Subgroups — C₃×D₃×D₄×Q₈ #11902640

Order 1152.

3276 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₃×Q₈	C₂	1	2	yes	maximal, complemented
2	C₃²×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₈×#67	C₂	1	2	yes	maximal, complemented
4	C₃×#5727	C₂	1	3	yes	maximal, complemented
5	C₃×D₃×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
6	C₃×#5632	C₂	1	6	yes	maximal, complemented
7	C₃×D₃×C₂²⋊Q₈	C₂	1	6	yes	maximal, complemented
8	C₃×Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×D₃×D₄	C₂	1	3	yes	maximal
11	C₃×D₄×Dic₆	C₂	1	3	yes	maximal, complemented
12	C₂×C₃×D₄×Q₈	—	3	1	no	maximal
13	D₃×D₄×Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃²×Q₈	C₂²	1	2	yes	complemented
15	C₂×C₃×D₃×Q₈	—	2	16	no	—
16	C₂×C₃×D₃×Q₈	C₂²	1	6	yes	—
17	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
19	C₂×C₃×D₃×Q₈	C₂²	1	6	yes	complemented
20	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×D₃	C₂²	1	6	yes	—
22	C₂²×C₃×Dic₆	C₂²	1	6	yes	complemented
23	C₃²×C₄⋊Q₈	C₂²	1	3	yes	complemented
24	C₃²×C₂²⋊Q₈	C₂²	1	6	yes	complemented
25	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×C₄×D₄	C₂²	1	3	yes	—
27	C₃×#946	C₂²	1	6	yes	complemented
28	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
29	C₃×#944	C₂²	1	6	yes	complemented
30	C₃×D₄×Dic₃	C₂²	1	3	yes	—
31	C₃×C₄×#67	C₂²	1	6	yes	—
32	C₃×#924	C₂²	1	6	yes	complemented
33	C₃×#897	C₂²	1	6	yes	complemented
34	C₃×#896	C₂²	1	12	yes	complemented
35	C₃×#893	C₂²	1	3	yes	—
36	C₃×D₃×C₄⋊C₄	C₂²	1	3	yes	—
37	C₃×D₃×C₄⋊C₄	C₂²	1	3	yes	—
38	C₃×D₃×C₄⋊C₄	C₂²	1	6	yes	—
39	C₃×#888	C₂²	1	6	yes	complemented
40	C₃×#888	C₂²	1	6	yes	complemented
41	C₃×#887	C₂²	1	3	yes	complemented
42	C₃×#67⋊C₄	C₂²	1	6	yes	—
43	C₃×D₃×C₂²⋊C₄	C₂²	1	6	yes	—
44	C₃×#878	C₂²	1	12	yes	complemented
45	C₃×C₄×D₁₂	C₂²	1	3	yes	—
46	C₃×C₄²×D₃	C₂²	1	3	yes	—
47	C₃×#869	C₂²	1	3	yes	complemented
48	C₃×C₄×Dic₆	C₂²	1	3	yes	complemented
49	C₂³×C₃×Q₈	—	3	2	no	—
50	C₂²×D₃×Q₈	C₂×C₃	1	2	yes	complemented
51	C₃×D₄×Q₈	—	2	1	no	—
52	C₃×D₄×Q₈	—	3	2	no	—
53	C₃×D₄×Q₈	—	3	3	no	—
54	C₃×D₄×Q₈	—	3	6	no	—
55	C₃×D₄×Q₈	—	3	1	no	—
56	C₃×D₄×Q₈	—	3	3	no	—
57	C₃×D₄×Q₈	D₃	1	1	yes	characteristic, direct product factor
58	C₃×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×C₄⋊Q₈	—	3	3	no	—
60	C₂×C₃×C₂²⋊Q₈	—	3	6	no	—
61	C₂×C₃×C₄×Q₈	—	3	1	no	—
62	C₂×C₃×C₄×D₄	—	3	3	no	—
63	Q₈×#67	C₂×C₃	1	2	yes	complemented
64	#5727	C₂×C₃	1	3	yes	complemented
65	D₃×C₄⋊Q₈	C₂×C₃	1	3	yes	complemented
66	#5632	C₂×C₃	1	6	yes	complemented
67	D₃×C₂²⋊Q₈	C₂×C₃	1	6	yes	complemented
68	Q₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
69	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
70	C₄×D₃×D₄	C₂×C₃	1	3	yes	—
71	D₄×Dic₆	C₂×C₃	1	3	yes	complemented
72	C₂³×C₃×D₃	C₂³	1	2	yes	—
73	C₂×C₃²×Q₈	—	2	8	no	—
74	C₂×C₃²×Q₈	C₂³	1	6	yes	—
75	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
76	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂³	1	6	yes	—
78	C₂×C₃×#67	C₂³	1	2	yes	—
79	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
80	C₃×D₃×Q₈	—	2	8	no	—
81	C₃×D₃×Q₈	—	2	24	no	—
82	C₃×D₃×Q₈	—	2	24	no	—
83	C₃×D₃×Q₈	D₄	1	8	yes	direct product factor
