Subgroups — #31720168

Order 17152.

2612 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574978	C₂	1	1	yes	maximal, characteristic
2	#22574922	C₂	1	2	yes	maximal, complemented
3	#22569127	C₂	1	1	yes	maximal, characteristic, complemented
4	#22569121	C₂	1	4	yes	maximal, complemented
5	#22569117	C₂	1	4	yes	maximal, complemented
6	#22569116	C₂	1	2	yes	maximal, complemented
7	#22569109	C₂	1	4	yes	maximal, complemented
8	#22569108	C₂	1	2	yes	maximal, complemented
9	C₂×#16863513	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16863512	C₂	1	1	yes	maximal, characteristic, complemented
11	#443×D₆₇	C₂	1	4	yes	maximal, complemented
12	#22568817	C₂	1	1	yes	maximal, characteristic, complemented
13	#22568755	C₂	1	2	yes	maximal, complemented
14	#22568631	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864232	C₂²	1	2	yes	—
17	#16864210	C₄	1	2	yes	complemented
18	#16864209	C₄	1	2	yes	complemented
19	#16864203	C₄	1	4	yes	complemented
20	#16864202	C₄	1	4	yes	complemented
21	#16864198	C₄	1	2	yes	complemented
22	#16864197	C₄	1	2	yes	complemented
23	#16864194	C₂²	1	2	yes	—
24	#16864193	C₂²	1	4	yes	—
25	C₂×#14524065	C₂²	1	1	yes	characteristic
26	#135×D₆₇	C₂²	1	4	yes	—
27	#16864162	—	2	4	no	—
28	#16864162	C₂²	1	2	yes	—
29	#16864162	C₂²	1	2	yes	complemented
30	#16864161	—	2	4	no	—
31	#16864161	C₂²	1	8	yes	complemented
32	C₂×#14524051	—	2	4	no	—
33	C₂×#14524051	C₂²	1	1	yes	characteristic
34	C₂×#14524051	C₂²	1	2	yes	complemented
35	C₂×#14524050	C₂²	1	2	yes	complemented
36	C₂×#14524049	C₂²	1	1	yes	characteristic
37	#131×D₆₇	—	2	4	no	—
38	#131×D₆₇	C₂²	1	8	yes	complemented
39	#16863864	C₂²	1	1	yes	characteristic
40	#16863519	C₂²	1	4	yes	complemented
41	#16863516	C₂²	1	8	yes	complemented
42	#16863515	C₂²	1	8	yes	complemented
43	#16863514	C₂²	1	4	yes	complemented
44	#16863513	C₂²	1	2	yes	complemented
45	#16863513	C₂²	1	2	yes	complemented
46	#16863513	C₂²	1	2	yes	complemented
47	#16863513	C₂²	1	2	yes	complemented
48	#16863512	C₂²	1	2	yes	complemented
49	#16863512	C₂²	1	2	yes	complemented
50	#16863512	C₂²	1	2	yes	complemented
51	#16863512	C₂²	1	2	yes	complemented
52	#16863511	C₂²	1	8	yes	complemented
53	#16863510	C₂²	1	8	yes	complemented
54	#16863444	C₂²	1	2	yes	complemented
55	#16863443	C₂²	1	4	yes	complemented
56	C₂×#14523979	C₂²	1	1	yes	characteristic, complemented
57	#108×D₆₇	C₂²	1	4	yes	complemented
58	#16863414	C₂²	1	2	yes	complemented
59	#16863411	C₂²	1	8	yes	complemented
60	C₂×#14523970	C₂²	1	2	yes	complemented
61	C₂×#14523969	C₂²	1	2	yes	complemented
62	#104×D₆₇	C₂²	1	8	yes	complemented
63	#16863353	C₂²	1	2	yes	complemented
64	#16863352	C₂²	1	1	yes	characteristic, complemented
65	#16863350	C₂²	1	2	yes	complemented
66	#16863348	C₂²	1	2	yes	complemented
67	M₁₆×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₈×D₆₇	C₂²	1	2	yes	complemented
70	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
71	#568×C₆₇	C₂²	1	2	yes	complemented
72	#444×C₆₇	C₂²	1	4	yes	complemented
73	#443×C₆₇	C₂²	1	4	yes	complemented
74	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#421×C₆₇	C₂²	1	2	yes	complemented
76	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#14524091	C₂×C₄	1	4	yes	—
78	#14524090	—	2	2	no	—
79	#14524090	C₂×C₄	1	4	yes	—
80	#14524089	—	2	2	no	—
81	#14524089	C₂×C₄	1	4	yes	—
82	#14524088	—	2	4	no	—
83	#14524088	C₂×C₄	1	4	yes	—
84	C₂×#11761628	—	2	4	no	—
85	C₂×#11761628	C₂³	1	2	yes	—
86	C₂×#11761628	C₂³	1	1	yes	characteristic
