Subgroups — C₂×C₃×#5192 #11867956

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#942	C₂	1	2	yes	maximal
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#836	C₂	1	2	yes	maximal, complemented
5	C₃×#5192	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#473	—	3	1	no	maximal
8	C₂×#5192	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
10	C₂×C₃×#235	C₂²	1	1	yes	characteristic
11	C₂×C₃²×Q₁₆	—	2	1	no	—
12	C₂×C₃²×Q₁₆	—	2	1	no	—
13	C₂×C₃²×Q₁₆	—	2	2	no	—
14	C₂×C₃²×Q₁₆	C₂²	1	4	yes	complemented
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×#216	—	2	2	no	—
17	C₃×#942	—	2	4	no	—
18	C₃×#942	C₂²	1	8	yes	—
19	C₂×C₃×#215	—	2	2	no	—
20	C₂×C₃×#208	C₂²	1	2	yes	—
21	C₂×C₃×#208	C₂²	1	1	yes	characteristic
22	C₃×#901	—	2	2	no	—
23	C₃×#901	C₂²	1	4	yes	—
24	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
25	C₂×C₃×D₃×C₈	—	2	1	no	—
26	C₃×#836	C₂²	1	8	yes	complemented
27	C₃×#819	C₂²	1	4	yes	complemented
28	C₂×C₃×#137	—	3	2	no	—
29	C₂²×C₃×Q₁₆	—	2	1	no	—
30	C₂²×C₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
31	C₂²×C₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×#131	—	3	1	no	—
33	C₂×#942	C₂×C₃	1	2	yes	—
34	C₂×#901	C₂×C₃	1	1	yes	characteristic
35	C₃×#473	—	3	8	no	—
36	C₂×C₃×#108	—	3	1	no	—
37	C₂×C₃×#101	—	3	2	no	—
38	C₂×#836	C₂×C₃	1	2	yes	complemented
39	#5192	C₂×C₃	1	8	yes	direct product factor
40	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₃²×Q₈	—	2	2	no	—
42	C₂×C₃²×Q₈	—	2	2	no	—
43	C₂×C₃²×Q₈	—	2	2	no	—
44	C₂×C₃²×Q₈	—	2	2	no	—
45	C₂×C₃²×Q₈	—	2	2	no	—
46	C₂×C₃²×Q₈	C₂³	1	4	yes	—
47	C₂²×C₃²×C₄	—	2	2	no	—
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃×#67	—	2	1	no	—
50	C₃×#235	—	2	1	no	—
51	C₃×#235	—	2	1	no	—
52	C₃×#235	D₄	1	2	yes	—
53	C₃×#235	C₂³	1	2	yes	—
54	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
55	C₂×C₃×C₄×D₃	—	2	1	no	—
56	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
57	C₃²×Q₁₆	—	2	4	no	—
58	C₃²×Q₁₆	—	2	4	no	—
59	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
60	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
61	C₂×C₃²×C₈	D₄	1	2	yes	—
62	C₂×C₃²×C₈	C₂³	1	2	yes	—
63	C₃×#216	—	2	8	no	—
64	C₃×#215	—	2	8	no	—
65	C₃×#208	—	2	1	no	—
66	C₃×#208	—	2	2	no	—
67	C₃×#208	C₂³	1	2	yes	—
68	C₃×#208	C₂³	1	4	yes	—
69	C₂×C₃×C₃⋊C₈	—	2	1	no	—
70	C₂×C₃×C₃⋊C₈	—	2	2	no	—
71	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
72	C₃×D₃×C₈	—	2	4	no	—
73	C₂×#473	—	3	1	no	Sylow
74	C₂×C₃×#41	—	3	1	no	—
75	C₂²×C₃×Q₈	—	2	2	no	—
76	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	—
77	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
78	C₂×#235	C₂²×C₃	1	1	yes	characteristic
79	C₃×#137	—	3	8	no	—
80	C₃×#137	—	6	4	no	—
81	C₂×C₃×Q₁₆	—	2	2	no	—
82	C₂×C₃×Q₁₆	—	2	2	no	—
83	C₂×C₃×Q₁₆	—	2	4	no	—
84	C₂×C₃×Q₁₆	—	2	1	no	—
85	C₂×C₃×Q₁₆	—	2	1	no	—
86	C₂×C₃×Q₁₆	—	2	2	no	—
