Subgroups — #30838069

Order 17152.

802 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570205	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#22559571	C₂	1	2	yes	maximal, complemented
4	#22559561	C₂	1	2	yes	maximal, complemented
5	#22559547	C₂	1	4	yes	maximal, complemented
6	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558858	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₈×D₆₇	—	2	1	no	—
10	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
11	#16863707	—	2	2	no	—
12	#16863673	C₂²	1	4	yes	—
13	#16863588	C₂²	1	4	yes	—
14	#16863529	—	2	2	no	—
15	C₄×#11761613	—	2	4	no	—
16	C₈×D₂₆₈	—	2	1	no	—
17	C₈×D₂₆₈	—	2	1	no	—
18	C₈×D₂₆₈	C₂²	1	2	yes	—
19	C₈×D₂₆₈	C₂²	1	2	yes	—
20	#16863449	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
23	#16863149	C₂²	1	2	yes	complemented
24	#16863147	C₂²	1	2	yes	complemented
25	#16863142	C₂²	1	4	yes	complemented
26	#16863140	C₂²	1	4	yes	complemented
27	C₂×#135×C₆₇	—	2	1	no	—
28	C₂×#135×C₆₇	—	2	1	no	—
29	#532×C₆₇	C₂²	1	2	yes	—
30	#495×C₆₇	—	2	1	no	—
31	#495×C₆₇	—	2	1	no	—
32	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#492×C₆₇	C₂²	1	2	yes	complemented
35	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×D₂₆₈	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₆₇	—	2	1	no	—
38	C₂×#11761613	—	2	4	no	—
39	C₂²×C₆₇⋊C₈	—	2	1	no	—
40	C₂×C₈×D₆₇	—	2	2	no	—
41	C₂×C₈×D₆₇	—	2	2	no	—
42	C₂×C₈×D₆₇	—	4	4	no	—
43	C₄×D₂₆₈	—	2	1	no	—
44	C₄×D₂₆₈	—	2	1	no	—
45	C₄×D₂₆₈	D₄	1	2	yes	—
46	C₄×D₂₆₈	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
48	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
49	#14523976	—	2	4	no	—
50	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
52	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
53	#14523964	—	2	4	no	—
54	#14523963	—	2	4	no	—
55	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
56	(C₂×D₆₇)⋊C₈	—	2	2	no	—
57	(C₂×D₆₇)⋊C₈	—	2	2	no	—
58	C₄×C₆₇⋊C₈	—	2	2	no	—
59	C₂×#41×C₆₇	—	2	2	no	—
60	#135×C₆₇	—	4	4	no	—
61	#135×C₆₇	—	4	4	no	—
62	C₂×Q₁₆×C₆₇	—	2	1	no	—
63	C₂×Q₁₆×C₆₇	—	2	1	no	—
64	C₂×SD₁₆×C₆₇	—	2	2	no	—
65	C₂×SD₁₆×C₆₇	—	2	2	no	—
66	C₂×D₈×C₆₇	—	2	1	no	—
67	C₂×D₈×C₆₇	—	2	1	no	—
68	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
71	#127×C₆₇	C₂³	1	2	yes	—
72	#124×C₆₇	—	2	2	no	—
73	#121×C₆₇	—	2	2	no	—
74	#121×C₆₇	—	2	2	no	—
75	C₄×D₄×C₆₇	—	2	2	no	—
76	C₄×D₄×C₆₇	—	2	2	no	—
77	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
80	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂³×D₆₇	—	2	1	no	—
83	C₂×D₂₆₈	—	2	1	no	—
84	C₂×D₂₆₈	—	2	4	no	—
85	C₂×D₂₆₈	C₂×D₄	1	2	yes	—
86	C₂²×Dic₆₇	—	2	1	no	—
87	C₂×C₄×D₆₇	—	2	2	no	—
88	C₂×C₄×D₆₇	—	2	2	no	—
89	C₂×C₄×D₆₇	—	4	2	no	—
90	C₂×C₄×D₆₇	—	4	2	no	—
91	#11761613	—	4	8	no	—
92	C₂×C₆₇⋊C₈	—	2	4	no	—
93	C₂×C₆₇⋊C₈	—	2	2	no	—
94	C₂×C₆₇⋊C₈	—	4	2	no	—
95	C₈×D₆₇	—	4	4	no	—
96	C₈×D₆₇	—	4	4	no	—
97	C₄⋊Dic₆₇	—	2	1	no	—
