Subgroups — #30884555

Order 17152.

960 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×#16863445	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863378	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863378	C₂	1	1	yes	maximal, characteristic
5	C₂×#16863378	C₂	1	1	yes	maximal, characteristic
6	#22561609	C₂	1	4	yes	maximal, complemented
7	#22561606	C₂	1	4	yes	maximal, complemented
8	C₂×C₆₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#430×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#11761628	C₂²	1	1	yes	characteristic
11	C₂²×#11761612	C₂²	1	1	yes	characteristic
12	C₂²×#11761612	C₂²	1	1	yes	characteristic
13	C₂²×#11761612	C₂²	1	1	yes	characteristic
14	#16863445	—	2	2	no	—
15	#16863445	C₂²	1	4	yes	—
16	#16863444	—	2	2	no	—
17	#16863444	C₂²	1	4	yes	—
18	C₂×#14523979	—	2	2	no	—
19	C₂×#14523978	—	2	2	no	—
20	#16863378	—	2	2	no	—
21	#16863378	—	2	2	no	—
22	#16863378	—	2	2	no	—
23	#16863378	—	2	2	no	—
24	#16863378	—	2	2	no	—
25	#16863378	—	2	2	no	—
26	C₂×#14523961	C₂²	1	2	yes	—
27	C₂×#14523961	C₂²	1	2	yes	—
28	C₂×#14523961	C₂²	1	2	yes	—
29	C₂×#14523959	C₂²	1	2	yes	—
30	C₂×#14523959	C₂²	1	2	yes	—
31	C₂×#14523959	C₂²	1	2	yes	—
32	C₆₇⋊#338	C₂²	1	4	yes	—
33	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
36	#430×C₆₇	—	2	2	no	—
37	#430×C₆₇	C₂²	1	4	yes	—
38	C₂×#108×C₆₇	—	2	2	no	—
39	C₂×#11761628	—	2	1	no	—
40	C₂×#11761628	—	2	1	no	—
41	C₂×#11761628	—	2	1	no	—
42	C₂×#11761628	—	2	1	no	—
43	C₂×#11761628	—	2	1	no	—
44	C₂×#11761628	—	2	1	no	—
45	C₂×#11761628	—	2	1	no	—
46	C₂×#11761628	—	2	1	no	—
47	C₂×#11761628	—	2	1	no	—
48	C₂×#11761628	—	2	1	no	—
49	C₂×#11761628	—	2	1	no	—
50	C₂×#11761628	—	2	1	no	—
51	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
52	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
53	C₂²×C₂²⋊D₆₇	Q₈	1	2	yes	—
54	C₂²×C₄×D₆₇	Q₈	1	2	yes	—
55	C₂×#11761612	—	2	1	no	—
56	C₂×#11761612	—	2	1	no	—
57	C₂×#11761612	—	2	1	no	—
58	C₂×#11761612	—	2	1	no	—
59	C₂×#11761612	—	2	1	no	—
60	C₂×#11761612	—	2	1	no	—
61	C₂×#11761612	—	2	1	no	—
62	C₂×#11761612	—	2	1	no	—
63	C₂×#11761612	—	2	1	no	—
64	C₂×#11761612	—	2	1	no	—
65	C₂×#11761612	—	2	1	no	—
66	C₂×#11761612	—	2	1	no	—
67	C₂×#11761612	—	2	1	no	—
68	C₂×#11761612	D₄	1	2	yes	—
69	C₂×#11761612	D₄	1	2	yes	—
70	C₂×#11761612	C₂³	1	2	yes	—
71	C₂×#11761612	C₂³	1	2	yes	—
72	C₂×#11761612	C₂³	1	2	yes	—
73	C₂²×C₆₇⋊C₈	—	2	1	no	—
74	C₂²×C₆₇⋊C₈	—	2	1	no	—
75	C₂²×C₆₇⋊C₈	—	2	1	no	—
76	#14523979	—	2	8	no	—
77	#14523978	—	2	8	no	—
78	#14523961	—	2	4	no	—
79	#14523961	—	2	4	no	—
80	#14523961	—	2	4	no	—
81	#14523959	—	2	4	no	—
82	#14523959	—	2	4	no	—
83	#14523959	—	2	4	no	—
84	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₆₇	—	2	1	no	—
86	C₂×M₁₆×C₆₇	—	2	1	no	—
87	C₂×M₁₆×C₆₇	—	2	1	no	—
88	C₂×M₁₆×C₆₇	—	2	1	no	—
89	C₂×M₁₆×C₆₇	—	2	1	no	—
90	C₂×M₁₆×C₆₇	—	2	1	no	—
