Finite Group Databasebeta

← #20256342

Subgroups — #20256342

Order 6016.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689833C211yesmaximal, characteristic, complemented
2#15689533C211yesmaximal, characteristic, complemented
3#15689529C211yesmaximal, characteristic, complemented
4#15689522C211yesmaximal, characteristic, complemented
5#15689423C211yesmaximal, characteristic, complemented
6#15689423C211yesmaximal, characteristic, complemented
7#15689420C211yesmaximal, characteristic, complemented
8#15689420C211yesmaximal, characteristic, complemented
9#15689403C211yesmaximal, characteristic, complemented
10#15689400C211yesmaximal, characteristic, complemented
11#15689254C211yesmaximal, characteristic, complemented
12#15689233C211yesmaximal, characteristic
13#15689233C211yesmaximal, characteristic
14C4×#10625334C211yesmaximal, characteristic
15C47×#554C211yesmaximal, characteristic, complemented
16C2×#10625334C2211yescharacteristic
17#13094024C2211yescharacteristic
18#13094016C2211yescharacteristic
19#13094016C2211yescharacteristic
20#13094002—21no—
21#13094002—21no—
22#13094000—21no—
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic
26C4⋊C4×D47—21no—
27#13093957C2211yescharacteristic
28#13093957C2211yescharacteristic
29#13093957C2211yescharacteristic
30#13093957C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093955C2211yescharacteristic
35#13093955C2211yescharacteristic
36C4⋊(C47⋊C8)C2211yescharacteristic
37C4⋊(C47⋊C8)C2211yescharacteristic
38C4⋊(C47⋊C8)C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45#13093935C2211yescharacteristic
46#13093935C2211yescharacteristic
47C4×C47⋊C8C2211yescharacteristic
48C4⋊Q8×C47C2211yescharacteristic
49#125×C47C2211yescharacteristic
50#125×C47C2211yescharacteristic
51C22⋊Q8×C47—21no—
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47—21no—
54C4×Q8×C47C2211yescharacteristic
55C4×D4×C47C2211yescharacteristic
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58C2×C4⋊C4×C47—21no—
59C2×Q8×C47—21no—
60C2×Q8×C47D411yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×Dic94—21no—
70C4⋊C4×C47—21no—
71C4⋊C4×C47—21no—
72C4⋊C4×C47—21no—
73C4⋊C4×C47—21no—
74C4⋊C4×C47—21no—
75C4⋊C4×C47D411yescharacteristic
76C4⋊C4×C47D411yescharacteristic
77C4⋊C4×C47D411yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C42×C47C2311yescharacteristic
85C42×C47C2311yescharacteristic
86C42×C47C2311yescharacteristic
87#10625334Q814yescomplemented
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99C2×C47⋊C8C2311yescharacteristic
100C2×C47⋊C8C2311yescharacteristic
101C2×C47⋊C8C2311yescharacteristic
102C2×C47⋊C8C2311yescharacteristic
103C23×C47—21no—
104C22×D47—21no—
105Q8×C47—41no—
106Q8×C47—81no—
107D4×C47—21no—
108D4×C47C2×Q812yes—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—42no—
113C2×C4×C47—81no—
114C2×C4×C47—81no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C2×Dic47—21no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125D188—21no—
126D188C2×Q812yes—
127C4×D47—42no—
128C4×D47—81no—
129C4×D47—81no—
130Dic94—81no—
131C47⋊C8—21no—
132C47⋊C8—21no—
133C47⋊C8—21no—
134C47⋊C8C2×Q812yes—
135C22×C47—22no—
136C22×C47—41no—
137C22×C47—41no—
138C22×C47C22×D411yescharacteristic
139C2×D47—22no—
140C2×D47—41no—
141C2×D47—41no—
142C4×C47—21no—
143C4×C47—21no—
144C4×C47—21no—
145C4×C47—21no—
146C4×C47—21no—
147C4×C47—21no—
148C4×C47—41no—
149C4×C47—41no—
150C4×C47—41no—
151C4×C47C22×Q811yescharacteristic
152C4×C472−1+411yescharacteristic
153Dic47—41no—
154Dic47—41no—
155Dic47—41no—
156#3389—471nomaximal, Sylow
157C2×C47—42no—
