Subgroups — #31720007

Order 17152.

2706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573412	C₂	1	2	yes	maximal, complemented
2	#22569093	C₂	1	4	yes	maximal, complemented
3	#22569085	C₂	1	4	yes	maximal, complemented
4	#22569077	C₂	1	2	yes	maximal, complemented
5	#22569069	C₂	1	4	yes	maximal, complemented
6	#22569061	C₂	1	2	yes	maximal, complemented
7	#22569010	C₂	1	4	yes	maximal, complemented
8	#135×Dic₆₇	C₂	1	4	yes	maximal, complemented
9	C₂×#16863434	C₂	1	1	yes	maximal, characteristic, complemented
10	#22568728	C₂	1	2	yes	maximal, complemented
11	C₂×#16863351	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
13	C₂²×#11761612	C₂²	1	1	yes	characteristic
14	#16863879	—	2	4	no	—
15	#16863879	C₂²	1	8	yes	complemented
16	#16863874	C₂²	1	4	yes	—
17	#16863871	—	2	4	no	—
18	#16863871	C₂²	1	4	yes	—
19	#41×Dic₆₇	—	2	4	no	—
20	#41×Dic₆₇	C₂²	1	8	yes	complemented
21	C₂×#14524002	—	2	4	no	—
22	C₂×#14524002	C₂²	1	2	yes	—
23	C₂×#14524002	C₂²	1	1	yes	characteristic
24	#16863508	C₂²	1	8	yes	complemented
25	#16863503	C₂²	1	8	yes	complemented
26	#16863497	C₂²	1	16	yes	complemented
27	Q₁₆×Dic₆₇	C₂²	1	8	yes	complemented
28	SD₁₆×Dic₆₇	C₂²	1	16	yes	complemented
29	D₈×Dic₆₇	C₂²	1	8	yes	complemented
30	#16863434	C₂²	1	2	yes	—
31	#16863434	C₂²	1	2	yes	—
32	#16863434	C₂²	1	2	yes	complemented
33	#16863434	C₂²	1	2	yes	complemented
34	C₂×#14523977	C₂²	1	2	yes	complemented
35	C₂×#14523975	C₂²	1	2	yes	complemented
36	#16863405	C₂²	1	4	yes	—
37	#16863401	C₂²	1	4	yes	—
38	#16863397	C₂²	1	8	yes	complemented
39	#16863392	C₂²	1	8	yes	complemented
40	#16863351	C₂²	1	2	yes	—
41	#16863351	C₂²	1	2	yes	—
42	#16863351	C₂²	1	2	yes	complemented
43	#16863351	C₂²	1	2	yes	complemented
44	C₂×#14523953	C₂²	1	2	yes	complemented
45	C₂×C₈×Dic₆₇	C₂²	1	2	yes	complemented
46	C₂²×#41×C₆₇	C₂²	1	2	yes	—
47	C₂×#135×C₆₇	C₄	1	16	yes	complemented
48	C₂×#135×C₆₇	C₂²	1	2	yes	—
49	C₂×#135×C₆₇	C₂²	1	2	yes	—
50	C₂×#135×C₆₇	C₂²	1	2	yes	—
51	C₂×#135×C₆₇	C₂²	1	2	yes	—
52	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
53	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	—
54	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
55	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×#11761612	—	2	4	no	—
57	C₂×#11761612	C₂³	1	2	yes	—
58	C₂×#11761612	C₂³	1	2	yes	—
59	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
60	Q₈×Dic₆₇	—	2	8	no	—
61	Q₈×Dic₆₇	C₂³	1	16	yes	—
62	D₄×Dic₆₇	—	2	16	no	—
63	D₄×Dic₆₇	—	2	8	no	—
64	D₄×Dic₆₇	—	2	16	no	—
65	D₄×Dic₆₇	C₂³	1	16	yes	—
66	#14524002	—	2	8	no	—
67	#14524002	—	2	8	no	—
68	#14524002	—	2	8	no	—
69	#14524002	—	2	2	no	—
70	#14524002	—	2	2	no	—
71	#14524002	D₄	1	2	yes	—
72	#14524002	D₄	1	2	yes	—
73	#14524002	C₂³	1	4	yes	—
74	#14524002	C₂³	1	4	yes	—
75	#14524002	C₂³	1	2	yes	—
76	#14524002	C₂³	1	2	yes	—
77	C₂×C₄⋊Dic₆₇	—	2	8	no	—
78	C₂×C₄⋊Dic₆₇	D₄	1	2	yes	—
79	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
80	C₂×C₂²⋊Dic₆₇	—	2	8	no	—
81	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
82	C₂×C₂²⋊Dic₆₇	D₄	1	2	yes	—
83	C₂×C₄×Dic₆₇	—	2	8	no	—
