Finite Group Databasebeta

← #19147321

Subgroups — #19147321

Order 5504.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583626C211yesmaximal, characteristic, complemented
2#14583569C211yesmaximal, characteristic
3#14583262C211yesmaximal, characteristic, complemented
4#14583244C211yesmaximal, characteristic, complemented
5#14583197C211yesmaximal, characteristic, complemented
6#14583196C211yesmaximal, characteristic, complemented
7#14583177C211yesmaximal, characteristic, complemented
8#14583098C211yesmaximal, characteristic, complemented
9#14583098C211yesmaximal, characteristic, complemented
10#14583096C211yesmaximal, characteristic, complemented
11#14583027C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13#14582996C211yesmaximal, characteristic, complemented
14#14582990C211yesmaximal, characteristic, complemented
15C43×#490C211yesmaximal, characteristic, complemented
16C2×#10621900—21no—
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20#13063324—21no—
21#13063324C2211yescharacteristic
22#13063321C2211yescharacteristic
23#13063321C2211yescharacteristic
24#13063316C2211yescharacteristic
25#13063315—21no—
26#13063315—21no—
27#13063297—21no—
28#13063297—21no—
29#13063296—21no—
30C4×Dic86C2211yescharacteristic
31C4×Dic86C2211yescharacteristic
32#13063290—21no—
33#13063290C2211yescharacteristic
34#13063290C2211yescharacteristic
35C4×D172C2211yescharacteristic
36D4×Dic43C2211yescharacteristic
37D4×Dic43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063256C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063250C2211yescharacteristic
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×C4×D43—21no—
72C2×Dic86—21no—
73C2×Dic86D411yescharacteristic
74C2×Dic86C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C42×C43C2311yescharacteristic
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84#10621883—22no—
85#10621883—22no—
86(C2×D43)⋊C4—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43D411yescharacteristic
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
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
105#10621873—22no—
106C23×C43—21no—
107C23×C43—21no—
108C22×D43—21no—
109D4×C43—21no—
110D4×C43—21no—
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—42no—
114D4×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2411yescharacteristic
120C22⋊D43—42no—
121C22⋊D43—42no—
122C22⋊D43—81no—
123C22⋊D43—81no—
124C2×Dic43—21no—
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—
135C4×D43—42no—
136Dic86—21no—
137Dic86—22no—
138Dic86—42no—
139Dic86#4112yescomplemented
140C8×C43—21no—
141C8×C43—21no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43C22×D411yescharacteristic
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C432−1+411yescharacteristic
160Dic43—22no—
161Dic43—21no—
162Dic43—21no—
163Dic43—21no—
164Dic43—41no—
165Dic43—41no—
166Dic43AGL(1,ℤ/8)12yes—
167#3368—431nomaximal, Sylow
168C2×C43—81no—
169C2×C43—81no—
170C2×C43#54811yescharacteristic
171C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
172C2×C43#57711yescharacteristic
173D43—81no—
174#557—431no—
175#550—431no—
176#490—431no—
177#490D4311yescharacteristic, complemented
178#486—431no—
179#478—431no—
180#478—431no—
181#474—431no—
182#460—431no—
183#460—431no—
184#460—431no—
185#446—431no—
186#440—431no—
187#440—431no—
188C4×SD16—431no—
189C43#336811yescharacteristic, complemented, Sylow
190C2×#41—861no—
191C2×SD16—431no—
192C2×SD16—431no—
193C2×SD16—431no—
194C4⋊Q8—431no—
195C4⋊Q8—861no—
196#127—431no—
197#127—431no—
198#127C2×D4311yescharacteristic
199#125—431no—
200#125—861no—
201#125—861no—
202#125C2×D4311yescharacteristic
203#121—861no—
204#121—861no—
205#121—861no—
206C4×Q8—431no—
207C4×Q8—431no—
208C4×Q8—431no—
209C4×Q8—431no—
210C4×Q8—861no—
211C4×D4—431no—
212C4×D4—431no—
213C4×D4—431no—
214#107—431no—
215#107—431no—
216#106—431no—
217C4⋊C8—431no—
218C4⋊C8—431no—
219C4⋊C8—431no—
220#103—431no—
221#102—431no—
222#102—431no—
223#102—431no—
224#102—431no—
225#102—431no—
226#102C2×D4311yescharacteristic
227#102C2×D4311yescharacteristic
228#102C2×D4311yescharacteristic
229#102C2×D4311yescharacteristic
230#97—431no—
231#97C2×D4311yescharacteristic
232C4×C8—431no—
233#41—1724no—
234C2×Q8—431no—
235C2×Q8—431no—
236C2×Q8—861no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—431no—
240C2×D4—861no—
241C2×D4—861no—
242C2×D4—861no—
243C2×D4—861no—
244C2×D4C22×D4311yescharacteristic
245C2×D4C22×D4311yescharacteristic
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249SD16—862no—
250SD16—862no—
251SD16—862no—
252C2×C8—431no—
253C2×C8—431no—
254C2×C8C22×D4311yescharacteristic
255C2×C8C22×D4311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22×D4311yescharacteristic
270C4⋊C4C22×D4311yescharacteristic
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C42—431no—
275C42—431no—
276C42—861no—
277C42—861no—
278C42—861no—
279C42C22×D4311yescharacteristic
280C23—21no—
281C23—21no—
282C23—861no—
283Q8—432no—
284Q8—862no—
285Q8—861no—
286Q8—1722no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—861no—
294D4—861no—
295D4—3441no—
296D4—3441no—
297D4—1722no—
298D4—1722no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—431no—
302C2×C4—431no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—1722no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4D4×D4311yescharacteristic
312C2×C4D4×D4311yescharacteristic
313C2×C4C23×D4311yescharacteristic
314C8—21no—
315C8—21no—
316C8—861no—
317C8—861no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22C2×D4×D4311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—432no—
333C4—862no—
334C4—861no—
335C4—861no—
336C4—861no—
337C4—1721no—
338C4—1721no—
339C4#41×D4311yescharacteristic
340C4#1306337211yescharacteristic
341C2—81no—
342C2—81no—
343C2—3441no—
344C2#1458355711yescharacteristic
345C2AGL(1,ℤ/8)×D4311yescharacteristic
346C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3368
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. #14583626C2semidirect
3. #14583262C2semidirect
4. #14583244C2semidirect
5. #14583197C2semidirect
6. #14583196C2semidirect
7. #14583177C2semidirect
8. #14583098C2semidirect
9. #14583098C2semidirect
10. #14583096C2semidirect
11. #14583027C2semidirect
12. #14583001C2semidirect
13. #14582996C2semidirect
14. #14582990C2semidirect
15. C43×#490C2semidirect
139. Dic86#41semidirect
177. #490D43semidirect
189. C43#3368semidirect