Subgroups — C₃×#33594 #10652201

Order 768.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3414	C₂	1	2	yes	maximal, complemented
2	C₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2214	C₂	1	2	yes	maximal, complemented
5	C₃×#2213	C₂	1	2	yes	maximal, complemented
6	C₃×#2212	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2148	C₂	1	2	yes	maximal, complemented
9	#33594	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂×C₃×#135	—	2	1	no	—
11	C₂×C₃×#135	C₂²	1	1	yes	characteristic
12	C₂×C₃×#135	C₂²	1	2	yes	—
13	C₂×C₃×#131	—	2	1	no	—
14	C₃×#532	—	2	1	no	—
15	C₃×#510	—	2	2	no	—
16	C₃×#510	C₂²	1	4	yes	—
17	C₃×#509	—	2	2	no	—
18	C₃×#509	C₂²	1	4	yes	—
19	C₃×#508	—	2	4	no	—
20	C₂×C₃×M₃₂	C₂²	1	2	yes	—
21	C₃×#495	—	2	1	no	—
22	C₃×#495	C₂²	1	2	yes	complemented
23	C₃×#494	C₂²	1	1	yes	characteristic, complemented
24	C₃×#493	C₂²	1	1	yes	characteristic, complemented
25	C₃×#492	—	2	1	no	—
26	C₃×#443	—	2	1	no	—
27	C₃×#443	—	2	1	no	—
28	C₃×#443	C₂²	1	2	yes	—
29	C₃×#443	C₂²	1	2	yes	—
30	C₂×C₃×#108	C₂²	1	1	yes	characteristic
31	C₂×C₃×#104	—	2	1	no	—
32	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
33	C₃×#364	C₂²	1	2	yes	complemented
34	C₃×#364	C₂²	1	2	yes	complemented
35	C₃×#362	C₂²	1	4	yes	complemented
36	C₃×#361	C₂²	1	4	yes	complemented
37	#3414	C₂×C₃	1	2	yes	complemented
38	#3147	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#443	C₂×C₃	1	1	yes	characteristic, complemented
40	#2214	C₂×C₃	1	2	yes	complemented
41	#2213	C₂×C₃	1	2	yes	complemented
42	#2212	C₂×C₃	1	4	yes	complemented
43	C₂×#364	C₂×C₃	1	1	yes	characteristic, complemented
44	#2148	C₂×C₃	1	2	yes	complemented
45	C₂×C₃×#41	—	2	1	no	—
46	C₂×C₃×#41	—	2	2	no	—
47	C₃×#135	—	2	1	no	—
48	C₃×#135	—	2	2	no	—
49	C₃×#135	—	2	2	no	—
50	C₃×#135	—	2	1	no	—
51	C₃×#135	—	2	2	no	—
52	C₃×#135	—	2	2	no	—
53	C₃×#135	—	4	1	no	—
54	C₃×#135	—	4	1	no	—
55	C₃×#135	—	4	1	no	—
56	C₃×#135	—	4	1	no	—
57	C₃×#135	D₄	1	2	yes	complemented
58	C₃×#135	C₂³	1	2	yes	—
59	C₂×C₃×Q₁₆	—	2	1	no	—
60	C₂×C₃×Q₁₆	D₄	1	1	yes	characteristic, complemented
61	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
62	C₂×C₃×SD₁₆	—	2	2	no	—
63	C₂×C₃×SD₁₆	—	2	2	no	—
64	C₂×C₃×SD₁₆	—	2	1	no	—
65	C₂×C₃×D₈	—	2	1	no	—
66	C₂×C₃×D₈	D₄	1	1	yes	characteristic, complemented
67	C₂×C₃×D₈	C₂³	1	2	yes	—
68	C₃×#131	—	2	2	no	—
69	C₃×#131	—	2	2	no	—
70	C₃×#131	—	4	1	no	—
71	C₃×#131	—	4	1	no	—
72	C₂×C₃×M₁₆	—	2	1	no	—
73	C₂×C₃×M₁₆	—	4	1	no	—
74	C₂²×C₃×C₈	—	4	1	no	—
75	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
