Subgroups — #30862609

Order 17152.

998 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863513	C₂	1	1	yes	maximal, characteristic, complemented
2	#22568904	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561098	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560958	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560915	C₂	1	2	yes	maximal, complemented
7	#22560653	C₂	1	2	yes	maximal, complemented
8	#22560247	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560090	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560049	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3050	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	2	yes	—
13	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
15	#16863513	—	2	4	no	—
16	#16863468	—	2	4	no	—
17	D₄×C₆₇⋊C₈	—	2	4	no	—
18	C₂×#14523979	C₂²	1	1	yes	characteristic
19	C₂×#14523979	C₂²	1	1	yes	characteristic
20	#16863423	C₂²	1	2	yes	—
21	C₂×#14523970	C₂²	1	2	yes	—
22	C₂×#14523970	C₂²	1	2	yes	—
23	#16863363	C₂²	1	2	yes	—
24	#16863360	C₂²	1	2	yes	—
25	#16863352	C₂²	1	2	yes	—
26	C₂×C₈×Dic₆₇	—	2	4	no	—
27	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
31	#16863161	C₂²	1	2	yes	—
32	#16863155	C₂²	1	2	yes	—
33	#16863155	C₂²	1	2	yes	—
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
36	#525×C₆₇	C₂²	1	2	yes	—
37	#467×C₆₇	C₄	1	2	yes	complemented
38	#466×C₆₇	C₄	1	2	yes	complemented
39	#465×C₆₇	C₄	1	4	yes	complemented
40	#427×C₆₇	C₂²	1	1	yes	characteristic
41	#416×C₆₇	C₂²	1	2	yes	—
42	C₂³×Dic₆₇	—	2	1	no	—
43	#14524050	—	2	4	no	—
44	#14524050	—	2	4	no	—
45	C₂×#11761612	—	2	2	no	—
46	C₂×#11761612	C₂³	1	2	yes	—
47	C₂×#11761612	C₂³	1	2	yes	—
48	C₂²×C₆₇⋊C₈	—	2	2	no	—
49	C₂²×C₆₇⋊C₈	—	2	2	no	—
50	C₂²×C₆₇⋊C₈	—	2	2	no	—
51	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
52	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
53	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₆₇	—	2	2	no	—
56	C₂×C₄×Dic₆₇	—	2	2	no	—
57	C₂×C₄×Dic₆₇	—	2	1	no	—
58	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
60	#14523979	—	2	2	no	—
61	#14523979	—	2	2	no	—
62	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
63	#14523970	—	2	4	no	—
64	#14523970	—	2	4	no	—
65	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
66	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
67	#14523954	—	2	2	no	—
68	C₄×C₆₇⋊C₈	—	2	2	no	—
69	C₈×Dic₆₇	—	2	2	no	—
70	C₈×Dic₆₇	—	2	2	no	—
71	C₈×Dic₆₇	—	2	2	no	—
72	C₈×Dic₆₇	D₄	1	4	yes	complemented
73	C₂×#41×C₆₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
75	#135×C₆₇	—	2	2	no	—
76	#135×C₆₇	—	2	2	no	—
77	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
79	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂²×C₈×C₆₇	—	2	2	no	—
81	C₂²×C₈×C₆₇	—	2	2	no	—
