Subgroups — C₂×C₆₇×#3484 #30742014

Order 17152.

14438 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3484	C₂	1	32	yes	maximal, direct product factor
4	C₂×#546×C₆₇	C₂	1	8	yes	maximal, complemented
5	C₂×D₄²×C₆₇	C₂	1	8	yes	maximal, complemented
6	C₂×#535×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#534×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#525×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂²×#120×C₆₇	C₂	1	4	yes	maximal, complemented
10	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₆₇	C₂²	1	2	yes	complemented
12	C₂×H(5,𝔽₂)×C₆₇	—	2	16	no	—
13	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	16	yes	complemented
14	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
15	C₂²×#41×C₆₇	C₂²	1	4	yes	complemented
16	C₂³×D₄×C₆₇	—	2	16	no	—
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₆₇	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₆₇	C₂²	1	8	yes	complemented
21	C₂³×D₄×C₆₇	C₂²	1	4	yes	complemented
22	C₂³×D₄×C₆₇	C₂²	1	16	yes	complemented
23	C₂³×D₄×C₆₇	C₂²	1	4	yes	complemented
24	C₂³×D₄×C₆₇	C₂²	1	8	yes	complemented
25	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	#546×C₆₇	C₂²	1	128	yes	complemented
27	D₄²×C₆₇	C₂²	1	128	yes	complemented
28	#535×C₆₇	C₂²	1	32	yes	complemented
29	#534×C₆₇	C₂²	1	64	yes	complemented
30	C₂×#127×C₆₇	C₂²	1	4	yes	complemented
31	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
32	#525×C₆₇	C₂²	1	32	yes	complemented
33	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
34	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
36	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
37	C₂×#121×C₆₇	C₂²	1	16	yes	complemented
38	C₂×#121×C₆₇	C₂²	1	8	yes	complemented
39	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
40	C₂×#120×C₆₇	C₂²	1	8	yes	complemented
41	C₂×#120×C₆₇	C₂²	1	16	yes	complemented
42	C₂×#120×C₆₇	C₂²	1	8	yes	complemented
43	C₂×#120×C₆₇	C₂²	1	64	yes	complemented
44	#518×C₆₇	C₂²	1	16	yes	complemented
45	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
46	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
47	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
49	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
50	C₂⁵×C₆₇	—	2	16	no	—
51	C₂⁵×C₆₇	—	4	16	no	—
52	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
53	C₂⁵×C₆₇	C₂³	1	8	yes	—
54	C₂⁵×C₆₇	C₂³	1	2	yes	—
55	C₂⁵×C₆₇	C₂³	1	2	yes	—
56	C₂⁵×C₆₇	C₂³	1	16	yes	complemented
57	C₂⁵×C₆₇	C₂³	1	4	yes	complemented
58	H(5,𝔽₂)×C₆₇	—	2	128	no	—
59	C₂×#41×C₆₇	—	2	32	no	—
60	C₂×#41×C₆₇	—	2	16	no	—
61	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
62	C₂×#41×C₆₇	C₂³	1	32	yes	complemented
63	C₂²×Q₈×C₆₇	C₂³	1	2	yes	complemented
64	C₂²×D₄×C₆₇	—	2	16	no	—
65	C₂²×D₄×C₆₇	—	2	32	no	—
66	C₂²×D₄×C₆₇	—	2	64	no	—
67	C₂²×D₄×C₆₇	—	2	128	no	—
68	C₂²×D₄×C₆₇	—	2	32	no	—
69	C₂²×D₄×C₆₇	—	2	8	no	—
70	C₂²×D₄×C₆₇	—	4	32	no	—
71	C₂²×D₄×C₆₇	D₄	1	16	yes	complemented
72	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
73	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
74	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
75	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
76	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
77	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
78	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
79	C₂²×D₄×C₆₇	C₂³	1	8	yes	complemented
80	C₂²×D₄×C₆₇	C₂³	1	64	yes	complemented
81	C₂²×D₄×C₆₇	C₂³	1	8	yes	complemented
82	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
83	C₂²×D₄×C₆₇	C₂³	1	16	yes	complemented
84	C₂²×D₄×C₆₇	C₂³	1	32	yes	complemented
85	C₂²×D₄×C₆₇	C₂³	1	32	yes	complemented
