Subgroups — C₂×#22562327 #31010386

Order 17152.

678 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523984	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863813	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863666	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562327	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863225	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#472×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524068	—	2	1	no	—
10	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
11	C₂×#14523984	—	2	1	no	—
12	C₂×#14523984	—	2	1	no	—
13	C₂×#14523984	—	2	2	no	—
14	C₂×#14523984	C₂²	1	4	yes	complemented
15	#16863813	—	2	2	no	—
16	#16863813	C₂²	1	4	yes	complemented
17	C₂×#14523983	—	2	1	no	—
18	C₂×#14523983	C₂²	1	1	yes	characteristic
19	C₂²×C₆₇⋊C₁₆	—	2	1	no	—
20	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
21	#16863666	—	2	2	no	—
22	#16863666	C₂²	1	4	yes	complemented
23	C₂×#14523979	C₂²	1	1	yes	characteristic
24	C₂×#14523959	—	2	1	no	—
25	#16863225	C₂²	1	4	yes	complemented
26	#16863209	C₂²	1	4	yes	complemented
27	#16863208	C₂²	1	4	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
29	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
31	#472×C₆₇	—	2	2	no	—
32	#472×C₆₇	C₂²	1	4	yes	complemented
33	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#100×C₆₇	—	2	1	no	—
35	C₂²×D₂₆₈	—	2	1	no	—
36	#14524068	—	2	4	no	—
37	#14524068	—	4	2	no	—
38	C₂×#11761615	—	4	1	no	—
39	C₂×D₅₃₆	—	2	1	no	—
40	C₂×D₅₃₆	—	2	1	no	—
41	C₂×D₅₃₆	—	2	1	no	—
42	C₂×D₅₃₆	—	2	1	no	—
43	C₂×D₅₃₆	—	2	1	no	—
44	C₂×D₅₃₆	C₂³	1	2	yes	—
45	C₂×#11761613	—	4	1	no	—
46	C₂×#11761612	—	2	1	no	—
47	#14523984	—	2	4	no	—
48	#14523984	—	2	4	no	—
49	#14523983	—	2	4	no	—
50	#14523983	—	2	1	no	—
51	#14523983	C₂³	1	2	yes	—
52	C₂×C₆₇⋊C₁₆	—	2	4	no	—
53	C₂×C₆₇⋊C₁₆	—	2	1	no	—
54	C₂×C₆₇⋊C₁₆	D₄	1	1	yes	characteristic
55	C₂×C₆₇⋊C₁₆	D₄	1	1	yes	characteristic
56	C₂×C₆₇⋊C₁₆	D₄	1	2	yes	—
57	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
58	#14523979	—	2	1	no	—
59	#14523979	C₂³	1	2	yes	—
60	#14523959	—	2	4	no	—
61	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₆₇	—	2	1	no	—
63	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
64	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
65	C₂×SD₁₆×C₆₇	—	4	1	no	—
66	C₂×D₈×C₆₇	—	2	1	no	—
67	C₂×D₈×C₆₇	—	2	1	no	—
68	C₂×D₈×C₆₇	—	2	1	no	—
69	C₂×D₈×C₆₇	—	2	1	no	—
70	C₂×D₈×C₆₇	—	2	1	no	—
71	C₂×D₈×C₆₇	—	4	1	no	—
72	C₂×D₈×C₆₇	C₂³	1	2	yes	—
73	#131×C₆₇	—	2	1	no	—
74	#131×C₆₇	—	2	1	no	—
75	#131×C₆₇	D₄	1	2	yes	—
76	#131×C₆₇	C₂³	1	2	yes	—
77	C₂×M₁₆×C₆₇	—	2	1	no	—
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	—	2	1	no	—
81	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	#108×C₆₇	—	2	1	no	—
83	#108×C₆₇	C₂³	1	2	yes	—
84	#100×C₆₇	—	2	4	no	—
85	C₂³×D₆₇	—	4	1	no	—
86	C₂×D₂₆₈	—	2	2	no	—
87	C₂×D₂₆₈	—	4	1	no	—
88	C₂×D₂₆₈	—	4	1	no	—
89	C₂×D₂₆₈	—	4	1	no	—
90	C₂×D₂₆₈	—	4	1	no	—
91	C₂×D₂₆₈	—	4	1	no	—
92	#11761615	—	4	4	no	—
93	D₅₃₆	—	2	2	no	—
94	D₅₃₆	—	2	2	no	—
95	D₅₃₆	—	4	1	no	—
96	D₅₃₆	—	4	1	no	—
