Subgroups — C₆₇×#10997 #30690248

Order 17152.

1630 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#100×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1736	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#339×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
12	#535×C₆₇	—	2	2	no	—
13	#535×C₆₇	—	2	2	no	—
14	#535×C₆₇	—	2	2	no	—
15	#535×C₆₇	C₄	1	4	yes	complemented
16	C₂×#127×C₆₇	—	2	1	no	—
17	C₂×#124×C₆₇	—	2	1	no	—
18	C₂×#121×C₆₇	—	2	2	no	—
19	C₂×#120×C₆₇	—	2	2	no	—
20	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₆₇	—	2	2	no	—
23	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#104×C₆₇	—	2	2	no	—
25	C₂×#104×C₆₇	—	2	2	no	—
26	C₂×#104×C₆₇	—	2	2	no	—
27	#417×C₆₇	—	2	2	no	—
28	#417×C₆₇	—	2	2	no	—
29	C₂×#103×C₆₇	—	2	1	no	—
30	C₂×#102×C₆₇	—	2	1	no	—
31	C₂×#100×C₆₇	—	2	2	no	—
32	C₂×#100×C₆₇	—	2	2	no	—
33	C₂×#100×C₆₇	—	2	2	no	—
34	#390×C₆₇	—	2	2	no	—
35	#390×C₆₇	—	2	2	no	—
36	#340×C₆₇	—	2	2	no	—
37	#339×C₆₇	—	2	2	no	—
38	C₂⁵×C₆₇	D₄	1	2	yes	—
39	C₂×#41×C₆₇	—	2	1	no	—
40	C₂×#41×C₆₇	—	2	1	no	—
41	C₂×#41×C₆₇	—	2	1	no	—
42	C₂×#41×C₆₇	—	2	1	no	—
43	C₂×#41×C₆₇	—	2	1	no	—
44	C₂×#41×C₆₇	—	2	1	no	—
45	C₂×#41×C₆₇	—	2	1	no	—
46	C₂×#41×C₆₇	—	2	1	no	—
47	C₂×#41×C₆₇	—	2	1	no	—
48	C₂×#41×C₆₇	—	2	1	no	—
49	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
50	C₂×#41×C₆₇	D₄	1	2	yes	—
51	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₆₇	—	2	1	no	—
53	C₂²×D₄×C₆₇	—	2	4	no	—
54	C₂²×D₄×C₆₇	—	2	1	no	—
55	C₂²×D₄×C₆₇	—	2	1	no	—
56	C₂²×D₄×C₆₇	—	2	1	no	—
57	C₂²×D₄×C₆₇	—	2	1	no	—
58	C₂²×D₄×C₆₇	—	2	1	no	—
59	C₂²×D₄×C₆₇	—	2	1	no	—
60	C₂²×D₄×C₆₇	—	2	1	no	—
61	C₂²×D₄×C₆₇	—	2	1	no	—
62	C₂²×D₄×C₆₇	—	2	1	no	—
63	C₂²×D₄×C₆₇	—	2	1	no	—
64	C₂²×D₄×C₆₇	—	2	1	no	—
65	C₂²×D₄×C₆₇	—	2	1	no	—
66	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
67	C₂²×D₄×C₆₇	D₄	1	2	yes	—
68	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	—	2	1	no	—
70	C₂³×C₄×C₆₇	—	2	1	no	—
71	C₂³×C₄×C₆₇	—	2	1	no	—
72	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₆₇	—	2	1	no	—
74	C₂×M₁₆×C₆₇	—	2	1	no	—
75	C₂×M₁₆×C₆₇	—	2	1	no	—
76	C₂×M₁₆×C₆₇	—	2	1	no	—
77	C₂×M₁₆×C₆₇	—	2	1	no	—
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂×M₁₆×C₆₇	—	2	1	no	—
80	C₂×M₁₆×C₆₇	—	2	1	no	—
81	C₂×M₁₆×C₆₇	—	2	1	no	—
82	C₂×M₁₆×C₆₇	—	2	1	no	—
83	C₂×M₁₆×C₆₇	D₄	1	2	yes	complemented
84	C₂×M₁₆×C₆₇	D₄	1	2	yes	complemented
85	C₂²×C₈×C₆₇	—	2	1	no	—
86	C₂²×C₈×C₆₇	—	2	1	no	—
87	#127×C₆₇	—	2	4	no	—
88	#127×C₆₇	—	2	4	no	—
89	#124×C₆₇	—	2	4	no	—
90	#124×C₆₇	—	2	4	no	—
91	#121×C₆₇	—	2	8	no	—
92	#121×C₆₇	—	2	8	no	—
93	#120×C₆₇	—	2	8	no	—
94	#120×C₆₇	—	2	8	no	—
95	#117×C₆₇	—	2	1	no	—
96	#117×C₆₇	—	2	1	no	—
97	#117×C₆₇	C₂×C₄	1	2	yes	—
98	#117×C₆₇	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
