Subgroups — C₂×C₃×#5197 #11861042

Order 1152.

1061 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	C₂×C₃²×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#948	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#837	C₂	1	2	yes	maximal, complemented
4	C₃×#5197	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#444	—	3	1	no	maximal
8	C₂×#5197	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃²×#41	C₂²	1	2	yes	—
10	C₃²×#135	C₄	1	4	yes	complemented
11	C₃²×#135	C₂²	1	4	yes	—
12	C₂×C₃²×Q₁₆	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃²×SD₁₆	C₄	1	2	yes	complemented
14	C₂×C₃²×D₈	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₃×#948	—	2	4	no	—
17	C₃×#948	C₂²	1	8	yes	complemented
18	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×#208	—	2	2	no	—
20	C₂×C₃×#208	C₂²	1	2	yes	—
21	C₂²×C₃×C₃⋊C₈	—	2	2	no	—
22	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×#837	C₂²	1	8	yes	complemented
24	C₃×#819	C₂²	1	4	yes	complemented
25	C₃×#815	C₂²	1	4	yes	complemented
26	C₂×C₃×#135	—	2	1	no	—
27	C₂×C₃×#135	D₃	1	1	yes	characteristic
28	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×#131	—	3	2	no	—
30	C₂×#948	C₂×C₃	1	2	yes	complemented
31	C₃×#444	—	3	8	no	—
32	C₂×C₃×#108	—	3	1	no	—
33	C₂×C₃×#104	—	3	2	no	—
34	C₂×C₃×#97	—	3	1	no	—
35	C₂×#837	C₂×C₃	1	2	yes	complemented
36	#5197	C₂×C₃	1	8	yes	direct product factor
37	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#815	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃²×#41	—	2	2	no	—
40	C₃²×#41	—	2	2	no	—
41	C₃²×#41	C₂×C₄	1	4	yes	—
42	C₃²×#41	C₂³	1	4	yes	—
43	C₂×C₃²×Q₈	C₂×C₄	1	2	yes	—
44	C₂×C₃²×D₄	—	2	2	no	—
45	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
46	C₂²×C₃²×C₄	—	2	2	no	—
47	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₃	—	2	1	no	—
49	C₃²×Q₁₆	C₂×C₄	1	4	yes	complemented
50	C₃²×SD₁₆	C₂×C₄	1	8	yes	complemented
51	C₃²×D₈	C₂×C₄	1	4	yes	complemented
52	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
55	C₂×C₃²×C₈	C₂³	1	2	yes	—
56	C₃×C₄×Dic₃	—	2	1	no	—
57	C₃×C₄×Dic₃	C₂³	1	2	yes	—
58	C₃×#208	—	2	2	no	—
59	C₃×#208	—	2	8	no	—
60	C₃×#208	C₂³	1	4	yes	—
61	C₂×C₃×C₃⋊C₈	—	2	2	no	—
62	C₂×C₃×C₃⋊C₈	—	2	8	no	—
63	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
64	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
65	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
66	C₂×#444	—	3	1	no	Sylow
67	C₂×C₃×#41	—	2	2	no	—
68	C₂×C₃×#41	C₂×D₃	1	2	yes	—
69	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
70	C₃×#135	—	2	4	no	—
71	C₃×#135	—	2	4	no	—
72	C₃×#135	Dic₃	1	4	yes	complemented
73	C₃×#135	C₃×C₄	1	4	yes	complemented
74	C₃×#135	C₂×D₃	1	4	yes	—
75	C₃×#135	C₂²×C₃	1	4	yes	—
76	C₂×C₃×Q₁₆	—	2	1	no	—
77	C₂×C₃×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
78	C₂×C₃×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
79	C₂×C₃×SD₁₆	—	2	2	no	—
80	C₂×C₃×SD₁₆	Dic₃	1	2	yes	complemented
81	C₂×C₃×SD₁₆	C₃×C₄	1	2	yes	complemented
82	C₂×C₃×D₈	—	2	1	no	—
83	C₂×C₃×D₈	Dic₃	1	1	yes	characteristic, complemented
84	C₂×C₃×D₈	C₃×C₄	1	1	yes	characteristic, complemented
