Subgroups — C₆₇×#33119 #30712370

Order 17152.

830 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×#484×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2621	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2274	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#1981	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1949	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1928	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1927	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1873	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#1873	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#1798	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
18	#484×C₆₇	—	2	4	no	—
19	#483×C₆₇	—	2	4	no	—
20	C₂×#107×C₆₇	C₂²	1	2	yes	—
21	C₂×#106×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
23	C₂×#103×C₆₇	C₂²	1	2	yes	—
24	C₂×#103×C₆₇	C₂²	1	2	yes	—
25	C₂×#103×C₆₇	C₂²	1	2	yes	—
26	C₂×#103×C₆₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
29	#398×C₆₇	—	2	2	no	—
30	#397×C₆₇	—	2	2	no	—
31	#391×C₆₇	C₂²	1	1	yes	characteristic
32	#391×C₆₇	C₂²	1	1	yes	characteristic
33	#382×C₆₇	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
35	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₆₇	—	2	2	no	—
38	#340×C₆₇	C₂²	1	2	yes	—
39	#340×C₆₇	C₂²	1	2	yes	—
40	#336×C₆₇	C₂²	1	2	yes	—
41	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	—	2	1	no	—
44	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₆₇	—	2	4	no	—
48	C₂²⋊Q₈×C₆₇	—	2	2	no	—
49	C₂²⋊Q₈×C₆₇	—	2	2	no	—
50	C₂²⋊Q₈×C₆₇	—	2	2	no	—
51	C₂²⋊Q₈×C₆₇	—	2	2	no	—
52	#117×C₆₇	—	2	4	no	—
53	#117×C₆₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₆₇	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
69	C₂×C₄²×C₆₇	—	2	1	no	—
70	C₂×C₄²×C₆₇	—	2	2	no	—
71	C₂×C₄²×C₆₇	—	2	2	no	—
72	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
74	#107×C₆₇	—	2	4	no	—
75	#106×C₆₇	—	2	4	no	—
76	C₄⋊C₈×C₆₇	—	2	4	no	—
77	#103×C₆₇	—	2	4	no	—
78	#103×C₆₇	—	2	4	no	—
79	#103×C₆₇	—	2	4	no	—
80	#103×C₆₇	—	2	4	no	—
81	C₂²⋊C₈×C₆₇	—	2	2	no	—
82	C₂²⋊C₈×C₆₇	—	2	2	no	—
83	#95×C₆₇	—	2	2	no	—
84	#95×C₆₇	—	2	2	no	—
85	#95×C₆₇	—	2	2	no	—
86	#95×C₆₇	—	2	2	no	—
87	#95×C₆₇	—	2	2	no	—
88	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₆₇	—	2	1	no	—
90	C₂×Q₈×C₆₇	—	2	1	no	—
91	C₂×Q₈×C₆₇	—	2	2	no	—
92	C₂×Q₈×C₆₇	—	2	2	no	—
93	C₂×Q₈×C₆₇	—	2	1	no	—
94	C₂×Q₈×C₆₇	—	2	1	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂×Q₈×C₆₇	—	2	2	no	—
97	C₂²×C₄×C₆₇	—	2	2	no	—
98	C₂²×C₄×C₆₇	—	2	2	no	—
99	C₂²×C₄×C₆₇	—	2	2	no	—
100	C₂²×C₄×C₆₇	—	2	2	no	—
101	C₂²×C₄×C₆₇	—	2	4	no	—
102	C₂²×C₄×C₆₇	—	2	1	no	—
103	C₂²×C₄×C₆₇	—	2	1	no	—
104	C₂²×C₄×C₆₇	—	2	1	no	—
105	C₂²×C₄×C₆₇	—	2	1	no	—
106	C₂²×C₄×C₆₇	—	8	2	no	—
107	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₇	#41	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₆₇	—	2	2	no	—
114	C₂×C₈×C₆₇	—	2	2	no	—
115	C₂×C₈×C₆₇	—	2	2	no	—
116	C₂×C₈×C₆₇	—	2	2	no	—
117	C₂×C₈×C₆₇	—	2	2	no	—
118	C₂×C₈×C₆₇	—	2	2	no	—
119	C₄⋊C₄×C₆₇	—	2	4	no	—
120	C₄⋊C₄×C₆₇	—	2	4	no	—
121	C₄⋊C₄×C₆₇	—	2	2	no	—
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	—	2	1	no	—
