Subgroups — C₂×C₃×#4717 #11861045

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#901	C₂	1	2	yes	maximal, complemented
3	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#805	C₂	1	2	yes	maximal, complemented
6	C₃×#4717	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#444	—	3	1	no	maximal
8	C₂×#4717	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×#235	C₂²	1	2	yes	—
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
13	C₂×C₃×#208	C₂²	1	2	yes	—
14	C₂×C₃×Dic₁₂	C₄	1	1	yes	characteristic, complemented
15	C₃×#904	C₄	1	4	yes	complemented
16	C₃×#904	C₂²	1	4	yes	—
17	C₂×C₃×D₂₄	C₄	1	1	yes	characteristic, complemented
18	C₂×C₃×#204	C₄	1	2	yes	complemented
19	C₃×#901	—	2	4	no	—
20	C₃×#901	C₂²	1	8	yes	complemented
21	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
22	C₂×C₃×D₃×C₈	—	2	2	no	—
23	C₃²×#97	C₂²	1	4	yes	complemented
24	C₃×#819	C₂²	1	4	yes	complemented
25	C₃×#805	C₂²	1	8	yes	complemented
26	C₂×C₃×#135	—	3	1	no	—
27	C₂×C₃×#131	—	3	2	no	—
28	C₂×#904	C₂×C₃	1	1	yes	characteristic
29	C₂×#901	C₂×C₃	1	2	yes	complemented
30	C₃×#444	—	3	8	no	—
31	C₂×C₃×#108	—	3	1	no	—
32	C₂×C₃×#104	—	3	2	no	—
33	C₂×C₃×#97	—	2	1	no	—
34	C₂×C₃×#97	D₃	1	1	yes	characteristic, complemented
35	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#805	C₂×C₃	1	2	yes	complemented
38	#4717	C₂×C₃	1	8	yes	direct product factor
39	C₂²×C₃²×C₄	—	2	1	no	—
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃×#67	—	2	2	no	—
42	C₃×#235	—	2	2	no	—
43	C₃×#235	—	2	2	no	—
44	C₃×#235	C₂×C₄	1	4	yes	—
45	C₃×#235	C₂³	1	4	yes	—
46	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₃	—	2	2	no	—
48	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
49	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
52	C₂×C₃²×C₈	D₄	1	2	yes	—
53	C₂×C₃²×C₈	D₄	1	2	yes	—
54	C₂×C₃²×C₈	C₂³	1	2	yes	—
55	C₂×C₃²×C₈	C₂³	1	2	yes	—
56	C₃²×C₄²	—	2	1	no	—
57	C₃²×C₄²	C₂³	1	2	yes	—
58	C₃×#208	—	2	2	no	—
59	C₃×#208	C₂³	1	4	yes	—
60	C₂×C₃×C₃⋊C₈	—	2	2	no	—
61	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
62	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
63	C₃×#204	C₂×C₄	1	8	yes	complemented
64	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
65	C₃×D₃×C₈	—	2	8	no	—
66	C₂×#444	—	3	1	no	Sylow
67	C₂×C₃×#41	—	3	2	no	—
68	C₂×#235	C₂²×C₃	1	2	yes	—
69	C₃×#135	—	3	4	no	—
70	C₃×#135	—	3	4	no	—
71	C₂×C₃×Q₁₆	—	3	1	no	—
72	C₂×C₃×SD₁₆	—	3	2	no	—
73	C₂×C₃×D₈	—	3	1	no	—
74	C₃×#131	—	3	8	no	—
75	C₃×#131	—	6	4	no	—
76	C₂×C₃×M₁₆	—	3	2	no	—
77	C₂×C₃×M₁₆	—	6	2	no	—
78	C₂²×C₃×C₈	—	2	1	no	—
79	C₂²×C₃×C₈	—	2	1	no	—
80	C₂²×C₃×C₈	—	6	2	no	—
81	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄²	—	2	1	no	—
86	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
87	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
88	C₂×#208	C₂²×C₃	1	2	yes	—
89	C₂×Dic₁₂	C₃×C₄	1	1	yes	characteristic, complemented
90	#904	C₃×C₄	1	4	yes	complemented
91	#904	C₂²×C₃	1	4	yes	—
92	C₂×D₂₄	C₃×C₄	1	1	yes	characteristic, complemented
93	C₂×#204	C₃×C₄	1	2	yes	complemented
94	#901	—	2	4	no	—
95	#901	C₂²×C₃	1	8	yes	complemented
96	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
97	C₂×D₃×C₈	—	2	2	no	—
98	C₃×#108	—	3	4	no	—
99	C₃×#104	—	3	8	no	—
100	C₃×#97	—	2	4	no	—
101	C₃×#97	C₂×D₃	1	4	yes	complemented
102	C₃×#97	C₂²×C₃	1	4	yes	complemented
103	#819	C₂²×C₃	1	4	yes	complemented
104	#805	C₂²×C₃	1	8	yes	complemented
105	C₂³×C₃²	#41	1	1	yes	characteristic
106	C₂²×C₃×D₃	—	2	2	no	—
107	C₂×C₃²×C₄	—	2	2	no	—
108	C₂×C₃²×C₄	—	4	2	no	—
