Finite Group Databasebeta

← #11796737

Subgroups — #11796737

Order 1152.

478 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 64 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×Q16×C3⋊D3C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic
3#10593762C211yesmaximal, characteristic
4#10590197C214yesmaximal, complemented
5C2×Q8×C3⋊D3—21no—
6#64286—21no—
7C2×C32×Q16C411yescharacteristic, complemented
8C2×#3756—21no—
9Q16×C3⋊D3—21no—
10Q16×C3⋊D3—21no—
11Q16×C3⋊D3C412yescomplemented
12Q16×C3⋊D3C2212yes—
13C2×#3746C411yescharacteristic, complemented
14C2×C8×C3⋊D3C2211yescharacteristic
15#63773—21no—
16#63769C2212yes—
17#63768—21no—
18#63765—21no—
19#63764C2212yes—
20C2×D3×Q16—62no—
21C2×C32×Q8—21no—
22Q8×C3⋊D3—22no—
23Q8×C3⋊D3—22no—
24Q8×C3⋊D3—41no—
25Q8×C3⋊D3—41no—
26C2×C4×C3⋊D3—41no—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×#634—21no—
29C2×#634—41no—
30C22⋊#157—41no—
31C4⋊#157—22no—
32C4×#157—41no—
33C32×Q16—21no—
34C32×Q16C2×C412yes—
35C2×C32×C8C2×C411yescharacteristic
36#3756—22no—
37#3756—22no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39#3746—21no—
40#3746C2×C412yes—
41C8×C3⋊D3C2×C411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C8×C3⋊D3D411yescharacteristic
44C8×C3⋊D3C2311yescharacteristic
45#3708—22no—
46#2141—91nomaximal, Sylow
47C2×D3×Q8—64no—
48C2×C3×Q16—22no—
49C2×#216—64no—
50D3×Q16—64no—
51D3×Q16—64no—
52D3×Q16—64no—
53D3×Q16—64no—
54C2×Dic12—62no—
55C2×D3×C8—62no—
56C22×C3⋊D3D811yescharacteristic
57C2×#157—42no—
58C32×Q8—22no—
59C32×Q8—41no—
60C2×C32×C4—41no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3SD1611yescharacteristic
64C4×C3⋊D3—42no—
65C4×C3⋊D3—42no—
66C4×C3⋊D3C22⋊C411yescharacteristic
67C4×C3⋊D3D811yescharacteristic
68C4×C3⋊D3SD1611yescharacteristic
69C4×C3⋊D3C2×D411yescharacteristic
70#634—22no—
71#634—41no—
72#634—42no—
73#634—42no—
74C32×C8C22⋊C411yescharacteristic
75C32×C8C22×C411yescharacteristic
76C3⋊(C3⋊C8)C22⋊C411yescharacteristic
77C3⋊(C3⋊C8)C2×D411yescharacteristic
78C22×Q16—91no—
79C2×M32—91no—
80#427—91no—
81#358—94no—
82C2×C3×Q8—24no—
83D3×Q8—68no—
84D3×Q8—68no—
85D3×Q8—124no—
86D3×Q8—124no—
87C2×C4×D3—62no—
88C2×C4×D3—124no—
89C2×Dic6—64no—
90C2×Dic6—124no—
91C3×Q16—24no—
92C3×Q16—24no—
93C2×C3×C8—22no—
94#216—68no—
95#216—68no—
96C2×C3⋊C8—62no—
97Dic12—64no—
98Dic12—64no—
99D3×C8—62no—
100D3×C8—62no—
101D3×C8—62no—
102D3×C8—62no—
103C22×C32#10211yescharacteristic
104C2×C3⋊D3—22no—
105C2×C3⋊D3#10211yescharacteristic
106C2×C3⋊D3C2×D811yescharacteristic
107#157—82no—
108C32×C4—42no—
109C32×C4#10211yescharacteristic
110C32×C4C2×C22⋊C411yescharacteristic
