Finite Group Databasebeta

← #26109450

Subgroups — #26109450

Order 12032.

432 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252355C211yesmaximal, characteristic
2#20243408C211yesmaximal, characteristic
3C4×#13093957C211yesmaximal, characteristic, complemented
4#20242143C211yesmaximal, characteristic, complemented
5#20241291C211yesmaximal, characteristic, complemented
6#20241289C211yesmaximal, characteristic, complemented
7C47×#1806C211yesmaximal, characteristic
8#15689254C411yescharacteristic, complemented
9#15689254C411yescharacteristic, complemented
10#15689201C411yescharacteristic, complemented
11#15689201C411yescharacteristic, complemented
12#15689195—21no—
13#15689195—21no—
14#15689176—21no—
15#15689176C2211yescharacteristic
16C2×#13093957—21no—
17#15689147C2211yescharacteristic
18C2×#13093951—21no—
19C4×#10625329—21no—
20C2×C4×C47⋊C8C2211yescharacteristic
21C4×C4⋊Dic47C2211yescharacteristic
22#15688885—21no—
23#15688882—21no—
24#15688873—21no—
25#15688873—21no—
26C4×#41×C47C2211yescharacteristic
27C47×#423C2211yescharacteristic
28C2×#104×C47—21no—
29C4×C4⋊C4×C47C2211yescharacteristic
30C47×#339—21no—
31C2×#10625329—21no—
32C2×#10625329—21no—
33C2×#10625329—21no—
34C22×C47⋊C8D411yescharacteristic
35C22×C47⋊C8D411yescharacteristic
36C2×C4⋊Dic47—21no—
37C2×C4×Dic47—21no—
38#13093957—24no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)C2×C411yescharacteristic
44C4⋊(C47⋊C8)C2×C411yescharacteristic
45#13093951—42no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C22⋊(C47⋊C8)—21no—
49#13093935—21no—
50#13093935—21no—
51C4×C47⋊C8—21no—
52C4×C47⋊C8C2×C411yescharacteristic
53C4×C47⋊C8C2×C411yescharacteristic
54C4×C47⋊C8D411yescharacteristic
55C4×C47⋊C8D411yescharacteristic
56C47⋊#95—21no—
57C2×#41×C47D411yescharacteristic
58C2×M16×C47—21no—
59C4×Q8×C47C2×C411yescharacteristic
60C4×Q8×C47Q811yescharacteristic
61C4×D4×C47—21no—
62C4×D4×C47—21no—
63C4×D4×C47C2×C411yescharacteristic
64C4×D4×C47Q811yescharacteristic
65#117×C47—21no—
66#117×C47D411yescharacteristic
67C2×C4⋊C4×C47—21no—
68C2×C42×C47—21no—
69C2×C42×C47—21no—
70C2×C42×C47C2311yescharacteristic
71C4⋊C8×C47—21no—
72C4⋊C8×C47—21no—
73#104×C47—42no—
74#95×C47—21no—
75#41×C47—21no—
76#41×C47—21no—
77#41×C47—21no—
78#41×C47—21no—
79C2×Q8×C47C4⋊C411yescharacteristic
80C2×D4×C47—21no—
81C2×D4×C47C4⋊C411yescharacteristic
82C22×C4×C47—21no—
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47—41no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47#4111yescharacteristic
89C22×Dic47—41no—
90M16×C47—41no—
91M16×C47—41no—
92C2×C8×C47—41no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—22no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47C4⋊C411yescharacteristic
98C4⋊C4×C47C4⋊C411yescharacteristic
99C22⋊C4×C47—21no—
100C22⋊C4×C47—21no—
101C22⋊C4×C47—21no—
102C42×C47—21no—
103C42×C47—21no—
104C42×C47—21no—
105C42×C47—41no—
106C42×C47—41no—
107C42×C47C22×C411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47C2×Q811yescharacteristic
110C42×C47#4111yescharacteristic
111C4⋊Dic47—22no—
112C4⋊Dic47—41no—
113C4×Dic47—41no—
