Subgroups — C₆₇×#21401 #30700652

Order 17152.

1518 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1990	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1957	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1893	C₂	1	4	yes	maximal, complemented
7	C₄×#102×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₆₇	—	2	1	no	—
9	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
10	#532×C₆₇	—	2	4	no	—
11	#532×C₆₇	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₆₇	—	2	1	no	—
15	C₂×#121×C₆₇	—	2	1	no	—
16	C₂×#121×C₆₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₆₇	—	2	1	no	—
18	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
19	C₂×#117×C₆₇	—	2	1	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₆₇	C₂²	1	8	yes	—
22	C₂×C₄×C₈×C₆₇	—	2	4	no	—
23	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
25	#384×C₆₇	C₂²	1	2	yes	—
26	#382×C₆₇	—	2	1	no	—
27	#380×C₆₇	—	2	1	no	—
28	#380×C₆₇	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
30	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
31	#340×C₆₇	C₂²	1	8	yes	—
32	C₂×#41×C₆₇	—	2	8	no	—
33	C₂×#41×C₆₇	—	4	4	no	—
34	C₂×#41×C₆₇	—	4	4	no	—
35	C₂²×Q₈×C₆₇	—	2	1	no	—
36	C₂²×D₄×C₆₇	—	2	2	no	—
37	C₂²×D₄×C₆₇	—	2	1	no	—
38	C₂²×D₄×C₆₇	—	2	1	no	—
39	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₆₇	—	2	2	no	—
41	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₆₇	—	2	4	no	—
45	C₂²×C₈×C₆₇	—	2	8	no	—
46	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
47	C₄⋊Q₈×C₆₇	—	2	2	no	—
48	C₄⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
49	#127×C₆₇	—	2	2	no	—
50	#127×C₆₇	C₂×C₄	1	4	yes	—
51	#124×C₆₇	—	2	8	no	—
52	#121×C₆₇	—	2	8	no	—
53	#121×C₆₇	—	2	4	no	—
54	#121×C₆₇	C₂×C₄	1	8	yes	—
55	C₄×D₄×C₆₇	—	2	8	no	—
56	C₄×D₄×C₆₇	—	2	4	no	—
57	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
58	#117×C₆₇	—	4	4	no	—
59	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
67	C₂×C₄²×C₆₇	—	2	2	no	—
68	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₇	D₄	1	4	yes	—
72	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
74	#102×C₆₇	—	2	16	no	—
75	C₄×C₈×C₆₇	—	2	4	no	—
76	C₄×C₈×C₆₇	—	2	4	no	—
77	#95×C₆₇	—	2	2	no	—
78	#95×C₆₇	—	2	2	no	—
79	C₂⁴×C₆₇	—	2	2	no	—
80	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
81	#41×C₆₇	—	4	32	no	—
82	C₂×Q₈×C₆₇	—	2	4	no	—
83	C₂×Q₈×C₆₇	—	4	2	no	—
84	C₂×Q₈×C₆₇	—	4	2	no	—
85	C₂×D₄×C₆₇	—	2	8	no	—
86	C₂×D₄×C₆₇	—	2	4	no	—
87	C₂×D₄×C₆₇	—	2	4	no	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	—	2	8	no	—
90	C₂×D₄×C₆₇	—	4	4	no	—
91	C₂×D₄×C₆₇	—	4	4	no	—
92	C₂×D₄×C₆₇	—	4	2	no	—
93	C₂×D₄×C₆₇	—	4	2	no	—
94	C₂×D₄×C₆₇	—	4	4	no	—
95	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₆₇	—	2	4	no	—
97	C₂²×C₄×C₆₇	—	2	4	no	—
98	C₂²×C₄×C₆₇	—	2	2	no	—
99	C₂²×C₄×C₆₇	—	2	8	no	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	4	4	no	—
102	C₂²×C₄×C₆₇	—	4	4	no	—
103	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₆₇	D₈	1	4	yes	—
106	C₂²×C₄×C₆₇	SD₁₆	1	4	yes	—
107	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₆₇	—	2	16	no	—
116	C₂×C₈×C₆₇	—	2	4	no	—
117	C₂×C₈×C₆₇	—	2	4	no	—
118	C₂×C₈×C₆₇	#41	1	8	yes	complemented
119	C₄⋊C₄×C₆₇	—	2	4	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	2	8	no	—
122	C₄⋊C₄×C₆₇	—	4	4	no	—
123	C₄⋊C₄×C₆₇	—	4	4	no	—
124	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
125	C₂²⋊C₄×C₆₇	—	2	8	no	—
126	C₂²⋊C₄×C₆₇	—	2	8	no	—
127	C₂²⋊C₄×C₆₇	—	4	4	no	—
128	C₄²×C₆₇	—	4	4	no	—
129	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
130	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
133	C₄²×C₆₇	C₂×D₄	1	2	yes	—
134	C₄²×C₆₇	C₂×D₄	1	2	yes	—
135	C₂³×C₆₇	—	2	2	no	—
136	C₂³×C₆₇	—	2	2	no	—
137	C₂³×C₆₇	—	2	4	no	—
138	C₂³×C₆₇	—	4	4	no	—
139	C₂³×C₆₇	—	4	2	no	—
