Subgroups — C₂×C₆₇×#2145 #30712638

Order 17152.

1170 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×M₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#427×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2145	C₂	1	8	yes	maximal, direct product factor
5	C₂×#360×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₆₇	—	2	1	no	—
7	C₂×#135×C₆₇	—	2	1	no	—
8	C₂×#135×C₆₇	—	2	2	no	—
9	C₂×#135×C₆₇	—	2	1	no	—
10	C₂×#135×C₆₇	—	2	2	no	—
11	C₂×#135×C₆₇	C₄	1	2	yes	complemented
12	C₂×#135×C₆₇	C₄	1	4	yes	complemented
13	C₂×#135×C₆₇	C₂²	1	2	yes	—
14	C₂×#135×C₆₇	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
16	C₂²×SD₁₆×C₆₇	—	2	1	no	—
17	C₂²×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
18	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₆₇	—	2	1	no	—
20	C₂×M₃₂×C₆₇	—	2	1	no	—
21	C₂×M₃₂×C₆₇	—	2	2	no	—
22	C₂×M₃₂×C₆₇	C₂²	1	2	yes	complemented
23	C₂×M₃₂×C₆₇	C₂²	1	4	yes	complemented
24	C₂²×C₁₆×C₆₇	—	2	1	no	—
25	#427×C₆₇	—	2	2	no	—
26	#427×C₆₇	C₂²	1	4	yes	complemented
27	C₂×#107×C₆₇	—	2	1	no	—
28	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
29	#360×C₆₇	C₂²	1	16	yes	complemented
30	C₂×#41×C₆₇	—	2	4	no	—
31	C₂×#41×C₆₇	—	2	2	no	—
32	C₂×#41×C₆₇	—	2	2	no	—
33	C₂×#41×C₆₇	—	2	4	no	—
34	C₂×#41×C₆₇	—	4	2	no	—
35	C₂×#41×C₆₇	—	4	1	no	—
36	C₂×#41×C₆₇	—	4	1	no	—
37	C₂×#41×C₆₇	—	4	2	no	—
38	C₂²×Q₈×C₆₇	—	2	1	no	—
39	C₂²×D₄×C₆₇	—	2	1	no	—
40	C₂²×D₄×C₆₇	—	4	1	no	—
41	C₂³×C₄×C₆₇	—	4	1	no	—
42	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
43	#135×C₆₇	—	2	4	no	—
44	#135×C₆₇	—	2	4	no	—
45	#135×C₆₇	—	2	4	no	—
46	#135×C₆₇	—	2	2	no	—
47	#135×C₆₇	—	2	4	no	—
48	#135×C₆₇	—	2	4	no	—
49	#135×C₆₇	—	2	2	no	—
50	#135×C₆₇	C₂×C₄	1	4	yes	—
51	#135×C₆₇	C₂×C₄	1	8	yes	complemented
52	#135×C₆₇	C₂³	1	4	yes	—
53	C₂×Q₁₆×C₆₇	—	2	2	no	—
54	C₂×Q₁₆×C₆₇	—	2	1	no	—
55	C₂×Q₁₆×C₆₇	C₂×C₄	1	2	yes	—
56	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	complemented
57	C₂×SD₁₆×C₆₇	—	2	4	no	—
58	C₂×SD₁₆×C₆₇	—	2	2	no	—
59	C₂×SD₁₆×C₆₇	—	2	2	no	—
60	C₂×SD₁₆×C₆₇	—	2	4	no	—
61	C₂×D₈×C₆₇	—	2	2	no	—
62	C₂×D₈×C₆₇	—	2	1	no	—
63	C₂×D₈×C₆₇	C₂×C₄	1	2	yes	—
64	C₂×D₈×C₆₇	C₂×C₄	1	4	yes	complemented
65	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
68	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₆₇	D₄	1	2	yes	—
70	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₆₇	D₄	1	2	yes	—
73	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
75	#117×C₆₇	—	2	4	no	—
76	#117×C₆₇	—	4	2	no	—
77	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₆₇	—	4	1	no	—
79	C₂×C₄²×C₆₇	—	4	1	no	—
80	M₃₂×C₆₇	—	2	4	no	—
81	M₃₂×C₆₇	—	2	2	no	—
82	M₃₂×C₆₇	C₂³	1	4	yes	complemented
83	C₂×C₁₆×C₆₇	—	2	2	no	—
84	C₂×C₁₆×C₆₇	—	2	4	no	—
85	#107×C₆₇	—	2	4	no	—
86	#106×C₆₇	—	2	2	no	—
87	#106×C₆₇	C₂³	1	4	yes	complemented
88	C₂⁴×C₆₇	—	4	1	no	—
89	C₂⁴×C₆₇	D₈	1	1	yes	characteristic
90	#41×C₆₇	—	2	4	no	—
91	#41×C₆₇	—	2	8	no	—
92	#41×C₆₇	—	2	4	no	—
93	#41×C₆₇	—	4	4	no	—
94	#41×C₆₇	—	4	4	no	—
95	#41×C₆₇	—	4	4	no	—
96	#41×C₆₇	—	4	4	no	—
97	#41×C₆₇	—	4	2	no	—
98	#41×C₆₇	—	4	2	no	—
99	#41×C₆₇	—	4	4	no	—