114C4×Dic47—41no—
115#10625329—42no—
116#10625329—42no—
117#10625329—41no—
118#10625329—41no—
119C2×C47⋊C8—22no—
120C2×C47⋊C8—21no—
121C2×C47⋊C8—21no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C2×C47⋊C8C22⋊C411yescharacteristic
125C2×C47⋊C8C22⋊C411yescharacteristic
126C2×C47⋊C8C22⋊C411yescharacteristic
127C2×C47⋊C8C22⋊C411yescharacteristic
128C23×C47—21no—
129C23×C47#12111yescharacteristic
130Q8×C47—21no—
131Q8×C47—21no—
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—41no—
135D4×C47—41no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—41no—
142C2×C4×C47—42no—
143C2×C4×C47—41no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—42no—
148C2×C4×C47—81no—
149C2×C4×C47—81no—
150C2×C4×C47C2×C22⋊C411yescharacteristic
151C2×C4×C47C2×C4⋊C411yescharacteristic
152C2×C4×C47#11711yescharacteristic
153C2×C4×C47#12111yescharacteristic
154C2×C4×C47C22⋊Q811yescharacteristic
155C2×C4×C47C22⋊Q811yescharacteristic
156C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C47#13711yescharacteristic
159C2×C4×C47#13711yescharacteristic
160C2×Dic47—42no—
161C2×Dic47—81no—
162C2×Dic47—81no—
163C8×C47—81no—
164C47⋊C8—21no—
165C47⋊C8—21no—
166C47⋊C8—21no—
167C47⋊C8—41no—
168C47⋊C8—41no—
169C47⋊C8—81no—
170C47⋊C8#10412yescomplemented
171#8668—471nomaximal, Sylow
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47#38011yescharacteristic
178C22×C47#46911yescharacteristic
179C22×C47#47011yescharacteristic
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—21no—
183C4×C47—41no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47—82no—
187C4×C47C2×#10411yescharacteristic
188C4×C47#42111yescharacteristic
189C4×C47#42811yescharacteristic
190C4×C47#42811yescharacteristic
191C4×C47#46811yescharacteristic
192C4×C47#46811yescharacteristic
193Dic47—82no—
194#2965—471no—
195#1806—471no—
196#1806D4711yescharacteristic
197C4×#107—471no—
198#1566—471no—
199#1303—471no—
200#1303—471no—
201C2×C47—21no—
202C2×C47—21no—
203C2×C47—81no—
204C2×C47#180611yescharacteristic
205C2×C47#180911yescharacteristic
206C2×C47#181411yescharacteristic
207C4×#41C2×D4711yescharacteristic
208#446—471no—
209#446—471no—
210#436—471no—
211#436—471no—
212#435—941no—
213#435—941no—
214#431—471no—
215#431—941no—
216C2×#107—941no—
217#423—471no—
218#423C2×D4711yescharacteristic
219C2×#104—21no—
220C2×#104—941no—
221C4×M16—941no—
222C2×C4×C8—471no—
223C4×C4⋊C4—471no—
224C4×C4⋊C4C2×D4711yescharacteristic
225#340—941no—
226#339—21no—
227#339—941no—
228#334—941no—
229#334—941no—
230C47#866811yescharacteristic, complemented, Sylow
231C2×#41C22⋊D4711yescharacteristic
232C2×M16—21no—
233C2×M16—941no—
234C2×M16—941no—
235C2×M16—941no—
236C22×C8—471no—
237C22×C8—471no—
238C4×Q8Dic9411yescharacteristic
239C4×Q8C4×D4711yescharacteristic
240C4×D4—21no—
241C4×D4—21no—
242C4×D4Dic9411yescharacteristic
243C4×D4C4×D4711yescharacteristic
244#117—21no—
245#117C22⋊D4711yescharacteristic
246C2×C4⋊C4—21no—
247C2×C4⋊C4—941no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—941no—
251C2×C42C22×D4711yescharacteristic
252#107—944no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—471no—
