Subgroups — C₂²×#16863397 #31719365

Order 17152.

5502 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863397	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#14523967	C₂	1	2	yes	maximal, complemented
5	C₂²×#14523964	C₂	1	2	yes	maximal, complemented
6	C₂³×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×Dic₆₇	—	2	1	no	—
8	C₂²×#11761612	—	2	8	no	—
9	C₂²×#11761612	C₂²	1	12	yes	complemented
10	C₂³×C₆₇⋊C₈	C₂²	1	2	yes	—
11	C₂²×C₄⋊Dic₆₇	—	2	1	no	—
12	C₂²×C₄⋊Dic₆₇	—	2	6	no	—
13	C₂²×C₄⋊Dic₆₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₆₇	C₂²	1	12	yes	complemented
15	#16863397	C₂²	1	64	yes	direct product factor
16	C₂×#14523967	C₂²	1	24	yes	complemented
17	C₂×#14523964	C₂²	1	24	yes	complemented
18	C₂²×#41×C₆₇	—	2	8	no	—
19	C₂²×#41×C₆₇	—	2	6	no	—
20	C₂²×#41×C₆₇	C₄	1	16	yes	complemented
21	C₂²×#41×C₆₇	C₂²	1	12	yes	—
22	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂³×D₄×C₆₇	—	2	1	no	—
24	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₆₇	—	2	1	no	—
26	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂³×Dic₆₇	—	2	2	no	—
28	C₂³×Dic₆₇	—	2	12	no	—
29	C₂³×Dic₆₇	—	4	8	no	—
30	C₂×#11761612	—	2	48	no	—
31	C₂×#11761612	C₂³	1	16	yes	complemented
32	C₂²×C₆₇⋊C₈	—	2	8	no	—
33	C₂²×C₆₇⋊C₈	C₂³	1	12	yes	—
34	C₂×C₄⋊Dic₆₇	—	2	6	no	—
35	C₂×C₄⋊Dic₆₇	—	2	12	no	—
36	C₂×C₄⋊Dic₆₇	—	2	24	no	—
37	C₂×C₄⋊Dic₆₇	C₂³	1	12	yes	—
38	C₂×C₄⋊Dic₆₇	C₂³	1	16	yes	complemented
39	#14523967	C₂³	1	32	yes	complemented
40	#14523964	C₂³	1	32	yes	complemented
41	C₂⁵×C₆₇	—	2	1	no	—
42	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
43	C₂×#41×C₆₇	—	2	96	no	—
44	C₂×#41×C₆₇	—	2	48	no	—
45	C₂×#41×C₆₇	—	2	24	no	—
46	C₂×#41×C₆₇	C₂×C₄	1	96	yes	complemented
47	C₂×#41×C₆₇	C₂³	1	16	yes	—
48	C₂²×Q₈×C₆₇	—	2	4	no	—
49	C₂²×Q₈×C₆₇	—	2	3	no	—
50	C₂²×Q₈×C₆₇	C₂×C₄	1	8	yes	complemented
51	C₂²×Q₈×C₆₇	C₂³	1	6	yes	—
52	C₂²×D₄×C₆₇	—	2	16	no	—
53	C₂²×D₄×C₆₇	—	2	12	no	—
54	C₂²×D₄×C₆₇	—	2	3	no	—
55	C₂²×D₄×C₆₇	—	2	4	no	—
56	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
57	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
58	C₂³×C₄×C₆₇	—	2	1	no	—
59	C₂³×C₄×C₆₇	—	2	16	no	—
60	C₂³×C₄×C₆₇	—	2	12	no	—
61	C₂³×C₄×C₆₇	C₂×C₄	1	8	yes	—
62	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₇	D₄	1	6	yes	—
64	C₂³×C₄×C₆₇	D₄	1	8	yes	—
65	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
67	C₂²×Dic₆₇	—	2	12	no	—
68	C₂²×Dic₆₇	—	2	16	no	—
69	C₂²×Dic₆₇	—	4	48	no	—
70	C₂²×Dic₆₇	—	4	8	no	—
71	#11761612	—	2	32	no	—
72	C₂×C₆₇⋊C₈	—	2	24	no	—
73	C₂×C₆₇⋊C₈	C₂⁴	1	8	yes	—
74	C₄⋊Dic₆₇	—	2	12	no	—
75	C₄⋊Dic₆₇	—	2	16	no	—
76	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
77	C₂⁴×C₆₇	—	2	4	no	—
78	C₂⁴×C₆₇	—	2	4	no	—
