Subgroups — C₂×C₆₇×#3288 #30740349

Order 17152.

2704 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₂×#576×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#3288	C₂	1	16	yes	maximal, direct product factor
4	C₂×#496×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#472×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#471×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#454×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#455×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#453×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#444×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
12	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
14	#577×C₆₇	—	2	8	no	—
15	#577×C₆₇	C₂²	1	16	yes	complemented
16	#576×C₆₇	—	2	8	no	—
17	#576×C₆₇	C₂²	1	16	yes	complemented
18	C₂×#137×C₆₇	—	2	2	no	—
19	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
20	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
21	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
22	C₂×AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
23	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
24	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
26	C₂×#135×C₆₇	—	2	2	no	—
27	C₂×#135×C₆₇	—	2	2	no	—
28	C₂×#135×C₆₇	C₂²	1	2	yes	—
29	C₂²×SD₁₆×C₆₇	—	2	2	no	—
30	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
31	C₂²×D₈×C₆₇	—	2	2	no	—
32	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
35	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#496×C₆₇	C₂²	1	8	yes	complemented
38	#472×C₆₇	C₂²	1	16	yes	complemented
39	#471×C₆₇	C₂²	1	16	yes	complemented
40	#455×C₆₇	C₂²	1	8	yes	complemented
41	#454×C₆₇	C₂²	1	8	yes	complemented
42	#453×C₆₇	C₂²	1	16	yes	complemented
43	#444×C₆₇	C₂²	1	16	yes	complemented
44	C₂×#108×C₆₇	C₂²	1	2	yes	complemented
45	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
46	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
47	C₂×#101×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×#100×C₆₇	C₂²	1	2	yes	complemented
49	C₂×#100×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	2₋¹⁺⁴×C₆₇	—	2	4	no	—
52	2₋¹⁺⁴×C₆₇	—	4	1	no	—
53	2₋¹⁺⁴×C₆₇	C₂³	1	4	yes	complemented
54	H(5,𝔽₂)×C₆₇	—	2	4	no	—
55	H(5,𝔽₂)×C₆₇	—	2	4	no	—
56	H(5,𝔽₂)×C₆₇	—	2	4	no	—
57	H(5,𝔽₂)×C₆₇	—	4	1	no	—
58	H(5,𝔽₂)×C₆₇	—	4	2	no	—
59	H(5,𝔽₂)×C₆₇	C₂³	1	4	yes	—
60	H(5,𝔽₂)×C₆₇	C₂³	1	8	yes	complemented
61	C₂×#41×C₆₇	—	2	2	no	—
62	C₂×#41×C₆₇	—	2	2	no	—
63	C₂×#41×C₆₇	—	2	2	no	—
64	C₂×#41×C₆₇	—	2	2	no	—
65	C₂×#41×C₆₇	—	4	1	no	—
66	C₂×#41×C₆₇	C₂³	1	2	yes	—
67	C₂×#41×C₆₇	C₂³	1	2	yes	—
68	C₂²×Q₈×C₆₇	—	2	2	no	—
69	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₆₇	—	2	2	no	—
71	C₂²×D₄×C₆₇	—	2	2	no	—
72	C₂²×D₄×C₆₇	—	2	2	no	—
73	C₂²×D₄×C₆₇	—	4	1	no	—
74	C₂²×D₄×C₆₇	—	4	1	no	—
75	C₂²×D₄×C₆₇	—	4	2	no	—
76	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
78	#137×C₆₇	—	2	4	no	—
79	#137×C₆₇	—	2	16	no	—
80	#137×C₆₇	C₂³	1	8	yes	complemented
81	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
82	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
