Subgroups — C₆₇×#11091 #30690342

Order 17152.

938 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#421×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#410×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#344×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#339×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×H(3,ℤ/4)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
12	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
15	#421×C₆₇	—	2	2	no	—
16	#421×C₆₇	—	2	2	no	—
17	C₂×#104×C₆₇	—	2	2	no	—
18	C₂×#104×C₆₇	—	2	2	no	—
19	C₂×#104×C₆₇	—	2	2	no	—
20	C₂×#104×C₆₇	—	2	2	no	—
21	#410×C₆₇	—	2	2	no	—
22	#410×C₆₇	C₄	1	4	yes	complemented
23	C₂×#99×C₆₇	—	2	2	no	—
24	#389×C₆₇	—	2	2	no	—
25	#385×C₆₇	—	2	2	no	—
26	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
27	#344×C₆₇	—	2	2	no	—
28	#339×C₆₇	—	2	2	no	—
29	H(3,ℤ/4)×C₆₇	—	2	2	no	—
30	C₂×#41×C₆₇	—	2	1	no	—
31	C₂×#41×C₆₇	—	2	1	no	—
32	C₂×#41×C₆₇	—	2	1	no	—
33	C₂×#41×C₆₇	—	2	1	no	—
34	C₂×#41×C₆₇	—	2	1	no	—
35	C₂×#41×C₆₇	—	2	1	no	—
36	C₂×#41×C₆₇	—	2	1	no	—
37	C₂×#41×C₆₇	—	2	1	no	—
38	C₂×#41×C₆₇	—	2	1	no	—
39	C₂×#41×C₆₇	—	2	1	no	—
40	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
41	C₂×#41×C₆₇	D₄	1	2	yes	—
42	C₂²×Q₈×C₆₇	Q₈	1	1	yes	characteristic
43	C₂²×D₄×C₆₇	—	2	1	no	—
44	C₂²×D₄×C₆₇	Q₈	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	—	2	1	no	—
46	C₂³×C₄×C₆₇	—	2	1	no	—
47	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₆₇	—	2	1	no	—
49	C₂×M₁₆×C₆₇	—	2	1	no	—
50	C₂×M₁₆×C₆₇	—	2	1	no	—
51	C₂×M₁₆×C₆₇	—	2	1	no	—
52	C₂×M₁₆×C₆₇	—	2	1	no	—
53	C₂×M₁₆×C₆₇	—	2	1	no	—
54	C₂×M₁₆×C₆₇	—	2	1	no	—
55	C₂×M₁₆×C₆₇	—	2	1	no	—
56	C₂×M₁₆×C₆₇	—	2	1	no	—
57	C₂×M₁₆×C₆₇	—	2	1	no	—
58	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
59	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
60	C₂²×C₈×C₆₇	—	2	1	no	—
61	C₂²×C₈×C₆₇	—	2	1	no	—
62	#117×C₆₇	—	2	1	no	—
63	#117×C₆₇	—	2	1	no	—
64	#117×C₆₇	—	2	1	no	—
65	#117×C₆₇	—	2	1	no	—
66	#117×C₆₇	—	2	1	no	—
67	#117×C₆₇	—	2	1	no	—
68	#117×C₆₇	—	2	1	no	—
69	#117×C₆₇	—	2	1	no	—
70	#117×C₆₇	—	2	1	no	—
71	#117×C₆₇	C₂×C₄	1	2	yes	—
72	#117×C₆₇	C₂×C₄	1	2	yes	—
73	#117×C₆₇	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
77	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
81	C₂×C₄²×C₆₇	—	2	1	no	—
82	C₂×C₄²×C₆₇	—	2	1	no	—
83	C₂×C₄²×C₆₇	—	2	1	no	—
84	C₂×C₄²×C₆₇	—	2	1	no	—
85	C₂×C₄²×C₆₇	—	2	1	no	—
86	C₂×C₄²×C₆₇	—	2	1	no	—
87	C₂×C₄²×C₆₇	—	2	1	no	—
88	C₂×C₄²×C₆₇	D₄	1	2	yes	—
89	C₂×C₄²×C₆₇	D₄	1	2	yes	—
90	#104×C₆₇	—	2	8	no	—
91	#104×C₆₇	—	2	8	no	—
92	#99×C₆₇	—	2	8	no	—
93	#95×C₆₇	—	2	4	no	—
94	C₂⁴×C₆₇	—	2	1	no	—
95	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
96	#41×C₆₇	—	2	2	no	—
97	#41×C₆₇	—	2	2	no	—
98	#41×C₆₇	—	2	2	no	—
99	#41×C₆₇	—	2	2	no	—
100	#41×C₆₇	—	2	2	no	—
101	#41×C₆₇	—	2	2	no	—
102	#41×C₆₇	—	2	2	no	—
103	#41×C₆₇	—	2	2	no	—
104	#41×C₆₇	—	4	1	no	—
105	#41×C₆₇	—	4	1	no	—
106	#41×C₆₇	—	4	1	no	—
107	#41×C₆₇	—	4	1	no	—
108	#41×C₆₇	—	4	1	no	—
109	#41×C₆₇	—	4	1	no	—
110	#41×C₆₇	—	4	1	no	—
111	#41×C₆₇	—	4	1	no	—