87	#41×D₆₇	—	2	4	no	—
88	#41×D₆₇	C₂³	1	8	yes	—
89	#14524075	C₂×C₄	1	8	yes	complemented
90	#14524074	C₂×C₄	1	4	yes	complemented
91	#14524073	C₂×C₄	1	4	yes	complemented
92	#14524072	C₂×C₄	1	8	yes	complemented
93	#14524070	C₂×C₄	1	8	yes	complemented
94	#14524069	C₂×C₄	1	4	yes	complemented
95	#14524068	C₂×C₄	1	4	yes	complemented
96	#14524067	C₂×C₄	1	8	yes	complemented
97	#14524066	C₂×C₄	1	4	yes	complemented
98	#14524065	C₂×C₄	1	2	yes	complemented
99	#14524065	C₂×C₄	1	2	yes	complemented
100	#14524065	C₂³	1	2	yes	—
101	#14524065	C₂³	1	2	yes	—
102	#14524064	C₂×C₄	1	8	yes	complemented
103	#14524063	C₂³	1	8	yes	—
104	#14524062	C₂×C₄	1	4	yes	complemented
105	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic, complemented
106	Q₁₆×D₆₇	C₂×C₄	1	4	yes	complemented
107	C₂×#11761617	C₂×C₄	1	2	yes	complemented
108	SD₁₆×D₆₇	C₂×C₄	1	8	yes	complemented
109	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic, complemented
110	D₈×D₆₇	C₂×C₄	1	4	yes	complemented
111	#14524051	—	2	4	no	—
112	#14524051	—	2	8	no	—
113	#14524051	—	2	2	no	—
114	#14524051	—	2	2	no	—
115	#14524051	—	2	8	no	—
116	#14524051	—	2	4	no	—
117	#14524051	D₄	1	2	yes	—
118	#14524051	D₄	1	2	yes	—
119	#14524051	D₄	1	2	yes	—
120	#14524051	D₄	1	2	yes	—
121	#14524051	C₂³	1	4	yes	—
122	#14524051	C₂³	1	4	yes	—
123	#14524050	—	2	2	no	—
124	#14524050	—	2	2	no	—
125	#14524050	C₂³	1	4	yes	—
126	#14524050	C₂³	1	4	yes	—
127	#14524049	—	2	4	no	—
128	#14524049	—	2	8	no	—
129	#14524049	—	2	8	no	—
130	#14524049	C₂×C₄	1	2	yes	—
131	#14524049	C₂×C₄	1	2	yes	—
132	#14524049	C₂×C₄	1	2	yes	—
133	#14524049	C₂×C₄	1	2	yes	—
134	#14524049	C₂³	1	8	yes	—
135	C₂×#11761612	—	2	2	no	—
136	C₂×#11761612	C₂³	1	2	yes	—
137	C₂×#11761612	C₂³	1	1	yes	characteristic
138	C₂×#11761611	—	2	8	no	—
139	C₂×#11761611	—	2	2	no	—
140	C₂×#11761611	C₂³	1	2	yes	—
141	C₂×#11761611	C₂³	1	2	yes	—
142	M₁₆×D₆₇	—	2	8	no	—
143	M₁₆×D₆₇	—	2	8	no	—
144	M₁₆×D₆₇	—	2	4	no	—
145	M₁₆×D₆₇	C₂³	1	8	yes	—
146	C₂²×C₆₇⋊C₈	—	2	2	no	—
147	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₆₇	—	2	2	no	—
149	C₂×C₈×D₆₇	—	2	8	no	—
150	C₂×C₈×D₆₇	C₂³	1	2	yes	—
151	C₂×C₈×D₆₇	C₂³	1	2	yes	—
152	#14524008	—	2	1	no	—
153	#14524005	—	2	1	no	—
154	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
155	#14524000	C₂³	1	2	yes	—
156	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
157	C₄²×D₆₇	C₂³	1	2	yes	—
158	#14523979	C₂³	1	2	yes	—
159	#14523979	C₂³	1	2	yes	—
160	#14523978	C₂³	1	8	yes	—
161	#14523971	C₂³	1	8	yes	—
162	#14523970	C₂³	1	4	yes	—
163	#14523970	C₂³	1	4	yes	—
164	#14523969	C₂³	1	4	yes	—
165	#14523969	C₂³	1	4	yes	—
166	#14523954	C₂³	1	2	yes	—
167	#14523953	C₂³	1	2	yes	—
168	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
169	C₈×Dic₆₇	C₂³	1	2	yes	—
170	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
171	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
172	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
173	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
174	C₂×#41×C₆₇	C₂³	1	2	yes	—
175	#135×C₆₇	C₂×C₄	1	2	yes	complemented
176	#135×C₆₇	C₂×C₄	1	2	yes	complemented
177	#135×C₆₇	C₂³	1	2	yes	—
178	#135×C₆₇	C₂³	1	2	yes	—
179	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
180	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	complemented
181	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
182	#131×C₆₇	—	2	4	no	—
183	#131×C₆₇	C₂³	1	8	yes	—
184	C₂×M₁₆×C₆₇	—	2	4	no	—
185	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
