Finite Group Databasebeta

← #19144824

Subgroups — #19144824

Order 5504.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583520C211yesmaximal, characteristic
2#14583240C211yesmaximal, characteristic, complemented
3#14583223C211yesmaximal, characteristic
4#14583194C211yesmaximal, characteristic, complemented
5#14583184C211yesmaximal, characteristic, complemented
6#14583121C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583055C211yesmaximal, characteristic, complemented
9#14583038C211yesmaximal, characteristic
10#14583004C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12C4×#10621885C211yesmaximal, characteristic, complemented
13C4×#10621884C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#519C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20#13063325C2211yescharacteristic
21#13063320—21no—
22#13063313C2211yescharacteristic
23#13063311—21no—
24#13063307—21no—
25#13063304C2211yescharacteristic
26#13063303—21no—
27#13063299C2211yescharacteristic
28C4×Dic86C2211yescharacteristic
29C4×D172C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35C4⋊(C43⋊C8)C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063249C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48C22×Q8×C43C2211yescharacteristic
49C4×Q8×C43—21no—
50C4×Q8×C43—21no—
51C4×Q8×C43C2211yescharacteristic
52C4×Q8×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55#117×C43—21no—
56#117×C43—21no—
57#117×C43C2211yescharacteristic
58#117×C43C2211yescharacteristic
59C2×Q8×C43—22no—
60C2×Q8×C43—22no—
61C2×Q8×C43—21no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×Dic86—21no—
70C2×Dic86C2311yescharacteristic
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊C4×C43D411yescharacteristic
81C22⋊C4×C43D411yescharacteristic
82C42×C43—21no—
83C42×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43—21no—
87C42×C43C2311yescharacteristic
88C42×C43C2311yescharacteristic
89C22⋊Dic43—21no—
90#10621885—22no—
91#10621885—22no—
92#10621884—22no—
93#10621884—22no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110Q8×C43—24no—
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43#4112yes—
114Q8×C43#4112yes—
115C2×C4×C43—24no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—81no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132D172—21no—
133D172—21no—
134C4×D43—81no—
135Dic86—21no—
136Dic86—21no—
137Dic86—81no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C43⋊C8—21no—
141C43⋊C8—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43C22×D411yescharacteristic
146C2×D43—41no—
147C2×D43—41no—
148C2×D43—41no—
149C4×C43—22no—
150C4×C43—22no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C43C2×#4111yescharacteristic
160Dic43—41no—
161Dic43—41no—
162Dic43—41no—
163#3121—431nomaximal, Sylow
164C2×C43—41no—
165C2×C43#52511yescharacteristic
166C2×C43#57711yescharacteristic
167C2×C43#57811yescharacteristic
168D43—81no—
169#542—431no—
170#519D4311yescharacteristic, complemented
171#485—431no—
172#482—431no—
173#477—431no—
174#475—431no—
175#464—431no—
176#464—431no—
177#451—431no—
178#448—431no—
179#441—431no—
180#440—431no—
181C4×Q16—431no—
182C4×SD16—431no—
183#433—431no—
184C43#312111yescharacteristic, complemented, Sylow
185C22×Q8C2×D4311yescharacteristic
186C2×Q16—431no—
187C2×Q16—431no—
188C2×SD16—431no—
189C2×SD16—431no—
190C4⋊Q8—431no—
191#126—861no—
192#124—431no—
193#124—861no—
194#123—861no—
195C22⋊Q8—431no—
196C22⋊Q8—861no—
197#121—431no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—431no—
201C4×Q8C2×D4311yescharacteristic
202C4×Q8C2×D4311yescharacteristic
203C4×Q8C2×D4311yescharacteristic
204C4×Q8C2×D4311yescharacteristic
205C4×D4—431no—
206#117—21no—
207#117—21no—
208#117C2×D4311yescharacteristic
209#117C2×D4311yescharacteristic
210#107—431no—
211#107—431no—
212#106—431no—
213#106—431no—
214C4⋊C8—431no—
215C4⋊C8—431no—
216#103—431no—
217#103—431no—
218#103—431no—
219#103—431no—
220#103—431no—
221#103—431no—
222#102—431no—
223#102—431no—
224C22⋊C8—431no—
225C22⋊C8—431no—
226#97—431no—
227C4×C8—431no—
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—431no—
232C2×Q8—861no—
233C2×Q8C22×D4311yescharacteristic
234C2×Q8C22×D4311yescharacteristic
235C2×D4—431no—
236C2×D4—861no—
237C22×C4—21no—
238C22×C4—861no—
239C22×C4C22×D4311yescharacteristic
240Q16—862no—
241Q16—862no—
242SD16—862no—
243SD16—862no—
244C2×C8—431no—
245C2×C8—431no—
246C2×C8—431no—
247C2×C8—431no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—431no—
253C4⋊C4—431no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4C22⋊D4311yescharacteristic
258C4⋊C4C22⋊D4311yescharacteristic
259C4⋊C4C22×D4311yescharacteristic
260C4⋊C4C22×D4311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—861no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C22⋊C4—861no—
266C22⋊C4—861no—
267C22⋊C4C22⋊D4311yescharacteristic
268C22⋊C4C22⋊D4311yescharacteristic
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—861no—
275C42C22×D4311yescharacteristic
276C42C22×D4311yescharacteristic
277C23—861no—
278C23C2×C22⋊D4311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—861no—
283Q8—861no—
284Q8—3441no—
285Q8#1062189812yes—
286Q8#1062189812yes—
287D4—861no—
288D4—861no—
289D4—3441no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—3441no—
301C2×C4C2×C22⋊D4311yescharacteristic
302C2×C4C2×C22⋊D4311yescharacteristic
303C2×C4C2×C22⋊D4311yescharacteristic
304C2×C4C2×C22⋊D4311yescharacteristic
305C2×C4C2×C22⋊D4311yescharacteristic
306C2×C4C23×D4311yescharacteristic
307C8—861no—
308C8—861no—
309C8—861no—
310C8—861no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—1721no—
315C22—1721no—
316C22—1721no—
317C22C22×C22⋊D4311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—1721no—
328C4—1721no—
329C4—1721no—
330C4C2×#1062189811yescharacteristic
331C4C2×#1062189811yescharacteristic
332C2—41no—
333C2—3441no—
334C2#1458341011yescharacteristic
335C2#1458370711yescharacteristic
336C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#519C2
socleC22×C43C22×D4
hypercenter#519D43
hypocenterC43#3121
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #14583240C2semidirect
4. #14583194C2semidirect
5. #14583184C2semidirect
6. #14583121C2semidirect
7. #14583121C2semidirect
8. #14583055C2semidirect
10. #14583004C2semidirect
11. #14582997C2semidirect
12. C4×#10621885C2semidirect
13. C4×#10621884C2semidirect
14. #14582960C2semidirect
15. C43×#519C2semidirect
170. #519D43semidirect
184. C43#3121semidirect