Finite Group Databasebeta

← #19144285

Subgroups — #19144285

Order 5504.

472 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
1C2×#13063357C211yesmaximal, characteristic, complemented
2C2×#13063331C211yesmaximal, characteristic, complemented
3#14583479C211yesmaximal, characteristic
4#14583472C211yesmaximal, characteristic, complemented
5#14583155C211yesmaximal, characteristic, complemented
6#14583154C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583146C211yesmaximal, characteristic, complemented
9#14583139C211yesmaximal, characteristic, complemented
10#14583131C211yesmaximal, characteristic, complemented
11#14583128C211yesmaximal, characteristic, complemented
12#14582940C211yesmaximal, characteristic, complemented
13#14582894C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#467C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19#13063357—24no—
20C2×#10621885C2211yescharacteristic
21C2×#10621873C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23#13063331—24no—
24C2×#10621877C2211yescharacteristic
25C2×#10621872C2211yescharacteristic
26C2×#10621872C2211yescharacteristic
27C2×C8×D43C2211yescharacteristic
28C2×C8×D43C2211yescharacteristic
29#13063324—21no—
30#13063311—21no—
31#13063310—21no—
32#13063307—21no—
33#13063305C2211yescharacteristic
34#13063304C2211yescharacteristic
35#13063303—21no—
36#13063301C2211yescharacteristic
37#13063301C2211yescharacteristic
38#13063300—21no—
39#13063300C2211yescharacteristic
40#13063299C2211yescharacteristic
41#13063298—21no—
42#13063298—21no—
43#13063283C2211yescharacteristic
44C4⋊C4×D43C2211yescharacteristic
45#13063258C2211yescharacteristic
46#13063257C2211yescharacteristic
47#13063256C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063249C2211yescharacteristic
50#13063249C2211yescharacteristic
51#13063248C2211yescharacteristic
52#13063247C2211yescharacteristic
53#13063245C2211yescharacteristic
54C2×Q16×C43C2211yescharacteristic
55C22×C8×C43C2211yescharacteristic
56C22⋊Q8×C43C2211yescharacteristic
57C22⋊Q8×C43C2211yescharacteristic
58#107×C43C2211yescharacteristic
59#103×C43C2211yescharacteristic
60#103×C43C2211yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43D411yescharacteristic
66C2×C22⋊D43D411yescharacteristic
67#10621902—22no—
68#10621902—22no—
69Q8×D43—22no—
70Q8×D43—22no—
71#10621898—22no—
72#10621898—22no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172D411yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×C4×D43C2311yescharacteristic
82C2×Dic86—21no—
83C2×Dic86D411yescharacteristic
84C2×Dic86C2311yescharacteristic
85Q16×C43—22no—
86C2×C8×C43—22no—
87C2×C8×C43C2311yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C4⋊C4×C43—21no—
90C4⋊C4×C43—21no—
91C4⋊C4×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊Dic43—21no—
96#10621885—22no—
97#10621884—22no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43C2311yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109Dic43⋊C4—21no—
110Dic43⋊C4—21no—
111C4×Dic43—21no—
112#10621877—22no—
113C2×C43⋊C8C2311yescharacteristic
114C2×C43⋊C8C2311yescharacteristic
115#10621873—22no—
116#10621872—22no—
117#10621872D414yescomplemented
118C8×D43—22no—
119C8×D43—22no—
120C23×C43C2×D411yescharacteristic
121C22×D43—21no—
122C22×D43C2×D411yescharacteristic
123C22×D43C2×D411yescharacteristic
124Q8×C43—21no—
125Q8×C43—21no—
126Q8×C43—21no—
127Q8×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2411yescharacteristic
136C22⋊D43—22no—
137C22⋊D43—22no—
138C22⋊D43—81no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—22no—
145D172—21no—
146D172—21no—
147D172—42no—
148D172—81no—
149C4×D43—21no—
150C4×D43—21no—
151C4×D43—42no—
152C4×D43—42no—
153C4×D43—81no—
154C4×D43C2×D412yes—
155C4×D43#4112yes—
156Dic86—22no—
157Dic86—21no—
158Dic86—21no—
159Dic86—42no—
160C8×C43—21no—
161C8×C43C2×D412yes—
162C43⋊C8—21no—
163C43⋊C8C2×D412yes—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43C22×D411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43#12112yes—
