Subgroups — C₆₇×#34929 #30714180

Order 17152.

2308 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2556	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2551	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2542	C₂	1	1	yes	maximal, characteristic
6	C₆₇×#2538	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#2506	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2492	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2452	C₂	1	2	yes	maximal
10	C₆₇×#2429	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2396	C₂	1	4	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₄⋊Q₈×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₄×C₂²⋊Q₈×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2293	C₂	1	2	yes	maximal
16	C₄²×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
18	#533×C₆₇	—	2	16	no	—
19	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
23	C₂×#125×C₆₇	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
32	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₆₇	C₂²	1	4	yes	—
37	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
38	#400×C₆₇	C₂²	1	4	yes	—
39	#399×C₆₇	C₂²	1	4	yes	—
40	#398×C₆₇	C₂²	1	4	yes	—
41	#398×C₆₇	C₂²	1	4	yes	—
42	#396×C₆₇	C₂²	1	4	yes	—
43	#396×C₆₇	C₂²	1	4	yes	—
44	#395×C₆₇	C₂²	1	4	yes	—
45	#393×C₆₇	C₂²	1	4	yes	—
46	#391×C₆₇	C₂²	1	2	yes	—
47	#391×C₆₇	C₂²	1	4	yes	—
48	#391×C₆₇	C₂²	1	2	yes	—
49	#390×C₆₇	C₂²	1	2	yes	—
50	#390×C₆₇	C₂²	1	2	yes	—
51	#389×C₆₇	C₂²	1	2	yes	—
52	#389×C₆₇	C₂²	1	2	yes	—
53	#389×C₆₇	C₂²	1	2	yes	—
54	#389×C₆₇	C₂²	1	2	yes	—
55	#389×C₆₇	C₂²	1	2	yes	—
56	#389×C₆₇	C₂²	1	2	yes	—
57	#389×C₆₇	C₂²	1	2	yes	—
58	#389×C₆₇	C₂²	1	4	yes	—
59	#388×C₆₇	C₂²	1	4	yes	—
60	#388×C₆₇	C₂²	1	4	yes	—
61	#387×C₆₇	C₂²	1	4	yes	—
62	#385×C₆₇	C₂²	1	4	yes	—
63	#384×C₆₇	C₂²	1	2	yes	—
64	#384×C₆₇	C₂²	1	1	yes	characteristic
65	#380×C₆₇	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
77	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
82	C₄³×C₆₇	C₂²	1	1	yes	characteristic
83	C₄³×C₆₇	C₂²	1	2	yes	—
84	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
85	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
86	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
91	C₄⋊Q₈×C₆₇	—	2	8	no	—
92	C₄⋊Q₈×C₆₇	—	2	8	no	—
93	C₄⋊Q₈×C₆₇	—	2	8	no	—
94	C₄⋊Q₈×C₆₇	—	2	4	no	—
95	#125×C₆₇	—	2	16	no	—
96	C₂²⋊Q₈×C₆₇	—	2	8	no	—
97	C₂²⋊Q₈×C₆₇	—	2	8	no	—
98	C₂²⋊Q₈×C₆₇	—	2	16	no	—
99	C₂²⋊Q₈×C₆₇	—	2	8	no	—
100	C₄×Q₈×C₆₇	—	2	4	no	—
101	C₄×Q₈×C₆₇	—	2	16	no	—
102	C₄×Q₈×C₆₇	—	2	8	no	—
103	C₄×Q₈×C₆₇	—	2	4	no	—
104	C₄×Q₈×C₆₇	D₄	1	8	yes	complemented
105	C₄×D₄×C₆₇	—	2	4	no	—
106	C₄×D₄×C₆₇	—	2	4	no	—
107	C₄×D₄×C₆₇	Q₈	1	8	yes	complemented
108	#117×C₆₇	—	2	16	no	—
109	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₆₇	—	2	8	no	—
139	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
156	#95×C₆₇	C₂³	1	2	yes	—
157	#95×C₆₇	C₂³	1	2	yes	—
158	#95×C₆₇	C₂³	1	2	yes	—
159	#95×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	4	yes	—
161	#95×C₆₇	C₂³	1	2	yes	—
162	#95×C₆₇	C₂³	1	2	yes	—
163	#95×C₆₇	C₂³	1	2	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	#95×C₆₇	C₂³	1	4	yes	—
166	#95×C₆₇	C₂³	1	4	yes	—
167	#95×C₆₇	C₂³	1	4	yes	—
168	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
169	C₂×Q₈×C₆₇	—	2	8	no	—
170	C₂×Q₈×C₆₇	—	2	4	no	—
171	C₂×Q₈×C₆₇	—	2	2	no	—
172	C₂×Q₈×C₆₇	—	2	2	no	—
173	C₂×Q₈×C₆₇	—	2	4	no	—
174	C₂×Q₈×C₆₇	—	2	8	no	—
175	C₂×Q₈×C₆₇	—	2	4	no	—
176	C₂×Q₈×C₆₇	—	4	4	no	—
177	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
178	C₂×D₄×C₆₇	—	2	2	no	—
179	C₂×D₄×C₆₇	—	2	2	no	—
180	C₂×D₄×C₆₇	C₂×Q₈	1	4	yes	—
181	C₂²×C₄×C₆₇	—	2	4	no	—
