Subgroups — #2224×D₆₇ #31010430

Order 17152.

638 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₈×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#22562347	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562346	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562345	C₂	1	2	yes	maximal, complemented
6	#22562344	C₂	1	2	yes	maximal, complemented
7	#22562343	C₂	1	1	yes	maximal, characteristic, complemented
8	#366×D₆₇	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#357×D₆₇	C₂	1	2	yes	maximal
11	C₆₇×#2224	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₆₇	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×D₆₇	—	2	1	no	—
14	C₄×D₄×D₆₇	—	2	1	no	—
15	C₂×C₁₆×D₆₇	C₂²	1	2	yes	—
16	#16863801	C₂²	1	1	yes	characteristic, complemented
17	#16863800	—	2	1	no	—
18	#16863800	C₂²	1	2	yes	complemented
19	#16863799	—	2	1	no	—
20	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
21	D₈×Dic₆₇	C₂²	1	1	yes	characteristic
22	#16863478	C₂²	1	1	yes	characteristic
23	C₄×#11761613	—	2	1	no	—
24	#16863476	—	2	1	no	—
25	#107×D₆₇	—	2	1	no	—
26	#107×D₆₇	C₂²	1	2	yes	—
27	#107×D₆₇	C₂²	1	1	yes	characteristic
28	#102×D₆₇	—	2	1	no	—
29	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
30	#16863222	C₂²	1	2	yes	complemented
31	#16863221	C₂²	1	2	yes	complemented
32	#16863221	C₂²	1	2	yes	complemented
33	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
34	Dic₆₇⋊C₁₆	C₂²	1	2	yes	complemented
35	#16863198	C₂²	1	2	yes	—
36	#16863197	C₂²	1	2	yes	—
37	#16863196	C₂²	1	2	yes	—
38	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
40	#366×C₆₇	C₂²	1	2	yes	complemented
41	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#357×C₆₇	C₂²	1	2	yes	—
43	C₂×Q₈×D₆₇	—	4	1	no	—
44	C₂×D₄×D₆₇	—	2	1	no	—
45	C₂²×C₄×D₆₇	—	4	1	no	—
46	C₂×D₅₃₆	C₂³	1	1	yes	characteristic
47	C₂×#11761613	—	2	1	no	—
48	D₈×D₆₇	—	2	2	no	—
49	D₈×D₆₇	Q₈	1	4	yes	complemented
50	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
51	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
52	#14524043	—	2	1	no	—
53	#14524042	—	2	2	no	—
54	#14524042	—	4	1	no	—
55	#14524041	—	4	1	no	—
56	C₄×D₂₆₈	—	2	1	no	—
57	D₄×Dic₆₇	—	2	1	no	—
58	#14524005	—	2	1	no	—
59	C₄×C₂²⋊D₆₇	—	4	1	no	—
60	(C₂²⋊D₆₇)⋊C₄	—	4	1	no	—
61	C₄⋊C₄×D₆₇	—	2	1	no	—
62	C₄⋊C₄×D₆₇	—	2	2	no	—
63	C₄⋊C₄×D₆₇	—	4	1	no	—
64	C₂²⋊C₄×D₆₇	—	4	1	no	—
65	C₄²×D₆₇	D₄	1	1	yes	characteristic
66	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
67	C₁₆×D₆₇	—	2	4	no	—
68	#14523977	—	2	1	no	—
69	#14523977	C₂³	1	2	yes	—
70	#14523977	C₂³	1	1	yes	characteristic
71	#14523976	—	2	2	no	—
72	#14523976	—	2	2	no	—
73	#14523976	—	2	1	no	—