86	C₂²×D₄×C₆₇	C₂³	1	64	yes	complemented
87	C₂³×C₄×C₆₇	—	2	8	no	—
88	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	8	yes	complemented
92	C₂³×C₄×C₆₇	C₂³	1	4	yes	complemented
93	C₂³×C₄×C₆₇	C₂³	1	4	yes	complemented
94	C₂³×C₄×C₆₇	C₂³	1	8	yes	complemented
95	#127×C₆₇	C₂³	1	32	yes	complemented
96	#124×C₆₇	C₂³	1	32	yes	complemented
97	#123×C₆₇	C₂³	1	32	yes	complemented
98	#123×C₆₇	C₂³	1	64	yes	complemented
99	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
100	#121×C₆₇	C₂³	1	32	yes	complemented
101	#121×C₆₇	C₂³	1	128	yes	complemented
102	#121×C₆₇	C₂³	1	64	yes	complemented
103	#120×C₆₇	C₂³	1	32	yes	complemented
104	#120×C₆₇	C₂³	1	64	yes	complemented
105	#120×C₆₇	C₂³	1	128	yes	complemented
106	#120×C₆₇	C₂³	1	64	yes	complemented
107	C₄×D₄×C₆₇	C₂³	1	64	yes	complemented
108	C₄×D₄×C₆₇	C₂³	1	64	yes	complemented
109	#117×C₆₇	C₂³	1	16	yes	complemented
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
112	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
115	C₂×C₂²⋊C₄×C₆₇	C₂³	1	64	yes	complemented
116	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
117	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	complemented
118	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	complemented
119	C₂×C₄²×C₆₇	C₂³	1	4	yes	complemented
120	C₂⁴×C₆₇	—	2	4	no	—
121	C₂⁴×C₆₇	—	2	8	no	—
122	C₂⁴×C₆₇	—	2	32	no	—
123	C₂⁴×C₆₇	—	2	8	no	—
124	C₂⁴×C₆₇	—	2	64	no	—
125	C₂⁴×C₆₇	—	2	32	no	—
126	C₂⁴×C₆₇	—	2	16	no	—
127	C₂⁴×C₆₇	—	4	8	no	—
128	C₂⁴×C₆₇	—	4	16	no	—
129	C₂⁴×C₆₇	—	4	8	no	—
130	C₂⁴×C₆₇	—	4	64	no	—
131	C₂⁴×C₆₇	—	4	16	no	—
132	C₂⁴×C₆₇	—	4	128	no	—
133	C₂⁴×C₆₇	C₂×D₄	1	16	yes	complemented
134	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
135	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
136	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
137	C₂⁴×C₆₇	C₂⁴	1	32	yes	—
138	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
139	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
140	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
141	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
142	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
143	C₂⁴×C₆₇	C₂⁴	1	16	yes	complemented
144	#41×C₆₇	—	2	128	no	—
145	#41×C₆₇	—	2	64	no	—
146	C₂×Q₈×C₆₇	—	2	8	no	—
147	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	complemented
148	C₂×D₄×C₆₇	—	2	32	no	—
149	C₂×D₄×C₆₇	—	2	16	no	—
150	C₂×D₄×C₆₇	—	2	32	no	—
151	C₂×D₄×C₆₇	—	2	64	no	—
152	C₂×D₄×C₆₇	—	2	128	no	—
153	C₂×D₄×C₆₇	—	2	32	no	—
154	C₂×D₄×C₆₇	—	2	256	no	—
155	C₂×D₄×C₆₇	—	2	128	no	—
156	C₂×D₄×C₆₇	—	2	16	no	—
157	C₂×D₄×C₆₇	—	2	8	no	—
158	C₂×D₄×C₆₇	—	2	32	no	—
159	C₂×D₄×C₆₇	—	4	32	no	—
160	C₂×D₄×C₆₇	—	4	128	no	—
161	C₂×D₄×C₆₇	C₂×D₄	1	32	yes	complemented
162	C₂×D₄×C₆₇	C₂×D₄	1	64	yes	complemented
163	C₂×D₄×C₆₇	C₂⁴	1	32	yes	—
164	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
165	C₂×D₄×C₆₇	C₂⁴	1	32	yes	—
166	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
167	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
168	C₂×D₄×C₆₇	C₂⁴	1	32	yes	complemented
169	C₂×D₄×C₆₇	C₂⁴	1	8	yes	complemented
170	C₂×D₄×C₆₇	C₂⁴	1	64	yes	complemented
171	C₂²×C₄×C₆₇	—	2	4	no	—
172	C₂²×C₄×C₆₇	—	2	16	no	—
173	C₂²×C₄×C₆₇	—	2	16	no	—
174	C₂²×C₄×C₆₇	—	2	16	no	—
175	C₂²×C₄×C₆₇	—	2	32	no	—
176	C₂²×C₄×C₆₇	—	4	16	no	—
177	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	complemented
178	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
181	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	complemented
186	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	complemented
187	C₂²×C₄×C₆₇	C₂⁴	1	32	yes	complemented
