Subgroups — C₂×C₆₇×#3002 #30739604

Order 17152.

5130 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3002	C₂	1	16	yes	maximal, direct product factor
5	C₂×#452×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#449×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#451×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#448×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#450×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#447×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#416×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₇	—	2	16	no	—
14	C₂²×#41×C₆₇	—	2	1	no	—
15	C₂²×#41×C₆₇	—	2	4	no	—
16	C₂²×#41×C₆₇	—	2	1	no	—
17	C₂²×#41×C₆₇	C₂²	1	2	yes	—
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂²×#41×C₆₇	C₂²	1	8	yes	complemented
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₆₇	—	2	1	no	—
23	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₆₇	—	2	1	no	—
25	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#135×C₆₇	—	2	16	no	—
27	C₂×#135×C₆₇	C₂²	1	16	yes	complemented
28	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
29	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
30	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
31	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
32	C₂³×C₈×C₆₇	C₂²	1	2	yes	complemented
33	#525×C₆₇	—	2	4	no	—
34	#525×C₆₇	C₂²	1	8	yes	complemented
35	C₂×#123×C₆₇	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#120×C₆₇	—	2	1	no	—
41	C₂×C₄×D₄×C₆₇	—	2	1	no	—
42	C₂×C₄×D₄×C₆₇	—	2	1	no	—
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	#452×C₆₇	C₂²	1	16	yes	complemented
45	#451×C₆₇	C₂²	1	8	yes	complemented
46	#450×C₆₇	C₂²	1	8	yes	complemented
47	#449×C₆₇	C₂²	1	16	yes	complemented
48	#448×C₆₇	C₂²	1	8	yes	complemented
49	#447×C₆₇	C₂²	1	8	yes	complemented
50	#416×C₆₇	C₂²	1	16	yes	complemented
51	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
54	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
58	C₂×C₂²⋊C₈×C₆₇	C₂²	1	8	yes	complemented
59	C₂⁵×C₆₇	—	2	1	no	—
60	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
61	C₂×#41×C₆₇	—	2	16	no	—
62	C₂×#41×C₆₇	—	2	64	no	—
63	C₂×#41×C₆₇	—	2	16	no	—
64	C₂×#41×C₆₇	—	2	64	no	—
65	C₂×#41×C₆₇	—	2	8	no	—
66	C₂×#41×C₆₇	—	2	8	no	—
67	C₂×#41×C₆₇	—	2	8	no	—
68	C₂×#41×C₆₇	—	2	4	no	—
69	C₂×#41×C₆₇	—	2	4	no	—
70	C₂×#41×C₆₇	—	2	8	no	—
71	C₂×#41×C₆₇	—	2	8	no	—
72	C₂×#41×C₆₇	—	2	2	no	—
73	C₂×#41×C₆₇	—	2	8	no	—
74	C₂×#41×C₆₇	D₄	1	16	yes	complemented
75	C₂×#41×C₆₇	C₂³	1	8	yes	—
76	C₂×#41×C₆₇	C₂³	1	8	yes	—
77	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
78	C₂²×Q₈×C₆₇	—	2	8	no	—
79	C₂²×Q₈×C₆₇	—	2	1	no	—
80	C₂²×Q₈×C₆₇	—	2	2	no	—
81	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
82	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
84	C₂²×D₄×C₆₇	—	2	16	no	—
85	C₂²×D₄×C₆₇	—	2	2	no	—
86	C₂²×D₄×C₆₇	—	2	2	no	—
87	C₂²×D₄×C₆₇	—	2	8	no	—
88	C₂²×D₄×C₆₇	—	2	8	no	—
89	C₂²×D₄×C₆₇	—	2	1	no	—
90	C₂²×D₄×C₆₇	—	2	1	no	—
91	C₂²×D₄×C₆₇	—	2	1	no	—
92	C₂²×D₄×C₆₇	—	2	1	no	—
93	C₂²×D₄×C₆₇	—	2	2	no	—
94	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₆₇	—	2	16	no	—
