Finite Group Databasebeta

← #11781552

Subgroups — #11781552

Order 1152.

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

normal subgroups only

This group has 268 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
1D4×#622C211yesmaximal, characteristic
2#10593379C211yesmaximal, characteristic, complemented
3#10591495C211yesmaximal, characteristic
4#10591494C211yesmaximal, characteristic
5#10590042C211yesmaximal, characteristic, complemented
6#10590040C211yesmaximal, characteristic, complemented
7#10590039C211yesmaximal, characteristic, complemented
8C22×#622—21no—
9D4×C3⋊Dic3C2211yescharacteristic
10#63919C2211yescharacteristic
11#63919C2211yescharacteristic
12C22⋊#622—21no—
13C4⋊#622C2211yescharacteristic
14C4×#622C2211yescharacteristic
15#63740—21no—
16#63740—21no—
17C3×#832—21no—
18C3×#832—21no—
19#63575—21no—
20#63573—21no—
21#63572C2211yescharacteristic
22#63572C2211yescharacteristic
23#4761—61no—
24#4759—61no—
25C2×C32×D4D411yescharacteristic
26C22×C3⋊Dic3—21no—
27C2×#627—21no—
28C2×#627—21no—
29C2×#622—21no—
30C2×#622—42no—
31C2×#622D411yescharacteristic
32C2×#622D411yescharacteristic
33#3757—21no—
34C4⋊(C3⋊Dic3)D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C3×C4⋊Dic3—21no—
37C3×C4⋊Dic3—21no—
38C2×C3×C3⋊C8—21no—
39C2×C3×C3⋊C8—21no—
40#3724—21no—
41#3724—21no—
42#1683—91nomaximal, Sylow
43D4×Dic3—61no—
44D4×Dic3—61no—
45#888—61no—
46#888—61no—
47C3×#102—61no—
48C3×#102—61no—
49#832—21no—
50#832—21no—
51#818—61no—
52#817—61no—
53Dic3⋊C8—61no—
54Dic3⋊C8—61no—
55#808—61no—
56#807—61no—
57C23×C32—21no—
58C32×D4—21no—
59C32×D4Q1612yes—
60C2×C32×C4C2×D411yescharacteristic
61C2×C3⋊Dic3—21no—
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3#4111yescharacteristic
66C2×C3×Dic3—41no—
67C2×C3×Dic3—41no—
68#627—41no—
69#627—41no—
70#627—81no—
71#622—21no—
72#622—21no—
73#622—41no—
74C3×C3⋊C8—41no—
75C3×C3⋊C8—41no—
76#487—91no—
77#476—91no—
78#474—91no—
79C8×D4—91no—
80#335—91no—
81#333—91no—
82#332—91no—
83C2×C3×D4—21no—
84C2×C3×D4—21no—
85C22×Dic3—121no—
86C22×Dic3—121no—
87C2×Dic6—121no—
88C2×Dic6—121no—
89C2×C3×C8—61no—
90C2×C3×C8—61no—
91C3×C4⋊C4—61no—
92C3×C4⋊C4—61no—
93#217—121no—
94#217—121no—
95C4⋊Dic3—21no—
96C4⋊Dic3—21no—
97C4⋊Dic3—61no—
98C4⋊Dic3—61no—
99Dic3⋊C4—121no—
100Dic3⋊C4—121no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C2×C3⋊C8—21no—
104C2×C3⋊C8—21no—
105C22×C32—22no—
106C22×C32—41no—
107C22×C32—41no—
108C22×C32#12111yescharacteristic
109C32×C4C2×Q1611yescharacteristic
110C32×C4#13511yescharacteristic
111C3⋊Dic3—21no—
112C3⋊Dic3—41no—
113C3⋊Dic3#13511yescharacteristic
114C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
115C3×Dic3—81no—
116C3×Dic3—81no—
117C22×C8—181no—
118C4⋊Q8—91no—
119C4⋊Q8—91no—
120C4×D4—91no—
121#107—181no—
122#106—181no—
123C4⋊C8—91no—
124C4⋊C8—91no—
125C4⋊C8—91no—
126#103—181no—
127#103—181no—
128#102—61no—
129#102—61no—
130C22⋊C8—181no—
131C4×C8—91no—
132C23×C3—41no—
133C23×C3—41no—
134C3×D4—22no—
135C3×D4—22no—
136C3×D4—41no—
137C3×D4—41no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—121no—
141C2×C3×C4—121no—
142C2×Dic3—41no—
143C2×Dic3—41no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—121no—
149C2×Dic3—121no—
150C2×Dic3—241no—
151C2×Dic3—241no—
152C2×Dic3—241no—
153C2×Dic3—241no—
154Dic6—241no—
155Dic6—241no—
156Dic6—242no—
157C3×C8—121no—
158C3×C8—121no—
159C3⋊C8—41no—
160C3⋊C8—41no—
161C2×C32—42no—
162C2×C32#46311yescharacteristic
163C2×C32#46711yescharacteristic
164C2×C32#47111yescharacteristic
165C2×Q8—181no—
166C2×Q8—181no—
167C2×D4GO+(4,𝔽2)11yescharacteristic
168C22×C4—181no—
169C2×C8—61no—
170C2×C8—61no—
171C2×C8—91no—
172C2×C8—91no—
173C2×C8—181no—
174C2×C8—362no—
175C4⋊C4—61no—
176C4⋊C4—61no—
177C4⋊C4—91no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C22⋊C4—181no—
181C42—91no—
182C22×C3—21no—
183C22×C3—21no—
184C22×C3—42no—
185C22×C3—42no—
186C22×C3—81no—
187C22×C3—81no—
188C22×C3—81no—
189C22×C3—81no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—241no—
195C3×C4—241no—
196Dic3—61no—
197Dic3—61no—
198Dic3—61no—
199Dic3—61no—
200Dic3—81no—
201Dic3—81no—
202Dic3—121no—
203Dic3—121no—
204Dic3—241no—
205Dic3—241no—
206C32#168311yescharacteristic, complemented, Sylow
207C23—21no—
208Q8—361no—
209Q8—361no—
210Q8—721no—
211D4—21no—
212D4#377612yes—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—121no—
216C2×C4—121no—
217C2×C4—181no—
218C2×C4—361no—
219C2×C4—361no—
220C2×C4C2×GO+(4,𝔽2)11yescharacteristic
221C8—121no—
222C8—121no—
223C8—181no—
224C8—181no—
225C8—361no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—21no—
232C2×C3—82no—
233C2×C3—82no—
234C22—22no—
235C22—41no—
236C22—41no—
237C22#6424211yescharacteristic
238C4—91no—
239C4—91no—
240C4—181no—
241C4—241no—
242C4—241no—
243C4—361no—
244C4#6423711yescharacteristic
245C4C2×#377611yescharacteristic
246C3—21no—
247C3—21no—
248C2—42no—
249C2#1059346211yescharacteristic
250C2#1059346711yescharacteristic
251C2#1059352711yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
Fitting, prime radicalC2×C32×D4D4
socleC22×C32#121
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1683
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593379C2semidirect
5. #10590042C2semidirect
6. #10590040C2semidirect
7. #10590039C2semidirect
206. C32#1683semidirect

Maximal subgroups

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

subgroupindex
D4×#6222
#105933792
#105914952
#105914942
#105900422
#105900402
#105900392
#16839