Finite Group Databasebeta

← #11785517

Subgroups — #11785517

Order 1152.

518 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 72 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×#64116C211yesmaximal, characteristic
2#10593808C212yesmaximal
3#10593771C212yesmaximal, complemented
4#10590186C212yesmaximal, complemented
5C2×#3828C2211yescharacteristic
6#64283C2214yes—
7C2×C32×M16C411yescharacteristic
8C22×C3⋊(C3⋊C8)C411yescharacteristic
9#64116—22no—
10#64116—22no—
11C2×#3743C411yescharacteristic
12C2×#3743C2211yescharacteristic
13C2×C8×C3⋊D3C411yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15#63788—22no—
16#63780—22no—
17#63771—22no—
18#63770—22no—
19C2×#907—62no—
20C22×C32×C4C2×C411yescharacteristic
21C2×#638D411yescharacteristic
22C2×#638Q811yescharacteristic
23#3828—22no—
24#3828—22no—
25C2×C4⋊(C3⋊D3)Q811yescharacteristic
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#634D411yescharacteristic
29#3792—24no—
30#3788—24no—
31#3787—24no—
32C32×M16—22no—
33C2×C32×C8C2×C411yescharacteristic
34C2×C32×C8C2×C411yescharacteristic
35C2×C3⋊(C3⋊C8)—21no—
36C2×C3⋊(C3⋊C8)—21no—
37C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39#3743—22no—
40#3743—22no—
41C8×C3⋊D3—21no—
42C8×C3⋊D3—21no—
43C8×C3⋊D3D412yes—
44C8×C3⋊D3D412yes—
45#1813—91nomaximal, Sylow
46C2×#235—62no—
47C2×C3×M16—22no—
48C22×C3⋊C8—62no—
49#907—68no—
50#907—68no—
51C2×ΓL(1,𝔽25)—62no—
52C2×ΓL(1,𝔽25)—62no—
53C2×D3×C8—62no—
54C2×D3×C8—62no—
55C23×C32C4⋊C411yescharacteristic
56C22×C3⋊D3C4⋊C411yescharacteristic
57C22×C3⋊D3C2×Q811yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4C4⋊C411yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62#638—22no—
63#638—22no—
64C2×C3⋊Dic3C4⋊C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C4⋊(C3⋊D3)—22no—
67C4×C3⋊D3—21no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3C2×D412yes—
70C4×C3⋊D3#4112yes—
71#634—22no—
72#622—44no—
73C32×C8—21no—
74C32×C8C22⋊C412yes—
75C3⋊(C3⋊C8)—21no—
76C3⋊(C3⋊C8)C22⋊C411yescharacteristic
77C3⋊(C3⋊C8)C22⋊C411yescharacteristic
78C2×#131—91no—
79C2×#108—92no—
80#413—92no—
81#338—92no—
82C22×C3×C4—22no—
83C2×#67—62no—
84C2×#67—62no—
85#235—68no—
86#235—68no—
87C2×D12—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×Dic6—62no—
91C3×M16—28no—
92C2×C3×C8—22no—
93C2×C3×C8—22no—
94C2×C3⋊C8—62no—
95C2×C3⋊C8—62no—
96C2×C3⋊C8—64no—
97C2×C3⋊C8—64no—
98ΓL(1,𝔽25)—68no—
99ΓL(1,𝔽25)—68no—
100D3×C8—64no—
101D3×C8—64no—
102D3×C8—64no—
103D3×C8—64no—
104C22×C32—21no—
105C22×C32—41no—
106C22×C32C2×C4⋊C411yescharacteristic
107C2×C3⋊D3—21no—
108C2×C3⋊D3—41no—
109C2×C3⋊D3—41no—
110C2×C3⋊D3C22⋊Q812yes—
111C32×C4—21no—
112C32×C4C2×C22⋊C411yescharacteristic
113C32×C4#11711yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3#12112yes—
116C2×#41—91no—
117#131—182no—
118#131—182no—
119C2×M16—91no—
120C2×M16—91no—
121C2×M16—94no—
122C2×M16#15711yescharacteristic
123C22×C8—91no—
124C22×C8—91no—
125C22×C8—91no—
126#108—182no—
127#108—182no—
128#101—182no—
129#100—182no—
130C23×C3—22no—
131C22×D3—62no—
132C22×D3—62no—
133C2×C3×C4—24no—
134C2×C3×C4—24no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137#67—68no—
138#67—68no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141D12—68no—
142C4×D3—64no—
143C4×D3—64no—
144C4×D3—64no—
145C4×D3—64no—
146Dic6—68no—
147C3×C8—24no—
148C3×C8—24no—
149C3⋊C8—62no—
150C3⋊C8—62no—
151C3⋊C8—64no—
152C2×C32—21no—
153C2×C32—41no—
154C2×C32#38011yescharacteristic
155C3⋊D3—22no—
156C3⋊D3—41no—
157#41—182no—
158#41—182no—
159C2×Q8—91no—
160C2×D4—91no—
161C2×D4—91no—
162C2×D4—91no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4C2×#15711yescharacteristic
166M16—22no—
167M16—182no—
168M16—182no—
169M16—184no—
170M16—184no—
171C2×C8—91no—
172C2×C8—92no—
173C2×C8—92no—
174C2×C8—91no—
175C2×C8—181no—
176C2×C8—181no—
177C2×C8—181no—
178C2×C8—181no—
179C2×C8—184no—
180C2×C8C2×#15711yescharacteristic
181C2×C8C2×#15711yescharacteristic
182C22×C3—24no—
183C22×C3—22no—
184C22×C3—44no—
185C2×D3—64no—
186C2×D3—64no—
187C2×D3—124no—
188C2×D3—124no—
189C3×C4—24no—
190C3×C4—22no—
191C3×C4—22no—
192Dic3—64no—
193Dic3—64no—
194C32#181311yescharacteristic, complemented, Sylow
195C23—91no—
196C23—91no—
197C23C4⋊#15711yescharacteristic
198Q8—182no—
199D4—182no—
200D4—182no—
201D4—182no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—91no—
205C2×C4—92no—
206C2×C4—92no—
207C2×C4—91no—
208C2×C4—181no—
209C2×C4—181no—
210C2×C4C4⋊#15711yescharacteristic
211C2×C4C22×#15711yescharacteristic
212C8—21no—
213C8—91no—
214C8—91no—
215C8—181no—
216C8—364no—
217C8C22⋊#15712yes—
218C2×C3—24no—
219C2×C3—22no—
220C2×C3—44no—
221D3—124no—
222D3—124no—
223C22—21no—
224C22—41no—
225C22—92no—
226C22—181no—
227C22—361no—
228C22—361no—
229C22C2×C4⋊#15711yescharacteristic
230C4—21no—
231C4—92no—
232C4—181no—
233C4#6428611yescharacteristic
234C4C2×C22⋊#15711yescharacteristic
235C3—22no—
236C2—21no—
237C2—41no—
238C2—182no—
239C2—361no—
240C2#1059381211yescharacteristic
subgroupG/H
centerC4#64286
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×M16C4
socleC2×C32#380
prime radicalC2×#3828C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×M16#157
hypocenterC32#1813
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10593771C2semidirect
4. #10590186C2semidirect
194. C32#1813semidirect

Maximal subgroups

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

subgroupindex
C2×#641162
#105938082
#105937712
#105901862
#18139