84	C₂×C₄×Dic₆₇	—	2	2	no	—
85	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
86	#14523977	C₂³	1	4	yes	—
87	#14523977	C₂³	1	4	yes	—
88	#14523975	C₂³	1	4	yes	—
89	#14523975	C₂³	1	4	yes	—
90	#14523967	C₂³	1	16	yes	—
91	#14523964	C₂³	1	16	yes	—
92	#14523953	C₂³	1	4	yes	—
93	#14523953	C₂³	1	4	yes	—
94	C₈×Dic₆₇	C₂³	1	4	yes	—
95	C₈×Dic₆₇	C₂³	1	4	yes	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	2	8	no	—
99	C₂×#41×C₆₇	C₂×C₄	1	16	yes	complemented
100	C₂×#41×C₆₇	C₂³	1	4	yes	—
101	C₂×#41×C₆₇	C₂³	1	4	yes	—
102	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
103	C₂²×D₄×C₆₇	—	2	2	no	—
104	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₆₇	—	2	2	no	—
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	#135×C₆₇	C₂×C₄	1	16	yes	complemented
108	#135×C₆₇	C₂×C₄	1	16	yes	complemented
109	#135×C₆₇	C₂×C₄	1	16	yes	complemented
110	#135×C₆₇	C₂×C₄	1	16	yes	complemented
111	C₂×Q₁₆×C₆₇	C₂×C₄	1	8	yes	complemented
112	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
113	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₆₇	C₂×C₄	1	16	yes	complemented
115	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
117	C₂×D₈×C₆₇	C₂×C₄	1	8	yes	complemented
118	C₂×D₈×C₆₇	C₂³	1	2	yes	—
119	C₂×D₈×C₆₇	C₂³	1	2	yes	—
120	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	complemented
121	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
127	C₂²×Dic₆₇	—	2	4	no	—
128	C₂²×Dic₆₇	—	2	16	no	—
129	C₂²×Dic₆₇	C₂×D₄	1	4	yes	—
130	#11761612	—	2	4	no	—
131	#11761612	—	2	4	no	—
132	C₂×C₆₇⋊C₈	—	2	4	no	—
133	C₂×C₆₇⋊C₈	C₂⁴	1	4	yes	—
134	C₄⋊Dic₆₇	—	2	4	no	—
135	C₄⋊Dic₆₇	—	2	16	no	—
136	C₄⋊Dic₆₇	C₂×D₄	1	4	yes	—
137	C₄⋊Dic₆₇	C₂×D₄	1	4	yes	—
138	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
139	C₂²⋊Dic₆₇	—	2	4	no	—
140	C₂²⋊Dic₆₇	—	2	4	no	—
141	C₂²⋊Dic₆₇	—	2	16	no	—
142	C₂²⋊Dic₆₇	C₂×D₄	1	4	yes	—
143	C₂²⋊Dic₆₇	C₂×D₄	1	4	yes	—
144	C₄×Dic₆₇	—	2	4	no	—
145	C₄×Dic₆₇	—	2	4	no	—
146	C₄×Dic₆₇	—	2	16	no	—
147	C₄×Dic₆₇	C₂×D₄	1	4	yes	—
148	C₄×Dic₆₇	C₂⁴	1	4	yes	—
149	C₂⁴×C₆₇	—	2	2	no	—
150	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
151	#41×C₆₇	—	2	16	no	—
152	#41×C₆₇	—	2	16	no	—
153	#41×C₆₇	—	2	8	no	—
154	#41×C₆₇	—	2	8	no	—
155	#41×C₆₇	C₂²×C₄	1	16	yes	—
156	#41×C₆₇	C₂²×C₄	1	16	yes	—
157	C₂×Q₈×C₆₇	—	2	2	no	—
158	C₂×Q₈×C₆₇	—	2	4	no	—
159	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
160	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
161	C₂×D₄×C₆₇	—	2	16	no	—
162	C₂×D₄×C₆₇	—	2	4	no	—
163	C₂×D₄×C₆₇	—	2	4	no	—
164	C₂×D₄×C₆₇	—	2	2	no	—
165	C₂×D₄×C₆₇	—	2	4	no	—
166	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
167	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₆₇	—	2	2	no	—
169	C₂²×C₄×C₆₇	—	2	16	no	—
170	C₂²×C₄×C₆₇	—	2	4	no	—
171	C₂²×C₄×C₆₇	—	2	4	no	—
172	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
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	#41	1	4	yes	—
177	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
180	Q₁₆×C₆₇	C₂²×C₄	1	8	yes	—
181	Q₁₆×C₆₇	C₂²×C₄	1	8	yes	—
182	SD₁₆×C₆₇	C₂²×C₄	1	16	yes	—
