Subgroups — C₂²×#456×C₆₇ #30739632

Order 17152.

4766 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#137×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#456×C₆₇	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#104×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂²×#101×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×2₋¹⁺⁴×C₆₇	—	2	12	no	—
8	C₂×2₋¹⁺⁴×C₆₇	—	2	6	no	—
9	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	12	yes	—
10	C₂²×#41×C₆₇	—	2	2	no	—
11	C₂²×#41×C₆₇	—	2	2	no	—
12	C₂²×#41×C₆₇	C₂²	1	2	yes	—
13	C₂³×Q₈×C₆₇	—	2	2	no	—
14	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×#137×C₆₇	—	2	12	no	—
17	C₂×#137×C₆₇	C₂²	1	24	yes	complemented
18	C₂²×Q₁₆×C₆₇	—	2	2	no	—
19	C₂²×SD₁₆×C₆₇	—	2	2	no	—
20	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄⋊Q₈×C₆₇	—	2	6	no	—
22	C₂×C₄⋊Q₈×C₆₇	C₂²	1	12	yes	complemented
23	C₂²×C₄⋊C₄×C₆₇	—	2	2	no	—
24	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
25	#456×C₆₇	C₂²	1	64	yes	direct product factor
26	C₂×#104×C₆₇	C₂²	1	24	yes	complemented
27	C₂×#101×C₆₇	C₂²	1	12	yes	complemented
28	2₋¹⁺⁴×C₆₇	—	2	48	no	—
29	2₋¹⁺⁴×C₆₇	—	2	48	no	—
30	2₋¹⁺⁴×C₆₇	—	2	24	no	—
31	2₋¹⁺⁴×C₆₇	C₂³	1	16	yes	—
32	C₂×#41×C₆₇	—	2	24	no	—
33	C₂×#41×C₆₇	—	2	24	no	—
34	C₂×#41×C₆₇	—	2	24	no	—
35	C₂×#41×C₆₇	—	2	24	no	—
36	C₂×#41×C₆₇	—	2	6	no	—
37	C₂×#41×C₆₇	—	2	6	no	—
38	C₂×#41×C₆₇	D₄	1	12	yes	—
39	C₂×#41×C₆₇	C₂³	1	12	yes	—
40	C₂²×Q₈×C₆₇	—	2	2	no	—
41	C₂²×Q₈×C₆₇	—	2	24	no	—
42	C₂²×Q₈×C₆₇	—	2	24	no	—
43	C₂²×Q₈×C₆₇	—	2	2	no	—
44	C₂²×Q₈×C₆₇	—	2	6	no	—
45	C₂²×Q₈×C₆₇	—	2	3	no	—
46	C₂²×Q₈×C₆₇	—	2	2	no	—
47	C₂²×Q₈×C₆₇	—	2	6	no	—
48	C₂²×Q₈×C₆₇	D₄	1	2	yes	—
49	C₂²×Q₈×C₆₇	D₄	1	6	yes	—
50	C₂²×Q₈×C₆₇	C₂³	1	6	yes	—
51	C₂²×Q₈×C₆₇	C₂³	1	6	yes	—
52	C₂²×D₄×C₆₇	—	2	2	no	—
53	C₂²×D₄×C₆₇	—	2	2	no	—
54	C₂²×D₄×C₆₇	D₄	1	2	yes	—
55	C₂³×C₄×C₆₇	—	2	4	no	—
56	C₂³×C₄×C₆₇	—	2	1	no	—
57	C₂³×C₄×C₆₇	—	2	2	no	—
58	C₂³×C₄×C₆₇	—	2	1	no	—
59	C₂³×C₄×C₆₇	D₄	1	2	yes	—
60	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
61	#137×C₆₇	—	2	48	no	—
62	#137×C₆₇	C₂³	1	32	yes	complemented
63	C₂×Q₁₆×C₆₇	—	2	24	no	—
64	C₂×SD₁₆×C₆₇	—	2	24	no	—
65	C₂×M₁₆×C₆₇	—	2	6	no	—
66	C₂×M₁₆×C₆₇	C₂³	1	12	yes	—
67	C₂²×C₈×C₆₇	—	2	2	no	—
68	C₄⋊Q₈×C₆₇	—	2	24	no	—
69	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
70	C₂×C₄⋊C₄×C₆₇	—	2	24	no	—
71	C₂×C₄²×C₆₇	—	2	3	no	—
72	C₂×C₄²×C₆₇	C₂³	1	6	yes	—
73	#104×C₆₇	C₂³	1	32	yes	complemented
74	#101×C₆₇	C₂³	1	16	yes	complemented
75	C₂⁴×C₆₇	—	2	2	no	—
76	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
77	#41×C₆₇	—	2	96	no	—
78	#41×C₆₇	—	2	96	no	—
