Subgroups — C₆₇×#22435 #30701686

Order 17152.

1472 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1962	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1897	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1871	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#1789	C₂	1	2	yes	maximal, complemented
11	C₄×#104×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₇	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
14	#550×C₆₇	C₄	1	1	yes	characteristic, complemented
15	D₄×Q₈×C₆₇	C₄	1	1	yes	characteristic, complemented
16	#548×C₆₇	C₄	1	2	yes	complemented
17	#547×C₆₇	—	2	1	no	—
18	#547×C₆₇	C₄	1	1	yes	characteristic, complemented
19	#546×C₆₇	—	2	2	no	—
20	#546×C₆₇	C₄	1	2	yes	complemented
21	D₄²×C₆₇	—	2	1	no	—
22	D₄²×C₆₇	C₄	1	1	yes	characteristic, complemented
23	#532×C₆₇	—	2	1	no	—
24	#532×C₆₇	C₂²	1	1	yes	characteristic
25	#525×C₆₇	—	2	2	no	—
26	#525×C₆₇	C₂²	1	2	yes	—
27	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	—	2	1	no	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
31	#436×C₆₇	—	2	1	no	—
32	#435×C₆₇	—	2	2	no	—
33	C₈×D₄×C₆₇	—	2	1	no	—
34	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#421×C₆₇	—	2	8	no	—
36	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#104×C₆₇	C₂²	1	2	yes	—
38	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
40	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#104×C₆₇	C₂²	1	2	yes	complemented
43	#407×C₆₇	C₂²	1	2	yes	complemented
44	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#390×C₆₇	—	2	1	no	—
46	#389×C₆₇	—	2	1	no	—
47	#388×C₆₇	—	2	2	no	—
48	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
50	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#339×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#339×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#339×C₆₇	C₂²	1	2	yes	complemented
54	C₂×#41×C₆₇	—	2	2	no	—
55	C₂×#41×C₆₇	—	2	2	no	—
56	C₂×#41×C₆₇	—	2	4	no	—
57	C₂×#41×C₆₇	—	2	4	no	—
58	C₂×#41×C₆₇	—	4	2	no	—
59	C₂×#41×C₆₇	—	4	2	no	—
60	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
61	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
62	C₂×#41×C₆₇	C₂³	1	2	yes	—
63	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
65	C₂²×D₄×C₆₇	—	2	2	no	—
66	C₂²×D₄×C₆₇	—	2	1	no	—
67	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
68	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	—	2	2	no	—
70	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
71	C₂×M₁₆×C₆₇	—	2	2	no	—
72	C₂×M₁₆×C₆₇	—	2	4	no	—
73	C₂×M₁₆×C₆₇	—	4	2	no	—
74	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
75	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₇	—	2	2	no	—
78	C₄⋊Q₈×C₆₇	—	2	1	no	—
79	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
80	#127×C₆₇	—	2	1	no	—
81	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
82	#124×C₆₇	—	2	2	no	—
83	#124×C₆₇	C₂×C₄	1	2	yes	—
84	#123×C₆₇	—	2	2	no	—
85	#123×C₆₇	—	2	2	no	—
86	#123×C₆₇	—	2	2	no	—
87	C₂²⋊Q₈×C₆₇	—	2	2	no	—
88	C₂²⋊Q₈×C₆₇	—	2	2	no	—
89	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
90	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
91	#121×C₆₇	—	2	2	no	—
92	#121×C₆₇	—	2	1	no	—
93	#121×C₆₇	—	2	1	no	—
94	#121×C₆₇	—	2	1	no	—
95	#121×C₆₇	—	2	1	no	—
96	#121×C₆₇	—	2	2	no	—
97	#121×C₆₇	—	2	2	no	—
98	#121×C₆₇	C₂×C₄	1	2	yes	—
99	#121×C₆₇	C₂×C₄	1	2	yes	—
100	#120×C₆₇	—	2	2	no	—
101	#120×C₆₇	—	2	2	no	—
