Subgroups — C₂²×#444×C₆₇ #30739429

Order 17152.

2710 conjugacy classes of subgroups.

The subgroup lattice has 300 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×#444×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×#97×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	#444×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×#97×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	2	no	—
33	C₂³×C₄×C₆₇	—	2	1	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	6	yes	—
51	C₂²×C₈×C₆₇	D₄	1	2	yes	—
52	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
53	C₂²×C₈×C₆₇	C₂³	1	6	yes	—
54	C₂×C₄²×C₆₇	—	2	3	no	—
55	C₂×C₄²×C₆₇	C₂³	1	6	yes	—
56	#108×C₆₇	C₂³	1	16	yes	complemented
57	#104×C₆₇	C₂³	1	32	yes	complemented
58	#97×C₆₇	C₂³	1	16	yes	complemented
59	C₂⁴×C₆₇	—	2	2	no	—
60	C₂⁴×C₆₇	#41	1	1	yes	characteristic
61	#41×C₆₇	—	2	24	no	—
62	#41×C₆₇	—	2	12	no	—
63	#41×C₆₇	—	2	12	no	—
64	#41×C₆₇	C₂²×C₄	1	24	yes	—
65	#41×C₆₇	C₂⁴	1	8	yes	—
66	C₂×Q₈×C₆₇	—	2	6	no	—
67	C₂×Q₈×C₆₇	C₂²×C₄	1	12	yes	—
68	C₂×D₄×C₆₇	—	2	12	no	—
69	C₂×D₄×C₆₇	—	2	12	no	—
70	C₂×D₄×C₆₇	—	2	6	no	—
71	C₂×D₄×C₆₇	C₂²×C₄	1	12	yes	—
72	C₂²×C₄×C₆₇	—	2	2	no	—
73	C₂²×C₄×C₆₇	—	2	12	no	—
74	C₂²×C₄×C₆₇	—	2	12	no	—
75	C₂²×C₄×C₆₇	—	2	6	no	—
76	C₂²×C₄×C₆₇	—	4	4	no	—
77	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₂²×C₄	1	3	yes	—
79	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
80	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	#41	1	3	yes	—
82	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
83	Q₁₆×C₆₇	C₂²×C₄	1	16	yes	complemented
84	SD₁₆×C₆₇	C₂²×C₄	1	32	yes	complemented
85	D₈×C₆₇	C₂²×C₄	1	16	yes	complemented
86	M₁₆×C₆₇	—	2	12	no	—
87	M₁₆×C₆₇	—	2	32	no	—
88	M₁₆×C₆₇	C₂⁴	1	8	yes	—
89	C₂×C₈×C₆₇	—	2	12	no	—
90	C₂×C₈×C₆₇	—	2	32	no	—
91	C₂×C₈×C₆₇	C₂²×C₄	1	6	yes	—
92	C₂×C₈×C₆₇	C₂²×C₄	1	6	yes	—
93	C₂×C₈×C₆₇	C₂²×C₄	1	12	yes	—
94	C₂×C₈×C₆₇	C₂×D₄	1	12	yes	—
95	C₂×C₈×C₆₇	C₂×D₄	1	12	yes	—
96	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
97	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
98	C₄²×C₆₇	—	2	6	no	—
99	C₄²×C₆₇	C₂⁴	1	4	yes	—
100	C₂³×C₆₇	—	2	4	no	—
101	C₂³×C₆₇	—	2	12	no	—
102	C₂³×C₆₇	—	4	8	no	—
103	C₂³×C₆₇	C₄×D₄	1	3	yes	—
104	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
105	C₂³×C₆₇	C₂×#41	1	3	yes	—
106	Q₈×C₆₇	—	2	12	no	—
107	Q₈×C₆₇	C₂³×C₄	1	8	yes	—
108	D₄×C₆₇	—	2	24	no	—
109	D₄×C₆₇	—	2	8	no	—
110	D₄×C₆₇	—	2	12	no	—
111	D₄×C₆₇	C₂³×C₄	1	8	yes	—
112	C₂×C₄×C₆₇	—	2	12	no	—
113	C₂×C₄×C₆₇	—	2	24	no	—
114	C₂×C₄×C₆₇	—	2	8	no	—
115	C₂×C₄×C₆₇	—	2	4	no	—
116	C₂×C₄×C₆₇	—	4	12	no	—
117	C₂×C₄×C₆₇	C₄×D₄	1	3	yes	—
118	C₂×C₄×C₆₇	C₄×D₄	1	3	yes	—
119	C₂×C₄×C₆₇	C₄×D₄	1	6	yes	—
120	C₂×C₄×C₆₇	C₂³×C₄	1	3	yes	—