84	C₃×D₃×D₄	Q₈	1	8	yes	direct product factor
85	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×D₃	—	2	24	no	—
87	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
88	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
89	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
90	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
91	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
92	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₆	—	2	24	no	—
94	C₂×C₃×Dic₆	C₂³	1	12	yes	—
95	C₂×C₃×Dic₆	C₂³	1	6	yes	—
96	C₂×C₃×Dic₆	C₂³	1	3	yes	—
97	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
98	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
99	C₃²×C₄⋊C₄	C₂³	1	6	yes	—
100	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
101	C₃²×C₄²	C₂³	1	3	yes	—
102	C₃×#217	C₂³	1	6	yes	—
103	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
104	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
105	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
106	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
107	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
108	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
109	C₃×Dic₃⋊C₄	C₂³	1	12	yes	—
110	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
111	C₃×C₄×Dic₃	C₂³	1	3	yes	—
112	C₃×C₄×Dic₃	C₂³	1	3	yes	—
113	C₃×C₄×Dic₃	C₂³	1	3	yes	—
114	C₂×D₄×Q₈	—	3	1	no	Sylow
115	C₂²×C₃×Q₈	—	2	2	no	—
116	C₂²×C₃×Q₈	—	3	1	no	—
117	C₂²×C₃×Q₈	—	3	6	no	—
118	C₂²×C₃×Q₈	—	3	6	no	—
119	C₂²×C₃×Q₈	—	3	2	no	—
120	C₂²×C₃×Q₈	—	3	6	no	—
121	C₂²×C₃×Q₈	—	6	16	no	—
122	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	complemented
123	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	complemented
124	C₂²×C₃×D₄	—	3	1	no	—
125	C₂³×C₃×C₄	—	3	6	no	—
126	C₂×D₃×Q₈	—	2	16	no	—
127	C₂×D₃×Q₈	C₂²×C₃	1	6	yes	—
128	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
129	C₂×D₃×Q₈	C₂²×C₃	1	6	yes	complemented
130	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
131	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₄×D₃	C₂²×C₃	1	6	yes	—
133	C₂²×Dic₆	C₂²×C₃	1	6	yes	complemented
134	C₃×C₄⋊Q₈	—	2	3	no	—
135	C₃×C₄⋊Q₈	—	3	6	no	—
136	C₃×C₄⋊Q₈	—	3	6	no	—
137	C₃×C₄⋊Q₈	—	3	6	no	—
138	C₃×C₄⋊Q₈	—	3	3	no	—
139	C₃×C₄⋊Q₈	C₂×D₃	1	3	yes	complemented
140	C₃×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
141	C₃×C₂²⋊Q₈	—	2	6	no	—
142	C₃×C₂²⋊Q₈	—	3	6	no	—
143	C₃×C₂²⋊Q₈	—	3	6	no	—
144	C₃×C₂²⋊Q₈	—	3	12	no	—
145	C₃×C₂²⋊Q₈	—	3	6	no	—
146	C₃×C₂²⋊Q₈	—	3	12	no	—
147	C₃×C₂²⋊Q₈	C₂×D₃	1	6	yes	complemented
148	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
149	C₃×C₄×Q₈	—	2	1	no	—
150	C₃×C₄×Q₈	—	3	1	no	—
151	C₃×C₄×Q₈	—	3	3	no	—
152	C₃×C₄×Q₈	—	3	3	no	—
153	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
154	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₃×C₄×D₄	—	2	3	no	—
156	C₃×C₄×D₄	—	3	3	no	—
157	C₃×C₄×D₄	—	3	6	no	—
158	C₃×C₄×D₄	—	3	3	no	—
159	C₃×C₄×D₄	—	3	6	no	—
160	C₃×C₄×D₄	—	3	3	no	—
161	C₃×C₄×D₄	C₂×D₃	1	3	yes	—
162	C₃×C₄×D₄	C₂²×C₃	1	3	yes	—
163	C₂×C₃×C₄⋊C₄	—	3	3	no	—
164	C₂×C₃×C₄⋊C₄	—	3	3	no	—
165	C₂×C₃×C₄⋊C₄	—	3	6	no	—
