Subgroups — #30827294

Order 17152.

652 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569228	C₂	1	2	yes	maximal, complemented
2	C₄×#14524066	C₂	1	1	yes	maximal, characteristic
3	#22559095	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559093	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559052	C₂	1	2	yes	maximal, complemented
6	#22559049	C₂	1	2	yes	maximal, complemented
7	Q₁₆×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558971	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558642	C₂	1	2	yes	maximal, complemented
10	C₈×#11761611	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524066	C₄	1	1	yes	characteristic
13	C₄×#11761629	C₂²	1	2	yes	—
14	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	—
15	Q₁₆×Dic₆₇	C₄	1	1	yes	characteristic
16	C₄×#11761615	C₂²	1	2	yes	—
17	#16863481	C₄	1	2	yes	—
18	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
19	#16863478	C₄	1	1	yes	characteristic
20	#16863475	—	2	2	no	—
21	#16863475	C₂²	1	2	yes	—
22	#16863473	—	2	2	no	—
23	#16863473	C₂²	1	2	yes	—
24	#16863452	—	2	2	no	—
25	#16863452	C₂²	1	2	yes	—
26	#16863447	C₂²	1	1	yes	characteristic
27	#16863433	C₄	1	1	yes	characteristic
28	#16863391	C₄	1	2	yes	—
29	C₄×#11761611	—	2	2	no	—
30	C₄×#11761611	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
32	#16863149	C₂²	1	1	yes	characteristic
33	#16863146	C₂²	1	2	yes	—
34	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
35	#16863125	C₂²	1	2	yes	—
36	#16863123	C₂²	1	2	yes	—
37	#16863118	C₂²	1	1	yes	characteristic
38	#16863117	C₂²	1	1	yes	characteristic
39	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
42	#335×C₆₇	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#11761629	C₂×C₄	1	2	yes	—
46	#14524066	—	2	4	no	—
47	C₂×#11761615	C₂×C₄	1	2	yes	—
48	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
49	C₂×#11761611	—	2	2	no	—
50	C₂×#11761611	—	2	2	no	—
51	C₂×#11761611	D₄	1	1	yes	characteristic
52	C₂×#11761611	D₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
55	Q₈×Dic₆₇	C₂×C₄	1	2	yes	—
56	C₄×D₂₆₈	—	2	2	no	—
57	C₄×D₂₆₈	C₂³	1	2	yes	—
58	#14524005	—	2	2	no	—
59	#14524005	C₂×C₄	1	2	yes	—
60	#14524001	—	2	2	no	—
61	#14524001	C₂×C₄	1	2	yes	—
62	C₄²×D₆₇	—	2	2	no	—
63	C₄²×D₆₇	C₂³	1	1	yes	characteristic
64	#14523977	C₂×C₄	1	1	yes	characteristic
65	#14523974	C₂×C₄	1	2	yes	—
66	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
67	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
68	Dic₆₇⋊C₈	—	2	1	no	—
69	#14523967	C₂×C₄	1	2	yes	—
70	#14523965	C₂×C₄	1	2	yes	—
71	#14523963	C₂×C₄	1	2	yes	—
72	(C₂×D₆₇)⋊C₈	—	2	2	no	—
73	(C₂×D₆₇)⋊C₈	—	2	1	no	—
74	(C₂×D₆₇)⋊C₈	—	2	2	no	—
75	(C₂×D₆₇)⋊C₈	—	2	2	no	—
76	#14523953	—	2	2	no	—
77	#14523953	D₄	1	1	yes	characteristic
78	#14523953	D₄	1	1	yes	characteristic
79	C₄×C₆₇⋊C₈	—	2	2	no	—
80	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
87	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₆₇	—	2	2	no	—
89	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
90	#103×C₆₇	C₂×C₄	1	2	yes	—
91	C₄×C₈×C₆₇	—	2	2	no	—
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	#11761629	—	2	4	no	—
