Subgroups — C₆₇×#21530 #30700781

Order 17152.

954 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#467×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#441×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2323	C₂	1	2	yes	maximal
5	C₆₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1933	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1894	C₂	1	2	yes	maximal
9	C₆₇×#1807	C₂	1	1	yes	maximal, characteristic
10	C₆₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
17	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
18	#467×C₆₇	C₄	1	8	yes	complemented
19	#441×C₆₇	—	2	4	no	—
20	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
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	#405×C₆₇	—	2	4	no	—
27	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
31	#391×C₆₇	C₂²	1	2	yes	—
32	#389×C₆₇	—	2	2	no	—
33	#389×C₆₇	C₂²	1	2	yes	—
34	#388×C₆₇	—	2	2	no	—
35	#388×C₆₇	—	2	2	no	—
36	#387×C₆₇	—	2	2	no	—
37	#380×C₆₇	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
39	#340×C₆₇	C₂²	1	2	yes	—
40	#340×C₆₇	C₂²	1	2	yes	—
41	#340×C₆₇	C₂²	1	2	yes	—
42	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₆₇	—	2	2	no	—
45	C₂×Q₁₆×C₆₇	—	2	2	no	—
46	C₂×Q₁₆×C₆₇	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₆₇	—	2	2	no	—
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂×M₁₆×C₆₇	—	2	2	no	—
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂²×C₈×C₆₇	—	2	2	no	—
52	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
57	C₂²⋊Q₈×C₆₇	—	2	4	no	—
58	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
59	C₄×Q₈×C₆₇	—	2	4	no	—
60	C₄×Q₈×C₆₇	—	2	4	no	—
61	#117×C₆₇	—	2	2	no	—
62	#117×C₆₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
73	C₂×C₄²×C₆₇	—	2	2	no	—
74	C₂×C₄²×C₆₇	—	2	2	no	—
75	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
77	#107×C₆₇	C₂×C₄	1	4	yes	—
78	#106×C₆₇	—	2	2	no	—
79	#106×C₆₇	—	2	2	no	—
80	#103×C₆₇	—	2	4	no	—
81	#103×C₆₇	—	2	4	no	—
82	#103×C₆₇	C₂×C₄	1	8	yes	—
83	#97×C₆₇	—	2	2	no	—
84	#97×C₆₇	D₄	1	4	yes	—
85	C₄×C₈×C₆₇	—	2	2	no	—
86	C₄×C₈×C₆₇	—	2	2	no	—
87	#95×C₆₇	—	2	2	no	—
88	#95×C₆₇	—	2	2	no	—
89	#95×C₆₇	—	2	2	no	—
90	#95×C₆₇	—	2	2	no	—
91	#95×C₆₇	—	2	2	no	—
92	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₆₇	—	2	2	no	—
94	C₂×Q₈×C₆₇	—	2	2	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂×Q₈×C₆₇	—	2	2	no	—
97	C₂×Q₈×C₆₇	—	2	2	no	—
98	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₆₇	—	2	1	no	—
100	C₂²×C₄×C₆₇	—	2	1	no	—
101	C₂²×C₄×C₆₇	—	2	1	no	—
102	C₂²×C₄×C₆₇	—	2	1	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	C₂²×C₄×C₆₇	—	2	2	no	—
105	C₂²×C₄×C₆₇	—	2	2	no	—
106	C₂²×C₄×C₆₇	—	2	2	no	—
107	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
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	Q₁₆×C₆₇	—	2	8	no	—
114	M₁₆×C₆₇	—	2	8	no	—
115	C₂×C₈×C₆₇	—	2	1	no	—
116	C₂×C₈×C₆₇	—	2	1	no	—
117	C₂×C₈×C₆₇	—	2	1	no	—
118	C₂×C₈×C₆₇	—	2	1	no	—
119	C₂×C₈×C₆₇	—	2	1	no	—
120	C₂×C₈×C₆₇	—	2	1	no	—
121	C₂×C₈×C₆₇	—	2	8	no	—
122	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₆₇	#41	1	2	yes	—
127	C₂×C₈×C₆₇	#41	1	2	yes	—
128	C₄⋊C₄×C₆₇	—	2	8	no	—
129	C₄⋊C₄×C₆₇	—	2	4	no	—
130	C₄⋊C₄×C₆₇	—	2	2	no	—
131	C₄⋊C₄×C₆₇	—	2	2	no	—
132	C₄⋊C₄×C₆₇	—	2	2	no	—
133	C₄⋊C₄×C₆₇	—	2	2	no	—
134	C₄⋊C₄×C₆₇	—	2	2	no	—
135	C₄⋊C₄×C₆₇	—	4	4	no	—
136	C₄⋊C₄×C₆₇	—	8	2	no	—
