Subgroups — C₂×#22561606 #30884547

Order 17152.

1078 conjugacy classes of subgroups.

The subgroup lattice has 592 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	C₂²×#14523959	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14523959	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14523959	C₂	1	1	yes	maximal, characteristic
6	#22561606	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₆₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#430×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
10	C₂²×#11761612	C₂²	1	1	yes	characteristic
11	C₂²×#11761612	C₂²	1	1	yes	characteristic
12	C₂²×#11761612	C₂²	1	1	yes	characteristic
13	#16863445	—	2	2	no	—
14	#16863445	C₂²	1	4	yes	complemented
15	#16863444	—	2	2	no	—
16	#16863444	C₂²	1	4	yes	complemented
17	C₂×#14523979	—	2	2	no	—
18	C₂×#14523978	—	2	2	no	—
19	C₂×#14523959	—	2	2	no	—
20	C₂×#14523959	—	2	2	no	—
21	C₂×#14523959	—	2	2	no	—
22	C₂×#14523959	—	2	2	no	—
23	C₂×#14523959	—	2	2	no	—
24	C₂×#14523959	—	2	2	no	—
25	C₂×#14523959	C₂²	1	4	yes	—
26	C₂×#14523959	C₂²	1	4	yes	—
27	C₂×#14523959	C₂²	1	4	yes	—
28	C₆₇⋊#338	C₂²	1	4	yes	complemented
29	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	#430×C₆₇	—	2	2	no	—
33	#430×C₆₇	C₂²	1	4	yes	complemented
34	C₂×#108×C₆₇	—	2	2	no	—
35	C₂⁴×D₆₇	Q₈	1	2	yes	—
36	C₂²×D₂₆₈	—	2	1	no	—
37	C₂²×D₂₆₈	—	2	1	no	—
38	C₂²×D₂₆₈	—	2	1	no	—
39	C₂²×D₂₆₈	—	2	1	no	—
40	C₂²×D₂₆₈	—	2	1	no	—
41	C₂²×D₂₆₈	—	2	1	no	—
42	C₂²×D₂₆₈	—	2	1	no	—
43	C₂²×D₂₆₈	—	2	1	no	—
44	C₂²×D₂₆₈	—	2	1	no	—
45	C₂²×D₂₆₈	—	2	1	no	—
46	C₂²×D₂₆₈	—	2	1	no	—
47	C₂²×D₂₆₈	—	2	1	no	—
48	C₂²×D₂₆₈	Q₈	1	2	yes	—
49	C₂²×D₂₆₈	C₂³	1	2	yes	—
50	C₂×#11761612	—	2	1	no	—
51	C₂×#11761612	—	2	1	no	—
52	C₂×#11761612	—	2	1	no	—
53	C₂×#11761612	—	2	1	no	—
54	C₂×#11761612	—	2	1	no	—
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	D₄	1	2	yes	—
64	C₂×#11761612	D₄	1	2	yes	—
65	C₂×#11761612	C₂³	1	2	yes	—
66	C₂×#11761612	C₂³	1	2	yes	—
67	C₂×#11761612	C₂³	1	2	yes	—
68	C₂²×C₆₇⋊C₈	—	2	1	no	—
69	C₂²×C₆₇⋊C₈	—	2	1	no	—
70	C₂²×C₆₇⋊C₈	—	2	1	no	—
71	#14523979	—	2	8	no	—
72	#14523978	—	2	8	no	—
73	#14523959	—	2	8	no	—
74	#14523959	—	2	8	no	—
75	#14523959	—	2	8	no	—
76	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₆₇	—	2	1	no	—
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂×M₁₆×C₆₇	—	2	1	no	—
80	C₂×M₁₆×C₆₇	—	2	1	no	—
81	C₂×M₁₆×C₆₇	—	2	1	no	—
82	C₂×M₁₆×C₆₇	—	2	1	no	—
83	C₂×M₁₆×C₆₇	—	2	1	no	—
84	C₂×M₁₆×C₆₇	—	2	1	no	—
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	D₄	1	2	yes	—
89	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
90	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
91	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
92	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
93	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