83	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
84	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
85	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
86	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
87	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	—
88	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	complemented
89	AGL(1,ℤ/8)×C₆₇	C₂³	1	8	yes	complemented
90	#135×C₆₇	—	2	16	no	—
91	#135×C₆₇	—	2	16	no	—
92	#135×C₆₇	D₄	1	8	yes	complemented
93	#135×C₆₇	C₂³	1	8	yes	—
94	C₂×Q₁₆×C₆₇	—	2	2	no	—
95	C₂×Q₁₆×C₆₇	D₄	1	2	yes	complemented
96	C₂×SD₁₆×C₆₇	—	2	2	no	—
97	C₂×SD₁₆×C₆₇	—	2	2	no	—
98	C₂×SD₁₆×C₆₇	—	2	2	no	—
99	C₂×SD₁₆×C₆₇	—	2	2	no	—
100	C₂×SD₁₆×C₆₇	—	2	16	no	—
101	C₂×SD₁₆×C₆₇	—	2	2	no	—
102	C₂×SD₁₆×C₆₇	—	2	2	no	—
103	C₂×SD₁₆×C₆₇	—	2	4	no	—
104	C₂×SD₁₆×C₆₇	D₄	1	2	yes	complemented
105	C₂×SD₁₆×C₆₇	D₄	1	2	yes	complemented
106	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
107	C₂×D₈×C₆₇	—	2	2	no	—
108	C₂×D₈×C₆₇	—	2	2	no	—
109	C₂×D₈×C₆₇	—	2	2	no	—
110	C₂×D₈×C₆₇	—	2	16	no	—
111	C₂×D₈×C₆₇	—	2	2	no	—
112	C₂×D₈×C₆₇	—	2	2	no	—
113	C₂×D₈×C₆₇	—	2	4	no	—
114	C₂×D₈×C₆₇	D₄	1	2	yes	complemented
115	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
116	#131×C₆₇	—	2	4	no	—
117	#131×C₆₇	—	2	4	no	—
118	#131×C₆₇	C₂³	1	8	yes	complemented
119	#131×C₆₇	C₂³	1	8	yes	complemented
120	C₂×M₁₆×C₆₇	—	2	2	no	—
121	C₂×M₁₆×C₆₇	—	2	2	no	—
122	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂²×C₈×C₆₇	—	2	2	no	—
125	C₂²×C₈×C₆₇	—	2	2	no	—
126	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
127	#127×C₆₇	—	4	1	no	—
128	#127×C₆₇	C₂³	1	4	yes	complemented
129	#124×C₆₇	—	4	1	no	—
130	#124×C₆₇	C₂³	1	4	yes	complemented
131	C₂×C₂²⋊C₄×C₆₇	—	4	1	no	—
132	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
133	#108×C₆₇	C₂³	1	8	yes	complemented
134	#104×C₆₇	C₂³	1	8	yes	complemented
135	#104×C₆₇	C₂³	1	8	yes	complemented
136	#101×C₆₇	C₂³	1	4	yes	complemented
137	#100×C₆₇	C₂³	1	8	yes	complemented
138	#100×C₆₇	C₂³	1	4	yes	complemented
139	#97×C₆₇	C₂³	1	4	yes	complemented
140	C₂⁴×C₆₇	—	2	1	no	—
141	C₂⁴×C₆₇	—	2	2	no	—
142	C₂⁴×C₆₇	—	4	2	no	—
143	C₂⁴×C₆₇	—	4	1	no	—
144	#41×C₆₇	—	2	2	no	—
145	#41×C₆₇	—	2	2	no	—
146	#41×C₆₇	—	2	2	no	—
147	#41×C₆₇	—	2	2	no	—
148	#41×C₆₇	—	2	8	no	—
149	#41×C₆₇	—	2	8	no	—
150	#41×C₆₇	—	2	8	no	—
151	#41×C₆₇	—	2	8	no	—
152	#41×C₆₇	—	4	4	no	—
153	#41×C₆₇	—	4	4	no	—
154	#41×C₆₇	—	4	4	no	—
155	#41×C₆₇	—	4	4	no	—
156	#41×C₆₇	—	4	4	no	—
157	#41×C₆₇	—	4	4	no	—
158	#41×C₆₇	C₂×D₄	1	4	yes	—
159	#41×C₆₇	C₂×D₄	1	4	yes	—
160	#41×C₆₇	C₂⁴	1	4	yes	—
161	#41×C₆₇	C₂⁴	1	4	yes	—
162	C₂×Q₈×C₆₇	—	2	1	no	—
163	C₂×Q₈×C₆₇	—	2	8	no	—
164	C₂×Q₈×C₆₇	—	2	2	no	—
165	C₂×Q₈×C₆₇	—	2	2	no	—
166	C₂×Q₈×C₆₇	—	4	1	no	—
167	C₂×Q₈×C₆₇	—	4	4	no	—
168	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
169	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
170	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
171	C₂×D₄×C₆₇	—	2	2	no	—
172	C₂×D₄×C₆₇	—	2	2	no	—
173	C₂×D₄×C₆₇	—	2	8	no	—
174	C₂×D₄×C₆₇	—	2	8	no	—
175	C₂×D₄×C₆₇	—	2	8	no	—