102	#120×C₆₇	—	2	2	no	—
103	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
104	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₆₇	—	2	1	no	—
106	C₄×D₄×C₆₇	—	2	2	no	—
107	C₄×D₄×C₆₇	—	2	1	no	—
108	C₄×D₄×C₆₇	—	2	1	no	—
109	C₄×D₄×C₆₇	—	2	2	no	—
110	C₄×D₄×C₆₇	—	2	1	no	—
111	C₄×D₄×C₆₇	—	2	2	no	—
112	C₄×D₄×C₆₇	—	2	1	no	—
113	C₄×D₄×C₆₇	—	2	1	no	—
114	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
115	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
116	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
118	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
120	C₄×D₄×C₆₇	D₄	1	2	yes	—
121	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
122	#117×C₆₇	—	2	1	no	—
123	#117×C₆₇	—	2	4	no	—
124	#117×C₆₇	—	4	2	no	—
125	#117×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
127	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
128	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
129	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
133	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
134	C₂×C₄²×C₆₇	—	2	1	no	—
135	C₂×C₄²×C₆₇	—	2	1	no	—
136	C₂×C₄²×C₆₇	—	2	1	no	—
137	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₄⋊C₈×C₆₇	—	2	1	no	—
142	C₄⋊C₈×C₆₇	—	2	1	no	—
143	#104×C₆₇	—	2	4	no	—
144	#104×C₆₇	—	2	2	no	—
145	#104×C₆₇	—	2	4	no	—
146	#104×C₆₇	—	2	4	no	—
147	#104×C₆₇	—	4	2	no	—
148	#104×C₆₇	—	4	2	no	—
149	#104×C₆₇	D₄	1	4	yes	complemented
150	C₂²⋊C₈×C₆₇	—	2	2	no	—
151	C₂²⋊C₈×C₆₇	—	2	2	no	—
152	#97×C₆₇	—	2	1	no	—
153	C₄×C₈×C₆₇	—	2	1	no	—
154	#95×C₆₇	—	2	2	no	—
155	#95×C₆₇	—	2	1	no	—
156	C₂⁴×C₆₇	—	2	2	no	—
157	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
158	#41×C₆₇	—	2	1	no	—
159	#41×C₆₇	—	2	1	no	—
160	#41×C₆₇	—	2	4	no	—
161	#41×C₆₇	—	2	4	no	—
162	#41×C₆₇	—	2	2	no	—
163	#41×C₆₇	—	2	2	no	—
164	#41×C₆₇	—	2	2	no	—
165	#41×C₆₇	—	2	2	no	—
166	#41×C₆₇	—	4	4	no	—
167	#41×C₆₇	—	4	4	no	—
168	#41×C₆₇	—	4	2	no	—
169	#41×C₆₇	—	4	2	no	—
170	#41×C₆₇	—	4	4	no	—
171	#41×C₆₇	—	4	4	no	—
172	#41×C₆₇	C₂×D₄	1	2	yes	—
173	#41×C₆₇	#41	1	2	yes	—
174	C₂×Q₈×C₆₇	—	2	2	no	—
175	C₂×Q₈×C₆₇	—	2	4	no	—
176	C₂×Q₈×C₆₇	—	4	2	no	—
177	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
178	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
179	C₂×D₄×C₆₇	—	2	1	no	—
180	C₂×D₄×C₆₇	—	2	4	no	—
181	C₂×D₄×C₆₇	—	2	2	no	—
182	C₂×D₄×C₆₇	—	2	2	no	—
183	C₂×D₄×C₆₇	—	2	2	no	—
184	C₂×D₄×C₆₇	—	2	2	no	—
185	C₂×D₄×C₆₇	—	2	2	no	—
186	C₂×D₄×C₆₇	—	2	1	no	—
187	C₂×D₄×C₆₇	—	2	2	no	—
188	C₂×D₄×C₆₇	—	2	1	no	—
189	C₂×D₄×C₆₇	—	4	2	no	—
190	C₂×D₄×C₆₇	—	4	2	no	—
191	C₂×D₄×C₆₇	—	4	4	no	—
192	C₂×D₄×C₆₇	—	4	4	no	—
193	C₂×D₄×C₆₇	—	4	4	no	—
194	C₂×D₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
195	C₂×D₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
196	C₂×D₄×C₆₇	C₂²⋊C₄	1	2	yes	—
197	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
198	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	—	2	2	no	—
200	C₂²×C₄×C₆₇	—	2	1	no	—
201	C₂²×C₄×C₆₇	—	2	2	no	—
202	C₂²×C₄×C₆₇	—	2	2	no	—
203	C₂²×C₄×C₆₇	—	2	2	no	—
204	C₂²×C₄×C₆₇	—	2	2	no	—
205	C₂²×C₄×C₆₇	—	2	1	no	—
206	C₂²×C₄×C₆₇	—	2	1	no	—
207	C₂²×C₄×C₆₇	—	2	1	no	—
208	C₂²×C₄×C₆₇	—	2	2	no	—
209	C₂²×C₄×C₆₇	—	2	2	no	—
210	C₂²×C₄×C₆₇	—	2	2	no	—
211	C₂²×C₄×C₆₇	—	2	1	no	—
212	C₂²×C₄×C₆₇	—	2	2	no	—
213	C₂²×C₄×C₆₇	—	4	4	no	—
214	C₂²×C₄×C₆₇	—	4	4	no	—
215	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
