Subgroups — #30745780

Order 17152.

634 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863449	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863420	C₂	1	1	yes	maximal, characteristic
3	#22558083	C₂	1	4	yes	maximal, complemented
4	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	—	2	1	no	—
6	#16863449	—	2	1	no	—
7	#16863449	—	2	1	no	—
8	#16863449	—	2	1	no	—
9	#16863449	—	2	1	no	—
10	#16863420	—	2	1	no	—
11	#16863420	—	2	1	no	—
12	#16863420	C₄	1	2	yes	—
13	#16863420	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
16	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄×C₆₇⋊C₈	C₄	1	2	yes	—
19	C₂²×M₁₆×C₆₇	—	2	1	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	#423×C₆₇	—	2	1	no	—
22	#423×C₆₇	—	2	1	no	—
23	#423×C₆₇	C₄	1	2	yes	—
24	#423×C₆₇	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₆₇	—	2	1	no	—
26	C₂×C₄⋊C₈×C₆₇	C₄	1	2	yes	—
27	C₂×#11761612	—	2	2	no	—
28	C₂×#11761612	—	2	2	no	—
29	C₂×#11761612	—	4	2	no	—
30	C₂×#11761612	—	4	2	no	—
31	C₂²×C₆₇⋊C₈	—	2	2	no	—
32	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
33	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
34	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
37	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
38	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
39	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₄×C₆₇⋊C₈	—	2	2	no	—
42	C₄×C₆₇⋊C₈	—	2	2	no	—
43	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
46	C₂×M₁₆×C₆₇	—	2	2	no	—
47	C₂×M₁₆×C₆₇	—	2	2	no	—
48	C₂×M₁₆×C₆₇	—	4	2	no	—
49	C₂×M₁₆×C₆₇	—	4	2	no	—
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₆₇	—	2	2	no	—
64	C₄⋊C₈×C₆₇	—	2	2	no	—
65	C₄⋊C₈×C₆₇	—	2	2	no	—
66	C₄⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
67	#11761612	—	4	4	no	—
68	#11761612	—	4	2	no	—
69	#11761612	—	4	2	no	—
70	C₂×C₆₇⋊C₈	—	2	4	no	—
71	C₂×C₆₇⋊C₈	—	2	4	no	—
72	C₂×C₆₇⋊C₈	—	4	4	no	—
73	C₂×C₆₇⋊C₈	—	4	4	no	—
74	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	—	4	2	no	—
76	C₂²×C₄×C₆₇	—	4	2	no	—
77	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	D₈	1	2	yes	—
93	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₆₇	Q₁₆	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
99	M₁₆×C₆₇	—	4	4	no	—
100	M₁₆×C₆₇	—	4	2	no	—
101	M₁₆×C₆₇	—	4	2	no	—
102	C₂×C₈×C₆₇	—	2	4	no	—
103	C₂×C₈×C₆₇	—	4	4	no	—
104	C₄²×C₆₇	C₄²	1	1	yes	characteristic
105	C₄²×C₆₇	C₄²	1	1	yes	characteristic
106	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₆₇	—	4	1	no	—
121	C₂³×C₆₇	—	4	1	no	—
122	C₂³×C₆₇	#95	1	1	yes	characteristic
123	C₂³×C₆₇	#95	1	1	yes	characteristic
124	C₂³×C₆₇	#106	1	2	yes	—
125	C₂³×C₆₇	#107	1	2	yes	—
126	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	4	1	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	1	no	—
136	C₂×C₄×C₆₇	—	4	1	no	—
137	C₂×C₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	4	1	no	—
139	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#102	1	2	yes	—
146	C₂×C₄×C₆₇	#102	1	2	yes	—
147	C₂×C₄×C₆₇	#102	1	2	yes	—
148	C₂×C₄×C₆₇	#102	1	2	yes	—
149	C₂×C₄×C₆₇	#103	1	2	yes	—
150	C₂×C₄×C₆₇	#103	1	2	yes	—
151	C₂×C₄×C₆₇	#103	1	2	yes	—
152	C₂×C₄×C₆₇	#103	1	2	yes	—
153	C₂×C₄×C₆₇	#106	1	2	yes	—
154	C₂×C₄×C₆₇	#107	1	2	yes	—
155	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
165	C₈×C₆₇	—	4	4	no	—
166	C₆₇⋊C₈	—	4	4	no	—
167	C₆₇⋊C₈	—	4	4	no	—
168	C₂²×C₆₇	—	2	1	no	—
169	C₂²×C₆₇	—	2	1	no	—
170	C₂²×C₆₇	—	2	1	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	—	4	2	no	—
175	C₂²×C₆₇	—	4	2	no	—
176	C₂²×C₆₇	#340	1	2	yes	—
177	C₂²×C₆₇	#340	1	2	yes	—
178	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
179	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
180	C₂²×C₆₇	C₂×#107	1	1	yes	characteristic
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	2	1	no	—
186	C₄×C₆₇	—	2	1	no	—
187	C₄×C₆₇	#338	1	2	yes	—
188	C₄×C₆₇	#340	1	2	yes	—
189	C₄×C₆₇	#340	1	2	yes	—
190	C₄×C₆₇	#413	1	2	yes	—
191	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
192	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
193	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
194	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
195	#8001	—	67	1	no	maximal, Sylow
196	C₂×C₆₇	—	2	2	no	—
197	C₂×C₆₇	—	2	2	no	—
198	C₂×C₆₇	—	2	1	no	—
199	C₂×C₆₇	—	2	1	no	—
200	C₂×C₆₇	C₂×#338	1	1	yes	characteristic
201	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
202	C₂×C₆₇	#1742	1	1	yes	characteristic
203	C₂×#431	—	67	1	no	—
204	C₂×#423	—	67	1	no	—
205	C₂×#423	D₆₇	1	1	yes	characteristic
206	#1292	—	67	4	no	—
207	C₆₇	#8001	1	1	yes	characteristic, complemented, Sylow
208	C₂²×M₁₆	—	2	1	no	—
209	C₂²×M₁₆	—	134	1	no	—
210	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
211	#431	—	134	1	no	—
212	#431	—	134	1	no	—
213	#431	—	134	1	no	—
214	#431	—	134	1	no	—
215	#423	—	2	1	no	—
216	#423	—	2	1	no	—
217	#423	—	67	2	no	—
218	#423	—	67	2	no	—
219	#423	—	134	1	no	—
220	#423	—	134	1	no	—
