Finite Group Databasebeta

← #19148707

Subgroups — #19148707

Order 5504.

1030 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583634C213yesmaximal, complemented
2#14583615C213yesmaximal, complemented
3#14583602C213yesmaximal, complemented
4#14583587C213yesmaximal, complemented
5#14583571C211yesmaximal, characteristic, complemented
6#14583561C211yesmaximal, characteristic, complemented
7#14583561C211yesmaximal, characteristic, complemented
8#14583523C213yesmaximal, complemented
9#14583505C213yesmaximal, complemented
10#14583436C213yesmaximal, complemented
11#14583434C213yesmaximal, complemented
12#14583381C211yesmaximal, characteristic, complemented
13#14583375C211yesmaximal, characteristic, complemented
14C4×#10621902C211yesmaximal, characteristic, complemented
15C43×#557C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621902C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19#13063322C2213yes—
20#13063320C2216yes—
21#13063320C2213yes—
22#13063320C2211yescharacteristic
23#13063316C2213yes—
24#13063314C2213yes—
25#13063314C2216yes—
26#13063313C2213yes—
27#13063313C2213yes—
28#13063310C2216yes—
29#13063310C2213yes—
30#13063310C2213yes—
31#13063310C2216yes—
32#13063305C2213yes—
33#13063305C2213yes—
34#13063301C2213yes—
35#13063300C2213yes—
36#13063300C2213yes—
37#13063300C2213yes—
38#13063300C2213yes—
39#13063300C2216yes—
40#13063300C2213yes—
41Q8×Dic43C2211yescharacteristic
42C4×Dic86C2213yes—
43#13063290C2213yes—
44C4×D172C2213yes—
45C4×D172C2213yes—
46C4×D172C2213yes—
47C4×D172C2213yes—
48C4×D172C2213yes—
49#13063287C2216yes—
50#13063287C2213yes—
51#13063287C2213yes—
52#13063283C2213yes—
53#13063283C2216yes—
54#13063283C2213yes—
55#13063282C2213yes—
56#13063282C2213yes—
57C4⋊C4×D43C2213yes—
58C42×D43C2213yes—
59C4⋊Q8×C43C2213yes—
60#125×C43C2213yes—
61#125×C43C2213yes—
62C4×Q8×C43C2211yescharacteristic
63C4×Q8×C43C2211yescharacteristic
64C4×Q8×C43C2211yescharacteristic
65C4×Q8×C43C2213yes—
66C2×Q8×C43C2313yes—
67C2×Q8×C43C2311yescharacteristic
68#10621902—24no—
69#10621902—24no—
70Q8×D43—24no—
71C2×D172C2313yes—
72C2×D172C2313yes—
73C2×D172C2316yes—
74C2×D172C2313yes—
75C2×D172C2313yes—
76C2×D172C2313yes—
77C2×C4×D43C2313yes—
78C2×C4×D43C2313yes—
79C2×C4×D43C2313yes—
80C2×C4×D43C2313yes—
81C2×C4×D43C2313yes—
82C2×C4×D43C2316yes—
83C2×Dic86C2313yes—
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2313yes—
86C4⋊C4×C43C2313yes—
87C4⋊C4×C43C2313yes—
88C4⋊C4×C43C2313yes—
89C4⋊C4×C43C2313yes—
90C4⋊C4×C43C2316yes—
91C42×C43C2313yes—
92C42×C43C2313yes—
93C42×C43C2313yes—
94(C2×D43)⋊C4C2311yescharacteristic
95(C2×D43)⋊C4C2313yes—
96(C2×D43)⋊C4C2313yes—
97(C2×D43)⋊C4C2313yes—
98(C2×D43)⋊C4C2313yes—
99(C2×D43)⋊C4C2316yes—
