Subgroups — C₂×#22558323 #30770765

Order 17152.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523983	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863434	C₂	1	1	yes	maximal, characteristic
3	#22558323	C₂	1	4	yes	maximal, direct product factor
4	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#14524002	—	2	1	no	—
6	C₂×#14523983	—	2	1	no	—
7	C₂×#14523983	—	2	1	no	—
8	C₂×#14523983	—	2	1	no	—
9	C₂×#14523983	C₄	1	2	yes	complemented
10	C₂×#14523983	C₄	1	2	yes	complemented
11	C₂×#14523983	C₂²	1	2	yes	—
12	C₂²×C₆₇⋊C₁₆	—	2	1	no	—
13	#16863434	—	2	1	no	—
14	#16863434	—	2	1	no	—
15	#16863434	C₄	1	2	yes	—
16	#16863434	C₂²	1	2	yes	—
17	C₂×#14523977	—	2	1	no	—
18	C₂×#14523975	C₄	1	2	yes	—
19	C₂²×M₁₆×C₆₇	—	2	1	no	—
20	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#108×C₆₇	—	2	1	no	—
22	C₂×#108×C₆₇	—	2	1	no	—
23	C₂×#108×C₆₇	—	2	1	no	—
24	C₂×#108×C₆₇	C₄	1	2	yes	complemented
25	C₂×#108×C₆₇	C₄	1	2	yes	complemented
26	C₂×#108×C₆₇	C₂²	1	2	yes	—
27	#14524002	—	2	2	no	—
28	#14524002	—	2	2	no	—
29	#14524002	—	4	1	no	—
30	#14524002	—	4	1	no	—
31	C₂×C₄⋊Dic₆₇	—	2	2	no	—
32	C₂×C₂²⋊Dic₆₇	—	4	1	no	—
33	C₂×C₄×Dic₆₇	—	4	1	no	—
34	#14523983	—	2	2	no	—
35	#14523983	—	2	2	no	—
36	#14523983	—	2	2	no	—
37	#14523983	C₂×C₄	1	4	yes	complemented
38	C₂×C₆₇⋊C₁₆	—	2	2	no	—
39	C₂×C₆₇⋊C₁₆	—	2	2	no	—
40	C₂×C₆₇⋊C₁₆	—	2	2	no	—
41	#14523977	—	2	2	no	—
42	#14523977	—	2	2	no	—
43	#14523975	—	2	2	no	—
44	#14523975	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₆₇	—	2	2	no	—
47	C₂×M₁₆×C₆₇	—	2	2	no	—
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂×M₁₆×C₆₇	—	4	1	no	—
50	C₂×M₁₆×C₆₇	—	4	1	no	—
51	C₂×M₁₆×C₆₇	—	4	1	no	—
52	C₂²×C₈×C₆₇	—	4	1	no	—
53	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₆₇	Q₈	1	1	yes	characteristic
65	C₂²×C₈×C₆₇	Q₈	1	1	yes	characteristic
66	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
67	#108×C₆₇	—	2	2	no	—
68	#108×C₆₇	—	2	2	no	—
69	#108×C₆₇	—	2	2	no	—
70	#108×C₆₇	C₂×C₄	1	4	yes	complemented
71	C₂²×Dic₆₇	—	4	2	no	—
72	C₄⋊Dic₆₇	—	2	4	no	—
73	C₄⋊Dic₆₇	—	4	2	no	—
74	C₂²⋊Dic₆₇	—	4	2	no	—
75	C₂²⋊Dic₆₇	—	4	2	no	—
76	C₄×Dic₆₇	—	4	2	no	—
77	C₄×Dic₆₇	—	4	2	no	—
78	C₆₇⋊C₁₆	—	2	4	no	—
79	C₂⁴×C₆₇	SD₁₆	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	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	SD₁₆	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	SD₁₆	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	SD₁₆	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	Q₁₆	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	Q₁₆	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	M₁₆×C₆₇	—	2	4	no	—
95	M₁₆×C₆₇	—	4	2	no	—
96	M₁₆×C₆₇	—	4	2	no	—
97	M₁₆×C₆₇	—	4	2	no	—
98	C₂×C₈×C₆₇	—	4	2	no	—
99	C₂×C₈×C₆₇	—	4	2	no	—
100	C₂×C₈×C₆₇	—	4	2	no	—
101	C₂×C₈×C₆₇	C₄²	1	1	yes	characteristic
102	C₂×C₈×C₆₇	C₄²	1	1	yes	characteristic
103	C₂×C₈×C₆₇	C₄²	1	1	yes	characteristic
104	C₂×C₈×C₆₇	C₄²	1	1	yes	characteristic
105	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
129	C₂³×C₆₇	—	4	2	no	—
130	C₂³×C₆₇	#102	1	1	yes	characteristic
131	C₂³×C₆₇	#102	1	1	yes	characteristic
132	C₂³×C₆₇	#103	1	1	yes	characteristic
133	C₂³×C₆₇	#103	1	1	yes	characteristic
134	C₂³×C₆₇	#106	1	1	yes	characteristic
135	C₂³×C₆₇	#106	1	1	yes	characteristic
136	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
137	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
138	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
139	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
