Finite Group Databasebeta

← #11777943

Subgroups — #11777943

Order 1152.

242 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×#3776C211yesmaximal, characteristic
2#10590788C211yesmaximal, characteristic
3#10590787C211yesmaximal, characteristic
4#10590169C211yesmaximal, characteristic
5#10590041C211yesmaximal, characteristic
6#10590032C211yesmaximal, characteristic
7#10590032C211yesmaximal, characteristic
8C2×#3776C411yescharacteristic
9C4×#627C2211yescharacteristic
10C4×#627C2211yescharacteristic
11C4×#622C2211yescharacteristic
12C4×#622C2211yescharacteristic
13#63743C411yescharacteristic
14#63740C411yescharacteristic
15#63740C411yescharacteristic
16C8×C3⋊Dic3C2211yescharacteristic
17C3×#815—21no—
18C3×Dic3⋊C8—21no—
19#63572C2211yescharacteristic
20#63572C2211yescharacteristic
21Dic3⋊(C3⋊C8)—21no—
22#63554—21no—
23#4828—61no—
24#4701—61no—
25C2×#627C2×C411yescharacteristic
26C2×#627C2×C411yescharacteristic
27C2×#622—21no—
28C2×#622C2×C411yescharacteristic
29C2×#622C2×C411yescharacteristic
30#3776—22no—
31C2×C32×C8D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C3×C4×Dic3—21no—
35C3×C4×Dic3—21no—
36C2×C3×C3⋊C8—21no—
37C2×C3×C3⋊C8—21no—
38#3724C2×C411yescharacteristic
39#3724C2×C411yescharacteristic
40Dic3⋊Dic3—21no—
41Dic3⋊Dic3—21no—
42#1593—91nomaximal, Sylow
43C4×Dic6—61no—
44C4×Dic6—61no—
45C3×C4⋊C8—61no—
46C3×#97—61no—
47#815—21no—
48#815—61no—
49Dic3⋊C8—21no—
50Dic3⋊C8—61no—
51Dic3⋊C8—61no—
52Dic3⋊C8—61no—
53C8×Dic3—61no—
54C8×Dic3—61no—
55C4⋊(C3⋊C8)—61no—
56#803—61no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3C22×C411yescharacteristic
59C2×C3⋊Dic3#4111yescharacteristic
60C2×C3×Dic3—21no—
61C2×C3×Dic3—21no—
62C2×C3×Dic3—21no—
63C2×C3×Dic3—21no—
64#627—21no—
65#627—21no—
66#627—21no—
67#627—21no—
68#622—21no—
69#622—41no—
70#622M1612yes—
71C32×C8—21no—
72C3⋊(C3⋊C8)—21no—
73C3×C3⋊C8—41no—
74C3×C3⋊C8—41no—
75#446—91no—
76#446—91no—
77C4×Q16—91no—
78#334—91no—
79Q8⋊C8—91no—
80Q8⋊C8—91no—
81#322—91no—
82C2×Dic6—61no—
83C2×Dic6—61no—
84C2×C3×C8—21no—
85C2×C3×C8—21no—
86C2×C3×C8—61no—
87C2×C3×C8—61no—
88C3×C42—61no—
89C3×C42—61no—
90C4⋊Dic3—61no—
91C4⋊Dic3—61no—
92Dic3⋊C4—61no—
93Dic3⋊C4—61no—
94Dic3⋊C4—61no—
95Dic3⋊C4—61no—
96C4×Dic3—21no—
97C4×Dic3—21no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C2×C3⋊C8—21no—
101C2×C3⋊C8—21no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—61no—
104C22×C32C4×D411yescharacteristic
105C32×C4#13711yescharacteristic
106C32×C4#13711yescharacteristic
107C3⋊Dic3—21no—
108C3⋊Dic3C2×M1611yescharacteristic
109C3⋊Dic3#13111yescharacteristic
110C3×Dic3—41no—
111C3×Dic3—41no—
112C3×Dic3—41no—
113C3×Dic3—41no—
114C2×Q16—91no—
115C4×Q8—91no—
116C4×Q8—91no—
117#107—91no—
118C4⋊C8—61no—
119C4⋊C8—91no—
120C4⋊C8—91no—
121C4⋊C8—181no—
122#103—91no—
123#103—91no—
124#97—61no—
125#97—181no—
126C4×C8—91no—
127C4×C8—91no—
128C4×C8—91no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—61no—
132C2×C3×C4—61no—
133C2×C3×C4—61no—
134C2×C3×C4—61no—
135C2×Dic3—21no—
136C2×Dic3—21no—
137C2×Dic3—21no—
138C2×Dic3—21no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143Dic6—121no—
144Dic6—121no—
145Dic6—121no—
146Dic6—121no—
147C3×C8—22no—
148C3×C8—41no—
149C3×C8—121no—
150C3×C8—121no—
151C3⋊C8—41no—
152C3⋊C8—41no—
153C3⋊C8—62no—
154C3⋊C8—121no—
155C2×C32#43611yescharacteristic
156C2×C32#44111yescharacteristic
157C2×C32#44411yescharacteristic
158C2×Q8—91no—
159C2×Q8—91no—
160Q16—182no—
161C2×C8—61no—
162C2×C8—61no—
163C2×C8—91no—
164C2×C8—91no—
165C2×C8—91no—
166C2×C8—181no—
167C2×C8GO+(4,𝔽2)11yescharacteristic
168C4⋊C4—91no—
169C4⋊C4—91no—
170C4⋊C4—181no—
171C4⋊C4—181no—
172C42—61no—
173C42—61no—
174C42—91no—
175C22×C3—21no—
176C22×C3—21no—
177C3×C4—21no—
178C3×C4—21no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—121no—
182C3×C4—121no—
183C3×C4—121no—
184C3×C4—121no—
185Dic3—41no—
186Dic3—41no—
187Dic3—41no—
188Dic3—41no—
189Dic3—61no—
190Dic3—61no—
191Dic3—61no—
192Dic3—61no—
193Dic3—121no—
194Dic3—121no—
195C32#159311yescharacteristic, complemented, Sylow
196Q8—181no—
197Q8—181no—
198Q8—181no—
199Q8—181no—
200C2×C4—61no—
201C2×C4—61no—
202C2×C4—61no—
203C2×C4—61no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4C2×GO+(4,𝔽2)11yescharacteristic
207C8—21no—
208C8—92no—
209C8—121no—
210C8—121no—
211C8—181no—
212C8—181no—
213C8—361no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C22C4×GO+(4,𝔽2)11yescharacteristic
221C4—91no—
222C4—91no—
223C4—121no—
224C4—121no—
225C4—121no—
226C4—121no—
227C4—181no—
228C4#6422611yescharacteristic
229C4#6423911yescharacteristic
230C3—21no—
231C3—21no—
232C2#1059328311yescharacteristic
233C2#1059329811yescharacteristic
234C2#1059336911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC2×C32×C8D4
socle, prime radicalC22×C32C4×D4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1593
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
195. C32#1593semidirect

Maximal subgroups

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

subgroupindex
C4×#37762
#105907882
#105907872
#105901692
#105900412
#105900322
#15939