Finite Group Databasebeta

← #19147404

Subgroups — #19147404

Order 5504.

350 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#14583631C211yesmaximal, characteristic
2Q8×Dic86C211yesmaximal, characteristic, complemented
3#14583260C211yesmaximal, characteristic, complemented
4#14583258C211yesmaximal, characteristic, complemented
5#14583244C211yesmaximal, characteristic
6#14583192C211yesmaximal, characteristic, complemented
7#14583180C211yesmaximal, characteristic, complemented
8#14583177C211yesmaximal, characteristic, complemented
9#14583123C211yesmaximal, characteristic, complemented
10#14583097C211yesmaximal, characteristic
11#14583028C211yesmaximal, characteristic, complemented
12#14583000C211yesmaximal, characteristic, complemented
13#14582997C211yesmaximal, characteristic, complemented
14Q16×Dic43C211yesmaximal, characteristic, complemented
15C43×#464C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17#13063325—21no—
18#13063325C2211yescharacteristic
19#13063324—21no—
20#13063324—21no—
21#13063324C2211yescharacteristic
22#13063324C2211yescharacteristic
23#13063321C2211yescharacteristic
24#13063314C2211yescharacteristic
25#13063311—21no—
26#13063309—21no—
27#13063307—21no—
28Q8×Dic43C2211yescharacteristic
29Q8×Dic43C2211yescharacteristic
30Q8×Dic43C2211yescharacteristic
31C4×Dic86—21no—
32C4×Dic86C2211yescharacteristic
33C4×D172C2211yescharacteristic
34D4×Dic43C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36#13063259C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063258C2211yescharacteristic
39Dic43⋊C8C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063236C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×Q16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54#124×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C22×Dic43—21no—
65C2×D172C2311yescharacteristic
66C2×C4×D43—21no—
67C2×Dic86—21no—
68C2×Dic86—21no—
69C2×Dic86—21no—
70C2×Dic86D411yescharacteristic
71Q16×C43—22no—
72SD16×C43—22no—
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43—21no—
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C42×C43—21no—
80C42×C43C2311yescharacteristic
81C22⋊Dic43—21no—
82#10621884—22no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43D411yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4D411yescharacteristic
97Dic43⋊C4D411yescharacteristic
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43C2311yescharacteristic
102C4×Dic43C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C23×C43—21no—
106C22×D43—21no—
107Q8×C43—21no—
108Q8×C43—21no—
109Q8×C43—21no—
110Q8×C43#4112yes—
111D4×C43—21no—
112D4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2411yescharacteristic
119C22⋊D43—42no—
120C22⋊D43—81no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—81no—
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129D172—21no—
130D172—21no—
131C4×D43—81no—
132Dic86—22no—
133Dic86—81no—
134Dic86—81no—
135Dic86—81no—
136C8×C43—21no—
137C8×C43—21no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43C22×D411yescharacteristic
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—41no—
147C4×C43—22no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43C2×#4111yescharacteristic
153C4×C432−1+411yescharacteristic
154Dic43—21no—
155Dic43—21no—
156Dic43—21no—
157Dic43—41no—
158Dic43—41no—
159Dic43—41no—
160Dic43#13712yes—
161#3375—431nomaximal, Sylow
162C2×C43—81no—
163C2×C43#54811yescharacteristic
164C2×C43C2×#13711yescharacteristic
