Subgroups — C₂²×C₃×#465 #10679041

Order 768.

3350 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#121	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×#465	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#465	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
11	C₂³×C₃×D₄	—	2	1	no	—
12	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
13	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×SD₁₆	—	2	8	no	—
15	C₂²×C₃×SD₁₆	C₂²	1	12	yes	complemented
16	C₂³×C₃×C₈	—	2	8	no	—
17	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₈	C₂²	1	12	yes	complemented
20	C₂×C₃×C₂²⋊Q₈	—	2	6	no	—
21	C₂×C₃×C₂²⋊Q₈	C₂²	1	12	yes	complemented
22	C₂×C₃×#121	—	2	6	no	—
23	C₂×C₃×#121	C₂²	1	12	yes	—
24	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
25	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
28	C₂²×C₃×C₂²⋊C₄	—	2	1	no	—
29	C₃×#465	C₂²	1	64	yes	direct product factor
30	C₂×C₃×#106	C₂²	1	12	yes	complemented
31	C₂×C₃×#103	C₂²	1	12	yes	complemented
32	C₂×C₃×#102	C₂²	1	12	yes	complemented
33	C₂³×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₈	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×#121	C₂×C₃	1	1	yes	characteristic
37	C₂×#465	C₂×C₃	1	24	yes	direct product factor
38	C₂²×#106	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×#103	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂²×#102	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁵×C₃	—	2	1	no	—
42	C₂⁵×C₃	D₄	1	1	yes	characteristic
43	C₂²×C₃×Q₈	—	2	3	no	—
44	C₂²×C₃×Q₈	—	2	4	no	—
45	C₂²×C₃×Q₈	—	2	4	no	—
46	C₂²×C₃×Q₈	C₂³	1	6	yes	—
47	C₂²×C₃×D₄	—	2	12	no	—
48	C₂²×C₃×D₄	—	2	4	no	—
49	C₂²×C₃×D₄	—	2	3	no	—
50	C₂²×C₃×D₄	—	2	4	no	—
51	C₂²×C₃×D₄	—	4	8	no	—
52	C₂²×C₃×D₄	C₂³	1	6	yes	—
53	C₂³×C₃×C₄	—	2	4	no	—
54	C₂³×C₃×C₄	—	2	4	no	—
55	C₂³×C₃×C₄	—	2	1	no	—
56	C₂³×C₃×C₄	—	2	1	no	—
57	C₂³×C₃×C₄	—	2	1	no	—
58	C₂³×C₃×C₄	D₄	1	6	yes	—
59	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
60	C₂³×C₃×C₄	C₂³	1	6	yes	—
61	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×SD₁₆	—	2	48	no	—
63	C₂×C₃×SD₁₆	C₂³	1	16	yes	complemented
64	C₂²×C₃×C₈	—	2	4	no	—
65	C₂²×C₃×C₈	—	2	48	no	—
66	C₂²×C₃×C₈	D₄	1	8	yes	complemented
67	C₂²×C₃×C₈	C₂³	1	6	yes	—
68	C₂²×C₃×C₈	C₂³	1	6	yes	—
69	C₂²×C₃×C₈	C₂³	1	16	yes	complemented
70	C₃×C₂²⋊Q₈	—	2	24	no	—
71	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
72	C₃×#121	—	2	24	no	—
73	C₃×#121	C₂³	1	16	yes	—
74	C₂×C₃×C₄⋊C₄	—	2	12	no	—
75	C₂×C₃×C₄⋊C₄	—	2	3	no	—
76	C₂×C₃×C₄⋊C₄	—	2	3	no	—
77	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
78	C₂×C₃×C₄⋊C₄	C₂³	1	6	yes	—
79	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
80	C₂×C₃×C₂²⋊C₄	—	2	12	no	—
81	C₃×#106	C₂³	1	16	yes	complemented
82	C₃×#103	C₂³	1	16	yes	complemented
