Subgroups — C₂×#22560859 #30858332

Order 17152.

1082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523979	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14523970	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863363	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863352	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560859	C₂	1	8	yes	maximal, direct product factor
6	C₂×#16863155	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761612	C₂²	1	1	yes	characteristic
10	C₂²×#11761612	C₂²	1	1	yes	characteristic
11	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
13	C₂×#14523979	—	2	4	no	—
14	C₂×#14523979	C₂²	1	4	yes	complemented
15	C₂×#14523970	—	2	4	no	—
16	C₂×#14523970	C₂²	1	4	yes	—
17	#16863363	—	2	2	no	—
18	#16863363	C₂²	1	4	yes	—
19	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
20	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
21	#16863352	—	2	2	no	—
22	#16863352	C₂²	1	4	yes	complemented
23	C₂×#14523954	—	2	1	no	—
24	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
25	#16863155	C₂²	1	4	yes	complemented
26	#16863150	C₂²	1	4	yes	complemented
27	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
30	#416×C₆₇	C₄	1	4	yes	complemented
31	#416×C₆₇	C₂²	1	4	yes	—
32	C₂×#103×C₆₇	C₄	1	1	yes	characteristic, complemented
33	C₂×#103×C₆₇	C₄	1	1	yes	characteristic, complemented
34	C₂×#102×C₆₇	C₄	1	1	yes	characteristic, complemented
35	C₂×#102×C₆₇	C₄	1	1	yes	characteristic, complemented
36	C₂³×Dic₆₇	—	2	1	no	—
37	C₂×#11761612	—	2	1	no	—
38	C₂×#11761612	—	2	1	no	—
39	C₂×#11761612	—	2	2	no	—
40	C₂×#11761612	—	2	2	no	—
41	C₂×#11761612	—	2	2	no	—
42	C₂×#11761612	D₄	1	4	yes	—
43	C₂×#11761612	C₂³	1	2	yes	—
44	C₂×#11761612	C₂³	1	2	yes	—
45	C₂²×C₆₇⋊C₈	—	2	1	no	—
46	C₂²×C₆₇⋊C₈	—	2	1	no	—
47	C₂²×C₆₇⋊C₈	—	2	2	no	—
48	C₂²×C₆₇⋊C₈	—	2	2	no	—
49	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
50	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
51	C₂²×C₆₇⋊C₈	D₄	1	2	yes	—
52	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
53	C₂×C₄×Dic₆₇	—	2	2	no	—
54	C₂×C₄×Dic₆₇	—	2	2	no	—
55	C₂×C₄×Dic₆₇	—	2	1	no	—
56	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
57	#14523979	—	2	8	no	—
58	#14523970	—	2	8	no	—
59	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
60	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
61	#14523954	—	2	4	no	—
62	C₄×C₆₇⋊C₈	—	2	4	no	—
63	C₂×#41×C₆₇	—	2	1	no	—
64	C₂×#41×C₆₇	—	2	1	no	—
65	C₂×#41×C₆₇	—	2	2	no	—
66	C₂×#41×C₆₇	—	2	2	no	—
67	C₂×#41×C₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	—	2	2	no	—
69	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
70	C₂×#41×C₆₇	C₂³	1	2	yes	—
71	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₆₇	—	2	1	no	—
73	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₆₇	—	2	1	no	—
75	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₇	—	2	2	no	—
77	C₂²×C₈×C₆₇	—	2	2	no	—
78	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
82	#117×C₆₇	—	2	1	no	—
83	#117×C₆₇	—	2	1	no	—
84	#117×C₆₇	C₂×C₄	1	2	yes	—
85	#117×C₆₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
