Finite Group Databasebeta

← #19146004

Subgroups — #19146004

Order 5504.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583521C211yesmaximal, characteristic, complemented
2#14583503C211yesmaximal, characteristic, complemented
3#14583206C211yesmaximal, characteristic, complemented
4#14583200C211yesmaximal, characteristic, complemented
5#14583187C211yesmaximal, characteristic, complemented
6#14583177C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic, complemented
8#14583142C211yesmaximal, characteristic, complemented
9#14583134C211yesmaximal, characteristic, complemented
10#14583125C211yesmaximal, characteristic, complemented
11#14583116C211yesmaximal, characteristic, complemented
12#14583116C211yesmaximal, characteristic, complemented
13#14583091C211yesmaximal, characteristic, complemented
14#14582924C211yesmaximal, characteristic, complemented
15C43×#460C211yesmaximal, characteristic, complemented
16C2×#10621882C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063319—21no—
22#13063317C2211yescharacteristic
23#13063314C2211yescharacteristic
24#13063313—21no—
25#13063310—21no—
26#13063306—21no—
27#13063306—21no—
28#13063303—21no—
29#13063301C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063297—21no—
32#13063297—21no—
33#13063296C2211yescharacteristic
34#13063296C2211yescharacteristic
35C4×D172C2211yescharacteristic
36D4×Dic43C2211yescharacteristic
37D4×Dic43C2211yescharacteristic
38#13063282C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063256C2211yescharacteristic
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063249C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063246C2211yescharacteristic
51#13063246C2211yescharacteristic
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—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×Dic86—21no—
73SD16×C43—41no—
74SD16×C43—41no—
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43C2311yescharacteristic
79C42×C43—21no—
80C42×C43C2311yescharacteristic
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85#10621882—41no—
86#10621882—41no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4D411yescharacteristic
93(C2×D43)⋊C4D411yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102Dic43⋊C4D411yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—41no—
107C8×D43—41no—
108C23×C43—21no—
109C23×C43—21no—
110C22×D43—21no—
111C22×D43C2×D411yescharacteristic
112Q8×C43—21no—
113Q8×C43—21no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—81no—
119D4×C43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—81no—
126C22⋊D43—81no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—21no—
136D172—21no—
137D172—81no—
138C4×D43—21no—
139C4×D43—21no—
140C4×D43—81no—
141Dic86—81no—
142C8×C43—21no—
143C8×C43—21no—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43H(5,𝔽2)11yescharacteristic
164C4×C432−1+411yescharacteristic
165Dic43—21no—
166Dic43—21no—
167Dic43—21no—
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171#3257—431nomaximal, Sylow
172C2×C43—81no—
173C2×C43—81no—
174C2×C43#53711yescharacteristic
175C2×C43#57611yescharacteristic
176C2×C43#57711yescharacteristic
177D43—41no—
178D43—81no—
179#542—431no—
180#540—431no—
181#479—431no—
182#478—431no—
183#476—431no—
184#474—431no—
185#469—431no—
186#468—431no—
187#466—431no—
188#465—431no—
189#463—431no—
190#463—431no—
191#460D4311yescharacteristic, complemented
192#459—431no—
193#424—431no—
194C43#325711yescharacteristic, complemented, Sylow
195C2×SD16C2×D4311yescharacteristic
196C2×SD16C2×D4311yescharacteristic
197C2×D8—431no—
198C2×D8—431no—
199C2×M16—431no—
200C22×C8—431no—
201C4⋊Q8—431no—
202#127C2×D4311yescharacteristic
203#126—861no—
204#125—431no—
205#124—431no—
206#124—861no—
207#123—861no—
208#123—861no—
209#123—861no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212#121—431no—
213#121—431no—
214#121—431no—
215#121—861no—
216#121—861no—
217C4×Q8C2×D4311yescharacteristic
218C4×D4—431no—
219C4×D4—431no—
220C4×D4—431no—
221#117—431no—
222#107—431no—
223#107—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228C4⋊C8—431no—
229C4⋊C8C2×D4311yescharacteristic
230#103—431no—
231#103—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236#102C2×D4311yescharacteristic
237#102C2×D4311yescharacteristic
238C2×Q8—861no—
239C2×Q8C22×D4311yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—431no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4—861no—
246C2×D4C22×D4311yescharacteristic
247C2×D4C22×D4311yescharacteristic
248C22×C4—431no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252SD16—41no—
253SD16—41no—
254D8—1721no—
255D8—1721no—
256M16—1721no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—1721no—
260C2×C8C22×D4311yescharacteristic
261C2×C8C22×D4311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—431no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4C22×D4311yescharacteristic
273C22⋊C4—431no—
274C22⋊C4—431no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C42—21no—
285C42—431no—
286C42C22×D4311yescharacteristic
287C23—21no—
288C23—21no—
289C23—431no—
290C23—861no—
291Q8—21no—
292Q8—21no—
293Q8—3441no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—861no—
301D4—861no—
302D4—3441no—
303D4—3441no—
304D4—3441no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—431no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4D4×D4311yescharacteristic
319C2×C4D4×D4311yescharacteristic
320C2×C4C23×D4311yescharacteristic
321C8—21no—
322C8—21no—
323C8—861no—
324C8—861no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—861no—
332C22—861no—
333C22—861no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—861no—
343C4—861no—
344C4—861no—
345C4—1721no—
346C4—1721no—
347C4—1721no—
348C4#1306337011yescharacteristic
349C4#1306337211yescharacteristic
350C2—81no—
351C2—81no—
352C2—3441no—
353C2—1721no—
354C2#1458347811yescharacteristic
355C2#1458370311yescharacteristic
356C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3257
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
1. #14583521C2semidirect
2. #14583503C2semidirect
3. #14583206C2semidirect
4. #14583200C2semidirect
5. #14583187C2semidirect
6. #14583177C2semidirect
7. #14583151C2semidirect
8. #14583142C2semidirect
9. #14583134C2semidirect
10. #14583125C2semidirect
11. #14583116C2semidirect
12. #14583116C2semidirect
13. #14583091C2semidirect
14. #14582924C2semidirect
15. C43×#460C2semidirect
191. #460D43semidirect
194. C43#3257semidirect