Subgroups — C₂²×#443×C₆₇ #30739428

Order 17152.

2750 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#131×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#443×C₆₇	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#104×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₆₇	C₂²	1	2	yes	—
8	C₂×#135×C₆₇	C₄	1	12	yes	complemented
9	C₂×#135×C₆₇	C₂²	1	12	yes	—
10	C₂²×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
11	C₂²×SD₁₆×C₆₇	C₄	1	2	yes	complemented
12	C₂²×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
13	C₂×#131×C₆₇	—	2	12	no	—
14	C₂×#131×C₆₇	C₂²	1	24	yes	complemented
15	C₂²×M₁₆×C₆₇	—	2	2	no	—
16	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
17	C₂³×C₈×C₆₇	—	2	2	no	—
18	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	#443×C₆₇	C₂²	1	64	yes	direct product factor
22	C₂×#108×C₆₇	C₂²	1	12	yes	complemented
23	C₂×#104×C₆₇	C₂²	1	24	yes	complemented
24	C₂×C₄×C₈×C₆₇	C₂²	1	12	yes	complemented
25	C₂×#41×C₆₇	—	2	6	no	—
26	C₂×#41×C₆₇	—	2	6	no	—
27	C₂×#41×C₆₇	C₂×C₄	1	12	yes	—
28	C₂×#41×C₆₇	C₂³	1	12	yes	—
29	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₆₇	—	2	2	no	—
31	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₆₇	—	2	1	no	—
33	C₂³×C₄×C₆₇	—	2	2	no	—
34	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
35	#135×C₆₇	C₂×C₄	1	48	yes	complemented
36	#135×C₆₇	C₂³	1	16	yes	—
37	C₂×Q₁₆×C₆₇	C₂×C₄	1	12	yes	complemented
38	C₂×SD₁₆×C₆₇	C₂×C₄	1	24	yes	complemented
39	C₂×D₈×C₆₇	C₂×C₄	1	12	yes	complemented
40	#131×C₆₇	—	2	48	no	—
41	#131×C₆₇	C₂³	1	32	yes	complemented
42	C₂×M₁₆×C₆₇	—	2	6	no	—
43	C₂×M₁₆×C₆₇	—	2	24	no	—
44	C₂×M₁₆×C₆₇	C₂³	1	12	yes	—
45	C₂²×C₈×C₆₇	—	2	2	no	—
46	C₂²×C₈×C₆₇	—	2	24	no	—
47	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₆₇	C₂×C₄	1	6	yes	—
50	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₆₇	D₄	1	6	yes	—
52	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
54	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
55	C₂×C₄²×C₆₇	—	2	3	no	—
56	C₂×C₄²×C₆₇	C₂³	1	6	yes	—
57	#108×C₆₇	C₂³	1	16	yes	complemented
58	#104×C₆₇	C₂³	1	32	yes	complemented
59	C₄×C₈×C₆₇	C₂³	1	16	yes	complemented
60	C₂⁴×C₆₇	—	2	2	no	—
61	C₂⁴×C₆₇	#41	1	1	yes	characteristic
62	#41×C₆₇	—	2	24	no	—
63	#41×C₆₇	—	2	12	no	—
64	#41×C₆₇	—	2	12	no	—
65	#41×C₆₇	C₂²×C₄	1	24	yes	—
66	#41×C₆₇	C₂⁴	1	8	yes	—
67	C₂×Q₈×C₆₇	—	2	6	no	—
68	C₂×Q₈×C₆₇	C₂²×C₄	1	12	yes	—
69	C₂×D₄×C₆₇	—	2	12	no	—
70	C₂×D₄×C₆₇	—	2	12	no	—
71	C₂×D₄×C₆₇	—	2	6	no	—
72	C₂×D₄×C₆₇	C₂²×C₄	1	12	yes	—
73	C₂²×C₄×C₆₇	—	2	8	no	—
74	C₂²×C₄×C₆₇	—	2	2	no	—
75	C₂²×C₄×C₆₇	—	2	6	no	—
