Finite Group Databasebeta

← #11789703

Subgroups — #11789703

Order 1152.

648 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 171 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#10592831C211yesmaximal, characteristic
2#10592824C211yesmaximal, characteristic, complemented
3#10592704C211yesmaximal, characteristic
4C2×#63632C211yesmaximal, characteristic
5C4×#3748C211yesmaximal, characteristic, complemented
6C32×#339C211yesmaximal, characteristic, complemented
7#10589399C211yesmaximal, characteristic, complemented
8#68750—34nomaximal
9C2×#3828C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16#63651C412yescomplemented
17#63650C412yescomplemented
18#63646—22no—
19#63632—21no—
20#63632—21no—
21#63632—22no—
22#63630—21no—
23C4×C3⋊(C3⋊C8)—21no—
24#5132—34no—
25#5125—34no—
26#5005—34no—
27C2×#805—34no—
28C4×#208—34no—
29C3×#339D314yescomplemented
30#4533—34no—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C2×#638—21no—
34#3828—21no—
35#3828—21no—
36#3828—21no—
37#3828—21no—
38C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
39C2×C4×C3⋊D3—21no—
40C2×#634C2×C411yescharacteristic
41C32×M16—21no—
42C32×M16C2×C412yes—
43C2×C32×C8—21no—
44C32×C4⋊C4—21no—
45C32×C22⋊C4—21no—
46C32×C42—21no—
47C32×C42—21no—
48C32×C42D411yescharacteristic
49C32×C42D411yescharacteristic
50#3748—21no—
51#3748—21no—
52#3748—21no—
53#3748—21no—
54#3748C2×C412yes—
55#3748D412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59#1932—91noSylow
60C2×#235—34no—
61C2×C3×M16C2×D314yes—
62C3×#117C2×D314yes—
63C2×C3×C42C2×D314yes—
64C2×#208—34no—
65C2×#208—34no—
66C2×#208—34no—
67#824—38no—
68#823—38no—
69#819—68no—
70#805—68no—
71#805—64no—
72#805—64no—
73#803—64no—
74C4×C3⋊C8—64no—
75C23×C32#4111yescharacteristic
76C22×C3⋊D3—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—42no—
80C2×C32×C4—41no—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4#4111yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C32×C4#4111yescharacteristic
87#638—41no—
88#638—41no—
89C2×C3⋊Dic3—21no—
90C4⋊(C3⋊D3)—21no—
91C4⋊(C3⋊D3)—21no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94#634—21no—
95#634—21no—
96C32×C8—22no—
97C3⋊(C3⋊C8)—22no—
98C3⋊(C3⋊C8)—22no—
99C3⋊(C3⋊C8)—41no—
100#430—91no—
101#421—91no—
102C2×#104—91no—
103#413—91no—
104C4×M16—91no—
105#344—91no—
106#339C3⋊D311yescharacteristic, complemented
107C22×C3×C4—24no—
108C22×C3×C4C22×D314yes—
109C2×#67—64no—
110#235—64no—
111#235—64no—
112#235—64no—
113#235—64no—
114C2×D12—34no—
115C2×C4×D3—64no—
116C2×Dic6—34no—
117C3×M16—24no—
118C3×M16C4×D318yes—
119C2×C3×C8—24no—
120C3×C4⋊C4—24no—
121C3×C22⋊C4—24no—
122C3×C42—24no—
123C3×C42—24no—
124C3×C42D1214yes—
125C3×C42D1214yes—
126#208—38no—
127#208—38no—
128#208—64no—
129#208—64no—
130#208—64no—
131#208—64no—
132C2×C3⋊C8—64no—
133C2×C3⋊C8—64no—
134C2×C3⋊C8—64no—
135C22×C32—41no—
136C22×C32#11711yescharacteristic
137C22×C32#12311yescharacteristic
138C22×C32#12411yescharacteristic
139C2×C3⋊D3—41no—
140C2×C3⋊D3—81no—
141C32×C4—22no—
142C32×C4—41no—
143C32×C4—81no—
144C32×C4C4×D411yescharacteristic
145C32×C4C4×D411yescharacteristic
146C32×C4#12111yescharacteristic
147C32×C4#12611yescharacteristic
148C3⋊Dic3—41no—
149C2×#41—91no—
150C2×M16—91no—
