Finite Group Databasebeta

← #11798955

Subgroups — #11798955

Order 1152.

270 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 47 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×#63736C212yesmaximal
2#10590387C211yesmaximal, characteristic
3C4×#3718C211yesmaximal, characteristic
4C4⋊#3708C211yesmaximal, characteristic
5#10590062C212yesmaximal
6C3×#869—21no—
7C3×C4×Dic6—21no—
8C2×#3718—21no—
9C2×#3718C2212yes—
10C2×#3718C2211yescharacteristic
11C2×#3708C2212yes—
12#63736—24no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14#63576C2211yescharacteristic
15#63565—21no—
16#5092—61no—
17C4×#216—61no—
18C2×C3×Dic6—21no—
19C2×C3×Dic6—22no—
20C32×C42D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23C3×C4⋊Dic3—21no—
24C3×C4⋊Dic3—41no—
25C3×C4⋊Dic3—41no—
26C3×Dic3⋊C4—41no—
27C3×C4×Dic3—41no—
28#3718—22no—
29#3718—21no—
30#3718—22no—
31#3718—42no—
32#3718D412yes—
33#3708—22no—
34#2209—91nomaximal, Sylow
35C3×C4⋊Q8—61no—
36C3×C4×Q8—61no—
37C2×#216—61no—
38C2×#216—62no—
39C2×#216—62no—
40#869—21no—
41C4×Dic6—21no—
42#835—61no—
43#810—61no—
44#807—61no—
45C4×C3⋊C8—61no—
46C4×C3⋊C8—61no—
47C2×C32×C4D811yescharacteristic
48C2×C32×C4D811yescharacteristic
49C2×C32×C4C2×D411yescharacteristic
50C2×C3×Dic3—41no—
51C2×C3×Dic3—41no—
52C2×C3×Dic3—42no—
53C3×Dic6—22no—
54C3×Dic6—41no—
55C3×Dic6—42no—
56C3×Dic6—42no—
57C3⋊(C3⋊C8)—21no—
58C3⋊(C3⋊C8)C2×D411yescharacteristic
59C3⋊(C3⋊C8)#4111yescharacteristic
60C2×Q32—92no—
61#494—91no—
62C4×Q16—91no—
63C4⋊C16—91no—
64#358—92no—
65C2×C3×Q8—61no—
66C2×C3×Q8—62no—
67C2×Dic6—21no—
68C2×Dic6—22no—
69C3×C4⋊C4—61no—
70C3×C4⋊C4—121no—
71C3×C4⋊C4—121no—
72C3×C4⋊C4—121no—
73C3×C42—21no—
74C3×C42—21no—
75C3×C42—121no—
76#216—62no—
77#216—62no—
78#216—122no—
79#216—122no—
80#216—124no—
81C4⋊Dic3—21no—
82C4⋊Dic3—41no—
83C4⋊Dic3—41no—
84Dic3⋊C4—41no—
85C4×Dic3—41no—
86C2×C3⋊C8—61no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8—61no—
89C2×C3⋊C8—61no—
90C22×C32C2×D811yescharacteristic
91C32×C4—21no—
92C32×C4Q3212yescomplemented
93C32×C4#12111yescharacteristic
94C32×C4AGL(1,ℤ/8)11yescharacteristic
95C3×Dic3—42no—
96C3×Dic3—82no—
97C3×Dic3—81no—
98C2×Q16—91no—
99C2×Q16—92no—
100C2×Q16—181no—
101C4⋊Q8—61no—
102C4×Q8—61no—
103Q32—184no—
104C2×C16—92no—
105#107—91no—
106#103—181no—
107C4×C8—91no—
108C3×Q8—62no—
109C3×Q8—121no—
110C3×Q8—122no—
111C3×Q8—122no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—121no—
119C2×C3×C4—121no—
120C2×C3×C4—122no—
121C2×Dic3—41no—
122C2×Dic3—41no—
123C2×Dic3—42no—
124Dic6—22no—
125Dic6—41no—
126Dic6—42no—
127Dic6—42no—
128C3⋊C8—61no—
129C3⋊C8—61no—
130C3⋊C8—61no—
131C3⋊C8—61no—
132C3⋊C8—62no—
133C3⋊C8—121no—
134C2×C32#45911yescharacteristic
135C2×C32C2×Q3211yescharacteristic
136C2×C32#51011yescharacteristic
137C2×Q8—61no—
138C2×Q8—62no—
139Q16—92no—
140Q16—181no—
141Q16—182no—
142Q16—182no—
143Q16—362no—
144C2×C8—91no—
145C2×C8—91no—
146C4⋊C4—61no—
147C4⋊C4—121no—
148C4⋊C4—121no—
149C4⋊C4—121no—
150C42—121no—
151C42GO+(4,𝔽2)11yescharacteristic
152C16—182no—
153C22×C3—21no—
154C22×C3—21no—
155C3×C4—22no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—22no—
161C3×C4—22no—
162C3×C4—41no—
163C3×C4—122no—
164C3×C4—242no—
165C3×C4—241no—
166Dic3—42no—
167Dic3—82no—
168Dic3—81no—
169C32#220911yescharacteristic, complemented, Sylow
170Q8—62no—
171Q8—121no—
172Q8—122no—
173Q8—122no—
174C2×C4—121no—
175C2×C4—121no—
176C2×C4—122no—
177C2×C4#377411yescharacteristic
178C2×C4#377411yescharacteristic
179C2×C4C2×GO+(4,𝔽2)11yescharacteristic
180C8—91no—
181C8—91no—
182C8—181no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—21no—
189C22C2×#377411yescharacteristic
190C4—21no—
191C4—122no—
192C4—241no—
193C4—242no—
194C4#6373612yescomplemented
195C4#6422411yescharacteristic
196C4#6423011yescharacteristic
197C3—21no—
198C3—21no—
199C2#1059333611yescharacteristic
200C2C2×#6373611yescharacteristic
201C2#1059341711yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socle, prime radicalC22×C32C2×D8
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2209
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
92. C32×C4Q32semidirect
169. C32#2209semidirect
194. C4#63736semidirect

Maximal subgroups

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

subgroupindex
C2×#637362
#105903872
C4×#37182
C4⋊#37082
#105900622
#22099