76	C₂²×C₄×C₆₇	—	2	12	no	—
77	C₂²×C₄×C₆₇	—	2	12	no	—
78	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₂²×C₄	1	3	yes	—
80	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
82	C₂²×C₄×C₆₇	#41	1	3	yes	—
83	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
84	Q₁₆×C₆₇	C₂²×C₄	1	16	yes	complemented
85	SD₁₆×C₆₇	C₂²×C₄	1	32	yes	complemented
86	D₈×C₆₇	C₂²×C₄	1	16	yes	complemented
87	M₁₆×C₆₇	—	2	12	no	—
88	M₁₆×C₆₇	—	2	32	no	—
89	M₁₆×C₆₇	C₂⁴	1	8	yes	—
90	C₂×C₈×C₆₇	—	2	12	no	—
91	C₂×C₈×C₆₇	—	2	32	no	—
92	C₂×C₈×C₆₇	C₂²×C₄	1	6	yes	—
93	C₂×C₈×C₆₇	C₂²×C₄	1	6	yes	—
94	C₂×C₈×C₆₇	C₂²×C₄	1	12	yes	—
95	C₂×C₈×C₆₇	C₂×D₄	1	6	yes	—
96	C₂×C₈×C₆₇	C₂×D₄	1	6	yes	—
97	C₂×C₈×C₆₇	C₂×D₄	1	12	yes	—
98	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
99	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
100	C₄²×C₆₇	—	2	6	no	—
101	C₄²×C₆₇	C₂⁴	1	4	yes	—
102	C₂³×C₆₇	—	2	4	no	—
103	C₂³×C₆₇	—	2	12	no	—
104	C₂³×C₆₇	—	4	8	no	—
105	C₂³×C₆₇	C₄×D₄	1	3	yes	—
106	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
107	C₂³×C₆₇	C₂×#41	1	3	yes	—
108	Q₈×C₆₇	—	2	12	no	—
109	Q₈×C₆₇	C₂³×C₄	1	8	yes	—
110	D₄×C₆₇	—	2	24	no	—
111	D₄×C₆₇	—	2	8	no	—
112	D₄×C₆₇	—	2	12	no	—
113	D₄×C₆₇	C₂³×C₄	1	8	yes	—
114	C₂×C₄×C₆₇	—	2	24	no	—
115	C₂×C₄×C₆₇	—	2	12	no	—
116	C₂×C₄×C₆₇	—	2	4	no	—
117	C₂×C₄×C₆₇	—	2	24	no	—
118	C₂×C₄×C₆₇	—	2	8	no	—
119	C₂×C₄×C₆₇	C₄×D₄	1	3	yes	—
120	C₂×C₄×C₆₇	C₄×D₄	1	3	yes	—
121	C₂×C₄×C₆₇	C₄×D₄	1	6	yes	—
122	C₂×C₄×C₆₇	C₂³×C₄	1	3	yes	—
123	C₂×C₄×C₆₇	C₂³×C₄	1	3	yes	—
124	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
125	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
126	C₂×C₄×C₆₇	C₂×#41	1	3	yes	—
127	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
128	C₈×C₆₇	—	2	8	no	—
129	C₈×C₆₇	C₂³×C₄	1	4	yes	—
130	C₈×C₆₇	C₂³×C₄	1	4	yes	—
131	C₈×C₆₇	C₂²×D₄	1	4	yes	—
132	C₈×C₆₇	C₂²×D₄	1	4	yes	—
133	C₂²×C₆₇	—	2	6	no	—
134	C₂²×C₆₇	—	2	6	no	—
135	C₂²×C₆₇	—	2	8	no	—
136	C₂²×C₆₇	—	4	24	no	—
137	C₂²×C₆₇	#443	1	4	yes	direct product factor
138	C₂²×C₆₇	C₂×C₄×D₄	1	3	yes	—
139	C₂²×C₆₇	C₂×C₄×D₄	1	3	yes	—
140	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
141	C₄×C₆₇	—	2	8	no	—
142	C₄×C₆₇	—	2	8	no	—
143	C₄×C₆₇	C₂×C₄×D₄	1	3	yes	—
144	C₄×C₆₇	C₂×C₄×D₄	1	3	yes	—
145	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
146	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
147	C₂²×#443	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂×C₆₇	—	2	1	no	—
149	C₂×C₆₇	—	2	3	no	—
150	C₂×C₆₇	—	4	8	no	—
151	C₂×C₆₇	C₂×#443	1	6	yes	direct product factor
152	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
