Subgroups — C₆₇×#61687 #30740938

Order 17152.

2068 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3308	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3299	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3287	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3269	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3203	C₂	1	4	yes	maximal, complemented
12	C₆₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3013	C₂	1	4	yes	maximal, complemented
15	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
17	C₂×#137×C₆₇	C₂²	1	4	yes	—
18	C₂×#135×C₆₇	C₂²	1	4	yes	—
19	#562×C₆₇	—	2	2	no	—
20	#554×C₆₇	—	2	1	no	—
21	#554×C₆₇	C₂²	1	2	yes	—
22	#550×C₆₇	—	2	1	no	—
23	#550×C₆₇	—	2	1	no	—
24	#550×C₆₇	C₂²	1	2	yes	—
25	#550×C₆₇	C₂²	1	2	yes	—
26	D₄×Q₈×C₆₇	—	2	1	no	—
27	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
28	#548×C₆₇	—	2	2	no	—
29	#548×C₆₇	C₂²	1	4	yes	—
30	#547×C₆₇	C₂²	1	2	yes	—
31	#547×C₆₇	C₂²	1	2	yes	—
32	#540×C₆₇	—	2	2	no	—
33	#537×C₆₇	—	2	2	no	—
34	#537×C₆₇	—	2	2	no	—
35	#537×C₆₇	C₂²	1	4	yes	—
36	#537×C₆₇	C₂²	1	2	yes	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	—	2	2	no	—
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	C₂²	1	1	yes	characteristic
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	#497×C₆₇	C₂²	1	2	yes	—
44	#493×C₆₇	C₂²	1	1	yes	characteristic
45	#492×C₆₇	C₂²	1	1	yes	characteristic
46	#489×C₆₇	C₂²	1	2	yes	—
47	#487×C₆₇	C₂²	1	1	yes	characteristic
48	#486×C₆₇	C₂²	1	1	yes	characteristic
49	#484×C₆₇	C₂²	1	4	yes	—
50	#484×C₆₇	C₂²	1	2	yes	—
51	#480×C₆₇	C₂²	1	4	yes	—
52	#480×C₆₇	C₂²	1	2	yes	—
53	#477×C₆₇	C₂²	1	2	yes	—
54	#477×C₆₇	C₂²	1	2	yes	—
55	#468×C₆₇	C₂²	1	4	yes	—
56	#468×C₆₇	C₂²	1	4	yes	—
57	#467×C₆₇	C₂²	1	4	yes	—
58	#466×C₆₇	C₂²	1	4	yes	—
59	#463×C₆₇	C₂²	1	4	yes	—
60	#462×C₆₇	C₂²	1	2	yes	—
61	#462×C₆₇	C₂²	1	2	yes	—
62	#460×C₆₇	C₂²	1	2	yes	—
63	#460×C₆₇	C₂²	1	2	yes	—
64	#452×C₆₇	C₂²	1	4	yes	—
65	#452×C₆₇	C₂²	1	4	yes	—
66	#452×C₆₇	C₂²	1	4	yes	—
67	#451×C₆₇	C₂²	1	2	yes	—
68	#451×C₆₇	C₂²	1	4	yes	—
69	#449×C₆₇	C₂²	1	4	yes	—
70	#449×C₆₇	C₂²	1	4	yes	—
71	#449×C₆₇	C₂²	1	4	yes	—
72	#448×C₆₇	C₂²	1	2	yes	—
73	#448×C₆₇	C₂²	1	4	yes	—
74	#440×C₆₇	C₂²	1	4	yes	—
75	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
76	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
77	#436×C₆₇	C₂²	1	2	yes	—
78	#435×C₆₇	C₂²	1	4	yes	—
79	C₈×D₄×C₆₇	C₂²	1	2	yes	—
80	#432×C₆₇	C₂²	1	1	yes	characteristic
81	#431×C₆₇	C₂²	1	1	yes	characteristic
82	#417×C₆₇	C₂²	1	4	yes	—
83	C₂×#103×C₆₇	C₂²	1	4	yes	—
84	#408×C₆₇	C₂²	1	4	yes	—
85	2₋¹⁺⁴×C₆₇	—	4	8	no	—
86	C₂×#41×C₆₇	—	2	4	no	—
87	C₂×#41×C₆₇	—	2	2	no	—
88	C₂×#41×C₆₇	—	2	2	no	—
89	C₂×#41×C₆₇	—	2	1	no	—
90	C₂×#41×C₆₇	C₂³	1	4	yes	—
91	C₂×#41×C₆₇	C₂³	1	2	yes	—
92	C₂×#41×C₆₇	C₂³	1	4	yes	—
93	C₂×#41×C₆₇	C₂³	1	2	yes	—
94	C₂²×Q₈×C₆₇	—	2	2	no	—
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
97	#137×C₆₇	—	4	8	no	—
98	#135×C₆₇	—	4	8	no	—
99	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×D₈×C₆₇	C₂³	1	4	yes	—
106	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
107	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₆₇	—	2	2	no	—
109	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	#127×C₆₇	—	2	2	no	—
115	#127×C₆₇	—	2	2	no	—