166	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
167	C₂×C₃×C₄²	—	3	3	no	—
168	#946	C₂²×C₃	1	6	yes	complemented
169	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
170	#944	C₂²×C₃	1	6	yes	complemented
171	D₄×Dic₃	C₂²×C₃	1	3	yes	—
172	C₄×#67	C₂²×C₃	1	6	yes	—
173	#924	C₂²×C₃	1	6	yes	complemented
174	#897	C₂²×C₃	1	6	yes	complemented
175	#896	C₂²×C₃	1	12	yes	complemented
176	#893	C₂²×C₃	1	3	yes	—
177	D₃×C₄⋊C₄	C₂²×C₃	1	3	yes	—
178	D₃×C₄⋊C₄	C₂²×C₃	1	6	yes	—
179	D₃×C₄⋊C₄	C₂²×C₃	1	3	yes	—
180	#888	C₂²×C₃	1	6	yes	complemented
181	#888	C₂²×C₃	1	6	yes	complemented
182	#887	C₂²×C₃	1	3	yes	complemented
183	#67⋊C₄	C₂²×C₃	1	6	yes	—
184	D₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
185	#878	C₂²×C₃	1	12	yes	complemented
186	C₄×D₁₂	C₂²×C₃	1	3	yes	—
187	C₄²×D₃	C₂²×C₃	1	3	yes	—
188	#869	C₂²×C₃	1	3	yes	complemented
189	C₄×Dic₆	C₂²×C₃	1	3	yes	complemented
190	C₂³×C₃²	C₂⁴	1	2	yes	—
191	C₂²×C₃×D₃	—	2	4	no	—
192	C₂²×C₃×D₃	—	2	4	no	—
193	C₂²×C₃×D₃	C₂×Q₈	1	8	yes	complemented
194	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
195	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
196	C₃²×Q₈	—	2	12	no	—
197	C₃²×Q₈	C₂×D₄	1	4	yes	complemented
198	C₃²×D₄	C₂×Q₈	1	4	yes	complemented
199	C₂×C₃²×C₄	—	2	12	no	—
200	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
201	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
202	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
203	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
204	C₃×#67	C₂×Q₈	1	8	yes	complemented
205	C₂×C₃×Dic₃	—	2	12	no	—
206	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
207	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
208	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
209	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
210	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
211	C₃×C₄×D₃	—	2	12	no	—
212	C₃×C₄×D₃	—	2	6	no	—
213	C₃×C₄×D₃	—	2	12	no	—
214	C₃×C₄×D₃	—	2	12	no	—
215	C₃×C₄×D₃	C₂×D₄	1	12	yes	—
216	C₃×C₄×D₃	C₂×Q₈	1	4	yes	complemented
217	C₃×Dic₆	—	2	12	no	—
218	C₃×Dic₆	—	2	24	no	—
219	C₃×Dic₆	C₂×D₄	1	12	yes	complemented
220	C₂³×Q₈	—	3	2	no	—
221	D₄×Q₈	—	3	2	no	—
222	D₄×Q₈	—	3	3	no	—
223	D₄×Q₈	—	3	6	no	—
224	D₄×Q₈	—	3	1	no	—
225	D₄×Q₈	—	3	3	no	—
226	D₄×Q₈	C₃×D₃	1	1	yes	characteristic, direct product factor
227	C₂×C₄⋊Q₈	—	3	3	no	—
228	C₂×C₂²⋊Q₈	—	3	6	no	—
229	C₂×C₄×Q₈	—	3	1	no	—
230	C₂×C₄×D₄	—	3	3	no	—
231	C₂⁴×C₃	—	3	2	no	—
232	C₂³×D₃	C₂³×C₃	1	2	yes	—
233	C₂×C₃×Q₈	—	2	8	no	—
234	C₂×C₃×Q₈	—	2	8	no	—
235	C₂×C₃×Q₈	—	2	1	no	—
236	C₂×C₃×Q₈	—	2	6	no	—
237	C₂×C₃×Q₈	—	3	8	no	—
238	C₂×C₃×Q₈	—	3	3	no	—
239	C₂×C₃×Q₈	—	3	12	no	—
240	C₂×C₃×Q₈	—	3	6	no	—
241	C₂×C₃×Q₈	—	4	8	no	—
242	C₂×C₃×Q₈	—	6	24	no	—
243	C₂×C₃×Q₈	—	6	24	no	—
244	C₂×C₃×Q₈	—	6	24	no	—
245	C₂×C₃×Q₈	—	6	8	no	—
246	C₂×C₃×Q₈	C₂²×D₃	1	6	yes	—
247	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
248	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
249	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	—	3	2	no	—
252	C₂×C₃×D₄	—	3	8	no	—
253	C₂×C₃×D₄	—	3	1	no	—
254	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