98	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
99	(C₂×D₆₇)⋊C₄	—	2	2	no	—
100	(C₂×D₆₇)⋊C₄	—	2	2	no	—
101	#41×C₆₇	—	4	4	no	—
102	#41×C₆₇	—	4	4	no	—
103	C₂×Q₈×C₆₇	—	2	2	no	—
104	C₂×D₄×C₆₇	—	2	2	no	—
105	C₂×D₄×C₆₇	—	2	2	no	—
106	C₂×D₄×C₆₇	—	2	2	no	—
107	C₂×D₄×C₆₇	—	4	2	no	—
108	C₂²×C₄×C₆₇	—	4	2	no	—
109	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
112	Q₁₆×C₆₇	—	4	2	no	—
113	Q₁₆×C₆₇	—	4	2	no	—
114	SD₁₆×C₆₇	—	4	4	no	—
115	SD₁₆×C₆₇	—	4	4	no	—
116	D₈×C₆₇	—	4	2	no	—
117	D₈×C₆₇	—	4	2	no	—
118	C₂×C₈×C₆₇	—	2	2	no	—
119	C₂×C₈×C₆₇	D₈	1	4	yes	complemented
120	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₆₇	—	2	2	no	—
125	C₄⋊C₄×C₆₇	—	2	2	no	—
126	C₂²⋊C₄×C₆₇	—	4	2	no	—
127	C₂²⋊C₄×C₆₇	—	4	2	no	—
128	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₆₇	#41	1	1	yes	characteristic
131	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
132	C₂³×C₆₇	—	4	2	no	—
133	C₂³×C₆₇	#121	1	1	yes	characteristic
134	C₂²×D₆₇	—	2	4	no	—
135	C₂²×D₆₇	—	2	2	no	—
136	C₂²×D₆₇	—	4	2	no	—
137	C₂²×D₆₇	—	4	2	no	—
138	Q₈×C₆₇	—	4	2	no	—
139	Q₈×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	4	2	no	—
141	D₄×C₆₇	—	4	4	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	8	2	no	—
144	D₄×C₆₇	—	8	4	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	8	4	no	—
149	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
157	C₂×Dic₆₇	—	2	2	no	—
158	C₂×Dic₆₇	—	4	2	no	—
159	D₂₆₈	—	2	4	no	—
160	D₂₆₈	—	2	2	no	—
161	D₂₆₈	#135	1	4	yes	complemented
162	C₄×D₆₇	—	4	2	no	—
163	C₄×D₆₇	—	4	2	no	—
164	C₄×D₆₇	—	4	4	no	—
165	C₈×C₆₇	—	2	1	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	C₂×D₈	1	2	yes	—
168	C₈×C₆₇	C₂×D₈	1	2	yes	—
169	C₆₇⋊C₈	—	4	2	no	—
170	C₆₇⋊C₈	—	4	4	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	8	2	no	—
174	C₂²×C₆₇	—	8	2	no	—
175	C₂²×C₆₇	—	8	2	no	—
176	C₂²×C₆₇	#459	1	2	yes	—
177	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
178	C₂×D₆₇	—	2	4	no	—
179	C₂×D₆₇	—	4	8	no	—
180	C₂×D₆₇	—	4	2	no	—
181	C₂×D₆₇	—	4	2	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	8	2	no	—
186	C₄×C₆₇	#459	1	2	yes	—
187	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₆₇	C₂×#135	1	2	yes	—
189	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	Dic₆₇	—	4	2	no	—
191	#19101	—	67	1	no	maximal, Sylow
192	C₂×C₆₇	—	2	2	no	—
193	C₂×C₆₇	—	16	2	no	—
194	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
195	C₂×C₆₇	#3050	1	1	yes	characteristic
196	C₂×C₆₇	#3067	1	1	yes	characteristic
197	D₆₇	—	4	4	no	—
198	#3147	D₆₇	1	1	yes	characteristic, complemented
199	#3100	—	67	2	no	—
200	C₂×C₈×D₄	—	67	1	no	—
201	#1669	—	67	2	no	—
202	#1667	—	67	2	no	—
203	#1665	—	67	4	no	—
204	#1564	—	67	1	no	—
205	#1540	—	67	2	no	—
206	C₆₇	#19101	1	1	yes	characteristic, complemented, Sylow
207	C₂×#135	—	2	1	no	—
208	C₂×#135	—	2	1	no	—
209	C₂³×C₈	—	134	1	no	—
210	#532	C₂×D₆₇	1	2	yes	—
211	C₂×C₄×D₄	—	67	1	no	—
