Finite Group Databasebeta

← #11876986

Subgroups — #11876986

Order 1152.

963 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 963 conjugacy classes of subgroups — too many to draw. Only its 162 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#10594929C212yesmaximal, complemented
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#5135C212yesmaximal, complemented
4#10591167C212yesmaximal, complemented
5#10590900C211yesmaximal, characteristic, complemented
6#10590886C211yesmaximal, characteristic, complemented
7#10590885C212yesmaximal, complemented
8#10590781C212yesmaximal, complemented
9#10590741C212yesmaximal, complemented
10#80853—32nomaximal
11C2×#3805—22no—
12C2×C32×M16C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#930C2214yes—
16C2×C3×D24C2212yes—
17#63980—22no—
18#63919C2212yes—
19#63915—22no—
20#63914C2212yes—
21#63902—22no—
22#63898C2214yes—
23C2×#3713C2212yes—
24#63642C2211yescharacteristic
25#63642C2211yescharacteristic
26C8×C3⋊Dic3C2211yescharacteristic
27C8×C3⋊Dic3C2211yescharacteristic
28C3×#821C2214yes—
29C3×#817C2212yes—
30#63574C2212yes—
31#63562C2214yes—
32#5596—34no—
33C3×#469—32no—
34#5152—32no—
35#5151—32no—
36#5135D312yescomplemented
37Dic3×M16—32no—
38Dic3×M16—61no—
39#5039—34no—
40#4869—32no—
41#4855—32no—
42#4785—34no—
43#4760—34no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D412yes—
46C2×C3×#67—24no—
47C2×C3×D12C2314yes—
48C2×#627—22no—
49C2×#625—22no—
50C2×#625—22no—
51#3805—48no—
52C2×D3×Dic3—24no—
53C32×M16—22no—
54C2×C32×C8C2311yescharacteristic
55C2×C32×C8C2311yescharacteristic
56C4×C3⋊Dic3D412yes—
57C4×C3⋊Dic3C2311yescharacteristic
58C4×C3⋊Dic3C2311yescharacteristic
59#3748—22no—
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61C2×C3⋊(C3⋊C8)C2311yescharacteristic
62C3×(C2×D3)⋊C4—24no—
63C3×C4⋊Dic3C2314yes—
64C3×D24—24no—
65#3724—22no—
66(C2×D3)⋊Dic3—24no—
67#3713—24no—
68#3184—91noSylow
69C2×#237—64no—
70C2×C3×D8—32no—
71C2×C3×M16—21no—
72C2×C3×M16C2×D312yes—
73C3×#121—34no—
74#940—34no—
75#939—64no—
76D4×Dic3—34no—
77C2×#213—34no—
78#930C2×D314yes—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C2×#208—32no—
82C2×#208—61no—
83C2×D24C2×D312yes—
84#893—34no—
85#888—34no—
86#885—64no—
87#67⋊C4—64no—
88C3×#106—32no—
89C3×#102—34no—
90#832—34no—
91#821C2×D314yes—
92#817C2×D312yes—
93#815—32no—
94#815—32no—
95#815—61no—
96#815—61no—
97C8×Dic3—32no—
98C8×Dic3—32no—
99C8×Dic3—61no—
100C8×Dic3—61no—
101#809—34no—
102#808—34no—
103C23×C32C2×D411yescharacteristic
104C22×C3×D3—24no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2411yescharacteristic
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3C2×D412yes—
111C2×C3⋊Dic3C2×D412yes—
112C3×#67—48no—
113C2×C3×Dic3—24no—
114C3×D12—24no—
115C3×D12—24no—
116#627—44no—
117#625—44no—
118#625—44no—
119D3×Dic3—48no—
120C32×C8—21no—
121C32×C8#4112yescomplemented
122C3⋊(C3⋊C8)—21no—
123C3⋊(C3⋊C8)#4112yescomplemented
124#532—92no—
125#498—91no—
126#493—91no—
127#486—92no—
128#469—32no—
129#469—92no—
130#442—92no—
131#442—92no—
132C4×M16—91no—
133C2×C3×D4—34no—
134C2×C3×D4—64no—
135C22×C3×C4—21no—
136C22×C3×C4C22×D312yes—
137C2×#67—24no—
138C2×#67—64no—
139C2×#67—64no—
140C22×Dic3—34no—
141C22×Dic3—62no—
142C22×Dic3—64no—
143#237—1216no—
144C2×D12C22×D314yes—
145C2×C4×D3—64no—
146C2×Dic6—64no—
147C3×D8—64no—
148C3×M16—24no—
149C3×M16—24no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8C22×D312yes—
153C2×C3×C8C22×D312yes—
154C3×C4⋊C4—34no—
155C3×C22⋊C4—64no—
156#217—64no—
157#213—68no—
158(C2×D3)⋊C4—24no—
159(C2×D3)⋊C4—64no—
160C4⋊Dic3C22×D314yes—
161Dic3⋊C4—64no—
162C4×Dic3—34no—
163C4×Dic3—32no—
164C4×Dic3—32no—
165C4×Dic3—61no—
166C4×Dic3—61no—
167C4×Dic3—62no—
168#208—64no—
169#208—64no—
170C2×C3⋊C8—32no—
