Finite Group Databasebeta

← #26120094

Subgroups — #26120094

Order 12032.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689325C211yesmaximal, characteristic
2#20244350C211yesmaximal, characteristic, complemented
3#20244181C211yesmaximal, characteristic
4#20243389C211yesmaximal, characteristic
5C2×#15688875C211yesmaximal, characteristic, complemented
6#20241272C211yesmaximal, characteristic, complemented
7C2×C47×#332C211yesmaximal, characteristic, complemented
8C22×#10625336—21no—
9C2×C4×D188C2211yescharacteristic
10#15689325—22no—
11#15689325—22no—
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093948—21no—
14C2×#13093946—21no—
15C2×(C2×D47)⋊C8—21no—
16C2×(C2×D47)⋊C8—21no—
17C2×C4×C47⋊C8C2211yescharacteristic
18#15688993C2211yescharacteristic
19#15688886—21no—
20#15688885—21no—
21#15688885—21no—
22#15688875—22no—
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C47×#332—22no—
27C22×D188D411yescharacteristic
28C22×C4×D47—21no—
29C2×#10625336—24no—
30C2×#10625336—42no—
31C2×#10625336—42no—
32C22×C47⋊C8—21no—
33C22×C47⋊C8D411yescharacteristic
34C22×C47⋊C8D411yescharacteristic
35C4×D188—21no—
36C4×D188—21no—
37C4×D188—21no—
38C4×D188—21no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47D411yescharacteristic
43C2×(C2×D47)⋊C4—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D412yes—
46#13093948—24no—
47#13093946—42no—
48(C2×D47)⋊C8—42no—
49(C2×D47)⋊C8—42no—
50C4×C47⋊C8—21no—
51C4×C47⋊C8—21no—
52C22×Q8×C47—21no—
53C22×C8×C47—21no—
54C22×C8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47D412yes—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C42×C47C2311yescharacteristic
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66C23×D47—21no—
67C2×Q8×C47—22no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C2×Q8×C47—41no—
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47#4111yescharacteristic
77C22×Dic47—21no—
78C22×Dic47—41no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188—21no—
84C2×D188D812yes—
85C2×C4×D47—41no—
86C2×C4×D47—41no—
87C2×C4×D47—41no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×C4×D47—41no—
91C2×C8×C47—41no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C4⋊C4×C47—22no—
98C4⋊C4×C47—22no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C42×C47C2×D411yescharacteristic
102C42×C47C2×D411yescharacteristic
103C42×C47#4111yescharacteristic
104C42×C47#4111yescharacteristic
105#10625336—48no—
106(C2×D47)⋊C4—41no—
107(C2×D47)⋊C4—41no—
108C4⋊Dic47—21no—
109C4⋊Dic47—21no—
110C4⋊Dic47—41no—
111C4⋊Dic47—41no—
112C4⋊Dic47—41no—
113C4⋊Dic47—41no—
114C4⋊Dic47—81no—
115C2×C47⋊C8—21no—
116C2×C47⋊C8—21no—
117C2×C47⋊C8—22no—
118C2×C47⋊C8—21no—
119C2×C47⋊C8—21no—
120C2×C47⋊C8—21no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8—41no—
123C2×C47⋊C8SD1612yescomplemented
124C23×C47#12111yescharacteristic
125C22×D47—22no—
126C22×D47—41no—
127C22×D47—41no—
128C22×D47—41no—
129C22×D47—41no—
130C22×D47—41no—
131C22×D47—41no—
132Q8×C47—42no—
133Q8×C47—42no—
134Q8×C47—81no—
135Q8×C47—81no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—42no—
139C2×C4×C47—81no—
140C2×C4×C47—81no—
141C2×C4×C47#12011yescharacteristic
142C2×C4×C47#12111yescharacteristic
143C2×C4×C47#12111yescharacteristic