98	C₂³×C₄×C₆₇	—	2	1	no	—
99	C₂³×C₄×C₆₇	—	2	2	no	—
100	C₂³×C₄×C₆₇	—	2	8	no	—
101	C₂³×C₄×C₆₇	—	2	8	no	—
102	C₂³×C₄×C₆₇	—	2	2	no	—
103	C₂³×C₄×C₆₇	—	2	1	no	—
104	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
105	C₂³×C₄×C₆₇	D₄	1	4	yes	—
106	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
112	#135×C₆₇	—	2	64	no	—
113	C₂×Q₁₆×C₆₇	—	2	8	no	—
114	C₂×Q₁₆×C₆₇	C₂³	1	8	yes	complemented
115	C₂×SD₁₆×C₆₇	—	2	8	no	—
116	C₂×SD₁₆×C₆₇	—	2	8	no	—
117	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
118	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
119	C₂×D₈×C₆₇	—	2	8	no	—
120	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
121	C₂²×C₈×C₆₇	—	2	8	no	—
122	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
123	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
124	C₂²×C₈×C₆₇	C₂³	1	8	yes	complemented
125	#123×C₆₇	—	2	8	no	—
126	C₂²⋊Q₈×C₆₇	—	2	2	no	—
127	C₂²⋊Q₈×C₆₇	—	2	2	no	—
128	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
129	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	complemented
130	#121×C₆₇	—	2	2	no	—
131	#121×C₆₇	—	2	2	no	—
132	#121×C₆₇	C₂³	1	4	yes	—
133	#121×C₆₇	C₂³	1	4	yes	complemented
134	#120×C₆₇	—	2	8	no	—
135	C₄×D₄×C₆₇	—	2	8	no	—
136	C₄×D₄×C₆₇	—	2	8	no	—
137	#117×C₆₇	—	2	2	no	—
138	#117×C₆₇	C₂³	1	4	yes	complemented
139	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
148	C₂×C₄²×C₆₇	—	2	1	no	—
149	#103×C₆₇	C₂³	1	8	yes	complemented
150	#103×C₆₇	C₂³	1	8	yes	complemented
151	#102×C₆₇	C₂³	1	8	yes	complemented
152	#102×C₆₇	C₂³	1	8	yes	complemented
153	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
154	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
155	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
156	C₂⁴×C₆₇	—	2	8	no	—
157	C₂⁴×C₆₇	—	2	4	no	—
158	C₂⁴×C₆₇	—	2	4	no	—
159	C₂⁴×C₆₇	—	2	4	no	—
160	C₂⁴×C₆₇	—	2	2	no	—
161	C₂⁴×C₆₇	—	2	1	no	—
162	C₂⁴×C₆₇	—	4	2	no	—
163	C₂⁴×C₆₇	—	4	4	no	—
164	C₂⁴×C₆₇	—	4	4	no	—
165	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
167	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
169	#41×C₆₇	—	2	64	no	—
170	#41×C₆₇	—	2	32	no	—
171	#41×C₆₇	—	2	64	no	—
172	#41×C₆₇	—	2	16	no	—
173	#41×C₆₇	—	2	16	no	—
174	#41×C₆₇	—	2	32	no	—
175	#41×C₆₇	—	2	16	no	—
176	#41×C₆₇	—	2	16	no	—
177	#41×C₆₇	—	4	8	no	—
178	#41×C₆₇	C₂×D₄	1	32	yes	complemented
179	C₂×Q₈×C₆₇	—	2	16	no	—
180	C₂×Q₈×C₆₇	—	2	8	no	—
181	C₂×Q₈×C₆₇	—	2	16	no	—
182	C₂×Q₈×C₆₇	—	2	4	no	—
183	C₂×Q₈×C₆₇	—	2	4	no	—
184	C₂×Q₈×C₆₇	—	2	2	no	—
185	C₂×Q₈×C₆₇	—	2	1	no	—
186	C₂×Q₈×C₆₇	—	2	4	no	—
187	C₂×Q₈×C₆₇	C₂×D₄	1	8	yes	—
188	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
189	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
190	C₂×D₄×C₆₇	—	2	64	no	—
191	C₂×D₄×C₆₇	—	2	16	no	—
192	C₂×D₄×C₆₇	—	2	8	no	—
193	C₂×D₄×C₆₇	—	2	16	no	—
194	C₂×D₄×C₆₇	—	2	16	no	—
195	C₂×D₄×C₆₇	—	2	8	no	—
196	C₂×D₄×C₆₇	—	2	8	no	—
197	C₂×D₄×C₆₇	—	2	16	no	—
198	C₂×D₄×C₆₇	—	2	4	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	2	no	—
203	C₂×D₄×C₆₇	—	2	4	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	1	no	—
206	C₂×D₄×C₆₇	—	4	4	no	—
