Subgroups — C₂×#22574566 #31763590

Order 17152.

7430 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574566	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864146	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864140	C₂	1	2	yes	maximal, complemented
4	C₂×#16864138	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864108	C₂	1	2	yes	maximal, complemented
6	C₂×#16864076	C₂	1	2	yes	maximal, complemented
7	C₂×#16864072	C₂	1	4	yes	maximal, complemented
8	C₂×#16864036	C₂	1	4	yes	maximal, complemented
9	C₂×#16864010	C₂	1	4	yes	maximal, complemented
10	C₂×#16863980	C₂	1	4	yes	maximal, complemented
11	C₂×#16863970	C₂	1	2	yes	maximal, complemented
12	C₂×#16863955	C₂	1	2	yes	maximal, complemented
13	C₂×#16863930	C₂	1	2	yes	maximal, complemented
14	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#11761628	C₂²	1	2	yes	—
16	C₂³×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
17	#16864146	C₂²	1	16	yes	complemented
18	#16864140	C₂²	1	32	yes	complemented
19	#16864138	C₂²	1	16	yes	complemented
20	#16864108	C₂²	1	32	yes	complemented
21	#16864076	C₂²	1	32	yes	complemented
22	#16864072	C₂²	1	64	yes	complemented
23	#16864036	C₂²	1	64	yes	complemented
24	#16864010	C₂²	1	64	yes	complemented
25	#16863980	C₂²	1	64	yes	complemented
26	#16863970	C₂²	1	32	yes	complemented
27	#16863955	C₂²	1	32	yes	complemented
28	C₂×#14524041	C₂²	1	2	yes	complemented
29	C₂×#14524041	C₂²	1	2	yes	complemented
30	#16863930	C₂²	1	32	yes	complemented
31	C₂×#14524037	C₂²	1	4	yes	complemented
32	C₂×#14524036	C₂²	1	4	yes	complemented
33	C₂×#14524036	C₂²	1	4	yes	complemented
34	C₂×#14524035	C₂²	1	2	yes	complemented
35	C₂×#14524032	C₂²	1	2	yes	complemented
36	C₂×#14524032	C₂²	1	2	yes	complemented
37	C₂×#14524031	C₂²	1	2	yes	complemented
38	C₂×#14524029	C₂²	1	4	yes	complemented
39	C₂×#14524029	C₂²	1	4	yes	complemented
40	C₂×#14524027	C₂²	1	4	yes	complemented
41	C₂×#14524026	C₂²	1	4	yes	complemented
42	C₂×#14524026	C₂²	1	4	yes	complemented
43	C₂×#14524025	C₂²	1	4	yes	complemented
44	C₂×#14524025	C₂²	1	4	yes	complemented
45	C₂×#14524024	C₂²	1	2	yes	—
46	C₂×#14524024	C₂²	1	2	yes	complemented
47	C₂×#14524022	C₂²	1	2	yes	complemented
48	C₂×#14524020	C₂²	1	4	yes	complemented
49	C₂×#14524020	C₂²	1	4	yes	complemented
50	C₂×#14524019	C₂²	1	4	yes	complemented
51	C₂×#14524019	C₂²	1	4	yes	complemented
52	C₂×#14524017	C₂²	1	2	yes	—
53	C₂×#14524016	C₂²	1	4	yes	complemented
54	C₂×#14524016	C₂²	1	4	yes	complemented
55	C₂×#14524015	C₂²	1	4	yes	—
56	C₂×#14524015	C₂²	1	4	yes	complemented
57	C₂×#14524013	C₂²	1	4	yes	complemented
58	C₂×#14524012	C₂²	1	4	yes	—
59	C₂×#14524011	C₂²	1	2	yes	—
60	C₂×#14524011	C₂²	1	2	yes	complemented
61	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
62	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
63	C₂×C₄×C₂²⋊D₆₇	C₂²	1	4	yes	complemented
64	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
65	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	complemented
66	C₂×#14524002	C₂²	1	2	yes	complemented
67	C₂×#14524000	C₂²	1	4	yes	complemented
68	C₂×#14523999	C₂²	1	4	yes	complemented
69	C₂²×C₂²⋊Dic₆₇	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊C₄×D₆₇	C₂²	1	4	yes	complemented
71	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
76	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	C₂×#124×C₆₇	C₂²	1	16	yes	complemented
79	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
80	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₂⁴×D₆₇	C₂³	1	2	yes	—
82	C₂×#11761628	—	4	8	no	—
83	C₂×#11761628	C₂³	1	16	yes	—
84	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
85	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
