Finite Group Databasebeta

← #26112448

Subgroups — #26112448

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689400C211yesmaximal, characteristic
2C2×C8×D188C211yesmaximal, characteristic
3#20243385C211yesmaximal, characteristic
4C2×#15688869C211yesmaximal, characteristic, complemented
5#20241271C211yesmaximal, characteristic, complemented
6#20241223C211yesmaximal, characteristic, complemented
7C47×#1956C211yesmaximal, characteristic, complemented
8C22×C8×D47—21no—
9C2×C4×D188C2211yescharacteristic
10#15689400—22no—
11#15689400C414yescomplemented
12C8×D188—22no—
13C8×D188—22no—
14C2×#13093957—21no—
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×C4⋊(C47⋊C8)C2211yescharacteristic
17C2×C4⋊(C47⋊C8)C2211yescharacteristic
18C2×#13093944—21no—
19C2×#13093944—21no—
20C2×(C2×D47)⋊C8—21no—
21#15688885—21no—
22#15688869—22no—
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×#103×C47—21no—
25C2×#103×C47—21no—
26C2×C4×C8×C47C2211yescharacteristic
27C47×#384C2211yescharacteristic
28C22×D188D411yescharacteristic
29C22×C4×D47—21no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32C22×C47⋊C8—21no—
33C2×C8×D47—24no—
34C2×C8×D47—42no—
35C2×C8×D47—42no—
36C4×D188—21no—
37C4×D188—21no—
38C4×D188C2×C412yes—
39C4×D188D412yes—
40C2×C4⋊Dic47D411yescharacteristic
41C2×(C2×D47)⋊C4—21no—
42#13093957—24no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)C2×C412yes—
48C4⋊(C47⋊C8)D412yes—
49#13093944—24no—
50#13093944—42no—
51(C2×D47)⋊C8—24no—
52C22×Q8×C47—21no—
53C22×C8×C47D411yescharacteristic
54C22×C8×C47D411yescharacteristic
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47C2×C412yes—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C42×C47C2311yescharacteristic
65#103×C47—42no—
66#103×C47—42no—
67C4×C8×C47—21no—
68C4×C8×C47—21no—
69C23×D47—21no—
70C2×Q8×C47—22no—
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C2×Q8×C47—41no—
74C2×Q8×C47—41no—
75C2×Q8×C47—41no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C22×Dic47—21no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188—21no—
85C2×D188C22⋊C412yes—
86C2×D188SD1612yes—
87C2×D188Q1612yes—
88C2×C4×D47—22no—
89C2×C4×D47—22no—
90C2×C4×D47—41no—
91C2×C4×D47—41no—
92C2×C4×D47—41no—
93C2×C4×D47—41no—
94C2×C8×C47—21no—
95C2×C8×C47—21no—
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47D812yes—
100C4⋊C4×C47—22no—
101C4⋊C4×C47—22no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47—41no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—81no—
109C42×C47C22×C411yescharacteristic
110C42×C47C2×D411yescharacteristic
111C42×C47C2×D411yescharacteristic
112C42×C47#4111yescharacteristic
113(C2×D47)⋊C4—22no—
114(C2×D47)⋊C4—22no—
115C4⋊Dic47—21no—
116C4⋊Dic47C22⋊C412yes—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—22no—
119C2×C47⋊C8—41no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8—41no—
124C2×C47⋊C8—41no—
125C2×C47⋊C8—41no—
126C8×D47—48no—
127C23×C47#12111yescharacteristic
128C22×D47—22no—
129C22×D47—22no—
130C22×D47—22no—
131C22×D47—41no—
132C22×D47—41no—
133C22×D47—41no—
134C22×D47—41no—
135Q8×C47—42no—
136Q8×C47—42no—
137Q8×C47—81no—
138Q8×C47—81no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—42no—
142C2×C4×C47—81no—
143C2×C4×C47—81no—
144C2×C4×C47—81no—
145C2×C4×C47—81no—
146C2×C4×C47—81no—
