Subgroups — C₂²×#448×C₆₇ #30739600

Order 17152.

5326 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	C₂⁴×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#121×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#448×C₆₇	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#103×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂²×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×Q₈×C₆₇	—	2	16	no	—
8	C₂³×Q₈×C₆₇	—	2	6	no	—
9	C₂³×Q₈×C₆₇	—	2	1	no	—
10	C₂³×Q₈×C₆₇	C₂²	1	2	yes	—
11	C₂³×Q₈×C₆₇	C₂²	1	12	yes	complemented
12	C₂³×D₄×C₆₇	—	2	1	no	—
13	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₆₇	—	2	1	no	—
15	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₆₇	—	2	16	no	—
17	C₂²×SD₁₆×C₆₇	C₂²	1	24	yes	complemented
18	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
19	C₂×#121×C₆₇	—	2	6	no	—
20	C₂×#121×C₆₇	C₂²	1	12	yes	—
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₆₇	—	2	1	no	—
23	#448×C₆₇	C₂²	1	64	yes	direct product factor
24	C₂×#103×C₆₇	C₂²	1	24	yes	complemented
25	C₂×C₂²⋊C₈×C₆₇	C₂²	1	12	yes	complemented
26	C₂⁵×C₆₇	—	2	1	no	—
27	C₂⁵×C₆₇	D₄	1	1	yes	characteristic
28	C₂²×Q₈×C₆₇	—	2	96	no	—
29	C₂²×Q₈×C₆₇	—	2	16	no	—
30	C₂²×Q₈×C₆₇	—	2	96	no	—
31	C₂²×Q₈×C₆₇	—	2	8	no	—
32	C₂²×Q₈×C₆₇	—	2	6	no	—
33	C₂²×Q₈×C₆₇	—	2	12	no	—
34	C₂²×Q₈×C₆₇	—	2	24	no	—
35	C₂²×Q₈×C₆₇	D₄	1	16	yes	complemented
36	C₂²×Q₈×C₆₇	C₂³	1	12	yes	—
37	C₂²×Q₈×C₆₇	C₂³	1	16	yes	complemented
38	C₂²×D₄×C₆₇	—	2	12	no	—
39	C₂²×D₄×C₆₇	—	2	8	no	—
40	C₂²×D₄×C₆₇	—	2	3	no	—
41	C₂²×D₄×C₆₇	—	4	8	no	—
42	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
43	C₂³×C₄×C₆₇	—	2	16	no	—
44	C₂³×C₄×C₆₇	—	2	12	no	—
45	C₂³×C₄×C₆₇	—	2	2	no	—
46	C₂³×C₄×C₆₇	—	2	8	no	—
47	C₂³×C₄×C₆₇	—	2	1	no	—
48	C₂³×C₄×C₆₇	D₄	1	6	yes	—
49	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
51	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₆₇	—	2	96	no	—
53	C₂×SD₁₆×C₆₇	C₂³	1	32	yes	complemented
54	C₂²×C₈×C₆₇	—	2	8	no	—
55	C₂²×C₈×C₆₇	C₂³	1	12	yes	—
56	#121×C₆₇	—	2	24	no	—
57	#121×C₆₇	C₂³	1	16	yes	—
58	C₂×C₄⋊C₄×C₆₇	—	2	3	no	—
59	C₂×C₄⋊C₄×C₆₇	C₂³	1	6	yes	—
60	C₂×C₂²⋊C₄×C₆₇	—	2	12	no	—
61	#103×C₆₇	C₂³	1	32	yes	complemented
62	C₂²⋊C₈×C₆₇	C₂³	1	16	yes	complemented
63	C₂⁴×C₆₇	—	2	4	no	—
64	C₂⁴×C₆₇	—	2	4	no	—
65	C₂⁴×C₆₇	—	2	6	no	—
66	C₂⁴×C₆₇	—	4	4	no	—
67	C₂⁴×C₆₇	—	4	4	no	—
68	C₂⁴×C₆₇	—	4	4	no	—
69	C₂⁴×C₆₇	SD₁₆	1	8	yes	complemented
70	C₂⁴×C₆₇	C₂×D₄	1	6	yes	—
71	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₆₇	—	2	192	no	—
73	C₂×Q₈×C₆₇	—	2	96	no	—