142	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
143	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#102	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#103	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#103	1	1	yes	characteristic
149	C₂×C₄×C₆₇	#103	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#103	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#103	1	1	yes	characteristic
152	C₂×C₄×C₆₇	#103	1	1	yes	characteristic
153	C₂×C₄×C₆₇	#106	1	1	yes	characteristic
154	C₂×C₄×C₆₇	#106	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#107	1	1	yes	characteristic
156	C₂×C₄×C₆₇	#107	1	1	yes	characteristic
157	C₂×C₄×C₆₇	#107	1	1	yes	characteristic
158	C₂×C₄×C₆₇	#107	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×D₈	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	C₂×Dic₆₇	—	4	4	no	—
166	C₂×Dic₆₇	—	8	4	no	—
167	C₈×C₆₇	—	4	4	no	—
168	C₈×C₆₇	#95	1	1	yes	characteristic
169	C₈×C₆₇	#95	1	1	yes	characteristic
170	C₈×C₆₇	#95	1	1	yes	characteristic
171	C₈×C₆₇	#95	1	1	yes	characteristic
172	C₈×C₆₇	C₂×C₄²	1	1	yes	characteristic
173	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₈×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₆₇	—	2	2	no	—
177	C₂²×C₆₇	—	2	2	no	—
178	C₂²×C₆₇	—	2	2	no	—
179	C₂²×C₆₇	—	4	1	no	—
180	C₂²×C₆₇	—	4	1	no	—
181	C₂²×C₆₇	—	4	1	no	—
182	C₂²×C₆₇	—	4	1	no	—
183	C₂²×C₆₇	#340	1	1	yes	characteristic
184	C₂²×C₆₇	#340	1	1	yes	characteristic
185	C₂²×C₆₇	#340	1	1	yes	characteristic
186	C₂²×C₆₇	#340	1	1	yes	characteristic
187	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
188	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
189	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
190	C₄×C₆₇	#340	1	1	yes	characteristic
191	C₄×C₆₇	#340	1	1	yes	characteristic
192	C₄×C₆₇	#340	1	1	yes	characteristic
193	C₄×C₆₇	#340	1	1	yes	characteristic
194	C₄×C₆₇	C₂×#95	1	1	yes	characteristic
195	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
196	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
197	C₄×C₆₇	C₂×#107	1	1	yes	characteristic
198	Dic₆₇	—	8	4	no	—
199	C₂×#1389	—	67	1	no	maximal, Sylow
200	C₂×C₆₇	—	2	1	no	—
201	C₂×C₆₇	—	2	1	no	—
202	C₂×C₆₇	—	2	1	no	—
203	C₂×C₆₇	—	2	1	no	—
204	C₂×C₆₇	—	2	1	no	—
205	C₂×C₆₇	—	2	1	no	—
206	C₂×C₆₇	#1389	1	2	yes	complemented
207	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
208	C₂²×M₃₂	—	67	1	no	—
209	C₂²×#108	D₆₇	1	1	yes	characteristic
210	C₂×#427	—	67	1	no	—
211	#1389	—	67	4	no	—
212	C₆₇	C₂×#1389	1	1	yes	characteristic, complemented, Sylow
213	C₂²×M₁₆	—	2	1	no	—
214	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
215	C₂×#117	—	134	1	no	—
216	C₂×M₃₂	—	67	2	no	—
217	C₂×M₃₂	—	67	2	no	—
218	C₂×M₃₂	—	67	2	no	—
219	C₂×M₃₂	—	134	1	no	—
220	C₂×M₃₂	—	134	1	no	—
221	C₂×M₃₂	—	134	1	no	—
222	C₂²×C₁₆	—	134	1	no	—
223	C₂×#108	—	2	1	no	—
224	C₂×#108	—	2	1	no	—
225	C₂×#108	—	2	1	no	—
226	C₂×#108	Dic₆₇	1	2	yes	complemented
227	C₂×#108	Dic₆₇	1	2	yes	complemented
228	C₂×#108	C₂×D₆₇	1	2	yes	—
229	#427	—	67	2	no	—
230	#427	—	67	2	no	—
231	#427	—	134	1	no	—
232	#427	—	134	1	no	—
233	C₂×#107	—	134	1	no	—
234	C₂×#106	—	67	2	no	—
235	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	4	1	no	—
240	C₂×M₁₆	—	4	1	no	—
241	C₂×M₁₆	—	4	1	no	—
242	C₂²×C₈	—	4	1	no	—
243	C₂²×C₈	Dic₁₃₄	1	1	yes	characteristic
244	C₂²×C₈	Dic₁₃₄	1	1	yes	characteristic
245	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
246	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
