Subgroups — C₃⋊D₃×#576 #11918780

Order 1152.

4536 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
2	C₃²×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	#10596306	C₂	1	2	yes	maximal, complemented
4	#10596245	C₂	1	6	yes	maximal, complemented
5	C₃⋊D₃×AGL(1,ℤ/8)	C₂	1	6	yes	maximal, complemented
6	#10596240	C₂	1	3	yes	maximal, complemented
7	C₃⋊D₃×#135	C₂	1	3	yes	maximal, complemented
8	#10596228	C₂	1	3	yes	maximal, complemented
9	C₂×D₈×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
10	#10596223	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃⋊D₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×#576	—	3	4	no	maximal
13	C₃²×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	#64366	—	2	2	no	—
15	#64366	C₂²	1	6	yes	complemented
16	#64366	C₂²	1	2	yes	complemented
17	#41×C₃⋊D₃	—	2	2	no	—
18	#41×C₃⋊D₃	C₂²	1	1	yes	characteristic
19	#41×C₃⋊D₃	C₂²	1	6	yes	complemented
20	#64361	—	2	6	no	—
21	#64361	C₂²	1	6	yes	complemented
22	C₂×D₄×C₃⋊D₃	—	2	6	no	—
23	C₂×D₄×C₃⋊D₃	C₂²	1	6	yes	complemented
24	C₃²×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
25	C₃²×#135	C₂²	1	3	yes	complemented
26	C₂×C₃²×D₈	C₂²	1	3	yes	complemented
27	C₃²×#131	C₂²	1	1	yes	characteristic, complemented
28	#64159	C₂²	1	6	yes	complemented
29	#64158	C₂²	1	6	yes	complemented
30	#64157	C₂²	1	1	yes	characteristic, complemented
31	#64141	C₂²	1	6	yes	complemented
32	C₂×#3753	C₂²	1	6	yes	complemented
33	#64128	C₂²	1	3	yes	complemented
34	Q₁₆×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
35	#64125	C₂²	1	6	yes	complemented
36	#64123	C₂²	1	12	yes	complemented
37	SD₁₆×C₃⋊D₃	C₂²	1	6	yes	complemented
38	#64121	C₂²	1	3	yes	complemented
39	#64120	C₂²	1	12	yes	complemented
40	D₈×C₃⋊D₃	C₂²	1	3	yes	complemented
41	D₈×C₃⋊D₃	C₂²	1	6	yes	complemented
42	D₈×C₃⋊D₃	C₂²	1	6	yes	complemented
43	D₈×C₃⋊D₃	C₂²	1	6	yes	complemented
44	#64117	C₂²	1	6	yes	complemented
45	#64116	C₂²	1	3	yes	complemented
46	M₁₆×C₃⋊D₃	C₂²	1	3	yes	complemented
47	#64113	C₂²	1	3	yes	complemented
48	C₂×#3745	C₂²	1	3	yes	complemented
49	#64110	C₂²	1	3	yes	complemented
50	C₂×C₈×C₃⋊D₃	C₂²	1	3	yes	complemented
51	D₃×H(5,𝔽₂)	—	3	8	no	—