74	C₂×Q₈×C₆₇	—	2	64	no	—
75	C₂×Q₈×C₆₇	—	2	48	no	—
76	C₂×Q₈×C₆₇	—	2	24	no	—
77	C₂×Q₈×C₆₇	—	2	12	no	—
78	C₂×Q₈×C₆₇	—	2	16	no	—
79	C₂×Q₈×C₆₇	C₂×D₄	1	48	yes	complemented
80	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
81	C₂×D₄×C₆₇	—	2	16	no	—
82	C₂×D₄×C₆₇	—	2	24	no	—
83	C₂×D₄×C₆₇	—	2	6	no	—
84	C₂×D₄×C₆₇	—	4	48	no	—
85	C₂×D₄×C₆₇	—	4	12	no	—
86	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
87	C₂²×C₄×C₆₇	—	2	96	no	—
88	C₂²×C₄×C₆₇	—	2	16	no	—
89	C₂²×C₄×C₆₇	—	2	4	no	—
90	C₂²×C₄×C₆₇	—	2	12	no	—
91	C₂²×C₄×C₆₇	—	2	16	no	—
92	C₂²×C₄×C₆₇	—	2	24	no	—
93	C₂²×C₄×C₆₇	—	2	24	no	—
94	C₂²×C₄×C₆₇	—	2	6	no	—
95	C₂²×C₄×C₆₇	—	4	4	no	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
97	C₂²×C₄×C₆₇	C₂×D₄	1	12	yes	—
98	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
99	C₂²×C₄×C₆₇	C₂×D₄	1	8	yes	—
100	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
102	SD₁₆×C₆₇	—	2	64	no	—
103	C₂×C₈×C₆₇	—	2	24	no	—
104	C₂×C₈×C₆₇	C₂⁴	1	8	yes	—
105	C₄⋊C₄×C₆₇	—	2	6	no	—
106	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
107	C₂²⋊C₄×C₆₇	—	2	16	no	—
108	C₂³×C₆₇	—	2	12	no	—
109	C₂³×C₆₇	—	2	12	no	—
110	C₂³×C₆₇	—	2	32	no	—
111	C₂³×C₆₇	—	2	4	no	—
112	C₂³×C₆₇	—	4	12	no	—
113	C₂³×C₆₇	—	4	12	no	—
114	C₂³×C₆₇	—	4	12	no	—
115	C₂³×C₆₇	—	8	16	no	—
116	C₂³×C₆₇	#120	1	4	yes	—
117	C₂³×C₆₇	C₂×SD₁₆	1	4	yes	—
118	C₂³×C₆₇	C₂×SD₁₆	1	24	yes	complemented
119	C₂³×C₆₇	#137	1	4	yes	—
120	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
121	C₂³×C₆₇	C₂²×D₄	1	3	yes	—
122	Q₈×C₆₇	—	2	64	no	—
123	Q₈×C₆₇	—	2	48	no	—
124	Q₈×C₆₇	—	2	8	no	—
125	Q₈×C₆₇	C₂²×D₄	1	16	yes	complemented
126	D₄×C₆₇	—	2	8	no	—
127	D₄×C₆₇	—	4	32	no	—
128	D₄×C₆₇	—	4	12	no	—
129	C₂×C₄×C₆₇	—	2	64	no	—
130	C₂×C₄×C₆₇	—	2	48	no	—
131	C₂×C₄×C₆₇	—	2	12	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	24	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	2	4	no	—
136	C₂×C₄×C₆₇	—	4	12	no	—
137	C₂×C₄×C₆₇	#120	1	12	yes	—
138	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
139	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
140	C₂×C₄×C₆₇	C₂²×D₄	1	12	yes	—
141	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
142	C₈×C₆₇	—	2	8	no	—
143	C₂²×C₆₇	—	2	4	no	—
144	C₂²×C₆₇	—	2	48	no	—
145	C₂²×C₆₇	—	2	4	no	—
146	C₂²×C₆₇	—	4	4	no	—
147	C₂²×C₆₇	—	4	4	no	—
148	C₂²×C₆₇	—	4	4	no	—
149	C₂²×C₆₇	—	8	24	no	—
150	C₂²×C₆₇	#448	1	16	yes	direct product factor
151	C₂²×C₆₇	C₂×#120	1	6	yes	—
152	C₂²×C₆₇	C₂²×SD₁₆	1	6	yes	—
153	C₂²×C₆₇	C₂²×SD₁₆	1	8	yes	complemented
154	C₂²×C₆₇	C₂×#137	1	6	yes	—