100(C2×D43)⋊C4C2316yes—
101(C2×D43)⋊C4C2313yes—
102(C2×D43)⋊C4C2316yes—
103(C2×D43)⋊C4C2311yescharacteristic
104(C2×D43)⋊C4C2311yescharacteristic
105(C2×D43)⋊C4C2313yes—
106(C2×D43)⋊C4C2313yes—
107C4⋊Dic43C2313yes—
108C4⋊Dic43C2313yes—
109C4⋊Dic43C2311yescharacteristic
110C4⋊Dic43C2313yes—
111Dic43⋊C4C2313yes—
112Dic43⋊C4C2311yescharacteristic
113Dic43⋊C4C2313yes—
114Dic43⋊C4C2313yes—
115C4×Dic43C2311yescharacteristic
116C4×Dic43C2313yes—
117C4×Dic43C2313yes—
118C4×Dic43C2316yes—
119C22×D43C2411yescharacteristic
120C22×D43C2413yes—
121C22×D43C2413yes—
122Q8×C43—43no—
123Q8×C43#4114yes—
124C2×C4×C43C2413yes—
125C2×C4×C43C2413yes—
126C2×C4×C43C2411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C2×C4×C43C2413yes—
129C2×C4×C43C2411yescharacteristic
130C2×C4×C43C2413yes—
131C2×Dic43C2411yescharacteristic
132C2×Dic43C2413yes—
133C2×Dic43C2411yescharacteristic
134C2×Dic43C2413yes—
135C2×Dic43C2411yescharacteristic
136D172—26no—
137D172—26no—
138D172—43no—
139D172—43no—
140D172—43no—
141D172—46no—
142C4×D43—26no—
143C4×D43—26no—
144C4×D43—26no—
145C4×D43—43no—
146C4×D43—46no—
147C4×D43—43no—
148Dic86—26no—
149C22×C43C2511yescharacteristic
150C2×D43—21no—
151C2×D43—23no—
152C2×D43—23no—
153C2×D43—23no—
154C2×D43—23no—
155C2×D43—23no—
156C2×D43—21no—
157C2×D43—23no—
158C2×D43—21no—
159C4×C43—21no—
160C4×C43—23no—
161C4×C43—23no—
162C4×C43—21no—
163C4×C43—23no—
164C4×C43—21no—
165C4×C43C2×#4116yes—
166Dic43—23no—
167Dic43—21no—
168Dic43—21no—
169Dic43—21no—
170Dic43—23no—
171#3524—431nomaximal, Sylow
172C2×C43C22×#4111yescharacteristic
173C2×C43#58511yescharacteristic
174C2×C43#58511yescharacteristic
175D43—41no—
176D43—43no—
177D43—43no—
178#559—433no—
179#557D4311yescharacteristic, complemented
180#555—433no—
181#553—433no—
182#552—433no—
183#550—431no—
184#548—431no—
185#548—431no—
186#542—433no—
187#540—433no—
188#529—433no—
189#529—433no—
190#520—431no—
191#519—431no—
192C4×#41—431no—
193C43#352411yescharacteristic, complemented, Sylow
194C2×#41—431no—
195C2×#41—431no—
196C22×Q8—431no—
197C4⋊Q8C2×D4313yes—
198#127—433no—
199#126—431no—
200#126—433no—
201#126—436no—
202#125—433no—
203#125C2×D4313yes—
204#125C2×D4313yes—
205#124—433no—
206#124—436no—
207#124—433no—
208#124—433no—
209#123—436no—
210#123—433no—
211#123—433no—
212#123—436no—
213C22⋊Q8—433no—
214C22⋊Q8—433no—
215C22⋊Q8—433no—
216#121—433no—
217#121—433no—
218#121—433no—
219#121—433no—
220#121—436no—
221#121—433no—
222C4×Q8—431no—
223C4×Q8—433no—
224C4×Q8—433no—
225C4×Q8C2×D4311yescharacteristic
226C4×Q8C2×D4311yescharacteristic
227C4×Q8C2×D4311yescharacteristic
228C4×Q8C2×D4313yes—
229C4×D4—433no—
230C4×D4—433no—
231C4×D4—436no—
232C4×D4—433no—
233C4×D4—433no—
234C4×D4—433no—
235C4×D4—433no—