96	#11761629	—	4	2	no	—
97	C₂×D₂₆₈	—	2	2	no	—
98	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
99	C₂×C₄×D₆₇	—	2	2	no	—
100	C₂×C₄×D₆₇	—	2	2	no	—
101	C₂×C₄×D₆₇	—	2	2	no	—
102	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
105	#11761615	—	2	4	no	—
106	D₅₃₆	—	2	2	no	—
107	#11761611	—	2	2	no	—
108	#11761611	—	2	2	no	—
109	#11761611	—	4	4	no	—
110	#11761611	—	4	4	no	—
111	C₂×C₆₇⋊C₈	—	2	2	no	—
112	C₂×C₆₇⋊C₈	—	2	1	no	—
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
116	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
117	C₈×D₆₇	—	2	2	no	—
118	C₈×D₆₇	—	4	1	no	—
119	C₄⋊Dic₆₇	—	2	2	no	—
120	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
121	(C₂×D₆₇)⋊C₄	—	2	2	no	—
122	(C₂×D₆₇)⋊C₄	—	2	2	no	—
123	(C₂×D₆₇)⋊C₄	—	2	2	no	—
124	C₄×Dic₆₇	—	2	2	no	—
125	C₄×Dic₆₇	—	2	2	no	—
126	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₆₇	#41	1	1	yes	characteristic
129	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
130	Q₁₆×C₆₇	M₁₆	1	4	yes	complemented
131	C₂×C₈×C₆₇	—	2	2	no	—
132	C₂×C₈×C₆₇	—	2	1	no	—
133	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₆₇	—	2	2	no	—
138	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₆₇	—	2	2	no	—
140	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
141	C₂²×D₆₇	—	2	2	no	—
142	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
143	Q₈×C₆₇	—	2	2	no	—
144	Q₈×C₆₇	C₂×M₁₆	1	4	yes	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	2	2	no	—
147	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂×Dic₆₇	—	2	2	no	—
151	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
154	D₂₆₈	—	2	2	no	—
155	D₂₆₈	—	2	2	no	—
156	D₂₆₈	—	4	4	no	—
157	C₄×D₆₇	—	2	1	no	—
158	C₄×D₆₇	—	2	1	no	—
159	C₄×D₆₇	—	2	1	no	—
160	C₄×D₆₇	—	2	1	no	—
161	C₄×D₆₇	—	4	1	no	—
162	C₄×D₆₇	—	4	4	no	—
163	C₄×D₆₇	—	4	2	no	—
164	C₄×D₆₇	—	4	2	no	—
165	C₄×D₆₇	—	8	2	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	2	1	no	—
168	C₈×C₆₇	—	4	1	no	—
169	C₈×C₆₇	—	4	2	no	—
170	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
171	C₈×C₆₇	#135	1	2	yes	complemented
172	C₆₇⋊C₈	—	2	1	no	—
173	C₆₇⋊C₈	—	2	1	no	—
174	C₆₇⋊C₈	—	2	1	no	—
175	C₆₇⋊C₈	—	4	1	no	—
176	C₆₇⋊C₈	—	4	2	no	—
177	C₆₇⋊C₈	#135	1	2	yes	complemented
178	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂×D₆₇	—	2	1	no	—
180	C₂×D₆₇	—	2	1	no	—
181	C₂×D₆₇	—	2	1	no	—
182	C₂×D₆₇	—	4	2	no	—
183	C₂×D₆₇	—	4	2	no	—
184	C₂×D₆₇	—	4	2	no	—
185	C₄×C₆₇	—	2	4	no	—
186	C₄×C₆₇	—	2	1	no	—
187	C₄×C₆₇	—	4	2	no	—
188	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
189	C₄×C₆₇	#568	1	1	yes	characteristic
190	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
191	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
192	Dic₆₇	—	2	1	no	—
193	Dic₆₇	—	2	1	no	—
194	Dic₆₇	—	2	1	no	—
195	Dic₆₇	—	4	2	no	—
196	#18039	—	67	1	no	maximal, Sylow
197	C₂×C₆₇	D₄×M₁₆	1	1	yes	characteristic
198	C₂×C₆₇	C₄×#135	1	1	yes	characteristic
199	C₂×C₆₇	#2957	1	1	yes	characteristic
200	D₆₇	—	4	1	no	—
201	D₆₇	—	8	2	no	—
202	#2971	—	67	2	no	—
203	C₄×#135	—	67	1	no	—
204	#1589	—	67	1	no	—
205	#1589	—	67	1	no	—
206	#1583	—	67	2	no	—
207	#1583	—	67	2	no	—
