Subgroups — C₂×#107×Dic₆₇ #30853877

Order 17152.

1358 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523977	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×Dic₆₇	C₂	1	2	yes	maximal
4	#107×Dic₆₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863158	C₂	1	2	yes	maximal
6	C₂²×#107×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₆₇	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₆₇	—	2	2	no	—
10	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
11	C₂×#14523977	C₄	1	8	yes	complemented
12	C₂×#14523977	C₂²	1	4	yes	—
13	C₂×C₈×Dic₆₇	C₄	1	8	yes	complemented
14	C₂×C₈×Dic₆₇	C₂²	1	4	yes	—
15	C₄⋊C₄×Dic₆₇	—	2	4	no	—
16	C₄⋊C₄×Dic₆₇	C₂²	1	8	yes	—
17	C₂×C₆₇⋊#95	—	2	2	no	—
18	#16863158	C₂²	1	8	yes	—
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
21	C₂×#107×C₆₇	C₄	1	8	yes	complemented
22	C₂×#107×C₆₇	C₂²	1	4	yes	—
23	C₂³×Dic₆₇	—	2	2	no	—
24	C₂³×Dic₆₇	D₄	1	1	yes	characteristic
25	C₂³×Dic₆₇	D₄	1	1	yes	characteristic
26	C₂²×C₆₇⋊C₈	—	2	2	no	—
27	C₂²×C₆₇⋊C₈	—	2	2	no	—
28	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
29	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
30	C₂×C₄⋊Dic₆₇	—	2	2	no	—
31	C₂×C₄⋊Dic₆₇	—	2	4	no	—
32	C₂×C₄⋊Dic₆₇	C₂×C₄	1	8	yes	—
33	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	—
34	C₂×C₄×Dic₆₇	—	2	8	no	—
35	C₂×C₄×Dic₆₇	—	4	8	no	—
36	C₂×C₄×Dic₆₇	C₂×C₄	1	4	yes	—
37	C₂×C₄×Dic₆₇	D₄	1	2	yes	—
38	C₂×C₄×Dic₆₇	Q₈	1	4	yes	—
39	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
40	#14523977	C₂×C₄	1	16	yes	complemented
41	C₈×Dic₆₇	C₂×C₄	1	16	yes	complemented
42	C₆₇⋊#95	—	2	8	no	—
43	C₂³×C₄×C₆₇	—	2	2	no	—
44	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	8	yes	—
52	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
53	#107×C₆₇	C₂×C₄	1	16	yes	complemented
54	C₂²×Dic₆₇	—	2	2	no	—
55	C₂²×Dic₆₇	—	2	2	no	—
56	C₂²×Dic₆₇	—	2	8	no	—
57	C₂²×Dic₆₇	—	2	4	no	—
58	C₂²×Dic₆₇	—	4	4	no	—
59	C₂²×Dic₆₇	—	4	4	no	—
60	C₂²×Dic₆₇	C₄⋊C₄	1	4	yes	—
61	C₂²×Dic₆₇	C₄⋊C₄	1	4	yes	—
62	C₂²×Dic₆₇	D₈	1	4	yes	—
63	C₂²×Dic₆₇	Q₁₆	1	4	yes	—
64	C₂²×Dic₆₇	C₂×D₄	1	2	yes	—
65	C₂²×Dic₆₇	C₂×D₄	1	2	yes	—
66	C₂×C₆₇⋊C₈	—	2	8	no	—
67	C₂×C₆₇⋊C₈	—	2	2	no	—
68	C₂×C₆₇⋊C₈	—	2	2	no	—
69	C₂×C₆₇⋊C₈	C₂²×C₄	1	4	yes	—
70	C₄⋊Dic₆₇	—	2	8	no	—
71	C₄⋊Dic₆₇	—	2	4	no	—
72	C₄⋊Dic₆₇	C₂²×C₄	1	8	yes	—
73	C₄×Dic₆₇	—	4	16	no	—
74	C₄×Dic₆₇	C₄⋊C₄	1	8	yes	—
75	C₄×Dic₆₇	C₂²×C₄	1	4	yes	—
76	C₄×Dic₆₇	C₂×Q₈	1	4	yes	—
77	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	—	2	8	no	—
79	C₂²×C₄×C₆₇	—	2	4	no	—
80	C₂²×C₄×C₆₇	—	4	4	no	—
81	C₂²×C₄×C₆₇	—	4	4	no	—
82	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₆₇	#41	1	2	yes	—
88	C₂²×C₄×C₆₇	#41	1	2	yes	—
89	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₆₇	C₄²	1	16	yes	complemented
91	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₆₇	—	2	8	no	—
95	C₄⋊C₄×C₆₇	—	2	4	no	—
96	C₄⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
97	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
98	C₂³×C₆₇	C₄×D₄	1	2	yes	—
99	C₂³×C₆₇	C₄×D₄	1	2	yes	—
100	C₂³×C₆₇	C₂×D₈	1	2	yes	—
101	C₂³×C₆₇	C₂×Q₁₆	1	2	yes	—