101	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
102	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
103	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
104	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
105	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
109	C₂×C₂²⋊C₄×C₆₇	—	4	8	no	—
110	C₂×C₄²×C₆₇	—	2	1	no	—
111	C₂×C₄²×C₆₇	—	2	1	no	—
112	C₂×C₄²×C₆₇	—	2	1	no	—
113	C₂×C₄²×C₆₇	—	2	1	no	—
114	C₂×C₄²×C₆₇	—	2	1	no	—
115	C₂×C₄²×C₆₇	—	2	1	no	—
116	C₂×C₄²×C₆₇	D₄	1	2	yes	complemented
117	#104×C₆₇	—	2	8	no	—
118	#103×C₆₇	—	2	4	no	—
119	#102×C₆₇	—	2	4	no	—
120	#100×C₆₇	—	2	8	no	—
121	C₂⁴×C₆₇	—	2	2	no	—
122	C₂⁴×C₆₇	—	2	2	no	—
123	C₂⁴×C₆₇	—	2	1	no	—
124	C₂⁴×C₆₇	—	2	2	no	—
125	C₂⁴×C₆₇	—	2	2	no	—
126	C₂⁴×C₆₇	—	2	2	no	—
127	C₂⁴×C₆₇	—	2	2	no	—
128	C₂⁴×C₆₇	—	4	4	no	—
129	C₂⁴×C₆₇	—	4	4	no	—
130	C₂⁴×C₆₇	C₂²⋊C₄	1	4	yes	—
131	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
132	#41×C₆₇	—	2	2	no	—
133	#41×C₆₇	—	2	2	no	—
134	#41×C₆₇	—	2	2	no	—
135	#41×C₆₇	—	2	2	no	—
136	#41×C₆₇	—	2	2	no	—
137	#41×C₆₇	—	2	2	no	—
138	#41×C₆₇	—	2	2	no	—
139	#41×C₆₇	—	2	2	no	—
140	#41×C₆₇	—	4	1	no	—
141	#41×C₆₇	—	4	1	no	—
142	#41×C₆₇	—	4	1	no	—
143	#41×C₆₇	—	4	1	no	—
144	#41×C₆₇	—	4	1	no	—
145	#41×C₆₇	—	4	1	no	—
146	#41×C₆₇	—	4	1	no	—
147	#41×C₆₇	—	4	1	no	—
148	C₂×Q₈×C₆₇	—	2	1	no	—
149	C₂×Q₈×C₆₇	—	2	1	no	—
150	C₂×Q₈×C₆₇	—	2	1	no	—
151	C₂×Q₈×C₆₇	—	2	1	no	—
152	C₂×Q₈×C₆₇	—	2	1	no	—
153	C₂×Q₈×C₆₇	C₂²⋊C₄	1	2	yes	complemented
154	C₂×D₄×C₆₇	—	2	2	no	—
155	C₂×D₄×C₆₇	—	2	2	no	—
156	C₂×D₄×C₆₇	—	2	16	no	—
157	C₂×D₄×C₆₇	—	2	2	no	—
158	C₂×D₄×C₆₇	—	2	2	no	—
159	C₂×D₄×C₆₇	—	2	2	no	—
160	C₂×D₄×C₆₇	—	2	2	no	—
161	C₂×D₄×C₆₇	—	2	2	no	—
162	C₂×D₄×C₆₇	—	2	2	no	—
163	C₂×D₄×C₆₇	—	2	1	no	—
164	C₂×D₄×C₆₇	—	2	2	no	—
165	C₂×D₄×C₆₇	—	2	2	no	—
166	C₂×D₄×C₆₇	—	2	2	no	—
167	C₂×D₄×C₆₇	—	2	1	no	—
168	C₂×D₄×C₆₇	—	2	1	no	—
169	C₂×D₄×C₆₇	—	2	1	no	—
170	C₂×D₄×C₆₇	—	2	2	no	—
171	C₂×D₄×C₆₇	—	2	2	no	—
172	C₂×D₄×C₆₇	—	2	1	no	—
173	C₂×D₄×C₆₇	—	2	2	no	—
174	C₂×D₄×C₆₇	—	4	1	no	—
175	C₂×D₄×C₆₇	—	4	1	no	—
176	C₂×D₄×C₆₇	—	4	1	no	—
177	C₂×D₄×C₆₇	—	4	1	no	—
178	C₂×D₄×C₆₇	—	4	1	no	—
179	C₂×D₄×C₆₇	—	4	1	no	—
180	C₂×D₄×C₆₇	—	4	1	no	—
181	C₂×D₄×C₆₇	—	4	1	no	—
182	C₂×D₄×C₆₇	—	4	1	no	—
183	C₂×D₄×C₆₇	—	4	1	no	—
184	C₂×D₄×C₆₇	—	4	1	no	—
185	C₂×D₄×C₆₇	—	4	1	no	—
186	C₂×D₄×C₆₇	—	4	1	no	—
187	C₂×D₄×C₆₇	—	4	1	no	—
188	C₂×D₄×C₆₇	—	4	1	no	—
189	C₂×D₄×C₆₇	—	4	1	no	—
190	C₂×D₄×C₆₇	—	4	1	no	—
191	C₂×D₄×C₆₇	—	4	1	no	—
192	C₂×D₄×C₆₇	—	4	1	no	—
193	C₂×D₄×C₆₇	—	4	1	no	—
194	C₂×D₄×C₆₇	—	8	4	no	—
195	C₂×D₄×C₆₇	—	8	4	no	—
196	C₂×D₄×C₆₇	C₂²⋊C₄	1	2	yes	complemented
197	C₂²×C₄×C₆₇	—	2	4	no	—
198	C₂²×C₄×C₆₇	—	2	2	no	—
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	—	4	2	no	—
205	C₂²×C₄×C₆₇	—	4	1	no	—
206	C₂²×C₄×C₆₇	—	4	1	no	—
207	C₂²×C₄×C₆₇	—	4	1	no	—