74	#14523965	—	2	1	no	—
75	#14523964	—	2	1	no	—
76	#14523963	—	2	1	no	—
77	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
78	C₈×Dic₆₇	D₄	1	1	yes	characteristic
79	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
80	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₆₇	—	2	1	no	—
82	C₄×D₄×C₆₇	—	2	1	no	—
83	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
84	#107×C₆₇	—	2	1	no	—
85	#107×C₆₇	C₂³	1	2	yes	—
86	#107×C₆₇	C₂³	1	1	yes	characteristic
87	#102×C₆₇	—	2	1	no	—
88	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂³×D₆₇	—	4	1	no	—
90	C₂×Dic₁₃₄	—	4	1	no	—
91	C₂×Dic₁₃₄	—	4	2	no	—
92	Q₈×D₆₇	—	8	4	no	—
93	C₂×D₂₆₈	—	2	1	no	—
94	C₂×C₂²⋊D₆₇	—	4	1	no	—
95	D₄×D₆₇	—	2	4	no	—
96	D₄×D₆₇	—	4	2	no	—
97	C₂²×Dic₆₇	—	4	1	no	—
98	C₂×C₄×D₆₇	—	4	1	no	—
99	C₂×C₄×D₆₇	—	4	2	no	—
100	C₂×C₄×D₆₇	—	4	1	no	—
101	C₂×C₄×D₆₇	—	4	1	no	—
102	C₂×C₄×D₆₇	—	8	4	no	—
103	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
104	C₂×C₄×D₆₇	D₈	1	1	yes	characteristic
105	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
106	D₅₃₆	—	2	1	no	—
107	D₅₃₆	C₂×Q₈	1	2	yes	complemented
108	#11761613	—	2	4	no	—
109	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
111	C₈×D₆₇	—	2	2	no	—
112	C₈×D₆₇	C₂×Q₈	1	2	yes	—
113	C₈×D₆₇	#41	1	2	yes	—
114	C₄⋊Dic₆₇	—	2	1	no	—
115	C₄⋊Dic₆₇	—	2	2	no	—
116	C₄⋊Dic₆₇	—	4	1	no	—
117	Dic₆₇⋊C₄	—	4	1	no	—
118	Dic₆₇⋊C₄	—	4	2	no	—
119	Dic₆₇⋊C₄	—	4	2	no	—
120	C₂²⋊Dic₆₇	—	4	1	no	—
121	(C₂×D₆₇)⋊C₄	—	4	1	no	—
122	(C₂×D₆₇)⋊C₄	—	4	1	no	—
123	C₄×Dic₆₇	D₈	1	1	yes	characteristic
124	C₄×Dic₆₇	D₈	1	1	yes	characteristic
125	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
126	C₆₇⋊C₁₆	—	2	2	no	—
127	C₂×Q₈×C₆₇	—	4	1	no	—
128	C₂×D₄×C₆₇	—	2	1	no	—
129	C₂²×C₄×C₆₇	—	4	1	no	—
130	D₈×C₆₇	—	2	1	no	—
131	D₈×C₆₇	C₂×Q₈	1	2	yes	complemented
132	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₄⋊C₄×C₆₇	—	2	2	no	—
136	C₄⋊C₄×C₆₇	—	4	1	no	—
137	C₂²⋊C₄×C₆₇	—	4	1	no	—
138	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₁₆×C₆₇	—	2	2	no	—
140	C₂³×C₆₇	—	4	1	no	—
141	C₂²×D₆₇	—	4	1	no	—
142	C₂²×D₆₇	—	4	4	no	—
143	C₂²×D₆₇	—	8	2	no	—
144	C₂²×D₆₇	—	8	2	no	—
145	C₂²×D₆₇	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₆₇	—	8	2	no	—
147	D₄×C₆₇	—	2	2	no	—
148	D₄×C₆₇	—	4	1	no	—
149	C₂×C₄×C₆₇	—	4	1	no	—
150	C₂×C₄×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	—	8	2	no	—
152	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂²⋊D₆₇	—	4	4	no	—
156	C₂×Dic₆₇	—	4	1	no	—
157	C₂×Dic₆₇	—	4	2	no	—
158	C₂×Dic₆₇	—	8	2	no	—
159	C₂×Dic₆₇	C₂×D₈	1	1	yes	characteristic
160	C₂×Dic₆₇	C₂×D₈	1	1	yes	characteristic
161	C₂×Dic₆₇	C₂×D₈	1	1	yes	characteristic