91	C₂×M₁₆×C₆₇	—	2	1	no	—
92	C₂×M₁₆×C₆₇	—	2	1	no	—
93	C₂×M₁₆×C₆₇	—	2	1	no	—
94	C₂×M₁₆×C₆₇	—	2	1	no	—
95	C₂×M₁₆×C₆₇	—	2	1	no	—
96	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
97	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
98	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
99	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
100	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
102	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂²×C₈×C₆₇	—	2	1	no	—
104	C₂²×C₈×C₆₇	—	2	1	no	—
105	C₂²×C₈×C₆₇	—	2	1	no	—
106	#108×C₆₇	—	2	8	no	—
107	C₂³×D₆₇	C₂×Q₈	1	2	yes	—
108	#11761628	—	4	1	no	—
109	#11761628	—	4	1	no	—
110	#11761628	—	4	1	no	—
111	#11761628	—	4	1	no	—
112	#11761628	—	4	1	no	—
113	#11761628	—	4	1	no	—
114	#11761628	—	4	1	no	—
115	#11761628	—	4	1	no	—
116	#11761628	—	4	1	no	—
117	#11761628	—	4	1	no	—
118	#11761628	—	4	1	no	—
119	#11761628	—	4	1	no	—
120	#11761628	—	4	1	no	—
121	#11761628	—	4	1	no	—
122	#11761628	—	4	1	no	—
123	#11761628	—	4	1	no	—
124	C₂×Dic₁₃₄	—	2	1	no	—
125	C₂×Dic₁₃₄	—	2	1	no	—
126	C₂×Dic₁₃₄	—	2	1	no	—
127	C₂×Dic₁₃₄	—	2	1	no	—
128	C₂×Dic₁₃₄	—	2	1	no	—
129	C₂×Dic₁₃₄	—	2	1	no	—
130	C₂×D₂₆₈	—	2	1	no	—
131	C₂×D₂₆₈	—	2	1	no	—
132	C₂×D₂₆₈	—	2	1	no	—
133	C₂×D₂₆₈	—	2	1	no	—
134	C₂×D₂₆₈	—	2	1	no	—
135	C₂×D₂₆₈	—	2	1	no	—
136	C₂×C₂²⋊D₆₇	—	2	2	no	—
137	C₂×C₂²⋊D₆₇	—	2	2	no	—
138	C₂×C₂²⋊D₆₇	—	2	2	no	—
139	C₂×C₂²⋊D₆₇	—	2	2	no	—
140	C₂×C₂²⋊D₆₇	—	2	2	no	—
141	C₂×C₂²⋊D₆₇	—	2	2	no	—
142	C₂²×Dic₆₇	C₂×Q₈	1	2	yes	—
143	C₂×C₄×D₆₇	—	2	2	no	—
144	C₂×C₄×D₆₇	—	2	2	no	—
145	C₂×C₄×D₆₇	—	2	2	no	—
146	C₂×C₄×D₆₇	—	2	2	no	—
147	C₂×C₄×D₆₇	—	2	2	no	—
148	C₂×C₄×D₆₇	—	2	2	no	—
149	#11761612	—	2	2	no	—
150	#11761612	—	2	2	no	—
151	#11761612	—	2	2	no	—
152	#11761612	—	2	2	no	—
153	#11761612	—	2	2	no	—
154	#11761612	—	2	2	no	—
155	#11761612	—	2	2	no	—
156	#11761612	—	4	1	no	—
157	#11761612	—	4	1	no	—
158	#11761612	—	4	1	no	—
159	#11761612	—	4	1	no	—
160	#11761612	C₂×D₄	1	4	yes	—
161	C₂×C₆₇⋊C₈	—	2	2	no	—
162	C₂×C₆₇⋊C₈	—	2	2	no	—
163	C₂×C₆₇⋊C₈	—	2	2	no	—
164	C₂×C₆₇⋊C₈	—	2	2	no	—
165	C₂×C₆₇⋊C₈	—	2	2	no	—
166	C₂×C₆₇⋊C₈	—	4	1	no	—
167	C₂×C₆₇⋊C₈	—	4	1	no	—
168	C₂×C₆₇⋊C₈	—	4	1	no	—
169	C₂×C₆₇⋊C₈	—	4	1	no	—
170	C₂⁴×C₆₇	C₂×Q₈	1	1	yes	characteristic
171	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
182	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
183	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
184	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
185	M₁₆×C₆₇	—	2	2	no	—
186	M₁₆×C₆₇	—	2	2	no	—
187	M₁₆×C₆₇	—	2	2	no	—
188	M₁₆×C₆₇	—	2	2	no	—
189	M₁₆×C₆₇	—	2	2	no	—
190	M₁₆×C₆₇	—	2	2	no	—
191	M₁₆×C₆₇	—	2	2	no	—
192	M₁₆×C₆₇	—	2	2	no	—
193	M₁₆×C₆₇	—	4	1	no	—
194	M₁₆×C₆₇	—	4	1	no	—
195	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
196	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
