Subgroups — C₂²×#394×C₆₇ #30713784

Order 17152.

8798 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂³×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#394×C₆₇	C₂	1	24	yes	maximal, direct product factor
6	C₂²×#95×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₆₇	C₂²	1	2	yes	—
8	C₂³×D₄×C₆₇	—	2	16	no	—
9	C₂³×D₄×C₆₇	—	2	8	no	—
10	C₂³×D₄×C₆₇	C₂²	1	12	yes	—
11	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₆₇	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₆₇	C₂²	1	12	yes	complemented
17	C₂²×C₂²⋊C₄×C₆₇	—	2	16	no	—
18	C₂²×C₂²⋊C₄×C₆₇	—	2	16	no	—
19	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	24	yes	complemented
20	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	24	yes	complemented
21	#394×C₆₇	C₂²	1	64	yes	direct product factor
22	C₂×#95×C₆₇	C₂²	1	12	yes	complemented
23	C₂⁵×C₆₇	—	2	8	no	—
24	C₂⁵×C₆₇	—	2	8	no	—
25	C₂⁵×C₆₇	—	2	8	no	—
26	C₂⁵×C₆₇	—	2	8	no	—
27	C₂⁵×C₆₇	—	2	8	no	—
28	C₂⁵×C₆₇	—	2	8	no	—
29	C₂⁵×C₆₇	D₄	1	16	yes	—
30	C₂⁵×C₆₇	C₂³	1	12	yes	—
31	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
32	C₂²×D₄×C₆₇	—	2	128	no	—
33	C₂²×D₄×C₆₇	—	2	96	no	—
34	C₂²×D₄×C₆₇	—	2	48	no	—
35	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
36	C₂³×C₄×C₆₇	—	2	4	no	—
37	C₂³×C₄×C₆₇	—	2	8	no	—
38	C₂³×C₄×C₆₇	—	2	4	no	—
39	C₂³×C₄×C₆₇	—	2	8	no	—
40	C₂³×C₄×C₆₇	—	2	8	no	—
41	C₂³×C₄×C₆₇	—	2	8	no	—
42	C₂³×C₄×C₆₇	—	2	4	no	—
43	C₂³×C₄×C₆₇	—	2	8	no	—
44	C₂³×C₄×C₆₇	D₄	1	8	yes	—
45	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
46	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	12	yes	—
48	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
49	C₂³×C₄×C₆₇	C₂³	1	6	yes	—
50	C₂×C₄⋊C₄×C₆₇	—	2	48	no	—
51	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
52	C₂×C₂²⋊C₄×C₆₇	—	2	96	no	—
53	C₂×C₂²⋊C₄×C₆₇	—	2	96	no	—
54	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
55	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
56	#95×C₆₇	C₂³	1	16	yes	complemented
57	C₂⁴×C₆₇	—	2	64	no	—
58	C₂⁴×C₆₇	—	2	64	no	—
59	C₂⁴×C₆₇	—	2	64	no	—
60	C₂⁴×C₆₇	—	2	24	no	—
61	C₂⁴×C₆₇	—	2	24	no	—
62	C₂⁴×C₆₇	—	2	24	no	—
63	C₂⁴×C₆₇	—	2	24	no	—
64	C₂⁴×C₆₇	—	2	24	no	—
65	C₂⁴×C₆₇	—	2	24	no	—
66	C₂⁴×C₆₇	—	4	32	no	—
67	C₂⁴×C₆₇	—	4	32	no	—
68	C₂⁴×C₆₇	—	4	32	no	—
69	C₂⁴×C₆₇	—	4	32	no	—
70	C₂⁴×C₆₇	C₂×D₄	1	48	yes	—
71	C₂⁴×C₆₇	C₂×D₄	1	8	yes	—
72	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
73	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
74	C₂⁴×C₆₇	#41	1	4	yes	—
75	C₂⁴×C₆₇	#41	1	8	yes	—
