Subgroups — C₂×#22558083 #30745774

Order 17152.

690 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863420	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#22558083	C₂	1	4	yes	maximal, direct product factor
4	C₂×#423×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11761612	—	2	1	no	—
6	C₂³×C₆₇⋊C₈	C₄	1	2	yes	—
7	#16863420	—	2	1	no	—
8	#16863420	—	2	1	no	—
9	#16863420	C₄	1	2	yes	—
10	#16863420	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
16	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
17	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	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	—	2	2	no	—
33	C₂²×C₆₇⋊C₈	—	2	2	no	—
34	C₂²×C₆₇⋊C₈	—	4	4	no	—
35	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
36	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
37	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
38	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
39	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
40	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
42	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
43	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
44	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
47	C₂×M₁₆×C₆₇	—	2	2	no	—
48	C₂×M₁₆×C₆₇	—	2	2	no	—
49	C₂×M₁₆×C₆₇	—	4	2	no	—
50	C₂×M₁₆×C₆₇	—	4	2	no	—
51	C₂²×C₈×C₆₇	—	2	2	no	—
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	C₂×C₄	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	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₆₇	—	2	2	no	—
65	C₄⋊C₈×C₆₇	—	2	2	no	—
66	C₄⋊C₈×C₆₇	—	2	2	no	—
67	C₄⋊C₈×C₆₇	C₂×C₄	1	4	yes	—
68	#11761612	—	4	4	no	—
69	#11761612	—	4	2	no	—
70	#11761612	—	4	2	no	—
71	C₂×C₆₇⋊C₈	—	2	4	no	—
72	C₂×C₆₇⋊C₈	—	2	4	no	—
73	C₂×C₆₇⋊C₈	—	4	4	no	—
74	C₂×C₆₇⋊C₈	—	4	4	no	—
75	C₂×C₆₇⋊C₈	—	4	4	no	—
76	C₂×C₆₇⋊C₈	—	4	4	no	—
77	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	—	2	2	no	—
79	C₂²×C₄×C₆₇	—	2	2	no	—
80	C₂²×C₄×C₆₇	—	4	2	no	—
81	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	D₈	1	2	yes	—
97	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
98	C₂²×C₄×C₆₇	SD₁₆	1	2	yes	—
99	C₂²×C₄×C₆₇	Q₁₆	1	2	yes	—
100	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
103	M₁₆×C₆₇	—	4	4	no	—
104	M₁₆×C₆₇	—	4	2	no	—
105	M₁₆×C₆₇	—	4	2	no	—
106	C₂×C₈×C₆₇	—	2	4	no	—
107	C₂×C₈×C₆₇	—	4	4	no	—
108	C₄²×C₆₇	C₄²	1	1	yes	characteristic
109	C₄²×C₆₇	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
113	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂³×C₆₇	—	2	2	no	—
125	C₂³×C₆₇	—	2	2	no	—
126	C₂³×C₆₇	#95	1	1	yes	characteristic
127	C₂³×C₆₇	#95	1	1	yes	characteristic
128	C₂³×C₆₇	#106	1	2	yes	—
129	C₂³×C₆₇	#107	1	2	yes	—
130	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	1	no	—
137	C₂×C₄×C₆₇	—	2	1	no	—
138	C₂×C₄×C₆₇	—	2	1	no	—
139	C₂×C₄×C₆₇	—	2	1	no	—
140	C₂×C₄×C₆₇	—	4	1	no	—
141	C₂×C₄×C₆₇	—	4	1	no	—
142	C₂×C₄×C₆₇	—	4	1	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#100	1	2	yes	—
151	C₂×C₄×C₆₇	#101	1	2	yes	—
152	C₂×C₄×C₆₇	#102	1	2	yes	—
153	C₂×C₄×C₆₇	#102	1	2	yes	—
154	C₂×C₄×C₆₇	#102	1	2	yes	—
155	C₂×C₄×C₆₇	#102	1	2	yes	—
156	C₂×C₄×C₆₇	#103	1	2	yes	—
157	C₂×C₄×C₆₇	#103	1	2	yes	—
158	C₂×C₄×C₆₇	#103	1	2	yes	—
159	C₂×C₄×C₆₇	#103	1	2	yes	—
160	C₂×C₄×C₆₇	#106	1	2	yes	—
161	C₂×C₄×C₆₇	#107	1	2	yes	—
162	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
172	C₈×C₆₇	—	4	4	no	—
173	C₆₇⋊C₈	—	4	4	no	—
174	C₆₇⋊C₈	—	4	4	no	—
175	C₂²×C₆₇	—	2	4	no	—
176	C₂²×C₆₇	—	2	4	no	—
177	C₂²×C₆₇	—	2	1	no	—
178	C₂²×C₆₇	—	2	1	no	—
179	C₂²×C₆₇	—	2	1	no	—
180	C₂²×C₆₇	—	2	1	no	—
181	C₂²×C₆₇	#338	1	2	yes	—
182	C₂²×C₆₇	#340	1	2	yes	—
183	C₂²×C₆₇	#340	1	2	yes	—
184	C₂²×C₆₇	#343	1	2	yes	—
185	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
