Subgroups — C₂×#22558076 #30745702

Order 17152.

1130 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊(C₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863256	C₂	1	1	yes	maximal, characteristic
3	#22558076	C₂	1	4	yes	maximal, direct product factor
4	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₆₇⋊C₈	C₄	1	2	yes	complemented
6	C₂²×C₄⋊Dic₆₇	—	2	1	no	—
7	C₂²×C₂²⋊Dic₆₇	—	2	1	no	—
8	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
11	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
12	C₂×C₂²⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
13	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
14	#16863256	—	2	1	no	—
15	#16863256	—	2	1	no	—
16	#16863256	C₄	1	2	yes	complemented
17	#16863256	C₂²	1	2	yes	—
18	C₂×C₆₇⋊#95	C₄	1	2	yes	complemented
19	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
22	#380×C₆₇	—	2	1	no	—
23	#380×C₆₇	—	2	1	no	—
24	#380×C₆₇	C₄	1	2	yes	complemented
25	#380×C₆₇	C₂²	1	2	yes	—
26	C₂×#95×C₆₇	C₄	1	2	yes	complemented
27	C₂³×Dic₆₇	—	2	2	no	—
28	C₂²×C₆₇⋊C₈	—	2	2	no	—
29	C₂²×C₆₇⋊C₈	—	2	2	no	—
30	C₂²×C₆₇⋊C₈	—	4	4	no	—
31	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	complemented
32	C₂×C₄⋊Dic₆₇	—	2	2	no	—
33	C₂×C₄⋊Dic₆₇	—	2	2	no	—
34	C₂×C₄⋊Dic₆₇	—	4	4	no	—
35	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
36	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₆₇	—	4	2	no	—
38	C₂×C₂²⋊Dic₆₇	—	4	2	no	—
39	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
43	C₆₇⋊#95	—	2	2	no	—
44	C₆₇⋊#95	C₂×C₄	1	4	yes	complemented
45	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	—	2	2	no	—
47	C₂³×C₄×C₆₇	—	4	4	no	—
48	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
60	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
61	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
65	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
68	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
69	#95×C₆₇	—	2	2	no	—
70	#95×C₆₇	C₂×C₄	1	4	yes	complemented
71	C₂²×Dic₆₇	—	2	4	no	—
72	C₂²×Dic₆₇	—	4	4	no	—
73	C₂²×Dic₆₇	—	4	4	no	—
74	C₂²×Dic₆₇	—	4	4	no	—
75	C₂×C₆₇⋊C₈	—	2	4	no	—
76	C₂×C₆₇⋊C₈	—	4	4	no	—
77	C₂×C₆₇⋊C₈	—	4	4	no	—
78	C₂×C₆₇⋊C₈	—	4	4	no	—
79	C₄⋊Dic₆₇	—	4	4	no	—
80	C₄⋊Dic₆₇	—	4	4	no	—
81	C₂²⋊Dic₆₇	—	4	4	no	—
82	C₂²⋊Dic₆₇	—	4	2	no	—
83	C₂²⋊Dic₆₇	—	4	2	no	—
84	C₂⁴×C₆₇	—	4	2	no	—
85	C₂⁴×C₆₇	—	4	2	no	—
86	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂⁴×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
90	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂⁴×C₆₇	D₈	1	2	yes	—
93	C₂⁴×C₆₇	SD₁₆	1	2	yes	—
94	C₂⁴×C₆₇	SD₁₆	1	2	yes	—
95	C₂⁴×C₆₇	Q₁₆	1	2	yes	—
96	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	—	2	4	no	—
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	4	no	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	4	2	no	—
102	C₂²×C₄×C₆₇	—	4	2	no	—
103	C₂²×C₄×C₆₇	—	4	2	no	—
104	C₂²×C₄×C₆₇	—	4	2	no	—
105	C₂²×C₄×C₆₇	—	4	2	no	—
106	C₂²×C₄×C₆₇	—	4	2	no	—
107	C₂²×C₄×C₆₇	—	4	2	no	—
108	C₂²×C₄×C₆₇	—	4	2	no	—
109	C₂²×C₄×C₆₇	—	4	2	no	—
110	C₂²×C₄×C₆₇	—	4	2	no	—
111	C₂²×C₄×C₆₇	—	4	2	no	—
112	C₂²×C₄×C₆₇	—	4	4	no	—
113	C₂²×C₄×C₆₇	—	4	4	no	—
114	C₂²×C₄×C₆₇	—	4	4	no	—
115	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