112	C₂×Q₈×C₆₇	—	2	1	no	—
113	C₂×Q₈×C₆₇	—	2	1	no	—
114	C₂×Q₈×C₆₇	—	2	1	no	—
115	C₂×Q₈×C₆₇	—	2	1	no	—
116	C₂×Q₈×C₆₇	—	2	1	no	—
117	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	complemented
118	C₂×D₄×C₆₇	—	2	2	no	—
119	C₂×D₄×C₆₇	—	2	2	no	—
120	C₂×D₄×C₆₇	—	2	1	no	—
121	C₂×D₄×C₆₇	—	2	1	no	—
122	C₂×D₄×C₆₇	—	2	1	no	—
123	C₂×D₄×C₆₇	—	2	1	no	—
124	C₂×D₄×C₆₇	—	2	1	no	—
125	C₂×D₄×C₆₇	—	4	1	no	—
126	C₂×D₄×C₆₇	—	4	1	no	—
127	C₂×D₄×C₆₇	—	4	1	no	—
128	C₂×D₄×C₆₇	—	4	1	no	—
129	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	complemented
130	C₂²×C₄×C₆₇	—	2	2	no	—
131	C₂²×C₄×C₆₇	—	2	2	no	—
132	C₂²×C₄×C₆₇	—	2	1	no	—
133	C₂²×C₄×C₆₇	—	2	2	no	—
134	C₂²×C₄×C₆₇	—	2	2	no	—
135	C₂²×C₄×C₆₇	—	2	2	no	—
136	C₂²×C₄×C₆₇	—	4	4	no	—
137	C₂²×C₄×C₆₇	—	4	1	no	—
138	C₂²×C₄×C₆₇	—	4	1	no	—
139	C₂²×C₄×C₆₇	—	4	1	no	—
140	C₂²×C₄×C₆₇	—	4	1	no	—
141	C₂²×C₄×C₆₇	—	4	1	no	—
142	C₂²×C₄×C₆₇	—	4	1	no	—
143	C₂²×C₄×C₆₇	—	4	1	no	—
144	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
152	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
153	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
154	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
155	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
158	M₁₆×C₆₇	—	2	2	no	—
159	M₁₆×C₆₇	—	2	2	no	—
160	M₁₆×C₆₇	—	2	2	no	—
161	M₁₆×C₆₇	—	2	2	no	—
162	M₁₆×C₆₇	—	4	1	no	—
163	M₁₆×C₆₇	—	4	1	no	—
164	M₁₆×C₆₇	—	4	1	no	—
165	M₁₆×C₆₇	—	4	1	no	—
166	C₂×C₈×C₆₇	—	2	2	no	—
167	C₂×C₈×C₆₇	—	2	2	no	—
168	C₂×C₈×C₆₇	—	4	1	no	—
169	C₂×C₈×C₆₇	—	4	1	no	—
170	C₂×C₈×C₆₇	—	4	1	no	—
171	C₂×C₈×C₆₇	—	4	1	no	—
172	C₄⋊C₄×C₆₇	—	2	2	no	—
173	C₄⋊C₄×C₆₇	—	2	2	no	—
174	C₄⋊C₄×C₆₇	—	2	2	no	—
175	C₄⋊C₄×C₆₇	—	4	8	no	—
176	C₄⋊C₄×C₆₇	—	4	1	no	—
177	C₄⋊C₄×C₆₇	—	4	1	no	—
178	C₄⋊C₄×C₆₇	—	4	1	no	—
179	C₂²⋊C₄×C₆₇	—	2	2	no	—
180	C₂²⋊C₄×C₆₇	—	2	2	no	—
181	C₂²⋊C₄×C₆₇	—	4	1	no	—
182	C₂²⋊C₄×C₆₇	—	4	1	no	—
183	C₂²⋊C₄×C₆₇	—	4	1	no	—
184	C₂²⋊C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
185	C₄²×C₆₇	—	2	2	no	—
186	C₄²×C₆₇	—	2	2	no	—
187	C₄²×C₆₇	—	2	2	no	—
188	C₄²×C₆₇	—	2	2	no	—
189	C₄²×C₆₇	—	2	2	no	—
190	C₄²×C₆₇	—	2	2	no	—
191	C₄²×C₆₇	—	2	2	no	—
192	C₄²×C₆₇	—	4	1	no	—
193	C₄²×C₆₇	—	4	1	no	—
194	C₄²×C₆₇	—	4	1	no	—
195	C₂³×C₆₇	—	2	2	no	—
196	C₂³×C₆₇	—	4	2	no	—
197	C₂³×C₆₇	—	4	1	no	—
198	C₂³×C₆₇	—	4	1	no	—
199	C₂³×C₆₇	—	8	2	no	—
200	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₆₇	#120	1	1	yes	characteristic
202	C₂³×C₆₇	#121	1	1	yes	characteristic
203	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂³×C₆₇	#123	1	1	yes	characteristic
205	C₂³×C₆₇	#124	1	1	yes	characteristic
206	C₂³×C₆₇	#127	1	1	yes	characteristic
207	Q₈×C₆₇	—	2	2	no	—
208	Q₈×C₆₇	—	2	2	no	—
209	Q₈×C₆₇	—	4	1	no	—
210	Q₈×C₆₇	—	4	1	no	—
211	D₄×C₆₇	—	2	2	no	—
212	D₄×C₆₇	—	2	2	no	—
213	D₄×C₆₇	—	4	2	no	—
214	D₄×C₆₇	—	4	2	no	—
215	D₄×C₆₇	—	4	2	no	—
216	D₄×C₆₇	—	4	2	no	—
217	D₄×C₆₇	—	4	1	no	—
218	D₄×C₆₇	—	4	1	no	—
219	C₂×C₄×C₆₇	—	2	4	no	—
220	C₂×C₄×C₆₇	—	2	2	no	—
221	C₂×C₄×C₆₇	—	2	4	no	—
222	C₂×C₄×C₆₇	—	4	4	no	—
223	C₂×C₄×C₆₇	—	4	2	no	—
224	C₂×C₄×C₆₇	—	4	4	no	—
