Subgroups — #30854408

Order 17152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863515	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863510	C₂	1	1	yes	maximal, characteristic
3	#22569007	C₂	1	1	yes	maximal, characteristic
4	#22568638	C₂	1	1	yes	maximal, characteristic, complemented
5	#22568637	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560116	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560092	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560087	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560054	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560050	C₂	1	1	yes	maximal, characteristic, complemented
11	#22560047	C₂	1	1	yes	maximal, characteristic, complemented
12	#22560043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#14523971	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14523954	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#104×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524063	C₂²	1	1	yes	characteristic
17	C₂×#14524051	C₂²	1	1	yes	characteristic
18	C₂×#14524051	C₂²	1	1	yes	characteristic
19	C₂×#14524050	C₂²	1	1	yes	characteristic
20	C₂×#14524050	C₂²	1	1	yes	characteristic
21	C₄×#11761628	C₂²	1	1	yes	characteristic
22	#16863515	C₄	1	8	yes	complemented
23	#16863510	C₄	1	8	yes	complemented
24	#16863506	C₄	1	2	yes	complemented
25	#16863501	C₄	1	2	yes	complemented
26	#16863496	C₄	1	2	yes	complemented
27	#16863494	C₄	1	2	yes	complemented
28	C₂×#14523978	C₂²	1	1	yes	characteristic
29	C₂×#14523978	C₂²	1	1	yes	characteristic
30	#16863432	C₂²	1	1	yes	characteristic
31	C₂×#14523971	C₂²	1	1	yes	characteristic
32	C₂×#14523971	C₂²	1	1	yes	characteristic
33	#16863392	C₂²	1	1	yes	characteristic
34	#16863390	C₂²	1	1	yes	characteristic
35	#16863354	C₂²	1	1	yes	characteristic
36	#16863354	C₂²	1	1	yes	characteristic
37	#16863352	—	2	1	no	—
38	#16863352	—	2	1	no	—
39	#16863352	C₂²	1	1	yes	characteristic
40	#16863352	C₂²	1	1	yes	characteristic
41	#16863350	—	2	1	no	—
42	#16863350	—	2	1	no	—
43	C₄×#11761612	—	2	1	no	—
44	C₄×#11761612	C₂²	1	1	yes	characteristic
45	#16863348	—	2	1	no	—
46	C₂×#14523954	—	2	1	no	—
47	C₂×#14523954	C₂²	1	1	yes	characteristic
48	C₂×#14523954	C₂²	1	1	yes	characteristic
49	C₂×#14523954	C₂²	1	1	yes	characteristic
50	C₂×#14523954	C₂²	1	1	yes	characteristic
51	#97×D₆₇	—	2	1	no	—
52	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
54	#16863160	C₂²	1	1	yes	characteristic
55	#16863160	C₂²	1	1	yes	characteristic
56	#16863156	C₂²	1	1	yes	characteristic
57	#16863156	C₂²	1	1	yes	characteristic
58	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#104×C₆₇	C₂²	1	1	yes	characteristic
61	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