82	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
86	#123×C₆₇	—	2	2	no	—
87	C₂²⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
88	#121×C₆₇	C₂×C₄	1	4	yes	—
89	#120×C₆₇	—	2	2	no	—
90	C₄×D₄×C₆₇	—	2	4	no	—
91	#117×C₆₇	C₂³	1	2	yes	—
92	#107×C₆₇	C₂×C₄	1	2	yes	complemented
93	#106×C₆₇	C₂×C₄	1	2	yes	complemented
94	#103×C₆₇	C₂×C₄	1	4	yes	complemented
95	#102×C₆₇	C₂×C₄	1	4	yes	complemented
96	C₂²×Dic₆₇	—	2	4	no	—
97	C₂²×Dic₆₇	—	2	8	no	—
98	C₂²×Dic₆₇	—	2	1	no	—
99	C₂²×Dic₆₇	—	2	1	no	—
100	#11761612	—	2	2	no	—
101	#11761612	—	2	2	no	—
102	#11761612	—	2	2	no	—
103	#11761612	—	2	2	no	—
104	#11761612	—	4	4	no	—
105	C₂×C₆₇⋊C₈	—	2	1	no	—
106	C₂×C₆₇⋊C₈	—	2	1	no	—
107	C₂×C₆₇⋊C₈	—	2	4	no	—
108	C₂×C₆₇⋊C₈	—	2	4	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₂×C₆₇⋊C₈	—	2	2	no	—
111	C₂×C₆₇⋊C₈	—	4	4	no	—
112	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
113	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
114	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
116	C₂×C₆₇⋊C₈	#41	1	2	yes	—
117	C₄×Dic₆₇	—	2	4	no	—
118	C₄×Dic₆₇	—	2	1	no	—
119	C₄×Dic₆₇	—	2	1	no	—
120	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
121	C₄×Dic₆₇	#41	1	2	yes	—
122	C₂⁴×C₆₇	#41	1	1	yes	characteristic
123	#41×C₆₇	—	2	2	no	—
124	#41×C₆₇	—	2	2	no	—
125	#41×C₆₇	—	2	2	no	—
126	#41×C₆₇	—	2	2	no	—
127	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
128	C₂×D₄×C₆₇	—	2	4	no	—
129	C₂×D₄×C₆₇	—	2	2	no	—
130	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₆₇	—	2	1	no	—
132	C₂²×C₄×C₆₇	—	2	1	no	—
133	C₂²×C₄×C₆₇	—	2	1	no	—
134	C₂²×C₄×C₆₇	—	2	1	no	—
135	C₂²×C₄×C₆₇	—	2	2	no	—
136	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₆₇	—	2	2	no	—
141	SD₁₆×C₆₇	—	2	4	no	—
142	D₈×C₆₇	—	2	2	no	—
143	C₂×C₈×C₆₇	—	2	1	no	—
144	C₂×C₈×C₆₇	—	2	1	no	—
145	C₂×C₈×C₆₇	—	2	4	no	—
146	C₂×C₈×C₆₇	—	2	4	no	—
147	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₆₇	#41	1	2	yes	—
152	C₄⋊C₄×C₆₇	—	2	4	no	—
153	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
154	C₂²⋊C₄×C₆₇	—	2	4	no	—
155	C₂²⋊C₄×C₆₇	—	2	2	no	—
156	C₂²⋊C₄×C₆₇	—	2	4	no	—
157	C₄²×C₆₇	—	2	2	no	—
158	C₂³×C₆₇	—	2	1	no	—
159	C₂³×C₆₇	—	2	1	no	—
160	C₂³×C₆₇	—	2	4	no	—
161	C₂³×C₆₇	—	2	2	no	—
162	C₂³×C₆₇	C₄×D₄	1	2	yes	—
163	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₆₇	—	2	2	no	—
165	Q₈×C₆₇	—	2	2	no	—
166	D₄×C₆₇	—	2	2	no	—
167	D₄×C₆₇	—	2	2	no	—
168	D₄×C₆₇	—	4	2	no	—
169	D₄×C₆₇	—	4	2	no	—
170	D₄×C₆₇	—	4	8	no	—
171	C₂×C₄×C₆₇	—	2	1	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	2	2	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	2	2	no	—
176	C₂×C₄×C₆₇	—	2	2	no	—
177	C₂×C₄×C₆₇	—	2	4	no	—
178	C₂×C₄×C₆₇	—	2	2	no	—
179	C₂×C₄×C₆₇	—	4	2	no	—
180	C₂×C₄×C₆₇	—	4	2	no	—
