Subgroups — C₆₇×#33229 #30712480

Order 17152.

888 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#491×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#489×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#488×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#487×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2660	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2658	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#1960	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1959	C₂	1	2	yes	maximal
9	C₆₇×#1958	C₂	1	2	yes	maximal
10	C₆₇×#1956	C₂	1	2	yes	maximal, complemented
11	C₆₇×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₆₇	C₂²	1	2	yes	—
18	#491×C₆₇	—	2	4	no	—
19	#489×C₆₇	—	2	4	no	—
20	#488×C₆₇	—	2	4	no	—
21	#487×C₆₇	—	2	4	no	—
22	C₂×#103×C₆₇	C₂²	1	2	yes	—
23	C₂×#103×C₆₇	C₂²	1	2	yes	—
24	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₇	C₂²	1	2	yes	—
27	C₂×#103×C₆₇	C₂²	1	2	yes	—
28	C₂×#103×C₆₇	C₂²	1	2	yes	—
29	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#102×C₆₇	C₂²	1	2	yes	—
32	C₂×#97×C₆₇	C₂²	1	2	yes	—
33	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
36	#399×C₆₇	—	2	2	no	—
37	#399×C₆₇	—	2	2	no	—
38	#398×C₆₇	—	2	2	no	—
39	#395×C₆₇	—	2	2	no	—
40	#384×C₆₇	C₂²	1	2	yes	—
41	#382×C₆₇	C₂²	1	2	yes	—
42	#376×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₆₇	—	2	1	no	—
44	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
46	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₆₇	—	2	2	no	—
51	C₄⋊Q₈×C₆₇	—	2	2	no	—
52	C₄⋊Q₈×C₆₇	—	2	2	no	—
53	C₄⋊Q₈×C₆₇	—	2	2	no	—
54	C₄⋊Q₈×C₆₇	—	2	4	no	—
55	C₄⋊Q₈×C₆₇	—	2	4	no	—
56	#125×C₆₇	—	2	2	no	—
57	#125×C₆₇	—	2	2	no	—
58	#124×C₆₇	—	2	2	no	—
59	#124×C₆₇	—	2	2	no	—
60	#124×C₆₇	—	2	4	no	—
61	#124×C₆₇	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
66	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
69	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
75	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
77	#103×C₆₇	—	2	4	no	—
78	#103×C₆₇	—	2	4	no	—
79	#103×C₆₇	—	2	2	no	—
80	#103×C₆₇	—	2	2	no	—
81	#103×C₆₇	—	2	4	no	—
82	#103×C₆₇	—	2	4	no	—
83	#103×C₆₇	—	2	4	no	—
84	#102×C₆₇	—	2	2	no	—
85	#102×C₆₇	—	2	2	no	—
86	#102×C₆₇	—	2	4	no	—
87	#97×C₆₇	—	2	4	no	—
88	#97×C₆₇	D₄	1	4	yes	—
89	C₄×C₈×C₆₇	—	2	4	no	—
90	C₄×C₈×C₆₇	D₄	1	4	yes	—
91	#95×C₆₇	—	2	4	no	—
92	#95×C₆₇	D₄	1	2	yes	—
93	#95×C₆₇	D₄	1	2	yes	—
94	C₂⁴×C₆₇	—	2	1	no	—
95	C₂×Q₈×C₆₇	—	2	1	no	—
96	C₂×Q₈×C₆₇	—	2	1	no	—
97	C₂×Q₈×C₆₇	—	2	2	no	—
98	C₂×Q₈×C₆₇	—	2	2	no	—
99	C₂×Q₈×C₆₇	—	2	2	no	—
100	C₂×Q₈×C₆₇	—	2	2	no	—
101	C₂×Q₈×C₆₇	—	2	2	no	—
102	C₂×Q₈×C₆₇	—	2	2	no	—
103	C₂×Q₈×C₆₇	—	2	2	no	—
104	C₂×Q₈×C₆₇	—	2	2	no	—
105	C₂×Q₈×C₆₇	—	4	2	no	—
106	C₂×Q₈×C₆₇	—	8	2	no	—
107	C₂×D₄×C₆₇	—	2	1	no	—
108	C₂×D₄×C₆₇	—	2	1	no	—
109	C₂×D₄×C₆₇	—	2	2	no	—
110	C₂×D₄×C₆₇	—	2	2	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	1	no	—
113	C₂²×C₄×C₆₇	—	2	1	no	—
114	C₂²×C₄×C₆₇	—	2	2	no	—
115	C₂²×C₄×C₆₇	—	2	1	no	—
116	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₆₇	—	2	2	no	—
121	C₂×C₈×C₆₇	—	2	2	no	—
122	C₂×C₈×C₆₇	—	2	2	no	—
123	C₂×C₈×C₆₇	—	2	2	no	—
124	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₆₇	—	2	1	no	—
128	C₄⋊C₄×C₆₇	—	2	1	no	—
129	C₄⋊C₄×C₆₇	—	2	2	no	—
130	C₄⋊C₄×C₆₇	—	2	1	no	—
131	C₄⋊C₄×C₆₇	—	2	1	no	—
132	C₄⋊C₄×C₆₇	—	2	2	no	—
133	C₄⋊C₄×C₆₇	—	4	8	no	—