76	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
77	C₂⁴×C₆₇	C₂⁴	1	3	yes	—
78	C₂×D₄×C₆₇	—	2	384	no	—
79	C₂×D₄×C₆₇	—	2	64	no	—
80	C₂×D₄×C₆₇	—	2	32	no	—
81	C₂²×C₄×C₆₇	—	2	32	no	—
82	C₂²×C₄×C₆₇	—	2	32	no	—
83	C₂²×C₄×C₆₇	—	2	12	no	—
84	C₂²×C₄×C₆₇	—	2	24	no	—
85	C₂²×C₄×C₆₇	—	2	12	no	—
86	C₂²×C₄×C₆₇	—	2	24	no	—
87	C₂²×C₄×C₆₇	—	2	24	no	—
88	C₂²×C₄×C₆₇	—	2	24	no	—
89	C₂²×C₄×C₆₇	—	2	12	no	—
90	C₂²×C₄×C₆₇	—	2	24	no	—
91	C₂²×C₄×C₆₇	—	4	16	no	—
92	C₂²×C₄×C₆₇	—	4	32	no	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	24	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	24	yes	complemented
95	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
98	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
99	C₄⋊C₄×C₆₇	—	2	32	no	—
100	C₂²⋊C₄×C₆₇	—	2	64	no	—
101	C₂²⋊C₄×C₆₇	—	2	64	no	—
102	C₂³×C₆₇	—	2	96	no	—
103	C₂³×C₆₇	—	2	96	no	—
104	C₂³×C₆₇	—	2	96	no	—
105	C₂³×C₆₇	—	2	8	no	—
106	C₂³×C₆₇	—	2	8	no	—
107	C₂³×C₆₇	—	2	8	no	—
108	C₂³×C₆₇	—	2	8	no	—
109	C₂³×C₆₇	—	2	8	no	—
110	C₂³×C₆₇	—	2	8	no	—
111	C₂³×C₆₇	—	4	48	no	—
112	C₂³×C₆₇	—	4	48	no	—
113	C₂³×C₆₇	—	4	48	no	—
114	C₂³×C₆₇	—	4	48	no	—
115	C₂³×C₆₇	—	4	256	no	—
116	C₂³×C₆₇	#120	1	16	yes	—
117	C₂³×C₆₇	#121	1	16	yes	—
118	C₂³×C₆₇	#121	1	32	yes	—
119	C₂³×C₆₇	#123	1	32	yes	—
120	C₂³×C₆₇	#124	1	16	yes	—
121	C₂³×C₆₇	C₂²×D₄	1	16	yes	—
122	C₂³×C₆₇	C₂²×D₄	1	12	yes	—
123	C₂³×C₆₇	C₂²×D₄	1	6	yes	—
124	C₂³×C₆₇	C₂²×D₄	1	6	yes	—
125	C₂³×C₆₇	C₂×#41	1	6	yes	—
126	C₂³×C₆₇	C₂×#41	1	12	yes	—
127	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
128	D₄×C₆₇	—	2	128	no	—
129	C₂×C₄×C₆₇	—	2	48	no	—
130	C₂×C₄×C₆₇	—	2	48	no	—
131	C₂×C₄×C₆₇	—	2	4	no	—
132	C₂×C₄×C₆₇	—	2	8	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	8	no	—
135	C₂×C₄×C₆₇	—	2	8	no	—
136	C₂×C₄×C₆₇	—	2	8	no	—
137	C₂×C₄×C₆₇	—	2	4	no	—
138	C₂×C₄×C₆₇	—	2	8	no	—
139	C₂×C₄×C₆₇	—	4	24	no	—
140	C₂×C₄×C₆₇	—	4	48	no	—
141	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	—
142	C₂×C₄×C₆₇	C₂²×D₄	1	8	yes	complemented
143	C₂²×C₆₇	—	2	16	no	—
144	C₂²×C₆₇	—	2	16	no	—
145	C₂²×C₆₇	—	2	16	no	—
146	C₂²×C₆₇	—	4	192	no	—
147	C₂²×C₆₇	—	4	8	no	—
148	C₂²×C₆₇	—	4	8	no	—
149	C₂²×C₆₇	—	4	8	no	—
150	C₂²×C₆₇	—	4	8	no	—
151	C₂²×C₆₇	#394	1	64	yes	direct product factor
152	C₂²×C₆₇	C₂×#120	1	12	yes	—
153	C₂²×C₆₇	C₂×#121	1	12	yes	—
154	C₂²×C₆₇	C₂×#121	1	24	yes	—
155	C₂²×C₆₇	C₂×#123	1	24	yes	—
156	C₂²×C₆₇	C₂×#124	1	12	yes	—
157	C₂²×C₆₇	C₂³×D₄	1	2	yes	—
158	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
159	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