52	C₃×#576	D₃	1	4	yes	complemented
53	#5835	—	3	8	no	—
54	#5774	—	3	24	no	—
55	D₃×AGL(1,ℤ/8)	—	3	24	no	—
56	#5769	—	3	12	no	—
57	D₃×#135	—	3	12	no	—
58	#5757	—	3	12	no	—
59	C₂×D₃×D₈	—	3	12	no	—
60	#5752	—	3	4	no	—
61	D₃×#131	—	3	4	no	—
62	C₂³×C₃⋊D₃	—	2	6	no	—
63	C₃²×#41	—	2	2	no	—
64	C₃²×#41	C₂³	1	1	yes	characteristic
65	C₃²×#41	C₂³	1	6	yes	complemented
66	C₂×C₃²×D₄	—	2	6	no	—
67	C₂×C₃²×D₄	C₂³	1	6	yes	complemented
68	C₂×#638	—	2	12	no	—
69	C₂×#638	—	2	6	no	—
70	#3832	—	2	2	no	—
71	#3832	D₄	1	1	yes	characteristic
72	#3832	C₂³	1	6	yes	complemented
73	Q₈×C₃⋊D₃	D₄	1	1	yes	characteristic
74	Q₈×C₃⋊D₃	C₂³	1	2	yes	—
75	#3830	—	2	6	no	—
76	#3830	—	2	6	no	—
77	#3830	D₄	1	3	yes	—
78	#3830	C₂³	1	6	yes	complemented
79	D₄×C₃⋊D₃	—	2	6	no	—
80	D₄×C₃⋊D₃	—	2	6	no	—
81	D₄×C₃⋊D₃	—	2	12	no	—
82	D₄×C₃⋊D₃	—	2	6	no	—
83	D₄×C₃⋊D₃	—	2	6	no	—
84	D₄×C₃⋊D₃	—	2	6	no	—
85	D₄×C₃⋊D₃	D₄	1	3	yes	—
86	D₄×C₃⋊D₃	C₂³	1	6	yes	—
87	D₄×C₃⋊D₃	C₂³	1	12	yes	complemented
88	#3828	—	2	6	no	—
89	#3828	—	2	6	no	—
90	#3828	C₂³	1	3	yes	—
91	#3828	C₂³	1	6	yes	complemented
92	C₂×C₄⋊(C₃⋊D₃)	—	2	6	no	—
93	C₂×C₄⋊(C₃⋊D₃)	C₂³	1	6	yes	complemented
94	C₂×C₄×C₃⋊D₃	—	2	6	no	—
95	C₂×C₄×C₃⋊D₃	C₂³	1	3	yes	—
96	C₃²×Q₁₆	C₂³	1	1	yes	characteristic, complemented
97	C₃²×SD₁₆	C₂³	1	6	yes	complemented
98	C₃²×D₈	C₂³	1	3	yes	complemented
99	C₃²×D₈	C₂³	1	6	yes	complemented
100	C₃²×M₁₆	C₂³	1	3	yes	complemented
101	C₂×C₃²×C₈	C₂³	1	3	yes	complemented
102	#3756	C₂³	1	2	yes	complemented
103	#3755	C₂³	1	6	yes	complemented
104	#3754	C₂³	1	6	yes	complemented
105	#3753	C₂³	1	6	yes	complemented
106	#3753	C₂³	1	12	yes	complemented
107	#3748	C₂³	1	3	yes	complemented
108	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	3	yes	complemented
109	#3746	C₂³	1	1	yes	characteristic, complemented
110	#3745	C₂³	1	3	yes	complemented
111	#3745	C₂³	1	6	yes	complemented
112	#3744	C₂³	1	6	yes	complemented
113	#3743	C₂³	1	6	yes	complemented
114	C₈×C₃⋊D₃	C₂³	1	1	yes	characteristic
115	C₈×C₃⋊D₃	C₂³	1	3	yes	—
116	C₈×C₃⋊D₃	C₂³	1	3	yes	complemented
117	C₈×C₃⋊D₃	C₂³	1	3	yes	complemented
118	C₂×#576	—	9	1	no	Sylow
119	C₃×H(5,𝔽₂)	C₂×D₃	1	8	yes	complemented
120	#1009	—	3	8	no	—
121	#1009	—	3	24	no	—