197	C₂×C₈×C₆₇	—	2	2	no	—
198	C₂×C₈×C₆₇	—	2	2	no	—
199	C₂×C₈×C₆₇	—	2	2	no	—
200	C₂×C₈×C₆₇	—	2	2	no	—
201	C₂×C₈×C₆₇	—	2	2	no	—
202	C₂×C₈×C₆₇	—	2	2	no	—
203	C₂×C₈×C₆₇	—	2	2	no	—
204	C₂×C₈×C₆₇	—	4	1	no	—
205	C₂×C₈×C₆₇	—	4	1	no	—
206	C₂³×C₆₇	—	8	1	no	—
207	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
209	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
210	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
211	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
212	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
214	C₂²×D₆₇	—	2	2	no	—
215	C₂²×D₆₇	—	2	2	no	—
216	C₂²×D₆₇	—	2	2	no	—
217	C₂²×D₆₇	—	8	2	no	—
218	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
225	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
226	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
227	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
228	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
229	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
230	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
231	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
237	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
238	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
239	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
246	C₂²⋊D₆₇	—	4	2	no	—
247	C₂²⋊D₆₇	—	4	2	no	—
248	C₂²⋊D₆₇	—	4	2	no	—
249	C₂²⋊D₆₇	—	4	2	no	—
250	C₂×Dic₆₇	—	2	2	no	—
251	C₂×Dic₆₇	—	2	2	no	—
252	C₂×Dic₆₇	—	2	2	no	—
253	D₂₆₈	—	4	1	no	—
254	D₂₆₈	—	4	1	no	—
255	D₂₆₈	—	4	1	no	—
256	D₂₆₈	—	4	1	no	—
257	C₄×D₆₇	—	4	2	no	—
258	C₄×D₆₇	—	4	2	no	—
259	C₄×D₆₇	—	4	2	no	—
260	C₄×D₆₇	—	4	2	no	—
261	Dic₁₃₄	—	4	1	no	—
262	Dic₁₃₄	—	4	1	no	—
263	Dic₁₃₄	—	4	1	no	—
264	Dic₁₃₄	—	4	1	no	—
265	C₈×C₆₇	—	2	4	no	—
266	C₈×C₆₇	—	2	4	no	—
267	C₈×C₆₇	—	4	2	no	—
268	C₆₇⋊C₈	—	2	4	no	—
269	C₆₇⋊C₈	—	4	2	no	—
270	C₆₇⋊C₈	—	4	2	no	—
271	C₂²×C₆₇	—	4	1	no	—
272	C₂²×C₆₇	—	4	1	no	—
273	C₂²×C₆₇	—	4	1	no	—
274	C₂²×C₆₇	—	4	1	no	—
275	C₂²×C₆₇	—	4	1	no	—
276	C₂²×C₆₇	—	4	1	no	—
277	C₂²×C₆₇	—	4	1	no	—
278	C₂²×C₆₇	#396	1	1	yes	characteristic
279	C₂²×C₆₇	#396	1	1	yes	characteristic
280	C₂²×C₆₇	#396	1	1	yes	characteristic
281	C₂²×C₆₇	#396	1	1	yes	characteristic
282	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
283	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
284	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
285	C₂×D₆₇	—	4	2	no	—
286	C₂×D₆₇	—	8	2	no	—
287	C₂×D₆₇	—	8	2	no	—
288	C₂×D₆₇	—	8	2	no	—
289	C₄×C₆₇	#396	1	1	yes	characteristic
290	C₄×C₆₇	#396	1	1	yes	characteristic
291	C₄×C₆₇	#396	1	1	yes	characteristic
292	C₄×C₆₇	#396	1	1	yes	characteristic
293	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
294	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
295	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
296	C₄×C₆₇	C₂×#126	1	1	yes	characteristic