153	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic
154	C₂²×#131	C₂×C₆₇	1	2	yes	complemented
155	C₂×#443	C₂×C₆₇	1	24	yes	direct product factor
156	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic, complemented
157	C₂²×#104	C₂×C₆₇	1	2	yes	complemented
158	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
159	C₆₇	C₂²×#443	1	1	yes	characteristic, direct product factor, Sylow
160	C₂²×#41	C₂²×C₆₇	1	2	yes	—
161	C₂×#135	C₄×C₆₇	1	12	yes	complemented
162	C₂×#135	C₂²×C₆₇	1	12	yes	—
163	C₂²×Q₁₆	C₄×C₆₇	1	1	yes	characteristic, complemented
164	C₂²×SD₁₆	C₄×C₆₇	1	2	yes	complemented
165	C₂²×D₈	C₄×C₆₇	1	1	yes	characteristic, complemented
166	C₂×#131	—	2	12	no	—
167	C₂×#131	C₂²×C₆₇	1	24	yes	complemented
168	C₂²×M₁₆	—	2	2	no	—
169	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
170	C₂³×C₈	—	2	2	no	—
171	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
173	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
174	#443	C₂²×C₆₇	1	64	yes	direct product factor
175	C₂×#108	C₂²×C₆₇	1	12	yes	complemented
176	C₂×#104	C₂²×C₆₇	1	24	yes	complemented
177	C₂×C₄×C₈	C₂²×C₆₇	1	12	yes	complemented
178	C₂×#41	—	2	6	no	—
179	C₂×#41	—	2	6	no	—
180	C₂×#41	C₂×C₄×C₆₇	1	12	yes	—
181	C₂×#41	C₂³×C₆₇	1	12	yes	—
182	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
183	C₂²×D₄	—	2	2	no	—
184	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
185	C₂³×C₄	—	2	1	no	—
186	C₂³×C₄	—	2	2	no	—
187	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
188	#135	C₂×C₄×C₆₇	1	48	yes	complemented
189	#135	C₂³×C₆₇	1	16	yes	—
190	C₂×Q₁₆	C₂×C₄×C₆₇	1	12	yes	complemented
191	C₂×SD₁₆	C₂×C₄×C₆₇	1	24	yes	complemented
192	C₂×D₈	C₂×C₄×C₆₇	1	12	yes	complemented
193	#131	—	2	48	no	—
194	#131	C₂³×C₆₇	1	32	yes	complemented
195	C₂×M₁₆	—	2	6	no	—
196	C₂×M₁₆	—	2	24	no	—
197	C₂×M₁₆	C₂³×C₆₇	1	12	yes	—
198	C₂²×C₈	—	2	2	no	—
199	C₂²×C₈	—	2	24	no	—
200	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
201	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
202	C₂²×C₈	C₂×C₄×C₆₇	1	6	yes	—
203	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
204	C₂²×C₈	D₄×C₆₇	1	6	yes	—
205	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
206	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
207	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
208	C₂×C₄²	—	2	3	no	—
209	C₂×C₄²	C₂³×C₆₇	1	6	yes	—
210	#108	C₂³×C₆₇	1	16	yes	complemented
211	#104	C₂³×C₆₇	1	32	yes	complemented
212	C₄×C₈	C₂³×C₆₇	1	16	yes	complemented
213	C₂⁴	—	2	2	no	—
214	C₂⁴	#41×C₆₇	1	1	yes	characteristic
215	#41	—	2	24	no	—