62	C₄³×C₆₇	C₂²	1	1	yes	characteristic
63	#339×C₆₇	C₂²	1	1	yes	characteristic
64	#339×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#11761628	C₂³	1	1	yes	characteristic
66	#14524063	C₂×C₄	1	4	yes	—
67	#14524063	C₂×C₄	1	4	yes	—
68	C₂×#11761618	C₂×C₄	1	1	yes	characteristic
69	C₂×#11761616	C₂×C₄	1	1	yes	characteristic
70	C₂×#11761615	C₂×C₄	1	1	yes	characteristic
71	C₂×#11761613	C₂×C₄	1	1	yes	characteristic
72	#14524051	—	2	2	no	—
73	#14524051	—	2	2	no	—
74	#14524051	C₂×C₄	1	4	yes	complemented
75	#14524051	C₂×C₄	1	4	yes	complemented
76	#14524050	—	2	2	no	—
77	#14524050	—	2	2	no	—
78	#14524050	C₂×C₄	1	4	yes	complemented
79	#14524050	C₂×C₄	1	4	yes	complemented
80	C₂×#11761612	—	2	1	no	—
81	C₂×#11761612	—	2	1	no	—
82	C₂×#11761612	C₂³	1	1	yes	characteristic
83	C₂×#11761612	C₂³	1	1	yes	characteristic
84	C₂×#11761611	—	2	1	no	—
85	C₂×#11761611	—	2	1	no	—
86	C₂²×C₆₇⋊C₈	—	2	1	no	—
87	C₂²×C₆₇⋊C₈	—	2	1	no	—
88	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
90	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
91	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₈×D₆₇	—	2	1	no	—
93	C₂×C₈×D₆₇	—	2	1	no	—
94	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
95	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
96	C₄×C₂²⋊D₆₇	—	2	2	no	—
97	#14524002	C₂³	1	1	yes	characteristic
98	#14524000	—	2	1	no	—
99	C₄²×D₆₇	—	2	1	no	—
100	#14523978	C₂×C₄	1	4	yes	complemented
101	#14523978	C₂×C₄	1	4	yes	complemented
102	#14523976	C₂×C₄	1	2	yes	—
103	#14523974	C₂×C₄	1	2	yes	—
104	#14523971	C₂×C₄	1	4	yes	complemented
105	#14523971	C₂×C₄	1	4	yes	complemented
106	#14523967	C₂×C₄	1	2	yes	—
107	#14523966	C₂×C₄	1	2	yes	—
108	#14523964	C₂×C₄	1	2	yes	—
109	#14523963	C₂×C₄	1	2	yes	—
110	#14523954	—	2	1	no	—
111	#14523954	—	2	1	no	—
112	#14523954	—	2	2	no	—
113	#14523954	—	2	1	no	—
114	#14523954	C₂×C₄	1	2	yes	—
115	#14523954	C₂×C₄	1	2	yes	—
116	#14523954	C₂×C₄	1	4	yes	complemented
117	#14523954	D₄	1	1	yes	characteristic
118	#14523954	D₄	1	1	yes	characteristic
119	#14523954	D₄	1	1	yes	characteristic
120	#14523954	D₄	1	1	yes	characteristic
121	#14523953	—	2	1	no	—
122	#14523953	—	2	1	no	—
123	C₄×C₆₇⋊C₈	—	2	1	no	—
124	C₄×C₆₇⋊C₈	—	2	1	no	—
125	C₄×C₆₇⋊C₈	—	2	2	no	—
126	C₄×C₆₇⋊C₈	—	2	1	no	—
127	C₄×C₆₇⋊C₈	C₂×C₄	1	4	yes	complemented
128	C₈×Dic₆₇	—	2	1	no	—
129	C₈×Dic₆₇	—	2	1	no	—
130	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
133	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
134	C₄×D₄×C₆₇	—	2	2	no	—
135	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
136	#117×C₆₇	—	2	1	no	—
137	#117×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₆₇	—	2	1	no	—
139	C₂×C₄²×C₆₇	—	2	2	no	—