79	#41×C₆₇	—	2	32	no	—
80	#41×C₆₇	—	2	24	no	—
81	#41×C₆₇	—	2	32	no	—
82	#41×C₆₇	—	2	12	no	—
83	#41×C₆₇	—	2	12	no	—
84	#41×C₆₇	C₂×D₄	1	24	yes	—
85	#41×C₆₇	C₂⁴	1	8	yes	—
86	C₂×Q₈×C₆₇	—	2	24	no	—
87	C₂×Q₈×C₆₇	—	2	96	no	—
88	C₂×Q₈×C₆₇	—	2	32	no	—
89	C₂×Q₈×C₆₇	—	2	6	no	—
90	C₂×Q₈×C₆₇	—	2	12	no	—
91	C₂×Q₈×C₆₇	—	2	12	no	—
92	C₂×Q₈×C₆₇	—	2	12	no	—
93	C₂×Q₈×C₆₇	—	2	12	no	—
94	C₂×Q₈×C₆₇	—	2	6	no	—
95	C₂×Q₈×C₆₇	—	2	12	no	—
96	C₂×Q₈×C₆₇	—	2	12	no	—
97	C₂×Q₈×C₆₇	—	4	6	no	—
98	C₂×Q₈×C₆₇	—	4	6	no	—
99	C₂×Q₈×C₆₇	C₂×D₄	1	12	yes	—
100	C₂×Q₈×C₆₇	C₂×D₄	1	12	yes	—
101	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
102	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
103	C₂×D₄×C₆₇	—	2	24	no	—
104	C₂×D₄×C₆₇	—	2	12	no	—
105	C₂×D₄×C₆₇	—	2	12	no	—
106	C₂×D₄×C₆₇	—	2	6	no	—
107	C₂×D₄×C₆₇	C₂×D₄	1	12	yes	—
108	C₂²×C₄×C₆₇	—	2	8	no	—
109	C₂²×C₄×C₆₇	—	2	48	no	—
110	C₂²×C₄×C₆₇	—	2	6	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	2	no	—
113	C₂²×C₄×C₆₇	—	2	6	no	—
114	C₂²×C₄×C₆₇	—	2	12	no	—
115	C₂²×C₄×C₆₇	—	2	12	no	—
116	C₂²×C₄×C₆₇	—	2	6	no	—
117	C₂²×C₄×C₆₇	—	4	3	no	—
118	C₂²×C₄×C₆₇	—	4	1	no	—
119	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
120	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
121	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
122	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
124	Q₁₆×C₆₇	—	2	32	no	—
125	SD₁₆×C₆₇	—	2	32	no	—
126	M₁₆×C₆₇	—	2	12	no	—
127	M₁₆×C₆₇	C₂⁴	1	8	yes	—
128	C₂×C₈×C₆₇	—	2	12	no	—
129	C₄⋊C₄×C₆₇	—	2	32	no	—
130	C₄²×C₆₇	—	2	6	no	—
131	C₄²×C₆₇	C₂⁴	1	4	yes	—
132	C₂³×C₆₇	—	2	4	no	—
133	C₂³×C₆₇	—	2	12	no	—
134	C₂³×C₆₇	—	4	8	no	—
135	C₂³×C₆₇	#120	1	3	yes	—
136	C₂³×C₆₇	#120	1	1	yes	characteristic
137	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
138	Q₈×C₆₇	—	2	32	no	—
139	Q₈×C₆₇	—	2	12	no	—
140	Q₈×C₆₇	—	2	24	no	—
141	Q₈×C₆₇	—	2	8	no	—
142	Q₈×C₆₇	—	2	8	no	—
143	Q₈×C₆₇	—	4	12	no	—
144	Q₈×C₆₇	C₂²×D₄	1	8	yes	—
145	D₄×C₆₇	—	2	32	no	—
146	D₄×C₆₇	—	2	24	no	—
147	D₄×C₆₇	—	2	8	no	—
148	D₄×C₆₇	—	2	12	no	—
149	D₄×C₆₇	C₂²×D₄	1	8	yes	—
150	C₂×C₄×C₆₇	—	2	24	no	—
151	C₂×C₄×C₆₇	—	2	64	no	—
152	C₂×C₄×C₆₇	—	2	12	no	—
153	C₂×C₄×C₆₇	—	2	12	no	—
154	C₂×C₄×C₆₇	—	2	12	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	24	no	—
157	C₂×C₄×C₆₇	—	2	8	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	4	6	no	—
160	C₂×C₄×C₆₇	—	4	6	no	—
161	C₂×C₄×C₆₇	#120	1	6	yes	—
162	C₂×C₄×C₆₇	#120	1	6	yes	—
163	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
164	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
165	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