225	C₂×C₄×C₆₇	—	4	4	no	—
226	C₂×C₄×C₆₇	—	4	2	no	—
227	C₂×C₄×C₆₇	—	4	1	no	—
228	C₂×C₄×C₆₇	—	4	1	no	—
229	C₂×C₄×C₆₇	—	4	2	no	—
230	C₂×C₄×C₆₇	—	4	2	no	—
231	C₂×C₄×C₆₇	—	4	2	no	—
232	C₂×C₄×C₆₇	—	4	2	no	—
233	C₂×C₄×C₆₇	—	4	4	no	—
234	C₂×C₄×C₆₇	—	4	2	no	—
235	C₂×C₄×C₆₇	—	4	2	no	—
236	C₂×C₄×C₆₇	—	8	2	no	—
237	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
239	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
244	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
245	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
246	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
247	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
248	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
249	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
250	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
251	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
258	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
259	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
260	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
261	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
262	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
263	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
264	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
265	C₈×C₆₇	—	4	2	no	—
266	C₈×C₆₇	—	4	2	no	—
267	C₂²×C₆₇	—	2	2	no	—
268	C₂²×C₆₇	—	2	2	no	—
269	C₂²×C₆₇	—	2	2	no	—
270	C₂²×C₆₇	—	4	1	no	—
271	C₂²×C₆₇	—	4	1	no	—
272	C₂²×C₆₇	—	4	1	no	—
273	C₂²×C₆₇	—	4	1	no	—
274	C₂²×C₆₇	—	4	2	no	—
275	C₂²×C₆₇	—	8	2	no	—
276	C₂²×C₆₇	—	8	2	no	—
277	C₂²×C₆₇	—	8	2	no	—
278	C₂²×C₆₇	#380	1	1	yes	characteristic
279	C₂²×C₆₇	#386	1	1	yes	characteristic
280	C₂²×C₆₇	#390	1	1	yes	characteristic
281	C₂²×C₆₇	#392	1	1	yes	characteristic
282	C₂²×C₆₇	#393	1	1	yes	characteristic
283	C₂²×C₆₇	#397	1	1	yes	characteristic
284	C₂²×C₆₇	#399	1	1	yes	characteristic
285	C₄×C₆₇	—	4	4	no	—
286	C₄×C₆₇	—	4	4	no	—
287	C₄×C₆₇	—	4	2	no	—
288	C₄×C₆₇	—	8	2	no	—
289	C₄×C₆₇	—	8	2	no	—
290	C₄×C₆₇	#385	1	1	yes	characteristic
291	C₄×C₆₇	#385	1	1	yes	characteristic
292	C₄×C₆₇	#388	1	1	yes	characteristic
293	C₄×C₆₇	#388	1	1	yes	characteristic
294	C₄×C₆₇	#394	1	1	yes	characteristic
295	C₄×C₆₇	#394	1	1	yes	characteristic
296	C₄×C₆₇	#396	1	1	yes	characteristic
297	C₄×C₆₇	#396	1	1	yes	characteristic
298	#11091	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂×C₆₇	—	2	1	no	—
300	C₂×C₆₇	—	2	1	no	—
301	C₂×C₆₇	—	2	1	no	—
302	C₂×C₆₇	—	2	1	no	—
303	C₂×C₆₇	—	2	1	no	—
304	C₂×C₆₇	—	2	1	no	—
305	C₂×C₆₇	—	8	2	no	—
306	C₂×C₆₇	#1439	1	1	yes	characteristic
307	C₂×C₆₇	#2031	1	2	yes	—
308	C₂×#421	C₂×C₆₇	1	1	yes	characteristic
309	C₂²×#104	C₂×C₆₇	1	1	yes	characteristic
310	C₂×#410	C₂×C₆₇	1	1	yes	characteristic
311	#2296	C₂×C₆₇	1	1	yes	characteristic, complemented
312	C₂×#344	C₂×C₆₇	1	1	yes	characteristic, complemented
313	C₂×#339	C₂×C₆₇	1	1	yes	characteristic, complemented
314	C₂×H(3,ℤ/4)	C₂×C₆₇	1	1	yes	characteristic, complemented
315	C₆₇	#11091	1	1	yes	characteristic, direct product factor, Sylow