140	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	#104×C₆₇	C₂×C₄	1	4	yes	complemented
144	#104×C₆₇	C₂×C₄	1	4	yes	complemented
145	#97×C₆₇	—	2	1	no	—
146	C₄×C₈×C₆₇	—	2	1	no	—
147	#11761628	—	2	1	no	—
148	#11761628	—	2	1	no	—
149	#11761628	C₂²×C₄	1	2	yes	—
150	#11761628	C₂²×C₄	1	2	yes	—
151	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₂²⋊D₆₇	—	2	1	no	—
154	C₂×C₄×D₆₇	—	2	1	no	—
155	C₂×C₄×D₆₇	—	2	2	no	—
156	#11761618	C₄²	1	4	yes	complemented
157	#11761616	C₄²	1	4	yes	complemented
158	#11761615	C₄²	1	4	yes	complemented
159	#11761613	C₄²	1	4	yes	complemented
160	#11761612	—	2	1	no	—
161	#11761612	—	2	1	no	—
162	#11761612	—	2	4	no	—
163	#11761612	—	2	4	no	—
164	#11761612	C₂²×C₄	1	2	yes	—
165	#11761612	C₂²×C₄	1	2	yes	—
166	#11761611	—	2	4	no	—
167	#11761611	—	2	4	no	—
168	C₂×C₆₇⋊C₈	—	2	1	no	—
169	C₂×C₆₇⋊C₈	—	2	1	no	—
170	C₂×C₆₇⋊C₈	—	2	1	no	—
171	C₂×C₆₇⋊C₈	—	2	1	no	—
172	C₂×C₆₇⋊C₈	—	2	4	no	—
173	C₂×C₆₇⋊C₈	—	2	4	no	—
174	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
176	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
181	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
182	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
183	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₆₇⋊C₈	#41	1	2	yes	—
186	C₂×C₆₇⋊C₈	#41	1	2	yes	—
187	C₈×D₆₇	—	2	4	no	—
188	C₈×D₆₇	—	2	4	no	—
189	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
190	Dic₆₇⋊C₄	—	2	2	no	—
191	C₂²⋊Dic₆₇	—	2	1	no	—
192	(C₂×D₆₇)⋊C₄	—	2	2	no	—
193	C₄×Dic₆₇	—	2	2	no	—
194	C₄×Dic₆₇	—	2	1	no	—
195	#41×C₆₇	—	2	1	no	—
196	#41×C₆₇	—	2	1	no	—
197	#41×C₆₇	C₂²×C₄	1	2	yes	—
198	#41×C₆₇	C₂²×C₄	1	2	yes	—
199	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
200	C₂×D₄×C₆₇	—	2	1	no	—
201	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	—	2	1	no	—
203	C₂²×C₄×C₆₇	—	2	1	no	—
204	C₂²×C₄×C₆₇	—	2	1	no	—
205	C₂²×C₄×C₆₇	—	2	2	no	—
206	C₂²×C₄×C₆₇	#41	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	M₁₆×C₆₇	—	2	1	no	—
209	M₁₆×C₆₇	—	2	1	no	—
210	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
211	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₆₇	—	2	1	no	—
213	C₂×C₈×C₆₇	—	2	1	no	—
214	C₄⋊C₄×C₆₇	—	2	2	no	—
215	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
216	C₂²⋊C₄×C₆₇	—	2	1	no	—
217	C₂²⋊C₄×C₆₇	—	2	2	no	—
218	C₄²×C₆₇	—	2	2	no	—
219	C₄²×C₆₇	—	2	1	no	—
220	C₄²×C₆₇	—	2	1	no	—
221	C₄²×C₆₇	—	2	1	no	—
222	C₄²×C₆₇	—	4	4	no	—
223	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
224	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
225	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
226	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₆₇	—	2	1	no	—
229	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
230	C₂²×D₆₇	—	2	1	no	—
