Finite Group Databasebeta

← #19144607

Subgroups — #19144607

Order 5504.

396 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
1C4×#10621898C211yesmaximal, characteristic, complemented
2#14583237C211yesmaximal, characteristic, complemented
3#14583220C211yesmaximal, characteristic, complemented
4#14583203C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583111C211yesmaximal, characteristic, complemented
8#14583059C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic
10C4×#10621885C211yesmaximal, characteristic, complemented
11C4×#10621884C211yesmaximal, characteristic, complemented
12C4×#10621883C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582952C211yesmaximal, characteristic, complemented
15C43×#529C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25C4×C22⋊D43—21no—
26C4×C22⋊D43—21no—
27#13063284C2211yescharacteristic
28#13063282—21no—
29C42×D43—21no—
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35C4⋊(C43⋊C8)C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C4×C43⋊C8C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48#126×C43—21no—
49#125×C43C2211yescharacteristic
50#124×C43C2211yescharacteristic
51#123×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55C4×D4×C43—21no—
56C4×D4×C43C2211yescharacteristic
57#117×C43—21no—
58C2×C42×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43D411yescharacteristic
64C22×C4×C43D411yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67#10621898—22no—
68#10621898—22no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×Dic86C2311yescharacteristic
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C42×C43—21no—
86C42×C43D411yescharacteristic
87C42×C43D411yescharacteristic
88C42×C43C2311yescharacteristic
89C42×C43C2311yescharacteristic
90C22⋊Dic43—21no—
91#10621885—22no—
92#10621884—22no—
93#10621883—22no—
94#10621882—22no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111Q8×C43—21no—
112Q8×C43—21no—
113D4×C43—21no—
114D4×C43—21no—
115D4×C43—42no—
116C2×C4×C43—22no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—41no—
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×C43C2411yescharacteristic
130C22⋊D43—24no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134D172—21no—
135D172#4112yes—
136C4×D43—24no—
137C4×D43—42no—
138C4×D43—42no—
139Dic86—21no—
140Dic86#4112yes—
141C43⋊C8—21no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43C22×D411yescharacteristic
152C2×D43—22no—
153C2×D43—41no—
154C2×D43—41no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43#13512yes—
163C4×C43C2×#4111yescharacteristic
164C4×C43C2×#4111yescharacteristic
165Dic43—22no—
166Dic43—41no—
167Dic43—41no—
168#3102—431nomaximal, Sylow
169C2×C43—41no—
170C2×C43—81no—
171C2×C43#52511yescharacteristic
172C2×C43C2×#13511yescharacteristic
173C2×C43#57511yescharacteristic
174D43—42no—
175#529D4311yescharacteristic, complemented
176C4×#41—431no—
177#485—431no—
178#482—431no—
179#479—431no—
180#478—431no—
181#464—431no—
182#463—431no—
183#452—431no—
184#449—431no—
185C4×Q16—431no—
186C4×SD16—431no—
187C4×SD16—431no—
188C4×D8—431no—
189#431—431no—
190C43#310211yescharacteristic, complemented, Sylow
191C2×#41—431no—
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×D8—431no—
196#126—21no—
197#125C2×D4311yescharacteristic
198#124C2×D4311yescharacteristic
199#123—21no—
200C22⋊Q8C2×D4311yescharacteristic
201#121C2×D4311yescharacteristic
202C4×Q8—431no—
203C4×Q8—431no—
204C4×Q8C2×D4311yescharacteristic
205C4×D4—21no—
206C4×D4—431no—
207C4×D4—431no—
208C4×D4—861no—
209C4×D4—861no—
210C4×D4C2×D4311yescharacteristic
211#117—21no—
212#117—431no—
213#117—861no—
214C2×C42—861no—
215C2×C42C2×D4311yescharacteristic
216#107—431no—
217#107—431no—
218#106—431no—
219#106—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#102—431no—
229#102—431no—
230C22⋊C8—431no—
231C22⋊C8—431no—
232C4×C8—431no—
233C4×C8—431no—
234#41—862no—
235#41—862no—
236C2×Q8—431no—
237C2×Q8C22×D4311yescharacteristic
238C2×D4—21no—
239C2×D4—431no—
240C2×D4—861no—
241C2×D4C22×D4311yescharacteristic
242C22×C4—21no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4C22⋊D4311yescharacteristic
247C22×C4C22⋊D4311yescharacteristic
248C22×C4C22×D4311yescharacteristic
249Q16—862no—
250SD16—862no—
251SD16—862no—
252D8—862no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8—431no—
256C2×C8—431no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4C22×D4311yescharacteristic
266C4⋊C4C22×D4311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C42—21no—
276C42—861no—
277C42—861no—
278C42—861no—
279C42C22⋊D4311yescharacteristic
280C42C22⋊D4311yescharacteristic
281C42C22×D4311yescharacteristic
282C42C22×D4311yescharacteristic
283C23—21no—
284C23—861no—
285C23C2×C22⋊D4311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—432no—
289Q8—861no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—432no—
294D4—864no—
295D4—861no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—864no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—1722no—
309C2×C4—1722no—
310C2×C4C2×C22⋊D4311yescharacteristic
311C2×C4C2×C22⋊D4311yescharacteristic
312C2×C4C2×C22⋊D4311yescharacteristic
313C2×C4C2×C22⋊D4311yescharacteristic
314C2×C4C2×C22⋊D4311yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—861no—
317C8—861no—
318C8—861no—
319C8—861no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—862no—
327C22—1721no—
328C22—1721no—
329C22C22×C22⋊D4311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—862no—
338C4—1721no—
339C4—1721no—
340C4#1306334512yes—
341C4#41×D4311yescharacteristic
342C4#41×D4311yescharacteristic
343C2—41no—
344C2—81no—
345C2—1722no—
346C2#1458340611yescharacteristic
347C2C2×#1306334511yescharacteristic
348C2#1458369711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#529C2
socleC22×C43C22×D4
hypercenter#529D43
hypocenterC43#3102
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#10621898C2semidirect
2. #14583237C2semidirect
3. #14583220C2semidirect
4. #14583203C2semidirect
5. #14583196C2semidirect
6. #14583118C2semidirect
7. #14583111C2semidirect
8. #14583059C2semidirect
10. C4×#10621885C2semidirect
11. C4×#10621884C2semidirect
12. C4×#10621883C2semidirect
13. C4×#10621882C2semidirect
14. #14582952C2semidirect
15. C43×#529C2semidirect
175. #529D43semidirect
190. C43#3102semidirect