186	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
187	C₂²×C₆₇	C₂×#107	1	1	yes	characteristic
188	C₄×C₆₇	—	2	1	no	—
189	C₄×C₆₇	—	2	1	no	—
190	C₄×C₆₇	—	2	1	no	—
191	C₄×C₆₇	—	2	1	no	—
192	C₄×C₆₇	—	2	1	no	—
193	C₄×C₆₇	—	2	1	no	—
194	C₄×C₆₇	#340	1	2	yes	—
195	C₄×C₆₇	#340	1	2	yes	—
196	C₄×C₆₇	#343	1	2	yes	—
197	C₄×C₆₇	C₂×#100	1	1	yes	characteristic
198	C₄×C₆₇	C₂×#101	1	1	yes	characteristic
199	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
200	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
201	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
202	C₄×C₆₇	C₂×#103	1	1	yes	characteristic
203	C₂×#1292	—	67	1	no	maximal, Sylow
204	C₂×C₆₇	—	2	2	no	—
205	C₂×C₆₇	—	2	1	no	—
206	C₂×C₆₇	—	2	1	no	—
207	C₂×C₆₇	#1292	1	4	yes	complemented
208	C₂×C₆₇	C₂×#338	1	1	yes	characteristic
209	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
210	C₂×C₆₇	C₂×#343	1	1	yes	characteristic
211	C₂×#423	—	67	1	no	—
212	C₂×#423	D₆₇	1	1	yes	characteristic
213	C₂²×C₄⋊C₈	—	67	1	no	—
214	#1292	—	67	4	no	—
215	C₆₇	C₂×#1292	1	1	yes	characteristic, complemented, Sylow
216	C₂²×M₁₆	—	2	1	no	—
217	C₂²×M₁₆	—	134	1	no	—
218	C₂³×C₈	—	67	2	no	—
219	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
220	#423	—	2	1	no	—
221	#423	—	2	1	no	—
222	#423	—	67	2	no	—
223	#423	—	67	2	no	—
224	#423	—	134	1	no	—
225	#423	—	134	1	no	—
226	#423	Dic₆₇	1	2	yes	—
227	#423	C₂×D₆₇	1	2	yes	—
228	C₂×C₄⋊C₈	—	2	1	no	—
229	C₂×C₄⋊C₈	—	67	2	no	—
230	C₂×C₄⋊C₈	—	67	2	no	—
231	C₂×C₄⋊C₈	—	67	2	no	—
232	C₂×C₄⋊C₈	—	134	1	no	—
233	C₂×C₄⋊C₈	—	134	1	no	—
234	C₂×C₄⋊C₈	—	134	1	no	—
235	C₂×C₄⋊C₈	—	134	1	no	—
236	C₂×C₄⋊C₈	—	134	1	no	—
237	C₂×C₄⋊C₈	Dic₆₇	1	2	yes	—
238	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
239	C₂³×C₄	C₄×D₆₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	4	2	no	—
244	C₂×M₁₆	—	4	2	no	—
245	C₂×M₁₆	—	268	2	no	—
246	C₂×M₁₆	—	268	2	no	—
247	C₂×M₁₆	—	134	2	no	—
248	C₂×M₁₆	—	134	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	268	4	no	—
251	C₂²×C₈	—	67	4	no	—
252	C₂²×C₈	—	134	2	no	—
253	C₂²×C₈	—	134	2	no	—
254	C₂²×C₈	—	134	2	no	—
255	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
256	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
257	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
259	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
260	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
261	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
262	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	67	4	no	—
271	C₄⋊C₈	—	134	2	no	—
272	C₄⋊C₈	—	134	2	no	—
273	C₄⋊C₈	—	134	2	no	—
274	C₄⋊C₈	—	134	2	no	—
275	C₄⋊C₈	—	134	2	no	—
276	C₄⋊C₈	—	134	2	no	—
277	C₄⋊C₈	—	134	2	no	—
278	C₄⋊C₈	C₂×Dic₆₇	1	4	yes	—
279	C₂⁴	Dic₆₇⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
284	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
285	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
288	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
291	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
294	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
297	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
298	C₂²×C₄	#11761613	1	2	yes	—
299	C₂²×C₄	#11761615	1	2	yes	—
300	C₂²×C₄	#11761616	1	2	yes	—
301	C₂²×C₄	#11761618	1	2	yes	—
302	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
305	M₁₆	—	4	4	no	—
306	M₁₆	—	4	2	no	—
307	M₁₆	—	4	2	no	—
308	M₁₆	—	268	4	no	—
309	M₁₆	—	268	2	no	—
310	M₁₆	—	268	2	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	—	268	4	no	—
314	C₂×C₈	—	268	4	no	—
315	C₂×C₈	—	268	4	no	—
316	C₂×C₈	—	268	4	no	—
317	C₂×C₈	—	134	4	no	—
318	C₂×C₈	—	134	4	no	—
319	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