207	C₂×D₄×C₆₇	—	4	4	no	—
208	C₂×D₄×C₆₇	—	4	4	no	—
209	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
210	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
211	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₆₇	—	2	8	no	—
213	C₂²×C₄×C₆₇	—	2	64	no	—
214	C₂²×C₄×C₆₇	—	2	16	no	—
215	C₂²×C₄×C₆₇	—	2	4	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	2	no	—
218	C₂²×C₄×C₆₇	—	2	4	no	—
219	C₂²×C₄×C₆₇	—	2	16	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	16	no	—
222	C₂²×C₄×C₆₇	—	2	8	no	—
223	C₂²×C₄×C₆₇	—	2	8	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	16	no	—
227	C₂²×C₄×C₆₇	—	2	1	no	—
228	C₂²×C₄×C₆₇	—	2	1	no	—
229	C₂²×C₄×C₆₇	—	2	1	no	—
230	C₂²×C₄×C₆₇	—	2	4	no	—
231	C₂²×C₄×C₆₇	—	4	4	no	—
232	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
241	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	Q₁₆×C₆₇	—	2	16	no	—
247	SD₁₆×C₆₇	—	2	16	no	—
248	SD₁₆×C₆₇	—	2	16	no	—
249	D₈×C₆₇	—	2	16	no	—
250	C₂×C₈×C₆₇	—	2	4	no	—
251	C₂×C₈×C₆₇	—	2	4	no	—
252	C₂×C₈×C₆₇	—	2	16	no	—
253	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
254	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₆₇	—	2	4	no	—
262	C₂²⋊C₄×C₆₇	—	2	4	no	—
263	C₂²⋊C₄×C₆₇	—	2	4	no	—
264	C₂²⋊C₄×C₆₇	—	2	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₄²×C₆₇	—	2	4	no	—
267	C₂³×C₆₇	—	2	2	no	—
268	C₂³×C₆₇	—	2	2	no	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	2	16	no	—
272	C₂³×C₆₇	—	2	8	no	—
273	C₂³×C₆₇	—	2	2	no	—
274	C₂³×C₆₇	—	2	8	no	—
275	C₂³×C₆₇	—	2	2	no	—
276	C₂³×C₆₇	—	2	8	no	—
277	C₂³×C₆₇	—	2	2	no	—
278	C₂³×C₆₇	—	2	4	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	4	4	no	—
281	C₂³×C₆₇	—	4	16	no	—
282	C₂³×C₆₇	—	4	32	no	—
283	C₂³×C₆₇	—	4	8	no	—
284	C₂³×C₆₇	—	4	4	no	—
285	C₂³×C₆₇	—	4	8	no	—
286	C₂³×C₆₇	—	4	4	no	—
287	C₂³×C₆₇	—	4	2	no	—
288	C₂³×C₆₇	—	4	2	no	—
289	C₂³×C₆₇	—	4	2	no	—
290	C₂³×C₆₇	#120	1	4	yes	—
291	C₂³×C₆₇	#135	1	4	yes	complemented
292	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
293	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
294	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
295	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₆₇	—	2	16	no	—
297	Q₈×C₆₇	—	2	8	no	—
298	Q₈×C₆₇	—	2	4	no	—
299	Q₈×C₆₇	—	2	4	no	—
300	Q₈×C₆₇	—	4	2	no	—
301	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
302	D₄×C₆₇	—	2	32	no	—
303	D₄×C₆₇	—	2	16	no	—
304	D₄×C₆₇	—	2	32	no	—
305	D₄×C₆₇	—	2	8	no	—
306	D₄×C₆₇	—	2	4	no	—
307	D₄×C₆₇	—	2	4	no	—
308	D₄×C₆₇	—	4	8	no	—
309	D₄×C₆₇	—	4	8	no	—
310	D₄×C₆₇	—	4	8	no	—
311	D₄×C₆₇	—	4	2	no	—
312	D₄×C₆₇	C₂²×D₄	1	8	yes	—
313	C₂×C₄×C₆₇	—	2	16	no	—
314	C₂×C₄×C₆₇	—	2	32	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	8	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	8	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	2	8	no	—
321	C₂×C₄×C₆₇	—	2	32	no	—
322	C₂×C₄×C₆₇	—	2	4	no	—
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	8	no	—
325	C₂×C₄×C₆₇	—	2	4	no	—
326	C₂×C₄×C₆₇	—	2	4	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	4	2	no	—
331	C₂×C₄×C₆₇	—	4	2	no	—
332	C₂×C₄×C₆₇	—	4	2	no	—
