Finite Group Databasebeta

← #11777804

Subgroups — #11777804

Order 1152.

288 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 56 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#10593835C211yesmaximal, characteristic, complemented
2#10593752C211yesmaximal, characteristic
3#10592487C211yesmaximal, characteristic
4Q8⋊#622C211yesmaximal, characteristic, complemented
5#10590172C211yesmaximal, characteristic, complemented
6C8×#622C211yesmaximal, characteristic, complemented
7#10590160C211yesmaximal, characteristic
8C2×#3788—21no—
9Q8×C3⋊Dic3C2211yescharacteristic
10C2×#3755C411yescharacteristic
11#64102C2211yescharacteristic
12#63779—21no—
13#63778—21no—
14#63777—21no—
15C4⋊#622C2211yescharacteristic
16C4⋊#622C2211yescharacteristic
17C4×#622C2211yescharacteristic
18C4×#622C2211yescharacteristic
19C32×#103C411yescharacteristic
20#63648C411yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22#63635C411yescharacteristic
23#4788—62no—
24C2×C32×Q8C2×C411yescharacteristic
25C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
26C2×C4×C3⋊D3—21no—
27C2×#622—21no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622D411yescharacteristic
31C2×#622D411yescharacteristic
32#3788—42no—
33C2×C32×C8C2×C411yescharacteristic
34C32×C4⋊C4C2×C411yescharacteristic
35#3755—22no—
36#3752—21no—
37C4⋊(C3⋊Dic3)—21no—
38C4⋊(C3⋊Dic3)C2×C411yescharacteristic
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3C2311yescharacteristic
41C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
42#1590—91nomaximal, Sylow
43Q8×Dic3—62no—
44C2×#215—62no—
45#893—62no—
46C3×#103—22no—
47#821—62no—
48C8×Dic3—62no—
49#808—62no—
50C22×C3⋊D3—21no—
51C32×Q8—21no—
52C32×Q8—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4C22×C411yescharacteristic
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3C2×D411yescharacteristic
58C2×C3⋊Dic3#4111yescharacteristic
59C4⋊(C3⋊D3)—21no—
60C4⋊(C3⋊D3)—21no—
61C4×C3⋊D3—41no—
62C4×C3⋊D3—41no—
63#622—22no—
64#622—21no—
65#622—41no—
66#622—41no—
67#622SD1612yescomplemented
68C32×C8—21no—
69C3⋊(C3⋊C8)M1612yescomplemented
70#446—91no—
71C4×SD16—91no—
72#436—91no—
73#334—91no—
74Q8⋊C8—91no—
75D4⋊C8—91no—
76C82—91no—
77C2×C3×Q8—22no—
78C2×D12—62no—
79C2×C4×D3—122no—
80C2×C3×C8—22no—
81C3×C4⋊C4—22no—
82#215—68no—
83(C2×D3)⋊C4—122no—
84C4⋊Dic3—62no—
85C4⋊Dic3—122no—
86C4×Dic3—62no—
87C4×Dic3—122no—
88C2×C3⋊C8—62no—
89C22×C32C4×D411yescharacteristic
90C2×C3⋊D3—41no—
91C2×C3⋊D3—41no—
92C2×C3⋊D3—41no—
93C32×C4—41no—
94C32×C4—41no—
95C32×C4C2×M1611yescharacteristic
96C32×C4#13111yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3—41no—
99C3⋊Dic3C2×SD1611yescharacteristic
100C3⋊Dic3#13511yescharacteristic
101C2×SD16—91no—
102C2×M16—181no—
103C4×Q8—91no—
104C4×D4—91no—
105#106—91no—
106C4⋊C8—91no—
107C4⋊C8—91no—
108C4⋊C8—181no—
109#103#15711yescharacteristic
110#102—91no—
111C22⋊C8—181no—
112#97—181no—
113C4×C8—91no—
114C4×C8—91no—
115C4×C8—91no—
116C22×D3—122no—
117C3×Q8—24no—
118C3×Q8—42no—
119C2×C3×C4—22no—
120C2×C3×C4—42no—
121C2×C3×C4—42no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—122no—
125D12—64no—
126D12—122no—
127C4×D3—242no—
128C4×D3—242no—
129C3×C8—42no—
130C3⋊C8—64no—
131C2×C32#43611yescharacteristic
132C2×C32C4×SD1611yescharacteristic
133C2×C32#44311yescharacteristic
134C3⋊D3—81no—
135C2×Q8C2×#15711yescharacteristic
136C2×D4—91no—
137C22×C4—181no—
138SD16—182no—
139M16—362no—
140C2×C8—91no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—181no—
144C2×C8—181no—
145C2×C8—181no—
146C2×C8C2×#15711yescharacteristic
147C4⋊C4—91no—
148C4⋊C4—181no—
149C4⋊C4C2×#15711yescharacteristic
150C22⋊C4—181no—
151C42—91no—
152C42—181no—
153C22×C3—22no—
154C2×D3—124no—
155C2×D3—242no—
156C2×D3—242no—
157C3×C4—22no—
158C3×C4—22no—
159C3×C4—44no—
160C3×C4—82no—
161Dic3—62no—
162Dic3—62no—
163Dic3—122no—
164Dic3—242no—
165C32#159011yescharacteristic, complemented, Sylow
166C23—181no—
167Q8—21no—
168Q8—21no—
169D4—181no—
170D4—181no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—181no—
176C2×C4—361no—
177C2×C4—361no—
178C2×C4C22×#15711yescharacteristic
179C8—21no—
180C8—92no—
181C8—92no—
182C8—181no—
183C8—182no—
184C8—361no—
185C8—361no—
186C2×C3—22no—
187C2×C3—22no—
188C2×C3—22no—
189D3—244no—
190C22—361no—
191C22—361no—
192C22—361no—
193C22D4×#15711yescharacteristic
194C4—41no—
195C4—41no—
196C4—91no—
197C4—91no—
198C4—181no—
199C4—361no—
200C4#6428311yescharacteristic
201C4#6428711yescharacteristic
202C3—22no—
203C2—721no—
204C2#1059374211yescharacteristic
205C2SD16×#15711yescharacteristic
206C2#1059378711yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#103C4
socleC22×C32C4×D4
prime radicalC2×C4⋊(C3⋊D3)C2×C4
cosocleC4×C3⋊Dic3C23
hypercenter#103#157
hypocenterC32#1590
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10593835C2semidirect
4. Q8⋊#622C2semidirect
5. #10590172C2semidirect
6. C8×#622C2semidirect
67. #622SD16semidirect
69. C3⋊(C3⋊C8)M16semidirect
165. C32#1590semidirect

Maximal subgroups

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

subgroupindex
#105938352
#105937522
#105924872
Q8⋊#6222
#105901722
C8×#6222
#105901602
#15909