182	C₂²×C₄×C₆₇	—	2	4	no	—
183	C₂²×C₄×C₆₇	—	2	4	no	—
184	C₂²×C₄×C₆₇	—	2	4	no	—
185	C₂²×C₄×C₆₇	—	2	4	no	—
186	C₂²×C₄×C₆₇	—	2	4	no	—
187	C₂²×C₄×C₆₇	—	2	4	no	—
188	C₂²×C₄×C₆₇	—	4	2	no	—
189	C₂²×C₄×C₆₇	C₂×Q₈	1	8	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
206	C₄⋊C₄×C₆₇	—	2	8	no	—
207	C₄⋊C₄×C₆₇	—	2	8	no	—
208	C₄⋊C₄×C₆₇	—	2	8	no	—
209	C₄⋊C₄×C₆₇	—	2	8	no	—
210	C₄⋊C₄×C₆₇	—	2	8	no	—
211	C₄⋊C₄×C₆₇	—	2	8	no	—
212	C₄⋊C₄×C₆₇	—	2	4	no	—
213	C₄⋊C₄×C₆₇	—	2	2	no	—
214	C₄⋊C₄×C₆₇	—	2	4	no	—
215	C₄⋊C₄×C₆₇	—	2	4	no	—
216	C₄⋊C₄×C₆₇	—	2	2	no	—
217	C₄⋊C₄×C₆₇	—	2	8	no	—
218	C₄⋊C₄×C₆₇	—	2	8	no	—
219	C₄⋊C₄×C₆₇	—	2	4	no	—
220	C₄⋊C₄×C₆₇	—	2	4	no	—
221	C₄⋊C₄×C₆₇	—	2	4	no	—
222	C₄⋊C₄×C₆₇	—	4	2	no	—
223	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
224	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
225	C₄⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
226	C₄⋊C₄×C₆₇	#41	1	4	yes	—
227	C₄⋊C₄×C₆₇	#41	1	4	yes	—
228	C₂²⋊C₄×C₆₇	—	2	8	no	—
229	C₂²⋊C₄×C₆₇	—	2	8	no	—
230	C₂²⋊C₄×C₆₇	—	2	4	no	—
231	C₂²⋊C₄×C₆₇	—	2	4	no	—
232	C₂²⋊C₄×C₆₇	—	2	8	no	—
233	C₂²⋊C₄×C₆₇	—	4	4	no	—
234	C₂²⋊C₄×C₆₇	C₂×Q₈	1	8	yes	—
235	C₄²×C₆₇	—	2	4	no	—
236	C₄²×C₆₇	—	2	4	no	—
237	C₄²×C₆₇	—	2	4	no	—
238	C₄²×C₆₇	—	2	8	no	—
239	C₄²×C₆₇	—	2	2	no	—
240	C₄²×C₆₇	—	2	4	no	—
241	C₄²×C₆₇	—	2	2	no	—
242	C₄²×C₆₇	—	2	4	no	—
243	C₄²×C₆₇	—	2	4	no	—
244	C₄²×C₆₇	—	2	2	no	—
245	C₄²×C₆₇	—	2	4	no	—
246	C₄²×C₆₇	—	4	1	no	—
247	C₄²×C₆₇	—	4	2	no	—
248	C₄²×C₆₇	C₂×D₄	1	4	yes	—
249	C₄²×C₆₇	C₂×D₄	1	8	yes	—
250	C₄²×C₆₇	C₂×Q₈	1	4	yes	—
251	C₄²×C₆₇	#41	1	4	yes	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	2	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	C₂²×Q₈	1	4	yes	—
259	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
260	Q₈×C₆₇	—	2	8	no	—
261	Q₈×C₆₇	—	4	16	no	—
262	Q₈×C₆₇	—	4	8	no	—
263	D₄×C₆₇	—	2	8	no	—
264	C₂×C₄×C₆₇	—	2	2	no	—
265	C₂×C₄×C₆₇	—	2	2	no	—
266	C₂×C₄×C₆₇	—	2	1	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	2	no	—
269	C₂×C₄×C₆₇	—	2	2	no	—
270	C₂×C₄×C₆₇	—	2	1	no	—
271	C₂×C₄×C₆₇	—	2	2	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	2	no	—
274	C₂×C₄×C₆₇	—	2	2	no	—
275	C₂×C₄×C₆₇	—	2	1	no	—
276	C₂×C₄×C₆₇	—	2	1	no	—
277	C₂×C₄×C₆₇	—	2	1	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	2	no	—
280	C₂×C₄×C₆₇	—	2	16	no	—
281	C₂×C₄×C₆₇	—	2	2	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	4	no	—
284	C₂×C₄×C₆₇	—	2	1	no	—
285	C₂×C₄×C₆₇	—	2	2	no	—
286	C₂×C₄×C₆₇	—	2	1	no	—
287	C₂×C₄×C₆₇	—	2	2	no	—
288	C₂×C₄×C₆₇	—	2	4	no	—
289	C₂×C₄×C₆₇	—	2	2	no	—
290	C₂×C₄×C₆₇	—	2	4	no	—
291	C₂×C₄×C₆₇	—	2	4	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	1	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	4	no	—
296	C₂×C₄×C₆₇	—	4	8	no	—
297	C₂×C₄×C₆₇	—	4	8	no	—
298	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
299	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
300	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
304	C₂×C₄×C₆₇	C₂²×Q₈	1	4	yes	—
305	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
306	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
307	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
308	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
309	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
310	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
311	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
312	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
313	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
314	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
315	C₂²×C₆₇	—	2	4	no	—
316	C₂²×C₆₇	—	2	4	no	—
317	C₂²×C₆₇	—	2	4	no	—