188	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	complemented
189	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	complemented
190	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
191	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
192	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	complemented
193	C₂²⋊C₄×C₆₇	C₂⁴	1	64	yes	complemented
194	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	complemented
195	C₄²×C₆₇	C₂⁴	1	16	yes	complemented
196	C₂³×C₆₇	—	2	32	no	—
197	C₂³×C₆₇	—	2	8	no	—
198	C₂³×C₆₇	—	2	4	no	—
199	C₂³×C₆₇	—	2	16	no	—
200	C₂³×C₆₇	—	2	4	no	—
201	C₂³×C₆₇	—	2	4	no	—
202	C₂³×C₆₇	—	2	16	no	—
203	C₂³×C₆₇	—	2	8	no	—
204	C₂³×C₆₇	—	2	64	no	—
205	C₂³×C₆₇	—	2	16	no	—
206	C₂³×C₆₇	—	2	8	no	—
207	C₂³×C₆₇	—	2	16	no	—
208	C₂³×C₆₇	—	2	16	no	—
209	C₂³×C₆₇	—	2	64	no	—
210	C₂³×C₆₇	—	2	32	no	—
211	C₂³×C₆₇	—	4	32	no	—
212	C₂³×C₆₇	—	4	16	no	—
213	C₂³×C₆₇	—	4	32	no	—
214	C₂³×C₆₇	—	4	16	no	—
215	C₂³×C₆₇	—	4	32	no	—
216	C₂³×C₆₇	—	4	128	no	—
217	C₂³×C₆₇	—	4	256	no	—
218	C₂³×C₆₇	—	4	32	no	—
219	C₂³×C₆₇	—	8	32	no	—
220	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
221	C₂³×C₆₇	C₂²×D₄	1	16	yes	—
222	C₂³×C₆₇	C₂²×D₄	1	32	yes	complemented
223	C₂³×C₆₇	H(5,𝔽₂)	1	8	yes	complemented
224	C₂³×C₆₇	C₂⁵	1	8	yes	—
225	C₂³×C₆₇	C₂⁵	1	8	yes	—
226	C₂³×C₆₇	C₂⁵	1	2	yes	—
227	C₂³×C₆₇	C₂⁵	1	8	yes	—
228	C₂³×C₆₇	C₂⁵	1	4	yes	—
229	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
230	Q₈×C₆₇	—	2	16	no	—
231	D₄×C₆₇	—	2	64	no	—
232	D₄×C₆₇	—	2	32	no	—
233	D₄×C₆₇	—	2	64	no	—
234	D₄×C₆₇	—	2	64	no	—
235	D₄×C₆₇	—	2	32	no	—
236	D₄×C₆₇	—	2	16	no	—
237	D₄×C₆₇	—	4	64	no	—
238	D₄×C₆₇	C₂²×D₄	1	64	yes	complemented
239	C₂×C₄×C₆₇	—	2	8	no	—
240	C₂×C₄×C₆₇	—	2	4	no	—
241	C₂×C₄×C₆₇	—	2	8	no	—
242	C₂×C₄×C₆₇	—	2	32	no	—
243	C₂×C₄×C₆₇	—	2	16	no	—
244	C₂×C₄×C₆₇	—	2	32	no	—
245	C₂×C₄×C₆₇	—	2	32	no	—
246	C₂×C₄×C₆₇	—	4	32	no	—
247	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
248	C₂×C₄×C₆₇	C₂²×D₄	1	16	yes	complemented
249	C₂×C₄×C₆₇	C₂⁵	1	16	yes	—
250	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
251	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
252	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
253	C₂²×C₆₇	—	2	32	no	—
254	C₂²×C₆₇	—	2	4	no	—
255	C₂²×C₆₇	—	2	16	no	—
256	C₂²×C₆₇	—	2	4	no	—
257	C₂²×C₆₇	—	2	4	no	—
258	C₂²×C₆₇	—	2	8	no	—
259	C₂²×C₆₇	—	2	16	no	—
260	C₂²×C₆₇	—	2	32	no	—
261	C₂²×C₆₇	—	2	8	no	—
262	C₂²×C₆₇	—	2	8	no	—
263	C₂²×C₆₇	—	2	16	no	—
264	C₂²×C₆₇	—	2	16	no	—
265	C₂²×C₆₇	—	4	32	no	—
266	C₂²×C₆₇	—	4	128	no	—
267	C₂²×C₆₇	—	4	32	no	—
268	C₂²×C₆₇	—	4	16	no	—
269	C₂²×C₆₇	—	4	16	no	—
270	C₂²×C₆₇	—	8	32	no	—
271	C₂²×C₆₇	C₂³×D₄	1	4	yes	—
272	C₂²×C₆₇	C₂³×D₄	1	16	yes	—
273	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
274	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
275	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	8	yes	complemented
276	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
277	C₄×C₆₇	—	2	4	no	—
278	C₄×C₆₇	—	2	8	no	—
279	C₄×C₆₇	—	2	16	no	—
280	C₄×C₆₇	C₂³×D₄	1	8	yes	—
281	C₂×#3484	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂×C₆₇	—	2	4	no	—
283	C₂×C₆₇	—	2	8	no	—
284	C₂×C₆₇	—	2	16	no	—
285	C₂×C₆₇	—	4	8	no	—
286	C₂×C₆₇	—	4	8	no	—
287	C₂×C₆₇	#3484	1	4	yes	direct product factor
288	C₂×C₆₇	C₂⁴×D₄	1	1	yes	characteristic
289	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	2	yes	—
290	C₂²×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
291	C₂⁴×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
292	#3484	C₂×C₆₇	1	32	yes	direct product factor
293	C₂×#546	C₂×C₆₇	1	8	yes	complemented
294	C₂×D₄²	C₂×C₆₇	1	8	yes	complemented