94	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
95	C₂²×C₈×C₆₇	—	2	1	no	—
96	C₂²×C₈×C₆₇	—	2	1	no	—
97	C₂²×C₈×C₆₇	—	2	1	no	—
98	#108×C₆₇	—	2	8	no	—
99	C₂³×D₆₇	—	2	2	no	—
100	C₂³×D₆₇	—	2	2	no	—
101	C₂³×D₆₇	—	2	2	no	—
102	C₂³×D₆₇	—	2	2	no	—
103	C₂³×D₆₇	—	2	2	no	—
104	C₂³×D₆₇	—	2	2	no	—
105	C₂³×D₆₇	—	8	4	no	—
106	C₂³×D₆₇	C₂×Q₈	1	4	yes	—
107	C₂×D₂₆₈	—	2	2	no	—
108	C₂×D₂₆₈	—	2	2	no	—
109	C₂×D₂₆₈	—	2	2	no	—
110	C₂×D₂₆₈	—	2	2	no	—
111	C₂×D₂₆₈	—	2	2	no	—
112	C₂×D₂₆₈	—	2	2	no	—
113	C₂×D₂₆₈	—	2	2	no	—
114	C₂×D₂₆₈	—	2	2	no	—
115	C₂×D₂₆₈	—	2	2	no	—
116	C₂×D₂₆₈	—	2	2	no	—
117	C₂×D₂₆₈	—	2	2	no	—
118	C₂×D₂₆₈	—	2	2	no	—
119	C₂×D₂₆₈	—	4	1	no	—
120	C₂×D₂₆₈	—	4	1	no	—
121	C₂×D₂₆₈	—	4	1	no	—
122	C₂×D₂₆₈	—	4	1	no	—
123	C₂×D₂₆₈	—	4	1	no	—
124	C₂×D₂₆₈	—	4	1	no	—
125	C₂×D₂₆₈	—	4	1	no	—
126	C₂×D₂₆₈	—	4	1	no	—
127	C₂×D₂₆₈	—	4	1	no	—
128	C₂×D₂₆₈	—	4	1	no	—
129	C₂×D₂₆₈	—	4	1	no	—
130	C₂×D₂₆₈	—	4	1	no	—
131	C₂×D₂₆₈	—	4	1	no	—
132	C₂×D₂₆₈	—	4	1	no	—
133	C₂×D₂₆₈	—	4	1	no	—
134	C₂×D₂₆₈	—	4	1	no	—
135	#11761612	—	2	2	no	—
136	#11761612	—	2	2	no	—
137	#11761612	—	2	2	no	—
138	#11761612	—	2	2	no	—
139	#11761612	—	2	2	no	—
140	#11761612	—	2	2	no	—
141	#11761612	—	2	2	no	—
142	#11761612	—	4	1	no	—
143	#11761612	—	4	1	no	—
144	#11761612	—	4	1	no	—
145	#11761612	—	4	1	no	—
146	#11761612	C₂×D₄	1	4	yes	—
147	C₂×C₆₇⋊C₈	—	2	2	no	—
148	C₂×C₆₇⋊C₈	—	2	2	no	—
149	C₂×C₆₇⋊C₈	—	2	2	no	—
150	C₂×C₆₇⋊C₈	—	2	2	no	—
151	C₂×C₆₇⋊C₈	—	2	2	no	—
152	C₂×C₆₇⋊C₈	—	4	1	no	—
153	C₂×C₆₇⋊C₈	—	4	1	no	—
154	C₂×C₆₇⋊C₈	—	4	1	no	—
155	C₂×C₆₇⋊C₈	—	4	1	no	—
156	C₂⁴×C₆₇	C₂×Q₈	1	1	yes	characteristic
157	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
164	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
165	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
166	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
167	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
168	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
169	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
170	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
171	M₁₆×C₆₇	—	2	2	no	—
172	M₁₆×C₆₇	—	2	2	no	—
173	M₁₆×C₆₇	—	2	2	no	—
174	M₁₆×C₆₇	—	2	2	no	—
175	M₁₆×C₆₇	—	2	2	no	—
176	M₁₆×C₆₇	—	2	2	no	—
177	M₁₆×C₆₇	—	2	2	no	—
178	M₁₆×C₆₇	—	2	2	no	—
179	M₁₆×C₆₇	—	4	1	no	—
180	M₁₆×C₆₇	—	4	1	no	—
181	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
182	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
183	C₂×C₈×C₆₇	—	2	2	no	—
184	C₂×C₈×C₆₇	—	2	2	no	—
185	C₂×C₈×C₆₇	—	2	2	no	—
186	C₂×C₈×C₆₇	—	2	2	no	—
187	C₂×C₈×C₆₇	—	2	2	no	—
188	C₂×C₈×C₆₇	—	2	2	no	—
189	C₂×C₈×C₆₇	—	2	2	no	—
190	C₂×C₈×C₆₇	—	4	1	no	—
191	C₂×C₈×C₆₇	—	4	1	no	—
192	C₂³×C₆₇	—	4	2	no	—
193	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
195	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
