Finite Group Databasebeta

← #11781598

Subgroups — #11781598

Order 1152.

240 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 45 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
1Q8×#622C211yesmaximal, characteristic
2#10593379C211yesmaximal, characteristic
3#10591631C211yesmaximal, characteristic
4#10591630C211yesmaximal, characteristic
5#10590042C211yesmaximal, characteristic
6#10590040C211yesmaximal, characteristic
7#10590039C211yesmaximal, characteristic
8Q8×C3⋊Dic3C2211yescharacteristic
9#63919C2211yescharacteristic
10#63919C2211yescharacteristic
11C4⋊#622—21no—
12C4⋊#622C2211yescharacteristic
13C4×#622—21no—
14C4×#622C2211yescharacteristic
15#63740—21no—
16#63740—21no—
17C3×#835—21no—
18C3×#835—21no—
19#63575—21no—
20#63573—21no—
21#63572C2211yescharacteristic
22#63572C2211yescharacteristic
23#4793—61no—
24#4791—61no—
25C2×C32×Q8D411yescharacteristic
26C2×#627—21no—
27C2×#627—21no—
28C2×#622—21no—
29C2×#622D411yescharacteristic
30C2×#622D411yescharacteristic
31C4⋊(C3⋊Dic3)—21no—
32C4⋊(C3⋊Dic3)D411yescharacteristic
33C4×C3⋊Dic3—21no—
34C4×C3⋊Dic3C2311yescharacteristic
35C3×C4⋊Dic3—21no—
36C3×C4⋊Dic3—21no—
37C2×C3×C3⋊C8—21no—
38C2×C3×C3⋊C8—21no—
39#3724—21no—
40#3724—21no—
41#1684—91nomaximal, Sylow
42Q8×Dic3—61no—
43Q8×Dic3—61no—
44#888—61no—
45#888—61no—
46C3×#103—61no—
47C3×#103—61no—
48#835—21no—
49#835—21no—
50#818—61no—
51#817—61no—
52Dic3⋊C8—61no—
53Dic3⋊C8—61no—
54#808—61no—
55#807—61no—
56C32×Q8—21no—
57C32×Q8Q1612yes—
58C2×C32×C4—21no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3—21no—
61C2×C3⋊Dic3C2×D411yescharacteristic
62C2×C3⋊Dic3#4111yescharacteristic
63C2×C3×Dic3—41no—
64C2×C3×Dic3—41no—
65#627—41no—
66#627—41no—
67#627—81no—
68#622—21no—
69#622—21no—
70#622—41no—
71C3×C3⋊C8—41no—
72C3×C3⋊C8—41no—
73#487—91no—
74#477—91no—
75#475—91no—
76C8×Q8—91no—
77#335—91no—
78#333—91no—
79#332—91no—
80C2×C3×Q8—21no—
81C2×C3×Q8—21no—
82C2×Dic6—121no—
83C2×Dic6—121no—
84C2×C3×C8—61no—
85C2×C3×C8—61no—
86C3×C4⋊C4—61no—
87C3×C4⋊C4—61no—
88C4⋊Dic3—21no—
89C4⋊Dic3—21no—
90C4⋊Dic3—61no—
91C4⋊Dic3—61no—
92C4⋊Dic3—121no—
93C4⋊Dic3—121no—
94Dic3⋊C4—121no—
95Dic3⋊C4—121no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—121no—
99C4×Dic3—121no—
100C2×C3⋊C8—21no—
101C2×C3⋊C8—21no—
102C22×C32#12111yescharacteristic
103C32×C4—22no—
104C32×C4C2×Q1611yescharacteristic
105C32×C4#13511yescharacteristic
106C3⋊Dic3—21no—
107C3⋊Dic3—41no—
108C3⋊Dic3#13511yescharacteristic
109C3⋊Dic3#13711yescharacteristic
110C3×Dic3—81no—
111C3×Dic3—81no—
112C4⋊Q8—91no—
113C4⋊Q8—91no—
114C4×Q8—91no—
115#107—181no—
116#106—181no—
117C4⋊C8—91no—
118C4⋊C8—91no—
119C4⋊C8—91no—
120C4⋊C8—181no—
121#103—61no—
122#103—61no—
123#103—181no—
124#103—181no—
125C4×C8—91no—
126C4×C8—181no—
127C3×Q8—22no—
128C3×Q8—22no—
129C3×Q8—41no—
130C3×Q8—41no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—41no—
134C2×C3×C4—41no—
135C2×C3×C4—121no—
136C2×C3×C4—121no—
137C2×Dic3—41no—
138C2×Dic3—41no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—121no—
144C2×Dic3—121no—
145Dic6—241no—
146Dic6—241no—
147Dic6—242no—
148C3×C8—121no—
149C3×C8—121no—
150C3⋊C8—41no—
151C3⋊C8—41no—
152C2×C32#46411yescharacteristic
153C2×C32#46711yescharacteristic
154C2×C32#47111yescharacteristic
155C2×Q8—181no—
156C2×Q8—181no—
157C2×Q8GO+(4,𝔽2)11yescharacteristic
158C2×C8—61no—
159C2×C8—61no—
160C2×C8—91no—
161C2×C8—91no—
162C2×C8—181no—
163C4⋊C4—61no—
164C4⋊C4—61no—
165C4⋊C4—91no—
166C4⋊C4—181no—
167C4⋊C4—181no—
168C4⋊C4—181no—
169C42—91no—
170C42—181no—
171C22×C3—21no—
172C22×C3—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—42no—
178C3×C4—42no—
179C3×C4—241no—
180C3×C4—241no—
181Dic3—61no—
182Dic3—61no—
183Dic3—61no—
184Dic3—61no—
185Dic3—81no—
186Dic3—81no—
187Dic3—121no—
188Dic3—121no—
189Dic3—241no—
190Dic3—241no—
191C32#168411yescharacteristic, complemented, Sylow
192Q8—21no—
193Q8—361no—
194Q8—361no—
195Q8—721no—
196Q8#377612yes—
197C2×C4—21no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—121no—
201C2×C4—121no—
202C2×C4—181no—
203C2×C4C2×GO+(4,𝔽2)11yescharacteristic
204C8—121no—
205C8—121no—
206C8—181no—
207C8—181no—
208C8—361no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—21no—
215C22#6424211yescharacteristic
216C4—22no—
217C4—91no—
218C4—91no—
219C4—181no—
220C4—241no—
221C4—241no—
222C4—361no—
223C4#6423711yescharacteristic
224C4C2×#377611yescharacteristic
225C3—21no—
226C3—21no—
227C2#1059347411yescharacteristic
228C2#1059348111yescharacteristic
229C2#1059352711yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socle, prime radicalC22×C32#121
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1684
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
191. C32#1684semidirect

Maximal subgroups

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

subgroupindex
Q8×#6222
#105933792
#105916312
#105916302
#105900422
#105900402
#105900392
#16849