140	C₂³×C₆₇	—	4	2	no	—
141	C₂³×C₆₇	—	4	4	no	—
142	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂³×C₆₇	C₂×D₈	1	2	yes	—
144	C₂³×C₆₇	C₂×SD₁₆	1	2	yes	—
145	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₆₇	—	4	8	no	—
147	D₄×C₆₇	—	2	8	no	—
148	D₄×C₆₇	—	4	16	no	—
149	D₄×C₆₇	—	4	4	no	—
150	D₄×C₆₇	—	4	8	no	—
151	D₄×C₆₇	—	4	8	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	2	2	no	—
154	C₂×C₄×C₆₇	—	2	4	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	8	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	—	4	2	no	—
160	C₂×C₄×C₆₇	—	4	16	no	—
161	C₂×C₄×C₆₇	—	4	4	no	—
162	C₂×C₄×C₆₇	—	4	4	no	—
163	C₂×C₄×C₆₇	—	4	4	no	—
164	C₂×C₄×C₆₇	#102	1	16	yes	complemented
165	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
172	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
173	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₆₇	#135	1	4	yes	—
175	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
178	C₈×C₆₇	—	2	8	no	—
179	C₂²×C₆₇	—	2	2	no	—
180	C₂²×C₆₇	—	2	4	no	—
181	C₂²×C₆₇	—	2	4	no	—
182	C₂²×C₆₇	—	2	2	no	—
183	C₂²×C₆₇	—	4	4	no	—
184	C₂²×C₆₇	—	4	4	no	—
185	C₂²×C₆₇	—	4	4	no	—
186	C₂²×C₆₇	—	8	4	no	—
187	C₂²×C₆₇	—	8	4	no	—
188	C₂²×C₆₇	C₂×#102	1	4	yes	—
189	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₆₇	#532	1	2	yes	—
191	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
192	C₂²×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
193	C₂²×C₆₇	C₂×#135	1	2	yes	—
194	C₄×C₆₇	—	2	2	no	—
195	C₄×C₆₇	—	2	2	no	—
196	C₄×C₆₇	—	4	4	no	—
197	C₄×C₆₇	—	8	4	no	—
198	C₄×C₆₇	C₂×#102	1	4	yes	—
199	C₄×C₆₇	C₂×#102	1	4	yes	—
200	C₄×C₆₇	#416	1	4	yes	—
201	C₄×C₆₇	C₄×#41	1	2	yes	—
202	C₄×C₆₇	#525	1	2	yes	—
203	#21401	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂×C₆₇	—	2	4	no	—
205	C₂×C₆₇	—	8	4	no	—
206	C₂×C₆₇	#2297	1	1	yes	characteristic
207	C₂×C₆₇	C₂²×#102	1	1	yes	characteristic
208	C₂×C₆₇	C₂×#416	1	1	yes	characteristic
209	C₂×C₆₇	#3167	1	2	yes	—
210	C₂×C₆₇	#3169	1	2	yes	—
211	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
212	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
213	#2285	C₂×C₆₇	1	1	yes	characteristic, complemented
214	#1990	C₂×C₆₇	1	2	yes	complemented
215	#1957	C₂×C₆₇	1	2	yes	complemented
216	#1893	C₂×C₆₇	1	4	yes	complemented
217	C₄×#102	C₂×C₆₇	1	4	yes	complemented
218	C₆₇	#21401	1	1	yes	characteristic, direct product factor, Sylow
219	C₂²×#41	—	2	1	no	—
220	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
221	#532	—	2	4	no	—
222	#532	C₄×C₆₇	1	8	yes	complemented
223	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
224	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
225	C₂×#124	—	2	1	no	—
226	C₂×#121	—	2	1	no	—
227	C₂×#121	C₂²×C₆₇	1	2	yes	—
228	C₂×C₄×D₄	—	2	1	no	—
229	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
230	C₂×#117	—	2	1	no	—
231	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
232	C₂×#102	C₂²×C₆₇	1	8	yes	—
233	C₂×C₄×C₈	—	2	4	no	—
234	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
235	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
236	#384	C₂²×C₆₇	1	2	yes	—
237	#382	—	2	1	no	—
238	#380	—	2	1	no	—
239	#380	C₂²×C₆₇	1	2	yes	—
240	C₄×C₄⋊C₄	—	2	1	no	—
241	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
242	#340	C₂²×C₆₇	1	8	yes	—
243	C₂×#41	—	2	8	no	—
244	C₂×#41	—	4	4	no	—
245	C₂×#41	—	4	4	no	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	—	2	8	no	—
257	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
260	#127	—	2	2	no	—
261	#127	C₂×C₄×C₆₇	1	4	yes	—
262	#124	—	2	8	no	—
263	#121	—	2	8	no	—
264	#121	—	2	4	no	—
265	#121	C₂×C₄×C₆₇	1	8	yes	—
266	C₄×D₄	—	2	8	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
269	#117	—	4	4	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
