Subgroups — C₂×C₄×#103×C₆₇ #30699658

Order 17152.

1726 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₆₇	C₂	1	2	yes	maximal
3	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₄×#103×C₆₇	C₂	1	8	yes	maximal, direct product factor
6	C₂×#340×C₆₇	C₂	1	2	yes	maximal
7	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
9	C₂×C₄×Q₈×C₆₇	—	2	4	no	—
10	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
11	C₂×C₄×Q₈×C₆₇	C₄	1	8	yes	complemented
12	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₆₇	—	2	1	no	—
17	C₂²×C₄²×C₆₇	—	2	1	no	—
18	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#103×C₆₇	C₄	1	16	yes	direct product factor
20	C₂×#103×C₆₇	C₂²	1	8	yes	—
21	C₂×C₄×C₈×C₆₇	—	2	4	no	—
22	C₂×C₄×C₈×C₆₇	C₂²	1	4	yes	—
23	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
24	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
25	C₂×#95×C₆₇	—	2	1	no	—
26	#340×C₆₇	C₂²	1	8	yes	—
27	C₂²×Q₈×C₆₇	—	2	2	no	—
28	C₂²×Q₈×C₆₇	—	2	1	no	—
29	C₂²×Q₈×C₆₇	—	2	4	no	—
30	C₂²×Q₈×C₆₇	C₂×C₄	1	4	yes	—
31	C₂²×Q₈×C₆₇	C₂×C₄	1	8	yes	—
32	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
33	C₂³×C₄×C₆₇	—	2	1	no	—
34	C₂³×C₄×C₆₇	—	2	1	no	—
35	C₂³×C₄×C₆₇	—	2	2	no	—
36	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₆₇	—	2	4	no	—
40	C₂²×C₈×C₆₇	—	2	4	no	—
41	C₂²×C₈×C₆₇	C₂×C₄	1	8	yes	—
42	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
43	C₄×Q₈×C₆₇	—	2	16	no	—
44	C₄×Q₈×C₆₇	—	2	8	no	—
45	C₄×Q₈×C₆₇	C₂×C₄	1	16	yes	complemented
46	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
56	C₂×C₄²×C₆₇	—	2	8	no	—
57	C₂×C₄²×C₆₇	—	2	4	no	—
58	C₂×C₄²×C₆₇	—	2	4	no	—
59	C₂×C₄²×C₆₇	—	4	4	no	—
60	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₆₇	D₄	1	2	yes	—
62	C₂×C₄²×C₆₇	D₄	1	4	yes	—
63	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
64	#103×C₆₇	C₂×C₄	1	32	yes	direct product factor
65	C₄×C₈×C₆₇	—	2	8	no	—
66	#95×C₆₇	—	2	4	no	—
67	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
68	C₂×Q₈×C₆₇	—	2	4	no	—
69	C₂×Q₈×C₆₇	—	2	8	no	—
70	C₂×Q₈×C₆₇	—	2	8	no	—
71	C₂×Q₈×C₆₇	—	2	16	no	—
72	C₂×Q₈×C₆₇	—	2	2	no	—
73	C₂×Q₈×C₆₇	—	2	4	no	—
74	C₂×Q₈×C₆₇	C₄²	1	16	yes	complemented
75	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
76	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
77	C₂²×C₄×C₆₇	—	2	4	no	—
78	C₂²×C₄×C₆₇	—	2	8	no	—
79	C₂²×C₄×C₆₇	—	2	4	no	—
80	C₂²×C₄×C₆₇	—	2	2	no	—
81	C₂²×C₄×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	—	2	8	no	—
83	C₂²×C₄×C₆₇	—	2	2	no	—
84	C₂²×C₄×C₆₇	—	2	4	no	—
85	C₂²×C₄×C₆₇	—	4	4	no	—
86	C₂²×C₄×C₆₇	—	4	4	no	—
87	C₂²×C₄×C₆₇	—	4	4	no	—
88	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₆₇	SD₁₆	1	4	yes	—
91	C₂²×C₄×C₆₇	Q₁₆	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₆₇	#41	1	4	yes	—
99	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₆₇	—	2	16	no	—
101	C₂×C₈×C₆₇	—	2	4	no	—
102	C₂×C₈×C₆₇	—	2	4	no	—
103	C₂×C₈×C₆₇	C₂²×C₄	1	8	yes	—
104	C₄⋊C₄×C₆₇	—	2	16	no	—
105	C₄⋊C₄×C₆₇	—	2	4	no	—
106	C₄⋊C₄×C₆₇	—	2	8	no	—
107	C₄⋊C₄×C₆₇	—	2	2	no	—