181	C₂×C₄×C₆₇	C₄×D₄	1	2	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	C₂²×D₄	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	C₂×Dic₆₇	—	2	16	no	—
189	C₂×Dic₆₇	—	2	4	no	—
190	C₂×Dic₆₇	—	2	4	no	—
191	C₂×Dic₆₇	—	2	2	no	—
192	C₂×Dic₆₇	—	2	2	no	—
193	C₈×C₆₇	—	2	2	no	—
194	C₈×C₆₇	C₄×D₄	1	2	yes	—
195	C₈×C₆₇	C₄×D₄	1	2	yes	—
196	C₆₇⋊C₈	—	2	2	no	—
197	C₆₇⋊C₈	—	4	2	no	—
198	C₆₇⋊C₈	—	4	2	no	—
199	C₆₇⋊C₈	#121	1	2	yes	—
200	C₆₇⋊C₈	#121	1	2	yes	—
201	C₂²×C₆₇	—	2	4	no	—
202	C₂²×C₆₇	—	2	4	no	—
203	C₂²×C₆₇	—	2	2	no	—
204	C₂²×C₆₇	—	2	2	no	—
205	C₂²×C₆₇	—	2	2	no	—
206	C₂²×C₆₇	—	4	4	no	—
207	C₂²×C₆₇	—	4	2	no	—
208	C₂²×C₆₇	#443	1	4	yes	complemented
209	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₆₇	#525	1	1	yes	characteristic
211	C₂²×C₆₇	#529	1	1	yes	characteristic
212	C₄×C₆₇	—	2	2	no	—
213	C₄×C₆₇	—	4	4	no	—
214	C₄×C₆₇	—	4	2	no	—
215	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
217	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
218	C₄×C₆₇	#532	1	1	yes	characteristic
219	Dic₆₇	—	2	4	no	—
220	Dic₆₇	—	2	4	no	—
221	#21544	—	67	1	no	maximal, Sylow
222	C₂×C₆₇	—	2	1	no	—
223	C₂×C₆₇	—	2	1	no	—
224	C₂×C₆₇	—	2	4	no	—
225	C₂×C₆₇	—	8	2	no	—
226	C₂×C₆₇	C₄×#121	1	1	yes	characteristic
227	C₂×C₆₇	C₂×#443	1	2	yes	—
228	#3050	D₆₇	1	1	yes	characteristic
229	C₂×#443	—	67	1	no	—
230	#2929	—	67	2	no	—
231	C₂²×C₄×C₈	—	67	1	no	—
232	#1974	—	67	1	no	—
233	#1945	—	67	1	no	—
234	#1937	—	67	2	no	—
235	#1896	—	67	2	no	—
236	#1810	—	67	1	no	—
237	#1772	—	67	1	no	—
238	#1764	—	67	2	no	—
239	C₆₇	#21544	1	1	yes	characteristic, complemented, Sylow
240	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
241	C₂×#131	—	67	2	no	—
242	C₂³×C₈	—	67	1	no	—
243	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
244	#525	C₂×D₆₇	1	2	yes	—
245	C₂²×C₄²	—	67	1	no	—
246	#467	Dic₆₇	1	2	yes	complemented
247	#466	Dic₆₇	1	2	yes	complemented
248	#465	Dic₆₇	1	4	yes	complemented
249	#443	—	134	4	no	—
250	#435	—	134	4	no	—
251	C₈×D₄	—	134	4	no	—
252	C₂×#108	—	67	1	no	—
253	C₂×#108	—	67	1	no	—
254	#427	C₂×D₆₇	1	1	yes	characteristic
255	#424	—	67	2	no	—
256	C₂×#104	—	67	2	no	—
257	C₂×#104	—	67	2	no	—
258	#416	C₂×D₆₇	1	2	yes	—
259	#408	—	67	2	no	—
260	#407	—	67	2	no	—
261	#405	—	67	2	no	—
262	C₂×C₄×C₈	—	67	1	no	—
263	C₂×C₄×C₈	—	67	1	no	—
264	C₂×C₄×C₈	—	67	1	no	—
265	C₂×C₄×C₈	—	67	1	no	—
266	C₂×C₄×C₈	—	134	4	no	—
267	#341	—	67	2	no	—
268	#339	—	67	2	no	—
269	#339	—	67	2	no	—
270	C₂×#41	C₂²×D₆₇	1	2	yes	—
271	C₂³×C₄	—	134	1	no	—
272	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
273	#135	—	2	2	no	—
274	#135	—	2	2	no	—
275	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic, complemented
276	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	complemented
