Finite Group Databasebeta

← #26110540

Subgroups — #26110540

Order 12032.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246339C211yesmaximal, characteristic
2#20244144C211yesmaximal, characteristic, complemented
3#20243385C211yesmaximal, characteristic
4C2×#15688852C211yesmaximal, characteristic
5#20241271C211yesmaximal, characteristic, complemented
6#20241228C211yesmaximal, characteristic, complemented
7C47×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D188C2211yescharacteristic
9C2×#13093982—21no—
10C2×#13093957—21no—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093944—21no—
14#15689024—21no—
15#15689013—22no—
16#15688980—21no—
17C4⋊C4×Dic47—21no—
18C4×C4⋊Dic47C2211yescharacteristic
19#15688885—21no—
20#15688885—21no—
21#15688852C414yescomplemented
22C2×C4×C8×C47C2211yescharacteristic
23C47×#384C2211yescharacteristic
24C47×#384C2211yescharacteristic
25C47×#340—22no—
26C22×D188D411yescharacteristic
27C22×C4×D47—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C4×D188—21no—
31C4×D188—21no—
32C4×D188C2×C412yes—
33C4×D188Q812yes—
34#13093982—42no—
35#13093982—42no—
36C2×C4⋊Dic47D411yescharacteristic
37C2×C4⋊Dic47D411yescharacteristic
38C2×C4⋊Dic47D411yescharacteristic
39C2×(C2×D47)⋊C4—21no—
40C2×(C2×D47)⋊C4—22no—
41C2×(C2×D47)⋊C4—22no—
42C2×C4×Dic47—22no—
43C2×C4×Dic47—21no—
44#13093957—42no—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)C2×C412yes—
49#13093944—42no—
50C47⋊#95—22no—
51C47⋊#95—21no—
52C22×C8×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47—21no—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47D412yes—
59C2×C42×C47C2311yescharacteristic
60C4×C8×C47—21no—
61C4×C8×C47C2×C412yes—
62C23×D47—21no—
63C22×C4×C47—22no—
64C22×C4×C47—41no—
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—21no—
76C2×D188C4⋊C412yes—
77C2×C4×D47—22no—
78C2×C4×D47—22no—
79C2×C4×D47—41no—
80C2×C4×D47—41no—
81C2×C4×D47—41no—
82C2×C4×D47—41no—
83C2×C8×C47—22no—
84C2×C8×C47—41no—
85C2×C8×C47—41no—
86C4⋊C4×C47—42no—
87C4⋊C4×C47—42no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C4⋊C4×C47—41no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96C42×C47C22×C411yescharacteristic
97C42×C47C2×Q811yescharacteristic
98C42×C47#4111yescharacteristic
99C42×C47#4111yescharacteristic
100(C2×D47)⋊C4—22no—
101(C2×D47)⋊C4—22no—
102(C2×D47)⋊C4—44no—
103(C2×D47)⋊C4—82no—
104C4⋊Dic47—21no—
105C4⋊Dic47—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47C4⋊C412yes—
109C4⋊Dic47D812yes—
110C4×Dic47—44no—
111C4×Dic47—41no—
112C4×Dic47—41no—
113C2×C47⋊C8—22no—
114C2×C47⋊C8—41no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C2×C47⋊C8—41no—
119C23×C47#12011yescharacteristic
120C22×D47—22no—
121C22×D47—41no—
122C22×D47—41no—
123C22×D47—41no—
124C22×D47—41no—
125C22×D47—41no—
126C22×D47—41no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47—81no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47C2×C4⋊C411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47C22⋊Q811yescharacteristic
139C2×C4×C47C22⋊Q811yescharacteristic
140C2×C4×C47#12311yescharacteristic
141C2×C4×C47C2×D811yescharacteristic
