Finite Group Databasebeta

← #11786004

Subgroups — #11786004

Order 1152.

302 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 62 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#10592388C211yesmaximal, characteristic
4#10590183C212yesmaximal
5#10590152C212yesmaximal
6#64286C2212yes—
7#64283C2212yes—
8C2×#3743C2211yescharacteristic
9C2×C8×C3⋊D3C2211yescharacteristic
10#64081C2211yescharacteristic
11#63771—21no—
12#63770—21no—
13#63769—21no—
14#63768—21no—
15C32×C4×C8C411yescharacteristic, complemented
16#63642C411yescharacteristic, complemented
17C8×C3⋊Dic3C411yescharacteristic, complemented
18#63630C411yescharacteristic, complemented
19#4689—62no—
20C2×C4×C3⋊D3C2311yescharacteristic
21C22⋊#157—22no—
22#3792—22no—
23C4⋊#157—22no—
24C4×#157—22no—
25#3788—22no—
26#3787—22no—
27C2×C32×C8C2×C411yescharacteristic
28C2×C32×C8C2×C411yescharacteristic
29C32×C42C2×C411yescharacteristic
30#3752—21no—
31#3750—21no—
32C4×C3⋊Dic3C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35#3743—21no—
36#3743—21no—
37C8×C3⋊D3D411yescharacteristic
38C8×C3⋊D3D411yescharacteristic
39C8×C3⋊D3Q811yescharacteristic
40C8×C3⋊D3Q811yescharacteristic
41#1833—91nomaximal, Sylow
42C2×ΓL(1,𝔽25)—62no—
43C2×D3×C8—62no—
44#872—62no—
45C3×C4×C8—22no—
46#815—62no—
47C8×Dic3—62no—
48#803—62no—
49C22×C3⋊D3#4111yescharacteristic
50C2×#157—42no—
51C2×C32×C4—21no—
52C2×C32×C4C22×C411yescharacteristic
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3#4111yescharacteristic
55C4×C3⋊D3C2×D411yescharacteristic
56C4×C3⋊D3C2×Q811yescharacteristic
57C4×C3⋊D3#4111yescharacteristic
58C4×C3⋊D3#4111yescharacteristic
59#622—42no—
60C32×C8—21no—
61C32×C8C4⋊C411yescharacteristic
62C32×C8C4⋊C411yescharacteristic
63C3⋊(C3⋊C8)—21no—
64C3⋊(C3⋊C8)C4⋊C411yescharacteristic
65C3⋊(C3⋊C8)C4⋊C411yescharacteristic
66C2×#108—91no—
67#427—91no—
68#405—91no—
69#344—92no—
70H(3,ℤ/4)—92no—
71C2×C4×D3—62no—
72C2×C3×C8—22no—
73C2×C3×C8—22no—
74C3×C42—22no—
75(C2×D3)⋊C4—64no—
76Dic3⋊C4—64no—
77C4×Dic3—62no—
78C2×C3⋊C8—62no—
79C2×C3⋊C8—62no—
80ΓL(1,𝔽25)—64no—
81ΓL(1,𝔽25)—64no—
82D3×C8—62no—
83D3×C8—62no—
84D3×C8—62no—
85D3×C8—62no—
86C22×C32#11711yescharacteristic
87C2×C3⋊D3—41no—
88C2×C3⋊D3#12411yescharacteristic
89C2×C3⋊D3#12511yescharacteristic
90#157—82no—
91C32×C4—41no—
92C32×C4C2×C4⋊C411yescharacteristic
93C32×C4#11711yescharacteristic
94C3⋊Dic3—41no—
95C3⋊Dic3#12411yescharacteristic
96C3⋊Dic3#12511yescharacteristic
97C2×M16—91no—
98C2×M16—92no—
99C22×C8—91no—
100#117—91no—
101#117—92no—
102#108—181no—
103#108—181no—
104#107—181no—
105#106—181no—
106#97—91no—
107#97—91no—
108C4×C8—91no—
109C4×C8#15711yescharacteristic, complemented
110C22×D3—62no—
111C2×C3×C4—24no—
112C2×C3×C4—22no—
113C2×Dic3—62no—
114C2×Dic3—64no—
115C4×D3—62no—
116C4×D3—62no—
117C4×D3—62no—
118C4×D3—62no—
119C3×C8—24no—
120C3×C8—22no—
121C3×C8—22no—
122C3⋊C8—62no—
123C3⋊C8—62no—
124C3⋊C8—64no—
125C2×C32—21no—
126C2×C32#38211yescharacteristic
127C3⋊D3—21no—
128C3⋊D3—21no—
129C22×C4—91no—
130M16—181no—
131M16—181no—
132M16—182no—
133M16—182no—
134C2×C8—91no—
135C2×C8—91no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—91no—
140C2×C8—182no—
141C2×C8C2×#15711yescharacteristic
142C2×C8C2×#15711yescharacteristic
143C4⋊C4—181no—
144C4⋊C4—182no—
145C22⋊C4—181no—
146C22⋊C4—182no—
147C42—91no—
148C42—182no—
149C42C2×#15711yescharacteristic
150C22×C3—22no—
151C2×D3—62no—
152C2×D3—62no—
153C2×D3—124no—
154C3×C4—22no—
155C3×C4—22no—
156C3×C4—44no—
157Dic3—62no—
158Dic3—62no—
159Dic3—124no—
160C32#183311yescharacteristic, complemented, Sylow
161C23—91no—
162C2×C4—21no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—181no—
169C2×C4—362no—
170C2×C4C22×#15711yescharacteristic
171C8—21no—
172C8—91no—
173C8—91no—
174C8—181no—
175C8—362no—
176C8C4⋊#15711yescharacteristic
177C8C4⋊#15711yescharacteristic
178C2×C3—24no—
179C2×C3—22no—
180D3—122no—
181D3—122no—
182C22—91no—
183C22—91no—
184C22—361no—
185C22#6428611yescharacteristic
186C4—41no—
187C4—91no—
188C4—91no—
189C4—361no—
190C4—722no—
191C4C2×C4⋊#15711yescharacteristic
192C4#6428611yescharacteristic
193C3—22no—
194C2—21no—
195C2—181no—
196C2—181no—
197C2#1059373611yescharacteristic
subgroupG/H
centerC4#64286
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×C8C4
socleC2×C32#382
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC4×C8#157
hypocenterC32#1833
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
15. C32×C4×C8C4semidirect
16. #63642C4semidirect
17. C8×C3⋊Dic3C4semidirect
18. #63630C4semidirect
109. C4×C8#157semidirect
160. C32#1833semidirect

Maximal subgroups

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

subgroupindex
#105937712
#105937682
#105923882
#105901832
#105901522
#18339