208	C₂²×C₄×C₆₇	—	4	1	no	—
209	C₂²×C₄×C₆₇	—	4	1	no	—
210	C₂²×C₄×C₆₇	—	4	1	no	—
211	C₂²×C₄×C₆₇	—	4	4	no	—
212	C₂²×C₄×C₆₇	—	4	1	no	—
213	C₂²×C₄×C₆₇	—	4	1	no	—
214	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
225	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
226	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
227	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
228	M₁₆×C₆₇	—	2	2	no	—
229	M₁₆×C₆₇	—	2	2	no	—
230	M₁₆×C₆₇	—	2	2	no	—
231	M₁₆×C₆₇	—	2	2	no	—
232	M₁₆×C₆₇	—	4	1	no	—
233	M₁₆×C₆₇	—	4	1	no	—
234	M₁₆×C₆₇	—	4	1	no	—
235	M₁₆×C₆₇	—	4	1	no	—
236	C₂×C₈×C₆₇	—	2	2	no	—
237	C₂×C₈×C₆₇	—	2	2	no	—
238	C₂×C₈×C₆₇	—	4	1	no	—
239	C₂×C₈×C₆₇	—	4	1	no	—
240	C₂×C₈×C₆₇	—	4	1	no	—
241	C₂×C₈×C₆₇	—	4	1	no	—
242	C₄⋊C₄×C₆₇	—	2	2	no	—
243	C₄⋊C₄×C₆₇	—	2	2	no	—
244	C₄⋊C₄×C₆₇	—	2	2	no	—
245	C₄⋊C₄×C₆₇	—	4	1	no	—
246	C₄⋊C₄×C₆₇	—	4	1	no	—
247	C₄⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	complemented
248	C₂²⋊C₄×C₆₇	—	2	16	no	—
249	C₂²⋊C₄×C₆₇	—	2	2	no	—
250	C₂²⋊C₄×C₆₇	—	2	2	no	—
251	C₂²⋊C₄×C₆₇	—	4	16	no	—
252	C₄²×C₆₇	—	2	2	no	—
253	C₄²×C₆₇	—	2	2	no	—
254	C₄²×C₆₇	—	2	2	no	—
255	C₄²×C₆₇	—	2	2	no	—
256	C₄²×C₆₇	—	4	1	no	—
257	C₄²×C₆₇	—	4	1	no	—
258	C₂³×C₆₇	—	2	2	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	2	4	no	—
261	C₂³×C₆₇	—	2	2	no	—
262	C₂³×C₆₇	—	2	4	no	—
263	C₂³×C₆₇	—	2	4	no	—
264	C₂³×C₆₇	—	4	8	no	—
265	C₂³×C₆₇	—	4	4	no	—
266	C₂³×C₆₇	—	4	4	no	—
267	C₂³×C₆₇	—	4	8	no	—
268	C₂³×C₆₇	—	4	1	no	—
269	C₂³×C₆₇	—	4	2	no	—
270	C₂³×C₆₇	—	4	2	no	—
271	C₂³×C₆₇	—	4	1	no	—
272	C₂³×C₆₇	—	4	2	no	—
273	C₂³×C₆₇	—	4	2	no	—
274	C₂³×C₆₇	—	4	2	no	—
275	C₂³×C₆₇	—	4	4	no	—
276	C₂³×C₆₇	—	4	2	no	—
277	C₂³×C₆₇	—	4	4	no	—
278	C₂³×C₆₇	—	8	4	no	—
279	C₂³×C₆₇	—	8	2	no	—
280	C₂³×C₆₇	—	8	2	no	—
281	C₂³×C₆₇	—	8	4	no	—
282	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂³×C₆₇	#120	1	1	yes	characteristic
284	C₂³×C₆₇	#120	1	1	yes	characteristic
285	C₂³×C₆₇	#120	1	1	yes	characteristic
286	C₂³×C₆₇	#121	1	1	yes	characteristic
287	C₂³×C₆₇	#121	1	1	yes	characteristic
288	C₂³×C₆₇	#123	1	1	yes	characteristic
289	Q₈×C₆₇	—	2	2	no	—
290	Q₈×C₆₇	—	2	2	no	—
291	Q₈×C₆₇	—	4	1	no	—
292	Q₈×C₆₇	—	4	1	no	—
293	D₄×C₆₇	—	2	2	no	—
294	D₄×C₆₇	—	2	2	no	—
295	D₄×C₆₇	—	4	2	no	—
296	D₄×C₆₇	—	4	2	no	—
297	D₄×C₆₇	—	4	2	no	—
298	D₄×C₆₇	—	4	2	no	—
299	D₄×C₆₇	—	4	2	no	—
300	D₄×C₆₇	—	4	2	no	—
301	D₄×C₆₇	—	4	2	no	—
302	D₄×C₆₇	—	4	2	no	—
303	D₄×C₆₇	—	4	2	no	—
304	D₄×C₆₇	—	4	2	no	—
305	D₄×C₆₇	—	4	1	no	—
306	D₄×C₆₇	—	4	2	no	—
307	D₄×C₆₇	—	4	2	no	—
308	D₄×C₆₇	—	4	1	no	—
309	D₄×C₆₇	—	8	16	no	—
310	C₂×C₄×C₆₇	—	2	4	no	—
311	C₂×C₄×C₆₇	—	2	4	no	—
312	C₂×C₄×C₆₇	—	2	2	no	—
313	C₂×C₄×C₆₇	—	4	4	no	—
314	C₂×C₄×C₆₇	—	4	2	no	—
315	C₂×C₄×C₆₇	—	4	4	no	—
316	C₂×C₄×C₆₇	—	4	2	no	—
317	C₂×C₄×C₆₇	—	4	1	no	—
318	C₂×C₄×C₆₇	—	4	1	no	—