100	C₂×Q₈×C₆₇	—	2	2	no	—
101	C₂×Q₈×C₆₇	—	2	4	no	—
102	C₂×Q₈×C₆₇	—	4	2	no	—
103	C₂×Q₈×C₆₇	—	4	1	no	—
104	C₂×D₄×C₆₇	—	2	2	no	—
105	C₂×D₄×C₆₇	—	2	4	no	—
106	C₂×D₄×C₆₇	—	4	2	no	—
107	C₂×D₄×C₆₇	—	4	4	no	—
108	C₂×D₄×C₆₇	—	4	2	no	—
109	C₂×D₄×C₆₇	—	4	4	no	—
110	C₂×D₄×C₆₇	—	4	2	no	—
111	C₂×D₄×C₆₇	—	4	1	no	—
112	C₂²×C₄×C₆₇	—	4	1	no	—
113	C₂²×C₄×C₆₇	—	4	4	no	—
114	C₂²×C₄×C₆₇	—	4	2	no	—
115	C₂²×C₄×C₆₇	—	4	4	no	—
116	C₂²×C₄×C₆₇	—	4	2	no	—
117	C₂²×C₄×C₆₇	—	4	2	no	—
118	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	D₈	1	2	yes	—
122	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	SD₁₆	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
125	C₂²×C₄×C₆₇	SD₁₆	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
128	Q₁₆×C₆₇	—	2	2	no	—
129	Q₁₆×C₆₇	—	2	4	no	—
130	Q₁₆×C₆₇	C₂²×C₄	1	4	yes	—
131	SD₁₆×C₆₇	—	2	4	no	—
132	SD₁₆×C₆₇	—	2	8	no	—
133	SD₁₆×C₆₇	—	2	4	no	—
134	D₈×C₆₇	—	2	2	no	—
135	D₈×C₆₇	—	2	4	no	—
136	D₈×C₆₇	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
139	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
141	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
142	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
143	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
144	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
155	C₄⋊C₄×C₆₇	—	2	4	no	—
156	C₄⋊C₄×C₆₇	—	4	2	no	—
157	C₂²⋊C₄×C₆₇	—	4	4	no	—
158	C₄²×C₆₇	—	4	4	no	—
159	C₁₆×C₆₇	—	2	4	no	—
160	C₂³×C₆₇	—	4	2	no	—
161	C₂³×C₆₇	—	4	4	no	—
162	C₂³×C₆₇	—	4	2	no	—
163	C₂³×C₆₇	—	8	4	no	—
164	C₂³×C₆₇	#102	1	1	yes	characteristic
165	C₂³×C₆₇	#102	1	1	yes	characteristic
166	C₂³×C₆₇	#102	1	2	yes	—
167	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
168	C₂³×C₆₇	C₂×D₈	1	2	yes	—
169	Q₈×C₆₇	—	2	4	no	—
170	Q₈×C₆₇	—	4	2	no	—
171	Q₈×C₆₇	—	4	4	no	—
172	D₄×C₆₇	—	2	4	no	—
173	D₄×C₆₇	—	4	4	no	—
174	D₄×C₆₇	—	4	4	no	—
175	D₄×C₆₇	—	4	8	no	—
176	D₄×C₆₇	—	4	2	no	—
177	D₄×C₆₇	—	4	4	no	—
178	C₂×C₄×C₆₇	—	4	4	no	—
179	C₂×C₄×C₆₇	—	4	2	no	—
180	C₂×C₄×C₆₇	—	4	4	no	—
181	C₂×C₄×C₆₇	—	4	4	no	—
182	C₂×C₄×C₆₇	—	4	8	no	—
183	C₂×C₄×C₆₇	—	4	4	no	—
184	C₂×C₄×C₆₇	—	8	4	no	—
185	C₂×C₄×C₆₇	#102	1	2	yes	—
186	C₂×C₄×C₆₇	#102	1	2	yes	—
187	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
188	C₂×C₄×C₆₇	#102	1	2	yes	—
189	C₂×C₄×C₆₇	#102	1	2	yes	—
190	C₂×C₄×C₆₇	#102	1	2	yes	—
191	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
192	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
197	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
199	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
201	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
205	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₈×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
207	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
208	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
209	C₂²×C₆₇	—	2	2	no	—
210	C₂²×C₆₇	—	2	2	no	—
211	C₂²×C₆₇	—	2	2	no	—
212	C₂²×C₆₇	—	4	2	no	—
213	C₂²×C₆₇	—	4	2	no	—
214	C₂²×C₆₇	—	4	4	no	—
215	C₂²×C₆₇	—	8	8	no	—
216	C₂²×C₆₇	—	8	4	no	—
217	C₂²×C₆₇	C₂×#102	1	2	yes	—