183	SD₁₆×C₆₇	C₂²×C₄	1	16	yes	—
184	D₈×C₆₇	C₂²×C₄	1	8	yes	—
185	D₈×C₆₇	C₂²×C₄	1	8	yes	—
186	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
187	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
188	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
189	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
190	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
191	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
192	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
193	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
195	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂³×C₆₇	—	2	4	no	—
197	C₂³×C₆₇	—	2	8	no	—
198	C₂³×C₆₇	—	4	2	no	—
199	C₂³×C₆₇	—	8	4	no	—
200	C₂³×C₆₇	C₄×D₄	1	4	yes	—
201	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
202	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
203	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₆₇	—	2	8	no	—
205	Q₈×C₆₇	—	2	4	no	—
206	Q₈×C₆₇	C₂³×C₄	1	8	yes	—
207	D₄×C₆₇	—	2	16	no	—
208	D₄×C₆₇	—	2	16	no	—
209	D₄×C₆₇	—	2	8	no	—
210	D₄×C₆₇	—	2	4	no	—
211	D₄×C₆₇	C₂³×C₄	1	8	yes	—
212	C₂×C₄×C₆₇	—	2	8	no	—
213	C₂×C₄×C₆₇	—	2	4	no	—
214	C₂×C₄×C₆₇	—	2	16	no	—
215	C₂×C₄×C₆₇	—	2	16	no	—
216	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
217	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
218	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
219	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
221	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
226	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
227	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
228	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
229	C₂×Dic₆₇	—	2	8	no	—
230	C₂×Dic₆₇	—	4	4	no	—
231	C₂×Dic₆₇	—	8	16	no	—
232	C₂×Dic₆₇	—	8	4	no	—
233	C₂×Dic₆₇	C₂²×D₄	1	8	yes	—
234	C₈×C₆₇	C₂³×C₄	1	2	yes	—
235	C₈×C₆₇	C₂³×C₄	1	2	yes	—
236	C₈×C₆₇	C₂³×C₄	1	2	yes	—
237	C₈×C₆₇	C₂³×C₄	1	2	yes	—
238	C₆₇⋊C₈	—	2	4	no	—
239	C₂²×C₆₇	—	2	2	no	—
240	C₂²×C₆₇	—	2	2	no	—
241	C₂²×C₆₇	—	2	2	no	—
242	C₂²×C₆₇	—	2	8	no	—
243	C₂²×C₆₇	—	4	4	no	—
244	C₂²×C₆₇	—	4	8	no	—
245	C₂²×C₆₇	—	8	8	no	—
246	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
247	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
248	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
249	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
250	C₄×C₆₇	—	2	8	no	—
251	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
252	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
253	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
254	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
255	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
256	Dic₆₇	—	2	8	no	—
257	Dic₆₇	—	4	8	no	—
258	#60167	—	67	1	no	maximal, Sylow
259	C₂×C₆₇	—	2	2	no	—
260	C₂×C₆₇	—	2	2	no	—
261	C₂×C₆₇	—	2	2	no	—
262	C₂×C₆₇	—	4	8	no	—
263	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
264	C₂×C₆₇	#3584	1	2	yes	—
265	C₂²×#135	D₆₇	1	1	yes	characteristic
266	#3428	—	67	2	no	—
267	#2952	—	67	4	no	—
268	#2951	—	67	4	no	—
269	#2950	—	67	2	no	—