76	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
77	C₃×C₄⋊Q₈	—	2	1	no	—
78	C₃×#127	—	2	1	no	—
79	C₃×#124	—	2	2	no	—
80	C₃×#121	—	4	2	no	—
81	C₃×C₄×D₄	—	4	2	no	—
82	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
83	C₃×Q₃₂	—	2	4	no	—
84	C₃×SD₃₂	—	2	4	no	—
85	C₃×SD₃₂	—	2	4	no	—
86	C₃×D₁₆	—	2	4	no	—
87	C₃×M₃₂	—	2	2	no	—
88	C₃×M₃₂	C₂³	1	4	yes	—
89	C₂×C₃×C₁₆	—	2	2	no	—
90	C₃×#108	—	2	1	no	—
91	C₃×#108	C₂³	1	2	yes	—
92	C₃×#104	—	2	2	no	—
93	C₃×#104	—	2	2	no	—
94	C₃×C₄×C₈	D₄	1	1	yes	characteristic
95	C₃×C₄×C₈	D₄	1	1	yes	characteristic
96	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
97	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
98	C₂×#135	—	2	1	no	—
99	C₂×#135	C₂²×C₃	1	1	yes	characteristic
100	C₂×#135	C₂²×C₃	1	2	yes	—
101	C₂×#131	—	2	1	no	—
102	#532	—	2	1	no	—
103	#510	—	2	2	no	—
104	#510	C₂²×C₃	1	4	yes	—
105	#509	—	2	2	no	—
106	#509	C₂²×C₃	1	4	yes	—
107	#508	—	2	4	no	—
108	C₂×M₃₂	C₂²×C₃	1	2	yes	—
109	#495	—	2	1	no	—
110	#495	C₂²×C₃	1	2	yes	complemented
111	#494	C₂²×C₃	1	1	yes	characteristic, complemented
112	#493	C₂²×C₃	1	1	yes	characteristic, complemented
113	#492	—	2	1	no	—
114	#443	—	2	1	no	—
115	#443	—	2	1	no	—
116	#443	C₂²×C₃	1	2	yes	—
117	#443	C₂²×C₃	1	2	yes	—
118	C₂×#108	C₂²×C₃	1	1	yes	characteristic
119	C₂×#104	—	2	1	no	—
120	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
121	#364	C₂²×C₃	1	2	yes	complemented
122	#364	C₂²×C₃	1	2	yes	complemented
123	#362	C₂²×C₃	1	4	yes	complemented
124	#361	C₂²×C₃	1	4	yes	complemented
125	C₃×#41	—	2	2	no	—
126	C₃×#41	—	2	2	no	—
127	C₃×#41	—	4	1	no	—
128	C₃×#41	—	4	1	no	—
129	C₃×#41	—	4	2	no	—
130	C₃×#41	—	4	2	no	—
131	C₃×#41	—	4	2	no	—
132	C₃×#41	—	4	2	no	—
133	C₂×C₃×Q₈	—	2	1	no	—
134	C₂×C₃×Q₈	—	2	2	no	—
135	C₂×C₃×D₄	—	2	1	no	—
136	C₂×C₃×D₄	—	2	2	no	—
137	C₂×C₃×D₄	—	4	2	no	—
138	C₂×C₃×D₄	—	4	1	no	—
139	C₂×C₃×D₄	—	4	2	no	—
140	C₂²×C₃×C₄	—	2	1	no	—
141	C₂²×C₃×C₄	—	4	1	no	—
142	C₂²×C₃×C₄	—	4	2	no	—
143	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
144	C₃×Q₁₆	—	2	1	no	—
145	C₃×Q₁₆	—	2	2	no	—
146	C₃×Q₁₆	—	2	2	no	—
147	C₃×Q₁₆	—	4	1	no	—
148	C₃×Q₁₆	—	4	1	no	—
149	C₃×Q₁₆	C₂×D₄	1	2	yes	—
150	C₃×SD₁₆	—	2	2	no	—
151	C₃×SD₁₆	—	2	2	no	—
152	C₃×SD₁₆	—	4	2	no	—
153	C₃×SD₁₆	—	4	2	no	—
154	C₃×SD₁₆	—	4	2	no	—
155	C₃×SD₁₆	—	4	2	no	—
156	C₃×D₈	—	2	1	no	—
157	C₃×D₈	—	2	2	no	—
158	C₃×D₈	—	2	2	no	—
159	C₃×D₈	—	4	1	no	—
160	C₃×D₈	—	4	1	no	—
161	C₃×D₈	C₂×D₄	1	2	yes	—
162	C₃×M₁₆	—	2	2	no	—
163	C₃×M₁₆	—	4	1	no	—
164	C₃×M₁₆	—	4	2	no	—
165	C₃×M₁₆	—	4	2	no	—
166	C₂×C₃×C₈	—	4	1	no	—
167	C₂×C₃×C₈	—	4	2	no	—
