Subgroups — #79486

Order 384.

464 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	#5128	C₂	1	1	yes	maximal, characteristic, complemented
4	#5126	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#5011	C₂	1	1	yes	maximal, characteristic, complemented
8	#4836	C₂	1	1	yes	maximal, characteristic, complemented
9	#4833	C₂	1	1	yes	maximal, characteristic, complemented
10	#4729	C₂	1	1	yes	maximal, characteristic, complemented
11	#4726	C₂	1	1	yes	maximal, characteristic, complemented
12	#67⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#4706	C₂	1	1	yes	maximal, characteristic, complemented
15	#4705	C₂	1	1	yes	maximal, characteristic, complemented
16	#2974	—	3	1	no	maximal, Sylow
17	C₂×D₃×D₄	C₄	1	1	yes	characteristic
18	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
23	D₄×Dic₃	C₄	1	1	yes	characteristic
24	C₄×#67	C₂²	1	1	yes	characteristic
25	C₄×#67	C₂²	1	1	yes	characteristic
26	C₂×#208	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
29	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
32	#893	C₄	1	1	yes	characteristic
33	D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
34	#67⋊C₄	C₄	1	1	yes	characteristic
35	#67⋊C₄	C₄	1	1	yes	characteristic
36	D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
37	D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
38	C₄×D₁₂	C₂²	1	1	yes	characteristic
39	C₄²×D₃	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
43	C₃×#97	C₂²	1	1	yes	characteristic, complemented
44	#830	C₂²	1	1	yes	characteristic, complemented
45	#830	C₂²	1	1	yes	characteristic, complemented
46	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
59	#803	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×D₄	—	3	1	no	—
61	#436	—	3	1	no	—
62	#436	—	3	1	no	—
63	#435	—	3	1	no	—
64	#435	—	3	1	no	—
65	#435	—	3	1	no	—
66	#435	D₃	1	1	yes	characteristic, complemented
67	C₈×D₄	—	3	1	no	—
68	C₈×D₄	—	3	1	no	—
69	#432	—	3	1	no	—
70	#431	—	3	1	no	—
71	#407	—	3	1	no	—
72	#407	—	3	1	no	—
73	C₂×C₂²⋊C₈	—	3	1	no	—
74	C₂×C₂²⋊C₈	—	3	1	no	—
75	C₂³×D₃	C₂×C₄	1	1	yes	characteristic
76	C₂³×D₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×D₄	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
80	C₂×#67	C₂×C₄	1	1	yes	characteristic
81	C₂×#67	C₂×C₄	1	1	yes	characteristic
82	C₂²×Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×Dic₃	C₂×C₄	1	1	yes	characteristic
84	D₃×D₄	—	2	4	no	—
85	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×D₃	—	4	1	no	—
87	C₂×C₄×D₃	—	4	1	no	—
88	C₂×C₄×D₃	—	4	1	no	—
89	C₂×C₄×D₃	—	4	1	no	—
90	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
99	C₃×M₁₆	—	4	1	no	—
100	C₂×C₃×C₈	—	4	1	no	—
101	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
105	C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₃×C₄²	C₂³	1	1	yes	characteristic
109	#217	C₂×C₄	1	1	yes	characteristic
110	#217	C₂×C₄	1	1	yes	characteristic
111	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