116	#127×C₆₇	D₄	1	1	yes	characteristic
117	#127×C₆₇	C₂³	1	1	yes	characteristic
118	#127×C₆₇	C₂³	1	1	yes	characteristic
119	#125×C₆₇	—	2	2	no	—
120	#125×C₆₇	—	2	1	no	—
121	#124×C₆₇	—	2	4	no	—
122	#124×C₆₇	—	2	1	no	—
123	#124×C₆₇	D₄	1	2	yes	—
124	#124×C₆₇	C₂³	1	2	yes	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	2	4	no	—
127	C₂²⋊Q₈×C₆₇	—	2	2	no	—
128	C₂²⋊Q₈×C₆₇	—	2	4	no	—
129	C₂²⋊Q₈×C₆₇	—	2	1	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	—	2	4	no	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
137	#121×C₆₇	—	2	4	no	—
138	#121×C₆₇	—	2	4	no	—
139	#121×C₆₇	—	2	4	no	—
140	#121×C₆₇	—	2	2	no	—
141	#121×C₆₇	—	2	4	no	—
142	#121×C₆₇	—	2	2	no	—
143	#121×C₆₇	—	2	4	no	—
144	#121×C₆₇	—	2	1	no	—
145	#121×C₆₇	—	2	1	no	—
146	#121×C₆₇	—	2	1	no	—
147	#121×C₆₇	—	2	4	no	—
148	#121×C₆₇	—	2	4	no	—
149	#121×C₆₇	D₄	1	2	yes	—
150	#121×C₆₇	D₄	1	2	yes	—
151	#121×C₆₇	C₂³	1	2	yes	—
152	#121×C₆₇	C₂³	1	4	yes	—
153	#121×C₆₇	C₂³	1	4	yes	—
154	C₄×Q₈×C₆₇	—	2	1	no	—
155	C₄×Q₈×C₆₇	—	2	1	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄×D₄×C₆₇	—	2	2	no	—
161	C₄×D₄×C₆₇	—	2	2	no	—
162	C₄×D₄×C₆₇	—	2	2	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	1	no	—
166	C₄×D₄×C₆₇	—	2	1	no	—
167	C₄×D₄×C₆₇	—	2	1	no	—
168	C₄×D₄×C₆₇	C₂³	1	2	yes	—
169	C₄×D₄×C₆₇	C₂³	1	2	yes	—
170	C₄×D₄×C₆₇	C₂³	1	2	yes	—
171	#117×C₆₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
176	C₂×C₄²×C₆₇	—	2	1	no	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	#107×C₆₇	C₂³	1	2	yes	—
179	#107×C₆₇	C₂³	1	4	yes	—
180	#107×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	#103×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	4	yes	—
185	#103×C₆₇	C₂³	1	4	yes	—
186	#103×C₆₇	C₂³	1	2	yes	—
187	#103×C₆₇	C₂³	1	2	yes	—
188	#103×C₆₇	C₂³	1	4	yes	—
189	#103×C₆₇	C₂³	1	2	yes	—
190	#102×C₆₇	C₂³	1	4	yes	—
191	#102×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
200	#41×C₆₇	—	2	8	no	—
201	#41×C₆₇	—	4	4	no	—
202	#41×C₆₇	—	4	4	no	—
203	#41×C₆₇	—	4	4	no	—
204	#41×C₆₇	—	4	16	no	—
205	#41×C₆₇	—	4	4	no	—
206	#41×C₆₇	—	4	4	no	—
207	#41×C₆₇	—	4	8	no	—
208	#41×C₆₇	—	8	2	no	—
209	#41×C₆₇	—	8	4	no	—
210	C₂×Q₈×C₆₇	—	2	4	no	—
211	C₂×Q₈×C₆₇	—	2	1	no	—
212	C₂×Q₈×C₆₇	—	2	1	no	—
213	C₂×Q₈×C₆₇	—	2	4	no	—
214	C₂×Q₈×C₆₇	—	2	1	no	—
215	C₂×Q₈×C₆₇	—	2	8	no	—
216	C₂×Q₈×C₆₇	—	4	4	no	—
217	C₂×Q₈×C₆₇	—	4	8	no	—
218	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
219	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
220	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
221	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
222	C₂×D₄×C₆₇	—	2	2	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	2	2	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	2	1	no	—
232	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
237	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₇	—	2	1	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
250	Q₁₆×C₆₇	—	2	4	no	—
251	Q₁₆×C₆₇	—	2	4	no	—
252	Q₁₆×C₆₇	—	4	4	no	—
253	SD₁₆×C₆₇	—	2	8	no	—
254	SD₁₆×C₆₇	—	4	4	no	—
255	SD₁₆×C₆₇	—	4	4	no	—
256	D₈×C₆₇	—	4	4	no	—
257	M₁₆×C₆₇	—	4	4	no	—
258	C₂×C₈×C₆₇	—	4	4	no	—
259	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
260	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