83	C₃×#102	C₂³	1	16	yes	complemented
84	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₂³×D₄	—	2	1	no	—
86	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
87	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂²×SD₁₆	—	2	8	no	—
89	C₂²×SD₁₆	C₂²×C₃	1	12	yes	complemented
90	C₂³×C₈	—	2	8	no	—
91	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
92	C₂³×C₈	C₂²×C₃	1	1	yes	characteristic
93	C₂³×C₈	C₂²×C₃	1	12	yes	complemented
94	C₂×C₂²⋊Q₈	—	2	6	no	—
95	C₂×C₂²⋊Q₈	C₂²×C₃	1	12	yes	complemented
96	C₂×#121	—	2	6	no	—
97	C₂×#121	C₂²×C₃	1	12	yes	—
98	C₂²×C₄⋊C₄	—	2	1	no	—
99	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₂²⋊C₄	—	2	1	no	—
102	C₂²×C₂²⋊C₄	—	2	1	no	—
103	#465	C₂²×C₃	1	64	yes	direct product factor
104	C₂×#106	C₂²×C₃	1	12	yes	complemented
105	C₂×#103	C₂²×C₃	1	12	yes	complemented
106	C₂×#102	C₂²×C₃	1	12	yes	complemented
107	C₂⁴×C₃	—	2	4	no	—
108	C₂⁴×C₃	—	2	4	no	—
109	C₂⁴×C₃	—	2	6	no	—
110	C₂⁴×C₃	—	4	4	no	—
111	C₂⁴×C₃	—	4	4	no	—
112	C₂⁴×C₃	—	4	4	no	—
113	C₂⁴×C₃	SD₁₆	1	8	yes	complemented
114	C₂⁴×C₃	C₂×D₄	1	6	yes	—
115	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×Q₈	—	2	6	no	—
117	C₂×C₃×Q₈	—	2	12	no	—
118	C₂×C₃×Q₈	—	2	12	no	—
119	C₂×C₃×Q₈	—	4	12	no	—
120	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
121	C₂×C₃×D₄	—	2	16	no	—
122	C₂×C₃×D₄	—	2	12	no	—
123	C₂×C₃×D₄	—	2	6	no	—
124	C₂×C₃×D₄	—	2	12	no	—
125	C₂×C₃×D₄	—	4	48	no	—
126	C₂×C₃×D₄	—	4	12	no	—
127	C₂×C₃×D₄	C₂⁴	1	4	yes	—
128	C₂²×C₃×C₄	—	2	4	no	—
129	C₂²×C₃×C₄	—	2	24	no	—
130	C₂²×C₃×C₄	—	2	12	no	—
131	C₂²×C₃×C₄	—	2	12	no	—
132	C₂²×C₃×C₄	—	2	6	no	—
133	C₂²×C₃×C₄	—	2	6	no	—
134	C₂²×C₃×C₄	—	2	6	no	—
135	C₂²×C₃×C₄	—	4	4	no	—
136	C₂²×C₃×C₄	—	4	4	no	—
137	C₂²×C₃×C₄	—	4	4	no	—
138	C₂²×C₃×C₄	C₂×D₄	1	6	yes	—
139	C₂²×C₃×C₄	C₂×D₄	1	12	yes	—
140	C₂²×C₃×C₄	C₂×D₄	1	3	yes	—
141	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
142	C₂²×C₃×C₄	#41	1	4	yes	—
143	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
144	C₂²×C₃×C₄	C₂⁴	1	3	yes	—
145	C₃×SD₁₆	—	2	32	no	—
146	C₂×C₃×C₈	—	2	12	no	—
147	C₂×C₃×C₈	—	2	32	no	—
148	C₂×C₃×C₈	C₂×D₄	1	24	yes	complemented
149	C₂×C₃×C₈	C₂⁴	1	4	yes	—
150	C₂×C₃×C₈	C₂⁴	1	4	yes	—
151	C₃×C₄⋊C₄	—	2	16	no	—
152	C₃×C₄⋊C₄	—	2	6	no	—
153	C₃×C₄⋊C₄	—	2	6	no	—
154	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₃×C₂²⋊C₄	—	2	16	no	—
157	C₃×C₂²⋊C₄	—	2	16	no	—
158	C₂⁵	—	2	1	no	—
159	C₂⁵	C₃×D₄	1	1	yes	characteristic
160	C₂²×Q₈	—	2	3	no	—
161	C₂²×Q₈	—	2	4	no	—
162	C₂²×Q₈	—	2	4	no	—
163	C₂²×Q₈	C₂³×C₃	1	6	yes	—
164	C₂²×D₄	—	2	12	no	—
165	C₂²×D₄	—	2	4	no	—
166	C₂²×D₄	—	2	3	no	—
167	C₂²×D₄	—	2	4	no	—
168	C₂²×D₄	—	4	8	no	—
169	C₂²×D₄	C₂³×C₃	1	6	yes	—
170	C₂³×C₄	—	2	4	no	—
171	C₂³×C₄	—	2	4	no	—
172	C₂³×C₄	—	2	1	no	—
173	C₂³×C₄	—	2	1	no	—