85	C₃×#131	—	3	8	no	—
86	C₃×#131	—	6	4	no	—
87	C₂×C₃×M₁₆	—	3	2	no	—
88	C₂×C₃×M₁₆	—	6	2	no	—
89	C₂²×C₃×C₈	—	2	1	no	—
90	C₂²×C₃×C₈	—	3	1	no	—
91	C₂²×C₃×C₈	—	6	2	no	—
92	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄²	—	3	1	no	—
95	#948	—	2	4	no	—
96	#948	C₂²×C₃	1	8	yes	complemented
97	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
98	C₂×#208	—	2	2	no	—
99	C₂×#208	C₂²×C₃	1	2	yes	—
100	C₂²×C₃⋊C₈	—	2	2	no	—
101	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
102	C₃×#108	—	3	4	no	—
103	C₃×#104	—	3	8	no	—
104	C₃×#97	—	3	4	no	—
105	#837	C₂²×C₃	1	8	yes	complemented
106	#819	C₂²×C₃	1	4	yes	complemented
107	#815	C₂²×C₃	1	4	yes	complemented
108	C₂³×C₃²	—	2	2	no	—
109	C₂³×C₃²	#41	1	1	yes	characteristic
110	C₃²×Q₈	—	2	2	no	—
111	C₃²×Q₈	C₂²×C₄	1	4	yes	—
112	C₃²×D₄	—	2	4	no	—
113	C₃²×D₄	—	2	4	no	—
114	C₃²×D₄	—	2	2	no	—
115	C₃²×D₄	C₂²×C₄	1	4	yes	—
116	C₂×C₃²×C₄	—	2	2	no	—
117	C₂×C₃²×C₄	—	2	4	no	—
118	C₂×C₃²×C₄	—	2	4	no	—
119	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	#41	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
125	C₂×C₃×Dic₃	—	2	2	no	—
126	C₂×C₃×Dic₃	—	4	2	no	—
127	C₃²×C₈	C₂²×C₄	1	2	yes	—
128	C₃²×C₈	C₂²×C₄	1	2	yes	—
129	C₃×C₃⋊C₈	—	2	4	no	—
130	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
131	C₂×#135	C₃×D₃	1	1	yes	characteristic
132	C₂×#131	—	3	2	no	—
133	#444	—	3	8	no	—
134	C₂×#108	—	3	1	no	—
135	C₂×#104	—	3	2	no	—
136	C₂×#97	—	3	1	no	—
137	C₃×#41	—	2	2	no	—
138	C₃×#41	—	2	2	no	—
139	C₃×#41	—	2	2	no	—
140	C₃×#41	—	2	2	no	—
141	C₃×#41	—	2	4	no	—
142	C₃×#41	—	2	4	no	—
143	C₃×#41	—	4	2	no	—
144	C₃×#41	—	4	2	no	—
145	C₃×#41	C₂×Dic₃	1	4	yes	—
146	C₃×#41	C₂×C₃×C₄	1	4	yes	—
147	C₃×#41	C₂²×D₃	1	4	yes	—
148	C₃×#41	C₂³×C₃	1	4	yes	—
149	C₂×C₃×Q₈	—	2	2	no	—
150	C₂×C₃×Q₈	C₂×Dic₃	1	2	yes	—
151	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
152	C₂×C₃×D₄	—	2	2	no	—
153	C₂×C₃×D₄	—	2	2	no	—
154	C₂×C₃×D₄	—	2	2	no	—
155	C₂×C₃×D₄	—	4	2	no	—
156	C₂×C₃×D₄	C₂×Dic₃	1	2	yes	—
157	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
158	C₂²×C₃×C₄	—	2	2	no	—
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	4	2	no	—
162	C₂²×C₃×C₄	—	6	1	no	—
163	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
165	C₂²×Dic₃	—	2	1	no	—
166	C₃×Q₁₆	—	2	4	no	—
167	C₃×Q₁₆	C₂×Dic₃	1	4	yes	complemented
168	C₃×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
169	C₃×SD₁₆	—	2	8	no	—
170	C₃×SD₁₆	C₂×Dic₃	1	8	yes	complemented
171	C₃×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
172	C₃×D₈	—	2	4	no	—
173	C₃×D₈	C₂×Dic₃	1	4	yes	complemented
174	C₃×D₈	C₂×C₃×C₄	1	4	yes	complemented
175	C₃×M₁₆	—	3	4	no	—
176	C₃×M₁₆	—	6	8	no	—
177	C₃×M₁₆	—	6	2	no	—
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₂×C₃×C₈	—	2	2	no	—
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	3	2	no	—
183	C₂×C₃×C₈	—	3	2	no	—
184	C₂×C₃×C₈	—	3	2	no	—
185	C₂×C₃×C₈	—	6	8	no	—
186	C₂×C₃×C₈	—	6	2	no	—
187	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
188	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
189	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
