Finite Group Databasebeta

← #20253105

Subgroups — #20253105

Order 6016.

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#15689921C211yesmaximal, characteristic, complemented
2C2×#13094044C211yesmaximal, characteristic, complemented
3C2×#13094031C211yesmaximal, characteristic, complemented
4#15689396C212yesmaximal, complemented
5#15689391C212yesmaximal, complemented
6#15689388C212yesmaximal, complemented
7#15689384C212yesmaximal, complemented
8C2×#13093959C211yesmaximal, characteristic, complemented
9#15689107C211yesmaximal, characteristic, complemented
10#15689105C211yesmaximal, characteristic, complemented
11C47×#575C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13#13094055—21no—
14#13094054C2212yes—
15#13094050—21no—
16#13094049C2212yes—
17#13094044—22no—
18#13094044—21no—
19#13094044—21no—
20#13094044—21no—
21#13094044—21no—
22C2×#10625337C2211yescharacteristic, complemented
23C2×#10625335C2211yescharacteristic, complemented
24C2×#10625336C2211yescharacteristic, complemented
25C2×#10625334C2211yescharacteristic, complemented
26#13094031—21no—
27#13094031—21no—
28#13094031C2212yes—
29#13094031C2212yes—
30C2×#10625329—21no—
31C2×#10625329C2211yescharacteristic
32C2×#10625329C2211yescharacteristic
33C22×C47⋊C8—21no—
34C22×C47⋊C8C2211yescharacteristic
35#13093959C2212yescomplemented
36#13093959C2212yescomplemented
37#13093943C2212yescomplemented
38#13093942C2212yescomplemented
39#13093941C2212yescomplemented
40#13093940C2212yescomplemented
41C2×#41×C47C2211yescharacteristic
42C2×#41×C47C2211yescharacteristic
43#137×C47—21no—
44#137×C47C2212yes—
45AGL(1,ℤ/8)×C47—21no—
46AGL(1,ℤ/8)×C47C2212yes—
47#135×C47—22no—
48C2×M16×C47C2211yescharacteristic
49#41×C47—21no—
50#41×C47—21no—
51#41×C47—21no—
52#41×C47—21no—
53#41×C47—21no—
54#41×C47—21no—
55#41×C47D412yes—
56#41×C47C2312yes—
57C2×Q8×C47D411yescharacteristic
58C2×Q8×C47C2311yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47—21no—
61C2×D4×C47D411yescharacteristic
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—21no—
67#10625350—21no—
68#10625350—21no—
69#10625350—21no—
70#10625350—21no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×Dic94C2311yescharacteristic
74Q16×C47—22no—
75SD16×C47—22no—
76SD16×C47—22no—
77D8×C47—22no—
78M16×C47—21no—
79M16×C47C2312yes—
80C2×C8×C47—21no—
81#10625337—22no—
82#10625337—21no—
83#10625337—21no—
84#10625336—22no—
85#10625336—21no—
86#10625336—21no—
87#10625335—22no—
88#10625335—21no—
89#10625335—21no—
90#10625334—22no—
91#10625334—21no—
92#10625334—21no—
93#10625329—21no—
94#10625329—21no—
95#10625329—22no—
96#10625329—22no—
97#10625329C2312yes—
98#10625329C2312yes—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—22no—
103C2×C47⋊C8D411yescharacteristic
104C2×C47⋊C8D411yescharacteristic
105C2×C47⋊C8D411yescharacteristic
106C2×C47⋊C8D411yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C23×C47—21no—
110C23×C47—21no—
111C23×C47#4111yescharacteristic
112C22×D47—21no—
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47C2×D412yes—
117D4×C47—22no—
118D4×C47—22no—
119D4×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—41no—
123D4×C47—41no—
124D4×C47C2×D412yes—
125C2×C4×C47—21no—
126C2×C4×C47—22no—
127C2×C4×C47—22no—
128C2×C4×C47—21no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47#4111yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—41no—
138C22⋊D47—41no—
139C2×Dic47—21no—
140D188—21no—
141D188—21no—
142C4×D47—41no—
143C4×D47—41no—
144Dic94—21no—
145Dic94—21no—
146C8×C47—22no—
147C47⋊C8—22no—
148C47⋊C8—22no—
149C47⋊C8C2×D411yescharacteristic
150C47⋊C8C2×D411yescharacteristic
151C47⋊C8C2×D411yescharacteristic
152C47⋊C8C2×D411yescharacteristic
153C22×C47—22no—
154C22×C47—41no—
155C22×C47—42no—
156C22×C47—41no—
157C22×C47—81no—
158C22×C47#12111yescharacteristic
159C22×C47#12111yescharacteristic
160C22×C47C2×#4111yescharacteristic
161C2×D47—41no—
162C2×D47—81no—
163C4×C47—22no—
164C4×C47—41no—
165C4×C47#12111yescharacteristic
166C4×C47#12111yescharacteristic
167C4×C47C22×D411yescharacteristic
168C4×C47C22×D411yescharacteristic
169Dic47—41no—
170#3067—471nomaximal, Sylow
171C2×C47—21no—
