Subgroups — C₆₇×#33121 #30712372

Order 17152.

872 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#481×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2620	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2274	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1983	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1948	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1927	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1926	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1875	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#121×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	#483×C₆₇	—	2	4	no	—
19	#481×C₆₇	—	2	4	no	—
20	C₂×#106×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×#102×C₆₇	C₂²	1	2	yes	—
26	C₂×#102×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	#396×C₆₇	—	2	2	no	—
30	#394×C₆₇	—	2	2	no	—
31	#391×C₆₇	C₂²	1	1	yes	characteristic
32	#390×C₆₇	C₂²	1	1	yes	characteristic
33	#384×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×D₄×C₆₇	—	2	1	no	—
43	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	—	2	1	no	—
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
48	#124×C₆₇	—	2	4	no	—
49	C₂²⋊Q₈×C₆₇	—	2	2	no	—
50	C₂²⋊Q₈×C₆₇	—	2	2	no	—
51	#121×C₆₇	—	2	2	no	—
52	#121×C₆₇	—	2	2	no	—
53	#117×C₆₇	—	2	4	no	—
54	#117×C₆₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	2	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	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
71	C₂×C₄²×C₆₇	—	2	1	no	—
72	C₂×C₄²×C₆₇	—	2	2	no	—
73	C₂×C₄²×C₆₇	—	2	2	no	—
74	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	#106×C₆₇	—	2	4	no	—
77	#106×C₆₇	—	2	4	no	—
78	C₄⋊C₈×C₆₇	—	2	4	no	—
79	#103×C₆₇	—	2	4	no	—
80	#103×C₆₇	—	2	4	no	—
81	#102×C₆₇	—	2	4	no	—
82	#102×C₆₇	—	2	4	no	—
83	C₂²⋊C₈×C₆₇	—	2	2	no	—
84	C₂²⋊C₈×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	—	2	1	no	—
89	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₆₇	—	2	1	no	—
91	C₂×Q₈×C₆₇	—	2	2	no	—
92	C₂×Q₈×C₆₇	—	2	1	no	—
93	C₂×Q₈×C₆₇	—	2	2	no	—
94	C₂×D₄×C₆₇	—	2	1	no	—
95	C₂×D₄×C₆₇	—	2	2	no	—
96	C₂×D₄×C₆₇	—	2	1	no	—
97	C₂×D₄×C₆₇	—	2	2	no	—
98	C₂×D₄×C₆₇	—	4	2	no	—
99	C₂×D₄×C₆₇	—	8	2	no	—
100	C₂²×C₄×C₆₇	—	2	2	no	—
101	C₂²×C₄×C₆₇	—	2	2	no	—
102	C₂²×C₄×C₆₇	—	2	2	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	C₂²×C₄×C₆₇	—	2	4	no	—
105	C₂²×C₄×C₆₇	—	2	1	no	—
106	C₂²×C₄×C₆₇	—	2	1	no	—
107	C₂²×C₄×C₆₇	—	2	1	no	—
108	C₂²×C₄×C₆₇	—	8	2	no	—
109	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₆₇	#41	1	2	yes	—
114	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₆₇	—	2	2	no	—
120	C₂×C₈×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	2	4	no	—
122	C₄⋊C₄×C₆₇	—	2	4	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₄⋊C₄×C₆₇	—	2	2	no	—
125	C₄⋊C₄×C₆₇	—	2	1	no	—
126	C₄⋊C₄×C₆₇	—	2	1	no	—
127	C₄⋊C₄×C₆₇	—	2	1	no	—
128	C₄⋊C₄×C₆₇	—	2	1	no	—
129	C₄⋊C₄×C₆₇	—	4	2	no	—
130	C₄⋊C₄×C₆₇	—	8	2	no	—
131	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₆₇	#41	1	4	yes	—
133	C₂²⋊C₄×C₆₇	—	2	4	no	—
134	C₂²⋊C₄×C₆₇	—	2	4	no	—
135	C₂²⋊C₄×C₆₇	—	4	2	no	—
136	C₂²⋊C₄×C₆₇	—	4	2	no	—
137	C₂²⋊C₄×C₆₇	—	4	4	no	—
138	C₂²⋊C₄×C₆₇	—	8	2	no	—
139	C₄²×C₆₇	—	2	4	no	—
140	C₄²×C₆₇	—	2	2	no	—
141	C₄²×C₆₇	—	8	2	no	—