196	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
200	C₂²×D₆₇	—	2	4	no	—
201	C₂²×D₆₇	—	2	4	no	—
202	C₂²×D₆₇	—	2	4	no	—
203	C₂²×D₆₇	—	4	2	no	—
204	C₂²×D₆₇	—	4	2	no	—
205	C₂²×D₆₇	—	4	2	no	—
206	C₂²×D₆₇	—	4	2	no	—
207	C₂²×D₆₇	—	8	4	no	—
208	C₂²×D₆₇	—	8	4	no	—
209	C₂²×D₆₇	—	8	4	no	—
210	C₂²×D₆₇	—	8	4	no	—
211	C₂²×D₆₇	—	8	4	no	—
212	C₂²×D₆₇	—	8	4	no	—
213	C₂²×D₆₇	—	8	4	no	—
214	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
215	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
216	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
217	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
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	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
229	C₂×C₄×C₆₇	C₂²⋊Q₈	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	#126	1	1	yes	characteristic
233	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
234	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
235	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
236	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
242	D₂₆₈	—	4	2	no	—
243	D₂₆₈	—	4	2	no	—
244	D₂₆₈	—	4	2	no	—
245	D₂₆₈	—	4	2	no	—
246	D₂₆₈	—	4	2	no	—
247	D₂₆₈	—	4	2	no	—
248	D₂₆₈	—	4	2	no	—
249	D₂₆₈	—	4	2	no	—
250	C₈×C₆₇	—	2	4	no	—
251	C₈×C₆₇	—	2	4	no	—
252	C₈×C₆₇	—	4	2	no	—
253	C₆₇⋊C₈	—	2	4	no	—
254	C₆₇⋊C₈	—	4	2	no	—
255	C₆₇⋊C₈	—	4	2	no	—
256	C₂²×C₆₇	—	2	2	no	—
257	C₂²×C₆₇	—	2	2	no	—
258	C₂²×C₆₇	—	2	2	no	—
259	C₂²×C₆₇	—	4	1	no	—
260	C₂²×C₆₇	—	4	1	no	—
261	C₂²×C₆₇	—	4	1	no	—
262	C₂²×C₆₇	—	4	1	no	—
263	C₂²×C₆₇	#396	1	1	yes	characteristic
264	C₂²×C₆₇	#396	1	1	yes	characteristic
265	C₂²×C₆₇	#396	1	1	yes	characteristic
266	C₂²×C₆₇	#396	1	1	yes	characteristic
267	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
268	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
269	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×D₆₇	—	4	4	no	—
271	C₂×D₆₇	—	8	4	no	—
272	C₂×D₆₇	—	8	4	no	—
273	C₂×D₆₇	—	8	4	no	—
274	C₂×D₆₇	—	8	4	no	—
275	C₂×D₆₇	—	8	4	no	—
276	C₂×D₆₇	—	8	4	no	—
277	C₂×D₆₇	—	8	4	no	—
278	C₄×C₆₇	#396	1	1	yes	characteristic
279	C₄×C₆₇	#396	1	1	yes	characteristic
280	C₄×C₆₇	#396	1	1	yes	characteristic
281	C₄×C₆₇	#396	1	1	yes	characteristic
282	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
283	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
284	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
285	C₄×C₆₇	C₂×#126	1	1	yes	characteristic
286	C₂×#2069	—	67	1	no	maximal, Sylow
287	C₂×C₆₇	—	2	1	no	—
288	C₂×C₆₇	—	2	1	no	—
289	C₂×C₆₇	—	2	1	no	—
290	C₂×C₆₇	—	2	1	no	—
291	C₂×C₆₇	—	2	1	no	—
292	C₂×C₆₇	—	2	1	no	—
293	C₂×C₆₇	#2069	1	2	yes	complemented
294	C₂×C₆₇	C₂×#396	1	1	yes	characteristic
295	D₆₇	—	8	4	no	—
296	C₂×#430	—	67	1	no	—
297	C₂×#430	—	67	1	no	—
298	C₂×#430	D₆₇	1	1	yes	characteristic, complemented
