Finite Group Databasebeta

← #20254816

Subgroups — #20254816

Order 6016.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689744C211yesmaximal, characteristic
2#15689735C211yesmaximal, characteristic, complemented
3#15689431C211yesmaximal, characteristic, complemented
4#15689424C211yesmaximal, characteristic, complemented
5#15689419C211yesmaximal, characteristic, complemented
6#15689409C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689369C211yesmaximal, characteristic
9#15689364C211yesmaximal, characteristic, complemented
10#15689352C211yesmaximal, characteristic
11#15689346C211yesmaximal, characteristic, complemented
12#15689346C211yesmaximal, characteristic, complemented
13#15689334C211yesmaximal, characteristic, complemented
14#15689329C211yesmaximal, characteristic, complemented
15C47×#424C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094024C2211yescharacteristic
22#13094019—21no—
23#13094017—21no—
24#13094017—21no—
25#13094016C2211yescharacteristic
26#13094014—21no—
27#13094014—21no—
28#13094012C2211yescharacteristic
29#13094010—21no—
30#13094006—21no—
31#13094003C2211yescharacteristic
32#13094003C2211yescharacteristic
33#13094003C2211yescharacteristic
34#13094002—21no—
35#13093998C2211yescharacteristic
36C4×Dic94C2211yescharacteristic
37C4×Dic94C2211yescharacteristic
38C4×Dic94C2211yescharacteristic
39C4×D188C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093949C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×M16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56C4⋊C8×C47C2211yescharacteristic
57C4⋊C8×C47C2211yescharacteristic
58C4⋊C8×C47C2211yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—21no—
61C2×D188C2311yescharacteristic
62C2×C4×D47—21no—
63C2×Dic94—21no—
64C2×Dic94C2311yescharacteristic
65C2×Dic94C2311yescharacteristic
66C2×Dic94C2311yescharacteristic
67M16×C47—41no—
68C2×C8×C47—41no—
69C2×C8×C47C2311yescharacteristic
70C2×C8×C47C2311yescharacteristic
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47D411yescharacteristic
74C4⋊C4×C47D411yescharacteristic
75C22⋊C4×C47D411yescharacteristic
76C22⋊C4×C47D411yescharacteristic
77C42×C47C2311yescharacteristic
78C42×C47C2311yescharacteristic
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82(C2×D47)⋊C4—21no—
83(C2×D47)⋊C4—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47C2311yescharacteristic
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
92C4⋊Dic47C2311yescharacteristic
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101C4×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104Dic188—41no—
105Dic188—41no—
106#10625325—41no—
107#10625325—41no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2×D411yescharacteristic
114C2×C4×C47C2×D411yescharacteristic
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2411yescharacteristic
118C22⋊D47—81no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126D188—21no—
127D188—21no—
128C4×D47—81no—
129Dic94—21no—
130Dic94—21no—
131Dic94—21no—
132Dic94—21no—
133Dic94—21no—
134Dic94—21no—
135Dic94—81no—
136C8×C47—21no—
137C8×C47—21no—
138C8×C47—21no—
139C8×C47—21no—
140C22×C47—21no—
141C22×C47—21no—
142C22×C47—21no—
143C22×C47C22×D411yescharacteristic
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—41no—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47H(5,𝔽2)11yescharacteristic
153C4×C472−1+411yescharacteristic
154Dic47—41no—
155Dic47—41no—
156Dic47—41no—
157Dic47—41no—
158Dic47—41no—
159Dic47—41no—
160Dic47—41no—
161#3258—471nomaximal, Sylow
162C2×C47—41no—
163C2×C47#53711yescharacteristic
164C2×C47#57711yescharacteristic