212	#495	—	2	1	no	—
213	#495	—	2	1	no	—
214	#494	C₂×D₆₇	1	1	yes	characteristic, complemented
215	#493	C₂×D₆₇	1	1	yes	characteristic, complemented
216	#492	C₂×D₆₇	1	2	yes	complemented
217	#480	—	134	2	no	—
218	#474	—	67	4	no	—
219	#459	—	67	4	no	—
220	#447	—	134	2	no	—
221	C₄×D₈	—	134	4	no	—
222	C₈×D₄	—	67	2	no	—
223	C₈×D₄	—	67	2	no	—
224	C₈×D₄	—	134	1	no	—
225	C₈×D₄	—	134	1	no	—
226	#431	—	67	2	no	—
227	C₂×C₄⋊C₈	—	67	1	no	—
228	C₂×C₂²⋊C₈	—	134	1	no	—
229	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
230	#335	—	67	2	no	—
231	#334	—	67	2	no	—
232	#332	—	67	4	no	—
233	#331	—	67	4	no	—
234	C₂×#41	—	2	2	no	—
235	C₂²×D₄	—	67	1	no	—
236	C₂³×C₄	—	134	1	no	—
237	#135	—	4	4	no	—
238	#135	—	4	4	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×D₈	—	2	1	no	—
244	C₂×D₈	—	2	1	no	—
245	C₂×D₈	—	134	4	no	—
246	C₂²×C₈	—	268	4	no	—
247	C₂²×C₈	—	134	1	no	—
248	C₂²×C₈	—	134	2	no	—
249	C₂²×C₈	—	134	2	no	—
250	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
251	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
252	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
253	#127	C₂²×D₆₇	1	2	yes	—
254	#124	—	2	2	no	—
255	#121	—	2	2	no	—
256	#121	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	67	2	no	—
260	C₄×D₄	—	67	2	no	—
261	C₄×D₄	—	134	1	no	—
262	C₄×D₄	—	134	1	no	—
263	C₂×C₄⋊C₄	—	67	1	no	—
264	C₂×C₂²⋊C₄	—	134	1	no	—
265	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
266	#107	—	134	4	no	—
267	C₄⋊C₈	—	67	2	no	—
268	C₄⋊C₈	—	67	4	no	—
269	C₄⋊C₈	—	134	1	no	—
270	#102	—	134	4	no	—
271	#102	—	134	4	no	—
272	C₂²⋊C₈	—	134	2	no	—
273	C₂²⋊C₈	—	134	2	no	—
274	C₂²⋊C₈	—	134	2	no	—
275	C₄×C₈	—	134	2	no	—
276	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
277	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
278	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
279	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
280	C₂⁴	—	134	1	no	—
281	#41	—	4	4	no	—
282	#41	—	4	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	67	2	no	—
289	C₂×D₄	—	134	4	no	—
290	C₂×D₄	—	134	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	268	2	no	—
293	C₂²×C₄	—	268	2	no	—
294	C₂²×C₄	—	134	1	no	—
295	C₂²×C₄	—	134	2	no	—
296	C₂²×C₄	—	134	2	no	—
297	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
299	C₂²×C₄	#11761627	1	1	yes	characteristic
300	Q₁₆	—	4	2	no	—
301	Q₁₆	—	4	2	no	—
302	SD₁₆	—	4	4	no	—
303	SD₁₆	—	4	4	no	—
304	D₈	—	4	2	no	—
305	D₈	—	4	2	no	—
306	D₈	—	268	8	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	268	2	no	—
309	C₂×C₈	—	268	4	no	—
310	C₂×C₈	—	268	4	no	—
311	C₂×C₈	—	134	4	no	—
312	C₂×C₈	—	134	2	no	—
313	C₂×C₈	#11761613	1	4	yes	complemented
314	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
315	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
316	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
