Subgroups — #10689113

Order 768.

552 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4834	C₂	1	1	yes	maximal, characteristic
2	C₂×#4480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#4459	C₂	1	1	yes	maximal, characteristic
4	#69484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#809	C₂	1	1	yes	maximal, characteristic
6	C₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	#8845	—	3	1	no	maximal, Sylow
9	C₂²×D₃×C₈	—	2	1	no	—
10	C₂×C₄×D₁₂	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₃)⋊C₈	—	2	1	no	—
15	C₂×#809	C₄	1	1	yes	characteristic
16	C₂×#809	C₄	1	1	yes	characteristic
17	C₂×C₄⋊(C₃⋊C₈)	—	2	1	no	—
18	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	#4834	—	2	2	no	—
22	#4834	—	2	2	no	—
23	#4529	C₄	1	1	yes	characteristic
24	#4529	C₄	1	1	yes	characteristic
25	#4524	—	2	1	no	—
26	#4480	—	2	2	no	—
27	#4459	—	2	2	no	—
28	C₂×C₈×D₄	—	3	1	no	—
29	#1939	—	3	1	no	—
30	C₄×#102	—	3	1	no	—
31	C₂×#334	—	3	1	no	—
32	C₂×D₄⋊C₈	—	3	1	no	—
33	#1279	D₃	1	1	yes	characteristic, complemented
34	#1273	—	3	1	no	—
35	C₂²×D₁₂	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₃	—	2	1	no	—
37	C₂²×C₃×C₈	—	2	1	no	—
38	C₂²×C₃×C₈	—	2	1	no	—
39	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄²	—	2	1	no	—
42	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
43	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
44	C₂×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃⋊C₈	—	2	1	no	—
46	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃⋊C₈	D₄	1	1	yes	characteristic
49	C₂²×C₃⋊C₈	D₄	1	1	yes	characteristic
50	C₂×D₃×C₈	—	2	4	no	—
51	C₂×D₃×C₈	—	4	2	no	—
52	C₂×D₃×C₈	—	4	2	no	—
53	C₄×D₁₂	—	2	1	no	—
54	C₄×D₁₂	—	2	1	no	—
55	C₄×D₁₂	D₄	1	2	yes	—
56	C₄×D₁₂	Q₈	1	2	yes	—
57	C₃×C₄⋊C₈	—	2	1	no	—
58	C₃×C₄⋊C₈	D₄	1	2	yes	—
59	C₃×C₄×C₈	—	2	1	no	—
60	C₃×C₄×C₈	—	2	1	no	—
61	C₃×#95	—	2	1	no	—
62	(C₂×D₃)⋊C₈	—	2	4	no	—
63	#809	—	2	2	no	—
64	#809	C₈	1	4	yes	complemented
65	C₄⋊(C₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₃⋊C₈)	—	2	1	no	—
67	C₄⋊(C₃⋊C₈)	—	4	2	no	—
68	C₄×C₃⋊C₈	—	2	1	no	—
69	C₄×C₃⋊C₈	—	2	1	no	—
70	C₄×C₃⋊C₈	—	2	1	no	—
71	C₄×C₃⋊C₈	—	2	1	no	—
72	C₂³×C₈	—	6	1	no	—
73	C₂×C₄×D₄	—	3	1	no	—
74	C₈×D₄	—	6	2	no	—
75	C₈×D₄	—	6	2	no	—
76	C₂×C₄⋊C₈	—	3	1	no	—
77	C₂×C₄⋊C₈	—	6	1	no	—
78	C₂×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
79	C₂×#102	—	3	1	no	—
80	C₂×#102	—	3	1	no	—