142C2×C4×C47#13511yescharacteristic
143C2×C4×C47#13511yescharacteristic
144C2×C4×C47#13511yescharacteristic
145C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C47#13711yescharacteristic
148C2×C4×C47#13711yescharacteristic
149C2×Dic47—22no—
150C2×Dic47—22no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—41no—
155C2×Dic47—41no—
156C2×Dic47—41no—
157C2×Dic47—41no—
158D188—22no—
159D188—22no—
160D188—41no—
161D188—41no—
162C4×D47—42no—
163C4×D47—42no—
164C4×D47—42no—
165C4×D47—42no—
166C8×C47—42no—
167C47⋊C8—42no—
168C47⋊C8—81no—
169#8897—471nomaximal, Sylow
170C22×C47#38511yescharacteristic
171C22×C47#44711yescharacteristic
172C22×C47#44911yescharacteristic
173C22×C47#45211yescharacteristic
174C22×C47#45211yescharacteristic
175C22×C47#45411yescharacteristic
176C22×C47#45511yescharacteristic
177C2×D47—42no—
178C2×D47—42no—
179C2×D47—42no—
180C2×D47—81no—
181C2×D47—81no—
182C2×D47—81no—
183C2×D47—81no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—82no—
187C4×C47—161no—
188C4×C47#42711yescharacteristic
189C4×C47#42811yescharacteristic
190C4×C47C4×D811yescharacteristic
191C4×C47#44011yescharacteristic
192C4×C47#47411yescharacteristic
193C4×C47#47811yescharacteristic
194C4×C47#48211yescharacteristic
195C4×C47#48511yescharacteristic
196Dic47—42no—
197Dic47—42no—
198Dic47—81no—
199#2354—471no—
200#1947—471no—
201#1834D4711yescharacteristic, complemented
202#1802—471no—
203C2×D4⋊C8—471no—
204#1296—471no—
205#1279—471no—
206C2×C47#162511yescharacteristic
207C2×C47#163811yescharacteristic
208C2×C47#164111yescharacteristic
209C2×C47#164611yescharacteristic
210C2×C47#185411yescharacteristic
211C2×C47#186011yescharacteristic
212C2×C47#186211yescharacteristic
213D47—82no—
214C2×C4×D4—471no—
215C2×#117—941no—
216C2×#107—941no—
217C2×C4⋊C8—471no—
218C2×C4⋊C8—471no—
219C2×#102—941no—
220C2×C4×C8C2×D4711yescharacteristic
221#390—941no—
222#388—942no—
223#384C2×D4711yescharacteristic
224#384C2×D4711yescharacteristic
225#380—941no—
226C4×C4⋊C4—471no—
227C4×C4⋊C4—941no—
228#340—22no—
229#340—941no—
230#340—941no—
231D4⋊C8—474no—
232C47#889711yescharacteristic, complemented, Sylow
233C22×D4—471no—
234C23×C4—941no—
235C22×C8—21no—
236C22×C8—941no—
237C22×C8—941no—
238C4×D4—472no—
239C4×D4—472no—
240C4×D4—941no—
241C4×D4—941no—
242#117—1882no—
243#117—1882no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—471no—
250C2×C4⋊C4—471no—
251C2×C4⋊C4—471no—
252C2×C4⋊C4C22⋊D4712yes—
253C2×C22⋊C4—941no—
254C2×C22⋊C4—942no—
255C2×C22⋊C4—942no—
256C2×C42—942no—
257C2×C42—941no—
258C2×C42C22×D4711yescharacteristic
259#107—1882no—
260C4⋊C8—472no—
261C4⋊C8—941no—
262C4⋊C8—941no—
263C4⋊C8—941no—
264#102—1882no—
265C4×C8—21no—
266C4×C8C4×D4712yes—
267#95—942no—
268#95—941no—
269C24—941no—
270C2×D4—472no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4—941no—
275C2×D4—941no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—941no—
279C22×C4—941no—
280C22×C4—942no—
281C22×C4—942no—
282C22×C4—941no—
283C22×C4—1881no—
284C22×C4—1881no—
285C22×C4—1881no—
286C22×C4—1881no—
287C22×C4D4×D4711yescharacteristic
288C22×C4D4×D4711yescharacteristic
289C22×C4C2×C22⋊D4711yescharacteristic