231	Q₈×C₆₇	—	2	1	no	—
232	Q₈×C₆₇	C₂×C₄²	1	2	yes	—
233	D₄×C₆₇	—	2	2	no	—
234	D₄×C₆₇	—	2	2	no	—
235	D₄×C₆₇	—	2	1	no	—
236	D₄×C₆₇	C₂×C₄²	1	2	yes	—
237	C₂×C₄×C₆₇	—	2	4	no	—
238	C₂×C₄×C₆₇	—	2	1	no	—
239	C₂×C₄×C₆₇	—	2	2	no	—
240	C₂×C₄×C₆₇	—	2	2	no	—
241	C₂×C₄×C₆₇	—	2	2	no	—
242	C₂×C₄×C₆₇	—	2	2	no	—
243	C₂×C₄×C₆₇	—	2	2	no	—
244	C₂×C₄×C₆₇	—	4	2	no	—
245	C₂×C₄×C₆₇	—	4	2	no	—
246	C₂×C₄×C₆₇	—	8	2	no	—
247	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
255	C₂²⋊D₆₇	—	2	2	no	—
256	C₂²⋊D₆₇	—	2	2	no	—
257	C₂×Dic₆₇	—	2	1	no	—
258	C₂×Dic₆₇	—	2	2	no	—
259	D₂₆₈	—	2	1	no	—
260	D₂₆₈	C₂×C₄²	1	2	yes	—
261	C₄×D₆₇	—	2	2	no	—
262	C₄×D₆₇	—	2	2	no	—
263	C₄×D₆₇	—	8	2	no	—
264	Dic₁₃₄	—	2	1	no	—
265	Dic₁₃₄	C₂×C₄²	1	2	yes	—
266	C₈×C₆₇	—	2	2	no	—
267	C₈×C₆₇	—	2	2	no	—
268	C₆₇⋊C₈	—	2	2	no	—
269	C₆₇⋊C₈	—	2	2	no	—
270	C₆₇⋊C₈	—	2	2	no	—
271	C₆₇⋊C₈	C₂×C₄²	1	2	yes	—
272	C₆₇⋊C₈	C₂×C₄²	1	2	yes	—
273	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
274	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
275	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
276	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
277	C₂²×C₆₇	—	2	2	no	—
278	C₂²×C₆₇	—	2	2	no	—
279	C₂²×C₆₇	—	4	2	no	—
280	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
282	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
283	C₂×D₆₇	—	2	2	no	—
284	C₂×D₆₇	—	4	2	no	—
285	C₄×C₆₇	—	2	4	no	—
286	C₄×C₆₇	—	2	2	no	—
287	C₄×C₆₇	—	2	2	no	—
288	C₄×C₆₇	—	2	2	no	—
289	C₄×C₆₇	—	4	2	no	—
290	C₄×C₆₇	—	4	2	no	—
291	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
292	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
294	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
295	Dic₆₇	—	2	2	no	—
296	Dic₆₇	—	4	2	no	—
297	#20512	—	67	1	no	maximal, Sylow
298	C₂×C₆₇	—	2	1	no	—
299	C₂×C₆₇	—	2	1	no	—
300	C₂×C₆₇	—	4	2	no	—
301	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
302	C₂×C₆₇	#2956	1	2	yes	—
303	D₆₇	—	4	2	no	—
304	C₂×#444	—	67	1	no	—
305	C₂×#443	—	67	1	no	—
306	#2943	—	67	1	no	—
307	#2875	—	67	1	no	—
308	#2875	—	67	1	no	—
309	#1778	—	67	1	no	—
310	#1773	—	67	1	no	—
311	#1772	—	67	1	no	—
312	#1765	—	67	1	no	—
313	#1765	—	67	1	no	—
314	#1764	—	67	1	no	—
315	#1764	—	67	1	no	—
316	C₄×#104	—	67	1	no	—
317	C₄×#104	D₆₇	1	1	yes	characteristic, complemented
318	C₄×#97	—	67	1	no	—
319	C₆₇	#20512	1	1	yes	characteristic, complemented, Sylow
320	C₂×#135	—	67	1	no	—
321	C₂×#131	—	67	1	no	—
322	C₂×#131	—	67	1	no	—
323	C₂×#131	—	67	1	no	—
324	C₂×#131	—	67	1	no	—
325	C₄×#41	—	67	1	no	—
326	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
327	#444	—	67	8	no	—
328	#443	—	67	8	no	—
329	#442	—	67	2	no	—
330	#441	—	67	2	no	—
331	#440	—	67	2	no	—
332	#440	—	67	2	no	—
333	C₂×#108	—	67	1	no	—
