Finite Group Databasebeta

← #11798425

Subgroups — #11798425

Order 1152.

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

normal subgroups only

This group has 648 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#10596228C211yesmaximal, characteristic
2C2×C32×SD32C211yesmaximal, characteristic, complemented
3#10592891C211yesmaximal, characteristic, complemented
4#10592878C211yesmaximal, characteristic, complemented
5#10589429C211yesmaximal, characteristic, complemented
6#10589376C211yesmaximal, characteristic, complemented
7#10589374C211yesmaximal, characteristic, complemented
8#71490—34nomaximal
9#64361—21no—
10C2×C32×Q16C2211yescharacteristic, complemented
11C2×C32×D8C2211yescharacteristic
12#64151—21no—
13#64141—21no—
14#64121—21no—
15#64120—22no—
16D8×C3⋊D3—21no—
17#64113C2211yescharacteristic
18#64110C2211yescharacteristic
19C32×SD32—22no—
20C2×C32×C16C2211yescharacteristic, complemented
21#63663—21no—
22#63656—21no—
23#63655—21no—
24#63646C2211yescharacteristic, complemented
25#63639C2211yescharacteristic, complemented
26#5757—34no—
27C2×C3×SD32D314yescomplemented
28#5192—34no—
29#5179—34no—
30#4563—34no—
31#4510—34no—
32#4508—34no—
33C2×C32×Q8—21no—
34C2×C32×D4—21no—
35C2×#638—42no—
36#3830—22no—
37#3830—41no—
38D4×C3⋊D3—22no—
39D4×C3⋊D3—41no—
40#3828—21no—
41#3828D411yescharacteristic
42C32×Q16—21no—
43C32×Q16—21no—
44C32×D8—21no—
45C32×D8D412yes—
46C2×C32×C8C2311yescharacteristic
47#3756—41no—
48#3755—41no—
49#3754—22no—
50#3753—22no—
51#3748—21no—
52#3748D411yescharacteristic
53#3746D411yescharacteristic
54#3745D411yescharacteristic
55#3744—21no—
56#3743—21no—
57C8×C3⋊D3—21no—
58C32×C16—21no—
59C3⋊(C3⋊C16)—21no—
60#2194—91noSylow
61#1004—64no—
62C2×C3×Q16C2×D314yescomplemented
63C2×C3×D8C2×D314yes—
64#942—64no—
65#932—64no—
66#912—64no—
67#911—68no—
68D3×D8—64no—
69#904—34no—
70#901—34no—
71C3×SD32—28no—
72C2×C3×C16C2×D314yescomplemented
73#836—64no—
74#829—64no—
75#828—64no—
76#819—34no—
77#812—34no—
78C23×C32—41no—
79C22×C3⋊D3—42no—
80C32×Q8—41no—
81C32×Q8—41no—
82C32×D4—22no—
83C32×D4—41no—
84C2×C32×C4—41no—
85C2×C32×C4C2×D411yescharacteristic
86#638—21no—
87#638—42no—
88#638—42no—
89#638—41no—
90C2×C3⋊Dic3—42no—
91C4⋊(C3⋊D3)—21no—
92C4⋊(C3⋊D3)D811yescharacteristic
93C4×C3⋊D3—21no—
94C4×C3⋊D3—41no—
95#634—21no—
96#634D811yescharacteristic
97C32×C8C2×D411yescharacteristic
98C32×C8C2×D411yescharacteristic
99C3⋊(C3⋊C8)—21no—
100C3⋊(C3⋊C8)—41no—
101#576—91no—
102#510—91no—
103C2×SD32C3⋊D311yescharacteristic, complemented
104#473—91no—
105#361—91no—
106#359—91no—
107#350—91no—
108C2×C3×Q8—24no—
109C2×C3×D4—24no—
110C2×#67—128no—
111#237—68no—
112#237—124no—
113D3×D4—68no—
114D3×D4—124no—
115#235—34no—
116#235—64no—
117C3×Q16—24no—
118C3×Q16—24no—
119C3×D8—24no—
120C3×D8#6718yes—
121C2×C3×C8C22×D314yes—
122#216—124no—
123#215—124no—
124#214—68no—
125#213—68no—
126#208—34no—
127#208—64no—
128Dic12—34no—
129D24—34no—
130#204—64no—
131ΓL(1,𝔽25)—64no—
132D3×C8—64no—
133C3×C16—24no—
134C3⋊C16—64no—
135C22×C32—42no—
136C22×C32—161no—
137C22×C32AGL(1,ℤ/8)11yescharacteristic
138C2×C3⋊D3—21no—
139C2×C3⋊D3—41no—
140C2×C3⋊D3—162no—
141C32×C4—81no—
142C32×C4#12011yescharacteristic
143C32×C4C2×D811yescharacteristic