166	C₂×C₄×C₆₇	C₂²×D₄	1	6	yes	—
167	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
168	C₈×C₆₇	—	2	8	no	—
169	C₂²×C₆₇	—	2	6	no	—
170	C₂²×C₆₇	—	2	6	no	—
171	C₂²×C₆₇	—	2	8	no	—
172	C₂²×C₆₇	—	4	24	no	—
173	C₂²×C₆₇	#456	1	4	yes	direct product factor
174	C₂²×C₆₇	C₂×#120	1	3	yes	—
175	C₂²×C₆₇	C₂×#120	1	3	yes	—
176	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
177	C₄×C₆₇	—	2	8	no	—
178	C₄×C₆₇	—	2	8	no	—
179	C₄×C₆₇	—	2	8	no	—
180	C₄×C₆₇	—	4	4	no	—
181	C₄×C₆₇	C₂×#120	1	6	yes	—
182	C₄×C₆₇	C₂³×D₄	1	2	yes	—
183	C₂²×#456	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂×C₆₇	—	2	1	no	—
185	C₂×C₆₇	—	2	3	no	—
186	C₂×C₆₇	—	4	8	no	—
187	C₂×C₆₇	C₂×#456	1	6	yes	direct product factor
188	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
189	C₂²×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic
190	C₂²×#137	C₂×C₆₇	1	2	yes	complemented
191	C₂²×C₄⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₂×#456	C₂×C₆₇	1	24	yes	direct product factor
193	C₂²×#104	C₂×C₆₇	1	2	yes	complemented
194	C₂²×#101	C₂×C₆₇	1	1	yes	characteristic, complemented
195	C₆₇	C₂²×#456	1	1	yes	characteristic, direct product factor, Sylow
196	C₂×2₋¹⁺⁴	—	2	12	no	—
197	C₂×2₋¹⁺⁴	—	2	6	no	—
198	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	12	yes	—
199	C₂²×#41	—	2	2	no	—
200	C₂²×#41	—	2	2	no	—
201	C₂²×#41	C₂²×C₆₇	1	2	yes	—
202	C₂³×Q₈	—	2	2	no	—
203	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
204	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
205	C₂×#137	—	2	12	no	—
206	C₂×#137	C₂²×C₆₇	1	24	yes	complemented
207	C₂²×Q₁₆	—	2	2	no	—
208	C₂²×SD₁₆	—	2	2	no	—
209	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
210	C₂×C₄⋊Q₈	—	2	6	no	—
211	C₂×C₄⋊Q₈	C₂²×C₆₇	1	12	yes	complemented
212	C₂²×C₄⋊C₄	—	2	2	no	—
213	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
214	#456	C₂²×C₆₇	1	64	yes	direct product factor
215	C₂×#104	C₂²×C₆₇	1	24	yes	complemented
216	C₂×#101	C₂²×C₆₇	1	12	yes	complemented
217	2₋¹⁺⁴	—	2	48	no	—
218	2₋¹⁺⁴	—	2	48	no	—
219	2₋¹⁺⁴	—	2	24	no	—
220	2₋¹⁺⁴	C₂³×C₆₇	1	16	yes	—
221	C₂×#41	—	2	24	no	—
222	C₂×#41	—	2	24	no	—
223	C₂×#41	—	2	24	no	—
224	C₂×#41	—	2	24	no	—
225	C₂×#41	—	2	6	no	—
226	C₂×#41	—	2	6	no	—
227	C₂×#41	D₄×C₆₇	1	12	yes	—
228	C₂×#41	C₂³×C₆₇	1	12	yes	—
229	C₂²×Q₈	—	2	2	no	—
230	C₂²×Q₈	—	2	24	no	—
231	C₂²×Q₈	—	2	24	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	6	no	—
234	C₂²×Q₈	—	2	3	no	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	—	2	6	no	—
237	C₂²×Q₈	D₄×C₆₇	1	2	yes	—
238	C₂²×Q₈	D₄×C₆₇	1	6	yes	—
239	C₂²×Q₈	C₂³×C₆₇	1	6	yes	—
