Subgroups — #30826490

Order 17152.

640 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570785	C₂	1	1	yes	maximal, characteristic
2	#22569286	C₂	1	2	yes	maximal, complemented
3	#22559121	C₂	1	2	yes	maximal, complemented
4	#22559095	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559030	C₂	1	2	yes	maximal, complemented
6	D₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559003	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558971	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558676	C₂	1	2	yes	maximal, complemented
10	#22558491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1589	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863943	C₂²	1	2	yes	—
13	#16863800	C₄	1	1	yes	characteristic
14	#16863771	C₄	1	1	yes	characteristic
15	#16863741	C₄	1	2	yes	—
16	#16863633	C₄	1	1	yes	characteristic
17	#16863631	C₄	1	2	yes	—
18	#16863629	C₄	1	1	yes	characteristic
19	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
20	C₄×#11761613	C₂²	1	2	yes	—
21	#16863475	C₂²	1	2	yes	—
22	#16863465	—	2	2	no	—
23	#16863464	—	2	2	no	—
24	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
25	#16863461	C₂²	1	2	yes	—
26	#16863452	C₂²	1	2	yes	—
27	#16863447	C₂²	1	1	yes	characteristic
28	#16863447	C₂²	1	1	yes	characteristic
29	#16863364	—	2	2	no	—
30	#16863361	—	2	2	no	—
31	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
32	#16863149	C₂²	1	1	yes	characteristic
33	#16863146	C₂²	1	2	yes	—
34	#16863125	C₂²	1	2	yes	—
35	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
36	#16863123	C₂²	1	2	yes	—
37	#16863118	C₂²	1	1	yes	characteristic
38	#16863118	C₂²	1	1	yes	characteristic
39	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
41	#436×C₆₇	C₂²	1	2	yes	—
42	#335×C₆₇	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#11761628	—	2	2	no	—
46	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
47	C₂×#11761613	C₂×C₄	1	2	yes	—
48	C₂×#11761611	—	2	2	no	—
49	C₂²×C₆₇⋊C₈	—	2	2	no	—
50	C₂×C₈×D₆₇	—	2	2	no	—
51	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
53	#14524042	C₂×C₄	1	2	yes	—
54	#14524039	C₂×C₄	1	2	yes	—
55	#14524029	—	2	2	no	—
56	#14524018	C₂×C₄	1	2	yes	—
57	#14524016	—	2	2	no	—
58	#14524014	C₂×C₄	1	2	yes	—
59	C₄×D₂₆₈	C₂³	1	2	yes	—
60	C₄×C₂²⋊D₆₇	—	2	2	no	—
61	C₄²×D₆₇	C₂³	1	1	yes	characteristic
62	#14523977	C₂×C₄	1	1	yes	characteristic
63	#14523976	C₂×C₄	1	2	yes	—
64	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
65	Dic₆₇⋊C₈	—	2	1	no	—
66	Dic₆₇⋊C₈	D₄	1	1	yes	characteristic
67	Dic₆₇⋊C₈	D₄	1	1	yes	characteristic
68	#14523965	C₂×C₄	1	2	yes	—
69	#14523964	C₂×C₄	1	2	yes	—
70	#14523963	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
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	(C₂×D₆₇)⋊C₈	D₄	1	1	yes	characteristic
77	(C₂×D₆₇)⋊C₈	D₄	1	1	yes	characteristic
78	#14523953	—	2	2	no	—
79	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
82	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
84	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
85	C₂×M₁₆×C₆₇	—	2	2	no	—