277	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic, complemented
278	#131	—	134	4	no	—
279	#131	—	134	4	no	—
280	C₂×M₁₆	—	67	2	no	—
281	C₂×M₁₆	—	67	2	no	—
282	C₂×M₁₆	—	134	2	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	67	1	no	—
286	C₂²×C₈	—	67	2	no	—
287	C₂²×C₈	—	67	2	no	—
288	C₂²×C₈	—	67	1	no	—
289	C₂²×C₈	—	134	2	no	—
290	C₂²×C₈	—	134	2	no	—
291	C₂²×C₈	—	134	2	no	—
292	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
293	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
294	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
296	#123	—	2	2	no	—
297	C₂²⋊Q₈	C₂×Dic₆₇	1	4	yes	—
298	#121	C₂×Dic₆₇	1	4	yes	—
299	#120	—	2	2	no	—
300	C₄×D₄	—	2	4	no	—
301	#117	C₂²×D₆₇	1	2	yes	—
302	C₂×C₄²	—	67	1	no	—
303	C₂×C₄²	—	67	1	no	—
304	C₂×C₄²	—	134	2	no	—
305	C₂×C₄²	—	134	2	no	—
306	C₂×C₄²	—	134	1	no	—
307	#108	—	134	2	no	—
308	#108	—	134	2	no	—
309	#107	C₂×Dic₆₇	1	2	yes	complemented
310	#106	C₂×Dic₆₇	1	2	yes	complemented
311	C₄⋊C₈	—	134	4	no	—
312	#104	—	134	4	no	—
313	#104	—	134	4	no	—
314	#103	C₂×Dic₆₇	1	4	yes	complemented
315	#102	C₂×Dic₆₇	1	4	yes	complemented
316	C₂²⋊C₈	—	134	4	no	—
317	C₂²⋊C₈	—	134	4	no	—
318	#97	—	134	2	no	—
319	C₄×C₈	—	67	4	no	—
320	C₄×C₈	—	134	2	no	—
321	C₄×C₈	—	134	2	no	—
322	C₄×C₈	—	134	2	no	—
323	C₄×C₈	—	134	2	no	—
324	C₂⁴	#11761627	1	1	yes	characteristic
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	134	4	no	—
339	C₂²×C₄	—	134	8	no	—
340	C₂²×C₄	—	134	1	no	—
341	C₂²×C₄	—	134	1	no	—
342	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
343	C₂²×C₄	D₄×D₆₇	1	2	yes	—
344	C₂²×C₄	#11761627	1	1	yes	characteristic
345	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
346	Q₁₆	—	2	2	no	—
347	SD₁₆	—	2	4	no	—
348	D₈	—	2	2	no	—
349	M₁₆	—	268	4	no	—
350	M₁₆	—	134	2	no	—
351	M₁₆	—	134	2	no	—
352	M₁₆	—	134	2	no	—
353	M₁₆	—	134	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	268	4	no	—
359	C₂×C₈	—	67	2	no	—
360	C₂×C₈	—	67	1	no	—
361	C₂×C₈	—	67	1	no	—
362	C₂×C₈	—	67	2	no	—
363	C₂×C₈	—	67	2	no	—
364	C₂×C₈	—	134	2	no	—
365	C₂×C₈	—	134	2	no	—
366	C₂×C₈	—	134	4	no	—
367	C₂×C₈	—	134	4	no	—
368	C₂×C₈	—	134	1	no	—
369	C₂×C₈	—	134	1	no	—
370	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
371	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
372	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
373	C₂×C₈	D₄×D₆₇	1	2	yes	—
374	C₂×C₈	#11761627	1	2	yes	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	C₂²×Dic₆₇	1	4	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	67	2	no	—
382	C₄²	—	67	2	no	—
383	C₄²	—	134	4	no	—
384	C₄²	—	134	1	no	—
385	C₄²	—	134	1	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	2	no	—
390	C₂³	D₄×Dic₆₇	1	2	yes	—
