Subgroups — C₂×C₆₇×#1911 #30700261

Order 17152.

1974 conjugacy classes of subgroups.

The subgroup lattice has 590 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	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂²×#100×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1911	C₂	1	8	yes	maximal, direct product factor
6	C₂×H(3,ℤ/4)×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
10	#535×C₆₇	—	2	2	no	—
11	#535×C₆₇	—	2	2	no	—
12	#535×C₆₇	C₄	1	4	yes	complemented
13	#535×C₆₇	C₂²	1	4	yes	—
14	C₂×#127×C₆₇	C₄	1	2	yes	complemented
15	C₂×#124×C₆₇	C₄	1	2	yes	complemented
16	C₂×#121×C₆₇	—	2	2	no	—
17	C₂×#120×C₆₇	—	2	2	no	—
18	#518×C₆₇	—	2	2	no	—
19	#518×C₆₇	—	2	4	no	—
20	#518×C₆₇	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₆₇	—	2	4	no	—
22	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₆₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₆₇	—	2	2	no	—
25	#421×C₆₇	—	2	4	no	—
26	#421×C₆₇	C₂²	1	8	yes	complemented
27	C₂×#104×C₆₇	—	2	4	no	—
28	C₂×#100×C₆₇	—	2	2	no	—
29	C₂×#100×C₆₇	—	2	2	no	—
30	C₂×#100×C₆₇	C₂²	1	4	yes	complemented
31	H(3,ℤ/4)×C₆₇	C₂²	1	8	yes	complemented
32	C₂⁵×C₆₇	D₄	1	2	yes	—
33	C₂×#41×C₆₇	—	2	1	no	—
34	C₂×#41×C₆₇	—	2	1	no	—
35	C₂×#41×C₆₇	—	2	2	no	—
36	C₂×#41×C₆₇	—	2	2	no	—
37	C₂×#41×C₆₇	—	2	2	no	—
38	C₂×#41×C₆₇	—	2	2	no	—
39	C₂×#41×C₆₇	C₂×C₄	1	2	yes	complemented
40	C₂×#41×C₆₇	C₂³	1	2	yes	—
41	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
42	C₂²×D₄×C₆₇	—	2	1	no	—
43	C₂²×D₄×C₆₇	—	2	4	no	—
44	C₂²×D₄×C₆₇	—	2	2	no	—
45	C₂²×D₄×C₆₇	—	2	2	no	—
46	C₂²×D₄×C₆₇	—	2	2	no	—
47	C₂²×D₄×C₆₇	—	2	2	no	—
48	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
49	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂²×D₄×C₆₇	D₄	1	2	yes	—
52	C₂²×D₄×C₆₇	D₄	1	2	yes	—
53	C₂²×D₄×C₆₇	D₄	1	2	yes	—
54	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₇	—	2	4	no	—
56	C₂³×C₄×C₆₇	—	2	1	no	—
57	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₆₇	—	2	2	no	—
59	C₂×M₁₆×C₆₇	—	2	2	no	—
60	C₂×M₁₆×C₆₇	—	2	2	no	—
61	C₂×M₁₆×C₆₇	—	2	2	no	—
62	C₂×M₁₆×C₆₇	—	2	2	no	—
63	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
64	C₂²×C₈×C₆₇	—	2	2	no	—
65	#127×C₆₇	—	2	4	no	—
66	#127×C₆₇	C₂×C₄	1	8	yes	complemented
67	#124×C₆₇	—	2	4	no	—
68	#124×C₆₇	C₂×C₄	1	8	yes	complemented
69	#121×C₆₇	—	2	8	no	—
70	#121×C₆₇	—	2	8	no	—
71	#120×C₆₇	—	2	8	no	—
72	#120×C₆₇	—	2	8	no	—
73	C₄×D₄×C₆₇	—	2	16	no	—
74	C₄×D₄×C₆₇	—	2	16	no	—
75	#117×C₆₇	—	2	2	no	—
76	#117×C₆₇	—	2	2	no	—
77	#117×C₆₇	—	2	1	no	—
78	#117×C₆₇	—	2	1	no	—
79	#117×C₆₇	C₂×C₄	1	2	yes	complemented
80	#117×C₆₇	D₄	1	4	yes	complemented
81	#117×C₆₇	C₂³	1	2	yes	—
82	#117×C₆₇	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
90	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
91	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	complemented
92	C₂×C₄²×C₆₇	D₄	1	4	yes	complemented
93	#104×C₆₇	—	2	16	no	—