102	C₂³×C₆₇	#135	1	2	yes	—
103	C₂³×C₆₇	#135	1	2	yes	—
104	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
105	C₂×C₄×C₆₇	—	2	8	no	—
106	C₂×C₄×C₆₇	—	4	4	no	—
107	C₂×C₄×C₆₇	—	4	4	no	—
108	C₂×C₄×C₆₇	—	4	16	no	—
109	C₂×C₄×C₆₇	C₂×C₄²	1	4	yes	—
110	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
111	C₂×C₄×C₆₇	#117	1	4	yes	—
112	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
113	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
114	C₂×C₄×C₆₇	C₄×Q₈	1	4	yes	—
115	C₂×C₄×C₆₇	C₄×Q₈	1	4	yes	—
116	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
117	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
118	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
119	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
120	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
121	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
122	C₂×Dic₆₇	—	2	2	no	—
123	C₂×Dic₆₇	—	2	2	no	—
124	C₂×Dic₆₇	—	2	8	no	—
125	C₂×Dic₆₇	—	2	8	no	—
126	C₂×Dic₆₇	—	4	4	no	—
127	C₂×Dic₆₇	—	4	4	no	—
128	C₂×Dic₆₇	—	4	16	no	—
129	C₂×Dic₆₇	#107	1	16	yes	direct product factor
130	C₂×Dic₆₇	C₂×C₄⋊C₄	1	4	yes	—
131	C₂×Dic₆₇	C₂×C₄⋊C₄	1	4	yes	—
132	C₂×Dic₆₇	C₂×D₈	1	4	yes	—
133	C₂×Dic₆₇	C₂×Q₁₆	1	4	yes	—
134	C₈×C₆₇	C₂×C₄²	1	8	yes	complemented
135	C₆₇⋊C₈	—	2	4	no	—
136	C₂²×C₆₇	C₄×C₄⋊C₄	1	4	yes	—
137	C₂²×C₆₇	C₂×#107	1	4	yes	—
138	C₂²×C₆₇	#427	1	4	yes	—
139	C₂²×C₆₇	C₄×D₈	1	4	yes	—
140	C₂²×C₆₇	C₄×D₈	1	4	yes	—
141	C₂²×C₆₇	C₄×Q₁₆	1	4	yes	—
142	C₂²×C₆₇	C₄×Q₁₆	1	4	yes	—
143	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
145	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
146	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
147	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
148	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
149	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
150	C₄×C₆₇	—	4	8	no	—
151	C₄×C₆₇	C₄×C₄⋊C₄	1	4	yes	—
152	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
153	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
154	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
155	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
156	Dic₆₇	—	2	4	no	—
157	Dic₆₇	—	4	8	no	—
158	Dic₆₇	C₂×#107	1	8	yes	direct product factor
159	C₂×C₄×#107	—	67	1	no	maximal, Sylow
160	C₂×C₆₇	C₄×#107	1	8	yes	complemented
161	C₂×C₆₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₆₇	C₂²×#107	1	1	yes	characteristic
163	C₂×C₆₇	C₂×#427	1	1	yes	characteristic
164	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
165	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
166	C₂×C₆₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
167	C₂×C₆₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
168	C₂²×#107	—	67	1	no	—
169	C₂²×#107	D₆₇	1	1	yes	characteristic
170	C₂²×C₄×C₈	—	67	1	no	—
171	C₂×C₄×C₄⋊C₄	—	67	2	no	—
172	C₄×#107	—	67	8	no	—
173	C₂×#340	—	67	2	no	—
174	C₆₇	C₂×C₄×#107	1	1	yes	characteristic, complemented, Sylow
175	C₂³×C₈	—	67	1	no	—
176	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