174	C₂³×C₄	—	2	1	no	—
175	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
176	C₂³×C₄	C₃×D₄	1	6	yes	—
177	C₂³×C₄	C₂³×C₃	1	6	yes	—
178	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂×SD₁₆	—	2	48	no	—
180	C₂×SD₁₆	C₂³×C₃	1	16	yes	complemented
181	C₂²×C₈	—	2	4	no	—
182	C₂²×C₈	—	2	48	no	—
183	C₂²×C₈	C₃×D₄	1	8	yes	complemented
184	C₂²×C₈	C₂³×C₃	1	6	yes	—
185	C₂²×C₈	C₂³×C₃	1	6	yes	—
186	C₂²×C₈	C₂³×C₃	1	16	yes	complemented
187	C₂²⋊Q₈	—	2	24	no	—
188	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
189	#121	—	2	24	no	—
190	#121	C₂³×C₃	1	16	yes	—
191	C₂×C₄⋊C₄	—	2	12	no	—
192	C₂×C₄⋊C₄	—	2	3	no	—
193	C₂×C₄⋊C₄	—	2	3	no	—
194	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
195	C₂×C₄⋊C₄	C₂³×C₃	1	6	yes	—
196	C₂×C₂²⋊C₄	—	2	12	no	—
197	C₂×C₂²⋊C₄	—	2	12	no	—
198	#106	C₂³×C₃	1	16	yes	complemented
199	#103	C₂³×C₃	1	16	yes	complemented
200	#102	C₂³×C₃	1	16	yes	complemented
201	C₂³×C₃	—	2	12	no	—
202	C₂³×C₃	—	2	12	no	—
203	C₂³×C₃	—	2	32	no	—
204	C₂³×C₃	—	2	4	no	—
205	C₂³×C₃	—	4	12	no	—
206	C₂³×C₃	—	4	12	no	—
207	C₂³×C₃	—	4	12	no	—
208	C₂³×C₃	—	8	16	no	—
209	C₂³×C₃	#121	1	4	yes	—
210	C₂³×C₃	C₂×SD₁₆	1	4	yes	—
211	C₂³×C₃	C₂×SD₁₆	1	24	yes	complemented
212	C₂³×C₃	#135	1	4	yes	—
213	C₂³×C₃	C₂²×D₄	1	4	yes	—
214	C₂³×C₃	C₂²×D₄	1	3	yes	—
215	C₃×Q₈	—	2	4	no	—
216	C₃×Q₈	—	2	4	no	—
217	C₃×Q₈	—	4	12	no	—
218	C₃×D₄	—	2	4	no	—
219	C₃×D₄	—	2	4	no	—
220	C₃×D₄	—	4	32	no	—
221	C₃×D₄	—	4	12	no	—
222	C₂×C₃×C₄	—	2	12	no	—
223	C₂×C₃×C₄	—	2	24	no	—
224	C₂×C₃×C₄	—	2	4	no	—
225	C₂×C₃×C₄	—	2	4	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	4	12	no	—
230	C₂×C₃×C₄	—	4	12	no	—
231	C₂×C₃×C₄	—	4	12	no	—
232	C₂×C₃×C₄	#121	1	12	yes	—
233	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
234	C₂×C₃×C₄	C₂²×D₄	1	3	yes	—
235	C₂×C₃×C₄	C₂²×D₄	1	6	yes	—
236	C₂×C₃×C₄	C₂×#41	1	6	yes	—
237	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
238	C₃×C₈	—	2	4	no	—
239	C₃×C₈	C₂²×D₄	1	8	yes	complemented
240	C₂⁴	—	2	4	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	2	6	no	—
243	C₂⁴	—	4	4	no	—
244	C₂⁴	—	4	4	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	C₃×SD₁₆	1	8	yes	complemented
247	C₂⁴	C₂×C₃×D₄	1	6	yes	—
248	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×Q₈	—	2	6	no	—
250	C₂×Q₈	—	2	12	no	—
251	C₂×Q₈	—	2	12	no	—
252	C₂×Q₈	—	4	12	no	—
253	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	—	2	12	no	—
256	C₂×D₄	—	2	6	no	—
257	C₂×D₄	—	2	12	no	—
258	C₂×D₄	—	4	48	no	—
259	C₂×D₄	—	4	12	no	—
260	C₂×D₄	C₂⁴×C₃	1	4	yes	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	24	no	—
263	C₂²×C₄	—	2	12	no	—
264	C₂²×C₄	—	2	12	no	—
265	C₂²×C₄	—	2	6	no	—
266	C₂²×C₄	—	2	6	no	—
267	C₂²×C₄	—	2	6	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	4	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	C₂×C₃×D₄	1	6	yes	—