319	C₂×C₄×C₆₇	—	4	2	no	—
320	C₂×C₄×C₆₇	—	4	2	no	—
321	C₂×C₄×C₆₇	—	4	2	no	—
322	C₂×C₄×C₆₇	—	4	2	no	—
323	C₂×C₄×C₆₇	—	4	2	no	—
324	C₂×C₄×C₆₇	—	4	2	no	—
325	C₂×C₄×C₆₇	—	4	4	no	—
326	C₂×C₄×C₆₇	—	4	2	no	—
327	C₂×C₄×C₆₇	—	8	2	no	—
328	C₂×C₄×C₆₇	—	8	2	no	—
329	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
330	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
333	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
334	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
336	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
337	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
338	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
339	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
340	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
341	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
342	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
343	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
344	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
345	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
346	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
347	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
348	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
349	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
350	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
351	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
352	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
353	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
354	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
355	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
356	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
357	C₈×C₆₇	—	4	2	no	—
358	C₈×C₆₇	—	4	2	no	—
359	C₂²×C₆₇	—	2	2	no	—
360	C₂²×C₆₇	—	2	2	no	—
361	C₂²×C₆₇	—	2	1	no	—
362	C₂²×C₆₇	—	2	1	no	—
363	C₂²×C₆₇	—	2	1	no	—
364	C₂²×C₆₇	—	2	1	no	—
365	C₂²×C₆₇	—	2	2	no	—
366	C₂²×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	4	8	no	—
368	C₂²×C₆₇	—	4	4	no	—
369	C₂²×C₆₇	—	4	8	no	—
370	C₂²×C₆₇	—	4	2	no	—
371	C₂²×C₆₇	—	4	4	no	—
372	C₂²×C₆₇	—	8	4	no	—
373	C₂²×C₆₇	—	8	4	no	—
374	C₂²×C₆₇	—	8	4	no	—
375	C₂²×C₆₇	—	8	1	no	—
376	C₂²×C₆₇	—	8	2	no	—
377	C₂²×C₆₇	—	8	1	no	—
378	C₂²×C₆₇	—	8	2	no	—
379	C₂²×C₆₇	—	8	2	no	—
380	C₂²×C₆₇	—	8	4	no	—
381	C₂²×C₆₇	#379	1	1	yes	characteristic
382	C₂²×C₆₇	#386	1	1	yes	characteristic
383	C₂²×C₆₇	#386	1	1	yes	characteristic
384	C₂²×C₆₇	#392	1	1	yes	characteristic
385	C₂²×C₆₇	#392	1	1	yes	characteristic
386	C₂²×C₆₇	#394	1	1	yes	characteristic
387	C₂²×C₆₇	#394	1	1	yes	characteristic
388	C₂²×C₆₇	#453	1	2	yes	—
389	C₂²×C₆₇	#455	1	2	yes	—
390	C₄×C₆₇	—	4	4	no	—
391	C₄×C₆₇	—	4	4	no	—
392	C₄×C₆₇	—	4	2	no	—
393	C₄×C₆₇	—	8	2	no	—