247	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
248	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
249	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
250	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
251	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
252	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
253	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
254	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
255	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
257	#117	—	268	1	no	—
258	#117	—	268	1	no	—
259	#117	—	134	2	no	—
260	#117	—	134	2	no	—
261	C₂×C₄⋊C₄	—	134	2	no	—
262	C₂×C₂²⋊C₄	—	268	1	no	—
263	C₂×C₄²	—	268	1	no	—
264	M₃₂	—	67	4	no	—
265	M₃₂	—	134	2	no	—
266	M₃₂	—	134	2	no	—
267	M₃₂	—	134	2	no	—
268	C₂×C₁₆	—	134	2	no	—
269	C₂×C₁₆	—	134	2	no	—
270	C₂×C₁₆	—	134	2	no	—
271	#108	—	2	2	no	—
272	#108	—	2	2	no	—
273	#108	—	2	2	no	—
274	#108	C₂×Dic₆₇	1	4	yes	complemented
275	#107	—	134	2	no	—
276	#107	—	134	2	no	—
277	#106	—	67	4	no	—
278	#106	—	134	2	no	—
279	C₂⁴	#11761615	1	1	yes	characteristic
280	C₂²×C₄	—	268	2	no	—
281	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
285	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	#11761613	1	1	yes	characteristic
288	C₂²×C₄	#11761613	1	1	yes	characteristic
289	C₂²×C₄	#11761615	1	1	yes	characteristic
290	C₂²×C₄	#11761616	1	1	yes	characteristic
291	C₂²×C₄	#11761616	1	1	yes	characteristic
292	C₂²×C₄	#11761618	1	1	yes	characteristic
293	C₂²×C₄	#11761618	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
295	M₁₆	—	2	4	no	—
296	M₁₆	—	4	2	no	—
297	M₁₆	—	4	2	no	—
298	M₁₆	—	4	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₄×Dic₆₇	1	1	yes	characteristic
303	C₂×C₈	C₄×Dic₆₇	1	1	yes	characteristic
304	C₂×C₈	C₄×Dic₆₇	1	1	yes	characteristic
305	C₂×C₈	C₄×Dic₆₇	1	1	yes	characteristic
306	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
307	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
308	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
309	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
310	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
311	C₂×C₈	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
312	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
313	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
314	C₂×C₈	Dic₆₇⋊C₄	1	1	yes	characteristic
315	C₂×C₈	Dic₆₇⋊C₄	1	1	yes	characteristic
316	C₂×C₈	Dic₆₇⋊C₄	1	1	yes	characteristic
317	C₂×C₈	Dic₆₇⋊C₄	1	1	yes	characteristic
318	C₂×C₈	Dic₆₇⋊C₄	1	1	yes	characteristic
319	C₂×C₈	Dic₆₇⋊C₄	1	1	yes	characteristic
320	C₂×C₈	C₄⋊Dic₆₇	1	1	yes	characteristic
321	C₂×C₈	C₄⋊Dic₆₇	1	1	yes	characteristic
322	C₂×C₈	C₄⋊Dic₆₇	1	1	yes	characteristic
323	C₂×C₈	C₄⋊Dic₆₇	1	1	yes	characteristic
324	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
325	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
327	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
328	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
329	C₂×C₈	C₂×Dic₁₃₄	1	1	yes	characteristic
330	C₄⋊C₄	—	268	2	no	—
331	C₄⋊C₄	—	134	4	no	—
332	C₂²⋊C₄	—	268	2	no	—
333	C₂²⋊C₄	—	268	2	no	—
334	C₄²	—	268	2	no	—
335	C₄²	—	268	2	no	—
336	C₁₆	—	134	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	#14523963	1	1	yes	characteristic
339	C₂³	#14523963	1	1	yes	characteristic
340	C₂³	#14523967	1	1	yes	characteristic
341	C₂³	#14523967	1	1	yes	characteristic
342	C₂³	#14523974	1	1	yes	characteristic
343	C₂³	#14523974	1	1	yes	characteristic