272	C₂²×C₄	C₂×C₃×D₄	1	12	yes	—
273	C₂²×C₄	C₂×C₃×D₄	1	3	yes	—
274	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
275	C₂²×C₄	C₃×#41	1	4	yes	—
276	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
277	C₂²×C₄	C₂⁴×C₃	1	3	yes	—
278	SD₁₆	—	2	32	no	—
279	C₂×C₈	—	2	12	no	—
280	C₂×C₈	—	2	32	no	—
281	C₂×C₈	C₂×C₃×D₄	1	24	yes	complemented
282	C₂×C₈	C₂⁴×C₃	1	4	yes	—
283	C₂×C₈	C₂⁴×C₃	1	4	yes	—
284	C₄⋊C₄	—	2	16	no	—
285	C₄⋊C₄	—	2	6	no	—
286	C₄⋊C₄	—	2	6	no	—
287	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
288	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
289	C₂²⋊C₄	—	2	16	no	—
290	C₂²⋊C₄	—	2	16	no	—
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	2	48	no	—
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	4	4	no	—
295	C₂²×C₃	—	4	4	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	—	8	24	no	—
298	C₂²×C₃	#465	1	16	yes	direct product factor
299	C₂²×C₃	C₂×#121	1	6	yes	—
300	C₂²×C₃	C₂²×SD₁₆	1	6	yes	—
301	C₂²×C₃	C₂²×SD₁₆	1	8	yes	complemented
302	C₂²×C₃	C₂×#135	1	6	yes	—
303	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	4	4	no	—
306	C₃×C₄	—	4	4	no	—
307	C₃×C₄	—	4	4	no	—
308	C₃×C₄	C₂×#121	1	6	yes	—
309	C₃×C₄	C₂³×D₄	1	1	yes	characteristic
310	C₃×C₄	C₂²×#41	1	1	yes	characteristic
311	C₂³	—	2	12	no	—
312	C₂³	—	2	32	no	—
313	C₂³	—	2	12	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	4	12	no	—
316	C₂³	—	4	12	no	—
317	C₂³	—	4	12	no	—
318	C₂³	—	8	16	no	—
319	C₂³	C₃×#121	1	4	yes	—
320	C₂³	C₂×C₃×SD₁₆	1	4	yes	—
321	C₂³	C₂×C₃×SD₁₆	1	24	yes	complemented
322	C₂³	C₃×#135	1	4	yes	—
323	C₂³	C₂²×C₃×D₄	1	4	yes	—
324	C₂³	C₂²×C₃×D₄	1	3	yes	—
325	Q₈	—	2	4	no	—
326	Q₈	—	2	4	no	—
327	Q₈	—	4	12	no	—
328	D₄	—	2	4	no	—
329	D₄	—	2	4	no	—
330	D₄	—	4	32	no	—
331	D₄	—	4	12	no	—
332	C₂×C₄	—	2	12	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	24	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	12	no	—
340	C₂×C₄	—	4	12	no	—
341	C₂×C₄	—	4	12	no	—
342	C₂×C₄	C₃×#121	1	12	yes	—
343	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
344	C₂×C₄	C₂²×C₃×D₄	1	6	yes	—
345	C₂×C₄	C₂²×C₃×D₄	1	3	yes	—
346	C₂×C₄	C₂×C₃×#41	1	6	yes	—
347	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	C₂²×C₃×D₄	1	8	yes	complemented
350	C₂×C₃	—	2	8	no	—
351	C₂×C₃	—	8	4	no	—
352	C₂×C₃	C₂×#465	1	12	yes	direct product factor
353	C₂×C₃	C₂²×#121	1	1	yes	characteristic
354	C₂×C₃	C₂³×SD₁₆	1	1	yes	characteristic
355	C₂×C₃	C₂²×#135	1	1	yes	characteristic
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	48	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	24	no	—
363	C₂²	C₃×#465	1	16	yes	direct product factor
364	C₂²	C₂×C₃×#121	1	6	yes	—
365	C₂²	C₂²×C₃×SD₁₆	1	6	yes	—
366	C₂²	C₂²×C₃×SD₁₆	1	8	yes	complemented