87	C₂×C₃×Q₁₆	—	2	1	no	—
88	C₂×C₃×Q₁₆	—	2	1	no	—
89	C₂×C₃×Q₁₆	—	2	2	no	—
90	C₂×C₃×Q₁₆	—	2	4	no	—
91	C₂×C₃×Q₁₆	—	6	2	no	—
92	C₂×C₃×Q₁₆	C₂×D₃	1	4	yes	complemented
93	C₂×C₃×Q₁₆	C₂²×C₃	1	4	yes	complemented
94	C₂×C₃×SD₁₆	—	6	2	no	—
95	C₃×#131	—	3	4	no	—
96	C₃×#131	—	6	2	no	—
97	C₂×C₃×M₁₆	—	3	1	no	—
98	C₂×C₃×M₁₆	—	3	2	no	—
99	C₂×C₃×M₁₆	—	6	1	no	—
100	C₂²×C₃×C₈	—	2	1	no	—
101	C₂²×C₃×C₈	—	6	1	no	—
102	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
104	C₂×#216	—	2	2	no	—
105	#942	—	2	4	no	—
106	#942	C₂²×C₃	1	8	yes	—
107	C₂×#215	—	2	2	no	—
108	C₂×#208	C₂²×C₃	1	1	yes	characteristic
109	C₂×#208	C₂²×C₃	1	2	yes	—
110	#901	—	2	2	no	—
111	#901	C₂²×C₃	1	4	yes	—
112	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
113	C₂×D₃×C₈	—	2	1	no	—
114	C₃×#108	—	3	4	no	—
115	C₃×#101	—	3	8	no	—
116	#836	C₂²×C₃	1	8	yes	complemented
117	#819	C₂²×C₃	1	4	yes	complemented
118	C₂³×C₃²	#41	1	1	yes	characteristic
119	C₂²×C₃×D₃	—	2	1	no	—
120	C₃²×Q₈	—	2	4	no	—
121	C₃²×Q₈	—	2	4	no	—
122	C₃²×Q₈	—	4	2	no	—
123	C₃²×Q₈	—	4	2	no	—
124	C₂×C₃²×C₄	—	2	4	no	—
125	C₂×C₃²×C₄	—	4	2	no	—
126	C₂×C₃²×C₄	—	4	2	no	—
127	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	#41	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
133	C₃×#67	—	2	2	no	—
134	C₃×#67	—	2	2	no	—
135	C₂×C₃×Dic₃	—	2	1	no	—
136	C₃×D₁₂	—	2	1	no	—
137	C₃×D₁₂	C₂×D₄	1	2	yes	—
138	C₃×C₄×D₃	—	2	2	no	—
139	C₃×C₄×D₃	—	2	2	no	—
140	C₃×Dic₆	—	2	1	no	—
141	C₃×Dic₆	C₂×D₄	1	2	yes	—
142	C₃²×C₈	C₂×D₄	1	2	yes	—
143	C₃²×C₈	C₂×D₄	1	2	yes	—
144	C₃×C₃⋊C₈	—	2	2	no	—
145	C₃×C₃⋊C₈	—	2	4	no	—
146	C₂×#137	—	3	2	no	—
147	C₂²×Q₁₆	C₃×D₃	1	1	yes	characteristic, complemented
148	C₂×#131	—	3	1	no	—
149	#473	—	3	8	no	—
150	C₂×#108	—	3	1	no	—
151	C₂×#101	—	3	2	no	—
152	C₃×#41	—	3	2	no	—
153	C₃×#41	—	3	2	no	—
154	C₃×#41	—	6	1	no	—
155	C₃×#41	—	6	1	no	—
156	C₂×C₃×Q₈	—	2	2	no	—
157	C₂×C₃×Q₈	—	2	2	no	—
158	C₂×C₃×Q₈	—	2	4	no	—
159	C₂×C₃×Q₈	—	2	4	no	—
160	C₂×C₃×Q₈	—	2	2	no	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	2	no	—
163	C₂×C₃×Q₈	—	2	2	no	—
164	C₂×C₃×Q₈	—	2	2	no	—
165	C₂×C₃×Q₈	—	2	2	no	—
166	C₂×C₃×Q₈	—	2	2	no	—
167	C₂×C₃×Q₈	—	2	2	no	—
168	C₂×C₃×Q₈	—	2	4	no	—
169	C₂×C₃×Q₈	—	3	1	no	—
170	C₂×C₃×Q₈	—	4	2	no	—
171	C₂×C₃×Q₈	—	4	2	no	—
172	C₂×C₃×Q₈	—	4	2	no	—
173	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
174	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
175	C₂×C₃×D₄	—	3	1	no	—
176	C₂×C₃×D₄	—	6	1	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	4	2	no	—
181	C₂²×C₃×C₄	—	6	1	no	—
182	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
184	C₂×#67	—	2	1	no	—
185	#235	—	2	1	no	—
186	#235	—	2	1	no	—
187	#235	C₃×D₄	1	2	yes	—
188	#235	C₂³×C₃	1	2	yes	—
189	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
190	C₂×C₄×D₃	—	2	1	no	—
191	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
192	C₃×Q₁₆	—	2	8	no	—
