Subgroups — #30754685

Order 17152.

554 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	C₂×C₄×#11761615	C₂	1	1	yes	maximal, characteristic
2	#22561003	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863146	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊(C₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16863123	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11761615	C₄	1	1	yes	characteristic
9	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
10	C₄×#11761615	—	2	2	no	—
11	C₄×#11761615	—	2	2	no	—
12	C₂×#14523974	C₄	1	1	yes	characteristic
13	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#14523967	C₄	1	1	yes	characteristic
15	C₂×#14523963	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₆₇)⋊C₈	—	2	2	no	—
17	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
19	#16863146	—	2	2	no	—
20	Q₈⋊(C₆₇⋊C₈)	—	2	2	no	—
21	#16863123	—	2	2	no	—
22	C₈×C₆₇⋊C₈	—	2	2	no	—
23	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
26	#336×C₆₇	—	2	2	no	—
27	C₂²×D₂₆₈	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₆₇	—	2	1	no	—
29	C₂×#11761615	—	2	2	no	—
30	C₂×#11761615	—	2	2	no	—
31	C₂×#11761615	C₈	1	4	yes	complemented
32	C₂²×C₆₇⋊C₈	—	2	1	no	—
33	C₂²×C₆₇⋊C₈	—	2	1	no	—
34	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×D₂₆₈	—	2	1	no	—
37	C₄×D₂₆₈	—	2	1	no	—
38	C₄×D₂₆₈	—	2	1	no	—
39	C₄×D₂₆₈	—	2	1	no	—
40	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
41	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
42	#14523974	—	2	2	no	—
43	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
44	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
45	#14523967	—	2	2	no	—
46	#14523963	—	2	2	no	—
47	(C₂×D₆₇)⋊C₈	—	4	4	no	—
48	C₄×C₆₇⋊C₈	—	2	1	no	—
49	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
50	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
51	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
52	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	—	2	1	no	—
54	C₂²×C₈×C₆₇	D₄	1	2	yes	—
55	C₄×Q₈×C₆₇	—	2	1	no	—
56	C₄×Q₈×C₆₇	—	2	1	no	—
57	C₄×Q₈×C₆₇	—	2	1	no	—
58	C₄×Q₈×C₆₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	—	2	1	no	—
62	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₆₇	—	2	1	no	—
64	C₄⋊C₈×C₆₇	—	2	1	no	—
65	C₄×C₈×C₆₇	—	2	1	no	—
66	C₄×C₈×C₆₇	—	2	1	no	—
67	C₂³×D₆₇	—	2	1	no	—
68	C₂×D₂₆₈	—	2	1	no	—
69	C₂×D₂₆₈	—	2	1	no	—
70	C₂×D₂₆₈	—	2	1	no	—
71	C₂×D₂₆₈	—	2	1	no	—
72	C₂×D₂₆₈	—	2	1	no	—
73	C₂×D₂₆₈	C₂×C₈	1	2	yes	—
74	C₂²×Dic₆₇	—	2	1	no	—
75	C₂×C₄×D₆₇	—	4	1	no	—
76	C₂×C₄×D₆₇	—	4	1	no	—
77	C₂×C₄×D₆₇	—	4	2	no	—
78	C₂×C₄×D₆₇	—	4	2	no	—
79	#11761615	—	2	8	no	—
80	C₂×C₆₇⋊C₈	—	2	4	no	—
81	C₂×C₆₇⋊C₈	—	2	2	no	—
82	C₂×C₆₇⋊C₈	—	2	1	no	—
83	C₂×C₆₇⋊C₈	—	2	1	no	—
84	C₂×C₆₇⋊C₈	—	4	1	no	—
85	C₂×C₆₇⋊C₈	—	4	2	no	—
86	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	2	yes	—
87	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	2	yes	—