121	C₂×C₄×C₆₇	C₂³×C₄	1	3	yes	—
122	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
123	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
124	C₂×C₄×C₆₇	C₂×#41	1	3	yes	—
125	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
126	C₈×C₆₇	—	2	8	no	—
127	C₈×C₆₇	C₂³×C₄	1	4	yes	—
128	C₈×C₆₇	C₂³×C₄	1	4	yes	—
129	C₈×C₆₇	C₂²×D₄	1	8	yes	—
130	C₂²×C₆₇	—	2	6	no	—
131	C₂²×C₆₇	—	2	6	no	—
132	C₂²×C₆₇	—	2	8	no	—
133	C₂²×C₆₇	—	4	24	no	—
134	C₂²×C₆₇	#444	1	4	yes	direct product factor
135	C₂²×C₆₇	C₂×C₄×D₄	1	3	yes	—
136	C₂²×C₆₇	C₂×C₄×D₄	1	3	yes	—
137	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
138	C₄×C₆₇	—	2	8	no	—
139	C₄×C₆₇	—	4	4	no	—
140	C₄×C₆₇	C₂×C₄×D₄	1	3	yes	—
141	C₄×C₆₇	C₂×C₄×D₄	1	3	yes	—
142	C₄×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
143	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
144	C₂²×#444	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂×C₆₇	—	2	1	no	—
146	C₂×C₆₇	—	2	3	no	—
147	C₂×C₆₇	—	4	8	no	—
148	C₂×C₆₇	C₂×#444	1	6	yes	direct product factor
149	C₂×C₆₇	C₂²×C₄×D₄	1	1	yes	characteristic
150	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic
151	C₂²×#131	C₂×C₆₇	1	2	yes	complemented
152	C₂×#444	C₂×C₆₇	1	24	yes	direct product factor
153	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic, complemented
154	C₂²×#104	C₂×C₆₇	1	2	yes	complemented
155	C₂²×#97	C₂×C₆₇	1	1	yes	characteristic, complemented
156	C₆₇	C₂²×#444	1	1	yes	characteristic, direct product factor, Sylow
157	C₂²×#41	C₂²×C₆₇	1	2	yes	—
158	C₂×#135	C₄×C₆₇	1	12	yes	complemented
159	C₂×#135	C₂²×C₆₇	1	12	yes	—
160	C₂²×Q₁₆	C₄×C₆₇	1	1	yes	characteristic, complemented
161	C₂²×SD₁₆	C₄×C₆₇	1	2	yes	complemented
162	C₂²×D₈	C₄×C₆₇	1	1	yes	characteristic, complemented
163	C₂×#131	—	2	12	no	—
164	C₂×#131	C₂²×C₆₇	1	24	yes	complemented
165	C₂²×M₁₆	—	2	2	no	—
166	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
167	C₂³×C₈	—	2	2	no	—
168	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
169	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
170	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
171	#444	C₂²×C₆₇	1	64	yes	direct product factor
172	C₂×#108	C₂²×C₆₇	1	12	yes	complemented
173	C₂×#104	C₂²×C₆₇	1	24	yes	complemented
174	C₂×#97	C₂²×C₆₇	1	12	yes	complemented
175	C₂×#41	—	2	6	no	—
176	C₂×#41	—	2	6	no	—
177	C₂×#41	C₂×C₄×C₆₇	1	12	yes	—
178	C₂×#41	C₂³×C₆₇	1	12	yes	—
179	C₂²×Q₈	C₂×C₄×C₆₇	1	2	yes	—
180	C₂²×D₄	—	2	2	no	—
181	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
182	C₂³×C₄	—	2	2	no	—
183	C₂³×C₄	—	2	1	no	—
184	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
185	#135	C₂×C₄×C₆₇	1	48	yes	complemented
186	#135	C₂³×C₆₇	1	16	yes	—
187	C₂×Q₁₆	C₂×C₄×C₆₇	1	12	yes	complemented