186	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
188	#117×C₆₇	C₂³	1	1	yes	characteristic
189	#108×C₆₇	C₂³	1	2	yes	—
190	#108×C₆₇	C₂³	1	2	yes	—
191	#104×C₆₇	C₂³	1	8	yes	—
192	#97×C₆₇	C₂³	1	2	yes	—
193	C₄×C₈×C₆₇	C₂³	1	2	yes	—
194	#11761629	—	2	4	no	—
195	#11761629	C₂²×C₄	1	8	yes	—
196	#11761628	—	2	2	no	—
197	#11761628	—	2	2	no	—
198	#11761628	—	2	8	no	—
199	#11761628	—	2	4	no	—
200	#11761628	—	2	8	no	—
201	#11761628	—	2	4	no	—
202	#11761628	C₂²×C₄	1	2	yes	—
203	#11761628	C₂²×C₄	1	2	yes	—
204	#11761628	C₂²×C₄	1	4	yes	—
205	#11761628	C₂×D₄	1	2	yes	—
206	#11761628	C₂×D₄	1	2	yes	—
207	#11761628	C₂⁴	1	4	yes	—
208	#11761627	—	2	8	no	—
209	#11761627	—	2	8	no	—
210	#11761627	—	2	4	no	—
211	#11761627	C₂²×C₄	1	8	yes	—
212	C₂×Dic₁₃₄	—	2	4	no	—
213	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
214	C₂×Dic₁₃₄	#41	1	1	yes	characteristic
215	Q₈×D₆₇	—	2	4	no	—
216	Q₈×D₆₇	C₂²×C₄	1	8	yes	—
217	C₂×D₂₆₈	—	2	4	no	—
218	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
219	C₂×D₂₆₈	#41	1	1	yes	characteristic
220	C₂×C₂²⋊D₆₇	—	2	2	no	—
221	C₂×C₂²⋊D₆₇	—	2	8	no	—
222	C₂×C₂²⋊D₆₇	#41	1	2	yes	—
223	D₄×D₆₇	—	2	8	no	—
224	D₄×D₆₇	—	2	8	no	—
225	D₄×D₆₇	—	2	4	no	—
226	D₄×D₆₇	C₂²×C₄	1	8	yes	—
227	C₂²×Dic₆₇	—	2	1	no	—
228	C₂×C₄×D₆₇	—	2	2	no	—
229	C₂×C₄×D₆₇	—	2	8	no	—
230	C₂×C₄×D₆₇	—	2	2	no	—
231	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
232	Dic₂₆₈	C₂²×C₄	1	2	yes	—
233	Dic₂₆₈	C₂²×C₄	1	2	yes	—
234	#11761618	C₂²×C₄	1	8	yes	—
235	#11761617	C₂²×C₄	1	4	yes	—
236	#11761617	C₂²×C₄	1	4	yes	—
237	#11761616	C₂²×C₄	1	8	yes	—
238	#11761615	C₂²×C₄	1	8	yes	—
239	D₅₃₆	C₂²×C₄	1	2	yes	—
240	D₅₃₆	C₂²×C₄	1	2	yes	—
241	#11761613	C₂²×C₄	1	8	yes	—
242	#11761612	—	2	2	no	—
243	#11761612	—	2	4	no	—
244	#11761612	—	2	4	no	—
245	#11761612	C₂²×C₄	1	2	yes	—
246	#11761612	C₂²×C₄	1	2	yes	—
247	#11761612	C₂⁴	1	4	yes	—
248	#11761611	—	2	8	no	—
249	#11761611	—	2	8	no	—
250	#11761611	—	2	4	no	—
251	#11761611	—	2	4	no	—
252	#11761611	C₂²×C₄	1	4	yes	—
253	#11761611	C₂²×C₄	1	4	yes	—
254	#11761611	C₂×D₄	1	4	yes	—
255	#11761611	C₂×D₄	1	4	yes	—
256	C₂×C₆₇⋊C₈	—	2	2	no	—
257	C₂×C₆₇⋊C₈	—	2	4	no	—
258	C₂×C₆₇⋊C₈	—	2	4	no	—
259	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
260	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
262	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
263	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
264	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
265	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
266	C₈×D₆₇	—	2	8	no	—
267	C₈×D₆₇	—	2	8	no	—
268	C₈×D₆₇	—	2	4	no	—
269	C₈×D₆₇	—	2	4	no	—
270	C₈×D₆₇	C₂²×C₄	1	4	yes	—
271	C₈×D₆₇	C₂²×C₄	1	4	yes	—
272	C₈×D₆₇	C₂×D₄	1	4	yes	—
273	C₈×D₆₇	C₂×D₄	1	4	yes	—
274	Dic₆₇⋊C₄	—	2	2	no	—
275	(C₂×D₆₇)⋊C₄	—	2	2	no	—
276	C₄×Dic₆₇	—	2	1	no	—
277	C₄×Dic₆₇	—	2	2	no	—
278	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
279	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
280	#41×C₆₇	—	2	2	no	—
281	#41×C₆₇	—	2	2	no	—
282	#41×C₆₇	C₂²×C₄	1	4	yes	—
283	#41×C₆₇	C₂⁴	1	4	yes	—
284	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
285	C₂×D₄×C₆₇	—	2	2	no	—
286	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
290	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
291	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
292	SD₁₆×C₆₇	C₂²×C₄	1	4	yes	—
293	D₈×C₆₇	C₂²×C₄	1	2	yes	—
294	D₈×C₆₇	C₂²×C₄	1	2	yes	—
295	M₁₆×C₆₇	—	2	2	no	—
296	M₁₆×C₆₇	—	2	8	no	—