94	#100×C₆₇	—	2	8	no	—
95	C₂⁴×C₆₇	—	2	2	no	—
96	C₂⁴×C₆₇	—	2	2	no	—
97	C₂⁴×C₆₇	—	2	2	no	—
98	C₂⁴×C₆₇	—	2	2	no	—
99	C₂⁴×C₆₇	—	2	1	no	—
100	C₂⁴×C₆₇	—	8	4	no	—
101	C₂⁴×C₆₇	C₂²⋊C₄	1	4	yes	—
102	C₂⁴×C₆₇	C₂²⋊C₄	1	4	yes	—
103	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
104	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
105	#41×C₆₇	—	2	4	no	—
106	#41×C₆₇	—	2	4	no	—
107	#41×C₆₇	—	2	4	no	—
108	#41×C₆₇	—	2	4	no	—
109	#41×C₆₇	—	4	2	no	—
110	#41×C₆₇	—	4	2	no	—
111	#41×C₆₇	—	4	2	no	—
112	#41×C₆₇	—	4	2	no	—
113	C₂×Q₈×C₆₇	—	2	1	no	—
114	C₂×Q₈×C₆₇	—	2	2	no	—
115	C₂×Q₈×C₆₇	—	2	2	no	—
116	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	complemented
117	C₂×D₄×C₆₇	—	2	2	no	—
118	C₂×D₄×C₆₇	—	2	2	no	—
119	C₂×D₄×C₆₇	—	2	16	no	—
120	C₂×D₄×C₆₇	—	2	1	no	—
121	C₂×D₄×C₆₇	—	2	4	no	—
122	C₂×D₄×C₆₇	—	2	4	no	—
123	C₂×D₄×C₆₇	—	2	4	no	—
124	C₂×D₄×C₆₇	—	2	4	no	—
125	C₂×D₄×C₆₇	—	2	2	no	—
126	C₂×D₄×C₆₇	—	2	2	no	—
127	C₂×D₄×C₆₇	—	2	4	no	—
128	C₂×D₄×C₆₇	—	2	4	no	—
129	C₂×D₄×C₆₇	—	2	4	no	—
130	C₂×D₄×C₆₇	—	2	4	no	—
131	C₂×D₄×C₆₇	—	2	4	no	—
132	C₂×D₄×C₆₇	—	2	4	no	—
133	C₂×D₄×C₆₇	—	2	4	no	—
134	C₂×D₄×C₆₇	—	2	4	no	—
135	C₂×D₄×C₆₇	—	4	1	no	—
136	C₂×D₄×C₆₇	—	4	1	no	—
137	C₂×D₄×C₆₇	—	4	1	no	—
138	C₂×D₄×C₆₇	—	4	1	no	—
139	C₂×D₄×C₆₇	—	8	8	no	—
140	C₂×D₄×C₆₇	C₂²⋊C₄	1	4	yes	—
141	C₂×D₄×C₆₇	C₂²⋊C₄	1	4	yes	—
142	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
143	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	complemented
144	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₆₇	—	2	2	no	—
146	C₂²×C₄×C₆₇	—	2	1	no	—
147	C₂²×C₄×C₆₇	—	2	4	no	—
148	C₂²×C₄×C₆₇	—	2	16	no	—
149	C₂²×C₄×C₆₇	—	2	2	no	—
150	C₂²×C₄×C₆₇	—	2	2	no	—
151	C₂²×C₄×C₆₇	—	4	2	no	—
152	C₂²×C₄×C₆₇	—	4	2	no	—
153	C₂²×C₄×C₆₇	—	8	8	no	—
154	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₆₇	#41	1	2	yes	—
162	C₂²×C₄×C₆₇	#41	1	2	yes	—
163	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
164	M₁₆×C₆₇	—	2	4	no	—
165	M₁₆×C₆₇	—	2	4	no	—
166	M₁₆×C₆₇	—	4	2	no	—
167	M₁₆×C₆₇	—	4	2	no	—
168	C₂×C₈×C₆₇	—	2	4	no	—
169	C₂×C₈×C₆₇	—	4	2	no	—
170	C₂×C₈×C₆₇	—	4	2	no	—
171	C₄⋊C₄×C₆₇	—	2	2	no	—
172	C₄⋊C₄×C₆₇	—	2	4	no	—
173	C₄⋊C₄×C₆₇	—	2	4	no	—
174	C₄⋊C₄×C₆₇	—	2	2	no	—
175	C₂²⋊C₄×C₆₇	—	2	16	no	—
176	C₂²⋊C₄×C₆₇	—	2	2	no	—
177	C₂²⋊C₄×C₆₇	—	2	16	no	—
178	C₂²⋊C₄×C₆₇	—	2	4	no	—
179	C₂²⋊C₄×C₆₇	—	2	4	no	—
180	C₂²⋊C₄×C₆₇	—	2	2	no	—
181	C₄²×C₆₇	—	2	2	no	—
182	C₄²×C₆₇	—	2	4	no	—
183	C₄²×C₆₇	C₂²×C₄	1	4	yes	complemented
184	C₄²×C₆₇	C₂×D₄	1	8	yes	complemented
185	C₂³×C₆₇	—	2	4	no	—
186	C₂³×C₆₇	—	2	4	no	—
187	C₂³×C₆₇	—	2	4	no	—
188	C₂³×C₆₇	—	2	4	no	—
189	C₂³×C₆₇	—	2	4	no	—
190	C₂³×C₆₇	—	2	4	no	—
191	C₂³×C₆₇	—	2	2	no	—
192	C₂³×C₆₇	—	4	2	no	—
193	C₂³×C₆₇	—	4	8	no	—
194	C₂³×C₆₇	—	4	8	no	—
195	C₂³×C₆₇	—	4	4	no	—
196	C₂³×C₆₇	—	4	1	no	—
197	C₂³×C₆₇	—	4	1	no	—
198	C₂³×C₆₇	—	8	4	no	—
199	C₂³×C₆₇	—	8	4	no	—
200	C₂³×C₆₇	—	8	4	no	—
201	C₂³×C₆₇	—	8	4	no	—
202	C₂³×C₆₇	—	8	4	no	—