144C3⋊Dic3—21no—
145C3⋊Dic3—41no—
146H(5,𝔽2)—181no—
147#137—181no—
148AGL(1,ℤ/8)—181no—
149AGL(1,ℤ/8)—182no—
150#135—91no—
151#135—181no—
152C2×Q16C2×C3⋊D311yescharacteristic, complemented
153C2×D8—181no—
154C2×D8C2×C3⋊D311yescharacteristic
155#131—91no—
156Q32—181no—
157SD32—22no—
158SD32—181no—
159M32—91no—
160C2×C16C2×C3⋊D311yescharacteristic, complemented
161#108—91no—
162#101—181no—
163C23×C3—44no—
164C22×D3—128no—
165C3×Q8—44no—
166C3×Q8—44no—
167C3×D4—28no—
168C3×D4—44no—
169C2×C3×C4—44no—
170C2×C3×C4D3×D414yes—
171#67—64no—
172#67—128no—
173#67—128no—
174#67—124no—
175C2×Dic3—128no—
176D12—34no—
177D12—64no—
178C4×D3—64no—
179C4×D3—124no—
180Dic6—34no—
181Dic6—64no—
182C3×C8D3×D414yes—
183C3×C8C2×#6714yes—
184C3⋊C8—64no—
185C3⋊C8—124no—
186C2×C32—21no—
187C2×C32—82no—
188C2×C32#44711yescharacteristic
189C3⋊D3—41no—
190C3⋊D3—81no—
191#41—91no—
192#41—182no—
193#41—181no—
194#41—361no—
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—182no—
198C2×D4—361no—
199C2×D4—362no—
200Q16—21no—
201Q16—21no—
202Q16—91no—
203Q16—361no—
204SD16—182no—
205SD16—181no—
206SD16—361no—
207D8—21no—
208D8—91no—
209D8—182no—
210D8#63812yes—
211M16—91no—
212M16—181no—
213M16—181no—
214C2×C8—181no—
215C2×C8C22×C3⋊D311yescharacteristic
216C16—21no—
217C16—181no—
218C22×C3—48no—
219C22×C3—164no—
220C22×C3#91114yes—
221C2×D3—64no—
222C2×D3—124no—
223C2×D3—488no—
224C3×C4—84no—
225C3×C4D3×D814yes—
226C3×C4#93714yes—
227Dic3—64no—
228Dic3—124no—
229C32#219411yescharacteristic, complemented, Sylow
230C23—41no—
231C23—362no—
232Q8—41no—
233Q8—41no—
234Q8—91no—
235Q8—181no—
236D4—22no—
237D4—41no—
238D4—91no—
239D4—181no—
240D4—181no—
241D4—362no—
242D4—362no—
243D4—361no—
244C2×C4—41no—
245C2×C4—181no—
246C2×C4—362no—
247C2×C4—361no—
248C2×C4D4×C3⋊D311yescharacteristic
249C8—181no—
250C8—361no—
251C8D4×C3⋊D311yescharacteristic
252C8C2×#63811yescharacteristic
253C2×C3—24no—
254C2×C3—88no—
255C2×C3#515614yes—
256D3—124no—
257D3—244no—
258C22—42no—
259C22—161no—
260C22—181no—
261C22—361no—
262C22—1442no—
263C22#6412011yescharacteristic
264C4—81no—
265C4—181no—
266C4—361no—
267C4D8×C3⋊D311yescharacteristic
268C4#6414611yescharacteristic
269C3#7149014yescomplemented
270C2—21no—
271C2—82no—
272C2—361no—
273C2—721no—
274C2#1059285511yescharacteristic
subgroupG/H
centerC2#10592855
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC2×C32×SD32C2
socleC2×C32#447
prime radical#10596228C2
hypercenterC2×SD32C3⋊D3
hypocenterC32#2194
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. C2×C32×SD32C2semidirect
3. #10592891C2semidirect
4. #10592878C2semidirect
5. #10589429C2semidirect
6. #10589376C2semidirect
7. #10589374C2semidirect
10. C2×C32×Q16C22semidirect
20. C2×C32×C16C22semidirect
24. #63646C22semidirect
25. #63639C22semidirect
27. C2×C3×SD32D3semidirect
62. C2×C3×Q16C2×D3semidirect
72. C2×C3×C16C2×D3semidirect
103. C2×SD32C3⋊D3semidirect
152. C2×Q16C2×C3⋊D3semidirect
160. C2×C16C2×C3⋊D3semidirect
229. C32#2194semidirect
269. C3#71490semidirect

Maximal subgroups

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

subgroupindex
#105962282
C2×C32×SD322
#105928912
#105928782
#105894292
#105893762
#105893742
#714903