Finite Group Databasebeta

← #11781553

Subgroups — #11781553

Order 1152.

268 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593749C211yesmaximal, characteristic
2#10593379C211yesmaximal, characteristic, complemented
3#10590433C211yesmaximal, characteristic
4#10590430C211yesmaximal, characteristic
5#10590042C211yesmaximal, characteristic, complemented
6#10590040C211yesmaximal, characteristic, complemented
7#10590039C211yesmaximal, characteristic, complemented
8C2×#3787—21no—
9#64102C2211yescharacteristic
10#63919C2211yescharacteristic
11#63919C2211yescharacteristic
12#63778—21no—
13C4⋊#622C2211yescharacteristic
14C4×#622C2211yescharacteristic
15#63740—21no—
16#63740—21no—
17C3×#808—21no—
18C3×#807—21no—
19#63572C2211yescharacteristic
20#63572C2211yescharacteristic
21#63564—21no—
22#63564—21no—
23#4890—61no—
24#4870—61no—
25C2×C4⋊(C3⋊D3)D411yescharacteristic
26C2×C4×C3⋊D3—21no—
27C2×#627—21no—
28C2×#627—21no—
29C2×#622—21no—
30C2×#622D411yescharacteristic
31C2×#622D411yescharacteristic
32#3787—42no—
33C32×C4⋊C4D411yescharacteristic
34#3752—21no—
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
43#893—61no—
44#893—61no—
45#888—61no—
46#888—61no—
47C3×#107—61no—
48C3×#106—61no—
49#821—61no—
50#821—61no—
51Dic3⋊C8—61no—
52Dic3⋊C8—61no—
53#809—61no—
54#809—61no—
55#808—21no—
56#807—21no—
57C22×C3⋊D3—21no—
58C2×C32×C4—21no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4111yescharacteristic
62C4⋊(C3⋊D3)—21no—
63C4⋊(C3⋊D3)Q1612yes—
64C4×C3⋊D3—41no—
65C4×C3⋊D3—41no—
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×D12—61no—
84C2×D12—61no—
85C2×C4×D3—121no—
86C2×C4×D3—121no—
87C2×Dic6—121no—
88C2×Dic6—121no—
89C2×C3×C8—61no—
90C2×C3×C8—61no—
91C3×C4⋊C4—21no—
92C3×C4⋊C4—21no—
93C3×C4⋊C4—61no—
94C3×C4⋊C4—61no—
95(C2×D3)⋊C4—121no—
96(C2×D3)⋊C4—121no—
97C4⋊Dic3—21no—
98C4⋊Dic3—21no—
99Dic3⋊C4—121no—
100Dic3⋊C4—121no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C2×C3⋊C8—21no—
104C2×C3⋊C8—21no—
105C22×C32#12111yescharacteristic
106C2×C3⋊D3—22no—
107C2×C3⋊D3—41no—
108C2×C3⋊D3—41no—
109C32×C4—41no—
110C32×C4C2×Q1611yescharacteristic
111C32×C4#13511yescharacteristic
112C3⋊Dic3—21no—
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—61no—
122#106—61no—
123C4⋊C8—91no—
124C4⋊C8—91no—
125C4⋊C8—91no—
126#103—181no—
127#103—181no—
128#102—181no—
129#102—181no—
130C22⋊C8—181no—
131C4×C8—91no—
132C22×D3—121no—
133C22×D3—121no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—41no—
137C2×C3×C4—41no—
138C2×C3×C4—121no—
139C2×C3×C4—121no—
140C2×Dic3—41no—
141C2×Dic3—41no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146D12—62no—
147D12—62no—
148D12—121no—
149D12—121no—
150C4×D3—241no—
151C4×D3—241no—
152C4×D3—241no—
153C4×D3—241no—
154Dic6—241no—
155Dic6—241no—
156Dic6—242no—
157C3×C8—121no—
158C3×C8—121no—
159C3⋊C8—41no—
160C3⋊C8—41no—
161C2×C32#46311yescharacteristic
162C2×C32#46711yescharacteristic
163C2×C32#47111yescharacteristic
164C3⋊D3—42no—
165C2×Q8—181no—
166C2×Q8—181no—
167C2×D4—91no—
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—181no—
178C4⋊C4—181no—
179C4⋊C4GO+(4,𝔽2)11yescharacteristic
180C22⋊C4—181no—
181C42—91no—
182C22×C3—21no—
183C22×C3—21no—
184C2×D3—122no—
185C2×D3—122no—
186C2×D3—241no—
187C2×D3—241no—
188C2×D3—241no—
189C2×D3—241no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—81no—
195C3×C4—81no—
196C3×C4—241no—
197C3×C4—241no—
198Dic3—61no—
199Dic3—61no—
200Dic3—61no—
201Dic3—61no—
202Dic3—81no—
203Dic3—81no—
204Dic3—121no—
205Dic3—121no—
206C32#168311yescharacteristic, complemented, Sylow
207C23—181no—
208Q8—361no—
209Q8—361no—
210Q8—721no—
211D4—92no—
212D4—181no—
213C2×C4—21no—
214C2×C4—91no—
215C2×C4—91no—
216C2×C4—121no—
217C2×C4—121no—
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—
232D3—242no—
233D3—242no—
234C22—182no—
235C22—361no—
236C22—361no—
237C22#6424211yescharacteristic
238C4—41no—
239C4—91no—
240C4—91no—
241C4—181no—
242C4—241no—
243C4—241no—
244C4#6422311yescharacteristic
245C4#6422811yescharacteristic
246C3—21no—
247C3—21no—
248C2—362no—
249C2#1059344611yescharacteristic
250C2#1059346211yescharacteristic
251C2#1059348111yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1683
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

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
#105937492
#105933792
#105904332
#105904302
#105900422
#105900402
#105900392
#16839