Finite Group Databasebeta

← #19145270

Subgroups — #19145270

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#14583523C211yesmaximal, characteristic
2#14583510C211yesmaximal, characteristic, complemented
3#14583305C211yesmaximal, characteristic, complemented
4#14583291C211yesmaximal, characteristic, complemented
5#14583254C211yesmaximal, characteristic, complemented
6#14583156C211yesmaximal, characteristic, complemented
7#14583148C211yesmaximal, characteristic
8#14583139C211yesmaximal, characteristic, complemented
9#14583131C211yesmaximal, characteristic
10#14583003C211yesmaximal, characteristic, complemented
11#14583002C211yesmaximal, characteristic, complemented
12#14582991C211yesmaximal, characteristic, complemented
13#14582984C211yesmaximal, characteristic, complemented
14#14582853C211yesmaximal, characteristic, complemented
15C43×#487C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063320—21no—
23#13063320—21no—
24#13063320—21no—
25#13063317C2211yescharacteristic
26#13063315—21no—
27#13063315—21no—
28#13063314—21no—
29#13063313C2211yescharacteristic
30#13063310—21no—
31#13063305C2211yescharacteristic
32#13063301—21no—
33#13063301C2211yescharacteristic
34#13063301C2211yescharacteristic
35#13063300C2211yescharacteristic
36Q8×Dic43C2211yescharacteristic
37Q8×Dic43C2211yescharacteristic
38#13063290C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063282C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063258C2211yescharacteristic
43#13063256C2211yescharacteristic
44#13063256C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063236C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53C4⋊Q8×C43C2211yescharacteristic
54#103×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D172—21no—
63C2×D172C2311yescharacteristic
64C2×C4×D43—21no—
65C2×C4×D43C2311yescharacteristic
66C2×Dic86C2311yescharacteristic
67C2×C8×C43C2311yescharacteristic
68C2×C8×C43C2311yescharacteristic
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43C2311yescharacteristic
73C4⋊C4×C43C2311yescharacteristic
74C42×C43C2311yescharacteristic
75#10621885—22no—
76#10621885—22no—
77#10621884—22no—
78#10621884—22no—
79(C2×D43)⋊C4—21no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4D411yescharacteristic
87(C2×D43)⋊C4D411yescharacteristic
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4D411yescharacteristic
99Dic43⋊C4D411yescharacteristic
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C22×D43—21no—
109C22×D43C2×D411yescharacteristic
110Q8×C43—21no—
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—21no—
129D172—21no—
130D172—81no—
131C4×D43—21no—
132C4×D43—21no—
133C4×D43—81no—
134Dic86—21no—
135Dic86—21no—
136C8×C43—21no—
137C8×C43—21no—
138C43⋊C8#4112yes—
139C43⋊C8#4112yes—
140C22×C43C22×D411yescharacteristic
141C2×D43—21no—
142C2×D43—21no—
143C2×D43—21no—
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—41no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43C2×#4111yescharacteristic
154C4×C43C2×#4111yescharacteristic
155Dic43—21no—
156Dic43—21no—
157Dic43—21no—
158Dic43—41no—
159Dic43—41no—
160Dic43—41no—
161#3178—431nomaximal, Sylow
162C2×C43#53211yescharacteristic
163C2×C43#57711yescharacteristic
164C2×C43#57811yescharacteristic
165D43—41no—
166D43—81no—
167#542—431no—
168#541—431no—
169#501—431no—
170#497—431no—
171#488—431no—
172#487D4311yescharacteristic, complemented
173#470—431no—
174#468—431no—
175#467—431no—
176#465—431no—
177#441—431no—
178#440—431no—
179C4×Q16—431no—
180C4×SD16—431no—
181#405—431no—
182C43#317811yescharacteristic, complemented, Sylow
183C2×Q16—431no—
184C2×Q16—431no—
185C2×SD16—431no—
186C2×SD16—431no—
187C2×M16—431no—
188C22×C8—431no—
189C4⋊Q8C2×D4311yescharacteristic
190C4⋊Q8C2×D4311yescharacteristic
191#126—861no—
192#126—861no—
193#126—861no—
194#125—431no—
195#125—861no—
196#125—861no—
197#124—431no—
198#124—861no—
199#123—861no—
200C22⋊Q8—431no—
201C22⋊Q8—431no—
202C22⋊Q8—431no—
203C22⋊Q8—861no—
204#121—431no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×Q8—431no—
208C4×D4—431no—
209#117—431no—
210#107—431no—
211#107—431no—
212#106—431no—
213#106—431no—
214#103—431no—
215#103—431no—
216#103C2×D4311yescharacteristic
217#103C2×D4311yescharacteristic
218#103C2×D4311yescharacteristic
219#103C2×D4311yescharacteristic
220#102—431no—
221#102—431no—
222#97—431no—
223#97—431no—
224C4×C8—431no—
225C4×C8C2×D4311yescharacteristic
226C2×Q8—21no—
227C2×Q8—431no—
228C2×Q8C22×D4311yescharacteristic
229C2×Q8C22×D4311yescharacteristic
230C2×D4—431no—
231C2×D4—861no—
232C22×C4—431no—
233C22×C4—861no—
234Q16—862no—
235Q16—862no—
236SD16—862no—
237SD16—862no—
238M16—862no—
239C2×C8—431no—
240C2×C8—431no—
241C2×C8—862no—
242C2×C8C22×D4311yescharacteristic
243C2×C8C22×D4311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—431no—
248C4⋊C4—431no—
249C4⋊C4—431no—
250C4⋊C4—431no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4C22×D4311yescharacteristic
260C4⋊C4C22×D4311yescharacteristic
261C22⋊C4—431no—
262C22⋊C4—431no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C22⋊C4—861no—
266C22⋊C4—861no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C42—431no—
271C42—861no—
272C42—861no—
273C42—861no—
274C42C22×D4311yescharacteristic
275C23—431no—
276C23—861no—
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—81no—
282Q8—861no—
283Q8—861no—
284D4—861no—
285D4—861no—
286D4—3441no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—431no—
292C2×C4—431no—
293C2×C4—431no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—3441no—
300C2×C4D4×D4311yescharacteristic
301C2×C4D4×D4311yescharacteristic
302C2×C4C23×D4311yescharacteristic
303C8—21no—
304C8—21no—
305C8—432no—
306C8—432no—
307C22—861no—
308C22—861no—
309C22—861no—
310C22—1721no—
311C22—1721no—
312C22—1721no—
313C22C2×D4×D4311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—861no—
321C4—861no—
322C4—861no—
323C4—1721no—
324C4—1721no—
325C4—1721no—
326C4#41×D4311yescharacteristic
327C4#41×D4311yescharacteristic
328C2—3441no—
329C2—1721no—
330C2#1458344811yescharacteristic
331C2#1458370511yescharacteristic
332C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3178
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #14583510C2semidirect
3. #14583305C2semidirect
4. #14583291C2semidirect
5. #14583254C2semidirect
6. #14583156C2semidirect
8. #14583139C2semidirect
10. #14583003C2semidirect
11. #14583002C2semidirect
12. #14582991C2semidirect
13. #14582984C2semidirect
14. #14582853C2semidirect
15. C43×#487C2semidirect
172. #487D43semidirect
182. C43#3178semidirect