394	C₄×C₆₇	#386	1	1	yes	characteristic
395	C₄×C₆₇	#386	1	1	yes	characteristic
396	C₄×C₆₇	#390	1	1	yes	characteristic
397	C₄×C₆₇	#390	1	1	yes	characteristic
398	C₄×C₆₇	#392	1	1	yes	characteristic
399	C₄×C₆₇	#392	1	1	yes	characteristic
400	C₄×C₆₇	#394	1	1	yes	characteristic
401	C₄×C₆₇	#394	1	1	yes	characteristic
402	#10997	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂×C₆₇	—	2	1	no	—
404	C₂×C₆₇	—	2	1	no	—
405	C₂×C₆₇	—	2	1	no	—
406	C₂×C₆₇	—	2	1	no	—
407	C₂×C₆₇	—	8	4	no	—
408	C₂×C₆₇	—	8	2	no	—
409	C₂×C₆₇	#1438	1	1	yes	characteristic
410	C₂×C₆₇	#1792	1	2	yes	—
411	C₂×C₆₇	#2002	1	1	yes	characteristic
412	C₂×C₆₇	#2004	1	1	yes	characteristic
413	C₂×C₆₇	#2037	1	2	yes	—
414	C₂×#535	C₂×C₆₇	1	1	yes	characteristic
415	C₂²×#104	C₂×C₆₇	1	1	yes	characteristic, complemented
416	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
417	C₂²×#100	C₂×C₆₇	1	1	yes	characteristic, complemented
418	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
419	#1736	C₂×C₆₇	1	1	yes	characteristic, complemented
420	C₂×#339	C₂×C₆₇	1	1	yes	characteristic, complemented
421	C₆₇	#10997	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
423	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
424	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
425	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
426	#535	—	2	2	no	—
427	#535	—	2	2	no	—
428	#535	—	2	2	no	—
429	#535	C₄×C₆₇	1	4	yes	complemented
430	C₂×#127	—	2	1	no	—
431	C₂×#124	—	2	1	no	—
432	C₂×#121	—	2	2	no	—
433	C₂×#120	—	2	2	no	—
434	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₂²×C₂²⋊C₄	—	2	2	no	—
437	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×#104	—	2	2	no	—
439	C₂×#104	—	2	2	no	—
440	C₂×#104	—	2	2	no	—
441	#417	—	2	2	no	—
442	#417	—	2	2	no	—
443	C₂×#103	—	2	1	no	—
444	C₂×#102	—	2	1	no	—
445	C₂×#100	—	2	2	no	—
446	C₂×#100	—	2	2	no	—
447	C₂×#100	—	2	2	no	—
448	#390	—	2	2	no	—
449	#390	—	2	2	no	—
450	#340	—	2	2	no	—
451	#339	—	2	2	no	—
452	C₂⁵	D₄×C₆₇	1	2	yes	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
464	C₂×#41	D₄×C₆₇	1	2	yes	—
465	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	4	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
481	C₂²×D₄	D₄×C₆₇	1	2	yes	—
482	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
487	C₂×M₁₆	—	2	1	no	—
488	C₂×M₁₆	—	2	1	no	—
489	C₂×M₁₆	—	2	1	no	—
490	C₂×M₁₆	—	2	1	no	—
491	C₂×M₁₆	—	2	1	no	—
492	C₂×M₁₆	—	2	1	no	—
493	C₂×M₁₆	—	2	1	no	—
494	C₂×M₁₆	—	2	1	no	—
495	C₂×M₁₆	—	2	1	no	—
496	C₂×M₁₆	—	2	1	no	—
497	C₂×M₁₆	D₄×C₆₇	1	2	yes	complemented
498	C₂×M₁₆	D₄×C₆₇	1	2	yes	complemented
499	C₂²×C₈	—	2	1	no	—
500	C₂²×C₈	—	2	1	no	—
501	#127	—	2	4	no	—
502	#127	—	2	4	no	—
503	#124	—	2	4	no	—
504	#124	—	2	4	no	—
505	#121	—	2	8	no	—
506	#121	—	2	8	no	—
507	#120	—	2	8	no	—
