Finite Group Databasebeta

← #19147437

Subgroups — #19147437

Order 5504.

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#14583622C211yesmaximal, characteristic
2#14583269C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic
4#14583256C211yesmaximal, characteristic
5#14583203C211yesmaximal, characteristic, complemented
6#14583196C211yesmaximal, characteristic
7#14583191C211yesmaximal, characteristic, complemented
8#14583121C211yesmaximal, characteristic
9#14583121C211yesmaximal, characteristic
10#14583109C211yesmaximal, characteristic, complemented
11#14583030C211yesmaximal, characteristic, complemented
12#14583004C211yesmaximal, characteristic, complemented
13#14582997C211yesmaximal, characteristic
14C4×#10621885C211yesmaximal, characteristic, complemented
15C43×#557C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19#13063325C2211yescharacteristic
20#13063320—21no—
21#13063320—21no—
22#13063313C2211yescharacteristic
23#13063313C2211yescharacteristic
24#13063301—21no—
25C4×Dic86C2211yescharacteristic
26C4×Dic86C2211yescharacteristic
27C4×D172C2211yescharacteristic
28#13063283—21no—
29#13063258C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063256C2211yescharacteristic
32C4⋊(C43⋊C8)C2211yescharacteristic
33C4⋊(C43⋊C8)C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063236C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48C4⋊Q8×C43—21no—
49C4⋊Q8×C43C2211yescharacteristic
50#125×C43—21no—
51#125×C43—21no—
52#125×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic
54C4×Q8×C43—21no—
55C4×Q8×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×Q8×C43C2211yescharacteristic
58C4×Q8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43D411yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D172C2311yescharacteristic
63C2×C4×D43—21no—
64C2×Dic86C2311yescharacteristic
65C2×Dic86C2311yescharacteristic
66C4⋊C4×C43—21no—
67C4⋊C4×C43—21no—
68C4⋊C4×C43—21no—
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43D411yescharacteristic
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C42×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43C2311yescharacteristic
84C42×C43C2311yescharacteristic
85C42×C43C2311yescharacteristic
86#10621885—22no—
87#10621885—22no—
88#10621884—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C22×D43—21no—
106Q8×C43—21no—
107Q8×C43—41no—
108Q8×C43—42no—
109Q8×C43#4112yes—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43C2×D411yescharacteristic
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2411yescharacteristic
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124D172—21no—
125D172—21no—
126C4×D43—42no—
127Dic86—21no—
128Dic86—21no—
129Dic86—21no—
130Dic86—21no—
131C43⋊C8—21no—
132C43⋊C8—21no—
133C43⋊C8—21no—
134C43⋊C8—21no—
135C22×C43C22×D411yescharacteristic
136C2×D43—41no—
137C2×D43—41no—
138C2×D43—41no—
139C4×C43—22no—
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43—41no—
149C4×C43C2×#4111yescharacteristic
150C4×C432−1+411yescharacteristic
151Dic43—41no—
152Dic43—41no—
153Dic43—41no—
154#3377—431nomaximal, Sylow
155C2×C43#54811yescharacteristic
156C2×C43#57511yescharacteristic
157C2×C43#57811yescharacteristic
158D43—81no—
159#557D4311yescharacteristic, complemented
160#556—431no—
161#491—431no—
162#489—431no—
163#488—431no—
164#479—431no—
165#478—431no—
166#477—431no—
167#464—431no—
168#464—431no—
169#462—431no—
170#446—431no—
171#441—431no—
172#440—431no—
173C4×Q16—431no—
174C43#337711yescharacteristic, complemented, Sylow
175C2×Q16—431no—
176C2×Q16—431no—
177C2×SD16—431no—
178C4⋊Q8—21no—
179C4⋊Q8—431no—
180C4⋊Q8C2×D4311yescharacteristic
181#126—861no—
182#126—861no—
183#125—21no—
184#125—21no—
185#125C2×D4311yescharacteristic
186#125C2×D4311yescharacteristic
187#124—431no—
188#124—431no—
189C22⋊Q8—861no—
190C4×Q8—21no—
191C4×Q8—431no—
192C4×Q8—431no—
193C4×Q8C2×D4311yescharacteristic
194C4×Q8C2×D4311yescharacteristic
195C4×Q8C2×D4311yescharacteristic
196C4×Q8C2×D4311yescharacteristic
197C4×D4—431no—
198#117—861no—
199#107—431no—
200#107—431no—
201#106—431no—
202C4⋊C8—431no—
203C4⋊C8—431no—
204C4⋊C8—431no—
205#103—431no—
206#103—431no—
207#103—431no—
208#103—431no—
209#103—431no—
210#103—431no—
211#103—431no—
212#102—431no—
213#102—431no—
214#102—431no—
215#97—431no—
216#97—431no—
217C4×C8—431no—
218C2×Q8—21no—
219C2×Q8—431no—
220C2×Q8—431no—
221C2×Q8C22⋊D4311yescharacteristic
222C2×Q8C22×D4311yescharacteristic
223C2×D4—431no—
224C22×C4—861no—
225Q16—862no—
226Q16—862no—
227SD16—862no—
228C2×C8—431no—
229C2×C8—431no—
230C2×C8—431no—
231C2×C8—431no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—431no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4C22⋊D4311yescharacteristic
246C4⋊C4C22⋊D4311yescharacteristic
247C4⋊C4C22⋊D4311yescharacteristic
248C4⋊C4C22×D4311yescharacteristic
249C4⋊C4C22×D4311yescharacteristic
250C4⋊C4C22×D4311yescharacteristic
251C22⋊C4—861no—
252C22⋊C4—861no—
253C22⋊C4—861no—
254C22⋊C4—861no—
255C22⋊C4—861no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—861no—
260C42—861no—
261C42C22×D4311yescharacteristic
262C42C22×D4311yescharacteristic
263C42C22×D4311yescharacteristic
264C23—861no—
265Q8—21no—
266Q8—41no—
267Q8—42no—
268Q8—861no—
269Q8—861no—
270Q8—861no—
271Q8—861no—
272Q8#1062190212yes—
273D4—861no—
274D4—861no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—861no—
280C2×C4—861no—
281C2×C4—861no—
282C2×C4—1722no—
283C2×C4C2×C22⋊D4311yescharacteristic
284C2×C4C2×C22⋊D4311yescharacteristic
285C2×C4C2×C22⋊D4311yescharacteristic
286C2×C4C2×C22⋊D4311yescharacteristic
287C2×C4C2×C22⋊D4311yescharacteristic
288C2×C4C2×C22⋊D4311yescharacteristic
289C2×C4C23×D4311yescharacteristic
290C8—861no—
291C8—861no—
292C8—861no—
293C8—861no—
294C22—1721no—
295C22—1721no—
296C22—1721no—
297C22C22×C22⋊D4311yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—1721no—
309C4—1721no—
310C4—1721no—
311C4C2×#1062190211yescharacteristic
312C4#1306337311yescharacteristic
313C2—3441no—
314C2#1458356011yescharacteristic
315C2#1458369711yescharacteristic
316C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#557C2
socleC22×C43C22×D4
hypercenter#557D43
hypocenterC43#3377
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
2. #14583269C2semidirect
5. #14583203C2semidirect
7. #14583191C2semidirect
10. #14583109C2semidirect
11. #14583030C2semidirect
12. #14583004C2semidirect
14. C4×#10621885C2semidirect
15. C43×#557C2semidirect
159. #557D43semidirect
174. C43#3377semidirect