295	C₂×#535	C₂×C₆₇	1	2	yes	complemented
296	C₂×#534	C₂×C₆₇	1	4	yes	complemented
297	C₂×#525	C₂×C₆₇	1	2	yes	complemented
298	C₂²×#120	C₂×C₆₇	1	4	yes	complemented
299	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
300	C₆₇	C₂×#3484	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁶	C₂²×C₆₇	1	2	yes	complemented
302	C₂×H(5,𝔽₂)	—	2	16	no	—
303	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	16	yes	complemented
304	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
305	C₂²×#41	C₂²×C₆₇	1	4	yes	complemented
306	C₂³×D₄	—	2	16	no	—
307	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
308	C₂³×D₄	C₂²×C₆₇	1	2	yes	complemented
309	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
310	C₂³×D₄	C₂²×C₆₇	1	8	yes	complemented
311	C₂³×D₄	C₂²×C₆₇	1	4	yes	complemented
312	C₂³×D₄	C₂²×C₆₇	1	16	yes	complemented
313	C₂³×D₄	C₂²×C₆₇	1	4	yes	complemented
314	C₂³×D₄	C₂²×C₆₇	1	8	yes	complemented
315	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
316	#546	C₂²×C₆₇	1	128	yes	complemented
317	D₄²	C₂²×C₆₇	1	128	yes	complemented
318	#535	C₂²×C₆₇	1	32	yes	complemented
319	#534	C₂²×C₆₇	1	64	yes	complemented
320	C₂×#127	C₂²×C₆₇	1	4	yes	complemented
321	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
322	#525	C₂²×C₆₇	1	32	yes	complemented
323	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
324	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
325	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
326	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
327	C₂×#121	C₂²×C₆₇	1	16	yes	complemented
328	C₂×#121	C₂²×C₆₇	1	8	yes	complemented
329	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
330	C₂×#120	C₂²×C₆₇	1	8	yes	complemented
331	C₂×#120	C₂²×C₆₇	1	16	yes	complemented
332	C₂×#120	C₂²×C₆₇	1	8	yes	complemented
333	C₂×#120	C₂²×C₆₇	1	64	yes	complemented
334	#518	C₂²×C₆₇	1	16	yes	complemented
335	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
336	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
337	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
338	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
339	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
340	C₂⁵	—	2	16	no	—
341	C₂⁵	—	4	16	no	—
342	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
343	C₂⁵	C₂³×C₆₇	1	8	yes	—
344	C₂⁵	C₂³×C₆₇	1	2	yes	—
345	C₂⁵	C₂³×C₆₇	1	2	yes	—
346	C₂⁵	C₂³×C₆₇	1	16	yes	complemented
347	C₂⁵	C₂³×C₆₇	1	4	yes	complemented
348	H(5,𝔽₂)	—	2	128	no	—
349	C₂×#41	—	2	32	no	—
350	C₂×#41	—	2	16	no	—
351	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
352	C₂×#41	C₂³×C₆₇	1	32	yes	complemented
353	C₂²×Q₈	C₂³×C₆₇	1	2	yes	complemented
354	C₂²×D₄	—	2	16	no	—
355	C₂²×D₄	—	2	32	no	—
356	C₂²×D₄	—	2	64	no	—
357	C₂²×D₄	—	2	128	no	—
358	C₂²×D₄	—	2	32	no	—
359	C₂²×D₄	—	2	8	no	—
360	C₂²×D₄	—	4	32	no	—
361	C₂²×D₄	D₄×C₆₇	1	16	yes	complemented
362	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
363	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
364	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
365	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
366	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
367	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
368	C₂²×D₄	C₂³×C₆₇	1	16	yes	complemented
369	C₂²×D₄	C₂³×C₆₇	1	8	yes	complemented
370	C₂²×D₄	C₂³×C₆₇	1	64	yes	complemented
371	C₂²×D₄	C₂³×C₆₇	1	8	yes	complemented
372	C₂²×D₄	C₂³×C₆₇	1	2	yes	complemented
373	C₂²×D₄	C₂³×C₆₇	1	16	yes	complemented
374	C₂²×D₄	C₂³×C₆₇	1	32	yes	complemented
375	C₂²×D₄	C₂³×C₆₇	1	32	yes	complemented
376	C₂²×D₄	C₂³×C₆₇	1	64	yes	complemented
377	C₂³×C₄	—	2	8	no	—