111C3⋊Dic3—42no—
112C3⋊Dic3#10211yescharacteristic
113C3⋊Dic3C2×SD1611yescharacteristic
114C22×Q8—181no—
115C2×Q16—92no—
116C2×Q16—92no—
117C2×Q16—91no—
118C2×Q16—181no—
119C2×Q16—181no—
120C2×Q16—181no—
121C2×Q16#15711yescharacteristic, complemented
122C22×C8—91no—
123#117—181no—
124M32—181no—
125M32—181no—
126C2×C16—92no—
127#107—92no—
128#106—181no—
129C22×D3—62no—
130C3×Q8—28no—
131C3×Q8—44no—
132C2×C3×C4—22no—
133C2×C3×C4—44no—
134C2×Dic3—62no—
135C2×Dic3—124no—
136C4×D3—62no—
137C4×D3—62no—
138C4×D3—62no—
139C4×D3—62no—
140C4×D3—128no—
141C4×D3—128no—
142Dic6—68no—
143Dic6—128no—
144Dic6—128no—
145Dic6—124no—
146C3×C8—22no—
147C3×C8—22no—
148C3⋊C8—62no—
149C3⋊C8—62no—
150C2×C32—21no—
151C2×C32C2×#10211yescharacteristic
152C3⋊D3—21no—
153C3⋊D3#51012yes—
154C2×Q8—21no—
155C2×Q8—182no—
156C2×Q8—182no—
157C2×Q8—181no—
158C2×Q8—361no—
159C2×Q8—361no—
160C2×Q8—361no—
161C22×C4—91no—
162C22×C4—361no—
163Q16—21no—
164Q16—92no—
165Q16—182no—
166Q16—182no—
167Q16—181no—
168Q16C2×#15712yes—
169C2×C8—91no—
170C2×C8—91no—
171C2×C8—91no—
172C2×C8—91no—
173C2×C8—91no—
174C2×C8C2×#15711yescharacteristic
175C4⋊C4—182no—
176C22⋊C4—361no—
177C42—361no—
178C16—182no—
179C22×C3—22no—
180C2×D3—62no—
181C2×D3—62no—
182C2×D3—68no—
183C3×C4—22no—
184C3×C4—22no—
185C3×C4—48no—
186Dic3—62no—
187Dic3—62no—
188Dic3—128no—
189C32#214111yescharacteristic, complemented, Sylow
190C23—91no—
191Q8—22no—
192Q8—41no—
193Q8—182no—
194Q8—362no—
195Q8—362no—
196Q8—361no—
197C2×C4—41no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—362no—
204C2×C4—362no—
205C2×C4—361no—
206C2×C4—362no—
207C2×C4C22⋊#15711yescharacteristic
208C8—91no—
209C8—91no—
210C8C22⋊#15711yescharacteristic
211C8C22×#15711yescharacteristic
212C2×C3—24no—
213C2×C3—22no—
214D3—64no—
215D3—64no—
216C22—91no—
217C22—91no—
218C22—182no—
219C22#6378211yescharacteristic
220C4—42no—
221C4—91no—
222C4—91no—
223C4—362no—
224C4—722no—
225C4#6378211yescharacteristic
226C4C2×C22⋊#15711yescharacteristic
227C3—22no—
228C2—21no—
229C2—92no—
230C2—181no—
231C2C2×#6378211yescharacteristic
subgroupG/H
centerC2C2×#63782
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC2×C32×Q16C4
socleC2×C32C2×#102
prime radicalC22×C3⋊D3D8
cosocleC8×C3⋊D3C23
hypercenterC2×Q16#157
hypocenterC32#2141
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
4. #10590197C2semidirect
7. C2×C32×Q16C4semidirect
11. Q16×C3⋊D3C4semidirect
13. C2×#3746C4semidirect
121. C2×Q16#157semidirect
189. C32#2141semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×C3⋊D32
#105937682
#105937622
#105901972
#21419