151C2×M16—91no—
152C2×M16—91no—
153C2×M16C2×C3⋊D311yescharacteristic
154#117C2×C3⋊D311yescharacteristic
155C2×C42C2×C3⋊D311yescharacteristic
156#108—182no—
157#104—182no—
158#104—181no—
159#104—181no—
160#101—92no—
161#100—92no—
162#97—181no—
163C4×C8—181no—
164C23×C3#23714yes—
165C22×D3—64no—
166C2×C3×C4—24no—
167C2×C3×C4—24no—
168C2×C3×C4—48no—
169C2×C3×C4—44no—
170C2×C3×C4C2×C4×D314yes—
171C2×C3×C4C2×D1214yes—
172C2×C3×C4#23514yes—
173C2×C3×C4D3×D414yes—
174C2×C3×C4#23714yes—
175C2×C3×C4#23914yes—
176#67—124no—
177#67—124no—
178C2×Dic3—64no—
179D12—64no—
180D12—64no—
181C4×D3—124no—
182C4×D3—124no—
183Dic6—64no—
184Dic6—64no—
185C3×C8—28no—
186C3⋊C8—68no—
187C3⋊C8—68no—
188C3⋊C8—124no—
189C2×C32—21no—
190C2×C32—21no—
191C2×C32—21no—
192C2×C32#38811yescharacteristic
193C3⋊D3—81no—
194#41—181no—
195#41—181no—
196#41—181no—
197#41—181no—
198C2×Q8—91no—
199C2×D4—91no—
200C2×D4—181no—
201C22×C4—21no—
202C22×C4—181no—
203C22×C4C22×C3⋊D311yescharacteristic
204M16—21no—
205M16—92no—
206M16—92no—
207M16—181no—
208M16—181no—
209M16—181no—
210M16—181no—
211M16C4×C3⋊D312yes—
212C2×C8—21no—
213C2×C8—181no—
214C2×C8—181no—
215C2×C8—181no—
216C4⋊C4—21no—
217C22⋊C4—21no—
218C42—21no—
219C42—21no—
220C42C4⋊(C3⋊D3)11yescharacteristic
221C42C4⋊(C3⋊D3)11yescharacteristic
222C22×C3—44no—
223C22×C3#88514yes—
224C22×C3#88614yes—
225C22×C3#89214yes—
226C2×D3—124no—
227C2×D3—244no—
228C3×C4—28no—
229C3×C4—44no—
230C3×C4—84no—
231C3×C4C4×D1214yes—
232C3×C4#67⋊C414yes—
233C3×C4#89514yes—
234C3×C4#89814yes—
235Dic3—124no—
236C32#193211yescharacteristic, complemented, Sylow
237C23—181no—
238C23#383011yescharacteristic
239Q8—181no—
240Q8—181no—
241D4—181no—
242D4—181no—
243D4—361no—
244D4—361no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—181no—
250C2×C4—361no—
251C2×C4—361no—
252C2×C4C2×C4×C3⋊D311yescharacteristic
253C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
254C2×C4#382811yescharacteristic
255C2×C4D4×C3⋊D311yescharacteristic
256C2×C4#383011yescharacteristic
257C2×C4#383211yescharacteristic
258C8—22no—
259C8—182no—
260C8—182no—
261C8—361no—
262C2×C3—24no—
263C2×C3—24no—
264C2×C3—24no—
265C2×C3#467014yes—
266D3—244no—
267C22—41no—
268C22—361no—
269C22—721no—
270C22#6409411yescharacteristic
271C22#6409511yescharacteristic
272C22#6410111yescharacteristic
273C4—22no—
274C4—41no—
275C4—81no—
276C4—361no—
277C4C4×C4⋊(C3⋊D3)11yescharacteristic
278C4#6409011yescharacteristic
279C4#6410411yescharacteristic
280C4#6410711yescharacteristic
281C3#6875014yescomplemented
282C2—21no—
283C2—21no—
284C2—21no—
285C2—721no—
286C2#1059236911yescharacteristic
subgroupG/H
centerC4#64104
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC2×C32#388
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1932
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #10592824C2semidirect
5. C4×#3748C2semidirect
6. C32×#339C2semidirect
7. #10589399C2semidirect
16. #63651C4semidirect
17. #63650C4semidirect
29. C3×#339D3semidirect
106. #339C3⋊D3semidirect
236. C32#1932semidirect
281. C3#68750semidirect

Maximal subgroups

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

subgroupindex
#105928312
#105928242
#105927042
C2×#636322
C4×#37482
C32×#3392
#105893992
#687503