218	C₂²×C₆₇	C₂×#102	1	2	yes	—
219	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
220	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
221	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
222	C₄×C₆₇	—	4	4	no	—
223	C₄×C₆₇	—	8	4	no	—
224	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
225	C₄×C₆₇	C₂×#102	1	2	yes	—
226	C₄×C₆₇	C₂×#102	1	2	yes	—
227	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
228	C₄×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
230	C₂×#2145	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₆₇	—	2	1	no	—
232	C₂×C₆₇	—	2	2	no	—
233	C₂×C₆₇	—	2	1	no	—
234	C₂×C₆₇	—	2	2	no	—
235	C₂×C₆₇	—	8	4	no	—
236	C₂×C₆₇	#2145	1	2	yes	direct product factor
237	C₂×C₆₇	C₂²×#102	1	1	yes	characteristic
238	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic
239	C₂²×M₃₂	C₂×C₆₇	1	1	yes	characteristic, complemented
240	C₂×#427	C₂×C₆₇	1	1	yes	characteristic, complemented
241	#2145	C₂×C₆₇	1	8	yes	direct product factor
242	C₂×#360	C₂×C₆₇	1	4	yes	complemented
243	C₆₇	C₂×#2145	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×#41	—	2	1	no	—
245	C₂×#135	—	2	1	no	—
246	C₂×#135	—	2	2	no	—
247	C₂×#135	—	2	1	no	—
248	C₂×#135	—	2	2	no	—
249	C₂×#135	C₄×C₆₇	1	2	yes	complemented
250	C₂×#135	C₄×C₆₇	1	4	yes	complemented
251	C₂×#135	C₂²×C₆₇	1	2	yes	—
252	C₂×#135	C₂²×C₆₇	1	4	yes	—
253	C₂²×Q₁₆	C₄×C₆₇	1	1	yes	characteristic, complemented
254	C₂²×SD₁₆	—	2	1	no	—
255	C₂²×D₈	C₄×C₆₇	1	1	yes	characteristic, complemented
256	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
257	C₂×#117	—	2	1	no	—
258	C₂×M₃₂	—	2	1	no	—
259	C₂×M₃₂	—	2	2	no	—
260	C₂×M₃₂	C₂²×C₆₇	1	2	yes	complemented
261	C₂×M₃₂	C₂²×C₆₇	1	4	yes	complemented
262	C₂²×C₁₆	—	2	1	no	—
263	#427	—	2	2	no	—
264	#427	C₂²×C₆₇	1	4	yes	complemented
265	C₂×#107	—	2	1	no	—
266	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
267	#360	C₂²×C₆₇	1	16	yes	complemented
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	4	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	4	1	no	—
273	C₂×#41	—	4	2	no	—
274	C₂×#41	—	4	1	no	—
275	C₂×#41	—	4	2	no	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	4	1	no	—
279	C₂³×C₄	—	4	1	no	—
280	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
281	#135	—	2	4	no	—
282	#135	—	2	4	no	—
283	#135	—	2	4	no	—
284	#135	—	2	2	no	—
285	#135	—	2	4	no	—
286	#135	—	2	4	no	—
287	#135	—	2	2	no	—
288	#135	C₂×C₄×C₆₇	1	4	yes	—
289	#135	C₂×C₄×C₆₇	1	8	yes	complemented
290	#135	C₂³×C₆₇	1	4	yes	—
291	C₂×Q₁₆	—	2	2	no	—
292	C₂×Q₁₆	—	2	1	no	—
293	C₂×Q₁₆	C₂×C₄×C₆₇	1	2	yes	—
294	C₂×Q₁₆	C₂×C₄×C₆₇	1	4	yes	complemented
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	1	no	—
301	C₂×D₈	C₂×C₄×C₆₇	1	2	yes	—
302	C₂×D₈	C₂×C₄×C₆₇	1	4	yes	complemented
303	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
304	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
305	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
306	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
307	C₂²×C₈	D₄×C₆₇	1	2	yes	—
308	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