299	C₂²×#100	—	67	1	no	—
300	C₂²×#100	—	67	1	no	—
301	C₂²×#100	—	67	1	no	—
302	#2069	—	67	8	no	—
303	C₂×#338	—	67	1	no	—
304	C₆₇	C₂×#2069	1	1	yes	characteristic, complemented, Sylow
305	C₂³×D₄	—	67	1	no	—
306	C₂²×M₁₆	—	67	1	no	—
307	C₂²×M₁₆	—	67	1	no	—
308	C₂²×M₁₆	—	67	1	no	—
309	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
310	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
311	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
312	#430	—	2	2	no	—
313	#430	—	67	4	no	—
314	#430	—	67	4	no	—
315	#430	—	134	2	no	—
316	#430	—	134	2	no	—
317	#430	C₂×D₆₇	1	4	yes	complemented
318	C₂×#108	—	2	2	no	—
319	C₂×#108	—	134	2	no	—
320	C₂×#108	—	134	2	no	—
321	C₂×#100	—	67	4	no	—
322	C₂×#100	—	67	4	no	—
323	C₂×#100	—	67	4	no	—
324	C₂×#100	—	134	2	no	—
325	C₂×#100	—	134	2	no	—
326	C₂×#100	—	134	2	no	—
327	C₂×#100	—	134	2	no	—
328	C₂×#100	—	134	2	no	—
329	C₂×#100	—	134	2	no	—
330	#338	—	67	4	no	—
331	C₂⁵	—	67	2	no	—
332	C₂²×D₄	—	67	2	no	—
333	C₂²×D₄	—	67	2	no	—
334	C₂²×D₄	—	134	1	no	—
335	C₂²×D₄	—	134	1	no	—
336	C₂²×D₄	—	134	1	no	—
337	C₂²×D₄	—	134	1	no	—
338	C₂²×D₄	—	134	1	no	—
339	C₂²×D₄	—	134	1	no	—
340	C₂²×D₄	—	134	1	no	—
341	C₂²×D₄	—	134	1	no	—
342	C₂²×D₄	—	134	1	no	—
343	C₂²×D₄	—	134	1	no	—
344	C₂²×D₄	—	134	1	no	—
345	C₂²×D₄	—	134	1	no	—
346	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	67	2	no	—
359	C₂×M₁₆	—	67	2	no	—
360	C₂×M₁₆	—	67	2	no	—
361	C₂×M₁₆	—	67	2	no	—
362	C₂×M₁₆	—	67	2	no	—
363	C₂×M₁₆	—	134	1	no	—
364	C₂×M₁₆	—	134	1	no	—
365	C₂×M₁₆	—	134	1	no	—
366	C₂×M₁₆	—	134	1	no	—
367	C₂×M₁₆	—	134	1	no	—
368	C₂×M₁₆	—	134	1	no	—
369	C₂×M₁₆	—	134	1	no	—
370	C₂×M₁₆	—	134	1	no	—
371	C₂×M₁₆	—	134	1	no	—
372	C₂×M₁₆	—	134	1	no	—
373	C₂×M₁₆	—	134	1	no	—
374	C₂×M₁₆	—	134	1	no	—
375	C₂×M₁₆	—	134	1	no	—
376	C₂×M₁₆	D₂₆₈	1	2	yes	—
377	C₂×M₁₆	D₂₆₈	1	2	yes	—
378	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
379	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
380	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
381	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
382	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	134	1	no	—
387	C₂²×C₈	—	134	1	no	—
388	C₂²×C₈	—	134	1	no	—
389	#108	—	2	8	no	—
390	#108	—	134	8	no	—
391	#108	—	134	8	no	—
392	#100	—	134	8	no	—
393	#100	—	134	8	no	—
394	#100	—	134	8	no	—
395	C₂⁴	—	536	4	no	—
396	C₂⁴	—	67	4	no	—
397	C₂⁴	—	134	2	no	—
398	C₂⁴	—	134	2	no	—
399	C₂⁴	—	134	2	no	—
400	C₂⁴	—	134	2	no	—
401	C₂⁴	—	134	2	no	—
402	C₂⁴	—	134	2	no	—
403	C₂⁴	Q₈×D₆₇	1	1	yes	characteristic
404	C₂×D₄	—	268	1	no	—
405	C₂×D₄	—	268	1	no	—
406	C₂×D₄	—	268	1	no	—
407	C₂×D₄	—	268	1	no	—
408	C₂×D₄	—	268	1	no	—
409	C₂×D₄	—	268	1	no	—
410	C₂×D₄	—	268	1	no	—
411	C₂×D₄	—	268	1	no	—
412	C₂×D₄	—	268	1	no	—
413	C₂×D₄	—	268	1	no	—
414	C₂×D₄	—	268	1	no	—
415	C₂×D₄	—	268	1	no	—