193	C₃×Q₁₆	—	2	8	no	—
194	C₃×Q₁₆	—	2	4	no	—
195	C₃×Q₁₆	—	2	4	no	—
196	C₃×Q₁₆	—	2	4	no	—
197	C₃×Q₁₆	—	2	4	no	—
198	C₃×Q₁₆	—	6	8	no	—
199	C₃×SD₁₆	—	6	8	no	—
200	C₃×M₁₆	—	3	2	no	—
201	C₃×M₁₆	—	3	4	no	—
202	C₃×M₁₆	—	6	2	no	—
203	C₃×M₁₆	—	6	1	no	—
204	C₃×M₁₆	—	6	4	no	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	—	2	1	no	—
207	C₂×C₃×C₈	—	2	2	no	—
208	C₂×C₃×C₈	—	2	2	no	—
209	C₂×C₃×C₈	—	6	2	no	—
210	C₂×C₃×C₈	—	6	1	no	—
211	C₂×C₃×C₈	—	6	4	no	—
212	C₂×C₃×C₈	#67	1	1	yes	characteristic
213	C₂×C₃×C₈	#67	1	1	yes	characteristic
214	C₂×C₃×C₈	#67	1	2	yes	—
215	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
216	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
217	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
218	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
219	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
220	#216	—	2	8	no	—
221	#215	—	2	8	no	—
222	#208	—	2	1	no	—
223	#208	—	2	2	no	—
224	#208	C₂³×C₃	1	4	yes	—
225	#208	C₂³×C₃	1	2	yes	—
226	C₂×C₃⋊C₈	—	2	1	no	—
227	C₂×C₃⋊C₈	—	2	2	no	—
228	ΓL(1,𝔽₂₅)	—	2	4	no	—
229	D₃×C₈	—	2	4	no	—
230	C₂²×C₃²	—	2	2	no	—
231	C₂²×C₃²	#121	1	1	yes	characteristic
232	C₂²×C₃²	#121	1	1	yes	characteristic
233	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
234	C₂×C₃×D₃	—	2	2	no	—
235	C₂×C₃×D₃	—	4	2	no	—
236	C₃²×C₄	—	4	4	no	—
237	C₃²×C₄	#121	1	1	yes	characteristic
238	C₃²×C₄	#121	1	1	yes	characteristic
239	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
241	C₃×Dic₃	—	2	2	no	—
242	C₂×#41	—	3	1	no	—
243	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	—
244	#137	—	3	8	no	—
245	#137	—	6	4	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	6	2	no	—
250	C₂×Q₁₆	C₂×C₃×D₃	1	4	yes	complemented
251	C₂×SD₁₆	—	6	2	no	—
252	#131	—	3	4	no	—
253	#131	—	6	2	no	—
254	C₂×M₁₆	—	3	1	no	—
255	C₂×M₁₆	—	3	2	no	—
256	C₂×M₁₆	—	6	1	no	—
257	C₂²×C₈	—	6	1	no	—
258	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
259	#108	—	3	4	no	—
260	#101	—	3	8	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	6	1	no	—
263	C₂³×C₃	#237	1	1	yes	characteristic
264	C₂³×C₃	C₃×#41	1	1	yes	characteristic
265	C₂²×D₃	—	2	1	no	—
266	C₃×Q₈	—	2	8	no	—
267	C₃×Q₈	—	2	4	no	—
268	C₃×Q₈	—	2	4	no	—
269	C₃×Q₈	—	2	4	no	—
270	C₃×Q₈	—	2	4	no	—
271	C₃×Q₈	—	3	2	no	—
272	C₃×Q₈	—	4	4	no	—
273	C₃×Q₈	—	4	4	no	—
274	C₃×Q₈	—	4	4	no	—
275	C₃×Q₈	—	4	2	no	—
276	C₃×Q₈	—	4	2	no	—
277	C₃×Q₈	—	4	2	no	—
278	C₃×Q₈	—	4	2	no	—
279	C₃×Q₈	—	6	1	no	—
280	C₃×D₄	—	3	2	no	—
281	C₃×D₄	—	6	2	no	—
282	C₃×D₄	—	6	2	no	—
283	C₃×D₄	—	6	1	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	4	4	no	—
293	C₂×C₃×C₄	—	4	4	no	—
294	C₂×C₃×C₄	—	4	4	no	—
295	C₂×C₃×C₄	—	4	2	no	—
296	C₂×C₃×C₄	—	4	2	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	—	4	2	no	—
299	C₂×C₃×C₄	—	6	1	no	—
300	C₂×C₃×C₄	—	6	2	no	—
301	C₂×C₃×C₄	—	6	2	no	—
