Finite Group Databasebeta

← #19145205

Subgroups — #19145205

Order 5504.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583522C211yesmaximal, characteristic, complemented
2#14583516C211yesmaximal, characteristic, complemented
3#14583296C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583260C211yesmaximal, characteristic, complemented
6#14583257C211yesmaximal, characteristic, complemented
7#14583155C211yesmaximal, characteristic, complemented
8#14583150C211yesmaximal, characteristic
9#14583128C211yesmaximal, characteristic, complemented
10#14583008C211yesmaximal, characteristic, complemented
11#14583003C211yesmaximal, characteristic, complemented
12SD16×Dic43C211yesmaximal, characteristic, complemented
13#14582986C211yesmaximal, characteristic, complemented
14#14582854C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063320—21no—
23#13063318—21no—
24#13063314C2211yescharacteristic
25#13063312—21no—
26#13063312C2211yescharacteristic
27#13063311—21no—
28#13063307—21no—
29#13063306—21no—
30#13063305—21no—
31#13063304C2211yescharacteristic
32#13063302—21no—
33#13063299C2211yescharacteristic
34Q8×Dic43C2211yescharacteristic
35#13063290C2211yescharacteristic
36D4×Dic43C2211yescharacteristic
37#13063287C2211yescharacteristic
38#13063284C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063235C2211yescharacteristic
49#13063235C2211yescharacteristic
50C8×Dic43C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C22×Dic43—21no—
65C2×D172C2311yescharacteristic
66C2×C4×D43—21no—
67C2×Dic86—21no—
68C2×Dic86—21no—
69C2×Dic86C2311yescharacteristic
70SD16×C43—22no—
71C2×C8×C43—22no—
72C2×C8×C43C2311yescharacteristic
73C2×C8×C43C2311yescharacteristic
74C4⋊C4×C43—21no—
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C22⋊Dic43—21no—
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43D411yescharacteristic
84C22⋊Dic43D411yescharacteristic
85#10621885—22no—
86#10621882—22no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43D411yescharacteristic
93C4⋊Dic43D411yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43C2311yescharacteristic
103C4×Dic43C2311yescharacteristic
104#10621877—22no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107#10621873—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111Q8×C43—21no—
112Q8×C43—21no—
113D4×C43—21no—
114D4×C43—21no—
115D4×C43—81no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2411yescharacteristic
123C22⋊D43—81no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—81no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132D172—21no—
133D172—21no—
134C4×D43—81no—
135Dic86—21no—
136Dic86—21no—
137Dic86—81no—
138Dic86—81no—
139C8×C43—21no—
140C8×C43#4112yes—
141C43⋊C8—21no—
142C43⋊C8#4112yes—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43C22×D411yescharacteristic
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C4×C43—21no—
154C4×C43—41no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43C2×#4111yescharacteristic
158C4×C43C2×#4111yescharacteristic
159Dic43—21no—
160Dic43—21no—
161Dic43—21no—
162Dic43—21no—
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166#3173—431nomaximal, Sylow
167C2×C43—41no—
168C2×C43—81no—
169C2×C43#53211yescharacteristic
170C2×C43#57711yescharacteristic
171C2×C43#57711yescharacteristic
172D43—81no—
173#542—431no—
174#542—431no—
175#498—431no—
176#495—431no—
177#489—431no—
178#489—431no—
179#470—431no—
180#469—431no—
181#465—431no—
182#465D4311yescharacteristic, complemented
183#442—431no—
184#441—431no—
185C4×SD16—431no—
186C4×SD16—431no—
187#405—431no—
188C43#317311yescharacteristic, complemented, Sylow
189C2×Q16—431no—
190C2×SD16—431no—
191C2×SD16C2×D4311yescharacteristic
192C2×D8—431no—
193C2×M16—431no—
194C22×C8C2×D4311yescharacteristic
195C4⋊Q8—431no—
196C4⋊Q8—431no—
197#126—861no—
198#126—861no—
199#124—431no—
200#124—431no—
201#124—861no—
202#124—861no—
203#123—861no—
204#123—861no—
205C22⋊Q8—431no—
206C22⋊Q8—861no—
207C22⋊Q8—861no—
208C22⋊Q8C2×D4311yescharacteristic
209#121—431no—
210#121C2×D4311yescharacteristic
211C4×Q8—431no—
212C4×Q8—431no—
213C4×D4—431no—
214C4×D4—431no—
215#117—431no—
216#106—431no—
217#106—431no—
218#106—431no—
219#106C2×D4311yescharacteristic
220#103—431no—
221#103—431no—
222#103—431no—
223#103C2×D4311yescharacteristic
224#102—431no—
225#102—431no—
226#102—431no—
227#102C2×D4311yescharacteristic
228#97—431no—
229#97—431no—
230C4×C8—431no—
231C4×C8—431no—
232C2×Q8—431no—
233C2×Q8—861no—
234C2×Q8—861no—
235C2×Q8C22×D4311yescharacteristic
236C2×D4—21no—
237C2×D4—431no—
238C2×D4—861no—
239C2×D4C22×D4311yescharacteristic
240C22×C4—861no—
241C22×C4—861no—
242C22×C4C22×D4311yescharacteristic
243Q16—862no—
244SD16—22no—
245SD16—862no—
246D8—862no—
247M16—862no—
248C2×C8—22no—
249C2×C8—431no—
250C2×C8—431no—
251C2×C8C22×D4311yescharacteristic
252C2×C8C22×D4311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—431no—
255C4⋊C4—431no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—431no—
268C22⋊C4—431no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C42—431no—
278C42—431no—
279C42—861no—
280C42—861no—
281C23—21no—
282C23—861no—
283C23D4×D4311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—861no—
287Q8—861no—
288Q8—3441no—
289Q8—3441no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—861no—
294D4—861no—
295D4—3441no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—431no—
302C2×C4—431no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—3441no—
309C2×C4—3441no—
310C2×C4D4×D4311yescharacteristic
311C2×C4C23×D4311yescharacteristic
312C8—21no—
313C8—432no—
314C8—861no—
315C8#1062190012yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—1721no—
323C22—1721no—
324C22—1721no—
325C22C2×D4×D4311yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—861no—
331C4—861no—
332C4—861no—
333C4—861no—
334C4—1721no—
335C4—1721no—
336C4—1721no—
337C4#41×D4311yescharacteristic
338C4C2×#1062190011yescharacteristic
339C2—41no—
340C2—81no—
341C2—3441no—
342C2#1458344411yescharacteristic
343C2#1458370511yescharacteristic
344C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3173
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14583522C2semidirect
2. #14583516C2semidirect
3. #14583296C2semidirect
4. #14583280C2semidirect
5. #14583260C2semidirect
6. #14583257C2semidirect
7. #14583155C2semidirect
9. #14583128C2semidirect
10. #14583008C2semidirect
11. #14583003C2semidirect
12. SD16×Dic43C2semidirect
13. #14582986C2semidirect
14. #14582854C2semidirect
15. C43×#465C2semidirect
182. #465D43semidirect
188. C43#3173semidirect