Finite Group Databasebeta

← #26246190

Subgroups — #26246190

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245869C211yesmaximal, characteristic
2#20245793C211yesmaximal, characteristic
3#20244959C212yesmaximal, complemented
4#20244958C212yesmaximal, complemented
5#20244952C211yesmaximal, characteristic, complemented
6#20244951C211yesmaximal, characteristic, complemented
7#20244945C211yesmaximal, characteristic, complemented
8#20243103C212yesmaximal
9#20243103C212yesmaximal
10#336×D47C211yesmaximal, characteristic
11C47×#2099C211yesmaximal, characteristic, complemented
12C22×C8×D47C2212yes—
13C2×#13093982C2212yes—
14C2×#13093982C2211yescharacteristic
15C2×#13093982C2211yescharacteristic
16C2×C42×D47C2211yescharacteristic
17#15689022C2211yescharacteristic
18#15689021C2211yescharacteristic
19#15689019C2211yescharacteristic
20#15688997—21no—
21#15688994—21no—
22#15688993C2211yescharacteristic
23#15688988C2212yes—
24#15688980—21no—
25#15688980—21no—
26C4⋊C4×Dic47—21no—
27C4⋊C4×Dic47—21no—
28C4⋊C4×Dic47—21no—
29#15688974—21no—
30#15688886C2212yes—
31#15688886C2212yes—
32#15688885C2212yes—
33#15688885C2212yes—
34#15688885C2212yes—
35#15688885C2212yes—
36#15688878C2211yescharacteristic
37#15688877C2212yes—
38C47×#389C2211yescharacteristic
39C47×#384C2211yescharacteristic
40C47×#340C2212yes—
41C47×#340C2212yes—
42C47×#336C2211yescharacteristic
43C22×C4×D47D411yescharacteristic
44C22×C4×D47D411yescharacteristic
45C22×C4×D47C2311yescharacteristic
46C22×C47⋊C8C2312yes—
47C2×C8×D47—24no—
48C2×C8×D47—24no—
49C2×C8×D47—24no—
50#13093982—22no—
51#13093982—24no—
52#13093982—28no—
53#13093982Q814yes—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47C2312yes—
58C2×C4⋊Dic47C2311yescharacteristic
59C2×C4⋊Dic47C2311yescharacteristic
60C2×Dic47⋊C4—21no—
61C2×Dic47⋊C4—21no—
62C2×(C2×D47)⋊C4—21no—
63C2×(C2×D47)⋊C4—22no—
64C2×(C2×D47)⋊C4—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47D411yescharacteristic
69C2×C4×Dic47D411yescharacteristic
70C2×C4×Dic47C2311yescharacteristic
71C42×D47—24no—
72C47⋊#95—21no—
73C47⋊#95—21no—
74C47⋊#95—22no—
75C47⋊#95—22no—
76C47⋊#95—21no—
77C22×C8×C47C2312yes—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47C2312yes—
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C42×C47C2311yescharacteristic
85#95×C47—21no—
86C23×D47C2×D411yescharacteristic
87C22×C4×C47—21no—
88C22×C4×C47—22no—
89C22×C4×C47—21no—
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2411yescharacteristic
93C22×Dic47—21no—
94C22×Dic47—21no—
95C22×Dic47—22no—
96C22×Dic47C2×D411yescharacteristic
97C22×Dic47C2×D411yescharacteristic
98C22×Dic47C2×D411yescharacteristic
99C2×C4×D47—22no—
100C2×C4×D47—22no—
101C2×C4×D47—22no—
102C2×C4×D47—22no—
103C2×C4×D47—41no—
104C2×C4×D47—41no—
105C2×C4×D47C2×Q812yes—
106C2×C4×D47#4114yes—
107C2×C4×D47#4114yes—
108C2×C4×D47#4112yes—
109C2×C8×C47—22no—
110C2×C8×C47—22no—
111C2×C8×C47—22no—
112C4⋊C4×C47—21no—
113C4⋊C4×C47—22no—
114C4⋊C4×C47—24no—
115C4⋊C4×C47—42no—
116C4⋊C4×C47—42no—
117C4⋊C4×C47—42no—
118C4⋊C4×C47C2×Q812yes—
119C42×C47—22no—
120(C2×D47)⋊C4—24no—
121(C2×D47)⋊C4—42no—
122(C2×D47)⋊C4—44no—
123C4⋊Dic47—21no—
124C4⋊Dic47—22no—
125C4⋊Dic47—24no—
126C4⋊Dic47—42no—
127C4⋊Dic47—42no—
128C4⋊Dic47—42no—
129C4⋊Dic47C2×Q812yes—
130Dic47⋊C4—42no—
131Dic47⋊C4—42no—
132C4×Dic47—22no—
133C4×Dic47—24no—
