Finite Group Databasebeta

← #19144312

Subgroups — #19144312

Order 5504.

452 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583697C211yesmaximal, characteristic, complemented
2C2×#13063345C211yesmaximal, characteristic, complemented
3C2×#13063332C211yesmaximal, characteristic, complemented
4#14583172C212yesmaximal, complemented
5#14583167C212yesmaximal, complemented
6#14583164C212yesmaximal, complemented
7#14583160C212yesmaximal, complemented
8C2×#13063260C211yesmaximal, characteristic, complemented
9#14582883C211yesmaximal, characteristic, complemented
10#14582881C211yesmaximal, characteristic, complemented
11C43×#575C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13#13063356—21no—
14#13063355C2212yes—
15#13063351—21no—
16#13063350C2212yes—
17#13063345—22no—
18#13063345—21no—
19#13063345—21no—
20#13063345—21no—
21#13063345—21no—
22C2×#10621885C2211yescharacteristic, complemented
23C2×#10621883C2211yescharacteristic, complemented
24C2×#10621884C2211yescharacteristic, complemented
25C2×#10621882C2211yescharacteristic, complemented
26#13063332—21no—
27#13063332—21no—
28#13063332C2212yes—
29#13063332C2212yes—
30C2×#10621877—21no—
31C2×#10621877C2211yescharacteristic
32C2×#10621877C2211yescharacteristic
33C22×C43⋊C8—21no—
34C22×C43⋊C8C2211yescharacteristic
35#13063260C2212yescomplemented
36#13063260C2212yescomplemented
37#13063244C2212yescomplemented
38#13063243C2212yescomplemented
39#13063242C2212yescomplemented
40#13063241C2212yescomplemented
41C2×#41×C43C2211yescharacteristic
42C2×#41×C43C2211yescharacteristic
43#137×C43—21no—
44#137×C43C2212yes—
45AGL(1,ℤ/8)×C43—21no—
46AGL(1,ℤ/8)×C43C2212yes—
47#135×C43—22no—
48C2×M16×C43C2211yescharacteristic
49#41×C43—21no—
50#41×C43—21no—
51#41×C43—21no—
52#41×C43—21no—
53#41×C43—21no—
54#41×C43—21no—
55#41×C43D412yes—
56#41×C43C2312yes—
57C2×Q8×C43D411yescharacteristic
58C2×Q8×C43C2311yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43D411yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67#10621898—21no—
68#10621898—21no—
69#10621898—21no—
70#10621898—21no—
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×Dic86C2311yescharacteristic
74Q16×C43—22no—
75SD16×C43—22no—
76SD16×C43—22no—
77D8×C43—22no—
78M16×C43—21no—
79M16×C43C2312yes—
80C2×C8×C43—21no—
81#10621885—22no—
82#10621885—21no—
83#10621885—21no—
84#10621884—22no—
85#10621884—21no—
86#10621884—21no—
87#10621883—22no—
88#10621883—21no—
89#10621883—21no—
90#10621882—22no—
91#10621882—21no—
92#10621882—21no—
93#10621877—21no—
94#10621877—21no—
95#10621877—22no—
96#10621877—22no—
97#10621877C2312yes—
98#10621877C2312yes—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8D411yescharacteristic
104C2×C43⋊C8D411yescharacteristic
105C2×C43⋊C8D411yescharacteristic
106C2×C43⋊C8D411yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C23×C43—21no—
110C23×C43—21no—
111C23×C43#4111yescharacteristic
112C22×D43—21no—
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43C2×D412yes—
117D4×C43—22no—
118D4×C43—22no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—41no—
123D4×C43—41no—
124D4×C43C2×D412yes—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43#4111yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—41no—
138C22⋊D43—41no—
139C2×Dic43—21no—
140D172—21no—
141D172—21no—
142C4×D43—41no—
143C4×D43—41no—
144Dic86—21no—
145Dic86—21no—
146C8×C43—22no—
147C43⋊C8—22no—
148C43⋊C8—22no—
149C43⋊C8C2×D411yescharacteristic
150C43⋊C8C2×D411yescharacteristic
151C43⋊C8C2×D411yescharacteristic
152C43⋊C8C2×D411yescharacteristic
153C22×C43—22no—
154C22×C43—41no—
155C22×C43—42no—
156C22×C43—41no—
157C22×C43—81no—
158C22×C43#12111yescharacteristic
159C22×C43#12111yescharacteristic
160C22×C43C2×#4111yescharacteristic
161C2×D43—41no—
162C2×D43—81no—
163C4×C43—22no—
164C4×C43—41no—
165C4×C43#12111yescharacteristic
166C4×C43#12111yescharacteristic
167C4×C43C22×D411yescharacteristic
168C4×C43C22×D411yescharacteristic
169Dic43—41no—
170#3067—431nomaximal, Sylow
171C2×C43—21no—
172C2×C43—21no—
173C2×C43—21no—