255	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	—	2	6	no	—
257	C₂²×C₃×C₄	—	3	1	no	—
258	C₂²×C₃×C₄	—	3	3	no	—
259	C₂²×C₃×C₄	—	3	6	no	—
260	C₂²×C₃×C₄	—	3	3	no	—
261	C₂²×C₃×C₄	—	3	6	no	—
262	C₂²×C₃×C₄	—	3	6	no	—
263	C₂²×C₃×C₄	—	3	6	no	—
264	C₂²×C₃×C₄	—	6	24	no	—
265	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
266	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
267	C₂×#67	C₂³×C₃	1	2	yes	—
268	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
269	D₃×Q₈	—	2	8	no	—
270	D₃×Q₈	—	2	24	no	—
271	D₃×Q₈	—	2	24	no	—
272	D₃×Q₈	C₃×D₄	1	8	yes	direct product factor
273	D₃×D₄	C₃×Q₈	1	8	yes	direct product factor
274	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₄×D₃	—	2	24	no	—
276	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
277	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
278	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
279	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
280	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
281	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
282	C₂×Dic₆	—	2	24	no	—
283	C₂×Dic₆	C₂³×C₃	1	6	yes	—
284	C₂×Dic₆	C₂³×C₃	1	12	yes	—
285	C₂×Dic₆	C₂³×C₃	1	3	yes	—
286	C₃×C₄⋊C₄	—	2	3	no	—
287	C₃×C₄⋊C₄	—	2	3	no	—
288	C₃×C₄⋊C₄	—	2	6	no	—
289	C₃×C₄⋊C₄	—	3	6	no	—
290	C₃×C₄⋊C₄	—	3	6	no	—
291	C₃×C₄⋊C₄	—	3	12	no	—
292	C₃×C₄⋊C₄	—	3	3	no	—
293	C₃×C₄⋊C₄	—	3	3	no	—
294	C₃×C₄⋊C₄	—	3	6	no	—
295	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
296	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
297	C₃×C₄⋊C₄	C₂²×D₃	1	6	yes	—
298	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
299	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
300	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
301	C₃×C₂²⋊C₄	—	2	6	no	—
302	C₃×C₂²⋊C₄	—	3	6	no	—
303	C₃×C₂²⋊C₄	—	3	6	no	—
304	C₃×C₂²⋊C₄	—	3	6	no	—
305	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
306	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
307	C₃×C₄²	—	2	3	no	—
308	C₃×C₄²	—	3	3	no	—
309	C₃×C₄²	—	3	3	no	—
310	C₃×C₄²	—	3	3	no	—
311	C₃×C₄²	C₂²×D₃	1	3	yes	—
312	C₃×C₄²	C₂³×C₃	1	3	yes	—
313	#217	C₂³×C₃	1	6	yes	—
314	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
315	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
316	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
317	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
318	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
319	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
320	Dic₃⋊C₄	C₂³×C₃	1	12	yes	—
321	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
322	C₄×Dic₃	C₂³×C₃	1	3	yes	—
323	C₄×Dic₃	C₂³×C₃	1	3	yes	—
324	C₄×Dic₃	C₂³×C₃	1	3	yes	—
325	C₂²×C₃²	—	2	2	no	—
326	C₂²×C₃²	—	2	2	no	—
327	C₂²×C₃²	C₂²×Q₈	1	4	yes	complemented
328	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
329	C₂×C₃×D₃	—	2	2	no	—
330	C₂×C₃×D₃	—	2	2	no	—
331	C₂×C₃×D₃	—	2	16	no	—
332	C₂×C₃×D₃	C₂²×D₄	1	2	yes	—
333	C₂×C₃×D₃	C₂²×Q₈	1	2	yes	—
334	C₂×C₃×D₃	C₂²×Q₈	1	4	yes	complemented
335	C₂×C₃×D₃	2₋¹⁺⁴	1	2	yes	—
336	C₃²×C₄	—	2	6	no	—
337	C₃²×C₄	—	2	3	no	—