144C2×C4×C47#12311yescharacteristic
145C2×C4×C47#12311yescharacteristic
146C2×C4×C47#12411yescharacteristic
147C2×C4×C47C2×D811yescharacteristic
148C2×C4×C47C2×SD1611yescharacteristic
149C2×C4×C47#13511yescharacteristic
150C2×C4×C47#13511yescharacteristic
151C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C47#13711yescharacteristic
154C2×C4×C47#13711yescharacteristic
155C2×Dic47—41no—
156C2×Dic47—41no—
157C2×Dic47—41no—
158C2×Dic47—81no—
159C2×Dic47—81no—
160C2×Dic47—81no—
161D188—22no—
162D188—22no—
163D188—41no—
164D188—41no—
165C4×D47—81no—
166C4×D47—81no—
167C4×D47—81no—
168C4×D47—81no—
169C8×C47—81no—
170C8×C47—81no—
171C47⋊C8—22no—
172C47⋊C8—42no—
173C47⋊C8—41no—
174#10476—471nomaximal, Sylow
175C22×C47#39411yescharacteristic
176C22×C47#46111yescharacteristic
177C22×C47#46311yescharacteristic
178C22×C47#46611yescharacteristic
179C22×C47#46811yescharacteristic
180C22×C47#47111yescharacteristic
181C22×C47#47311yescharacteristic
182C2×D47—42no—
183C2×D47—42no—
184C2×D47—42no—
185C2×D47—81no—
186C2×D47—81no—
187C2×D47—81no—
188C2×D47—81no—
189C4×C47—21no—
190C4×C47—21no—
191C4×C47—82no—
192C4×C47#44711yescharacteristic
193C4×C47#45211yescharacteristic
194C4×C47#46011yescharacteristic
195C4×C47#46411yescharacteristic
196C4×C47#46511yescharacteristic
197C4×C47#46811yescharacteristic
198C4×C47#48011yescharacteristic
199C4×C47#48211yescharacteristic
200Dic47—81no—
201Dic47—161no—
202C2×#461—471no—
203#1990—471no—
204#1954—471no—
205#1802—471no—
206C2×#335—471no—
207C2×#332D4711yescharacteristic, complemented
208#1296—471no—
209C2×C47#167311yescharacteristic
210C2×C47#168111yescharacteristic
211C2×C47#169111yescharacteristic
212C2×C47#169911yescharacteristic
213C2×C47#203311yescharacteristic
214C2×C47#205211yescharacteristic
215C2×C47#205511yescharacteristic
216D47—82no—
217C22×SD16—941no—
218C2×C4⋊Q8C2×D4711yescharacteristic
219C2×C4×D4—471no—
220#461—942no—
221#461—942no—
222C2×C4⋊C8—471no—
223C2×C4⋊C8C2×D4711yescharacteristic
224C2×C4⋊C8C2×D4711yescharacteristic
225C2×#103—941no—
226C2×#102—941no—
227C2×C22⋊C8—941no—
228C2×C22⋊C8—941no—
229C2×C4×C8—471no—
230#384—471no—
231#340—941no—
232#340—941no—
233#340—941no—
234#335—942no—
235#332—22no—
236C47#1047611yescharacteristic, complemented, Sylow
237C22×Q8—21no—
238C22×D4—471no—
239C23×C4—941no—
240C2×SD16—944no—
241C2×SD16—1882no—
242C2×SD16—1882no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—471no—
246C22×C8—471no—
247C22×C8—941no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8C22⋊D4712yes—
252C4×D4—941no—
253C4×D4—941no—
254C4×D4—941no—
255C4×D4—941no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—471no—
259C2×C4⋊C4—941no—
260C2×C4⋊C4—941no—
261C2×C4⋊C4—941no—
262C2×C22⋊C4—941no—
263C2×C42C22×D4711yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—472no—
269C4⋊C8—941no—
270#103—944no—
271#102—1882no—
272C22⋊C8—1882no—
273C22⋊C8—1882no—
274C4×C8—941no—
275C4×C8—941no—
276C24—941no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—472no—
284C2×D4—941no—
285C2×D4—941no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C22×C4—41no—
290C22×C4—941no—
291C22×C4—1881no—
292C22×C4—1881no—
293C22×C4—1881no—
294C22×C4—1881no—
295C22×C4—1881no—
296C22×C4—1881no—
297C22×C4—1881no—