86	C₂²×D₂₆₈	C₂³	1	2	yes	—
87	C₂²×D₂₆₈	C₂³	1	2	yes	—
88	C₂²×C₂²⋊D₆₇	—	4	8	no	—
89	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
90	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
91	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
92	C₂²×C₂²⋊D₆₇	C₂³	1	4	yes	—
93	C₂²×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
94	C₂³×Dic₆₇	C₂³	1	4	yes	—
95	C₂³×Dic₆₇	C₂³	1	2	yes	—
96	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
97	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
98	#14524041	C₂³	1	16	yes	complemented
99	#14524041	C₂³	1	16	yes	complemented
100	#14524037	C₂³	1	32	yes	complemented
101	#14524036	C₂³	1	32	yes	complemented
102	#14524036	C₂³	1	32	yes	complemented
103	#14524035	C₂³	1	16	yes	complemented
104	#14524032	C₂³	1	16	yes	complemented
105	#14524032	C₂³	1	16	yes	complemented
106	#14524031	C₂³	1	16	yes	complemented
107	#14524029	C₂³	1	32	yes	complemented
108	#14524029	C₂³	1	32	yes	complemented
109	#14524027	C₂³	1	32	yes	complemented
110	#14524026	C₂³	1	32	yes	complemented
111	#14524026	C₂³	1	32	yes	complemented
112	#14524025	C₂³	1	32	yes	complemented
113	#14524025	C₂³	1	32	yes	complemented
114	#14524024	C₂³	1	16	yes	—
115	#14524024	C₂³	1	16	yes	complemented
116	#14524022	C₂³	1	16	yes	complemented
117	#14524020	C₂³	1	32	yes	complemented
118	#14524020	C₂³	1	32	yes	complemented
119	#14524019	C₂³	1	32	yes	complemented
120	#14524019	C₂³	1	32	yes	complemented
121	#14524017	C₂³	1	16	yes	—
122	#14524016	C₂³	1	32	yes	complemented
123	#14524016	C₂³	1	32	yes	complemented
124	#14524015	C₂³	1	32	yes	—
125	#14524015	C₂³	1	32	yes	complemented
126	#14524013	C₂³	1	32	yes	complemented
127	#14524012	C₂³	1	32	yes	—
128	#14524011	C₂³	1	16	yes	—
129	#14524011	C₂³	1	16	yes	complemented
130	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
131	C₄×D₂₆₈	C₂³	1	16	yes	complemented
132	C₄×C₂²⋊D₆₇	C₂³	1	32	yes	complemented
133	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	complemented
134	(C₂²⋊D₆₇)⋊C₄	C₂³	1	32	yes	complemented
135	#14524002	C₂³	1	16	yes	complemented
136	#14524000	C₂³	1	32	yes	complemented
137	#14523999	C₂³	1	32	yes	complemented
138	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
139	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
140	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
141	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
142	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
143	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
144	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
145	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
146	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
147	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊Dic₆₇	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₆₇	C₂³	1	16	yes	complemented
153	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
154	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
155	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
156	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
157	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
158	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
159	C₂²⋊C₄×D₆₇	C₂³	1	32	yes	complemented
160	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
161	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
162	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
163	C₂⁵×C₆₇	C₂³	1	2	yes	—
164	C₂²×Q₈×C₆₇	—	4	4	no	—
165	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
168	C₂²×Q₈×C₆₇	C₂³	1	8	yes	complemented
169	C₂²×D₄×C₆₇	—	4	4	no	—
170	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
