Subgroups — C₂×C₄×#101×C₆₇ #30699646

Order 17152.

1538 conjugacy classes of subgroups.

The subgroup lattice has 350 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×#101×C₆₇	C₂	1	2	yes	maximal
3	C₂×C₄×M₁₆×C₆₇	C₂	1	2	yes	maximal
4	C₄×#101×C₆₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×#343×C₆₇	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₆₇	C₂²	1	4	yes	—
8	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
9	C₂×C₄×Q₈×C₆₇	—	2	4	no	—
10	C₂×C₄×Q₈×C₆₇	—	2	2	no	—
11	C₂×C₄×Q₈×C₆₇	C₄	1	4	yes	—
12	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₆₇	C₄	1	2	yes	—
16	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#101×C₆₇	C₄	1	16	yes	direct product factor
18	C₂×#101×C₆₇	C₂²	1	8	yes	—
19	C₄×M₁₆×C₆₇	—	2	4	no	—
20	C₄×M₁₆×C₆₇	C₂²	1	8	yes	—
21	C₂×#97×C₆₇	—	2	2	no	—
22	C₂×C₄×C₈×C₆₇	—	2	2	no	—
23	#343×C₆₇	C₂²	1	8	yes	—
24	C₂²×Q₈×C₆₇	—	2	2	no	—
25	C₂²×Q₈×C₆₇	—	2	2	no	—
26	C₂²×Q₈×C₆₇	—	2	4	no	—
27	C₂²×Q₈×C₆₇	C₂×C₄	1	8	yes	—
28	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
29	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
30	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₆₇	—	2	4	no	—
36	C₂×M₁₆×C₆₇	—	2	8	no	—
37	C₂×M₁₆×C₆₇	C₂×C₄	1	16	yes	—
38	C₂×M₁₆×C₆₇	C₂³	1	8	yes	—
39	C₂²×C₈×C₆₇	—	2	4	no	—
40	C₄×Q₈×C₆₇	—	2	8	no	—
41	C₄×Q₈×C₆₇	—	2	8	no	—
42	C₄×Q₈×C₆₇	—	2	8	no	—
43	C₄×Q₈×C₆₇	—	2	8	no	—
44	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
51	C₂×C₄²×C₆₇	—	2	2	no	—
52	C₂×C₄²×C₆₇	—	2	4	no	—
53	C₂×C₄²×C₆₇	—	2	2	no	—
54	C₂×C₄²×C₆₇	C₂×C₄	1	8	yes	—
55	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₆₇	D₄	1	2	yes	—
57	C₂×C₄²×C₆₇	D₄	1	4	yes	—
58	C₂×C₄²×C₆₇	D₄	1	2	yes	—
59	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
60	#101×C₆₇	C₂×C₄	1	32	yes	direct product factor
61	#97×C₆₇	—	2	8	no	—
62	C₄×C₈×C₆₇	—	2	8	no	—
63	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
64	C₂×Q₈×C₆₇	—	2	4	no	—
65	C₂×Q₈×C₆₇	—	2	4	no	—
66	C₂×Q₈×C₆₇	—	2	16	no	—
67	C₂×Q₈×C₆₇	—	2	16	no	—
68	C₂×Q₈×C₆₇	—	2	4	no	—
69	C₂×Q₈×C₆₇	—	2	4	no	—
70	C₂×Q₈×C₆₇	C₄²	1	8	yes	—
71	C₂×Q₈×C₆₇	C₂²×C₄	1	8	yes	—
72	C₂²×C₄×C₆₇	—	2	2	no	—
73	C₂²×C₄×C₆₇	—	2	2	no	—
74	C₂²×C₄×C₆₇	—	2	4	no	—
75	C₂²×C₄×C₆₇	—	2	4	no	—
76	C₂²×C₄×C₆₇	—	2	2	no	—
77	C₂²×C₄×C₆₇	—	2	2	no	—
78	C₂²×C₄×C₆₇	—	4	2	no	—
79	C₂²×C₄×C₆₇	—	4	4	no	—
80	C₂²×C₄×C₆₇	C₄²	1	8	yes	—
81	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	#41	1	4	yes	—
95	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₆₇	—	2	16	no	—
97	M₁₆×C₆₇	—	2	8	no	—
98	M₁₆×C₆₇	C₂²×C₄	1	16	yes	—
99	C₂×C₈×C₆₇	—	2	16	no	—
100	C₂×C₈×C₆₇	—	2	8	no	—
101	C₄⋊C₄×C₆₇	—	2	16	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	4	no	—
104	C₄²×C₆₇	—	2	8	no	—
105	C₄²×C₆₇	—	2	8	no	—
106	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
107	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
108	C₄²×C₆₇	C₂×D₄	1	4	yes	—
109	C₄²×C₆₇	C₂×D₄	1	4	yes	—
110	C₂³×C₆₇	—	2	2	no	—
111	C₂³×C₆₇	—	2	2	no	—
112	C₂³×C₆₇	C₂×C₄²	1	2	yes	—
113	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₆₇	#117	1	2	yes	—
116	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
117	Q₈×C₆₇	—	2	16	no	—
118	Q₈×C₆₇	—	2	16	no	—
119	C₂×C₄×C₆₇	—	2	4	no	—
120	C₂×C₄×C₆₇	—	2	4	no	—
121	C₂×C₄×C₆₇	—	2	8	no	—
122	C₂×C₄×C₆₇	—	2	8	no	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	4	no	—
125	C₂×C₄×C₆₇	—	2	4	no	—
126	C₂×C₄×C₆₇	—	2	4	no	—
127	C₂×C₄×C₆₇	—	2	4	no	—
128	C₂×C₄×C₆₇	—	4	2	no	—
129	C₂×C₄×C₆₇	—	4	2	no	—
130	C₂×C₄×C₆₇	—	4	4	no	—
131	C₂×C₄×C₆₇	—	4	4	no	—
132	C₂×C₄×C₆₇	—	4	4	no	—
133	C₂×C₄×C₆₇	#101	1	4	yes	direct product factor
134	C₂×C₄×C₆₇	C₂×C₄²	1	8	yes	—