334	C₂×#108	—	67	1	no	—
335	#427	—	67	1	no	—
336	C₂×#104	—	67	1	no	—
337	C₂×#104	—	67	1	no	—
338	C₂×#104	C₂×D₆₇	1	1	yes	characteristic
339	C₂×#104	C₂×D₆₇	1	1	yes	characteristic
340	#416	—	67	1	no	—
341	#416	—	67	1	no	—
342	#405	—	67	1	no	—
343	#405	—	67	1	no	—
344	#405	—	67	1	no	—
345	#405	—	67	1	no	—
346	#405	—	134	1	no	—
347	#405	—	134	1	no	—
348	#405	—	134	1	no	—
349	#405	—	134	1	no	—
350	C₄×M₁₆	—	67	1	no	—
351	C₄×M₁₆	—	134	1	no	—
352	C₄×M₁₆	—	134	1	no	—
353	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
354	C₂×#97	—	67	1	no	—
355	C₂×#97	—	67	1	no	—
356	C₂×#97	—	67	1	no	—
357	C₂×#97	—	67	1	no	—
358	C₂×#97	—	134	1	no	—
359	C₂×#97	—	134	1	no	—
360	C₂×C₄×C₈	—	67	1	no	—
361	C₂×C₄×C₈	—	67	1	no	—
362	C₄³	C₂×D₆₇	1	1	yes	characteristic
363	#341	—	67	1	no	—
364	#341	—	67	1	no	—
365	#339	—	67	1	no	—
366	#339	—	67	1	no	—
367	#339	C₂×D₆₇	1	1	yes	characteristic
368	#339	C₂×D₆₇	1	1	yes	characteristic
369	C₂×#41	—	67	1	no	—
370	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
371	#135	—	67	4	no	—
372	#135	—	67	4	no	—
373	C₂×Q₁₆	—	67	1	no	—
374	C₂×SD₁₆	—	67	1	no	—
375	C₂×SD₁₆	—	67	1	no	—
376	C₂×D₈	—	67	1	no	—
377	#131	—	67	4	no	—
378	#131	—	67	4	no	—
379	#131	—	67	4	no	—
380	#131	—	67	4	no	—
381	#131	—	134	2	no	—
382	#131	—	134	2	no	—
383	#131	—	134	2	no	—
384	#131	—	134	2	no	—
385	C₂×M₁₆	—	67	1	no	—
386	C₂×M₁₆	—	67	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	C₂²×D₆₇	1	1	yes	characteristic
392	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
393	C₂²×C₈	—	67	1	no	—
394	C₂²×C₈	—	67	1	no	—
395	C₂²×C₈	—	67	1	no	—
396	C₂²×C₈	—	67	1	no	—
397	C₂²×C₈	—	134	1	no	—
398	C₂²×C₈	—	134	1	no	—
399	C₂²×C₈	—	134	1	no	—
400	C₂²×C₈	—	134	1	no	—
401	C₄×Q₈	—	67	2	no	—
402	C₄×Q₈	C₄×D₆₇	1	2	yes	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	67	2	no	—
405	C₄×D₄	—	134	2	no	—
406	C₄×D₄	C₄×D₆₇	1	2	yes	—
407	#117	—	2	1	no	—
408	#117	—	67	1	no	—
409	#117	—	134	1	no	—
410	#117	C₂²×D₆₇	1	1	yes	characteristic
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	—	134	1	no	—
414	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
415	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
416	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
417	#108	—	67	4	no	—
418	#108	—	67	4	no	—
419	#107	—	67	2	no	—
420	#106	—	67	2	no	—
421	#104	—	67	4	no	—
422	#104	—	67	4	no	—
423	#104	C₄×D₆₇	1	4	yes	complemented
424	#104	C₄×D₆₇	1	4	yes	complemented
425	#103	—	67	2	no	—
426	#103	—	67	2	no	—
427	#102	—	67	2	no	—
428	#102	—	67	2	no	—
429	#97	—	2	1	no	—
430	#97	—	67	2	no	—
431	#97	—	67	2	no	—
432	#97	—	67	4	no	—
433	#97	—	67	1	no	—
434	#97	—	67	1	no	—
435	#97	—	67	1	no	—
436	#97	—	67	1	no	—
437	#97	—	134	2	no	—
438	#97	—	134	1	no	—