122	#1009	—	6	8	no	—
123	D₃×#41	—	3	4	no	—
124	D₃×#41	—	3	24	no	—
125	D₃×#41	—	6	8	no	—
126	#1004	—	3	24	no	—
127	#1004	—	6	24	no	—
128	C₂×D₃×D₄	—	3	24	no	—
129	C₂×D₃×D₄	—	6	24	no	—
130	C₃×AGL(1,ℤ/8)	C₂×D₃	1	24	yes	complemented
131	C₃×#135	C₂×D₃	1	12	yes	complemented
132	C₂×C₃×D₈	C₂×D₃	1	12	yes	complemented
133	C₃×#131	C₂×D₃	1	4	yes	complemented
134	#950	—	3	24	no	—
135	#949	—	3	24	no	—
136	#948	—	3	4	no	—
137	#932	—	3	24	no	—
138	C₂×#213	—	3	24	no	—
139	#919	—	3	12	no	—
140	D₃×Q₁₆	—	3	4	no	—
141	#916	—	3	24	no	—
142	#914	—	3	48	no	—
143	D₃×SD₁₆	—	3	24	no	—
144	#912	—	3	12	no	—
145	#911	—	3	48	no	—
146	D₃×D₈	—	3	12	no	—
147	D₃×D₈	—	3	24	no	—
148	D₃×D₈	—	3	24	no	—
149	D₃×D₈	—	3	24	no	—
150	#908	—	3	24	no	—
151	#907	—	3	12	no	—
152	D₃×M₁₆	—	3	12	no	—
153	#904	—	3	12	no	—
154	C₂×D₂₄	—	3	12	no	—
155	#901	—	3	12	no	—
156	C₂×D₃×C₈	—	3	12	no	—
157	C₂³×C₃²	—	2	6	no	—
158	C₂²×C₃⋊D₃	—	2	6	no	—
159	C₂²×C₃⋊D₃	—	2	6	no	—
160	C₂²×C₃⋊D₃	—	2	12	no	—
161	C₂²×C₃⋊D₃	—	8	12	no	—
162	C₂²×C₃⋊D₃	C₂×D₄	1	3	yes	—
163	C₃²×Q₈	C₂×D₄	1	1	yes	characteristic
164	C₃²×Q₈	C₂⁴	1	2	yes	—
165	C₃²×D₄	—	2	6	no	—
166	C₃²×D₄	—	2	6	no	—
167	C₃²×D₄	C₂×D₄	1	3	yes	—
168	C₃²×D₄	C₂⁴	1	6	yes	—
169	C₂×C₃²×C₄	—	2	6	no	—
170	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
171	#638	—	2	6	no	—
172	#638	—	2	6	no	—
173	#638	—	2	6	no	—
174	#638	—	2	12	no	—
175	#638	C₂×D₄	1	6	yes	—
176	C₂×C₃⋊Dic₃	—	2	6	no	—
177	C₂×C₃⋊Dic₃	C₂×D₄	1	3	yes	—
178	C₄⋊(C₃⋊D₃)	—	2	6	no	—
179	C₄⋊(C₃⋊D₃)	—	2	6	no	—
180	C₄⋊(C₃⋊D₃)	C₂×D₄	1	3	yes	—
181	C₄⋊(C₃⋊D₃)	C₂⁴	1	6	yes	—
182	C₄×C₃⋊D₃	—	2	2	no	—
183	C₄×C₃⋊D₃	—	2	6	no	—
184	C₄×C₃⋊D₃	—	2	6	no	—
185	C₄×C₃⋊D₃	C₂×D₄	1	3	yes	—
186	C₄×C₃⋊D₃	C₂×D₄	1	3	yes	—
187	C₄×C₃⋊D₃	C₂⁴	1	1	yes	characteristic
188	C₄×C₃⋊D₃	C₂⁴	1	3	yes	—
189	#634	—	2	2	no	—
190	#634	C₂×D₄	1	3	yes	—
191	#634	C₂⁴	1	2	yes	—
192	C₃²×C₈	C₂⁴	1	1	yes	characteristic
193	C₃²×C₈	C₂⁴	1	3	yes	—
194	C₃⋊(C₃⋊C₈)	C₂⁴	1	1	yes	characteristic
195	C₃⋊(C₃⋊C₈)	C₂⁴	1	3	yes	—
196	C₂×H(5,𝔽₂)	—	9	2	no	—
197	#576	—	9	2	no	—
198	#576	—	9	6	no	—
199	#576	—	9	3	no	—
200	#576	—	9	3	no	—
201	#576	—	9	1	no	—
202	#576	C₃⋊D₃	1	1	yes	characteristic, direct product factor
203	C₂×AGL(1,ℤ/8)	—	9	6	no	—
