yescharacteristic
65C4×Q8×C47D411yescharacteristic
66C4×D4×C47—21no—
67C4×D4×C47—21no—
68C4×D4×C47—21no—
69C4×D4×C47—21no—
70C4×D4×C47C2×C411yescharacteristic
71C4×D4×C47D411yescharacteristic
72#117×C47—21no—
73#117×C47D411yescharacteristic
74C2×C42×C47—21no—
75C2×C42×C47C2311yescharacteristic
76C4⋊C8×C47—21no—
77C4⋊C8×C47C2×C411yescharacteristic
78C4⋊C8×C47C2×C411yescharacteristic
79#103×C47—21no—
80#103×C47—21no—
81#102×C47—21no—
82#102×C47—21no—
83#41×C47—21no—
84#41×C47—21no—
85#41×C47—21no—
86#41×C47—21no—
87#41×C47—41no—
88#41×C47—41no—
89#41×C47—41no—
90#41×C47—41no—
91C2×Q8×C47—21no—
92C2×Q8×C47C22⋊C411yescharacteristic
93C2×D4×C47—21no—
94C2×D4×C47—21no—
95C2×D4×C47—21no—
96C2×D4×C47—21no—
97C2×D4×C47—41no—
98C2×D4×C47C22⋊C411yescharacteristic
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—41no—
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×C4×C47#4111yescharacteristic
106Q16×C47—42no—
107SD16×C47—42no—
108SD16×C47—42no—
109D8×C47—42no—
110C2×C8×C47—21no—
111C2×C8×C47—21no—
112C2×C8×C47—41no—
113C2×C8×C47—41no—
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—41no—
124C22⋊C4×C47—41no—
125C42×C47—21no—
126C42×C47—21no—
127C42×C47—21no—
128C42×C47C22×C411yescharacteristic
129C42×C47C2×D411yescharacteristic
130C42×C47C2×D411yescharacteristic
131C42×C47C2×D411yescharacteristic
132#10625329—41no—
133#10625329—41no—
134C2×C47⋊C8—22no—
135C2×C47⋊C8—21no—
136C2×C47⋊C8—22no—
137C2×C47⋊C8—21no—
138C2×C47⋊C8—41no—
139C2×C47⋊C8—41no—
140C2×C47⋊C8—41no—
141C2×C47⋊C8—41no—
142C2×C47⋊C8—41no—
143C23×C47—21no—
144C23×C47—41no—
145C23×C47#12311yescharacteristic
146Q8×C47—21no—
147Q8×C47—21no—
148Q8×C47—41no—
149Q8×C47—41no—
150D4×C47—21no—
151D4×C47—21no—
152D4×C47—42no—
153D4×C47—41no—
154D4×C47—41no—
155D4×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—41no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47—81no—
173C2×C4×C47—81no—
174C2×C4×C47—81no—
175C2×C4×C47C2×C22⋊C411yescharacteristic
176C2×C4×C47C4×D411yescharacteristic
177C2×C4×C47C4×D411yescharacteristic
178C2×C4×C47#12011yescharacteristic
179C2×C4×C47#12111yescharacteristic
180C2×C4×C47#12111yescharacteristic
181C2×C4×C47#13511yescharacteristic
182C2×C4×C47#13511yescharacteristic
183C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
185C8×C47—41no—
186C8×C47—41no—
187C47⋊C8—42no—
188C47⋊C8—41no—
189C47⋊C8—41no—
190C47⋊C8—42no—
191C47⋊C8—81no—
192#8996—471nomaximal, Sylow
193C22×C47—21no—
194C22×C47—21no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—81no—
199C22×C47—81no—
200C22×C47—81no—
201C22×C47#38611yescharacteristic
202C22×C47#48211yescharacteristic
203C22×C47#48211yescharacteristic
204C4×C47—21no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—41no—
208C4×C47—41no—
209C4×C47—41no—
210C4×C47—81no—
211C4×C47#41611yescharacteristic
212C4×C47#41811yescharacteristic
213C4×C47#44311yescharacteristic
214C4×C47#44411yescharacteristic
215C4×C47#44911yescharacteristic
216C4×C47#44911yescharacteristic
217#3035D4711yescharacteristic
218#2925—471no—
219#1492—471no—
220#1480—471no—
221#1476—471no—
222#1301—471no—
223#1277—471no—
224C2×C47—21no—
225C2×C47—21no—
226C2×C47—81no—
227C2×C47—161no—
228C2×C47#187511yescharacteristic
229C2×C47#187611yescharacteristic
230C2×C47#188111yescharacteristic
231C2×#135—21no—
232#532C2×D4711yescharacteristic
233C4×#41C2×D4711yescharacteristic
234#464—21no—
235#463—21no—
236#462Dic4711yescharacteristic
237#461Dic4711yescharacteristic
238#460Dic4711yescharacteristic
239#459Dic4711yescharacteristic
240#433—942no—
241#432—941no—
242#431—471no—
243#431—941no—
244#423—471no—
245C2×C4⋊C8—471no—
246C2×C4⋊C8C2×D4711yescharacteristic
247#416—21no—
248#408—941no—
249#405—941no—
250C2×C4×C8—471no—
251Q8⋊C8—941no—
252D4⋊C8—941no—
253D4⋊C8—941no—
254D4⋊C8—942no—
255D4⋊C8—941no—
256C47#899611yescharacteristic, complemented, Sylow