188	C₂×SD₁₆	C₂×C₄×C₆₇	1	24	yes	complemented
189	C₂×D₈	C₂×C₄×C₆₇	1	12	yes	complemented
190	#131	—	2	48	no	—
191	#131	C₂³×C₆₇	1	32	yes	complemented
192	C₂×M₁₆	—	2	6	no	—
193	C₂×M₁₆	—	2	24	no	—
194	C₂×M₁₆	C₂³×C₆₇	1	12	yes	—
195	C₂²×C₈	—	2	2	no	—
196	C₂²×C₈	—	2	24	no	—
197	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
198	C₂²×C₈	C₂×C₄×C₆₇	1	1	yes	characteristic
199	C₂²×C₈	C₂×C₄×C₆₇	1	6	yes	—
200	C₂²×C₈	D₄×C₆₇	1	2	yes	—
201	C₂²×C₈	D₄×C₆₇	1	6	yes	—
202	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
203	C₂²×C₈	C₂³×C₆₇	1	6	yes	—
204	C₂×C₄²	—	2	3	no	—
205	C₂×C₄²	C₂³×C₆₇	1	6	yes	—
206	#108	C₂³×C₆₇	1	16	yes	complemented
207	#104	C₂³×C₆₇	1	32	yes	complemented
208	#97	C₂³×C₆₇	1	16	yes	complemented
209	C₂⁴	—	2	2	no	—
210	C₂⁴	#41×C₆₇	1	1	yes	characteristic
211	#41	—	2	24	no	—
212	#41	—	2	12	no	—
213	#41	—	2	12	no	—
214	#41	C₂²×C₄×C₆₇	1	24	yes	—
215	#41	C₂⁴×C₆₇	1	8	yes	—
216	C₂×Q₈	—	2	6	no	—
217	C₂×Q₈	C₂²×C₄×C₆₇	1	12	yes	—
218	C₂×D₄	—	2	12	no	—
219	C₂×D₄	—	2	12	no	—
220	C₂×D₄	—	2	6	no	—
221	C₂×D₄	C₂²×C₄×C₆₇	1	12	yes	—
222	C₂²×C₄	—	2	2	no	—
223	C₂²×C₄	—	2	12	no	—
224	C₂²×C₄	—	2	12	no	—
225	C₂²×C₄	—	2	6	no	—
226	C₂²×C₄	—	4	4	no	—
227	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
228	C₂²×C₄	C₂²×C₄×C₆₇	1	3	yes	—
229	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
230	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
231	C₂²×C₄	#41×C₆₇	1	3	yes	—
232	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
233	Q₁₆	C₂²×C₄×C₆₇	1	16	yes	complemented
234	SD₁₆	C₂²×C₄×C₆₇	1	32	yes	complemented
235	D₈	C₂²×C₄×C₆₇	1	16	yes	complemented
236	M₁₆	—	2	12	no	—
237	M₁₆	—	2	32	no	—
238	M₁₆	C₂⁴×C₆₇	1	8	yes	—
239	C₂×C₈	—	2	12	no	—
240	C₂×C₈	—	2	32	no	—
241	C₂×C₈	C₂²×C₄×C₆₇	1	6	yes	—
242	C₂×C₈	C₂²×C₄×C₆₇	1	6	yes	—
243	C₂×C₈	C₂²×C₄×C₆₇	1	12	yes	—
244	C₂×C₈	C₂×D₄×C₆₇	1	12	yes	—
245	C₂×C₈	C₂×D₄×C₆₇	1	12	yes	—
246	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
247	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
248	C₄²	—	2	6	no	—
249	C₄²	C₂⁴×C₆₇	1	4	yes	—
250	C₂³	—	2	4	no	—
251	C₂³	—	2	12	no	—
252	C₂³	—	4	8	no	—
253	C₂³	C₄×D₄×C₆₇	1	3	yes	—
254	C₂³	C₄×D₄×C₆₇	1	1	yes	characteristic
255	C₂³	C₂×#41×C₆₇	1	3	yes	—
256	Q₈	—	2	12	no	—
257	Q₈	C₂³×C₄×C₆₇	1	8	yes	—
258	D₄	—	2	24	no	—
259	D₄	—	2	8	no	—
260	D₄	—	2	12	no	—
261	D₄	C₂³×C₄×C₆₇	1	8	yes	—
262	C₂×C₄	—	2	12	no	—
263	C₂×C₄	—	2	24	no	—
264	C₂×C₄	—	2	8	no	—
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	4	12	no	—
267	C₂×C₄	C₄×D₄×C₆₇	1	3	yes	—
268	C₂×C₄	C₄×D₄×C₆₇	1	3	yes	—
269	C₂×C₄	C₄×D₄×C₆₇	1	6	yes	—
270	C₂×C₄	C₂³×C₄×C₆₇	1	3	yes	—
271	C₂×C₄	C₂³×C₄×C₆₇	1	3	yes	—
272	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
273	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