89	C₂×C₄²×C₆₇	—	2	1	no	—
90	#103×C₆₇	C₂×C₄	1	4	yes	complemented
91	#103×C₆₇	C₂×C₄	1	4	yes	complemented
92	#102×C₆₇	C₂×C₄	1	4	yes	complemented
93	#102×C₆₇	C₂×C₄	1	4	yes	complemented
94	C₂²×Dic₆₇	—	2	4	no	—
95	C₂²×Dic₆₇	—	2	2	no	—
96	C₂²×Dic₆₇	—	4	2	no	—
97	C₂²×Dic₆₇	—	4	2	no	—
98	#11761612	—	2	4	no	—
99	#11761612	—	2	2	no	—
100	#11761612	—	2	2	no	—
101	#11761612	—	2	2	no	—
102	#11761612	—	4	2	no	—
103	#11761612	C₂×D₄	1	4	yes	—
104	C₂×C₆₇⋊C₈	—	2	4	no	—
105	C₂×C₆₇⋊C₈	—	2	2	no	—
106	C₂×C₆₇⋊C₈	—	2	2	no	—
107	C₂×C₆₇⋊C₈	—	2	4	no	—
108	C₂×C₆₇⋊C₈	—	2	2	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₂×C₆₇⋊C₈	—	2	2	no	—
111	C₂×C₆₇⋊C₈	—	2	2	no	—
112	C₂×C₆₇⋊C₈	—	4	2	no	—
113	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
114	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
115	C₄×Dic₆₇	—	2	2	no	—
116	C₄×Dic₆₇	—	2	2	no	—
117	C₄×Dic₆₇	—	4	2	no	—
118	C₂⁴×C₆₇	—	2	1	no	—
119	C₂⁴×C₆₇	#41	1	1	yes	characteristic
120	#41×C₆₇	—	2	4	no	—
121	#41×C₆₇	—	2	4	no	—
122	#41×C₆₇	—	2	2	no	—
123	#41×C₆₇	—	2	2	no	—
124	#41×C₆₇	—	2	2	no	—
125	#41×C₆₇	—	2	2	no	—
126	#41×C₆₇	—	4	2	no	—
127	#41×C₆₇	—	4	2	no	—
128	#41×C₆₇	—	4	2	no	—
129	#41×C₆₇	—	4	2	no	—
130	C₂×Q₈×C₆₇	—	2	1	no	—
131	C₂×Q₈×C₆₇	—	2	2	no	—
132	C₂×Q₈×C₆₇	—	2	2	no	—
133	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₆₇	—	2	2	no	—
135	C₂×D₄×C₆₇	—	2	2	no	—
136	C₂×D₄×C₆₇	—	2	2	no	—
137	C₂×D₄×C₆₇	—	2	2	no	—
138	C₂×D₄×C₆₇	—	2	1	no	—
139	C₂×D₄×C₆₇	—	4	2	no	—
140	C₂×D₄×C₆₇	—	4	2	no	—
141	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₆₇	—	2	1	no	—
143	C₂²×C₄×C₆₇	—	2	1	no	—
144	C₂²×C₄×C₆₇	—	2	1	no	—
145	C₂²×C₄×C₆₇	—	2	2	no	—
146	C₂²×C₄×C₆₇	—	2	2	no	—
147	C₂²×C₄×C₆₇	—	4	2	no	—
148	C₂²×C₄×C₆₇	—	4	2	no	—
149	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₇	#41	1	2	yes	—
155	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
156	C₂²×C₄×C₆₇	#41	1	2	yes	—
157	C₂²×C₄×C₆₇	#41	1	2	yes	—
158	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₆₇	—	2	2	no	—
160	C₂×C₈×C₆₇	—	2	2	no	—
161	C₂×C₈×C₆₇	—	2	4	no	—
162	C₂×C₈×C₆₇	—	2	2	no	—
163	C₂×C₈×C₆₇	—	2	2	no	—
164	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
166	C₄⋊C₄×C₆₇	—	2	1	no	—
167	C₄⋊C₄×C₆₇	—	2	1	no	—
168	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
169	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
170	C₂²⋊C₄×C₆₇	—	2	2	no	—
171	C₂²⋊C₄×C₆₇	—	2	2	no	—
172	C₄²×C₆₇	—	2	2	no	—
173	C₄²×C₆₇	—	2	2	no	—
174	C₂³×C₆₇	—	2	2	no	—
175	C₂³×C₆₇	—	2	2	no	—
176	C₂³×C₆₇	—	2	2	no	—
177	C₂³×C₆₇	—	4	2	no	—
178	C₂³×C₆₇	—	4	2	no	—
179	C₂³×C₆₇	—	4	2	no	—
180	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
181	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
182	C₂³×C₆₇	#124	1	2	yes	—
183	C₂³×C₆₇	#126	1	2	yes	—
184	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
185	Q₈×C₆₇	—	2	2	no	—
186	Q₈×C₆₇	—	2	2	no	—
187	Q₈×C₆₇	—	4	2	no	—
188	D₄×C₆₇	—	2	2	no	—
189	D₄×C₆₇	—	2	2	no	—
190	D₄×C₆₇	—	4	2	no	—
191	D₄×C₆₇	—	4	2	no	—
192	D₄×C₆₇	—	4	4	no	—
193	D₄×C₆₇	—	4	2	no	—
194	C₂×C₄×C₆₇	—	2	2	no	—
195	C₂×C₄×C₆₇	—	2	2	no	—
196	C₂×C₄×C₆₇	—	2	2	no	—
197	C₂×C₄×C₆₇	—	4	2	no	—