116	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
117	Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
119	C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
120	C₄×Dic₃	C₂³	1	1	yes	characteristic
121	#208	—	4	1	no	—
122	C₂×C₃⋊C₈	—	4	1	no	—
123	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	ΓL(1,𝔽₂₅)	—	4	1	no	—
128	ΓL(1,𝔽₂₅)	—	4	1	no	—
129	D₃×C₈	—	4	1	no	—
130	D₃×C₈	—	4	1	no	—
131	C₂²×D₄	—	3	1	no	—
132	C₂³×C₄	—	3	1	no	—
133	C₂³×C₄	—	3	1	no	—
134	C₂×M₁₆	—	3	1	no	—
135	C₂×M₁₆	—	3	1	no	—
136	C₂×M₁₆	—	3	1	no	—
137	C₂×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
138	C₂²×C₈	—	3	1	no	—
139	C₂²×C₈	—	3	1	no	—
140	C₂²×C₈	—	3	1	no	—
141	C₂²×C₈	C₂×D₃	1	1	yes	characteristic, complemented
142	C₄×D₄	—	3	1	no	—
143	C₄×D₄	—	3	1	no	—
144	C₄×D₄	—	3	1	no	—
145	C₄×D₄	—	3	1	no	—
146	C₄×D₄	—	3	1	no	—
147	C₄×D₄	—	3	1	no	—
148	C₄×D₄	—	3	1	no	—
149	C₄×D₄	C₂×D₃	1	1	yes	characteristic
150	C₂×C₄⋊C₄	—	3	1	no	—
151	C₂×C₂²⋊C₄	—	3	1	no	—
152	C₂×C₂²⋊C₄	—	3	1	no	—
153	C₂×C₄²	—	3	1	no	—
154	C₄⋊C₈	—	3	1	no	—
155	C₄⋊C₈	—	3	1	no	—
156	C₄⋊C₈	—	3	1	no	—
157	C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
158	C₂²⋊C₈	—	3	1	no	—
159	C₂²⋊C₈	—	3	1	no	—
160	C₂²⋊C₈	—	3	1	no	—
161	C₂²⋊C₈	—	3	1	no	—
162	C₂²⋊C₈	—	3	1	no	—
163	C₂²⋊C₈	—	3	1	no	—
164	C₂²⋊C₈	—	3	1	no	—
165	C₂²⋊C₈	—	3	1	no	—
166	C₂²⋊C₈	—	3	1	no	—
167	C₂²⋊C₈	—	3	1	no	—
168	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
169	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
170	#97	—	3	1	no	—
171	#97	C₂×D₃	1	1	yes	characteristic, complemented
172	C₄×C₈	—	3	1	no	—
173	C₄×C₈	—	3	1	no	—
174	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
175	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×D₃	—	2	2	no	—
177	C₂²×D₃	—	2	2	no	—
178	C₂²×D₃	—	2	2	no	—
179	C₂²×D₃	—	2	2	no	—
180	C₂²×D₃	—	4	1	no	—
181	C₂²×D₃	—	4	1	no	—
182	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
183	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
184	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
185	C₃×D₄	—	2	2	no	—
186	C₂×C₃×C₄	—	2	1	no	—
187	C₂×C₃×C₄	—	2	1	no	—
188	C₂×C₃×C₄	—	2	1	no	—
189	C₂×C₃×C₄	—	2	1	no	—
190	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
195	#67	—	2	2	no	—
196	#67	M₁₆	1	4	yes	complemented
197	C₂×Dic₃	—	4	1	no	—
198	C₂×Dic₃	—	4	1	no	—
199	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
202	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
204	D₁₂	—	2	2	no	—
205	C₄×D₃	—	2	2	no	—
206	C₄×D₃	—	2	1	no	—
207	C₄×D₃	—	2	1	no	—
208	C₄×D₃	—	2	1	no	—
209	C₄×D₃	—	2	1	no	—
210	C₄×D₃	—	2	1	no	—
211	C₄×D₃	—	2	1	no	—
212	C₄×D₃	—	2	2	no	—
213	C₄×D₃	—	4	1	no	—
214	C₄×D₃	—	4	1	no	—
215	C₄×D₃	—	4	1	no	—
216	C₄×D₃	—	4	1	no	—
217	C₃×C₈	—	2	1	no	—
218	C₃×C₈	—	2	1	no	—
219	C₃×C₈	—	2	1	no	—
220	C₃×C₈	—	2	1	no	—
221	C₃⋊C₈	—	2	1	no	—
222	C₃⋊C₈	—	2	1	no	—
223	C₃⋊C₈	—	2	1	no	—
224	C₃⋊C₈	—	2	1	no	—
225	C₂⁴	—	3	1	no	—
226	C₂⁴	—	3	1	no	—
227	C₂×D₄	—	3	1	no	—