216	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
223	M₁₆×C₆₇	—	2	1	no	—
224	M₁₆×C₆₇	—	2	2	no	—
225	M₁₆×C₆₇	—	2	1	no	—
226	M₁₆×C₆₇	—	2	1	no	—
227	M₁₆×C₆₇	—	2	2	no	—
228	M₁₆×C₆₇	—	4	4	no	—
229	M₁₆×C₆₇	C₂×D₄	1	2	yes	complemented
230	C₂×C₈×C₆₇	—	2	1	no	—
231	C₂×C₈×C₆₇	—	2	2	no	—
232	C₂×C₈×C₆₇	—	2	1	no	—
233	C₂×C₈×C₆₇	—	4	4	no	—
234	C₄⋊C₄×C₆₇	—	2	1	no	—
235	C₄⋊C₄×C₆₇	—	2	2	no	—
236	C₄⋊C₄×C₆₇	—	2	1	no	—
237	C₄⋊C₄×C₆₇	—	2	1	no	—
238	C₄⋊C₄×C₆₇	—	2	1	no	—
239	C₄⋊C₄×C₆₇	—	2	2	no	—
240	C₄⋊C₄×C₆₇	—	4	4	no	—
241	C₄⋊C₄×C₆₇	—	4	2	no	—
242	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
243	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
244	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
245	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
246	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
247	C₂²⋊C₄×C₆₇	—	2	2	no	—
248	C₂²⋊C₄×C₆₇	—	2	2	no	—
249	C₂²⋊C₄×C₆₇	—	2	1	no	—
250	C₂²⋊C₄×C₆₇	—	2	2	no	—
251	C₂²⋊C₄×C₆₇	—	2	2	no	—
252	C₂²⋊C₄×C₆₇	—	2	1	no	—
253	C₂²⋊C₄×C₆₇	—	2	1	no	—
254	C₂²⋊C₄×C₆₇	—	2	2	no	—
255	C₂²⋊C₄×C₆₇	—	2	2	no	—
256	C₂²⋊C₄×C₆₇	—	4	4	no	—
257	C₂²⋊C₄×C₆₇	—	4	4	no	—
258	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
259	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
260	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
261	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
262	C₄²×C₆₇	—	2	1	no	—
263	C₄²×C₆₇	—	2	1	no	—
264	C₄²×C₆₇	—	2	1	no	—
265	C₄²×C₆₇	—	2	1	no	—
266	C₄²×C₆₇	—	2	2	no	—
267	C₄²×C₆₇	—	2	1	no	—
268	C₄²×C₆₇	—	2	1	no	—
269	C₄²×C₆₇	—	2	2	no	—
270	C₄²×C₆₇	—	4	2	no	—
271	C₄²×C₆₇	—	4	2	no	—
272	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
273	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
274	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₆₇	C₂×D₄	1	2	yes	complemented
277	C₂³×C₆₇	—	2	1	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	4	2	no	—
282	C₂³×C₆₇	—	4	2	no	—
283	C₂³×C₆₇	—	4	4	no	—
284	C₂³×C₆₇	—	4	4	no	—
285	C₂³×C₆₇	—	8	2	no	—
286	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
287	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₆₇	—	2	1	no	—
290	Q₈×C₆₇	—	2	2	no	—
291	Q₈×C₆₇	—	2	2	no	—
292	Q₈×C₆₇	—	4	4	no	—
293	Q₈×C₆₇	C₄×D₄	1	2	yes	—
294	D₄×C₆₇	—	2	2	no	—
295	D₄×C₆₇	—	2	2	no	—
296	D₄×C₆₇	—	2	2	no	—
297	D₄×C₆₇	—	2	1	no	—
298	D₄×C₆₇	—	2	2	no	—
299	D₄×C₆₇	—	2	2	no	—
300	D₄×C₆₇	—	2	2	no	—
301	D₄×C₆₇	—	4	2	no	—
302	D₄×C₆₇	—	4	4	no	—
303	D₄×C₆₇	—	4	4	no	—
304	D₄×C₆₇	—	4	4	no	—
305	D₄×C₆₇	—	4	4	no	—
306	D₄×C₆₇	—	4	2	no	—
307	D₄×C₆₇	—	4	2	no	—
308	D₄×C₆₇	—	4	2	no	—
309	D₄×C₆₇	—	8	1	no	—
310	D₄×C₆₇	—	8	2	no	—
311	D₄×C₆₇	C₄×D₄	1	2	yes	—
312	C₂×C₄×C₆₇	—	2	1	no	—
313	C₂×C₄×C₆₇	—	2	2	no	—
314	C₂×C₄×C₆₇	—	2	2	no	—
315	C₂×C₄×C₆₇	—	2	2	no	—
316	C₂×C₄×C₆₇	—	2	2	no	—
317	C₂×C₄×C₆₇	—	2	2	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	2	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	1	no	—
328	C₂×C₄×C₆₇	—	2	1	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	4	1	no	—
332	C₂×C₄×C₆₇	—	4	4	no	—
333	C₂×C₄×C₆₇	—	4	4	no	—
334	C₂×C₄×C₆₇	—	4	4	no	—
335	C₂×C₄×C₆₇	—	4	1	no	—
336	C₂×C₄×C₆₇	—	4	1	no	—
337	C₂×C₄×C₆₇	—	4	1	no	—
338	C₂×C₄×C₆₇	—	4	1	no	—
339	C₂×C₄×C₆₇	—	4	2	no	—
340	C₂×C₄×C₆₇	—	4	2	no	—
341	C₂×C₄×C₆₇	—	4	2	no	—
342	C₂×C₄×C₆₇	—	4	2	no	—
343	C₂×C₄×C₆₇	—	4	2	no	—
344	C₂×C₄×C₆₇	—	4	2	no	—
345	C₂×C₄×C₆₇	—	8	1	no	—
346	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
