Finite Group Databasebeta

← #11798261

Subgroups — #11798261

Order 1152.

678 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 107 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#10596239C211yesmaximal, characteristic, complemented
2C32×#509C211yesmaximal, characteristic, complemented
3#10592858C211yesmaximal, characteristic, complemented
4#10592846C211yesmaximal, characteristic, complemented
5#10589432C211yesmaximal, characteristic, complemented
6#10589384C211yesmaximal, characteristic, complemented
7#10589380C211yesmaximal, characteristic, complemented
8#71516—34nomaximal
9#41×C3⋊D3—21no—
10C32×#135C2211yescharacteristic
11C2×C32×D8C2211yescharacteristic, complemented
12#64159—21no—
13#64147—21no—
14#64127—21no—
15#64124—21no—
16#64123—21no—
17#64120—21no—
18#64113C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20C32×SD32—21no—
21C32×D16—21no—
22C32×M32C2211yescharacteristic, complemented
23#63659—21no—
24#63654—21no—
25#63653—21no—
26#63644C2211yescharacteristic, complemented
27#63639C2211yescharacteristic, complemented
28#5768—34no—
29C3×#509D314yescomplemented
30#5159—34no—
31#5147—34no—
32#4566—34no—
33#4518—34no—
34#4514—34no—
35C32×#41—21no—
36C2×C32×D4—21no—
37C2×#638—41no—
38#3832—21no—
39Q8×C3⋊D3—21no—
40#3830—21no—
41#3830—41no—
42D4×C3⋊D3—21no—
43D4×C3⋊D3—41no—
44#3828—21no—
45#3828—41no—
46C2×C4×C3⋊D3—41no—
47C2×C4×C3⋊D3D411yescharacteristic
48C32×Q16D411yescharacteristic, complemented
49C32×SD16—21no—
50C32×D8—21no—
51C32×D8—21no—
52C32×D8D411yescharacteristic, complemented
53C2×C32×C8C2311yescharacteristic
54#3757—41no—
55#3756—21no—
56#3755—21no—
57#3754—21no—
58#3753—21no—
59C4⋊(C3⋊Dic3)—21no—
60C2×C3⋊(C3⋊C8)D411yescharacteristic
61#3746D411yescharacteristic, complemented
62#3745D411yescharacteristic, complemented
63#3744—21no—
64#3743—21no—
65#3743—21no—
66C32×C16—21no—
67C3⋊(C3⋊C16)—21no—
68#2190—91noSylow
69D3×#41—64no—
70C3×#135C2×D314yes—
71C2×C3×D8C2×D314yescomplemented
72#950—64no—
73#938—64no—
74#918—64no—
75#915—64no—
76#914—64no—
77#911—64no—
78#904—34no—
79C2×ΓL(1,𝔽25)—34no—
80C3×SD32—24no—
81C3×D16—24no—
82C3×M32C2×D314yescomplemented
83#832—64no—
84#827—64no—
85#826—64no—
86#817—34no—
87#812—34no—
88C23×C32—41no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3D811yescharacteristic
91C32×Q8—21no—
92C32×D4—21no—
93C32×D4—41no—
94C32×D4—41no—
95C32×D4—41no—
96C2×C32×C4—41no—
97C2×C32×C4C2×D411yescharacteristic
98#638—41no—
99#638—41no—
100#638—41no—
101#638—82no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3D811yescharacteristic
105C4⋊(C3⋊D3)—21no—
106C4⋊(C3⋊D3)—41no—
107C4×C3⋊D3—21no—
108C4×C3⋊D3—21no—
109C4×C3⋊D3—41no—
110C4×C3⋊D3—41no—
111C4×C3⋊D3—41no—
112#634—21no—
113#634—41no—
114C32×C8C2×D411yescharacteristic
115C32×C8C2×D411yescharacteristic
116C3⋊(C3⋊C8)—21no—
117#575—91no—
118#509—91no—
119#509C3⋊D311yescharacteristic, complemented
120#469—91no—
121#360—91no—
122#360—91no—
123#349—91no—
124C3×#41—24no—
125C2×C3×D4—24no—
126C2×#67—124no—
127#239—64no—
128D3×Q8—64no—
129#237—64no—
130#237—124no—
131D3×D4—64no—
132D3×D4—124no—
133#235—64no—
134#235—124no—
135C2×C4×D3—34no—
136C2×C4×D3—124no—
137C3×Q16#6714yescomplemented
138C3×SD16—24no—
139C3×D8—24no—
140C3×D8—24no—
141C3×D8#6714yescomplemented
142C2×C3×C8C22×D314yes—
143#217—124no—
144#216—64no—
145#215—64no—
146#214—64no—
147#213—64no—
148C4⋊Dic3—64no—
149C2×C3⋊C8—34no—
150Dic12—34no—
151D24—34no—
152#204—64no—
153ΓL(1,𝔽25)—64no—
154ΓL(1,𝔽25)—64no—
155C3×C16—24no—
156C3⋊C16—64no—
157C22×C32—41no—
158C22×C32—81no—
159C22×C32—81no—
160C22×C32—81no—
161C22×C32C2×D811yescharacteristic
162C2×C3⋊D3—21no—
163C2×C3⋊D3—41no—
164C2×C3⋊D3—41no—
165C2×C3⋊D3—82no—
166C32×C4—41no—
167C32×C4#12011yescharacteristic
168C32×C4AGL(1,ℤ/8)11yescharacteristic
169C3⋊Dic3—21no—
170C3⋊Dic3—41no—
171C3⋊Dic3—81no—