176	C₂×D₄×C₆₇	—	2	2	no	—
177	C₂×D₄×C₆₇	—	2	2	no	—
178	C₂×D₄×C₆₇	—	2	2	no	—
179	C₂×D₄×C₆₇	—	2	2	no	—
180	C₂×D₄×C₆₇	—	2	2	no	—
181	C₂×D₄×C₆₇	—	2	2	no	—
182	C₂×D₄×C₆₇	—	2	1	no	—
183	C₂×D₄×C₆₇	—	2	2	no	—
184	C₂×D₄×C₆₇	—	4	4	no	—
185	C₂×D₄×C₆₇	—	4	4	no	—
186	C₂×D₄×C₆₇	—	4	4	no	—
187	C₂×D₄×C₆₇	—	4	2	no	—
188	C₂×D₄×C₆₇	—	4	2	no	—
189	C₂×D₄×C₆₇	—	4	2	no	—
190	C₂×D₄×C₆₇	—	4	4	no	—
191	C₂×D₄×C₆₇	—	4	4	no	—
192	C₂×D₄×C₆₇	—	4	8	no	—
193	C₂×D₄×C₆₇	—	4	4	no	—
194	C₂×D₄×C₆₇	—	4	8	no	—
195	C₂×D₄×C₆₇	—	4	1	no	—
196	C₂×D₄×C₆₇	—	8	4	no	—
197	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₆₇	—	2	2	no	—
202	C₂²×C₄×C₆₇	—	2	2	no	—
203	C₂²×C₄×C₆₇	—	2	1	no	—
204	C₂²×C₄×C₆₇	—	2	1	no	—
205	C₂²×C₄×C₆₇	—	4	1	no	—
206	C₂²×C₄×C₆₇	—	4	2	no	—
207	C₂²×C₄×C₆₇	—	4	2	no	—
208	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	Q₁₆×C₆₇	—	2	8	no	—
210	Q₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
211	SD₁₆×C₆₇	—	2	8	no	—
212	SD₁₆×C₆₇	—	2	8	no	—
213	SD₁₆×C₆₇	—	2	8	no	—
214	SD₁₆×C₆₇	—	2	8	no	—
215	SD₁₆×C₆₇	—	2	8	no	—
216	SD₁₆×C₆₇	—	2	8	no	—
217	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
218	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
219	D₈×C₆₇	—	2	8	no	—
220	D₈×C₆₇	—	2	8	no	—
221	D₈×C₆₇	—	2	8	no	—
222	D₈×C₆₇	—	2	8	no	—
223	D₈×C₆₇	—	2	8	no	—
224	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
225	M₁₆×C₆₇	—	2	2	no	—
226	M₁₆×C₆₇	—	2	2	no	—
227	M₁₆×C₆₇	—	2	8	no	—
228	M₁₆×C₆₇	—	2	8	no	—
229	M₁₆×C₆₇	C₂⁴	1	4	yes	—
230	M₁₆×C₆₇	C₂⁴	1	4	yes	—
231	C₂×C₈×C₆₇	—	2	2	no	—
232	C₂×C₈×C₆₇	—	2	2	no	—
233	C₂×C₈×C₆₇	—	2	8	no	—
234	C₂×C₈×C₆₇	—	2	8	no	—
235	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
237	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
238	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
239	C₂²⋊C₄×C₆₇	—	4	4	no	—
240	C₄²×C₆₇	—	2	1	no	—
241	C₄²×C₆₇	C₂⁴	1	2	yes	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	2	no	—
244	C₂³×C₆₇	—	2	2	no	—
245	C₂³×C₆₇	—	2	4	no	—
246	C₂³×C₆₇	—	4	8	no	—
247	C₂³×C₆₇	—	4	4	no	—
248	C₂³×C₆₇	—	4	1	no	—
249	C₂³×C₆₇	—	4	2	no	—
250	C₂³×C₆₇	—	4	1	no	—
251	C₂³×C₆₇	—	4	2	no	—
252	C₂³×C₆₇	—	8	4	no	—
253	C₂³×C₆₇	—	8	2	no	—
254	C₂³×C₆₇	—	16	4	no	—
255	C₂³×C₆₇	—	16	2	no	—
256	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
257	Q₈×C₆₇	—	2	2	no	—
258	Q₈×C₆₇	—	2	2	no	—
259	Q₈×C₆₇	—	2	4	no	—
260	Q₈×C₆₇	—	4	4	no	—
261	Q₈×C₆₇	—	4	2	no	—
262	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
263	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
264	D₄×C₆₇	—	2	4	no	—
265	D₄×C₆₇	—	2	4	no	—
266	D₄×C₆₇	—	2	4	no	—
267	D₄×C₆₇	—	2	4	no	—
268	D₄×C₆₇	—	2	2	no	—
269	D₄×C₆₇	—	2	2	no	—
270	D₄×C₆₇	—	2	4	no	—
271	D₄×C₆₇	—	2	4	no	—
272	D₄×C₆₇	—	2	4	no	—
273	D₄×C₆₇	—	4	8	no	—
274	D₄×C₆₇	—	4	8	no	—
275	D₄×C₆₇	—	4	8	no	—
276	D₄×C₆₇	—	4	4	no	—
277	D₄×C₆₇	—	4	2	no	—
278	D₄×C₆₇	—	4	2	no	—
279	D₄×C₆₇	—	4	2	no	—
280	D₄×C₆₇	—	8	8	no	—
281	D₄×C₆₇	C₂²×D₄	1	4	yes	—
282	D₄×C₆₇	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	2	4	no	—
286	C₂×C₄×C₆₇	—	2	4	no	—
