Finite Group Databasebeta

← #20254071

Subgroups — #20254071

Order 6016.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689744C211yesmaximal, characteristic, complemented
2#15689728C211yesmaximal, characteristic, complemented
3#15689532C211yesmaximal, characteristic, complemented
4#15689512C211yesmaximal, characteristic, complemented
5#15689478C211yesmaximal, characteristic, complemented
6#15689470C211yesmaximal, characteristic, complemented
7#15689376C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic, complemented
9#15689359C211yesmaximal, characteristic, complemented
10#15689352C211yesmaximal, characteristic, complemented
11#15689236C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13C4×#10625325C211yesmaximal, characteristic, complemented
14C4×D376C211yesmaximal, characteristic, complemented
15C47×#405C211yesmaximal, characteristic, complemented
16C2×#10625325C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×D376C2211yescharacteristic
19C2×D376C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094021C2211yescharacteristic
22#13094019—21no—
23#13094016C2211yescharacteristic
24#13094012C2211yescharacteristic
25#13094010—21no—
26#13094009—21no—
27#13094009—21no—
28#13094006—21no—
29#13094003C2211yescharacteristic
30#13094002—21no—
31#13093998C2211yescharacteristic
32#13093998C2211yescharacteristic
33#13093998C2211yescharacteristic
34#13093997—21no—
35#13093997—21no—
36C4×Dic94C2211yescharacteristic
37C4×D188C2211yescharacteristic
38C4×D188C2211yescharacteristic
39C4×D188C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#97×C47C2211yescharacteristic
56#97×C47C2211yescharacteristic
57C4×C8×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—21no—
61C2×C22⋊D47—21no—
62C2×C22⋊D47—21no—
63C2×D188—21no—
64C2×D188—21no—
65C2×D188C2311yescharacteristic
66C2×D188C2311yescharacteristic
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×Dic94—21no—
72C2×Dic94C2311yescharacteristic
73M16×C47—22no—
74C2×C8×C47—22no—
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47D411yescharacteristic
80C4⋊C4×C47D411yescharacteristic
81C22⋊C4×C47D411yescharacteristic
82C22⋊C4×C47D411yescharacteristic
83C42×C47C2311yescharacteristic
84C42×C47C2311yescharacteristic
85C22⋊Dic47—21no—
86(C2×D47)⋊C4—21no—
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—
93(C2×D47)⋊C4—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—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—81no—
121C22⋊D47—81no—
122C22⋊D47—81no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128D188—21no—
129D188—21no—
130D188—21no—
131D188—21no—
132D188—21no—
133D188—21no—
134D188—81no—
135D188—81no—
136C4×D47—81no—
137C4×D47—81no—
138C4×D47—81no—
139Dic94—21no—
140Dic94—21no—
141Dic94—81no—
142C8×C47—21no—
143C8×C47—21no—
144C8×C47#4112yes—
145C8×C47#4112yes—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47C22×D411yescharacteristic
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47C2×#4111yescharacteristic
165C4×C47C2×#4111yescharacteristic
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171#3179—471nomaximal, Sylow
172C2×C47—41no—
173C2×C47#53211yescharacteristic
174C2×C47#57611yescharacteristic
175C2×C47#57711yescharacteristic
176D47—81no—
177D47—81no—
178D47—81no—
179#542—471no—
180#540—471no—
181#501—471no—
182#496—471no—
183#488—471no—
184#486—471no—
185#469—471no—
186#468—471no—
187#466—471no—
188#465—471no—
189#442—471no—
190#440—471no—
191C4×SD16—471no—
192C4×D8—471no—
193#405D4711yescharacteristic, complemented
194C47#317911yescharacteristic, complemented, Sylow
195C2×SD16—471no—
196C2×SD16—471no—
197C2×D8—471no—
198C2×D8—471no—
199C2×M16C2×D4711yescharacteristic
200C22×C8C2×D4711yescharacteristic
201C4⋊Q8—471no—
202#127—471no—
203#126—941no—
204#125—471no—
205#124—471no—
206#124—941no—
207#123—941no—
208#123—941no—
209#123—941no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212#121—471no—
213#121—471no—
214#121—471no—
215#121—941no—
216#121—941no—
217C4×Q8—471no—
218C4×D4—471no—
219C4×D4—471no—
220C4×D4—471no—
221#117C2×D4711yescharacteristic
222#107—471no—
223#107—471no—
224#106—471no—
225#106—471no—
226#103—471no—
227#103—471no—
228#102—471no—
229#102—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#97C2×D4711yescharacteristic
235#97C2×D4711yescharacteristic
236C4×C8C2×D4711yescharacteristic
237C4×C8C2×D4711yescharacteristic
238C2×Q8—471no—
239C2×Q8—941no—
240C2×D4—471no—
241C2×D4—471no—
242C2×D4—471no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4—941no—
246C2×D4—941no—
247C2×D4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252SD16—942no—
253SD16—942no—
254D8—942no—
255D8—942no—
256M16—22no—
257C2×C8—22no—
258C2×C8C22×D4711yescharacteristic
259C2×C8C22×D4711yescharacteristic
260C2×C8C22×D4711yescharacteristic
261C2×C8C22×D4711yescharacteristic
262C4⋊C4—471no—
263C4⋊C4—471no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4D18811yescharacteristic
272C4⋊C4D18811yescharacteristic
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C22⋊C4—941no—
282C22⋊C4D18811yescharacteristic
283C22⋊C4D18811yescharacteristic
284C42—941no—
285C42C22×D4711yescharacteristic
286C42C22×D4711yescharacteristic
287C23—941no—
288C23—941no—
289C23—941no—
290C23C2×D18811yescharacteristic
291Q8—941no—
292Q8—941no—
293Q8—3761no—
294D4—941no—
295D4—941no—
296D4—941no—
297D4—941no—
298D4—941no—
299D4—941no—
300D4—3761no—
301D4—3761no—
302D4—3761no—
303D4—3761no—
304D4—3761no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4—3761no—
315C2×C4C2×D18811yescharacteristic
316C2×C4C2×D18811yescharacteristic
317C2×C4C2×D18811yescharacteristic
318C2×C4C2×D18811yescharacteristic
319C2×C4C2×D18811yescharacteristic
320C2×C4C23×D4711yescharacteristic
321C8—21no—
322C8—21no—
323C8#1062535012yes—
324C8#1062535012yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—1881no—
329C22—1881no—
330C22—1881no—
331C22—1881no—
332C22—1881no—
333C22—1881no—
334C22—1881no—
335C22—1881no—
336C22—1881no—
337C22C22×D18811yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—1881no—
344C4—1881no—
345C4—1881no—
346C4—1881no—
347C4—1881no—
348C4C2×#1062535011yescharacteristic
349C4C2×#1062535011yescharacteristic
350C2—41no—
351C2—3761no—
352C2—3761no—
353C2—3761no—
354C2#1568967311yescharacteristic
355C2#1568992811yescharacteristic
356C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#405C2
socleC22×C47C22×D4
hypercenter#405D47
hypocenterC47#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689728C2semidirect
3. #15689532C2semidirect
4. #15689512C2semidirect
5. #15689478C2semidirect
6. #15689470C2semidirect
7. #15689376C2semidirect
8. #15689369C2semidirect
9. #15689359C2semidirect
10. #15689352C2semidirect
11. #15689236C2semidirect
12. #15689225C2semidirect
13. C4×#10625325C2semidirect
14. C4×D376C2semidirect
15. C47×#405C2semidirect
193. #405D47semidirect
194. C47#3179semidirect