Finite Group Databasebeta

← #19144884

Subgroups — #19144884

Order 5504.

382 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
1#14583503C211yesmaximal, characteristic
2#14583375C211yesmaximal, characteristic, complemented
3#14583222C211yesmaximal, characteristic, complemented
4#14583221C211yesmaximal, characteristic, complemented
5#14583207C211yesmaximal, characteristic, complemented
6#14583206C211yesmaximal, characteristic, complemented
7#14583096C211yesmaximal, characteristic, complemented
8#14583036C211yesmaximal, characteristic, complemented
9#14583036C211yesmaximal, characteristic, complemented
10#14583000C211yesmaximal, characteristic, complemented
11#14582996C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13SD16×Dic43C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#460C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19#13063317C2211yescharacteristic
20#13063306—21no—
21#13063306—21no—
22#13063297—21no—
23#13063297—21no—
24#13063296C2211yescharacteristic
25#13063296C2211yescharacteristic
26Q8×Dic43C2211yescharacteristic
27C4×Dic86—21no—
28C4×Dic86C2211yescharacteristic
29#13063290—21no—
30#13063290C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32D4×Dic43C2211yescharacteristic
33#13063283—21no—
34#13063283C2211yescharacteristic
35#13063282—21no—
36#13063282C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54#127×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67C22×Dic43—21no—
68Q8×D43—22no—
69Q8×D43—22no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×Dic86—21no—
73C2×Dic86C2311yescharacteristic
74SD16×C43—22no—
75SD16×C43—22no—
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C42×C43—21no—
81C42×C43C2311yescharacteristic
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86#10621883—22no—
87#10621883—22no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4D411yescharacteristic
90(C2×D43)⋊C4D411yescharacteristic
91C4⋊Dic43—21no—
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4D411yescharacteristic
100Dic43⋊C4D411yescharacteristic
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43—21no—
110C22×D43C2×D411yescharacteristic
111Q8×C43—21no—
112Q8×C43#4112yes—
113D4×C43—21no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—81no—
118D4×C43—81no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C22⋊D43—81no—
125C22⋊D43—81no—
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135C4×D43—24no—
136C4×D43—21no—
137C4×D43—21no—
138Dic86—24no—
139Dic86—21no—
140Dic86#4112yes—
141C8×C43—21no—
142C8×C43—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43C22×D411yescharacteristic
152C2×D43—21no—
153C2×D43—21no—
154C2×D43—21no—
155C4×C43—22no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C43C2×#4111yescharacteristic
161Dic43—21no—
162Dic43—22no—
163Dic43—21no—
164Dic43—21no—
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168#3126—431nomaximal, Sylow
169C2×C43—81no—
170C2×C43—81no—
171C2×C43#52511yescharacteristic
172C2×C43#57711yescharacteristic
173C2×C43#57711yescharacteristic
174D43—41no—
175#540—431no—
176#519—431no—
177#482—431no—
178#482—431no—
179#479—431no—
180#479—431no—
181#460—431no—
182#460D4311yescharacteristic, complemented
183#448—431no—
184#448—431no—
185#440—431no—
186#440—431no—
187C4×SD16—431no—
188C4×SD16—431no—
189#433—431no—
190C43#312611yescharacteristic, complemented, Sylow
191C22×Q8—431no—
192C2×SD16—431no—
193C2×SD16—431no—
194C2×SD16C2×D4311yescharacteristic
195C2×SD16C2×D4311yescharacteristic
196#127C2×D4311yescharacteristic
197#125—431no—
198#123—861no—
199#123—861no—
200#121—431no—
201#121—431no—
202#121—861no—
203#121—861no—
204C4×Q8—431no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×Q8—861no—
208C4×Q8—861no—
209C4×Q8C2×D4311yescharacteristic
210C4×D4—431no—
211C4×D4—431no—
212#117—431no—
213#117—431no—
214#117—861no—
215#117—861no—
216#107—431no—
217#107—431no—
218#106—431no—
219#106—431no—
220C4⋊C8—431no—
221C4⋊C8C2×D4311yescharacteristic
222#103—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#102—431no—
227#102—431no—
228#102C2×D4311yescharacteristic
229#102C2×D4311yescharacteristic
230C22⋊C8—431no—
231C22⋊C8—431no—
232#97—431no—
233C4×C8—431no—
234C2×Q8—431no—
235C2×Q8—861no—
236C2×Q8—862no—
237C2×Q8—862no—
238C2×Q8C22×D4311yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—861no—
242C2×D4—861no—
243C2×D4C22×D4311yescharacteristic
244C2×D4C22×D4311yescharacteristic
245C22×C4—431no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249SD16—22no—
250SD16—22no—
251SD16—862no—
252SD16—862no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8C22×D4311yescharacteristic
256C2×C8C22×D4311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4C22×D4311yescharacteristic
269C22⋊C4—431no—
270C22⋊C4—431no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C42—21no—
277C42—431no—
278C42—861no—
279C42—861no—
280C42—861no—
281C42—861no—
282C42C22×D4311yescharacteristic
283C23—21no—
284C23—21no—
285C23—431no—
286Q8—21no—
287Q8—432no—
288Q8—864no—
289Q8—861no—
290Q8#1062190012yes—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4—81no—
297D4—3441no—
298D4—3441no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—431no—
302C2×C4—431no—
303C2×C4—431no—
304C2×C4—864no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4D4×D4311yescharacteristic
314C2×C4D4×D4311yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—861no—
319C8—861no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—861no—
327C22—861no—
328C22—861no—
329C22C2×D4×D4311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—861no—
335C4—862no—
336C4—861no—
337C4—861no—
338C4—1721no—
339C4—1721no—
340C4—1721no—
341C4#41×D4311yescharacteristic
342C4C2×#1062190011yescharacteristic
343C2—81no—
344C2—81no—
345C2—1721no—
346C2#1458340911yescharacteristic
347C2#1458370511yescharacteristic
348C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3126
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #14583375C2semidirect
3. #14583222C2semidirect
4. #14583221C2semidirect
5. #14583207C2semidirect
6. #14583206C2semidirect
7. #14583096C2semidirect
8. #14583036C2semidirect
9. #14583036C2semidirect
10. #14583000C2semidirect
11. #14582996C2semidirect
12. #14582990C2semidirect
13. SD16×Dic43C2semidirect
14. #14582959C2semidirect
15. C43×#460C2semidirect
182. #460D43semidirect
190. C43#3126semidirect