137	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
138	C₂²⋊C₄×C₆₇	—	2	8	no	—
139	C₂²⋊C₄×C₆₇	—	2	4	no	—
140	C₂²⋊C₄×C₆₇	—	8	2	no	—
141	C₄²×C₆₇	—	2	1	no	—
142	C₄²×C₆₇	—	2	1	no	—
143	C₄²×C₆₇	—	4	4	no	—
144	C₄²×C₆₇	—	8	2	no	—
145	C₄²×C₆₇	C₂×D₄	1	2	yes	—
146	C₄²×C₆₇	#41	1	2	yes	—
147	C₂³×C₆₇	—	2	1	no	—
148	C₂³×C₆₇	—	2	1	no	—
149	C₂³×C₆₇	—	2	2	no	—
150	C₂³×C₆₇	—	2	2	no	—
151	C₂³×C₆₇	C₄×D₄	1	2	yes	—
152	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₆₇	—	2	4	no	—
154	Q₈×C₆₇	—	2	4	no	—
155	Q₈×C₆₇	—	4	2	no	—
156	Q₈×C₆₇	—	4	2	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	2	2	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	2	no	—
169	C₂×C₄×C₆₇	—	2	2	no	—
170	C₂×C₄×C₆₇	—	4	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	2	no	—
176	C₂×C₄×C₆₇	—	4	2	no	—
177	C₂×C₄×C₆₇	—	4	2	no	—
178	C₂×C₄×C₆₇	—	4	2	no	—
179	C₂×C₄×C₆₇	—	4	2	no	—
180	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₆₇	#121	1	4	yes	—
182	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
188	C₈×C₆₇	—	2	2	no	—
189	C₈×C₆₇	—	2	2	no	—
190	C₈×C₆₇	—	2	2	no	—
191	C₈×C₆₇	C₄×D₄	1	4	yes	—
192	C₂²×C₆₇	—	2	2	no	—
193	C₂²×C₆₇	—	2	2	no	—
194	C₂²×C₆₇	—	2	2	no	—
195	C₂²×C₆₇	—	4	2	no	—
196	C₂²×C₆₇	—	4	2	no	—
197	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
199	C₂²×C₆₇	#532	1	1	yes	characteristic
200	C₂²×C₆₇	#577	1	2	yes	—
201	C₂²×C₆₇	#578	1	2	yes	—
202	C₄×C₆₇	—	2	4	no	—
203	C₄×C₆₇	—	2	2	no	—
204	C₄×C₆₇	—	4	4	no	—
205	C₄×C₆₇	—	4	2	no	—
206	C₄×C₆₇	—	4	4	no	—
207	C₄×C₆₇	—	8	2	no	—
208	C₄×C₆₇	—	8	2	no	—
209	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
211	C₄×C₆₇	#525	1	1	yes	characteristic
212	C₄×C₆₇	#529	1	1	yes	characteristic
213	#21530	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₆₇	—	4	2	no	—
215	C₂×C₆₇	C₄×#121	1	1	yes	characteristic
216	C₂×C₆₇	#2950	1	1	yes	characteristic
217	C₂×C₆₇	#2952	1	1	yes	characteristic
218	C₂×C₆₇	#3063	1	2	yes	—
219	C₂×C₆₇	#3178	1	2	yes	—
220	C₂×#467	C₂×C₆₇	1	1	yes	characteristic
221	C₂×#441	C₂×C₆₇	1	1	yes	characteristic, complemented
222	C₂×#405	C₂×C₆₇	1	1	yes	characteristic
223	#2323	C₂×C₆₇	1	2	yes	—
224	#1971	C₂×C₆₇	1	1	yes	characteristic, complemented
225	#1943	C₂×C₆₇	1	1	yes	characteristic, complemented
226	#1933	C₂×C₆₇	1	2	yes	complemented
227	#1894	C₂×C₆₇	1	2	yes	—
228	#1807	C₂×C₆₇	1	1	yes	characteristic
229	#1776	C₂×C₆₇	1	1	yes	characteristic, complemented
230	C₄×#103	C₂×C₆₇	1	2	yes	complemented
231	C₆₇	#21530	1	1	yes	characteristic, direct product factor, Sylow
232	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
233	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
234	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
236	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
237	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
238	#467	C₄×C₆₇	1	8	yes	complemented
239	#441	—	2	4	no	—
240	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
241	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
242	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
243	C₂×#103	C₂²×C₆₇	1	2	yes	—
244	C₂×#103	C₂²×C₆₇	1	2	yes	—
245	C₂×#103	C₂²×C₆₇	1	2	yes	—
246	#405	—	2	4	no	—
247	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
248	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
251	#391	C₂²×C₆₇	1	2	yes	—
252	#389	—	2	2	no	—
253	#389	C₂²×C₆₇	1	2	yes	—
254	#388	—	2	2	no	—