172	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
174	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
176	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
177	#124×C₆₇	C₂³	1	8	yes	—
178	#124×C₆₇	C₂³	1	8	yes	—
179	#124×C₆₇	C₂³	1	32	yes	complemented
180	#124×C₆₇	C₂³	1	8	yes	complemented
181	#124×C₆₇	C₂³	1	8	yes	complemented
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
191	C₂³×D₆₇	—	4	4	no	—
192	C₂³×D₆₇	—	4	8	no	—
193	C₂³×D₆₇	C₂⁴	1	4	yes	—
194	C₂³×D₆₇	C₂⁴	1	8	yes	—
195	#11761628	—	4	32	no	—
196	C₂×Dic₁₃₄	—	4	4	no	—
197	C₂×Dic₁₃₄	—	4	4	no	—
198	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
199	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
200	C₂×D₂₆₈	—	4	4	no	—
201	C₂×D₂₆₈	—	4	4	no	—
202	C₂×D₂₆₈	C₂⁴	1	8	yes	—
203	C₂×D₂₆₈	C₂⁴	1	8	yes	—
204	C₂×C₂²⋊D₆₇	—	2	16	no	—
205	C₂×C₂²⋊D₆₇	—	4	8	no	—
206	C₂×C₂²⋊D₆₇	—	4	8	no	—
207	C₂×C₂²⋊D₆₇	—	4	8	no	—
208	C₂×C₂²⋊D₆₇	—	4	32	no	—
209	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
210	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
211	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
212	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
213	C₂²×Dic₆₇	—	4	8	no	—
214	C₂²×Dic₆₇	—	4	4	no	—
215	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
216	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
217	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
218	C₂²×Dic₆₇	C₂⁴	1	16	yes	—
219	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
220	C₂×C₄×D₆₇	—	4	8	no	—
221	C₂×C₄×D₆₇	—	4	8	no	—
222	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
223	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
224	C₄⋊Dic₆₇	C₂⁴	1	16	yes	—
225	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
226	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
227	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
228	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
229	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
230	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
231	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
232	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
233	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
234	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
235	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
236	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
237	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
238	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
239	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
240	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
241	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
242	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
243	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
244	C₄×Dic₆₇	C₂⁴	1	8	yes	—
245	C₄×Dic₆₇	C₂⁴	1	16	yes	—
246	C₄×Dic₆₇	C₂⁴	1	8	yes	—
247	C₂⁴×C₆₇	—	2	8	no	—
248	C₂⁴×C₆₇	—	4	8	no	—
249	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
250	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
251	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
253	C₂×Q₈×C₆₇	—	4	2	no	—
254	C₂×Q₈×C₆₇	—	4	4	no	—
255	C₂×Q₈×C₆₇	—	4	2	no	—
256	C₂×Q₈×C₆₇	—	4	16	no	—
257	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
258	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
259	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
260	C₂×D₄×C₆₇	—	4	2	no	—
261	C₂×D₄×C₆₇	—	4	4	no	—
262	C₂×D₄×C₆₇	—	4	2	no	—
263	C₂×D₄×C₆₇	—	4	16	no	—
264	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₆₇	—	2	4	no	—
268	C₂²×C₄×C₆₇	—	2	8	no	—
269	C₂²×C₄×C₆₇	—	4	4	no	—