318	C₂²×C₆₇	—	4	2	no	—
319	C₂²×C₆₇	—	4	2	no	—
320	C₂²×C₆₇	—	4	2	no	—
321	C₂²×C₆₇	—	4	2	no	—
322	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
323	C₂²×C₆₇	C₂³×Q₈	1	1	yes	characteristic
324	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
325	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
326	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
328	C₂²×C₆₇	#585	1	1	yes	characteristic
329	C₄×C₆₇	—	2	4	no	—
330	C₄×C₆₇	—	2	2	no	—
331	C₄×C₆₇	—	2	4	no	—
332	C₄×C₆₇	—	2	2	no	—
333	C₄×C₆₇	—	2	4	no	—
334	C₄×C₆₇	—	2	4	no	—
335	C₄×C₆₇	—	2	2	no	—
336	C₄×C₆₇	—	2	4	no	—
337	C₄×C₆₇	—	4	2	no	—
338	C₄×C₆₇	—	4	4	no	—
339	C₄×C₆₇	—	4	2	no	—
340	C₄×C₆₇	—	4	4	no	—
341	C₄×C₆₇	—	4	1	no	—
342	C₄×C₆₇	#532	1	4	yes	—
343	C₄×C₆₇	#533	1	4	yes	complemented
344	C₄×C₆₇	D₄×Q₈	1	4	yes	—
345	#34929	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂×C₆₇	—	4	4	no	—
347	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
348	C₂×C₆₇	C₂×#533	1	1	yes	characteristic
349	C₂×C₆₇	#3461	1	1	yes	characteristic
350	C₂×C₆₇	C₂×D₄×Q₈	1	1	yes	characteristic
351	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
352	C₂×C₆₇	Q₈×#41	1	1	yes	characteristic
353	C₂×C₆₇	#3482	1	1	yes	characteristic
354	C₂×#533	C₂×C₆₇	1	2	yes	complemented
355	#2556	C₂×C₆₇	1	4	yes	complemented
356	#2551	C₂×C₆₇	1	1	yes	characteristic, complemented
357	#2546	C₂×C₆₇	1	1	yes	characteristic, complemented
358	#2542	C₂×C₆₇	1	1	yes	characteristic
359	#2538	C₂×C₆₇	1	1	yes	characteristic
360	#2506	C₂×C₆₇	1	2	yes	complemented
361	#2492	C₂×C₆₇	1	2	yes	complemented
362	#2452	C₂×C₆₇	1	2	yes	—
363	#2429	C₂×C₆₇	1	2	yes	complemented
364	#2396	C₂×C₆₇	1	4	yes	complemented
365	C₄×C₄⋊Q₈	C₂×C₆₇	1	2	yes	complemented
366	C₄×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
367	C₄×C₂²⋊Q₈	C₂×C₆₇	1	2	yes	complemented
368	#2293	C₂×C₆₇	1	2	yes	—
369	C₄²×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
370	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic
371	C₆₇	#34929	1	1	yes	characteristic, direct product factor, Sylow
372	#533	—	2	16	no	—
373	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
374	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
375	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
376	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
377	C₂×#125	C₂²×C₆₇	1	4	yes	—
378	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
379	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
380	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
381	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
382	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
383	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
384	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
386	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
387	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
388	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
389	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
390	C₂×#117	C₂²×C₆₇	1	4	yes	—
391	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
392	#400	C₂²×C₆₇	1	4	yes	—
393	#399	C₂²×C₆₇	1	4	yes	—
394	#398	C₂²×C₆₇	1	4	yes	—
395	#398	C₂²×C₆₇	1	4	yes	—
396	#396	C₂²×C₆₇	1	4	yes	—
397	#396	C₂²×C₆₇	1	4	yes	—
398	#395	C₂²×C₆₇	1	4	yes	—
399	#393	C₂²×C₆₇	1	4	yes	—
400	#391	C₂²×C₆₇	1	2	yes	—
401	#391	C₂²×C₆₇	1	4	yes	—
402	#391	C₂²×C₆₇	1	2	yes	—
403	#390	C₂²×C₆₇	1	2	yes	—
404	#390	C₂²×C₆₇	1	2	yes	—
405	#389	C₂²×C₆₇	1	4	yes	—
406	#389	C₂²×C₆₇	1	2	yes	—
407	#389	C₂²×C₆₇	1	2	yes	—
408	#389	C₂²×C₆₇	1	2	yes	—
409	#389	C₂²×C₆₇	1	2	yes	—
410	#389	C₂²×C₆₇	1	2	yes	—
411	#389	C₂²×C₆₇	1	2	yes	—