81	C₂×C₂²⋊C₈	—	6	1	no	—
82	C₂×C₄×C₈	—	3	1	no	—
83	C₂×C₄×C₈	—	3	1	no	—
84	C₂×C₄×C₈	C₂×D₃	1	1	yes	characteristic
85	C₄×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	#340	—	3	1	no	—
87	#340	—	3	1	no	—
88	#336	—	6	1	no	—
89	#334	—	6	2	no	—
90	D₄⋊C₈	—	6	2	no	—
91	C₂³×D₃	—	2	1	no	—
92	C₂²×C₃×C₄	—	2	1	no	—
93	C₂²×C₃×C₄	—	2	1	no	—
94	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₃×C₄	#41	1	1	yes	characteristic
97	C₂²×Dic₃	—	2	1	no	—
98	C₂×D₁₂	—	2	1	no	—
99	C₂×D₁₂	—	2	1	no	—
100	C₂×D₁₂	—	2	1	no	—
101	C₂×D₁₂	C₄⋊C₄	1	2	yes	—
102	C₂×D₁₂	C₂×C₈	1	2	yes	—
103	C₂×D₁₂	M₁₆	1	2	yes	—
104	C₂×C₄×D₃	—	2	2	no	—
105	C₂×C₄×D₃	—	2	2	no	—
106	C₂×C₄×D₃	—	4	1	no	—
107	C₂×C₄×D₃	—	4	1	no	—
108	C₂×C₄×D₃	—	4	1	no	—
109	C₂×C₄×D₃	—	4	1	no	—
110	C₂×C₃×C₈	—	2	2	no	—
111	C₂×C₃×C₈	—	2	2	no	—
112	C₂×C₃×C₈	—	4	1	no	—
113	C₂×C₃×C₈	—	4	1	no	—
114	C₂×C₃×C₈	—	4	1	no	—
115	C₂×C₃×C₈	—	4	1	no	—
116	C₃×C₄⋊C₄	—	2	1	no	—
117	C₃×C₄⋊C₄	—	2	1	no	—
118	C₃×C₄⋊C₄	—	2	1	no	—
119	C₃×C₄⋊C₄	C₂×C₈	1	2	yes	complemented
120	C₃×C₄²	—	4	1	no	—
121	C₃×C₄²	—	4	1	no	—
122	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
123	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
124	C₃×C₄²	C₂×Q₈	1	1	yes	characteristic
125	C₃×C₄²	#41	1	1	yes	characteristic
126	(C₂×D₃)⋊C₄	—	2	2	no	—
127	(C₂×D₃)⋊C₄	—	2	2	no	—
128	C₄⋊Dic₃	—	2	1	no	—
129	C₄⋊Dic₃	C₄⋊C₄	1	2	yes	—
130	C₂×C₃⋊C₈	—	2	1	no	—
131	C₂×C₃⋊C₈	—	2	1	no	—
132	C₂×C₃⋊C₈	—	2	1	no	—
133	C₂×C₃⋊C₈	—	2	1	no	—
134	C₂×C₃⋊C₈	—	2	1	no	—
135	C₂×C₃⋊C₈	—	2	1	no	—
136	C₂×C₃⋊C₈	—	2	1	no	—
137	C₂×C₃⋊C₈	—	2	1	no	—
138	C₂×C₃⋊C₈	—	2	1	no	—
139	C₂×C₃⋊C₈	—	2	1	no	—
140	C₂×C₃⋊C₈	—	4	1	no	—
141	C₂×C₃⋊C₈	—	4	1	no	—
142	C₂×C₃⋊C₈	—	4	1	no	—
143	C₂×C₃⋊C₈	C₂×C₈	1	2	yes	complemented
144	C₂×C₃⋊C₈	SD₁₆	1	2	yes	—
145	D₃×C₈	—	4	8	no	—
146	C₂²×D₄	—	3	1	no	—
147	C₂³×C₄	—	6	1	no	—
148	C₂²×C₈	—	2	1	no	—
149	C₂²×C₈	—	2	1	no	—
150	C₂²×C₈	—	3	1	no	—
151	C₂²×C₈	—	3	1	no	—
152	C₂²×C₈	—	3	1	no	—
153	C₂²×C₈	—	3	1	no	—
154	C₂²×C₈	—	6	4	no	—
155	C₂²×C₈	—	6	1	no	—
156	C₂²×C₈	—	12	2	no	—
157	C₂²×C₈	—	12	2	no	—
158	C₄×D₄	—	3	2	no	—
159	C₄×D₄	—	3	2	no	—
160	C₄×D₄	—	6	1	no	—
161	C₄×D₄	—	6	1	no	—
162	C₂×C₄⋊C₄	—	3	1	no	—
163	C₂×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
164	C₂×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
165	C₂×C₂²⋊C₄	—	6	1	no	—
166	C₂×C₄²	—	2	1	no	—
167	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