177	C₂²×C₄⋊C₄	—	67	2	no	—
178	C₂²×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
179	C₂²×C₄²	—	67	1	no	—
180	C₂²×C₄²	—	134	2	no	—
181	C₂×#107	—	67	8	no	—
182	C₂×#107	—	67	4	no	—
183	C₂×#107	Dic₆₇	1	8	yes	direct product factor
184	C₂×#107	C₂×D₆₇	1	4	yes	—
185	C₂×C₄×C₈	—	67	8	no	—
186	C₂×C₄×C₈	—	67	4	no	—
187	C₄×C₄⋊C₄	—	67	8	no	—
188	C₄×C₄⋊C₄	—	134	4	no	—
189	C₂×#95	—	134	2	no	—
190	#340	—	67	8	no	—
191	C₂³×C₄	—	2	2	no	—
192	C₂³×C₄	—	67	1	no	—
193	C₂³×C₄	—	67	1	no	—
194	C₂³×C₄	—	134	2	no	—
195	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
196	C₂²×C₈	—	67	4	no	—
197	C₂²×C₈	—	67	2	no	—
198	C₂²×C₈	—	134	2	no	—
199	C₂²×C₈	—	134	2	no	—
200	C₂²×C₈	C₄×D₆₇	1	4	yes	—
201	C₂²×C₈	C₄×D₆₇	1	4	yes	—
202	C₂²×C₈	C₂×Dic₆₇	1	4	yes	—
203	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	67	8	no	—
207	C₂×C₄⋊C₄	—	67	4	no	—
208	C₂×C₄⋊C₄	—	134	2	no	—
209	C₂×C₄⋊C₄	—	134	4	no	—
210	C₂×C₄⋊C₄	C₂×Dic₆₇	1	8	yes	—
211	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
212	C₂×C₄²	—	268	8	no	—
213	C₂×C₄²	—	67	4	no	—
214	C₂×C₄²	—	67	2	no	—
215	C₂×C₄²	—	67	4	no	—
216	C₂×C₄²	—	67	2	no	—
217	C₂×C₄²	—	134	8	no	—
218	#107	—	67	16	no	—
219	#107	C₂×Dic₆₇	1	16	yes	direct product factor
220	C₄×C₈	—	67	16	no	—
221	#95	—	134	8	no	—
222	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
223	C₂²×C₄	—	2	8	no	—
224	C₂²×C₄	—	2	4	no	—
225	C₂²×C₄	—	4	4	no	—
226	C₂²×C₄	—	4	4	no	—
227	C₂²×C₄	—	268	4	no	—
228	C₂²×C₄	—	268	4	no	—
229	C₂²×C₄	—	67	4	no	—
230	C₂²×C₄	—	67	4	no	—
231	C₂²×C₄	—	67	4	no	—
232	C₂²×C₄	—	67	2	no	—
233	C₂²×C₄	—	67	4	no	—
234	C₂²×C₄	—	67	2	no	—
235	C₂²×C₄	—	134	8	no	—
236	C₂²×C₄	—	134	4	no	—
237	C₂²×C₄	—	134	2	no	—
238	C₂²×C₄	—	134	2	no	—
239	C₂²×C₄	C₂×C₄×D₆₇	1	2	yes	—
240	C₂²×C₄	C₂×C₄×D₆₇	1	2	yes	—
241	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
242	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
243	C₂²×C₄	Q₈×D₆₇	1	2	yes	—
244	C₂²×C₄	#11761627	1	2	yes	—
245	C₂²×C₄	#11761629	1	2	yes	—
246	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
247	C₂×C₈	—	67	4	no	—
248	C₂×C₈	—	134	8	no	—
249	C₂×C₈	—	134	2	no	—
250	C₂×C₈	—	134	2	no	—
251	C₂×C₈	C₄×Dic₆₇	1	16	yes	complemented
252	C₂×C₈	C₂×C₄×D₆₇	1	4	yes	—
253	C₂×C₈	C₂×C₄×D₆₇	1	4	yes	—
254	C₂×C₈	C₂²×Dic₆₇	1	4	yes	—
255	C₄⋊C₄	—	2	8	no	—
256	C₄⋊C₄	—	2	4	no	—
257	C₄⋊C₄	—	67	8	no	—
258	C₄⋊C₄	—	134	8	no	—
259	C₄⋊C₄	—	134	4	no	—
260	C₄⋊C₄	C₂²×Dic₆₇	1	8	yes	—
261	C₄²	—	268	16	no	—
262	C₄²	—	67	8	no	—
263	C₄²	—	67	4	no	—
264	C₄²	—	67	4	no	—
265	C₂³	C₄⋊C₄×D₆₇	1	2	yes	—
266	C₂³	#14524005	1	2	yes	—
267	C₂³	D₄×Dic₆₇	1	2	yes	—
268	C₂³	D₈×D₆₇	1	2	yes	—
269	C₂³	Q₁₆×D₆₇	1	2	yes	—
270	C₂³	#14524062	1	2	yes	—
271	C₂³	#14524066	1	2	yes	—
272	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
273	C₂×C₄	—	2	8	no	—
274	C₂×C₄	—	4	4	no	—
275	C₂×C₄	—	4	4	no	—
276	C₂×C₄	—	4	16	no	—
277	C₂×C₄	—	268	4	no	—
278	C₂×C₄	—	268	4	no	—
279	C₂×C₄	—	268	16	no	—
280	C₂×C₄	—	67	4	no	—
281	C₂×C₄	—	67	4	no	—
282	C₂×C₄	—	67	4	no	—
283	C₂×C₄	—	67	16	no	—
284	C₂×C₄	—	67	4	no	—
285	C₂×C₄	—	134	8	no	—
286	C₂×C₄	—	134	2	no	—