204	C₂×#135	—	9	3	no	—
205	C₂²×D₈	—	9	3	no	—
206	C₂×#131	—	9	1	no	—
207	C₂³×D₃	—	6	24	no	—
208	C₃×#41	—	2	8	no	—
209	C₃×#41	C₂²×D₃	1	4	yes	—
210	C₃×#41	C₂²×D₃	1	24	yes	complemented
211	C₂×C₃×D₄	—	2	24	no	—
212	C₂×C₃×D₄	C₂²×D₃	1	24	yes	complemented
213	C₂×#67	—	6	24	no	—
214	C₂×#67	—	6	48	no	—
215	#239	—	3	4	no	—
216	#239	—	3	24	no	—
217	#239	—	6	8	no	—
218	D₃×Q₈	—	3	4	no	—
219	D₃×Q₈	—	3	8	no	—
220	#237	—	3	12	no	—
221	#237	—	3	24	no	—
222	#237	—	6	24	no	—
223	#237	—	6	24	no	—
224	D₃×D₄	—	3	12	no	—
225	D₃×D₄	—	3	24	no	—
226	D₃×D₄	—	3	48	no	—
227	D₃×D₄	—	6	24	no	—
228	D₃×D₄	—	6	24	no	—
229	D₃×D₄	—	6	24	no	—
230	D₃×D₄	—	6	48	no	—
231	D₃×D₄	—	6	24	no	—
232	D₃×D₄	—	6	24	no	—
233	#235	—	3	12	no	—
234	#235	—	3	24	no	—
235	#235	—	6	24	no	—
236	#235	—	6	24	no	—
237	C₂×D₁₂	—	3	24	no	—
238	C₂×D₁₂	—	6	24	no	—
239	C₂×C₄×D₃	—	3	12	no	—
240	C₂×C₄×D₃	—	6	24	no	—
241	C₃×Q₁₆	C₂²×D₃	1	4	yes	complemented
242	C₃×SD₁₆	C₂²×D₃	1	24	yes	complemented
243	C₃×D₈	C₂²×D₃	1	12	yes	complemented
244	C₃×D₈	C₂²×D₃	1	24	yes	complemented
245	C₃×M₁₆	C₂²×D₃	1	12	yes	complemented
246	C₂×C₃×C₈	C₂²×D₃	1	12	yes	complemented
247	#216	—	3	8	no	—
248	#215	—	3	24	no	—
249	#214	—	3	24	no	—
250	#213	—	3	24	no	—
251	#213	—	3	48	no	—
252	#208	—	3	12	no	—
253	C₂×C₃⋊C₈	—	3	12	no	—
254	Dic₁₂	—	3	4	no	—
255	D₂₄	—	3	12	no	—
256	D₂₄	—	3	24	no	—
257	#204	—	3	24	no	—
258	ΓL(1,𝔽₂₅)	—	3	24	no	—
259	D₃×C₈	—	3	4	no	—
260	D₃×C₈	—	3	12	no	—
261	D₃×C₈	—	3	12	no	—
262	D₃×C₈	—	3	12	no	—
263	C₂²×C₃²	—	2	6	no	—
264	C₂²×C₃²	—	8	6	no	—
265	C₂²×C₃²	C₂²×D₄	1	3	yes	—
266	C₂×C₃⋊D₃	—	2	6	no	—
267	C₂×C₃⋊D₃	—	2	6	no	—
268	C₂×C₃⋊D₃	—	4	12	no	—
269	C₂×C₃⋊D₃	—	8	12	no	—
270	C₂×C₃⋊D₃	—	8	6	no	—
271	C₂×C₃⋊D₃	C₂²×D₄	1	3	yes	—
272	C₂×C₃⋊D₃	C₂²×D₄	1	1	yes	characteristic
273	C₃²×C₄	—	2	2	no	—
274	C₃²×C₄	C₂²×D₄	1	3	yes	—
275	C₃²×C₄	C₂⁵	1	1	yes	characteristic
276	C₃⋊Dic₃	—	2	2	no	—
277	C₃⋊Dic₃	C₂²×D₄	1	1	yes	characteristic
278	C₃⋊Dic₃	C₂²×D₄	1	3	yes	—
279	H(5,𝔽₂)	—	9	2	no	—
280	H(5,𝔽₂)	—	9	6	no	—
281	H(5,𝔽₂)	—	9	6	no	—
282	H(5,𝔽₂)	—	18	6	no	—
283	H(5,𝔽₂)	—	18	2	no	—
284	H(5,𝔽₂)	C₂×C₃⋊D₃	1	2	yes	complemented
285	C₂×#41	—	9	1	no	—
286	C₂×#41	—	9	6	no	—
287	C₂×#41	—	18	2	no	—