261	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₄⋊C₄×C₆₇	—	2	2	no	—
264	C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₄⋊C₄×C₆₇	—	2	4	no	—
266	C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₄⋊C₄×C₆₇	—	2	4	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	4	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²⋊C₄×C₆₇	—	2	2	no	—
282	C₂²⋊C₄×C₆₇	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	2	no	—
285	C₂²⋊C₄×C₆₇	—	2	2	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
291	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
292	C₄²×C₆₇	—	2	2	no	—
293	C₄²×C₆₇	—	2	2	no	—
294	C₄²×C₆₇	—	2	2	no	—
295	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
296	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
302	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₆₇	—	2	4	no	—
304	Q₈×C₆₇	—	2	2	no	—
305	Q₈×C₆₇	—	2	2	no	—
306	Q₈×C₆₇	—	2	4	no	—
307	Q₈×C₆₇	—	2	2	no	—
308	Q₈×C₆₇	—	4	2	no	—
309	Q₈×C₆₇	—	4	8	no	—
310	Q₈×C₆₇	—	4	2	no	—
311	Q₈×C₆₇	—	8	1	no	—
312	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
313	D₄×C₆₇	—	2	4	no	—
314	D₄×C₆₇	—	2	4	no	—
315	D₄×C₆₇	—	2	4	no	—
316	D₄×C₆₇	—	4	2	no	—
317	D₄×C₆₇	—	4	4	no	—
318	D₄×C₆₇	—	4	2	no	—
319	D₄×C₆₇	—	4	8	no	—
320	D₄×C₆₇	—	4	4	no	—
321	D₄×C₆₇	—	4	2	no	—
322	D₄×C₆₇	—	4	2	no	—
323	D₄×C₆₇	—	8	1	no	—
324	D₄×C₆₇	—	8	1	no	—
325	D₄×C₆₇	—	8	4	no	—
326	D₄×C₆₇	—	8	4	no	—
327	D₄×C₆₇	—	8	2	no	—
328	D₄×C₆₇	—	8	4	no	—
329	C₂×C₄×C₆₇	—	2	4	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	4	no	—
333	C₂×C₄×C₆₇	—	2	4	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	4	1	no	—
341	C₂×C₄×C₆₇	—	4	8	no	—
342	C₂×C₄×C₆₇	—	4	8	no	—
343	C₂×C₄×C₆₇	—	4	4	no	—
344	C₂×C₄×C₆₇	—	4	4	no	—
345	C₂×C₄×C₆₇	—	8	4	no	—
346	C₂×C₄×C₆₇	—	8	1	no	—
347	C₂×C₄×C₆₇	—	8	4	no	—
348	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
353	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
355	C₈×C₆₇	—	2	2	no	—
356	C₈×C₆₇	—	2	4	no	—
357	C₈×C₆₇	—	2	2	no	—
358	C₂²×C₆₇	—	2	1	no	—
359	C₂²×C₆₇	—	2	4	no	—
360	C₂²×C₆₇	—	2	1	no	—
361	C₂²×C₆₇	—	2	4	no	—
362	C₂²×C₆₇	—	2	1	no	—
363	C₂²×C₆₇	—	2	4	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	4	2	no	—
369	C₂²×C₆₇	—	4	2	no	—
370	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₆₇	—	2	1	no	—
372	C₄×C₆₇	—	2	1	no	—
373	C₄×C₆₇	—	2	4	no	—
374	C₄×C₆₇	—	2	1	no	—
375	C₄×C₆₇	—	2	4	no	—
376	C₄×C₆₇	—	2	1	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	2	no	—
379	C₄×C₆₇	—	4	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	#578	1	2	yes	—
383	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
384	#61687	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
385	C₂×C₆₇	—	4	1	no	—
386	C₂×C₆₇	—	4	4	no	—
387	C₂×C₆₇	—	8	2	no	—
388	C₂×C₆₇	—	8	2	no	—
389	C₂×C₆₇	#3484	1	1	yes	characteristic
390	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
391	C₂×C₆₇	#3585	1	1	yes	characteristic
392	#3548	C₂×C₆₇	1	1	yes	characteristic, complemented
393	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
394	#3333	C₂×C₆₇	1	2	yes	complemented
395	#3308	C₂×C₆₇	1	4	yes	complemented
396	#3299	C₂×C₆₇	1	2	yes	complemented
397	#3287	C₂×C₆₇	1	2	yes	complemented
398	#3278	C₂×C₆₇	1	2	yes	complemented
399	#3269	C₂×C₆₇	1	4	yes	complemented
400	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