97	#11761613	—	4	4	no	—
98	#11761612	—	2	2	no	—
99	#11761612	—	4	1	no	—
100	C₂×C₆₇⋊C₈	—	4	1	no	—
101	C₆₇⋊C₁₆	—	2	2	no	—
102	C₆₇⋊C₁₆	C₂×D₄	1	2	yes	—
103	C₆₇⋊C₁₆	C₂×D₄	1	2	yes	—
104	C₂⁴×C₆₇	—	4	1	no	—
105	#41×C₆₇	—	2	1	no	—
106	#41×C₆₇	—	2	1	no	—
107	#41×C₆₇	D₈	1	2	yes	—
108	#41×C₆₇	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₆₇	D₈	1	1	yes	characteristic
110	C₂×D₄×C₆₇	—	2	1	no	—
111	C₂×D₄×C₆₇	—	2	2	no	—
112	C₂×D₄×C₆₇	—	4	1	no	—
113	C₂×D₄×C₆₇	—	4	1	no	—
114	C₂×D₄×C₆₇	—	4	1	no	—
115	C₂×D₄×C₆₇	—	4	1	no	—
116	C₂×D₄×C₆₇	—	4	1	no	—
117	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	—	2	1	no	—
119	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
120	SD₁₆×C₆₇	—	4	4	no	—
121	D₈×C₆₇	—	2	2	no	—
122	D₈×C₆₇	—	2	2	no	—
123	D₈×C₆₇	—	4	4	no	—
124	D₈×C₆₇	—	4	1	no	—
125	D₈×C₆₇	—	4	1	no	—
126	M₁₆×C₆₇	—	2	1	no	—
127	M₁₆×C₆₇	—	2	2	no	—
128	M₁₆×C₆₇	—	2	2	no	—
129	M₁₆×C₆₇	—	2	2	no	—
130	M₁₆×C₆₇	—	4	1	no	—
131	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₆₇	—	2	1	no	—
133	C₂×C₈×C₆₇	—	2	2	no	—
134	C₂×C₈×C₆₇	—	2	2	no	—
135	C₂×C₈×C₆₇	—	4	1	no	—
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
140	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
142	C₂³×C₆₇	—	2	1	no	—
143	C₂³×C₆₇	—	4	2	no	—
144	C₂³×C₆₇	—	8	1	no	—
145	C₂³×C₆₇	—	8	1	no	—
146	C₂³×C₆₇	—	16	2	no	—
147	C₂³×C₆₇	#135	1	1	yes	characteristic
148	C₂²×D₆₇	—	4	2	no	—
149	C₂²×D₆₇	—	8	1	no	—
150	C₂²×D₆₇	—	8	1	no	—
151	C₂²×D₆₇	—	16	2	no	—
152	Q₈×C₆₇	—	2	1	no	—
153	Q₈×C₆₇	C₂×D₈	1	2	yes	—
154	D₄×C₆₇	—	2	2	no	—
155	D₄×C₆₇	—	2	2	no	—
156	D₄×C₆₇	—	2	1	no	—
157	D₄×C₆₇	—	4	2	no	—
158	D₄×C₆₇	—	4	2	no	—
159	D₄×C₆₇	—	8	1	no	—
160	D₄×C₆₇	—	8	1	no	—
161	D₄×C₆₇	C₂×D₈	1	2	yes	—
162	C₂×C₄×C₆₇	—	2	1	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
171	D₂₆₈	—	4	2	no	—
172	D₂₆₈	—	4	2	no	—
173	D₂₆₈	—	8	1	no	—
174	D₂₆₈	—	8	1	no	—
175	C₈×C₆₇	—	2	2	no	—
176	C₈×C₆₇	—	4	2	no	—
177	C₈×C₆₇	#121	1	1	yes	characteristic
178	C₈×C₆₇	#121	1	1	yes	characteristic
179	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
180	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
181	C₆₇⋊C₈	—	4	2	no	—
182	C₂²×C₆₇	—	2	2	no	—
183	C₂²×C₆₇	—	2	2	no	—
184	C₂²×C₆₇	—	4	2	no	—
185	C₂²×C₆₇	—	8	2	no	—
186	C₂²×C₆₇	—	16	2	no	—
187	C₂²×C₆₇	—	16	2	no	—
188	C₂²×C₆₇	—	16	2	no	—
189	C₂²×C₆₇	#466	1	1	yes	characteristic
190	C₂²×C₆₇	#466	1	1	yes	characteristic
191	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
192	C₂×D₆₇	—	8	2	no	—
193	C₂×D₆₇	—	16	2	no	—
194	C₂×D₆₇	—	16	2	no	—
195	C₂×D₆₇	—	16	2	no	—
196	C₄×C₆₇	—	2	2	no	—
197	C₄×C₆₇	#466	1	1	yes	characteristic
198	C₄×C₆₇	#466	1	1	yes	characteristic
199	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
200	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
201	C₂×#2221	—	67	1	no	maximal, Sylow
202	C₂×C₆₇	—	2	1	no	—
203	C₂×C₆₇	—	2	1	no	—
204	C₂×C₆₇	—	4	2	no	—
205	C₂×C₆₇	—	16	2	no	—
206	C₂×C₆₇	#2221	1	2	yes	complemented
207	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
208	D₆₇	—	16	2	no	—
209	C₂²×D₁₆	—	67	1	no	—
210	C₂×#504	—	67	1	no	—
211	C₂×#472	—	67	1	no	—
