Finite Group Databasebeta

← #26109837

Subgroups — #26109837

Order 12032.

472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246330C211yesmaximal, characteristic
2#20243373C211yesmaximal, characteristic
3#20241704C211yesmaximal, characteristic
4#20241268C211yesmaximal, characteristic, complemented
5#20241266C211yesmaximal, characteristic, complemented
6#20241255C211yesmaximal, characteristic, complemented
7C47×#1289C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D47C2211yescharacteristic
9C2×#13093938—21no—
10C2×C22⋊(C47⋊C8)C2211yescharacteristic
11#15689013—21no—
12#15689004—21no—
13#15689000—21no—
14#15688990C411yescharacteristic, complemented
15#15688985C411yescharacteristic, complemented
16#15688983C2211yescharacteristic
17C22⋊C4×Dic47—21no—
18#15688970C411yescharacteristic, complemented
19#15688968C411yescharacteristic, complemented
20C2×C47⋊#95C2211yescharacteristic
21#15688889—21no—
22#15688848—21no—
23#15688846—21no—
24C2×C22⋊C8×C47C2211yescharacteristic
25C47×#380C2211yescharacteristic
26C47×#380C2211yescharacteristic
27C22×C22⋊D47D411yescharacteristic
28C23×Dic47—21no—
29C22×C4×D47C2×C411yescharacteristic
30C22×C47⋊C8—21no—
31C4×C22⋊D47—21no—
32C4×C22⋊D47—21no—
33C4×C22⋊D47—21no—
34C4×C22⋊D47—21no—
35C2×C4⋊Dic47—21no—
36C2×Dic47⋊C4D411yescharacteristic
37C2×C22⋊Dic47—21no—
38C2×C22⋊Dic47D411yescharacteristic
39C2×(C2×D47)⋊C4—21no—
40C2×(C2×D47)⋊C4—21no—
41C2×(C2×D47)⋊C4D411yescharacteristic
42C2×C4×Dic47—21no—
43C2×C4×Dic47—21no—
44C2×C4×Dic47C2×C411yescharacteristic
45#13093938—42no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C47⋊#95—21no—
52C47⋊#95—21no—
53C47⋊#95—21no—
54C47⋊#95C2×C411yescharacteristic
55C47⋊#95C2×C411yescharacteristic
56C23×C4×C47C2311yescharacteristic
57C22×C8×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C22⋊C4×C47—21no—
61C2×C22⋊C4×C47—21no—
62C22⋊C8×C47—21no—
63C22⋊C8×C47—21no—
64#95×C47—21no—
65#95×C47C2×C411yescharacteristic
66#95×C47C2×C411yescharacteristic
67C24×C47C2×D411yescharacteristic
68C23×D47C22⋊C411yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—41no—
72C22×C4×C47—81no—
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47#4111yescharacteristic
76C22×C4×C47#4111yescharacteristic
77C22×C4×C47#4111yescharacteristic
78C22×C4×C47#4111yescharacteristic
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C2×C22⋊D47—21no—
82C2×C22⋊D47—21no—
83C2×C22⋊D47—21no—
84C2×C22⋊D47—21no—
85C22×Dic47—21no—
86C22×Dic47—21no—
87C22×Dic47—42no—
88C22×Dic47—41no—
89C22×Dic47—41no—
90C22×Dic47—41no—
91C22×Dic47—81no—
92C22×Dic47C22⋊C411yescharacteristic
93C22×Dic47C22⋊C411yescharacteristic
94C22×Dic47C22⋊C411yescharacteristic
95C2×C4×D47—21no—
96C2×C4×D47—21no—
97C2×C4×D47—81no—
98C2×C8×C47—41no—
99C2×C8×C47—81no—
100C4⋊C4×C47—81no—
101C4⋊C4×C47—81no—
102C22⋊C4×C47—41no—
103C22⋊C4×C47—41no—
104C22⋊C4×C47—41no—
105C22⋊C4×C47—41no—
106C22⋊Dic47—21no—
107C22⋊Dic47—21no—
108C22⋊Dic47—41no—
109C22⋊Dic47—41no—
110(C2×D47)⋊C4—21no—
111(C2×D47)⋊C4—21no—
112(C2×D47)⋊C4—42no—
113(C2×D47)⋊C4—81no—
114C4⋊Dic47—81no—
115Dic47⋊C4—21no—
116Dic47⋊C4—21no—
117C4×Dic47—21no—
118C4×Dic47—21no—
119C4×Dic47—42no—
120C4×Dic47—81no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—81no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47C2×C22⋊C411yescharacteristic