256C4⋊C8—471no—
257C4⋊C8—941no—
258C4⋊C8—941no—
259C4⋊C8—941no—
260C4⋊C8—941no—
261#104—42no—
262#104—1882no—
263C22⋊C8—941no—
264C22⋊C8—941no—
265C22⋊C8—941no—
266#97—941no—
267#97—941no—
268C4×C8—471no—
269C4×C8—471no—
270C4×C8—471no—
271C4×C8—471no—
272C4×C8—941no—
273#95—21no—
274#95—941no—
275#41—21no—
276#41—21no—
277#41—21no—
278#41—21no—
279C2×Q8Dic47⋊C411yescharacteristic
280C2×D4—21no—
281C2×D4Dic47⋊C411yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—1881no—
287C22×C4D4×D4711yescharacteristic
288C22×C4#1062535211yescharacteristic
289C22×C4C2×C22⋊D4711yescharacteristic
290M16—41no—
291M16—41no—
292M16—1882no—
293M16—1882no—
294M16—1881no—
295M16—1881no—
296C2×C8—41no—
297C2×C8—471no—
298C2×C8—471no—
299C2×C8—471no—
300C2×C8—471no—
301C2×C8—942no—
302C2×C8—941no—
303C2×C8—941no—
304C2×C8—1881no—
305C2×C8—1881no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—942no—
311C4⋊C4—1881no—
312C4⋊C4Dic47⋊C411yescharacteristic
313C4⋊C4Dic47⋊C411yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—41no—
321C42—41no—
322C42—1881no—
323C42—1881no—
324C42C2×Dic9411yescharacteristic
325C42C2×C4×D4711yescharacteristic
326C42D4×D4711yescharacteristic
327C42#1062535211yescharacteristic
328C23—21no—
329C23#1309399611yescharacteristic
330Q8—21no—
331Q8—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—3761no—
351C2×C4—3761no—
352C2×C4—1882no—
353C2×C4C22⋊C4×D4711yescharacteristic
354C2×C4C2×Dic47⋊C411yescharacteristic
355C2×C4#1309398011yescharacteristic
356C2×C4#1309399611yescharacteristic
357C2×C4#1309400111yescharacteristic
358C2×C4#1309400111yescharacteristic
359C2×C4#1309404911yescharacteristic
360C2×C4#1309405011yescharacteristic
361C2×C4#1309405411yescharacteristic
362C2×C4#1309405511yescharacteristic
363C8—81no—
364C8—472no—
365C8—941no—
366C8—941no—
367C8—941no—
368C8—3761no—
369C8—1881no—
370C8—1881no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22#1568898111yescharacteristic
377C22#1568937411yescharacteristic
378C22#1568937911yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—82no—
386C4—3762no—
387C4#104×D4711yescharacteristic
388C4#1568913811yescharacteristic
389C4#1568916311yescharacteristic
390C4#1568916611yescharacteristic
391C4#1568936711yescharacteristic
392C4#1568937111yescharacteristic
393C2—21no—
394C2—21no—
395C2—81no—
396C2#2024340611yescharacteristic
397C2#2024341911yescharacteristic
398C2#2024344011yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1806C2
socleC22×C47#380
prime radicalC2×#41×C47D4
cosocleC2×C42×C47C23
hypercenter#1806D47
hypocenterC47#8668
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. C4×#13093957C2semidirect
4. #20242143C2semidirect
5. #20241291C2semidirect
6. #20241289C2semidirect
8. #15689254C4semidirect
9. #15689254C4semidirect
10. #15689201C4semidirect
11. #15689201C4semidirect
170. C47⋊C8#104semidirect
230. C47#8668semidirect

Maximal subgroups

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

subgroupindex
#202523552
#202434082
C4×#130939572
#202421432
#202412912
#202412892
C47×#18062
#866847