333	C₂×C₄×C₆₇	—	4	8	no	—
334	C₂×C₄×C₆₇	#120	1	4	yes	—
335	C₂×C₄×C₆₇	#120	1	8	yes	—
336	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
341	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
342	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
343	C₈×C₆₇	—	2	4	no	—
344	C₈×C₆₇	—	2	4	no	—
345	C₂²×C₆₇	—	2	2	no	—
346	C₂²×C₆₇	—	2	8	no	—
347	C₂²×C₆₇	—	2	8	no	—
348	C₂²×C₆₇	—	2	2	no	—
349	C₂²×C₆₇	—	2	2	no	—
350	C₂²×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	2	2	no	—
352	C₂²×C₆₇	—	2	8	no	—
353	C₂²×C₆₇	—	2	2	no	—
354	C₂²×C₆₇	—	2	2	no	—
355	C₂²×C₆₇	—	4	16	no	—
356	C₂²×C₆₇	—	4	32	no	—
357	C₂²×C₆₇	—	4	4	no	—
358	C₂²×C₆₇	—	4	16	no	—
359	C₂²×C₆₇	—	4	4	no	—
360	C₂²×C₆₇	—	4	4	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	—	4	2	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	8	4	no	—
365	C₂²×C₆₇	C₂×#120	1	4	yes	—
366	C₂²×C₆₇	C₂×#120	1	2	yes	—
367	C₂²×C₆₇	C₂×#135	1	2	yes	—
368	C₂²×C₆₇	C₂×#135	1	4	yes	complemented
369	C₂²×C₆₇	#575	1	2	yes	—
370	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₆₇	—	2	2	no	—
372	C₄×C₆₇	—	2	8	no	—
373	C₄×C₆₇	—	2	2	no	—
374	C₄×C₆₇	—	4	2	no	—
375	C₄×C₆₇	—	4	2	no	—
376	C₄×C₆₇	—	4	2	no	—
377	C₄×C₆₇	C₂×#120	1	4	yes	—
378	C₄×C₆₇	C₂×#120	1	2	yes	—
379	C₄×C₆₇	C₂³×D₄	1	2	yes	—
380	C₂×#3002	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₆₇	—	2	4	no	—
382	C₂×C₆₇	—	2	4	no	—
383	C₂×C₆₇	—	4	2	no	—
384	C₂×C₆₇	—	4	8	no	—
385	C₂×C₆₇	—	8	2	no	—
386	C₂×C₆₇	#3002	1	4	yes	direct product factor
387	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
388	C₂×C₆₇	C₂²×#135	1	1	yes	characteristic
389	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
390	C₂³×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
391	C₂²×#135	C₂×C₆₇	1	2	yes	complemented
392	C₂×#525	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#3002	C₂×C₆₇	1	16	yes	direct product factor
394	C₂×#452	C₂×C₆₇	1	2	yes	complemented
395	C₂×#449	C₂×C₆₇	1	2	yes	complemented
396	C₂×#451	C₂×C₆₇	1	1	yes	characteristic, complemented
397	C₂×#448	C₂×C₆₇	1	1	yes	characteristic, complemented
398	C₂×#450	C₂×C₆₇	1	1	yes	characteristic, complemented
399	C₂×#447	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₂×#416	C₂×C₆₇	1	2	yes	complemented
401	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₆₇	C₂×#3002	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²×#41	—	2	16	no	—
404	C₂²×#41	—	2	1	no	—
405	C₂²×#41	—	2	1	no	—
406	C₂²×#41	—	2	4	no	—
407	C₂²×#41	C₂²×C₆₇	1	2	yes	—
408	C₂²×#41	C₂²×C₆₇	1	2	yes	—
409	C₂²×#41	C₂²×C₆₇	1	8	yes	complemented
410	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
411	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
412	C₂³×D₄	—	2	1	no	—
413	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
414	C₂⁴×C₄	—	2	1	no	—
415	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
416	C₂×#135	—	2	16	no	—
417	C₂×#135	C₂²×C₆₇	1	16	yes	complemented
418	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
419	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
420	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