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
279	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
280	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
281	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
282	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
283	C₄²×C₆₇	C₂⁴	1	4	yes	—
284	C₄²×C₆₇	C₂⁴	1	4	yes	—
285	C₄²×C₆₇	C₂⁴	1	8	yes	—
286	C₂³×C₆₇	—	2	4	no	—
287	C₂³×C₆₇	—	2	4	no	—
288	C₂³×C₆₇	—	2	4	no	—
289	C₂³×C₆₇	—	2	8	no	—
290	C₂³×C₆₇	—	2	8	no	—
291	C₂³×C₆₇	—	2	16	no	—
292	C₂³×C₆₇	—	4	16	no	—
293	C₂³×C₆₇	—	8	16	no	—
294	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
295	C₂³×C₆₇	C₂⁵	1	4	yes	—
296	C₂³×C₆₇	C₂⁵	1	4	yes	—
297	C₂³×C₆₇	C₂⁵	1	2	yes	—
298	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
299	C₂²×D₆₇	—	2	8	no	—
300	C₂²×D₆₇	—	2	8	no	—
301	C₂²×D₆₇	—	2	8	no	—
302	C₂²×D₆₇	—	4	8	no	—
303	C₂²×D₆₇	—	4	16	no	—
304	C₂²×D₆₇	—	8	16	no	—
305	C₂²×D₆₇	C₂⁵	1	8	yes	—
306	Q₈×C₆₇	—	4	4	no	—
307	Q₈×C₆₇	—	4	8	no	—
308	Q₈×C₆₇	—	4	4	no	—
309	D₄×C₆₇	—	4	4	no	—
310	D₄×C₆₇	—	4	8	no	—
311	D₄×C₆₇	—	4	4	no	—
312	C₂×C₄×C₆₇	—	2	8	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	4	no	—
316	C₂×C₄×C₆₇	—	2	4	no	—
317	C₂×C₄×C₆₇	—	2	16	no	—
318	C₂×C₄×C₆₇	—	2	4	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	4	8	no	—
321	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
322	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
323	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
324	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
325	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
326	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
327	C₂²⋊D₆₇	—	2	32	no	—
328	C₂²⋊D₆₇	—	4	16	no	—
329	C₂²⋊D₆₇	—	4	16	no	—
330	C₂²⋊D₆₇	—	4	16	no	—
331	C₂×Dic₆₇	—	2	8	no	—
332	C₂×Dic₆₇	—	2	8	no	—
333	C₂×Dic₆₇	—	2	8	no	—
334	C₂×Dic₆₇	—	4	16	no	—
335	C₂×Dic₆₇	—	4	8	no	—
336	C₂×Dic₆₇	C₂⁵	1	8	yes	—
337	C₂×Dic₆₇	C₂⁵	1	8	yes	—
338	C₂×Dic₆₇	C₂⁵	1	8	yes	—
339	D₂₆₈	—	4	8	no	—
340	D₂₆₈	—	4	8	no	—
341	C₄×D₆₇	—	4	16	no	—
342	C₄×D₆₇	—	4	16	no	—
343	Dic₁₃₄	—	4	8	no	—
344	Dic₁₃₄	—	4	8	no	—
345	C₂²×C₆₇	—	2	4	no	—
346	C₂²×C₆₇	—	2	8	no	—
347	C₂²×C₆₇	—	2	4	no	—
348	C₂²×C₆₇	—	2	4	no	—
349	C₂²×C₆₇	—	2	8	no	—
350	C₂²×C₆₇	—	2	8	no	—
351	C₂²×C₆₇	—	4	8	no	—
352	C₂²×C₆₇	—	4	8	no	—
353	C₂²×C₆₇	—	8	16	no	—
354	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
355	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
356	C₂²×C₆₇	#585	1	4	yes	—
357	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
358	C₂×D₆₇	—	2	8	no	—
359	C₂×D₆₇	—	2	8	no	—
360	C₂×D₆₇	—	2	8	no	—
361	C₂×D₆₇	—	4	16	no	—
362	C₂×D₆₇	—	8	16	no	—
363	C₄×C₆₇	—	2	4	no	—
364	C₄×C₆₇	—	2	4	no	—
365	C₄×C₆₇	—	2	2	no	—
366	C₄×C₆₇	—	2	2	no	—
367	C₄×C₆₇	—	2	4	no	—
368	C₄×C₆₇	—	2	4	no	—
369	Dic₆₇	—	2	8	no	—
370	Dic₆₇	—	2	8	no	—
371	Dic₆₇	—	2	8	no	—
372	C₂×#3545	—	67	1	no	maximal, Sylow
373	C₂×C₆₇	—	2	4	no	—
374	C₂×C₆₇	—	4	4	no	—
375	C₂×C₆₇	—	4	4	no	—
376	C₂×C₆₇	#3545	1	4	yes	complemented
377	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₆₇	C₂×#585	1	2	yes	—
379	D₆₇	—	4	8	no	—
380	#3545	—	67	32	no	—
381	C₂×#563	—	67	1	no	—
382	C₂×#562	—	67	2	no	—
383	C₂×H(3,𝔽₄)	—	67	1	no	—
384	C₂×#555	—	67	2	no	—
385	C₂×#551	—	67	2	no	—
386	C₂×#551	—	67	4	no	—
387	C₂×#546	—	67	4	no	—
388	C₂×#542	—	67	4	no	—
389	C₂×#538	—	67	4	no	—
390	C₂×#536	—	67	2	no	—
391	C₂×#534	—	67	2	no	—
392	C₂×#529	—	67	2	no	—
393	C₂²×#124	D₆₇	1	1	yes	characteristic, complemented
394	C₆₇	C₂×#3545	1	1	yes	characteristic, complemented, Sylow
395	C₂²×#41	—	67	2	no	—
396	C₂³×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
397	C₂³×D₄	—	67	2	no	—
398	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic
399	#563	—	67	16	no	—
400	#562	—	67	32	no	—
401	H(3,𝔽₄)	—	67	16	no	—
402	#555	—	67	32	no	—
403	#551	—	67	32	no	—
404	#551	—	67	64	no	—
405	#546	—	67	64	no	—
406	#542	—	67	64	no	—
407	#538	—	67	64	no	—
408	#536	—	67	32	no	—
409	#534	—	67	32	no	—
410	C₂×C₄⋊Q₈	—	67	2	no	—
411	C₂×C₄⋊Q₈	—	67	2	no	—
412	#529	—	67	32	no	—
413	C₂×#126	—	67	4	no	—
414	C₂×#126	—	67	4	no	—
415	C₂×#126	—	67	4	no	—
416	C₂×#125	—	67	2	no	—
417	C₂×#124	—	67	2	no	—
418	C₂×#124	—	67	2	no	—
419	C₂×#124	—	67	4	no	—
420	C₂×#124	—	67	4	no	—
421	C₂×#124	—	67	2	no	—
422	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
423	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
424	C₂×#124	C₂×D₆₇	1	4	yes	complemented
425	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
426	C₂×#124	C₂×D₆₇	1	1	yes	characteristic, complemented
427	C₂×#124	C₂×D₆₇	1	16	yes	complemented
428	C₂×#123	—	67	2	no	—
429	C₂×#123	—	67	2	no	—
430	C₂×#123	—	67	4	no	—
431	C₂×#123	—	67	4	no	—
432	C₂×#123	—	67	4	no	—
433	C₂×#123	—	67	4	no	—
434	C₂×#123	—	67	4	no	—
435	C₂×C₂²⋊Q₈	—	67	4	no	—
436	C₂×C₂²⋊Q₈	—	67	4	no	—
437	C₂×C₂²⋊Q₈	—	67	2	no	—
438	C₂×C₂²⋊Q₈	—	67	4	no	—
439	C₂×C₂²⋊Q₈	—	67	4	no	—
440	C₂×#121	—	67	4	no	—
441	C₂×#121	—	67	4	no	—
442	C₂×#121	—	67	2	no	—
443	C₂×#121	—	67	4	no	—
444	C₂×#121	—	67	4	no	—
445	C₂×#120	—	67	4	no	—
446	C₂×#120	—	67	2	no	—
447	C₂×#120	—	67	2	no	—
448	C₂×#120	—	67	4	no	—
449	C₂×C₄×Q₈	—	67	2	no	—
450	C₂×C₄×D₄	—	67	4	no	—
451	C₂×C₄×D₄	—	67	4	no	—
452	C₂×C₄×D₄	—	67	4	no	—
453	C₂×C₄×D₄	—	67	2	no	—
454	C₂×#117	—	67	2	no	—
455	C₂×#117	—	67	4	no	—
456	C₂×#117	—	67	4	no	—
457	C₂²×C₂²⋊C₄	—	67	2	no	—
458	C₂²×C₂²⋊C₄	—	67	4	no	—
459	C₂²×C₂²⋊C₄	C₂×D₆₇	1	4	yes	complemented
460	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
461	C₂⁵	—	67	2	no	—
462	C₂⁵	C₂²×D₆₇	1	2	yes	—
463	C₂×#41	—	268	8	no	—
464	C₂×#41	—	67	16	no	—
465	C₂²×Q₈	—	4	4	no	—
466	C₂²×Q₈	—	67	2	no	—
467	C₂²×Q₈	—	67	2	no	—
468	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
469	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
470	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
471	C₂²×Q₈	C₂²×D₆₇	1	8	yes	complemented
472	C₂²×D₄	—	4	4	no	—
473	C₂²×D₄	—	268	8	no	—
474	C₂²×D₄	—	67	4	no	—
475	C₂²×D₄	—	67	4	no	—
476	C₂²×D₄	—	67	4	no	—
477	C₂²×D₄	—	67	16	no	—
478	C₂²×D₄	—	67	4	no	—
479	C₂²×D₄	—	67	2	no	—
480	C₂²×D₄	—	67	2	no	—
481	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
482	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
483	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
484	C₂²×D₄	C₂²×D₆₇	1	8	yes	—
485	C₂³×C₄	—	67	4	no	—
486	C₂³×C₄	—	67	2	no	—
487	C₂³×C₄	—	67	4	no	—
488	C₂³×C₄	—	67	4	no	—
489	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
490	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
491	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
492	C₄⋊Q₈	—	67	16	no	—
493	C₄⋊Q₈	—	67	16	no	—
494	#126	—	67	32	no	—
495	#126	—	67	32	no	—
496	#126	—	67	32	no	—
497	#125	—	67	16	no	—
498	#124	—	67	16	no	—
499	#124	—	67	16	no	—
500	#124	—	67	32	no	—
501	#124	—	67	32	no	—
502	#124	—	67	16	no	—
503	#124	C₂²×D₆₇	1	8	yes	—
504	#124	C₂²×D₆₇	1	8	yes	—
505	#124	C₂²×D₆₇	1	32	yes	complemented
506	#124	C₂²×D₆₇	1	8	yes	complemented
507	#124	C₂²×D₆₇	1	8	yes	complemented
508	#123	—	67	16	no	—
509	#123	—	67	16	no	—
510	#123	—	67	32	no	—
511	#123	—	67	32	no	—
512	#123	—	67	32	no	—
513	#123	—	67	32	no	—
514	#123	—	67	32	no	—
515	C₂²⋊Q₈	—	67	32	no	—
516	C₂²⋊Q₈	—	67	32	no	—
517	C₂²⋊Q₈	—	67	16	no	—
518	C₂²⋊Q₈	—	67	32	no	—
519	C₂²⋊Q₈	—	67	32	no	—
520	#121	—	67	32	no	—
521	#121	—	67	32	no	—
522	#121	—	67	16	no	—
523	#121	—	67	32	no	—
524	#121	—	67	32	no	—