378	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
379	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₆₇	1	8	yes	complemented
382	C₂³×C₄	C₂³×C₆₇	1	4	yes	complemented
383	C₂³×C₄	C₂³×C₆₇	1	4	yes	complemented
384	C₂³×C₄	C₂³×C₆₇	1	8	yes	complemented
385	#127	C₂³×C₆₇	1	32	yes	complemented
386	#124	C₂³×C₆₇	1	32	yes	complemented
387	#123	C₂³×C₆₇	1	32	yes	complemented
388	#123	C₂³×C₆₇	1	64	yes	complemented
389	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
390	#121	C₂³×C₆₇	1	32	yes	complemented
391	#121	C₂³×C₆₇	1	128	yes	complemented
392	#121	C₂³×C₆₇	1	64	yes	complemented
393	#120	C₂³×C₆₇	1	32	yes	complemented
394	#120	C₂³×C₆₇	1	64	yes	complemented
395	#120	C₂³×C₆₇	1	128	yes	complemented
396	#120	C₂³×C₆₇	1	64	yes	complemented
397	C₄×D₄	C₂³×C₆₇	1	64	yes	complemented
398	C₄×D₄	C₂³×C₆₇	1	64	yes	complemented
399	#117	C₂³×C₆₇	1	16	yes	complemented
400	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
401	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
402	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
405	C₂×C₂²⋊C₄	C₂³×C₆₇	1	64	yes	complemented
406	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
407	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	complemented
408	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	complemented
409	C₂×C₄²	C₂³×C₆₇	1	4	yes	complemented
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	8	no	—
412	C₂⁴	—	2	32	no	—
413	C₂⁴	—	2	8	no	—
414	C₂⁴	—	2	64	no	—
415	C₂⁴	—	2	32	no	—
416	C₂⁴	—	2	16	no	—
417	C₂⁴	—	4	8	no	—
418	C₂⁴	—	4	16	no	—
419	C₂⁴	—	4	8	no	—
420	C₂⁴	—	4	64	no	—
421	C₂⁴	—	4	16	no	—
422	C₂⁴	—	4	128	no	—
423	C₂⁴	C₂×D₄×C₆₇	1	16	yes	complemented
424	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
425	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
426	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
427	C₂⁴	C₂⁴×C₆₇	1	32	yes	—
428	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
429	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
430	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
431	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
432	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
433	C₂⁴	C₂⁴×C₆₇	1	16	yes	complemented
434	#41	—	2	128	no	—
435	#41	—	2	64	no	—
436	C₂×Q₈	—	2	8	no	—
437	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	complemented
438	C₂×D₄	—	2	32	no	—
439	C₂×D₄	—	2	16	no	—
440	C₂×D₄	—	2	32	no	—
441	C₂×D₄	—	2	64	no	—
442	C₂×D₄	—	2	128	no	—
443	C₂×D₄	—	2	32	no	—
444	C₂×D₄	—	2	256	no	—
445	C₂×D₄	—	2	128	no	—
446	C₂×D₄	—	2	16	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	32	no	—
449	C₂×D₄	—	4	32	no	—
450	C₂×D₄	—	4	128	no	—
451	C₂×D₄	C₂×D₄×C₆₇	1	32	yes	complemented
452	C₂×D₄	C₂×D₄×C₆₇	1	64	yes	complemented
453	C₂×D₄	C₂⁴×C₆₇	1	32	yes	—
454	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
455	C₂×D₄	C₂⁴×C₆₇	1	32	yes	—
456	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
457	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
458	C₂×D₄	C₂⁴×C₆₇	1	32	yes	complemented
459	C₂×D₄	C₂⁴×C₆₇	1	8	yes	complemented
460	C₂×D₄	C₂⁴×C₆₇	1	64	yes	complemented
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	16	no	—
463	C₂²×C₄	—	2	16	no	—
464	C₂²×C₄	—	2	16	no	—
465	C₂²×C₄	—	2	32	no	—
466	C₂²×C₄	—	4	16	no	—
467	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	complemented
468	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
469	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
472	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	complemented
476	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	complemented
477	C₂²×C₄	C₂⁴×C₆₇	1	32	yes	complemented