88	C₂×C₆₇⋊C₈	C₂×C₈	1	2	yes	—
89	C₂×C₆₇⋊C₈	M₁₆	1	2	yes	—
90	C₄⋊Dic₆₇	—	2	1	no	—
91	C₄⋊Dic₆₇	—	2	1	no	—
92	(C₂×D₆₇)⋊C₄	—	4	1	no	—
93	(C₂×D₆₇)⋊C₄	—	4	1	no	—
94	C₂×Q₈×C₆₇	—	2	1	no	—
95	C₂×Q₈×C₆₇	—	2	1	no	—
96	C₂×Q₈×C₆₇	—	2	1	no	—
97	C₂×Q₈×C₆₇	—	2	1	no	—
98	C₂×Q₈×C₆₇	—	2	1	no	—
99	C₂×Q₈×C₆₇	C₂×C₈	1	2	yes	—
100	C₂²×C₄×C₆₇	—	2	1	no	—
101	C₂²×C₄×C₆₇	—	2	1	no	—
102	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
105	C₂×C₈×C₆₇	—	2	2	no	—
106	C₂×C₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	—	4	1	no	—
108	C₂×C₈×C₆₇	—	4	2	no	—
109	C₂×C₈×C₆₇	SD₁₆	1	4	yes	complemented
110	C₄⋊C₄×C₆₇	—	2	1	no	—
111	C₄⋊C₄×C₆₇	—	2	1	no	—
112	C₄⋊C₄×C₆₇	—	4	1	no	—
113	C₄⋊C₄×C₆₇	—	4	1	no	—
114	C₄²×C₆₇	—	4	1	no	—
115	C₄²×C₆₇	—	4	1	no	—
116	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₆₇	#41	1	1	yes	characteristic
120	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
121	C₂²×D₆₇	—	2	2	no	—
122	C₂²×D₆₇	—	4	1	no	—
123	C₂²×D₆₇	—	4	1	no	—
124	C₂²×D₆₇	—	4	2	no	—
125	C₂²×D₆₇	—	4	2	no	—
126	Q₈×C₆₇	—	2	2	no	—
127	Q₈×C₆₇	—	2	2	no	—
128	Q₈×C₆₇	—	4	1	no	—
129	Q₈×C₆₇	—	4	1	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	4	1	no	—
133	C₂×C₄×C₆₇	—	4	1	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	2	no	—
136	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
139	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
140	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
141	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#131	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#131	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
147	C₂×C₄×C₆₇	#135	1	2	yes	—
148	C₂×Dic₆₇	—	4	1	no	—
149	C₂×Dic₆₇	—	4	2	no	—
150	D₂₆₈	—	2	2	no	—
151	D₂₆₈	—	2	2	no	—
152	D₂₆₈	—	4	1	no	—
153	D₂₆₈	—	4	1	no	—
154	C₄×D₆₇	—	8	2	no	—
155	C₄×D₆₇	—	8	1	no	—
156	C₄×D₆₇	—	8	1	no	—
157	C₈×C₆₇	—	2	4	no	—
158	C₈×C₆₇	—	8	1	no	—
159	C₆₇⋊C₈	—	2	4	no	—
160	C₆₇⋊C₈	—	2	2	no	—
161	C₆₇⋊C₈	—	8	1	no	—
162	C₆₇⋊C₈	C₂²⋊C₈	1	4	yes	complemented
163	C₂²×C₆₇	#390	1	1	yes	characteristic
164	C₂²×C₆₇	C₈×D₄	1	1	yes	characteristic
165	C₂²×C₆₇	#436	1	1	yes	characteristic
166	C₂²×C₆₇	C₄×SD₁₆	1	2	yes	—
167	C₂²×C₆₇	#443	1	2	yes	—
168	C₂×D₆₇	—	4	4	no	—
169	C₂×D₆₇	—	4	2	no	—
170	C₂×D₆₇	—	8	2	no	—
171	C₂×D₆₇	—	8	1	no	—
172	C₂×D₆₇	—	8	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	—	4	2	no	—
176	C₄×C₆₇	—	8	1	no	—
177	C₄×C₆₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
178	C₄×C₆₇	#408	1	1	yes	characteristic
179	C₄×C₆₇	C₈×D₄	1	1	yes	characteristic
180	C₄×C₆₇	#436	1	1	yes	characteristic
181	C₄×C₆₇	#465	1	2	yes	—
182	C₄×C₆₇	#492	1	1	yes	characteristic
183	C₄×C₆₇	#495	1	1	yes	characteristic
184	Dic₆₇	—	8	1	no	—
185	#9655	—	67	1	no	maximal, Sylow
186	C₂×C₆₇	C₈×SD₁₆	1	2	yes	—
187	C₂×C₆₇	#1590	1	2	yes	—
188	C₂×C₆₇	#1954	1	1	yes	characteristic
189	C₂×C₆₇	#1968	1	1	yes	characteristic