168	C₂×C₃×C₈	—	4	2	no	—
169	C₂×C₃×C₈	D₈	1	1	yes	characteristic
170	C₂×C₃×C₈	D₈	1	1	yes	characteristic
171	C₂×C₃×C₈	D₈	1	1	yes	characteristic
172	C₂×C₃×C₈	D₈	1	1	yes	characteristic
173	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
178	C₂×C₃×C₈	#41	1	1	yes	characteristic
179	C₂×C₃×C₈	#41	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
181	C₃×C₄⋊C₄	—	4	2	no	—
182	C₃×C₂²⋊C₄	—	4	4	no	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
185	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
186	C₃×C₁₆	—	2	4	no	—
187	C₂×#41	—	2	1	no	—
188	C₂×#41	—	2	2	no	—
189	#135	—	2	1	no	—
190	#135	—	2	2	no	—
191	#135	—	2	2	no	—
192	#135	—	2	1	no	—
193	#135	—	2	2	no	—
194	#135	—	2	2	no	—
195	#135	—	4	1	no	—
196	#135	—	4	1	no	—
197	#135	—	4	1	no	—
198	#135	—	4	1	no	—
199	#135	C₃×D₄	1	2	yes	complemented
200	#135	C₂³×C₃	1	2	yes	—
201	C₂×Q₁₆	—	2	1	no	—
202	C₂×Q₁₆	C₃×D₄	1	1	yes	characteristic, complemented
203	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
204	C₂×SD₁₆	—	2	2	no	—
205	C₂×SD₁₆	—	2	2	no	—
206	C₂×SD₁₆	—	2	1	no	—
207	C₂×D₈	—	2	1	no	—
208	C₂×D₈	C₃×D₄	1	1	yes	characteristic, complemented
209	C₂×D₈	C₂³×C₃	1	2	yes	—
210	#131	—	2	2	no	—
211	#131	—	2	2	no	—
212	#131	—	4	1	no	—
213	#131	—	4	1	no	—
214	C₂×M₁₆	—	2	1	no	—
215	C₂×M₁₆	—	4	1	no	—
216	C₂²×C₈	—	4	1	no	—
217	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
219	C₄⋊Q₈	—	2	1	no	—
220	#127	—	2	1	no	—
221	#124	—	2	2	no	—
222	#121	—	4	2	no	—
223	C₄×D₄	—	4	2	no	—
224	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
225	Q₃₂	—	2	4	no	—
226	SD₃₂	—	2	4	no	—
227	SD₃₂	—	2	4	no	—
228	D₁₆	—	2	4	no	—
229	M₃₂	—	2	2	no	—
230	M₃₂	C₂³×C₃	1	4	yes	—
231	C₂×C₁₆	—	2	2	no	—
232	#108	—	2	1	no	—
233	#108	C₂³×C₃	1	2	yes	—
234	#104	—	2	2	no	—
235	#104	—	2	2	no	—
236	C₄×C₈	C₃×D₄	1	1	yes	characteristic
237	C₄×C₈	C₃×D₄	1	1	yes	characteristic
238	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
239	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
240	C₂³×C₃	—	4	1	no	—
241	C₂³×C₃	—	4	2	no	—
242	C₂³×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	4	1	no	—
245	C₃×Q₈	—	4	2	no	—
246	C₃×Q₈	—	4	2	no	—
247	C₃×D₄	—	2	2	no	—
248	C₃×D₄	—	4	2	no	—
249	C₃×D₄	—	4	2	no	—
250	C₃×D₄	—	4	2	no	—
251	C₃×D₄	—	4	2	no	—
252	C₃×D₄	—	4	1	no	—
253	C₃×D₄	—	8	4	no	—
254	C₃×D₄	—	8	2	no	—
255	C₃×D₄	—	8	2	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	—	8	2	no	—
264	C₂×C₃×C₄	—	8	2	no	—
265	C₂×C₃×C₄	#121	1	1	yes	characteristic
266	C₂×C₃×C₄	#121	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