270	#2949	—	67	4	no	—
271	#2948	—	67	2	no	—
272	#2943	—	67	4	no	—
273	C₄×#135	—	67	4	no	—
274	C₂×#427	—	67	1	no	—
275	#2896	—	67	2	no	—
276	C₂×#405	—	67	1	no	—
277	C₆₇	#60167	1	1	yes	characteristic, complemented, Sylow
278	C₂²×#41	C₂×D₆₇	1	2	yes	—
279	C₂×#135	Dic₆₇	1	16	yes	complemented
280	C₂×#135	C₂×D₆₇	1	2	yes	—
281	C₂×#135	C₂×D₆₇	1	2	yes	—
282	C₂×#135	C₂×D₆₇	1	2	yes	—
283	C₂×#135	C₂×D₆₇	1	2	yes	—
284	C₂²×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
285	C₂²×SD₁₆	C₂×D₆₇	1	2	yes	—
286	C₂²×D₈	C₂×D₆₇	1	1	yes	characteristic
287	C₂²×M₁₆	—	67	1	no	—
288	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
289	#520	—	67	8	no	—
290	#520	—	134	4	no	—
291	#519	—	67	4	no	—
292	#518	—	67	4	no	—
293	#518	—	134	4	no	—
294	C₄×#41	—	67	8	no	—
295	C₄×#41	—	134	4	no	—
296	C₂×#117	—	67	1	no	—
297	C₂×#117	—	67	2	no	—
298	C₂×#117	—	134	4	no	—
299	#442	—	67	8	no	—
300	#441	—	67	8	no	—
301	#440	—	67	16	no	—
302	C₄×Q₁₆	—	67	8	no	—
303	C₄×SD₁₆	—	67	16	no	—
304	C₄×D₈	—	67	8	no	—
305	#427	—	67	2	no	—
306	#427	—	67	2	no	—
307	#427	—	67	2	no	—
308	#427	—	67	2	no	—
309	C₂×#107	—	67	2	no	—
310	C₂×#106	—	67	2	no	—
311	#419	—	67	4	no	—
312	#418	—	67	4	no	—
313	#417	—	67	8	no	—
314	#416	—	67	8	no	—
315	#405	—	67	2	no	—
316	#405	—	67	2	no	—
317	#405	—	67	2	no	—
318	#405	—	67	2	no	—
319	C₂×#97	—	67	2	no	—
320	C₂×C₄×C₈	—	67	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	8	no	—
324	C₂×#41	C₂×Dic₆₇	1	16	yes	complemented
325	C₂×#41	C₂²×D₆₇	1	4	yes	—
326	C₂×#41	C₂²×D₆₇	1	4	yes	—
327	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
330	C₂³×C₄	—	2	2	no	—
331	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
332	#135	C₂×Dic₆₇	1	16	yes	complemented
333	#135	C₂×Dic₆₇	1	16	yes	complemented
334	#135	C₂×Dic₆₇	1	16	yes	complemented
335	#135	C₂×Dic₆₇	1	16	yes	complemented
336	C₂×Q₁₆	C₂×Dic₆₇	1	8	yes	complemented
337	C₂×Q₁₆	C₂²×D₆₇	1	2	yes	—
338	C₂×Q₁₆	C₂²×D₆₇	1	2	yes	—
339	C₂×SD₁₆	C₂×Dic₆₇	1	16	yes	complemented
340	C₂×SD₁₆	C₂²×D₆₇	1	4	yes	—
341	C₂×SD₁₆	C₂²×D₆₇	1	4	yes	—
342	C₂×D₈	C₂×Dic₆₇	1	8	yes	complemented
343	C₂×D₈	C₂²×D₆₇	1	2	yes	—
344	C₂×D₈	C₂²×D₆₇	1	2	yes	—
345	C₂×M₁₆	—	67	2	no	—
346	C₂×M₁₆	—	67	2	no	—
347	C₂×M₁₆	—	134	4	no	—
348	C₂²×C₈	—	67	2	no	—
349	C₂²×C₈	C₂×Dic₆₇	1	8	yes	complemented
350	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
354	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
356	C₄×Q₈	—	67	16	no	—
357	C₄×Q₈	—	134	8	no	—
358	C₄×D₄	—	67	16	no	—
359	C₄×D₄	—	134	16	no	—
360	C₄×D₄	—	134	8	no	—
361	C₄×D₄	—	134	16	no	—
362	#117	—	67	2	no	—
363	#117	—	67	2	no	—
364	#117	—	67	2	no	—
365	#117	—	67	2	no	—
366	#117	—	67	4	no	—
367	#117	—	67	4	no	—
368	#117	—	134	8	no	—
369	#117	—	134	8	no	—
370	#117	—	134	8	no	—
371	#117	—	134	2	no	—
372	#117	—	134	2	no	—
373	C₂×C₄⋊C₄	—	67	2	no	—
374	C₂×C₄⋊C₄	—	67	4	no	—
375	C₂×C₄⋊C₄	—	134	8	no	—
376	C₂×C₂²⋊C₄	—	67	2	no	—
377	C₂×C₂²⋊C₄	—	134	8	no	—
378	C₂×C₂²⋊C₄	—	134	2	no	—
379	C₂×C₄²	—	67	2	no	—
380	C₂×C₄²	—	134	8	no	—
381	C₂×C₄²	—	134	2	no	—
382	#107	—	67	4	no	—
383	#107	—	67	4	no	—
384	#106	—	67	4	no	—