134	C₄⋊C₄×C₆₇	—	4	2	no	—
135	C₄⋊C₄×C₆₇	—	4	2	no	—
136	C₄⋊C₄×C₆₇	—	4	2	no	—
137	C₄⋊C₄×C₆₇	—	4	2	no	—
138	C₄⋊C₄×C₆₇	—	4	2	no	—
139	C₄⋊C₄×C₆₇	—	8	4	no	—
140	C₂²⋊C₄×C₆₇	—	4	8	no	—
141	C₂²⋊C₄×C₆₇	—	4	2	no	—
142	C₂²⋊C₄×C₆₇	—	4	2	no	—
143	C₄²×C₆₇	C₂×D₄	1	2	yes	—
144	C₄²×C₆₇	C₂×D₄	1	2	yes	—
145	C₄²×C₆₇	#41	1	4	yes	—
146	C₄²×C₆₇	#41	1	4	yes	—
147	C₂³×C₆₇	—	4	2	no	—
148	C₂³×C₆₇	—	4	1	no	—
149	C₂³×C₆₇	—	4	2	no	—
150	C₂³×C₆₇	—	4	2	no	—
151	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₆₇	—	4	1	no	—
153	Q₈×C₆₇	—	4	1	no	—
154	Q₈×C₆₇	—	4	2	no	—
155	Q₈×C₆₇	—	4	2	no	—
156	Q₈×C₆₇	—	4	2	no	—
157	Q₈×C₆₇	—	4	2	no	—
158	Q₈×C₆₇	—	4	2	no	—
159	Q₈×C₆₇	—	8	4	no	—
160	D₄×C₆₇	—	4	1	no	—
161	D₄×C₆₇	—	4	1	no	—
162	D₄×C₆₇	—	4	2	no	—
163	C₂×C₄×C₆₇	—	2	4	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	—	2	4	no	—
166	C₂×C₄×C₆₇	—	2	2	no	—
167	C₂×C₄×C₆₇	—	4	2	no	—
168	C₂×C₄×C₆₇	—	4	2	no	—
169	C₂×C₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	4	1	no	—
171	C₂×C₄×C₆₇	—	4	1	no	—
172	C₂×C₄×C₆₇	—	4	1	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	—	4	2	no	—
175	C₂×C₄×C₆₇	—	4	2	no	—
176	C₂×C₄×C₆₇	—	4	4	no	—
177	C₂×C₄×C₆₇	—	4	2	no	—
178	C₂×C₄×C₆₇	#124	1	8	yes	—
179	C₂×C₄×C₆₇	#127	1	2	yes	—
180	C₂×C₄×C₆₇	#127	1	2	yes	—
181	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
184	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
185	C₈×C₆₇	—	2	2	no	—
186	C₈×C₆₇	—	2	4	no	—
187	C₈×C₆₇	—	2	2	no	—
188	C₂²×C₆₇	—	8	1	no	—
189	C₂²×C₆₇	—	8	4	no	—
190	C₂²×C₆₇	—	8	1	no	—
191	C₂²×C₆₇	—	8	1	no	—
192	C₂²×C₆₇	C₂×#124	1	2	yes	—
193	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
194	C₂²×C₆₇	#577	1	2	yes	—
195	C₂²×C₆₇	#578	1	2	yes	—
196	C₄×C₆₇	—	2	8	no	—
197	C₄×C₆₇	—	2	2	no	—
198	C₄×C₆₇	—	2	2	no	—
199	C₄×C₆₇	—	8	2	no	—
200	C₄×C₆₇	—	8	1	no	—
201	C₄×C₆₇	—	8	1	no	—
202	C₄×C₆₇	—	8	2	no	—
203	C₄×C₆₇	—	8	1	no	—
204	C₄×C₆₇	#532	1	1	yes	characteristic
205	C₄×C₆₇	#532	1	2	yes	—
206	C₄×C₆₇	#532	1	1	yes	characteristic
207	#33229	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₆₇	—	16	1	no	—
209	C₂×C₆₇	#2858	1	1	yes	characteristic
210	C₂×C₆₇	#3137	1	4	yes	—
211	C₂×C₆₇	#3154	1	1	yes	characteristic
212	C₂×C₆₇	#3156	1	1	yes	characteristic
213	C₂×#491	C₂×C₆₇	1	1	yes	characteristic, complemented
214	C₂×#489	C₂×C₆₇	1	1	yes	characteristic
215	C₂×#488	C₂×C₆₇	1	1	yes	characteristic
216	C₂×#487	C₂×C₆₇	1	1	yes	characteristic, complemented
217	#2660	C₂×C₆₇	1	1	yes	characteristic, complemented
218	#2658	C₂×C₆₇	1	1	yes	characteristic
219	#1960	C₂×C₆₇	1	2	yes	complemented
220	#1959	C₂×C₆₇	1	2	yes	—
221	#1958	C₂×C₆₇	1	2	yes	—
222	#1956	C₂×C₆₇	1	2	yes	complemented
223	#1726	C₂×C₆₇	1	1	yes	characteristic, complemented
224	C₆₇	#33229	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
227	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
228	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
229	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
230	C₂×#124	C₂²×C₆₇	1	2	yes	—
231	#491	—	2	4	no	—
232	#489	—	2	4	no	—
233	#488	—	2	4	no	—
234	#487	—	2	4	no	—
235	C₂×#103	C₂²×C₆₇	1	2	yes	—
236	C₂×#103	C₂²×C₆₇	1	2	yes	—
237	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
238	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
239	C₂×#103	C₂²×C₆₇	1	2	yes	—
240	C₂×#103	C₂²×C₆₇	1	2	yes	—
241	C₂×#103	C₂²×C₆₇	1	2	yes	—
242	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