162	D₂₆₈	—	2	2	no	—
163	D₂₆₈	—	4	1	no	—
164	C₄×D₆₇	—	2	2	no	—
165	C₄×D₆₇	—	8	2	no	—
166	C₄×D₆₇	—	8	4	no	—
167	C₄×D₆₇	—	8	2	no	—
168	C₄×D₆₇	—	8	2	no	—
169	C₄×D₆₇	D₁₆	1	4	yes	—
170	C₄×D₆₇	C₂²⋊Q₈	1	2	yes	—
171	C₄×D₆₇	#137	1	2	yes	—
172	Dic₁₃₄	—	8	2	no	—
173	Dic₁₃₄	—	8	4	no	—
174	C₈×C₆₇	—	2	1	no	—
175	C₈×C₆₇	C₂²×Q₈	1	1	yes	characteristic
176	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
177	C₆₇⋊C₈	—	2	1	no	—
178	C₆₇⋊C₈	C₂²⋊Q₈	1	2	yes	—
179	C₂²×C₆₇	—	4	2	no	—
180	C₂²×C₆₇	—	8	1	no	—
181	C₂²×C₆₇	—	8	1	no	—
182	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
183	C₂×D₆₇	—	4	2	no	—
184	C₂×D₆₇	—	8	1	no	—
185	C₂×D₆₇	—	8	1	no	—
186	C₂×D₆₇	—	8	8	no	—
187	C₂×D₆₇	#474	1	2	yes	—
188	C₂×D₆₇	C₂×D₁₆	1	2	yes	—
189	C₂×D₆₇	#510	1	2	yes	—
190	C₄×C₆₇	—	2	1	no	—
191	C₄×C₆₇	—	8	2	no	—
192	C₄×C₆₇	—	8	1	no	—
193	C₄×C₆₇	C₂×D₁₆	1	2	yes	—
194	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
196	Dic₆₇	—	2	1	no	—
197	Dic₆₇	—	8	2	no	—
198	Dic₆₇	—	8	1	no	—
199	Dic₆₇	#474	1	2	yes	—
200	Dic₆₇	C₂×D₁₆	1	2	yes	—
201	C₂×#2224	—	67	1	no	maximal, Sylow
202	C₂×C₆₇	—	8	2	no	—
203	C₂×C₆₇	C₂×#474	1	1	yes	characteristic
204	C₂×C₆₇	C₂²×D₁₆	1	1	yes	characteristic
205	C₂×C₆₇	C₂×#510	1	1	yes	characteristic
206	D₆₇	—	8	2	no	—
207	D₆₇	#2224	1	4	yes	direct product factor
208	C₂×#500	—	67	1	no	—
209	C₂×C₄×D₈	—	67	1	no	—
210	#2224	—	67	1	no	—
211	#2224	—	67	1	no	—
212	#2224	—	67	2	no	—
213	#2224	—	67	1	no	—
214	#2224	—	67	2	no	—
215	#2224	D₆₇	1	1	yes	characteristic, direct product factor
216	C₂×#366	—	67	2	no	—
217	C₂×C₄⋊C₁₆	—	67	1	no	—
218	C₂×#357	—	67	2	no	—
219	C₆₇	C₂×#2224	1	1	yes	characteristic, complemented, Sylow
220	C₂²×D₈	—	67	1	no	—
221	C₂×C₄⋊Q₈	—	134	1	no	—
222	C₂×C₄×D₄	—	134	1	no	—
223	C₂²×C₁₆	—	67	2	no	—
224	#500	—	67	2	no	—
225	#500	—	67	1	no	—
226	#500	—	134	1	no	—
227	#500	—	134	1	no	—
228	#500	C₂×D₆₇	1	1	yes	characteristic, complemented
229	C₄×D₈	—	67	1	no	—
230	C₄×D₈	—	67	1	no	—
231	C₄×D₈	—	67	1	no	—
232	C₄×D₈	—	134	1	no	—
233	C₄×D₈	—	134	1	no	—
234	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
235	C₂×#107	—	67	2	no	—
236	C₂×#107	—	67	1	no	—
237	C₂×#107	—	134	1	no	—
238	C₂×#102	—	134	1	no	—
239	C₂×C₄×C₈	—	67	1	no	—
240	#366	—	67	2	no	—
241	#366	—	67	2	no	—
242	#366	—	67	2	no	—
243	#366	C₂×D₆₇	1	2	yes	complemented
244	C₄⋊C₁₆	—	67	2	no	—
245	C₄⋊C₁₆	—	67	1	no	—
246	C₄⋊C₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
247	#357	—	67	2	no	—
248	#357	—	67	2	no	—
249	#357	—	67	2	no	—
250	#357	C₂×D₆₇	1	2	yes	—
251	C₂²×Q₈	—	268	1	no	—
252	C₂²×D₄	—	134	1	no	—
253	C₂³×C₄	—	268	1	no	—
254	C₂×D₈	—	67	4	no	—
255	C₂×D₈	—	67	1	no	—
256	C₂×D₈	—	134	2	no	—