297	Dic₆₇	—	4	2	no	—
298	#23622	—	67	1	no	maximal, 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	—	2	1	no	—
306	C₂×C₆₇	C₂×#396	1	1	yes	characteristic
307	D₆₇	—	8	2	no	—
308	C₂×#430	—	67	1	no	—
309	C₂×#430	—	67	1	no	—
310	C₂×#430	D₆₇	1	1	yes	characteristic, complemented
311	C₂×#413	—	67	1	no	—
312	C₂×#413	—	67	1	no	—
313	C₂×#413	—	67	1	no	—
314	#2070	—	67	4	no	—
315	#2069	—	67	4	no	—
316	C₂×#338	—	67	1	no	—
317	C₆₇	#23622	1	1	yes	characteristic, complemented, Sylow
318	C₂²×#41	—	67	1	no	—
319	C₂²×M₁₆	—	67	1	no	—
320	C₂²×M₁₆	—	67	1	no	—
321	C₂²×M₁₆	—	67	1	no	—
322	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
323	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
324	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
325	#430	—	2	2	no	—
326	#430	—	67	4	no	—
327	#430	—	67	4	no	—
328	#430	—	134	2	no	—
329	#430	—	134	2	no	—
330	#430	C₂×D₆₇	1	4	yes	—
331	C₂×#108	—	2	2	no	—
332	C₂×#108	—	134	2	no	—
333	C₂×#108	—	134	2	no	—
334	#413	—	134	2	no	—
335	#413	—	134	2	no	—
336	#413	—	134	2	no	—
337	#413	—	134	2	no	—
338	#413	—	134	2	no	—
339	#413	—	134	2	no	—
340	C₂×#101	—	67	2	no	—
341	C₂×#101	—	67	2	no	—
342	C₂×#101	—	67	2	no	—
343	C₂×#100	—	67	2	no	—
344	C₂×#100	—	67	2	no	—
345	C₂×#100	—	67	2	no	—
346	#338	—	67	4	no	—
347	C₂×#41	—	134	1	no	—
348	C₂×#41	—	134	1	no	—
349	C₂×#41	—	134	1	no	—
350	C₂×#41	—	134	1	no	—
351	C₂×#41	—	134	1	no	—
352	C₂×#41	—	134	1	no	—
353	C₂×#41	—	134	1	no	—
354	C₂×#41	—	134	1	no	—
355	C₂×#41	—	134	1	no	—
356	C₂×#41	—	134	1	no	—
357	C₂×#41	—	134	1	no	—
358	C₂×#41	—	134	1	no	—
359	C₂²×Q₈	—	67	1	no	—
360	C₂²×D₄	—	67	2	no	—
361	C₂²×D₄	—	67	1	no	—
362	C₂³×C₄	—	67	2	no	—
363	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	67	2	no	—
376	C₂×M₁₆	—	67	2	no	—
377	C₂×M₁₆	—	67	2	no	—
378	C₂×M₁₆	—	67	2	no	—
379	C₂×M₁₆	—	67	2	no	—
380	C₂×M₁₆	—	134	1	no	—
381	C₂×M₁₆	—	134	1	no	—
382	C₂×M₁₆	—	134	1	no	—
383	C₂×M₁₆	—	134	1	no	—
384	C₂×M₁₆	—	134	1	no	—
385	C₂×M₁₆	—	134	1	no	—
386	C₂×M₁₆	—	134	1	no	—
387	C₂×M₁₆	—	134	1	no	—
388	C₂×M₁₆	—	134	1	no	—
389	C₂×M₁₆	—	134	1	no	—
390	C₂×M₁₆	—	134	1	no	—
391	C₂×M₁₆	—	134	1	no	—
392	C₂×M₁₆	—	134	1	no	—
393	C₂×M₁₆	D₂₆₈	1	2	yes	—
394	C₂×M₁₆	D₂₆₈	1	2	yes	—
395	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
396	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
397	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
398	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
399	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	134	1	no	—
404	C₂²×C₈	—	134	1	no	—
405	C₂²×C₈	—	134	1	no	—
406	#108	—	2	8	no	—
407	#108	—	134	8	no	—
408	#108	—	134	8	no	—
409	#101	—	134	4	no	—
410	#101	—	134	4	no	—
411	#101	—	134	4	no	—
412	#100	—	134	4	no	—
413	#100	—	134	4	no	—
414	#100	—	134	4	no	—
415	C₂⁴	—	67	2	no	—
416	C₂⁴	Q₈×D₆₇	1	1	yes	characteristic
417	#41	—	268	1	no	—