320	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
321	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
322	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
323	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
324	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
325	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
326	C₄²	C₂²⋊Dic₆₇	1	1	yes	characteristic
327	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
328	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
329	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
330	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
332	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
333	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
334	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	C₆₇⋊#95	1	1	yes	characteristic
338	C₂³	C₆₇⋊#95	1	1	yes	characteristic
339	C₂³	#14523974	1	2	yes	—
340	C₂³	#14523976	1	2	yes	—
341	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
356	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
357	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
358	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
359	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
360	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
361	C₂×C₄	#14523959	1	2	yes	—
362	C₂×C₄	#14523961	1	2	yes	—
363	C₂×C₄	#14523963	1	2	yes	—
364	C₂×C₄	#14523963	1	2	yes	—
365	C₂×C₄	#14523964	1	2	yes	—
366	C₂×C₄	#14523964	1	2	yes	—
367	C₂×C₄	#14523966	1	2	yes	—
368	C₂×C₄	#14523966	1	2	yes	—
369	C₂×C₄	#14523967	1	2	yes	—
370	C₂×C₄	#14523967	1	2	yes	—
371	C₂×C₄	#14523974	1	2	yes	—
372	C₂×C₄	#14523976	1	2	yes	—
373	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
374	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
375	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
377	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
379	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
380	C₂×C₄	C₂×#11761615	1	1	yes	characteristic
381	C₂×C₄	C₂×#11761616	1	1	yes	characteristic
382	C₂×C₄	C₂×#11761618	1	1	yes	characteristic
383	C₈	—	4	4	no	—
384	C₈	—	268	4	no	—
385	C₈	—	268	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	C₆₇⋊#338	1	2	yes	—
393	C₂²	#16863158	1	2	yes	—
394	C₂²	#16863158	1	2	yes	—
395	C₂²	#16863164	1	2	yes	—
396	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
397	C₂²	C₂×#14523974	1	1	yes	characteristic
398	C₂²	C₂×#14523976	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	#16863158	1	2	yes	—
406	C₄	#16863158	1	2	yes	—
407	C₄	#16863164	1	2	yes	—
408	C₄	C₂×#14523959	1	1	yes	characteristic
409	C₄	C₂×#14523961	1	1	yes	characteristic
410	C₄	C₂×#14523963	1	1	yes	characteristic
411	C₄	C₂×#14523964	1	1	yes	characteristic
412	C₄	C₂×#14523966	1	1	yes	characteristic
413	C₄	C₂×#14523967	1	1	yes	characteristic
414	C₂	—	2	2	no	—
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	#22558083	1	4	yes	direct product factor
418	C₂	C₂×C₆₇⋊#338	1	1	yes	characteristic
419	C₂	C₂×#16863158	1	1	yes	characteristic
420	C₂	C₂×#16863164	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₆₇⋊#95
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×#423×C₆₇	C₂
socle	C₂³×C₆₇	#95
prime radical	C₂⁴×C₆₇	C₄⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×#423	D₆₇
hypocenter	C₆₇	C₂×#1292
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #22558083	C₂	direct (N × H)
207. C₂×C₆₇	#1292	semidirect
215. C₆₇	C₂×#1292	semidirect
417. C₂	#22558083	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×#16863420	2
C₂²×C₄⋊(C₆₇⋊C₈)	2
#22558083	2
C₂×#423×C₆₇	2
C₂×#1292	67

Subgroups — C2×#22558083 #30745774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22558083 #30745774