257	C₂×D₈	—	134	1	no	—
258	C₂×D₈	C₂²×D₆₇	1	1	yes	characteristic
259	C₂²×C₈	—	67	1	no	—
260	C₂²×C₈	—	67	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	268	1	no	—
263	C₄⋊Q₈	—	268	1	no	—
264	C₄⋊Q₈	—	134	2	no	—
265	C₄⋊Q₈	—	134	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	268	1	no	—
268	C₄×D₄	—	268	1	no	—
269	C₄×D₄	—	134	1	no	—
270	C₄×D₄	—	134	1	no	—
271	C₄×D₄	—	134	1	no	—
272	C₂×C₄⋊C₄	—	268	1	no	—
273	C₂×C₄⋊C₄	—	134	1	no	—
274	C₂×C₄⋊C₄	—	134	2	no	—
275	C₂×C₂²⋊C₄	—	268	1	no	—
276	C₂×C₄²	—	67	1	no	—
277	C₂×C₁₆	—	67	2	no	—
278	C₂×C₁₆	—	134	4	no	—
279	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
280	#107	—	2	1	no	—
281	#107	—	67	2	no	—
282	#107	—	67	1	no	—
283	#107	—	134	1	no	—
284	#107	—	134	2	no	—
285	#107	—	134	2	no	—
286	#107	—	134	1	no	—
287	#107	C₂²×D₆₇	1	2	yes	—
288	#107	C₂²×D₆₇	1	1	yes	characteristic
289	#102	—	2	1	no	—
290	#102	—	134	1	no	—
291	#102	—	134	1	no	—
292	#102	—	134	1	no	—
293	C₄×C₈	—	67	1	no	—
294	C₄×C₈	—	67	1	no	—
295	C₄×C₈	—	67	1	no	—
296	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
297	C₂⁴	—	268	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	268	2	no	—
300	C₂×Q₈	—	268	1	no	—
301	C₂×Q₈	—	536	4	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	268	2	no	—
304	C₂×D₄	—	268	1	no	—
305	C₂×D₄	—	134	4	no	—
306	C₂×D₄	—	134	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	268	1	no	—
309	C₂²×C₄	—	268	2	no	—
310	C₂²×C₄	—	268	1	no	—
311	C₂²×C₄	—	268	1	no	—
312	C₂²×C₄	—	268	1	no	—
313	C₂²×C₄	—	536	4	no	—
314	C₂²×C₄	—	67	1	no	—
315	C₂²×C₄	—	67	1	no	—
316	C₂²×C₄	—	67	1	no	—
317	D₈	—	2	1	no	—
318	D₈	—	67	2	no	—
319	D₈	—	134	4	no	—
320	D₈	—	134	1	no	—
321	D₈	Q₈×D₆₇	1	2	yes	complemented
322	C₂×C₈	—	67	1	no	—
323	C₂×C₈	—	67	2	no	—
324	C₂×C₈	—	67	2	no	—
325	C₂×C₈	—	67	1	no	—
326	C₂×C₈	—	134	2	no	—
327	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	268	2	no	—
333	C₄⋊C₄	—	268	1	no	—
334	C₄⋊C₄	—	268	2	no	—
335	C₄⋊C₄	—	268	1	no	—
336	C₄⋊C₄	—	134	1	no	—
337	C₄⋊C₄	—	134	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	268	1	no	—
340	C₂²⋊C₄	—	268	1	no	—
341	C₂²⋊C₄	—	268	1	no	—
342	C₄²	—	67	1	no	—
343	C₄²	—	67	1	no	—
344	C₄²	—	67	1	no	—
345	C₄²	D₄×D₆₇	1	1	yes	characteristic
346	C₁₆	—	2	2	no	—
347	C₁₆	—	134	2	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	268	4	no	—
350	C₂³	—	268	1	no	—
351	C₂³	—	536	2	no	—
352	C₂³	—	536	2	no	—
353	C₂³	—	67	1	no	—
354	Q₈	—	8	2	no	—
355	Q₈	—	536	4	no	—
356	Q₈	—	536	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	268	4	no	—
360	D₄	—	268	1	no	—
361	D₄	—	134	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	268	1	no	—