158C2×C47D4×Q811yescharacteristic
159C2×C47#57511yescharacteristic
160C2×C47#57611yescharacteristic
161D47—42no—
162#554—471no—
163#554D4711yescharacteristic, complemented
164#501—471no—
165#501—471no—
166#499—471no—
167#478—471no—
168#478—471no—
169#478—471no—
170#478—471no—
171#474—471no—
172#474—471no—
173#446—471no—
174#442—471no—
175#442—471no—
176C4×D8—471no—
177C47#338911yescharacteristic, complemented, Sylow
178C2×D8—471no—
179C4⋊Q8—471no—
180C4⋊Q8C2×D4711yescharacteristic
181#125—471no—
182#125—471no—
183#125C2×D4711yescharacteristic
184#125C2×D4711yescharacteristic
185C22⋊Q8—21no—
186C22⋊Q8—21no—
187C22⋊Q8—21no—
188C22⋊Q8—941no—
189C22⋊Q8—941no—
190C22⋊Q8—941no—
191C4×Q8C2×D4711yescharacteristic
192C4×D4—471no—
193C4×D4—471no—
194C4×D4—471no—
195C4×D4C2×D4711yescharacteristic
196C4×D4C2×D4711yescharacteristic
197C4×D4C2×D4711yescharacteristic
198C2×C4⋊C4—21no—
199C2×C4⋊C4—941no—
200#107—471no—
201#107—471no—
202#107—471no—
203#107—471no—
204#107—471no—
205#106—471no—
206#106—471no—
207#106—471no—
208#106—471no—
209C4⋊C8—471no—
210C4⋊C8—471no—
211C4⋊C8—471no—
212#102—471no—
213#102—471no—
214#102—471no—
215#102—471no—
216#102—471no—
217#102—471no—
218#97—471no—
219#97—471no—
220C4×C8—471no—
221C2×Q8—21no—
222C2×Q8—941no—
223C2×Q8C22⋊D4711yescharacteristic
224C2×D4—471no—
225C2×D4C22×D4711yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—941no—
230C22×C4—941no—
231C22×C4—941no—
232D8—474no—
233C2×C8—471no—
234C2×C8—471no—
235C2×C8—471no—
236C2×C8—471no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—471no—
243C4⋊C4—471no—
244C4⋊C4—471no—
245C4⋊C4—941no—
246C4⋊C4—941no—
247C4⋊C4—941no—
248C4⋊C4—941no—
249C4⋊C4—941no—
250C4⋊C4C22⋊D4711yescharacteristic
251C4⋊C4C22⋊D4711yescharacteristic
252C4⋊C4C22⋊D4711yescharacteristic
253C4⋊C4C22×D4711yescharacteristic
254C4⋊C4C22×D4711yescharacteristic
255C4⋊C4C22×D4711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—941no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C42C22×D4711yescharacteristic
263C42C22×D4711yescharacteristic
264C42C22×D4711yescharacteristic
265C23—21no—
266C23—941no—
267Q8—41no—
268Q8—81no—
269Q8—3761no—
270D4—21no—
271D4—472no—
272D4—941no—
273D4Q8×D4712yes—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—941no—
281C2×C4—941no—
282C2×C4—941no—
283C2×C4—3761no—
284C2×C4—3761no—
285C2×C4—1882no—
286C2×C4C2×C22⋊D4711yescharacteristic
287C2×C4C2×C22⋊D4711yescharacteristic
288C2×C4C2×C22⋊D4711yescharacteristic
289C2×C4C2×C22⋊D4711yescharacteristic
290C2×C4C2×C22⋊D4711yescharacteristic
291C2×C4C2×C22⋊D4711yescharacteristic
292C2×C4C23×D4711yescharacteristic
293C8—472no—
294C8—941no—
295C8—941no—
296C8—941no—
297C22—22no—
298C22—41no—
299C22—41no—
300C22—942no—
301C22—1881no—
302C22—1881no—
303C22C22×C22⋊D4711yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—1881no—
314C4—1881no—
315C4—1881no—
316C4C2×Q8×D4711yescharacteristic
317C4#1309407211yescharacteristic
318C2—42no—
319C2—1882no—
320C2Q8×C22⋊D4711yescharacteristic
321C2#1568992111yescharacteristic
322C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#554C2
socleC22×C47C22×D4
hypercenter#554D47
hypocenterC47#3389
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #15689833C2semidirect
2. #15689533C2semidirect
3. #15689529C2semidirect
4. #15689522C2semidirect
5. #15689423C2semidirect
6. #15689423C2semidirect
7. #15689420C2semidirect
8. #15689420C2semidirect
9. #15689403C2semidirect
10. #15689400C2semidirect
11. #15689254C2semidirect
15. C47×#554C2semidirect
87. #10625334Q8semidirect
163. #554D47semidirect
177. C47#3389semidirect