302	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	#237	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
314	#67	—	2	2	no	—
315	#67	—	2	2	no	—
316	C₂×Dic₃	—	2	1	no	—
317	D₁₂	—	2	1	no	—
318	D₁₂	C₂×C₃×D₄	1	2	yes	—
319	C₄×D₃	—	2	2	no	—
320	C₄×D₃	—	2	2	no	—
321	Dic₆	—	2	1	no	—
322	Dic₆	C₂×C₃×D₄	1	2	yes	—
323	C₃×C₈	—	2	2	no	—
324	C₃×C₈	—	2	2	no	—
325	C₃×C₈	—	6	4	no	—
326	C₃×C₈	—	6	2	no	—
327	C₃×C₈	C₂×#67	1	2	yes	—
328	C₃×C₈	C₂×#67	1	2	yes	—
329	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
330	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
331	C₃⋊C₈	—	2	2	no	—
332	C₃⋊C₈	—	2	4	no	—
333	C₂×C₃²	—	2	1	no	—
334	C₂×C₃²	—	2	1	no	—
335	C₂×C₃²	#473	1	2	yes	complemented
336	C₂×C₃²	C₂×#121	1	1	yes	characteristic
337	C₃×D₃	—	4	2	no	—
338	#41	—	3	2	no	—
339	#41	—	3	2	no	—
340	#41	—	6	1	no	—
341	#41	—	6	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	3	1	no	—
348	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
349	C₂×D₄	—	3	1	no	—
350	C₂×D₄	—	6	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	6	1	no	—
353	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
354	Q₁₆	—	2	4	no	—
355	Q₁₆	—	2	4	no	—
356	Q₁₆	—	6	8	no	—
357	SD₁₆	—	6	8	no	—
358	M₁₆	—	3	2	no	—
359	M₁₆	—	3	4	no	—
360	M₁₆	—	6	2	no	—
361	M₁₆	—	6	1	no	—
362	M₁₆	—	6	4	no	—
363	C₂×C₈	—	6	2	no	—
364	C₂×C₈	—	6	1	no	—
365	C₂×C₈	—	6	4	no	—
366	C₂×C₈	C₃×#67	1	1	yes	characteristic
367	C₂×C₈	C₃×#67	1	1	yes	characteristic
368	C₂×C₈	C₃×#67	1	2	yes	—
369	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
370	C₂²×C₃	—	2	4	no	—
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	6	2	no	—
377	C₂²×C₃	—	12	2	no	—
378	C₂²×C₃	#938	1	1	yes	characteristic
379	C₂²×C₃	#938	1	1	yes	characteristic
380	C₂²×C₃	C₃×#121	1	1	yes	characteristic
381	C₂²×C₃	C₃×#121	1	1	yes	characteristic
382	C₂²×C₃	C₂×#237	1	1	yes	characteristic
383	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
384	C₂×D₃	—	2	2	no	—
385	C₂×D₃	—	4	2	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	4	8	no	—
391	C₃×C₄	—	4	4	no	—
392	C₃×C₄	—	4	4	no	—
393	C₃×C₄	—	6	2	no	—
394	C₃×C₄	#938	1	1	yes	characteristic
395	C₃×C₄	#938	1	1	yes	characteristic
396	C₃×C₄	C₃×#121	1	1	yes	characteristic
397	C₃×C₄	C₃×#121	1	1	yes	characteristic
398	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
399	C₃×C₄	C₂²×#67	1	1	yes	characteristic
400	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
401	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
402	Dic₃	—	2	2	no	—
403	C₃²	C₂×#473	1	1	yes	characteristic, complemented, Sylow
404	C₂³	—	6	1	no	—
405	C₂³	C₃×#237	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	3	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	6	1	no	—
412	D₄	—	3	2	no	—
413	D₄	—	6	2	no	—
414	D₄	—	6	2	no	—
415	D₄	—	6	1	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	6	1	no	—