155	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
156	C₄×C₆₇	—	2	16	no	—
157	C₄×C₆₇	—	2	4	no	—
158	C₄×C₆₇	—	4	4	no	—
159	C₄×C₆₇	C₂×#120	1	6	yes	—
160	C₄×C₆₇	C₂³×D₄	1	2	yes	—
161	C₂²×#448	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂×C₆₇	—	2	8	no	—
163	C₂×C₆₇	—	8	4	no	—
164	C₂×C₆₇	C₂×#448	1	12	yes	direct product factor
165	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
166	C₂×C₆₇	C₂³×SD₁₆	1	1	yes	characteristic
167	C₂×C₆₇	C₂²×#137	1	1	yes	characteristic
168	C₂⁴×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
169	C₂³×SD₁₆	C₂×C₆₇	1	2	yes	complemented
170	C₂²×#121	C₂×C₆₇	1	1	yes	characteristic
171	C₂×#448	C₂×C₆₇	1	24	yes	direct product factor
172	C₂²×#103	C₂×C₆₇	1	2	yes	complemented
173	C₂²×C₂²⋊C₈	C₂×C₆₇	1	1	yes	characteristic, complemented
174	C₆₇	C₂²×#448	1	1	yes	characteristic, direct product factor, Sylow
175	C₂³×Q₈	—	2	16	no	—
176	C₂³×Q₈	—	2	1	no	—
177	C₂³×Q₈	—	2	6	no	—
178	C₂³×Q₈	C₂²×C₆₇	1	2	yes	—
179	C₂³×Q₈	C₂²×C₆₇	1	12	yes	complemented
180	C₂³×D₄	—	2	1	no	—
181	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
182	C₂⁴×C₄	—	2	1	no	—
183	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
184	C₂²×SD₁₆	—	2	16	no	—
185	C₂²×SD₁₆	C₂²×C₆₇	1	24	yes	complemented
186	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
187	C₂×#121	—	2	6	no	—
188	C₂×#121	C₂²×C₆₇	1	12	yes	—
189	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
190	C₂²×C₂²⋊C₄	—	2	1	no	—
191	#448	C₂²×C₆₇	1	64	yes	direct product factor
192	C₂×#103	C₂²×C₆₇	1	24	yes	complemented
193	C₂×C₂²⋊C₈	C₂²×C₆₇	1	12	yes	complemented
194	C₂⁵	—	2	1	no	—
195	C₂⁵	D₄×C₆₇	1	1	yes	characteristic
196	C₂²×Q₈	—	2	96	no	—
197	C₂²×Q₈	—	2	16	no	—
198	C₂²×Q₈	—	2	96	no	—
199	C₂²×Q₈	—	2	8	no	—
200	C₂²×Q₈	—	2	6	no	—
201	C₂²×Q₈	—	2	12	no	—
202	C₂²×Q₈	—	2	24	no	—
203	C₂²×Q₈	D₄×C₆₇	1	16	yes	complemented
204	C₂²×Q₈	C₂³×C₆₇	1	12	yes	—
205	C₂²×Q₈	C₂³×C₆₇	1	16	yes	complemented
206	C₂²×D₄	—	2	12	no	—
207	C₂²×D₄	—	2	8	no	—
208	C₂²×D₄	—	2	3	no	—
209	C₂²×D₄	—	4	8	no	—
210	C₂²×D₄	C₂³×C₆₇	1	6	yes	—
211	C₂³×C₄	—	2	16	no	—
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	—	2	12	no	—
214	C₂³×C₄	—	2	8	no	—
215	C₂³×C₄	—	2	1	no	—
216	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
217	C₂³×C₄	D₄×C₆₇	1	6	yes	—
218	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
219	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
220	C₂×SD₁₆	—	2	96	no	—
221	C₂×SD₁₆	C₂³×C₆₇	1	32	yes	complemented
222	C₂²×C₈	—	2	8	no	—
223	C₂²×C₈	C₂³×C₆₇	1	12	yes	—
224	#121	—	2	24	no	—