351	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
353	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
358	C₈×C₆₇	—	2	2	no	—
359	C₈×C₆₇	—	4	2	no	—
360	C₈×C₆₇	—	4	1	no	—
361	C₂²×C₆₇	—	2	1	no	—
362	C₂²×C₆₇	—	2	1	no	—
363	C₂²×C₆₇	—	2	2	no	—
364	C₂²×C₆₇	—	2	2	no	—
365	C₂²×C₆₇	—	2	2	no	—
366	C₂²×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	2	2	no	—
368	C₂²×C₆₇	—	2	2	no	—
369	C₂²×C₆₇	—	2	2	no	—
370	C₂²×C₆₇	—	4	1	no	—
371	C₂²×C₆₇	—	4	1	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	8	2	no	—
376	C₂²×C₆₇	—	8	2	no	—
377	C₂²×C₆₇	—	8	8	no	—
378	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
379	C₂²×C₆₇	D₄²	1	1	yes	characteristic
380	C₂²×C₆₇	#546	1	1	yes	characteristic
381	C₄×C₆₇	—	2	2	no	—
382	C₄×C₆₇	—	2	2	no	—
383	C₄×C₆₇	—	2	2	no	—
384	C₄×C₆₇	—	2	1	no	—
385	C₄×C₆₇	—	2	1	no	—
386	C₄×C₆₇	—	2	1	no	—
387	C₄×C₆₇	—	4	2	no	—
388	C₄×C₆₇	—	4	2	no	—
389	C₄×C₆₇	—	4	2	no	—
390	C₄×C₆₇	—	4	1	no	—
391	C₄×C₆₇	—	4	1	no	—
392	C₄×C₆₇	—	8	2	no	—
393	C₄×C₆₇	#421	1	2	yes	complemented
394	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
395	C₄×C₆₇	#518	1	1	yes	characteristic
396	C₄×C₆₇	D₄²	1	1	yes	characteristic
397	C₄×C₆₇	#546	1	1	yes	characteristic
398	#22435	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂×C₆₇	—	2	1	no	—
400	C₂×C₆₇	—	2	1	no	—
401	C₂×C₆₇	—	4	2	no	—
402	C₂×C₆₇	—	4	2	no	—
403	C₂×C₆₇	—	4	2	no	—
404	C₂×C₆₇	—	8	2	no	—
405	C₂×C₆₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
406	C₂×C₆₇	C₂×#421	1	1	yes	characteristic
407	C₂×C₆₇	#2901	1	1	yes	characteristic
408	D₄×#41	C₂×C₆₇	1	1	yes	characteristic
409	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
410	C₂×#421	C₂×C₆₇	1	2	yes	complemented
411	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#1980	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#1962	C₂×C₆₇	1	1	yes	characteristic, complemented
414	#1897	C₂×C₆₇	1	2	yes	complemented
415	#1871	C₂×C₆₇	1	2	yes	complemented
416	#1806	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#1789	C₂×C₆₇	1	2	yes	complemented
418	C₄×#104	C₂×C₆₇	1	1	yes	characteristic, complemented
419	C₆₇	#22435	1	1	yes	characteristic, direct product factor, Sylow
420	C₂²×#41	C₂²×C₆₇	1	2	yes	—
421	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
422	#550	C₄×C₆₇	1	1	yes	characteristic, complemented
423	D₄×Q₈	C₄×C₆₇	1	1	yes	characteristic, complemented
424	#548	C₄×C₆₇	1	2	yes	complemented
425	#547	—	2	1	no	—
426	#547	C₄×C₆₇	1	1	yes	characteristic, complemented
427	#546	—	2	2	no	—
428	#546	C₄×C₆₇	1	2	yes	complemented
429	D₄²	—	2	1	no	—
430	D₄²	C₄×C₆₇	1	1	yes	characteristic, complemented
431	#532	—	2	1	no	—
432	#532	C₂²×C₆₇	1	1	yes	characteristic
433	#525	—	2	2	no	—
434	#525	C₂²×C₆₇	1	2	yes	—
435	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×C₄×D₄	—	2	1	no	—
437	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
439	#436	—	2	1	no	—
440	#435	—	2	2	no	—
441	C₈×D₄	—	2	1	no	—
442	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
443	#421	—	2	8	no	—
444	C₂×#104	C₂²×C₆₇	1	2	yes	—
445	C₂×#104	C₂²×C₆₇	1	1	yes	characteristic
446	C₂×#104	C₂²×C₆₇	1	1	yes	characteristic
447	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
448	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
449	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
450	C₂×#104	C₂²×C₆₇	1	2	yes	complemented
451	#407	C₂²×C₆₇	1	2	yes	complemented
