Finite Group Databasebeta

← #11886578

Subgroups — #11886578

Order 1152.

1392 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1392 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596308C212yesmaximal, complemented
2#10596245C212yesmaximal, complemented
3C32×#454C211yesmaximal, characteristic, complemented
4#10592898C212yesmaximal, complemented
5#10592760C211yesmaximal, characteristic, complemented
6#10592757C211yesmaximal, characteristic, complemented
7#10592522C212yesmaximal, complemented
8#10592521C212yesmaximal, complemented
9#10592453C212yesmaximal, complemented
10#80287—34nomaximal
11C32×2−1+4C2211yescharacteristic, complemented
12#64366C2212yescomplemented
13#64361C2211yescharacteristic
14C32×AGL(1,ℤ/8)C2212yescomplemented
15C32×#124C2211yescharacteristic, complemented
16#64159—22no—
17#64159C2212yes—
18#64158—22no—
19#64158C2212yescomplemented
20#64157C2212yescomplemented
21#64151—22no—
22#64151C2212yescomplemented
23C2×#3755—22no—
24C2×#3755C2212yescomplemented
25C2×#3753C2212yescomplemented
26#64125—22no—
27#64123—22no—
28#64120—22no—
29D8×C3⋊D3—22no—
30#64117C2212yes—
31#64116C2212yescomplemented
32#64083C2211yescharacteristic, complemented
33C32×#104C2212yescomplemented
34C32×#101C2211yescharacteristic, complemented
35#63660C2211yescharacteristic, complemented
36#63650C2212yescomplemented
37#63649C2212yescomplemented
38#63632C2212yescomplemented
39#63630C2211yescharacteristic, complemented
40#5837—38no—
41#5774—38no—
42C3×#454D314yescomplemented
43#5199—38no—
44#5061—34no—
45#5058—34no—
46#4823—38no—
47#4822—38no—
48#4754—38no—
49C32×#41—22no—
50C32×#41—41no—
51C32×#41C2312yes—
52C2×C32×Q8—22no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4C2311yescharacteristic
55C2×#638—41no—
56#3832—22no—
57#3830—22no—
58D4×C3⋊D3—22no—
59D4×C3⋊D3—22no—
60D4×C3⋊D3—42no—
61#3828—22no—
62#3828C2312yes—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)—41no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C32×SD16—22no—
67C32×D8—22no—
68C32×M16C2312yes—
69C32×C22⋊C4—41no—
70C32×C42C2311yescharacteristic
71#3756—22no—
72#3756D412yescomplemented
73#3755—22no—
74#3755—22no—
75#3755—22no—
76#3755—22no—
77#3755D412yescomplemented
78#3754D412yescomplemented
79#3753—22no—
80#3753—22no—
81#3753—22no—
82#3753D412yescomplemented
83#3748—22no—
84#3748C2312yes—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87#3745—22no—
88#3744—22no—
89#3743—22no—
90C8×C3⋊D3—22no—
91#3288—91noSylow
92C3×2−1+4C2×D314yescomplemented
93#1009—38no—
94#1004—34no—
95C3×AGL(1,ℤ/8)C2×D318yescomplemented
96C3×#124C2×D314yescomplemented
97#950—38no—
98#950—68no—
99#949—38no—
100#949—68no—
101#948—38no—
102#942—38no—
103#942—68no—
104C2×#215—38no—
105C2×#215—68no—
106C2×#213—38no—
107#916—68no—
108#914—68no—
109#911—68no—
110D3×D8—68no—
111#908—38no—
112#907—38no—
113#874—34no—
114C3×#104C2×D318yescomplemented
115C3×#101C2×D314yescomplemented
116#833—34no—
117#823—38no—
118#822—38no—
119#805—38no—
120#803—34no—
121C23×C32—21no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—42no—
125C32×Q8—22no—
126C32×Q8—41no—
127C32×Q8C2×D412yes—