401	#3207	C₂×C₆₇	1	1	yes	characteristic, complemented
402	#3203	C₂×C₆₇	1	4	yes	complemented
403	#3112	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#3104	C₂×C₆₇	1	1	yes	characteristic, complemented
405	#3013	C₂×C₆₇	1	4	yes	complemented
406	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
407	C₆₇	#61687	1	1	yes	characteristic, direct product factor, Sylow
408	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
409	C₂×#137	C₂²×C₆₇	1	4	yes	—
410	C₂×#135	C₂²×C₆₇	1	4	yes	—
411	#562	—	2	2	no	—
412	#554	—	2	1	no	—
413	#554	C₂²×C₆₇	1	2	yes	—
414	#550	—	2	1	no	—
415	#550	—	2	1	no	—
416	#550	C₂²×C₆₇	1	2	yes	—
417	#550	C₂²×C₆₇	1	2	yes	—
418	D₄×Q₈	—	2	1	no	—
419	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
420	#548	—	2	2	no	—
421	#548	C₂²×C₆₇	1	4	yes	—
422	#547	C₂²×C₆₇	1	2	yes	—
423	#547	C₂²×C₆₇	1	2	yes	—
424	#540	—	2	2	no	—
425	#537	—	2	2	no	—
426	#537	—	2	2	no	—
427	#537	C₂²×C₆₇	1	2	yes	—
428	#537	C₂²×C₆₇	1	4	yes	—
429	#533	C₂²×C₆₇	1	1	yes	characteristic
430	#532	—	2	2	no	—
431	#532	C₂²×C₆₇	1	1	yes	characteristic
432	#532	C₂²×C₆₇	1	1	yes	characteristic
433	#532	C₂²×C₆₇	1	1	yes	characteristic
434	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
435	#497	C₂²×C₆₇	1	2	yes	—
436	#493	C₂²×C₆₇	1	1	yes	characteristic
437	#492	C₂²×C₆₇	1	1	yes	characteristic
438	#489	C₂²×C₆₇	1	2	yes	—
439	#487	C₂²×C₆₇	1	1	yes	characteristic
440	#486	C₂²×C₆₇	1	1	yes	characteristic
441	#484	C₂²×C₆₇	1	2	yes	—
442	#484	C₂²×C₆₇	1	4	yes	—
443	#480	C₂²×C₆₇	1	4	yes	—
444	#480	C₂²×C₆₇	1	2	yes	—
445	#477	C₂²×C₆₇	1	2	yes	—
446	#477	C₂²×C₆₇	1	2	yes	—
447	#468	C₂²×C₆₇	1	4	yes	—
448	#468	C₂²×C₆₇	1	4	yes	—
449	#467	C₂²×C₆₇	1	4	yes	—
450	#466	C₂²×C₆₇	1	4	yes	—
451	#463	C₂²×C₆₇	1	4	yes	—
452	#462	C₂²×C₆₇	1	2	yes	—
453	#462	C₂²×C₆₇	1	2	yes	—
454	#460	C₂²×C₆₇	1	2	yes	—
455	#460	C₂²×C₆₇	1	2	yes	—
456	#452	C₂²×C₆₇	1	4	yes	—
457	#452	C₂²×C₆₇	1	4	yes	—
458	#452	C₂²×C₆₇	1	4	yes	—
459	#451	C₂²×C₆₇	1	2	yes	—
460	#451	C₂²×C₆₇	1	4	yes	—
461	#449	C₂²×C₆₇	1	4	yes	—
462	#449	C₂²×C₆₇	1	4	yes	—
463	#449	C₂²×C₆₇	1	4	yes	—
464	#448	C₂²×C₆₇	1	2	yes	—
465	#448	C₂²×C₆₇	1	4	yes	—
466	#440	C₂²×C₆₇	1	4	yes	—
467	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
468	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
469	#436	C₂²×C₆₇	1	2	yes	—
470	#435	C₂²×C₆₇	1	4	yes	—
471	C₈×D₄	C₂²×C₆₇	1	2	yes	—
472	#432	C₂²×C₆₇	1	1	yes	characteristic
473	#431	C₂²×C₆₇	1	1	yes	characteristic
474	#417	C₂²×C₆₇	1	4	yes	—
475	C₂×#103	C₂²×C₆₇	1	4	yes	—
476	#408	C₂²×C₆₇	1	4	yes	—
477	2₋¹⁺⁴	—	4	8	no	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	—	2	1	no	—
482	C₂×#41	C₂³×C₆₇	1	4	yes	—
483	C₂×#41	C₂³×C₆₇	1	2	yes	—
484	C₂×#41	C₂³×C₆₇	1	4	yes	—
485	C₂×#41	C₂³×C₆₇	1	2	yes	—
486	C₂²×Q₈	—	2	2	no	—
487	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
488	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
489	#137	—	4	8	no	—
490	#135	—	4	8	no	—
491	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
492	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
493	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
494	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
495	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
497	C₂×D₈	C₂³×C₆₇	1	4	yes	—