171C2×C3⋊C8—32no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8—61no—
174D24—24no—
175C22×C32—21no—
176C22×C32—22no—
177C22×C32C22×D411yescharacteristic
178C2×C3×D3—44no—
179C2×C3×D3—44no—
180C2×C3×D3—44no—
181C32×C4—21no—
182C32×C4C2×#4111yescharacteristic
183C32×C4C2×#4111yescharacteristic
184C3⋊Dic3—22no—
185C3⋊Dic3AGL(1,ℤ/8)14yes—
186C3×Dic3—44no—
187C2×#41—182no—
188C2×D8—32no—
189C2×D8—92no—
190C2×M16—91no—
191C2×M16D3211yescharacteristic
192C4⋊Q8—92no—
193#127—92no—
194#124—182no—
195#121—34no—
196#121—182no—
197C4×D4—94no—
198C4×D4—182no—
199C2×C42—91no—
200#106—32no—
201#106—92no—
202#102—34no—
203#102—94no—
204#97—91no—
205#97—91no—
206C4×C8—91no—
207C4×C8—91no—
208C23×C3—21no—
209C23×C3—64no—
210C23×C3D3×D412yes—
211C22×D3—24no—
212C3×D4—64no—
213C3×D4—64no—
214C3×D4—128no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—64no—
222C2×C3×C4D3×D412yes—
223C2×C3×C4C23×D312yes—
224#67—48no—
225#67—128no—
226#67—128no—
227C2×Dic3—24no—
228C2×Dic3—34no—
229C2×Dic3—34no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—68no—
233C2×Dic3—124no—
234C2×Dic3—128no—
235D12—24no—
236D12—24no—
237C4×D3—128no—
238Dic6—128no—
239C3×C8—22no—
240C3×C8—22no—
241C3×C8—22no—
242C3×C8#23714yescomplemented
243C3⋊C8—34no—
244C3⋊C8—62no—
245C3⋊C8—62no—
246C3⋊C8—62no—
247C2×C32—41no—
248C2×C32#53211yescharacteristic
249C2×C32C2×AGL(1,ℤ/8)12yes—
250C3×D3—84no—
251#41—368no—
252C2×Q8—182no—
253C2×D4—34no—
254C2×D4—64no—
255C2×D4—182no—
256C2×D4—182no—
257C22×C4—92no—
258C22×C4—184no—
259C22×C4C2×D3211yescharacteristic
260D8—64no—
261D8—184no—
262M16—22no—
263M16—182no—
264C2×C8—91no—
265C2×C8—91no—
266C2×C8C2×D3211yescharacteristic
267C2×C8C2×D3211yescharacteristic
268C4⋊C4—34no—
269C4⋊C4—182no—
270C22⋊C4—64no—
271C22⋊C4—184no—
272C42—91no—
273C42—91no—
274C42—92no—
275C22×C3—22no—
276C22×C3—24no—
277C22×C3—22no—
278C22×C3—21no—
279C22×C3—42no—
280C22×C3—124no—
281C22×C3—124no—
282C22×C3—124no—
283C22×C3C2×D3×D412yes—
284C2×D3—44no—
285C2×D3—44no—
286C2×D3—44no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—124no—
292C3×C4C2×#23712yes—
293C3×C4D3×#4112yes—
294Dic3—38no—
295Dic3—44no—
296Dic3—64no—
297Dic3—64no—
298Dic3—122no—
299C32#318411yescharacteristic, complemented, Sylow
300C23—64no—
301C23#380211yescharacteristic
302Q8—364no—
303D4—64no—
304D4—64no—
305D4—128no—
306D4—364no—
307D4—364no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—64no—
311C2×C4—92no—
312C2×C4—92no—
313C2×C4—184no—
314C2×C4—368no—
315C2×C4#380211yescharacteristic
316C2×C4C22×D3211yescharacteristic
317C8—21no—
318C8—92no—
319C8—181no—
320C8#380512yescomplemented
321C2×C3—21no—
322C2×C3—22no—
323C2×C3—42no—
324C2×C3—42no—
325C2×C3—244no—
326C2×C3#559612yes—
327C2×C3D3×AGL(1,ℤ/8)14yes—
328D3—84no—
329C22—21no—
330C22—22no—
331C22—124no—
332C22—124no—
333C22—124no—
334C22C2×#380211yescharacteristic
335C4—21no—
336C4—94no—
337C4—124no—
338C4—182no—
339C4#6430611yescharacteristic
340C4C2×#380511yescharacteristic
341C3—21no—
342C3#8085312yescomplemented
343C2—41no—
344C2—244no—
345C2#1059471612yes—
346C2#1059492911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594929C2semidirect
2. M16×C3⋊Dic3C2semidirect
3. C3×#5135C2semidirect
4. #10591167C2semidirect
5. #10590900C2semidirect
6. #10590886C2semidirect
7. #10590885C2semidirect
8. #10590781C2semidirect
9. #10590741C2semidirect
36. #5135D3semidirect
121. C32×C8#41semidirect
123. C3⋊(C3⋊C8)#41semidirect
242. C3×C8#237semidirect
299. C32#3184semidirect
320. C8#3805semidirect
342. C3#80853semidirect

Maximal subgroups

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

subgroupindex
#105949292
M16×C3⋊Dic32
C3×#51352
#105911672
#105909002
#105908862
#105908852
#105907812
#105907412
#808533