525	#120	—	67	32	no	—
526	#120	—	67	16	no	—
527	#120	—	67	16	no	—
528	#120	—	67	32	no	—
529	C₄×Q₈	—	67	16	no	—
530	C₄×D₄	—	67	32	no	—
531	C₄×D₄	—	67	32	no	—
532	C₄×D₄	—	67	32	no	—
533	C₄×D₄	—	67	16	no	—
534	#117	—	67	16	no	—
535	#117	—	67	32	no	—
536	#117	—	67	32	no	—
537	C₂×C₄⋊C₄	—	67	4	no	—
538	C₂×C₄⋊C₄	—	67	4	no	—
539	C₂×C₄⋊C₄	—	67	4	no	—
540	C₂×C₄⋊C₄	—	67	4	no	—
541	C₂×C₄⋊C₄	—	67	4	no	—
542	C₂×C₄⋊C₄	—	67	4	no	—
543	C₂×C₄⋊C₄	—	67	2	no	—
544	C₂×C₄⋊C₄	—	67	2	no	—
545	C₂×C₄⋊C₄	—	67	4	no	—
546	C₂×C₂²⋊C₄	—	67	4	no	—
547	C₂×C₂²⋊C₄	—	67	4	no	—
548	C₂×C₂²⋊C₄	—	67	2	no	—
549	C₂×C₂²⋊C₄	—	67	2	no	—
550	C₂×C₂²⋊C₄	—	67	16	no	—
551	C₂×C₂²⋊C₄	—	67	4	no	—
552	C₂×C₂²⋊C₄	—	67	4	no	—
553	C₂×C₂²⋊C₄	—	67	4	no	—
554	C₂×C₂²⋊C₄	—	67	4	no	—
555	C₂×C₂²⋊C₄	—	67	4	no	—
556	C₂×C₂²⋊C₄	—	67	4	no	—
557	C₂×C₂²⋊C₄	—	67	4	no	—
558	C₂×C₂²⋊C₄	—	67	32	no	—
559	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂²×D₆₇	1	32	yes	complemented
564	C₂×C₄²	—	67	2	no	—
565	C₂×C₄²	—	67	4	no	—
566	C₂×C₄²	—	67	2	no	—
567	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
568	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
569	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
570	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
571	C₂⁴	—	2	8	no	—
572	C₂⁴	—	4	8	no	—
573	C₂⁴	—	268	4	no	—
574	C₂⁴	—	268	8	no	—
575	C₂⁴	—	67	8	no	—
576	C₂⁴	—	67	4	no	—
577	C₂⁴	C₂³×D₆₇	1	2	yes	—
578	C₂⁴	C₂³×D₆₇	1	2	yes	—
579	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
580	C₂⁴	C₂³×D₆₇	1	8	yes	—
581	#41	—	268	32	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	—	4	16	no	—
586	C₂×Q₈	—	268	4	no	—
587	C₂×Q₈	—	268	4	no	—
588	C₂×Q₈	—	67	8	no	—
589	C₂×Q₈	—	67	8	no	—
590	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
591	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
592	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	4	4	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	16	no	—
597	C₂×D₄	—	268	4	no	—
598	C₂×D₄	—	268	4	no	—
599	C₂×D₄	—	268	32	no	—
600	C₂×D₄	—	268	8	no	—
601	C₂×D₄	—	268	8	no	—
602	C₂×D₄	—	268	8	no	—
603	C₂×D₄	—	67	16	no	—
604	C₂×D₄	—	67	16	no	—
605	C₂×D₄	—	67	16	no	—
606	C₂×D₄	—	67	16	no	—
607	C₂×D₄	—	67	8	no	—
608	C₂×D₄	—	67	8	no	—
609	C₂×D₄	—	134	16	no	—
610	C₂×D₄	C₂³×D₆₇	1	4	yes	—
611	C₂×D₄	C₂³×D₆₇	1	8	yes	—
612	C₂×D₄	C₂³×D₆₇	1	4	yes	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	8	no	—
615	C₂²×C₄	—	4	4	no	—
616	C₂²×C₄	—	268	8	no	—
617	C₂²×C₄	—	268	8	no	—
618	C₂²×C₄	—	268	4	no	—
619	C₂²×C₄	—	268	8	no	—
620	C₂²×C₄	—	67	16	no	—
621	C₂²×C₄	—	67	8	no	—
622	C₂²×C₄	—	67	16	no	—
623	C₂²×C₄	—	67	16	no	—
624	C₂²×C₄	—	67	4	no	—
625	C₂²×C₄	—	67	4	no	—
626	C₂²×C₄	—	67	4	no	—
627	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
628	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
629	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
630	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
631	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
632	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
633	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
634	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
635	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
636	C₄⋊C₄	—	67	16	no	—
637	C₄⋊C₄	—	67	16	no	—
638	C₄⋊C₄	—	67	16	no	—
639	C₄⋊C₄	—	67	16	no	—
640	C₄⋊C₄	—	67	16	no	—
641	C₄⋊C₄	—	67	16	no	—
642	C₄⋊C₄	—	67	8	no	—
643	C₄⋊C₄	—	67	8	no	—
644	C₄⋊C₄	—	67	16	no	—
645	C₂²⋊C₄	—	67	16	no	—
646	C₂²⋊C₄	—	67	16	no	—
647	C₂²⋊C₄	—	67	8	no	—
648	C₂²⋊C₄	—	67	8	no	—
649	C₂²⋊C₄	—	67	16	no	—
650	C₂²⋊C₄	—	67	16	no	—
651	C₂²⋊C₄	—	67	16	no	—
652	C₂²⋊C₄	—	67	16	no	—
653	C₂²⋊C₄	—	67	16	no	—
654	C₂²⋊C₄	—	67	16	no	—