452	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
453	#390	—	2	1	no	—
454	#389	—	2	1	no	—
455	#388	—	2	2	no	—
456	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
457	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
458	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
459	#339	C₂²×C₆₇	1	2	yes	complemented
460	#339	C₂²×C₆₇	1	1	yes	characteristic, complemented
461	#339	C₂²×C₆₇	1	1	yes	characteristic, complemented
462	C₂×#41	—	2	2	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	4	no	—
465	C₂×#41	—	2	4	no	—
466	C₂×#41	—	4	2	no	—
467	C₂×#41	—	4	2	no	—
468	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
469	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
470	C₂×#41	C₂³×C₆₇	1	2	yes	—
471	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
472	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
473	C₂²×D₄	—	2	2	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
476	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
477	C₂³×C₄	—	2	2	no	—
478	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×M₁₆	—	2	2	no	—
480	C₂×M₁₆	—	2	4	no	—
481	C₂×M₁₆	—	4	2	no	—
482	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
483	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
484	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
485	C₂²×C₈	—	2	2	no	—
486	C₄⋊Q₈	—	2	1	no	—
487	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
488	#127	—	2	1	no	—
489	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
490	#124	—	2	2	no	—
491	#124	C₂×C₄×C₆₇	1	2	yes	—
492	#123	—	2	2	no	—
493	#123	—	2	2	no	—
494	#123	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
498	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
499	#121	—	2	2	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	—	2	2	no	—
505	#121	—	2	2	no	—
506	#121	C₂×C₄×C₆₇	1	2	yes	—
507	#121	C₂×C₄×C₆₇	1	2	yes	—
508	#120	—	2	2	no	—
509	#120	—	2	2	no	—
510	#120	—	2	2	no	—
511	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
512	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
523	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
524	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
525	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
526	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
527	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
528	C₄×D₄	D₄×C₆₇	1	2	yes	—
529	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
530	#117	—	2	1	no	—
531	#117	—	2	4	no	—
532	#117	—	4	2	no	—
533	#117	C₂³×C₆₇	1	1	yes	characteristic
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	—	2	2	no	—
539	C₂×C₂²⋊C₄	—	2	2	no	—
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
542	C₂×C₄²	—	2	1	no	—
543	C₂×C₄²	—	2	1	no	—
544	C₂×C₄²	—	2	1	no	—
545	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
546	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
549	C₄⋊C₈	—	2	1	no	—
550	C₄⋊C₈	—	2	1	no	—
551	#104	—	2	4	no	—
552	#104	—	2	2	no	—
553	#104	—	2	4	no	—
554	#104	—	2	4	no	—
555	#104	—	4	2	no	—
556	#104	—	4	2	no	—
557	#104	D₄×C₆₇	1	4	yes	complemented
558	C₂²⋊C₈	—	2	2	no	—
559	C₂²⋊C₈	—	2	2	no	—
560	#97	—	2	1	no	—
561	C₄×C₈	—	2	1	no	—
562	#95	—	2	2	no	—
563	#95	—	2	1	no	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
566	#41	—	2	1	no	—
567	#41	—	2	1	no	—
568	#41	—	2	4	no	—
569	#41	—	2	4	no	—
570	#41	—	2	2	no	—
571	#41	—	2	2	no	—
572	#41	—	2	2	no	—