109	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	#41	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
115	C₃×#67	—	2	4	no	—
116	C₃×#67	—	2	4	no	—
117	C₂×C₃×Dic₃	—	2	2	no	—
118	C₃×D₁₂	—	2	2	no	—
119	C₃×D₁₂	C₂²×C₄	1	4	yes	—
120	C₃×C₄×D₃	—	2	4	no	—
121	C₃×C₄×D₃	—	2	4	no	—
122	C₃×Dic₆	—	2	2	no	—
123	C₃×Dic₆	C₂²×C₄	1	4	yes	—
124	C₃²×C₈	C₂²×C₄	1	2	yes	—
125	C₃²×C₈	C₂²×C₄	1	2	yes	—
126	C₃²×C₈	C₂×D₄	1	4	yes	—
127	C₃×C₃⋊C₈	—	2	4	no	—
128	C₂×#135	—	3	1	no	—
129	C₂×#131	—	3	2	no	—
130	#444	—	3	8	no	—
131	C₂×#108	—	3	1	no	—
132	C₂×#104	—	3	2	no	—
133	C₂×#97	C₃×D₃	1	1	yes	characteristic, complemented
134	C₃×#41	—	3	4	no	—
135	C₃×#41	—	3	4	no	—
136	C₃×#41	—	6	2	no	—
137	C₃×#41	—	6	2	no	—
138	C₂×C₃×Q₈	—	3	2	no	—
139	C₂×C₃×D₄	—	3	2	no	—
140	C₂×C₃×D₄	—	6	2	no	—
141	C₂²×C₃×C₄	—	2	2	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	2	1	no	—
145	C₂²×C₃×C₄	—	6	2	no	—
146	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂×#67	—	2	2	no	—
149	#235	—	2	2	no	—
150	#235	—	2	2	no	—
151	#235	C₂×C₃×C₄	1	4	yes	—
152	#235	C₂³×C₃	1	4	yes	—
153	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
154	C₂×C₄×D₃	—	2	2	no	—
155	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
156	C₃×Q₁₆	—	3	4	no	—
157	C₃×SD₁₆	—	3	8	no	—
158	C₃×D₈	—	3	4	no	—
159	C₃×M₁₆	—	3	4	no	—
160	C₃×M₁₆	—	6	2	no	—
161	C₃×M₁₆	—	6	8	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	1	no	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	2	2	no	—
167	C₂×C₃×C₈	—	2	2	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	6	2	no	—
170	C₂×C₃×C₈	—	6	8	no	—
171	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
172	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
173	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
174	C₂×C₃×C₈	D₁₂	1	2	yes	—
175	C₂×C₃×C₈	D₁₂	1	2	yes	—
176	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
179	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
180	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
181	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
182	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
183	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
184	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	—	2	1	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	C₂²×D₃	1	2	yes	—
190	C₃×C₄²	C₂³×C₃	1	2	yes	—
191	#208	—	2	2	no	—
192	#208	C₂³×C₃	1	4	yes	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
195	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
196	#204	C₂×C₃×C₄	1	8	yes	complemented
197	ΓL(1,𝔽₂₅)	—	2	8	no	—
198	D₃×C₈	—	2	8	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
201	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
202	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
203	C₂×C₃×D₃	—	2	4	no	—
204	C₂×C₃×D₃	—	4	4	no	—
205	C₃²×C₄	—	4	2	no	—
206	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
207	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
208	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
209	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
210	C₃×Dic₃	—	2	4	no	—
211	C₂×#41	—	3	2	no	—
212	#135	—	3	4	no	—
213	#135	—	3	4	no	—
214	C₂×Q₁₆	—	3	1	no	—
215	C₂×SD₁₆	—	3	2	no	—
216	C₂×D₈	—	3	1	no	—
217	#131	—	3	8	no	—
218	#131	—	6	4	no	—
219	C₂×M₁₆	—	3	2	no	—
220	C₂×M₁₆	—	6	2	no	—
221	C₂²×C₈	—	6	2	no	—
222	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
223	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
225	#108	—	3	4	no	—
226	#104	—	3	8	no	—