160	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
161	C₂²×C₆₇	C₂²×#41	1	2	yes	—
162	C₄×C₆₇	—	2	8	no	—
163	C₄×C₆₇	—	2	8	no	—
164	C₄×C₆₇	—	4	4	no	—
165	C₄×C₆₇	—	4	8	no	—
166	C₂²×#394	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂×C₆₇	—	4	16	no	—
168	C₂×C₆₇	C₂×#394	1	24	yes	direct product factor
169	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
170	C₂×C₆₇	C₂²×#121	1	1	yes	characteristic
171	C₂×C₆₇	C₂²×#121	1	2	yes	—
172	C₂×C₆₇	C₂²×#123	1	2	yes	—
173	C₂×C₆₇	C₂²×#124	1	1	yes	characteristic
174	C₂⁴×D₄	C₂×C₆₇	1	1	yes	characteristic
175	C₂³×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
176	C₂³×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
177	C₂³×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
178	C₂×#394	C₂×C₆₇	1	24	yes	direct product factor
179	C₂²×#95	C₂×C₆₇	1	1	yes	characteristic, complemented
180	C₆₇	C₂²×#394	1	1	yes	characteristic, direct product factor, Sylow
181	C₂⁶	C₂²×C₆₇	1	2	yes	—
182	C₂³×D₄	—	2	16	no	—
183	C₂³×D₄	—	2	8	no	—
184	C₂³×D₄	C₂²×C₆₇	1	12	yes	—
185	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
186	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
187	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
188	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
189	C₂²×C₄⋊C₄	—	2	8	no	—
190	C₂²×C₄⋊C₄	C₂²×C₆₇	1	12	yes	complemented
191	C₂²×C₂²⋊C₄	—	2	16	no	—
192	C₂²×C₂²⋊C₄	—	2	16	no	—
193	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	24	yes	complemented
194	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	24	yes	complemented
195	#394	C₂²×C₆₇	1	64	yes	direct product factor
196	C₂×#95	C₂²×C₆₇	1	12	yes	complemented
197	C₂⁵	—	2	8	no	—
198	C₂⁵	—	2	8	no	—
199	C₂⁵	—	2	8	no	—
200	C₂⁵	—	2	8	no	—
201	C₂⁵	—	2	8	no	—
202	C₂⁵	—	2	8	no	—
203	C₂⁵	D₄×C₆₇	1	16	yes	—
204	C₂⁵	C₂³×C₆₇	1	12	yes	—
205	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
206	C₂²×D₄	—	2	128	no	—
207	C₂²×D₄	—	2	96	no	—
208	C₂²×D₄	—	2	48	no	—
209	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
210	C₂³×C₄	—	2	4	no	—
211	C₂³×C₄	—	2	8	no	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	—	2	8	no	—
214	C₂³×C₄	—	2	8	no	—
215	C₂³×C₄	—	2	8	no	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	—	2	8	no	—
218	C₂³×C₄	D₄×C₆₇	1	8	yes	—
219	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
220	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
221	C₂³×C₄	C₂³×C₆₇	1	12	yes	—
222	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
223	C₂³×C₄	C₂³×C₆₇	1	6	yes	—
224	C₂×C₄⋊C₄	—	2	48	no	—