236C4×D4—433no—
237#117—433no—
238#117—433no—
239#117—436no—
240#117—433no—
241#117—433no—
242C2×C4⋊C4—433no—
243C2×C42—433no—
244#41—864no—
245#41—864no—
246C2×Q8—433no—
247C2×Q8—864no—
248C2×Q8C22×D4313yes—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—433no—
251C2×D4—433no—
252C2×D4—433no—
253C2×D4—433no—
254C2×D4—436no—
255C2×D4—433no—
256C22×C4—433no—
257C22×C4—433no—
258C22×C4—433no—
259C22×C4—433no—
260C22×C4—433no—
261C22×C4—436no—
262C4⋊C4—433no—
263C4⋊C4—433no—
264C4⋊C4—431no—
265C4⋊C4—433no—
266C4⋊C4—433no—
267C4⋊C4—433no—
268C4⋊C4—431no—
269C4⋊C4—433no—
270C4⋊C4C22×D4313yes—
271C4⋊C4C22×D4313yes—
272C4⋊C4C22×D4313yes—
273C4⋊C4C22×D4316yes—
274C4⋊C4C22×D4313yes—
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4313yes—
277C22⋊C4—431no—
278C22⋊C4—433no—
279C22⋊C4—433no—
280C22⋊C4—433no—
281C22⋊C4—436no—
282C22⋊C4—433no—
283C22⋊C4—436no—
284C22⋊C4—431no—
285C22⋊C4—433no—
286C22⋊C4—431no—
287C22⋊C4—433no—
288C22⋊C4—436no—
289C22⋊C4—433no—
290C42—431no—
291C42—433no—
292C42—433no—
293C42—436no—
294C42C22×D4313yes—
295C42C22×D4313yes—
296C42C22×D4313yes—
297C23—431no—
298C23—433no—
299C23—433no—
300Q8—43no—
301Q8—866no—
302Q8#1062190214yes—
303D4—866no—
304D4—866no—
305D4—1723no—
306D4—1726no—
307D4—1723no—
308D4—1723no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—433no—
312C2×C4—433no—
313C2×C4—431no—
314C2×C4—866no—
315C2×C4—866no—
316C2×C4—866no—
317C2×C4—1723no—
318C2×C4—1723no—
319C2×C4—1726no—
320C2×C4C23×D4313yes—
321C2×C4C23×D4311yescharacteristic
322C2×C4C23×D4313yes—
323C2×C4C23×D4311yescharacteristic
324C2×C4C23×D4311yescharacteristic
325C2×C4C23×D4313yes—
326C2×C4C23×D4313yes—
327C22—861no—
328C22—863no—
329C22—863no—
330C22—863no—
331C22—861no—
332C22—863no—
333C22—863no—
334C22—863no—
335C22—861no—
336C22C24×D4311yescharacteristic
337C4—23no—
338C4—23no—
339C4—21no—
340C4—21no—
341C4—23no—
342C4—21no—
343C4—861no—
344C4—861no—
345C4—863no—
346C4—861no—
347C4—863no—
348C4C2×#1062190216yes—
349C2—1721no—
350C2—1723no—
351C2—1723no—
352C2C22×#1062190211yescharacteristic
353C2#1458373511yescharacteristic
354C2#1458373611yescharacteristic
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×#557C2
hypercenter#557D43
hypocenterC43#3524
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #14583634C2semidirect
2. #14583615C2semidirect
3. #14583602C2semidirect
4. #14583587C2semidirect
5. #14583571C2semidirect
6. #14583561C2semidirect
7. #14583561C2semidirect
8. #14583523C2semidirect
9. #14583505C2semidirect
10. #14583436C2semidirect
11. #14583434C2semidirect
12. #14583381C2semidirect
13. #14583375C2semidirect
14. C4×#10621902C2semidirect
15. C43×#557C2semidirect
179. #557D43semidirect
193. C43#3524semidirect