297	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
298	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
299	M₁₆×C₆₇	C₂⁴	1	4	yes	—
300	C₂×C₈×C₆₇	—	2	2	no	—
301	C₂×C₈×C₆₇	—	2	8	no	—
302	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
303	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
304	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
305	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
306	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
309	C₄⋊C₄×C₆₇	—	2	1	no	—
310	C₂²⋊C₄×C₆₇	—	2	1	no	—
311	C₄²×C₆₇	C₂⁴	1	2	yes	—
312	C₂³×C₆₇	—	2	2	no	—
313	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
314	C₂²×D₆₇	—	2	2	no	—
315	C₂²×D₆₇	—	2	8	no	—
316	C₂²×D₆₇	C₂×#41	1	2	yes	—
317	Q₈×C₆₇	—	2	2	no	—
318	Q₈×C₆₇	C₂³×C₄	1	4	yes	—
319	D₄×C₆₇	—	2	4	no	—
320	D₄×C₆₇	—	2	4	no	—
321	D₄×C₆₇	—	2	2	no	—
322	D₄×C₆₇	C₂³×C₄	1	4	yes	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	2	4	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
328	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
329	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
333	C₂²⋊D₆₇	—	2	4	no	—
334	C₂²⋊D₆₇	—	2	4	no	—
335	C₂²⋊D₆₇	—	2	8	no	—
336	C₂²⋊D₆₇	—	2	8	no	—
337	C₂²⋊D₆₇	C₄×D₄	1	4	yes	—
338	C₂²⋊D₆₇	C₄×D₄	1	4	yes	—
339	C₂×Dic₆₇	—	2	2	no	—
340	C₂×Dic₆₇	—	2	1	no	—
341	C₂×Dic₆₇	—	2	8	no	—
342	C₂×Dic₆₇	—	2	1	no	—
343	C₂×Dic₆₇	—	4	2	no	—
344	C₂×Dic₆₇	C₂×#41	1	2	yes	—
345	D₂₆₈	—	2	8	no	—
346	D₂₆₈	—	2	2	no	—
347	D₂₆₈	C₄×D₄	1	2	yes	—
348	D₂₆₈	C₄×D₄	1	2	yes	—
349	D₂₆₈	C₂³×C₄	1	4	yes	—
350	C₄×D₆₇	—	2	8	no	—
351	C₄×D₆₇	—	2	4	no	—
352	C₄×D₆₇	—	2	4	no	—
353	C₄×D₆₇	—	2	8	no	—
354	C₄×D₆₇	—	4	4	no	—
355	C₄×D₆₇	C₂³×C₄	1	4	yes	—
356	C₄×D₆₇	C₂²×D₄	1	4	yes	—
357	Dic₁₃₄	—	2	2	no	—
358	Dic₁₃₄	—	2	8	no	—
359	Dic₁₃₄	C₄×D₄	1	2	yes	—
360	Dic₁₃₄	C₄×D₄	1	2	yes	—
361	Dic₁₃₄	C₂³×C₄	1	4	yes	—
362	C₈×C₆₇	—	2	4	no	—
363	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
364	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
365	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
366	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
367	C₈×C₆₇	C₂²×D₄	1	4	yes	—
368	C₆₇⋊C₈	—	2	4	no	—
369	C₆₇⋊C₈	C₂³×C₄	1	4	yes	—
370	C₆₇⋊C₈	C₂²×D₄	1	1	yes	characteristic
371	C₆₇⋊C₈	C₂²×D₄	1	1	yes	characteristic
372	C₆₇⋊C₈	C₂²×D₄	1	1	yes	characteristic
373	C₆₇⋊C₈	C₂²×D₄	1	1	yes	characteristic
374	C₂²×C₆₇	—	2	4	no	—
375	C₂²×C₆₇	—	4	1	no	—
376	C₂²×C₆₇	—	8	2	no	—
377	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
378	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
379	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
380	C₂×D₆₇	—	2	4	no	—
381	C₂×D₆₇	—	4	2	no	—
382	C₂×D₆₇	—	8	8	no	—
383	C₂×D₆₇	—	8	2	no	—
384	C₂×D₆₇	C₂×C₄×D₄	1	4	yes	—
385	C₄×C₆₇	—	2	4	no	—
386	C₄×C₆₇	—	4	2	no	—
387	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
388	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
389	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
390	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
391	Dic₆₇	—	2	2	no	—
392	Dic₆₇	—	2	4	no	—
393	Dic₆₇	—	4	1	no	—
394	Dic₆₇	C₂×C₄×D₄	1	4	yes	—
395	#60183	—	67	1	no	maximal, Sylow
396	C₂×C₆₇	—	2	1	no	—
397	C₂×C₆₇	—	2	1	no	—
398	C₂×C₆₇	—	2	1	no	—
399	C₂×C₆₇	—	4	4	no	—
400	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
401	D₆₇	—	2	4	no	—
402	D₆₇	—	4	4	no	—
403	#3584	—	67	1	no	—
404	#3573	—	67	2	no	—
405	#2957	—	67	4	no	—
406	#2957	—	67	1	no	—
407	#2957	D₆₇	1	1	yes	characteristic, complemented
