Subgroups — #30745708

Order 17152.

714 conjugacy classes of subgroups.

The subgroup lattice has 434 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	#22562616	C₂	1	1	yes	maximal, characteristic
3	#22558076	C₂	1	4	yes	maximal
4	C₆₇×#2285	C₂	1	1	yes	maximal, characteristic
5	C₂×#14524002	—	2	1	no	—
6	#16863449	—	2	1	no	—
7	#16863449	—	2	1	no	—
8	#16863449	—	2	1	no	—
9	#16863449	—	2	1	no	—
10	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
11	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄×C₆₇⋊C₈	C₄	1	2	yes	complemented
13	#16863266	—	2	1	no	—
14	#16863262	C₄	1	2	yes	complemented
15	#16863256	—	2	1	no	—
16	#16863256	C₂²	1	2	yes	—
17	C₄×C₄⋊Dic₆₇	—	2	1	no	—
18	C₄×C₄⋊Dic₆₇	C₄	1	2	yes	complemented
19	C₂×#117×C₆₇	—	2	1	no	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	#384×C₆₇	—	2	1	no	—
22	#382×C₆₇	C₄	1	2	yes	complemented
23	#380×C₆₇	—	2	1	no	—
24	#380×C₆₇	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
26	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	complemented
27	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
28	#14524002	—	4	2	no	—
29	#14524002	—	4	2	no	—
30	C₂×C₄⋊Dic₆₇	—	2	2	no	—
31	C₂×C₄⋊Dic₆₇	—	2	2	no	—
32	C₂×C₄⋊Dic₆₇	—	2	2	no	—
33	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
34	C₂×C₄×Dic₆₇	—	2	2	no	—
35	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
38	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
39	C₄×C₆₇⋊C₈	—	2	2	no	—
40	C₄×C₆₇⋊C₈	—	2	2	no	—
41	C₆₇⋊#95	—	2	2	no	—
42	C₆₇⋊#95	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	#117×C₆₇	—	4	2	no	—
47	#117×C₆₇	—	4	2	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄²×C₆₇	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	C₂×C₄	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	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
65	#95×C₆₇	—	2	2	no	—
66	#95×C₆₇	C₂×C₄	1	4	yes	—
67	C₂²×Dic₆₇	—	2	4	no	—
68	C₂×C₆₇⋊C₈	—	2	4	no	—
69	C₂×C₆₇⋊C₈	—	4	4	no	—
70	C₄⋊Dic₆₇	—	4	4	no	—
71	C₄⋊Dic₆₇	—	4	4	no	—
72	C₄⋊Dic₆₇	—	4	4	no	—
73	C₂²⋊Dic₆₇	—	4	2	no	—
74	C₂²⋊Dic₆₇	—	4	2	no	—
75	C₄×Dic₆₇	—	4	4	no	—
76	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	—	2	4	no	—
78	C₂²×C₄×C₆₇	—	4	2	no	—
79	C₂²×C₄×C₆₇	—	4	2	no	—
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	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	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	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
102	C₄⋊C₄×C₆₇	—	4	4	no	—
103	C₄⋊C₄×C₆₇	—	4	4	no	—
104	C₄⋊C₄×C₆₇	—	4	4	no	—
105	C₂²⋊C₄×C₆₇	—	4	2	no	—
106	C₂²⋊C₄×C₆₇	—	4	2	no	—
107	C₄²×C₆₇	—	4	4	no	—
108	C₄²×C₆₇	C₄²	1	1	yes	characteristic
109	C₄²×C₆₇	C₄²	1	1	yes	characteristic
110	C₄²×C₆₇	C₄²	1	1	yes	characteristic
111	C₄²×C₆₇	C₄²	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	C₄⋊C₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
122	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₆₇	—	4	1	no	—
125	C₂³×C₆₇	—	4	1	no	—
126	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
130	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
131	C₂³×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
132	C₂³×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
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	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	2	no	—
139	C₂×C₄×C₆₇	—	4	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	—	4	1	no	—
145	C₂×C₄×C₆₇	—	4	4	no	—
146	C₂×C₄×C₆₇	—	4	4	no	—
147	C₂×C₄×C₆₇	—	4	4	no	—
148	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
152	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
153	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
154	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
156	C₂×C₄×C₆₇	#102	1	2	yes	—
157	C₂×C₄×C₆₇	#102	1	2	yes	—
158	C₂×C₄×C₆₇	#102	1	2	yes	—
159	C₂×C₄×C₆₇	#102	1	2	yes	—
160	C₂×C₄×C₆₇	#103	1	2	yes	—
161	C₂×C₄×C₆₇	#103	1	2	yes	—
162	C₂×C₄×C₆₇	#103	1	2	yes	—
163	C₂×C₄×C₆₇	#103	1	2	yes	—
164	C₂×C₄×C₆₇	#106	1	2	yes	—
165	C₂×C₄×C₆₇	#106	1	2	yes	—
166	C₂×C₄×C₆₇	#107	1	2	yes	—
167	C₂×C₄×C₆₇	#107	1	2	yes	—