216	#41	—	2	12	no	—
217	#41	—	2	12	no	—
218	#41	C₂²×C₄×C₆₇	1	24	yes	—
219	#41	C₂⁴×C₆₇	1	8	yes	—
220	C₂×Q₈	—	2	6	no	—
221	C₂×Q₈	C₂²×C₄×C₆₇	1	12	yes	—
222	C₂×D₄	—	2	12	no	—
223	C₂×D₄	—	2	12	no	—
224	C₂×D₄	—	2	6	no	—
225	C₂×D₄	C₂²×C₄×C₆₇	1	12	yes	—
226	C₂²×C₄	—	2	8	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	6	no	—
229	C₂²×C₄	—	2	12	no	—
230	C₂²×C₄	—	2	12	no	—
231	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
232	C₂²×C₄	C₂²×C₄×C₆₇	1	3	yes	—
233	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
235	C₂²×C₄	#41×C₆₇	1	3	yes	—
236	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
237	Q₁₆	C₂²×C₄×C₆₇	1	16	yes	complemented
238	SD₁₆	C₂²×C₄×C₆₇	1	32	yes	complemented
239	D₈	C₂²×C₄×C₆₇	1	16	yes	complemented
240	M₁₆	—	2	12	no	—
241	M₁₆	—	2	32	no	—
242	M₁₆	C₂⁴×C₆₇	1	8	yes	—
243	C₂×C₈	—	2	12	no	—
244	C₂×C₈	—	2	32	no	—
245	C₂×C₈	C₂²×C₄×C₆₇	1	6	yes	—
246	C₂×C₈	C₂²×C₄×C₆₇	1	6	yes	—
247	C₂×C₈	C₂²×C₄×C₆₇	1	12	yes	—
248	C₂×C₈	C₂×D₄×C₆₇	1	6	yes	—
249	C₂×C₈	C₂×D₄×C₆₇	1	6	yes	—
250	C₂×C₈	C₂×D₄×C₆₇	1	12	yes	—
251	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
252	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
253	C₄²	—	2	6	no	—
254	C₄²	C₂⁴×C₆₇	1	4	yes	—
255	C₂³	—	2	4	no	—
256	C₂³	—	2	12	no	—
257	C₂³	—	4	8	no	—
258	C₂³	C₄×D₄×C₆₇	1	3	yes	—
259	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
260	C₂³	C₂×#41×C₆₇	1	3	yes	—
261	Q₈	—	2	12	no	—
262	Q₈	C₂³×C₄×C₆₇	1	8	yes	—
263	D₄	—	2	24	no	—
264	D₄	—	2	8	no	—
265	D₄	—	2	12	no	—
266	D₄	C₂³×C₄×C₆₇	1	8	yes	—
267	C₂×C₄	—	2	24	no	—
268	C₂×C₄	—	2	12	no	—
269	C₂×C₄	—	2	4	no	—
270	C₂×C₄	—	2	24	no	—
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	C₄×D₄×C₆₇	1	3	yes	—
273	C₂×C₄	C₄×D₄×C₆₇	1	3	yes	—
274	C₂×C₄	C₄×D₄×C₆₇	1	6	yes	—
275	C₂×C₄	C₂³×C₄×C₆₇	1	3	yes	—
276	C₂×C₄	C₂³×C₄×C₆₇	1	3	yes	—
277	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
278	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
279	C₂×C₄	C₂×#41×C₆₇	1	3	yes	—
280	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
281	C₈	—	2	8	no	—
282	C₈	C₂³×C₄×C₆₇	1	4	yes	—
283	C₈	C₂³×C₄×C₆₇	1	4	yes	—
284	C₈	C₂²×D₄×C₆₇	1	4	yes	—
285	C₈	C₂²×D₄×C₆₇	1	4	yes	—
286	C₂²	—	2	6	no	—
287	C₂²	—	2	6	no	—
288	C₂²	—	2	8	no	—
289	C₂²	—	4	24	no	—
290	C₂²	#443×C₆₇	1	4	yes	direct product factor
291	C₂²	C₂×C₄×D₄×C₆₇	1	3	yes	—
292	C₂²	C₂×C₄×D₄×C₆₇	1	3	yes	—
293	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
294	C₄	—	2	8	no	—
295	C₄	—	2	8	no	—
296	C₄	C₂×C₄×D₄×C₆₇	1	3	yes	—
297	C₄	C₂×C₄×D₄×C₆₇	1	3	yes	—
298	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