385	#106	—	67	4	no	—
386	#103	—	67	16	no	—
387	#102	—	67	16	no	—
388	#97	—	67	4	no	—
389	#97	—	67	4	no	—
390	C₄×C₈	—	67	4	no	—
391	C₄×C₈	—	67	4	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
394	#41	—	2	16	no	—
395	#41	—	2	16	no	—
396	#41	—	2	8	no	—
397	#41	—	2	8	no	—
398	#41	C₂²×Dic₆₇	1	16	yes	—
399	#41	C₂²×Dic₆₇	1	16	yes	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	C₂²×Dic₆₇	1	8	yes	—
403	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
404	C₂×D₄	—	2	16	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	C₂²×Dic₆₇	1	8	yes	—
410	C₂×D₄	C₂³×D₆₇	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	16	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	67	4	no	—
416	C₂²×C₄	—	134	16	no	—
417	C₂²×C₄	—	134	4	no	—
418	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
419	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
420	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
421	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
422	C₂²×C₄	#11761627	1	4	yes	—
423	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
426	Q₁₆	C₂²×Dic₆₇	1	8	yes	—
427	Q₁₆	C₂²×Dic₆₇	1	8	yes	—
428	SD₁₆	C₂²×Dic₆₇	1	16	yes	—
429	SD₁₆	C₂²×Dic₆₇	1	16	yes	—
430	D₈	C₂²×Dic₆₇	1	8	yes	—
431	D₈	C₂²×Dic₆₇	1	8	yes	—
432	M₁₆	—	134	4	no	—
433	M₁₆	—	134	4	no	—
434	C₂×C₈	—	67	4	no	—
435	C₂×C₈	—	134	4	no	—
436	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
437	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
438	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
439	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
440	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
441	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
442	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
443	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
444	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
445	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
446	C₄⋊C₄	—	67	4	no	—
447	C₄⋊C₄	—	67	4	no	—
448	C₄⋊C₄	—	67	8	no	—
449	C₄⋊C₄	—	134	16	no	—
450	C₄⋊C₄	—	134	4	no	—
451	C₂²⋊C₄	—	67	4	no	—
452	C₂²⋊C₄	—	67	4	no	—
453	C₂²⋊C₄	—	134	16	no	—
454	C₂²⋊C₄	—	134	4	no	—
455	C₂²⋊C₄	—	134	4	no	—
456	C₄²	—	67	4	no	—
457	C₄²	—	67	4	no	—
458	C₄²	—	134	16	no	—
459	C₄²	—	134	4	no	—
460	C₄²	—	134	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	8	4	no	—
465	C₂³	D₄×Dic₆₇	1	4	yes	—
466	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
467	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
468	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	Q₈	—	2	4	no	—
471	Q₈	C₂³×Dic₆₇	1	8	yes	—
472	D₄	—	2	16	no	—
473	D₄	—	2	16	no	—
474	D₄	—	2	8	no	—
475	D₄	—	2	4	no	—
476	D₄	C₂³×Dic₆₇	1	8	yes	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	16	no	—
480	C₂×C₄	—	2	16	no	—
481	C₂×C₄	—	268	4	no	—
482	C₂×C₄	—	536	4	no	—
483	C₂×C₄	—	536	16	no	—
484	C₂×C₄	—	67	8	no	—
485	C₂×C₄	—	134	8	no	—
486	C₂×C₄	D₄×Dic₆₇	1	4	yes	—
487	C₂×C₄	D₄×Dic₆₇	1	4	yes	—
488	C₂×C₄	D₄×Dic₆₇	1	4	yes	—
489	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