287	C₂×C₄×C₆₇	—	2	4	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	4	4	no	—
292	C₂×C₄×C₆₇	—	4	8	no	—
293	C₂×C₄×C₆₇	—	4	8	no	—
294	C₂×C₄×C₆₇	—	4	2	no	—
295	C₂×C₄×C₆₇	—	4	1	no	—
296	C₂×C₄×C₆₇	—	4	1	no	—
297	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
301	C₈×C₆₇	—	2	4	no	—
302	C₈×C₆₇	—	2	4	no	—
303	C₈×C₆₇	C₂²×D₄	1	4	yes	—
304	C₈×C₆₇	C₂²×D₄	1	4	yes	—
305	C₂²×C₆₇	—	2	2	no	—
306	C₂²×C₆₇	—	2	4	no	—
307	C₂²×C₆₇	—	2	4	no	—
308	C₂²×C₆₇	—	4	4	no	—
309	C₂²×C₆₇	—	4	4	no	—
310	C₂²×C₆₇	—	4	2	no	—
311	C₂²×C₆₇	—	4	4	no	—
312	C₂²×C₆₇	—	8	4	no	—
313	C₂²×C₆₇	—	8	2	no	—
314	C₂²×C₆₇	—	8	4	no	—
315	C₂²×C₆₇	—	8	2	no	—
316	C₂²×C₆₇	—	16	2	no	—
317	C₂²×C₆₇	—	16	1	no	—
318	C₂²×C₆₇	—	16	8	no	—
319	C₂²×C₆₇	—	16	4	no	—
320	C₂²×C₆₇	D₄²	1	1	yes	characteristic
321	C₂²×C₆₇	D₄²	1	1	yes	characteristic
322	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₄×C₆₇	—	2	4	no	—
324	C₄×C₆₇	—	2	4	no	—
325	C₄×C₆₇	—	4	2	no	—
326	C₄×C₆₇	—	4	2	no	—
327	C₄×C₆₇	D₄²	1	2	yes	—
328	C₄×C₆₇	C₂³×D₄	1	2	yes	—
329	C₂×#3288	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂×C₆₇	—	2	1	no	—
331	C₂×C₆₇	—	2	1	no	—
332	C₂×C₆₇	—	4	4	no	—
333	C₂×C₆₇	—	4	4	no	—
334	C₂×C₆₇	—	8	4	no	—
335	C₂×C₆₇	—	8	2	no	—
336	C₂×C₆₇	#3288	1	2	yes	direct product factor
337	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
338	C₂×#577	C₂×C₆₇	1	2	yes	complemented
339	C₂×#576	C₂×C₆₇	1	2	yes	complemented
340	#3288	C₂×C₆₇	1	16	yes	direct product factor
341	C₂×#496	C₂×C₆₇	1	1	yes	characteristic, complemented
342	C₂×#472	C₂×C₆₇	1	2	yes	complemented
343	C₂×#471	C₂×C₆₇	1	2	yes	complemented
344	C₂×#454	C₂×C₆₇	1	1	yes	characteristic, complemented
345	C₂×#455	C₂×C₆₇	1	1	yes	characteristic, complemented
346	C₂×#453	C₂×C₆₇	1	2	yes	complemented
347	C₂×#444	C₂×C₆₇	1	2	yes	complemented
348	C₆₇	C₂×#3288	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
350	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
351	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
352	#577	—	2	8	no	—
353	#577	C₂²×C₆₇	1	16	yes	complemented
354	#576	—	2	8	no	—
355	#576	C₂²×C₆₇	1	16	yes	complemented
356	C₂×#137	—	2	2	no	—
357	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
358	C₂×AGL(1,ℤ/8)	—	2	2	no	—
359	C₂×AGL(1,ℤ/8)	—	2	2	no	—
360	C₂×AGL(1,ℤ/8)	—	2	2	no	—
361	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
362	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
363	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
364	C₂×#135	—	2	2	no	—
365	C₂×#135	—	2	2	no	—
366	C₂×#135	C₂²×C₆₇	1	2	yes	—
367	C₂²×SD₁₆	—	2	2	no	—
368	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
369	C₂²×D₈	—	2	2	no	—
370	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
371	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
372	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
373	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
374	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
375	#496	C₂²×C₆₇	1	8	yes	complemented
376	#472	C₂²×C₆₇	1	16	yes	complemented
377	#471	C₂²×C₆₇	1	16	yes	complemented
378	#455	C₂²×C₆₇	1	8	yes	complemented