288	C₂²×D₄	—	9	6	no	—
289	C₂²×D₄	—	18	6	no	—
290	AGL(1,ℤ/8)	—	9	6	no	—
291	AGL(1,ℤ/8)	—	9	6	no	—
292	AGL(1,ℤ/8)	—	9	12	no	—
293	AGL(1,ℤ/8)	—	9	12	no	—
294	AGL(1,ℤ/8)	—	9	6	no	—
295	AGL(1,ℤ/8)	C₂×C₃⋊D₃	1	6	yes	complemented
296	#135	—	9	6	no	—
297	#135	—	9	3	no	—
298	#135	—	9	6	no	—
299	#135	—	9	3	no	—
300	#135	—	9	3	no	—
301	#135	C₂×C₃⋊D₃	1	3	yes	complemented
302	C₂×Q₁₆	—	9	1	no	—
303	C₂×SD₁₆	—	9	6	no	—
304	C₂×D₈	—	9	6	no	—
305	C₂×D₈	—	9	3	no	—
306	C₂×D₈	—	9	6	no	—
307	C₂×D₈	—	9	6	no	—
308	C₂×D₈	—	9	6	no	—
309	C₂×D₈	—	9	3	no	—
310	C₂×D₈	C₂×C₃⋊D₃	1	3	yes	complemented
311	#131	—	9	1	no	—
312	#131	—	9	3	no	—
313	#131	—	9	3	no	—
314	#131	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
315	C₂×M₁₆	—	9	3	no	—
316	C₂²×C₈	—	9	3	no	—
317	C₂³×C₃	—	2	24	no	—
318	C₂²×D₃	—	3	12	no	—
319	C₂²×D₃	—	6	24	no	—
320	C₂²×D₃	—	6	48	no	—
321	C₂²×D₃	—	6	24	no	—
322	C₂²×D₃	—	24	48	no	—
323	C₃×Q₈	D₃×D₄	1	4	yes	—
324	C₃×Q₈	C₂³×D₃	1	8	yes	—
325	C₃×D₄	—	2	24	no	—
326	C₃×D₄	—	2	24	no	—
327	C₃×D₄	D₃×D₄	1	12	yes	—
328	C₃×D₄	C₂³×D₃	1	24	yes	—
329	C₂×C₃×C₄	—	2	24	no	—
330	C₂×C₃×C₄	C₂³×D₃	1	12	yes	—
331	#67	—	3	24	no	—
332	#67	—	6	48	no	—
333	#67	—	6	24	no	—
334	#67	—	6	24	no	—
335	#67	—	6	24	no	—
336	C₂×Dic₃	—	3	12	no	—
337	C₂×Dic₃	—	6	24	no	—
338	D₁₂	—	3	12	no	—
339	D₁₂	—	3	24	no	—
340	D₁₂	—	6	24	no	—
341	D₁₂	—	6	24	no	—
342	C₄×D₃	—	3	12	no	—
343	C₄×D₃	—	3	12	no	—
344	C₄×D₃	—	3	4	no	—
345	C₄×D₃	—	3	12	no	—
346	C₄×D₃	—	6	24	no	—
347	C₄×D₃	—	6	8	no	—
348	C₄×D₃	—	6	24	no	—
349	Dic₆	—	3	12	no	—
350	Dic₆	—	3	8	no	—
351	Dic₆	—	6	8	no	—
352	C₃×C₈	C₂³×D₃	1	4	yes	—
353	C₃×C₈	C₂³×D₃	1	12	yes	—
354	C₃⋊C₈	—	3	4	no	—
355	C₃⋊C₈	—	3	12	no	—
356	C₂×C₃²	—	2	3	no	—
357	C₂×C₃²	—	4	6	no	—
358	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
359	C₃⋊D₃	—	2	3	no	—
360	C₃⋊D₃	—	4	6	no	—
361	C₃⋊D₃	#576	1	2	yes	direct product factor
362	C₂⁴	—	18	6	no	—
363	#41	—	2	2	no	—
364	#41	—	9	1	no	—
365	#41	—	9	3	no	—
366	#41	—	9	3	no	—
367	#41	—	9	6	no	—
368	#41	—	9	6	no	—
369	#41	—	9	6	no	—
370	#41	—	18	6	no	—
371	#41	—	18	6	no	—
372	#41	—	18	6	no	—
373	#41	—	18	6	no	—
374	#41	—	18	2	no	—
375	#41	C₂²×C₃⋊D₃	1	1	yes	characteristic