243	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
244	C₂×#102	C₂²×C₆₇	1	2	yes	—
245	C₂×#97	C₂²×C₆₇	1	2	yes	—
246	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
248	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
249	#399	—	2	2	no	—
250	#399	—	2	2	no	—
251	#398	—	2	2	no	—
252	#395	—	2	2	no	—
253	#384	C₂²×C₆₇	1	2	yes	—
254	#382	C₂²×C₆₇	1	2	yes	—
255	#376	C₂²×C₆₇	1	1	yes	characteristic
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
258	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
259	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	—	2	4	no	—
269	#125	—	2	2	no	—
270	#125	—	2	2	no	—
271	#124	—	2	2	no	—
272	#124	—	2	2	no	—
273	#124	—	2	4	no	—
274	#124	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
290	#103	—	2	4	no	—
291	#103	—	2	4	no	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	—	2	4	no	—
295	#103	—	2	4	no	—
296	#103	—	2	4	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	4	no	—
300	#97	—	2	4	no	—
301	#97	D₄×C₆₇	1	4	yes	—
302	C₄×C₈	—	2	4	no	—
303	C₄×C₈	D₄×C₆₇	1	4	yes	—
304	#95	—	2	4	no	—
305	#95	D₄×C₆₇	1	2	yes	—
306	#95	D₄×C₆₇	1	2	yes	—
307	C₂⁴	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	8	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
330	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	8	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	8	4	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	C₂×D₄×C₆₇	1	2	yes	—
357	C₄²	C₂×D₄×C₆₇	1	2	yes	—
358	C₄²	#41×C₆₇	1	4	yes	—
359	C₄²	#41×C₆₇	1	4	yes	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
365	Q₈	—	4	1	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	4	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	#124×C₆₇	1	8	yes	—
392	C₂×C₄	#127×C₆₇	1	2	yes	—
393	C₂×C₄	#127×C₆₇	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
397	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
398	C₈	—	2	2	no	—
399	C₈	—	2	4	no	—
400	C₈	—	2	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₂×#124×C₆₇	1	2	yes	—
406	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
407	C₂²	#577×C₆₇	1	2	yes	—
408	C₂²	#578×C₆₇	1	2	yes	—
409	C₄	—	2	8	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	2	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	#532×C₆₇	1	1	yes	characteristic
418	C₄	#532×C₆₇	1	2	yes	—
419	C₄	#532×C₆₇	1	1	yes	characteristic
420	C₂	—	16	1	no	—
421	C₂	C₆₇×#2858	1	1	yes	characteristic
422	C₂	C₆₇×#3137	1	4	yes	—
423	C₂	C₆₇×#3154	1	1	yes	characteristic
424	C₂	C₆₇×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ #376×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#491×C₆₇	C₂	semidirect
4. C₂×#487×C₆₇	C₂	semidirect
5. C₆₇×#2660	C₂	semidirect
7. C₆₇×#1960	C₂	semidirect
10. C₆₇×#1956	C₂	semidirect
11. C₆₇×#1726	C₂	semidirect
207. #33229	C₆₇	direct (N × H)
213. C₂×#491	C₂×C₆₇	semidirect
216. C₂×#487	C₂×C₆₇	semidirect
217. #2660	C₂×C₆₇	semidirect
219. #1960	C₂×C₆₇	semidirect
222. #1956	C₂×C₆₇	semidirect
223. #1726	C₂×C₆₇	semidirect
224. C₆₇	#33229	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×#491×C₆₇	2
C₂×#489×C₆₇	2
C₂×#488×C₆₇	2
C₂×#487×C₆₇	2
C₆₇×#2660	2
C₆₇×#2658	2
C₆₇×#1960	2
C₆₇×#1959	2
C₆₇×#1958	2
C₆₇×#1956	2
C₆₇×#1726	2
#33229	67

Subgroups — C67×#33229 #30712480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33229 #30712480