Finite Group Databasebeta

← #19146926

Subgroups — #19146926

Order 5504.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583607C211yesmaximal, characteristic, complemented
2#14583568C211yesmaximal, characteristic
3#14583244C211yesmaximal, characteristic, complemented
4#14583213C211yesmaximal, characteristic, complemented
5#14583211C211yesmaximal, characteristic, complemented
6#14583192C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583142C211yesmaximal, characteristic, complemented
9#14583097C211yesmaximal, characteristic, complemented
10#14583060C211yesmaximal, characteristic, complemented
11Q16×Dic43C211yesmaximal, characteristic, complemented
12#14582974C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14#14582899C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621877C2211yescharacteristic
19C2×#10621872C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063321—21no—
22#13063321C2211yescharacteristic
23#13063315—21no—
24#13063305—21no—
25#13063302—21no—
26#13063301C2211yescharacteristic
27#13063299—21no—
28#13063299C2211yescharacteristic
29#13063296—21no—
30#13063296C2211yescharacteristic
31Q8×Dic43C2211yescharacteristic
32Q8×Dic43C2211yescharacteristic
33C4×C22⋊D43—21no—
34C4×C22⋊D43C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43D411yescharacteristic
72C22×Dic43—21no—
73#10621902—22no—
74#10621902—41no—
75C2×D172—21no—
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43C2311yescharacteristic
80C2×Dic86—21no—
81Q16×C43—22no—
82SD16×C43—41no—
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621884—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107#10621877—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43#4112yes—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—42no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—42no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—22no—
131C22⋊D43—42no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—81no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142D172—21no—
143D172—21no—
144D172—42no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—42no—
148C4×D43—81no—
149Dic86—81no—
150C8×C43—21no—
151C8×C43—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C4×C43—22no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178Dic43#13712yes—
179#3333—431nomaximal, Sylow
180C2×C43—41no—
181C2×C43—81no—
182C2×C43#54611yescharacteristic
183C2×C43C2×#13711yescharacteristic
184C2×C43#57611yescharacteristic
185D43—41no—
186D43—81no—
187#554—431no—
188#550—431no—
189#486—431no—
190#480—431no—
191#480—431no—
192#477—431no—
193#468—431no—
194#468—431no—
195#460—431no—
196#452—431no—
197#452D4311yescharacteristic, complemented
198C4×Q16—431no—
199#436—431no—
200#417—431no—
201#417—431no—
202C43#333311yescharacteristic, complemented, Sylow
203C2×#41—431no—
204C2×#41C2×D4311yescharacteristic
205C2×Q16C2×D4311yescharacteristic
206C2×SD16—431no—
207C2×SD16C2×D4311yescharacteristic
208C2×M16—431no—
209C2×M16—431no—
210C4⋊Q8—431no—
211#127—431no—
212#127—861no—
213#125—861no—
214C22⋊Q8—431no—
215C22⋊Q8—861no—
216C22⋊Q8—861no—
217C22⋊Q8C2×D4311yescharacteristic
218#121—431no—
219#121—431no—
220#121—861no—
221#121—861no—
222C4×Q8—431no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—861no—
226C4×D4—861no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229#107—431no—
230#107—431no—
231#107—431no—
232C4⋊C8—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103C2×D4311yescharacteristic
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102C2×D4311yescharacteristic
243C22⋊C8—431no—
244C22⋊C8C2×D4311yescharacteristic
245C4×C8—431no—
246#41—22no—
247#41—41no—
248#41—862no—
249#41—1721no—
250C2×Q8—861no—
251C2×Q8C22×D4311yescharacteristic
252C2×Q8C22×D4311yescharacteristic
253C2×D4—21no—
254C2×D4—431no—
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4C22×D4311yescharacteristic
262C22×C4—21no—
263C22×C4—431no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4C22×D4311yescharacteristic
268Q16—22no—
269SD16—41no—
270SD16—1721no—
271M16—1721no—
272M16—1721no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8C22×D4311yescharacteristic
276C2×C8C22×D4311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—431no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C42—431no—
296C42—861no—
297C42—861no—
298C23—21no—
299C23—431no—
300C23—861no—
301C23D4×D4311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—3441no—
306Q8#1062190012yes—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—862no—
311D4—861no—
312D4—861no—
313D4—3441no—
314D4—3441no—
315D4—3441no—
316D4—1722no—
317D4—1722no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—1722no—
335C2×C4D4×D4311yescharacteristic
336C2×C4C23×D4311yescharacteristic
337C8—21no—
338C8—21no—
339C8—861no—
340C8—861no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22C2×D4×D4311yescharacteristic
354C4—21no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—432no—
359C4—861no—
360C4—861no—
361C4—1721no—
362C4—1721no—
363C4—1721no—
364C4C2×#1062190011yescharacteristic
365C4#1306337011yescharacteristic
366C2—41no—
367C2—81no—
368C2—3441no—
369C2—1721no—
370C2#1458353611yescharacteristic
371C2#137×D4311yescharacteristic
372C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3333
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #14583607C2semidirect
3. #14583244C2semidirect
4. #14583213C2semidirect
5. #14583211C2semidirect
6. #14583192C2semidirect
7. #14583147C2semidirect
8. #14583142C2semidirect
9. #14583097C2semidirect
10. #14583060C2semidirect
11. Q16×Dic43C2semidirect
12. #14582974C2semidirect
13. #14582900C2semidirect
14. #14582899C2semidirect
15. C43×#452C2semidirect
197. #452D43semidirect
202. C43#3333semidirect