416	C₂×D₄	—	268	1	no	—
417	C₂×D₄	—	268	1	no	—
418	C₂×D₄	—	268	1	no	—
419	C₂×D₄	—	268	1	no	—
420	C₂×D₄	—	134	2	no	—
421	C₂×D₄	—	134	2	no	—
422	C₂×D₄	—	134	2	no	—
423	C₂×D₄	—	134	2	no	—
424	C₂×D₄	—	134	2	no	—
425	C₂×D₄	—	134	2	no	—
426	C₂×D₄	—	134	2	no	—
427	C₂×D₄	—	134	2	no	—
428	C₂×D₄	—	134	2	no	—
429	C₂×D₄	—	134	2	no	—
430	C₂×D₄	—	134	2	no	—
431	C₂×D₄	—	134	2	no	—
432	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
433	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
438	C₂²×C₄	Q₈×D₆₇	1	1	yes	characteristic
439	C₂²×C₄	#11761627	1	1	yes	characteristic
440	C₂²×C₄	#11761627	1	1	yes	characteristic
441	C₂²×C₄	#11761628	1	1	yes	characteristic
442	C₂²×C₄	#11761628	1	1	yes	characteristic
443	C₂²×C₄	#11761629	1	1	yes	characteristic
444	C₂²×C₄	#11761629	1	1	yes	characteristic
445	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	4	1	no	—
455	M₁₆	—	4	1	no	—
456	M₁₆	—	268	1	no	—
457	M₁₆	—	268	1	no	—
458	M₁₆	—	268	1	no	—
459	M₁₆	—	268	1	no	—
460	M₁₆	—	67	4	no	—
461	M₁₆	—	134	2	no	—
462	M₁₆	—	134	2	no	—
463	M₁₆	—	134	2	no	—
464	M₁₆	—	134	2	no	—
465	M₁₆	—	134	2	no	—
466	M₁₆	—	134	2	no	—
467	M₁₆	—	134	2	no	—
468	M₁₆	C₂×C₂²⋊D₆₇	1	4	yes	—
469	M₁₆	C₂×D₂₆₈	1	4	yes	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	268	1	no	—
480	C₂×C₈	—	268	1	no	—
481	C₂×C₈	—	268	1	no	—
482	C₂×C₈	—	268	1	no	—
483	C₂×C₈	—	134	2	no	—
484	C₂×C₈	—	134	2	no	—
485	C₂×C₈	—	134	2	no	—
486	C₂×C₈	—	134	2	no	—
487	C₂×C₈	—	134	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	268	2	no	—
490	C₂³	—	268	2	no	—
491	C₂³	—	268	2	no	—
492	C₂³	—	268	2	no	—
493	C₂³	—	536	4	no	—
494	C₂³	—	536	4	no	—
495	C₂³	—	536	4	no	—
496	C₂³	—	536	4	no	—
497	C₂³	—	536	4	no	—
498	C₂³	—	536	4	no	—
499	C₂³	—	536	4	no	—
500	C₂³	—	134	4	no	—
501	C₂³	—	134	4	no	—
502	C₂³	—	134	4	no	—
503	C₂³	#14524019	1	1	yes	characteristic
504	C₂³	#14524019	1	1	yes	characteristic
505	C₂³	#14524021	1	1	yes	characteristic
506	C₂³	#14524021	1	1	yes	characteristic
507	C₂³	#14524023	1	1	yes	characteristic
508	C₂³	#14524023	1	1	yes	characteristic
509	C₂³	C₂×Q₈×D₆₇	1	1	yes	characteristic
510	D₄	—	268	2	no	—
511	D₄	—	268	2	no	—
512	D₄	—	268	2	no	—
513	D₄	—	268	2	no	—
514	D₄	—	268	2	no	—
515	D₄	—	268	2	no	—
516	D₄	—	268	2	no	—
517	D₄	—	268	2	no	—
518	C₂×C₄	#14524015	1	1	yes	characteristic
519	C₂×C₄	#14524015	1	1	yes	characteristic
520	C₂×C₄	#14524015	1	1	yes	characteristic
521	C₂×C₄	#14524015	1	1	yes	characteristic
522	C₂×C₄	#14524017	1	1	yes	characteristic
523	C₂×C₄	#14524017	1	1	yes	characteristic
524	C₂×C₄	#14524017	1	1	yes	characteristic
525	C₂×C₄	#14524017	1	1	yes	characteristic
526	C₂×C₄	#14524018	1	1	yes	characteristic
527	C₂×C₄	#14524018	1	1	yes	characteristic
528	C₂×C₄	#14524018	1	1	yes	characteristic
529	C₂×C₄	#14524018	1	1	yes	characteristic
530	C₂×C₄	#14524019	1	1	yes	characteristic
