Finite Group Databasebeta

← #19147299

Subgroups — #19147299

Order 5504.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583605C211yesmaximal, characteristic, complemented
2#14583569C211yesmaximal, characteristic, complemented
3#14583262C211yesmaximal, characteristic, complemented
4#14583244C211yesmaximal, characteristic, complemented
5#14583201C211yesmaximal, characteristic, complemented
6#14583196C211yesmaximal, characteristic, complemented
7#14583187C211yesmaximal, characteristic, complemented
8#14583093C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583091C211yesmaximal, characteristic, complemented
11#14583027C211yesmaximal, characteristic, complemented
12#14583012C211yesmaximal, characteristic, complemented
13#14583008C211yesmaximal, characteristic, complemented
14#14582979C211yesmaximal, characteristic, complemented
15C43×#490C211yesmaximal, characteristic, complemented
16C2×#10621900—21no—
17C2×D344C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063321C2211yescharacteristic
22#13063321C2211yescharacteristic
23#13063316C2211yescharacteristic
24#13063305—21no—
25#13063303—21no—
26#13063303—21no—
27#13063297—21no—
28#13063297—21no—
29#13063296—21no—
30C4×Dic86C2211yescharacteristic
31C4×D172C2211yescharacteristic
32C4×D172C2211yescharacteristic
33D4×Dic43C2211yescharacteristic
34D4×Dic43C2211yescharacteristic
35#13063287C2211yescharacteristic
36#13063287C2211yescharacteristic
37C4⋊C4×D43—21no—
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
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—44no—
70C2×D172C2311yescharacteristic
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×Dic86—21no—
77C2×Dic86D411yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87#10621882—22no—
88#10621882—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43D411yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4D411yescharacteristic
100Dic43⋊C4D411yescharacteristic
101C4×Dic43C2311yescharacteristic
102C4×Dic43C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105D344—22no—
106C23×C43—21no—
107C23×C43—21no—
108C22×D43—21no—
109C22×D43—21no—
110D4×C43—21no—
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—21no—
114D4×C43—42no—
115D4×C43—81no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2411yescharacteristic
121C22⋊D43—42no—
122C22⋊D43—42no—
123C22⋊D43—81no—
124C22⋊D43—81no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—42no—
128C2×Dic43—42no—
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—21no—
135D172—21no—
136D172#4112yescomplemented
137C4×D43—42no—
138C4×D43—42no—
139C4×D43—81no—
140C4×D43—81no—
141Dic86—22no—
142Dic86—81no—
143C8×C43—21no—
144C8×C43—21no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43C22×D411yescharacteristic
154C2×D43—22no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43C2×#4111yescharacteristic
165C4×C432−1+411yescharacteristic
166Dic43—21no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171Dic43AGL(1,ℤ/8)12yes—
172#3366—431nomaximal, Sylow
173C2×C43—81no—
174C2×C43—81no—
175C2×C43#54811yescharacteristic
176C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C43#57611yescharacteristic
178D43—42no—
179D43—81no—
180#554—431no—
181#550—431no—
182#490—431no—
183#490D4311yescharacteristic, complemented
184#486—431no—
185#478—431no—
186#478—431no—
187#476—431no—
188#459—431no—
189#459—431no—
190#459—431no—
191#446—431no—
192#442—431no—
193#442—431no—
194C4×D8—431no—
195C43#336611yescharacteristic, complemented, Sylow
196C2×#41—861no—
197C2×D8—431no—
198C2×D8—431no—
199C2×D8—431no—
200C4⋊Q8—431no—
201#127—431no—
202#127—431no—
203#127C2×D4311yescharacteristic
204#125—431no—
205#125C2×D4311yescharacteristic
206C22⋊Q8—861no—
207C22⋊Q8—861no—
208C22⋊Q8—861no—
209#121—861no—
210#121—861no—
211#121—861no—
212C4×Q8—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—431no—
217C4×D4—431no—
218C4×D4—431no—
219C2×C4⋊C4—861no—
220#107—431no—
221#106—431no—
222#106—431no—
223C4⋊C8—431no—
224C4⋊C8—431no—
225C4⋊C8—431no—
226#102—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102C2×D4311yescharacteristic
233#102C2×D4311yescharacteristic
234#102C2×D4311yescharacteristic
235#102C2×D4311yescharacteristic
236#97—431no—
237#97C2×D4311yescharacteristic
238C4×C8—431no—
239#41—1724no—
240C2×Q8—431no—
241C2×Q8—861no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—431no—
245C2×D4—431no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4C22×D4311yescharacteristic
251C2×D4C22×D4311yescharacteristic
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258D8—862no—
259D8—862no—
260D8—862no—
261C2×C8—431no—
262C2×C8—431no—
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—431no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C42—431no—
284C42—431no—
285C42C22×D4311yescharacteristic
286C23—21no—
287C23—21no—
288C23—861no—
289C23—861no—
290Q8—862no—
291Q8—3441no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—81no—
298D4—432no—
299D4—861no—
300D4—861no—
301D4—861no—
302D4—3441no—
303D4—3441no—
304D4—1722no—
305D4—1722no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—431no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—3441no—
315C2×C4—3441no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4D4×D4311yescharacteristic
321C2×C4D4×D4311yescharacteristic
322C2×C4C23×D4311yescharacteristic
323C8—21no—
324C8—21no—
325C8—861no—
326C8—861no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—862no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22—1721no—
338C22—1721no—
339C22C2×D4×D4311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—432no—
345C4—861no—
346C4—861no—
347C4—861no—
348C4—1721no—
349C4—1721no—
350C4#41×D4311yescharacteristic
351C4#1306337211yescharacteristic
352C2—81no—
353C2—81no—
354C2—3441no—
355C2—1722no—
356C2#1458355711yescharacteristic
357C2AGL(1,ℤ/8)×D4311yescharacteristic
358C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3366
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. #14583605C2semidirect
2. #14583569C2semidirect
3. #14583262C2semidirect
4. #14583244C2semidirect
5. #14583201C2semidirect
6. #14583196C2semidirect
7. #14583187C2semidirect
8. #14583093C2semidirect
9. #14583093C2semidirect
10. #14583091C2semidirect
11. #14583027C2semidirect
12. #14583012C2semidirect
13. #14583008C2semidirect
14. #14582979C2semidirect
15. C43×#490C2semidirect
136. D172#41semidirect
183. #490D43semidirect
195. C43#3366semidirect