134C4×Dic47—22no—
135C4×Dic47—22no—
136C4×Dic47—42no—
137C4×Dic47—44no—
138C2×C47⋊C8—22no—
139C2×C47⋊C8—22no—
140C2×C47⋊C8—22no—
141C8×D47—48no—
142C23×C47C22×D411yescharacteristic
143C22×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146C22×D47—21no—
147C22×D47C22⋊Q812yes—
148C22×D47#12312yes—
149C22×D47#12412yes—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—22no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—41no—
158C2×C4×C47—42no—
159C2×C4×C47—41no—
160C2×C4×C47—42no—
161C2×C4×C47—42no—
162C2×C4×C47—41no—
163C2×C4×C47#13512yes—
164C2×C4×C47#13512yes—
165C2×C4×C47C22×Q811yescharacteristic
166C2×C4×C47C2×#4112yes—
167C2×C4×C47C2×#4112yes—
168C2×C4×C47C2×#4111yescharacteristic
169C2×Dic47—22no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—41no—
177C2×Dic47—41no—
178C2×Dic47—41no—
179C2×Dic47—42no—
180C2×Dic47—41no—
181C2×Dic47—41no—
182C2×Dic47—42no—
183C2×Dic47—42no—
184C2×Dic47C22⋊Q812yes—
185C2×Dic47#12312yes—
186C2×Dic47#12412yes—
187C4×D47—44no—
188C4×D47—44no—
189C4×D47#12518yes—
190C4×D47#12618yes—
191C8×C47—42no—
192C47⋊C8—42no—
193#23744—471nomaximal, Sylow
194C22×C47C2×C22⋊Q811yescharacteristic
195C22×C47C2×#12311yescharacteristic
196C22×C47C2×#12411yescharacteristic
197C22×C47C2×#13511yescharacteristic
198C22×C47C2×#13511yescharacteristic
199C22×C47#57511yescharacteristic
200C22×C47#57511yescharacteristic
201C2×D47—22no—
202C2×D47—22no—
203C2×D47—22no—
204C2×D47—22no—
205C2×D47—22no—
206C2×D47—22no—
207C2×D47#40014yes—
208C4×C47—22no—
209C4×C47—22no—
210C4×C47—42no—
211C4×C47—81no—
212C4×C47—82no—
213C4×C47C2×#12512yes—
214C4×C47C2×#12612yes—
215Dic47—42no—
216Dic47—41no—
217Dic47—41no—
218Dic47—81no—
219Dic47—82no—
220Dic47#40014yes—
221#2296—471no—
222#2285—471no—
223#2101—472no—
224#2101—472no—
225#2100—471no—
226#2100—471no—
227#2099—471no—
228#2099D4711yescharacteristic, complemented
229#1735—472no—
230#1735—472no—
231C2×#336—471no—
232C2×C47C2×#40011yescharacteristic
233C2×C47#307611yescharacteristic
234C2×C47#307611yescharacteristic
235C2×C47#309111yescharacteristic
236C2×C47#309111yescharacteristic
237C2×C47#313111yescharacteristic
238C2×C47#313511yescharacteristic
239D47—24no—
240C23×C8—472no—
241C2×#117—471no—
242C2×#117—472no—
243C2×#117—471no—
244C22×C42—471no—
245#389—471no—
246#389—471no—
247#389—471no—
248#389C2×D4711yescharacteristic
249#385—941no—
250#385—941no—
251#384—471no—
252#384C2×D4711yescharacteristic
253#382—472no—
254#380—941no—
255#380—941no—
256C4×C4⋊C4—941no—
257C4×C4⋊C4—941no—
258C4×C4⋊C4—941no—
259C4×C4⋊C4—941no—
260#340—472no—
261#340—472no—
262#340—472no—
263#340—472no—
264#340—472no—
265#340—472no—
266#340C2×D4712yes—
267#340C2×D4712yes—
268#336—472no—
269#336—471no—
270#336C2×D4711yescharacteristic
271C47#2374411yescharacteristic, complemented, Sylow
272C23×C4—471no—
273C23×C4—471no—
274C23×C4—471no—
275C22×C8—472no—
276C22×C8—944no—
277C22×C8—944no—
278C22×C8—944no—
279C22×C8C22×D4712yes—
280#117—474no—
281#117—942no—
282#117—944no—
283#117—948no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—471no—
288C2×C4⋊C4—472no—
289C2×C4⋊C4—471no—
290C2×C4⋊C4—941no—
291C2×C4⋊C4—941no—
292C2×C4⋊C4—941no—
293C2×C4⋊C4—941no—
294C2×C4⋊C4—941no—
295C2×C4⋊C4C22×D4712yes—
296C2×C4⋊C4C22×D4711yescharacteristic
297C2×C4⋊C4C22×D4711yescharacteristic
298C2×C22⋊C4—941no—
299C2×C22⋊C4—942no—