79	C₂⁴×C₆₇	—	2	8	no	—
80	C₂⁴×C₆₇	—	2	6	no	—
81	C₂⁴×C₆₇	—	4	4	no	—
82	C₂⁴×C₆₇	—	4	4	no	—
83	C₂⁴×C₆₇	C₂²⋊C₄	1	8	yes	—
84	C₂⁴×C₆₇	C₂×D₄	1	6	yes	—
85	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
86	#41×C₆₇	—	2	192	no	—
87	#41×C₆₇	—	2	32	no	—
88	#41×C₆₇	C₂²×C₄	1	64	yes	complemented
89	C₂×Q₈×C₆₇	—	2	24	no	—
90	C₂×Q₈×C₆₇	—	2	12	no	—
91	C₂×Q₈×C₆₇	—	2	6	no	—
92	C₂×Q₈×C₆₇	C₂²×C₄	1	24	yes	complemented
93	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
94	C₂×D₄×C₆₇	—	2	96	no	—
95	C₂×D₄×C₆₇	—	2	16	no	—
96	C₂×D₄×C₆₇	—	2	24	no	—
97	C₂×D₄×C₆₇	—	2	6	no	—
98	C₂×D₄×C₆₇	—	2	12	no	—
99	C₂×D₄×C₆₇	C₂²×C₄	1	24	yes	complemented
100	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₆₇	—	2	8	no	—
102	C₂²×C₄×C₆₇	—	2	6	no	—
103	C₂²×C₄×C₆₇	—	2	96	no	—
104	C₂²×C₄×C₆₇	—	2	16	no	—
105	C₂²×C₄×C₆₇	C₂²⋊C₄	1	8	yes	—
106	C₂²×C₄×C₆₇	C₂²⋊C₄	1	48	yes	—
107	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₆₇	C₂²×C₄	1	24	yes	—
109	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
112	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	24	yes	—
114	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
115	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
116	C₂³×C₆₇	—	2	12	no	—
117	C₂³×C₆₇	—	2	12	no	—
118	C₂³×C₆₇	—	2	32	no	—
119	C₂³×C₆₇	—	2	24	no	—
120	C₂³×C₆₇	—	2	4	no	—
121	C₂³×C₆₇	—	4	12	no	—
122	C₂³×C₆₇	—	4	12	no	—
123	C₂³×C₆₇	—	4	32	no	—
124	C₂³×C₆₇	C₂×C₂²⋊C₄	1	24	yes	—
125	C₂³×C₆₇	C₂×C₂²⋊C₄	1	4	yes	—
126	C₂³×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
127	C₂³×C₆₇	#137	1	4	yes	—
128	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
129	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
130	Q₈×C₆₇	—	2	24	no	—
131	Q₈×C₆₇	—	2	4	no	—
132	Q₈×C₆₇	C₂³×C₄	1	8	yes	complemented
133	D₄×C₆₇	—	2	64	no	—
134	D₄×C₆₇	—	2	24	no	—
135	D₄×C₆₇	—	2	4	no	—
136	D₄×C₆₇	C₂³×C₄	1	8	yes	complemented
137	C₂×C₄×C₆₇	—	2	24	no	—
138	C₂×C₄×C₆₇	—	2	4	no	—
139	C₂×C₄×C₆₇	—	2	64	no	—
140	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	24	yes	—
141	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	12	yes	—
142	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	48	yes	—
143	C₂×C₄×C₆₇	C₂³×C₄	1	6	yes	—
144	C₂×C₄×C₆₇	C₂³×C₄	1	8	yes	—
145	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
147	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
148	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
149	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
150	C₂×Dic₆₇	—	2	8	no	—
151	C₂×Dic₆₇	—	4	32	no	—
152	C₂×Dic₆₇	—	4	24	no	—
153	C₆₇⋊C₈	—	2	8	no	—
154	C₂²×C₆₇	—	2	48	no	—
155	C₂²×C₆₇	—	2	4	no	—
156	C₂²×C₆₇	—	2	4	no	—
157	C₂²×C₆₇	—	2	8	no	—
158	C₂²×C₆₇	—	4	48	no	—