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—942no—
294C2×C8—1881no—
295C2×C8—1881no—
296C2×C8—1881no—
297C2×C8—1881no—
298C2×C8—1881no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—472no—
310C4⋊C4—472no—
311C4⋊C4—941no—
312C4⋊C4—941no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C22⋊C4—942no—
316C22⋊C4—942no—
317C22⋊C4—3762no—
318C22⋊C4—1884no—
319C42—1884no—
320C42—1881no—
321C42—1881no—
322C42C2×C4×D4711yescharacteristic
323C42#1062535011yescharacteristic
324C42Q8×D4711yescharacteristic
325C42#1062535411yescharacteristic
326C23—942no—
327C23—1881no—
328C23—1881no—
329C23—1881no—
330C23—1881no—
331C23—1881no—
332C23—1881no—
333C23#1309399211yescharacteristic
334D4—942no—
335D4—942no—
336D4—1881no—
337D4—1881no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—942no—
347C2×C4—942no—
348C2×C4—1881no—
349C2×C4—1881no—
350C2×C4—1881no—
351C2×C4—1881no—
352C2×C4—1881no—
353C2×C4—1881no—
354C2×C4—1881no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4—1882no—
358C2×C4—1882no—
359C2×C4C4⋊C4×D4711yescharacteristic
360C2×C4C4×C22⋊D4711yescharacteristic
361C2×C4#1309398611yescharacteristic
362C2×C4#1309400011yescharacteristic
363C2×C4#1309400211yescharacteristic
364C2×C4#1309400911yescharacteristic
365C2×C4D8×D4711yescharacteristic
366C2×C4#1309404511yescharacteristic
367C2×C4#1309404511yescharacteristic
368C2×C4#1309404711yescharacteristic
369C2×C4#1309404811yescharacteristic
370C2×C4#1309405111yescharacteristic
371C2×C4#1309405311yescharacteristic
372C2×C4#1309405611yescharacteristic
373C8—42no—
374C8—3761no—
375C8—1882no—
376C22—3761no—
377C22—3761no—
378C22—3761no—
379C22—3761no—
380C22—1882no—
381C22—1882no—
382C22—1882no—
383C22#1568899411yescharacteristic
384C22#1568925511yescharacteristic
385C22#1568926711yescharacteristic
386C22#1568928211yescharacteristic
387C22#1568928411yescharacteristic
388C22#1568929511yescharacteristic
389C22#1568930011yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—161no—
394C4—3761no—
395C4—1882no—
396C4—1882no—
397C4#1568915811yescharacteristic
398C4#1568916211yescharacteristic
399C4#1568920511yescharacteristic
400C4#1568922211yescharacteristic
401C4#1568940211yescharacteristic
402C4#1568942611yescharacteristic
403C4#1568944911yescharacteristic
404C4#1568946711yescharacteristic
405C2—3762no—
406C2#2024247411yescharacteristic
407C2#2024255711yescharacteristic
408C2#2024257811yescharacteristic
409C2#2024261311yescharacteristic
410C2#2024358611yescharacteristic
411C2#2024362011yescharacteristic
412C2#2024363211yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1834C2
socleC23×C47#120
prime radicalC22×D188D4
cosocleC2×C42×C47C23
hypercenter#1834D47
hypocenterC47#8897
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #20244144C2semidirect
5. #20241271C2semidirect
6. #20241228C2semidirect
7. C47×#1834C2semidirect
21. #15688852C4semidirect
201. #1834D47semidirect
232. C47#8897semidirect

Maximal subgroups

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

subgroupindex
#202463392
#202441442
#202433852
C2×#156888522
#202412712
#202412282
C47×#18342
#889747