168	C₄⋊C₈	—	2	1	no	—
169	C₄⋊C₈	—	6	1	no	—
170	C₄⋊C₈	—	6	1	no	—
171	C₄⋊C₈	—	12	2	no	—
172	C₄⋊C₈	D₁₂	1	2	yes	—
173	#102	—	3	4	no	—
174	#102	—	6	2	no	—
175	C₂²⋊C₈	—	6	4	no	—
176	C₄×C₈	—	2	1	no	—
177	C₄×C₈	—	2	1	no	—
178	C₄×C₈	—	6	1	no	—
179	C₄×C₈	—	6	1	no	—
180	C₄×C₈	—	6	1	no	—
181	C₄×C₈	—	6	1	no	—
182	#95	—	2	1	no	—
183	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
184	C₂²×D₃	—	2	2	no	—
185	C₂²×D₃	—	2	2	no	—
186	C₂²×D₃	—	2	2	no	—
187	C₂²×D₃	—	4	1	no	—
188	C₂²×D₃	—	4	1	no	—
189	C₂²×D₃	—	4	1	no	—
190	C₂²×D₃	—	4	1	no	—
191	C₂×C₃×C₄	—	2	1	no	—
192	C₂×C₃×C₄	—	2	1	no	—
193	C₂×C₃×C₄	—	2	2	no	—
194	C₂×C₃×C₄	—	4	1	no	—
195	C₂×C₃×C₄	—	4	1	no	—
196	C₂×C₃×C₄	—	4	1	no	—
197	C₂×C₃×C₄	—	4	1	no	—
198	C₂×C₃×C₄	—	4	1	no	—
199	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
201	C₂×C₃×C₄	#120	1	1	yes	characteristic
202	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₃×C₄	#123	1	1	yes	characteristic
205	C₂×C₃×C₄	C₂²×C₈	1	1	yes	characteristic
206	C₂×C₃×C₄	C₂×M₁₆	1	1	yes	characteristic
207	C₂×C₃×C₄	#131	1	1	yes	characteristic
208	C₂×C₃×C₄	#131	1	1	yes	characteristic
209	C₂×C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
210	C₂×C₃×C₄	#135	1	1	yes	characteristic
211	C₂×C₃×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×C₃×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×Dic₃	—	2	2	no	—
214	C₂×Dic₃	—	4	1	no	—
215	C₂×Dic₃	—	4	1	no	—
216	D₁₂	—	2	2	no	—
217	D₁₂	—	2	2	no	—
218	D₁₂	—	2	2	no	—
219	D₁₂	C₄⋊C₈	1	4	yes	complemented
220	C₄×D₃	—	4	2	no	—
221	C₄×D₃	—	4	2	no	—
222	C₄×D₃	—	4	2	no	—
223	C₄×D₃	—	4	2	no	—
224	C₃×C₈	—	4	2	no	—
225	C₃×C₈	—	4	2	no	—
226	C₃⋊C₈	—	2	2	no	—
227	C₃⋊C₈	—	2	2	no	—
228	C₃⋊C₈	—	4	1	no	—
229	C₃⋊C₈	—	4	1	no	—
230	C₃⋊C₈	—	8	1	no	—
231	C₂⁴	—	6	1	no	—
232	C₂×D₄	—	3	2	no	—
233	C₂×D₄	—	3	2	no	—
234	C₂×D₄	—	3	2	no	—
235	C₂×D₄	—	6	1	no	—
236	C₂×D₄	—	6	1	no	—
237	C₂×D₄	—	6	1	no	—
238	C₂²×C₄	—	2	1	no	—
239	C₂²×C₄	—	2	1	no	—
240	C₂²×C₄	—	6	1	no	—
241	C₂²×C₄	—	6	2	no	—
242	C₂²×C₄	—	6	2	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	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂²×C₄	D₃×D₄	1	1	yes	characteristic
249	C₂²×C₄	#237	1	1	yes	characteristic
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	3	2	no	—
253	C₂×C₈	—	3	2	no	—
254	C₂×C₈	—	4	1	no	—
255	C₂×C₈	—	4	1	no	—
256	C₂×C₈	—	4	1	no	—
257	C₂×C₈	—	4	1	no	—
258	C₂×C₈	—	6	1	no	—