299	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
300	C₂	—	2	1	no	—
301	C₂	—	2	3	no	—
302	C₂	—	4	8	no	—
303	C₂	C₂×#443×C₆₇	1	6	yes	direct product factor
304	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₆₇	D₄
commutator	C₄	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂³×C₆₇	C₄×D₄
prime radical	C₂²×#135×C₆₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₆₇ ◁ C₂³×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#131×C₆₇	C₂	semidirect
3. C₂×#443×C₆₇	C₂	direct (N × H)
4. C₂²×#108×C₆₇	C₂	semidirect
5. C₂²×#104×C₆₇	C₂	semidirect
6. C₂²×C₄×C₈×C₆₇	C₂	semidirect
8. C₂×#135×C₆₇	C₄	semidirect
10. C₂²×Q₁₆×C₆₇	C₄	semidirect
11. C₂²×SD₁₆×C₆₇	C₄	semidirect
12. C₂²×D₈×C₆₇	C₄	semidirect
14. C₂×#131×C₆₇	C₂²	semidirect
21. #443×C₆₇	C₂²	direct (N × H)
22. C₂×#108×C₆₇	C₂²	semidirect
23. C₂×#104×C₆₇	C₂²	semidirect
24. C₂×C₄×C₈×C₆₇	C₂²	semidirect
35. #135×C₆₇	C₂×C₄	semidirect
37. C₂×Q₁₆×C₆₇	C₂×C₄	semidirect
38. C₂×SD₁₆×C₆₇	C₂×C₄	semidirect
39. C₂×D₈×C₆₇	C₂×C₄	semidirect
41. #131×C₆₇	C₂³	semidirect
57. #108×C₆₇	C₂³	semidirect
58. #104×C₆₇	C₂³	semidirect
59. C₄×C₈×C₆₇	C₂³	semidirect
84. Q₁₆×C₆₇	C₂²×C₄	semidirect
85. SD₁₆×C₆₇	C₂²×C₄	semidirect
86. D₈×C₆₇	C₂²×C₄	semidirect
137. C₂²×C₆₇	#443	direct (N × H)
147. C₂²×#443	C₆₇	direct (N × H)
151. C₂×C₆₇	C₂×#443	direct (N × H)
154. C₂²×#131	C₂×C₆₇	semidirect
155. C₂×#443	C₂×C₆₇	direct (N × H)
156. C₂²×#108	C₂×C₆₇	semidirect
157. C₂²×#104	C₂×C₆₇	semidirect
158. C₂²×C₄×C₈	C₂×C₆₇	semidirect
159. C₆₇	C₂²×#443	direct (N × H)
161. C₂×#135	C₄×C₆₇	semidirect
163. C₂²×Q₁₆	C₄×C₆₇	semidirect
164. C₂²×SD₁₆	C₄×C₆₇	semidirect
165. C₂²×D₈	C₄×C₆₇	semidirect
167. C₂×#131	C₂²×C₆₇	semidirect
174. #443	C₂²×C₆₇	direct (N × H)
175. C₂×#108	C₂²×C₆₇	semidirect
176. C₂×#104	C₂²×C₆₇	semidirect
177. C₂×C₄×C₈	C₂²×C₆₇	semidirect
188. #135	C₂×C₄×C₆₇	semidirect
190. C₂×Q₁₆	C₂×C₄×C₆₇	semidirect
191. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
192. C₂×D₈	C₂×C₄×C₆₇	semidirect
194. #131	C₂³×C₆₇	semidirect
210. #108	C₂³×C₆₇	semidirect
211. #104	C₂³×C₆₇	semidirect
212. C₄×C₈	C₂³×C₆₇	semidirect
237. Q₁₆	C₂²×C₄×C₆₇	semidirect
238. SD₁₆	C₂²×C₄×C₆₇	semidirect
239. D₈	C₂²×C₄×C₆₇	semidirect
290. C₂²	#443×C₆₇	direct (N × H)
303. C₂	C₂×#443×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×#135×C₆₇	2
C₂²×#131×C₆₇	2
C₂×#443×C₆₇	2
C₂²×#108×C₆₇	2
C₂²×#104×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₂²×#443	67

Subgroups — C22×#443×C67 #30739428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#443×C₆₇ #30739428