117	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
119	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
143	C₄⋊C₄×C₆₇	—	4	4	no	—
144	C₄⋊C₄×C₆₇	—	4	4	no	—
145	C₂²⋊C₄×C₆₇	—	4	4	no	—
146	C₂²⋊C₄×C₆₇	—	4	2	no	—
147	C₂²⋊C₄×C₆₇	—	4	2	no	—
148	C₂³×C₆₇	—	2	2	no	—
149	C₂³×C₆₇	—	2	2	no	—
150	C₂³×C₆₇	—	2	2	no	—
151	C₂³×C₆₇	—	2	2	no	—
152	C₂³×C₆₇	—	2	2	no	—
153	C₂³×C₆₇	—	2	2	no	—
154	C₂³×C₆₇	—	4	1	no	—
155	C₂³×C₆₇	—	4	1	no	—
156	C₂³×C₆₇	—	4	1	no	—
157	C₂³×C₆₇	—	4	1	no	—
158	C₂³×C₆₇	—	4	1	no	—
159	C₂³×C₆₇	—	4	1	no	—
160	C₂³×C₆₇	—	4	1	no	—
161	C₂³×C₆₇	—	4	4	no	—
162	C₂³×C₆₇	—	4	4	no	—
163	C₂³×C₆₇	—	4	4	no	—
164	C₂³×C₆₇	—	4	4	no	—
165	C₂³×C₆₇	—	4	1	no	—
166	C₂³×C₆₇	#95	1	1	yes	characteristic
167	C₂³×C₆₇	#95	1	1	yes	characteristic
168	C₂³×C₆₇	#95	1	1	yes	characteristic
169	C₂³×C₆₇	#95	1	1	yes	characteristic
170	C₂³×C₆₇	#102	1	2	yes	—
171	C₂³×C₆₇	#102	1	2	yes	—
172	C₂³×C₆₇	#102	1	2	yes	—
173	C₂³×C₆₇	#102	1	2	yes	—
174	C₂³×C₆₇	#103	1	2	yes	—
175	C₂³×C₆₇	#103	1	2	yes	—
176	C₂³×C₆₇	#103	1	2	yes	—
177	C₂³×C₆₇	#103	1	2	yes	—
178	C₂³×C₆₇	#106	1	2	yes	—
179	C₂³×C₆₇	#106	1	2	yes	—
180	C₂³×C₆₇	#107	1	2	yes	—
181	C₂³×C₆₇	#107	1	2	yes	—
182	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
186	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
187	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
188	C₂³×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
189	C₂×C₄×C₆₇	—	2	2	no	—
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	—	2	2	no	—
192	C₂×C₄×C₆₇	—	2	2	no	—
193	C₂×C₄×C₆₇	—	2	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	—	2	2	no	—
198	C₂×C₄×C₆₇	—	2	2	no	—
199	C₂×C₄×C₆₇	—	2	2	no	—
200	C₂×C₄×C₆₇	—	2	2	no	—
201	C₂×C₄×C₆₇	—	2	2	no	—
202	C₂×C₄×C₆₇	—	2	2	no	—
203	C₂×C₄×C₆₇	—	2	2	no	—
204	C₂×C₄×C₆₇	—	4	1	no	—
205	C₂×C₄×C₆₇	—	4	1	no	—
206	C₂×C₄×C₆₇	—	4	1	no	—
207	C₂×C₄×C₆₇	—	4	1	no	—
208	C₂×C₄×C₆₇	—	4	1	no	—
209	C₂×C₄×C₆₇	—	4	1	no	—
210	C₂×C₄×C₆₇	—	4	1	no	—
211	C₂×C₄×C₆₇	—	4	1	no	—
212	C₂×C₄×C₆₇	—	4	1	no	—
213	C₂×C₄×C₆₇	—	4	1	no	—
214	C₂×C₄×C₆₇	—	4	1	no	—
215	C₂×C₄×C₆₇	—	4	1	no	—
216	C₂×C₄×C₆₇	—	4	4	no	—
217	C₂×C₄×C₆₇	—	4	4	no	—
218	C₂×C₄×C₆₇	—	4	4	no	—
219	C₂×C₄×C₆₇	—	8	8	no	—
220	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
221	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
222	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
223	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
224	C₂×C₄×C₆₇	#99	1	4	yes	—
225	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
226	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₆₇	—	4	4	no	—
230	C₂×Dic₆₇	—	4	4	no	—
231	C₂×Dic₆₇	—	4	4	no	—
232	C₂×Dic₆₇	—	8	8	no	—
233	C₆₇⋊C₈	—	4	4	no	—
234	C₂²×C₆₇	—	2	4	no	—
235	C₂²×C₆₇	—	2	4	no	—
236	C₂²×C₆₇	—	2	4	no	—
237	C₂²×C₆₇	—	2	4	no	—
238	C₂²×C₆₇	—	2	4	no	—
239	C₂²×C₆₇	—	2	4	no	—
240	C₂²×C₆₇	—	2	1	no	—
241	C₂²×C₆₇	—	2	1	no	—
242	C₂²×C₆₇	—	2	1	no	—
243	C₂²×C₆₇	—	2	1	no	—
244	C₂²×C₆₇	—	2	1	no	—
245	C₂²×C₆₇	—	2	1	no	—
246	C₂²×C₆₇	—	2	1	no	—
247	C₂²×C₆₇	—	2	1	no	—
248	C₂²×C₆₇	—	2	1	no	—
249	C₂²×C₆₇	—	2	1	no	—
250	C₂²×C₆₇	—	2	1	no	—
251	C₂²×C₆₇	—	2	1	no	—
252	C₂²×C₆₇	—	4	2	no	—
253	C₂²×C₆₇	—	4	2	no	—
254	C₂²×C₆₇	—	4	2	no	—
255	C₂²×C₆₇	—	4	2	no	—
256	C₂²×C₆₇	—	4	2	no	—
257	C₂²×C₆₇	—	4	2	no	—
258	C₂²×C₆₇	—	4	1	no	—