227	#97	C₂×C₃×D₃	1	4	yes	complemented
228	C₂³×C₃	—	2	1	no	—
229	C₂³×C₃	—	6	2	no	—
230	C₂³×C₃	#235	1	1	yes	characteristic
231	C₂³×C₃	C₃×#41	1	1	yes	characteristic
232	C₂²×D₃	—	2	2	no	—
233	C₃×Q₈	—	3	4	no	—
234	C₃×Q₈	—	6	2	no	—
235	C₃×D₄	—	3	4	no	—
236	C₃×D₄	—	6	4	no	—
237	C₃×D₄	—	6	4	no	—
238	C₃×D₄	—	6	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	4	4	no	—
249	C₂×C₃×C₄	—	4	2	no	—
250	C₂×C₃×C₄	—	4	2	no	—
251	C₂×C₃×C₄	—	6	2	no	—
252	C₂×C₃×C₄	—	6	4	no	—
253	C₂×C₃×C₄	—	6	4	no	—
254	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
258	C₂×C₃×C₄	#235	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
266	#67	—	2	4	no	—
267	#67	—	2	4	no	—
268	C₂×Dic₃	—	2	2	no	—
269	D₁₂	—	2	2	no	—
270	D₁₂	C₂²×C₃×C₄	1	4	yes	—
271	C₄×D₃	—	2	4	no	—
272	C₄×D₃	—	2	4	no	—
273	Dic₆	—	2	2	no	—
274	Dic₆	C₂²×C₃×C₄	1	4	yes	—
275	C₃×C₈	—	2	2	no	—
276	C₃×C₈	—	2	2	no	—
277	C₃×C₈	—	2	4	no	—
278	C₃×C₈	—	6	4	no	—
279	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
280	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
281	C₃×C₈	C₂×D₁₂	1	4	yes	—
282	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
283	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
284	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
285	C₃⋊C₈	—	2	4	no	—
286	C₂×C₃²	—	2	1	no	—
287	C₂×C₃²	—	2	1	no	—
288	C₂×C₃²	#444	1	2	yes	complemented
289	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
290	C₃×D₃	—	4	4	no	—
291	#41	—	3	4	no	—
292	#41	—	3	4	no	—
293	#41	—	6	2	no	—
294	#41	—	6	2	no	—
295	C₂×Q₈	—	3	2	no	—
296	C₂×D₄	—	3	2	no	—
297	C₂×D₄	—	6	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	6	2	no	—
300	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
301	Q₁₆	—	3	4	no	—
302	SD₁₆	—	3	8	no	—
303	D₈	—	3	4	no	—
304	M₁₆	—	3	4	no	—
305	M₁₆	—	6	2	no	—
306	M₁₆	—	6	8	no	—
307	C₂×C₈	—	6	2	no	—
308	C₂×C₈	—	6	8	no	—
309	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
310	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
311	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
312	C₂×C₈	C₃×D₁₂	1	2	yes	—
313	C₂×C₈	C₃×D₁₂	1	2	yes	—
314	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
315	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
316	C₄²	—	2	1	no	—
317	C₄²	C₂²×C₃×D₃	1	2	yes	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	6	4	no	—
325	C₂²×C₃	—	12	4	no	—
326	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
327	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
328	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
329	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
330	C₂²×C₃	C₂×#235	1	1	yes	characteristic
331	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
332	C₂×D₃	—	2	4	no	—
333	C₂×D₃	—	4	4	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	4	4	no	—
339	C₃×C₄	—	4	2	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	6	4	no	—
342	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
343	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
344	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
345	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
346	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
347	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
348	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
349	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
350	Dic₃	—	2	4	no	—
351	C₃²	C₂×#444	1	1	yes	characteristic, complemented, Sylow
352	C₂³	—	6	2	no	—
353	C₂³	C₃×#235	1	1	yes	characteristic