203	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂³×C₆₇	C₂×C₂²⋊C₄	1	8	yes	—
205	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₆₇	#120	1	1	yes	characteristic
207	C₂³×C₆₇	#120	1	1	yes	characteristic
208	C₂³×C₆₇	#123	1	1	yes	characteristic
209	C₂³×C₆₇	#123	1	1	yes	characteristic
210	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₆₇	—	2	4	no	—
212	Q₈×C₆₇	—	4	2	no	—
213	D₄×C₆₇	—	2	8	no	—
214	D₄×C₆₇	—	2	4	no	—
215	D₄×C₆₇	—	2	8	no	—
216	D₄×C₆₇	—	2	8	no	—
217	D₄×C₆₇	—	2	8	no	—
218	D₄×C₆₇	—	4	2	no	—
219	D₄×C₆₇	—	4	2	no	—
220	D₄×C₆₇	—	4	2	no	—
221	D₄×C₆₇	—	4	2	no	—
222	D₄×C₆₇	—	4	2	no	—
223	D₄×C₆₇	—	8	16	no	—
224	C₂×C₄×C₆₇	—	2	4	no	—
225	C₂×C₄×C₆₇	—	2	2	no	—
226	C₂×C₄×C₆₇	—	2	8	no	—
227	C₂×C₄×C₆₇	—	4	8	no	—
228	C₂×C₄×C₆₇	—	4	4	no	—
229	C₂×C₄×C₆₇	—	4	1	no	—
230	C₂×C₄×C₆₇	—	4	1	no	—
231	C₂×C₄×C₆₇	—	4	4	no	—
232	C₂×C₄×C₆₇	—	4	4	no	—
233	C₂×C₄×C₆₇	—	8	16	no	—
234	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
237	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
238	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
239	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
240	C₂×C₄×C₆₇	#120	1	2	yes	—
241	C₂×C₄×C₆₇	#121	1	2	yes	—
242	C₂×C₄×C₆₇	#121	1	2	yes	—
243	C₂×C₄×C₆₇	#121	1	2	yes	—
244	C₂×C₄×C₆₇	#121	1	2	yes	—
245	C₂×C₄×C₆₇	#123	1	2	yes	—
246	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
250	C₈×C₆₇	—	4	4	no	—
251	C₂²×C₆₇	—	2	2	no	—
252	C₂²×C₆₇	—	2	2	no	—
253	C₂²×C₆₇	—	2	2	no	—
254	C₂²×C₆₇	—	2	8	no	—
255	C₂²×C₆₇	—	4	1	no	—
256	C₂²×C₆₇	—	4	1	no	—
257	C₂²×C₆₇	—	4	1	no	—
258	C₂²×C₆₇	—	4	1	no	—
259	C₂²×C₆₇	—	4	8	no	—
260	C₂²×C₆₇	—	4	8	no	—
261	C₂²×C₆₇	—	4	8	no	—
262	C₂²×C₆₇	—	4	4	no	—
263	C₂²×C₆₇	—	4	8	no	—
264	C₂²×C₆₇	—	4	2	no	—
265	C₂²×C₆₇	—	8	4	no	—
266	C₂²×C₆₇	—	8	4	no	—
267	C₂²×C₆₇	—	8	4	no	—
268	C₂²×C₆₇	—	8	2	no	—
269	C₂²×C₆₇	—	8	2	no	—
270	C₂²×C₆₇	#386	1	1	yes	characteristic
271	C₂²×C₆₇	#386	1	1	yes	characteristic
272	C₂²×C₆₇	#386	1	1	yes	characteristic
273	C₂²×C₆₇	#386	1	1	yes	characteristic
274	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₆₇	C₂×#120	1	1	yes	characteristic
276	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
277	C₄×C₆₇	—	4	8	no	—
278	C₄×C₆₇	—	4	4	no	—
279	C₄×C₆₇	—	4	2	no	—
280	C₄×C₆₇	#386	1	2	yes	—
281	C₄×C₆₇	#386	1	2	yes	—
282	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
283	C₄×C₆₇	C₂×#121	1	2	yes	—
284	C₂×#1911	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂×C₆₇	—	2	1	no	—
286	C₂×C₆₇	—	2	1	no	—
287	C₂×C₆₇	—	2	1	no	—
288	C₂×C₆₇	—	2	1	no	—
289	C₂×C₆₇	—	2	1	no	—
290	C₂×C₆₇	—	2	1	no	—
291	C₂×C₆₇	—	4	8	no	—
292	C₂×C₆₇	—	8	2	no	—
293	C₂×C₆₇	#1911	1	2	yes	direct product factor
294	C₂×C₆₇	C₂×#386	1	1	yes	characteristic
295	C₂×#535	C₂×C₆₇	1	1	yes	characteristic
296	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
297	C₂×#421	C₂×C₆₇	1	2	yes	complemented