421	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
422	C₂³×C₈	C₂²×C₆₇	1	2	yes	complemented
423	#525	—	2	4	no	—
424	#525	C₂²×C₆₇	1	8	yes	complemented
425	C₂×#123	—	2	1	no	—
426	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
428	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
429	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
430	C₂×#120	—	2	1	no	—
431	C₂×C₄×D₄	—	2	1	no	—
432	C₂×C₄×D₄	—	2	1	no	—
433	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
434	#452	C₂²×C₆₇	1	16	yes	complemented
435	#451	C₂²×C₆₇	1	8	yes	complemented
436	#450	C₂²×C₆₇	1	8	yes	complemented
437	#449	C₂²×C₆₇	1	16	yes	complemented
438	#448	C₂²×C₆₇	1	8	yes	complemented
439	#447	C₂²×C₆₇	1	8	yes	complemented
440	#416	C₂²×C₆₇	1	16	yes	complemented
441	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
442	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
443	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
444	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
445	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₆₇	1	8	yes	complemented
448	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
449	C₂⁵	—	2	1	no	—
450	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
451	C₂×#41	—	2	16	no	—
452	C₂×#41	—	2	64	no	—
453	C₂×#41	—	2	16	no	—
454	C₂×#41	—	2	64	no	—
455	C₂×#41	—	2	8	no	—
456	C₂×#41	—	2	8	no	—
457	C₂×#41	—	2	8	no	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	8	no	—
461	C₂×#41	—	2	8	no	—
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	2	8	no	—
464	C₂×#41	D₄×C₆₇	1	16	yes	complemented
465	C₂×#41	C₂³×C₆₇	1	8	yes	—
466	C₂×#41	C₂³×C₆₇	1	8	yes	—
467	C₂×#41	C₂³×C₆₇	1	4	yes	complemented
468	C₂²×Q₈	—	2	8	no	—
469	C₂²×Q₈	—	2	1	no	—
470	C₂²×Q₈	—	2	2	no	—
471	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
473	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
474	C₂²×D₄	—	2	16	no	—
475	C₂²×D₄	—	2	2	no	—
476	C₂²×D₄	—	2	2	no	—
477	C₂²×D₄	—	2	8	no	—
478	C₂²×D₄	—	2	8	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	—	2	2	no	—
484	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
486	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
487	C₂³×C₄	—	2	16	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	2	no	—
490	C₂³×C₄	—	2	2	no	—
491	C₂³×C₄	—	2	8	no	—
492	C₂³×C₄	—	2	8	no	—
493	C₂³×C₄	—	2	1	no	—
494	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
495	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
496	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
497	C₂³×C₄	D₄×C₆₇	1	4	yes	—
498	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
501	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
502	#135	—	2	64	no	—
503	C₂×Q₁₆	—	2	8	no	—
504	C₂×Q₁₆	C₂³×C₆₇	1	8	yes	complemented
505	C₂×SD₁₆	—	2	8	no	—
506	C₂×SD₁₆	—	2	8	no	—
507	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
508	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
509	C₂×D₈	—	2	8	no	—
510	C₂×D₈	C₂³×C₆₇	1	8	yes	complemented
511	C₂²×C₈	—	2	8	no	—
512	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
513	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