379	#454	C₂²×C₆₇	1	8	yes	complemented
380	#453	C₂²×C₆₇	1	16	yes	complemented
381	#444	C₂²×C₆₇	1	16	yes	complemented
382	C₂×#108	C₂²×C₆₇	1	2	yes	complemented
383	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
384	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
385	C₂×#101	C₂²×C₆₇	1	1	yes	characteristic, complemented
386	C₂×#100	C₂²×C₆₇	1	2	yes	complemented
387	C₂×#100	C₂²×C₆₇	1	1	yes	characteristic, complemented
388	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
389	2₋¹⁺⁴	—	2	4	no	—
390	2₋¹⁺⁴	—	4	1	no	—
391	2₋¹⁺⁴	C₂³×C₆₇	1	4	yes	complemented
392	H(5,𝔽₂)	—	2	4	no	—
393	H(5,𝔽₂)	—	2	4	no	—
394	H(5,𝔽₂)	—	2	4	no	—
395	H(5,𝔽₂)	—	4	1	no	—
396	H(5,𝔽₂)	—	4	2	no	—
397	H(5,𝔽₂)	C₂³×C₆₇	1	4	yes	—
398	H(5,𝔽₂)	C₂³×C₆₇	1	8	yes	complemented
399	C₂×#41	—	2	2	no	—
400	C₂×#41	—	2	2	no	—
401	C₂×#41	—	2	2	no	—
402	C₂×#41	—	2	2	no	—
403	C₂×#41	—	4	1	no	—
404	C₂×#41	C₂³×C₆₇	1	2	yes	—
405	C₂×#41	C₂³×C₆₇	1	2	yes	—
406	C₂²×Q₈	—	2	2	no	—
407	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
408	C₂²×D₄	—	2	2	no	—
409	C₂²×D₄	—	2	2	no	—
410	C₂²×D₄	—	2	2	no	—
411	C₂²×D₄	—	4	1	no	—
412	C₂²×D₄	—	4	1	no	—
413	C₂²×D₄	—	4	2	no	—
414	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
415	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
416	#137	—	2	4	no	—
417	#137	—	2	16	no	—
418	#137	C₂³×C₆₇	1	8	yes	complemented
419	AGL(1,ℤ/8)	—	2	4	no	—
420	AGL(1,ℤ/8)	—	2	4	no	—
421	AGL(1,ℤ/8)	—	2	4	no	—
422	AGL(1,ℤ/8)	—	2	16	no	—
423	AGL(1,ℤ/8)	—	2	16	no	—
424	AGL(1,ℤ/8)	—	2	16	no	—
425	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	—
426	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	complemented
427	AGL(1,ℤ/8)	C₂³×C₆₇	1	8	yes	complemented
428	#135	—	2	16	no	—
429	#135	—	2	16	no	—
430	#135	D₄×C₆₇	1	8	yes	complemented
431	#135	C₂³×C₆₇	1	8	yes	—
432	C₂×Q₁₆	—	2	2	no	—
433	C₂×Q₁₆	D₄×C₆₇	1	2	yes	complemented
434	C₂×SD₁₆	—	2	2	no	—
435	C₂×SD₁₆	—	2	2	no	—
436	C₂×SD₁₆	—	2	2	no	—
437	C₂×SD₁₆	—	2	2	no	—
438	C₂×SD₁₆	—	2	16	no	—
439	C₂×SD₁₆	—	2	2	no	—
440	C₂×SD₁₆	—	2	2	no	—
441	C₂×SD₁₆	—	2	4	no	—
442	C₂×SD₁₆	D₄×C₆₇	1	2	yes	complemented
443	C₂×SD₁₆	D₄×C₆₇	1	2	yes	complemented
444	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
445	C₂×D₈	—	2	2	no	—
446	C₂×D₈	—	2	2	no	—
447	C₂×D₈	—	2	2	no	—
448	C₂×D₈	—	2	16	no	—
449	C₂×D₈	—	2	2	no	—
450	C₂×D₈	—	2	2	no	—
451	C₂×D₈	—	2	4	no	—
452	C₂×D₈	D₄×C₆₇	1	2	yes	complemented
453	C₂×D₈	C₂³×C₆₇	1	8	yes	complemented
454	#131	—	2	4	no	—
455	#131	—	2	4	no	—
456	#131	C₂³×C₆₇	1	8	yes	complemented
457	#131	C₂³×C₆₇	1	8	yes	complemented
458	C₂×M₁₆	—	2	2	no	—
459	C₂×M₁₆	—	2	2	no	—
460	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
461	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
462	C₂²×C₈	—	2	2	no	—
463	C₂²×C₈	—	2	2	no	—
464	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
465	#127	—	4	1	no	—
466	#127	C₂³×C₆₇	1	4	yes	complemented
467	#124	—	4	1	no	—
468	#124	C₂³×C₆₇	1	4	yes	complemented
469	C₂×C₂²⋊C₄	—	4	1	no	—
470	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
471	#108	C₂³×C₆₇	1	8	yes	complemented