478	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	complemented
479	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	complemented
480	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
481	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
482	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	complemented
483	C₂²⋊C₄	C₂⁴×C₆₇	1	64	yes	complemented
484	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	complemented
485	C₄²	C₂⁴×C₆₇	1	16	yes	complemented
486	C₂³	—	2	32	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	16	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	16	no	—
493	C₂³	—	2	8	no	—
494	C₂³	—	2	64	no	—
495	C₂³	—	2	16	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	16	no	—
498	C₂³	—	2	16	no	—
499	C₂³	—	2	64	no	—
500	C₂³	—	2	32	no	—
501	C₂³	—	4	32	no	—
502	C₂³	—	4	16	no	—
503	C₂³	—	4	32	no	—
504	C₂³	—	4	16	no	—
505	C₂³	—	4	32	no	—
506	C₂³	—	4	128	no	—
507	C₂³	—	4	256	no	—
508	C₂³	—	4	32	no	—
509	C₂³	—	8	32	no	—
510	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
511	C₂³	C₂²×D₄×C₆₇	1	16	yes	—
512	C₂³	C₂²×D₄×C₆₇	1	32	yes	complemented
513	C₂³	H(5,𝔽₂)×C₆₇	1	8	yes	complemented
514	C₂³	C₂⁵×C₆₇	1	8	yes	—
515	C₂³	C₂⁵×C₆₇	1	8	yes	—
516	C₂³	C₂⁵×C₆₇	1	2	yes	—
517	C₂³	C₂⁵×C₆₇	1	8	yes	—
518	C₂³	C₂⁵×C₆₇	1	4	yes	—
519	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
520	Q₈	—	2	16	no	—
521	D₄	—	2	64	no	—
522	D₄	—	2	32	no	—
523	D₄	—	2	64	no	—
524	D₄	—	2	64	no	—
525	D₄	—	2	32	no	—
526	D₄	—	2	16	no	—
527	D₄	—	4	64	no	—
528	D₄	C₂²×D₄×C₆₇	1	64	yes	complemented
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	2	32	no	—
533	C₂×C₄	—	2	16	no	—
534	C₂×C₄	—	2	32	no	—
535	C₂×C₄	—	2	32	no	—
536	C₂×C₄	—	4	32	no	—
537	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
538	C₂×C₄	C₂²×D₄×C₆₇	1	16	yes	complemented
539	C₂×C₄	C₂⁵×C₆₇	1	16	yes	—
540	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
541	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
542	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
543	C₂²	—	2	32	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	16	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	16	no	—
550	C₂²	—	2	32	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	2	16	no	—
554	C₂²	—	2	16	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	128	no	—
557	C₂²	—	4	32	no	—
558	C₂²	—	4	16	no	—
559	C₂²	—	4	16	no	—
560	C₂²	—	8	32	no	—
561	C₂²	C₂³×D₄×C₆₇	1	4	yes	—
562	C₂²	C₂³×D₄×C₆₇	1	16	yes	—
563	C₂²	C₂³×D₄×C₆₇	1	2	yes	—
564	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
565	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	8	yes	complemented
566	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
567	C₄	—	2	4	no	—
568	C₄	—	2	8	no	—
569	C₄	—	2	16	no	—
570	C₄	C₂³×D₄×C₆₇	1	8	yes	—
571	C₂	—	2	4	no	—
572	C₂	—	2	8	no	—
573	C₂	—	2	16	no	—
574	C₂	—	4	8	no	—
575	C₂	—	4	8	no	—
576	C₂	C₆₇×#3484	1	4	yes	direct product factor
577	C₂	C₂⁴×D₄×C₆₇	1	1	yes	characteristic
578	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×H(5,𝔽₂)×C₆₇	C₂	semidirect
2. C₂⁴×D₄×C₆₇	C₂	semidirect
3. C₆₇×#3484	C₂	direct (N × H)
4. C₂×#546×C₆₇	C₂	semidirect
5. C₂×D₄²×C₆₇	C₂	semidirect
6. C₂×#535×C₆₇	C₂	semidirect
7. C₂×#534×C₆₇	C₂	semidirect
8. C₂×#525×C₆₇	C₂	semidirect
9. C₂²×#120×C₆₇	C₂	semidirect
10. C₂×#518×C₆₇	C₂	semidirect
11. C₂⁶×C₆₇	C₂²	semidirect
13. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
14. C₂²×#41×C₆₇	C₂²	semidirect
15. C₂²×#41×C₆₇	C₂²	semidirect
18. C₂³×D₄×C₆₇	C₂²	semidirect
19. C₂³×D₄×C₆₇	C₂²	semidirect
20. C₂³×D₄×C₆₇	C₂²	semidirect
21. C₂³×D₄×C₆₇	C₂²	semidirect
22. C₂³×D₄×C₆₇	C₂²	semidirect