269	C₂×C₃×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
271	C₃×C₈	—	4	2	no	—
272	C₃×C₈	#121	1	1	yes	characteristic
273	C₃×C₈	#121	1	1	yes	characteristic
274	C₃×C₈	C₂×D₈	1	1	yes	characteristic
275	C₃×C₈	C₂×D₈	1	1	yes	characteristic
276	C₃×C₈	C₂×D₈	1	1	yes	characteristic
277	C₃×C₈	C₂×D₈	1	1	yes	characteristic
278	C₃×C₈	C₂²×D₄	1	1	yes	characteristic
279	C₃×C₈	C₂×#41	1	1	yes	characteristic
280	#41	—	2	2	no	—
281	#41	—	2	2	no	—
282	#41	—	4	1	no	—
283	#41	—	4	1	no	—
284	#41	—	4	2	no	—
285	#41	—	4	2	no	—
286	#41	—	4	2	no	—
287	#41	—	4	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
299	Q₁₆	—	2	1	no	—
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	2	2	no	—
302	Q₁₆	—	4	1	no	—
303	Q₁₆	—	4	1	no	—
304	Q₁₆	C₂×C₃×D₄	1	2	yes	—
305	SD₁₆	—	2	2	no	—
306	SD₁₆	—	2	2	no	—
307	SD₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	SD₁₆	—	4	2	no	—
310	SD₁₆	—	4	2	no	—
311	D₈	—	2	1	no	—
312	D₈	—	2	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	4	1	no	—
315	D₈	—	4	1	no	—
316	D₈	C₂×C₃×D₄	1	2	yes	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	4	2	no	—
320	M₁₆	—	4	2	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	C₃×D₈	1	1	yes	characteristic
325	C₂×C₈	C₃×D₈	1	1	yes	characteristic
326	C₂×C₈	C₃×D₈	1	1	yes	characteristic
327	C₂×C₈	C₃×D₈	1	1	yes	characteristic
328	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
330	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
332	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
333	C₂×C₈	C₃×#41	1	1	yes	characteristic
334	C₂×C₈	C₃×#41	1	1	yes	characteristic
335	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
336	C₄⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₄²	—	2	1	no	—
339	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
340	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
341	C₁₆	—	2	4	no	—
342	C₂²×C₃	—	4	1	no	—
343	C₂²×C₃	—	4	2	no	—
344	C₂²×C₃	—	8	2	no	—
345	C₂²×C₃	—	8	4	no	—
346	C₂²×C₃	—	8	2	no	—
347	C₂²×C₃	#459	1	1	yes	characteristic
348	C₂²×C₃	#459	1	1	yes	characteristic
349	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₃×C₄	—	2	2	no	—
351	C₃×C₄	—	4	1	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	—	8	2	no	—
354	C₃×C₄	#459	1	1	yes	characteristic
355	C₃×C₄	#459	1	1	yes	characteristic
356	C₃×C₄	C₂×#121	1	1	yes	characteristic
357	C₃×C₄	C₂²×D₈	1	1	yes	characteristic
358	C₂³	—	4	1	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	8	4	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	C₃×#121	1	1	yes	characteristic