531	C₂×C₄	#14524019	1	1	yes	characteristic
532	C₂×C₄	#14524021	1	1	yes	characteristic
533	C₂×C₄	#14524021	1	1	yes	characteristic
534	C₂×C₄	#14524023	1	1	yes	characteristic
535	C₂×C₄	#14524023	1	1	yes	characteristic
536	C₂×C₄	#14524038	1	1	yes	characteristic
537	C₂×C₄	#14524038	1	1	yes	characteristic
538	C₂×C₄	#14524038	1	1	yes	characteristic
539	C₂×C₄	#14524038	1	1	yes	characteristic
540	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
541	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
543	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
544	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
545	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
546	C₈	—	2	4	no	—
547	C₈	—	2	4	no	—
548	C₈	—	4	2	no	—
549	C₈	—	268	2	no	—
550	C₈	—	268	2	no	—
551	C₈	—	134	4	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	268	4	no	—
560	C₂²	—	536	4	no	—
561	C₂²	—	536	4	no	—
562	C₂²	—	536	4	no	—
563	C₂²	—	536	4	no	—
564	C₂²	—	536	4	no	—
565	C₂²	—	536	4	no	—
566	C₂²	—	536	4	no	—
567	C₂²	#16863318	1	1	yes	characteristic
568	C₂²	#16863318	1	1	yes	characteristic
569	C₂²	#16863318	1	1	yes	characteristic
570	C₂²	#16863318	1	1	yes	characteristic
571	C₂²	C₂×#14524019	1	1	yes	characteristic
572	C₂²	C₂×#14524021	1	1	yes	characteristic
573	C₂²	C₂×#14524023	1	1	yes	characteristic
574	C₄	#16863318	1	1	yes	characteristic
575	C₄	#16863318	1	1	yes	characteristic
576	C₄	#16863318	1	1	yes	characteristic
577	C₄	#16863318	1	1	yes	characteristic
578	C₄	C₂×#14524015	1	1	yes	characteristic
579	C₄	C₂×#14524017	1	1	yes	characteristic
580	C₄	C₂×#14524018	1	1	yes	characteristic
581	C₄	C₂×#14524038	1	1	yes	characteristic
582	C₂	—	2	1	no	—
583	C₂	—	2	1	no	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	536	4	no	—
589	C₂	#22561606	1	2	yes	direct product factor
590	C₂	C₂×#16863318	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863318
commutator, cosocle	C₂²×C₄×C₆₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#430×C₆₇	C₂
socle	C₂²×C₆₇	#396
prime radical	C₂³×D₂₆₈	C₂²
hypercenter	C₂×#430	D₆₇
hypocenter	C₆₇	C₂×#2069
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ 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. #22561606	C₂	direct (N × H)
7. C₂×C₆₇⋊#338	C₂	semidirect
8. C₂×#430×C₆₇	C₂	semidirect
14. #16863445	C₂²	semidirect
16. #16863444	C₂²	semidirect
28. C₆₇⋊#338	C₂²	semidirect
33. #430×C₆₇	C₂²	semidirect
293. C₂×C₆₇	#2069	semidirect
298. C₂×#430	D₆₇	semidirect
304. C₆₇	C₂×#2069	semidirect
317. #430	C₂×D₆₇	semidirect
589. C₂	#22561606	direct (N × H)

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
C₂²×#14523959	2
#22561606	2
C₂×C₆₇⋊#338	2
C₂×#430×C₆₇	2
C₂×#2069	67

Subgroups — C2×#22561606 #30884547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22561606 #30884547