655	C₂²⋊C₄	—	67	16	no	—
656	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
657	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
658	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
659	C₂²⋊C₄	C₂³×D₆₇	1	16	yes	—
660	C₄²	—	67	8	no	—
661	C₄²	—	67	16	no	—
662	C₄²	—	67	8	no	—
663	C₄²	C₂³×D₆₇	1	4	yes	—
664	C₄²	C₂³×D₆₇	1	8	yes	—
665	C₄²	C₂³×D₆₇	1	4	yes	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	16	no	—
672	C₂³	—	4	16	no	—
673	C₂³	—	8	16	no	—
674	C₂³	—	268	8	no	—
675	C₂³	—	268	16	no	—
676	C₂³	—	536	16	no	—
677	C₂³	—	67	8	no	—
678	C₂³	—	134	8	no	—
679	C₂³	—	134	8	no	—
680	C₂³	—	134	8	no	—
681	C₂³	#14524088	1	4	yes	—
682	C₂³	C₂⁴×D₆₇	1	4	yes	—
683	C₂³	C₂⁴×D₆₇	1	4	yes	—
684	C₂³	C₂⁴×D₆₇	1	2	yes	—
685	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
686	Q₈	—	4	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	4	no	—
689	Q₈	—	268	8	no	—
690	Q₈	—	268	8	no	—
691	D₄	—	4	4	no	—
692	D₄	—	4	8	no	—
693	D₄	—	4	4	no	—
694	D₄	—	268	8	no	—
695	D₄	—	268	8	no	—
696	D₄	—	268	16	no	—
697	D₄	—	268	16	no	—
698	D₄	—	268	16	no	—
699	D₄	—	134	32	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	16	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	268	16	no	—
710	C₂×C₄	—	268	16	no	—
711	C₂×C₄	—	268	8	no	—
712	C₂×C₄	—	268	16	no	—
713	C₂×C₄	—	67	8	no	—
714	C₂×C₄	—	67	8	no	—
715	C₂×C₄	—	67	8	no	—
716	C₂×C₄	—	134	8	no	—
717	C₂×C₄	—	134	8	no	—
718	C₂×C₄	—	134	8	no	—
719	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
720	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
721	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
722	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
723	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
724	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	8	no	—
730	C₂²	—	2	8	no	—
731	C₂²	—	4	8	no	—
732	C₂²	—	4	8	no	—
733	C₂²	—	8	16	no	—
734	C₂²	—	268	16	no	—
735	C₂²	—	536	16	no	—
736	C₂²	—	134	8	no	—
737	C₂²	—	134	8	no	—
738	C₂²	—	134	8	no	—
739	C₂²	C₂×#14524088	1	4	yes	—
740	C₂²	C₂×#14524088	1	2	yes	—
741	C₂²	#16864232	1	4	yes	—
742	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	134	8	no	—
750	C₄	—	134	8	no	—
751	C₄	—	134	8	no	—
752	C₂	—	2	4	no	—
753	C₂	—	4	4	no	—
754	C₂	—	4	4	no	—
755	C₂	—	268	8	no	—
756	C₂	#22574566	1	4	yes	direct product factor
757	C₂	C₂²×#14524088	1	1	yes	characteristic
758	C₂	C₂×#16864232	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂²×#124×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂²×#124	D₆₇
hypocenter	C₆₇	C₂×#3545
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. #22574566	C₂	direct (N × H)
2. C₂×#16864146	C₂	semidirect
3. C₂×#16864140	C₂	semidirect
4. C₂×#16864138	C₂	semidirect
5. C₂×#16864108	C₂	semidirect
6. C₂×#16864076	C₂	semidirect
7. C₂×#16864072	C₂	semidirect
8. C₂×#16864036	C₂	semidirect
9. C₂×#16864010	C₂	semidirect
10. C₂×#16863980	C₂	semidirect
11. C₂×#16863970	C₂	semidirect
12. C₂×#16863955	C₂	semidirect
13. C₂×#16863930	C₂	semidirect
14. C₂²×#124×C₆₇	C₂	semidirect
16. C₂³×C₂²⋊D₆₇	C₂²	semidirect
17. #16864146	C₂²	semidirect
18. #16864140	C₂²	semidirect
19. #16864138	C₂²	semidirect
20. #16864108	C₂²	semidirect
21. #16864076	C₂²	semidirect
22. #16864072	C₂²	semidirect
23. #16864036	C₂²	semidirect
24. #16864010	C₂²	semidirect
25. #16863980	C₂²	semidirect
26. #16863970	C₂²	semidirect
27. #16863955	C₂²	semidirect
28. C₂×#14524041	C₂²	semidirect
29. C₂×#14524041	C₂²	semidirect
30. #16863930	C₂²	semidirect
31. C₂×#14524037	C₂²	semidirect
32. C₂×#14524036	C₂²	semidirect
33. C₂×#14524036	C₂²	semidirect
34. C₂×#14524035	C₂²	semidirect
35. C₂×#14524032	C₂²	semidirect
36. C₂×#14524032	C₂²	semidirect