508	#120	—	2	8	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	C₂×C₄×C₆₇	1	2	yes	—
512	#117	D₄×C₆₇	1	2	yes	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
519	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	complemented
520	C₂×C₂²⋊C₄	—	2	4	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	8	no	—
523	C₂×C₂²⋊C₄	—	4	8	no	—
524	C₂×C₄²	—	2	1	no	—
525	C₂×C₄²	—	2	1	no	—
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	D₄×C₆₇	1	2	yes	complemented
531	#104	—	2	8	no	—
532	#103	—	2	4	no	—
533	#102	—	2	4	no	—
534	#100	—	2	8	no	—
535	C₂⁴	—	2	2	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	1	no	—
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	2	no	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	—	4	4	no	—
543	C₂⁴	—	4	4	no	—
544	C₂⁴	C₂²⋊C₄×C₆₇	1	4	yes	—
545	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
546	#41	—	2	2	no	—
547	#41	—	2	2	no	—
548	#41	—	2	2	no	—
549	#41	—	2	2	no	—
550	#41	—	2	2	no	—
551	#41	—	2	2	no	—
552	#41	—	2	2	no	—
553	#41	—	2	2	no	—
554	#41	—	4	1	no	—
555	#41	—	4	1	no	—
556	#41	—	4	1	no	—
557	#41	—	4	1	no	—
558	#41	—	4	1	no	—
559	#41	—	4	1	no	—
560	#41	—	4	1	no	—
561	#41	—	4	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	C₂²⋊C₄×C₆₇	1	2	yes	complemented
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	16	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	—	4	1	no	—
595	C₂×D₄	—	4	1	no	—
596	C₂×D₄	—	4	1	no	—
597	C₂×D₄	—	4	1	no	—
598	C₂×D₄	—	4	1	no	—
599	C₂×D₄	—	4	1	no	—
600	C₂×D₄	—	4	1	no	—
601	C₂×D₄	—	4	1	no	—
602	C₂×D₄	—	4	1	no	—
603	C₂×D₄	—	4	1	no	—
604	C₂×D₄	—	4	1	no	—
605	C₂×D₄	—	4	1	no	—
606	C₂×D₄	—	4	1	no	—
607	C₂×D₄	—	4	1	no	—
608	C₂×D₄	—	8	4	no	—
609	C₂×D₄	—	8	4	no	—
610	C₂×D₄	C₂²⋊C₄×C₆₇	1	2	yes	complemented
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	—	4	1	no	—
623	C₂²×C₄	—	4	1	no	—
624	C₂²×C₄	—	4	1	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	—	4	1	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
629	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
638	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
639	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
640	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
641	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
642	M₁₆	—	2	2	no	—
643	M₁₆	—	2	2	no	—
644	M₁₆	—	2	2	no	—
645	M₁₆	—	2	2	no	—
646	M₁₆	—	4	1	no	—
647	M₁₆	—	4	1	no	—
648	M₁₆	—	4	1	no	—
649	M₁₆	—	4	1	no	—
650	C₂×C₈	—	2	2	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	—	4	1	no	—
653	C₂×C₈	—	4	1	no	—
654	C₂×C₈	—	4	1	no	—
655	C₂×C₈	—	4	1	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	4	1	no	—
660	C₄⋊C₄	—	4	1	no	—
661	C₄⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	complemented