408	#2956	—	67	4	no	—
409	#2956	—	67	2	no	—
410	#2955	—	67	4	no	—
411	#2955	—	67	2	no	—
412	C₂×#443	—	67	4	no	—
413	C₂×#443	—	67	1	no	—
414	C₂×#443	—	67	1	no	—
415	#2916	—	67	1	no	—
416	#2901	—	67	2	no	—
417	C₄×#131	—	67	1	no	—
418	C₆₇	#60183	1	1	yes	characteristic, complemented, Sylow
419	#585	—	67	2	no	—
420	#578	—	67	2	no	—
421	#578	—	67	2	no	—
422	#577	—	67	4	no	—
423	#577	—	67	4	no	—
424	#576	—	67	2	no	—
425	#576	—	67	2	no	—
426	#575	—	67	2	no	—
427	#575	—	67	4	no	—
428	C₂×#135	—	67	4	no	—
429	C₂×#135	—	67	1	no	—
430	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
431	#568	—	67	2	no	—
432	#568	—	67	8	no	—
433	#568	—	67	2	no	—
434	#568	—	134	4	no	—
435	#568	—	134	4	no	—
436	#568	C₂×D₆₇	1	2	yes	complemented
437	C₂×#131	—	67	1	no	—
438	C₂×#131	—	67	1	no	—
439	C₂×#131	—	67	2	no	—
440	C₂×#131	—	67	8	no	—
441	C₂×#131	—	67	2	no	—
442	C₂×#131	—	134	4	no	—
443	C₂×#131	—	134	4	no	—
444	C₄×#41	—	67	1	no	—
445	#444	—	67	8	no	—
446	#444	—	67	8	no	—
447	#444	—	67	4	no	—
448	#444	C₂×D₆₇	1	4	yes	complemented
449	#443	—	67	2	no	—
450	#443	—	67	2	no	—
451	#443	—	67	2	no	—
452	#443	—	67	2	no	—
453	#443	—	67	8	no	—
454	#443	—	67	2	no	—
455	#443	—	67	2	no	—
456	#443	—	67	2	no	—
457	#443	—	67	2	no	—
458	#443	—	67	8	no	—
459	#443	—	67	4	no	—
460	#443	C₂×D₆₇	1	4	yes	complemented
461	#430	—	67	2	no	—
462	#430	—	67	4	no	—
463	C₂×#108	—	67	1	no	—
464	C₂×#108	—	67	4	no	—
465	C₂×#108	C₂×D₆₇	1	1	yes	characteristic, complemented
466	#421	—	67	2	no	—
467	#421	—	67	8	no	—
468	#421	C₂×D₆₇	1	2	yes	complemented
469	C₂×#104	—	67	2	no	—
470	C₂×#104	—	67	2	no	—
471	C₂×#104	—	67	8	no	—
472	#405	—	67	1	no	—
473	#405	—	67	2	no	—
474	#405	—	67	2	no	—
475	#405	C₂×D₆₇	1	1	yes	characteristic, complemented
476	C₄×M₁₆	—	67	1	no	—
477	C₄×M₁₆	—	67	2	no	—
478	C₂×C₄×C₈	—	67	1	no	—
479	C₂×C₄×C₈	—	67	2	no	—
480	2₋¹⁺⁴	—	67	4	no	—
481	2₋¹⁺⁴	—	67	4	no	—
482	2₋¹⁺⁴	—	134	2	no	—
483	H(5,𝔽₂)	—	67	4	no	—
484	H(5,𝔽₂)	—	67	4	no	—
485	H(5,𝔽₂)	—	134	4	no	—
486	H(5,𝔽₂)	—	134	2	no	—
487	C₂×#41	—	67	1	no	—
488	C₂×#41	—	67	8	no	—
489	C₂×#41	—	67	2	no	—
490	C₂×#41	—	134	4	no	—
491	C₂×#41	—	134	4	no	—
492	C₂×#41	C₂²×D₆₇	1	2	yes	—
493	#137	—	67	4	no	—
494	#137	—	67	4	no	—
495	#137	—	67	8	no	—
496	#137	—	67	8	no	—
497	AGL(1,ℤ/8)	—	67	4	no	—
498	AGL(1,ℤ/8)	—	67	4	no	—
499	AGL(1,ℤ/8)	—	67	8	no	—
500	AGL(1,ℤ/8)	—	67	8	no	—
501	#135	—	67	8	no	—
502	#135	—	67	4	no	—
503	#135	—	67	8	no	—
504	#135	—	67	4	no	—
505	#135	—	67	2	no	—
506	#135	—	67	2	no	—
507	#135	—	67	2	no	—
508	#135	—	67	2	no	—
509	#135	C₄×D₆₇	1	2	yes	complemented
510	#135	C₄×D₆₇	1	2	yes	complemented
511	#135	C₂²×D₆₇	1	2	yes	—
512	#135	C₂²×D₆₇	1	2	yes	—
513	C₂×Q₁₆	—	67	4	no	—
514	C₂×Q₁₆	—	67	1	no	—
515	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic, complemented
516	C₂×SD₁₆	—	67	8	no	—
517	C₂×SD₁₆	—	67	2	no	—
518	C₂×SD₁₆	C₄×D₆₇	1	2	yes	complemented
519	C₂×D₈	—	67	4	no	—
520	C₂×D₈	—	67	1	no	—
521	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic, complemented
522	#131	—	2	4	no	—
523	#131	—	67	2	no	—
524	#131	—	67	2	no	—
525	#131	—	67	2	no	—
526	#131	—	67	2	no	—
527	#131	—	67	2	no	—
528	#131	—	67	2	no	—
529	#131	—	67	2	no	—
530	#131	—	67	2	no	—
531	#131	—	67	4	no	—
532	#131	—	67	4	no	—
533	#131	—	67	4	no	—
534	#131	—	67	4	no	—
535	#131	—	67	8	no	—
536	#131	—	134	8	no	—
537	#131	—	134	8	no	—
538	#131	—	134	4	no	—
539	#131	—	134	2	no	—
540	#131	—	134	8	no	—
541	#131	—	134	2	no	—
542	#131	—	134	2	no	—
543	#131	—	134	2	no	—