174C2×C43—42no—
175C2×C43—81no—
176C2×C43C2×#12111yescharacteristic
177D43—81no—
178#575—431no—
179#575D4311yescharacteristic, complemented
180C2×#135—431no—
181C2×#131—431no—
182#473—432no—
183#472—432no—
184#471—432no—
185#471—432no—
186C2×#108—431no—
187#413—431no—
188#413—431no—
189C43#306711yescharacteristic, complemented, Sylow
190C2×#41—431no—
191C2×#41C2×D4311yescharacteristic
192C2×#41C2×D4311yescharacteristic
193#137—21no—
194#137—432no—
195#137—861no—
196#137C2×D4312yes—
197AGL(1,ℤ/8)—21no—
198AGL(1,ℤ/8)—432no—
199AGL(1,ℤ/8)—861no—
200AGL(1,ℤ/8)C2×D4312yes—
201#135—22no—
202#135—861no—
203#135—861no—
204#135—861no—
205#135—861no—
206#135—862no—
207C2×Q16—431no—
208C2×SD16—431no—
209C2×SD16—431no—
210C2×D8—431no—
211#131—432no—
212#131—432no—
213#131—861no—
214#131—861no—
215C2×M16—431no—
216C2×M16—431no—
217C2×M16—861no—
218C2×M16C2×D4311yescharacteristic
219C22×C8—431no—
220C22×C8—861no—
221#108—432no—
222#108—432no—
223#101—432no—
224#101—432no—
225#100—432no—
226#100—432no—
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—21no—
232#41—21no—
233#41—861no—
234#41—861no—
235#41—861no—
236#41—861no—
237#41C22⋊D4312yes—
238#41C22×D4312yes—
239C2×Q8—431no—
240C2×Q8C22⋊D4311yescharacteristic
241C2×Q8C22×D4311yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—431no—
245C2×D4—861no—
246C2×D4C22⋊D4311yescharacteristic
247C2×D4C22×D4311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—861no—
251C22×C4C22×D4311yescharacteristic
252Q16—22no—
253Q16—861no—
254Q16—861no—
255Q16—862no—
256SD16—22no—
257SD16—22no—
258SD16—861no—
259SD16—861no—
260SD16—861no—
261SD16—861no—
262SD16—862no—
263SD16—862no—
264D8—22no—
265D8—861no—
266D8—861no—
267D8—862no—
268M16—21no—
269M16—432no—
270M16—432no—
271M16—862no—
272M16—862no—
273M16—861no—
274M16—861no—
275M16C22×D4312yes—
276C2×C8—21no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8—431no—
281C2×C8—431no—
282C2×C8—431no—
283C2×C8—862no—
284C2×C8—862no—
285C2×C8—861no—
286C2×C8—861no—
287C23—21no—
288C23—21no—
289C23—861no—
290C23#1062190011yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—861no—
295Q8—861no—
296Q8C2×C22⋊D4312yes—
297D4—22no—
298D4—22no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—41no—
304D4—861no—
305D4—861no—
306D4—1721no—
307D4—1721no—
308D4C2×C22⋊D4312yes—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—861no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4D4×D4311yescharacteristic
319C2×C4D4×D4311yescharacteristic
320C2×C4#1062190011yescharacteristic
321C2×C4C2×C22⋊D4311yescharacteristic
322C2×C4C2×C22⋊D4311yescharacteristic
323C2×C4C23×D4311yescharacteristic
324C8—22no—
325C8—431no—
326C8—431no—
327C8—431no—
328C8—431no—
329C8—862no—
330C8—862no—
331C22—22no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22—81no—
336C22—3441no—
337C22—1721no—
338C22#1306329711yescharacteristic
339C22#1306329711yescharacteristic
340C22C2×#1062190011yescharacteristic
341C4—22no—
342C4—41no—
343C4—1721no—
344C4#1306329711yescharacteristic
345C4#1306329711yescharacteristic
346C4C2×D4×D4311yescharacteristic
347C4C22×C22⋊D4311yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—42no—
352C2—81no—
353C2—3441no—
354C2C2×#1306329711yescharacteristic
subgroupG/H
centerC4#13063297
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#575C2
socleC2×C43C2×#121
hypercenter#575D43
hypocenterC43#3067
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. C2×#13063345C2semidirect
3. C2×#13063332C2semidirect
4. #14583172C2semidirect
5. #14583167C2semidirect
6. #14583164C2semidirect
7. #14583160C2semidirect
8. C2×#13063260C2semidirect
9. #14582883C2semidirect
10. #14582881C2semidirect
11. C43×#575C2semidirect
22. C2×#10621885C22semidirect
23. C2×#10621883C22semidirect
24. C2×#10621884C22semidirect
25. C2×#10621882C22semidirect
35. #13063260C22semidirect
36. #13063260C22semidirect
37. #13063244C22semidirect
38. #13063243C22semidirect
39. #13063242C22semidirect
40. #13063241C22semidirect
179. #575D43semidirect
189. C43#3067semidirect