Subgroups — #30827346

Order 17152.

786 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#11761612	C₂	1	2	yes	maximal, complemented
2	#22559123	C₂	1	2	yes	maximal, complemented
3	#22559074	C₂	1	4	yes	maximal, complemented
4	#22559033	C₂	1	2	yes	maximal, complemented
5	#22558965	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558634	C₂	1	2	yes	maximal, complemented
7	#22558498	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761612	—	2	2	no	—
10	#16863474	C₂²	1	4	yes	complemented
11	#16863468	—	2	4	no	—
12	D₄×C₆₇⋊C₈	C₂²	1	4	yes	complemented
13	#16863449	C₂²	1	1	yes	characteristic
14	#16863420	C₂²	1	2	yes	—
15	#16863360	—	2	2	no	—
16	C₄×#11761612	C₂²	1	1	yes	characteristic
17	#16863147	C₂²	1	2	yes	complemented
18	#16863147	C₂²	1	2	yes	complemented
19	D₄⋊(C₆₇⋊C₈)	C₂²	1	4	yes	complemented
20	D₄⋊(C₆₇⋊C₈)	C₂²	1	4	yes	complemented
21	#16863118	C₂²	1	2	yes	complemented
22	#16863117	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₆₇	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
25	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic
26	C₄×D₈×C₆₇	C₄	1	2	yes	—
27	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic
28	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₆₇	C₂²	1	2	yes	—
30	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#107×C₆₇	C₄	1	1	yes	characteristic
32	C₂×#102×C₆₇	C₄	1	2	yes	—
33	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#11761612	—	2	4	no	—
35	C₂×#11761612	—	2	2	no	—
36	C₂×#11761612	—	4	8	no	—
37	C₂×#11761612	D₄	1	2	yes	—
38	C₂²×C₆₇⋊C₈	—	2	4	no	—
39	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
40	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
41	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
42	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
43	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
44	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
45	#14523954	D₄	1	2	yes	—
46	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
47	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₆₇	—	2	2	no	—
50	C₂×D₈×C₆₇	—	2	4	no	—
51	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
52	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₄×D₄×C₆₇	—	2	2	no	—
57	C₄×D₄×C₆₇	—	2	2	no	—
58	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
59	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₆₇	C₂³	1	2	yes	—
61	C₄×D₄×C₆₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	#107×C₆₇	C₂×C₄	1	2	yes	—
66	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
67	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
68	#102×C₆₇	C₂×C₄	1	2	yes	—
69	#102×C₆₇	C₂×C₄	1	2	yes	—
70	#102×C₆₇	C₂×C₄	1	2	yes	—
71	#102×C₆₇	C₂×C₄	1	2	yes	—
72	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
76	#11761612	—	2	4	no	—
77	#11761612	—	4	8	no	—
78	#11761612	—	4	4	no	—
79	C₂×C₆₇⋊C₈	—	2	4	no	—
80	C₂×C₆₇⋊C₈	—	2	2	no	—
81	C₂×C₆₇⋊C₈	—	4	8	no	—
82	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
83	C₂⁴×C₆₇	—	2	2	no	—
84	C₂×D₄×C₆₇	—	2	4	no	—
85	C₂×D₄×C₆₇	—	2	2	no	—
86	C₂×D₄×C₆₇	—	4	2	no	—
87	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₆₇	—	2	2	no	—
90	C₂²×C₄×C₆₇	—	2	2	no	—
91	C₂²×C₄×C₆₇	—	2	2	no	—
92	C₂²×C₄×C₆₇	—	2	2	no	—
93	C₂²×C₄×C₆₇	—	2	2	no	—
94	C₂²×C₄×C₆₇	—	4	4	no	—
95	C₂²×C₄×C₆₇	—	4	4	no	—
96	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
99	D₈×C₆₇	—	2	4	no	—
100	D₈×C₆₇	—	2	2	no	—
101	D₈×C₆₇	M₁₆	1	4	yes	complemented
102	C₂×C₈×C₆₇	—	2	2	no	—
103	C₂×C₈×C₆₇	—	4	1	no	—
104	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
108	C₄⋊C₄×C₆₇	—	2	2	no	—
109	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
111	C₂²⋊C₄×C₆₇	—	2	2	no	—
112	C₂²⋊C₄×C₆₇	—	2	2	no	—
113	C₂²⋊C₄×C₆₇	—	2	2	no	—
114	C₂²⋊C₄×C₆₇	—	2	2	no	—
