Finite Group Databasebeta

← #19144651

Subgroups — #19144651

Order 5504.

434 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#14583446C211yesmaximal, characteristic, complemented
2C4×#10621900C211yesmaximal, characteristic, complemented
3#14583226C211yesmaximal, characteristic, complemented
4#14583222C211yesmaximal, characteristic, complemented
5#14583193C211yesmaximal, characteristic, complemented
6#14583187C211yesmaximal, characteristic, complemented
7#14583098C211yesmaximal, characteristic, complemented
8#14583092C211yesmaximal, characteristic, complemented
9#14583045C211yesmaximal, characteristic, complemented
10#14583041C211yesmaximal, characteristic, complemented
11C4×#10621873C211yesmaximal, characteristic, complemented
12C4×#10621883C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582950C211yesmaximal, characteristic, complemented
15C4×D8×C43C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621900C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063321C2211yescharacteristic
23#13063311—21no—
24#13063300C2211yescharacteristic
25#13063298—21no—
26#13063296C2211yescharacteristic
27C4×Dic86C2211yescharacteristic
28#13063290C2211yescharacteristic
29C4×D172C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31C4×C22⋊D43—21no—
32C4×C22⋊D43—21no—
33(C22⋊D43)⋊C4—21no—
34#13063283C2211yescharacteristic
35#13063281—21no—
36C2×C4×Dic43—21no—
37C42×D43C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C4×C43⋊C8C2211yescharacteristic
52C2×D8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×D4×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69#10621900—22no—
70#10621900—22no—
71#10621898—44no—
72C2×D172—21no—
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43D411yescharacteristic
76C2×C4×D43D411yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×Dic86—21no—
79C2×Dic86C2311yescharacteristic
80D8×C43—22no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C42×C43C2311yescharacteristic
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90#10621883—22no—
91#10621882—22no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43D411yescharacteristic
104C4×Dic43D411yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108#10621873—22no—
109C23×C43—21no—
110C23×C43—21no—
111C22×D43—21no—
112C22×D43C2×D411yescharacteristic
113D4×C43—21no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43#4112yescomplemented
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C22⋊D43—24no—
125C22⋊D43—42no—
126C22⋊D43—42no—
127C22⋊D43—42no—
128C2×Dic43—24no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—42no—
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136D172—21no—
137D172—21no—
138D172—42no—
139C4×D43—22no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—22no—
143C4×D43—42no—
144Dic86—21no—
145Dic86—42no—
146Dic86#4112yescomplemented
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—22no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43AGL(1,ℤ/8)12yes—
168C4×C43C2×#4111yescharacteristic
169C4×C43C2×#4111yescharacteristic
170Dic43—22no—
171Dic43—21no—
172Dic43—21no—
173Dic43—41no—
174Dic43—41no—
175Dic43#13512yes—
176#3106—431nomaximal, Sylow
177C2×C43—42no—
178C2×C43—81no—
179C2×C43#52511yescharacteristic
180C2×C43C2×#13511yescharacteristic
181C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
182D43—41no—
183D43—81no—
184#532—431no—
185C4×#41—431no—
186#482—431no—
187#482—431no—
188#477—431no—
189#476—431no—
190#460—431no—
191#459—431no—
192#449—431no—
193#449—431no—
194C4×SD16—431no—
195C4×SD16—431no—
196C4×D8—431no—
197C4×D8D4311yescharacteristic, complemented
198#431—431no—
199C43#310611yescharacteristic, complemented, Sylow
200C2×#41—431no—
201C2×#41—861no—
202C2×SD16—431no—
203C2×SD16—431no—
204C2×D8—431no—
205C2×D8C2×D4311yescharacteristic
206C4⋊Q8—431no—
207#127—431no—
208#124—861no—
209#121—431no—
210#121—431no—
211#121—861no—
212C4×Q8—431no—
213C4×Q8—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—861no—
217C4×D4—861no—
218C4×D4—861no—
219C4×D4C2×D4311yescharacteristic
220C4×D4C2×D4311yescharacteristic
221#117—431no—
222#117—861no—
223C2×C42—431no—
224C2×C42—861no—
225#107—431no—
226#107C2×D4311yescharacteristic
227#106—431no—
228#106—431no—
229C4⋊C8—431no—
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236#102—431no—
237#102C2×D4311yescharacteristic
238#102C2×D4311yescharacteristic
239C22⋊C8—431no—
240C22⋊C8—431no—
241C4×C8—431no—
242C4×C8C2×D4311yescharacteristic
243#41—862no—
244#41—862no—
245#41—1724no—
246C2×Q8—431no—
247C2×Q8—861no—
248C2×D4—431no—
249C2×D4—861no—
250C2×D4—861no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4C22×D4311yescharacteristic
255C2×D4C22×D4311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264SD16—862no—
265SD16—862no—
266D8—22no—
267D8—862no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—431no—
273C4⋊C4—431no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4C22×D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—431no—
287C42—431no—
288C42—431no—
289C42—861no—
290C42—861no—
291C42—861no—
292C42C22×D4311yescharacteristic
293C23—21no—
294C23—21no—
295C23—431no—
296C23—861no—
297Q8—432no—
298Q8—861no—
299Q8—1722no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—864no—
304D4—861no—
305D4—861no—
306D4—1722no—
307D4—1722no—
308D4—1722no—
309D4—1722no—
310D4#1062189812yescomplemented
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—431no—
316C2×C4—431no—
317C2×C4—431no—
318C2×C4—862no—
319C2×C4—864no—
320C2×C4—861no—
321C2×C4—862no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4D4×D4311yescharacteristic
329C2×C4D4×D4311yescharacteristic
330C2×C4C23×D4311yescharacteristic
331C8—21no—
332C8—21no—
333C8—861no—
334C8—861no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—861no—
342C22—861no—
343C22—861no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C2×D4×D4311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—432no—
352C4—861no—
353C4—862no—
354C4—861no—
355C4—1721no—
356C4—1721no—
357C4#1306334912yes—
358C4#41×D4311yescharacteristic
359C4C2×#1062189811yescharacteristic
360C2—42no—
361C2—81no—
362C2—3441no—
363C2—1721no—
364C2#1458340811yescharacteristic
365C2#135×D4311yescharacteristic
366C2C2×#1306334911yescharacteristic
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC4×D8×C43C2
socleC22×C43C22×D4
hypercenterC4×D8D43
hypocenterC43#3106
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14583446C2semidirect
2. C4×#10621900C2semidirect
3. #14583226C2semidirect
4. #14583222C2semidirect
5. #14583193C2semidirect
6. #14583187C2semidirect
7. #14583098C2semidirect
8. #14583092C2semidirect
9. #14583045C2semidirect
10. #14583041C2semidirect
11. C4×#10621873C2semidirect
12. C4×#10621883C2semidirect
13. C4×#10621882C2semidirect
14. #14582950C2semidirect
15. C4×D8×C43C2semidirect
116. D4×C43#41semidirect
146. Dic86#41semidirect
197. C4×D8D43semidirect
199. C43#3106semidirect
310. D4#10621898semidirect