316	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
317	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
319	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
320	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
321	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
322	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
323	#421	—	2	2	no	—
324	#421	—	2	2	no	—
325	C₂×#104	—	2	2	no	—
326	C₂×#104	—	2	2	no	—
327	C₂×#104	—	2	2	no	—
328	C₂×#104	—	2	2	no	—
329	#410	—	2	2	no	—
330	#410	C₄×C₆₇	1	4	yes	complemented
331	C₂×#99	—	2	2	no	—
332	#389	—	2	2	no	—
333	#385	—	2	2	no	—
334	C₄×C₄⋊C₄	—	2	2	no	—
335	#344	—	2	2	no	—
336	#339	—	2	2	no	—
337	H(3,ℤ/4)	—	2	2	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
349	C₂×#41	D₄×C₆₇	1	2	yes	—
350	C₂²×Q₈	Q₈×C₆₇	1	1	yes	characteristic
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	Q₈×C₆₇	1	1	yes	characteristic
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
367	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	C₂×C₄×C₆₇	1	2	yes	—
380	#117	C₂×C₄×C₆₇	1	2	yes	—
381	#117	D₄×C₆₇	1	2	yes	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	4	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	D₄×C₆₇	1	2	yes	—
397	C₂×C₄²	D₄×C₆₇	1	2	yes	—
398	#104	—	2	8	no	—
399	#104	—	2	8	no	—
400	#99	—	2	8	no	—
401	#95	—	2	4	no	—
402	C₂⁴	—	2	1	no	—
403	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	C₄⋊C₄×C₆₇	1	2	yes	complemented
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	—	4	1	no	—
436	C₂×D₄	—	4	1	no	—
437	C₂×D₄	C₄⋊C₄×C₆₇	1	2	yes	complemented
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
460	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
461	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
462	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
463	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
464	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
465	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	M₁₆	—	4	1	no	—
473	M₁₆	—	4	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	4	8	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	—	4	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	8	2	no	—
508	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
509	C₂³	#120×C₆₇	1	1	yes	characteristic
510	C₂³	#121×C₆₇	1	1	yes	characteristic
511	C₂³	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
512	C₂³	#123×C₆₇	1	1	yes	characteristic
513	C₂³	#124×C₆₇	1	1	yes	characteristic
514	C₂³	#127×C₆₇	1	1	yes	characteristic
515	Q₈	—	2	2	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
546	C₂×C₄	#117×C₆₇	1	1	yes	characteristic
547	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
548	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
549	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
550	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
551	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
552	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
553	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
