Finite Group Databasebeta

← #11800032

Subgroups — #11800032

Order 1152.

230 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 37 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#10591189C211yesmaximal, characteristic
2#10591143C211yesmaximal, characteristic
3#10590201C211yesmaximal, characteristic
4#10590067C212yesmaximal, complemented
5#10590066C212yesmaximal, complemented
6C2×#3748C2211yescharacteristic
7C3×#924—21no—
8C2×C3×#208—21no—
9C2×#3718C2211yescharacteristic
10#63773C2212yes—
11#63578—21no—
12#63578C2212yes—
13#63574C2211yescharacteristic
14#63565—21no—
15#5124—61no—
16#5052—61no—
17C22×C32×C4D411yescharacteristic
18C2×C3×Dic6—21no—
19#3748—22no—
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22C3×#217—41no—
23C3×C4⋊Dic3—21no—
24C3×Dic3⋊C4—41no—
25C3×#208—22no—
26C3×#208—41no—
27C2×C3×C3⋊C8—41no—
28#3718—22no—
29#3708—22no—
30#2239—91nomaximal, Sylow
31C2×C3×M16—61no—
32C3×C22⋊Q8—61no—
33C2×#216—61no—
34#924—21no—
35C2×#208—21no—
36C2×#208—61no—
37C2×#208—61no—
38#835—61no—
39#822—62no—
40#822—62no—
41#810—61no—
42#808—61no—
43C23×C32SD1611yescharacteristic
44C2×C32×C4—21no—
45C2×C32×C4—21no—
46C2×C32×C4SD1611yescharacteristic
47C2×C32×C4C2×D411yescharacteristic
48C2×C3×Dic3—41no—
49C2×C3×Dic3—41no—
50C3×Dic6—41no—
51C3×Dic6—41no—
52C3⋊(C3⋊C8)—21no—
53C3⋊(C3⋊C8)#4112yes—
54C3×C3⋊C8—42no—
55#470—91no—
56#430—91no—
57#365—92no—
58#362—92no—
59#349—91no—
60C2×C3×Q8—61no—
61C22×C3×C4—21no—
62C22×C3×C4—21no—
63C2×Dic6—21no—
64C3×M16—62no—
65C3×M16—121no—
66C2×C3×C8—121no—
67C3×C4⋊C4—61no—
68C3×C4⋊C4—121no—
69C3×C22⋊C4—121no—
70#217—41no—
71#216—122no—
72C4⋊Dic3—21no—
73Dic3⋊C4—41no—
74#208—22no—
75#208—41no—
76#208—62no—
77#208—62no—
78#208—122no—
79C2×C3⋊C8—41no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84C22×C32—21no—
85C22×C32—41no—
86C22×C32C2×SD1611yescharacteristic
87C32×C4—21no—
88C32×C4#12311yescharacteristic
89C32×C4AGL(1,ℤ/8)11yescharacteristic
90C3×Dic3—81no—
91C3×Dic3—81no—
92C2×Q16—91no—
93C2×M16—61no—
94C2×M16—91no—
95C22⋊Q8—61no—
96M32—92no—
97#108—92no—
98#108—181no—
99#106—91no—
100#103—181no—
101C23×C3—21no—
102C23×C3—21no—
103C3×Q8—121no—
104C3×Q8—121no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—41no—
114C2×C3×C4—41no—
115C2×C3×C4—121no—
116C2×C3×C4—121no—
117C2×Dic3—41no—
118C2×Dic3—41no—
119Dic6—41no—
120Dic6—41no—
121C3×C8—122no—
122C3⋊C8—42no—
123C3⋊C8—62no—
124C3⋊C8—62no—
125C3⋊C8—62no—
126C3⋊C8—121no—
127C2×C32—21no—
128C2×C32—41no—
129C2×C32#48111yescharacteristic
130C2×Q8—61no—
131C22×C4GO+(4,𝔽2)11yescharacteristic
132Q16—182no—
133M16—62no—
134M16—121no—
135M16—182no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—121no—
139C4⋊C4—61no—
140C4⋊C4—121no—
141C22⋊C4—121no—
142C16—182no—
143C22×C3—21no—
144C22×C3—21no—
145C22×C3—21no—
146C22×C3—21no—
147C22×C3—41no—
148C22×C3—41no—
149C22×C3—41no—
150C22×C3—81no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—41no—
158C3×C4—241no—
159C3×C4—241no—
160Dic3—81no—
161Dic3—81no—
162C32#223911yescharacteristic, complemented, Sylow
163C23#377511yescharacteristic
164Q8—121no—
165Q8—121no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—121no—
169C2×C4—121no—
170C2×C4#377511yescharacteristic
171C2×C4C2×GO+(4,𝔽2)11yescharacteristic
172C8—92no—
173C8—122no—
174C8—181no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—41no—
180C2×C3—41no—
181C2×C3—41no—
182C2×C3—81no—
183C22—21no—
184C22—41no—
185C22C2×#377511yescharacteristic
186C4—21no—
187C4—241no—
188C4—241no—
189C4#6423311yescharacteristic
190C4#6423611yescharacteristic
191C3—21no—
192C3—21no—
193C2—21no—
194C2—41no—
195C2#1059349711yescharacteristic
subgroupG/H
centerC2#10593497
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32#481
prime radicalC23×C32SD16
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2239
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590067C2semidirect
5. #10590066C2semidirect
162. C32#2239semidirect

Maximal subgroups

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

subgroupindex
#105911892
#105911432
#105902012
#105900672
#105900662
#22399