490	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
491	C₂×C₄	C₂³×Dic₆₇	1	2	yes	—
492	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
494	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
495	C₂×C₄	C₂×#11761627	1	2	yes	—
496	C₂×C₄	C₂×#11761627	1	2	yes	—
497	C₂×C₄	C₂×#11761627	1	2	yes	—
498	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
499	C₈	—	134	4	no	—
500	C₈	C₂³×Dic₆₇	1	2	yes	—
501	C₈	C₂³×Dic₆₇	1	2	yes	—
502	C₈	C₂³×Dic₆₇	1	2	yes	—
503	C₈	C₂³×Dic₆₇	1	2	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₂×D₄×Dic₆₇	1	2	yes	—
512	C₂²	C₂×D₄×Dic₆₇	1	2	yes	—
513	C₂²	C₂×D₄×Dic₆₇	1	2	yes	—
514	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	268	8	no	—
517	C₄	—	134	8	no	—
518	C₄	C₂×D₄×Dic₆₇	1	2	yes	—
519	C₄	C₂×D₄×Dic₆₇	1	2	yes	—
520	C₄	C₂×D₄×Dic₆₇	1	2	yes	—
521	C₄	C₂⁴×Dic₆₇	1	1	yes	characteristic
522	C₄	C₂²×#11761627	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	4	8	no	—
527	C₂	C₂²×D₄×Dic₆₇	1	1	yes	characteristic
528	C₂	#22574978	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting, prime radical	C₂²×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂³×D₄
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂²×#135	D₆₇
hypocenter	C₆₇	#60167
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. #22573412	C₂	semidirect
2. #22569093	C₂	semidirect
3. #22569085	C₂	semidirect
4. #22569077	C₂	semidirect
5. #22569069	C₂	semidirect
6. #22569061	C₂	semidirect
7. #22569010	C₂	semidirect
8. #135×Dic₆₇	C₂	semidirect
9. C₂×#16863434	C₂	semidirect
10. #22568728	C₂	semidirect
11. C₂×#16863351	C₂	semidirect
15. #16863879	C₂²	semidirect
20. #41×Dic₆₇	C₂²	semidirect
24. #16863508	C₂²	semidirect
25. #16863503	C₂²	semidirect
26. #16863497	C₂²	semidirect
27. Q₁₆×Dic₆₇	C₂²	semidirect
28. SD₁₆×Dic₆₇	C₂²	semidirect
29. D₈×Dic₆₇	C₂²	semidirect
32. #16863434	C₂²	semidirect
33. #16863434	C₂²	semidirect
34. C₂×#14523977	C₂²	semidirect
35. C₂×#14523975	C₂²	semidirect
38. #16863397	C₂²	semidirect
39. #16863392	C₂²	semidirect
42. #16863351	C₂²	semidirect
43. #16863351	C₂²	semidirect
44. C₂×#14523953	C₂²	semidirect
45. C₂×C₈×Dic₆₇	C₂²	semidirect
47. C₂×#135×C₆₇	C₄	semidirect
99. C₂×#41×C₆₇	C₂×C₄	semidirect
107. #135×C₆₇	C₂×C₄	semidirect
108. #135×C₆₇	C₂×C₄	semidirect
109. #135×C₆₇	C₂×C₄	semidirect
110. #135×C₆₇	C₂×C₄	semidirect
111. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
114. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
117. C₂×D₈×C₆₇	C₂×C₄	semidirect
120. C₂²×C₈×C₆₇	C₂×C₄	semidirect
277. C₆₇	#60167	semidirect
279. C₂×#135	Dic₆₇	semidirect
324. C₂×#41	C₂×Dic₆₇	semidirect
332. #135	C₂×Dic₆₇	semidirect
333. #135	C₂×Dic₆₇	semidirect
334. #135	C₂×Dic₆₇	semidirect
335. #135	C₂×Dic₆₇	semidirect
336. C₂×Q₁₆	C₂×Dic₆₇	semidirect
339. C₂×SD₁₆	C₂×Dic₆₇	semidirect
342. C₂×D₈	C₂×Dic₆₇	semidirect
349. C₂²×C₈	C₂×Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573412	2
#22569093	2
#22569085	2
#22569077	2
#22569069	2
#22569061	2
#22569010	2
#135×Dic₆₇	2
C₂×#16863434	2
#22568728	2
C₂×#16863351	2
C₂²×#135×C₆₇	2
#60167	67