498	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
499	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
506	#127	—	2	2	no	—
507	#127	—	2	2	no	—
508	#127	D₄×C₆₇	1	1	yes	characteristic
509	#127	C₂³×C₆₇	1	1	yes	characteristic
510	#127	C₂³×C₆₇	1	1	yes	characteristic
511	#125	—	2	2	no	—
512	#125	—	2	1	no	—
513	#124	—	2	4	no	—
514	#124	—	2	1	no	—
515	#124	D₄×C₆₇	1	2	yes	—
516	#124	C₂³×C₆₇	1	2	yes	—
517	#123	—	2	4	no	—
518	#123	—	2	4	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	—	2	1	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	—	2	4	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
527	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
528	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
529	#121	—	2	4	no	—
530	#121	—	2	4	no	—
531	#121	—	2	4	no	—
532	#121	—	2	2	no	—
533	#121	—	2	4	no	—
534	#121	—	2	2	no	—
535	#121	—	2	4	no	—
536	#121	—	2	1	no	—
537	#121	—	2	1	no	—
538	#121	—	2	1	no	—
539	#121	—	2	4	no	—
540	#121	—	2	4	no	—
541	#121	D₄×C₆₇	1	2	yes	—
542	#121	D₄×C₆₇	1	2	yes	—
543	#121	C₂³×C₆₇	1	2	yes	—
544	#121	C₂³×C₆₇	1	4	yes	—
545	#121	C₂³×C₆₇	1	4	yes	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
550	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
551	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	C₂³×C₆₇	1	2	yes	—
561	C₄×D₄	C₂³×C₆₇	1	2	yes	—
562	C₄×D₄	C₂³×C₆₇	1	2	yes	—
563	#117	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
570	#107	C₂³×C₆₇	1	2	yes	—
571	#107	C₂³×C₆₇	1	2	yes	—
572	#107	C₂³×C₆₇	1	4	yes	—
573	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
574	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
575	#103	C₂³×C₆₇	1	2	yes	—
576	#103	C₂³×C₆₇	1	4	yes	—
577	#103	C₂³×C₆₇	1	4	yes	—
578	#103	C₂³×C₆₇	1	4	yes	—
579	#103	C₂³×C₆₇	1	2	yes	—
580	#103	C₂³×C₆₇	1	2	yes	—
581	#103	C₂³×C₆₇	1	2	yes	—
582	#102	C₂³×C₆₇	1	4	yes	—
583	#102	C₂³×C₆₇	1	4	yes	—
584	#102	C₂³×C₆₇	1	4	yes	—
585	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
586	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
587	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
589	#97	C₂³×C₆₇	1	2	yes	—
590	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
591	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
592	#41	—	2	8	no	—
593	#41	—	4	4	no	—
594	#41	—	4	4	no	—
595	#41	—	4	4	no	—
596	#41	—	4	16	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	8	no	—
600	#41	—	8	2	no	—
601	#41	—	8	4	no	—
602	C₂×Q₈	—	2	4	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	4	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	8	no	—
608	C₂×Q₈	—	4	4	no	—
609	C₂×Q₈	—	4	8	no	—
610	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
611	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
612	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
625	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
626	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
627	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
628	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
629	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
642	Q₁₆	—	2	4	no	—
643	Q₁₆	—	2	4	no	—
644	Q₁₆	—	4	4	no	—
645	SD₁₆	—	2	8	no	—
646	SD₁₆	—	4	4	no	—
647	SD₁₆	—	4	4	no	—
648	D₈	—	4	4	no	—
649	M₁₆	—	4	4	no	—