412	#389	C₂²×C₆₇	1	2	yes	—
413	#388	C₂²×C₆₇	1	4	yes	—
414	#388	C₂²×C₆₇	1	4	yes	—
415	#387	C₂²×C₆₇	1	4	yes	—
416	#385	C₂²×C₆₇	1	4	yes	—
417	#384	C₂²×C₆₇	1	2	yes	—
418	#384	C₂²×C₆₇	1	1	yes	characteristic
419	#380	C₂²×C₆₇	1	2	yes	—
420	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
422	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
423	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
424	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
425	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
436	C₄³	C₂²×C₆₇	1	1	yes	characteristic
437	C₄³	C₂²×C₆₇	1	2	yes	—
438	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
439	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
440	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
443	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
444	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
445	C₄⋊Q₈	—	2	8	no	—
446	C₄⋊Q₈	—	2	8	no	—
447	C₄⋊Q₈	—	2	8	no	—
448	C₄⋊Q₈	—	2	4	no	—
449	#125	—	2	16	no	—
450	C₂²⋊Q₈	—	2	8	no	—
451	C₂²⋊Q₈	—	2	8	no	—
452	C₂²⋊Q₈	—	2	16	no	—
453	C₂²⋊Q₈	—	2	8	no	—
454	C₄×Q₈	—	2	4	no	—
455	C₄×Q₈	—	2	16	no	—
456	C₄×Q₈	—	2	8	no	—
457	C₄×Q₈	—	2	4	no	—
458	C₄×Q₈	D₄×C₆₇	1	8	yes	complemented
459	C₄×D₄	—	2	4	no	—
460	C₄×D₄	—	2	4	no	—
461	C₄×D₄	Q₈×C₆₇	1	8	yes	complemented
462	#117	—	2	16	no	—
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
492	C₂×C₄²	—	2	8	no	—
493	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
494	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
496	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
498	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
499	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
500	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
501	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
502	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
504	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
506	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
507	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
510	#95	C₂³×C₆₇	1	2	yes	—
511	#95	C₂³×C₆₇	1	2	yes	—
512	#95	C₂³×C₆₇	1	2	yes	—
513	#95	C₂³×C₆₇	1	4	yes	—
514	#95	C₂³×C₆₇	1	4	yes	—
515	#95	C₂³×C₆₇	1	2	yes	—
516	#95	C₂³×C₆₇	1	2	yes	—
517	#95	C₂³×C₆₇	1	2	yes	—
518	#95	C₂³×C₆₇	1	4	yes	—
519	#95	C₂³×C₆₇	1	4	yes	—
520	#95	C₂³×C₆₇	1	4	yes	—
521	#95	C₂³×C₆₇	1	4	yes	—
522	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
523	C₂×Q₈	—	2	8	no	—
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	4	no	—
528	C₂×Q₈	—	2	8	no	—
529	C₂×Q₈	—	2	4	no	—
530	C₂×Q₈	—	4	4	no	—
531	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	C₂×Q₈×C₆₇	1	4	yes	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	C₂×Q₈×C₆₇	1	8	yes	—
544	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
549	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
555	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	8	no	—
562	C₄⋊C₄	—	2	8	no	—
563	C₄⋊C₄	—	2	8	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	8	no	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
578	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
579	C₄⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
580	C₄⋊C₄	#41×C₆₇	1	4	yes	—
581	C₄⋊C₄	#41×C₆₇	1	4	yes	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	8	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	4	4	no	—
588	C₂²⋊C₄	C₂×Q₈×C₆₇	1	8	yes	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	8	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	4	1	no	—
601	C₄²	—	4	2	no	—
602	C₄²	C₂×D₄×C₆₇	1	4	yes	—
603	C₄²	C₂×D₄×C₆₇	1	8	yes	—