212	C₂×#472	D₆₇	1	1	yes	characteristic, complemented
213	#2221	—	67	8	no	—
214	C₂×#368	—	67	1	no	—
215	C₂×#361	—	67	1	no	—
216	C₂×#361	—	67	1	no	—
217	C₆₇	C₂×#2221	1	1	yes	characteristic, complemented, Sylow
218	C₂×AGL(1,ℤ/8)	—	2	1	no	—
219	C₂×AGL(1,ℤ/8)	—	134	1	no	—
220	C₂²×D₈	—	67	1	no	—
221	C₂²×D₈	C₂×D₆₇	1	1	yes	characteristic
222	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
223	C₂×D₁₆	—	67	4	no	—
224	C₂×D₁₆	—	134	1	no	—
225	C₂×D₁₆	—	134	1	no	—
226	C₂×D₁₆	—	134	2	no	—
227	#504	—	67	4	no	—
228	#504	—	134	2	no	—
229	C₂×M₃₂	—	67	1	no	—
230	C₂×M₃₂	—	134	1	no	—
231	C₂²×C₁₆	—	67	1	no	—
232	C₂²×C₁₆	—	134	1	no	—
233	#472	—	2	2	no	—
234	#472	—	67	4	no	—
235	#472	—	134	2	no	—
236	#472	C₂×D₆₇	1	4	yes	complemented
237	C₂×#108	—	67	1	no	—
238	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
239	C₂×#100	—	2	1	no	—
240	C₂×#100	—	134	1	no	—
241	#368	—	67	4	no	—
242	#361	—	67	4	no	—
243	#361	—	67	4	no	—
244	C₂×#41	C₂²⋊D₆₇	1	1	yes	characteristic
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	134	1	no	—
247	AGL(1,ℤ/8)	—	2	4	no	—
248	AGL(1,ℤ/8)	—	4	2	no	—
249	AGL(1,ℤ/8)	—	268	2	no	—
250	AGL(1,ℤ/8)	—	134	4	no	—
251	C₂×SD₁₆	—	4	1	no	—
252	C₂×SD₁₆	—	268	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	4	1	no	—
259	C₂×D₈	—	268	1	no	—
260	C₂×D₈	—	67	2	no	—
261	C₂×D₈	—	134	1	no	—
262	C₂×D₈	—	134	1	no	—
263	C₂×D₈	—	134	1	no	—
264	C₂×D₈	—	134	1	no	—
265	C₂×D₈	—	134	1	no	—
266	C₂×D₈	C₂²×D₆₇	1	2	yes	—
267	#131	—	2	1	no	—
268	#131	—	2	1	no	—
269	#131	C₂²⋊D₆₇	1	2	yes	—
270	#131	C₂²×D₆₇	1	2	yes	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	2	1	no	—
273	C₂×M₁₆	—	134	1	no	—
274	C₂×M₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
277	D₁₆	—	134	4	no	—
278	D₁₆	—	134	4	no	—
279	M₃₂	—	67	2	no	—
280	M₃₂	—	134	4	no	—
281	M₃₂	—	134	1	no	—
282	C₂×C₁₆	—	67	1	no	—
283	C₂×C₁₆	—	67	1	no	—
284	C₂×C₁₆	—	67	2	no	—
285	C₂×C₁₆	—	67	2	no	—
286	C₂×C₁₆	—	134	4	no	—
287	C₂×C₁₆	—	134	1	no	—
288	#108	—	2	1	no	—
289	#108	—	67	2	no	—
290	#108	—	134	1	no	—
291	#108	C₂²×D₆₇	1	2	yes	—
292	#100	—	2	4	no	—
293	#100	—	134	4	no	—
294	C₂⁴	—	4	1	no	—
295	C₂⁴	—	268	1	no	—
296	#41	—	2	1	no	—
297	#41	—	2	1	no	—
298	#41	#11761613	1	2	yes	—
299	#41	C₂×C₂²⋊D₆₇	1	2	yes	—
300	C₂×Q₈	#11761613	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	268	1	no	—
309	C₂×D₄	—	268	1	no	—
310	C₂×D₄	—	268	1	no	—
311	C₂×D₄	—	268	1	no	—
312	C₂×D₄	—	268	1	no	—
313	C₂×D₄	—	134	2	no	—
314	C₂×D₄	#11761613	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
317	SD₁₆	—	4	4	no	—
318	SD₁₆	—	268	4	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	4	no	—
322	D₈	—	4	1	no	—
323	D₈	—	4	1	no	—
324	D₈	—	268	4	no	—
325	D₈	—	268	1	no	—
326	D₈	—	268	1	no	—
327	D₈	—	134	2	no	—
328	D₈	—	134	2	no	—
329	M₁₆	—	2	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	4	1	no	—
334	M₁₆	—	268	1	no	—
335	M₁₆	—	134	2	no	—
336	M₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	268	1	no	—
342	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
343	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