514	C₂²×C₈	C₂³×C₆₇	1	8	yes	complemented
515	#123	—	2	8	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
519	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	complemented
520	#121	—	2	2	no	—
521	#121	—	2	2	no	—
522	#121	C₂³×C₆₇	1	4	yes	—
523	#121	C₂³×C₆₇	1	4	yes	complemented
524	#120	—	2	8	no	—
525	C₄×D₄	—	2	8	no	—
526	C₄×D₄	—	2	8	no	—
527	#117	—	2	2	no	—
528	#117	C₂³×C₆₇	1	4	yes	complemented
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₄²	—	2	1	no	—
539	#103	C₂³×C₆₇	1	8	yes	complemented
540	#103	C₂³×C₆₇	1	8	yes	complemented
541	#102	C₂³×C₆₇	1	8	yes	complemented
542	#102	C₂³×C₆₇	1	8	yes	complemented
543	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
545	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
546	C₂⁴	—	2	8	no	—
547	C₂⁴	—	2	4	no	—
548	C₂⁴	—	2	4	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	1	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	4	no	—
554	C₂⁴	—	4	4	no	—
555	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
556	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
557	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
558	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
559	#41	—	2	64	no	—
560	#41	—	2	32	no	—
561	#41	—	2	64	no	—
562	#41	—	2	16	no	—
563	#41	—	2	16	no	—
564	#41	—	2	32	no	—
565	#41	—	2	16	no	—
566	#41	—	2	16	no	—
567	#41	—	4	8	no	—
568	#41	C₂×D₄×C₆₇	1	32	yes	complemented
569	C₂×Q₈	—	2	16	no	—
570	C₂×Q₈	—	2	8	no	—
571	C₂×Q₈	—	2	16	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	C₂×D₄×C₆₇	1	8	yes	—
578	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
579	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
580	C₂×D₄	—	2	64	no	—
581	C₂×D₄	—	2	16	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	16	no	—
584	C₂×D₄	—	2	16	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	16	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
600	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
601	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
602	C₂²×C₄	—	2	8	no	—
603	C₂²×C₄	—	2	64	no	—
604	C₂²×C₄	—	2	16	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	16	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	16	no	—
612	C₂²×C₄	—	2	8	no	—
613	C₂²×C₄	—	2	8	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	16	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
627	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
635	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
636	Q₁₆	—	2	16	no	—
637	SD₁₆	—	2	16	no	—
638	SD₁₆	—	2	16	no	—
639	D₈	—	2	16	no	—
640	C₂×C₈	—	2	4	no	—
641	C₂×C₈	—	2	4	no	—
642	C₂×C₈	—	2	16	no	—
643	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
644	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
650	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	16	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	8	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	4	no	—
671	C₂³	—	4	16	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	4	32	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	8	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	#120×C₆₇	1	4	yes	—