115	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₆₇	#41	1	1	yes	characteristic
118	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
119	C₂³×C₆₇	—	2	2	no	—
120	C₂³×C₆₇	—	2	2	no	—
121	C₂³×C₆₇	—	4	4	no	—
122	C₂³×C₆₇	—	4	4	no	—
123	C₂³×C₆₇	—	8	2	no	—
124	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
125	D₄×C₆₇	—	2	2	no	—
126	D₄×C₆₇	—	2	2	no	—
127	D₄×C₆₇	—	2	2	no	—
128	D₄×C₆₇	—	4	4	no	—
129	D₄×C₆₇	C₂×M₁₆	1	4	yes	complemented
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	4	no	—
136	C₂×C₄×C₆₇	—	4	2	no	—
137	C₂×C₄×C₆₇	—	4	2	no	—
138	C₂×C₄×C₆₇	—	4	2	no	—
139	C₂×C₄×C₆₇	—	4	2	no	—
140	C₂×C₄×C₆₇	—	4	4	no	—
141	C₂×C₄×C₆₇	—	4	4	no	—
142	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
146	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
149	C₈×C₆₇	—	2	1	no	—
150	C₈×C₆₇	—	2	1	no	—
151	C₈×C₆₇	—	2	1	no	—
152	C₈×C₆₇	C₂×M₁₆	1	2	yes	complemented
153	C₆₇⋊C₈	—	2	4	no	—
154	C₆₇⋊C₈	—	4	2	no	—
155	C₆₇⋊C₈	—	4	4	no	—
156	C₂²×C₆₇	—	2	1	no	—
157	C₂²×C₆₇	—	2	1	no	—
158	C₂²×C₆₇	—	2	4	no	—
159	C₂²×C₆₇	—	4	2	no	—
160	C₂²×C₆₇	—	4	2	no	—
161	C₂²×C₆₇	—	4	2	no	—
162	C₂²×C₆₇	—	4	2	no	—
163	C₂²×C₆₇	—	4	2	no	—
164	C₂²×C₆₇	—	8	8	no	—
165	C₂²×C₆₇	#442	1	2	yes	—
166	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
167	C₄×C₆₇	—	2	1	no	—
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	4	2	no	—
171	C₄×C₆₇	—	4	2	no	—
172	C₄×C₆₇	#442	1	2	yes	—
173	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
174	C₄×C₆₇	#568	1	1	yes	characteristic
175	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
176	#18044	—	67	1	no	maximal, Sylow
177	C₂×C₆₇	—	2	2	no	—
178	C₂×C₆₇	—	4	4	no	—
179	C₂×C₆₇	—	8	2	no	—
180	C₂×C₆₇	D₄×M₁₆	1	1	yes	characteristic
181	C₂×C₆₇	C₂×#442	1	1	yes	characteristic
182	C₂×C₆₇	#2957	1	1	yes	characteristic
183	C₂×C₄×D₈	D₆₇	1	1	yes	characteristic
184	D₄×M₁₆	—	67	2	no	—
185	#1594	—	67	2	no	—
186	#1586	—	67	4	no	—
187	#1580	—	67	2	no	—
188	#1566	—	67	1	no	—
189	#1486	—	67	2	no	—
190	#1451	—	67	1	no	—
191	C₆₇	#18044	1	1	yes	characteristic, complemented, Sylow
192	C₂²×D₈	Dic₆₇	1	1	yes	characteristic
193	C₂²×M₁₆	—	134	2	no	—
194	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	—
195	C₄×D₈	Dic₆₇	1	2	yes	—
196	C₄×D₈	Dic₆₇	1	1	yes	characteristic
197	C₄×D₈	Dic₆₇	1	1	yes	characteristic
198	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
199	C₄×D₈	C₂×D₆₇	1	2	yes	—
200	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
201	#436	—	67	4	no	—
202	#435	—	134	4	no	—
203	C₈×D₄	—	67	4	no	—
204	#431	—	67	1	no	—
205	C₂×#107	Dic₆₇	1	1	yes	characteristic
206	#423	—	67	2	no	—
207	C₂×#102	Dic₆₇	1	2	yes	—
208	#407	—	134	2	no	—
209	C₄×M₁₆	—	67	1	no	—
210	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
211	#334	—	67	2	no	—
212	#334	—	67	2	no	—
213	D₄⋊C₈	—	67	4	no	—
214	D₄⋊C₈	—	67	4	no	—
215	#322	—	67	2	no	—
216	#322	—	67	2	no	—
217	C₂²×D₄	C₂×Dic₆₇	1	2	yes	—
218	C₂³×C₄	—	2	2	no	—
219	C₂×D₈	—	2	4	no	—
220	C₂×D₈	C₂×Dic₆₇	1	2	yes	—
221	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
222	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
223	C₂×M₁₆	—	268	8	no	—
224	C₂×M₁₆	—	67	2	no	—
225	C₂×M₁₆	—	134	4	no	—
226	C₂×M₁₆	—	134	2	no	—
227	C₂²×C₈	—	134	4	no	—
228	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
229	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
233	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
234	C₄×D₄	C₂²×D₆₇	1	2	yes	—
235	C₄×D₄	C₂²×D₆₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
239	#107	C₂×Dic₆₇	1	2	yes	—
240	#107	C₂×Dic₆₇	1	1	yes	characteristic
241	#107	C₂×Dic₆₇	1	1	yes	characteristic
242	C₄⋊C₈	—	67	4	no	—
243	C₄⋊C₈	—	134	2	no	—
244	C₄⋊C₈	—	134	1	no	—
245	#102	C₂×Dic₆₇	1	2	yes	—
246	#102	C₂×Dic₆₇	1	2	yes	—
247	#102	C₂×Dic₆₇	1	2	yes	—