159	C₂²×C₆₇	—	4	4	no	—
160	C₂²×C₆₇	—	4	4	no	—
161	C₂²×C₆₇	#417	1	16	yes	complemented
162	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	8	yes	—
163	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	6	yes	—
164	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
165	C₂²×C₆₇	C₂×#137	1	6	yes	—
166	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
167	C₄×C₆₇	—	2	8	no	—
168	C₄×C₆₇	C₂²×C₂²⋊C₄	1	8	yes	—
169	C₄×C₆₇	C₂²×C₂²⋊C₄	1	6	yes	—
170	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
171	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
172	Dic₆₇	—	4	8	no	—
173	C₂²×#417	—	67	1	no	maximal, Sylow
174	C₂×C₆₇	—	2	8	no	—
175	C₂×C₆₇	—	4	8	no	—
176	C₂×C₆₇	C₂×#417	1	12	yes	complemented
177	C₂×C₆₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
180	C₂³×#41	D₆₇	1	1	yes	characteristic
181	C₂³×M₁₆	—	67	1	no	—
182	C₂³×C₄⋊C₄	—	67	1	no	—
183	C₂×#417	—	67	24	no	—
184	C₂²×#103	—	67	2	no	—
185	C₂²×#102	—	67	2	no	—
186	C₆₇	C₂²×#417	1	1	yes	characteristic, complemented, Sylow
187	C₂²×#41	—	2	8	no	—
188	C₂²×#41	—	2	6	no	—
189	C₂²×#41	Dic₆₇	1	16	yes	complemented
190	C₂²×#41	C₂×D₆₇	1	12	yes	—
191	C₂³×Q₈	C₂×D₆₇	1	1	yes	characteristic
192	C₂³×D₄	—	2	1	no	—
193	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic
194	C₂⁴×C₄	—	2	1	no	—
195	C₂⁴×C₄	—	134	1	no	—
196	C₂⁴×C₄	C₂×D₆₇	1	1	yes	characteristic
197	C₂²×M₁₆	—	67	12	no	—
198	C₂²×M₁₆	—	134	8	no	—
199	C₂³×C₈	—	67	2	no	—
200	C₂²×C₄⋊C₄	—	67	2	no	—
201	C₂²×C₄⋊C₄	—	67	12	no	—
202	C₂²×C₄⋊C₄	—	134	6	no	—
203	C₂²×C₄⋊C₄	—	134	1	no	—
204	#417	—	67	64	no	—
205	C₂×#103	—	67	24	no	—
206	C₂×#102	—	67	24	no	—
207	C₂⁵	—	2	1	no	—
208	C₂⁵	C₂²⋊D₆₇	1	1	yes	characteristic
209	C₂×#41	—	2	96	no	—
210	C₂×#41	—	2	48	no	—
211	C₂×#41	—	2	24	no	—
212	C₂×#41	C₂×Dic₆₇	1	96	yes	complemented
213	C₂×#41	C₂²×D₆₇	1	16	yes	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	3	no	—
216	C₂²×Q₈	C₂×Dic₆₇	1	8	yes	complemented
217	C₂²×Q₈	C₂²×D₆₇	1	6	yes	—
218	C₂²×D₄	—	2	16	no	—
219	C₂²×D₄	—	2	12	no	—
220	C₂²×D₄	—	2	3	no	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	C₂×Dic₆₇	1	8	yes	complemented
223	C₂²×D₄	C₂²×D₆₇	1	6	yes	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	—	2	16	no	—
226	C₂³×C₄	—	2	12	no	—
227	C₂³×C₄	—	268	8	no	—
228	C₂³×C₄	—	134	12	no	—
229	C₂³×C₄	—	134	2	no	—
230	C₂³×C₄	C₂×Dic₆₇	1	8	yes	—
231	C₂³×C₄	C₂²⋊D₆₇	1	6	yes	—
232	C₂³×C₄	C₂²⋊D₆₇	1	1	yes	characteristic
233	C₂³×C₄	C₂²⋊D₆₇	1	8	yes	—
234	C₂³×C₄	C₂²×D₆₇	1	6	yes	—
235	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
236	C₂×M₁₆	—	67	16	no	—
237	C₂×M₁₆	—	134	48	no	—
238	C₂²×C₈	—	67	12	no	—
239	C₂²×C₈	—	134	8	no	—
240	C₂×C₄⋊C₄	—	67	12	no	—
241	C₂×C₄⋊C₄	—	67	16	no	—
