Finite Group Databasebeta

← #19146783

Subgroups — #19146783

Order 5504.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583614C211yesmaximal, characteristic, complemented
2#14583558C211yesmaximal, characteristic, complemented
3#14583259C211yesmaximal, characteristic, complemented
4#14583241C211yesmaximal, characteristic, complemented
5#14583224C211yesmaximal, characteristic, complemented
6#14583185C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583128C211yesmaximal, characteristic, complemented
9#14583115C211yesmaximal, characteristic, complemented
10#14583046C211yesmaximal, characteristic, complemented
11#14583040C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13#14582909C211yesmaximal, characteristic, complemented
14#14582896C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×D344C2211yescharacteristic
21#13063325C2211yescharacteristic
22#13063313C2211yescharacteristic
23#13063311—21no—
24#13063311—21no—
25#13063311—21no—
26#13063304C2211yescharacteristic
27#13063303—21no—
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic
30#13063299C2211yescharacteristic
31#13063297—21no—
32#13063296—21no—
33C4×Dic86C2211yescharacteristic
34C4×D172C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36#13063284C2211yescharacteristic
37#13063284C2211yescharacteristic
38#13063283—21no—
39#13063259C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52C2×M16×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×D4×C43D411yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67#10621898—22no—
68#10621898—41no—
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×Dic86—22no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—41no—
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79M16×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43D411yescharacteristic
86C22⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C42×C43C2311yescharacteristic
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
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
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108D344—41no—
109#10621873—22no—
110#10621873—41no—
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115D4×C43—41no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—42no—
126C22⋊D43—42no—
127C22⋊D43—81no—
128C22⋊D43—81no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—42no—
136D172—21no—
137D172—21no—
138D172—21no—
139D172—21no—
140C4×D43—42no—
141C4×D43—42no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—42no—
146Dic86—81no—
147Dic86#4112yes—
148C8×C43—21no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43C22×D411yescharacteristic
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—22no—
172Dic43—41no—
173Dic43—41no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177#3321—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43—41no—
180C2×C43#54611yescharacteristic
181C2×C43#57511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—81no—
184D43—81no—
185#555—431no—
186#548—431no—
187#489—431no—
188#485—431no—
189#482—431no—
190#475—431no—
191#469—431no—
192#465—431no—
193#463—431no—
194#449—431no—
195#448—431no—
196#440—431no—
197#435D4311yescharacteristic, complemented
198#419—431no—
199#416—431no—
200C43#332111yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C22×Q8—431no—
203C2×SD16—431no—
204C2×SD16—431no—
205C2×D8—431no—
206C2×M16C2×D4311yescharacteristic
207C22×C8C2×D4311yescharacteristic
208C4⋊Q8—431no—
209#124—431no—
210#124—861no—
211#124—861no—
212#124—861no—
213C22⋊Q8—431no—
214C22⋊Q8—861no—
215#121—431no—
216#121—431no—
217#121—431no—
218#121—861no—
219#121—861no—
220C4×Q8—431no—
221C4×D4—431no—
222C4×D4—861no—
223C4×D4C2×D4311yescharacteristic
224#117—431no—
225#117—431no—
226#117—861no—
227#107—431no—
228#106—431no—
229#106—431no—
230C4⋊C8C2×D4311yescharacteristic
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241C22⋊C8C2×D4311yescharacteristic
242C22⋊C8C2×D4311yescharacteristic
243#97C2×D4311yescharacteristic
244#41—862no—
245#41—1721no—
246C2×Q8—431no—
247C2×Q8—431no—
248C2×Q8—862no—
249C2×Q8—861no—
250C2×Q8—861no—
251C2×Q8—1721no—
252C2×D4—431no—
253C2×D4—431no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4D17211yescharacteristic
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263C22×C4C22×D4311yescharacteristic
264SD16—862no—
265SD16—1721no—
266D8—1721no—
267M16—41no—
268C2×C8—41no—
269C2×C8C22×D4311yescharacteristic
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4D17211yescharacteristic
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4D17211yescharacteristic
291C22⋊C4D17211yescharacteristic
292C42—861no—
293C42—861no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—861no—
297C23—861no—
298C23C2×D17211yescharacteristic
299C23C2×D17211yescharacteristic
300Q8—432no—
301Q8—861no—
302Q8—861no—
303Q8—861no—
304Q8—3441no—
305Q8—1722no—
306D4—41no—
307D4—861no—
308D4—861no—
309D4—861no—
310D4—861no—
311D4—3441no—
312D4—3441no—
313D4—1722no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—1722no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4C2×D17211yescharacteristic
329C2×C4C2×D17211yescharacteristic
330C2×C4C2×D17211yescharacteristic
331C2×C4C2×D17211yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22C22×D17211yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—862no—
355C4—1721no—
356C4—1721no—
357C4—1721no—
358C4—1721no—
359C4—1721no—
360C4#41×D4311yescharacteristic
361C4#1306337011yescharacteristic
362C2—41no—
363C2—41no—
364C2—3441no—
365C2—3441no—
366C2#1458354411yescharacteristic
367C2#1458369911yescharacteristic
368C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3321
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14583614C2semidirect
2. #14583558C2semidirect
3. #14583259C2semidirect
4. #14583241C2semidirect
5. #14583224C2semidirect
6. #14583185C2semidirect
7. #14583152C2semidirect
8. #14583128C2semidirect
9. #14583115C2semidirect
10. #14583046C2semidirect
11. #14583040C2semidirect
12. #14583001C2semidirect
13. #14582909C2semidirect
14. #14582896C2semidirect
15. C43×#435C2semidirect
197. #435D43semidirect
200. C43#3321semidirect