86	C₄×D₄×C₆₇	C₂³	1	2	yes	—
87	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
89	#102×C₆₇	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₆₇	—	2	2	no	—
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	#11761628	—	8	2	no	—
95	#11761628	—	8	2	no	—
96	C₂×Dic₁₃₄	—	2	2	no	—
97	C₂×D₂₆₈	—	2	2	no	—
98	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
99	C₂×C₂²⋊D₆₇	—	2	2	no	—
100	C₂×C₂²⋊D₆₇	—	2	2	no	—
101	C₂×C₂²⋊D₆₇	—	2	2	no	—
102	C₂×C₄×D₆₇	—	2	2	no	—
103	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
106	D₅₃₆	—	2	2	no	—
107	#11761613	—	2	4	no	—
108	#11761611	—	8	2	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₂×C₆₇⋊C₈	—	2	1	no	—
111	C₂×C₆₇⋊C₈	—	8	2	no	—
112	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
116	C₈×D₆₇	—	2	2	no	—
117	C₈×D₆₇	—	2	2	no	—
118	C₈×D₆₇	—	8	2	no	—
119	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
120	Dic₆₇⋊C₄	—	2	2	no	—
121	C₂²⋊Dic₆₇	—	2	2	no	—
122	(C₂×D₆₇)⋊C₄	—	2	2	no	—
123	(C₂×D₆₇)⋊C₄	—	2	2	no	—
124	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₆₇	#41	1	1	yes	characteristic
127	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₆₇	—	2	2	no	—
129	D₈×C₆₇	—	2	2	no	—
130	M₁₆×C₆₇	—	8	2	no	—
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	C₂²×C₄	1	2	yes	—
138	C₂²⋊C₄×C₆₇	—	2	2	no	—
139	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
140	C₂³×C₆₇	—	2	2	no	—
141	C₂²×D₆₇	—	2	2	no	—
142	C₂²×D₆₇	C₄×D₄	1	1	yes	characteristic
143	D₄×C₆₇	—	2	2	no	—
144	D₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
151	C₂²⋊D₆₇	—	8	2	no	—
152	C₂²⋊D₆₇	—	8	2	no	—
153	C₂²⋊D₆₇	—	8	2	no	—
154	C₂×Dic₆₇	—	2	2	no	—
155	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
156	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
157	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
158	D₂₆₈	—	2	2	no	—
159	D₂₆₈	—	2	2	no	—
160	D₂₆₈	—	8	2	no	—
161	C₄×D₆₇	—	2	1	no	—
162	C₄×D₆₇	—	2	1	no	—
163	C₄×D₆₇	—	2	1	no	—
164	C₄×D₆₇	—	2	1	no	—
165	C₄×D₆₇	—	4	1	no	—
166	C₄×D₆₇	—	4	2	no	—
167	C₄×D₆₇	—	4	2	no	—
168	Dic₁₃₄	—	8	2	no	—
169	C₈×C₆₇	—	2	1	no	—
170	C₈×C₆₇	—	2	1	no	—
171	C₈×C₆₇	—	2	1	no	—
172	C₈×C₆₇	—	4	1	no	—
173	C₈×C₆₇	—	4	2	no	—
174	C₈×C₆₇	#131	1	2	yes	—
175	C₆₇⋊C₈	—	2	1	no	—
176	C₆₇⋊C₈	—	2	1	no	—
177	C₆₇⋊C₈	—	2	1	no	—
178	C₆₇⋊C₈	—	4	1	no	—
179	C₆₇⋊C₈	—	4	2	no	—
180	C₆₇⋊C₈	#131	1	2	yes	—
181	C₂²×C₆₇	—	4	2	no	—
182	C₂²×C₆₇	—	4	2	no	—
183	C₂²×C₆₇	—	4	2	no	—
184	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂×D₆₇	—	2	1	no	—
186	C₂×D₆₇	—	2	1	no	—
187	C₂×D₆₇	—	2	1	no	—
188	C₂×D₆₇	—	4	2	no	—
189	C₂×D₆₇	—	4	2	no	—
190	C₂×D₆₇	—	4	2	no	—
191	C₄×C₆₇	—	2	1	no	—
192	C₄×C₆₇	—	4	2	no	—
193	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
194	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
195	C₄×C₆₇	#576	1	1	yes	characteristic
196	C₄×C₆₇	#576	1	1	yes	characteristic
197	Dic₆₇	—	2	1	no	—
198	Dic₆₇	—	2	1	no	—
199	Dic₆₇	—	2	1	no	—
200	Dic₆₇	—	4	2	no	—
201	#17970	—	67	1	no	maximal, Sylow
202	C₂×C₆₇	—	8	2	no	—
203	C₂×C₆₇	#2931	1	1	yes	characteristic