168	C₂×C₄×C₆₇	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₆₇	—	4	4	no	—
173	C₂×Dic₆₇	—	4	4	no	—
174	C₂×Dic₆₇	—	4	4	no	—
175	C₆₇⋊C₈	—	4	4	no	—
176	C₂²×C₆₇	—	2	1	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	—	2	1	no	—
182	C₂²×C₆₇	—	4	1	no	—
183	C₂²×C₆₇	—	4	1	no	—
184	C₂²×C₆₇	—	4	1	no	—
185	C₂²×C₆₇	—	4	1	no	—
186	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
187	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
188	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
189	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
190	C₂²×C₆₇	C₂×#103	1	1	yes	characteristic
191	C₂²×C₆₇	C₂×#106	1	1	yes	characteristic
192	C₂²×C₆₇	C₂×#107	1	1	yes	characteristic
193	C₄×C₆₇	—	2	1	no	—
194	C₄×C₆₇	—	2	1	no	—
195	C₄×C₆₇	—	2	1	no	—
196	C₄×C₆₇	—	2	1	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	2	1	no	—
199	C₄×C₆₇	—	8	4	no	—
200	C₄×C₆₇	H(3,ℤ/4)	1	2	yes	—
201	C₄×C₆₇	#340	1	2	yes	—
202	C₄×C₆₇	#340	1	2	yes	—
203	C₄×C₆₇	#340	1	2	yes	—
204	C₄×C₆₇	#340	1	2	yes	—
205	C₄×C₆₇	#410	1	2	yes	—
206	Dic₆₇	—	8	4	no	—
207	#7981	—	67	1	no	maximal, Sylow
208	C₂×C₆₇	—	2	1	no	—
209	C₂×C₆₇	—	2	1	no	—
210	C₂×C₆₇	—	2	1	no	—
211	C₂×C₆₇	—	2	1	no	—
212	C₂×C₆₇	—	2	1	no	—
213	C₂×C₆₇	—	2	1	no	—
214	C₂×C₆₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
215	C₂×C₆₇	C₂×#340	1	1	yes	characteristic
216	C₂×C₆₇	#1740	1	1	yes	characteristic
217	C₂×#431	—	67	1	no	—
218	#2285	—	67	1	no	—
219	#2285	D₆₇	1	1	yes	characteristic
220	#1289	—	67	4	no	—
221	C₆₇	#7981	1	1	yes	characteristic, complemented, Sylow
222	C₂×#117	—	2	1	no	—
223	C₂×#117	—	134	1	no	—
224	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
225	#431	—	134	1	no	—
226	#431	—	134	1	no	—
227	#431	—	134	1	no	—
228	#431	—	134	1	no	—
229	C₂×C₄⋊C₈	—	67	2	no	—
230	C₂×C₂²⋊C₈	—	67	2	no	—
231	C₂×C₄×C₈	—	67	2	no	—
232	#384	—	2	1	no	—
233	#384	—	134	1	no	—
234	#382	—	67	2	no	—
235	#382	Dic₆₇	1	2	yes	complemented
236	#380	—	2	1	no	—
237	#380	—	67	2	no	—
238	#380	—	134	1	no	—
239	#380	C₂×D₆₇	1	2	yes	—
240	C₄×C₄⋊C₄	—	2	1	no	—
241	C₄×C₄⋊C₄	—	67	2	no	—
242	C₄×C₄⋊C₄	—	134	1	no	—
243	C₄×C₄⋊C₄	Dic₆₇	1	2	yes	complemented
244	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
245	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
246	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
247	C₂²×C₈	—	67	4	no	—
248	#117	—	4	2	no	—
249	#117	—	4	2	no	—
250	#117	—	268	2	no	—
251	#117	—	268	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	134	2	no	—
256	C₂×C₄⋊C₄	—	134	2	no	—
257	C₂×C₄⋊C₄	—	134	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	134	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	134	2	no	—
262	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
263	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
264	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
265	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
266	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
267	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
268	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
269	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
270	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
271	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
272	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
273	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
274	C₄⋊C₈	—	134	2	no	—
275	C₄⋊C₈	—	134	2	no	—
276	C₂²⋊C₈	—	134	2	no	—
277	C₂²⋊C₈	—	134	2	no	—
278	C₄×C₈	—	134	2	no	—
279	C₄×C₈	—	134	2	no	—
280	#95	—	2	2	no	—
281	#95	—	67	4	no	—
282	#95	—	134	2	no	—
283	#95	C₂×Dic₆₇	1	4	yes	—
284	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	134	4	no	—
289	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
295	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
297	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
299	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
300	C₂²×C₄	Dic₆₇⋊C₄	1	1	yes	characteristic
301	C₂²×C₄	#11761613	1	2	yes	—
302	C₂²×C₄	#11761615	1	2	yes	—
303	C₂²×C₄	#11761616	1	2	yes	—
304	C₂²×C₄	#11761618	1	2	yes	—
305	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
