Finite Group Databasebeta

← #26133334

Subgroups — #26133334

Order 12032.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D752C211yesmaximal, characteristic
2C2×C4×D376C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic, complemented
4C2×#15688925C211yesmaximal, characteristic, complemented
5#20244254C211yesmaximal, characteristic, complemented
6#20241480C211yesmaximal, characteristic, complemented
7C47×#1374C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C22×D376C2211yescharacteristic
10C2×C4×D188—21no—
11C2×D752—22no—
12C2×D752—22no—
13C2×D752C414yescomplemented
14C4×D376—22no—
15C4×D376—22no—
16C2×#13093958C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093946—21no—
19C2×#13093946—21no—
20#15689025—21no—
21#15688925—22no—
22#15688925—22no—
23C22×C16×C47C2211yescharacteristic
24C22×C16×C47C2211yescharacteristic
25C2×C4×C8×C47C2211yescharacteristic
26C22×D188—21no—
27C22×D188—21no—
28C22×C4×D47—41no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376—21no—
34C2×D376—21no—
35C2×D376—21no—
36C2×D376—21no—
37C2×D376C2×C412yes—
38C2×D376C2×C412yescomplemented
39C2×D376D412yes—
40C2×D376D412yes—
41C4×D188—24no—
42C4×D188—42no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×(C2×D47)⋊C4—41no—
46C2×(C2×D47)⋊C4—41no—
47C2×(C2×D47)⋊C4—41no—
48D752—28no—
49#13093958—21no—
50#13093958—21no—
51#13093958—21no—
52#13093958D412yes—
53#13093946—24no—
54#13093946—42no—
55C22×C8×C47D411yescharacteristic
56C22×C8×C47C2311yescharacteristic
57C2×C42×C47D411yescharacteristic
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47—21no—
63C2×C16×C47C2×C412yescomplemented
64C4×C8×C47—21no—
65C4×C8×C47—21no—
66C23×D47—41no—
67C23×D47—41no—
68C22×C4×C47D811yescharacteristic
69C22×C4×C47D811yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×Dic47—41no—
72C22×Dic47—41no—
73C2×D188—22no—
74C2×D188—22no—
75C2×D188—22no—
76C2×D188—22no—
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×C4×D47—44no—
86C2×C4×D47—82no—
87C2×C4×D47—82no—
88C2×C8×C47—21no—
89C2×C8×C47—21no—
90C2×C8×C47—21no—
91C2×C8×C47C22×C411yescharacteristic
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C2×C8×C47#4111yescharacteristic
97C42×C47—21no—
98C42×C47—21no—
99(C2×D47)⋊C4—44no—
100(C2×D47)⋊C4—82no—
101(C2×D47)⋊C4—82no—
102C4⋊Dic47—22no—
103C4⋊Dic47—41no—
104C4⋊Dic47—41no—
105C4⋊Dic47—41no—
106D376—22no—
107D376—22no—
108D376—22no—
109D376—22no—
110D376—22no—
111D376—41no—
112D376—41no—
113D376C22⋊C414yescomplemented
114C16×C47—22no—
115C16×C47—41no—
116C23×C47C2×D811yescharacteristic
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123C22×D47—81no—
124C22×D47—81no—
125C22×D47—81no—
126C22×D47—81no—
127C22×D47—81no—
128C22×D47—81no—
129C22×D47—81no—
130C22×D47—81no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47D1612yescomplemented
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47#12011yescharacteristic
139C2×C4×C47#12111yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×Dic47—42no—
144C2×Dic47—81no—
145C2×Dic47—81no—
146C2×Dic47—81no—
147C2×Dic47—81no—
148C2×Dic47—81no—
