Finite Group Databasebeta

← #19144850

Subgroups — #19144850

Order 5504.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583516C211yesmaximal, characteristic, complemented
2#14583382C211yesmaximal, characteristic, complemented
3#14583235C211yesmaximal, characteristic, complemented
4#14583210C211yesmaximal, characteristic, complemented
5#14583192C211yesmaximal, characteristic, complemented
6#14583177C211yesmaximal, characteristic, complemented
7#14583119C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583000C211yesmaximal, characteristic, complemented
11#14582996C211yesmaximal, characteristic, complemented
12#14582991C211yesmaximal, characteristic, complemented
13D8×Dic43C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic
16C2×#10621885C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18#13063324C2211yescharacteristic
19#13063318—21no—
20#13063312—21no—
21#13063312C2211yescharacteristic
22#13063306—21no—
23#13063304C2211yescharacteristic
24#13063302—21no—
25Q8×Dic43C2211yescharacteristic
26Q8×Dic43C2211yescharacteristic
27#13063290C2211yescharacteristic
28D4×Dic43—21no—
29D4×Dic43—21no—
30D4×Dic43C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32D4×Dic43C2211yescharacteristic
33#13063284—21no—
34#13063284C2211yescharacteristic
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×D8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—22no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×Dic86—21no—
73C2×Dic86C2311yescharacteristic
74SD16×C43—22no—
75D8×C43—22no—
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43D411yescharacteristic
87C22⋊Dic43D411yescharacteristic
88#10621885—22no—
89#10621883—22no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43D411yescharacteristic
94C4⋊Dic43D411yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43—21no—
110C23×C43C2×D411yescharacteristic
111Q8×C43—21no—
112Q8×C43#4112yes—
113D4×C43—24no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—81no—
118D4×C43#4112yes—
119C2×C4×C43—24no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138Dic86—21no—
139Dic86—21no—
140Dic86—81no—
141C8×C43—21no—
142C8×C43—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—22no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C4×C43—21no—
156C4×C43—22no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C43C2×#4111yescharacteristic
160Dic43—21no—
161Dic43—21no—
162Dic43—21no—
163Dic43—21no—
164Dic43—41no—
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168#3124—431nomaximal, Sylow
169C2×C43—41no—
170C2×C43—42no—
171C2×C43—81no—
172C2×C43#52511yescharacteristic
173C2×C43#57611yescharacteristic
174C2×C43#57811yescharacteristic
175#542—431no—
176#520—431no—
177#484—431no—
178#480—431no—
179#477—431no—
180#474—431no—
181#464—431no—
182#463—431no—
183#452—431no—
184#449D4311yescharacteristic
185#440—431no—
186#440—431no—
187C4×Q16—431no—
188C4×D8—431no—
189#433—431no—
190C43#312411yescharacteristic, complemented, Sylow
191C2×#41C2×D4311yescharacteristic
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16C2×D4311yescharacteristic
195C2×D8C2×D4311yescharacteristic
196C4⋊Q8—431no—
197#126—861no—
198#124—431no—
199#124—861no—
200#123—861no—
201C22⋊Q8—431no—
202C22⋊Q8—861no—
203#121C2×D4311yescharacteristic
204C4×Q8—431no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×D4—431no—
208C4×D4—431no—
209C4×D4—431no—
210C4×D4—861no—
211C4×D4—861no—
212#117—431no—
213#117—861no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216#107—431no—
217#107—431no—
218#107—431no—
219#107—431no—
220C4⋊C8—431no—
221C4⋊C8—431no—
222#103—431no—
223#103—431no—
224#103—431no—
225#103C2×D4311yescharacteristic
226#102—431no—
227#102—431no—
228#102—431no—
229#102C2×D4311yescharacteristic
230C22⋊C8—431no—
231C22⋊C8C2×D4311yescharacteristic
232#97—431no—
233C4×C8—431no—
234#41—22no—
235#41—22no—
236C2×Q8—431no—
237C2×Q8—861no—
238C2×Q8C22×D4311yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C22×D4311yescharacteristic
242C2×D4C22×D4311yescharacteristic
243C22×C4—21no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4C22×D4311yescharacteristic
249Q16—862no—
250SD16—22no—
251SD16—862no—
252D8—22no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8C22×D4311yescharacteristic
256C2×C8C22×D4311yescharacteristic
257C4⋊C4—431no—
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
269C22⋊C4—21no—
270C22⋊C4—431no—
271C22⋊C4—431no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C42—431no—
279C42—431no—
280C42—861no—
281C42—861no—
282C42—861no—
283C23—21no—
284C23—21no—
285C23D4×D4311yescharacteristic
286Q8—21no—
287Q8—861no—
288Q8—861no—
289Q8—3441no—
290Q8#1062190012yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#1062190012yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—431no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—3441no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4—3441no—
314C2×C4D4×D4311yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—861no—
319C8—861no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D4311yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—861no—
334C4—861no—
335C4—861no—
336C4—861no—
337C4—1721no—
338C4—1721no—
339C4—1721no—
340C4—1721no—
341C4C2×#1062190011yescharacteristic
342C4C2×#1062190011yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1458340511yescharacteristic
347C2#1458370311yescharacteristic
348C2#1458371311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3124
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14583516C2semidirect
2. #14583382C2semidirect
3. #14583235C2semidirect
4. #14583210C2semidirect
5. #14583192C2semidirect
6. #14583177C2semidirect
7. #14583119C2semidirect
8. #14583112C2semidirect
9. #14583061C2semidirect
10. #14583000C2semidirect
11. #14582996C2semidirect
12. #14582991C2semidirect
13. D8×Dic43C2semidirect
14. #14582957C2semidirect
190. C43#3124semidirect