228	C₂×D₄	—	3	1	no	—
229	C₂×D₄	—	3	1	no	—
230	C₂×D₄	—	6	4	no	—
231	C₂×D₄	C₄×D₃	1	1	yes	characteristic
232	C₂²×C₄	—	3	1	no	—
233	C₂²×C₄	—	3	1	no	—
234	C₂²×C₄	—	3	1	no	—
235	C₂²×C₄	—	3	1	no	—
236	C₂²×C₄	—	3	1	no	—
237	C₂²×C₄	—	3	1	no	—
238	C₂²×C₄	—	3	1	no	—
239	C₂²×C₄	—	3	1	no	—
240	C₂²×C₄	—	3	1	no	—
241	C₂²×C₄	—	3	1	no	—
242	C₂²×C₄	—	3	1	no	—
243	C₂²×C₄	—	12	1	no	—
244	C₂²×C₄	—	12	1	no	—
245	C₂²×C₄	—	12	1	no	—
246	C₂²×C₄	—	12	1	no	—
247	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
248	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
249	M₁₆	—	4	1	no	—
250	M₁₆	—	12	1	no	—
251	M₁₆	—	12	1	no	—
252	M₁₆	—	12	1	no	—
253	C₂×C₈	—	3	1	no	—
254	C₂×C₈	—	3	1	no	—
255	C₂×C₈	—	3	1	no	—
256	C₂×C₈	—	3	1	no	—
257	C₂×C₈	—	4	1	no	—
258	C₂×C₈	—	12	1	no	—
259	C₂×C₈	—	12	1	no	—
260	C₂×C₈	—	12	1	no	—
261	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
262	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
263	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
264	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
265	C₄⋊C₄	—	3	1	no	—
266	C₄⋊C₄	—	3	1	no	—
267	C₄⋊C₄	—	3	1	no	—
268	C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
269	C₂²⋊C₄	—	3	1	no	—
270	C₂²⋊C₄	—	3	1	no	—
271	C₂²⋊C₄	—	3	1	no	—
272	C₂²⋊C₄	—	3	1	no	—
273	C₂²⋊C₄	—	3	1	no	—
274	C₂²⋊C₄	—	3	1	no	—
275	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
276	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
277	C₄²	—	3	1	no	—
278	C₄²	—	3	1	no	—
279	C₄²	—	3	1	no	—
280	C₄²	C₂²×D₃	1	1	yes	characteristic
281	C₂²×C₃	—	2	1	no	—
282	C₂²×C₃	—	2	1	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	C₂×M₁₆	1	2	yes	—
287	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
288	C₂×D₃	—	2	1	no	—
289	C₂×D₃	—	2	1	no	—
290	C₂×D₃	—	2	1	no	—
291	C₂×D₃	—	2	1	no	—
292	C₂×D₃	—	2	1	no	—
293	C₂×D₃	—	2	1	no	—
294	C₂×D₃	—	2	1	no	—
295	C₂×D₃	—	4	4	no	—
296	C₂×D₃	—	4	4	no	—
297	C₂×D₃	C₂×M₁₆	1	2	yes	—
298	C₂×D₃	#131	1	2	yes	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
304	C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
305	Dic₃	—	2	1	no	—
306	Dic₃	—	2	1	no	—
307	Dic₃	—	2	1	no	—
308	Dic₃	—	2	1	no	—
309	Dic₃	C₂×M₁₆	1	2	yes	—
310	C₂³	—	3	1	no	—
311	C₂³	—	3	1	no	—
312	C₂³	—	3	1	no	—
313	C₂³	—	6	2	no	—
314	C₂³	—	6	2	no	—
315	C₂³	—	6	2	no	—
316	C₂³	—	6	2	no	—
317	C₂³	—	12	1	no	—
318	C₂³	—	12	1	no	—
319	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
320	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
321	D₄	—	2	2	no	—
322	D₄	—	3	4	no	—
323	D₄	—	6	2	no	—
324	D₄	—	6	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	3	1	no	—
330	C₂×C₄	—	3	1	no	—
331	C₂×C₄	—	3	1	no	—
332	C₂×C₄	—	3	1	no	—
333	C₂×C₄	—	3	1	no	—
334	C₂×C₄	—	6	2	no	—
335	C₂×C₄	—	6	2	no	—
336	C₂×C₄	—	6	1	no	—
337	C₂×C₄	—	6	1	no	—
338	C₂×C₄	—	6	1	no	—
339	C₂×C₄	—	6	1	no	—
340	C₂×C₄	—	6	1	no	—
341	C₂×C₄	—	6	1	no	—
342	C₂×C₄	—	12	1	no	—
343	C₂×C₄	—	12	1	no	—
344	C₂×C₄	—	12	1	no	—
345	C₂×C₄	—	12	1	no	—