149D188—24no—
150D188—42no—
151D188—42no—
152D188—42no—
153D188—42no—
154D188—42no—
155D188—81no—
156D188—81no—
157C4×D47—88no—
158C8×C47—41no—
159C8×C47C2×C22⋊C411yescharacteristic
160C8×C47C4×D411yescharacteristic
161C8×C47#12111yescharacteristic
162C8×C47#12311yescharacteristic
163#13012—471nomaximal, Sylow
164C22×C47C4×D811yescharacteristic
165C22×C47#44711yescharacteristic
166C22×C47#45911yescharacteristic
167C22×C47C2×D1611yescharacteristic
168C22×C47#50811yescharacteristic
169C22×C47#50911yescharacteristic
170C22×C47#50911yescharacteristic
171C2×D47—44no—
172C2×D47—82no—
173C2×D47—82no—
174C2×D47—82no—
175C2×D47—82no—
176C2×D47—82no—
177C2×D47—82no—
178C2×D47—82no—
179C2×D47—82no—
180C2×D47—82no—
181C2×D47—161no—
182C2×D47—161no—
183C2×D47—161no—
184C2×D47—161no—
185C4×C47—22no—
186C4×C47—41no—
187C4×C47#38611yescharacteristic
188C4×C47#44211yescharacteristic
189C4×C47#44911yescharacteristic
190C4×C47#46311yescharacteristic
191Dic47—82no—
192Dic47—161no—
193C22×D16—471no—
194C2×C4×D8—471no—
195C2×#357—471no—
196C2×#357—471no—
197#1970—471no—
198#1380—471no—
199#1374D4711yescharacteristic, complemented
200C2×C47#187911yescharacteristic
201C2×C47C4×D1611yescharacteristic
202C2×C47#217711yescharacteristic
203C2×C47#218411yescharacteristic
204C2×C47#218611yescharacteristic
205C2×C47#220611yescharacteristic
206C2×C47#221011yescharacteristic
207D47—84no—
208D47—162no—
209C22×D8—471no—
210C22×D8—471no—
211C2×C4×D4—941no—
212C2×D16—474no—
213C2×D16—942no—
214C2×D16—942no—
215C22×C16C2×D4711yescharacteristic
216C22×C16C2×D4711yescharacteristic
217C4×D8—942no—
218C4×D8—942no—
219C2×#107—471no—
220C2×#107—471no—
221C2×#102—941no—
222C2×#102—941no—
223C2×C4×C8C2×D4711yescharacteristic
224#390—941no—
225#357—942no—
226#357—942no—
227C47#1301211yescharacteristic, complemented, Sylow
228C22×D4—941no—
229C22×D4—941no—
230C23×C4—1881no—
231C2×D8—472no—
232C2×D8—472no—
233C2×D8—472no—
234C2×D8—472no—
235C2×D8—941no—
236C2×D8—941no—
237C2×D8—941no—
238C2×D8—941no—
239C2×D8—941no—
240C2×D8—941no—
241C2×D8—941no—
242C2×D8—941no—
243C22×C8D18811yescharacteristic
244C22×C8C22×D4711yescharacteristic
245C4×D4—944no—
246C4×D4—1882no—
247C2×C4⋊C4—941no—
248C2×C4⋊C4—941no—
249C2×C22⋊C4—1881no—
250C2×C22⋊C4—1881no—
251C2×C22⋊C4—1881no—
252C2×C42D18811yescharacteristic
253D16—948no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16C4×D4712yescomplemented
260#107—472no—
261#107—941no—
262#107—941no—
263#107—941no—
264#102—944no—
265#102—1882no—
266C4×C8—21no—
267C4×C8—21no—
268C24—1881no—
269C24—1881no—
270C2×D4—942no—
271C2×D4—942no—
272C2×D4—942no—
273C2×D4—942no—
274C2×D4—1881no—
275C2×D4—1881no—
276C2×D4—1881no—
277C2×D4—1881no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4—1881no—
281C2×D4—1881no—
282C22×C4—3762no—
283C22×C4—3762no—
284C22×C4—1884no—
285C22×C4—1881no—
286C22×C4—1881no—
287C22×C4D37611yescharacteristic
288C22×C4D37611yescharacteristic
289C22×C4C2×D18811yescharacteristic
290D8—474no—
291D8—942no—
292D8—942no—
293D8—942no—
294D8—942no—
295D8—942no—
296D8—1881no—