204	C₂×C₆₇	#2948	1	1	yes	characteristic
205	C₂×C₆₇	#2957	1	1	yes	characteristic
206	D₆₇	—	4	1	no	—
207	D₆₇	—	8	2	no	—
208	#3169	—	67	1	no	—
209	#2981	—	67	2	no	—
210	#1594	—	67	2	no	—
211	#1589	—	67	1	no	—
212	#1589	D₆₇	1	1	yes	characteristic, complemented
213	#1580	—	67	2	no	—
214	C₈×D₈	—	67	1	no	—
215	C₈×D₈	—	67	1	no	—
216	#1568	—	67	1	no	—
217	#1496	—	67	2	no	—
218	#1450	—	67	1	no	—
219	C₆₇	#17970	1	1	yes	characteristic, complemented, Sylow
220	#532	—	67	2	no	—
221	#500	—	67	1	no	—
222	#493	—	67	1	no	—
223	#486	—	67	2	no	—
224	#466	—	67	1	no	—
225	#466	—	67	1	no	—
226	#466	—	67	2	no	—
227	C₄×D₈	—	67	2	no	—
228	C₄×D₈	—	67	1	no	—
229	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
230	#436	—	67	2	no	—
231	#436	C₂×D₆₇	1	2	yes	—
232	#435	—	134	2	no	—
233	#435	—	134	2	no	—
234	C₈×D₄	—	67	2	no	—
235	C₈×D₄	—	67	2	no	—
236	#432	—	67	2	no	—
237	#431	—	67	1	no	—
238	#431	—	67	1	no	—
239	#408	—	134	2	no	—
240	#408	—	134	2	no	—
241	C₂×C₄×C₈	—	67	1	no	—
242	#335	—	67	1	no	—
243	#335	C₂×D₆₇	1	1	yes	characteristic
244	#334	—	67	2	no	—
245	D₄⋊C₈	—	67	2	no	—
246	D₄⋊C₈	—	67	2	no	—
247	D₄⋊C₈	—	67	2	no	—
248	D₄⋊C₈	C₂×D₆₇	1	2	yes	—
249	#322	—	67	1	no	—
250	#322	—	67	1	no	—
251	C₈²	—	67	1	no	—
252	C₈²	C₂×D₆₇	1	1	yes	characteristic
253	C₂×#41	—	134	2	no	—
254	C₂×D₈	—	67	2	no	—
255	C₂×D₈	—	67	1	no	—
256	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	134	2	no	—
259	C₂²×C₈	—	67	1	no	—
260	C₂²×C₈	—	67	1	no	—
261	C₂²×C₈	—	134	2	no	—
262	C₂²×C₈	—	134	2	no	—
263	C₄⋊Q₈	—	67	2	no	—
264	#127	—	67	2	no	—
265	#124	—	134	2	no	—
266	#121	—	67	2	no	—
267	#121	—	67	2	no	—
268	#121	—	134	2	no	—
269	C₄×D₄	—	67	2	no	—
270	C₄×D₄	—	134	2	no	—
271	C₄×D₄	C₂²×D₆₇	1	2	yes	—
272	C₂×C₄²	—	67	1	no	—
273	#107	—	67	1	no	—
274	#107	—	67	2	no	—
275	#107	C₄×D₆₇	1	1	yes	characteristic
276	C₄⋊C₈	—	67	1	no	—
277	C₄⋊C₈	—	67	1	no	—
278	C₄⋊C₈	—	67	2	no	—
279	C₄⋊C₈	—	134	1	no	—
280	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
281	#102	—	67	2	no	—
282	#102	—	67	2	no	—
283	#102	—	67	2	no	—
284	#102	C₄×D₆₇	1	2	yes	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	67	1	no	—
287	C₂²⋊C₈	—	67	1	no	—
288	C₂²⋊C₈	—	134	2	no	—
289	C₂²⋊C₈	—	134	2	no	—
290	C₂²⋊C₈	—	134	1	no	—
291	C₂²⋊C₈	—	134	2	no	—
292	C₂²⋊C₈	—	134	2	no	—
293	#97	—	134	2	no	—
294	C₄×C₈	—	67	1	no	—
295	C₄×C₈	—	67	1	no	—
296	C₄×C₈	—	67	1	no	—
297	C₄×C₈	—	67	1	no	—
298	C₄×C₈	—	67	1	no	—
299	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
300	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
302	#41	—	536	2	no	—
303	#41	—	536	2	no	—
304	C₂×Q₈	—	134	2	no	—
305	C₂×D₄	—	67	2	no	—
306	C₂×D₄	—	134	2	no	—
307	C₂×D₄	—	134	2	no	—
308	C₂×D₄	—	134	2	no	—
309	C₂×D₄	—	134	2	no	—
310	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	67	1	no	—
313	C₂²×C₄	—	67	1	no	—
314	C₂²×C₄	—	67	1	no	—
315	C₂²×C₄	—	134	2	no	—
316	D₈	—	2	2	no	—
317	D₈	—	134	4	no	—
318	D₈	—	134	2	no	—
319	M₁₆	—	8	2	no	—
320	M₁₆	—	536	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	536	2	no	—
324	C₂×C₈	—	536	2	no	—
325	C₂×C₈	—	67	1	no	—
