Finite Group Databasebeta

← #19144708

Subgroups — #19144708

Order 5504.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583436C211yesmaximal, characteristic, complemented
2C4×#10621900C211yesmaximal, characteristic, complemented
3#14583239C211yesmaximal, characteristic, complemented
4#14583226C211yesmaximal, characteristic, complemented
5#14583205C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583124C211yesmaximal, characteristic, complemented
8#14583116C211yesmaximal, characteristic, complemented
9#14583058C211yesmaximal, characteristic, complemented
10#14583045C211yesmaximal, characteristic
11#14583009C211yesmaximal, characteristic, complemented
12#14583004C211yesmaximal, characteristic, complemented
13#14583001C211yesmaximal, characteristic, complemented
14#14582954C211yesmaximal, characteristic, complemented
15C43×#440C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20#13063320—21no—
21#13063316C2211yescharacteristic
22#13063314C2211yescharacteristic
23#13063310—21no—
24#13063301C2211yescharacteristic
25#13063300C2211yescharacteristic
26C4×Dic86C2211yescharacteristic
27#13063290C2211yescharacteristic
28C4×D172—21no—
29C4×D172C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31C4×C22⋊D43—21no—
32(C22⋊D43)⋊C4—21no—
33#13063283C2211yescharacteristic
34#13063282—21no—
35#13063281—21no—
36C2×C4×Dic43—21no—
37C42×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063256C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65#10621900—22no—
66#10621900—22no—
67C2×D172—21no—
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43D411yescharacteristic
71C2×C4×D43D411yescharacteristic
72C2×C4×D43C2311yescharacteristic
73C2×Dic86C2311yescharacteristic
74SD16×C43—22no—
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C42×C43—21no—
82C42×C43C2311yescharacteristic
83C22⋊Dic43—21no—
84#10621885—22no—
85#10621882—22no—
86(C2×D43)⋊C4—21no—
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—
92C4⋊Dic43—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43D411yescharacteristic
103C4×Dic43D411yescharacteristic
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107#10621873—22no—
108C23×C43—21no—
109C22×D43—21no—
110C22×D43C2×D411yescharacteristic
111Q8×C43—21no—
112Q8×C43—21no—
113D4×C43—21no—
114D4×C43#4112yes—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—42no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—24no—
123C2×Dic43—24no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—42no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131D172—21no—
132D172—21no—
133D172—42no—
134C4×D43—21no—
135C4×D43—21no—
136C4×D43—41no—
137C4×D43—41no—
138C4×D43—42no—
139Dic86—21no—
140Dic86#4112yes—
141C8×C43—21no—
142C8×C43—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—22no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43C22×D411yescharacteristic
149C2×D43—21no—
150C2×D43—21no—
151C2×D43—21no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43C2×#4111yescharacteristic
161C4×C43C2×#4111yescharacteristic
162Dic43—22no—
163Dic43—21no—
164Dic43—21no—
165Dic43—21no—
166Dic43—41no—
167Dic43—41no—
168#3111—431nomaximal, Sylow
169C2×C43—42no—
170C2×C43#52511yescharacteristic
171C2×C43#57511yescharacteristic
172C2×C43#57511yescharacteristic
173D43—41no—
174D43—81no—
175#529—431no—
176C4×#41—431no—
177#485—431no—
178#482—431no—
179#479—431no—
180#478—431no—
181#464—431no—
182#463—431no—
183#452—431no—
184#449—431no—
185#442—431no—
186#441—431no—
187#440—431no—
188#440D4311yescharacteristic, complemented
189#432—431no—
190C43#311111yescharacteristic, complemented, Sylow
191C2×#41—431no—
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16C2×D4311yescharacteristic
195C2×D8—431no—
196#126—861no—
197#125—431no—
198#124—431no—
199#123—861no—
200C22⋊Q8—431no—
201#121—431no—
202C4×Q8—431no—
203C4×Q8—431no—
204C4×Q8C2×D4311yescharacteristic
205C4×D4—431no—
206C4×D4—431no—
207C4×D4—861no—
208C4×D4—861no—
209C4×D4—861no—
210C4×D4C2×D4311yescharacteristic
211#117—431no—
212#117—861no—
213#117—861no—
214C2×C42—431no—
215C2×C42—861no—
216#107—431no—
217#107C2×D4311yescharacteristic
218#106—431no—
219#106—431no—
220C4⋊C8—431no—
221C4⋊C8—431no—
222#103—431no—
223#103—431no—
224#103—431no—
225#103C2×D4311yescharacteristic
226#102—431no—
227#102—431no—
228#102—431no—
229#102C2×D4311yescharacteristic
230C22⋊C8—431no—
231C22⋊C8—431no—
232#97—431no—
233#97C2×D4311yescharacteristic
234#41—862no—
235#41—862no—
236C2×Q8—431no—
237C2×Q8C22×D4311yescharacteristic
238C2×D4—431no—
239C2×D4—861no—
240C2×D4—861no—
241C2×D4C22×D4311yescharacteristic
242C22×C4—21no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249Q16—862no—
250SD16—22no—
251SD16—862no—
252D8—862no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8C22×D4311yescharacteristic
256C2×C8C22×D4311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4C22×D4311yescharacteristic
266C4⋊C4C22×D4311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C42—21no—
276C42—431no—
277C42—431no—
278C42—431no—
279C42—861no—
280C42—861no—
281C42—861no—
282C42C22×D4311yescharacteristic
283C23—21no—
284C23—431no—
285C23—861no—
286Q8—21no—
287Q8—21no—
288Q8—432no—
289Q8—861no—
290D4—21no—
291D4—864no—
292D4—861no—
293D4—861no—
294D4—1722no—
295D4#1062189812yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—431no—
301C2×C4—431no—
302C2×C4—431no—
303C2×C4—864no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1722no—
312C2×C4—1722no—
313C2×C4D4×D4311yescharacteristic
314C2×C4D4×D4311yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—861no—
319C8—861no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—861no—
324C22—861no—
325C22—861no—
326C22—1721no—
327C22—1721no—
328C22—1721no—
329C22C2×D4×D4311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—861no—
336C4—862no—
337C4—861no—
338C4—861no—
339C4—1721no—
340C4—1721no—
341C4#41×D4311yescharacteristic
342C4C2×#1062189811yescharacteristic
343C2—42no—
344C2—3441no—
345C2—1721no—
346C2#1458340811yescharacteristic
347C2#1458369511yescharacteristic
348C2#1458369811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#440C2
socleC22×C43C22×D4
hypercenter#440D43
hypocenterC43#3111
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14583436C2semidirect
2. C4×#10621900C2semidirect
3. #14583239C2semidirect
4. #14583226C2semidirect
5. #14583205C2semidirect
6. #14583197C2semidirect
7. #14583124C2semidirect
8. #14583116C2semidirect
9. #14583058C2semidirect
11. #14583009C2semidirect
12. #14583004C2semidirect
13. #14583001C2semidirect
14. #14582954C2semidirect
15. C43×#440C2semidirect
188. #440D43semidirect
190. C43#3111semidirect