Finite Group Databasebeta

← #19147327

Subgroups — #19147327

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#14583570C211yesmaximal, characteristic
3#14583265C211yesmaximal, characteristic, complemented
4#14583262C211yesmaximal, characteristic, complemented
5#14583244C211yesmaximal, characteristic, complemented
6#14583198C211yesmaximal, characteristic, complemented
7#14583178C211yesmaximal, characteristic, complemented
8#14583100C211yesmaximal, characteristic, complemented
9#14583098C211yesmaximal, characteristic, complemented
10#14583098C211yesmaximal, characteristic, complemented
11#14583028C211yesmaximal, characteristic, complemented
12#14582999C211yesmaximal, characteristic, complemented
13#14582998C211yesmaximal, characteristic, complemented
14#14582986C211yesmaximal, characteristic, complemented
15C43×#478C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621873C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20#13063324—21no—
21#13063324C2211yescharacteristic
22#13063322C2211yescharacteristic
23#13063321C2211yescharacteristic
24#13063321C2211yescharacteristic
25#13063316C2211yescharacteristic
26#13063315—21no—
27#13063315—21no—
28#13063299—21no—
29#13063298—21no—
30#13063298—21no—
31C4×Dic86C2211yescharacteristic
32C4×Dic86C2211yescharacteristic
33#13063290—21no—
34#13063290C2211yescharacteristic
35#13063290C2211yescharacteristic
36#13063287C2211yescharacteristic
37#13063287C2211yescharacteristic
38#13063258C2211yescharacteristic
39Dic43⋊C8C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063247C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063246C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063236C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×D4×C43C2311yescharacteristic
60C22×C4×C43—21no—
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65#10621898—44no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172C2311yescharacteristic
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
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
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C42×C43C2311yescharacteristic
84#10621883—22no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43D411yescharacteristic
89C4⋊Dic43C2311yescharacteristic
90Dic43⋊C4—21no—
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4D411yescharacteristic
96Dic43⋊C4D411yescharacteristic
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43C2311yescharacteristic
101C4×Dic43C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104#10621873—22no—
105#10621873—22no—
106C23×C43—21no—
107C22×D43—21no—
108C22×D43—21no—
109D4×C43—21no—
110D4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—42no—
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2411yescharacteristic
118C22⋊D43—42no—
119C22⋊D43—42no—
120C22⋊D43—81no—
121C22⋊D43—81no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—21no—
129D172—21no—
130D172—21no—
131D172—21no—
132D172—42no—
133D172—81no—
134C4×D43—42no—
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×C43C22×D411yescharacteristic
148C2×D43—41no—
149C2×D43—41no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C432−1+411yescharacteristic
161Dic43—22no—
162Dic43—21no—
163Dic43—21no—
164Dic43—21no—
165Dic43—41no—
166Dic43AGL(1,ℤ/8)12yes—
167#3368—431nomaximal, Sylow
168C2×C43—81no—
169C2×C43#54811yescharacteristic
170C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C43#57711yescharacteristic
172D43—81no—
173D43—81no—
174#557—431no—
175#550—431no—
176#490—431no—
177#490—431no—
178#486—431no—
179#478—431no—
180#478D4311yescharacteristic, complemented
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#127—431no—
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×D4C2×D4311yescharacteristic
214#107—431no—
215#107C2×D4311yescharacteristic
216#106C2×D4311yescharacteristic
217C4⋊C8—431no—
218C4⋊C8—431no—
219C4⋊C8C2×D4311yescharacteristic
220#103—431no—
221#102—431no—
222#102—431no—
223#102—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228#102C2×D4311yescharacteristic
229#102C2×D4311yescharacteristic
230#97—431no—
231#97—431no—
232C4×C8—431no—
233#41—1724no—
234C2×Q8—431no—
235C2×Q8—431no—
236C2×Q8—861no—
237C2×D4—431no—
238C2×D4—431no—
239C2×D4—861no—
240C2×D4—861no—
241C2×D4—861no—
242C2×D4—861no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4C22×D4311yescharacteristic
246C22×C4—21no—
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—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4C22×D4311yescharacteristic
269C4⋊C4C22×D4311yescharacteristic
270C4⋊C4C22×D4311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C42—431no—
275C42—431no—
276C42—861no—
277C42—861no—
278C42—861no—
279C42C22×D4311yescharacteristic
280C23—21no—
281C23—861no—
282C23—861no—
283Q8—432no—
284Q8—862no—
285Q8—861no—
286Q8—1722no—
287D4—21no—
288D4—21no—
289D4—861no—
290D4—861no—
291D4—861no—
292D4—861no—
293D4—3441no—
294D4—3441no—
295D4—3441no—
296D4—1722no—
297D4—1722no—
298D4—1722no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—431no—
307C2×C4—861no—
308C2×C4—861no—
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—1721no—
322C22—1721no—
323C22—1721no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22C2×D4×D4311yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—432no—
334C4—862no—
335C4—861no—
336C4—861no—
337C4—861no—
338C4—1721no—
339C4#41×D4311yescharacteristic
340C4#1306337311yescharacteristic
341C2—81no—
342C2—3441no—
343C2—3441no—
344C2#1458355911yescharacteristic
345C2AGL(1,ℤ/8)×D4311yescharacteristic
346C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#478C2
socleC22×C43C22×D4
hypercenter#478D43
hypocenterC43#3368
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14583626C2semidirect
3. #14583265C2semidirect
4. #14583262C2semidirect
5. #14583244C2semidirect
6. #14583198C2semidirect
7. #14583178C2semidirect
8. #14583100C2semidirect
9. #14583098C2semidirect
10. #14583098C2semidirect
11. #14583028C2semidirect
12. #14582999C2semidirect
13. #14582998C2semidirect
14. #14582986C2semidirect
15. C43×#478C2semidirect
139. Dic86#41semidirect
180. #478D43semidirect
189. C43#3368semidirect