298	C₂²×#100	C₂×C₆₇	1	1	yes	characteristic, complemented
299	#1911	C₂×C₆₇	1	8	yes	direct product factor
300	C₂×H(3,ℤ/4)	C₂×C₆₇	1	2	yes	complemented
301	C₆₇	C₂×#1911	1	1	yes	characteristic, direct product factor, Sylow
302	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
303	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
304	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
305	#535	—	2	2	no	—
306	#535	—	2	2	no	—
307	#535	C₄×C₆₇	1	4	yes	complemented
308	#535	C₂²×C₆₇	1	4	yes	—
309	C₂×#127	C₄×C₆₇	1	2	yes	complemented
310	C₂×#124	C₄×C₆₇	1	2	yes	complemented
311	C₂×#121	—	2	2	no	—
312	C₂×#120	—	2	2	no	—
313	#518	—	2	2	no	—
314	#518	—	2	4	no	—
315	#518	C₂²×C₆₇	1	4	yes	complemented
316	C₂×C₄×D₄	—	2	4	no	—
317	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
318	C₂×#117	C₂²×C₆₇	1	2	yes	—
319	C₂²×C₂²⋊C₄	—	2	2	no	—
320	#421	—	2	4	no	—
321	#421	C₂²×C₆₇	1	8	yes	complemented
322	C₂×#104	—	2	4	no	—
323	C₂×#100	—	2	2	no	—
324	C₂×#100	—	2	2	no	—
325	C₂×#100	C₂²×C₆₇	1	4	yes	complemented
326	H(3,ℤ/4)	C₂²×C₆₇	1	8	yes	complemented
327	C₂⁵	D₄×C₆₇	1	2	yes	—
328	C₂×#41	—	2	1	no	—
329	C₂×#41	—	2	1	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	C₂×C₄×C₆₇	1	2	yes	complemented
335	C₂×#41	C₂³×C₆₇	1	2	yes	—
336	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	4	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
344	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
345	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
346	C₂²×D₄	D₄×C₆₇	1	2	yes	—
347	C₂²×D₄	D₄×C₆₇	1	2	yes	—
348	C₂²×D₄	D₄×C₆₇	1	2	yes	—
349	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
350	C₂³×C₄	—	2	4	no	—
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
353	C₂×M₁₆	—	2	2	no	—
354	C₂×M₁₆	—	2	2	no	—
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
359	C₂²×C₈	—	2	2	no	—
360	#127	—	2	4	no	—
361	#127	C₂×C₄×C₆₇	1	8	yes	complemented
362	#124	—	2	4	no	—
363	#124	C₂×C₄×C₆₇	1	8	yes	complemented
364	#121	—	2	8	no	—
365	#121	—	2	8	no	—
366	#120	—	2	8	no	—
367	#120	—	2	8	no	—
368	C₄×D₄	—	2	16	no	—
369	C₄×D₄	—	2	16	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	C₂×C₄×C₆₇	1	2	yes	complemented
375	#117	D₄×C₆₇	1	4	yes	complemented
376	#117	C₂³×C₆₇	1	2	yes	—
377	#117	C₂³×C₆₇	1	4	yes	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	—	2	4	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	8	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	complemented
387	C₂×C₄²	D₄×C₆₇	1	4	yes	complemented
388	#104	—	2	16	no	—
389	#100	—	2	8	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	1	no	—
395	C₂⁴	—	8	4	no	—
396	C₂⁴	C₂²⋊C₄×C₆₇	1	4	yes	—
397	C₂⁴	C₂²⋊C₄×C₆₇	1	4	yes	—
398	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
399	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
400	#41	—	2	4	no	—
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	#41	—	4	2	no	—
405	#41	—	4	2	no	—
406	#41	—	4	2	no	—