165C2×C43#57611yescharacteristic
166D43—81no—
167#559—431no—
168Q82—431no—
169#489—431no—
170#489—431no—
171#486—431no—
172#477—431no—
173#474—431no—
174#474—431no—
175#464—431no—
176#464D4311yescharacteristic, complemented
177#460—431no—
178#446—431no—
179#440—431no—
180#440—431no—
181C4×Q16—431no—
182C43#337511yescharacteristic, complemented, Sylow
183C2×Q16C2×D4311yescharacteristic
184C2×SD16—431no—
185C2×SD16C2×D4311yescharacteristic
186C4⋊Q8—431no—
187C4⋊Q8—431no—
188C4⋊Q8—431no—
189C4⋊Q8—861no—
190C4⋊Q8—861no—
191C4⋊Q8—861no—
192#127—431no—
193#124—431no—
194#124—861no—
195#124C2×D4311yescharacteristic
196#123—861no—
197#123—861no—
198C4×Q8—431no—
199C4×Q8—431no—
200C4×Q8—431no—
201C4×Q8—431no—
202C4×Q8—861no—
203C4×Q8C2×D4311yescharacteristic
204C4×D4—431no—
205C4×D4—431no—
206C4×D4—861no—
207#107—431no—
208#107—431no—
209#107—431no—
210C4⋊C8—431no—
211C4⋊C8—431no—
212C4⋊C8C2×D4311yescharacteristic
213#103—431no—
214#103—431no—
215#103—431no—
216#103C2×D4311yescharacteristic
217#102—431no—
218#102—431no—
219#102—431no—
220#102—431no—
221#102—431no—
222#102C2×D4311yescharacteristic
223#97—431no—
224#97—431no—
225C4×C8—431no—
226C2×Q8—431no—
227C2×Q8—861no—
228C2×Q8—861no—
229C2×Q8—861no—
230C2×Q8C22×D4311yescharacteristic
231C2×Q8C22×D4311yescharacteristic
232C2×D4—431no—
233C2×D4—861no—
234C2×D4—861no—
235C2×D4C22×D4311yescharacteristic
236C22×C4—861no—
237C22×C4—861no—
238Q16—22no—
239SD16—22no—
240SD16—862no—
241C2×C8—431no—
242C2×C8—431no—
243C2×C8C22×D4311yescharacteristic
244C2×C8C22×D4311yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—431no—
247C4⋊C4—431no—
248C4⋊C4—431no—
249C4⋊C4—431no—
250C4⋊C4—431no—
251C4⋊C4—431no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4C22×D4311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—861no—
262C22⋊C4—861no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C42—21no—
266C42—431no—
267C42—431no—
268C42—861no—
269C42—861no—
270C42—861no—
271C42C22×D4311yescharacteristic
272C23—21no—
273C23—861no—
274Q8—21no—
275Q8—21no—
276Q8—21no—
277Q8—862no—
278Q8—3441no—
279Q8—3441no—
280Q8—3441no—
281Q8#1062190012yes—
282D4—21no—
283D4—21no—
284D4—861no—
285D4—861no—
286D4—3441no—
287D4—1722no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—431no—
292C2×C4—431no—
293C2×C4—431no—
294C2×C4—431no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—3441no—
299C2×C4—3441no—
300C2×C4D4×D4311yescharacteristic
301C2×C4D4×D4311yescharacteristic
302C2×C4C23×D4311yescharacteristic
303C8—21no—
304C8—21no—
305C8—861no—
306C8—861no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—1721no—
311C22—1721no—
312C22—1721no—
313C22C2×D4×D4311yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—432no—
320C4—861no—
321C4—861no—
322C4—861no—
323C4—1721no—
324C4—1721no—
325C4—1721no—
326C4C2×#1062190011yescharacteristic
327C4#1306337211yescharacteristic
328C2—81no—
329C2—3441no—
330C2#1458355511yescharacteristic
331C2#137×D4311yescharacteristic
332C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#464C2
socleC22×C43C22×D4
hypercenter#464D43
hypocenterC43#3375
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. Q8×Dic86C2semidirect
3. #14583260C2semidirect
4. #14583258C2semidirect
6. #14583192C2semidirect
7. #14583180C2semidirect
8. #14583177C2semidirect
9. #14583123C2semidirect
11. #14583028C2semidirect
12. #14583000C2semidirect
13. #14582997C2semidirect
14. Q16×Dic43C2semidirect
15. C43×#464C2semidirect
176. #464D43semidirect
182. C43#3375semidirect