124	C₄⋊C₄×C₆₇	—	2	1	no	—
125	C₄⋊C₄×C₆₇	—	2	1	no	—
126	C₄⋊C₄×C₆₇	—	2	1	no	—
127	C₄⋊C₄×C₆₇	—	4	2	no	—
128	C₄⋊C₄×C₆₇	—	4	2	no	—
129	C₄⋊C₄×C₆₇	—	4	4	no	—
130	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₆₇	#41	1	4	yes	—
132	C₂²⋊C₄×C₆₇	—	2	4	no	—
133	C₂²⋊C₄×C₆₇	—	2	4	no	—
134	C₂²⋊C₄×C₆₇	—	4	2	no	—
135	C₂²⋊C₄×C₆₇	—	4	2	no	—
136	C₄²×C₆₇	—	2	4	no	—
137	C₄²×C₆₇	—	2	2	no	—
138	C₄²×C₆₇	—	8	2	no	—
139	C₄²×C₆₇	—	8	2	no	—
140	C₄²×C₆₇	#41	1	4	yes	—
141	C₂³×C₆₇	—	2	1	no	—
142	C₂³×C₆₇	—	2	1	no	—
143	C₂³×C₆₇	—	2	2	no	—
144	C₂³×C₆₇	—	2	2	no	—
145	C₂³×C₆₇	#121	1	2	yes	—
146	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₆₇	—	4	2	no	—
148	Q₈×C₆₇	—	4	2	no	—
149	Q₈×C₆₇	—	4	2	no	—
150	Q₈×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	—	2	1	no	—
152	C₂×C₄×C₆₇	—	2	1	no	—
153	C₂×C₄×C₆₇	—	2	2	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	4	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	2	2	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	4	2	no	—
163	C₂×C₄×C₆₇	—	4	2	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	—	4	2	no	—
166	C₂×C₄×C₆₇	—	4	1	no	—
167	C₂×C₄×C₆₇	—	4	1	no	—
168	C₂×C₄×C₆₇	—	4	1	no	—
169	C₂×C₄×C₆₇	—	4	1	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	1	no	—
174	C₂×C₄×C₆₇	—	4	2	no	—
175	C₂×C₄×C₆₇	—	4	2	no	—
176	C₂×C₄×C₆₇	—	8	4	no	—
177	C₂×C₄×C₆₇	#121	1	2	yes	—
178	C₂×C₄×C₆₇	#123	1	4	yes	—
179	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
182	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
183	C₈×C₆₇	—	4	2	no	—
184	C₈×C₆₇	—	4	2	no	—
185	C₂²×C₆₇	—	2	2	no	—
186	C₂²×C₆₇	—	2	2	no	—
187	C₂²×C₆₇	—	2	2	no	—
188	C₂²×C₆₇	—	4	2	no	—
189	C₂²×C₆₇	—	4	2	no	—
190	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
191	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
192	C₂²×C₆₇	#525	1	1	yes	characteristic
193	C₂²×C₆₇	#577	1	2	yes	—
194	C₂²×C₆₇	#578	1	2	yes	—
195	C₄×C₆₇	—	2	4	no	—
196	C₄×C₆₇	—	2	2	no	—
197	C₄×C₆₇	—	4	2	no	—
198	C₄×C₆₇	—	4	4	no	—
199	C₄×C₆₇	—	4	4	no	—
200	C₄×C₆₇	—	8	1	no	—
201	C₄×C₆₇	—	8	1	no	—
202	C₄×C₆₇	—	8	1	no	—
203	C₄×C₆₇	—	8	1	no	—
204	C₄×C₆₇	#529	1	2	yes	—
205	C₄×C₆₇	#532	1	2	yes	—
206	#33119	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₆₇	—	4	2	no	—
208	C₂×C₆₇	#2854	1	1	yes	characteristic
209	C₂×C₆₇	#3042	1	1	yes	characteristic
210	C₂×C₆₇	#3044	1	1	yes	characteristic
211	C₂×C₆₇	#3097	1	2	yes	—
212	C₂×C₆₇	#3120	1	2	yes	—
213	C₂×#484	C₂×C₆₇	1	1	yes	characteristic
214	C₂×#483	C₂×C₆₇	1	1	yes	characteristic
215	#2621	C₂×C₆₇	1	1	yes	characteristic
216	#2274	C₂×C₆₇	1	1	yes	characteristic
217	#1981	C₂×C₆₇	1	2	yes	complemented
218	#1949	C₂×C₆₇	1	2	yes	complemented
219	#1928	C₂×C₆₇	1	2	yes	complemented
220	#1927	C₂×C₆₇	1	2	yes	complemented
221	#1873	C₂×C₆₇	1	1	yes	characteristic
222	#1873	C₂×C₆₇	1	1	yes	characteristic
223	#1798	C₂×C₆₇	1	1	yes	characteristic
224	C₆₇	#33119	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
226	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
228	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
229	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
231	#484	—	2	4	no	—