472	#104	C₂³×C₆₇	1	8	yes	complemented
473	#104	C₂³×C₆₇	1	8	yes	complemented
474	#101	C₂³×C₆₇	1	4	yes	complemented
475	#100	C₂³×C₆₇	1	8	yes	complemented
476	#100	C₂³×C₆₇	1	4	yes	complemented
477	#97	C₂³×C₆₇	1	4	yes	complemented
478	C₂⁴	—	2	1	no	—
479	C₂⁴	—	2	2	no	—
480	C₂⁴	—	4	2	no	—
481	C₂⁴	—	4	1	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	—	2	2	no	—
485	#41	—	2	2	no	—
486	#41	—	2	8	no	—
487	#41	—	2	8	no	—
488	#41	—	2	8	no	—
489	#41	—	2	8	no	—
490	#41	—	4	4	no	—
491	#41	—	4	4	no	—
492	#41	—	4	4	no	—
493	#41	—	4	4	no	—
494	#41	—	4	4	no	—
495	#41	—	4	4	no	—
496	#41	C₂×D₄×C₆₇	1	4	yes	—
497	#41	C₂×D₄×C₆₇	1	4	yes	—
498	#41	C₂⁴×C₆₇	1	4	yes	—
499	#41	C₂⁴×C₆₇	1	4	yes	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	8	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	2	no	—
504	C₂×Q₈	—	4	1	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
507	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
508	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	8	no	—
512	C₂×D₄	—	2	8	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	4	4	no	—
523	C₂×D₄	—	4	4	no	—
524	C₂×D₄	—	4	4	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂×D₄	—	4	2	no	—
528	C₂×D₄	—	4	4	no	—
529	C₂×D₄	—	4	4	no	—
530	C₂×D₄	—	4	8	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	—	4	8	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂×D₄	—	8	4	no	—
535	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
536	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
537	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
538	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	4	1	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
547	Q₁₆	—	2	8	no	—
548	Q₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
549	SD₁₆	—	2	8	no	—
550	SD₁₆	—	2	8	no	—
551	SD₁₆	—	2	8	no	—
552	SD₁₆	—	2	8	no	—
553	SD₁₆	—	2	8	no	—
554	SD₁₆	—	2	8	no	—
555	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
556	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
557	D₈	—	2	8	no	—
558	D₈	—	2	8	no	—
559	D₈	—	2	8	no	—
560	D₈	—	2	8	no	—
561	D₈	—	2	8	no	—
562	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
563	M₁₆	—	2	2	no	—
564	M₁₆	—	2	2	no	—
565	M₁₆	—	2	8	no	—
566	M₁₆	—	2	8	no	—
567	M₁₆	C₂⁴×C₆₇	1	4	yes	—
568	M₁₆	C₂⁴×C₆₇	1	4	yes	—
569	C₂×C₈	—	2	2	no	—
570	C₂×C₈	—	2	2	no	—
571	C₂×C₈	—	2	8	no	—
572	C₂×C₈	—	2	8	no	—
573	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
574	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
575	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
576	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
577	C₂²⋊C₄	—	4	4	no	—
578	C₄²	—	2	1	no	—
579	C₄²	C₂⁴×C₆₇	1	2	yes	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	4	8	no	—
585	C₂³	—	4	4	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	8	4	no	—
591	C₂³	—	8	2	no	—
592	C₂³	—	16	2	no	—
593	C₂³	—	16	4	no	—
594	C₂³	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
595	Q₈	—	2	2	no	—
596	Q₈	—	2	2	no	—
597	Q₈	—	2	4	no	—
598	Q₈	—	4	4	no	—
599	Q₈	—	4	2	no	—