681	C₂³	#135×C₆₇	1	4	yes	complemented
682	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
683	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
684	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
685	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
686	Q₈	—	2	16	no	—
687	Q₈	—	2	8	no	—
688	Q₈	—	2	4	no	—
689	Q₈	—	2	4	no	—
690	Q₈	—	4	2	no	—
691	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
692	D₄	—	2	32	no	—
693	D₄	—	2	16	no	—
694	D₄	—	2	32	no	—
695	D₄	—	2	8	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	4	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	8	no	—
700	D₄	—	4	8	no	—
701	D₄	—	4	2	no	—
702	D₄	C₂²×D₄×C₆₇	1	8	yes	—
703	C₂×C₄	—	2	16	no	—
704	C₂×C₄	—	2	32	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	2	32	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	#120×C₆₇	1	4	yes	—
725	C₂×C₄	#120×C₆₇	1	8	yes	—
726	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
731	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
732	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
733	C₈	—	2	4	no	—
734	C₈	—	2	4	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	8	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	8	no	—
745	C₂²	—	4	16	no	—
746	C₂²	—	4	32	no	—
747	C₂²	—	4	4	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	16	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	8	4	no	—
755	C₂²	C₂×#120×C₆₇	1	4	yes	—
756	C₂²	C₂×#120×C₆₇	1	2	yes	—
757	C₂²	C₂×#135×C₆₇	1	2	yes	—
758	C₂²	C₂×#135×C₆₇	1	4	yes	complemented
759	C₂²	#575×C₆₇	1	2	yes	—
760	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
761	C₄	—	2	2	no	—
762	C₄	—	2	8	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	C₂×#120×C₆₇	1	4	yes	—
768	C₄	C₂×#120×C₆₇	1	2	yes	—
769	C₄	C₂³×D₄×C₆₇	1	2	yes	—
770	C₂	—	2	4	no	—
771	C₂	—	2	4	no	—
772	C₂	—	4	2	no	—
773	C₂	—	4	8	no	—
774	C₂	—	8	2	no	—
775	C₂	C₆₇×#3002	1	4	yes	direct product factor
776	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
777	C₂	C₂²×#135×C₆₇	1	1	yes	characteristic
778	C₂	C₂×#575×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₆₇	C₂	semidirect
2. C₂²×#135×C₆₇	C₂	semidirect
3. C₂×#525×C₆₇	C₂	semidirect
4. C₆₇×#3002	C₂	direct (N × H)
5. C₂×#452×C₆₇	C₂	semidirect
6. C₂×#449×C₆₇	C₂	semidirect
7. C₂×#451×C₆₇	C₂	semidirect
8. C₂×#448×C₆₇	C₂	semidirect
9. C₂×#450×C₆₇	C₂	semidirect
10. C₂×#447×C₆₇	C₂	semidirect
11. C₂×#416×C₆₇	C₂	semidirect
12. C₂²×C₂²⋊C₈×C₆₇	C₂	semidirect
19. C₂²×#41×C₆₇	C₂²	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
27. C₂×#135×C₆₇	C₂²	semidirect
28. C₂²×Q₁₆×C₆₇	C₂²	semidirect
29. C₂²×SD₁₆×C₆₇	C₂²	semidirect
30. C₂²×SD₁₆×C₆₇	C₂²	semidirect
31. C₂²×D₈×C₆₇	C₂²	semidirect
32. C₂³×C₈×C₆₇	C₂²	semidirect
34. #525×C₆₇	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
39. C₂×#121×C₆₇	C₂²	semidirect
43. C₂×#117×C₆₇	C₂²	semidirect
44. #452×C₆₇	C₂²	semidirect
45. #451×C₆₇	C₂²	semidirect
46. #450×C₆₇	C₂²	semidirect
47. #449×C₆₇	C₂²	semidirect
48. #448×C₆₇	C₂²	semidirect
49. #447×C₆₇	C₂²	semidirect
50. #416×C₆₇	C₂²	semidirect