298C22×C4#1062535011yescharacteristic
299C22×C4D4×D4711yescharacteristic
300C22×C4D4×D4711yescharacteristic
301SD16—1888no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—472no—
309C2×C8—941no—
310C2×C8—941no—
311C2×C8—942no—
312C2×C8—941no—
313C2×C8—941no—
314C2×C8—941no—
315C2×C8—1881no—
316C2×C8—1881no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—941no—
322C4⋊C4—941no—
323C4⋊C4—3761no—
324C4⋊C4—1881no—
325C4⋊C4—1881no—
326C4⋊C4—1881no—
327C4⋊C4—1881no—
328C22⋊C4—1881no—
329C22⋊C4—1881no—
330C42#1062535011yescharacteristic
331C42D4×D4711yescharacteristic
332C42#1062535211yescharacteristic
333C42C2×C22⋊D4711yescharacteristic
334C23—942no—
335C23—1881no—
336C23—1881no—
337C23—1881no—
338C23—1881no—
339C23—1881no—
340C23—1881no—
341C23#1309399711yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—942no—
347D4—942no—
348D4—1881no—
349D4—1881no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—3761no—
356C2×C4—3761no—
357C2×C4—3761no—
358C2×C4—3761no—
359C2×C4—3761no—
360C2×C4—3761no—
361C2×C4—3761no—
362C2×C4—1881no—
363C2×C4—1881no—
364C2×C4—1881no—
365C2×C4#1309399211yescharacteristic
366C2×C4#1309399611yescharacteristic
367C2×C4#1309399711yescharacteristic
368C2×C4#1309400611yescharacteristic
369C2×C4#1309400711yescharacteristic
370C2×C4#1309401011yescharacteristic
371C2×C4D8×D4711yescharacteristic
372C2×C4SD16×D4711yescharacteristic
373C2×C4#1309404511yescharacteristic
374C2×C4#1309404711yescharacteristic
375C2×C4#1309404811yescharacteristic
376C2×C4#1309405111yescharacteristic
377C2×C4#1309405311yescharacteristic
378C2×C4#1309405611yescharacteristic
379C8—81no—
380C8—81no—
381C8—942no—
382C8—1882no—
383C8—1881no—
384C22—3761no—
385C22—3761no—
386C22—3761no—
387C22—3761no—
388C22—1882no—
389C22—1882no—
390C22—1882no—
391C22#1568903811yescharacteristic
392C22#1568932711yescharacteristic
393C22#1568934111yescharacteristic
394C22#1568935811yescharacteristic
395C22#1568936811yescharacteristic
396C22#1568938911yescharacteristic
397C22#1568939711yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—3761no—
402C4—7521no—
403C4#1568925511yescharacteristic
404C4#1568928211yescharacteristic
405C4#1568932111yescharacteristic
406C4#1568934711yescharacteristic
407C4#1568935511yescharacteristic
408C4#1568937211yescharacteristic
409C4#1568943511yescharacteristic
410C4#1568944611yescharacteristic
411C2—3762no—
412C2#2024277611yescharacteristic
413C2#2024282811yescharacteristic
414C2#2024288611yescharacteristic
415C2#2024293811yescharacteristic
416C2#2024456811yescharacteristic
417C2#2024468711yescharacteristic
418C2#2024470211yescharacteristic
subgroupG/H
centerC23#13093997
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC2×C47×#332C2
socleC23×C47#121
prime radicalC22×D188D4
hypercenterC2×#332D47
hypocenterC47#10476
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #20244350C2semidirect
5. C2×#15688875C2semidirect
6. #20241272C2semidirect
7. C2×C47×#332C2semidirect
123. C2×C47⋊C8SD16semidirect
207. C2×#332D47semidirect
236. C47#10476semidirect

Maximal subgroups

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

subgroupindex
C2×#156893252
#202443502
#202441812
#202433892
C2×#156888752
#202412722
C2×C47×#3322
#1047647