259	C₂×C₈	—	6	1	no	—
260	C₂×C₈	—	6	1	no	—
261	C₂×C₈	—	6	1	no	—
262	C₂×C₈	—	6	1	no	—
263	C₂×C₈	—	6	1	no	—
264	C₂×C₈	—	6	1	no	—
265	C₂×C₈	—	6	1	no	—
266	C₂×C₈	—	6	1	no	—
267	C₂×C₈	—	6	1	no	—
268	C₂×C₈	—	12	8	no	—
269	C₂×C₈	—	12	1	no	—
270	C₂×C₈	—	12	1	no	—
271	C₂×C₈	—	12	1	no	—
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	3	2	no	—
276	C₄⋊C₄	—	6	1	no	—
277	C₄⋊C₄	D₃×C₈	1	2	yes	complemented
278	C₂²⋊C₄	—	6	2	no	—
279	C₂²⋊C₄	—	6	2	no	—
280	C₄²	—	4	1	no	—
281	C₄²	—	4	1	no	—
282	C₄²	C₂×D₁₂	1	1	yes	characteristic
283	C₄²	#235	1	1	yes	characteristic
284	C₄²	D₃×D₄	1	1	yes	characteristic
285	C₄²	D₃×Q₈	1	1	yes	characteristic
286	C₂²×C₃	#385	1	1	yes	characteristic
287	C₂²×C₃	C₈×D₄	1	1	yes	characteristic
288	C₂²×C₃	#435	1	1	yes	characteristic
289	C₂²×C₃	C₄×SD₁₆	1	1	yes	characteristic
290	C₂²×C₃	#442	1	1	yes	characteristic
291	C₂²×C₃	#443	1	1	yes	characteristic
292	C₂²×C₃	#444	1	1	yes	characteristic
293	C₂×D₃	—	2	4	no	—
294	C₂×D₃	—	4	2	no	—
295	C₂×D₃	—	4	2	no	—
296	C₂×D₃	—	4	2	no	—
297	C₂×D₃	—	4	2	no	—
298	C₂×D₃	—	4	2	no	—
299	C₂×D₃	—	4	2	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	—	8	1	no	—
304	C₃×C₄	C₂×C₄⋊C₈	1	1	yes	characteristic
305	C₃×C₄	#424	1	1	yes	characteristic
306	C₃×C₄	C₈×D₄	1	1	yes	characteristic
307	C₃×C₄	#435	1	1	yes	characteristic
308	C₃×C₄	#449	1	1	yes	characteristic
309	C₃×C₄	#450	1	1	yes	characteristic
310	C₃×C₄	#476	1	1	yes	characteristic
311	C₃×C₄	#478	1	1	yes	characteristic
312	Dic₃	—	4	2	no	—
313	C₂³	—	6	2	no	—
314	C₂³	—	6	2	no	—
315	C₂³	—	6	2	no	—
316	C₂³	—	12	1	no	—
317	C₂³	—	12	1	no	—
318	C₂³	—	12	1	no	—
319	C₂³	—	12	1	no	—
320	C₂³	#67⋊C₄	1	1	yes	characteristic
321	D₄	—	3	4	no	—
322	D₄	—	6	2	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	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	6	2	no	—
334	C₂×C₄	—	12	1	no	—
335	C₂×C₄	—	12	1	no	—
336	C₂×C₄	—	12	2	no	—
337	C₂×C₄	—	12	2	no	—
338	C₂×C₄	—	12	2	no	—
339	C₂×C₄	—	12	2	no	—
340	C₂×C₄	C₄×D₁₂	1	1	yes	characteristic
341	C₂×C₄	#882	1	1	yes	characteristic
342	C₂×C₄	#883	1	1	yes	characteristic
343	C₂×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
344	C₂×C₄	#896	1	1	yes	characteristic
345	C₂×C₄	#897	1	1	yes	characteristic
346	C₂×C₄	C₂×D₃×C₈	1	1	yes	characteristic
347	C₂×C₄	#901	1	1	yes	characteristic
348	C₂×C₄	D₃×M₁₆	1	1	yes	characteristic
349	C₂×C₄	#907	1	1	yes	characteristic
