Finite Group Databasebeta

← #19145708

Subgroups — #19145708

Order 5504.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583522C211yesmaximal, characteristic, complemented
2#14583470C211yesmaximal, characteristic, complemented
3#14583292C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583257C211yesmaximal, characteristic, complemented
6#14583248C211yesmaximal, characteristic, complemented
7#14583119C211yesmaximal, characteristic, complemented
8#14583113C211yesmaximal, characteristic, complemented
9#14583107C211yesmaximal, characteristic, complemented
10#14583103C211yesmaximal, characteristic, complemented
11#14583054C211yesmaximal, characteristic, complemented
12#14583044C211yesmaximal, characteristic
13#14583040C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23#13063324C2211yescharacteristic
24#13063323C2211yescharacteristic
25#13063323C2211yescharacteristic
26#13063320—21no—
27#13063314C2211yescharacteristic
28#13063312C2211yescharacteristic
29#13063312C2211yescharacteristic
30#13063311—21no—
31#13063307—21no—
32#13063306—21no—
33#13063306—21no—
34#13063305—21no—
35#13063304—21no—
36#13063304—21no—
37#13063299C2211yescharacteristic
38Q8×Dic43C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063284C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
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—41no—
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—
68C22×Dic43—21no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×Dic86—21no—
72C2×Dic86—21no—
73C2×Dic86—41no—
74C2×Dic86—41no—
75C2×Dic86C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77Q16×C43—41no—
78SD16×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43D411yescharacteristic
89C22⋊Dic43D411yescharacteristic
90#10621885—41no—
91#10621885—41no—
92#10621884—41no—
93#10621882—41no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43D411yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107C4×Dic43—21no—
108C4×Dic43C2311yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112#10621873—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117Q8×C43—21no—
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—42no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—81no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—42no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141D172—21no—
142D172—21no—
143C4×D43—81no—
144Dic86—21no—
145Dic86—21no—
146Dic86—21no—
147Dic86—21no—
148Dic86—42no—
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—41no—
162C2×D43—41no—
163C2×D43—41no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43H(5,𝔽2)11yescharacteristic
169C4×C43H(5,𝔽2)11yescharacteristic
170Dic43—21no—
171Dic43—21no—
172Dic43—21no—
173Dic43—21no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177#3225—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43—81no—
180C2×C43#53511yescharacteristic
181C2×C43#57711yescharacteristic
182C2×C43#57811yescharacteristic
183D43—81no—
184#542—431no—
185#536—431no—
186#497—431no—
187#495—431no—
188#489—431no—
189#487—431no—
190#464—431no—
191#463—431no—
192#462—431no—
193#461—431no—
194#452D4311yescharacteristic, complemented
195#451—431no—
196#449—431no—
197#448—431no—
198#433—431no—
199C43#322511yescharacteristic, complemented, Sylow
200C2×#41C2×D4311yescharacteristic
201C22×Q8—431no—
202C2×Q16—431no—
203C2×Q16—431no—
204C2×Q16C2×D4311yescharacteristic
205C2×SD16—431no—
206C2×SD16—431no—
207C2×SD16—431no—
208C2×SD16C2×D4311yescharacteristic
209C2×D8—431no—
210C4⋊Q8—431no—
211C4⋊Q8—431no—
212C4⋊Q8—431no—
213#126—861no—
214#124—431no—
215#124—431no—
216#124—431no—
217#124—861no—
218#123—861no—
219#123—861no—
220#123—861no—
221C22⋊Q8—861no—
222C22⋊Q8—861no—
223C22⋊Q8—861no—
224C22⋊Q8C2×D4311yescharacteristic
225#121—431no—
226C4×Q8—431no—
227C4×D4—431no—
228#117—431no—
229C4⋊C8—431no—
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103C2×D4311yescharacteristic
237#102—431no—
238#102C2×D4311yescharacteristic
239C22⋊C8—431no—
240C22⋊C8C2×D4311yescharacteristic
241#97—431no—
242C4×C8—431no—
243#41—41no—
244#41—41no—
245C2×Q8—431no—
246C2×Q8—431no—
247C2×Q8—861no—
248C2×Q8—861no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8C22×D4311yescharacteristic
252C2×Q8C22×D4311yescharacteristic
253C2×D4—21no—
254C2×D4—431no—
255C2×D4—861no—
256C2×D4C22×D4311yescharacteristic
257C22×C4—21no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4C22×D4311yescharacteristic
261Q16—41no—
262Q16—1721no—
263Q16—1721no—
264SD16—41no—
265SD16—1721no—
266SD16—1721no—
267SD16—1721no—
268D8—1721no—
269C2×C8—431no—
270C2×C8—431no—
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—431no—
286C22⋊C4—431no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C42—431no—
296C42—431no—
297C42—861no—
298C23—21no—
299C23—861no—
300C23D4×D4311yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—861no—
306Q8—861no—
307Q8—861no—
308Q8—861no—
309Q8—3441no—
310Q8—1722no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—861no—
315D4—861no—
316D4—3441no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—3441no—
331C2×C4—1722no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C2×D4×D4311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—861no—
353C4—861no—
354C4—861no—
355C4—861no—
356C4—1721no—
357C4—1721no—
358C4—1721no—
359C4#1306337011yescharacteristic
360C4#1306337011yescharacteristic
361C2—41no—
362C2—81no—
363C2—3441no—
364C2#1458346411yescharacteristic
365C2#1458370611yescharacteristic
366C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3225
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. #14583522C2semidirect
2. #14583470C2semidirect
3. #14583292C2semidirect
4. #14583280C2semidirect
5. #14583257C2semidirect
6. #14583248C2semidirect
7. #14583119C2semidirect
8. #14583113C2semidirect
9. #14583107C2semidirect
10. #14583103C2semidirect
11. #14583054C2semidirect
13. #14583040C2semidirect
14. #14582957C2semidirect
15. C43×#452C2semidirect
194. #452D43semidirect
199. C43#3225semidirect