128C32×D4—22no—
129C32×D4—22no—
130C32×D4—41no—
131C32×D4C2×D412yes—
132C2×C32×C4—22no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—42no—
136C2×C32×C4C2411yescharacteristic
137#638—22no—
138#638—42no—
139#638—42no—
140C2×C3⋊Dic3—41no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—42no—
144C4⋊(C3⋊D3)—82no—
145C4⋊(C3⋊D3)C2×D412yes—
146C4×C3⋊D3—22no—
147C4×C3⋊D3—42no—
148#634C2×D412yes—
149C32×C8—22no—
150C3⋊(C3⋊C8)—22no—
151C3⋊(C3⋊C8)C2×D412yes—
152C3⋊(C3⋊C8)C2×D412yes—
153#577—92no—
154#576—92no—
155#496—91no—
156#472—92no—
157#471—92no—
158#455—91no—
159#454C3⋊D311yescharacteristic, complemented
160#453—92no—
161#444—92no—
162C3×#41—28no—
163C3×#41—44no—
164C3×#41C22×D318yes—
165C2×C3×Q8—28no—
166C2×C3×Q8C22×D314yes—
167C2×C3×D4C22×D314yes—
168C2×#67—124no—
169#239—68no—
170#237—68no—
171D3×D4—68no—
172D3×D4—68no—
173D3×D4—128no—
174#235—38no—
175#235—68no—
176C2×D12—38no—
177C2×D12—68no—
178C2×D12—124no—
179C3×SD16—28no—
180C3×D8—28no—
181C3×M16C22×D318yes—
182C3×C22⋊C4—44no—
183C3×C42C22×D314yes—
184#216—38no—
185#216—68no—
186#215—38no—
187#215—68no—
188#215—68no—
189#215—68no—
190#215—68no—
191#214—38no—
192#213—38no—
193#213—68no—
194#213—68no—
195#213—68no—
196#208—38no—
197#208—68no—
198C2×C3⋊C8—38no—
199C2×C3⋊C8—68no—
200D24—68no—
201#204—68no—
202ΓL(1,𝔽25)—68no—
203D3×C8—68no—
204C22×C32—22no—
205C22×C32—41no—
206C22×C32—81no—
207C22×C32H(5,𝔽2)11yescharacteristic
208C2×C3⋊D3—22no—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—82no—
211C2×C3⋊D3—161no—
212C2×C3⋊D3—162no—
213C32×C4—22no—
214C32×C4—41no—
215C32×C4—41no—
216C32×C4C22×D412yes—
217C3⋊Dic3—22no—
2182−1+4C2×C3⋊D311yescharacteristic, complemented
219H(5,𝔽2)—92no—
220H(5,𝔽2)—91no—
221#137—92no—
222#137—182no—
223AGL(1,ℤ/8)—92no—
224AGL(1,ℤ/8)—92no—
225AGL(1,ℤ/8)—182no—
226AGL(1,ℤ/8)—182no—
227AGL(1,ℤ/8)—182no—
228AGL(1,ℤ/8)C2×C3⋊D312yescomplemented
229#135—92no—
230#135—182no—
231#135—182no—
232C2×SD16—92no—
233C2×SD16—182no—
234C2×D8—92no—
235C2×D8—182no—
236#131—92no—
237#131—92no—
238#127—91no—
239#124C2×C3⋊D311yescharacteristic, complemented
240#108—92no—
241#104—92no—
242#104C2×C3⋊D312yescomplemented
243#101C2×C3⋊D311yescharacteristic, complemented
244#100—91no—
245#100—92no—
246#97—91no—
247C23×C3—24no—
248C22×D3—68no—
249C22×D3—124no—
250C22×D3—128no—
251C3×Q8—28no—
252C3×Q8—44no—
253C3×Q8D3×D418yes—
254C3×D4—28no—
255C3×D4—28no—
256C3×D4—44no—
257C3×D4D3×D418yes—
258C2×C3×C4—28no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—48no—
262C2×C3×C4C23×D314yes—
263#67—68no—
264#67—128no—
265#67—128no—
266C2×Dic3—124no—
267D12—38no—
268D12—68no—
269D12—68no—
270D12—128no—
271D12—248no—
272C4×D3—68no—
273C4×D3—128no—
274Dic6—38no—
275C3×C8—28no—
276C3⋊C8—38no—
277C3⋊C8—38no—
278C3⋊C8—68no—
279C2×C32—21no—
280C2×C32—42no—
281C2×C32—81no—
282C2×C32D4211yescharacteristic
283C3⋊D3—42no—
284C3⋊D3—82no—
285#41—22no—
286#41—41no—
287#41—92no—
288#41—182no—
289#41—182no—
290#41—182no—
291#41C22×C3⋊D312yes—
292C2×Q8—22no—
293C2×Q8C22×C3⋊D311yescharacteristic
294C2×D4—92no—
295C2×D4—182no—
296C2×D4—182no—
297C2×D4—182no—
298C2×D4—361no—
299C2×D4—362no—