544	#131	—	134	8	no	—
545	#131	—	134	4	no	—
546	#131	—	134	4	no	—
547	#131	C₂²×D₆₇	1	8	yes	—
548	C₂×M₁₆	—	2	4	no	—
549	C₂×M₁₆	—	67	1	no	—
550	C₂×M₁₆	—	67	2	no	—
551	C₂×M₁₆	—	67	2	no	—
552	C₂×M₁₆	—	67	2	no	—
553	C₂×M₁₆	—	67	8	no	—
554	C₂×M₁₆	—	134	2	no	—
555	C₂×M₁₆	—	134	8	no	—
556	C₂×M₁₆	—	134	8	no	—
557	C₂×M₁₆	—	134	2	no	—
558	C₂×M₁₆	—	134	8	no	—
559	C₂×M₁₆	—	134	4	no	—
560	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
561	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
562	C₂²×C₈	—	67	1	no	—
563	C₂²×C₈	—	67	2	no	—
564	C₂²×C₈	—	67	2	no	—
565	C₂²×C₈	—	134	2	no	—
566	C₂²×C₈	—	134	8	no	—
567	C₂²×C₈	—	134	2	no	—
568	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
569	C₄×Q₈	—	134	1	no	—
570	C₄×D₄	—	134	2	no	—
571	C₄×D₄	—	134	1	no	—
572	#117	—	67	2	no	—
573	#117	C₂²×D₆₇	1	1	yes	characteristic
574	C₂×C₄²	—	67	1	no	—
575	C₂×C₄²	—	67	2	no	—
576	#108	—	67	8	no	—
577	#108	—	67	2	no	—
578	#108	—	67	2	no	—
579	#108	C₂²×D₆₇	1	2	yes	—
580	#108	C₂²×D₆₇	1	2	yes	—
581	#104	—	67	4	no	—
582	#104	—	67	4	no	—
583	#104	—	67	4	no	—
584	#104	—	67	4	no	—
585	#104	—	67	8	no	—
586	#104	C₂²×D₆₇	1	8	yes	—
587	#97	—	67	2	no	—
588	#97	—	67	2	no	—
589	#97	C₂²×D₆₇	1	2	yes	—
590	C₄×C₈	—	67	1	no	—
591	C₄×C₈	—	67	2	no	—
592	C₄×C₈	—	67	1	no	—
593	C₄×C₈	—	67	1	no	—
594	C₄×C₈	—	67	1	no	—
595	C₄×C₈	—	67	2	no	—
596	C₄×C₈	C₂²×D₆₇	1	2	yes	—
597	#41	—	2	2	no	—
598	#41	—	2	2	no	—
599	#41	—	67	2	no	—
600	#41	—	67	2	no	—
601	#41	—	67	2	no	—
602	#41	—	67	2	no	—
603	#41	—	67	8	no	—
604	#41	—	67	8	no	—
605	#41	—	67	4	no	—
606	#41	—	67	4	no	—
607	#41	—	134	8	no	—
608	#41	—	134	8	no	—
609	#41	—	134	4	no	—
610	#41	—	134	4	no	—
611	#41	—	134	8	no	—
612	#41	—	134	8	no	—
613	#41	—	134	4	no	—
614	#41	—	134	4	no	—
615	#41	—	134	2	no	—
616	#41	—	134	2	no	—
617	#41	C₂×C₄×D₆₇	1	4	yes	—
618	#41	C₂³×D₆₇	1	4	yes	—
619	C₂×Q₈	—	67	1	no	—
620	C₂×Q₈	—	67	8	no	—
621	C₂×Q₈	—	67	2	no	—
622	C₂×Q₈	—	134	4	no	—
623	C₂×Q₈	—	134	4	no	—
624	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	67	2	no	—
627	C₂×D₄	—	67	8	no	—
628	C₂×D₄	—	67	2	no	—
629	C₂×D₄	—	67	1	no	—
630	C₂×D₄	—	134	4	no	—
631	C₂×D₄	—	134	8	no	—
632	C₂×D₄	—	134	4	no	—
633	C₂×D₄	—	134	8	no	—
634	C₂×D₄	—	134	8	no	—
635	C₂×D₄	—	134	2	no	—
636	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	67	2	no	—
639	C₂²×C₄	—	134	2	no	—
640	C₂²×C₄	—	134	8	no	—
641	C₂²×C₄	—	134	1	no	—
642	C₂²×C₄	—	134	2	no	—
643	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
644	Q₁₆	—	67	8	no	—
645	Q₁₆	—	67	2	no	—
646	Q₁₆	—	67	2	no	—
647	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
648	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
649	SD₁₆	—	67	8	no	—
650	SD₁₆	—	67	8	no	—
651	SD₁₆	—	67	4	no	—
652	SD₁₆	—	67	4	no	—
653	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
654	SD₁₆	C₂×C₄×D₆₇	1	4	yes	—
655	D₈	—	67	8	no	—
656	D₈	—	67	2	no	—
657	D₈	—	67	2	no	—
658	D₈	C₂×C₄×D₆₇	1	2	yes	—
659	D₈	C₂×C₄×D₆₇	1	2	yes	—
660	M₁₆	—	2	2	no	—
661	M₁₆	—	2	8	no	—
662	M₁₆	—	67	2	no	—
663	M₁₆	—	67	2	no	—
664	M₁₆	—	67	4	no	—
665	M₁₆	—	67	4	no	—
666	M₁₆	—	67	4	no	—
667	M₁₆	—	67	4	no	—
668	M₁₆	—	67	4	no	—
669	M₁₆	—	134	4	no	—
670	M₁₆	—	134	4	no	—
671	M₁₆	—	134	8	no	—
672	M₁₆	—	134	4	no	—
673	M₁₆	—	134	4	no	—
674	M₁₆	—	134	2	no	—
675	M₁₆	—	134	8	no	—
676	M₁₆	D₄×D₆₇	1	2	yes	—
677	M₁₆	D₄×D₆₇	1	2	yes	—
678	M₁₆	C₂³×D₆₇	1	4	yes	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	2	8	no	—
681	C₂×C₈	—	67	1	no	—
682	C₂×C₈	—	67	1	no	—
