Finite Group Databasebeta

← #20256232

Subgroups — #20256232

Order 6016.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689851C211yesmaximal, characteristic, complemented
2#15689846C211yesmaximal, characteristic
3#15689492C211yesmaximal, characteristic, complemented
4#15689483C211yesmaximal, characteristic
5#15689478C211yesmaximal, characteristic
6#15689431C211yesmaximal, characteristic, complemented
7#15689424C211yesmaximal, characteristic
8#15689419C211yesmaximal, characteristic, complemented
9#15689346C211yesmaximal, characteristic
10#15689346C211yesmaximal, characteristic
11#15689334C211yesmaximal, characteristic, complemented
12#15689231C211yesmaximal, characteristic, complemented
13#15689225C211yesmaximal, characteristic
14C4×Dic188C211yesmaximal, characteristic, complemented
15C47×#446C211yesmaximal, characteristic, complemented
16C2×Dic188C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094024C2211yescharacteristic
21#13094022—21no—
22#13094019—21no—
23#13094019—21no—
24#13094016C2211yescharacteristic
25#13094016C2211yescharacteristic
26#13094014—21no—
27#13094014—21no—
28#13094012C2211yescharacteristic
29#13094012C2211yescharacteristic
30#13094000—21no—
31C4×Dic94C2211yescharacteristic
32C4×Dic94C2211yescharacteristic
33C4×Dic94C2211yescharacteristic
34C4×Dic94C2211yescharacteristic
35C4×Dic94C2211yescharacteristic
36#13093989—21no—
37C4×D188C2211yescharacteristic
38#13093982—21no—
39#13093958C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093956C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093949C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C4×Q8×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C4⋊C8×C47C2211yescharacteristic
56#97×C47C2211yescharacteristic
57#97×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C2×Q8×C47D411yescharacteristic
60C2×D188C2311yescharacteristic
61C2×C4×D47—21no—
62C2×Dic94—21no—
63C2×Dic94C2311yescharacteristic
64C2×Dic94C2311yescharacteristic
65C2×Dic94C2311yescharacteristic
66C2×C8×C47C2311yescharacteristic
67C2×C8×C47C2311yescharacteristic
68C2×C8×C47C2311yescharacteristic
69C2×C8×C47C2311yescharacteristic
70C4⋊C4×C47D411yescharacteristic
71C4⋊C4×C47D411yescharacteristic
72C4⋊C4×C47D411yescharacteristic
73C42×C47C2311yescharacteristic
74C42×C47C2311yescharacteristic
75C42×C47C2311yescharacteristic
76(C2×D47)⋊C4—21no—
77(C2×D47)⋊C4—21no—
78(C2×D47)⋊C4—21no—
79(C2×D47)⋊C4—21no—
80(C2×D47)⋊C4—21no—
81C4⋊Dic47—21no—
82C4⋊Dic47—21no—
83C4⋊Dic47—21no—
84C4⋊Dic47C2311yescharacteristic
85C4⋊Dic47C2311yescharacteristic
86C4⋊Dic47C2311yescharacteristic
87C4⋊Dic47C2311yescharacteristic
88Dic47⋊C4—21no—
89Dic47⋊C4—21no—
90Dic47⋊C4—21no—
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—21no—
101C4×Dic47—21no—
102Dic188—22no—
103Dic188—22no—
104#10625325—22no—
105C22×D47—21no—
106Q8×C47—41no—
107C2×C4×C47C2×D411yescharacteristic
108C2×C4×C47C2×D411yescharacteristic
109C2×C4×C47C2×D411yescharacteristic
110C2×C4×C47C2×D411yescharacteristic
111C2×C4×C47C2×D411yescharacteristic
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2411yescharacteristic
114C2×Dic47—21no—
115C2×Dic47—21no—
116C2×Dic47—21no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47—21no—
120C2×Dic47—21no—
121D188—21no—
122D188—21no—
123C4×D47—42no—
124Dic94—21no—
125Dic94—21no—
126Dic94—21no—
127Dic94—21no—
128Dic94—21no—
129Dic94—42no—
130Dic94#4112yes—
131C8×C47—21no—
132C8×C47—21no—
133C8×C47—21no—
134C8×C47—21no—
135C22×C47C22×D411yescharacteristic
136C2×D47—41no—
137C2×D47—41no—
138C2×D47—41no—
139C4×C47—21no—
140C4×C47—21no—
141C4×C47—21no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47C2×#4111yescharacteristic
