Finite Group Databasebeta

← #11784408

Subgroups — #11784408

Order 1152.

370 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593771C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic
3#10593765C212yesmaximal
4C3⋊D3×#97C211yesmaximal, characteristic
5#10590151C212yesmaximal
6#64286C2212yes—
7#64283C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C2×C8×C3⋊D3C2211yescharacteristic
10C42×C3⋊D3C2211yescharacteristic
11#63771C412yescomplemented
12#63770C412yescomplemented
13#63769C412yescomplemented
14#63768C412yescomplemented
15#63767—22no—
16C8×#157—22no—
17C32×#97C411yescharacteristic, complemented
18#63642C411yescharacteristic, complemented
19#63642C411yescharacteristic, complemented
20#63630C411yescharacteristic, complemented
21D3×#97—62no—
22C2×C4×C3⋊D3—21no—
23C2×C4×C3⋊D3C2311yescharacteristic
24C22⋊#157—22no—
25#3792—22no—
26C4⋊#157C2×C414yes—
27C4×#157—22no—
28#3788C2×C414yes—
29#3787—22no—
30C2×C32×C8C2×C411yescharacteristic
31C2×C32×C8C2×C411yescharacteristic
32C32×C42C2×C411yescharacteristic
33C4×C3⋊Dic3—21no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
37C8×C3⋊D3C2×C411yescharacteristic
38C8×C3⋊D3C2×C411yescharacteristic
39C8×C3⋊D3C2×C411yescharacteristic
40C8×C3⋊D3C2×C411yescharacteristic
41C8×C3⋊D3D412yes—
42C8×C3⋊D3Q812yes—
43#1773—91nomaximal, Sylow
44C2×D3×C8—62no—
45C2×D3×C8—62no—
46C42×D3—62no—
47C3×#97—22no—
48#815—62no—
49#815—62no—
50#803—62no—
51C22×C3⋊D3#4111yescharacteristic
52C2×#157—24no—
53C2×C32×C4—21no—
54C2×C32×C4C22×C411yescharacteristic
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3#4111yescharacteristic
57C4×C3⋊D3—42no—
58C4×C3⋊D3C22×C411yescharacteristic
59C4×C3⋊D3C22×C411yescharacteristic
60C4×C3⋊D3C2×D411yescharacteristic
61C4×C3⋊D3C2×Q811yescharacteristic
62#622—24no—
63C32×C8C4211yescharacteristic
64C32×C8C4211yescharacteristic
65C32×C8C4⋊C412yes—
66C3⋊(C3⋊C8)C4211yescharacteristic
67C3⋊(C3⋊C8)C4211yescharacteristic
68C3⋊(C3⋊C8)C4⋊C412yes—
69C2×#108—91no—
70#427—91no—
71#405—92no—
72C2×#97—91no—
73#339—92no—
74C2×C4×D3—62no—
75C2×C4×D3—64no—
76C2×C3×C8—22no—
77C2×C3×C8—22no—
78C3×C42—22no—
79C4×Dic3—62no—
80C4×Dic3—64no—
81C2×C3⋊C8—62no—
82C2×C3⋊C8—62no—
83D3×C8—62no—
84D3×C8—62no—
85D3×C8—62no—
86D3×C8—62no—
87D3×C8—64no—
88D3×C8—64no—
89C22×C32#11711yescharacteristic
90C2×C3⋊D3—22no—
91C2×C3⋊D3C4×D411yescharacteristic
92C2×C3⋊D3C4×Q811yescharacteristic
93#157—44no—
94C32×C4—41no—
95C32×C4C2×C4211yescharacteristic
96C32×C4C2×C4⋊C411yescharacteristic
97C3⋊Dic3—41no—
98C3⋊Dic3C4×D411yescharacteristic
99C3⋊Dic3C4×Q811yescharacteristic
100C2×M16—92no—
101C22×C8—91no—
102C22×C8—91no—
103#117—92no—
104C2×C42—91no—
105#108—92no—
106#108—92no—
107#107—92no—
108#106—92no—
109#97—91no—
110#97—91no—
111#97—91no—
112#97—182no—
113#97#15711yescharacteristic, complemented
114C4×C8—182no—
115C22×D3—62no—
116C2×C3×C4—24no—
117C2×C3×C4—22no—
118C2×Dic3—62no—
119C2×Dic3—64no—
120C4×D3—62no—
121C4×D3—62no—
122C4×D3—62no—
123C4×D3—62no—
124C4×D3—128no—
125C3×C8—22no—
126C3×C8—22no—
127C3×C8—24no—
128C3⋊C8—62no—
129C3⋊C8—62no—
130C3⋊C8—64no—
131C2×C32—21no—
132C2×C32C4×C4⋊C411yescharacteristic
133C3⋊D3—21no—
134C3⋊D3#44412yes—
135C22×C4—91no—
136C22×C4—181no—
137M16—94no—
138M16—182no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—91no—
142C2×C8—91no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—92no—
146C2×C8—92no—
147C2×C8—182no—
148C2×C8C2×#15711yescharacteristic
149C2×C8C2×#15711yescharacteristic
150C4⋊C4—94no—
151C22⋊C4—182no—
152C42—91no—
153C42—181no—
154C42—182no—
155C42C2×#15711yescharacteristic
156C22×C3—22no—
157C2×D3—62no—
158C2×D3—62no—
159C2×D3—68no—
160C3×C4—22no—
161C3×C4—22no—
162C3×C4—44no—
163Dic3—62no—
164Dic3—62no—
165Dic3—124no—
166C32#177311yescharacteristic, complemented, Sylow
167C23—91no—
168C2×C4—21no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—184no—
175C2×C4—181no—
176C2×C4—362no—
177C2×C4C22×#15711yescharacteristic
178C8—91no—
179C8—91no—
180C8—92no—
181C8—184no—
182C8C4×#15711yescharacteristic
183C8C4×#15711yescharacteristic
184C8C4⋊#15712yes—
185C2×C3—24no—
186C2×C3—22no—
187D3—64no—
188D3—64no—
189C22—91no—
190C22—91no—
191C22—182no—
192C22#6428611yescharacteristic
193C4—41no—
194C4—91no—
195C4—91no—
196C4—361no—
197C4—364no—
198C4C2×C4×#15711yescharacteristic
199C4C2×C4⋊#15711yescharacteristic
200C3—22no—
201C2—21no—
202C2—92no—
203C2—181no—
204C2C4×C4⋊#15711yescharacteristic
subgroupG/H
centerC4C2×C4⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#97C4
socleC2×C32C4×C4⋊C4
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenter#97#157
hypocenterC32#1773
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ #97

Complements

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

NH ≅ G/Ntype
11. #63771C4semidirect
12. #63770C4semidirect
13. #63769C4semidirect
14. #63768C4semidirect
17. C32×#97C4semidirect
18. #63642C4semidirect
19. #63642C4semidirect
20. #63630C4semidirect
113. #97#157semidirect
166. C32#1773semidirect

Maximal subgroups

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

subgroupindex
#105937712
#105937682
#105937652
C3⋊D3×#972
#105901512
#17739