198	C₂×C₄×C₆₇	—	4	2	no	—
199	C₂×C₄×C₆₇	—	4	2	no	—
200	C₂×C₄×C₆₇	—	4	2	no	—
201	C₂×C₄×C₆₇	—	4	2	no	—
202	C₂×C₄×C₆₇	—	4	4	no	—
203	C₂×C₄×C₆₇	#117	1	2	yes	—
204	C₂×C₄×C₆₇	#117	1	2	yes	—
205	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₆₇	#121	1	2	yes	—
210	C₂×C₄×C₆₇	#121	1	2	yes	—
211	C₂×C₄×C₆₇	#123	1	2	yes	—
212	C₂×C₄×C₆₇	#123	1	2	yes	—
213	C₂×C₄×C₆₇	#124	1	2	yes	—
214	C₂×C₄×C₆₇	#126	1	2	yes	—
215	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
221	C₂×Dic₆₇	—	2	4	no	—
222	C₂×Dic₆₇	—	4	8	no	—
223	C₂×Dic₆₇	—	4	2	no	—
224	C₂×Dic₆₇	—	4	2	no	—
225	C₈×C₆₇	—	2	2	no	—
226	C₈×C₆₇	—	2	2	no	—
227	C₆₇⋊C₈	—	2	4	no	—
228	C₆₇⋊C₈	—	2	2	no	—
229	C₆₇⋊C₈	—	2	2	no	—
230	C₆₇⋊C₈	—	4	2	no	—
231	C₂²×C₆₇	—	2	4	no	—
232	C₂²×C₆₇	—	2	4	no	—
233	C₂²×C₆₇	—	2	1	no	—
234	C₂²×C₆₇	—	2	1	no	—
235	C₂²×C₆₇	—	2	1	no	—
236	C₂²×C₆₇	—	2	1	no	—
237	C₂²×C₆₇	—	4	2	no	—
238	C₂²×C₆₇	—	4	2	no	—
239	C₂²×C₆₇	—	4	2	no	—
240	C₂²×C₆₇	—	8	4	no	—
241	C₂²×C₆₇	#388	1	2	yes	—
242	C₂²×C₆₇	#388	1	2	yes	—
243	C₂²×C₆₇	#443	1	2	yes	—
244	C₂²×C₆₇	#444	1	2	yes	—
245	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₆₇	C₂×#124	1	1	yes	characteristic
247	C₂²×C₆₇	C₂×#126	1	1	yes	characteristic
248	C₄×C₆₇	—	4	2	no	—
249	C₄×C₆₇	—	4	2	no	—
250	C₄×C₆₇	—	4	2	no	—
251	C₄×C₆₇	#388	1	2	yes	—
252	C₄×C₆₇	#388	1	2	yes	—
253	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
254	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
256	C₄×C₆₇	C₂×#123	1	1	yes	characteristic
257	Dic₆₇	—	4	4	no	—
258	C₂×#1929	—	67	1	no	maximal, Sylow
259	C₂×C₆₇	—	2	1	no	—
260	C₂×C₆₇	—	2	1	no	—
261	C₂×C₆₇	—	2	2	no	—
262	C₂×C₆₇	—	8	2	no	—
263	C₂×C₆₇	#1929	1	4	yes	complemented
264	C₂×C₆₇	C₂×#388	1	1	yes	characteristic
265	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
266	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
267	C₂²×#108	—	67	1	no	—
268	C₂²×#104	—	67	1	no	—
269	C₂×#416	D₆₇	1	1	yes	characteristic
270	C₂×#408	—	67	1	no	—
271	C₂×#405	—	67	1	no	—
272	#1929	—	67	8	no	—
273	C₂×#339	—	67	1	no	—
274	C₂×#336	—	67	1	no	—
275	C₆₇	C₂×#1929	1	1	yes	characteristic, complemented, Sylow
276	C₂²×#41	C₂×D₆₇	1	1	yes	characteristic
277	C₂²×M₁₆	—	67	1	no	—
278	C₂²×M₁₆	—	67	1	no	—
279	C₂³×C₈	—	67	1	no	—
280	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
281	C₂×#117	C₂×D₆₇	1	1	yes	characteristic
282	C₂²×C₄²	—	67	1	no	—
283	C₂×#108	—	67	4	no	—
284	C₂×#108	—	134	4	no	—
285	C₂×#104	—	67	4	no	—
286	C₂×#104	—	134	4	no	—
287	#416	Dic₆₇	1	4	yes	complemented
288	#416	C₂×D₆₇	1	4	yes	—
289	C₂×#103	Dic₆₇	1	1	yes	characteristic, complemented
290	C₂×#103	Dic₆₇	1	1	yes	characteristic, complemented
291	C₂×#102	Dic₆₇	1	1	yes	characteristic, complemented
292	C₂×#102	Dic₆₇	1	1	yes	characteristic, complemented
293	#408	—	67	4	no	—
294	#408	—	134	2	no	—
295	C₂×C₂²⋊C₈	—	134	1	no	—
296	C₂×C₂²⋊C₈	—	134	1	no	—
297	#405	—	67	4	no	—
298	#405	—	134	2	no	—
299	C₂×#97	—	134	1	no	—
300	C₂×C₄×C₈	—	134	1	no	—
301	#339	—	67	4	no	—
302	#336	—	67	4	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	C₂×Dic₆₇	1	2	yes	—
310	C₂×#41	C₂²×D₆₇	1	2	yes	—
311	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	134	1	no	—