23. C₂³×D₄×C₆₇	C₂²	semidirect
24. C₂³×D₄×C₆₇	C₂²	semidirect
25. C₂⁴×C₄×C₆₇	C₂²	semidirect
26. #546×C₆₇	C₂²	semidirect
27. D₄²×C₆₇	C₂²	semidirect
28. #535×C₆₇	C₂²	semidirect
29. #534×C₆₇	C₂²	semidirect
30. C₂×#127×C₆₇	C₂²	semidirect
31. C₂×#124×C₆₇	C₂²	semidirect
32. #525×C₆₇	C₂²	semidirect
33. C₂×#123×C₆₇	C₂²	semidirect
34. C₂×#123×C₆₇	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
36. C₂×#121×C₆₇	C₂²	semidirect
37. C₂×#121×C₆₇	C₂²	semidirect
38. C₂×#121×C₆₇	C₂²	semidirect
39. C₂×#120×C₆₇	C₂²	semidirect
40. C₂×#120×C₆₇	C₂²	semidirect
41. C₂×#120×C₆₇	C₂²	semidirect
42. C₂×#120×C₆₇	C₂²	semidirect
43. C₂×#120×C₆₇	C₂²	semidirect
44. #518×C₆₇	C₂²	semidirect
45. C₂×C₄×D₄×C₆₇	C₂²	semidirect
46. C₂×C₄×D₄×C₆₇	C₂²	semidirect
47. C₂×#117×C₆₇	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
56. C₂⁵×C₆₇	C₂³	semidirect
57. C₂⁵×C₆₇	C₂³	semidirect
61. C₂×#41×C₆₇	C₂³	semidirect
62. C₂×#41×C₆₇	C₂³	semidirect
63. C₂²×Q₈×C₆₇	C₂³	semidirect
71. C₂²×D₄×C₆₇	D₄	semidirect
78. C₂²×D₄×C₆₇	C₂³	semidirect
79. C₂²×D₄×C₆₇	C₂³	semidirect
80. C₂²×D₄×C₆₇	C₂³	semidirect
81. C₂²×D₄×C₆₇	C₂³	semidirect
82. C₂²×D₄×C₆₇	C₂³	semidirect
83. C₂²×D₄×C₆₇	C₂³	semidirect
84. C₂²×D₄×C₆₇	C₂³	semidirect
85. C₂²×D₄×C₆₇	C₂³	semidirect
86. C₂²×D₄×C₆₇	C₂³	semidirect
91. C₂³×C₄×C₆₇	C₂³	semidirect
92. C₂³×C₄×C₆₇	C₂³	semidirect
93. C₂³×C₄×C₆₇	C₂³	semidirect
94. C₂³×C₄×C₆₇	C₂³	semidirect
95. #127×C₆₇	C₂³	semidirect
96. #124×C₆₇	C₂³	semidirect
97. #123×C₆₇	C₂³	semidirect
98. #123×C₆₇	C₂³	semidirect
99. C₂²⋊Q₈×C₆₇	C₂³	semidirect
100. #121×C₆₇	C₂³	semidirect
101. #121×C₆₇	C₂³	semidirect
102. #121×C₆₇	C₂³	semidirect
103. #120×C₆₇	C₂³	semidirect
104. #120×C₆₇	C₂³	semidirect
105. #120×C₆₇	C₂³	semidirect
106. #120×C₆₇	C₂³	semidirect
107. C₄×D₄×C₆₇	C₂³	semidirect
108. C₄×D₄×C₆₇	C₂³	semidirect
109. #117×C₆₇	C₂³	semidirect
110. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
111. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
114. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
115. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
116. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
117. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
118. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
119. C₂×C₄²×C₆₇	C₂³	semidirect
133. C₂⁴×C₆₇	C₂×D₄	semidirect
143. C₂⁴×C₆₇	C₂⁴	semidirect
147. C₂×Q₈×C₆₇	C₂⁴	semidirect
161. C₂×D₄×C₆₇	C₂×D₄	semidirect
162. C₂×D₄×C₆₇	C₂×D₄	semidirect
168. C₂×D₄×C₆₇	C₂⁴	semidirect
169. C₂×D₄×C₆₇	C₂⁴	semidirect
170. C₂×D₄×C₆₇	C₂⁴	semidirect
177. C₂²×C₄×C₆₇	C₂×D₄	semidirect
185. C₂²×C₄×C₆₇	C₂⁴	semidirect
186. C₂²×C₄×C₆₇	C₂⁴	semidirect
187. C₂²×C₄×C₆₇	C₂⁴	semidirect
188. C₄⋊C₄×C₆₇	C₂⁴	semidirect
189. C₄⋊C₄×C₆₇	C₂⁴	semidirect
192. C₂²⋊C₄×C₆₇	C₂⁴	semidirect
193. C₂²⋊C₄×C₆₇	C₂⁴	semidirect
194. C₂²⋊C₄×C₆₇	C₂⁴	semidirect
195. C₄²×C₆₇	C₂⁴	semidirect
222. C₂³×C₆₇	C₂²×D₄	semidirect
223. C₂³×C₆₇	H(5,𝔽₂)	semidirect
238. D₄×C₆₇	C₂²×D₄	semidirect
248. C₂×C₄×C₆₇	C₂²×D₄	semidirect
275. C₂²×C₆₇	C₂×H(5,𝔽₂)	semidirect
281. C₂×#3484	C₆₇	direct (N × H)
287. C₂×C₆₇	#3484	direct (N × H)
290. C₂²×H(5,𝔽₂)	C₂×C₆₇	semidirect
291. C₂⁴×D₄	C₂×C₆₇	semidirect
292. #3484	C₂×C₆₇	direct (N × H)
293. C₂×#546	C₂×C₆₇	semidirect
294. C₂×D₄²	C₂×C₆₇	semidirect
295. C₂×#535	C₂×C₆₇	semidirect
296. C₂×#534	C₂×C₆₇	semidirect
297. C₂×#525	C₂×C₆₇	semidirect
298. C₂²×#120	C₂×C₆₇	semidirect
299. C₂×#518	C₂×C₆₇	semidirect
300. C₆₇	C₂×#3484	direct (N × H)
301. C₂⁶	C₂²×C₆₇	semidirect
303. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
304. C₂²×#41	C₂²×C₆₇	semidirect
305. C₂²×#41	C₂²×C₆₇	semidirect
308. C₂³×D₄	C₂²×C₆₇	semidirect
309. C₂³×D₄	C₂²×C₆₇	semidirect