190	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
191	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
192	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
193	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
194	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
195	C₃×C₄²	—	3	2	no	—
196	C₃×C₄²	—	6	1	no	—
197	C₄×Dic₃	—	2	1	no	—
198	C₄×Dic₃	C₂³×C₃	1	2	yes	—
199	#208	—	2	2	no	—
200	#208	—	2	8	no	—
201	#208	C₂³×C₃	1	4	yes	—
202	C₂×C₃⋊C₈	—	2	2	no	—
203	C₂×C₃⋊C₈	—	2	8	no	—
204	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
205	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
206	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	—	2	4	no	—
209	C₂²×C₃²	—	4	4	no	—
210	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
211	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
212	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
213	C₃²×C₄	—	2	4	no	—
214	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
215	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
216	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
217	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
218	C₃×Dic₃	—	4	2	no	—
219	C₂×#41	C₂×C₃×D₃	1	2	yes	—
220	#135	C₃×Dic₃	1	4	yes	complemented
221	#135	C₂×C₃×D₃	1	4	yes	—
222	C₂×Q₁₆	C₃×Dic₃	1	1	yes	characteristic, complemented
223	C₂×SD₁₆	C₃×Dic₃	1	2	yes	complemented
224	C₂×D₈	C₃×Dic₃	1	1	yes	characteristic, complemented
225	#131	—	3	8	no	—
226	#131	—	6	4	no	—
227	C₂×M₁₆	—	3	2	no	—
228	C₂×M₁₆	—	6	2	no	—
229	C₂²×C₈	—	3	1	no	—
230	C₂²×C₈	—	6	2	no	—
231	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂×C₄²	—	3	1	no	—
233	#108	—	3	4	no	—
234	#104	—	3	8	no	—
235	#97	—	3	4	no	—
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	1	no	—
239	C₂³×C₃	—	4	2	no	—
240	C₂³×C₃	#237	1	1	yes	characteristic
241	C₂³×C₃	C₃×#41	1	1	yes	characteristic
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	2	4	no	—
245	C₃×Q₈	—	4	2	no	—
246	C₃×Q₈	C₂²×Dic₃	1	4	yes	—
247	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
248	C₃×D₄	—	2	4	no	—
249	C₃×D₄	—	2	4	no	—
250	C₃×D₄	—	2	4	no	—
251	C₃×D₄	—	2	4	no	—
252	C₃×D₄	—	2	2	no	—
253	C₃×D₄	—	2	2	no	—
254	C₃×D₄	—	2	4	no	—
255	C₃×D₄	—	4	2	no	—
256	C₃×D₄	—	4	4	no	—
257	C₃×D₄	—	4	4	no	—
258	C₃×D₄	C₂²×Dic₃	1	4	yes	—
259	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	4	4	no	—
273	C₂×C₃×C₄	—	4	4	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	6	2	no	—
276	C₂×C₃×C₄	—	12	2	no	—
277	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
278	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
279	C₂×C₃×C₄	#237	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
289	C₂×Dic₃	—	2	2	no	—
290	C₂×Dic₃	—	4	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₃×C₈	—	2	2	no	—
293	C₃×C₈	—	3	4	no	—
294	C₃×C₈	—	6	4	no	—
295	C₃×C₈	C₂²×Dic₃	1	2	yes	—
296	C₃×C₈	C₂²×Dic₃	1	2	yes	—
297	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
298	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
299	C₃⋊C₈	—	2	4	no	—
300	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