338	C₃²×C₄	C₂²×D₄	1	6	yes	—
339	C₃²×C₄	C₂²×Q₈	1	2	yes	complemented
340	C₃×Dic₃	—	2	6	no	—
341	C₃×Dic₃	—	2	3	no	—
342	C₃×Dic₃	C₂²×D₄	1	6	yes	—
343	C₃×Dic₃	C₂²×Q₈	1	2	yes	complemented
344	C₂²×Q₈	—	3	1	no	—
345	C₂²×Q₈	—	3	6	no	—
346	C₂²×Q₈	—	3	6	no	—
347	C₂²×Q₈	—	3	2	no	—
348	C₂²×Q₈	—	3	6	no	—
349	C₂²×Q₈	—	6	16	no	—
350	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	complemented
351	C₂²×D₄	—	3	1	no	—
352	C₂³×C₄	—	3	6	no	—
353	C₄⋊Q₈	—	3	6	no	—
354	C₄⋊Q₈	—	3	6	no	—
355	C₄⋊Q₈	—	3	6	no	—
356	C₄⋊Q₈	—	3	3	no	—
357	C₄⋊Q₈	C₂×C₃×D₃	1	3	yes	complemented
358	C₂²⋊Q₈	—	3	6	no	—
359	C₂²⋊Q₈	—	3	6	no	—
360	C₂²⋊Q₈	—	3	12	no	—
361	C₂²⋊Q₈	—	3	6	no	—
362	C₂²⋊Q₈	—	3	12	no	—
363	C₂²⋊Q₈	C₂×C₃×D₃	1	6	yes	complemented
364	C₄×Q₈	—	3	1	no	—
365	C₄×Q₈	—	3	3	no	—
366	C₄×Q₈	—	3	3	no	—
367	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
368	C₄×D₄	—	3	3	no	—
369	C₄×D₄	—	3	6	no	—
370	C₄×D₄	—	3	3	no	—
371	C₄×D₄	—	3	6	no	—
372	C₄×D₄	—	3	3	no	—
373	C₄×D₄	C₂×C₃×D₃	1	3	yes	—
374	C₂×C₄⋊C₄	—	3	3	no	—
375	C₂×C₄⋊C₄	—	3	3	no	—
376	C₂×C₄⋊C₄	—	3	6	no	—
377	C₂×C₂²⋊C₄	—	3	6	no	—
378	C₂×C₄²	—	3	3	no	—
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	3	1	no	—
381	C₂³×C₃	—	3	8	no	—
382	C₂³×C₃	—	3	2	no	—
383	C₂³×C₃	—	6	4	no	—
384	C₂³×C₃	—	6	4	no	—
385	C₂³×C₃	C₂³×D₃	1	2	yes	—
386	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
387	C₂²×D₃	—	2	4	no	—
388	C₂²×D₃	—	2	4	no	—
389	C₂²×D₃	C₂×C₃×Q₈	1	8	yes	complemented
390	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
391	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
392	C₃×Q₈	—	2	12	no	—
393	C₃×Q₈	—	2	12	no	—
394	C₃×Q₈	—	2	4	no	—
395	C₃×Q₈	—	3	12	no	—
396	C₃×Q₈	—	4	12	no	—
397	C₃×Q₈	—	6	24	no	—
398	C₃×Q₈	—	6	12	no	—
399	C₃×Q₈	D₃×D₄	1	4	yes	direct product factor
400	C₃×Q₈	C₂×C₃×D₄	1	4	yes	complemented
401	C₃×D₄	—	2	4	no	—
402	C₃×D₄	—	3	8	no	—
403	C₃×D₄	—	3	4	no	—
404	C₃×D₄	D₃×Q₈	1	4	yes	direct product factor
405	C₃×D₄	C₂×C₃×Q₈	1	4	yes	complemented
406	C₂×C₃×C₄	—	2	12	no	—
407	C₂×C₃×C₄	—	2	12	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	3	no	—
410	C₂×C₃×C₄	—	2	3	no	—
411	C₂×C₃×C₄	—	2	6	no	—
412	C₂×C₃×C₄	—	3	1	no	—
413	C₂×C₃×C₄	—	3	3	no	—
414	C₂×C₃×C₄	—	3	12	no	—
415	C₂×C₃×C₄	—	3	4	no	—
416	C₂×C₃×C₄	—	3	3	no	—
417	C₂×C₃×C₄	—	3	6	no	—
418	C₂×C₃×C₄	—	4	12	no	—
419	C₂×C₃×C₄	—	6	12	no	—
420	C₂×C₃×C₄	—	6	6	no	—
421	C₂×C₃×C₄	—	6	12	no	—
422	C₂×C₃×C₄	—	6	12	no	—
423	C₂×C₃×C₄	—	6	12	no	—
424	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
425	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
426	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
427	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
429	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
430	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
431	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
432	#67	C₂×C₃×Q₈	1	8	yes	complemented
433	C₂×Dic₃	—	2	12	no	—
434	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
435	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
436	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
437	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