418	#41	—	268	1	no	—
419	#41	—	268	1	no	—
420	#41	—	268	1	no	—
421	#41	—	268	1	no	—
422	#41	—	268	1	no	—
423	#41	—	268	1	no	—
424	#41	—	268	1	no	—
425	#41	—	268	1	no	—
426	#41	—	268	1	no	—
427	#41	—	268	1	no	—
428	#41	—	268	1	no	—
429	#41	—	268	1	no	—
430	#41	—	268	1	no	—
431	#41	—	268	1	no	—
432	#41	—	268	1	no	—
433	C₂×Q₈	—	134	1	no	—
434	C₂×Q₈	—	134	1	no	—
435	C₂×Q₈	—	134	1	no	—
436	C₂×Q₈	—	134	1	no	—
437	C₂×Q₈	—	134	1	no	—
438	C₂×Q₈	—	134	1	no	—
439	C₂×D₄	—	134	2	no	—
440	C₂×D₄	—	134	2	no	—
441	C₂×D₄	—	134	2	no	—
442	C₂×D₄	—	134	2	no	—
443	C₂×D₄	—	134	2	no	—
444	C₂×D₄	—	134	2	no	—
445	C₂×D₄	—	134	1	no	—
446	C₂×D₄	—	134	1	no	—
447	C₂×D₄	—	134	1	no	—
448	C₂×D₄	—	134	1	no	—
449	C₂×D₄	—	134	1	no	—
450	C₂×D₄	—	134	1	no	—
451	C₂²×C₄	—	67	2	no	—
452	C₂²×C₄	—	134	2	no	—
453	C₂²×C₄	—	134	2	no	—
454	C₂²×C₄	—	134	2	no	—
455	C₂²×C₄	—	134	2	no	—
456	C₂²×C₄	—	134	2	no	—
457	C₂²×C₄	—	134	2	no	—
458	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
464	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
465	C₂²×C₄	#11761627	1	1	yes	characteristic
466	C₂²×C₄	#11761627	1	1	yes	characteristic
467	C₂²×C₄	#11761628	1	1	yes	characteristic
468	C₂²×C₄	#11761628	1	1	yes	characteristic
469	C₂²×C₄	#11761629	1	1	yes	characteristic
470	C₂²×C₄	#11761629	1	1	yes	characteristic
471	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	4	1	no	—
481	M₁₆	—	4	1	no	—
482	M₁₆	—	268	1	no	—
483	M₁₆	—	268	1	no	—
484	M₁₆	—	268	1	no	—
485	M₁₆	—	268	1	no	—
486	M₁₆	—	67	4	no	—
487	M₁₆	—	134	2	no	—
488	M₁₆	—	134	2	no	—
489	M₁₆	—	134	2	no	—
490	M₁₆	—	134	2	no	—
491	M₁₆	—	134	2	no	—
492	M₁₆	—	134	2	no	—
493	M₁₆	—	134	2	no	—
494	M₁₆	C₂×C₂²⋊D₆₇	1	4	yes	—
495	M₁₆	C₂×D₂₆₈	1	4	yes	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	268	1	no	—
506	C₂×C₈	—	268	1	no	—
507	C₂×C₈	—	268	1	no	—
508	C₂×C₈	—	268	1	no	—
509	C₂×C₈	—	134	2	no	—
510	C₂×C₈	—	134	2	no	—
511	C₂×C₈	—	134	2	no	—
512	C₂×C₈	—	134	2	no	—
513	C₂×C₈	—	134	2	no	—
514	C₂³	—	8	1	no	—
515	C₂³	—	536	2	no	—
516	C₂³	—	134	2	no	—
517	C₂³	—	134	2	no	—
518	C₂³	—	134	2	no	—
519	C₂³	#14524019	1	1	yes	characteristic
520	C₂³	#14524019	1	1	yes	characteristic
521	C₂³	#14524021	1	1	yes	characteristic
522	C₂³	#14524021	1	1	yes	characteristic
523	C₂³	#14524023	1	1	yes	characteristic
524	C₂³	#14524023	1	1	yes	characteristic
525	C₂³	C₂×Q₈×D₆₇	1	1	yes	characteristic
526	Q₈	—	268	1	no	—
527	Q₈	—	268	1	no	—
528	Q₈	—	268	1	no	—
529	Q₈	—	268	1	no	—
530	D₄	—	268	2	no	—
531	D₄	—	268	2	no	—
532	D₄	—	268	2	no	—
533	D₄	—	268	2	no	—
534	D₄	—	268	1	no	—
535	D₄	—	268	1	no	—
536	D₄	—	268	1	no	—
537	D₄	—	268	1	no	—
538	C₂×C₄	—	268	2	no	—
539	C₂×C₄	—	268	2	no	—
540	C₂×C₄	—	268	2	no	—
541	C₂×C₄	—	268	2	no	—
542	C₂×C₄	—	134	2	no	—
543	C₂×C₄	—	134	2	no	—
544	C₂×C₄	—	134	2	no	—
545	C₂×C₄	#14524015	1	1	yes	characteristic
546	C₂×C₄	#14524015	1	1	yes	characteristic