366	C₂×C₄	—	268	2	no	—
367	C₂×C₄	—	536	2	no	—
368	C₂×C₄	—	536	4	no	—
369	C₂×C₄	—	536	2	no	—
370	C₂×C₄	—	536	2	no	—
371	C₂×C₄	—	536	2	no	—
372	C₂×C₄	—	67	1	no	—
373	C₂×C₄	—	67	1	no	—
374	C₂×C₄	—	67	4	no	—
375	C₂×C₄	—	67	2	no	—
376	C₂×C₄	—	67	2	no	—
377	C₂×C₄	—	67	1	no	—
378	C₂×C₄	—	134	2	no	—
379	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
380	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	67	2	no	—
384	C₈	—	134	1	no	—
385	C₈	C₂×Q₈×D₆₇	1	1	yes	characteristic
386	C₈	#41×D₆₇	1	1	yes	characteristic
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	268	2	no	—
391	C₂²	—	536	8	no	—
392	C₂²	—	536	1	no	—
393	C₂²	—	536	1	no	—
394	C₂²	—	67	2	no	—
395	C₂²	—	67	2	no	—
396	C₂²	—	67	2	no	—
397	C₂²	C₂×D₈×D₆₇	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	536	1	no	—
402	C₄	—	536	2	no	—
403	C₄	—	67	2	no	—
404	C₄	—	67	2	no	—
405	C₄	—	134	1	no	—
406	C₄	D₁₆×D₆₇	1	2	yes	—
407	C₄	C₂²⋊Q₈×D₆₇	1	1	yes	characteristic
408	C₄	#137×D₆₇	1	1	yes	characteristic
409	C₂	—	8	2	no	—
410	C₂	—	536	2	no	—
411	C₂	—	67	4	no	—
412	C₂	#474×D₆₇	1	1	yes	characteristic
413	C₂	C₂×D₁₆×D₆₇	1	1	yes	characteristic
414	C₂	#510×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₆₇
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#2224	C₂
socle	C₂²×C₆₇	C₂²×D₈
prime radical	C₂×D₈×D₆₇	C₂²
hypercenter	#2224	D₆₇
hypocenter	C₆₇	C₂×#2224
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2224

Complements

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

N	H ≅ G/N	type
1. #500×D₆₇	C₂	semidirect
3. #22562347	C₂	semidirect
4. #22562346	C₂	semidirect
5. #22562345	C₂	semidirect
6. #22562344	C₂	semidirect
7. #22562343	C₂	semidirect
8. #366×D₆₇	C₂	semidirect
9. C₄⋊C₁₆×D₆₇	C₂	semidirect
11. C₆₇×#2224	C₂	semidirect
16. #16863801	C₂²	semidirect
18. #16863800	C₂²	semidirect
30. #16863222	C₂²	semidirect
31. #16863221	C₂²	semidirect
32. #16863221	C₂²	semidirect
33. C₄⋊(C₆₇⋊C₁₆)	C₂²	semidirect
34. Dic₆₇⋊C₁₆	C₂²	semidirect
38. #500×C₆₇	C₂²	semidirect
40. #366×C₆₇	C₂²	semidirect
41. C₄⋊C₁₆×C₆₇	C₂²	semidirect
49. D₈×D₆₇	Q₈	semidirect
107. D₅₃₆	C₂×Q₈	semidirect
131. D₈×C₆₇	C₂×Q₈	semidirect
207. D₆₇	#2224	direct (N × H)
215. #2224	D₆₇	direct (N × H)
219. C₆₇	C₂×#2224	semidirect
228. #500	C₂×D₆₇	semidirect
243. #366	C₂×D₆₇	semidirect
246. C₄⋊C₁₆	C₂×D₆₇	semidirect
321. D₈	Q₈×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#500×D₆₇	2
C₄×D₈×D₆₇	2
#22562347	2
#22562346	2
#22562345	2
#22562344	2
#22562343	2
#366×D₆₇	2
C₄⋊C₁₆×D₆₇	2
#357×D₆₇	2
C₆₇×#2224	2
C₂×#2224	67

Subgroups — #2224×D67 #31010430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2224×D₆₇ #31010430