Finite Group Databasebeta

← #11798110

Subgroups — #11798110

Order 1152.

690 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#64113C211yesmaximal, characteristic, complemented
2C32×#466C211yesmaximal, characteristic, complemented
3C2×#63654C211yesmaximal, characteristic, complemented
4C2×#63653C211yesmaximal, characteristic, complemented
5#10589415C211yesmaximal, characteristic, complemented
6#10589358C211yesmaximal, characteristic, complemented
7#10589357C211yesmaximal, characteristic, complemented
8#71076—34nomaximal
9C2×#3828—21no—
10C2×C32×D8C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C32×#121—21no—
13C2×#3746C2211yescharacteristic
14#64113—22no—
15#64113—22no—
16C2×#3745C2211yescharacteristic
17C2×#3744—21no—
18C32×#107C2211yescharacteristic
19C32×#102—21no—
20#63654—22no—
21#63653—22no—
22C2×C3⋊(C3⋊C16)C2211yescharacteristic
23C2×C3⋊(C3⋊C16)C2211yescharacteristic
24C2×#904—34no—
25C3×#466D314yescomplemented
26C2×#827—34no—
27C2×#826—34no—
28#4549—34no—
29#4492—34no—
30#4491—34no—
31C2×C32×D4—21no—
32C2×C32×D4—41no—
33C22×C32×C4D411yescharacteristic
34C2×#638—41no—
35#3828—24no—
36#3828—42no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4×C3⋊D3—41no—
39C2×#634—21no—
40C32×D8—21no—
41C32×D8—21no—
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8C2311yescharacteristic
46C32×C4⋊C4—21no—
47C32×C22⋊C4—41no—
48#3746—21no—
49#3746D412yescomplemented
50#3745—21no—
51#3745D412yescomplemented
52#3744—24no—
53C3⋊(C3⋊C16)—21no—
54C3⋊(C3⋊C16)—21no—
55#2186—91noSylow
56C2×#235—64no—
57C2×C3×D8C2×D314yes—
58C22×C3×C8C2×D314yes—
59C3×#121—24no—
60C2×Dic12—34no—
61#904—68no—
62#904—68no—
63C2×D24—34no—
64C2×#204—64no—
65C3×#107C2×D314yes—
66C3×#102—24no—
67#827—68no—
68#826—68no—
69C2×C3⋊C16—34no—
70C2×C3⋊C16—34no—
71C23×C32—41no—
72C23×C32D811yescharacteristic
73C22×C3⋊D3—41no—
74C32×D4—41no—
75C32×D4—41no—
76C32×D4—82no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—41no—
80C2×C32×C4D811yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82#638—44no—
83C2×C3⋊Dic3—41no—
84C4⋊(C3⋊D3)—22no—
85C4⋊(C3⋊D3)—41no—
86C4×C3⋊D3—44no—
87#634—22no—
88#634—41no—
89C32×C8—21no—
90C32×C8C2×D411yescharacteristic
91C32×C8C2×D411yescharacteristic
92C2×#135—91no—
93C2×SD32—91no—
94C2×D16—91no—
95#466C3⋊D311yescharacteristic, complemented
96#358—91no—
97#357—91no—
98C22⋊C16—91no—
99C2×C3×D4—24no—
100C2×C3×D4—44no—
101C22×C3×C4#6714yes—
102C2×#67—124no—
103#235—616no—
104#235—128no—
105C2×D12—64no—
106C2×C4×D3—124no—
107C2×Dic6—64no—
108C3×D8—24no—
109C3×D8—24no—
110C2×C3×C8—24no—
111C2×C3×C8—24no—
112C2×C3×C8#6714yes—
113C2×C3×C8C22×D314yes—
114C3×C4⋊C4—24no—
115C3×C22⋊C4—44no—
116Dic12—38no—
117Dic12—64no—
118D24—38no—
119D24—64no—
120#204—616no—
121C3⋊C16—64no—
122C3⋊C16—64no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—81no—
127C22×C32—81no—
128C22×C32—81no—
129C22×C32C2×D811yescharacteristic
130C2×C3⋊D3—42no—
131C2×C3⋊D3—81no—
132C2×C3⋊D3—81no—
133C32×C4—21no—
134C32×C4—81no—
135C32×C4#12011yescharacteristic
136C32×C4AGL(1,ℤ/8)11yescharacteristic
137C3⋊Dic3—42no—
138C2×#41—181no—