438	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
439	C₄×D₃	—	2	12	no	—
440	C₄×D₃	—	2	6	no	—
441	C₄×D₃	—	2	12	no	—
442	C₄×D₃	—	2	12	no	—
443	C₄×D₃	C₂×C₃×D₄	1	12	yes	—
444	C₄×D₃	C₂×C₃×Q₈	1	4	yes	complemented
445	Dic₆	—	2	12	no	—
446	Dic₆	—	2	24	no	—
447	Dic₆	C₂×C₃×D₄	1	12	yes	complemented
448	C₂×C₃²	—	2	4	no	—
449	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
450	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
451	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
452	C₃×D₃	—	2	4	no	—
453	C₃×D₃	D₄×Q₈	1	4	yes	direct product factor
454	C₂⁴	—	3	2	no	—
455	C₂×Q₈	—	2	8	no	—
456	C₂×Q₈	—	3	8	no	—
457	C₂×Q₈	—	3	3	no	—
458	C₂×Q₈	—	3	12	no	—
459	C₂×Q₈	—	3	6	no	—
460	C₂×Q₈	—	6	24	no	—
461	C₂×Q₈	—	6	24	no	—
462	C₂×Q₈	—	6	24	no	—
463	C₂×Q₈	—	6	8	no	—
464	C₂×Q₈	C₂²×C₃×D₃	1	6	yes	—
465	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
466	C₂×D₄	—	3	2	no	—
467	C₂×D₄	—	3	8	no	—
468	C₂×D₄	—	3	1	no	—
469	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
470	C₂²×C₄	—	3	1	no	—
471	C₂²×C₄	—	3	3	no	—
472	C₂²×C₄	—	3	6	no	—
473	C₂²×C₄	—	3	3	no	—
474	C₂²×C₄	—	3	6	no	—
475	C₂²×C₄	—	3	6	no	—
476	C₂²×C₄	—	3	6	no	—
477	C₂²×C₄	—	6	24	no	—
478	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
479	C₄⋊C₄	—	3	6	no	—
480	C₄⋊C₄	—	3	3	no	—
481	C₄⋊C₄	—	3	6	no	—
482	C₄⋊C₄	—	3	3	no	—
483	C₄⋊C₄	—	3	12	no	—
484	C₄⋊C₄	—	3	6	no	—
485	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
486	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
487	C₄⋊C₄	C₂²×C₃×D₃	1	6	yes	—
488	C₂²⋊C₄	—	3	6	no	—
489	C₂²⋊C₄	—	3	6	no	—
490	C₂²⋊C₄	—	3	6	no	—
491	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
492	C₄²	—	3	3	no	—
493	C₄²	—	3	3	no	—
494	C₄²	—	3	3	no	—
495	C₄²	C₂²×C₃×D₃	1	3	yes	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	4	no	—
501	C₂²×C₃	—	2	1	no	—
502	C₂²×C₃	—	3	2	no	—
503	C₂²×C₃	—	3	2	no	—
504	C₂²×C₃	—	3	2	no	—
505	C₂²×C₃	—	3	4	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	4	2	no	—
508	C₂²×C₃	—	6	16	no	—
509	C₂²×C₃	—	6	2	no	—
510	C₂²×C₃	—	6	2	no	—
511	C₂²×C₃	C₂×D₃×Q₈	1	4	yes	complemented
512	C₂²×C₃	C₂²×C₃×Q₈	1	4	yes	complemented
513	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
514	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
515	C₂×D₃	—	2	2	no	—
516	C₂×D₃	—	2	2	no	—
517	C₂×D₃	—	2	16	no	—
518	C₂×D₃	C₂²×C₃×D₄	1	2	yes	—
519	C₂×D₃	C₂²×C₃×Q₈	1	2	yes	—
520	C₂×D₃	C₂²×C₃×Q₈	1	4	yes	complemented
521	C₂×D₃	C₃×2₋¹⁺⁴	1	2	yes	—
522	C₃×C₄	—	2	6	no	—
523	C₃×C₄	—	2	3	no	—
524	C₃×C₄	—	2	6	no	—
525	C₃×C₄	—	2	3	no	—
526	C₃×C₄	—	2	6	no	—
527	C₃×C₄	—	2	2	no	—
528	C₃×C₄	—	3	6	no	—
529	C₃×C₄	—	3	2	no	—
530	C₃×C₄	—	4	6	no	—
531	C₃×C₄	—	4	3	no	—
532	C₃×C₄	—	6	6	no	—
533	C₃×C₄	—	6	3	no	—
534	C₃×C₄	C₂×D₃×D₄	1	6	yes	—
535	C₃×C₄	C₂×D₃×Q₈	1	2	yes	complemented
536	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
537	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	complemented
538	Dic₃	—	2	6	no	—
539	Dic₃	—	2	3	no	—
540	Dic₃	C₂²×C₃×D₄	1	6	yes	—
541	Dic₃	C₂²×C₃×Q₈	1	2	yes	complemented
542	C₃²	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