135	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂×C₄×C₆₇	#117	1	2	yes	—
141	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
142	C₂×C₄×C₆₇	C₄×D₄	1	8	yes	—
143	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
144	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
145	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
146	C₈×C₆₇	—	2	16	no	—
147	C₂²×C₆₇	—	2	1	no	—
148	C₂²×C₆₇	—	2	1	no	—
149	C₂²×C₆₇	—	2	1	no	—
150	C₂²×C₆₇	—	2	1	no	—
151	C₂²×C₆₇	—	2	4	no	—
152	C₂²×C₆₇	—	2	4	no	—
153	C₂²×C₆₇	C₄×C₂²⋊C₄	1	2	yes	—
154	C₂²×C₆₇	C₄×C₂²⋊C₄	1	2	yes	—
155	C₂²×C₆₇	C₂×#101	1	2	yes	—
156	C₂²×C₆₇	#413	1	2	yes	—
157	C₂²×C₆₇	C₂²×C₄²	1	1	yes	characteristic
158	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₆₇	C₂×#117	1	1	yes	characteristic
160	C₄×C₆₇	—	2	2	no	—
161	C₄×C₆₇	—	2	4	no	—
162	C₄×C₆₇	—	2	8	no	—
163	C₄×C₆₇	—	4	4	no	—
164	C₄×C₆₇	C₄×C₂²⋊C₄	1	4	yes	—
165	C₄×C₆₇	C₂×#101	1	4	yes	direct product factor
166	C₄×C₆₇	C₂×C₄×D₄	1	4	yes	—
167	C₂×C₄×#101	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂×C₆₇	—	2	1	no	—
169	C₂×C₆₇	—	2	2	no	—
170	C₂×C₆₇	—	2	1	no	—
171	C₂×C₆₇	C₄×#101	1	4	yes	direct product factor
172	C₂×C₆₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₆₇	C₂²×#101	1	1	yes	characteristic
174	C₂×C₆₇	C₂×#413	1	1	yes	characteristic
175	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic
176	C₂²×#101	C₂×C₆₇	1	2	yes	—
177	C₂×C₄×M₁₆	C₂×C₆₇	1	2	yes	—
178	C₄×#101	C₂×C₆₇	1	8	yes	direct product factor
179	C₂×#343	C₂×C₆₇	1	2	yes	—
180	C₆₇	C₂×C₄×#101	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
182	C₂²×M₁₆	C₂²×C₆₇	1	4	yes	—
183	C₂×C₄×Q₈	—	2	2	no	—
184	C₂×C₄×Q₈	—	2	2	no	—
185	C₂×C₄×Q₈	—	2	4	no	—
186	C₂×C₄×Q₈	C₄×C₆₇	1	4	yes	—
187	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
188	C₂²×C₄⋊C₄	C₄×C₆₇	1	2	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
190	C₂²×C₄²	C₄×C₆₇	1	2	yes	—
191	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
192	C₂×#101	C₄×C₆₇	1	16	yes	direct product factor
193	C₂×#101	C₂²×C₆₇	1	8	yes	—
194	C₄×M₁₆	—	2	4	no	—
195	C₄×M₁₆	C₂²×C₆₇	1	8	yes	—
196	C₂×#97	—	2	2	no	—
197	C₂×C₄×C₈	—	2	2	no	—
198	#343	C₂²×C₆₇	1	8	yes	—
199	C₂²×Q₈	—	2	2	no	—
200	C₂²×Q₈	—	2	2	no	—
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	C₂×C₄×C₆₇	1	8	yes	—
203	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
204	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
205	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
206	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
207	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	—
208	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
210	C₂×M₁₆	—	2	4	no	—
211	C₂×M₁₆	—	2	8	no	—
212	C₂×M₁₆	C₂×C₄×C₆₇	1	16	yes	—
213	C₂×M₁₆	C₂³×C₆₇	1	8	yes	—
214	C₂²×C₈	—	2	4	no	—
215	C₄×Q₈	—	2	8	no	—
216	C₄×Q₈	—	2	8	no	—
217	C₄×Q₈	—	2	8	no	—
218	C₄×Q₈	—	2	8	no	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	8	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
225	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	4	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂×C₄×C₆₇	1	8	yes	—
230	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	—
231	C₂×C₄²	D₄×C₆₇	1	2	yes	—
232	C₂×C₄²	D₄×C₆₇	1	2	yes	—
233	C₂×C₄²	D₄×C₆₇	1	4	yes	—
234	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
235	#101	C₂×C₄×C₆₇	1	32	yes	direct product factor
236	#97	—	2	8	no	—
237	C₄×C₈	—	2	8	no	—
238	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	—	2	16	no	—
242	C₂×Q₈	—	2	16	no	—
243	C₂×Q₈	—	2	4	no	—
244	C₂×Q₈	—	2	4	no	—
245	C₂×Q₈	C₄²×C₆₇	1	8	yes	—