420	C₂×C₄	—	6	2	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
423	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
424	C₂×C₄	C₃×#237	1	1	yes	characteristic
425	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
426	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
427	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
428	C₈	—	6	4	no	—
429	C₈	—	6	2	no	—
430	C₈	C₂×C₃×#67	1	2	yes	—
431	C₈	C₂×C₃×#67	1	2	yes	—
432	C₂×C₃	—	2	2	no	—
433	C₂×C₃	—	2	2	no	—
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	2	2	no	—
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	12	2	no	—
441	C₂×C₃	#5192	1	2	yes	direct product factor
442	C₂×C₃	C₃×#473	1	2	yes	complemented
443	C₂×C₃	C₂×#938	1	1	yes	characteristic
444	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
445	D₃	—	4	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	6	2	no	—
448	C₂²	—	12	2	no	—
449	C₂²	C₃×#938	1	1	yes	characteristic
450	C₂²	C₃×#938	1	1	yes	characteristic
451	C₂²	C₂×C₃×#237	1	1	yes	characteristic
452	C₄	—	4	4	no	—
453	C₄	—	6	2	no	—
454	C₄	C₃×#938	1	1	yes	characteristic
455	C₄	C₃×#938	1	1	yes	characteristic
456	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
457	C₄	C₂²×C₃×#67	1	1	yes	characteristic
458	C₃	—	2	1	no	—
459	C₃	C₂×#5192	1	1	yes	characteristic, direct product factor
460	C₃	C₂×C₃×#473	1	1	yes	characteristic, complemented
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	12	2	no	—
464	C₂	C₃×#5192	1	2	yes	direct product factor
465	C₂	C₂×C₃×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#938
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×Q₁₆	C₂
socle	C₂²×C₃²	#121
prime radical	C₂×C₃×#235	C₂²
hypercenter	C₂²×C₃×Q₁₆	D₃
hypocenter	C₃	C₂×C₃×#473
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×Q₁₆	C₂	semidirect
4. C₂×C₃×#836	C₂	semidirect
5. C₃×#5192	C₂	direct (N × H)
6. C₂×C₃×#819	C₂	semidirect
8. C₂×#5192	C₃	direct (N × H)
14. C₂×C₃²×Q₁₆	C₂²	semidirect
26. C₃×#836	C₂²	semidirect
27. C₃×#819	C₂²	semidirect
30. C₂²×C₃×Q₁₆	D₃	semidirect
31. C₂²×C₃×Q₁₆	C₂×C₃	semidirect
38. C₂×#836	C₂×C₃	semidirect
39. #5192	C₂×C₃	direct (N × H)
40. C₂×#819	C₂×C₃	semidirect
92. C₂×C₃×Q₁₆	C₂×D₃	semidirect
93. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
116. #836	C₂²×C₃	semidirect
117. #819	C₂²×C₃	semidirect
147. C₂²×Q₁₆	C₃×D₃	semidirect
250. C₂×Q₁₆	C₂×C₃×D₃	semidirect
335. C₂×C₃²	#473	semidirect
403. C₃²	C₂×#473	semidirect
441. C₂×C₃	#5192	direct (N × H)
442. C₂×C₃	C₃×#473	semidirect
459. C₃	C₂×#5192	direct (N × H)
460. C₃	C₂×C₃×#473	semidirect
464. C₂	C₃×#5192	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×Q₁₆	2
C₂×C₃×#942	2
C₂×C₃×#901	2
C₂×C₃×#836	2
C₃×#5192	2
C₂×C₃×#819	2
C₂×C₃×#473	3
C₂×#5192	3

Subgroups — C2×C3×#5192 #11867956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5192 #11867956