147C2×C4×C47C2×C22⋊C411yescharacteristic
148C2×C4×C47C4×D411yescharacteristic
149C2×C4×C47C4×D411yescharacteristic
150C2×C4×C47#12011yescharacteristic
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47#12311yescharacteristic
153C2×C4×C47C2×D811yescharacteristic
154C2×C4×C47C2×SD1611yescharacteristic
155C2×C4×C47C2×Q1611yescharacteristic
156C2×C4×C47#13511yescharacteristic
157C2×C4×C47#13511yescharacteristic
158C2×C4×C47#13511yescharacteristic
159C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
161C2×Dic47—22no—
162C2×Dic47—41no—
163C2×Dic47—41no—
164D188—22no—
165D188—22no—
166D188—22no—
167D188#10314yescomplemented
168C4×D47—42no—
169C4×D47—42no—
170C4×D47—42no—
171C4×D47—42no—
172C8×C47—22no—
173C8×C47—41no—
174C47⋊C8—42no—
175C47⋊C8—42no—
176C47⋊C8—81no—
177#9219—471nomaximal, Sylow
178C22×C47#38611yescharacteristic
179C22×C47#45911yescharacteristic
180C22×C47#46311yescharacteristic
181C22×C47#46511yescharacteristic
182C22×C47#46711yescharacteristic
183C22×C47#47111yescharacteristic
184C22×C47#47311yescharacteristic
185C2×D47—24no—
186C2×D47—42no—
187C2×D47—42no—
188C2×D47—42no—
189C2×D47—42no—
190C2×D47—42no—
191C2×D47—42no—
192C4×C47—21no—
193C4×C47—21no—
194C4×C47—82no—
195C4×C47—161no—
196C4×C47C2×#10311yescharacteristic
197C4×C47#41611yescharacteristic
198C4×C47C4×D811yescharacteristic
199C4×C47#44211yescharacteristic
200C4×C47#44711yescharacteristic
201C4×C47#44911yescharacteristic
202C4×C47#46511yescharacteristic
203C4×C47#46711yescharacteristic
204Dic47—42no—
205C2×#474—471no—
206C2×C8×D4—471no—
207#1956D4711yescharacteristic, complemented
208#1802—471no—
209C2×#332—471no—
210#1296—471no—
211#1277—471no—
212C2×C47#166511yescharacteristic
213C2×C47#166911yescharacteristic
214C2×C47#167911yescharacteristic
215C2×C47#168311yescharacteristic
216C2×C47#187911yescharacteristic
217C2×C47#189211yescharacteristic
218C2×C47#190811yescharacteristic
219D47—44no—
220C23×C8—941no—
221C2×C4⋊Q8C2×D4711yescharacteristic
222C2×C4×D4—471no—
223#474—474no—
224#474—942no—
225C8×D4—942no—
226C8×D4—942no—
227C2×#107—941no—
228C2×C4⋊C8—471no—
229C2×C4⋊C8—471no—
230C2×C4⋊C8—471no—
231C2×#103—21no—
232C2×#103—21no—
233C2×#102—941no—
234C2×#102—941no—
235C2×C22⋊C8—941no—
236C2×C4×C8C2×D4711yescharacteristic
237#384C2×D4711yescharacteristic
238#340—941no—
239#332—942no—
240C47#921911yescharacteristic, complemented, Sylow
241C22×Q8—21no—
242C22×D4—471no—
243C23×C4—941no—
244C22×C8—944no—
245C22×C8—941no—
246C22×C8—941no—
247C22×C8—941no—
248C22×C8—1882no—
249C22×C8—1882no—
250C22×C8C22⋊D4711yescharacteristic
251C22×C8C22⋊D4711yescharacteristic
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C4×D4712yes—
256C4×D4—472no—
257C4×D4—472no—
258C4×D4—941no—
259C4×D4—941no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—471no—
266C2×C22⋊C4—941no—
267C2×C42C22×D4711yescharacteristic
268#107—944no—
269C4⋊C8—472no—
270C4⋊C8—472no—
271C4⋊C8—941no—
272C4⋊C8—941no—
273C4⋊C8—941no—
274C4⋊C8—941no—
275#103—42no—
276#103—42no—
277#102—944no—
278#102—1882no—
279C22⋊C8—944no—
280C4×C8—21no—
281C4×C8—21no—
282C24—941no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—472no—
290C2×D4—472no—
291C2×D4—472no—
292C2×D4—941no—
293C2×D4—941no—
294C2×D4—941no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—941no—