274	C₂×C₄	C₂×#41×C₆₇	1	3	yes	—
275	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
276	C₈	—	2	8	no	—
277	C₈	C₂³×C₄×C₆₇	1	4	yes	—
278	C₈	C₂³×C₄×C₆₇	1	4	yes	—
279	C₈	C₂²×D₄×C₆₇	1	8	yes	—
280	C₂²	—	2	6	no	—
281	C₂²	—	2	6	no	—
282	C₂²	—	2	8	no	—
283	C₂²	—	4	24	no	—
284	C₂²	#444×C₆₇	1	4	yes	direct product factor
285	C₂²	C₂×C₄×D₄×C₆₇	1	3	yes	—
286	C₂²	C₂×C₄×D₄×C₆₇	1	3	yes	—
287	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
288	C₄	—	2	8	no	—
289	C₄	—	4	4	no	—
290	C₄	C₂×C₄×D₄×C₆₇	1	3	yes	—
291	C₄	C₂×C₄×D₄×C₆₇	1	3	yes	—
292	C₄	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
293	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
294	C₂	—	2	1	no	—
295	C₂	—	2	3	no	—
296	C₂	—	4	8	no	—
297	C₂	C₂×#444×C₆₇	1	6	yes	direct product factor
298	C₂	C₂²×C₄×D₄×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₇	C₂×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×C₄×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×#444×C₆₇	C₂	direct (N × H)
4. C₂²×#108×C₆₇	C₂	semidirect
5. C₂²×#104×C₆₇	C₂	semidirect
6. C₂²×#97×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. #444×C₆₇	C₂²	direct (N × H)
22. C₂×#108×C₆₇	C₂²	semidirect
23. C₂×#104×C₆₇	C₂²	semidirect
24. C₂×#97×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
56. #108×C₆₇	C₂³	semidirect
57. #104×C₆₇	C₂³	semidirect
58. #97×C₆₇	C₂³	semidirect
83. Q₁₆×C₆₇	C₂²×C₄	semidirect
84. SD₁₆×C₆₇	C₂²×C₄	semidirect
85. D₈×C₆₇	C₂²×C₄	semidirect
134. C₂²×C₆₇	#444	direct (N × H)
144. C₂²×#444	C₆₇	direct (N × H)
148. C₂×C₆₇	C₂×#444	direct (N × H)
151. C₂²×#131	C₂×C₆₇	semidirect
152. C₂×#444	C₂×C₆₇	direct (N × H)
153. C₂²×#108	C₂×C₆₇	semidirect
154. C₂²×#104	C₂×C₆₇	semidirect
155. C₂²×#97	C₂×C₆₇	semidirect
156. C₆₇	C₂²×#444	direct (N × H)
158. C₂×#135	C₄×C₆₇	semidirect
160. C₂²×Q₁₆	C₄×C₆₇	semidirect
161. C₂²×SD₁₆	C₄×C₆₇	semidirect
162. C₂²×D₈	C₄×C₆₇	semidirect
164. C₂×#131	C₂²×C₆₇	semidirect
171. #444	C₂²×C₆₇	direct (N × H)
172. C₂×#108	C₂²×C₆₇	semidirect
173. C₂×#104	C₂²×C₆₇	semidirect
174. C₂×#97	C₂²×C₆₇	semidirect
185. #135	C₂×C₄×C₆₇	semidirect
187. C₂×Q₁₆	C₂×C₄×C₆₇	semidirect
188. C₂×SD₁₆	C₂×C₄×C₆₇	semidirect
189. C₂×D₈	C₂×C₄×C₆₇	semidirect
191. #131	C₂³×C₆₇	semidirect
206. #108	C₂³×C₆₇	semidirect
207. #104	C₂³×C₆₇	semidirect
208. #97	C₂³×C₆₇	semidirect
233. Q₁₆	C₂²×C₄×C₆₇	semidirect
234. SD₁₆	C₂²×C₄×C₆₇	semidirect
235. D₈	C₂²×C₄×C₆₇	semidirect
284. C₂²	#444×C₆₇	direct (N × H)
297. C₂	C₂×#444×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×#444×C₆₇	2
C₂²×#108×C₆₇	2
C₂²×#104×C₆₇	2
C₂²×#97×C₆₇	2
C₂²×#444	67

Subgroups — C22×#444×C67 #30739429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#444×C₆₇ #30739429