391	C₂³	C₂×#11761627	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	4	8	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	134	16	no	—
410	C₂×C₄	—	134	4	no	—
411	C₂×C₄	—	134	4	no	—
412	C₂×C₄	—	134	2	no	—
413	C₂×C₄	—	134	2	no	—
414	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
415	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
418	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
419	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
420	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	268	2	no	—
423	C₈	—	268	2	no	—
424	C₈	—	67	2	no	—
425	C₈	—	67	2	no	—
426	C₈	—	134	2	no	—
427	C₈	D₄×Dic₆₇	1	2	yes	—
428	C₈	D₄×Dic₆₇	1	2	yes	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	#16863513	1	4	yes	complemented
437	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
438	C₂²	#16863906	1	1	yes	characteristic
439	C₂²	#16863927	1	1	yes	characteristic
440	C₄	—	2	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	2	no	—
443	C₄	—	134	4	no	—
444	C₄	—	134	4	no	—
445	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
446	C₄	#41×Dic₆₇	1	1	yes	characteristic
447	C₄	#121×D₆₇	1	1	yes	characteristic
448	C₄	#16863941	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	4	no	—
451	C₂	—	2	1	no	—
452	C₂	—	8	2	no	—
453	C₂	#121×Dic₆₇	1	1	yes	characteristic
454	C₂	C₂×#16863513	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting, prime radical	C₆₇×#3050	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#3050	D₆₇
hypocenter	C₆₇	#21544
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. C₂×#16863513	C₂	semidirect
2. #22568904	C₂	semidirect
3. C₂²×C₈×Dic₆₇	C₂	semidirect
4. #22561098	C₂	semidirect
5. #22560958	C₂	semidirect
6. #22560915	C₂	semidirect
7. #22560653	C₂	semidirect
8. #22560247	C₂	semidirect
9. #22560090	C₂	semidirect
10. #22560049	C₂	semidirect
37. #467×C₆₇	C₄	semidirect
38. #466×C₆₇	C₄	semidirect
39. #465×C₆₇	C₄	semidirect
72. C₈×Dic₆₇	D₄	semidirect
77. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
78. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
79. C₂×D₈×C₆₇	C₂×C₄	semidirect
92. #107×C₆₇	C₂×C₄	semidirect
93. #106×C₆₇	C₂×C₄	semidirect
94. #103×C₆₇	C₂×C₄	semidirect
95. #102×C₆₇	C₂×C₄	semidirect
208. C₂²×C₆₇	#443	semidirect
239. C₆₇	#21544	semidirect
246. #467	Dic₆₇	semidirect
247. #466	Dic₆₇	semidirect
248. #465	Dic₆₇	semidirect
275. C₂×Q₁₆	C₂×Dic₆₇	semidirect
276. C₂×SD₁₆	C₂×Dic₆₇	semidirect
277. C₂×D₈	C₂×Dic₆₇	semidirect
309. #107	C₂×Dic₆₇	semidirect
310. #106	C₂×Dic₆₇	semidirect
314. #103	C₂×Dic₆₇	semidirect
315. #102	C₂×Dic₆₇	semidirect
436. C₂²	#16863513	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863513	2
#22568904	2
C₂²×C₈×Dic₆₇	2
#22561098	2
#22560958	2
#22560915	2
#22560653	2
#22560247	2
#22560090	2
#22560049	2
C₆₇×#3050	2
#21544	67