172C2×#41—181no—
173#137—181no—
174#137—181no—
175AGL(1,ℤ/8)—181no—
176AGL(1,ℤ/8)—181no—
177#135—91no—
178#135—181no—
179#135C2×C3⋊D311yescharacteristic
180C2×D8C2×C3⋊D311yescharacteristic, complemented
181C2×M16—91no—
182#121—181no—
183SD32—21no—
184SD32—181no—
185D16—21no—
186D16—181no—
187M32—91no—
188M32C2×C3⋊D311yescharacteristic, complemented
189#106—91no—
190#102—181no—
191C23×C3—44no—
192C22×D3—34no—
193C22×D3—124no—
194C3×Q8—24no—
195C3×D4—24no—
196C3×D4—44no—
197C3×D4—44no—
198C3×D4—44no—
199C2×C3×C4—44no—
200C2×C3×C4D3×D414yes—
201#67—124no—
202#67—124no—
203#67—124no—
204#67—248no—
205C2×Dic3—34no—
206C2×Dic3—124no—
207C2×Dic3—124no—
208D12—64no—
209D12—124no—
210C4×D3—64no—
211C4×D3—64no—
212C4×D3—124no—
213C4×D3—124no—
214C4×D3—124no—
215Dic6—64no—
216Dic6—124no—
217C3×C8D3×D414yes—
218C3×C8C2×#6714yes—
219C3⋊C8—64no—
220C2×C32—21no—
221C2×C32—81no—
222C2×C32—161no—
223C2×C32#44711yescharacteristic
224C3⋊D3—41no—
225C3⋊D3—81no—
226#41—21no—
227#41—181no—
228#41—181no—
229#41—181no—
230#41—361no—
231#41—361no—
232C2×Q8—181no—
233C2×D4—21no—
234C2×D4—181no—
235C2×D4—361no—
236C2×D4—361no—
237C22×C4—91no—
238C22×C4—361no—
239Q16—91no—
240Q16—181no—
241Q16#63811yescharacteristic, complemented
242SD16—21no—
243SD16—181no—
244SD16—181no—
245SD16—181no—
246D8—21no—
247D8—21no—
248D8—91no—
249D8—181no—
250D8#63811yescharacteristic, complemented
251M16—181no—
252M16—181no—
253C2×C8—91no—
254C2×C8C22×C3⋊D311yescharacteristic
255C4⋊C4—181no—
256C22⋊C4—361no—
257C16—21no—
258C16—181no—
259C22×C3—44no—
260C22×C3—84no—
261C22×C3—84no—
262C22×C3—84no—
263C22×C3D3×D814yes—
264C2×D3—64no—
265C2×D3—124no—
266C2×D3—124no—
267C2×D3—248no—
268C3×C4—44no—
269C3×C4#91114yes—
270C3×C4#93714yes—
271Dic3—64no—
272Dic3—124no—
273Dic3—244no—
274C32#219011yescharacteristic, complemented, Sylow
275C23—41no—
276C23—91no—
277C23—361no—
278Q8—21no—
279Q8—181no—
280Q8—361no—
281D4—21no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—181no—
286D4—361no—
287D4—361no—
288D4—361no—
289D4—361no—
290D4—722no—
291C2×C4—41no—
292C2×C4—91no—
293C2×C4—181no—
294C2×C4—181no—
295C2×C4—361no—
296C2×C4—361no—
297C2×C4—361no—
298C2×C4—361no—
299C2×C4—361no—
300C2×C4D4×C3⋊D311yescharacteristic
301C8—181no—
302C8D4×C3⋊D311yescharacteristic
303C8C2×#63811yescharacteristic
304C2×C3—24no—
305C2×C3—84no—
306C2×C3—164no—
307C2×C3#515614yes—
308D3—124no—
309D3—244no—
310C22—41no—
311C22—81no—
312C22—81no—
313C22—81no—
314C22—181no—
315C22—361no—
316C22—361no—
317C22—722no—
318C22D8×C3⋊D311yescharacteristic
319C4—41no—
320C4—181no—
321C4—361no—
322C4—721no—
323C4#6412011yescharacteristic
324C4#6414611yescharacteristic
325C3#7151614yescomplemented
326C2—21no—
327C2—81no—
328C2—161no—
329C2—361no—
330C2—721no—
331C2#1059285511yescharacteristic
subgroupG/H
centerC2#10592855
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#509C2
socleC2×C32#447
hypercenter#509C3⋊D3
hypocenterC32#2190
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #10596239C2semidirect
2. C32×#509C2semidirect
3. #10592858C2semidirect
4. #10592846C2semidirect
5. #10589432C2semidirect
6. #10589384C2semidirect
7. #10589380C2semidirect
11. C2×C32×D8C22semidirect
22. C32×M32C22semidirect
26. #63644C22semidirect
27. #63639C22semidirect
29. C3×#509D3semidirect
48. C32×Q16D4semidirect
52. C32×D8D4semidirect
61. #3746D4semidirect
62. #3745D4semidirect
71. C2×C3×D8C2×D3semidirect
82. C3×M32C2×D3semidirect
119. #509C3⋊D3semidirect
137. C3×Q16#67semidirect
141. C3×D8#67semidirect
180. C2×D8C2×C3⋊D3semidirect
188. M32C2×C3⋊D3semidirect
241. Q16#638semidirect
250. D8#638semidirect
274. C32#2190semidirect
325. C3#71516semidirect

Maximal subgroups

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

subgroupindex
#105962392
C32×#5092
#105928582
#105928462
#105894322
#105893842
#105893802
#715163