Finite Group Databasebeta

← #19147534

Subgroups — #19147534

Order 5504.

334 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583609C211yesmaximal, characteristic
2#14583309C211yesmaximal, characteristic, complemented
3#14583305C211yesmaximal, characteristic, complemented
4#14583298C211yesmaximal, characteristic, complemented
5#14583206C211yesmaximal, characteristic, complemented
6#14583206C211yesmaximal, characteristic, complemented
7#14583196C211yesmaximal, characteristic
8#14583196C211yesmaximal, characteristic
9#14583186C211yesmaximal, characteristic
10#14583184C211yesmaximal, characteristic, complemented
11#14583030C211yesmaximal, characteristic, complemented
12#14582997C211yesmaximal, characteristic
13#14582997C211yesmaximal, characteristic
14C4×#10621884C211yesmaximal, characteristic
15C43×#557C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17#13063325C2211yescharacteristic
18#13063317C2211yescharacteristic
19#13063317C2211yescharacteristic
20#13063303—21no—
21#13063303—21no—
22#13063301—21no—
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25C4×D172C2211yescharacteristic
26C4⋊C4×D43—21no—
27#13063258C2211yescharacteristic
28#13063258C2211yescharacteristic
29#13063258C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063256C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊(C43⋊C8)C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063249C2211yescharacteristic
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×C4×D43—21no—
65C2×C4×D43—21no—
66C2×Dic86—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×C43—21no—
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43D411yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C42×C43—21no—
82C42×C43—21no—
83C42×C43—21no—
84C42×C43C2311yescharacteristic
85C42×C43C2311yescharacteristic
86C42×C43C2311yescharacteristic
87#10621884Q814yescomplemented
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99C2×C43⋊C8C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C22×D43—21no—
104Q8×C43—21no—
105Q8×C43—41no—
106Q8×C43—42no—
107Q8×C43C2×Q812yes—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43C2×D411yescharacteristic
113C2×C4×C43C2×D411yescharacteristic
114C2×C4×C43C2×D411yescharacteristic
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2411yescharacteristic
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122D172—21no—
123D172C2×Q812yes—
124C4×D43—42no—
125C4×D43—81no—
126C4×D43—81no—
127Dic86—81no—
128C43⋊C8—21no—
129C43⋊C8—21no—
130C43⋊C8—21no—
131C43⋊C8C2×Q812yes—
132C22×C43C22×D411yescharacteristic
133C2×D43—22no—
134C2×D43—41no—
135C2×D43—41no—
136C4×C43—22no—
137C4×C43—21no—
138C4×C43—21no—
139C4×C43—21no—
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—41no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C43C22×Q811yescharacteristic
147C4×C432−1+411yescharacteristic
148Dic43—41no—
149Dic43—41no—
150Dic43—41no—
151#3388—431nomaximal, Sylow
152C2×C43D4×Q811yescharacteristic
153C2×C43#57511yescharacteristic
154C2×C43#57711yescharacteristic
155D43—42no—
156#557D4311yescharacteristic, complemented
157#554—431no—
158#501—431no—
159#501—431no—
160#499—431no—
161#479—431no—
162#479—431no—
163#478—431no—
164#478—431no—
165#476—431no—
166#475—431no—
167#446—431no—
168#440—431no—
169#440—431no—
170C4×SD16—431no—
171C43#338811yescharacteristic, complemented, Sylow
172C2×SD16—431no—
173C4⋊Q8—21no—
174C4⋊Q8—431no—
175C4⋊Q8C2×D4311yescharacteristic
176#125—21no—
177#125—21no—
178#125—431no—
179#125—431no—
180#125C2×D4311yescharacteristic
181#125C2×D4311yescharacteristic
182C22⋊Q8—861no—
183C22⋊Q8—861no—
184C22⋊Q8—861no—
185C4×Q8—21no—
186C4×Q8C2×D4311yescharacteristic
187C4×Q8C2×D4311yescharacteristic
188C4×Q8C2×D4311yescharacteristic
189C4×Q8C2×D4311yescharacteristic
190C4×D4—431no—
191C4×D4—431no—
192C4×D4—431no—
193C2×C4⋊C4—861no—
194#107—431no—
195#107—431no—
196#107—431no—
197#107—431no—
198#106—431no—
199#106—431no—
200#106—431no—
201#106—431no—
202#106—431no—
203C4⋊C8—431no—
204C4⋊C8—431no—
205C4⋊C8—431no—
206#103—431no—
207#103—431no—
208#103—431no—
209#102—431no—
210#102—431no—
211#102—431no—
212#97—431no—
213#97—431no—
214C4×C8—431no—
215C2×Q8—21no—
216C2×Q8—861no—
217C2×Q8C22⋊D4311yescharacteristic
218C2×Q8C22×D4311yescharacteristic
219C2×D4—431no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4—861no—
223SD16—434no—
224C2×C8—431no—
225C2×C8—431no—
226C2×C8—431no—
227C2×C8—431no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—431no—
237C4⋊C4—431no—
238C4⋊C4—431no—
239C4⋊C4—861no—
240C4⋊C4—861no—
241C4⋊C4—861no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4C22⋊D4311yescharacteristic
245C4⋊C4C22⋊D4311yescharacteristic
246C4⋊C4C22⋊D4311yescharacteristic
247C4⋊C4C22×D4311yescharacteristic
248C4⋊C4C22×D4311yescharacteristic
249C4⋊C4C22×D4311yescharacteristic
250C22⋊C4—861no—
251C22⋊C4—861no—
252C22⋊C4—861no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42C22×D4311yescharacteristic
257C42C22×D4311yescharacteristic
258C42C22×D4311yescharacteristic
259C23—861no—
260Q8—21no—
261Q8—41no—
262Q8—42no—
263Q8—3441no—
264Q8Q8×D4312yes—
265D4—432no—
266D4—861no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—861no—
272C2×C4—861no—
273C2×C4—861no—
274C2×C4—3441no—
275C2×C4—3441no—
276C2×C4—1722no—
277C2×C4C2×C22⋊D4311yescharacteristic
278C2×C4C2×C22⋊D4311yescharacteristic
279C2×C4C2×C22⋊D4311yescharacteristic
280C2×C4C2×C22⋊D4311yescharacteristic
281C2×C4C2×C22⋊D4311yescharacteristic
282C2×C4C2×C22⋊D4311yescharacteristic
283C2×C4C23×D4311yescharacteristic
284C8—432no—
285C8—861no—
286C8—861no—
287C8—861no—
288C22—862no—
289C22—1721no—
290C22—1721no—
291C22C22×C22⋊D4311yescharacteristic
292C4—22no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—1721no—
303C4—1721no—
304C4—1721no—
305C4C2×Q8×D4311yescharacteristic
306C4#1306337311yescharacteristic
307C2—1722no—
308C2Q8×C22⋊D4311yescharacteristic
309C2#1458369711yescharacteristic
310C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#557C2
socleC22×C43C22×D4
hypercenter#557D43
hypocenterC43#3388
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. #14583309C2semidirect
3. #14583305C2semidirect
4. #14583298C2semidirect
5. #14583206C2semidirect
6. #14583206C2semidirect
10. #14583184C2semidirect
11. #14583030C2semidirect
15. C43×#557C2semidirect
87. #10621884Q8semidirect
156. #557D43semidirect
171. C43#3388semidirect