573	#41	—	2	2	no	—
574	#41	—	4	4	no	—
575	#41	—	4	4	no	—
576	#41	—	4	2	no	—
577	#41	—	4	2	no	—
578	#41	—	4	4	no	—
579	#41	—	4	4	no	—
580	#41	C₂×D₄×C₆₇	1	2	yes	—
581	#41	#41×C₆₇	1	2	yes	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
586	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	4	no	—
602	C₂×D₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
603	C₂×D₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
604	C₂×D₄	C₂²⋊C₄×C₆₇	1	2	yes	—
605	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
606	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
624	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
625	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
626	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
627	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
629	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
631	M₁₆	—	2	1	no	—
632	M₁₆	—	2	2	no	—
633	M₁₆	—	2	1	no	—
634	M₁₆	—	2	1	no	—
635	M₁₆	—	2	2	no	—
636	M₁₆	—	4	4	no	—
637	M₁₆	C₂×D₄×C₆₇	1	2	yes	complemented
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	4	4	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	4	4	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
651	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
652	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
653	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
654	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
667	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
668	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
669	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	—	2	1	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	1	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	—	4	2	no	—
680	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
681	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
684	C₄²	C₂×D₄×C₆₇	1	2	yes	complemented
685	C₂³	—	2	1	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	8	2	no	—
694	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
695	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
696	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
697	Q₈	—	2	1	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	4	no	—
701	Q₈	C₄×D₄×C₆₇	1	2	yes	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	1	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	2	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	4	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	4	no	—
714	D₄	—	4	2	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	8	1	no	—
718	D₄	—	8	2	no	—
719	D₄	C₄×D₄×C₆₇	1	2	yes	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	4	2	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
755	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
756	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
757	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
758	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
759	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
760	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
763	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
764	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
765	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
766	C₈	—	2	2	no	—
767	C₈	—	4	2	no	—
768	C₈	—	4	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	8	2	no	—