439	#97	—	134	1	no	—
440	#97	—	134	1	no	—
441	#97	—	134	1	no	—
442	#97	—	134	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	—	67	4	no	—
445	C₄×C₈	—	134	2	no	—
446	C₄×C₈	—	134	1	no	—
447	C₄×C₈	—	134	1	no	—
448	C₄×C₈	—	134	1	no	—
449	C₄×C₈	—	134	1	no	—
450	C₄×C₈	—	134	1	no	—
451	#41	—	2	1	no	—
452	#41	—	2	1	no	—
453	#41	—	67	2	no	—
454	#41	—	67	2	no	—
455	#41	—	134	1	no	—
456	#41	—	134	1	no	—
457	#41	C₂×C₄×D₆₇	1	2	yes	—
458	#41	C₂×C₄×D₆₇	1	2	yes	—
459	C₂×Q₈	—	67	1	no	—
460	C₂×Q₈	C₂×C₄×D₆₇	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	67	1	no	—
463	C₂×D₄	—	134	1	no	—
464	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	134	2	no	—
470	C₂²×C₄	—	134	1	no	—
471	C₂²×C₄	#11761627	1	2	yes	—
472	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
473	Q₁₆	—	67	4	no	—
474	SD₁₆	—	67	4	no	—
475	SD₁₆	—	67	4	no	—
476	D₈	—	67	4	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	67	2	no	—
480	M₁₆	—	67	2	no	—
481	M₁₆	—	134	4	no	—
482	M₁₆	—	134	4	no	—
483	M₁₆	—	134	4	no	—
484	M₁₆	—	134	4	no	—
485	M₁₆	—	134	1	no	—
486	M₁₆	—	134	1	no	—
487	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
488	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	67	2	no	—
492	C₂×C₈	—	67	2	no	—
493	C₂×C₈	—	67	1	no	—
494	C₂×C₈	—	67	1	no	—
495	C₂×C₈	—	67	2	no	—
496	C₂×C₈	—	67	2	no	—
497	C₂×C₈	—	67	1	no	—
498	C₂×C₈	—	67	1	no	—
499	C₂×C₈	—	67	1	no	—
500	C₂×C₈	—	67	1	no	—
501	C₂×C₈	—	67	2	no	—
502	C₂×C₈	—	67	2	no	—
503	C₂×C₈	—	67	2	no	—
504	C₂×C₈	—	134	4	no	—
505	C₂×C₈	—	134	4	no	—
506	C₂×C₈	—	134	4	no	—
507	C₂×C₈	—	134	4	no	—
508	C₂×C₈	—	134	1	no	—
509	C₂×C₈	—	134	1	no	—
510	C₂×C₈	—	134	1	no	—
511	C₂×C₈	—	134	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	67	2	no	—
514	C₄⋊C₄	—	134	2	no	—
515	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	134	1	no	—
519	C₂²⋊C₄	—	134	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	4	4	no	—
525	C₄²	—	134	2	no	—
526	C₄²	—	134	1	no	—
527	C₄²	C₂×C₄×D₆₇	1	2	yes	—
528	C₄²	C₂×C₄×D₆₇	1	2	yes	—
529	C₄²	C₂×C₄×D₆₇	1	2	yes	—
530	C₄²	D₄×D₆₇	1	1	yes	characteristic
531	C₄²	D₄×D₆₇	1	1	yes	characteristic
532	C₂³	—	2	1	no	—
533	C₂³	—	134	1	no	—
534	C₂³	C₂×#11761627	1	1	yes	characteristic
535	Q₈	—	2	1	no	—
536	Q₈	—	67	2	no	—
537	Q₈	—	134	1	no	—
538	Q₈	C₄²×D₆₇	1	2	yes	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	1	no	—
542	D₄	—	67	2	no	—
543	D₄	—	134	2	no	—
544	D₄	—	134	2	no	—
545	D₄	—	134	1	no	—
546	D₄	C₄²×D₆₇	1	2	yes	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	536	2	no	—
558	C₂×C₄	—	134	2	no	—
559	C₂×C₄	—	134	1	no	—
560	C₂×C₄	—	134	2	no	—
561	C₂×C₄	—	134	2	no	—
562	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	2	yes	—
563	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	2	yes	—