367	C₂²	C₂×C₃×#135	1	6	yes	—
368	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	4	no	—
373	C₄	C₂×C₃×#121	1	6	yes	—
374	C₄	C₂³×C₃×D₄	1	1	yes	characteristic
375	C₄	C₂²×C₃×#41	1	1	yes	characteristic
376	C₃	C₂²×#465	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	2	8	no	—
378	C₂	—	8	4	no	—
379	C₂	C₂×C₃×#465	1	12	yes	direct product factor
380	C₂	C₂²×C₃×#121	1	1	yes	characteristic
381	C₂	C₂³×C₃×SD₁₆	1	1	yes	characteristic
382	C₂	C₂²×C₃×#135	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂²×C₃×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂⁴×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×SD₁₆	C₂	semidirect
2. C₂⁴×C₃×C₈	C₂	semidirect
3. C₂²×C₃×C₂²⋊Q₈	C₂	semidirect
5. C₂×C₃×#465	C₂	direct (N × H)
6. C₂²×C₃×#106	C₂	semidirect
7. C₂²×C₃×#103	C₂	semidirect
8. C₂²×C₃×#102	C₂	semidirect
9. C₂²×#465	C₃	direct (N × H)
15. C₂²×C₃×SD₁₆	C₂²	semidirect
19. C₂³×C₃×C₈	C₂²	semidirect
21. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
29. C₃×#465	C₂²	direct (N × H)
30. C₂×C₃×#106	C₂²	semidirect
31. C₂×C₃×#103	C₂²	semidirect
32. C₂×C₃×#102	C₂²	semidirect
33. C₂³×SD₁₆	C₂×C₃	semidirect
34. C₂⁴×C₈	C₂×C₃	semidirect
35. C₂²×C₂²⋊Q₈	C₂×C₃	semidirect
37. C₂×#465	C₂×C₃	direct (N × H)
38. C₂²×#106	C₂×C₃	semidirect
39. C₂²×#103	C₂×C₃	semidirect
40. C₂²×#102	C₂×C₃	semidirect
63. C₂×C₃×SD₁₆	C₂³	semidirect
66. C₂²×C₃×C₈	D₄	semidirect
69. C₂²×C₃×C₈	C₂³	semidirect
71. C₃×C₂²⋊Q₈	C₂³	semidirect
81. C₃×#106	C₂³	semidirect
82. C₃×#103	C₂³	semidirect
83. C₃×#102	C₂³	semidirect
89. C₂²×SD₁₆	C₂²×C₃	semidirect
93. C₂³×C₈	C₂²×C₃	semidirect
95. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
103. #465	C₂²×C₃	direct (N × H)
104. C₂×#106	C₂²×C₃	semidirect
105. C₂×#103	C₂²×C₃	semidirect
106. C₂×#102	C₂²×C₃	semidirect
113. C₂⁴×C₃	SD₁₆	semidirect
148. C₂×C₃×C₈	C₂×D₄	semidirect
180. C₂×SD₁₆	C₂³×C₃	semidirect
183. C₂²×C₈	C₃×D₄	semidirect
186. C₂²×C₈	C₂³×C₃	semidirect
188. C₂²⋊Q₈	C₂³×C₃	semidirect
198. #106	C₂³×C₃	semidirect
199. #103	C₂³×C₃	semidirect
200. #102	C₂³×C₃	semidirect
211. C₂³×C₃	C₂×SD₁₆	semidirect
239. C₃×C₈	C₂²×D₄	semidirect
246. C₂⁴	C₃×SD₁₆	semidirect
281. C₂×C₈	C₂×C₃×D₄	semidirect
298. C₂²×C₃	#465	direct (N × H)
301. C₂²×C₃	C₂²×SD₁₆	semidirect
321. C₂³	C₂×C₃×SD₁₆	semidirect
349. C₈	C₂²×C₃×D₄	semidirect
352. C₂×C₃	C₂×#465	direct (N × H)
363. C₂²	C₃×#465	direct (N × H)
366. C₂²	C₂²×C₃×SD₁₆	semidirect
376. C₃	C₂²×#465	direct (N × H)
379. C₂	C₂×C₃×#465	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×SD₁₆	2
C₂⁴×C₃×C₈	2
C₂²×C₃×C₂²⋊Q₈	2
C₂²×C₃×#121	2
C₂×C₃×#465	2
C₂²×C₃×#106	2
C₂²×C₃×#103	2
C₂²×C₃×#102	2
C₂²×#465	3

Subgroups — C22×C3×#465 #10679041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#465 #10679041