Finite Group Databasebeta

← #19147110

Subgroups — #19147110

Order 5504.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583589C211yesmaximal, characteristic, complemented
2#14583305C211yesmaximal, characteristic, complemented
3#14583240C211yesmaximal, characteristic, complemented
4#14583240C211yesmaximal, characteristic, complemented
5#14583220C211yesmaximal, characteristic, complemented
6#14583215C211yesmaximal, characteristic, complemented
7#14583199C211yesmaximal, characteristic, complemented
8#14583181C211yesmaximal, characteristic, complemented
9#14583143C211yesmaximal, characteristic, complemented
10#14583126C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582942C211yesmaximal, characteristic, complemented
14#14582935C211yesmaximal, characteristic, complemented
15C43×#555C211yesmaximal, characteristic
16C2×#10621883C2211yescharacteristic
17C2×#10621877C2211yescharacteristic
18C22×C43⋊C8C2211yescharacteristic
19#13063318—21no—
20#13063317C2211yescharacteristic
21#13063315—21no—
22#13063306—21no—
23#13063304C2211yescharacteristic
24#13063304C2211yescharacteristic
25C4×Dic86C2211yescharacteristic
26#13063284C2211yescharacteristic
27#13063281—21no—
28C2×C4⋊Dic43C2211yescharacteristic
29#13063258C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063256C2211yescharacteristic
34#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063256C2211yescharacteristic
37#13063256C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063246C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C4⋊Q8×C43C2211yescharacteristic
49#124×C43—21no—
50#124×C43—21no—
51#121×C43—21no—
52#121×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic
56#117×C43—21no—
57#117×C43C2211yescharacteristic
58#117×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43D411yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×Dic43—21no—
68C2×Dic86C2311yescharacteristic
69C4⋊C4×C43—21no—
70C4⋊C4×C43D411yescharacteristic
71C4⋊C4×C43C2311yescharacteristic
72C4⋊C4×C43C2311yescharacteristic
73C4⋊C4×C43C2311yescharacteristic
74C22⋊C4×C43—21no—
75C22⋊C4×C43—21no—
76C22⋊C4×C43—21no—
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C22⋊C4×C43D411yescharacteristic
80C22⋊C4×C43D411yescharacteristic
81C42×C43—21no—
82C42×C43—21no—
83C42×C43C2311yescharacteristic
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87#10621883—22no—
88C4⋊Dic43—21no—
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99#10621877—22no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C23×C43—21no—
106C23×C43C2×D411yescharacteristic
107C23×C43C2×D411yescharacteristic
108Q8×C43—81no—
109D4×C43—21no—
110D4×C43—21no—
111D4×C43—41no—
112D4×C43—81no—
113D4×C43—81no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—42no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—42no—
132Dic86—21no—
133Dic86—21no—
134C43⋊C8—21no—
135C43⋊C8—21no—
136C43⋊C8—21no—
137C43⋊C8#4112yes—
138C22×C43—21no—
139C22×C43—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43C22×D411yescharacteristic
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43—41no—
155C4×C43C2×#4111yescharacteristic
156C4×C432−1+411yescharacteristic
157Dic43—41no—
158Dic43—41no—
159Dic43—41no—
160Dic43—41no—
161#3348—431nomaximal, Sylow
162C2×C43—41no—
163C2×C43—41no—
164C2×C43—81no—
165C2×C43#54711yescharacteristic
166C2×C43#57511yescharacteristic
167C2×C43#57711yescharacteristic
168#555D4311yescharacteristic
169#552—431no—
170#501—431no—
171#485—431no—
172#485—431no—
173#482—431no—
174#481—431no—
175#478—431no—
176#475—431no—
177#468—431no—
178#465—431no—
179#440—431no—
180#435—431no—
181#428—431no—
182#427—431no—
183C43#334811yescharacteristic, complemented, Sylow
184C2×SD16—431no—
185C2×M16—431no—
186C22×C8—431no—
187C4⋊Q8C2×D4311yescharacteristic
188#126—861no—
189#125—431no—
190#125—861no—
191#124—21no—
192#124—21no—
193#123—861no—
194C22⋊Q8—431no—
195C22⋊Q8—431no—
196#121—21no—
197#121C2×D4311yescharacteristic
198#121C2×D4311yescharacteristic
199C4×Q8—431no—
200C4×D4C2×D4311yescharacteristic
201C4×D4C2×D4311yescharacteristic
202#117—21no—
203#117—431no—
204#117—861no—
205#117C2×D4311yescharacteristic
206#117C2×D4311yescharacteristic
207C2×C4⋊C4—431no—
208#107—431no—
209#107—431no—
210#107—431no—
211#107—431no—
212#106—431no—
213#106—431no—
214#106—431no—
215#106—431no—
216#106—431no—
217C4⋊C8—431no—
218#103—431no—
219#103—431no—
220#103—431no—
221#102—431no—
222#102—431no—
223#102—431no—
224C22⋊C8—431no—
225C22⋊C8—431no—
226#97—431no—
227C2×Q8—21no—
228C2×Q8—431no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C22⋊D4311yescharacteristic
232C2×D4C22×D4311yescharacteristic
233C22×C4—21no—
234C22×C4—861no—
235C22×C4C22×D4311yescharacteristic
236C22×C4C22×D4311yescharacteristic
237SD16—862no—
238M16—862no—
239C2×C8—431no—
240C2×C8—431no—
241C2×C8—431no—
242C2×C8—431no—
243C2×C8—862no—
244C4⋊C4—21no—
245C4⋊C4—431no—
246C4⋊C4—431no—
247C4⋊C4—431no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4C22⋊D4311yescharacteristic
255C4⋊C4C22×D4311yescharacteristic
256C4⋊C4C22×D4311yescharacteristic
257C4⋊C4C22×D4311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C22⋊C4—861no—
266C22⋊C4C22⋊D4311yescharacteristic
267C22⋊C4C22⋊D4311yescharacteristic
268C42—21no—
269C42—21no—
270C42—861no—
271C42—861no—
272C42C22×D4311yescharacteristic
273C23—21no—
274C23C2×C22⋊D4311yescharacteristic
275C23C2×C22⋊D4311yescharacteristic
276Q8—81no—
277Q8—861no—
278Q8—861no—
279D4—21no—
280D4—21no—
281D4—41no—
282D4—81no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—1722no—
297C2×C4C2×C22⋊D4311yescharacteristic
298C2×C4C2×C22⋊D4311yescharacteristic
299C2×C4C2×C22⋊D4311yescharacteristic
300C2×C4C2×C22⋊D4311yescharacteristic
301C2×C4C23×D4311yescharacteristic
302C8—432no—
303C8—861no—
304C8—861no—
305C8—861no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C22×C22⋊D4311yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—1721no—
324C4—1721no—
325C4—1721no—
326C4—1721no—
327C4#41×D4311yescharacteristic
328C4#1306337211yescharacteristic
329C2—41no—
330C2—41no—
331C2—81no—
332C2#1458354811yescharacteristic
333C2#1458369711yescharacteristic
334C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#555C2
socleC22×C43C22×D4
hypercenter#555D43
hypocenterC43#3348
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #14583589C2semidirect
2. #14583305C2semidirect
3. #14583240C2semidirect
4. #14583240C2semidirect
5. #14583220C2semidirect
6. #14583215C2semidirect
7. #14583199C2semidirect
8. #14583181C2semidirect
9. #14583143C2semidirect
10. #14583126C2semidirect
11. #14582999C2semidirect
12. #14582971C2semidirect
13. #14582942C2semidirect
14. #14582935C2semidirect
183. C43#3348semidirect