300C2×D4—361no—
301C2×D4C22×C3⋊D311yescharacteristic
302Q16—92no—
303Q16—182no—
304SD16—22no—
305SD16—92no—
306SD16—92no—
307SD16—182no—
308SD16—182no—
309SD16—182no—
310SD16—182no—
311SD16—182no—
312D8—22no—
313D8—92no—
314D8—182no—
315D8—182no—
316D8—182no—
317D8—182no—
318M16—92no—
319M16—182no—
320M16—182no—
321M16C22×C3⋊D312yes—
322C2×C8—92no—
323C2×C8—182no—
324C2×C8—182no—
325C22⋊C4—41no—
326C42C22×C3⋊D311yescharacteristic
327C22×C3—28no—
328C22×C3—44no—
329C22×C3—84no—
330C22×C3#100414yes—
331C2×D3—68no—
332C2×D3—128no—
333C2×D3—248no—
334C2×D3—484no—
335C2×D3—488no—
336C3×C4—28no—
337C3×C4—44no—
338C3×C4—44no—
339C3×C4C2×D3×D418yes—
340Dic3—68no—
341C32#328811yescharacteristic, complemented, Sylow
342C23—21no—
343C23—182no—
344C23—362no—
345C23—361no—
346Q8—22no—
347Q8—41no—
348Q8—92no—
349Q8D4×C3⋊D312yes—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—92no—
354D4—182no—
355D4—182no—
356D4—182no—
357D4—362no—
358D4—362no—
359D4—362no—
360D4—722no—
361D4D4×C3⋊D312yes—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—182no—
367C2×C4—362no—
368C2×C4—361no—
369C2×C4C23×C3⋊D311yescharacteristic
370C8—22no—
371C8—92no—
372C8—92no—
373C8—182no—
374C2×C3—24no—
375C2×C3—48no—
376C2×C3—84no—
377C2×C3#559014yes—
378D3—128no—
379D3—248no—
380C22—22no—
381C22—41no—
382C22—81no—
383C22—182no—
384C22—362no—
385C22—722no—
386C22—1442no—
387C22—1441no—
388C22#6436111yescharacteristic
389C4—22no—
390C4—41no—
391C4—41no—
392C4—182no—
393C4C2×D4×C3⋊D312yes—
394C3#8028714yescomplemented
395C2—21no—
396C2—42no—
397C2—81no—
398C2—362no—
399C2—722no—
400C2#1059606111yescharacteristic
subgroupG/H
centerC2#10596061
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#454C2
socleC2×C32D42
hypercenter#454C3⋊D3
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #10596308C2semidirect
2. #10596245C2semidirect
3. C32×#454C2semidirect
4. #10592898C2semidirect
5. #10592760C2semidirect
6. #10592757C2semidirect
7. #10592522C2semidirect
8. #10592521C2semidirect
9. #10592453C2semidirect
11. C32×2−1+4C22semidirect
12. #64366C22semidirect
14. C32×AGL(1,ℤ/8)C22semidirect
15. C32×#124C22semidirect
19. #64158C22semidirect
20. #64157C22semidirect
22. #64151C22semidirect
24. C2×#3755C22semidirect
25. C2×#3753C22semidirect
31. #64116C22semidirect
32. #64083C22semidirect
33. C32×#104C22semidirect
34. C32×#101C22semidirect
35. #63660C22semidirect
36. #63650C22semidirect
37. #63649C22semidirect
38. #63632C22semidirect
39. #63630C22semidirect
42. C3×#454D3semidirect
72. #3756D4semidirect
77. #3755D4semidirect
78. #3754D4semidirect
82. #3753D4semidirect
92. C3×2−1+4C2×D3semidirect
95. C3×AGL(1,ℤ/8)C2×D3semidirect
96. C3×#124C2×D3semidirect
114. C3×#104C2×D3semidirect
115. C3×#101C2×D3semidirect
159. #454C3⋊D3semidirect
218. 2−1+4C2×C3⋊D3semidirect
228. AGL(1,ℤ/8)C2×C3⋊D3semidirect
239. #124C2×C3⋊D3semidirect
242. #104C2×C3⋊D3semidirect
243. #101C2×C3⋊D3semidirect
341. C32#3288semidirect
394. C3#80287semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105963082
#105962452
C32×#4542
#105928982
#105927602
#105927572
#105925222
#105925212
#105924532
#802873