51. C₂×#103×C₆₇	C₂²	semidirect
52. C₂×#103×C₆₇	C₂²	semidirect
53. C₂×#102×C₆₇	C₂²	semidirect
54. C₂×#102×C₆₇	C₂²	semidirect
57. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
58. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
74. C₂×#41×C₆₇	D₄	semidirect
77. C₂×#41×C₆₇	C₂³	semidirect
114. C₂×Q₁₆×C₆₇	C₂³	semidirect
117. C₂×SD₁₆×C₆₇	C₂³	semidirect
118. C₂×SD₁₆×C₆₇	C₂³	semidirect
120. C₂×D₈×C₆₇	C₂³	semidirect
124. C₂²×C₈×C₆₇	C₂³	semidirect
129. C₂²⋊Q₈×C₆₇	C₂³	semidirect
133. #121×C₆₇	C₂³	semidirect
138. #117×C₆₇	C₂³	semidirect
149. #103×C₆₇	C₂³	semidirect
150. #103×C₆₇	C₂³	semidirect
151. #102×C₆₇	C₂³	semidirect
152. #102×C₆₇	C₂³	semidirect
155. C₂²⋊C₈×C₆₇	C₂³	semidirect
178. #41×C₆₇	C₂×D₄	semidirect
291. C₂³×C₆₇	#135	semidirect
368. C₂²×C₆₇	C₂×#135	semidirect
380. C₂×#3002	C₆₇	direct (N × H)
386. C₂×C₆₇	#3002	direct (N × H)
390. C₂³×#41	C₂×C₆₇	semidirect
391. C₂²×#135	C₂×C₆₇	semidirect
392. C₂×#525	C₂×C₆₇	semidirect
393. #3002	C₂×C₆₇	direct (N × H)
394. C₂×#452	C₂×C₆₇	semidirect
395. C₂×#449	C₂×C₆₇	semidirect
396. C₂×#451	C₂×C₆₇	semidirect
397. C₂×#448	C₂×C₆₇	semidirect
398. C₂×#450	C₂×C₆₇	semidirect
399. C₂×#447	C₂×C₆₇	semidirect
400. C₂×#416	C₂×C₆₇	semidirect
401. C₂²×C₂²⋊C₈	C₂×C₆₇	semidirect
402. C₆₇	C₂×#3002	direct (N × H)
409. C₂²×#41	C₂²×C₆₇	semidirect
410. C₂²×#41	C₂²×C₆₇	semidirect
417. C₂×#135	C₂²×C₆₇	semidirect
418. C₂²×Q₁₆	C₂²×C₆₇	semidirect
419. C₂²×SD₁₆	C₂²×C₆₇	semidirect
420. C₂²×SD₁₆	C₂²×C₆₇	semidirect
421. C₂²×D₈	C₂²×C₆₇	semidirect
422. C₂³×C₈	C₂²×C₆₇	semidirect
424. #525	C₂²×C₆₇	semidirect
427. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
429. C₂×#121	C₂²×C₆₇	semidirect
433. C₂×#117	C₂²×C₆₇	semidirect
434. #452	C₂²×C₆₇	semidirect
435. #451	C₂²×C₆₇	semidirect
436. #450	C₂²×C₆₇	semidirect
437. #449	C₂²×C₆₇	semidirect
438. #448	C₂²×C₆₇	semidirect
439. #447	C₂²×C₆₇	semidirect
440. #416	C₂²×C₆₇	semidirect
441. C₂×#103	C₂²×C₆₇	semidirect
442. C₂×#103	C₂²×C₆₇	semidirect
443. C₂×#102	C₂²×C₆₇	semidirect
444. C₂×#102	C₂²×C₆₇	semidirect
447. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
448. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
464. C₂×#41	D₄×C₆₇	semidirect
467. C₂×#41	C₂³×C₆₇	semidirect
504. C₂×Q₁₆	C₂³×C₆₇	semidirect
507. C₂×SD₁₆	C₂³×C₆₇	semidirect
508. C₂×SD₁₆	C₂³×C₆₇	semidirect
510. C₂×D₈	C₂³×C₆₇	semidirect
514. C₂²×C₈	C₂³×C₆₇	semidirect
519. C₂²⋊Q₈	C₂³×C₆₇	semidirect
523. #121	C₂³×C₆₇	semidirect
528. #117	C₂³×C₆₇	semidirect
539. #103	C₂³×C₆₇	semidirect
540. #103	C₂³×C₆₇	semidirect
541. #102	C₂³×C₆₇	semidirect
542. #102	C₂³×C₆₇	semidirect
545. C₂²⋊C₈	C₂³×C₆₇	semidirect
568. #41	C₂×D₄×C₆₇	semidirect
681. C₂³	#135×C₆₇	semidirect
758. C₂²	C₂×#135×C₆₇	semidirect
775. C₂	C₆₇×#3002	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₆₇	2
C₂²×#135×C₆₇	2
C₂×#525×C₆₇	2
C₆₇×#3002	2
C₂×#452×C₆₇	2
C₂×#449×C₆₇	2
C₂×#451×C₆₇	2
C₂×#448×C₆₇	2
C₂×#450×C₆₇	2
C₂×#447×C₆₇	2
C₂×#416×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂×#3002	67

Subgroups — C2×C67×#3002 #30739604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3002 #30739604