208	C₈×Q₁₆	—	67	1	no	—
209	C₈×Q₁₆	D₆₇	1	1	yes	characteristic, complemented
210	#1568	—	67	1	no	—
211	#1488	—	67	2	no	—
212	C₈×M₁₆	—	67	1	no	—
213	C₆₇	#18039	1	1	yes	characteristic, complemented, Sylow
214	C₂×#135	—	67	1	no	—
215	C₄×#41	—	67	2	no	—
216	C₈×Q₈	—	67	2	no	—
217	C₈×Q₈	C₂×D₆₇	1	2	yes	—
218	C₄×Q₁₆	—	67	1	no	—
219	C₄×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
220	C₄×SD₁₆	—	67	2	no	—
221	C₄×SD₁₆	—	67	2	no	—
222	C₄×D₈	—	67	1	no	—
223	C₄×D₈	—	67	1	no	—
224	#436	—	67	2	no	—
225	#436	—	67	2	no	—
226	#436	—	134	2	no	—
227	#436	—	134	2	no	—
228	#432	—	67	2	no	—
229	#432	—	134	2	no	—
230	#431	—	67	1	no	—
231	#427	—	67	1	no	—
232	#416	—	67	2	no	—
233	C₄×M₁₆	—	67	1	no	—
234	C₄×M₁₆	—	134	2	no	—
235	C₂×C₄×C₈	—	67	1	no	—
236	#335	—	67	1	no	—
237	#335	C₂×D₆₇	1	1	yes	characteristic
238	#334	—	67	2	no	—
239	Q₈⋊C₈	—	67	2	no	—
240	Q₈⋊C₈	C₂×D₆₇	1	2	yes	—
241	D₄⋊C₈	—	67	2	no	—
242	D₄⋊C₈	—	67	2	no	—
243	#322	—	67	1	no	—
244	#322	—	67	1	no	—
245	C₈²	—	67	1	no	—
246	C₈²	C₂×D₆₇	1	1	yes	characteristic
247	C₂×#41	—	67	2	no	—
248	#135	—	134	4	no	—
249	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic
250	C₂×SD₁₆	—	67	2	no	—
251	C₂×D₈	—	67	1	no	—
252	C₂×M₁₆	—	67	1	no	—
253	C₂×M₁₆	—	67	1	no	—
254	C₂×M₁₆	—	134	2	no	—
255	C₂×M₁₆	—	134	2	no	—
256	C₂²×C₈	—	67	1	no	—
257	C₂²×C₈	—	67	1	no	—
258	C₄×Q₈	—	67	2	no	—
259	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
260	C₄×D₄	—	67	2	no	—
261	C₄×D₄	—	67	2	no	—
262	C₄×D₄	—	134	2	no	—
263	C₄×D₄	—	134	2	no	—
264	#117	—	67	2	no	—
265	#117	—	134	2	no	—
266	C₂×C₄²	—	67	1	no	—
267	C₂×C₄²	—	134	2	no	—
268	#107	—	67	1	no	—
269	#107	C₄×D₆₇	1	1	yes	characteristic
270	#106	—	67	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	67	2	no	—
273	C₄⋊C₈	—	134	2	no	—
274	C₄⋊C₈	—	134	1	no	—
275	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
276	#103	—	67	2	no	—
277	#103	C₄×D₆₇	1	2	yes	—
278	#102	—	67	2	no	—
279	#102	—	67	2	no	—
280	C₂²⋊C₈	—	134	2	no	—
281	C₂²⋊C₈	—	134	1	no	—
282	C₂²⋊C₈	—	134	2	no	—
283	C₂²⋊C₈	—	134	2	no	—
284	#97	—	67	1	no	—
285	#97	—	67	1	no	—
286	#97	—	134	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	67	1	no	—
289	C₄×C₈	—	67	1	no	—
290	C₄×C₈	—	67	1	no	—
291	C₄×C₈	—	67	1	no	—
292	C₄×C₈	—	67	1	no	—
293	C₄×C₈	—	134	2	no	—
294	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
295	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
296	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
297	#41	—	268	2	no	—
298	#41	—	134	4	no	—
299	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
300	C₂×D₄	—	67	2	no	—
301	C₂×D₄	—	134	2	no	—
302	C₂²×C₄	—	67	1	no	—
303	C₂²×C₄	—	67	1	no	—
304	C₂²×C₄	—	67	1	no	—
305	C₂²×C₄	—	134	2	no	—
306	C₂²×C₄	—	134	2	no	—
307	C₂²×C₄	—	134	2	no	—
308	Q₁₆	#11761611	1	4	yes	complemented
309	SD₁₆	—	134	4	no	—
310	D₈	—	134	2	no	—
311	M₁₆	—	268	4	no	—
312	M₁₆	—	268	4	no	—
313	M₁₆	—	134	2	no	—
314	M₁₆	—	134	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	268	1	no	—
318	C₂×C₈	—	67	1	no	—
319	C₂×C₈	—	67	1	no	—
320	C₂×C₈	—	67	1	no	—
321	C₂×C₈	—	67	1	no	—
322	C₂×C₈	—	134	2	no	—
323	C₂×C₈	—	134	1	no	—