326	C₂×C₈	—	67	1	no	—
327	C₂×C₈	—	67	1	no	—
328	C₂×C₈	—	67	1	no	—
329	C₂×C₈	—	134	2	no	—
330	C₂×C₈	—	134	2	no	—
331	C₂×C₈	—	134	1	no	—
332	C₂×C₈	—	134	2	no	—
333	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
335	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
336	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
337	C₄⋊C₄	—	67	2	no	—
338	C₄⋊C₄	—	134	2	no	—
339	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	134	2	no	—
342	C₂²⋊C₄	—	134	2	no	—
343	C₂²⋊C₄	—	134	2	no	—
344	C₄²	—	67	1	no	—
345	C₄²	—	67	1	no	—
346	C₄²	—	67	1	no	—
347	C₄²	C₂³×D₆₇	1	1	yes	characteristic
348	C₂³	—	2	2	no	—
349	C₂³	—	67	1	no	—
350	C₂³	—	134	2	no	—
351	Q₈	—	536	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	536	2	no	—
355	D₄	—	536	2	no	—
356	D₄	—	536	2	no	—
357	D₄	—	536	2	no	—
358	D₄	—	134	2	no	—
359	D₄	—	134	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	268	1	no	—
364	C₂×C₄	—	268	2	no	—
365	C₂×C₄	—	268	2	no	—
366	C₂×C₄	—	67	1	no	—
367	C₂×C₄	—	67	1	no	—
368	C₂×C₄	—	67	1	no	—
369	C₂×C₄	—	134	2	no	—
370	C₂×C₄	—	134	1	no	—
371	C₂×C₄	—	134	1	no	—
372	C₂×C₄	—	134	1	no	—
373	C₂×C₄	—	134	1	no	—
374	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
375	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
376	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	2	no	—
382	C₈	—	268	1	no	—
383	C₈	—	268	2	no	—
384	C₈	—	67	2	no	—
385	C₈	—	134	1	no	—
386	C₈	—	134	1	no	—
387	C₈	—	134	1	no	—
388	C₈	#14524051	1	2	yes	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	268	2	no	—
393	C₂²	—	268	2	no	—
394	C₂²	—	268	2	no	—
395	C₂²	—	134	1	no	—
396	C₂²	—	134	1	no	—
397	C₂²	—	134	1	no	—
398	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	268	2	no	—
402	C₄	—	134	1	no	—
403	C₄	—	134	1	no	—
404	C₄	—	134	1	no	—
405	C₄	#131×D₆₇	1	1	yes	characteristic
406	C₄	C₂×#14524051	1	1	yes	characteristic
407	C₄	#16864197	1	1	yes	characteristic
408	C₄	#16864198	1	1	yes	characteristic
409	C₂	—	8	2	no	—
410	C₂	—	268	1	no	—
411	C₂	—	536	2	no	—
412	C₂	#22568918	1	1	yes	characteristic
413	C₂	#22569056	1	1	yes	characteristic
414	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	C₆₇×#1589	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#22570785	C₂
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1589	D₆₇
hypocenter	C₆₇	#17970
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1589

Complements

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

N	H ≅ G/N	type
2. #22569286	C₂	semidirect
3. #22559121	C₂	semidirect
4. #22559095	C₂	semidirect
5. #22559030	C₂	semidirect
6. D₈×C₆₇⋊C₈	C₂	semidirect
7. #22559003	C₂	semidirect
8. #22558971	C₂	semidirect
9. #22558676	C₂	semidirect
10. #22558491	C₂	semidirect
11. C₆₇×#1589	C₂	semidirect
212. #1589	D₆₇	semidirect
219. C₆₇	#17970	semidirect

Maximal subgroups

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

subgroup	index
#22570785	2
#22569286	2
#22559121	2
#22559095	2
#22559030	2
D₈×C₆₇⋊C₈	2
#22559003	2
#22558971	2
#22558676	2
#22558491	2
C₆₇×#1589	2
#17970	67