662	C₂²⋊C₄	—	2	16	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	4	16	no	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	2	no	—
669	C₄²	—	2	2	no	—
670	C₄²	—	4	1	no	—
671	C₄²	—	4	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	4	8	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	8	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	—	8	4	no	—
693	C₂³	—	8	2	no	—
694	C₂³	—	8	2	no	—
695	C₂³	—	8	4	no	—
696	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
697	C₂³	#120×C₆₇	1	1	yes	characteristic
698	C₂³	#120×C₆₇	1	1	yes	characteristic
699	C₂³	#120×C₆₇	1	1	yes	characteristic
700	C₂³	#121×C₆₇	1	1	yes	characteristic
701	C₂³	#121×C₆₇	1	1	yes	characteristic
702	C₂³	#123×C₆₇	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	4	1	no	—
706	Q₈	—	4	1	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	2	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	2	no	—
711	D₄	—	4	2	no	—
712	D₄	—	4	2	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	1	no	—
723	D₄	—	8	16	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	4	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	8	2	no	—
742	C₂×C₄	—	8	2	no	—
743	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
744	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
745	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
746	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
747	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
748	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
749	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
750	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
751	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
752	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
753	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
754	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
755	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
756	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
757	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
758	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
759	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
760	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
761	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
762	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
763	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
764	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
765	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
766	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
767	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
768	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
769	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
770	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