221	#423	Dic₆₇	1	2	yes	—
222	#423	C₂×D₆₇	1	2	yes	—
223	C₂×C₄⋊C₈	—	2	1	no	—
224	C₂×C₄⋊C₈	—	67	2	no	—
225	C₂×C₄⋊C₈	—	67	2	no	—
226	C₂×C₄⋊C₈	—	134	1	no	—
227	C₂×C₄⋊C₈	Dic₆₇	1	2	yes	—
228	C₂×C₂²⋊C₈	—	67	2	no	—
229	C₂×C₄×C₈	—	67	2	no	—
230	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
231	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	4	2	no	—
236	C₂×M₁₆	—	4	2	no	—
237	C₂×M₁₆	—	268	2	no	—
238	C₂×M₁₆	—	268	2	no	—
239	C₂×M₁₆	—	134	2	no	—
240	C₂×M₁₆	—	134	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	67	4	no	—
243	C₂²×C₈	—	134	2	no	—
244	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
248	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
249	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
251	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	67	4	no	—
260	C₄⋊C₈	—	134	2	no	—
261	C₄⋊C₈	—	134	2	no	—
262	C₄⋊C₈	—	134	2	no	—
263	C₄⋊C₈	—	134	2	no	—
264	C₄⋊C₈	—	134	2	no	—
265	C₄⋊C₈	C₂×Dic₆₇	1	4	yes	—
266	C₂²⋊C₈	—	134	2	no	—
267	C₂²⋊C₈	—	134	2	no	—
268	C₄×C₈	—	134	2	no	—
269	C₄×C₈	—	134	2	no	—
270	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
275	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
281	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
287	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
288	C₂²×C₄	#11761613	1	2	yes	—
289	C₂²×C₄	#11761615	1	2	yes	—
290	C₂²×C₄	#11761616	1	2	yes	—
291	C₂²×C₄	#11761618	1	2	yes	—
292	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
295	M₁₆	—	4	4	no	—
296	M₁₆	—	4	2	no	—
297	M₁₆	—	4	2	no	—
298	M₁₆	—	268	4	no	—
299	M₁₆	—	268	2	no	—
300	M₁₆	—	268	2	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	4	4	no	—
303	C₂×C₈	—	268	4	no	—
304	C₂×C₈	—	268	4	no	—
305	C₂×C₈	—	134	4	no	—
306	C₂×C₈	—	134	4	no	—
307	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
308	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
309	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
310	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
311	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
312	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
313	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
314	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
315	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
316	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
317	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
318	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
320	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
322	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	C₆₇⋊#95	1	1	yes	characteristic
326	C₂³	C₆₇⋊#95	1	1	yes	characteristic
327	C₂³	#14523974	1	2	yes	—
328	C₂³	#14523976	1	2	yes	—
329	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
343	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
344	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
345	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
346	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
347	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
348	C₂×C₄	#14523963	1	2	yes	—
349	C₂×C₄	#14523963	1	2	yes	—
350	C₂×C₄	#14523964	1	2	yes	—
351	C₂×C₄	#14523964	1	2	yes	—
352	C₂×C₄	#14523966	1	2	yes	—
353	C₂×C₄	#14523966	1	2	yes	—
354	C₂×C₄	#14523967	1	2	yes	—
355	C₂×C₄	#14523967	1	2	yes	—
356	C₂×C₄	#14523974	1	2	yes	—
357	C₂×C₄	#14523976	1	2	yes	—
358	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
364	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
365	C₂×C₄	C₂×#11761615	1	1	yes	characteristic
366	C₂×C₄	C₂×#11761616	1	1	yes	characteristic
367	C₂×C₄	C₂×#11761618	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₈	—	268	4	no	—
370	C₈	—	268	4	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	#16863158	1	2	yes	—
380	C₂²	#16863158	1	2	yes	—
381	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
382	C₂²	C₂×#14523974	1	1	yes	characteristic
383	C₂²	C₂×#14523976	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	C₆₇⋊#338	1	2	yes	—
391	C₄	#16863158	1	2	yes	—
392	C₄	#16863158	1	2	yes	—
393	C₄	#16863378	1	2	yes	—
394	C₄	C₂×#14523963	1	1	yes	characteristic
395	C₄	C₂×#14523964	1	1	yes	characteristic
396	C₄	C₂×#14523966	1	1	yes	characteristic
397	C₄	C₂×#14523967	1	1	yes	characteristic
398	C₂	—	2	2	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	C₂×C₆₇⋊#338	1	1	yes	characteristic
403	C₂	C₂×#16863158	1	1	yes	characteristic
404	C₂	#22559947	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₆₇⋊#95
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×#423×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₄⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×#423	D₆₇
hypocenter	C₆₇	#8001
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #22558083	C₂	semidirect
207. C₆₇	#8001	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863449	2
C₂×#16863420	2
#22558083	2
C₂×#423×C₆₇	2
#8001	67