108	C₄⋊C₄×C₆₇	—	2	4	no	—
109	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
110	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
111	C₄²×C₆₇	—	2	16	no	—
112	C₄²×C₆₇	—	4	8	no	—
113	C₄²×C₆₇	C₂²⋊C₄	1	8	yes	—
114	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
115	C₄²×C₆₇	C₂×D₄	1	4	yes	—
116	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₆₇	C₄×D₄	1	4	yes	—
118	C₂³×C₆₇	C₂×SD₁₆	1	2	yes	—
119	C₂³×C₆₇	C₂×Q₁₆	1	2	yes	—
120	C₂³×C₆₇	#135	1	4	yes	—
121	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₆₇	—	2	4	no	—
123	Q₈×C₆₇	—	2	8	no	—
124	Q₈×C₆₇	—	2	16	no	—
125	Q₈×C₆₇	C₂×C₄²	1	8	yes	complemented
126	C₂×C₄×C₆₇	—	2	4	no	—
127	C₂×C₄×C₆₇	—	2	8	no	—
128	C₂×C₄×C₆₇	—	2	4	no	—
129	C₂×C₄×C₆₇	—	2	16	no	—
130	C₂×C₄×C₆₇	—	2	8	no	—
131	C₂×C₄×C₆₇	—	2	4	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	4	4	no	—
134	C₂×C₄×C₆₇	—	4	4	no	—
135	C₂×C₄×C₆₇	—	4	4	no	—
136	C₂×C₄×C₆₇	—	4	8	no	—
137	C₂×C₄×C₆₇	—	4	16	no	—
138	C₂×C₄×C₆₇	#103	1	16	yes	direct product factor
139	C₂×C₄×C₆₇	C₂×C₄²	1	4	yes	—
140	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
141	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
143	C₂×C₄×C₆₇	#117	1	4	yes	—
144	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
145	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₆₇	C₂×SD₁₆	1	4	yes	—
147	C₂×C₄×C₆₇	C₂×Q₁₆	1	4	yes	—
148	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
152	C₈×C₆₇	—	2	8	no	—
153	C₂²×C₆₇	C₄×C₂²⋊C₄	1	4	yes	—
154	C₂²×C₆₇	C₂×#103	1	4	yes	—
155	C₂²×C₆₇	#416	1	4	yes	—
156	C₂²×C₆₇	C₄×SD₁₆	1	8	yes	—
157	C₂²×C₆₇	C₄×Q₁₆	1	8	yes	—
158	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₆₇	C₂×C₄×D₄	1	2	yes	—
160	C₂²×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
161	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
162	C₂²×C₆₇	C₂×#135	1	2	yes	—
163	C₄×C₆₇	—	2	4	no	—
164	C₄×C₆₇	—	2	8	no	—
165	C₄×C₆₇	—	4	4	no	—
166	C₄×C₆₇	—	4	8	no	—
167	C₄×C₆₇	C₄×C₂²⋊C₄	1	4	yes	—
168	C₄×C₆₇	C₂×#103	1	8	yes	direct product factor
169	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
170	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
171	C₄×C₆₇	C₂×C₄×D₄	1	2	yes	—
172	C₂×C₄×#103	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂×C₆₇	C₄×#103	1	8	yes	direct product factor
174	C₂×C₆₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₆₇	C₂²×#103	1	1	yes	characteristic
176	C₂×C₆₇	C₂×#416	1	1	yes	characteristic
177	C₂×C₆₇	C₂×C₄×SD₁₆	1	2	yes	—
178	C₂×C₆₇	C₂×C₄×Q₁₆	1	2	yes	—
179	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic
180	C₂²×#103	C₂×C₆₇	1	2	yes	—
181	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic
182	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic
183	C₄×#103	C₂×C₆₇	1	8	yes	direct product factor
184	C₂×#340	C₂×C₆₇	1	2	yes	—
185	C₆₇	C₂×C₄×#103	1	1	yes	characteristic, direct product factor, Sylow
186	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
188	C₂×C₄×Q₈	—	2	4	no	—
189	C₂×C₄×Q₈	—	2	2	no	—
190	C₂×C₄×Q₈	C₄×C₆₇	1	8	yes	complemented