287	C₂×C₄	—	134	2	no	—
288	C₂×C₄	—	134	8	no	—
289	C₂×C₄	C₂×C₄×Dic₆₇	1	4	yes	—
290	C₂×C₄	C₄⋊C₄×D₆₇	1	2	yes	—
291	C₂×C₄	#14524001	1	4	yes	—
292	C₂×C₄	#14524005	1	2	yes	—
293	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
294	C₂×C₄	#14524008	1	4	yes	—
295	C₂×C₄	Q₈×Dic₆₇	1	4	yes	—
296	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
297	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
298	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
299	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
300	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
301	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
302	C₈	—	134	4	no	—
303	C₈	C₂×C₄×Dic₆₇	1	8	yes	complemented
304	C₂²	C₄⋊C₄×Dic₆₇	1	4	yes	—
305	C₂²	#107×D₆₇	1	4	yes	—
306	C₂²	#16863433	1	4	yes	—
307	C₂²	#16863478	1	4	yes	—
308	C₂²	D₈×Dic₆₇	1	4	yes	—
309	C₂²	#16863490	1	4	yes	—
310	C₂²	Q₁₆×Dic₆₇	1	4	yes	—
311	C₂²	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
312	C₂²	C₂×#14524005	1	1	yes	characteristic
313	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
314	C₂²	C₂×D₈×D₆₇	1	1	yes	characteristic
315	C₂²	C₂×Q₁₆×D₆₇	1	1	yes	characteristic
316	C₂²	C₂×#14524062	1	1	yes	characteristic
317	C₂²	C₂×#14524066	1	1	yes	characteristic
318	C₄	—	4	8	no	—
319	C₄	—	268	8	no	—
320	C₄	—	67	8	no	—
321	C₄	—	134	4	no	—
322	C₄	C₄⋊C₄×Dic₆₇	1	4	yes	—
323	C₄	C₂²×C₄×Dic₆₇	1	1	yes	characteristic
324	C₄	C₂×#14524001	1	1	yes	characteristic
325	C₄	C₂×#14524008	1	1	yes	characteristic
326	C₄	C₂×Q₈×Dic₆₇	1	1	yes	characteristic
327	C₂	#107×Dic₆₇	1	8	yes	direct product factor
328	C₂	C₂×C₄⋊C₄×Dic₆₇	1	1	yes	characteristic
329	C₂	C₂×#107×D₆₇	1	1	yes	characteristic
330	C₂	C₂×#16863433	1	1	yes	characteristic
331	C₂	C₂×#16863478	1	1	yes	characteristic
332	C₂	C₂×D₈×Dic₆₇	1	1	yes	characteristic
333	C₂	C₂×#16863490	1	1	yes	characteristic
334	C₂	C₂×Q₁₆×Dic₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂²×#107×C₆₇	C₂
socle, prime radical	C₂⁴×C₆₇	C₂×D₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂²×#107	D₆₇
hypocenter	C₆₇	C₂×C₄×#107
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#107

Complements

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

N	H ≅ G/N	type
4. #107×Dic₆₇	C₂	direct (N × H)
11. C₂×#14523977	C₄	semidirect
13. C₂×C₈×Dic₆₇	C₄	semidirect
21. C₂×#107×C₆₇	C₄	semidirect
40. #14523977	C₂×C₄	semidirect
41. C₈×Dic₆₇	C₂×C₄	semidirect
53. #107×C₆₇	C₂×C₄	semidirect
90. C₂×C₈×C₆₇	C₄²	semidirect
129. C₂×Dic₆₇	#107	direct (N × H)
134. C₈×C₆₇	C₂×C₄²	semidirect
158. Dic₆₇	C₂×#107	direct (N × H)
160. C₂×C₆₇	C₄×#107	semidirect
174. C₆₇	C₂×C₄×#107	semidirect
183. C₂×#107	Dic₆₇	direct (N × H)
219. #107	C₂×Dic₆₇	direct (N × H)
251. C₂×C₈	C₄×Dic₆₇	semidirect
303. C₈	C₂×C₄×Dic₆₇	semidirect
327. C₂	#107×Dic₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523977	2
C₂²×C₈×Dic₆₇	2
C₂×C₄⋊C₄×Dic₆₇	2
#107×Dic₆₇	2
C₂×#16863158	2
C₂²×#107×C₆₇	2
C₂×C₄×#107	67

Subgroups — C2×#107×Dic67 #30853877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#107×Dic₆₇ #30853877