Finite Group Databasebeta

← #19147133

Subgroups — #19147133

Order 5504.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583617C211yesmaximal, characteristic, complemented
2#14583601C211yesmaximal, characteristic
3#14583307C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583230C211yesmaximal, characteristic, complemented
6#14583222C211yesmaximal, characteristic, complemented
7#14583209C211yesmaximal, characteristic, complemented
8#14583187C211yesmaximal, characteristic, complemented
9#14583143C211yesmaximal, characteristic, complemented
10#14583127C211yesmaximal, characteristic, complemented
11#14582996C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582942C211yesmaximal, characteristic, complemented
14#14582934C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C2×#10621883C2211yescharacteristic
17C2×#10621877C2211yescharacteristic
18C2×C8×D43C2211yescharacteristic
19#13063324C2211yescharacteristic
20#13063319—21no—
21#13063318—21no—
22#13063318—21no—
23#13063316C2211yescharacteristic
24#13063311—21no—
25#13063309—21no—
26#13063305C2211yescharacteristic
27#13063304C2211yescharacteristic
28#13063297—21no—
29#13063296C2211yescharacteristic
30C4×Dic86—21no—
31#13063290C2211yescharacteristic
32D4×Dic43—21no—
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35#13063283C2211yescharacteristic
36#13063283C2211yescharacteristic
37C2×C4⋊Dic43C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063256C2211yescharacteristic
44#13063256C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063248C2211yescharacteristic
49#13063246C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43D411yescharacteristic
64C22×Dic43—21no—
65C22×Dic43—21no—
66C2×C4×D43C2311yescharacteristic
67C2×Dic86—21no—
68C2×Dic86C2311yescharacteristic
69C2×C8×C43C2311yescharacteristic
70C2×C8×C43C2311yescharacteristic
71C4⋊C4×C43C2311yescharacteristic
72C4⋊C4×C43C2311yescharacteristic
73C4⋊C4×C43C2311yescharacteristic
74C22⋊C4×C43—21no—
75C22⋊C4×C43—21no—
76C42×C43—21no—
77C22⋊Dic43—21no—
78C22⋊Dic43—21no—
79C22⋊Dic43—21no—
80C22⋊Dic43D411yescharacteristic
81#10621883—22no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4D411yescharacteristic
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4D411yescharacteristic
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43C2311yescharacteristic
101#10621877—22no—
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C8×D43—22no—
105C23×C43—21no—
106C23×C43C2×D411yescharacteristic
107C22×D43C2×D411yescharacteristic
108D4×C43—21no—
109D4×C43—21no—
110D4×C43—42no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2411yescharacteristic
118C22⋊D43—41no—
119C22⋊D43—81no—
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—81no—
125C2×Dic43—81no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129C4×D43—21no—
130C4×D43—21no—
131Dic86—21no—
132Dic86—21no—
133Dic86—42no—
134C8×C43—21no—
135C8×C43—21no—
136C43⋊C8—21no—
137C43⋊C8#4112yes—
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—41no—
144C22×C43C22×D411yescharacteristic
145C2×D43—21no—
146C2×D43—21no—
147C2×D43—21no—
148C4×C43—21no—
149C4×C43—41no—
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—41no—
161#3350—431nomaximal, Sylow
162C2×C43—41no—
163C2×C43—81no—
164C2×C43#54711yescharacteristic
165C2×C43#57511yescharacteristic
166C2×C43#57711yescharacteristic
167D43—41no—
168#556—431no—
169#553—431no—
170#501—431no—
171#485—431no—
172#483—431no—
173#482—431no—
174#482D4311yescharacteristic, complemented
175#479—431no—
176#476—431no—
177#468—431no—
178#465—431no—
179#440—431no—
180#435—431no—
181#428—431no—
182#427—431no—
183C43#335011yescharacteristic, complemented, Sylow
184C2×SD16—431no—
185C2×M16—431no—
186C22×C8—431no—
187C4⋊Q8—431no—
188#126—861no—
189#126—861no—
190#126—861no—
191#125—431no—
192#124—861no—
193#123—861no—
194C22⋊Q8—431no—
195C22⋊Q8—431no—
196#121—431no—
197#121—861no—
198#121C2×D4311yescharacteristic
199C4×Q8—431no—
200C4×Q8—861no—
201C4×D4—431no—
202C4×D4—431no—
203C4×D4—861no—
204#117—431no—
205#117—431no—
206#117C2×D4311yescharacteristic
207C2×C4⋊C4—431no—
208#107—431no—
209#107—431no—
210#107—431no—
211#107C2×D4311yescharacteristic
212#106—431no—
213#106—431no—
214#106—431no—
215#106—431no—
216#106C2×D4311yescharacteristic
217C4⋊C8—431no—
218#103—431no—
219#103—431no—
220#103—431no—
221#102—431no—
222#102C2×D4311yescharacteristic
223#102C2×D4311yescharacteristic
224C22⋊C8—431no—
225C22⋊C8C2×D4311yescharacteristic
226#97—431no—
227C2×Q8—431no—
228C2×Q8—861no—
229C2×D4—21no—
230C2×D4—431no—
231C2×D4—861no—
232C2×D4C22×D4311yescharacteristic
233C22×C4—431no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4C22×D4311yescharacteristic
237SD16—862no—
238M16—862no—
239C2×C8—431no—
240C2×C8—431no—
241C2×C8—862no—
242C2×C8C22×D4311yescharacteristic
243C2×C8C22×D4311yescharacteristic
244C4⋊C4—431no—
245C4⋊C4—431no—
246C4⋊C4—431no—
247C4⋊C4—431no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4C22×D4311yescharacteristic
256C4⋊C4C22×D4311yescharacteristic
257C4⋊C4C22×D4311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—431no—
261C22⋊C4—431no—
262C22⋊C4—861no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C22⋊C4—861no—
266C22⋊C4—861no—
267C22⋊C4—861no—
268C42—21no—
269C42—431no—
270C42—861no—
271C42—861no—
272C42—861no—
273C23—21no—
274C23—431no—
275C23D4×D4311yescharacteristic
276Q8—861no—
277Q8—861no—
278Q8—1722no—
279D4—21no—
280D4—21no—
281D4—42no—
282D4—3441no—
283D4—1721no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—431no—
290C2×C4—431no—
291C2×C4—431no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—3441no—
299C2×C4—3441no—
300C2×C4D4×D4311yescharacteristic
301C2×C4C23×D4311yescharacteristic
302C8—21no—
303C8—21no—
304C8—432no—
305C8—861no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—861no—
313C22—861no—
314C22—861no—
315C22C2×D4×D4311yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—861no—
321C4—861no—
322C4—861no—
323C4—1721no—
324C4—1721no—
325C4—1721no—
326C4—1721no—
327C4#41×D4311yescharacteristic
328C4#1306337211yescharacteristic
329C2—41no—
330C2—81no—
331C2—1721no—
332C2#1458354711yescharacteristic
333C2#1458369511yescharacteristic
334C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3350
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14583617C2semidirect
3. #14583307C2semidirect
4. #14583242C2semidirect
5. #14583230C2semidirect
6. #14583222C2semidirect
7. #14583209C2semidirect
8. #14583187C2semidirect
9. #14583143C2semidirect
10. #14583127C2semidirect
11. #14582996C2semidirect
12. #14582973C2semidirect
13. #14582942C2semidirect
14. #14582934C2semidirect
15. C43×#482C2semidirect
174. #482D43semidirect
183. C43#3350semidirect