600	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
601	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
602	D₄	—	2	4	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	4	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	4	no	—
609	D₄	—	2	4	no	—
610	D₄	—	2	4	no	—
611	D₄	—	4	8	no	—
612	D₄	—	4	8	no	—
613	D₄	—	4	8	no	—
614	D₄	—	4	4	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	8	8	no	—
619	D₄	C₂²×D₄×C₆₇	1	4	yes	—
620	D₄	C₂²×D₄×C₆₇	1	4	yes	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	8	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
636	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
637	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
638	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
639	C₈	—	2	4	no	—
640	C₈	—	2	4	no	—
641	C₈	C₂²×D₄×C₆₇	1	4	yes	—
642	C₈	C₂²×D₄×C₆₇	1	4	yes	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	4	no	—
650	C₂²	—	8	4	no	—
651	C₂²	—	8	2	no	—
652	C₂²	—	8	4	no	—
653	C₂²	—	8	2	no	—
654	C₂²	—	16	2	no	—
655	C₂²	—	16	1	no	—
656	C₂²	—	16	4	no	—
657	C₂²	—	16	8	no	—
658	C₂²	D₄²×C₆₇	1	1	yes	characteristic
659	C₂²	D₄²×C₆₇	1	1	yes	characteristic
660	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
661	C₄	—	2	4	no	—
662	C₄	—	2	4	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	D₄²×C₆₇	1	2	yes	—
666	C₄	C₂³×D₄×C₆₇	1	2	yes	—
667	C₂	—	2	1	no	—
668	C₂	—	2	1	no	—
669	C₂	—	4	4	no	—
670	C₂	—	4	4	no	—
671	C₂	—	8	4	no	—
672	C₂	—	8	2	no	—
673	C₂	C₆₇×#3288	1	2	yes	direct product factor
674	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#577×C₆₇	C₂	semidirect
2. C₂×#576×C₆₇	C₂	semidirect
3. C₆₇×#3288	C₂	direct (N × H)
4. C₂×#496×C₆₇	C₂	semidirect
5. C₂×#472×C₆₇	C₂	semidirect
6. C₂×#471×C₆₇	C₂	semidirect
7. C₂×#454×C₆₇	C₂	semidirect
8. C₂×#455×C₆₇	C₂	semidirect
9. C₂×#453×C₆₇	C₂	semidirect
10. C₂×#444×C₆₇	C₂	semidirect
11. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
13. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
15. #577×C₆₇	C₂²	semidirect
17. #576×C₆₇	C₂²	semidirect
19. C₂×#137×C₆₇	C₂²	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
30. C₂²×SD₁₆×C₆₇	C₂²	semidirect
32. C₂²×D₈×C₆₇	C₂²	semidirect
33. C₂×#131×C₆₇	C₂²	semidirect
34. C₂×#131×C₆₇	C₂²	semidirect
35. C₂×#127×C₆₇	C₂²	semidirect
36. C₂×#124×C₆₇	C₂²	semidirect
37. #496×C₆₇	C₂²	semidirect
38. #472×C₆₇	C₂²	semidirect
39. #471×C₆₇	C₂²	semidirect
40. #455×C₆₇	C₂²	semidirect
41. #454×C₆₇	C₂²	semidirect
42. #453×C₆₇	C₂²	semidirect
43. #444×C₆₇	C₂²	semidirect
44. C₂×#108×C₆₇	C₂²	semidirect
45. C₂×#104×C₆₇	C₂²	semidirect
46. C₂×#104×C₆₇	C₂²	semidirect
47. C₂×#101×C₆₇	C₂²	semidirect
48. C₂×#100×C₆₇	C₂²	semidirect
49. C₂×#100×C₆₇	C₂²	semidirect
50. C₂×#97×C₆₇	C₂²	semidirect
53. 2₋¹⁺⁴×C₆₇	C₂³	semidirect
60. H(5,𝔽₂)×C₆₇	C₂³	semidirect
80. #137×C₆₇	C₂³	semidirect
88. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
89. AGL(1,ℤ/8)×C₆₇	C₂³	semidirect
92. #135×C₆₇	D₄	semidirect
95. C₂×Q₁₆×C₆₇	D₄	semidirect
104. C₂×SD₁₆×C₆₇	D₄	semidirect
105. C₂×SD₁₆×C₆₇	D₄	semidirect
106. C₂×SD₁₆×C₆₇	C₂³	semidirect