376	#41	C₂²×C₃⋊D₃	1	6	yes	complemented
377	C₂×Q₈	—	9	1	no	—
378	C₂×Q₈	—	9	2	no	—
379	C₂×D₄	—	2	6	no	—
380	C₂×D₄	—	9	3	no	—
381	C₂×D₄	—	9	6	no	—
382	C₂×D₄	—	9	12	no	—
383	C₂×D₄	—	9	6	no	—
384	C₂×D₄	—	18	6	no	—
385	C₂×D₄	—	18	6	no	—
386	C₂×D₄	—	18	6	no	—
387	C₂×D₄	—	18	6	no	—
388	C₂×D₄	—	18	12	no	—
389	C₂×D₄	—	18	6	no	—
390	C₂×D₄	—	18	6	no	—
391	C₂×D₄	—	18	12	no	—
392	C₂×D₄	—	18	6	no	—
393	C₂×D₄	C₂²×C₃⋊D₃	1	6	yes	complemented
394	C₂²×C₄	—	9	3	no	—
395	C₂²×C₄	—	18	6	no	—
396	Q₁₆	—	9	2	no	—
397	Q₁₆	—	9	1	no	—
398	Q₁₆	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented
399	SD₁₆	—	9	6	no	—
400	SD₁₆	—	9	6	no	—
401	SD₁₆	—	9	6	no	—
402	SD₁₆	C₂²×C₃⋊D₃	1	6	yes	complemented
403	D₈	—	9	6	no	—
404	D₈	—	9	12	no	—
405	D₈	—	9	3	no	—
406	D₈	—	9	6	no	—
407	D₈	C₂²×C₃⋊D₃	1	3	yes	complemented
408	D₈	C₂²×C₃⋊D₃	1	6	yes	complemented
409	M₁₆	—	9	3	no	—
410	M₁₆	—	9	6	no	—
411	M₁₆	C₂²×C₃⋊D₃	1	3	yes	complemented
412	C₂×C₈	—	9	3	no	—
413	C₂×C₈	—	9	1	no	—
414	C₂×C₈	—	9	3	no	—
415	C₂×C₈	—	9	3	no	—
416	C₂×C₈	—	9	3	no	—
417	C₂×C₈	C₂²×C₃⋊D₃	1	3	yes	complemented
418	C₂²×C₃	—	2	24	no	—
419	C₂²×C₃	—	8	24	no	—
420	C₂²×C₃	C₂×D₃×D₄	1	12	yes	—
421	C₂×D₃	—	3	4	no	—
422	C₂×D₃	—	3	12	no	—
423	C₂×D₃	—	6	24	no	—
424	C₂×D₃	—	6	24	no	—
425	C₂×D₃	—	12	48	no	—
426	C₂×D₃	—	24	48	no	—
427	C₂×D₃	—	24	24	no	—
428	C₃×C₄	—	2	8	no	—
429	C₃×C₄	C₂×D₃×D₄	1	12	yes	—
430	C₃×C₄	C₂⁴×D₃	1	4	yes	—
431	Dic₃	—	3	12	no	—
432	Dic₃	—	3	4	no	—
433	Dic₃	—	6	8	no	—
434	C₃²	C₂×#576	1	1	yes	characteristic, complemented, Sylow
435	C₂³	—	2	6	no	—
436	C₂³	—	9	3	no	—
437	C₂³	—	18	6	no	—
438	C₂³	—	18	12	no	—
439	C₂³	—	18	6	no	—
440	C₂³	—	72	12	no	—
441	Q₈	—	9	3	no	—
442	Q₈	—	9	2	no	—
443	Q₈	—	18	2	no	—
444	Q₈	D₄×C₃⋊D₃	1	1	yes	characteristic
445	Q₈	C₂³×C₃⋊D₃	1	2	yes	—
446	D₄	—	2	6	no	—
447	D₄	—	2	6	no	—
448	D₄	—	9	6	no	—
449	D₄	—	9	3	no	—
450	D₄	—	9	6	no	—
451	D₄	—	18	6	no	—
452	D₄	—	18	6	no	—
453	D₄	—	18	12	no	—
454	D₄	—	18	6	no	—
455	D₄	—	18	6	no	—
456	D₄	—	18	6	no	—
457	D₄	D₄×C₃⋊D₃	1	3	yes	—
458	D₄	C₂³×C₃⋊D₃	1	6	yes	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	9	3	no	—
461	C₂×C₄	—	9	3	no	—
462	C₂×C₄	—	9	3	no	—
463	C₂×C₄	—	9	1	no	—
464	C₂×C₄	—	9	3	no	—