257C2×#41—21no—
258C2×#41C22⋊D4711yescharacteristic
259#135—42no—
260#135—42no—
261C2×Q16—21no—
262C2×SD16—21no—
263C2×SD16—21no—
264C2×D8—21no—
265C2×M16—941no—
266C22×C8—21no—
267C22×C8—941no—
268C22×C8—941no—
269C4⋊Q8C2×Dic4711yescharacteristic
270#127C2×Dic4711yescharacteristic
271#124—21no—
272#121—21no—
273#121—21no—
274C4×Q8C2×Dic4711yescharacteristic
275C4×Q8C22⋊D4711yescharacteristic
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4C2×Dic4711yescharacteristic
281C4×D4C22⋊D4711yescharacteristic
282#117—21no—
283#117C22⋊D4711yescharacteristic
284C2×C42—21no—
285C2×C42C22×D4711yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—471no—
288C4⋊C8—471no—
289C4⋊C8—472no—
290C4⋊C8—941no—
291C4⋊C8—941no—
292C4⋊C8—941no—
293C4⋊C8C2×Dic4711yescharacteristic
294C4⋊C8C2×Dic4711yescharacteristic
295#103—21no—
296#103—21no—
297#102—21no—
298#102—21no—
299C22⋊C8—942no—
300C22⋊C8—942no—
301C22⋊C8—941no—
302#97—942no—
303C4×C8—942no—
304C4×C8—941no—
305C4×C8—941no—
306C4×C8—941no—
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—41no—
312#41—41no—
313#41—41no—
314#41—41no—
315C2×Q8—21no—
316C2×Q8C22⋊Dic4711yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4C22⋊Dic4711yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4#1062535211yescharacteristic
328C22×C4#1062535211yescharacteristic
329C22×C4C2×C22⋊D4711yescharacteristic
330Q16—42no—
331SD16—42no—
332SD16—42no—
333D8—42no—
334M16—1881no—
335M16—1881no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—942no—
341C2×C8—941no—
342C2×C8—942no—
343C2×C8—941no—
344C2×C8—1881no—
345C2×C8—1881no—
346C2×C8—1881no—
347C2×C8—1881no—
348C2×C8—1881no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4C22⋊Dic4711yescharacteristic
354C4⋊C4C22⋊Dic4711yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C42—21no—
361C42—21no—
362C42—21no—
363C42D4×D4711yescharacteristic
364C42D4×D4711yescharacteristic
365C42C22×Dic4711yescharacteristic
366C42C2×C22⋊D4711yescharacteristic
367C23—21no—
368C23—41no—
369C23#1309400511yescharacteristic
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—41no—
374D4—21no—
375D4—21no—
376D4—42no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—41no—
381D4—41no—
382D4—41no—
383D4—81no—
384D4—81no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C2×C22⋊Dic4711yescharacteristic
400C2×C4D4×Dic4711yescharacteristic
401C2×C4D4×Dic4711yescharacteristic
402C2×C4#1309399211yescharacteristic
403C2×C4#1309399611yescharacteristic
404C2×C4#1309399611yescharacteristic
405C2×C4#1309404411yescharacteristic
406C2×C4#1309404411yescharacteristic
407C2×C4#1309405011yescharacteristic
408C2×C4#1309405011yescharacteristic
409C8—41no—
410C8—41no—
411C8—3761no—
412C8—1882no—
413C8—1881no—
414C8—1881no—
415C8—1882no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22#1568900311yescharacteristic
425C22#1568944411yescharacteristic
426C22#1568944411yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4#1568911911yescharacteristic
435C4#1568912811yescharacteristic
436C4#1568924011yescharacteristic
437C4#1568924511yescharacteristic
438C4#1568926611yescharacteristic
439C4#1568926611yescharacteristic
440C2—21no—
441C2—21no—
442C2—81no—
443C2—161no—
444C2#2024371111yescharacteristic
445C2#2024371711yescharacteristic
446C2#2024375211yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3035C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenter#3035D47
hypocenterC47#8996
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #20252054C2semidirect
2. #20241839C2semidirect
3. #20241787C2semidirect
4. #20241770C2semidirect
5. #20241285C2semidirect
6. #20241222C2semidirect
256. C47#8996semidirect

Maximal subgroups

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

subgroupindex
#202520542
#202418392
#202417872
#202417702
#202412852
#202412222
C47×#30352
#899647