316	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
317	C₂×M₁₆	—	67	4	no	—
318	C₂×M₁₆	—	67	2	no	—
319	C₂×M₁₆	—	67	2	no	—
320	C₂×M₁₆	—	134	2	no	—
321	C₂×M₁₆	—	134	2	no	—
322	C₂×M₁₆	—	134	1	no	—
323	C₂×M₁₆	—	134	1	no	—
324	C₂×M₁₆	—	134	2	no	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	—	67	2	no	—
328	C₂²×C₈	—	67	1	no	—
329	C₂²×C₈	—	67	1	no	—
330	C₂²×C₈	—	67	2	no	—
331	C₂²×C₈	—	134	1	no	—
332	C₂²×C₈	—	134	1	no	—
333	C₂²×C₈	—	134	2	no	—
334	C₂²×C₈	—	134	2	no	—
335	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
336	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
337	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
338	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
339	#117	—	2	1	no	—
340	#117	—	2	1	no	—
341	#117	C₂×Dic₆₇	1	2	yes	—
342	#117	C₂²×D₆₇	1	2	yes	—
343	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	67	2	no	—
348	C₂×C₄²	—	134	1	no	—
349	C₂×C₄²	—	134	2	no	—
350	C₂×C₄²	—	134	2	no	—
351	#108	—	134	8	no	—
352	#104	—	134	8	no	—
353	#103	C₂×Dic₆₇	1	4	yes	complemented
354	#103	C₂×Dic₆₇	1	4	yes	complemented
355	#102	C₂×Dic₆₇	1	4	yes	complemented
356	#102	C₂×Dic₆₇	1	4	yes	complemented
357	C₂²⋊C₈	—	134	4	no	—
358	C₂²⋊C₈	—	134	4	no	—
359	#97	—	134	4	no	—
360	C₄×C₈	—	134	4	no	—
361	C₂⁴	—	2	1	no	—
362	C₂⁴	#11761627	1	1	yes	characteristic
363	#41	—	2	4	no	—
364	#41	—	2	4	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	#41	—	4	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	268	2	no	—
393	C₂²×C₄	—	268	2	no	—
394	C₂²×C₄	—	134	4	no	—
395	C₂²×C₄	—	134	2	no	—
396	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
397	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
398	C₂²×C₄	D₄×D₆₇	1	2	yes	—
399	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
400	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
401	C₂²×C₄	#11761627	1	2	yes	—
402	C₂²×C₄	#11761627	1	1	yes	characteristic
403	C₂²×C₄	#11761628	1	2	yes	—
404	C₂²×C₄	#11761628	1	2	yes	—
405	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
406	M₁₆	—	268	2	no	—
407	M₁₆	—	67	4	no	—
408	M₁₆	—	134	2	no	—
409	M₁₆	—	134	2	no	—
410	M₁₆	—	134	4	no	—
411	M₁₆	—	134	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	268	2	no	—
418	C₂×C₈	—	67	2	no	—
419	C₂×C₈	—	67	2	no	—
420	C₂×C₈	—	134	2	no	—
421	C₂×C₈	—	134	4	no	—
422	C₂×C₈	—	134	2	no	—
423	C₂×C₈	—	134	2	no	—
424	C₂×C₈	—	134	4	no	—
425	C₂×C₈	—	134	2	no	—
426	C₂×C₈	—	134	2	no	—
427	C₂×C₈	—	134	2	no	—
428	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
429	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
433	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	268	2	no	—
439	C₄²	—	134	2	no	—
440	C₄²	—	134	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
448	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
449	C₂³	#14524029	1	2	yes	—
450	C₂³	#14524036	1	2	yes	—
451	C₂³	C₂×#11761627	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	268	8	no	—
471	C₂×C₄	—	268	2	no	—
472	C₂×C₄	—	268	2	no	—
473	C₂×C₄	—	134	4	no	—
474	C₂×C₄	#14524002	1	2	yes	—
475	C₂×C₄	#14524002	1	2	yes	—