784	C₂²	—	8	2	no	—
785	C₂²	—	8	8	no	—
786	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
787	C₂²	D₄²×C₆₇	1	1	yes	characteristic
788	C₂²	#546×C₆₇	1	1	yes	characteristic
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	8	2	no	—
801	C₄	#421×C₆₇	1	2	yes	complemented
802	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
803	C₄	#518×C₆₇	1	1	yes	characteristic
804	C₄	D₄²×C₆₇	1	1	yes	characteristic
805	C₄	#546×C₆₇	1	1	yes	characteristic
806	C₂	—	2	1	no	—
807	C₂	—	2	1	no	—
808	C₂	—	4	2	no	—
809	C₂	—	4	2	no	—
810	C₂	—	4	2	no	—
811	C₂	—	8	2	no	—
812	C₂	D₄×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
813	C₂	C₂×#421×C₆₇	1	1	yes	characteristic
814	C₂	C₆₇×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂²×C₂²⋊C₄
prime radical	D₄×#41×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×M₁₆×C₆₇	C₂	semidirect
3. C₂×#421×C₆₇	C₂	semidirect
4. C₆₇×#2293	C₂	semidirect
5. C₆₇×#1980	C₂	semidirect
6. C₆₇×#1962	C₂	semidirect
7. C₆₇×#1897	C₂	semidirect
8. C₆₇×#1871	C₂	semidirect
9. C₆₇×#1806	C₂	semidirect
10. C₆₇×#1789	C₂	semidirect
11. C₄×#104×C₆₇	C₂	semidirect
13. C₂²×M₁₆×C₆₇	C₂²	semidirect
14. #550×C₆₇	C₄	semidirect
15. D₄×Q₈×C₆₇	C₄	semidirect
16. #548×C₆₇	C₄	semidirect
18. #547×C₆₇	C₄	semidirect
20. #546×C₆₇	C₄	semidirect
22. D₄²×C₆₇	C₄	semidirect
30. C₂×#117×C₆₇	C₂²	semidirect
34. #423×C₆₇	C₂²	semidirect
39. C₂×#104×C₆₇	C₂²	semidirect
40. C₂×#104×C₆₇	C₂²	semidirect
41. C₂×#104×C₆₇	C₂²	semidirect
42. C₂×#104×C₆₇	C₂²	semidirect
43. #407×C₆₇	C₂²	semidirect
44. C₄×M₁₆×C₆₇	C₂²	semidirect
48. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
49. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
50. C₄³×C₆₇	C₂²	semidirect
51. #339×C₆₇	C₂²	semidirect
52. #339×C₆₇	C₂²	semidirect
53. #339×C₆₇	C₂²	semidirect
149. #104×C₆₇	D₄	semidirect
229. M₁₆×C₆₇	C₂×D₄	semidirect
276. C₄²×C₆₇	C₂×D₄	semidirect
393. C₄×C₆₇	#421	semidirect
398. #22435	C₆₇	direct (N × H)
409. D₄×M₁₆	C₂×C₆₇	semidirect
410. C₂×#421	C₂×C₆₇	semidirect
411. #2293	C₂×C₆₇	semidirect
412. #1980	C₂×C₆₇	semidirect
413. #1962	C₂×C₆₇	semidirect
414. #1897	C₂×C₆₇	semidirect
415. #1871	C₂×C₆₇	semidirect
416. #1806	C₂×C₆₇	semidirect
417. #1789	C₂×C₆₇	semidirect
418. C₄×#104	C₂×C₆₇	semidirect
419. C₆₇	#22435	direct (N × H)
421. C₂²×M₁₆	C₂²×C₆₇	semidirect
422. #550	C₄×C₆₇	semidirect
423. D₄×Q₈	C₄×C₆₇	semidirect
424. #548	C₄×C₆₇	semidirect
426. #547	C₄×C₆₇	semidirect
428. #546	C₄×C₆₇	semidirect
430. D₄²	C₄×C₆₇	semidirect
438. C₂×#117	C₂²×C₆₇	semidirect
442. #423	C₂²×C₆₇	semidirect
447. C₂×#104	C₂²×C₆₇	semidirect
448. C₂×#104	C₂²×C₆₇	semidirect
449. C₂×#104	C₂²×C₆₇	semidirect
450. C₂×#104	C₂²×C₆₇	semidirect
451. #407	C₂²×C₆₇	semidirect
452. C₄×M₁₆	C₂²×C₆₇	semidirect
456. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
457. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
458. C₄³	C₂²×C₆₇	semidirect
459. #339	C₂²×C₆₇	semidirect
460. #339	C₂²×C₆₇	semidirect
461. #339	C₂²×C₆₇	semidirect
557. #104	D₄×C₆₇	semidirect
637. M₁₆	C₂×D₄×C₆₇	semidirect
684. C₄²	C₂×D₄×C₆₇	semidirect
801. C₄	#421×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₆₇	2
D₄×M₁₆×C₆₇	2
C₂×#421×C₆₇	2
C₆₇×#2293	2
C₆₇×#1980	2
C₆₇×#1962	2
C₆₇×#1897	2
C₆₇×#1871	2
C₆₇×#1806	2
C₆₇×#1789	2
C₄×#104×C₆₇	2
#22435	67

Subgroups — C67×#22435 #30701686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#22435 #30701686