255	#388	—	2	2	no	—
256	#387	—	2	2	no	—
257	#380	C₂²×C₆₇	1	2	yes	—
258	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
259	#340	C₂²×C₆₇	1	2	yes	—
260	#340	C₂²×C₆₇	1	2	yes	—
261	#340	C₂²×C₆₇	1	2	yes	—
262	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
263	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	C₂×C₄×C₆₇	1	4	yes	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
273	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
277	C₂²⋊Q₈	—	2	4	no	—
278	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	4	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
297	#107	C₂×C₄×C₆₇	1	4	yes	—
298	#106	—	2	2	no	—
299	#106	—	2	2	no	—
300	#103	—	2	4	no	—
301	#103	—	2	4	no	—
302	#103	C₂×C₄×C₆₇	1	8	yes	—
303	#97	—	2	2	no	—
304	#97	D₄×C₆₇	1	4	yes	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
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	C₂²×C₄×C₆₇	1	4	yes	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
331	C₂²×C₄	#41×C₆₇	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
333	Q₁₆	—	2	8	no	—
334	M₁₆	—	2	8	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	8	no	—
342	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
343	C₂×C₈	C₂²×C₄×C₆₇	1	2	yes	—
344	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
345	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
346	C₂×C₈	#41×C₆₇	1	2	yes	—
347	C₂×C₈	#41×C₆₇	1	2	yes	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	8	2	no	—
365	C₄²	C₂×D₄×C₆₇	1	2	yes	—
366	C₄²	#41×C₆₇	1	2	yes	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	C₄×D₄×C₆₇	1	2	yes	—
372	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	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	2	no	—
400	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
401	C₂×C₄	#121×C₆₇	1	4	yes	—
402	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	C₄×D₄×C₆₇	1	4	yes	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
418	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
419	C₂²	#532×C₆₇	1	1	yes	characteristic
420	C₂²	#577×C₆₇	1	2	yes	—
421	C₂²	#578×C₆₇	1	2	yes	—
422	C₄	—	2	4	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
430	C₄	C₄×#41×C₆₇	1	1	yes	characteristic
431	C₄	#525×C₆₇	1	1	yes	characteristic
432	C₄	#529×C₆₇	1	1	yes	characteristic
433	C₂	—	4	2	no	—
434	C₂	C₄×#121×C₆₇	1	1	yes	characteristic
435	C₂	C₆₇×#2950	1	1	yes	characteristic
436	C₂	C₆₇×#2952	1	1	yes	characteristic
437	C₂	C₆₇×#3063	1	2	yes	—
438	C₂	C₆₇×#3178	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂×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×#441×C₆₇	C₂	semidirect
5. C₆₇×#1971	C₂	semidirect
6. C₆₇×#1943	C₂	semidirect
7. C₆₇×#1933	C₂	semidirect
10. C₆₇×#1776	C₂	semidirect
11. C₄×#103×C₆₇	C₂	semidirect
18. #467×C₆₇	C₄	semidirect
213. #21530	C₆₇	direct (N × H)
221. C₂×#441	C₂×C₆₇	semidirect
224. #1971	C₂×C₆₇	semidirect
225. #1943	C₂×C₆₇	semidirect
226. #1933	C₂×C₆₇	semidirect
229. #1776	C₂×C₆₇	semidirect
230. C₄×#103	C₂×C₆₇	semidirect
231. C₆₇	#21530	direct (N × H)
238. #467	C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#467×C₆₇	2
C₂×#441×C₆₇	2
C₂×#405×C₆₇	2
C₆₇×#2323	2
C₆₇×#1971	2
C₆₇×#1943	2
C₆₇×#1933	2
C₆₇×#1894	2
C₆₇×#1807	2
C₆₇×#1776	2
C₄×#103×C₆₇	2
#21530	67

Subgroups — C67×#21530 #30700781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21530 #30700781