172C2×C47—21no—
173C2×C47—21no—
174C2×C47—42no—
175C2×C47—81no—
176C2×C47C2×#12111yescharacteristic
177D47—81no—
178#575—471no—
179#575D4711yescharacteristic, complemented
180C2×#135—471no—
181C2×#131—471no—
182#473—472no—
183#472—472no—
184#471—472no—
185#471—472no—
186C2×#108—471no—
187#413—471no—
188#413—471no—
189C47#306711yescharacteristic, complemented, Sylow
190C2×#41—471no—
191C2×#41C2×D4711yescharacteristic
192C2×#41C2×D4711yescharacteristic
193#137—21no—
194#137—472no—
195#137—941no—
196#137C2×D4712yes—
197AGL(1,ℤ/8)—21no—
198AGL(1,ℤ/8)—472no—
199AGL(1,ℤ/8)—941no—
200AGL(1,ℤ/8)C2×D4712yes—
201#135—22no—
202#135—941no—
203#135—941no—
204#135—941no—
205#135—941no—
206#135—942no—
207C2×Q16—471no—
208C2×SD16—471no—
209C2×SD16—471no—
210C2×D8—471no—
211#131—472no—
212#131—472no—
213#131—941no—
214#131—941no—
215C2×M16—471no—
216C2×M16—471no—
217C2×M16—941no—
218C2×M16C2×D4711yescharacteristic
219C22×C8—471no—
220C22×C8—941no—
221#108—472no—
222#108—472no—
223#101—472no—
224#101—472no—
225#100—472no—
226#100—472no—
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—21no—
232#41—21no—
233#41—941no—
234#41—941no—
235#41—941no—
236#41—941no—
237#41C22⋊D4712yes—
238#41C22×D4712yes—
239C2×Q8—471no—
240C2×Q8C22⋊D4711yescharacteristic
241C2×Q8C22×D4711yescharacteristic
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—471no—
245C2×D4—941no—
246C2×D4C22⋊D4711yescharacteristic
247C2×D4C22×D4711yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—941no—
251C22×C4C22×D4711yescharacteristic
252Q16—22no—
253Q16—941no—
254Q16—941no—
255Q16—942no—
256SD16—22no—
257SD16—22no—
258SD16—941no—
259SD16—941no—
260SD16—941no—
261SD16—941no—
262SD16—942no—
263SD16—942no—
264D8—22no—
265D8—941no—
266D8—941no—
267D8—942no—
268M16—21no—
269M16—472no—
270M16—472no—
271M16—942no—
272M16—942no—
273M16—941no—
274M16—941no—
275M16C22×D4712yes—
276C2×C8—21no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8—471no—
280C2×C8—471no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—942no—
284C2×C8—942no—
285C2×C8—941no—
286C2×C8—941no—
287C23—21no—
288C23—21no—
289C23—941no—
290C23#1062535211yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—941no—
295Q8—941no—
296Q8C2×C22⋊D4712yes—
297D4—22no—
298D4—22no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—41no—
303D4—41no—
304D4—941no—
305D4—941no—
306D4—1881no—
307D4—1881no—
308D4C2×C22⋊D4712yes—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—941no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4D4×D4711yescharacteristic
319C2×C4D4×D4711yescharacteristic
320C2×C4#1062535211yescharacteristic
321C2×C4C2×C22⋊D4711yescharacteristic
322C2×C4C2×C22⋊D4711yescharacteristic
323C2×C4C23×D4711yescharacteristic
324C8—22no—
325C8—471no—
326C8—471no—
327C8—471no—
328C8—471no—
329C8—942no—
330C8—942no—
331C22—22no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22—81no—
336C22—3761no—
337C22—1881no—
338C22#1309399611yescharacteristic
339C22#1309399611yescharacteristic
340C22C2×#1062535211yescharacteristic
341C4—22no—
342C4—41no—
343C4—1881no—
344C4#1309399611yescharacteristic
345C4#1309399611yescharacteristic
346C4C2×D4×D4711yescharacteristic
347C4C22×C22⋊D4711yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—42no—
352C2—81no—
353C2—3761no—
354C2C2×#1309399611yescharacteristic
subgroupG/H
centerC4#13093996
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#575C2
socleC2×C47C2×#121
hypercenter#575D47
hypocenterC47#3067
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #15689921C2semidirect
2. C2×#13094044C2semidirect
3. C2×#13094031C2semidirect
4. #15689396C2semidirect
5. #15689391C2semidirect
6. #15689388C2semidirect
7. #15689384C2semidirect
8. C2×#13093959C2semidirect
9. #15689107C2semidirect
10. #15689105C2semidirect
11. C47×#575C2semidirect
22. C2×#10625337C22semidirect
23. C2×#10625335C22semidirect
24. C2×#10625336C22semidirect
25. C2×#10625334C22semidirect
35. #13093959C22semidirect
36. #13093959C22semidirect
37. #13093943C22semidirect
38. #13093942C22semidirect
39. #13093941C22semidirect
40. #13093940C22semidirect
179. #575D47semidirect
189. C47#3067semidirect