301	C₂×C₃²	—	2	1	no	—
302	C₂×C₃²	—	2	1	no	—
303	C₂×C₃²	—	4	4	no	—
304	C₂×C₃²	#444	1	2	yes	complemented
305	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
306	#41	—	2	2	no	—
307	#41	—	2	2	no	—
308	#41	C₂×C₃×Dic₃	1	4	yes	—
309	#41	C₂²×C₃×D₃	1	4	yes	—
310	C₂×Q₈	C₂×C₃×Dic₃	1	2	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	C₂×C₃×Dic₃	1	2	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	6	1	no	—
315	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
316	Q₁₆	C₂×C₃×Dic₃	1	4	yes	complemented
317	SD₁₆	C₂×C₃×Dic₃	1	8	yes	complemented
318	D₈	C₂×C₃×Dic₃	1	4	yes	complemented
319	M₁₆	—	3	4	no	—
320	M₁₆	—	6	8	no	—
321	M₁₆	—	6	2	no	—
322	C₂×C₈	—	3	2	no	—
323	C₂×C₈	—	3	2	no	—
324	C₂×C₈	—	3	2	no	—
325	C₂×C₈	—	6	8	no	—
326	C₂×C₈	—	6	2	no	—
327	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
328	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
329	C₂×C₈	C₂×C₃×Dic₃	1	2	yes	—
330	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
331	C₄²	—	3	2	no	—
332	C₄²	—	6	1	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	4	no	—
336	C₂²×C₃	—	2	4	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	1	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	—	4	4	no	—
342	C₂²×C₃	—	4	4	no	—
343	C₂²×C₃	—	4	4	no	—
344	C₂²×C₃	—	8	4	no	—
345	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
346	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
347	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
348	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
349	C₂²×C₃	C₂×#237	1	1	yes	characteristic
350	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
351	C₃×C₄	—	2	4	no	—
352	C₃×C₄	—	2	4	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	4	4	no	—
358	C₃×C₄	—	12	2	no	—
359	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
360	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
361	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
362	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
363	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
364	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
365	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
366	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
367	Dic₃	—	4	2	no	—
368	C₃²	C₂×#444	1	1	yes	characteristic, complemented, Sylow
369	C₂³	—	2	2	no	—
370	C₂³	C₃×#237	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	C₂²×C₃×Dic₃	1	4	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	2	no	—
376	D₄	C₂²×C₃×Dic₃	1	4	yes	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	6	2	no	—
381	C₂×C₄	—	12	2	no	—
382	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
383	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
384	C₂×C₄	C₃×#237	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
387	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
388	C₈	—	3	4	no	—
389	C₈	—	6	4	no	—
390	C₈	C₂²×C₃×Dic₃	1	2	yes	—
391	C₈	C₂²×C₃×Dic₃	1	2	yes	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	2	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	4	1	no	—
