Finite Group Databasebeta

← D3×#458⋊C3 #11921231

Subgroups — D3×#458⋊C3 #11921231

Order 1152.

369 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 28 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
1D3×#997C211yesmaximal, characteristic
2C3×#458⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#458⋊C3)C211yesmaximal, characteristic, complemented
4D3×#458C311yesmaximal, characteristic, complemented
5C2×#458⋊C3—31nomaximal
6C3×#997C2211yescharacteristic
7C4×D3×A4—41nomaximal
8D3×H(5,𝔽2)C2×C311yescharacteristic
9C2×#997—31no—
10D3×#123—31no—
11C3×#458C2×C311yescharacteristic, complemented
12#5243C2×C311yescharacteristic, complemented
13#5053—31no—
14D3×#99—31no—
15#4742—31no—
16#458⋊C3—21no—
17#458⋊C3—31no—
18#458⋊C3D311yescharacteristic, direct product factor
19C2×D3×A4—41no—
20C2×D3×A4—81no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23D3×SL(2,𝔽3)—81no—
24C2×#458—31noSylow
25C3×H(5,𝔽2)C22×C311yescharacteristic
26#1009—61no—
27D3×#41—61no—
28#1004—31no—
29#1004—61no—
30C2×D3×D4—31no—
31C2×D3×D4—61no—
32C22×C4×D3A411yescharacteristic, complemented
33#997—21no—
34#997C2×D311yescharacteristic
35C2×C4×A4—121no—
36C3×#123—31no—
37#935—31no—
38#929—31no—
39#894—61no—
40D3×C4⋊C4—61no—
41#886—31no—
42#883—61no—
43D3×C22⋊C4—31no—
44D3×C22⋊C4—61no—
45C3×#99—31no—
46#834—31no—
47#806—32no—
48C2×C3×A4—41no—
49C2×C3×A4—81no—
50D3×A4—42no—
51D3×A4—82no—
52C3×C4×D3—161no—
53C3×SL(2,𝔽3)—81no—
54C2×H(5,𝔽2)—31no—
55C2×#123—91no—
56#458—31no—
57#458—91no—
58#458—91no—
59#458C3×D311yescharacteristic, complemented
60C2×#99—91no—
61C23×D3—21no—
62C23×D3—31no—
63C23×D3C2×A411yescharacteristic
64C22×A4—121no—
65C22×A4—241no—
66C3×#41—61no—
67C2×C3×D4—31no—
68C2×C3×D4—61no—
69C22×C3×C4C2×A411yescharacteristic, complemented
70C2×#67—31no—
71C2×#67—31no—
72C2×#67—61no—
73C2×#67—61no—
74C22×Dic3C2×A411yescharacteristic, complemented
75#239—61no—
76D3×Q8—21no—
77#237—62no—
78#237—61no—
79D3×D4—62no—
80D3×D4—62no—
81D3×D4—62no—
82D3×D4—61no—
83D3×D4—62no—
84#235—61no—
85#235—62no—
86C2×D12—31no—
87C2×D12—61no—
88C2×C4×D3—31no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—61no—
93C2×SL(2,𝔽3)—241no—
94C4×A4—41no—
95C4×A4—81no—
96C4×A4—121no—
97C3×C4⋊C4—61no—
98C3×C22⋊C4—31no—
99C3×C22⋊C4—61no—
100#217—31no—
101#217—61no—
102(C2×D3)⋊C4—61no—
103(C2×D3)⋊C4—61no—
104(C2×D3)⋊C4—61no—
105C4⋊Dic3—61no—
106Dic3⋊C4—61no—
107Dic3⋊C4—61no—
108C2×C3×D3—161no—
109C3×A4—41no—
110C3×A4—81no—
111C32×C4—161no—
112C3×Dic3—161no—
113H(5,𝔽2)—91no—
114H(5,𝔽2)—181no—
115H(5,𝔽2)—181no—
116H(5,𝔽2)C2×C3×D311yescharacteristic
117C2×#41—181no—
118C22×D4—91no—
119C22×D4—181no—
120C23×C4—31no—
121#123—31no—
122#123—91no—
123#123—91no—
124#123—91no—
125#123—181no—
126#123—181no—
127C2×C4⋊C4—181no—
128C2×C22⋊C4—91no—
129C2×C22⋊C4—181no—
130#99—31no—
131#99—92no—
132#99—91no—
133C23×C3—21no—
134C23×C3—31no—
135C23×C3C22×A411yescharacteristic
136C22×D3—31no—
137C22×D3—31no—
138C22×D3—31no—
139C22×D3—42no—
140C22×D3—61no—
141C22×D3—61no—
142C22×D3—61no—
143C22×D3—82no—
144C22×D3—122no—
145C2×A4—41no—
146C2×A4—81no—
147C2×A4—81no—
148C2×A4—122no—
149C2×A4—161no—
150C2×A4—242no—
151C3×Q8—21no—
152C3×D4—62no—
153C3×D4—61no—
154C2×C3×C4—31no—
155C2×C3×C4—61no—
156C2×C3×C4—61no—
157C2×C3×C4—61no—
158C2×C3×C4—481no—
159#67—62no—
160#67—62no—
161#67—62no—