476	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
477	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
478	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
479	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
480	C₂×C₄	#14524016	1	2	yes	—
481	C₂×C₄	#14524016	1	2	yes	—
482	C₂×C₄	#14524025	1	2	yes	—
483	C₂×C₄	#14524025	1	2	yes	—
484	C₂×C₄	#14524029	1	2	yes	—
485	C₂×C₄	#14524036	1	2	yes	—
486	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
489	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
490	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
491	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₈	—	268	2	no	—
495	C₈	—	134	4	no	—
496	C₈	—	134	2	no	—
497	C₈	—	134	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	#16863289	1	2	yes	—
509	C₂²	#16863289	1	2	yes	—
510	C₂²	#16863513	1	2	yes	—
511	C₂²	#16863518	1	2	yes	—
512	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
513	C₂²	C₂×#14524029	1	1	yes	characteristic
514	C₂²	C₂×#14524036	1	1	yes	characteristic
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	268	4	no	—
519	C₄	#16863289	1	2	yes	—
520	C₄	#16863289	1	2	yes	—
521	C₄	C₂×#14524002	1	1	yes	characteristic
522	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
523	C₄	C₂×#14524016	1	1	yes	characteristic
524	C₄	C₂×#14524025	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	1	no	—
528	C₂	—	8	2	no	—
529	C₂	#22560859	1	4	yes	direct product factor
530	C₂	C₂×#16863289	1	1	yes	characteristic
531	C₂	C₂×#16863513	1	1	yes	characteristic
532	C₂	C₂×#16863518	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#416×C₆₇	C₂
socle	C₂³×C₆₇	C₄×D₄
prime radical	C₂²×#41×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#416	D₆₇
hypocenter	C₆₇	C₂×#1929
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#416

Complements

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

N	H ≅ G/N	type
1. C₂²×#14523979	C₂	semidirect
4. C₂×#16863352	C₂	semidirect
5. #22560859	C₂	direct (N × H)
6. C₂×#16863155	C₂	semidirect
7. C₂×#16863150	C₂	semidirect
14. C₂×#14523979	C₂²	semidirect
22. #16863352	C₂²	semidirect
25. #16863155	C₂²	semidirect
26. #16863150	C₂²	semidirect
30. #416×C₆₇	C₄	semidirect
32. C₂×#103×C₆₇	C₄	semidirect
33. C₂×#103×C₆₇	C₄	semidirect
34. C₂×#102×C₆₇	C₄	semidirect
35. C₂×#102×C₆₇	C₄	semidirect
90. #103×C₆₇	C₂×C₄	semidirect
91. #103×C₆₇	C₂×C₄	semidirect
92. #102×C₆₇	C₂×C₄	semidirect
93. #102×C₆₇	C₂×C₄	semidirect
263. C₂×C₆₇	#1929	semidirect
275. C₆₇	C₂×#1929	semidirect
287. #416	Dic₆₇	semidirect
289. C₂×#103	Dic₆₇	semidirect
290. C₂×#103	Dic₆₇	semidirect
291. C₂×#102	Dic₆₇	semidirect
292. C₂×#102	Dic₆₇	semidirect
353. #103	C₂×Dic₆₇	semidirect
354. #103	C₂×Dic₆₇	semidirect
355. #102	C₂×Dic₆₇	semidirect
356. #102	C₂×Dic₆₇	semidirect
529. C₂	#22560859	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523979	2
C₂²×#14523970	2
C₂×#16863363	2
C₂×#16863352	2
#22560859	2
C₂×#16863155	2
C₂×#16863150	2
C₂×#416×C₆₇	2
C₂×#1929	67

Subgroups — C2×#22560859 #30858332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22560859 #30858332