126C23×C47#12311yescharacteristic
127C23×C47#12311yescharacteristic
128C23×C47#13511yescharacteristic
129C23×C47#13511yescharacteristic
130C23×C47AGL(1,ℤ/8)11yescharacteristic
131C23×C47#13711yescharacteristic
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—41no—
136C22×D47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
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—41no—
148C2×C4×C47—41no—
149C2×C4×C47—81no—
150C2×C4×C47—81no—
151C2×C4×C47—81no—
152C2×C4×C47#11711yescharacteristic
153C2×C4×C47#11711yescharacteristic
154C2×C4×C47#12311yescharacteristic
155C2×C4×C47#12311yescharacteristic
156C22⋊D47—41no—
157C22⋊D47—41no—
158C22⋊D47—41no—
159C22⋊D47—41no—
160C2×Dic47—22no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—21no—
165C2×Dic47—21no—
166C2×Dic47—41no—
167C2×Dic47—41no—
168C2×Dic47—41no—
169C2×Dic47—41no—
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47—41no—
173C2×Dic47—82no—
174C2×Dic47—82no—
175C2×Dic47—81no—
176C2×Dic47—81no—
177C2×Dic47—81no—
178C4×D47—81no—
179C4×D47—81no—
180C8×C47—81no—
181C47⋊C8—81no—
182#8763—471nomaximal, Sylow
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47#38111yescharacteristic
194C22×C47#41611yescharacteristic
195C22×C47#41711yescharacteristic
196C22×C47#48211yescharacteristic
197C22×C47#48211yescharacteristic
198C22×C47#48511yescharacteristic
199C22×C47#48511yescharacteristic
200C2×D47—41no—
201C2×D47—41no—
202C2×D47—41no—
203C2×D47—81no—
204C2×D47—81no—
205C4×C47—21no—
206C4×C47—21no—
207C4×C47—21no—
208C4×C47—21no—
209C4×C47—81no—
210C4×C47—81no—
211C4×C47—161no—
212Dic47—42no—
213Dic47—41no—
214Dic47—41no—
215Dic47—41no—
216Dic47—81no—
217Dic47—161no—
218#2353—471no—
219#1799—471no—
220#1459—471no—
221#1294—471no—
222#1294—471no—
223#1289—471no—
224#1289D4711yescharacteristic, complemented
225C2×C47—21no—
226C2×C47—21no—
227C2×C47—21no—
228C2×C47—21no—
229C2×C47—21no—
230C2×C47—21no—
231C2×C47#182511yescharacteristic
232C2×C47#182711yescharacteristic
233C2×C47#182811yescharacteristic
234D47—81no—
235C2×C4×D4—471no—
236C2×#99—941no—
237C2×C22⋊C8—471no—
238C2×C22⋊C8C2×D4711yescharacteristic
239#388—941no—
240#387—941no—
241#386—941no—
242#383—471no—
243#381—471no—
244#380—471no—
245#380C2×D4711yescharacteristic
246#380C2×D4711yescharacteristic
247C4×C22⋊C4—471no—
248C4×C22⋊C4—941no—
249#376—471no—
250C2×#95—471no—
251#342—941no—
252#324—941no—
253#323—941no—
254C47#876311yescharacteristic, complemented, Sylow
255C22×D4—471no—
256C23×C4—471no—
257C23×C4—941no—
258C23×C4C22×D4711yescharacteristic
259C22×C8—21no—
260C22×C8—941no—
261C4×D4—941no—
262C4×D4—941no—
263C4×D4—941no—
264C4×D4—941no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—471no—
268C2×C4⋊C4—941no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—471no—
272C2×C22⋊C4—471no—
273C2×C22⋊C4—941no—
274C2×C22⋊C4—941no—
275C2×C22⋊C4—941no—
276C2×C42—471no—
277C2×C42—941no—
278C2×C42—941no—
279#99—1882no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—941no—
283C22⋊C8—941no—
284#95—21no—
285#95—471no—
286#95—471no—
287#95—941no—
288#95—941no—
289#95—941no—
290#95—941no—
291#95—941no—
292#95—941no—
293#95C4×D4711yescharacteristic
294#95C4×D4711yescharacteristic
295C24—471no—
296C24D4×D4711yescharacteristic
297C2×D4—941no—
298C2×D4—941no—