139#135—182no—
140#135—182no—
141C2×Q16—91no—
142C2×SD16—181no—
143C2×D8—91no—
144C2×D8C2×C3⋊D311yescharacteristic
145C22×C8C2×C3⋊D311yescharacteristic
146#121—21no—
147SD32—182no—
148D16—182no—
149C2×C16—91no—
150C2×C16—91no—
151#107C2×C3⋊D311yescharacteristic
152#102—21no—
153C23×C3—44no—
154C23×C3#21314yes—
155C22×D3—124no—
156C3×D4—44no—
157C3×D4—44no—
158C3×D4—88no—
159C2×C3×C4—24no—
160C2×C3×C4—24no—
161C2×C3×C4—44no—
162C2×C3×C4#21314yes—
163C2×C3×C4C2×#6714yes—
164#67—1216no—
165C2×Dic3—124no—
166D12—68no—
167D12—124no—
168C4×D3—1216no—
169Dic6—68no—
170Dic6—124no—
171C3×C8—24no—
172C3×C8D3×D414yes—
173C3×C8D3×D414yes—
174C2×C32—41no—
175C2×C32—161no—
176C2×C32#44711yescharacteristic
177C2×C32#50811yescharacteristic
178C2×C32#50911yescharacteristic
179C3⋊D3—82no—
180#41—184no—
181#41—362no—
182C2×Q8—181no—
183C2×D4—21no—
184C2×D4—41no—
185C2×D4—181no—
186C2×D4—361no—
187C22×C4—361no—
188C22×C4#63811yescharacteristic
189Q16—92no—
190Q16—181no—
191SD16—184no—
192D8—21no—
193D8—21no—
194D8—92no—
195D8—181no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8#63811yescharacteristic
199C2×C8C22×C3⋊D311yescharacteristic
200C4⋊C4—21no—
201C22⋊C4—41no—
202C16—181no—
203C16—181no—
204C22×C3—24no—
205C22×C3—24no—
206C22×C3—24no—
207C22×C3—84no—
208C22×C3—84no—
209C22×C3—84no—
210C22×C3C2×#21314yes—
211C2×D3—128no—
212C2×D3—244no—
213C2×D3—244no—
214C3×C4—24no—
215C3×C4—84no—
216C3×C4#93714yes—
217C3×C4#94914yes—
218Dic3—128no—
219C32#218611yescharacteristic, complemented, Sylow
220C23—41no—
221C23—361no—
222C23#375311yescharacteristic
223Q8—182no—
224Q8—361no—
225D4—41no—
226D4—41no—
227D4—82no—
228D4—182no—
229D4—364no—
230D4—361no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—364no—
235C2×C4—361no—
236C2×C4#375311yescharacteristic
237C2×C4C2×#63811yescharacteristic
238C8—21no—
239C8D4×C3⋊D311yescharacteristic
240C8D4×C3⋊D311yescharacteristic
241C2×C3—44no—
242C2×C3—164no—
243C2×C3#503614yes—
244C2×C3#514714yes—
245C2×C3#519414yes—
246D3—248no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—81no—
251C22—81no—
252C22—81no—
253C22—362no—
254C22—721no—
255C22—721no—
256C22C2×#375311yescharacteristic
257C4—21no—
258C4—81no—
259C4—362no—
260C4#6414611yescharacteristic
261C4#6415811yescharacteristic
262C3#7107614yescomplemented
263C2—41no—
264C2—161no—
265C2—722no—
266C2#1059273511yescharacteristic
267C2#1059284611yescharacteristic
268C2#1059289311yescharacteristic
subgroupG/H
centerC22C2×#3753
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#466C2
socleC22×C32C2×D8
hypercenter#466C3⋊D3
hypocenterC32#2186
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#64113C2semidirect
2. C32×#466C2semidirect
3. C2×#63654C2semidirect
4. C2×#63653C2semidirect
5. #10589415C2semidirect
6. #10589358C2semidirect
7. #10589357C2semidirect
25. C3×#466D3semidirect
49. #3746D4semidirect
51. #3745D4semidirect
95. #466C3⋊D3semidirect
219. C32#2186semidirect
262. C3#71076semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
C32×#4662
C2×#636542
C2×#636532
#105894152
#105893582
#105893572
#710763