547	C₂×C₄	#14524015	1	1	yes	characteristic
548	C₂×C₄	#14524015	1	1	yes	characteristic
549	C₂×C₄	#14524017	1	1	yes	characteristic
550	C₂×C₄	#14524017	1	1	yes	characteristic
551	C₂×C₄	#14524017	1	1	yes	characteristic
552	C₂×C₄	#14524017	1	1	yes	characteristic
553	C₂×C₄	#14524018	1	1	yes	characteristic
554	C₂×C₄	#14524018	1	1	yes	characteristic
555	C₂×C₄	#14524018	1	1	yes	characteristic
556	C₂×C₄	#14524018	1	1	yes	characteristic
557	C₂×C₄	#14524019	1	1	yes	characteristic
558	C₂×C₄	#14524019	1	1	yes	characteristic
559	C₂×C₄	#14524021	1	1	yes	characteristic
560	C₂×C₄	#14524021	1	1	yes	characteristic
561	C₂×C₄	#14524023	1	1	yes	characteristic
562	C₂×C₄	#14524023	1	1	yes	characteristic
563	C₂×C₄	#14524038	1	1	yes	characteristic
564	C₂×C₄	#14524038	1	1	yes	characteristic
565	C₂×C₄	#14524038	1	1	yes	characteristic
566	C₂×C₄	#14524038	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
568	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
570	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
571	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
572	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
573	C₈	—	2	4	no	—
574	C₈	—	2	4	no	—
575	C₈	—	4	2	no	—
576	C₈	—	268	2	no	—
577	C₈	—	268	2	no	—
578	C₈	—	134	4	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	268	2	no	—
587	C₂²	—	536	2	no	—
588	C₂²	—	536	2	no	—
589	C₂²	—	536	2	no	—
590	C₂²	#16863318	1	1	yes	characteristic
591	C₂²	#16863318	1	1	yes	characteristic
592	C₂²	#16863318	1	1	yes	characteristic
593	C₂²	#16863318	1	1	yes	characteristic
594	C₂²	C₂×#14524019	1	1	yes	characteristic
595	C₂²	C₂×#14524021	1	1	yes	characteristic
596	C₂²	C₂×#14524023	1	1	yes	characteristic
597	C₄	—	268	2	no	—
598	C₄	#16863318	1	1	yes	characteristic
599	C₄	#16863318	1	1	yes	characteristic
600	C₄	#16863318	1	1	yes	characteristic
601	C₄	#16863318	1	1	yes	characteristic
602	C₄	C₂×#14524015	1	1	yes	characteristic
603	C₄	C₂×#14524017	1	1	yes	characteristic
604	C₄	C₂×#14524018	1	1	yes	characteristic
605	C₄	C₂×#14524038	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	—	2	1	no	—
613	C₂	—	536	2	no	—
614	C₂	C₂×#16863318	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16863318
commutator, cosocle	C₂²×C₄×C₆₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#430×C₆₇	C₂
socle	C₂×C₆₇	C₂×#396
prime radical	C₂²×#11761628	C₂²
hypercenter	C₂×#430	D₆₇
hypocenter	C₆₇	#23622
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
1. C₂×#16863445	C₂	semidirect
2. C₂×#16863444	C₂	semidirect
6. #22561609	C₂	semidirect
7. #22561606	C₂	semidirect
8. C₂×C₆₇⋊#338	C₂	semidirect
9. C₂×#430×C₆₇	C₂	semidirect
310. C₂×#430	D₆₇	semidirect
317. C₆₇	#23622	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863445	2
C₂×#16863444	2
C₂×#16863378	2
#22561609	2
#22561606	2
C₂×C₆₇⋊#338	2
C₂×#430×C₆₇	2
#23622	67