309	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
310	C₂²×C₈	D₄×C₆₇	1	2	yes	—
311	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
313	#117	—	2	4	no	—
314	#117	—	4	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	4	1	no	—
317	C₂×C₄²	—	4	1	no	—
318	M₃₂	—	2	4	no	—
319	M₃₂	—	2	2	no	—
320	M₃₂	C₂³×C₆₇	1	4	yes	complemented
321	C₂×C₁₆	—	2	2	no	—
322	C₂×C₁₆	—	2	4	no	—
323	#107	—	2	4	no	—
324	#106	—	2	2	no	—
325	#106	C₂³×C₆₇	1	4	yes	complemented
326	C₂⁴	—	4	1	no	—
327	C₂⁴	D₈×C₆₇	1	1	yes	characteristic
328	#41	—	2	4	no	—
329	#41	—	2	8	no	—
330	#41	—	2	4	no	—
331	#41	—	4	4	no	—
332	#41	—	4	4	no	—
333	#41	—	4	4	no	—
334	#41	—	4	4	no	—
335	#41	—	4	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	4	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
357	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
358	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
359	C₂²×C₄	D₈×C₆₇	1	1	yes	characteristic
360	C₂²×C₄	D₈×C₆₇	1	2	yes	—
361	C₂²×C₄	SD₁₆×C₆₇	1	1	yes	characteristic
362	C₂²×C₄	SD₁₆×C₆₇	1	1	yes	characteristic
363	C₂²×C₄	SD₁₆×C₆₇	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
366	Q₁₆	—	2	2	no	—
367	Q₁₆	—	2	4	no	—
368	Q₁₆	C₂²×C₄×C₆₇	1	4	yes	—
369	SD₁₆	—	2	4	no	—
370	SD₁₆	—	2	8	no	—
371	SD₁₆	—	2	4	no	—
372	D₈	—	2	2	no	—
373	D₈	—	2	4	no	—
374	D₈	C₂²×C₄×C₆₇	1	4	yes	—
375	C₂×C₈	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
376	C₂×C₈	C₂²⋊C₄×C₆₇	1	2	yes	—
377	C₂×C₈	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
378	C₂×C₈	C₂²⋊C₄×C₆₇	1	2	yes	—
379	C₂×C₈	C₂²⋊C₄×C₆₇	1	2	yes	—
380	C₂×C₈	C₂²⋊C₄×C₆₇	1	2	yes	—
381	C₂×C₈	C₂²⋊C₄×C₆₇	1	2	yes	—
382	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
383	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
384	C₂×C₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
385	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
387	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
388	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
389	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
390	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
391	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
392	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₄²	—	4	4	no	—
397	C₁₆	—	2	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	8	4	no	—
402	C₂³	#102×C₆₇	1	1	yes	characteristic
403	C₂³	#102×C₆₇	1	1	yes	characteristic
404	C₂³	#102×C₆₇	1	2	yes	—
405	C₂³	C₂×D₈×C₆₇	1	1	yes	characteristic
406	C₂³	C₂×D₈×C₆₇	1	2	yes	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	8	4	no	—
423	C₂×C₄	#102×C₆₇	1	2	yes	—
424	C₂×C₄	#102×C₆₇	1	1	yes	characteristic
425	C₂×C₄	#102×C₆₇	1	2	yes	—
426	C₂×C₄	#102×C₆₇	1	1	yes	characteristic
427	C₂×C₄	#102×C₆₇	1	2	yes	—
428	C₂×C₄	#102×C₆₇	1	2	yes	—
429	C₂×C₄	#102×C₆₇	1	2	yes	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
432	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
433	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
434	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