240	C₂²×Q₈	C₂³×C₆₇	1	6	yes	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	D₄×C₆₇	1	2	yes	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	—	2	1	no	—
248	C₂³×C₄	D₄×C₆₇	1	2	yes	—
249	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
250	#137	—	2	48	no	—
251	#137	C₂³×C₆₇	1	32	yes	complemented
252	C₂×Q₁₆	—	2	24	no	—
253	C₂×SD₁₆	—	2	24	no	—
254	C₂×M₁₆	—	2	6	no	—
255	C₂×M₁₆	C₂³×C₆₇	1	12	yes	—
256	C₂²×C₈	—	2	2	no	—
257	C₄⋊Q₈	—	2	24	no	—
258	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
259	C₂×C₄⋊C₄	—	2	24	no	—
260	C₂×C₄²	—	2	3	no	—
261	C₂×C₄²	C₂³×C₆₇	1	6	yes	—
262	#104	C₂³×C₆₇	1	32	yes	complemented
263	#101	C₂³×C₆₇	1	16	yes	complemented
264	C₂⁴	—	2	2	no	—
265	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
266	#41	—	2	96	no	—
267	#41	—	2	96	no	—
268	#41	—	2	32	no	—
269	#41	—	2	24	no	—
270	#41	—	2	32	no	—
271	#41	—	2	12	no	—
272	#41	—	2	12	no	—
273	#41	C₂×D₄×C₆₇	1	24	yes	—
274	#41	C₂⁴×C₆₇	1	8	yes	—
275	C₂×Q₈	—	2	24	no	—
276	C₂×Q₈	—	2	96	no	—
277	C₂×Q₈	—	2	32	no	—
278	C₂×Q₈	—	2	6	no	—
279	C₂×Q₈	—	2	12	no	—
280	C₂×Q₈	—	2	12	no	—
281	C₂×Q₈	—	2	12	no	—
282	C₂×Q₈	—	2	12	no	—
283	C₂×Q₈	—	2	6	no	—
284	C₂×Q₈	—	2	12	no	—
285	C₂×Q₈	—	2	12	no	—
286	C₂×Q₈	—	4	6	no	—
287	C₂×Q₈	—	4	6	no	—
288	C₂×Q₈	C₂×D₄×C₆₇	1	12	yes	—
289	C₂×Q₈	C₂×D₄×C₆₇	1	12	yes	—
290	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
291	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
292	C₂×D₄	—	2	24	no	—
293	C₂×D₄	—	2	12	no	—
294	C₂×D₄	—	2	12	no	—
295	C₂×D₄	—	2	6	no	—
296	C₂×D₄	C₂×D₄×C₆₇	1	12	yes	—
297	C₂²×C₄	—	2	48	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	6	no	—
302	C₂²×C₄	—	2	6	no	—
303	C₂²×C₄	—	2	12	no	—
304	C₂²×C₄	—	2	12	no	—
305	C₂²×C₄	—	2	6	no	—
306	C₂²×C₄	—	4	3	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
309	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
310	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
312	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
313	Q₁₆	—	2	32	no	—
314	SD₁₆	—	2	32	no	—
315	M₁₆	—	2	12	no	—
316	M₁₆	C₂⁴×C₆₇	1	8	yes	—
317	C₂×C₈	—	2	12	no	—
318	C₄⋊C₄	—	2	32	no	—
319	C₄²	—	2	6	no	—
320	C₄²	C₂⁴×C₆₇	1	4	yes	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	12	no	—
323	C₂³	—	4	8	no	—
324	C₂³	#120×C₆₇	1	3	yes	—
325	C₂³	#120×C₆₇	1	1	yes	characteristic
326	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
327	Q₈	—	2	32	no	—
328	Q₈	—	2	12	no	—
329	Q₈	—	2	24	no	—
330	Q₈	—	2	8	no	—
331	Q₈	—	2	8	no	—
332	Q₈	—	4	12	no	—
333	Q₈	C₂²×D₄×C₆₇	1	8	yes	—
334	D₄	—	2	32	no	—
335	D₄	—	2	24	no	—
336	D₄	—	2	8	no	—
337	D₄	—	2	12	no	—
338	D₄	C₂²×D₄×C₆₇	1	8	yes	—