554	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
555	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
556	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
557	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
558	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
559	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
560	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
561	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
562	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
563	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
564	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
565	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
566	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
567	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
568	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
569	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
570	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
571	C₂×C₄	#126×C₆₇	1	1	yes	characteristic
572	C₂×C₄	#126×C₆₇	1	1	yes	characteristic
573	C₈	—	4	2	no	—
574	C₈	—	4	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	8	2	no	—
584	C₂²	—	8	2	no	—
585	C₂²	—	8	2	no	—
586	C₂²	#380×C₆₇	1	1	yes	characteristic
587	C₂²	#386×C₆₇	1	1	yes	characteristic
588	C₂²	#390×C₆₇	1	1	yes	characteristic
589	C₂²	#392×C₆₇	1	1	yes	characteristic
590	C₂²	#393×C₆₇	1	1	yes	characteristic
591	C₂²	#397×C₆₇	1	1	yes	characteristic
592	C₂²	#399×C₆₇	1	1	yes	characteristic
593	C₄	—	4	4	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	2	no	—
596	C₄	—	8	2	no	—
597	C₄	—	8	2	no	—
598	C₄	#385×C₆₇	1	1	yes	characteristic
599	C₄	#385×C₆₇	1	1	yes	characteristic
600	C₄	#388×C₆₇	1	1	yes	characteristic
601	C₄	#388×C₆₇	1	1	yes	characteristic
602	C₄	#394×C₆₇	1	1	yes	characteristic
603	C₄	#394×C₆₇	1	1	yes	characteristic
604	C₄	#396×C₆₇	1	1	yes	characteristic
605	C₄	#396×C₆₇	1	1	yes	characteristic
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	8	2	no	—
613	C₂	C₆₇×#1439	1	1	yes	characteristic
614	C₂	C₆₇×#2031	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	#124
commutator	C₂²×C₄	C₂²×C₄×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
socle	C₂²×C₆₇	#393
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₇×#2296	C₂	semidirect
5. C₂×#344×C₆₇	C₂	semidirect
6. C₂×#339×C₆₇	C₂	semidirect
7. C₂×H(3,ℤ/4)×C₆₇	C₂	semidirect
22. #410×C₆₇	C₄	semidirect
117. C₂×Q₈×C₆₇	C₄⋊C₄	semidirect
129. C₂×D₄×C₆₇	C₄⋊C₄	semidirect
298. #11091	C₆₇	direct (N × H)
311. #2296	C₂×C₆₇	semidirect
312. C₂×#344	C₂×C₆₇	semidirect
313. C₂×#339	C₂×C₆₇	semidirect
314. C₂×H(3,ℤ/4)	C₂×C₆₇	semidirect
315. C₆₇	#11091	direct (N × H)
330. #410	C₄×C₆₇	semidirect
425. C₂×Q₈	C₄⋊C₄×C₆₇	semidirect
437. C₂×D₄	C₄⋊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×#421×C₆₇	2
C₂²×#104×C₆₇	2
C₂×#410×C₆₇	2
C₆₇×#2296	2
C₂×#344×C₆₇	2
C₂×#339×C₆₇	2
C₂×H(3,ℤ/4)×C₆₇	2
#11091	67

Subgroups — C67×#11091 #30690342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#11091 #30690342