604	C₄²	C₂×Q₈×C₆₇	1	4	yes	—
605	C₄²	#41×C₆₇	1	4	yes	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	C₂²×Q₈×C₆₇	1	4	yes	—
613	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
614	Q₈	—	2	8	no	—
615	Q₈	—	4	16	no	—
616	Q₈	—	4	8	no	—
617	D₄	—	2	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	16	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
654	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
655	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
657	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
658	C₂×C₄	C₂²×Q₈×C₆₇	1	4	yes	—
659	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
660	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
661	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
662	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
663	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
664	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
665	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
666	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
667	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
668	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
677	C₂²	C₂³×Q₈×C₆₇	1	1	yes	characteristic
678	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
679	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
680	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
681	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
682	C₂²	#585×C₆₇	1	1	yes	characteristic
683	C₄	—	2	4	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	4	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	4	no	—
695	C₄	—	4	1	no	—
696	C₄	#532×C₆₇	1	4	yes	—
697	C₄	#533×C₆₇	1	4	yes	complemented
698	C₄	D₄×Q₈×C₆₇	1	4	yes	—
699	C₂	—	4	4	no	—
700	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
701	C₂	C₂×#533×C₆₇	1	1	yes	characteristic
702	C₂	C₆₇×#3461	1	1	yes	characteristic
703	C₂	C₂×D₄×Q₈×C₆₇	1	1	yes	characteristic
704	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
705	C₂	Q₈×#41×C₆₇	1	1	yes	characteristic
706	C₂	C₆₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂²×D₄×C₆₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₆₇	C₂	semidirect
2. C₆₇×#2556	C₂	semidirect
3. C₆₇×#2551	C₂	semidirect
4. C₆₇×#2546	C₂	semidirect
7. C₆₇×#2506	C₂	semidirect
8. C₆₇×#2492	C₂	semidirect
10. C₆₇×#2429	C₂	semidirect
11. C₆₇×#2396	C₂	semidirect
12. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
13. C₄×C₄⋊Q₈×C₆₇	C₂	semidirect
14. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
16. C₄²×Q₈×C₆₇	C₂	semidirect
104. C₄×Q₈×C₆₇	D₄	semidirect
107. C₄×D₄×C₆₇	Q₈	semidirect
343. C₄×C₆₇	#533	semidirect
345. #34929	C₆₇	direct (N × H)
354. C₂×#533	C₂×C₆₇	semidirect
355. #2556	C₂×C₆₇	semidirect
356. #2551	C₂×C₆₇	semidirect
357. #2546	C₂×C₆₇	semidirect
360. #2506	C₂×C₆₇	semidirect
361. #2492	C₂×C₆₇	semidirect
363. #2429	C₂×C₆₇	semidirect
364. #2396	C₂×C₆₇	semidirect
365. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
366. C₄×C₄⋊Q₈	C₂×C₆₇	semidirect
367. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
369. C₄²×Q₈	C₂×C₆₇	semidirect
371. C₆₇	#34929	direct (N × H)
458. C₄×Q₈	D₄×C₆₇	semidirect
461. C₄×D₄	Q₈×C₆₇	semidirect
697. C₄	#533×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#533×C₆₇	2
C₆₇×#2556	2
C₆₇×#2551	2
C₆₇×#2546	2
C₆₇×#2542	2
C₆₇×#2538	2
C₆₇×#2506	2
C₆₇×#2492	2
C₆₇×#2452	2
C₆₇×#2429	2
C₆₇×#2396	2
C₄×C₄⋊Q₈×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₆₇×#2293	2
C₄²×Q₈×C₆₇	2
C₄²×D₄×C₆₇	2
#34929	67

Subgroups — C67×#34929 #30714180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34929 #30714180