771	C₈	—	4	2	no	—
772	C₈	—	4	2	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	4	8	no	—
782	C₂²	—	4	4	no	—
783	C₂²	—	4	8	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	8	4	no	—
788	C₂²	—	8	4	no	—
789	C₂²	—	8	2	no	—
790	C₂²	—	8	1	no	—
791	C₂²	—	8	2	no	—
792	C₂²	—	8	1	no	—
793	C₂²	—	8	4	no	—
794	C₂²	—	8	2	no	—
795	C₂²	#379×C₆₇	1	1	yes	characteristic
796	C₂²	#386×C₆₇	1	1	yes	characteristic
797	C₂²	#386×C₆₇	1	1	yes	characteristic
798	C₂²	#392×C₆₇	1	1	yes	characteristic
799	C₂²	#392×C₆₇	1	1	yes	characteristic
800	C₂²	#394×C₆₇	1	1	yes	characteristic
801	C₂²	#394×C₆₇	1	1	yes	characteristic
802	C₂²	#453×C₆₇	1	2	yes	—
803	C₂²	#455×C₆₇	1	2	yes	—
804	C₄	—	4	4	no	—
805	C₄	—	4	4	no	—
806	C₄	—	4	2	no	—
807	C₄	—	8	2	no	—
808	C₄	#386×C₆₇	1	1	yes	characteristic
809	C₄	#386×C₆₇	1	1	yes	characteristic
810	C₄	#390×C₆₇	1	1	yes	characteristic
811	C₄	#390×C₆₇	1	1	yes	characteristic
812	C₄	#392×C₆₇	1	1	yes	characteristic
813	C₄	#392×C₆₇	1	1	yes	characteristic
814	C₄	#394×C₆₇	1	1	yes	characteristic
815	C₄	#394×C₆₇	1	1	yes	characteristic
816	C₂	—	2	1	no	—
817	C₂	—	2	1	no	—
818	C₂	—	2	1	no	—
819	C₂	—	2	1	no	—
820	C₂	—	8	4	no	—
821	C₂	—	8	2	no	—
822	C₂	C₆₇×#1438	1	1	yes	characteristic
823	C₂	C₆₇×#1792	1	2	yes	—
824	C₂	C₆₇×#2002	1	1	yes	characteristic
825	C₂	C₆₇×#2004	1	1	yes	characteristic
826	C₂	C₆₇×#2037	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	#120
commutator	C₂²×C₄	C₂²×C₄×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
prime radical	C₂×#535×C₆₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#104×C₆₇	C₂	semidirect
3. C₂×#417×C₆₇	C₂	semidirect
4. C₂²×#100×C₆₇	C₂	semidirect
5. C₂×#390×C₆₇	C₂	semidirect
6. C₆₇×#1736	C₂	semidirect
7. C₂×#339×C₆₇	C₂	semidirect
15. #535×C₆₇	C₄	semidirect
83. C₂×M₁₆×C₆₇	D₄	semidirect
84. C₂×M₁₆×C₆₇	D₄	semidirect
105. C₂×C₄⋊C₄×C₆₇	D₄	semidirect
116. C₂×C₄²×C₆₇	D₄	semidirect
153. C₂×Q₈×C₆₇	C₂²⋊C₄	semidirect
196. C₂×D₄×C₆₇	C₂²⋊C₄	semidirect
247. C₄⋊C₄×C₆₇	C₂²⋊C₄	semidirect
402. #10997	C₆₇	direct (N × H)
415. C₂²×#104	C₂×C₆₇	semidirect
416. C₂×#417	C₂×C₆₇	semidirect
417. C₂²×#100	C₂×C₆₇	semidirect
418. C₂×#390	C₂×C₆₇	semidirect
419. #1736	C₂×C₆₇	semidirect
420. C₂×#339	C₂×C₆₇	semidirect
421. C₆₇	#10997	direct (N × H)
429. #535	C₄×C₆₇	semidirect
497. C₂×M₁₆	D₄×C₆₇	semidirect
498. C₂×M₁₆	D₄×C₆₇	semidirect
519. C₂×C₄⋊C₄	D₄×C₆₇	semidirect
530. C₂×C₄²	D₄×C₆₇	semidirect
567. C₂×Q₈	C₂²⋊C₄×C₆₇	semidirect
610. C₂×D₄	C₂²⋊C₄×C₆₇	semidirect
661. C₄⋊C₄	C₂²⋊C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₆₇	2
C₂²×#104×C₆₇	2
C₂×#417×C₆₇	2
C₂²×#100×C₆₇	2
C₂×#390×C₆₇	2
C₆₇×#1736	2
C₂×#339×C₆₇	2
#10997	67

Subgroups — C67×#10997 #30690248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#10997 #30690248