317	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	67	2	no	—
321	C₄⋊C₄	—	134	1	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	134	2	no	—
325	C₂²⋊C₄	—	134	2	no	—
326	C₄²	D₄×D₆₇	1	1	yes	characteristic
327	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
328	C₄²	#11761627	1	1	yes	characteristic
329	C₄²	C₂³×D₆₇	1	1	yes	characteristic
330	C₂³	—	4	2	no	—
331	C₂³	—	268	2	no	—
332	C₂³	—	268	2	no	—
333	C₂³	—	134	4	no	—
334	C₂³	—	134	2	no	—
335	C₂³	#14524014	1	1	yes	characteristic
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	4	no	—
343	D₄	—	67	4	no	—
344	D₄	—	134	4	no	—
345	D₄	—	134	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	—	268	2	no	—
351	C₂×C₄	—	268	4	no	—
352	C₂×C₄	—	268	2	no	—
353	C₂×C₄	—	268	2	no	—
354	C₂×C₄	—	134	2	no	—
355	C₂×C₄	#14524014	1	1	yes	characteristic
356	C₂×C₄	#14524014	1	1	yes	characteristic
357	C₂×C₄	#14524014	1	1	yes	characteristic
358	C₂×C₄	C₂×#11761613	1	2	yes	—
359	C₂×C₄	#14524069	1	2	yes	—
360	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
362	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	268	2	no	—
366	C₈	—	268	4	no	—
367	C₈	C₂×#11761613	1	2	yes	—
368	C₈	C₂×#11761613	1	2	yes	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	268	8	no	—
375	C₂²	—	268	2	no	—
376	C₂²	—	268	2	no	—
377	C₂²	—	134	4	no	—
378	C₂²	#16863588	1	2	yes	—
379	C₂²	C₂×#14524014	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	8	2	no	—
384	C₄	—	268	2	no	—
385	C₄	#16863588	1	2	yes	—
386	C₄	C₂²×#11761613	1	1	yes	characteristic
387	C₄	#135×D₆₇	1	2	yes	—
388	C₄	C₂×#14524069	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	268	4	no	—
391	C₂	—	16	2	no	—
392	C₂	C₂×#16863588	1	1	yes	characteristic
393	C₂	#22569786	1	1	yes	characteristic
394	C₂	#22569925	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14524014
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#3147	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	#3147	D₆₇
hypocenter	C₆₇	#19101
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #22570205	C₂	semidirect
2. C₂×C₈×D₂₆₈	C₂	semidirect
3. #22559571	C₂	semidirect
4. #22559561	C₂	semidirect
5. #22559547	C₂	semidirect
6. #22558957	C₂	semidirect
7. #22558858	C₂	semidirect
8. C₆₇×#3147	C₂	semidirect
23. #16863149	C₂²	semidirect
24. #16863147	C₂²	semidirect
25. #16863142	C₂²	semidirect
26. #16863140	C₂²	semidirect
32. #494×C₆₇	C₂²	semidirect
33. #493×C₆₇	C₂²	semidirect
34. #492×C₆₇	C₂²	semidirect
119. C₂×C₈×C₆₇	D₈	semidirect
161. D₂₆₈	#135	semidirect
198. #3147	D₆₇	semidirect
206. C₆₇	#19101	semidirect
214. #494	C₂×D₆₇	semidirect
215. #493	C₂×D₆₇	semidirect
216. #492	C₂×D₆₇	semidirect
313. C₂×C₈	#11761613	semidirect

Maximal subgroups

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

subgroup	index
#22570205	2
C₂×C₈×D₂₆₈	2
#22559571	2
#22559561	2
#22559547	2
#22558957	2
#22558858	2
C₆₇×#3147	2
#19101	67