650	C₂×C₈	—	4	4	no	—
651	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
652	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
653	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	2	no	—
678	C₂²⋊C₄	—	2	4	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
683	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
684	C₄²	—	2	2	no	—
685	C₄²	—	2	2	no	—
686	C₄²	—	2	2	no	—
687	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
689	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
690	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
694	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
695	Q₈	—	2	4	no	—
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	4	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	8	no	—
702	Q₈	—	4	2	no	—
703	Q₈	—	8	1	no	—
704	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
705	D₄	—	2	4	no	—
706	D₄	—	2	4	no	—
707	D₄	—	2	4	no	—
708	D₄	—	4	2	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	2	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	8	1	no	—
716	D₄	—	8	1	no	—
717	D₄	—	8	4	no	—
718	D₄	—	8	2	no	—
719	D₄	—	8	4	no	—
720	D₄	—	8	4	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	8	no	—
734	C₂×C₄	—	4	8	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
741	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
745	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
746	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
747	C₈	—	2	2	no	—
748	C₈	—	2	4	no	—
749	C₈	—	2	2	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	4	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	4	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	#578×C₆₇	1	2	yes	—
775	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
776	C₂	—	4	1	no	—
777	C₂	—	4	4	no	—
778	C₂	—	8	2	no	—
779	C₂	—	8	2	no	—
780	C₂	C₆₇×#3484	1	1	yes	characteristic
781	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
782	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3548	C₂	semidirect
2. C₆₇×#3497	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3308	C₂	semidirect
5. C₆₇×#3299	C₂	semidirect
6. C₆₇×#3287	C₂	semidirect
7. C₆₇×#3278	C₂	semidirect
8. C₆₇×#3269	C₂	semidirect
9. C₆₇×#3216	C₂	semidirect
10. C₆₇×#3207	C₂	semidirect
11. C₆₇×#3203	C₂	semidirect
12. C₆₇×#3112	C₂	semidirect
13. C₆₇×#3104	C₂	semidirect
14. C₆₇×#3013	C₂	semidirect
15. C₆₇×#2981	C₂	semidirect
384. #61687	C₆₇	direct (N × H)
392. #3548	C₂×C₆₇	semidirect
393. #3497	C₂×C₆₇	semidirect
394. #3333	C₂×C₆₇	semidirect
395. #3308	C₂×C₆₇	semidirect
396. #3299	C₂×C₆₇	semidirect
397. #3287	C₂×C₆₇	semidirect
398. #3278	C₂×C₆₇	semidirect
399. #3269	C₂×C₆₇	semidirect
400. #3216	C₂×C₆₇	semidirect
401. #3207	C₂×C₆₇	semidirect
402. #3203	C₂×C₆₇	semidirect
403. #3112	C₂×C₆₇	semidirect
404. #3104	C₂×C₆₇	semidirect
405. #3013	C₂×C₆₇	semidirect
406. #2981	C₂×C₆₇	semidirect
407. C₆₇	#61687	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3548	2
C₆₇×#3497	2
C₆₇×#3333	2
C₆₇×#3308	2
C₆₇×#3299	2
C₆₇×#3287	2
C₆₇×#3278	2
C₆₇×#3269	2
C₆₇×#3216	2
C₆₇×#3207	2
C₆₇×#3203	2
C₆₇×#3112	2
C₆₇×#3104	2
C₆₇×#3013	2
C₆₇×#2981	2
#61687	67

Subgroups — C67×#61687 #30740938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61687 #30740938