346	C₂×C₄	—	12	1	no	—
347	C₂×C₄	—	12	1	no	—
348	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
352	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	6	1	no	—
358	C₈	—	6	1	no	—
359	C₈	—	6	1	no	—
360	C₈	—	6	1	no	—
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	4	1	no	—
363	C₂×C₃	#518	1	1	yes	characteristic
364	C₂×C₃	C₂²×M₁₆	1	1	yes	characteristic
365	C₂×C₃	C₂×#131	1	1	yes	characteristic
366	D₃	—	2	2	no	—
367	D₃	—	2	2	no	—
368	D₃	—	4	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	3	2	no	—
375	C₂²	—	3	2	no	—
376	C₂²	—	6	1	no	—
377	C₂²	—	6	1	no	—
378	C₂²	—	6	1	no	—
379	C₂²	—	6	1	no	—
380	C₂²	—	6	1	no	—
381	C₂²	—	6	1	no	—
382	C₂²	—	6	1	no	—
383	C₂²	—	12	4	no	—
384	C₂²	—	12	4	no	—
385	C₂²	D₃×M₁₆	1	2	yes	—
386	C₂²	C₂²×C₄×D₃	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	3	2	no	—
392	C₄	—	6	1	no	—
393	C₄	—	6	1	no	—
394	C₄	—	6	1	no	—
395	C₄	—	6	1	no	—
396	C₄	#1004	1	1	yes	characteristic
397	C₄	#1009	1	1	yes	characteristic
398	C₃	#2974	1	1	yes	characteristic, complemented, Sylow
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	6	2	no	—
402	C₂	—	6	2	no	—
403	C₂	—	12	1	no	—
404	C₂	#5545	1	1	yes	characteristic
405	C₂	C₂×D₃×M₁₆	1	1	yes	characteristic
406	C₂	D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₄
Fitting	C₃×#435	C₂
prime radical	C₂×D₃×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#435	D₃
hypocenter	C₃	#2974
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. C₃×#435	C₂	semidirect
3. #5128	C₂	semidirect
4. #5126	C₂	semidirect
5. C₈×#67	C₂	semidirect
6. C₂×(C₂×D₃)⋊C₈	C₂	semidirect
7. #5011	C₂	semidirect
8. #4836	C₂	semidirect
9. #4833	C₂	semidirect
10. #4729	C₂	semidirect
11. #4726	C₂	semidirect
12. #67⋊C₈	C₂	semidirect
13. D₃×C₂²⋊C₈	C₂	semidirect
14. #4706	C₂	semidirect
15. #4705	C₂	semidirect
20. C₂×C₃×M₁₆	C₂²	semidirect
21. C₂²×C₃×C₈	C₂²	semidirect
26. C₂×#208	C₂²	semidirect
27. C₂²×C₃⋊C₈	C₂²	semidirect
28. C₂×ΓL(1,𝔽₂₅)	C₂²	semidirect
29. C₂×ΓL(1,𝔽₂₅)	C₂²	semidirect
30. C₂×D₃×C₈	C₂²	semidirect
31. C₂×D₃×C₈	C₂²	semidirect
40. C₃×C₄⋊C₈	C₂²	semidirect
41. C₃×C₂²⋊C₈	C₂²	semidirect
42. C₃×C₂²⋊C₈	C₂²	semidirect
43. C₃×#97	C₂²	semidirect
44. #830	C₂²	semidirect
45. #830	C₂²	semidirect
50. (C₂×D₃)⋊C₈	C₂²	semidirect
51. (C₂×D₃)⋊C₈	C₂²	semidirect
52. (C₂×D₃)⋊C₈	C₂²	semidirect
53. (C₂×D₃)⋊C₈	C₂²	semidirect
54. Dic₃⋊C₈	C₂²	semidirect
55. Dic₃⋊C₈	C₂²	semidirect
56. C₈×Dic₃	C₂²	semidirect
57. C₈×Dic₃	C₂²	semidirect
58. C₄⋊(C₃⋊C₈)	C₂²	semidirect
59. #803	C₂²	semidirect
66. #435	D₃	semidirect
137. C₂×M₁₆	C₂×D₃	semidirect
141. C₂²×C₈	C₂×D₃	semidirect
157. C₄⋊C₈	C₂×D₃	semidirect
168. C₂²⋊C₈	C₂×D₃	semidirect
169. C₂²⋊C₈	C₂×D₃	semidirect
171. #97	C₂×D₃	semidirect
196. #67	M₁₆	semidirect
398. C₃	#2974	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₃×D₄	2
C₃×#435	2
#5128	2
#5126	2
C₈×#67	2
C₂×(C₂×D₃)⋊C₈	2
#5011	2
#4836	2
#4833	2
#4729	2
#4726	2
#67⋊C₈	2
D₃×C₂²⋊C₈	2
#4706	2
#4705	2
#2974	3