465	C₂×C₄	—	18	6	no	—
466	C₂×C₄	—	18	2	no	—
467	C₂×C₄	—	18	6	no	—
468	C₂×C₄	—	18	6	no	—
469	C₂×C₄	C₂³×C₃⋊D₃	1	3	yes	—
470	C₈	—	9	1	no	—
471	C₈	—	9	3	no	—
472	C₈	C₂³×C₃⋊D₃	1	1	yes	characteristic
473	C₈	C₂³×C₃⋊D₃	1	3	yes	—
474	C₂×C₃	—	2	12	no	—
475	C₂×C₃	—	4	24	no	—
476	C₂×C₃	C₂²×D₃×D₄	1	4	yes	—
477	D₃	—	3	8	no	—
478	D₃	—	6	12	no	—
479	D₃	—	12	24	no	—
480	C₂²	—	2	6	no	—
481	C₂²	—	8	6	no	—
482	C₂²	—	9	1	no	—
483	C₂²	—	9	3	no	—
484	C₂²	—	18	6	no	—
485	C₂²	—	18	6	no	—
486	C₂²	—	36	12	no	—
487	C₂²	—	72	6	no	—
488	C₂²	—	72	12	no	—
489	C₂²	C₂×D₄×C₃⋊D₃	1	3	yes	—
490	C₄	—	2	2	no	—
491	C₄	—	9	1	no	—
492	C₄	—	9	3	no	—
493	C₄	—	18	2	no	—
494	C₄	C₂×D₄×C₃⋊D₃	1	3	yes	—
495	C₄	C₂⁴×C₃⋊D₃	1	1	yes	characteristic
496	C₃	D₃×#576	1	4	yes	complemented
497	C₂	—	2	3	no	—
498	C₂	—	4	6	no	—
499	C₂	—	9	2	no	—
500	C₂	—	18	3	no	—
501	C₂	—	36	6	no	—
502	C₂	C₂²×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁵
Frattini	C₄	C₂⁴×C₃⋊D₃
Fitting	C₃²×#576	C₂
socle	C₂×C₃²	C₂³×D₄
hypercenter	#576	C₃⋊D₃
hypocenter	C₃²	C₂×#576
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×H(5,𝔽₂)	C₂	semidirect
2. C₃²×#576	C₂	semidirect
3. #10596306	C₂	semidirect
4. #10596245	C₂	semidirect
5. C₃⋊D₃×AGL(1,ℤ/8)	C₂	semidirect
6. #10596240	C₂	semidirect
7. C₃⋊D₃×#135	C₂	semidirect
8. #10596228	C₂	semidirect
9. C₂×D₈×C₃⋊D₃	C₂	semidirect
10. #10596223	C₂	semidirect
11. C₃⋊D₃×#131	C₂	semidirect
13. C₃²×H(5,𝔽₂)	C₂²	semidirect
15. #64366	C₂²	semidirect
16. #64366	C₂²	semidirect
19. #41×C₃⋊D₃	C₂²	semidirect
21. #64361	C₂²	semidirect
23. C₂×D₄×C₃⋊D₃	C₂²	semidirect
24. C₃²×AGL(1,ℤ/8)	C₂²	semidirect
25. C₃²×#135	C₂²	semidirect
26. C₂×C₃²×D₈	C₂²	semidirect
27. C₃²×#131	C₂²	semidirect
28. #64159	C₂²	semidirect
29. #64158	C₂²	semidirect
30. #64157	C₂²	semidirect
31. #64141	C₂²	semidirect
32. C₂×#3753	C₂²	semidirect
33. #64128	C₂²	semidirect
34. Q₁₆×C₃⋊D₃	C₂²	semidirect
35. #64125	C₂²	semidirect
36. #64123	C₂²	semidirect
37. SD₁₆×C₃⋊D₃	C₂²	semidirect
38. #64121	C₂²	semidirect
39. #64120	C₂²	semidirect
40. D₈×C₃⋊D₃	C₂²	semidirect
41. D₈×C₃⋊D₃	C₂²	semidirect
42. D₈×C₃⋊D₃	C₂²	semidirect
43. D₈×C₃⋊D₃	C₂²	semidirect
44. #64117	C₂²	semidirect
45. #64116	C₂²	semidirect