564	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
568	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
569	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	67	2	no	—
573	C₈	—	67	2	no	—
574	C₈	—	67	2	no	—
575	C₈	—	67	2	no	—
576	C₈	—	67	2	no	—
577	C₈	—	67	2	no	—
578	C₈	—	134	2	no	—
579	C₈	—	134	2	no	—
580	C₈	—	134	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	268	2	no	—
585	C₂²	—	134	2	no	—
586	C₂²	C₂×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
587	C₂²	C₄×#11761627	1	1	yes	characteristic
588	C₂²	C₄×#11761627	1	1	yes	characteristic
589	C₄	—	2	4	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	268	2	no	—
596	C₄	—	134	2	no	—
597	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
598	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
599	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
600	C₄	#16863864	1	1	yes	characteristic
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	268	2	no	—
605	C₂	C₄×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
606	C₂	#22569115	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₄×#104×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524063	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#104	D₆₇
hypocenter	C₆₇	#20512
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
4. #22568638	C₂	semidirect
5. #22568637	C₂	semidirect
6. #22560116	C₂	semidirect
7. #22560092	C₂	semidirect
8. #22560087	C₂	semidirect
9. #22560054	C₂	semidirect
10. #22560050	C₂	semidirect
11. #22560047	C₂	semidirect
12. #22560043	C₂	semidirect
13. C₄×#14523971	C₂	semidirect
14. C₄×#14523954	C₂	semidirect
15. C₄×#104×C₆₇	C₂	semidirect
22. #16863515	C₄	semidirect
23. #16863510	C₄	semidirect
24. #16863506	C₄	semidirect
25. #16863501	C₄	semidirect
26. #16863496	C₄	semidirect
27. #16863494	C₄	semidirect
74. #14524051	C₂×C₄	semidirect
75. #14524051	C₂×C₄	semidirect
78. #14524050	C₂×C₄	semidirect
79. #14524050	C₂×C₄	semidirect
100. #14523978	C₂×C₄	semidirect
101. #14523978	C₂×C₄	semidirect
104. #14523971	C₂×C₄	semidirect
105. #14523971	C₂×C₄	semidirect
116. #14523954	C₂×C₄	semidirect
127. C₄×C₆₇⋊C₈	C₂×C₄	semidirect
143. #104×C₆₇	C₂×C₄	semidirect
144. #104×C₆₇	C₂×C₄	semidirect
156. #11761618	C₄²	semidirect
157. #11761616	C₄²	semidirect
158. #11761615	C₄²	semidirect
159. #11761613	C₄²	semidirect
317. C₄×#104	D₆₇	semidirect
319. C₆₇	#20512	semidirect
423. #104	C₄×D₆₇	semidirect
424. #104	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863515	2
C₂×#16863510	2
#22569007	2
#22568638	2
#22568637	2
#22560116	2
#22560092	2
#22560087	2
#22560054	2
#22560050	2
#22560047	2
#22560043	2
C₄×#14523971	2
C₄×#14523954	2
C₄×#104×C₆₇	2
#20512	67