683	C₂×C₈	—	67	1	no	—
684	C₂×C₈	—	67	1	no	—
685	C₂×C₈	—	67	1	no	—
686	C₂×C₈	—	67	2	no	—
687	C₂×C₈	—	67	1	no	—
688	C₂×C₈	—	67	4	no	—
689	C₂×C₈	—	67	4	no	—
690	C₂×C₈	—	67	4	no	—
691	C₂×C₈	—	67	4	no	—
692	C₂×C₈	—	134	4	no	—
693	C₂×C₈	—	134	4	no	—
694	C₂×C₈	—	134	8	no	—
695	C₂×C₈	—	134	4	no	—
696	C₂×C₈	—	134	4	no	—
697	C₂×C₈	—	134	2	no	—
698	C₂×C₈	—	134	8	no	—
699	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
700	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
701	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
702	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
703	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
704	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
705	C₂×C₈	C₂³×D₆₇	1	2	yes	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	134	2	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	134	2	no	—
710	C₄²	—	67	1	no	—
711	C₄²	—	67	1	no	—
712	C₄²	—	134	2	no	—
713	C₄²	—	134	1	no	—
714	C₄²	C₂³×D₆₇	1	2	yes	—
715	C₂³	—	2	2	no	—
716	C₂³	—	67	2	no	—
717	C₂³	—	134	8	no	—
718	C₂³	—	134	2	no	—
719	C₂³	#41×D₆₇	1	1	yes	characteristic
720	Q₈	—	2	2	no	—
721	Q₈	—	67	2	no	—
722	Q₈	—	67	2	no	—
723	Q₈	—	67	4	no	—
724	Q₈	—	134	8	no	—
725	Q₈	—	134	2	no	—
726	Q₈	C₂²×C₄×D₆₇	1	4	yes	—
727	D₄	—	2	4	no	—
728	D₄	—	2	4	no	—
729	D₄	—	2	2	no	—
730	D₄	—	67	4	no	—
731	D₄	—	67	4	no	—
732	D₄	—	67	2	no	—
733	D₄	—	67	2	no	—
734	D₄	—	67	4	no	—
735	D₄	—	134	8	no	—
736	D₄	—	134	8	no	—
737	D₄	—	134	8	no	—
738	D₄	—	134	4	no	—
739	D₄	—	134	4	no	—
740	D₄	—	134	2	no	—
741	D₄	C₂²×C₄×D₆₇	1	4	yes	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	268	4	no	—
747	C₂×C₄	—	268	2	no	—
748	C₂×C₄	—	67	2	no	—
749	C₂×C₄	—	67	4	no	—
750	C₂×C₄	—	67	4	no	—
751	C₂×C₄	—	134	8	no	—
752	C₂×C₄	—	134	8	no	—
753	C₂×C₄	—	134	1	no	—
754	C₂×C₄	—	134	8	no	—
755	C₂×C₄	—	134	2	no	—
756	C₂×C₄	—	134	1	no	—
757	C₂×C₄	—	134	4	no	—
758	C₂×C₄	—	134	4	no	—
759	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
760	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
761	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
762	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
763	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
764	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
765	C₈	—	2	4	no	—
766	C₈	—	67	4	no	—
767	C₈	—	67	1	no	—
768	C₈	—	67	1	no	—
769	C₈	—	67	1	no	—
770	C₈	—	67	1	no	—
771	C₈	—	134	4	no	—
772	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
773	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
774	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
775	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
776	C₈	C₂×D₄×D₆₇	1	4	yes	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	8	2	no	—
780	C₂²	—	268	2	no	—
781	C₂²	—	536	2	no	—
782	C₂²	—	536	8	no	—
783	C₂²	—	67	4	no	—
784	C₂²	—	134	4	no	—
785	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
786	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
787	C₂²	C₂×#41×D₆₇	1	1	yes	characteristic
788	C₄	—	2	4	no	—
789	C₄	—	4	2	no	—
790	C₄	—	268	1	no	—
791	C₄	—	67	4	no	—
792	C₄	—	134	2	no	—
793	C₄	—	134	4	no	—
794	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
795	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
796	C₄	C₂³×C₄×D₆₇	1	1	yes	characteristic
797	C₄	C₂²×D₄×D₆₇	1	1	yes	characteristic
798	C₂	—	2	1	no	—
799	C₂	—	2	1	no	—
800	C₂	—	2	1	no	—
801	C₂	—	4	4	no	—
802	C₂	—	268	4	no	—
803	C₂	—	134	4	no	—