177C4×C43—21no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43C22×D411yescharacteristic
183C4×C43C2×#4111yescharacteristic
184Dic43—21no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188Dic43#12112yes—
189#3063—431nomaximal, Sylow
190C2×C43—41no—
191C2×C43C2×#12111yescharacteristic
192C2×C43#57711yescharacteristic
193C2×C43#57811yescharacteristic
194D43—22no—
195D43—41no—
196D43—81no—
197C2×#137—431no—
198C2×#131—431no—
199#537—431no—
200#536—431no—
201#470—431no—
202#470—431no—
203#468—431no—
204#468—431no—
205#467—431no—
206#467D4311yescharacteristic, complemented
207#465—431no—
208#465—431no—
209#428—431no—
210#416—431no—
211C2×#103—431no—
212C43#306311yescharacteristic, complemented, Sylow
213C2×#41—431no—
214C2×#41—431no—
215C22×Q8—431no—
216#137—864no—
217C2×Q16—431no—
218C2×Q16C2×D4311yescharacteristic
219C2×SD16—431no—
220C2×SD16—431no—
221#131—864no—
222C2×M16—431no—
223C2×M16—431no—
224C2×M16—431no—
225C22×C8—431no—
226C22×C8—431no—
227C22×C8C2×D4311yescharacteristic
228C4⋊Q8—861no—
229#124—861no—
230#123—861no—
231#123—861no—
232C22⋊Q8—431no—
233C22⋊Q8—431no—
234C22⋊Q8—431no—
235C22⋊Q8—431no—
236C22⋊Q8—861no—
237C22⋊Q8C2×D4311yescharacteristic
238C22⋊Q8C2×D4311yescharacteristic
239#121—431no—
240#121—431no—
241#121—861no—
242#121—861no—
243#121—861no—
244#117—431no—
245C2×C4⋊C4—431no—
246#107—431no—
247#107C2×D4311yescharacteristic
248#106—431no—
249#106—431no—
250#103—431no—
251#103—431no—
252#103—431no—
253#103—431no—
254#103C2×D4311yescharacteristic
255#103C2×D4311yescharacteristic
256#102—431no—
257#102—431no—
258#41—862no—
259#41—862no—
260#41—862no—
261#41—862no—
262C2×Q8—431no—
263C2×Q8—431no—
264C2×Q8—861no—
265C2×Q8—862no—
266C2×Q8—862no—
267C2×Q8C22×D4311yescharacteristic
268C2×Q8C22×D4311yescharacteristic
269C2×D4—431no—
270C2×D4—431no—
271C2×D4—431no—
272C2×D4—431no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4C22×D4311yescharacteristic
282Q16—22no—
283Q16—862no—
284SD16—862no—
285SD16—862no—
286M16—434no—
287M16—862no—
288M16—862no—
289C2×C8—22no—
290C2×C8—431no—
291C2×C8—431no—
292C2×C8—862no—
293C2×C8—862no—
294C2×C8C22×D4311yescharacteristic
295C2×C8C22×D4311yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—431no—
299C4⋊C4—431no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4C22×D4311yescharacteristic
306C4⋊C4C22×D4311yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C42—861no—
317C23—431no—
318C23—431no—
319C23—861no—
320C23D4×D4311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—862no—
326Q8—861no—
327Q8—861no—
328Q8—1722no—
329D4—862no—
330D4—862no—
331D4—862no—
332D4—861no—
333D4—861no—
334D4—3441no—
335D4—3441no—
336D4—1722no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—431no—
344C2×C4—432no—
345C2×C4—432no—
346C2×C4—431no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—3441no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4D4×D4311yescharacteristic
356C2×C4C23×D4311yescharacteristic
357C8—21no—
358C8—432no—
359C8—861no—
360C8D4×D4312yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—432no—
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—41no—
379C4—432no—
380C4—861no—
381C4—1721no—
382C4—1721no—
383C4—1721no—
384C4C2×D4×D4311yescharacteristic
385C4#41×D4311yescharacteristic
386C2—41no—
387C2—862no—
388C2—3441no—
389C2—1721no—
390C2#121×D4311yescharacteristic
391C2#1458370611yescharacteristic
392C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#467C2
socleC22×C43C22×D4
hypercenter#467D43
hypocenterC43#3063
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#13063357C2semidirect
2. C2×#13063331C2semidirect
4. #14583472C2semidirect
5. #14583155C2semidirect
6. #14583154C2semidirect
7. #14583147C2semidirect
8. #14583146C2semidirect
9. #14583139C2semidirect
10. #14583131C2semidirect
11. #14583128C2semidirect
12. #14582940C2semidirect
13. #14582894C2semidirect
14. #103×D43C2semidirect
15. C43×#467C2semidirect
117. #10621872D4semidirect
206. #467D43semidirect
212. C43#3063semidirect