543	C₂³	—	3	1	no	—
544	C₂³	—	3	8	no	—
545	C₂³	—	3	2	no	—
546	C₂³	—	6	4	no	—
547	C₂³	—	6	4	no	—
548	C₂³	C₂³×C₃×D₃	1	2	yes	—
549	Q₈	—	2	12	no	—
550	Q₈	—	3	12	no	—
551	Q₈	—	6	24	no	—
552	Q₈	—	6	12	no	—
553	Q₈	C₃×D₃×D₄	1	4	yes	direct product factor
554	D₄	—	3	8	no	—
555	D₄	—	3	4	no	—
556	D₄	C₃×D₃×Q₈	1	4	yes	direct product factor
557	C₂×C₄	—	2	12	no	—
558	C₂×C₄	—	3	1	no	—
559	C₂×C₄	—	3	3	no	—
560	C₂×C₄	—	3	12	no	—
561	C₂×C₄	—	3	4	no	—
562	C₂×C₄	—	3	3	no	—
563	C₂×C₄	—	3	6	no	—
564	C₂×C₄	—	6	12	no	—
565	C₂×C₄	—	6	12	no	—
566	C₂×C₄	—	6	6	no	—
567	C₂×C₄	—	6	12	no	—
568	C₂×C₄	—	6	12	no	—
569	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
570	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
571	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
572	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
573	C₂×C₃	—	2	4	no	—
574	C₂×C₃	—	2	4	no	—
575	C₂×C₃	—	2	1	no	—
576	C₂×C₃	—	2	1	no	—
577	C₂×C₃	—	2	1	no	—
578	C₂×C₃	—	3	4	no	—
579	C₂×C₃	—	4	4	no	—
580	C₂×C₃	—	6	4	no	—
581	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
582	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
583	C₂×C₃	D₃×2₋¹⁺⁴	1	1	yes	characteristic
584	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
585	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
586	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
587	D₃	—	2	4	no	—
588	D₃	C₃×D₄×Q₈	1	4	yes	direct product factor
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	3	2	no	—
592	C₂²	—	3	2	no	—
593	C₂²	—	3	2	no	—
594	C₂²	—	3	4	no	—
595	C₂²	—	6	16	no	—
596	C₂²	—	6	2	no	—
597	C₂²	—	6	2	no	—
598	C₂²	C₂×C₃×D₃×Q₈	1	4	yes	complemented
599	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
600	C₄	—	2	6	no	—
601	C₄	—	2	3	no	—
602	C₄	—	3	6	no	—
603	C₄	—	3	2	no	—
604	C₄	—	6	6	no	—
605	C₄	—	6	3	no	—
606	C₄	C₂×C₃×D₃×D₄	1	6	yes	—
607	C₄	C₂×C₃×D₃×Q₈	1	2	yes	complemented
608	C₃	—	2	1	no	—
609	C₃	D₃×D₄×Q₈	1	1	yes	characteristic, direct product factor
610	C₃	C₂×C₃×D₄×Q₈	1	1	yes	characteristic, complemented
611	C₂	—	2	4	no	—
612	C₂	—	3	4	no	—
613	C₂	—	6	4	no	—
614	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
615	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
616	C₂	C₃×D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×D₄×Q₈	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×D₃×D₄	C₂²
hypercenter	C₃×D₄×Q₈	D₃
hypocenter	C₃	C₂×C₃×D₄×Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₃×Q₈	C₂	semidirect
2. C₃²×D₄×Q₈	C₂	semidirect
3. C₃×Q₈×#67	C₂	semidirect
4. C₃×#5727	C₂	semidirect
5. C₃×D₃×C₄⋊Q₈	C₂	semidirect
6. C₃×#5632	C₂	semidirect
7. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
8. C₃×Q₈×D₁₂	C₂	semidirect
9. C₃×C₄×D₃×Q₈	C₂	semidirect
11. C₃×D₄×Dic₆	C₂	semidirect
13. D₃×D₄×Q₈	C₃	direct (N × H)
14. C₂²×C₃²×Q₈	C₂²	semidirect
18. C₂×C₃×D₃×Q₈	C₂²	semidirect
19. C₂×C₃×D₃×Q₈	C₂²	semidirect
22. C₂²×C₃×Dic₆	C₂²	semidirect
23. C₃²×C₄⋊Q₈	C₂²	semidirect
24. C₃²×C₂²⋊Q₈	C₂²	semidirect
25. C₃²×C₄×Q₈	C₂²	semidirect
27. C₃×#946	C₂²	semidirect
28. C₃×Q₈×Dic₃	C₂²	semidirect
29. C₃×#944	C₂²	semidirect
32. C₃×#924	C₂²	semidirect