300C2×C22⋊C4—941no—
301C2×C42—471no—
302C2×C42—471no—
303C2×C42—471no—
304C2×C42—944no—
305C2×C42—941no—
306C2×C42—941no—
307C2×C42—942no—
308C2×C42C22×D4711yescharacteristic
309#95—21no—
310#95—942no—
311#95—942no—
312#95—941no—
313#95—941no—
314#95—941no—
315C24—471no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—471no—
320C22×C4—472no—
321C22×C4—474no—
322C22×C4—474no—
323C22×C4—472no—
324C22×C4—471no—
325C22×C4—471no—
326C22×C4—942no—
327C22×C4—942no—
328C22×C4—941no—
329C22×C4—942no—
330C22×C4—942no—
331C22×C4—941no—
332C22×C4—942no—
333C22×C4—1881no—
334C22×C4—1881no—
335C22×C4D4×D4711yescharacteristic
336C22×C4D4×D4711yescharacteristic
337C22×C4C23×D4711yescharacteristic
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—942no—
342C2×C8—942no—
343C2×C8—942no—
344C2×C8—1888no—
345C4⋊C4—21no—
346C4⋊C4—22no—
347C4⋊C4—24no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—472no—
352C4⋊C4—941no—
353C4⋊C4—942no—
354C4⋊C4—944no—
355C4⋊C4—1882no—
356C4⋊C4—1882no—
357C4⋊C4—1882no—
358C4⋊C4—1882no—
359C4⋊C4—1882no—
360C4⋊C4Q8×D4712yes—
361C22⋊C4—944no—
362C22⋊C4—1882no—
363C22⋊C4—1884no—
364C42—22no—
365C42—942no—
366C42—942no—
367C42—944no—
368C42—942no—
369C42—1882no—
370C42—1884no—
371C23—472no—
372C23—472no—
373C23—472no—
374C23—941no—
375C23—941no—
376C23—941no—
377C23—941no—
378C23C2×D4×D4711yescharacteristic
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—472no—
393C2×C4—472no—
394C2×C4—472no—
395C2×C4—478no—
396C2×C4—478no—
397C2×C4—942no—
398C2×C4—941no—
399C2×C4—941no—
400C2×C4—941no—
401C2×C4—941no—
402C2×C4—941no—
403C2×C4—941no—
404C2×C4—1884no—
405C2×C4—1884no—
406C2×C4—1881no—
407C2×C4—1882no—
408C2×C4—1881no—
409C2×C4—1882no—
410C2×C4—1882no—
411C2×C4—1881no—
412C2×C4—1881no—
413C2×C4—1881no—
414C2×C4#1309404312yes—
415C2×C4#1309404512yes—
416C2×C4C2×Q8×D4711yescharacteristic
417C2×C4#41×D4712yes—
418C2×C4#41×D4712yes—
419C2×C4#41×D4711yescharacteristic
420C8—42no—
421C8—1882no—
422C22—474no—
423C22—942no—
424C22—942no—
425C22—942no—
426C22—942no—
427C22—942no—
428C22—942no—
429C22C22⋊Q8×D4711yescharacteristic
430C22#123×D4711yescharacteristic
431C22#124×D4711yescharacteristic
432C22C2×#1309404311yescharacteristic
433C22C2×#1309404511yescharacteristic
434C22#1568992211yescharacteristic
435C22#1568992211yescharacteristic
436C4—22no—
437C4—22no—
438C4—42no—
439C4—82no—
440C4—81no—
441C4—474no—
442C4—3762no—
443C4—3761no—
444C4—1881no—
445C4—1881no—
446C4—1882no—
447C4#125×D4712yes—
448C4#126×D4712yes—
449C2—944no—
450C2#400×D4711yescharacteristic
451C2#2025316911yescharacteristic
452C2#2025317111yescharacteristic
453C2#2025329611yescharacteristic
454C2#2025330211yescharacteristic
455C2#2025370711yescharacteristic
456C2#2025373511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2099C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#2099D47
hypocenterC47#23744
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #20244959C2semidirect
4. #20244958C2semidirect
5. #20244952C2semidirect
6. #20244951C2semidirect
7. #20244945C2semidirect
11. C47×#2099C2semidirect
228. #2099D47semidirect
271. C47#23744semidirect

Maximal subgroups

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

subgroupindex
#202458692
#202457932
#202449592
#202449582
#202449522
#202449512
#202449452
#202431032
#336×D472
C47×#20992
#2374447