191	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
192	C₂²×C₄⋊C₄	—	2	1	no	—
193	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
195	C₂²×C₄²	—	2	1	no	—
196	C₂²×C₄²	—	2	1	no	—
197	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
198	C₂×#103	C₄×C₆₇	1	16	yes	direct product factor
199	C₂×#103	C₂²×C₆₇	1	8	yes	—
200	C₂×C₄×C₈	—	2	4	no	—
201	C₂×C₄×C₈	C₂²×C₆₇	1	4	yes	—
202	C₄×C₄⋊C₄	—	2	2	no	—
203	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
204	C₂×#95	—	2	1	no	—
205	#340	C₂²×C₆₇	1	8	yes	—
206	C₂²×Q₈	—	2	2	no	—
207	C₂²×Q₈	—	2	1	no	—
208	C₂²×Q₈	—	2	4	no	—
209	C₂²×Q₈	C₂×C₄×C₆₇	1	4	yes	—
210	C₂²×Q₈	C₂×C₄×C₆₇	1	8	yes	—
211	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
212	C₂³×C₄	—	2	1	no	—
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
216	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
217	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	C₂×C₄×C₆₇	1	8	yes	—
221	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
222	C₄×Q₈	—	2	16	no	—
223	C₄×Q₈	—	2	8	no	—
224	C₄×Q₈	C₂×C₄×C₆₇	1	16	yes	complemented
225	C₂×C₄⋊C₄	—	2	8	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	4	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	—
233	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
235	C₂×C₄²	—	2	8	no	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	2	4	no	—
238	C₂×C₄²	—	4	4	no	—
239	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
240	C₂×C₄²	D₄×C₆₇	1	2	yes	—
241	C₂×C₄²	D₄×C₆₇	1	4	yes	—
242	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
243	#103	C₂×C₄×C₆₇	1	32	yes	direct product factor
244	C₄×C₈	—	2	8	no	—
245	#95	—	2	4	no	—
246	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	—	2	8	no	—
249	C₂×Q₈	—	2	8	no	—
250	C₂×Q₈	—	2	16	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	2	4	no	—
253	C₂×Q₈	C₄²×C₆₇	1	16	yes	complemented
254	C₂×Q₈	C₂²×C₄×C₆₇	1	8	yes	—
255	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	—	4	4	no	—
267	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
268	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
269	C₂²×C₄	SD₁₆×C₆₇	1	4	yes	—
270	C₂²×C₄	Q₁₆×C₆₇	1	4	yes	—
271	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
273	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
277	C₂²×C₄	#41×C₆₇	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
279	C₂×C₈	—	2	16	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	C₂²×C₄×C₆₇	1	8	yes	—
283	C₄⋊C₄	—	2	16	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
289	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
290	C₄²	—	2	16	no	—
291	C₄²	—	4	8	no	—
292	C₄²	C₂²⋊C₄×C₆₇	1	8	yes	—
293	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
294	C₄²	C₂×D₄×C₆₇	1	4	yes	—
295	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
296	C₂³	C₄×D₄×C₆₇	1	4	yes	—
297	C₂³	C₂×SD₁₆×C₆₇	1	2	yes	—
298	C₂³	C₂×Q₁₆×C₆₇	1	2	yes	—
299	C₂³	#135×C₆₇	1	4	yes	—
300	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
