Finite Group Databasebeta

← #19147670

Subgroups — #19147670

Order 5504.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583622C211yesmaximal, characteristic, complemented
2#14583294C211yesmaximal, characteristic, complemented
3#14583291C211yesmaximal, characteristic, complemented
4#14583281C211yesmaximal, characteristic
5#14583121C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic
8#14583111C211yesmaximal, characteristic
9#14583109C211yesmaximal, characteristic, complemented
10#14583106C211yesmaximal, characteristic, complemented
11#14583030C211yesmaximal, characteristic, complemented
12#14582999C211yesmaximal, characteristic, complemented
13#14582997C211yesmaximal, characteristic, complemented
14C4×#10621885C211yesmaximal, characteristic, complemented
15C43×#556C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621884C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25#13063325C2211yescharacteristic
26#13063320—21no—
27#13063320—21no—
28#13063313C2211yescharacteristic
29#13063313C2211yescharacteristic
30#13063301—21no—
31C4×Dic86C2211yescharacteristic
32C4×Dic86C2211yescharacteristic
33C4×D172C2211yescharacteristic
34#13063283—21no—
35#13063258C2211yescharacteristic
36C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊(C43⋊C8)C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063248C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063236C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48C4⋊Q8×C43C2211yescharacteristic
49#126×C43—21no—
50#126×C43—21no—
51#124×C43C2211yescharacteristic
52#124×C43C2211yescharacteristic
53C22⋊Q8×C43—21no—
54C4×Q8×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58#117×C43—21no—
59C2×Q8×C43D411yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C2×D172C2311yescharacteristic
65C2×C4×D43—21no—
66C2×Dic86C2311yescharacteristic
67C2×Dic86C2311yescharacteristic
68C4⋊C4×C43—21no—
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43D411yescharacteristic
73C4⋊C4×C43D411yescharacteristic
74C4⋊C4×C43D411yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C22⋊C4×C43—21no—
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C42×C43—21no—
82C42×C43—21no—
83C42×C43C2311yescharacteristic
84C42×C43C2311yescharacteristic
85C42×C43C2311yescharacteristic
86#10621885—22no—
87#10621885—41no—
88#10621885—41no—
89#10621885—41no—
90#10621884—22no—
91#10621884—41no—
92#10621883—22no—
93#10621883—41no—
94#10621882—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C22×D43—21no—
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—41no—
118D4×C43—21no—
119D4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134D172—21no—
135D172—21no—
136C4×D43—42no—
137Dic86—21no—
138Dic86—21no—
139Dic86—21no—
140Dic86—21no—
141C43⋊C8—21no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C43⋊C8#4112yes—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43C22×D411yescharacteristic
149C2×D43—41no—
150C2×D43—41no—
151C2×D43—41no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43C2×#4111yescharacteristic
162C4×C43H(5,𝔽2)11yescharacteristic
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166#3402—431nomaximal, Sylow
167C2×C43—81no—
168C2×C43#55011yescharacteristic
169C2×C43#57511yescharacteristic
170C2×C43#57811yescharacteristic
171D43—81no—
172#556—431no—
173#556D4311yescharacteristic, complemented
174#497—431no—
175#497—431no—
176#495—431no—
177#464—431no—
178#464—431no—
179#463—431no—
180#463—431no—
181#462—431no—
182#462—431no—
183#446—431no—
184#440—431no—
185#440—431no—
186C4×Q16—431no—
187C43#340211yescharacteristic, complemented, Sylow
188C2×Q16—431no—
189C2×Q16—431no—
190C2×Q16—431no—
191C2×Q16—431no—
192C2×SD16—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×SD16—431no—
196C2×D8—431no—
197C4⋊Q8—431no—
198C4⋊Q8C2×D4311yescharacteristic
199#126—21no—
200#126—21no—
201#126—861no—
202#126—861no—
203#124—431no—
204#124—431no—
205#124C2×D4311yescharacteristic
206#124C2×D4311yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—861no—
209C4×Q8—431no—
210C4×Q8—431no—
211C4×Q8C2×D4311yescharacteristic
212C4×Q8C2×D4311yescharacteristic
213C4×Q8C2×D4311yescharacteristic
214C4×D4—431no—
215C4×D4C2×D4311yescharacteristic
216#117—21no—
217#117—861no—
218#107—431no—
219C4⋊C8—431no—
220C4⋊C8—431no—
221C4⋊C8—431no—
222#103—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#102—431no—
227#102—431no—
228#97—431no—
229#97—431no—
230C4×C8—431no—
231C2×Q8—431no—
232C2×Q8—431no—
233C2×Q8C22⋊D4311yescharacteristic
234C2×Q8C22×D4311yescharacteristic
235C2×Q8C22×D4311yescharacteristic
236C2×D4—431no—
237C2×D4C22×D4311yescharacteristic
238C22×C4—21no—
239C22×C4—861no—
240Q16—862no—
241Q16—1721no—
242Q16—1721no—
243Q16—1721no—
244SD16—862no—
245SD16—862no—
246SD16—1721no—
247SD16—1721no—
248D8—1721no—
249C2×C8—431no—
250C2×C8—431no—
251C2×C8—431no—
252C2×C8—431no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—431no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4C22⋊D4311yescharacteristic
263C4⋊C4C22⋊D4311yescharacteristic
264C4⋊C4C22⋊D4311yescharacteristic
265C4⋊C4C22×D4311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C42—21no—
277C42—21no—
278C42—861no—
279C42—861no—
280C42C22×D4311yescharacteristic
281C42C22×D4311yescharacteristic
282C42C22×D4311yescharacteristic
283C23—21no—
284C23—861no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—861no—
291Q8—861no—
292Q8—861no—
293Q8—861no—
294D4—21no—
295D4—21no—
296D4—861no—
297D4—861no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—1722no—
306C2×C4C2×C22⋊D4311yescharacteristic
307C2×C4C2×C22⋊D4311yescharacteristic
308C2×C4C2×C22⋊D4311yescharacteristic
309C2×C4C2×C22⋊D4311yescharacteristic
310C2×C4C2×C22⋊D4311yescharacteristic
311C2×C4C2×C22⋊D4311yescharacteristic
312C2×C4C23×D4311yescharacteristic
313C8—432no—
314C8—861no—
315C8—861no—
316C8—861no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—1721no—
321C22—1721no—
322C22—1721no—
323C22C22×C22⋊D4311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1721no—
334C4—1721no—
335C4—1721no—
336C4#41×D4311yescharacteristic
337C4#1306337111yescharacteristic
338C2—81no—
339C2—3441no—
340C2#1458356811yescharacteristic
341C2#1458369711yescharacteristic
342C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#556C2
socleC22×C43C22×D4
hypercenter#556D43
hypocenterC43#3402
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #14583622C2semidirect
2. #14583294C2semidirect
3. #14583291C2semidirect
5. #14583121C2semidirect
6. #14583118C2semidirect
9. #14583109C2semidirect
10. #14583106C2semidirect
11. #14583030C2semidirect
12. #14582999C2semidirect
13. #14582997C2semidirect
14. C4×#10621885C2semidirect
15. C43×#556C2semidirect
173. #556D43semidirect
187. C43#3402semidirect