299C2×D4—941no—
300C2×D4—941no—
301C2×D4—941no—
302C2×D4—941no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—81no—
307C22×C4—471no—
308C22×C4—471no—
309C22×C4—471no—
310C22×C4—941no—
311C22×C4—941no—
312C22×C4—941no—
313C22×C4—941no—
314C22×C4—3761no—
315C22×C4—3761no—
316C22×C4—1882no—
317C22×C4—1881no—
318C22×C4—1881no—
319C22×C4—1881no—
320C22×C4C2×C4×D4711yescharacteristic
321C22×C4#1062535011yescharacteristic
322C22×C4#1062535011yescharacteristic
323C22×C4D4×D4711yescharacteristic
324C22×C4#1062535211yescharacteristic
325C22×C4#1062535411yescharacteristic
326C2×C8—41no—
327C2×C8—81no—
328C2×C8—3761no—
329C2×C8—1881no—
330C4⋊C4—81no—
331C4⋊C4—81no—
332C4⋊C4—941no—
333C4⋊C4—941no—
334C4⋊C4—3761no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—941no—
340C22⋊C4—941no—
341C22⋊C4—941no—
342C22⋊C4—941no—
343C22⋊C4—3761no—
344C22⋊C4—1882no—
345C22⋊C4—1881no—
346C22⋊C4—1881no—
347C42—941no—
348C42—941no—
349C42—3761no—
350C42—1882no—
351C23—41no—
352C23—41no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23—1881no—
357C23—1881no—
358C23C22⋊C4×D4711yescharacteristic
359C23#1309400611yescharacteristic
360C23#1309400911yescharacteristic
361C23#1309404511yescharacteristic
362C23#1309404711yescharacteristic
363C23#1309404811yescharacteristic
364C23#1309405311yescharacteristic
365D4—1881no—
366D4—1881no—
367D4—1881no—
368D4—1881no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—942no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—941no—
389C2×C4—941no—
390C2×C4—3761no—
391C2×C4—3761no—
392C2×C4—3762no—
393C2×C4—3762no—
394C2×C4—3761no—
395C2×C4—3761no—
396C2×C4—3761no—
397C2×C4—1881no—
398C2×C4—1881no—
399C2×C4—1881no—
400C2×C4—1881no—
401C2×C4—1881no—
402C2×C4—1881no—
403C2×C4—1881no—
404C2×C4#1309398111yescharacteristic
405C2×C4#1309398211yescharacteristic
406C2×C4#1309400611yescharacteristic
407C2×C4#1309400911yescharacteristic
408C8—81no—
409C8—3761no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—3761no—
421C22—3761no—
422C22—1881no—
423C22—1881no—
424C22—1881no—
425C22#1568898511yescharacteristic
426C22#1568911811yescharacteristic
427C22#1568912111yescharacteristic
428C22#1568944611yescharacteristic
429C22#1568945011yescharacteristic
430C22#1568946311yescharacteristic
431C22#1568946711yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—161no—
439C4—3761no—
440C4—1882no—
441C4—1881no—
442C4—1881no—
443C4—1881no—
444C4—7521no—
445C2—21no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—3761no—
452C2#2024348211yescharacteristic
453C2#2024349011yescharacteristic
454C2#2024349511yescharacteristic
subgroupG/H
centerC22#15688985
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1289C2
socleC22×C47#381
prime radicalC22×C22⋊D47D4
cosocleC23×C4×C47C23
hypercenter#1289D47
hypocenterC47#8763
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
4. #20241268C2semidirect
5. #20241266C2semidirect
6. #20241255C2semidirect
7. C47×#1289C2semidirect
14. #15688990C4semidirect
15. #15688985C4semidirect
18. #15688970C4semidirect
19. #15688968C4semidirect
224. #1289D47semidirect
254. C47#8763semidirect

Maximal subgroups

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

subgroupindex
#202463302
#202433732
#202417042
#202412682
#202412662
#202412552
C47×#12892
#876347