146C4×C472−1+411yescharacteristic
147Dic47—22no—
148Dic47—41no—
149Dic47—41no—
150Dic47—41no—
151Dic47—41no—
152Dic47—41no—
153Dic47—41no—
154#3377—471nomaximal, Sylow
155C2×C47#54811yescharacteristic
156C2×C47#57511yescharacteristic
157C2×C47#57811yescharacteristic
158D47—81no—
159#557—471no—
160#556—471no—
161#491—471no—
162#489—471no—
163#488—471no—
164#479—471no—
165#478—471no—
166#477—471no—
167#464—471no—
168#464—471no—
169#462—471no—
170#446D4711yescharacteristic, complemented
171#441—471no—
172#440—471no—
173C4×Q16—471no—
174C47#337711yescharacteristic, complemented, Sylow
175C2×Q16—471no—
176C2×Q16—471no—
177C2×SD16—471no—
178C4⋊Q8—471no—
179C4⋊Q8—471no—
180C4⋊Q8—941no—
181#126—941no—
182#126—941no—
183#125—471no—
184#125—471no—
185#125—941no—
186#125—941no—
187#124—471no—
188#124—471no—
189C22⋊Q8—941no—
190C4×Q8—471no—
191C4×Q8—471no—
192C4×Q8—471no—
193C4×Q8—471no—
194C4×Q8—471no—
195C4×Q8—941no—
196C4×Q8C2×D4711yescharacteristic
197C4×D4—471no—
198#117—941no—
199#107—471no—
200#107—471no—
201#106—471no—
202C4⋊C8C2×D4711yescharacteristic
203C4⋊C8C2×D4711yescharacteristic
204C4⋊C8C2×D4711yescharacteristic
205#103—471no—
206#103—471no—
207#103—471no—
208#103—471no—
209#103—471no—
210#103—471no—
211#103—471no—
212#102—471no—
213#102—471no—
214#102—471no—
215#97C2×D4711yescharacteristic
216#97C2×D4711yescharacteristic
217C4×C8C2×D4711yescharacteristic
218C2×Q8—471no—
219C2×Q8—471no—
220C2×Q8—471no—
221C2×Q8—941no—
222C2×Q8D18811yescharacteristic
223C2×D4—471no—
224C22×C4—941no—
225Q16—942no—
226Q16—942no—
227SD16—942no—
228C2×C8C22×D4711yescharacteristic
229C2×C8C22×D4711yescharacteristic
230C2×C8C22×D4711yescharacteristic
231C2×C8C22×D4711yescharacteristic
232C4⋊C4—471no—
233C4⋊C4—471no—
234C4⋊C4—471no—
235C4⋊C4—471no—
236C4⋊C4—941no—
237C4⋊C4—941no—
238C4⋊C4—941no—
239C4⋊C4—941no—
240C4⋊C4—941no—
241C4⋊C4—941no—
242C4⋊C4—941no—
243C4⋊C4—941no—
244C4⋊C4—941no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4D18811yescharacteristic
249C4⋊C4D18811yescharacteristic
250C4⋊C4D18811yescharacteristic
251C22⋊C4—941no—
252C22⋊C4—941no—
253C22⋊C4—941no—
254C22⋊C4—941no—
255C22⋊C4—941no—
256C42—941no—
257C42—941no—
258C42—941no—
259C42—941no—
260C42—941no—
261C42C22×D4711yescharacteristic
262C42C22×D4711yescharacteristic
263C42C22×D4711yescharacteristic
264C23—941no—
265Q8—41no—
266Q8—472no—
267Q8—941no—
268Q8—941no—
269Q8—941no—
270Q8—941no—
271Q8—941no—
272Q8—1882no—
273D4—941no—
274D4—941no—
275C2×C4—941no—
276C2×C4—941no—
277C2×C4—941no—
278C2×C4—941no—
279C2×C4—941no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—1882no—
283C2×C4C2×D18811yescharacteristic
284C2×C4C2×D18811yescharacteristic
285C2×C4C2×D18811yescharacteristic
286C2×C4C2×D18811yescharacteristic
287C2×C4C2×D18811yescharacteristic
288C2×C4C2×D18811yescharacteristic
289C2×C4C23×D4711yescharacteristic
290C8—21no—
291C8—21no—
292C8—21no—
293C8—21no—
294C22—1881no—
295C22—1881no—
296C22—1881no—
297C22C22×D18811yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—942no—
305C4—1881no—
306C4—1881no—
307C4—1881no—
308C4—1881no—
309C4—1881no—
310C4—1881no—
311C4#41×D4711yescharacteristic
312C4#1309407211yescharacteristic
313C2—3761no—
314C2#1568978511yescharacteristic
315C2#1568992311yescharacteristic
316C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3377
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #15689851C2semidirect
3. #15689492C2semidirect
6. #15689431C2semidirect
8. #15689419C2semidirect
11. #15689334C2semidirect
12. #15689231C2semidirect
14. C4×Dic188C2semidirect
15. C47×#446C2semidirect
170. #446D47semidirect
174. C47#3377semidirect