407	#41	—	4	2	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	complemented
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	16	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	8	8	no	—
435	C₂×D₄	C₂²⋊C₄×C₆₇	1	4	yes	—
436	C₂×D₄	C₂²⋊C₄×C₆₇	1	4	yes	—
437	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
438	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	complemented
439	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	16	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	8	8	no	—
449	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
455	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
456	C₂²×C₄	#41×C₆₇	1	2	yes	—
457	C₂²×C₄	#41×C₆₇	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
459	M₁₆	—	2	4	no	—
460	M₁₆	—	2	4	no	—
461	M₁₆	—	4	2	no	—
462	M₁₆	—	4	2	no	—
463	C₂×C₈	—	2	4	no	—
464	C₂×C₈	—	4	2	no	—
465	C₂×C₈	—	4	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	16	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	16	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	4	no	—
478	C₄²	C₂²×C₄×C₆₇	1	4	yes	complemented
479	C₄²	C₂×D₄×C₆₇	1	8	yes	complemented
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	8	4	no	—
494	C₂³	—	8	4	no	—
495	C₂³	—	8	4	no	—
496	C₂³	—	8	4	no	—
497	C₂³	—	8	4	no	—
498	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
499	C₂³	C₂×C₂²⋊C₄×C₆₇	1	8	yes	—
500	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
501	C₂³	#120×C₆₇	1	1	yes	characteristic
502	C₂³	#120×C₆₇	1	1	yes	characteristic
503	C₂³	#123×C₆₇	1	1	yes	characteristic
504	C₂³	#123×C₆₇	1	1	yes	characteristic
505	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
506	Q₈	—	2	4	no	—
507	Q₈	—	4	2	no	—
508	D₄	—	2	8	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	8	no	—
511	D₄	—	2	8	no	—
512	D₄	—	2	8	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	8	16	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	8	16	no	—
529	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
530	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
531	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
532	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
533	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
534	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
535	C₂×C₄	#120×C₆₇	1	2	yes	—
536	C₂×C₄	#121×C₆₇	1	2	yes	—
537	C₂×C₄	#121×C₆₇	1	2	yes	—
538	C₂×C₄	#121×C₆₇	1	2	yes	—
539	C₂×C₄	#121×C₆₇	1	2	yes	—
540	C₂×C₄	#123×C₆₇	1	2	yes	—
541	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
544	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
545	C₈	—	4	4	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	8	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	8	no	—
555	C₂²	—	4	8	no	—
556	C₂²	—	4	8	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	8	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	—	8	4	no	—