259	C₂²×C₆₇	—	4	1	no	—
260	C₂²×C₆₇	—	4	1	no	—
261	C₂²×C₆₇	—	4	1	no	—
262	C₂²×C₆₇	H(3,ℤ/4)	1	2	yes	—
263	C₂²×C₆₇	#340	1	2	yes	—
264	C₂²×C₆₇	#340	1	2	yes	—
265	C₂²×C₆₇	#340	1	2	yes	—
266	C₂²×C₆₇	#340	1	2	yes	—
267	C₂²×C₆₇	#342	1	2	yes	—
268	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
269	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
270	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
271	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
272	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
273	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
274	C₂²×C₆₇	C₂×#107	1	1	yes	characteristic
275	C₄×C₆₇	—	2	1	no	—
276	C₄×C₆₇	—	2	1	no	—
277	C₄×C₆₇	—	2	1	no	—
278	C₄×C₆₇	—	2	1	no	—
279	C₄×C₆₇	—	2	1	no	—
280	C₄×C₆₇	—	2	1	no	—
281	C₄×C₆₇	—	8	4	no	—
282	C₄×C₆₇	#342	1	2	yes	—
283	C₄×C₆₇	C₂×#99	1	2	yes	—
284	Dic₆₇	—	8	4	no	—
285	C₂×#1289	—	67	1	no	maximal, Sylow
286	C₂×C₆₇	—	2	1	no	—
287	C₂×C₆₇	—	2	1	no	—
288	C₂×C₆₇	—	2	2	no	—
289	C₂×C₆₇	—	2	2	no	—
290	C₂×C₆₇	—	2	2	no	—
291	C₂×C₆₇	—	2	1	no	—
292	C₂×C₆₇	—	2	1	no	—
293	C₂×C₆₇	—	2	1	no	—
294	C₂×C₆₇	—	2	1	no	—
295	C₂×C₆₇	#1289	1	4	yes	complemented
296	C₂×C₆₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
297	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
298	C₂×C₆₇	C₂×#342	1	1	yes	characteristic
299	C₂²×C₂²⋊C₈	—	67	1	no	—
300	C₂×#380	—	67	1	no	—
301	C₂×#380	D₆₇	1	1	yes	characteristic
302	#1289	—	67	4	no	—
303	C₆₇	C₂×#1289	1	1	yes	characteristic, complemented, Sylow
304	C₂⁴×C₄	C₂×D₆₇	1	1	yes	characteristic
305	C₂³×C₈	—	67	2	no	—
306	C₂²×C₄⋊C₄	—	2	1	no	—
307	C₂²×C₄⋊C₄	—	134	1	no	—
308	C₂²×C₂²⋊C₄	—	2	1	no	—
309	C₂²×C₂²⋊C₄	—	134	1	no	—
310	C₂×C₂²⋊C₈	—	67	2	no	—
311	C₂×C₂²⋊C₈	—	67	2	no	—
312	C₂×C₂²⋊C₈	—	134	1	no	—
313	C₂×C₂²⋊C₈	—	134	1	no	—
314	C₂×C₂²⋊C₈	—	134	1	no	—
315	C₂×C₂²⋊C₈	—	134	1	no	—
316	#380	—	2	1	no	—
317	#380	—	2	1	no	—
318	#380	—	67	2	no	—
319	#380	—	67	2	no	—
320	#380	—	134	1	no	—
321	#380	—	134	1	no	—
322	#380	Dic₆₇	1	2	yes	complemented
323	#380	C₂×D₆₇	1	2	yes	—
324	C₂×#95	—	67	2	no	—
325	C₂×#95	Dic₆₇	1	2	yes	complemented
326	C₂⁵	C₂²⋊D₆₇	1	1	yes	characteristic
327	C₂³×C₄	—	2	2	no	—
328	C₂³×C₄	—	4	4	no	—
329	C₂³×C₄	—	134	2	no	—
330	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
331	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
332	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
333	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
334	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
335	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
336	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
337	C₂³×C₄	D₂₆₈	1	1	yes	characteristic
338	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
339	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
340	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
341	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
342	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
343	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
344	C₂²×C₈	—	268	4	no	—
345	C₂²×C₈	—	67	4	no	—
346	C₂²×C₈	—	134	2	no	—
347	C₂²×C₈	—	134	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	4	4	no	—
351	C₂×C₄⋊C₄	—	268	4	no	—
352	C₂×C₄⋊C₄	—	134	2	no	—