399	C₂×C₃	—	4	1	no	—
400	C₂×C₃	—	4	4	no	—
401	C₂×C₃	—	4	4	no	—
402	C₂×C₃	—	8	4	no	—
403	C₂×C₃	#5197	1	2	yes	direct product factor
404	C₂×C₃	C₃×#444	1	2	yes	complemented
405	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
406	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
407	C₂²	—	2	2	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	C₃×D₄×Dic₃	1	1	yes	characteristic
411	C₂²	C₃×D₄×Dic₃	1	1	yes	characteristic
412	C₂²	C₂×C₃×#237	1	1	yes	characteristic
413	C₄	—	2	4	no	—
414	C₄	—	12	2	no	—
415	C₄	C₃×D₄×Dic₃	1	1	yes	characteristic
416	C₄	C₃×D₄×Dic₃	1	1	yes	characteristic
417	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
418	C₄	C₂³×C₃×Dic₃	1	1	yes	characteristic
419	C₃	—	2	1	no	—
420	C₃	C₂×#5197	1	1	yes	characteristic, direct product factor
421	C₃	C₂×C₃×#444	1	1	yes	characteristic, complemented
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	4	4	no	—
425	C₂	C₃×#5197	1	2	yes	direct product factor
426	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting, prime radical	C₂×C₃²×#135	C₂
socle	C₂²×C₃²	C₄×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#135	D₃
hypocenter	C₃	C₂×C₃×#444
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#948	C₂	semidirect
3. C₂×C₃×#837	C₂	semidirect
4. C₃×#5197	C₂	direct (N × H)
5. C₂×C₃×#819	C₂	semidirect
6. C₂×C₃×#815	C₂	semidirect
8. C₂×#5197	C₃	direct (N × H)
10. C₃²×#135	C₄	semidirect
12. C₂×C₃²×Q₁₆	C₄	semidirect
13. C₂×C₃²×SD₁₆	C₄	semidirect
14. C₂×C₃²×D₈	C₄	semidirect
17. C₃×#948	C₂²	semidirect
23. C₃×#837	C₂²	semidirect
24. C₃×#819	C₂²	semidirect
25. C₃×#815	C₂²	semidirect
30. C₂×#948	C₂×C₃	semidirect
35. C₂×#837	C₂×C₃	semidirect
36. #5197	C₂×C₃	direct (N × H)
37. C₂×#819	C₂×C₃	semidirect
38. C₂×#815	C₂×C₃	semidirect
49. C₃²×Q₁₆	C₂×C₄	semidirect
50. C₃²×SD₁₆	C₂×C₄	semidirect
51. C₃²×D₈	C₂×C₄	semidirect
72. C₃×#135	Dic₃	semidirect
73. C₃×#135	C₃×C₄	semidirect
77. C₂×C₃×Q₁₆	Dic₃	semidirect
78. C₂×C₃×Q₁₆	C₃×C₄	semidirect
80. C₂×C₃×SD₁₆	Dic₃	semidirect
81. C₂×C₃×SD₁₆	C₃×C₄	semidirect
83. C₂×C₃×D₈	Dic₃	semidirect
84. C₂×C₃×D₈	C₃×C₄	semidirect
96. #948	C₂²×C₃	semidirect
105. #837	C₂²×C₃	semidirect
106. #819	C₂²×C₃	semidirect
107. #815	C₂²×C₃	semidirect
167. C₃×Q₁₆	C₂×Dic₃	semidirect
168. C₃×Q₁₆	C₂×C₃×C₄	semidirect
170. C₃×SD₁₆	C₂×Dic₃	semidirect
171. C₃×SD₁₆	C₂×C₃×C₄	semidirect
173. C₃×D₈	C₂×Dic₃	semidirect
174. C₃×D₈	C₂×C₃×C₄	semidirect
220. #135	C₃×Dic₃	semidirect
222. C₂×Q₁₆	C₃×Dic₃	semidirect
223. C₂×SD₁₆	C₃×Dic₃	semidirect
224. C₂×D₈	C₃×Dic₃	semidirect
304. C₂×C₃²	#444	semidirect
316. Q₁₆	C₂×C₃×Dic₃	semidirect
317. SD₁₆	C₂×C₃×Dic₃	semidirect
318. D₈	C₂×C₃×Dic₃	semidirect
368. C₃²	C₂×#444	semidirect
403. C₂×C₃	#5197	direct (N × H)
404. C₂×C₃	C₃×#444	semidirect
420. C₃	C₂×#5197	direct (N × H)
421. C₃	C₂×C₃×#444	semidirect
425. C₂	C₃×#5197	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#135	2
C₂×C₃×#948	2
C₂×C₃×#837	2
C₃×#5197	2
C₂×C₃×#819	2
C₂×C₃×#815	2
C₂×C₃×#444	3
C₂×#5197	3

Subgroups — C2×C3×#5197 #11861042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5197 #11861042