435	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
436	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
437	C₂×C₄	C₂×SD₁₆×C₆₇	1	1	yes	characteristic
438	C₂×C₄	C₂×SD₁₆×C₆₇	1	1	yes	characteristic
439	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
440	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
441	C₈	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
442	C₈	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
443	C₈	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
444	C₈	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
445	C₈	C₂³×C₄×C₆₇	1	1	yes	characteristic
446	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	8	no	—
454	C₂²	—	8	4	no	—
455	C₂²	C₂×#102×C₆₇	1	2	yes	—
456	C₂²	C₂×#102×C₆₇	1	2	yes	—
457	C₂²	C₂×#102×C₆₇	1	1	yes	characteristic
458	C₂²	C₂×#102×C₆₇	1	1	yes	characteristic
459	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
460	C₄	—	4	4	no	—
461	C₄	—	8	4	no	—
462	C₄	C₂×#102×C₆₇	1	1	yes	characteristic
463	C₄	C₂×#102×C₆₇	1	2	yes	—
464	C₄	C₂×#102×C₆₇	1	2	yes	—
465	C₄	C₂×#102×C₆₇	1	1	yes	characteristic
466	C₄	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
467	C₄	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	2	no	—
472	C₂	—	8	4	no	—
473	C₂	C₆₇×#2145	1	2	yes	direct product factor
474	C₂	C₂²×#102×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	#102
commutator	C₈	C₂³×C₄×C₆₇
Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂×#102
prime radical	C₂²×#135×C₆₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ C₂³×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×M₃₂×C₆₇	C₂	semidirect
3. C₂×#427×C₆₇	C₂	semidirect
4. C₆₇×#2145	C₂	direct (N × H)
5. C₂×#360×C₆₇	C₂	semidirect
11. C₂×#135×C₆₇	C₄	semidirect
12. C₂×#135×C₆₇	C₄	semidirect
15. C₂²×Q₁₆×C₆₇	C₄	semidirect
17. C₂²×D₈×C₆₇	C₄	semidirect
22. C₂×M₃₂×C₆₇	C₂²	semidirect
23. C₂×M₃₂×C₆₇	C₂²	semidirect
26. #427×C₆₇	C₂²	semidirect
28. C₂×#106×C₆₇	C₂²	semidirect
29. #360×C₆₇	C₂²	semidirect
51. #135×C₆₇	C₂×C₄	semidirect
56. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
64. C₂×D₈×C₆₇	C₂×C₄	semidirect
82. M₃₂×C₆₇	C₂³	semidirect
87. #106×C₆₇	C₂³	semidirect
230. C₂×#2145	C₆₇	direct (N × H)
236. C₂×C₆₇	#2145	direct (N × H)
239. C₂²×M₃₂	C₂×C₆₇	semidirect
240. C₂×#427	C₂×C₆₇	semidirect
241. #2145	C₂×C₆₇	direct (N × H)
242. C₂×#360	C₂×C₆₇	semidirect
243. C₆₇	C₂×#2145	direct (N × H)
249. C₂×#135	C₄×C₆₇	semidirect
250. C₂×#135	C₄×C₆₇	semidirect
253. C₂²×Q₁₆	C₄×C₆₇	semidirect
255. C₂²×D₈	C₄×C₆₇	semidirect
260. C₂×M₃₂	C₂²×C₆₇	semidirect
261. C₂×M₃₂	C₂²×C₆₇	semidirect
264. #427	C₂²×C₆₇	semidirect
266. C₂×#106	C₂²×C₆₇	semidirect
267. #360	C₂²×C₆₇	semidirect
289. #135	C₂×C₄×C₆₇	semidirect
294. C₂×Q₁₆	C₂×C₄×C₆₇	semidirect
302. C₂×D₈	C₂×C₄×C₆₇	semidirect
320. M₃₂	C₂³×C₆₇	semidirect
325. #106	C₂³×C₆₇	semidirect
473. C₂	C₆₇×#2145	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₆₇	2
C₂²×M₃₂×C₆₇	2
C₂×#427×C₆₇	2
C₆₇×#2145	2
C₂×#360×C₆₇	2
C₂×#2145	67

Subgroups — C2×C67×#2145 #30712638

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2145 #30712638