350	C₂×C₄	#911	1	1	yes	characteristic
351	C₂×C₄	D₃×SD₁₆	1	1	yes	characteristic
352	C₂×C₄	#914	1	1	yes	characteristic
353	C₂×C₄	#919	1	1	yes	characteristic
354	C₈	—	4	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	6	2	no	—
357	C₈	—	6	2	no	—
358	C₈	—	12	1	no	—
359	C₈	—	12	1	no	—
360	C₈	—	24	1	no	—
361	C₂×C₃	C₈×SD₁₆	1	1	yes	characteristic
362	C₂×C₃	#1580	1	1	yes	characteristic
363	C₂×C₃	#1582	1	1	yes	characteristic
364	C₂×C₃	#1586	1	1	yes	characteristic
365	C₂×C₃	#1850	1	1	yes	characteristic
366	C₂×C₃	#1864	1	1	yes	characteristic
367	C₂×C₃	#1866	1	1	yes	characteristic
368	D₃	—	4	4	no	—
369	C₂²	—	6	4	no	—
370	C₂²	—	12	2	no	—
371	C₂²	—	12	2	no	—
372	C₂²	—	12	2	no	—
373	C₂²	—	12	2	no	—
374	C₂²	—	12	2	no	—
375	C₂²	—	12	2	no	—
376	C₂²	#4668	1	1	yes	characteristic
377	C₂²	#67⋊C₈	1	1	yes	characteristic
378	C₂²	#4728	1	1	yes	characteristic
379	C₂²	#4785	1	1	yes	characteristic
380	C₂²	#4788	1	1	yes	characteristic
381	C₂²	#4823	1	1	yes	characteristic
382	C₂²	#4824	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	12	2	no	—
388	C₄	C₈×D₁₂	1	1	yes	characteristic
389	C₄	#4706	1	1	yes	characteristic
390	C₄	#4776	1	1	yes	characteristic
391	C₄	#4810	1	1	yes	characteristic
392	C₄	D₃×C₄⋊C₈	1	1	yes	characteristic
393	C₄	#4839	1	1	yes	characteristic
394	C₄	#4870	1	1	yes	characteristic
395	C₄	#4891	1	1	yes	characteristic
396	C₃	#8845	1	1	yes	characteristic, complemented, Sylow
397	C₂	—	12	4	no	—
398	C₂	#68151	1	1	yes	characteristic
399	C₂	#68158	1	1	yes	characteristic
400	C₂	#68212	1	1	yes	characteristic
401	C₂	#68216	1	1	yes	characteristic
402	C₂	#68666	1	1	yes	characteristic
403	C₂	#68774	1	1	yes	characteristic
404	C₂	#68895	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₃
Fitting	C₃×#1279	C₂
socle	C₂³×C₃	C₄×D₄
prime radical	C₂²×D₁₂	C₂×C₄
cosocle	C₂×C₃×C₄²	C₂³
hypercenter	#1279	D₃
hypocenter	C₃	#8845
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. C₂×#4480	C₂	semidirect
4. #69484	C₂	semidirect
6. C₃×#1279	C₂	semidirect
7. C₃⋊#1273	C₂	semidirect
33. #1279	D₃	semidirect
64. #809	C₈	semidirect
119. C₃×C₄⋊C₄	C₂×C₈	semidirect
143. C₂×C₃⋊C₈	C₂×C₈	semidirect
219. D₁₂	C₄⋊C₈	semidirect
277. C₄⋊C₄	D₃×C₈	semidirect
396. C₃	#8845	semidirect

Maximal subgroups

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

subgroup	index
C₂×#4834	2
C₂×#4480	2
C₂×#4459	2
#69484	2
C₄×#809	2
C₃×#1279	2
C₃⋊#1273	2
#8845	3