563	C₂²	—	8	2	no	—
564	C₂²	—	8	2	no	—
565	C₂²	#386×C₆₇	1	1	yes	characteristic
566	C₂²	#386×C₆₇	1	1	yes	characteristic
567	C₂²	#386×C₆₇	1	1	yes	characteristic
568	C₂²	#386×C₆₇	1	1	yes	characteristic
569	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
570	C₂²	C₂×#120×C₆₇	1	1	yes	characteristic
571	C₂²	C₂×#123×C₆₇	1	1	yes	characteristic
572	C₄	—	4	8	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	#386×C₆₇	1	2	yes	—
576	C₄	#386×C₆₇	1	2	yes	—
577	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
578	C₄	C₂×#121×C₆₇	1	2	yes	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	4	8	no	—
586	C₂	—	8	2	no	—
587	C₂	C₆₇×#1911	1	2	yes	direct product factor
588	C₂	C₂×#386×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	#386
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#535×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₆₇	C₂	semidirect
3. C₂×#421×C₆₇	C₂	semidirect
4. C₂²×#100×C₆₇	C₂	semidirect
5. C₆₇×#1911	C₂	direct (N × H)
6. C₂×H(3,ℤ/4)×C₆₇	C₂	semidirect
12. #535×C₆₇	C₄	semidirect
14. C₂×#127×C₆₇	C₄	semidirect
15. C₂×#124×C₆₇	C₄	semidirect
20. #518×C₆₇	C₂²	semidirect
26. #421×C₆₇	C₂²	semidirect
30. C₂×#100×C₆₇	C₂²	semidirect
31. H(3,ℤ/4)×C₆₇	C₂²	semidirect
39. C₂×#41×C₆₇	C₂×C₄	semidirect
41. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
50. C₂²×D₄×C₆₇	C₂×C₄	semidirect
66. #127×C₆₇	C₂×C₄	semidirect
68. #124×C₆₇	C₂×C₄	semidirect
79. #117×C₆₇	C₂×C₄	semidirect
80. #117×C₆₇	D₄	semidirect
91. C₂×C₄²×C₆₇	C₂×C₄	semidirect
92. C₂×C₄²×C₆₇	D₄	semidirect
116. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
143. C₂×D₄×C₆₇	C₂²×C₄	semidirect
183. C₄²×C₆₇	C₂²×C₄	semidirect
184. C₄²×C₆₇	C₂×D₄	semidirect
284. C₂×#1911	C₆₇	direct (N × H)
293. C₂×C₆₇	#1911	direct (N × H)
296. C₂×#518	C₂×C₆₇	semidirect
297. C₂×#421	C₂×C₆₇	semidirect
298. C₂²×#100	C₂×C₆₇	semidirect
299. #1911	C₂×C₆₇	direct (N × H)
300. C₂×H(3,ℤ/4)	C₂×C₆₇	semidirect
301. C₆₇	C₂×#1911	direct (N × H)
307. #535	C₄×C₆₇	semidirect
309. C₂×#127	C₄×C₆₇	semidirect
310. C₂×#124	C₄×C₆₇	semidirect
315. #518	C₂²×C₆₇	semidirect
321. #421	C₂²×C₆₇	semidirect
325. C₂×#100	C₂²×C₆₇	semidirect
326. H(3,ℤ/4)	C₂²×C₆₇	semidirect
334. C₂×#41	C₂×C₄×C₆₇	semidirect
336. C₂²×Q₈	C₂×C₄×C₆₇	semidirect
345. C₂²×D₄	C₂×C₄×C₆₇	semidirect
361. #127	C₂×C₄×C₆₇	semidirect
363. #124	C₂×C₄×C₆₇	semidirect
374. #117	C₂×C₄×C₆₇	semidirect
375. #117	D₄×C₆₇	semidirect
386. C₂×C₄²	C₂×C₄×C₆₇	semidirect
387. C₂×C₄²	D₄×C₆₇	semidirect
411. C₂×Q₈	C₂²×C₄×C₆₇	semidirect
438. C₂×D₄	C₂²×C₄×C₆₇	semidirect
478. C₄²	C₂²×C₄×C₆₇	semidirect
479. C₄²	C₂×D₄×C₆₇	semidirect
587. C₂	C₆₇×#1911	direct (N × H)

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
C₂×#518×C₆₇	2
C₂×#421×C₆₇	2
C₂²×#100×C₆₇	2
C₆₇×#1911	2
C₂×H(3,ℤ/4)×C₆₇	2
C₂×#1911	67

Subgroups — C2×C67×#1911 #30700261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1911 #30700261