353	C₂×C₄⋊C₄	—	134	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	4	2	no	—
357	C₂×C₂²⋊C₄	—	4	2	no	—
358	C₂×C₂²⋊C₄	—	268	2	no	—
359	C₂×C₂²⋊C₄	—	268	2	no	—
360	C₂×C₂²⋊C₄	—	134	2	no	—
361	C₂×C₂²⋊C₄	—	134	2	no	—
362	C₂²⋊C₈	—	134	2	no	—
363	C₂²⋊C₈	—	134	2	no	—
364	C₂²⋊C₈	—	134	2	no	—
365	C₂²⋊C₈	—	134	2	no	—
366	#95	—	2	2	no	—
367	#95	—	67	4	no	—
368	#95	—	134	2	no	—
369	#95	C₂×Dic₆₇	1	4	yes	complemented
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
373	C₂⁴	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
374	C₂⁴	C₂²⋊Dic₆₇	1	1	yes	characteristic
375	C₂⁴	C₂²⋊Dic₆₇	1	1	yes	characteristic
376	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
377	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
378	C₂⁴	#11761613	1	2	yes	—
379	C₂⁴	#11761615	1	2	yes	—
380	C₂⁴	#11761616	1	2	yes	—
381	C₂⁴	#11761618	1	2	yes	—
382	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	268	4	no	—
402	C₂²×C₄	—	268	4	no	—
403	C₂²×C₄	—	268	4	no	—
404	C₂²×C₄	—	134	4	no	—
405	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
406	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
407	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
408	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
409	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
410	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
411	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
412	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
413	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
414	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
415	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
416	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
417	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
418	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
419	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
420	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
421	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
422	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
423	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
424	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
425	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
426	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
429	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
432	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
433	C₂×C₈	—	268	4	no	—
434	C₂×C₈	—	268	4	no	—
435	C₂×C₈	—	268	4	no	—
436	C₂×C₈	—	134	4	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	268	4	no	—
440	C₄⋊C₄	—	268	4	no	—
441	C₂²⋊C₄	—	4	4	no	—
442	C₂²⋊C₄	—	4	2	no	—
443	C₂²⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	268	4	no	—
445	C₂²⋊C₄	—	268	2	no	—
446	C₂²⋊C₄	—	268	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	4	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	4	4	no	—
463	C₂³	—	4	4	no	—
464	C₂³	—	4	1	no	—
465	C₂³	C₆₇⋊#95	1	1	yes	characteristic
466	C₂³	C₆₇⋊#95	1	1	yes	characteristic
467	C₂³	C₆₇⋊#95	1	1	yes	characteristic
468	C₂³	C₆₇⋊#95	1	1	yes	characteristic
469	C₂³	#14523963	1	2	yes	—
470	C₂³	#14523963	1	2	yes	—
471	C₂³	#14523964	1	2	yes	—
472	C₂³	#14523964	1	2	yes	—
473	C₂³	#14523966	1	2	yes	—
474	C₂³	#14523966	1	2	yes	—