33. C₃×#897	C₂²	semidirect
34. C₃×#896	C₂²	semidirect
39. C₃×#888	C₂²	semidirect
40. C₃×#888	C₂²	semidirect
41. C₃×#887	C₂²	semidirect
44. C₃×#878	C₂²	semidirect
47. C₃×#869	C₂²	semidirect
48. C₃×C₄×Dic₆	C₂²	semidirect
50. C₂²×D₃×Q₈	C₂×C₃	semidirect
57. C₃×D₄×Q₈	D₃	direct (N × H)
58. C₃×D₄×Q₈	C₂×C₃	semidirect
63. Q₈×#67	C₂×C₃	semidirect
64. #5727	C₂×C₃	semidirect
65. D₃×C₄⋊Q₈	C₂×C₃	semidirect
66. #5632	C₂×C₃	semidirect
67. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
68. Q₈×D₁₂	C₂×C₃	semidirect
69. C₄×D₃×Q₈	C₂×C₃	semidirect
71. D₄×Dic₆	C₂×C₃	semidirect
83. C₃×D₃×Q₈	D₄	direct (N × H)
84. C₃×D₃×D₄	Q₈	direct (N × H)
122. C₂²×C₃×Q₈	C₂×D₃	semidirect
123. C₂²×C₃×Q₈	C₂²×C₃	semidirect
129. C₂×D₃×Q₈	C₂²×C₃	semidirect
130. C₂×D₃×Q₈	C₂²×C₃	semidirect
133. C₂²×Dic₆	C₂²×C₃	semidirect
139. C₃×C₄⋊Q₈	C₂×D₃	semidirect
140. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
147. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
148. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
153. C₃×C₄×Q₈	C₂×D₃	semidirect
154. C₃×C₄×Q₈	C₂²×C₃	semidirect
168. #946	C₂²×C₃	semidirect
169. Q₈×Dic₃	C₂²×C₃	semidirect
170. #944	C₂²×C₃	semidirect
173. #924	C₂²×C₃	semidirect
174. #897	C₂²×C₃	semidirect
175. #896	C₂²×C₃	semidirect
180. #888	C₂²×C₃	semidirect
181. #888	C₂²×C₃	semidirect
182. #887	C₂²×C₃	semidirect
185. #878	C₂²×C₃	semidirect
188. #869	C₂²×C₃	semidirect
189. C₄×Dic₆	C₂²×C₃	semidirect
193. C₂²×C₃×D₃	C₂×Q₈	semidirect
197. C₃²×Q₈	C₂×D₄	semidirect
198. C₃²×D₄	C₂×Q₈	semidirect
204. C₃×#67	C₂×Q₈	semidirect
210. C₃×D₁₂	C₂×Q₈	semidirect
216. C₃×C₄×D₃	C₂×Q₈	semidirect
219. C₃×Dic₆	C₂×D₄	semidirect
226. D₄×Q₈	C₃×D₃	direct (N × H)
272. D₃×Q₈	C₃×D₄	direct (N × H)
273. D₃×D₄	C₃×Q₈	direct (N × H)
327. C₂²×C₃²	C₂²×Q₈	semidirect
334. C₂×C₃×D₃	C₂²×Q₈	semidirect
339. C₃²×C₄	C₂²×Q₈	semidirect
343. C₃×Dic₃	C₂²×Q₈	semidirect
350. C₂²×Q₈	C₂×C₃×D₃	semidirect
357. C₄⋊Q₈	C₂×C₃×D₃	semidirect
363. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
367. C₄×Q₈	C₂×C₃×D₃	semidirect
389. C₂²×D₃	C₂×C₃×Q₈	semidirect
399. C₃×Q₈	D₃×D₄	direct (N × H)
400. C₃×Q₈	C₂×C₃×D₄	semidirect
404. C₃×D₄	D₃×Q₈	direct (N × H)
405. C₃×D₄	C₂×C₃×Q₈	semidirect
432. #67	C₂×C₃×Q₈	semidirect
438. D₁₂	C₂×C₃×Q₈	semidirect
444. C₄×D₃	C₂×C₃×Q₈	semidirect
447. Dic₆	C₂×C₃×D₄	semidirect
453. C₃×D₃	D₄×Q₈	direct (N × H)
511. C₂²×C₃	C₂×D₃×Q₈	semidirect
512. C₂²×C₃	C₂²×C₃×Q₈	semidirect
520. C₂×D₃	C₂²×C₃×Q₈	semidirect
535. C₃×C₄	C₂×D₃×Q₈	semidirect
537. C₃×C₄	C₂²×C₃×Q₈	semidirect
541. Dic₃	C₂²×C₃×Q₈	semidirect
542. C₃²	C₂×D₄×Q₈	semidirect
553. Q₈	C₃×D₃×D₄	direct (N × H)
556. D₄	C₃×D₃×Q₈	direct (N × H)
588. D₃	C₃×D₄×Q₈	direct (N × H)
598. C₂²	C₂×C₃×D₃×Q₈	semidirect
607. C₄	C₂×C₃×D₃×Q₈	semidirect
609. C₃	D₃×D₄×Q₈	direct (N × H)
610. C₃	C₂×C₃×D₄×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×Q₈	2
C₃²×D₄×Q₈	2
C₃×Q₈×#67	2
C₃×#5727	2
C₃×D₃×C₄⋊Q₈	2
C₃×#5632	2
C₃×D₃×C₂²⋊Q₈	2
C₃×Q₈×D₁₂	2
C₃×C₄×D₃×Q₈	2
C₃×C₄×D₃×D₄	2
C₃×D₄×Dic₆	2
C₂×C₃×D₄×Q₈	3
D₃×D₄×Q₈	3

Subgroups — C3×D3×D4×Q8 #11902640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₄×Q₈ #11902640