301	Q₈	—	2	4	no	—
302	Q₈	—	2	8	no	—
303	Q₈	—	2	16	no	—
304	Q₈	C₂×C₄²×C₆₇	1	8	yes	complemented
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	16	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	8	no	—
316	C₂×C₄	—	4	16	no	—
317	C₂×C₄	#103×C₆₇	1	16	yes	direct product factor
318	C₂×C₄	C₂×C₄²×C₆₇	1	4	yes	—
319	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
320	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
321	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
322	C₂×C₄	#117×C₆₇	1	4	yes	—
323	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
324	C₂×C₄	C₄×D₄×C₆₇	1	4	yes	—
325	C₂×C₄	C₂×SD₁₆×C₆₇	1	4	yes	—
326	C₂×C₄	C₂×Q₁₆×C₆₇	1	4	yes	—
327	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
328	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
329	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
331	C₈	—	2	8	no	—
332	C₂²	C₄×C₂²⋊C₄×C₆₇	1	4	yes	—
333	C₂²	C₂×#103×C₆₇	1	4	yes	—
334	C₂²	#416×C₆₇	1	4	yes	—
335	C₂²	C₄×SD₁₆×C₆₇	1	8	yes	—
336	C₂²	C₄×Q₁₆×C₆₇	1	8	yes	—
337	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
338	C₂²	C₂×C₄×D₄×C₆₇	1	2	yes	—
339	C₂²	C₂²×SD₁₆×C₆₇	1	1	yes	characteristic
340	C₂²	C₂²×Q₁₆×C₆₇	1	1	yes	characteristic
341	C₂²	C₂×#135×C₆₇	1	2	yes	—
342	C₄	—	2	8	no	—
343	C₄	—	2	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	C₄×C₂²⋊C₄×C₆₇	1	4	yes	—
347	C₄	C₂×#103×C₆₇	1	8	yes	direct product factor
348	C₄	C₂²×C₄²×C₆₇	1	1	yes	characteristic
349	C₄	C₂×#117×C₆₇	1	1	yes	characteristic
350	C₄	C₂×C₄×D₄×C₆₇	1	2	yes	—
351	C₂	C₄×#103×C₆₇	1	8	yes	direct product factor
352	C₂	C₂×C₄×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
353	C₂	C₂²×#103×C₆₇	1	1	yes	characteristic
354	C₂	C₂×#416×C₆₇	1	1	yes	characteristic
355	C₂	C₂×C₄×SD₁₆×C₆₇	1	2	yes	—
356	C₂	C₂×C₄×Q₁₆×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₆₇	D₄
commutator	C₄	C₂²×C₄²×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle, prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄×#103×C₆₇	C₂	direct (N × H)
11. C₂×C₄×Q₈×C₆₇	C₄	semidirect
19. C₂×#103×C₆₇	C₄	direct (N × H)
45. C₄×Q₈×C₆₇	C₂×C₄	semidirect
64. #103×C₆₇	C₂×C₄	direct (N × H)
74. C₂×Q₈×C₆₇	C₄²	semidirect
125. Q₈×C₆₇	C₂×C₄²	semidirect
138. C₂×C₄×C₆₇	#103	direct (N × H)
168. C₄×C₆₇	C₂×#103	direct (N × H)
172. C₂×C₄×#103	C₆₇	direct (N × H)
173. C₂×C₆₇	C₄×#103	direct (N × H)
183. C₄×#103	C₂×C₆₇	direct (N × H)
185. C₆₇	C₂×C₄×#103	direct (N × H)
190. C₂×C₄×Q₈	C₄×C₆₇	semidirect
198. C₂×#103	C₄×C₆₇	direct (N × H)
224. C₄×Q₈	C₂×C₄×C₆₇	semidirect
243. #103	C₂×C₄×C₆₇	direct (N × H)
253. C₂×Q₈	C₄²×C₆₇	semidirect
304. Q₈	C₂×C₄²×C₆₇	semidirect
317. C₂×C₄	#103×C₆₇	direct (N × H)
347. C₄	C₂×#103×C₆₇	direct (N × H)
351. C₂	C₄×#103×C₆₇	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×C₄×Q₈×C₆₇	2
C₂²×#103×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₄×#103×C₆₇	2
C₂×#340×C₆₇	2
C₂×C₄×#103	67

Subgroups — C2×C4×#103×C67 #30699658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#103×C₆₇ #30699658