298C22×C4—942no—
299C22×C4—942no—
300C22×C4—1881no—
301C22×C4—1881no—
302C22×C4—1881no—
303C22×C4—1881no—
304C22×C4D4×D4711yescharacteristic
305C22×C4#1062535211yescharacteristic
306C22×C4C2×C22⋊D4711yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—942no—
313C2×C8—942no—
314C2×C8—1888no—
315C2×C8—1881no—
316C2×C8—1881no—
317C2×C8—1881no—
318C2×C8—1881no—
319C2×C8—1881no—
320C2×C8—1881no—
321C2×C8—1881no—
322C2×C8#1062533412yes—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—81no—
332C4⋊C4—472no—
333C4⋊C4—941no—
334C22⋊C4—942no—
335C22⋊C4—942no—
336C42C2×C4×D4711yescharacteristic
337C42#1062535011yescharacteristic
338C42D4×D4711yescharacteristic
339C42D4×D4711yescharacteristic
340C23—942no—
341C23—942no—
342C23—942no—
343C23—1881no—
344C23—1881no—
345C23—1881no—
346C23—1881no—
347C23#1309399511yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—474no—
353D4—942no—
354D4—942no—
355D4—942no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—942no—
365C2×C4—1881no—
366C2×C4—1881no—
367C2×C4—1882no—
368C2×C4—1882no—
369C2×C4—1882no—
370C2×C4—1882no—
371C2×C4C22⋊C4×D4711yescharacteristic
372C2×C4(C22⋊D47)⋊C411yescharacteristic
373C2×C4C4×C22⋊D4711yescharacteristic
374C2×C4#1309399211yescharacteristic
375C2×C4#1309399711yescharacteristic
376C2×C4#1309400611yescharacteristic
377C2×C4C2×#1062533411yescharacteristic
378C2×C4SD16×D4711yescharacteristic
379C2×C4Q16×D4711yescharacteristic
380C2×C4#1309404411yescharacteristic
381C2×C4#1309404511yescharacteristic
382C2×C4#1309404711yescharacteristic
383C2×C4#1309404911yescharacteristic
384C2×C4#1309405011yescharacteristic
385C8—22no—
386C8—41no—
387C8—3761no—
388C8—1882no—
389C8—1882no—
390C22—944no—
391C22—1882no—
392C22—1882no—
393C22—1882no—
394C22—1882no—
395C22—1882no—
396C22—1882no—
397C22#1568899911yescharacteristic
398C22#1568931511yescharacteristic
399C22#1568933511yescharacteristic
400C22#1568934911yescharacteristic
401C22#1568936111yescharacteristic
402C22#1568938311yescharacteristic
403C22#1568939511yescharacteristic
404C4—21no—
405C4—21no—
406C4—82no—
407C4—161no—
408C4—1882no—
409C4#103×D4711yescharacteristic
410C4#1568911811yescharacteristic
411C4C4×#1062533411yescharacteristic
412C4#1568923311yescharacteristic
413C4#1568925611yescharacteristic
414C4#1568926611yescharacteristic
415C4#1568935511yescharacteristic
416C4#1568936311yescharacteristic
417C2—1884no—
418C2#2024272611yescharacteristic
419C2#2024275011yescharacteristic
420C2#2024280811yescharacteristic
421C2#2024283611yescharacteristic
422C2#2024373911yescharacteristic
423C2#2024380811yescharacteristic
424C2#2024390611yescharacteristic
subgroupG/H
centerC23#13093995
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1956C2
socleC23×C47#121
prime radicalC22×D188D4
cosocleC2×C42×C47C23
hypercenter#1956D47
hypocenterC47#9219
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
4. C2×#15688869C2semidirect
5. #20241271C2semidirect
6. #20241223C2semidirect
7. C47×#1956C2semidirect
11. #15689400C4semidirect
167. D188#103semidirect
207. #1956D47semidirect
240. C47#9219semidirect

Maximal subgroups

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

subgroupindex
C2×#156894002
C2×C8×D1882
#202433852
C2×#156888692
#202412712
#202412232
C47×#19562
#921947