Finite Group Databasebeta

← #11785531

Subgroups — #11785531

Order 1152.

334 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 67 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×#64287C211yesmaximal, characteristic
2#10593824C212yesmaximal
3C2×#63748C212yesmaximal, complemented
4#10590096C212yesmaximal, complemented
5C2×#3830C2211yescharacteristic
6C2×#3792C411yescharacteristic
7C2×#3792C2214yes—
8C2×#3792C2211yescharacteristic
9C22×#622C411yescharacteristic
10C22×#622C2211yescharacteristic
11#64287—24no—
12C2×#3788C411yescharacteristic
13C2×#3787C411yescharacteristic
14#63788—22no—
15#63780—22no—
16#63748—24no—
17C2×C32×D4Q811yescharacteristic
18C2×#638D411yescharacteristic
19C2×#638Q811yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22#3830—22no—
23#3830—22no—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×#634D411yescharacteristic
26#3792—22no—
27#3792—22no—
28#3792—24no—
29#3792—24no—
30C2×#622—22no—
31C2×#622—24no—
32C2×#622C2×C411yescharacteristic
33C2×#622C2×C411yescharacteristic
34C2×#622C2×C411yescharacteristic
35C2×#622C2×C411yescharacteristic
36C2×#622D414yes—
37#3788—22no—
38#3787—22no—
39#1813—91nomaximal, Sylow
40C2×#237—121no—
41C23×C32C4⋊C411yescharacteristic
42C23×C32C2×Q811yescharacteristic
43C22×C3⋊D3C4⋊C411yescharacteristic
44C32×D4—22no—
45C2×C32×C4C4⋊C411yescharacteristic
46#638—22no—
47#638—22no—
48C2×C3⋊Dic3—21no—
49C2×C3⋊Dic3—21no—
50C2×C3⋊Dic3C4⋊C411yescharacteristic
51C2×C3⋊Dic3C22×C411yescharacteristic
52C2×C3⋊Dic3C2×D412yes—
53C2×C3⋊Dic3C2×D411yescharacteristic
54C2×C3⋊Dic3#4112yes—
55C4×C3⋊D3—21no—
56C4×C3⋊D3—21no—
57#634—22no—
58#622—21no—
59#622—21no—
60#622—44no—
61#622C22⋊C412yes—
62#622C22⋊C412yes—
63C2×#131—91no—
64C2×#108—92no—
65#413—92no—
66#338—92no—
67C2×C3×D4—41no—
68C2×#67—121no—
69C2×#67—121no—
70C22×Dic3—121no—
71C22×Dic3—121no—
72#237—124no—
73#237—124no—
74C2×C4×D3—121no—
75C2×Dic6—121no—
76C22×C32—21no—
77C22×C32—41no—
78C22×C32—41no—
79C22×C32C2×C4⋊C411yescharacteristic
80C22×C32C22⋊Q812yes—
81C2×C3⋊D3—21no—
82C2×C3⋊D3—41no—
83C32×C4—21no—
84C3⋊Dic3—21no—
85C3⋊Dic3C2×C22⋊C411yescharacteristic
86C3⋊Dic3#11711yescharacteristic
87C3⋊Dic3#12112yes—
88C2×#41—91no—
89#131—184no—
90C2×M16—91no—
91C2×M16—91no—
92C2×M16—91no—
93C2×M16—94no—
94C22×C8—91no—
95C22×C8—91no—
96C22×C8—91no—
97#108—184no—
98#101—182no—
99#100—182no—
100C23×C3—41no—
101C23×C3—41no—
102C22×D3—121no—
103C3×D4—44no—
104C2×C3×C4—41no—
105#67—124no—
106#67—124no—
107C2×Dic3—121no—
108C2×Dic3—121no—
109C2×Dic3—121no—
110C2×Dic3—122no—
111C2×Dic3—122no—
112C2×Dic3—122no—
113C2×Dic3—122no—
114C4×D3—122no—
115C4×D3—122no—
116Dic6—124no—
117C2×C32—21no—
118C2×C32—22no—
119C2×C32—41no—
120C2×C32#38011yescharacteristic
121C3⋊D3—41no—
122#41—182no—
123#41—182no—
124C2×Q8—91no—
125C2×D4—91no—
126C2×D4—91no—
127C2×D4PSU(3,𝔽2)11yescharacteristic
128C22×C4—91no—
129C22×C4—91no—
130C22×C4—91no—
131M16—182no—
132M16—182no—
133M16—182no—
134M16—184no—
135M16—184no—
136C2×C8—94no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—182no—
142C2×C8—182no—
143C2×C8—184no—
144C22×C3—42no—
145C22×C3—41no—
146C22×C3—42no—
147C22×C3—82no—
148C22×C3—82no—
149C2×D3—122no—
150C2×D3—242no—
151C3×C4—42no—
152Dic3—122no—
153Dic3—121no—
154Dic3—121no—
155Dic3—122no—
156C32#181311yescharacteristic, complemented, Sylow
157C23—91no—
158C23#377711yescharacteristic
159C23C2×PSU(3,𝔽2)11yescharacteristic
160Q8—182no—
161D4—22no—
162D4—182no—
163D4—182no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—92no—
167C2×C4—92no—
168C2×C4—91no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4#377711yescharacteristic
174C8—92no—
175C8—92no—
176C8—181no—
177C8—181no—
178C8—364no—
179C2×C3—42no—
180C2×C3—41no—
181C2×C3—82no—
182C2×C3—82no—
183D3—242no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—181no—
188C22—361no—
189C22C2×#377711yescharacteristic
190C22C22⋊PSU(3,𝔽2)12yes—
191C4—21no—
192C4—91no—
193C4—92no—
194C4—91no—
195C4—181no—
196C3—41no—
197C2—21no—
198C2—22no—
199C2—41no—
200C2—361no—
201C2#1059356811yescharacteristic
subgroupG/H
centerC2#10593568
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×PSU(3,𝔽2)
FittingC2×C32×D4Q8
socleC2×C32#380
prime radicalC2×#3830C22
cosocleC22×C3⋊Dic3C23
hypercenterC2×D4PSU(3,𝔽2)
hypocenterC32#1813
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
3. C2×#63748C2semidirect
4. #10590096C2semidirect
156. C32#1813semidirect

Maximal subgroups

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

subgroupindex
C2×#642872
#105938242
C2×#637482
#105900962
#18139