37. C₂×#14524031	C₂²	semidirect
38. C₂×#14524029	C₂²	semidirect
39. C₂×#14524029	C₂²	semidirect
40. C₂×#14524027	C₂²	semidirect
41. C₂×#14524026	C₂²	semidirect
42. C₂×#14524026	C₂²	semidirect
43. C₂×#14524025	C₂²	semidirect
44. C₂×#14524025	C₂²	semidirect
46. C₂×#14524024	C₂²	semidirect
47. C₂×#14524022	C₂²	semidirect
48. C₂×#14524020	C₂²	semidirect
49. C₂×#14524020	C₂²	semidirect
50. C₂×#14524019	C₂²	semidirect
51. C₂×#14524019	C₂²	semidirect
53. C₂×#14524016	C₂²	semidirect
54. C₂×#14524016	C₂²	semidirect
56. C₂×#14524015	C₂²	semidirect
57. C₂×#14524013	C₂²	semidirect
60. C₂×#14524011	C₂²	semidirect
61. C₂×C₄×Dic₁₃₄	C₂²	semidirect
62. C₂×C₄×D₂₆₈	C₂²	semidirect
63. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
64. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
65. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
66. C₂×#14524002	C₂²	semidirect
67. C₂×#14524000	C₂²	semidirect
68. C₂×#14523999	C₂²	semidirect
69. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
71. C₂³×Q₈×C₆₇	C₂²	semidirect
75. C₂×#124×C₆₇	C₂²	semidirect
76. C₂×#124×C₆₇	C₂²	semidirect
77. C₂×#124×C₆₇	C₂²	semidirect
78. C₂×#124×C₆₇	C₂²	semidirect
79. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
80. C₂²×C₄²×C₆₇	C₂²	semidirect
93. C₂²×C₂²⋊D₆₇	C₂³	semidirect
98. #14524041	C₂³	semidirect
99. #14524041	C₂³	semidirect
100. #14524037	C₂³	semidirect
101. #14524036	C₂³	semidirect
102. #14524036	C₂³	semidirect
103. #14524035	C₂³	semidirect
104. #14524032	C₂³	semidirect
105. #14524032	C₂³	semidirect
106. #14524031	C₂³	semidirect
107. #14524029	C₂³	semidirect
108. #14524029	C₂³	semidirect
109. #14524027	C₂³	semidirect
110. #14524026	C₂³	semidirect
111. #14524026	C₂³	semidirect
112. #14524025	C₂³	semidirect
113. #14524025	C₂³	semidirect
115. #14524024	C₂³	semidirect
116. #14524022	C₂³	semidirect
117. #14524020	C₂³	semidirect
118. #14524020	C₂³	semidirect
119. #14524019	C₂³	semidirect
120. #14524019	C₂³	semidirect
122. #14524016	C₂³	semidirect
123. #14524016	C₂³	semidirect
125. #14524015	C₂³	semidirect
126. #14524013	C₂³	semidirect
129. #14524011	C₂³	semidirect
130. C₄×Dic₁₃₄	C₂³	semidirect
131. C₄×D₂₆₈	C₂³	semidirect
132. C₄×C₂²⋊D₆₇	C₂³	semidirect
133. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
134. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
135. #14524002	C₂³	semidirect
136. #14524000	C₂³	semidirect
137. #14523999	C₂³	semidirect
152. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
159. C₂²⋊C₄×D₆₇	C₂³	semidirect
168. C₂²×Q₈×C₆₇	C₂³	semidirect
179. #124×C₆₇	C₂³	semidirect
180. #124×C₆₇	C₂³	semidirect
181. #124×C₆₇	C₂³	semidirect
186. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
190. C₂×C₄²×C₆₇	C₂³	semidirect
376. C₂×C₆₇	#3545	semidirect
393. C₂²×#124	D₆₇	semidirect
394. C₆₇	C₂×#3545	semidirect
396. C₂³×Q₈	C₂×D₆₇	semidirect
424. C₂×#124	C₂×D₆₇	semidirect
425. C₂×#124	C₂×D₆₇	semidirect
426. C₂×#124	C₂×D₆₇	semidirect
427. C₂×#124	C₂×D₆₇	semidirect
459. C₂²×C₂²⋊C₄	C₂×D₆₇	semidirect
460. C₂²×C₄²	C₂×D₆₇	semidirect
471. C₂²×Q₈	C₂²×D₆₇	semidirect
505. #124	C₂²×D₆₇	semidirect
506. #124	C₂²×D₆₇	semidirect
507. #124	C₂²×D₆₇	semidirect
563. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
570. C₂×C₄²	C₂²×D₆₇	semidirect
756. C₂	#22574566	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574566	2
C₂×#16864146	2
C₂×#16864140	2
C₂×#16864138	2
C₂×#16864108	2
C₂×#16864076	2
C₂×#16864072	2
C₂×#16864036	2
C₂×#16864010	2
C₂×#16863980	2
C₂×#16863970	2
C₂×#16863955	2
C₂×#16863930	2
C₂²×#124×C₆₇	2
C₂×#3545	67

Subgroups — C2×#22574566 #31763590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574566 #31763590