Finite Group Databasebeta

← #20253589

Subgroups — #20253589

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689728C211yesmaximal, characteristic, complemented
2#15689603C211yesmaximal, characteristic, complemented
3#15689442C211yesmaximal, characteristic, complemented
4#15689437C211yesmaximal, characteristic, complemented
5#15689431C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689324C211yesmaximal, characteristic, complemented
8#15689319C211yesmaximal, characteristic, complemented
9#15689270C211yesmaximal, characteristic, complemented
10#15689270C211yesmaximal, characteristic, complemented
11#15689236C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13C4×#10625325C211yesmaximal, characteristic, complemented
14C4×D376C211yesmaximal, characteristic, complemented
15C47×#433C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×D376C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094021C2211yescharacteristic
22#13094016C2211yescharacteristic
23#13094009—21no—
24#13094009—21no—
25#13093998C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093997—21no—
28#13093997—21no—
29C4×Dic94C2211yescharacteristic
30C4×Dic94C2211yescharacteristic
31C4×D188C2211yescharacteristic
32C4×D188C2211yescharacteristic
33C4×D188C2211yescharacteristic
34C4×D188C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36(C22⋊D47)⋊C4—21no—
37#13093982—21no—
38C2×C4⋊Dic47C2211yescharacteristic
39C4⋊C4×D47—21no—
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52#117×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—21no—
61C2×C22⋊D47—21no—
62C2×C22⋊D47—21no—
63C22×Dic47—21no—
64#10625350—22no—
65#10625350—22no—
66C2×D188—21no—
67C2×D188—21no—
68C2×D188C2311yescharacteristic
69C2×D188C2311yescharacteristic
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×Dic94C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47D411yescharacteristic
83C22⋊C4×C47D411yescharacteristic
84C22⋊C4×C47D411yescharacteristic
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104D376—22no—
105D376—22no—
106#10625325—22no—
107#10625325—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2411yescharacteristic
120C22⋊D47—24no—
121C22⋊D47—81no—
122C22⋊D47—81no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—81no—
129D188—21no—
130D188—21no—
131D188—21no—
132D188—21no—
133D188—21no—
134D188—81no—
135D188—81no—
136D188#4112yes—
137C4×D47—24no—
138C4×D47—81no—
139C4×D47—81no—
140C4×D47—81no—
141C4×D47—81no—
142Dic94—21no—
143Dic94#4112yes—
144C8×C47—21no—
145C8×C47—21no—
146C8×C47—21no—
147C8×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47C22×D411yescharacteristic
152C2×D47—22no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47C2×#4111yescharacteristic
167C4×C47C2×#4111yescharacteristic
168Dic47—22no—
169Dic47—41no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173#3119—471nomaximal, Sylow
174C2×C47—41no—
175C2×C47#52511yescharacteristic
176C2×C47#57611yescharacteristic
177C2×C47#57711yescharacteristic
178D47—42no—
179D47—81no—
180D47—81no—
181#540—471no—
182#520—471no—
183#481—471no—
184#480—471no—
185#479—471no—
186#478—471no—
187#460—471no—
188#459—471no—
189#449—471no—
190#449—471no—
191#442—471no—
192#440—471no—
193C4×SD16—471no—
194C4×D8—471no—
195#433D4711yescharacteristic, complemented
196C47#311911yescharacteristic, complemented, Sylow
197C2×#41—471no—
198C2×SD16—471no—
199C2×SD16—471no—
200C2×D8—471no—
201C2×D8—471no—
202#127—471no—
203#125—471no—
204#123—941no—
205#123—941no—
206#121—471no—
207#121—471no—
208#121—941no—
209#121—941no—
210C4×Q8—471no—
211C4×Q8—471no—
212C4×D4—471no—
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—941no—
217C4×D4—941no—
218#117—941no—
219#117C2×D4711yescharacteristic
220C2×C4⋊C4—471no—
221C2×C4⋊C4—941no—
222#107—471no—
223#107—471no—
224#106—471no—
225#106—471no—
226C4⋊C8C2×D4711yescharacteristic
227C4⋊C8C2×D4711yescharacteristic
228#103—471no—
229#103—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102—471no—
235#102—471no—
236C22⋊C8C2×D4711yescharacteristic
237C22⋊C8C2×D4711yescharacteristic
238#97C2×D4711yescharacteristic
239C4×C8C2×D4711yescharacteristic
240#41—942no—
241#41—942no—
242C2×Q8—471no—
243C2×D4—471no—
244C2×D4—471no—
245C2×D4—471no—
246C2×D4—941no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4—941no—
250C2×D4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258SD16—942no—
259SD16—942no—
260D8—942no—
261D8—942no—
262C2×C8C22×D4711yescharacteristic
263C2×C8C22×D4711yescharacteristic
264C2×C8C22×D4711yescharacteristic
265C2×C8C22×D4711yescharacteristic
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4D18811yescharacteristic
276C4⋊C4D18811yescharacteristic
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4D18811yescharacteristic
284C22⋊C4D18811yescharacteristic
285C42—941no—
286C42—941no—
287C42C22×D4711yescharacteristic
288C42C22×D4711yescharacteristic
289C23—941no—
290C23—941no—
291C23—941no—
292C23C2×D18811yescharacteristic
293Q8—472no—
294Q8—941no—
295D4—472no—
296D4—944no—
297D4—941no—
298D4—941no—
299D4—941no—
300D4—941no—
301D4—941no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305D4—3761no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—944no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—3761no—
315C2×C4—3761no—
316C2×C4—3761no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4C2×D18811yescharacteristic
320C2×C4C2×D18811yescharacteristic
321C2×C4C2×D18811yescharacteristic
322C2×C4C2×D18811yescharacteristic
323C2×C4C2×D18811yescharacteristic
324C2×C4C23×D4711yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—942no—
333C22—1881no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22—1881no—
341C22C22×D18811yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—942no—
348C4—1881no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4#41×D4711yescharacteristic
353C4#41×D4711yescharacteristic
354C2—41no—
355C2—3761no—
356C2—3761no—
357C2—1882no—
358C2#1568963511yescharacteristic
359C2#1568992811yescharacteristic
360C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3119
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #15689728C2semidirect
2. #15689603C2semidirect
3. #15689442C2semidirect
4. #15689437C2semidirect
5. #15689431C2semidirect
6. #15689424C2semidirect
7. #15689324C2semidirect
8. #15689319C2semidirect
9. #15689270C2semidirect
10. #15689270C2semidirect
11. #15689236C2semidirect
12. #15689225C2semidirect
13. C4×#10625325C2semidirect
14. C4×D376C2semidirect
15. C47×#433C2semidirect
195. #433D47semidirect
196. C47#3119semidirect