46. M₁₆×C₃⋊D₃	C₂²	semidirect
47. #64113	C₂²	semidirect
48. C₂×#3745	C₂²	semidirect
49. #64110	C₂²	semidirect
50. C₂×C₈×C₃⋊D₃	C₂²	semidirect
52. C₃×#576	D₃	semidirect
65. C₃²×#41	C₂³	semidirect
67. C₂×C₃²×D₄	C₂³	semidirect
72. #3832	C₂³	semidirect
78. #3830	C₂³	semidirect
87. D₄×C₃⋊D₃	C₂³	semidirect
91. #3828	C₂³	semidirect
93. C₂×C₄⋊(C₃⋊D₃)	C₂³	semidirect
96. C₃²×Q₁₆	C₂³	semidirect
97. C₃²×SD₁₆	C₂³	semidirect
98. C₃²×D₈	C₂³	semidirect
99. C₃²×D₈	C₂³	semidirect
100. C₃²×M₁₆	C₂³	semidirect
101. C₂×C₃²×C₈	C₂³	semidirect
102. #3756	C₂³	semidirect
103. #3755	C₂³	semidirect
104. #3754	C₂³	semidirect
105. #3753	C₂³	semidirect
106. #3753	C₂³	semidirect
107. #3748	C₂³	semidirect
108. C₂×C₃⋊(C₃⋊C₈)	C₂³	semidirect
109. #3746	C₂³	semidirect
110. #3745	C₂³	semidirect
111. #3745	C₂³	semidirect
112. #3744	C₂³	semidirect
113. #3743	C₂³	semidirect
116. C₈×C₃⋊D₃	C₂³	semidirect
117. C₈×C₃⋊D₃	C₂³	semidirect
119. C₃×H(5,𝔽₂)	C₂×D₃	semidirect
130. C₃×AGL(1,ℤ/8)	C₂×D₃	semidirect
131. C₃×#135	C₂×D₃	semidirect
132. C₂×C₃×D₈	C₂×D₃	semidirect
133. C₃×#131	C₂×D₃	semidirect
202. #576	C₃⋊D₃	direct (N × H)
210. C₃×#41	C₂²×D₃	semidirect
212. C₂×C₃×D₄	C₂²×D₃	semidirect
241. C₃×Q₁₆	C₂²×D₃	semidirect
242. C₃×SD₁₆	C₂²×D₃	semidirect
243. C₃×D₈	C₂²×D₃	semidirect
244. C₃×D₈	C₂²×D₃	semidirect
245. C₃×M₁₆	C₂²×D₃	semidirect
246. C₂×C₃×C₈	C₂²×D₃	semidirect
284. H(5,𝔽₂)	C₂×C₃⋊D₃	semidirect
295. AGL(1,ℤ/8)	C₂×C₃⋊D₃	semidirect
301. #135	C₂×C₃⋊D₃	semidirect
310. C₂×D₈	C₂×C₃⋊D₃	semidirect
314. #131	C₂×C₃⋊D₃	semidirect
361. C₃⋊D₃	#576	direct (N × H)
376. #41	C₂²×C₃⋊D₃	semidirect
393. C₂×D₄	C₂²×C₃⋊D₃	semidirect
398. Q₁₆	C₂²×C₃⋊D₃	semidirect
402. SD₁₆	C₂²×C₃⋊D₃	semidirect
407. D₈	C₂²×C₃⋊D₃	semidirect
408. D₈	C₂²×C₃⋊D₃	semidirect
411. M₁₆	C₂²×C₃⋊D₃	semidirect
417. C₂×C₈	C₂²×C₃⋊D₃	semidirect
434. C₃²	C₂×#576	semidirect
496. C₃	D₃×#576	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×H(5,𝔽₂)	2
C₃²×#576	2
#10596306	2
#10596245	2
C₃⋊D₃×AGL(1,ℤ/8)	2
#10596240	2
C₃⋊D₃×#135	2
#10596228	2
C₂×D₈×C₃⋊D₃	2
#10596223	2
C₃⋊D₃×#131	2
D₃×#576	3

Subgroups — C3⋊D3×#576 #11918780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×#576 #11918780