310	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
311	C₂×C₈	—	268	4	no	—
312	C₂×C₈	—	134	4	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	4	no	—
316	C₄⋊C₄	—	268	4	no	—
317	C₄⋊C₄	—	268	4	no	—
318	C₄⋊C₄	—	268	4	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	268	2	no	—
322	C₂²⋊C₄	—	268	2	no	—
323	C₄²	—	4	4	no	—
324	C₄²	—	268	4	no	—
325	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
326	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
327	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
328	C₄²	C₄×Dic₆₇	1	1	yes	characteristic
329	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
330	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
331	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
332	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
333	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
334	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
335	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
336	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
337	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
338	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
339	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
340	C₄²	C₄⋊Dic₆₇	1	1	yes	characteristic
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
344	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
345	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
346	C₂³	C₂×#11761613	1	1	yes	characteristic
347	C₂³	C₂×#11761615	1	1	yes	characteristic
348	C₂³	C₂×#11761616	1	1	yes	characteristic
349	C₂³	C₂×#11761618	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	268	4	no	—
366	C₂×C₄	—	268	4	no	—
367	C₂×C₄	—	268	4	no	—
368	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
369	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
370	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
371	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
372	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
373	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
374	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
375	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
376	C₂×C₄	#14523963	1	2	yes	—
377	C₂×C₄	#14523963	1	2	yes	—
378	C₂×C₄	#14523964	1	2	yes	—
379	C₂×C₄	#14523964	1	2	yes	—
380	C₂×C₄	#14523966	1	2	yes	—
381	C₂×C₄	#14523966	1	2	yes	—
382	C₂×C₄	#14523967	1	2	yes	—
383	C₂×C₄	#14523967	1	2	yes	—
384	C₂×C₄	#14523974	1	2	yes	—
385	C₂×C₄	#14523974	1	2	yes	—
386	C₂×C₄	#14523976	1	2	yes	—
387	C₂×C₄	#14523976	1	2	yes	—
388	C₂×C₄	C₂×C₄×Dic₆₇	1	1	yes	characteristic
389	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
390	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
392	C₈	—	268	4	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
404	C₂²	C₂×#14523963	1	1	yes	characteristic
405	C₂²	C₂×#14523964	1	1	yes	characteristic
406	C₂²	C₂×#14523966	1	1	yes	characteristic
407	C₂²	C₂×#14523967	1	1	yes	characteristic
408	C₂²	C₂×#14523974	1	1	yes	characteristic
409	C₂²	C₂×#14523976	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	4	no	—
417	C₄	—	536	4	no	—
418	C₄	#16863152	1	2	yes	—
419	C₄	#16863158	1	2	yes	—
420	C₄	#16863158	1	2	yes	—
421	C₄	#16863158	1	2	yes	—
422	C₄	#16863158	1	2	yes	—
423	C₄	#16863369	1	2	yes	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	2	1	no	—
430	C₂	C₂×#16863152	1	1	yes	characteristic
431	C₂	C₂×#16863158	1	1	yes	characteristic
432	C₂	#22559941	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₆₇⋊#95
commutator	C₂×C₄×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₆₇×#2285	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	#2285	D₆₇
hypocenter	C₆₇	#7981
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
10. C₂×C₄⋊(C₆₇⋊C₈)	C₄	semidirect
12. C₂×C₄×C₆₇⋊C₈	C₄	semidirect
14. #16863262	C₄	semidirect
18. C₄×C₄⋊Dic₆₇	C₄	semidirect
22. #382×C₆₇	C₄	semidirect
26. C₄×C₄⋊C₄×C₆₇	C₄	semidirect
221. C₆₇	#7981	semidirect
235. #382	Dic₆₇	semidirect
243. C₄×C₄⋊C₄	Dic₆₇	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
#22562616	2
#22558076	2
C₆₇×#2285	2
#7981	67