162C2×Dic3—31no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166D12—62no—
167D12—61no—
168C4×D3—41no—
169C4×D3—61no—
170C4×D3—62no—
171C4×D3—61no—
172C4×D3—121no—
173C4×D3—122no—
174Dic6—61no—
175SL(2,𝔽3)—81no—
176SL(2,𝔽3)—161no—
177C2×C32—161no—
178C3×D3—162no—
179C24—31no—
180C24—61no—
181C24—91no—
182#41—61no—
183#41—181no—
184#41—182no—
185#41—182no—
186#41—181no—
187#41—181no—
188C2×Q8—61no—
189C2×D4—31no—
190C2×D4—61no—
191C2×D4—91no—
192C2×D4—91no—
193C2×D4—91no—
194C2×D4—181no—
195C2×D4—182no—
196C2×D4—182no—
197C2×D4—182no—
198C2×D4—181no—
199C2×D4—182no—
200C2×D4—181no—
201C2×D4—181no—
202C22×C4—31no—
203C22×C4—91no—
204C22×C4—181no—
205C22×C4—181no—
206C22×C4—181no—
207C22×C4—181no—
208C22×C4D3×A411yescharacteristic, complemented
209C4⋊C4—61no—
210C4⋊C4—181no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C22⋊C4—31no—
214C22⋊C4—61no—
215C22⋊C4—91no—
216C22⋊C4—181no—
217C22⋊C4—181no—
218C22⋊C4—181no—
219C22⋊C4—181no—
220C22×C3—31no—
221C22×C3—41no—
222C22×C3—61no—
223C22×C3—81no—
224C22×C3—121no—
225C22×C3—481no—
226C2×D3—31no—
227C2×D3—62no—
228C2×D3—61no—
229C2×D3—121no—
230C2×D3—122no—
231C2×D3—121no—
232C2×D3—241no—
233C2×D3—241no—
234C2×D3#120⋊C311yescharacteristic
235A4—41no—
236A4—81no—
237A4—81no—
238A4—161no—
239C3×C4—41no—
240C3×C4—61no—
241C3×C4—121no—
242C3×C4—161no—
243C3×C4—321no—
244C3×C4—481no—
245Dic3—41no—
246Dic3—61no—
247Dic3—121no—
248C32—161noSylow
249C23—21no—
250C23—31no—
251C23—91no—
252C23—91no—
253C23—91no—
254C23—122no—
255C23—181no—
256C23—181no—
257C23—181no—
258C23—242no—
259C23—362no—
260C23C2×D3×A411yescharacteristic
261Q8—21no—
262Q8—181no—
263D4—62no—
264D4—61no—
265D4—182no—
266D4—181no—
267D4—182no—
268D4—182no—
269D4—182no—
270C2×C4—31no—
271C2×C4—61no—
272C2×C4—61no—
273C2×C4—61no—
274C2×C4—91no—
275C2×C4—121no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—182no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—361no—
283C2×C4—362no—
284C2×C3—61no—
285C2×C3—121no—
286C2×C3—161no—
287C2×C3—321no—
288C2×C3—482no—
289C2×C3C2×#120⋊C311yescharacteristic
290D3—61no—
291D3—121no—
292D3#458⋊C312yesdirect product factor
293C22—31no—
294C22—31no—
295C22—41no—
296C22—61no—
297C22—81no—
298C22—91no—
299C22—121no—
300C22—182no—
301C22—181no—
302C22—362no—
303C22—361no—
304C22—361no—
305C22—721no—
306C22—721no—
307C4—41no—
308C4—61no—
309C4—121no—
310C4—121no—
311C4—181no—
312C4—361no—
313C3—161no—
314C3—321no—
315C3C2×#458⋊C311yescharacteristic, complemented
316C2—32no—
317C2—61no—
318C2—121no—
319C2—181no—
320C2—361no—
321C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
commutator, cosocle, hypocenterC3×H(5,𝔽2)C22×C3
FrattiniC23C2×D3×A4
FittingC3×#458C2×C3
socleC2×C3C2×#120⋊C3
prime radicalD3×#997C2
LCSG ▷ C3×H(5,𝔽2)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×#458⋊C3C2semidirect
3. C3⋊(#458⋊C3)C2semidirect
4. D3×#458C3semidirect
11. C3×#458C2×C3semidirect
12. #5243C2×C3semidirect
18. #458⋊C3D3direct (N × H)
32. C22×C4×D3A4semidirect
59. #458C3×D3semidirect
69. C22×C3×C4C2×A4semidirect
74. C22×Dic3C2×A4semidirect
208. C22×C4D3×A4semidirect
292. D3#458⋊C3direct (N × H)
315. C3C2×#458⋊C3semidirect

Maximal subgroups

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

subgroupindex
D3×#9972
C3×#458⋊C32
C3⋊(#458⋊C3)2
D3×#4583
C2×#458⋊C33
C4×D3×A44