297D8—1881no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8C2×C4×D4711yescharacteristic
302C2×C8#1062535011yescharacteristic
303C2×C8D4×D4711yescharacteristic
304C2×C8D4×D4711yescharacteristic
305C2×C8D4×D4711yescharacteristic
306C2×C8#1062535411yescharacteristic
307C4⋊C4—942no—
308C4⋊C4—1881no—
309C4⋊C4—1881no—
310C4⋊C4—1881no—
311C22⋊C4—3762no—
312C22⋊C4—3762no—
313C22⋊C4—1884no—
314C42—21no—
315C42—21no—
316C16—22no—
317C16—41no—
318C23—3761no—
319C23—3761no—
320C23—3761no—
321C23—3761no—
322C23—3761no—
323C23—3761no—
324C23—3761no—
325C23—3761no—
326C23—3761no—
327C23—3761no—
328C23—1882no—
329C23—1882no—
330C23—1882no—
331C23—1882no—
332C23C2×D37611yescharacteristic
333D4—944no—
334D4—3761no—
335D4—3761no—
336D4—1882no—
337D4—1882no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—3768no—
347C2×C4—3761no—
348C2×C4—3761no—
349C2×C4—3761no—
350C2×C4—3761no—
351C2×C4—3761no—
352C2×C4—1882no—
353C2×C4D75212yescomplemented
354C2×C4C4×D18811yescharacteristic
355C2×C4#1309399411yescharacteristic
356C2×C4#1309399911yescharacteristic
357C2×C4#1309404611yescharacteristic
358C2×C4#1309405211yescharacteristic
359C2×C4#1309405211yescharacteristic
360C8—41no—
361C8C22⋊C4×D4711yescharacteristic
362C8#1309398611yescharacteristic
363C8#1309399711yescharacteristic
364C8#1309400911yescharacteristic
365C22—3762no—
366C22—3762no—
367C22—3762no—
368C22—3762no—
369C22—3762no—
370C22—3762no—
371C22—3762no—
372C22—3762no—
373C22—3762no—
374C22—1884no—
375C22—7521no—
376C22—7521no—
377C22—7521no—
378C22—7521no—
379C22C4×D37611yescharacteristic
380C22#1568925911yescharacteristic
381C22#1568931911yescharacteristic
382C22C2×D75211yescharacteristic
383C22#1568955511yescharacteristic
384C22#1568956111yescharacteristic
385C22#1568956111yescharacteristic
386C4—22no—
387C4—41no—
388C4—3762no—
389C4—7521no—
390C4#1568900111yescharacteristic
391C4#1568923611yescharacteristic
392C4#1568927011yescharacteristic
393C4#1568933911yescharacteristic
394C2—3764no—
395C2—7522no—
396C2#2024373511yescharacteristic
397C2C4×D75211yescharacteristic
398C2#2024526511yescharacteristic
399C2#2024530211yescharacteristic
400C2#2024531311yescharacteristic
401C2#2024542411yescharacteristic
402C2#2024544411yescharacteristic
subgroupG/H
centerC23C2×D376
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1374C2
socleC23×C47C2×D8
prime radicalC22×D752C2
cosocleC22×C8×C47C23
hypercenter#1374D47
hypocenterC47#13012
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×C4×D376C2semidirect
3. C2×#15688925C2semidirect
4. C2×#15688925C2semidirect
5. #20244254C2semidirect
6. #20241480C2semidirect
7. C47×#1374C2semidirect
13. C2×D752C4semidirect
38. C2×D376C2×C4semidirect
63. C2×C16×C47C2×C4semidirect
113. D376C22⋊C4semidirect
136. C2×C4×C47D16semidirect
199. #1374D47semidirect
227. C47#13012semidirect
259. C2×C16C4×D47semidirect
353. C2×C4D752semidirect

Maximal subgroups

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

subgroupindex
C22×D7522
C2×C4×D3762
C2×#156889252
#202442542
#202414802
C47×#13742
#1301247