142	C₄²×C₆₇	—	8	2	no	—
143	C₄²×C₆₇	#41	1	4	yes	—
144	C₂³×C₆₇	—	2	1	no	—
145	C₂³×C₆₇	—	2	1	no	—
146	C₂³×C₆₇	—	2	2	no	—
147	C₂³×C₆₇	—	2	2	no	—
148	C₂³×C₆₇	—	4	1	no	—
149	C₂³×C₆₇	—	4	1	no	—
150	C₂³×C₆₇	—	4	1	no	—
151	C₂³×C₆₇	—	4	2	no	—
152	C₂³×C₆₇	—	4	2	no	—
153	C₂³×C₆₇	#121	1	2	yes	—
154	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₆₇	—	4	2	no	—
156	Q₈×C₆₇	—	4	2	no	—
157	D₄×C₆₇	—	4	2	no	—
158	D₄×C₆₇	—	4	2	no	—
159	D₄×C₆₇	—	8	4	no	—
160	C₂×C₄×C₆₇	—	2	1	no	—
161	C₂×C₄×C₆₇	—	2	1	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	2	4	no	—
165	C₂×C₄×C₆₇	—	2	4	no	—
166	C₂×C₄×C₆₇	—	2	4	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	2	4	no	—
169	C₂×C₄×C₆₇	—	2	2	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	4	2	no	—
172	C₂×C₄×C₆₇	—	4	2	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	—	4	2	no	—
175	C₂×C₄×C₆₇	—	4	1	no	—
176	C₂×C₄×C₆₇	—	4	1	no	—
177	C₂×C₄×C₆₇	—	4	1	no	—
178	C₂×C₄×C₆₇	—	4	1	no	—
179	C₂×C₄×C₆₇	—	4	1	no	—
180	C₂×C₄×C₆₇	—	4	2	no	—
181	C₂×C₄×C₆₇	—	4	2	no	—
182	C₂×C₄×C₆₇	—	8	4	no	—
183	C₂×C₄×C₆₇	#121	1	2	yes	—
184	C₂×C₄×C₆₇	#123	1	4	yes	—
185	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
188	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
189	C₈×C₆₇	—	4	2	no	—
190	C₈×C₆₇	—	4	2	no	—
191	C₂²×C₆₇	—	2	2	no	—
192	C₂²×C₆₇	—	2	2	no	—
193	C₂²×C₆₇	—	2	2	no	—
194	C₂²×C₆₇	—	4	2	no	—
195	C₂²×C₆₇	—	4	2	no	—
196	C₂²×C₆₇	—	8	2	no	—
197	C₂²×C₆₇	—	8	1	no	—
198	C₂²×C₆₇	—	8	2	no	—
199	C₂²×C₆₇	—	8	1	no	—
200	C₂²×C₆₇	—	8	1	no	—
201	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
202	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
203	C₂²×C₆₇	#525	1	1	yes	characteristic
204	C₂²×C₆₇	#577	1	2	yes	—
205	C₂²×C₆₇	#577	1	2	yes	—
206	C₄×C₆₇	—	2	4	no	—
207	C₄×C₆₇	—	2	2	no	—
208	C₄×C₆₇	—	4	2	no	—
209	C₄×C₆₇	—	4	4	no	—
210	C₄×C₆₇	—	4	4	no	—
211	C₄×C₆₇	—	8	1	no	—
212	C₄×C₆₇	—	8	1	no	—
213	C₄×C₆₇	—	8	1	no	—
214	C₄×C₆₇	#529	1	2	yes	—
215	C₄×C₆₇	#532	1	2	yes	—
216	#33121	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂×C₆₇	—	4	2	no	—
218	C₂×C₆₇	—	16	1	no	—
219	C₂×C₆₇	#2854	1	1	yes	characteristic
220	C₂×C₆₇	#3042	1	1	yes	characteristic
221	C₂×C₆₇	#3043	1	1	yes	characteristic
222	C₂×C₆₇	#3099	1	2	yes	—
223	C₂×C₆₇	#3125	1	2	yes	—
224	C₂×#481	C₂×C₆₇	1	1	yes	characteristic
225	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
226	#2620	C₂×C₆₇	1	1	yes	characteristic
227	#2274	C₂×C₆₇	1	1	yes	characteristic, complemented
228	#1983	C₂×C₆₇	1	2	yes	complemented
229	#1948	C₂×C₆₇	1	2	yes	complemented
230	#1927	C₂×C₆₇	1	2	yes	complemented
231	#1926	C₂×C₆₇	1	2	yes	complemented
232	#1875	C₂×C₆₇	1	1	yes	characteristic
233	#1873	C₂×C₆₇	1	1	yes	characteristic, complemented
234	#1798	C₂×C₆₇	1	1	yes	characteristic, complemented
235	C₆₇	#33121	1	1	yes	characteristic, direct product factor, Sylow
236	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
238	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
239	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
240	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
242	#483	—	2	4	no	—
243	#481	—	2	4	no	—
244	C₂×#106	C₂²×C₆₇	1	2	yes	—
245	C₂×#106	C₂²×C₆₇	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
247	C₂×#103	C₂²×C₆₇	1	2	yes	—