165C2×C47#57811yescharacteristic
166D47—81no—
167#542—471no—
168#541—471no—
169#479—471no—
170#478—471no—
171#477—471no—
172#475—471no—
173#470—471no—
174#468—471no—
175#467—471no—
176#465—471no—
177#464—471no—
178#464—471no—
179#462—471no—
180#461—471no—
181#424D4711yescharacteristic, complemented
182C47#325811yescharacteristic, complemented, Sylow
183C2×Q16—471no—
184C2×Q16—471no—
185C2×SD16—471no—
186C2×SD16—471no—
187C2×M16C2×D4711yescharacteristic
188C22×C8C2×D4711yescharacteristic
189C4⋊Q8—471no—
190C4⋊Q8—471no—
191#126—941no—
192#126—941no—
193#126—941no—
194#125—471no—
195#125—941no—
196#125—941no—
197#124—471no—
198#124—941no—
199#123—941no—
200C22⋊Q8—471no—
201C22⋊Q8—471no—
202C22⋊Q8—471no—
203C22⋊Q8—941no—
204#121—471no—
205C4×Q8—471no—
206C4×Q8—471no—
207C4×Q8—471no—
208C4×D4—471no—
209#117C2×D4711yescharacteristic
210#107—471no—
211#107—471no—
212#106—471no—
213#106—471no—
214C4⋊C8C2×D4711yescharacteristic
215C4⋊C8C2×D4711yescharacteristic
216C4⋊C8C2×D4711yescharacteristic
217C4⋊C8C2×D4711yescharacteristic
218#103—471no—
219#103—471no—
220#103—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#102—471no—
225#102—471no—
226C2×Q8—471no—
227C2×Q8—471no—
228C2×Q8—471no—
229C2×Q8—941no—
230C2×D4—471no—
231C2×D4—941no—
232C22×C4—941no—
233C22×C4C22×D4711yescharacteristic
234Q16—1881no—
235Q16—1881no—
236SD16—1881no—
237SD16—1881no—
238M16—41no—
239C2×C8—41no—
240C2×C8C22×D4711yescharacteristic
241C2×C8C22×D4711yescharacteristic
242C2×C8C22×D4711yescharacteristic
243C2×C8C22×D4711yescharacteristic
244C4⋊C4—471no—
245C4⋊C4—471no—
246C4⋊C4—471no—
247C4⋊C4—471no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4—941no—
251C4⋊C4—941no—
252C4⋊C4—941no—
253C4⋊C4—941no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4—941no—
259C4⋊C4D18811yescharacteristic
260C4⋊C4D18811yescharacteristic
261C22⋊C4—941no—
262C22⋊C4—941no—
263C22⋊C4—941no—
264C22⋊C4—941no—
265C22⋊C4—941no—
266C22⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4D18811yescharacteristic
269C22⋊C4D18811yescharacteristic
270C42—941no—
271C42—941no—
272C42—941no—
273C42C22×D4711yescharacteristic
274C42C22×D4711yescharacteristic
275C23—941no—
276C23C2×D18811yescharacteristic
277Q8—941no—
278Q8—941no—
279Q8—941no—
280Q8—941no—
281Q8—941no—
282Q8—941no—
283Q8—3761no—
284D4—941no—
285D4—941no—
286D4—3761no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—3761no—
297C2×C4C2×D18811yescharacteristic
298C2×C4C2×D18811yescharacteristic
299C2×C4C2×D18811yescharacteristic
300C2×C4C2×D18811yescharacteristic
301C2×C4C2×D18811yescharacteristic
302C2×C4C23×D4711yescharacteristic
303C8—21no—
304C8—21no—
305C8—21no—
306C8—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—1881no—
311C22—1881no—
312C22—1881no—
313C22C22×D18811yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—1881no—
320C4—1881no—
321C4—1881no—
322C4—1881no—
323C4—1881no—
324C4—1881no—
325C4—1881no—
326C4#1309406911yescharacteristic
327C4#1309407211yescharacteristic
328C2—41no—
329C2—3761no—
330C2#1568970411yescharacteristic
331C2#1568993511yescharacteristic
332C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#424C2
socleC22×C47C22×D4
hypercenter#424D47
hypocenterC47#3258
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #15689735C2semidirect
3. #15689431C2semidirect
4. #15689424C2semidirect
5. #15689419C2semidirect
6. #15689409C2semidirect
7. #15689381C2semidirect
9. #15689364C2semidirect
11. #15689346C2semidirect
12. #15689346C2semidirect
13. #15689334C2semidirect
14. #15689329C2semidirect
15. C47×#424C2semidirect
181. #424D47semidirect
182. C47#3258semidirect