Finite Group Databasebeta

← #19145503

Subgroups — #19145503

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583479C211yesmaximal, characteristic, complemented
2#14583477C211yesmaximal, characteristic, complemented
3#14583228C211yesmaximal, characteristic, complemented
4#14583227C211yesmaximal, characteristic, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583216C211yesmaximal, characteristic, complemented
7#14583154C211yesmaximal, characteristic, complemented
8#14583151C211yesmaximal, characteristic, complemented
9#14583131C211yesmaximal, characteristic, complemented
10#14583125C211yesmaximal, characteristic, complemented
11#14583060C211yesmaximal, characteristic, complemented
12#14583044C211yesmaximal, characteristic, complemented
13#14583043C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063304—21no—
23#13063303—21no—
24#13063301C2211yescharacteristic
25#13063301C2211yescharacteristic
26#13063301C2211yescharacteristic
27#13063300—21no—
28#13063300C2211yescharacteristic
29#13063299—21no—
30#13063299C2211yescharacteristic
31#13063298—21no—
32#13063298—21no—
33#13063297—21no—
34#13063297—21no—
35#13063296C2211yescharacteristic
36#13063296C2211yescharacteristic
37C2×C4⋊Dic43C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
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—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43D411yescharacteristic
71C2×C22⋊D43D411yescharacteristic
72C22×Dic43—21no—
73#10621902—41no—
74#10621902—41no—
75#10621898—41no—
76#10621898—41no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172D411yescharacteristic
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43C2311yescharacteristic
84C2×C4×D43C2311yescharacteristic
85C2×Dic86D411yescharacteristic
86Q16×C43—41no—
87SD16×C43—41no—
88C2×C8×C43C2311yescharacteristic
89C2×C8×C43C2311yescharacteristic
90C4⋊C4×C43—21no—
91C4⋊C4×C43C2311yescharacteristic
92C22⋊C4×C43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95#10621884—41no—
96#10621882—41no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112#10621872—41no—
113C8×D43—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117C22×D43C2×D411yescharacteristic
118C22×D43C2×D411yescharacteristic
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122Q8×C43—21no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—42no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—42no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—41no—
135C22⋊D43—41no—
136C22⋊D43—81no—
137C22⋊D43—81no—
138C22⋊D43—81no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—81no—
143C2×Dic43C2×D411yescharacteristic
144C2×Dic43C2×D411yescharacteristic
145D172—21no—
146D172—21no—
147D172—41no—
148D172—42no—
149D172—81no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—42no—
155C4×D43—81no—
156Dic86—41no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43C22×D411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C4×C43—21no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43H(5,𝔽2)11yescharacteristic
182C4×C43H(5,𝔽2)11yescharacteristic
183Dic43—21no—
184Dic43—21no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#3204—431nomaximal, Sylow
189C2×C43—41no—
190C2×C43—81no—
191C2×C43#53411yescharacteristic
192C2×C43#57711yescharacteristic
193C2×C43#57711yescharacteristic
194D43—41no—
195D43—41no—
196D43—81no—
197#537—431no—
198#537—431no—
199#483—431no—
200#483—431no—
201#481—431no—
202#481—431no—
203#470—431no—
204#469—431no—
205#465—431no—
206#465—431no—
207#452—431no—
208#452D4311yescharacteristic, complemented
209#449—431no—
210#449—431no—
211#408—431no—
212C43#320411yescharacteristic, complemented, Sylow
213C2×#41—431no—
214C2×#41—431no—
215C2×#41C2×D4311yescharacteristic
216C2×Q16C2×D4311yescharacteristic
217C2×SD16—431no—
218C2×SD16C2×D4311yescharacteristic
219C2×D8—431no—
220C2×M16—431no—
221C22×C8—431no—
222C22⋊Q8—431no—
223C22⋊Q8—431no—
224C22⋊Q8—431no—
225C22⋊Q8—861no—
226C22⋊Q8—861no—
227C22⋊Q8C2×D4311yescharacteristic
228#121—431no—
229#121—431no—
230#121—431no—
231#121—431no—
232#121—861no—
233#121—861no—
234#121—861no—
235#121—861no—
236#121—861no—
237#121—861no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240#106—431no—
241#106—431no—
242#106—431no—
243#106—431no—
244#103—431no—
245#103—431no—
246#103—431no—
247#103C2×D4311yescharacteristic
248#102—431no—
249#102—431no—
250#102—431no—
251#102C2×D4311yescharacteristic
252C22⋊C8—431no—
253C22⋊C8—431no—
254C22⋊C8—431no—
255C22⋊C8C2×D4311yescharacteristic
256#41—41no—
257#41—41no—
258#41—1721no—
259#41—1721no—
260#41—1721no—
261#41—1721no—
262C2×Q8—431no—
263C2×Q8C22×D4311yescharacteristic
264C2×Q8C22×D4311yescharacteristic
265C2×D4—21no—
266C2×D4—431no—
267C2×D4—431no—
268C2×D4—431no—
269C2×D4—431no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4C22×D4311yescharacteristic
276C22×C4—21no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4C22×D4311yescharacteristic
283Q16—41no—
284SD16—41no—
285SD16—1721no—
286D8—1721no—
287M16—1721no—
288C2×C8—431no—
289C2×C8—431no—
290C2×C8—1721no—
291C2×C8C22×D4311yescharacteristic
292C2×C8C22×D4311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—431no—
295C4⋊C4—431no—
296C4⋊C4—431no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4C22×D4311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C23—21no—
312C23—431no—
313C23—431no—
314C23—861no—
315C23D4×D4311yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—1721no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—861no—
325D4—861no—
326D4—3441no—
327D4—3441no—
328D4—3441no—
329D4—3441no—
330D4—1721no—
331D4—1722no—
332D4—1721no—
333D4—1721no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—431no—
341C2×C4—431no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—1722no—
352C2×C4D4×D4311yescharacteristic
353C2×C4C23×D4311yescharacteristic
354C8—21no—
355C8—21no—
356C8—861no—
357C8—861no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—861no—
365C22—861no—
366C22—861no—
367C22—861no—
368C22—861no—
369C22—861no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C2×D4×D4311yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—861no—
379C4—861no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1306337011yescharacteristic
384C4#1306337011yescharacteristic
385C2—41no—
386C2—81no—
387C2—3441no—
388C2—1721no—
389C2—1721no—
390C2#1458345911yescharacteristic
391C2#1458370611yescharacteristic
392C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3204
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. #14583479C2semidirect
2. #14583477C2semidirect
3. #14583228C2semidirect
4. #14583227C2semidirect
5. #14583218C2semidirect
6. #14583216C2semidirect
7. #14583154C2semidirect
8. #14583151C2semidirect
9. #14583131C2semidirect
10. #14583125C2semidirect
11. #14583060C2semidirect
12. #14583044C2semidirect
13. #14583043C2semidirect
14. #14582864C2semidirect
15. C43×#452C2semidirect
208. #452D43semidirect
212. C43#3204semidirect