190	C₂×C₆₇	#1974	1	1	yes	characteristic
191	D₆₇	—	8	2	no	—
192	C₂×C₄×SD₁₆	—	67	1	no	—
193	#1984	D₆₇	1	1	yes	characteristic, complemented
194	#1954	—	67	1	no	—
195	C₂×#334	—	67	1	no	—
196	C₂×Q₈⋊C₈	—	67	1	no	—
197	C₂×D₄⋊C₈	—	67	1	no	—
198	C₂×C₈²	—	67	1	no	—
199	C₆₇	#9655	1	1	yes	characteristic, complemented, Sylow
200	C₂²×SD₁₆	—	67	1	no	—
201	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
202	C₂×C₄×D₄	—	67	1	no	—
203	C₄×SD₁₆	—	134	2	no	—
204	C₄×SD₁₆	—	134	2	no	—
205	C₂×#106	—	67	1	no	—
206	C₂×C₄⋊C₈	—	67	1	no	—
207	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
208	C₂×#103	—	67	1	no	—
209	C₂×#102	—	67	1	no	—
210	C₂×C₂²⋊C₈	—	134	2	no	—
211	C₂×C₄×C₈	—	67	1	no	—
212	C₂×C₄×C₈	—	67	1	no	—
213	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
214	#336	—	2	2	no	—
215	#334	—	134	2	no	—
216	Q₈⋊C₈	—	134	2	no	—
217	D₄⋊C₈	—	134	2	no	—
218	C₈²	—	134	2	no	—
219	C₂²×Q₈	C₄×D₆₇	1	1	yes	characteristic
220	C₂²×D₄	—	67	1	no	—
221	C₂³×C₄	—	134	1	no	—
222	C₂×SD₁₆	—	67	4	no	—
223	C₂×SD₁₆	—	134	2	no	—
224	C₂×SD₁₆	—	134	2	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	67	1	no	—
227	C₂²×C₈	—	67	1	no	—
228	C₂²×C₈	—	134	1	no	—
229	C₂²×C₈	—	134	1	no	—
230	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×D₄	—	134	1	no	—
236	C₄×D₄	—	134	1	no	—
237	C₄×D₄	—	134	1	no	—
238	C₄×D₄	—	134	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	67	1	no	—
241	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	—	134	1	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
245	#106	—	134	2	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	134	1	no	—
249	C₄⋊C₈	—	134	1	no	—
250	#103	—	134	2	no	—
251	#102	—	134	2	no	—
252	C₂²⋊C₈	—	268	4	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	67	2	no	—
256	C₄×C₈	—	67	2	no	—
257	C₄×C₈	—	67	2	no	—
258	C₄×C₈	—	134	1	no	—
259	C₂⁴	—	134	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	C₈×D₆₇	1	2	yes	—
266	C₂×D₄	—	67	2	no	—
267	C₂×D₄	—	134	1	no	—
268	C₂×D₄	—	134	1	no	—
269	C₂×D₄	—	134	1	no	—
270	C₂×D₄	—	134	1	no	—
271	C₂×D₄	—	134	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	268	1	no	—
275	C₂²×C₄	—	268	1	no	—
276	C₂²×C₄	—	268	2	no	—
277	C₂²×C₄	—	268	2	no	—
278	C₂²×C₄	—	134	1	no	—
279	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
281	C₂²×C₄	#11761628	1	1	yes	characteristic
282	SD₁₆	—	134	8	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	268	1	no	—
288	C₂×C₈	—	268	2	no	—
289	C₂×C₈	—	67	2	no	—
290	C₂×C₈	—	67	2	no	—
291	C₂×C₈	—	67	2	no	—
292	C₂×C₈	—	67	2	no	—
293	C₂×C₈	—	134	4	no	—
294	C₂×C₈	—	134	2	no	—
295	C₂×C₈	—	134	1	no	—
296	C₂×C₈	—	134	1	no	—
297	C₂×C₈	#11761615	1	4	yes	complemented
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	134	1	no	—
303	C₄⋊C₄	—	134	1	no	—
304	C₂²⋊C₄	—	268	1	no	—
305	C₂²⋊C₄	—	268	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	D₄×D₆₇	1	1	yes	characteristic