225	#121	C₂³×C₆₇	1	16	yes	—
226	C₂×C₄⋊C₄	—	2	3	no	—
227	C₂×C₄⋊C₄	C₂³×C₆₇	1	6	yes	—
228	C₂×C₂²⋊C₄	—	2	12	no	—
229	#103	C₂³×C₆₇	1	32	yes	complemented
230	C₂²⋊C₈	C₂³×C₆₇	1	16	yes	complemented
231	C₂⁴	—	2	4	no	—
232	C₂⁴	—	2	4	no	—
233	C₂⁴	—	2	6	no	—
234	C₂⁴	—	4	4	no	—
235	C₂⁴	—	4	4	no	—
236	C₂⁴	—	4	4	no	—
237	C₂⁴	SD₁₆×C₆₇	1	8	yes	complemented
238	C₂⁴	C₂×D₄×C₆₇	1	6	yes	—
239	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
240	C₂×Q₈	—	2	192	no	—
241	C₂×Q₈	—	2	96	no	—
242	C₂×Q₈	—	2	64	no	—
243	C₂×Q₈	—	2	48	no	—
244	C₂×Q₈	—	2	24	no	—
245	C₂×Q₈	—	2	12	no	—
246	C₂×Q₈	—	2	16	no	—
247	C₂×Q₈	C₂×D₄×C₆₇	1	48	yes	complemented
248	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
249	C₂×D₄	—	2	16	no	—
250	C₂×D₄	—	2	24	no	—
251	C₂×D₄	—	2	6	no	—
252	C₂×D₄	—	4	48	no	—
253	C₂×D₄	—	4	12	no	—
254	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
255	C₂²×C₄	—	2	96	no	—
256	C₂²×C₄	—	2	16	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	12	no	—
259	C₂²×C₄	—	2	16	no	—
260	C₂²×C₄	—	2	24	no	—
261	C₂²×C₄	—	2	24	no	—
262	C₂²×C₄	—	2	6	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
265	C₂²×C₄	C₂×D₄×C₆₇	1	12	yes	—
266	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
267	C₂²×C₄	C₂×D₄×C₆₇	1	8	yes	—
268	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
269	C₂²×C₄	C₂⁴×C₆₇	1	3	yes	—
270	SD₁₆	—	2	64	no	—
271	C₂×C₈	—	2	24	no	—
272	C₂×C₈	C₂⁴×C₆₇	1	8	yes	—
273	C₄⋊C₄	—	2	6	no	—
274	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₂³	—	2	32	no	—
277	C₂³	—	2	12	no	—
278	C₂³	—	2	12	no	—
279	C₂³	—	2	4	no	—
280	C₂³	—	4	12	no	—
281	C₂³	—	4	12	no	—
282	C₂³	—	4	12	no	—
283	C₂³	—	8	16	no	—
284	C₂³	#120×C₆₇	1	4	yes	—
285	C₂³	C₂×SD₁₆×C₆₇	1	4	yes	—
286	C₂³	C₂×SD₁₆×C₆₇	1	24	yes	complemented
287	C₂³	#137×C₆₇	1	4	yes	—
288	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
289	C₂³	C₂²×D₄×C₆₇	1	3	yes	—
290	Q₈	—	2	64	no	—
291	Q₈	—	2	48	no	—
292	Q₈	—	2	8	no	—
293	Q₈	C₂²×D₄×C₆₇	1	16	yes	complemented
294	D₄	—	2	8	no	—
295	D₄	—	4	32	no	—
296	D₄	—	4	12	no	—
297	C₂×C₄	—	2	64	no	—
298	C₂×C₄	—	2	48	no	—
299	C₂×C₄	—	2	12	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	24	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	4	12	no	—
305	C₂×C₄	#120×C₆₇	1	12	yes	—
306	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
308	C₂×C₄	C₂²×D₄×C₆₇	1	12	yes	—
309	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
310	C₈	—	2	8	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	2	48	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	4	no	—