344	C₂³	C₂×#11761615	1	1	yes	characteristic
345	C₂×C₄	—	268	4	no	—
346	C₂×C₄	—	536	4	no	—
347	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
348	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
349	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
350	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
351	C₂×C₄	#14523963	1	1	yes	characteristic
352	C₂×C₄	#14523963	1	1	yes	characteristic
353	C₂×C₄	#14523964	1	1	yes	characteristic
354	C₂×C₄	#14523964	1	1	yes	characteristic
355	C₂×C₄	#14523964	1	1	yes	characteristic
356	C₂×C₄	#14523964	1	1	yes	characteristic
357	C₂×C₄	#14523966	1	1	yes	characteristic
358	C₂×C₄	#14523966	1	1	yes	characteristic
359	C₂×C₄	#14523966	1	1	yes	characteristic
360	C₂×C₄	#14523966	1	1	yes	characteristic
361	C₂×C₄	#14523967	1	1	yes	characteristic
362	C₂×C₄	#14523967	1	1	yes	characteristic
363	C₂×C₄	#14523974	1	1	yes	characteristic
364	C₂×C₄	#14523974	1	1	yes	characteristic
365	C₂×C₄	#14523976	1	1	yes	characteristic
366	C₂×C₄	#14523976	1	1	yes	characteristic
367	C₂×C₄	#14523976	1	1	yes	characteristic
368	C₂×C₄	#14523976	1	1	yes	characteristic
369	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
371	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
372	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
373	C₂×C₄	C₂×#11761616	1	1	yes	characteristic
374	C₂×C₄	C₂×#11761618	1	1	yes	characteristic
375	C₈	—	4	4	no	—
376	C₈	C₆₇⋊#95	1	1	yes	characteristic
377	C₈	C₆₇⋊#95	1	1	yes	characteristic
378	C₈	C₆₇⋊#95	1	1	yes	characteristic
379	C₈	C₆₇⋊#95	1	1	yes	characteristic
380	C₈	C₂×C₄×Dic₆₇	1	1	yes	characteristic
381	C₈	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
382	C₈	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
383	C₈	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	#16863158	1	1	yes	characteristic
392	C₂²	#16863158	1	1	yes	characteristic
393	C₂²	#16863158	1	1	yes	characteristic
394	C₂²	#16863158	1	1	yes	characteristic
395	C₂²	C₂×#14523963	1	1	yes	characteristic
396	C₂²	C₂×#14523967	1	1	yes	characteristic
397	C₂²	C₂×#14523974	1	1	yes	characteristic
398	C₄	—	536	4	no	—
399	C₄	#16863158	1	1	yes	characteristic
400	C₄	#16863158	1	1	yes	characteristic
401	C₄	#16863158	1	1	yes	characteristic
402	C₄	#16863158	1	1	yes	characteristic
403	C₄	C₂×C₆₇⋊#95	1	1	yes	characteristic
404	C₄	C₂×#14523964	1	1	yes	characteristic
405	C₄	C₂×#14523966	1	1	yes	characteristic
406	C₄	C₂×#14523976	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	#22558323	1	2	yes	direct product factor
414	C₂	C₂×#16863158	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14523964
commutator	C₈×C₆₇	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂²×#108×C₆₇	C₂
socle	C₂²×C₆₇	#340
prime radical	C₂⁴×C₆₇	SD₁₆
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂²×#108	D₆₇
hypocenter	C₆₇	C₂×#1389
LCS	G ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
3. #22558323	C₂	direct (N × H)
9. C₂×#14523983	C₄	semidirect
10. C₂×#14523983	C₄	semidirect
24. C₂×#108×C₆₇	C₄	semidirect
25. C₂×#108×C₆₇	C₄	semidirect
37. #14523983	C₂×C₄	semidirect
70. #108×C₆₇	C₂×C₄	semidirect
206. C₂×C₆₇	#1389	semidirect
212. C₆₇	C₂×#1389	semidirect
226. C₂×#108	Dic₆₇	semidirect
227. C₂×#108	Dic₆₇	semidirect
274. #108	C₂×Dic₆₇	semidirect
413. C₂	#22558323	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×#14523983	2
C₂×#16863434	2
#22558323	2
C₂²×#108×C₆₇	2
C₂×#1389	67

Subgroups — C2×#22558323 #30770765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22558323 #30770765