248	#102	C₂×Dic₆₇	1	2	yes	—
249	C₂²⋊C₈	—	134	4	no	—
250	C₂²⋊C₈	—	134	4	no	—
251	C₂²⋊C₈	—	134	1	no	—
252	#97	—	67	2	no	—
253	C₄×C₈	—	67	2	no	—
254	C₄×C₈	—	67	2	no	—
255	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
256	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
257	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
258	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
259	C₂⁴	—	2	2	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
264	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
273	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
274	C₂²×C₄	#11761627	1	1	yes	characteristic
275	D₈	—	2	4	no	—
276	D₈	—	2	2	no	—
277	D₈	#11761612	1	4	yes	complemented
278	M₁₆	—	268	4	no	—
279	M₁₆	—	268	8	no	—
280	M₁₆	—	134	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	268	8	no	—
284	C₂×C₈	—	67	4	no	—
285	C₂×C₈	—	134	4	no	—
286	C₂×C₈	—	134	2	no	—
287	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
288	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
289	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
290	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
293	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	2	2	no	—
296	C₂²⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
299	C₄²	D₄×D₆₇	1	1	yes	characteristic
300	C₄²	#11761627	1	1	yes	characteristic
301	C₄²	C₂³×D₆₇	1	1	yes	characteristic
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	4	no	—
306	C₂³	—	8	2	no	—
307	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
308	D₄	—	2	2	no	—
309	D₄	—	2	2	no	—
310	D₄	—	2	2	no	—
311	D₄	—	4	4	no	—
312	D₄	C₂×#11761612	1	4	yes	complemented
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
326	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
327	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
328	C₂×C₄	#14524067	1	4	yes	—
329	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
331	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
332	C₈	—	2	1	no	—
333	C₈	—	2	1	no	—
334	C₈	—	2	1	no	—
335	C₈	—	268	2	no	—
336	C₈	—	268	4	no	—
337	C₈	—	134	4	no	—
338	C₈	C₂×#11761612	1	2	yes	complemented
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	8	8	no	—
348	C₂²	#16863508	1	2	yes	—
349	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	#16863508	1	2	yes	—
356	C₄	C₂²×#11761612	1	1	yes	characteristic
357	C₄	#16864163	1	1	yes	characteristic
358	C₄	C₂×#14524067	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	4	4	no	—
361	C₂	—	8	2	no	—
362	C₂	D₄×#11761612	1	1	yes	characteristic
363	C₂	C₂×#16863508	1	1	yes	characteristic
364	C₂	#22569126	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×C₄×D₈×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂²×D₈×C₆₇	C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₂×C₄×D₈	D₆₇
hypocenter	C₆₇	#18044
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#11761612	C₂	semidirect
2. #22559123	C₂	semidirect
3. #22559074	C₂	semidirect
4. #22559033	C₂	semidirect
5. #22558965	C₂	semidirect
6. #22558634	C₂	semidirect
7. #22558498	C₂	semidirect
10. #16863474	C₂²	semidirect
12. D₄×C₆₇⋊C₈	C₂²	semidirect
17. #16863147	C₂²	semidirect
18. #16863147	C₂²	semidirect
19. D₄⋊(C₆₇⋊C₈)	C₂²	semidirect
20. D₄⋊(C₆₇⋊C₈)	C₂²	semidirect
21. #16863118	C₂²	semidirect
22. #16863117	C₂²	semidirect
101. D₈×C₆₇	M₁₆	semidirect
129. D₄×C₆₇	C₂×M₁₆	semidirect
152. C₈×C₆₇	C₂×M₁₆	semidirect
191. C₆₇	#18044	semidirect
277. D₈	#11761612	semidirect
312. D₄	C₂×#11761612	semidirect
338. C₈	C₂×#11761612	semidirect

Maximal subgroups

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

subgroup	index
D₄×#11761612	2
#22559123	2
#22559074	2
#22559033	2
#22558965	2
#22558634	2
#22558498	2
C₂×C₄×D₈×C₆₇	2
#18044	67