280	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₆₇	1	4	yes	—
283	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
285	#102	—	2	16	no	—
286	C₄×C₈	—	2	4	no	—
287	C₄×C₈	—	2	4	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	C₂⁴	—	2	2	no	—
291	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
292	#41	—	4	32	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
315	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
316	C₂²×C₄	D₈×C₆₇	1	4	yes	—
317	C₂²×C₄	SD₁₆×C₆₇	1	4	yes	—
318	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
326	C₂×C₈	—	2	16	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	#41×C₆₇	1	8	yes	complemented
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	4	4	no	—
339	C₄²	—	4	4	no	—
340	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
341	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
342	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
343	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
344	C₄²	C₂×D₄×C₆₇	1	2	yes	—
345	C₄²	C₂×D₄×C₆₇	1	2	yes	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	4	no	—
353	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
354	C₂³	C₂×D₈×C₆₇	1	2	yes	—
355	C₂³	C₂×SD₁₆×C₆₇	1	2	yes	—
356	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
357	Q₈	—	4	8	no	—
358	D₄	—	2	8	no	—
359	D₄	—	4	16	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	8	no	—
362	D₄	—	4	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	16	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	#102×C₆₇	1	16	yes	complemented
376	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
378	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
381	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
382	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
383	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
384	C₂×C₄	C₂×SD₁₆×C₆₇	1	2	yes	—
385	C₂×C₄	#135×C₆₇	1	4	yes	—
386	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
389	C₈	—	2	8	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	4	no	—
398	C₂²	—	8	4	no	—
399	C₂²	C₂×#102×C₆₇	1	4	yes	—
400	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
401	C₂²	#532×C₆₇	1	2	yes	—
402	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
403	C₂²	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
404	C₂²	C₂×#135×C₆₇	1	2	yes	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	4	no	—
408	C₄	—	8	4	no	—
409	C₄	C₂×#102×C₆₇	1	4	yes	—
410	C₄	C₂×#102×C₆₇	1	4	yes	—
411	C₄	#416×C₆₇	1	4	yes	—
412	C₄	C₄×#41×C₆₇	1	2	yes	—
413	C₄	#525×C₆₇	1	2	yes	—
414	C₂	—	2	4	no	—
415	C₂	—	8	4	no	—
416	C₂	C₆₇×#2297	1	1	yes	characteristic
417	C₂	C₂²×#102×C₆₇	1	1	yes	characteristic
418	C₂	C₂×#416×C₆₇	1	1	yes	characteristic
419	C₂	C₆₇×#3167	1	2	yes	—
420	C₂	C₆₇×#3169	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂²×D₄
prime radical	C₂×#532×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₈×C₆₇	C₂	semidirect
3. C₆₇×#2285	C₂	semidirect
4. C₆₇×#1990	C₂	semidirect
5. C₆₇×#1957	C₂	semidirect
6. C₆₇×#1893	C₂	semidirect
7. C₄×#102×C₆₇	C₂	semidirect
11. #532×C₆₇	C₄	semidirect
118. C₂×C₈×C₆₇	#41	semidirect
164. C₂×C₄×C₆₇	#102	semidirect
203. #21401	C₆₇	direct (N × H)
212. C₂²×C₄×C₈	C₂×C₆₇	semidirect
213. #2285	C₂×C₆₇	semidirect
214. #1990	C₂×C₆₇	semidirect
215. #1957	C₂×C₆₇	semidirect
216. #1893	C₂×C₆₇	semidirect
217. C₄×#102	C₂×C₆₇	semidirect
218. C₆₇	#21401	direct (N × H)
222. #532	C₄×C₆₇	semidirect
329. C₂×C₈	#41×C₆₇	semidirect
375. C₂×C₄	#102×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₆₇×#2285	2
C₆₇×#1990	2
C₆₇×#1957	2
C₆₇×#1893	2
C₄×#102×C₆₇	2
#21401	67

Subgroups — C67×#21401 #30700652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21401 #30700652