Finite Group Databasebeta

← #19146720

Subgroups — #19146720

Order 5504.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583587C211yesmaximal, characteristic, complemented
2#14583569C211yesmaximal, characteristic
3#14583222C211yesmaximal, characteristic, complemented
4#14583216C211yesmaximal, characteristic, complemented
5#14583203C211yesmaximal, characteristic, complemented
6#14583144C211yesmaximal, characteristic, complemented
7#14583127C211yesmaximal, characteristic, complemented
8#14583096C211yesmaximal, characteristic, complemented
9#14583062C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14583007C211yesmaximal, characteristic, complemented
12#14582972C211yesmaximal, characteristic, complemented
13#14582897C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#490C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063321—21no—
24#13063320—21no—
25#13063316—21no—
26#13063310—21no—
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic
29#13063297—21no—
30#13063297—21no—
31#13063296C2211yescharacteristic
32#13063296C2211yescharacteristic
33C4×Dic86C2211yescharacteristic
34C4×Dic86C2211yescharacteristic
35C4×D172C2211yescharacteristic
36D4×Dic43—21no—
37#13063283—21no—
38#13063283C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063256C2211yescharacteristic
43C4⋊(C43⋊C8)C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#127×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic
54#102×C43C2211yescharacteristic
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69#10621900—22no—
70#10621900—22no—
71#10621900—41no—
72#10621900—41no—
73C2×D172D411yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×C4×D43C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C42×C43C2311yescharacteristic
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88#10621883—41no—
89#10621883—41no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43D411yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108Dic172—22no—
109#10621872—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C22×D43C2×D411yescharacteristic
114C22×D43C2×D411yescharacteristic
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—42no—
120D4×C43—81no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—42no—
127C22⋊D43—42no—
128C22⋊D43—81no—
129C22⋊D43—81no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—41no—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—42no—
144Dic86—21no—
145Dic86—21no—
146Dic86—21no—
147Dic86#4112yes—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—22no—
172Dic43—21no—
173Dic43—21no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177#3317—431nomaximal, Sylow
178C2×C43—81no—
179C2×C43—81no—
180C2×C43#54611yescharacteristic
181C2×C43#57511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—41no—
185#552—431no—
186#550—431no—
187#490D4311yescharacteristic, complemented
188#482—431no—
189#481—431no—
190#479—431no—
191#468—431no—
192#465—431no—
193#460—431no—
194#452—431no—
195#452—431no—
196#441—431no—
197#435—431no—
198#417—431no—
199#416—431no—
200C43#331711yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C2×#41—431no—
203C2×Q16—431no—
204C2×SD16—431no—
205C2×SD16—431no—
206C2×M16—431no—
207C22×C8—431no—
208#127—861no—
209#127C2×D4311yescharacteristic
210#126—861no—
211#125—861no—
212#125C2×D4311yescharacteristic
213#123—861no—
214C22⋊Q8—431no—
215C22⋊Q8—431no—
216#121—431no—
217#121—431no—
218#121—861no—
219#121—861no—
220C4×Q8—431no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—861no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227#107—431no—
228#106—431no—
229#106—431no—
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#102—431no—
236#102—431no—
237#102C2×D4311yescharacteristic
238#102C2×D4311yescharacteristic
239#102C2×D4311yescharacteristic
240#102C2×D4311yescharacteristic
241C22⋊C8—431no—
242C22⋊C8—431no—
243#97C2×D4311yescharacteristic
244#41—862no—
245#41—862no—
246#41—1721no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8—431no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4C22×D4311yescharacteristic
258C2×D4C22×D4311yescharacteristic
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264Q16—862no—
265SD16—1721no—
266SD16—1721no—
267M16—1721no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—1721no—
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—431no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4C22×D4311yescharacteristic
284C4⋊C4C22×D4311yescharacteristic
285C22⋊C4—431no—
286C22⋊C4—431no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C42—861no—
293C42—861no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—21no—
297C23—21no—
298C23—431no—
299C23—431no—
300Q8—432no—
301Q8—861no—
302Q8—861no—
303Q8—861no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3441no—
311D4—3441no—
312D4—1721no—
313D4—1722no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—431no—
318C2×C4—431no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4D4×D4311yescharacteristic
331C2×C4D4×D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—861no—
336C8—861no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—861no—
348C22—861no—
349C22C2×D4×D4311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—861no—
355C4—861no—
356C4—862no—
357C4—1721no—
358C4—1721no—
359C4—1721no—
360C4#41×D4311yescharacteristic
361C4#1306337111yescharacteristic
362C2—81no—
363C2—81no—
364C2—1721no—
365C2—1721no—
366C2#1458354211yescharacteristic
367C2#1458369511yescharacteristic
368C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3317
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14583587C2semidirect
3. #14583222C2semidirect
4. #14583216C2semidirect
5. #14583203C2semidirect
6. #14583144C2semidirect
7. #14583127C2semidirect
8. #14583096C2semidirect
9. #14583062C2semidirect
10. #14583062C2semidirect
11. #14583007C2semidirect
12. #14582972C2semidirect
13. #14582897C2semidirect
14. #14582892C2semidirect
15. C43×#490C2semidirect
187. #490D43semidirect
200. C43#3317semidirect