310. C₂³×D₄	C₂²×C₆₇	semidirect
311. C₂³×D₄	C₂²×C₆₇	semidirect
312. C₂³×D₄	C₂²×C₆₇	semidirect
313. C₂³×D₄	C₂²×C₆₇	semidirect
314. C₂³×D₄	C₂²×C₆₇	semidirect
315. C₂⁴×C₄	C₂²×C₆₇	semidirect
316. #546	C₂²×C₆₇	semidirect
317. D₄²	C₂²×C₆₇	semidirect
318. #535	C₂²×C₆₇	semidirect
319. #534	C₂²×C₆₇	semidirect
320. C₂×#127	C₂²×C₆₇	semidirect
321. C₂×#124	C₂²×C₆₇	semidirect
322. #525	C₂²×C₆₇	semidirect
323. C₂×#123	C₂²×C₆₇	semidirect
324. C₂×#123	C₂²×C₆₇	semidirect
325. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
326. C₂×#121	C₂²×C₆₇	semidirect
327. C₂×#121	C₂²×C₆₇	semidirect
328. C₂×#121	C₂²×C₆₇	semidirect
329. C₂×#120	C₂²×C₆₇	semidirect
330. C₂×#120	C₂²×C₆₇	semidirect
331. C₂×#120	C₂²×C₆₇	semidirect
332. C₂×#120	C₂²×C₆₇	semidirect
333. C₂×#120	C₂²×C₆₇	semidirect
334. #518	C₂²×C₆₇	semidirect
335. C₂×C₄×D₄	C₂²×C₆₇	semidirect
336. C₂×C₄×D₄	C₂²×C₆₇	semidirect
337. C₂×#117	C₂²×C₆₇	semidirect
338. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
339. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
346. C₂⁵	C₂³×C₆₇	semidirect
347. C₂⁵	C₂³×C₆₇	semidirect
351. C₂×#41	C₂³×C₆₇	semidirect
352. C₂×#41	C₂³×C₆₇	semidirect
353. C₂²×Q₈	C₂³×C₆₇	semidirect
361. C₂²×D₄	D₄×C₆₇	semidirect
368. C₂²×D₄	C₂³×C₆₇	semidirect
369. C₂²×D₄	C₂³×C₆₇	semidirect
370. C₂²×D₄	C₂³×C₆₇	semidirect
371. C₂²×D₄	C₂³×C₆₇	semidirect
372. C₂²×D₄	C₂³×C₆₇	semidirect
373. C₂²×D₄	C₂³×C₆₇	semidirect
374. C₂²×D₄	C₂³×C₆₇	semidirect
375. C₂²×D₄	C₂³×C₆₇	semidirect
376. C₂²×D₄	C₂³×C₆₇	semidirect
381. C₂³×C₄	C₂³×C₆₇	semidirect
382. C₂³×C₄	C₂³×C₆₇	semidirect
383. C₂³×C₄	C₂³×C₆₇	semidirect
384. C₂³×C₄	C₂³×C₆₇	semidirect
385. #127	C₂³×C₆₇	semidirect
386. #124	C₂³×C₆₇	semidirect
387. #123	C₂³×C₆₇	semidirect
388. #123	C₂³×C₆₇	semidirect
389. C₂²⋊Q₈	C₂³×C₆₇	semidirect
390. #121	C₂³×C₆₇	semidirect
391. #121	C₂³×C₆₇	semidirect
392. #121	C₂³×C₆₇	semidirect
393. #120	C₂³×C₆₇	semidirect
394. #120	C₂³×C₆₇	semidirect
395. #120	C₂³×C₆₇	semidirect
396. #120	C₂³×C₆₇	semidirect
397. C₄×D₄	C₂³×C₆₇	semidirect
398. C₄×D₄	C₂³×C₆₇	semidirect
399. #117	C₂³×C₆₇	semidirect
400. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
401. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
404. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
405. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
406. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
407. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
408. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
409. C₂×C₄²	C₂³×C₆₇	semidirect
423. C₂⁴	C₂×D₄×C₆₇	semidirect
433. C₂⁴	C₂⁴×C₆₇	semidirect
437. C₂×Q₈	C₂⁴×C₆₇	semidirect
451. C₂×D₄	C₂×D₄×C₆₇	semidirect
452. C₂×D₄	C₂×D₄×C₆₇	semidirect
458. C₂×D₄	C₂⁴×C₆₇	semidirect
459. C₂×D₄	C₂⁴×C₆₇	semidirect
460. C₂×D₄	C₂⁴×C₆₇	semidirect
467. C₂²×C₄	C₂×D₄×C₆₇	semidirect
475. C₂²×C₄	C₂⁴×C₆₇	semidirect
476. C₂²×C₄	C₂⁴×C₆₇	semidirect
477. C₂²×C₄	C₂⁴×C₆₇	semidirect
478. C₄⋊C₄	C₂⁴×C₆₇	semidirect
479. C₄⋊C₄	C₂⁴×C₆₇	semidirect
482. C₂²⋊C₄	C₂⁴×C₆₇	semidirect
483. C₂²⋊C₄	C₂⁴×C₆₇	semidirect
484. C₂²⋊C₄	C₂⁴×C₆₇	semidirect
485. C₄²	C₂⁴×C₆₇	semidirect
512. C₂³	C₂²×D₄×C₆₇	semidirect
513. C₂³	H(5,𝔽₂)×C₆₇	semidirect
528. D₄	C₂²×D₄×C₆₇	semidirect
538. C₂×C₄	C₂²×D₄×C₆₇	semidirect
565. C₂²	C₂×H(5,𝔽₂)×C₆₇	semidirect
576. C₂	C₆₇×#3484	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×H(5,𝔽₂)×C₆₇	2
C₂⁴×D₄×C₆₇	2
C₆₇×#3484	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₂×#535×C₆₇	2
C₂×#534×C₆₇	2
C₂×#525×C₆₇	2
C₂²×#120×C₆₇	2
C₂×#518×C₆₇	2
C₂×#3484	67

Subgroups — C2×C67×#3484 #30742014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3484 #30742014