242	C₂×C₄⋊C₄	—	134	12	no	—
243	C₂×C₄⋊C₄	—	134	6	no	—
244	C₂×C₄⋊C₄	—	134	24	no	—
245	#103	—	67	32	no	—
246	#102	—	67	32	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	—	2	8	no	—
250	C₂⁴	—	2	6	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	C₂²⋊Dic₆₇	1	8	yes	—
254	C₂⁴	C₂×C₂²⋊D₆₇	1	6	yes	—
255	C₂⁴	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
256	#41	—	2	192	no	—
257	#41	—	2	32	no	—
258	#41	C₂²×Dic₆₇	1	64	yes	complemented
259	C₂×Q₈	—	2	24	no	—
260	C₂×Q₈	—	2	12	no	—
261	C₂×Q₈	—	2	6	no	—
262	C₂×Q₈	C₂²×Dic₆₇	1	24	yes	complemented
263	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
264	C₂×D₄	—	2	96	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	24	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	2	12	no	—
269	C₂×D₄	C₂²×Dic₆₇	1	24	yes	complemented
270	C₂×D₄	C₂³×D₆₇	1	4	yes	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	6	no	—
273	C₂²×C₄	—	2	96	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	268	48	no	—
276	C₂²×C₄	—	268	8	no	—
277	C₂²×C₄	—	134	16	no	—
278	C₂²×C₄	—	134	12	no	—
279	C₂²×C₄	C₂²⋊Dic₆₇	1	8	yes	—
280	C₂²×C₄	C₂²⋊Dic₆₇	1	48	yes	—
281	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
282	C₂²×C₄	C₂²×Dic₆₇	1	24	yes	—
283	C₂²×C₄	C₂×C₂²⋊D₆₇	1	6	yes	—
284	C₂²×C₄	C₂×C₂²⋊D₆₇	1	3	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₆₇	1	12	yes	—
286	C₂²×C₄	C₂×C₂²⋊D₆₇	1	4	yes	—
287	C₂²×C₄	C₂×C₂²⋊D₆₇	1	24	yes	—
288	C₂²×C₄	C₂³×D₆₇	1	3	yes	—
289	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
290	M₁₆	—	134	32	no	—
291	C₂×C₈	—	67	8	no	—
292	C₂×C₈	—	134	24	no	—
293	C₄⋊C₄	—	67	8	no	—
294	C₄⋊C₄	—	134	16	no	—
295	C₄⋊C₄	—	134	12	no	—
296	C₂³	—	2	32	no	—
297	C₂³	—	2	12	no	—
298	C₂³	—	2	12	no	—
299	C₂³	—	2	24	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	4	32	no	—
302	C₂³	—	4	12	no	—
303	C₂³	—	4	12	no	—
304	C₂³	C₂×C₂²⋊Dic₆₇	1	24	yes	—
305	C₂³	C₂×C₂²⋊Dic₆₇	1	4	yes	—
306	C₂³	#14524068	1	4	yes	—
307	C₂³	#14524073	1	4	yes	—
308	C₂³	C₂²×C₂²⋊D₆₇	1	4	yes	—
309	C₂³	C₂²×C₂²⋊D₆₇	1	3	yes	—
310	Q₈	—	2	24	no	—
311	Q₈	—	2	4	no	—
312	Q₈	C₂³×Dic₆₇	1	8	yes	complemented
313	D₄	—	2	64	no	—
314	D₄	—	2	24	no	—
315	D₄	—	2	4	no	—
316	D₄	C₂³×Dic₆₇	1	8	yes	complemented
317	C₂×C₄	—	2	24	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	64	no	—
320	C₂×C₄	—	268	32	no	—
321	C₂×C₄	—	268	24	no	—
322	C₂×C₄	—	134	8	no	—
323	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	24	yes	—
324	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	12	yes	—
325	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	48	yes	—
326	C₂×C₄	C₂³×Dic₆₇	1	6	yes	—
327	C₂×C₄	C₂³×Dic₆₇	1	8	yes	—
328	C₂×C₄	C₂²×C₂²⋊D₆₇	1	4	yes	—
329	C₂×C₄	C₂²×C₂²⋊D₆₇	1	3	yes	—