354	Q₈	—	3	4	no	—
355	Q₈	—	6	2	no	—
356	D₄	—	3	4	no	—
357	D₄	—	6	4	no	—
358	D₄	—	6	4	no	—
359	D₄	—	6	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	6	2	no	—
363	C₂×C₄	—	6	4	no	—
364	C₂×C₄	—	6	4	no	—
365	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
366	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
368	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
369	C₂×C₄	C₃×#235	1	1	yes	characteristic
370	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
371	C₈	—	6	4	no	—
372	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
373	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
374	C₈	C₂×C₃×D₁₂	1	4	yes	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	2	1	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	2	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	12	4	no	—
384	C₂×C₃	#4717	1	2	yes	direct product factor
385	C₂×C₃	C₃×#444	1	2	yes	complemented
386	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
387	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
388	D₃	—	4	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	6	4	no	—
391	C₂²	—	12	4	no	—
392	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
393	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
394	C₂²	C₂×C₃×#235	1	1	yes	characteristic
395	C₄	—	4	2	no	—
396	C₄	—	6	4	no	—
397	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
398	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
399	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
400	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
401	C₃	—	2	1	no	—
402	C₃	C₂×#4717	1	1	yes	characteristic, direct product factor
403	C₃	C₂×C₃×#444	1	1	yes	characteristic, complemented
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	12	4	no	—
407	C₂	C₃×#4717	1	2	yes	direct product factor
408	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₂×C₃×#444
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#901	C₂	semidirect
3. C₂×C₃²×#97	C₂	semidirect
4. C₂×C₃×#819	C₂	semidirect
5. C₂×C₃×#805	C₂	semidirect
6. C₃×#4717	C₂	direct (N × H)
8. C₂×#4717	C₃	direct (N × H)
14. C₂×C₃×Dic₁₂	C₄	semidirect
15. C₃×#904	C₄	semidirect
17. C₂×C₃×D₂₄	C₄	semidirect
18. C₂×C₃×#204	C₄	semidirect
20. C₃×#901	C₂²	semidirect
23. C₃²×#97	C₂²	semidirect
24. C₃×#819	C₂²	semidirect
25. C₃×#805	C₂²	semidirect
29. C₂×#901	C₂×C₃	semidirect
34. C₂×C₃×#97	D₃	semidirect
35. C₂×C₃×#97	C₂×C₃	semidirect
36. C₂×#819	C₂×C₃	semidirect
37. C₂×#805	C₂×C₃	semidirect
38. #4717	C₂×C₃	direct (N × H)
61. C₃×Dic₁₂	C₂×C₄	semidirect
62. C₃×D₂₄	C₂×C₄	semidirect
63. C₃×#204	C₂×C₄	semidirect
89. C₂×Dic₁₂	C₃×C₄	semidirect
90. #904	C₃×C₄	semidirect
92. C₂×D₂₄	C₃×C₄	semidirect
93. C₂×#204	C₃×C₄	semidirect
95. #901	C₂²×C₃	semidirect
101. C₃×#97	C₂×D₃	semidirect
102. C₃×#97	C₂²×C₃	semidirect
103. #819	C₂²×C₃	semidirect
104. #805	C₂²×C₃	semidirect
133. C₂×#97	C₃×D₃	semidirect
194. Dic₁₂	C₂×C₃×C₄	semidirect
195. D₂₄	C₂×C₃×C₄	semidirect
196. #204	C₂×C₃×C₄	semidirect
227. #97	C₂×C₃×D₃	semidirect
288. C₂×C₃²	#444	semidirect
351. C₃²	C₂×#444	semidirect
384. C₂×C₃	#4717	direct (N × H)
385. C₂×C₃	C₃×#444	semidirect
402. C₃	C₂×#4717	direct (N × H)
403. C₃	C₂×C₃×#444	semidirect
407. C₂	C₃×#4717	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×C₃×#904	2
C₂×C₃×#901	2
C₂×C₃²×#97	2
C₂×C₃×#819	2
C₂×C₃×#805	2
C₃×#4717	2
C₂×C₃×#444	3
C₂×#4717	3

Subgroups — C2×C3×#4717 #11861045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4717 #11861045