232	#483	—	2	4	no	—
233	C₂×#107	C₂²×C₆₇	1	2	yes	—
234	C₂×#106	C₂²×C₆₇	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
236	C₂×#103	C₂²×C₆₇	1	2	yes	—
237	C₂×#103	C₂²×C₆₇	1	2	yes	—
238	C₂×#103	C₂²×C₆₇	1	2	yes	—
239	C₂×#103	C₂²×C₆₇	1	2	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
241	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
242	#398	—	2	2	no	—
243	#397	—	2	2	no	—
244	#391	C₂²×C₆₇	1	1	yes	characteristic
245	#391	C₂²×C₆₇	1	1	yes	characteristic
246	#382	C₂²×C₆₇	1	1	yes	characteristic
247	C₄×C₄⋊C₄	—	2	2	no	—
248	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
249	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
250	C₄×C₂²⋊C₄	—	2	2	no	—
251	#340	C₂²×C₆₇	1	2	yes	—
252	#340	C₂²×C₆₇	1	2	yes	—
253	#336	C₂²×C₆₇	1	2	yes	—
254	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
255	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
259	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
260	C₄⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	C₂²⋊Q₈	—	2	2	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	C₂²⋊Q₈	—	2	2	no	—
265	#117	—	2	4	no	—
266	#117	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
273	C₂×C₄⋊C₄	D₄×C₆₇	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
287	#107	—	2	4	no	—
288	#106	—	2	4	no	—
289	C₄⋊C₈	—	2	4	no	—
290	#103	—	2	4	no	—
291	#103	—	2	4	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	8	2	no	—
320	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
324	C₂²×C₄	#41×C₆₇	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
344	C₄⋊C₄	#41×C₆₇	1	4	yes	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	8	2	no	—
352	C₄²	—	8	2	no	—
353	C₄²	#41×C₆₇	1	4	yes	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	#121×C₆₇	1	2	yes	—
359	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	8	4	no	—
390	C₂×C₄	#121×C₆₇	1	2	yes	—
391	C₂×C₄	#123×C₆₇	1	4	yes	—
392	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
395	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
404	C₂²	C₂×#123×C₆₇	1	1	yes	characteristic
405	C₂²	#525×C₆₇	1	1	yes	characteristic
406	C₂²	#577×C₆₇	1	2	yes	—
407	C₂²	#578×C₆₇	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	4	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	#529×C₆₇	1	2	yes	—
418	C₄	#532×C₆₇	1	2	yes	—
419	C₂	—	4	2	no	—
420	C₂	C₆₇×#2854	1	1	yes	characteristic
421	C₂	C₆₇×#3042	1	1	yes	characteristic
422	C₂	C₆₇×#3044	1	1	yes	characteristic
423	C₂	C₆₇×#3097	1	2	yes	—
424	C₂	C₆₇×#3120	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₇×#1981	C₂	semidirect
6. C₆₇×#1949	C₂	semidirect
7. C₆₇×#1928	C₂	semidirect
8. C₆₇×#1927	C₂	semidirect
206. #33119	C₆₇	direct (N × H)
217. #1981	C₂×C₆₇	semidirect
218. #1949	C₂×C₆₇	semidirect
219. #1928	C₂×C₆₇	semidirect
220. #1927	C₂×C₆₇	semidirect
224. C₆₇	#33119	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×#484×C₆₇	2
C₂×#483×C₆₇	2
C₆₇×#2621	2
C₆₇×#2274	2
C₆₇×#1981	2
C₆₇×#1949	2
C₆₇×#1928	2
C₆₇×#1927	2
C₆₇×#1873	2
C₆₇×#1798	2
#33119	67

Subgroups — C67×#33119 #30712370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33119 #30712370