316	C₂²	—	4	4	no	—
317	C₂²	—	8	24	no	—
318	C₂²	#448×C₆₇	1	16	yes	direct product factor
319	C₂²	C₂×#120×C₆₇	1	6	yes	—
320	C₂²	C₂²×SD₁₆×C₆₇	1	6	yes	—
321	C₂²	C₂²×SD₁₆×C₆₇	1	8	yes	complemented
322	C₂²	C₂×#137×C₆₇	1	6	yes	—
323	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
324	C₄	—	2	16	no	—
325	C₄	—	2	4	no	—
326	C₄	—	4	4	no	—
327	C₄	C₂×#120×C₆₇	1	6	yes	—
328	C₄	C₂³×D₄×C₆₇	1	2	yes	—
329	C₂	—	2	8	no	—
330	C₂	—	8	4	no	—
331	C₂	C₂×#448×C₆₇	1	12	yes	direct product factor
332	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
333	C₂	C₂³×SD₁₆×C₆₇	1	1	yes	characteristic
334	C₂	C₂²×#137×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂²×#121×C₆₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Q₈×C₆₇	C₂	semidirect
2. C₂³×SD₁₆×C₆₇	C₂	semidirect
4. C₂×#448×C₆₇	C₂	direct (N × H)
5. C₂²×#103×C₆₇	C₂	semidirect
6. C₂²×C₂²⋊C₈×C₆₇	C₂	semidirect
11. C₂³×Q₈×C₆₇	C₂²	semidirect
17. C₂²×SD₁₆×C₆₇	C₂²	semidirect
23. #448×C₆₇	C₂²	direct (N × H)
24. C₂×#103×C₆₇	C₂²	semidirect
25. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
35. C₂²×Q₈×C₆₇	D₄	semidirect
37. C₂²×Q₈×C₆₇	C₂³	semidirect
53. C₂×SD₁₆×C₆₇	C₂³	semidirect
61. #103×C₆₇	C₂³	semidirect
62. C₂²⋊C₈×C₆₇	C₂³	semidirect
69. C₂⁴×C₆₇	SD₁₆	semidirect
79. C₂×Q₈×C₆₇	C₂×D₄	semidirect
118. C₂³×C₆₇	C₂×SD₁₆	semidirect
125. Q₈×C₆₇	C₂²×D₄	semidirect
150. C₂²×C₆₇	#448	direct (N × H)
153. C₂²×C₆₇	C₂²×SD₁₆	semidirect
161. C₂²×#448	C₆₇	direct (N × H)
164. C₂×C₆₇	C₂×#448	direct (N × H)
168. C₂⁴×Q₈	C₂×C₆₇	semidirect
169. C₂³×SD₁₆	C₂×C₆₇	semidirect
171. C₂×#448	C₂×C₆₇	direct (N × H)
172. C₂²×#103	C₂×C₆₇	semidirect
173. C₂²×C₂²⋊C₈	C₂×C₆₇	semidirect
174. C₆₇	C₂²×#448	direct (N × H)
179. C₂³×Q₈	C₂²×C₆₇	semidirect
185. C₂²×SD₁₆	C₂²×C₆₇	semidirect
191. #448	C₂²×C₆₇	direct (N × H)
192. C₂×#103	C₂²×C₆₇	semidirect
193. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
203. C₂²×Q₈	D₄×C₆₇	semidirect
205. C₂²×Q₈	C₂³×C₆₇	semidirect
221. C₂×SD₁₆	C₂³×C₆₇	semidirect
229. #103	C₂³×C₆₇	semidirect
230. C₂²⋊C₈	C₂³×C₆₇	semidirect
237. C₂⁴	SD₁₆×C₆₇	semidirect
247. C₂×Q₈	C₂×D₄×C₆₇	semidirect
286. C₂³	C₂×SD₁₆×C₆₇	semidirect
293. Q₈	C₂²×D₄×C₆₇	semidirect
318. C₂²	#448×C₆₇	direct (N × H)
321. C₂²	C₂²×SD₁₆×C₆₇	semidirect
331. C₂	C₂×#448×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
C₂⁴×Q₈×C₆₇	2
C₂³×SD₁₆×C₆₇	2
C₂²×#121×C₆₇	2
C₂×#448×C₆₇	2
C₂²×#103×C₆₇	2
C₂²×C₂²⋊C₈×C₆₇	2
C₂²×#448	67

Subgroups — C22×#448×C67 #30739600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#448×C₆₇ #30739600