475	C₂³	#14523967	1	2	yes	—
476	C₂³	#14523967	1	2	yes	—
477	C₂³	#14523974	1	2	yes	—
478	C₂³	#14523974	1	2	yes	—
479	C₂³	#14523976	1	2	yes	—
480	C₂³	#14523976	1	2	yes	—
481	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
482	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
483	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
484	C₂³	C₂×#11761613	1	1	yes	characteristic
485	C₂³	C₂×#11761615	1	1	yes	characteristic
486	C₂³	C₂×#11761616	1	1	yes	characteristic
487	C₂³	C₂×#11761618	1	1	yes	characteristic
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	8	8	no	—
519	C₂×C₄	—	268	4	no	—
520	C₂×C₄	—	268	4	no	—
521	C₂×C₄	—	268	4	no	—
522	C₂×C₄	—	536	8	no	—
523	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
524	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
525	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
526	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
527	C₂×C₄	#14523957	1	4	yes	—
528	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
529	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
531	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
532	C₈	—	268	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	#16863152	1	2	yes	—
562	C₂²	#16863158	1	2	yes	—
563	C₂²	#16863158	1	2	yes	—
564	C₂²	#16863158	1	2	yes	—
565	C₂²	#16863158	1	2	yes	—
566	C₂²	#16863162	1	2	yes	—
567	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
568	C₂²	C₂×#14523963	1	1	yes	characteristic
569	C₂²	C₂×#14523964	1	1	yes	characteristic
570	C₂²	C₂×#14523966	1	1	yes	characteristic
571	C₂²	C₂×#14523967	1	1	yes	characteristic
572	C₂²	C₂×#14523974	1	1	yes	characteristic
573	C₂²	C₂×#14523976	1	1	yes	characteristic
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	8	4	no	—
581	C₄	—	536	4	no	—
582	C₄	#16863162	1	2	yes	—
583	C₄	C₂×#14523957	1	2	yes	—
584	C₂	—	2	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	2	2	no	—
590	C₂	—	2	2	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	#22558076	1	4	yes	direct product factor
594	C₂	C₂×#16863152	1	1	yes	characteristic
595	C₂	C₂×#16863158	1	1	yes	characteristic
596	C₂	C₂×#16863162	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₆₇⋊#95
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#380×C₆₇	C₂
socle	C₂³×C₆₇	#95
prime radical	C₂⁵×C₆₇	D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#380	D₆₇
hypocenter	C₆₇	C₂×#1289
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#380

Complements

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

N	H ≅ G/N	type
3. #22558076	C₂	direct (N × H)
5. C₂³×C₆₇⋊C₈	C₄	semidirect
12. C₂×C₂²⋊(C₆₇⋊C₈)	C₄	semidirect
16. #16863256	C₄	semidirect
18. C₂×C₆₇⋊#95	C₄	semidirect
24. #380×C₆₇	C₄	semidirect
26. C₂×#95×C₆₇	C₄	semidirect
31. C₂²×C₆₇⋊C₈	C₂×C₄	semidirect
44. C₆₇⋊#95	C₂×C₄	semidirect
70. #95×C₆₇	C₂×C₄	semidirect
295. C₂×C₆₇	#1289	semidirect
303. C₆₇	C₂×#1289	semidirect
322. #380	Dic₆₇	semidirect
325. C₂×#95	Dic₆₇	semidirect
369. #95	C₂×Dic₆₇	semidirect
593. C₂	#22558076	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×C₂²⋊(C₆₇⋊C₈)	2
C₂×#16863256	2
#22558076	2
C₂×#380×C₆₇	2
C₂×#1289	67

Subgroups — C2×#22558076 #30745702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22558076 #30745702