804	C₂	C₂×C₄×D₄×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#2957	C₂
socle	C₂×C₆₇	C₂²×C₄×D₄
prime radical	#22574978	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#2957	D₆₇
hypocenter	C₆₇	#60183
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #22574922	C₂	semidirect
3. #22569127	C₂	semidirect
4. #22569121	C₂	semidirect
5. #22569117	C₂	semidirect
6. #22569116	C₂	semidirect
7. #22569109	C₂	semidirect
8. #22569108	C₂	semidirect
9. C₂×#16863513	C₂	semidirect
10. C₂×#16863512	C₂	semidirect
11. #443×D₆₇	C₂	semidirect
12. #22568817	C₂	semidirect
13. #22568755	C₂	semidirect
14. #22568631	C₂	semidirect
15. C₆₇×#2957	C₂	semidirect
17. #16864210	C₄	semidirect
18. #16864209	C₄	semidirect
19. #16864203	C₄	semidirect
20. #16864202	C₄	semidirect
21. #16864198	C₄	semidirect
22. #16864197	C₄	semidirect
29. #16864162	C₂²	semidirect
31. #16864161	C₂²	semidirect
34. C₂×#14524051	C₂²	semidirect
35. C₂×#14524050	C₂²	semidirect
38. #131×D₆₇	C₂²	semidirect
40. #16863519	C₂²	semidirect
41. #16863516	C₂²	semidirect
42. #16863515	C₂²	semidirect
43. #16863514	C₂²	semidirect
44. #16863513	C₂²	semidirect
45. #16863513	C₂²	semidirect
46. #16863513	C₂²	semidirect
47. #16863513	C₂²	semidirect
48. #16863512	C₂²	semidirect
49. #16863512	C₂²	semidirect
50. #16863512	C₂²	semidirect
51. #16863512	C₂²	semidirect
52. #16863511	C₂²	semidirect
53. #16863510	C₂²	semidirect
54. #16863444	C₂²	semidirect
55. #16863443	C₂²	semidirect
56. C₂×#14523979	C₂²	semidirect
57. #108×D₆₇	C₂²	semidirect
58. #16863414	C₂²	semidirect
59. #16863411	C₂²	semidirect
60. C₂×#14523970	C₂²	semidirect
61. C₂×#14523969	C₂²	semidirect
62. #104×D₆₇	C₂²	semidirect
63. #16863353	C₂²	semidirect
64. #16863352	C₂²	semidirect
65. #16863350	C₂²	semidirect
66. #16863348	C₂²	semidirect
67. M₁₆×Dic₆₇	C₂²	semidirect
68. C₂×C₈×Dic₆₇	C₂²	semidirect
69. C₄×C₈×D₆₇	C₂²	semidirect
71. #568×C₆₇	C₂²	semidirect
72. #444×C₆₇	C₂²	semidirect
73. #443×C₆₇	C₂²	semidirect
74. C₂×#108×C₆₇	C₂²	semidirect
75. #421×C₆₇	C₂²	semidirect
76. #405×C₆₇	C₂²	semidirect
89. #14524075	C₂×C₄	semidirect
90. #14524074	C₂×C₄	semidirect
91. #14524073	C₂×C₄	semidirect
92. #14524072	C₂×C₄	semidirect
93. #14524070	C₂×C₄	semidirect
94. #14524069	C₂×C₄	semidirect
95. #14524068	C₂×C₄	semidirect
96. #14524067	C₂×C₄	semidirect
97. #14524066	C₂×C₄	semidirect
98. #14524065	C₂×C₄	semidirect
99. #14524065	C₂×C₄	semidirect
102. #14524064	C₂×C₄	semidirect
104. #14524062	C₂×C₄	semidirect
105. C₂×Dic₂₆₈	C₂×C₄	semidirect
106. Q₁₆×D₆₇	C₂×C₄	semidirect
107. C₂×#11761617	C₂×C₄	semidirect
108. SD₁₆×D₆₇	C₂×C₄	semidirect
109. C₂×D₅₃₆	C₂×C₄	semidirect
110. D₈×D₆₇	C₂×C₄	semidirect
175. #135×C₆₇	C₂×C₄	semidirect
176. #135×C₆₇	C₂×C₄	semidirect
179. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
180. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
181. C₂×D₈×C₆₇	C₂×C₄	semidirect
407. #2957	D₆₇	semidirect
418. C₆₇	#60183	semidirect
436. #568	C₂×D₆₇	semidirect
448. #444	C₂×D₆₇	semidirect
460. #443	C₂×D₆₇	semidirect
465. C₂×#108	C₂×D₆₇	semidirect
468. #421	C₂×D₆₇	semidirect
475. #405	C₂×D₆₇	semidirect
509. #135	C₄×D₆₇	semidirect
510. #135	C₄×D₆₇	semidirect
515. C₂×Q₁₆	C₄×D₆₇	semidirect
518. C₂×SD₁₆	C₄×D₆₇	semidirect
521. C₂×D₈	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22574978	2
#22574922	2
#22569127	2
#22569121	2
#22569117	2
#22569116	2
#22569109	2
#22569108	2
C₂×#16863513	2
C₂×#16863512	2
#443×D₆₇	2
#22568817	2
#22568755	2
#22568631	2
C₆₇×#2957	2
#60183	67