114. C₂×D₈×C₆₇	D₄	semidirect
115. C₂×D₈×C₆₇	C₂³	semidirect
118. #131×C₆₇	C₂³	semidirect
119. #131×C₆₇	C₂³	semidirect
128. #127×C₆₇	C₂³	semidirect
130. #124×C₆₇	C₂³	semidirect
133. #108×C₆₇	C₂³	semidirect
134. #104×C₆₇	C₂³	semidirect
135. #104×C₆₇	C₂³	semidirect
136. #101×C₆₇	C₂³	semidirect
137. #100×C₆₇	C₂³	semidirect
138. #100×C₆₇	C₂³	semidirect
139. #97×C₆₇	C₂³	semidirect
210. Q₁₆×C₆₇	C₂×D₄	semidirect
217. SD₁₆×C₆₇	C₂×D₄	semidirect
218. SD₁₆×C₆₇	C₂×D₄	semidirect
224. D₈×C₆₇	C₂×D₄	semidirect
329. C₂×#3288	C₆₇	direct (N × H)
336. C₂×C₆₇	#3288	direct (N × H)
338. C₂×#577	C₂×C₆₇	semidirect
339. C₂×#576	C₂×C₆₇	semidirect
340. #3288	C₂×C₆₇	direct (N × H)
341. C₂×#496	C₂×C₆₇	semidirect
342. C₂×#472	C₂×C₆₇	semidirect
343. C₂×#471	C₂×C₆₇	semidirect
344. C₂×#454	C₂×C₆₇	semidirect
345. C₂×#455	C₂×C₆₇	semidirect
346. C₂×#453	C₂×C₆₇	semidirect
347. C₂×#444	C₂×C₆₇	semidirect
348. C₆₇	C₂×#3288	direct (N × H)
349. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
351. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
353. #577	C₂²×C₆₇	semidirect
355. #576	C₂²×C₆₇	semidirect
357. C₂×#137	C₂²×C₆₇	semidirect
362. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
363. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
368. C₂²×SD₁₆	C₂²×C₆₇	semidirect
370. C₂²×D₈	C₂²×C₆₇	semidirect
371. C₂×#131	C₂²×C₆₇	semidirect
372. C₂×#131	C₂²×C₆₇	semidirect
373. C₂×#127	C₂²×C₆₇	semidirect
374. C₂×#124	C₂²×C₆₇	semidirect
375. #496	C₂²×C₆₇	semidirect
376. #472	C₂²×C₆₇	semidirect
377. #471	C₂²×C₆₇	semidirect
378. #455	C₂²×C₆₇	semidirect
379. #454	C₂²×C₆₇	semidirect
380. #453	C₂²×C₆₇	semidirect
381. #444	C₂²×C₆₇	semidirect
382. C₂×#108	C₂²×C₆₇	semidirect
383. C₂×#104	C₂²×C₆₇	semidirect
384. C₂×#104	C₂²×C₆₇	semidirect
385. C₂×#101	C₂²×C₆₇	semidirect
386. C₂×#100	C₂²×C₆₇	semidirect
387. C₂×#100	C₂²×C₆₇	semidirect
388. C₂×#97	C₂²×C₆₇	semidirect
391. 2₋¹⁺⁴	C₂³×C₆₇	semidirect
398. H(5,𝔽₂)	C₂³×C₆₇	semidirect
418. #137	C₂³×C₆₇	semidirect
426. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
427. AGL(1,ℤ/8)	C₂³×C₆₇	semidirect
430. #135	D₄×C₆₇	semidirect
433. C₂×Q₁₆	D₄×C₆₇	semidirect
442. C₂×SD₁₆	D₄×C₆₇	semidirect
443. C₂×SD₁₆	D₄×C₆₇	semidirect
444. C₂×SD₁₆	C₂³×C₆₇	semidirect
452. C₂×D₈	D₄×C₆₇	semidirect
453. C₂×D₈	C₂³×C₆₇	semidirect
456. #131	C₂³×C₆₇	semidirect
457. #131	C₂³×C₆₇	semidirect
466. #127	C₂³×C₆₇	semidirect
468. #124	C₂³×C₆₇	semidirect
471. #108	C₂³×C₆₇	semidirect
472. #104	C₂³×C₆₇	semidirect
473. #104	C₂³×C₆₇	semidirect
474. #101	C₂³×C₆₇	semidirect
475. #100	C₂³×C₆₇	semidirect
476. #100	C₂³×C₆₇	semidirect
477. #97	C₂³×C₆₇	semidirect
548. Q₁₆	C₂×D₄×C₆₇	semidirect
555. SD₁₆	C₂×D₄×C₆₇	semidirect
556. SD₁₆	C₂×D₄×C₆₇	semidirect
562. D₈	C₂×D₄×C₆₇	semidirect
673. C₂	C₆₇×#3288	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₂×#576×C₆₇	2
C₆₇×#3288	2
C₂×#496×C₆₇	2
C₂×#472×C₆₇	2
C₂×#471×C₆₇	2
C₂×#454×C₆₇	2
C₂×#455×C₆₇	2
C₂×#453×C₆₇	2
C₂×#444×C₆₇	2
C₂×#3288	67

Subgroups — C2×C67×#3288 #30740349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3288 #30740349