384	C₂×C₄	C₃×#121	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
387	C₂×C₄	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
389	C₈	—	4	2	no	—
390	C₈	C₃×#121	1	1	yes	characteristic
391	C₈	C₃×#121	1	1	yes	characteristic
392	C₈	C₂×C₃×D₈	1	1	yes	characteristic
393	C₈	C₂×C₃×D₈	1	1	yes	characteristic
394	C₈	C₂×C₃×D₈	1	1	yes	characteristic
395	C₈	C₂×C₃×D₈	1	1	yes	characteristic
396	C₈	C₂²×C₃×D₄	1	1	yes	characteristic
397	C₈	C₂×C₃×#41	1	1	yes	characteristic
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	8	2	no	—
402	C₂×C₃	—	16	2	no	—
403	C₂×C₃	C₂×#459	1	1	yes	characteristic
404	C₂²	—	4	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	4	no	—
408	C₂²	—	8	2	no	—
409	C₂²	C₃×#459	1	1	yes	characteristic
410	C₂²	C₃×#459	1	1	yes	characteristic
411	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	C₃×#459	1	1	yes	characteristic
417	C₄	C₃×#459	1	1	yes	characteristic
418	C₄	C₂×C₃×#121	1	1	yes	characteristic
419	C₄	C₂²×C₃×D₈	1	1	yes	characteristic
420	C₃	#33594	1	1	yes	characteristic, direct product factor, Sylow
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	16	2	no	—
426	C₂	C₂×C₃×#459	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
socle	C₂×C₃	C₂×#459
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3414	C₂	semidirect
2. C₃×#3147	C₂	semidirect
3. C₂×C₃×#443	C₂	semidirect
4. C₃×#2214	C₂	semidirect
5. C₃×#2213	C₂	semidirect
6. C₃×#2212	C₂	semidirect
7. C₂×C₃×#364	C₂	semidirect
8. C₃×#2148	C₂	semidirect
9. #33594	C₃	direct (N × H)
22. C₃×#495	C₂²	semidirect
23. C₃×#494	C₂²	semidirect
24. C₃×#493	C₂²	semidirect
33. C₃×#364	C₂²	semidirect
34. C₃×#364	C₂²	semidirect
35. C₃×#362	C₂²	semidirect
36. C₃×#361	C₂²	semidirect
37. #3414	C₂×C₃	semidirect
38. #3147	C₂×C₃	semidirect
39. C₂×#443	C₂×C₃	semidirect
40. #2214	C₂×C₃	semidirect
41. #2213	C₂×C₃	semidirect
42. #2212	C₂×C₃	semidirect
43. C₂×#364	C₂×C₃	semidirect
44. #2148	C₂×C₃	semidirect
57. C₃×#135	D₄	semidirect
60. C₂×C₃×Q₁₆	D₄	semidirect
66. C₂×C₃×D₈	D₄	semidirect
110. #495	C₂²×C₃	semidirect
111. #494	C₂²×C₃	semidirect
112. #493	C₂²×C₃	semidirect
121. #364	C₂²×C₃	semidirect
122. #364	C₂²×C₃	semidirect
123. #362	C₂²×C₃	semidirect
124. #361	C₂²×C₃	semidirect
199. #135	C₃×D₄	semidirect
202. C₂×Q₁₆	C₃×D₄	semidirect
208. C₂×D₈	C₃×D₄	semidirect
420. C₃	#33594	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3414	2
C₃×#3147	2
C₂×C₃×#443	2
C₃×#2214	2
C₃×#2213	2
C₃×#2212	2
C₂×C₃×#364	2
C₃×#2148	2
#33594	3

Subgroups — C3×#33594 #10652201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33594 #10652201