339	C₂×C₄	—	2	64	no	—
340	C₂×C₄	—	2	24	no	—
341	C₂×C₄	—	2	12	no	—
342	C₂×C₄	—	2	12	no	—
343	C₂×C₄	—	2	12	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	24	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	4	6	no	—
349	C₂×C₄	—	4	6	no	—
350	C₂×C₄	#120×C₆₇	1	6	yes	—
351	C₂×C₄	#120×C₆₇	1	6	yes	—
352	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
353	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
354	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
355	C₂×C₄	C₂²×D₄×C₆₇	1	6	yes	—
356	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
357	C₈	—	2	8	no	—
358	C₂²	—	2	6	no	—
359	C₂²	—	2	6	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	4	24	no	—
362	C₂²	#456×C₆₇	1	4	yes	direct product factor
363	C₂²	C₂×#120×C₆₇	1	3	yes	—
364	C₂²	C₂×#120×C₆₇	1	3	yes	—
365	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
366	C₄	—	2	8	no	—
367	C₄	—	2	8	no	—
368	C₄	—	2	8	no	—
369	C₄	—	4	4	no	—
370	C₄	C₂×#120×C₆₇	1	6	yes	—
371	C₄	C₂³×D₄×C₆₇	1	2	yes	—
372	C₂	—	2	1	no	—
373	C₂	—	2	3	no	—
374	C₂	—	4	8	no	—
375	C₂	C₂×#456×C₆₇	1	6	yes	direct product factor
376	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×2₋¹⁺⁴×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#137×C₆₇	C₂	semidirect
3. C₂²×C₄⋊Q₈×C₆₇	C₂	semidirect
4. C₂×#456×C₆₇	C₂	direct (N × H)
5. C₂²×#104×C₆₇	C₂	semidirect
6. C₂²×#101×C₆₇	C₂	semidirect
17. C₂×#137×C₆₇	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
25. #456×C₆₇	C₂²	direct (N × H)
26. C₂×#104×C₆₇	C₂²	semidirect
27. C₂×#101×C₆₇	C₂²	semidirect
62. #137×C₆₇	C₂³	semidirect
69. C₄⋊Q₈×C₆₇	C₂³	semidirect
73. #104×C₆₇	C₂³	semidirect
74. #101×C₆₇	C₂³	semidirect
173. C₂²×C₆₇	#456	direct (N × H)
183. C₂²×#456	C₆₇	direct (N × H)
187. C₂×C₆₇	C₂×#456	direct (N × H)
190. C₂²×#137	C₂×C₆₇	semidirect
191. C₂²×C₄⋊Q₈	C₂×C₆₇	semidirect
192. C₂×#456	C₂×C₆₇	direct (N × H)
193. C₂²×#104	C₂×C₆₇	semidirect
194. C₂²×#101	C₂×C₆₇	semidirect
195. C₆₇	C₂²×#456	direct (N × H)
206. C₂×#137	C₂²×C₆₇	semidirect
211. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
214. #456	C₂²×C₆₇	direct (N × H)
215. C₂×#104	C₂²×C₆₇	semidirect
216. C₂×#101	C₂²×C₆₇	semidirect
251. #137	C₂³×C₆₇	semidirect
258. C₄⋊Q₈	C₂³×C₆₇	semidirect
262. #104	C₂³×C₆₇	semidirect
263. #101	C₂³×C₆₇	semidirect
362. C₂²	#456×C₆₇	direct (N × H)
375. C₂	C₂×#456×C₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×2₋¹⁺⁴×C₆₇	2
C₂²×#137×C₆₇	2
C₂²×C₄⋊Q₈×C₆₇	2
C₂×#456×C₆₇	2
C₂²×#104×C₆₇	2
C₂²×#101×C₆₇	2
C₂²×#456	67

Subgroups — C22×#456×C67 #30739632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#456×C₆₇ #30739632