324	C₂×C₈	—	134	2	no	—
325	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
326	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
327	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
328	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	67	2	no	—
331	C₄⋊C₄	—	134	2	no	—
332	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
333	C₂²⋊C₄	—	134	2	no	—
334	C₂²⋊C₄	—	134	2	no	—
335	C₂²⋊C₄	—	134	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	67	1	no	—
338	C₄²	—	67	1	no	—
339	C₄²	—	67	1	no	—
340	C₄²	—	134	2	no	—
341	C₄²	—	134	2	no	—
342	C₄²	C₂³×D₆₇	1	1	yes	characteristic
343	C₂³	—	67	1	no	—
344	C₂³	—	134	2	no	—
345	Q₈	—	2	2	no	—
346	Q₈	C₂×#11761611	1	4	yes	—
347	D₄	—	268	4	no	—
348	D₄	—	134	2	no	—
349	D₄	—	134	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	268	4	no	—
353	C₂×C₄	—	268	1	no	—
354	C₂×C₄	—	268	2	no	—
355	C₂×C₄	—	268	2	no	—
356	C₂×C₄	—	536	2	no	—
357	C₂×C₄	—	67	1	no	—
358	C₂×C₄	—	67	1	no	—
359	C₂×C₄	—	67	1	no	—
360	C₂×C₄	—	134	2	no	—
361	C₂×C₄	—	134	1	no	—
362	C₂×C₄	—	134	1	no	—
363	C₂×C₄	—	134	1	no	—
364	C₂×C₄	—	134	1	no	—
365	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
366	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
367	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	4	1	no	—
371	C₈	—	4	2	no	—
372	C₈	—	268	1	no	—
373	C₈	—	268	2	no	—
374	C₈	—	67	2	no	—
375	C₈	—	134	1	no	—
376	C₈	—	134	1	no	—
377	C₈	—	134	1	no	—
378	C₈	C₂×#11761611	1	2	yes	—
379	C₈	#14524066	1	2	yes	complemented
380	C₂²	—	268	2	no	—
381	C₂²	—	268	2	no	—
382	C₂²	—	268	2	no	—
383	C₂²	—	134	1	no	—
384	C₂²	—	134	1	no	—
385	C₂²	—	134	1	no	—
386	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	4	no	—
389	C₄	—	4	2	no	—
390	C₄	—	268	2	no	—
391	C₄	—	134	1	no	—
392	C₄	—	134	1	no	—
393	C₄	—	134	1	no	—
394	C₄	C₂²×#11761611	1	1	yes	characteristic
395	C₄	#16864161	1	1	yes	characteristic
396	C₄	#135×D₆₇	1	1	yes	characteristic
397	C₄	C₂×#14524066	1	1	yes	characteristic
398	C₂	—	268	1	no	—
399	C₂	—	536	2	no	—
400	C₂	D₄×#11761611	1	1	yes	characteristic
401	C₂	C₄×#14524066	1	1	yes	characteristic
402	C₂	#22569121	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×Q₁₆×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524066	C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₈×Q₁₆	D₆₇
hypocenter	C₆₇	#18039
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
1. #22569228	C₂	semidirect
3. #22559095	C₂	semidirect
4. #22559093	C₂	semidirect
5. #22559052	C₂	semidirect
6. #22559049	C₂	semidirect
7. Q₁₆×C₆₇⋊C₈	C₂	semidirect
8. #22558971	C₂	semidirect
9. #22558642	C₂	semidirect
10. C₈×#11761611	C₂	semidirect
11. C₈×Q₁₆×C₆₇	C₂	semidirect
130. Q₁₆×C₆₇	M₁₆	semidirect
171. C₈×C₆₇	#135	semidirect
177. C₆₇⋊C₈	#135	semidirect
209. C₈×Q₁₆	D₆₇	semidirect
213. C₆₇	#18039	semidirect
308. Q₁₆	#11761611	semidirect
379. C₈	#14524066	semidirect

Maximal subgroups

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

subgroup	index
#22569228	2
C₄×#14524066	2
#22559095	2
#22559093	2
#22559052	2
#22559049	2
Q₁₆×C₆₇⋊C₈	2
#22558971	2
#22558642	2
C₈×#11761611	2
C₈×Q₁₆×C₆₇	2
#18039	67