246	C₂×Q₈	C₂²×C₄×C₆₇	1	8	yes	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	C₄²×C₆₇	1	8	yes	—
256	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
257	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
258	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
259	C₂²×C₄	C₂²⋊C₄×C₆₇	1	2	yes	—
260	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
262	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
264	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
267	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
269	C₂²×C₄	#41×C₆₇	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
271	M₁₆	—	2	16	no	—
272	M₁₆	—	2	8	no	—
273	M₁₆	C₂²×C₄×C₆₇	1	16	yes	—
274	C₂×C₈	—	2	16	no	—
275	C₂×C₈	—	2	8	no	—
276	C₄⋊C₄	—	2	16	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄²	—	2	8	no	—
280	C₄²	—	2	8	no	—
281	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
282	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
283	C₄²	C₂×D₄×C₆₇	1	4	yes	—
284	C₄²	C₂×D₄×C₆₇	1	4	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	C₂×C₄²×C₆₇	1	2	yes	—
288	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
289	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
290	C₂³	#117×C₆₇	1	2	yes	—
291	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
292	Q₈	—	2	16	no	—
293	Q₈	—	2	16	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	#101×C₆₇	1	4	yes	direct product factor
309	C₂×C₄	C₂×C₄²×C₆₇	1	8	yes	—
310	C₂×C₄	C₂×C₄²×C₆₇	1	2	yes	—
311	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
312	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	4	yes	—
313	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
314	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
315	C₂×C₄	#117×C₆₇	1	2	yes	—
316	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
317	C₂×C₄	C₄×D₄×C₆₇	1	8	yes	—
318	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
319	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
320	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
321	C₈	—	2	16	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	1	no	—
328	C₂²	C₄×C₂²⋊C₄×C₆₇	1	2	yes	—
329	C₂²	C₄×C₂²⋊C₄×C₆₇	1	2	yes	—
330	C₂²	C₂×#101×C₆₇	1	2	yes	—
331	C₂²	#413×C₆₇	1	2	yes	—
332	C₂²	C₂²×C₄²×C₆₇	1	1	yes	characteristic
333	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
334	C₂²	C₂×#117×C₆₇	1	1	yes	characteristic
335	C₄	—	2	8	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	4	no	—
338	C₄	—	4	4	no	—
339	C₄	C₄×C₂²⋊C₄×C₆₇	1	4	yes	—
340	C₄	C₂×#101×C₆₇	1	4	yes	direct product factor
341	C₄	C₂×C₄×D₄×C₆₇	1	4	yes	—
342	C₂	—	2	1	no	—
343	C₂	—	2	1	no	—
344	C₂	—	2	2	no	—
345	C₂	C₄×#101×C₆₇	1	4	yes	direct product factor
346	C₂	C₂×C₄×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
347	C₂	C₂²×#101×C₆₇	1	1	yes	characteristic
348	C₂	C₂×#413×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₄×#101×C₆₇	C₂	direct (N × H)
17. C₂×#101×C₆₇	C₄	direct (N × H)
60. #101×C₆₇	C₂×C₄	direct (N × H)
133. C₂×C₄×C₆₇	#101	direct (N × H)
165. C₄×C₆₇	C₂×#101	direct (N × H)
167. C₂×C₄×#101	C₆₇	direct (N × H)
171. C₂×C₆₇	C₄×#101	direct (N × H)
178. C₄×#101	C₂×C₆₇	direct (N × H)
180. C₆₇	C₂×C₄×#101	direct (N × H)
192. C₂×#101	C₄×C₆₇	direct (N × H)
235. #101	C₂×C₄×C₆₇	direct (N × H)
308. C₂×C₄	#101×C₆₇	direct (N × H)
340. C₄	C₂×#101×C₆₇	direct (N × H)
345. C₂	C₄×#101×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×#101×C₆₇	2
C₂×C₄×M₁₆×C₆₇	2
C₄×#101×C₆₇	2
C₂×#343×C₆₇	2
C₂×C₄×#101	67

Subgroups — C2×C4×#101×C67 #30699646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#101×C₆₇ #30699646