248	C₂×#103	C₂²×C₆₇	1	2	yes	—
249	C₂×#102	C₂²×C₆₇	1	2	yes	—
250	C₂×#102	C₂²×C₆₇	1	2	yes	—
251	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
253	#396	—	2	2	no	—
254	#394	—	2	2	no	—
255	#391	C₂²×C₆₇	1	1	yes	characteristic
256	#390	C₂²×C₆₇	1	1	yes	characteristic
257	#384	C₂²×C₆₇	1	1	yes	characteristic
258	C₄×C₄⋊C₄	—	2	2	no	—
259	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
260	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
261	C₄×C₂²⋊C₄	—	2	2	no	—
262	#340	C₂²×C₆₇	1	2	yes	—
263	#340	C₂²×C₆₇	1	2	yes	—
264	#336	C₂²×C₆₇	1	2	yes	—
265	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
271	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
272	#124	—	2	4	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	#121	—	2	2	no	—
276	#121	—	2	2	no	—
277	#117	—	2	4	no	—
278	#117	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
284	C₂×C₄⋊C₄	D₄×C₆₇	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
300	#106	—	2	4	no	—
301	#106	—	2	4	no	—
302	C₄⋊C₈	—	2	4	no	—
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	4	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂⁴	—	2	1	no	—
313	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
337	C₂²×C₄	#41×C₆₇	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
356	C₄⋊C₄	#41×C₆₇	1	4	yes	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	8	2	no	—
366	C₄²	—	8	2	no	—
367	C₄²	#41×C₆₇	1	4	yes	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	#121×C₆₇	1	2	yes	—
378	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	4	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	#121×C₆₇	1	2	yes	—
408	C₂×C₄	#123×C₆₇	1	4	yes	—
409	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
412	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
426	C₂²	C₂×#123×C₆₇	1	1	yes	characteristic
427	C₂²	#525×C₆₇	1	1	yes	characteristic
428	C₂²	#577×C₆₇	1	2	yes	—
429	C₂²	#577×C₆₇	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	4	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	#529×C₆₇	1	2	yes	—
439	C₄	#532×C₆₇	1	2	yes	—
440	C₂	—	4	2	no	—
441	C₂	—	16	1	no	—
442	C₂	C₆₇×#2854	1	1	yes	characteristic
443	C₂	C₆₇×#3042	1	1	yes	characteristic
444	C₂	C₆₇×#3043	1	1	yes	characteristic
445	C₂	C₆₇×#3099	1	2	yes	—
446	C₂	C₆₇×#3125	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂×#121×C₆₇	C₂²
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
2. C₂×#483×C₆₇	C₂	semidirect
4. C₆₇×#2274	C₂	semidirect
5. C₆₇×#1983	C₂	semidirect
6. C₆₇×#1948	C₂	semidirect
7. C₆₇×#1927	C₂	semidirect
8. C₆₇×#1926	C₂	semidirect
10. C₆₇×#1873	C₂	semidirect
11. C₆₇×#1798	C₂	semidirect
216. #33121	C₆₇	direct (N × H)
225. C₂×#483	C₂×C₆₇	semidirect
227. #2274	C₂×C₆₇	semidirect
228. #1983	C₂×C₆₇	semidirect
229. #1948	C₂×C₆₇	semidirect
230. #1927	C₂×C₆₇	semidirect
231. #1926	C₂×C₆₇	semidirect
233. #1873	C₂×C₆₇	semidirect
234. #1798	C₂×C₆₇	semidirect
235. C₆₇	#33121	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×#481×C₆₇	2
C₂×#483×C₆₇	2
C₆₇×#2620	2
C₆₇×#2274	2
C₆₇×#1983	2
C₆₇×#1948	2
C₆₇×#1927	2
C₆₇×#1926	2
C₆₇×#1875	2
C₆₇×#1873	2
C₆₇×#1798	2
#33121	67

Subgroups — C67×#33121 #30712372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33121 #30712372