309	C₄²	D₄×D₆₇	1	1	yes	characteristic
310	C₄²	D₄×D₆₇	1	1	yes	characteristic
311	C₄²	#11761627	1	1	yes	characteristic
312	C₂³	—	268	2	no	—
313	C₂³	—	268	1	no	—
314	C₂³	—	268	1	no	—
315	C₂³	—	268	2	no	—
316	C₂³	—	134	2	no	—
317	C₂³	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	4	1	no	—
321	Q₈	—	4	1	no	—
322	D₄	—	268	1	no	—
323	D₄	—	268	1	no	—
324	D₄	—	134	2	no	—
325	D₄	—	134	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	268	1	no	—
333	C₂×C₄	—	268	2	no	—
334	C₂×C₄	—	536	1	no	—
335	C₂×C₄	—	536	1	no	—
336	C₂×C₄	—	536	2	no	—
337	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
338	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
339	C₂×C₄	#14524015	1	1	yes	characteristic
340	C₂×C₄	#14524016	1	1	yes	characteristic
341	C₂×C₄	#14524029	1	1	yes	characteristic
342	C₂×C₄	#14524039	1	1	yes	characteristic
343	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
344	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
345	C₂×C₄	#14524049	1	1	yes	characteristic
346	C₂×C₄	#14524051	1	1	yes	characteristic
347	C₂×C₄	C₂×#11761615	1	2	yes	—
348	C₂×C₄	#14524063	1	2	yes	—
349	C₈	—	2	4	no	—
350	C₈	—	8	1	no	—
351	C₈	—	536	1	no	—
352	C₈	—	67	4	no	—
353	C₈	—	134	4	no	—
354	C₈	—	134	2	no	—
355	C₂²	—	268	4	no	—
356	C₂²	—	268	2	no	—
357	C₂²	—	536	1	no	—
358	C₂²	—	536	1	no	—
359	C₂²	—	536	2	no	—
360	C₂²	#16863296	1	1	yes	characteristic
361	C₂²	C₈×C₂²⋊D₆₇	1	1	yes	characteristic
362	C₂²	#16863472	1	1	yes	characteristic
363	C₂²	C₄×#11761615	1	2	yes	—
364	C₂²	#16863511	1	2	yes	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	2	no	—
368	C₄	—	8	1	no	—
369	C₄	—	536	1	no	—
370	C₄	C₂²⋊C₈×D₆₇	1	1	yes	characteristic
371	C₄	#16863361	1	1	yes	characteristic
372	C₄	(C₂²⋊D₆₇)⋊C₈	1	1	yes	characteristic
373	C₄	#16863471	1	1	yes	characteristic
374	C₄	#16863627	1	2	yes	—
375	C₄	#16863770	1	1	yes	characteristic
376	C₄	#16863778	1	1	yes	characteristic
377	C₂	—	536	2	no	—
378	C₂	C₈×#11761615	1	2	yes	—
379	C₂	#22559099	1	2	yes	—
380	C₂	#22561001	1	1	yes	characteristic
381	C₂	#22561066	1	1	yes	characteristic
382	C₂	#22561096	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1984	C₂
socle	C₂³×C₆₇	C₄×D₄
prime radical	C₂²×D₂₆₈	C₂×C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#1984	D₆₇
hypocenter	C₆₇	#9655
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1984

Complements

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

N	H ≅ G/N	type
3. C₂×#16863146	C₂	semidirect
4. C₂×Q₈⋊(C₆₇⋊C₈)	C₂	semidirect
6. C₂×C₈×C₆₇⋊C₈	C₂	semidirect
7. C₆₇×#1984	C₂	semidirect
31. C₂×#11761615	C₈	semidirect
109. C₂×C₈×C₆₇	SD₁₆	semidirect
162. C₆₇⋊C₈	C₂²⋊C₈	semidirect
193. #1984	D₆₇	semidirect
199. C₆₇	#9655	semidirect
297. C₂×C₈	#11761615	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#11761615	2
#22561003	2
C₂×#16863146	2
C₂×Q₈⋊(C₆₇⋊C₈)	2
C₂×#16863123	2
C₂×C₈×C₆₇⋊C₈	2
C₆₇×#1984	2
#9655	67