330	C₂×C₄	C₂²×C₂²⋊D₆₇	1	6	yes	—
331	C₂×C₄	C₂²×C₂²⋊D₆₇	1	8	yes	—
332	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
333	C₈	—	134	8	no	—
334	C₂²	—	2	48	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	4	48	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	4	4	no	—
341	C₂²	#16863397	1	16	yes	direct product factor
342	C₂²	C₂²×C₂²⋊Dic₆₇	1	8	yes	—
343	C₂²	C₂²×C₂²⋊Dic₆₇	1	6	yes	—
344	C₂²	C₂×#14524068	1	6	yes	—
345	C₂²	C₂×#14524073	1	6	yes	—
346	C₂²	C₂³×C₂²⋊D₆₇	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	268	8	no	—
349	C₄	C₂²×C₂²⋊Dic₆₇	1	8	yes	—
350	C₄	C₂²×C₂²⋊Dic₆₇	1	6	yes	—
351	C₄	C₂⁴×Dic₆₇	1	1	yes	characteristic
352	C₄	C₂³×C₂²⋊D₆₇	1	1	yes	characteristic
353	C₂	—	2	8	no	—
354	C₂	—	4	8	no	—
355	C₂	C₂×#16863397	1	12	yes	direct product factor
356	C₂	C₂³×C₂²⋊Dic₆₇	1	1	yes	characteristic
357	C₂	C₂²×#14524068	1	1	yes	characteristic
358	C₂	C₂²×#14524073	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₆₇
commutator	C₄×C₆₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting, prime radical	C₂³×#41×C₆₇	C₂
socle	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂³×#41	D₆₇
hypocenter	C₆₇	C₂²×#417
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×#11761612	C₂	semidirect
2. C₂³×C₄⋊Dic₆₇	C₂	semidirect
3. C₂×#16863397	C₂	direct (N × H)
4. C₂²×#14523967	C₂	semidirect
5. C₂²×#14523964	C₂	semidirect
9. C₂²×#11761612	C₂²	semidirect
14. C₂²×C₄⋊Dic₆₇	C₂²	semidirect
15. #16863397	C₂²	direct (N × H)
16. C₂×#14523967	C₂²	semidirect
17. C₂×#14523964	C₂²	semidirect
20. C₂²×#41×C₆₇	C₄	semidirect
31. C₂×#11761612	C₂³	semidirect
38. C₂×C₄⋊Dic₆₇	C₂³	semidirect
39. #14523967	C₂³	semidirect
40. #14523964	C₂³	semidirect
46. C₂×#41×C₆₇	C₂×C₄	semidirect
50. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
56. C₂²×D₄×C₆₇	C₂×C₄	semidirect
88. #41×C₆₇	C₂²×C₄	semidirect
92. C₂×Q₈×C₆₇	C₂²×C₄	semidirect
99. C₂×D₄×C₆₇	C₂²×C₄	semidirect
132. Q₈×C₆₇	C₂³×C₄	semidirect
136. D₄×C₆₇	C₂³×C₄	semidirect
161. C₂²×C₆₇	#417	semidirect
176. C₂×C₆₇	C₂×#417	semidirect
186. C₆₇	C₂²×#417	semidirect
189. C₂²×#41	Dic₆₇	semidirect
212. C₂×#41	C₂×Dic₆₇	semidirect
216. C₂²×Q₈	C₂×Dic₆₇	semidirect
222. C₂²×D₄	C₂×Dic₆₇	semidirect
258. #41	C₂²×Dic₆₇	semidirect
262. C₂×Q₈	C₂²×Dic₆₇	semidirect
269. C₂×D₄	C₂²×Dic₆₇	semidirect
312. Q₈	C₂³×Dic₆₇	semidirect
316. D₄	C₂³×Dic₆₇	semidirect
341. C₂²	#16863397	direct (N × H)
355. C₂	C₂×#16863397	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11761612	2
C₂³×C₄⋊Dic₆₇	2
C₂×#16863397	2
C₂²×#14523967	2
C₂²×#14523964	2
C₂³×#41×C₆₇	2
C₂²×#417	67

Subgroups — C22×#16863397 #31719365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16863397 #31719365