345	C₂×C₈	#11761627	1	1	yes	characteristic
346	C₂×C₈	#11761627	1	1	yes	characteristic
347	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
348	C₁₆	—	67	2	no	—
349	C₁₆	—	67	2	no	—
350	C₁₆	—	134	2	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	8	1	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	268	2	no	—
356	C₂³	—	16	2	no	—
357	C₂³	—	536	1	no	—
358	C₂³	—	536	1	no	—
359	C₂³	—	1072	2	no	—
360	C₂³	#14524063	1	1	yes	characteristic
361	Q₈	—	2	1	no	—
362	Q₈	C₂×#11761613	1	2	yes	—
363	D₄	—	2	2	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	1	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	8	1	no	—
369	D₄	—	8	1	no	—
370	D₄	—	268	2	no	—
371	D₄	—	268	2	no	—
372	D₄	—	536	1	no	—
373	D₄	—	536	1	no	—
374	D₄	C₂×#11761613	1	2	yes	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	#14524015	1	1	yes	characteristic
379	C₂×C₄	#14524015	1	1	yes	characteristic
380	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
381	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
382	C₂×C₄	#14524063	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	268	2	no	—
387	C₈	#14524015	1	1	yes	characteristic
388	C₈	#14524015	1	1	yes	characteristic
389	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
390	C₈	C₂×#11761627	1	1	yes	characteristic
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	2	no	—
396	C₂²	—	16	2	no	—
397	C₂²	—	16	2	no	—
398	C₂²	—	536	2	no	—
399	C₂²	—	1072	2	no	—
400	C₂²	—	1072	2	no	—
401	C₂²	—	1072	2	no	—
402	C₂²	#16863630	1	1	yes	characteristic
403	C₂²	#16863630	1	1	yes	characteristic
404	C₂²	C₂×#14524063	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	#16863630	1	1	yes	characteristic
407	C₄	#16863630	1	1	yes	characteristic
408	C₄	C₂×#14524015	1	1	yes	characteristic
409	C₄	C₂²×#11761613	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	4	2	no	—
413	C₂	—	16	2	no	—
414	C₂	—	1072	2	no	—
415	C₂	#22562327	1	2	yes	direct product factor
416	C₂	C₂×#16863630	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863630
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂×#472×C₆₇	C₂
socle	C₂²×C₆₇	#466
hypercenter	C₂×#472	D₆₇
hypocenter	C₆₇	C₂×#2221
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. C₂²×#14523984	C₂	semidirect
2. C₂×#16863813	C₂	semidirect
3. C₂×#16863666	C₂	semidirect
4. #22562327	C₂	direct (N × H)
5. C₂×#16863225	C₂	semidirect
6. C₂×#16863209	C₂	semidirect
7. C₂×#16863208	C₂	semidirect
8. C₂×#472×C₆₇	C₂	semidirect
14. C₂×#14523984	C₂²	semidirect
16. #16863813	C₂²	semidirect
22. #16863666	C₂²	semidirect
25. #16863225	C₂²	semidirect
26. #16863209	C₂²	semidirect
27. #16863208	C₂²	semidirect
32. #472×C₆₇	C₂²	semidirect
206. C₂×C₆₇	#2221	semidirect
212. C₂×#472	D₆₇	semidirect
217. C₆₇	C₂×#2221	semidirect
236. #472	C₂×D₆₇	semidirect
415. C₂	#22562327	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523984	2
C₂×#16863813	2
C₂×#16863666	2
#22562327	2
C₂×#16863225	2
C₂×#16863209	2
C₂×#16863208	2
C₂×#472×C₆₇	2
C₂×#2221	67

Subgroups — C2×#22562327 #31010386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562327 #31010386