225	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
226	C₂×C₂²⋊C₄	—	2	96	no	—
227	C₂×C₂²⋊C₄	—	2	96	no	—
228	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
229	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
230	#95	C₂³×C₆₇	1	16	yes	complemented
231	C₂⁴	—	2	64	no	—
232	C₂⁴	—	2	64	no	—
233	C₂⁴	—	2	64	no	—
234	C₂⁴	—	2	24	no	—
235	C₂⁴	—	2	24	no	—
236	C₂⁴	—	2	24	no	—
237	C₂⁴	—	2	24	no	—
238	C₂⁴	—	2	24	no	—
239	C₂⁴	—	2	24	no	—
240	C₂⁴	—	4	32	no	—
241	C₂⁴	—	4	32	no	—
242	C₂⁴	—	4	32	no	—
243	C₂⁴	—	4	32	no	—
244	C₂⁴	C₂×D₄×C₆₇	1	48	yes	—
245	C₂⁴	C₂×D₄×C₆₇	1	8	yes	—
246	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
247	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
248	C₂⁴	#41×C₆₇	1	4	yes	—
249	C₂⁴	#41×C₆₇	1	8	yes	—
250	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
251	C₂⁴	C₂⁴×C₆₇	1	3	yes	—
252	C₂×D₄	—	2	384	no	—
253	C₂×D₄	—	2	64	no	—
254	C₂×D₄	—	2	32	no	—
255	C₂²×C₄	—	2	32	no	—
256	C₂²×C₄	—	2	32	no	—
257	C₂²×C₄	—	2	12	no	—
258	C₂²×C₄	—	2	24	no	—
259	C₂²×C₄	—	2	12	no	—
260	C₂²×C₄	—	2	24	no	—
261	C₂²×C₄	—	2	24	no	—
262	C₂²×C₄	—	2	24	no	—
263	C₂²×C₄	—	2	12	no	—
264	C₂²×C₄	—	2	24	no	—
265	C₂²×C₄	—	4	16	no	—
266	C₂²×C₄	—	4	32	no	—
267	C₂²×C₄	C₂×D₄×C₆₇	1	24	yes	—
268	C₂²×C₄	C₂×D₄×C₆₇	1	24	yes	complemented
269	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
271	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
273	C₄⋊C₄	—	2	32	no	—
274	C₂²⋊C₄	—	2	64	no	—
275	C₂²⋊C₄	—	2	64	no	—
276	C₂³	—	2	96	no	—
277	C₂³	—	2	96	no	—
278	C₂³	—	2	96	no	—
279	C₂³	—	2	8	no	—
280	C₂³	—	2	8	no	—
281	C₂³	—	2	8	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	8	no	—
284	C₂³	—	2	8	no	—
285	C₂³	—	4	48	no	—
286	C₂³	—	4	48	no	—
287	C₂³	—	4	48	no	—
288	C₂³	—	4	48	no	—
289	C₂³	—	4	256	no	—
290	C₂³	#120×C₆₇	1	16	yes	—
291	C₂³	#121×C₆₇	1	16	yes	—
292	C₂³	#121×C₆₇	1	32	yes	—
293	C₂³	#123×C₆₇	1	32	yes	—
294	C₂³	#124×C₆₇	1	16	yes	—
295	C₂³	C₂²×D₄×C₆₇	1	16	yes	—
296	C₂³	C₂²×D₄×C₆₇	1	12	yes	—
297	C₂³	C₂²×D₄×C₆₇	1	6	yes	—
298	C₂³	C₂²×D₄×C₆₇	1	6	yes	—
299	C₂³	C₂×#41×C₆₇	1	6	yes	—
300	C₂³	C₂×#41×C₆₇	1	12	yes	—
301	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
302	D₄	—	2	128	no	—
303	C₂×C₄	—	2	48	no	—
304	C₂×C₄	—	2	48	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	4	24	no	—
314	C₂×C₄	—	4	48	no	—
315	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	—
316	C₂×C₄	C₂²×D₄×C₆₇	1	8	yes	complemented
317	C₂²	—	2	16	no	—
318	C₂²	—	2	16	no	—
319	C₂²	—	2	16	no	—
320	C₂²	—	4	192	no	—
321	C₂²	—	4	8	no	—
322	C₂²	—	4	8	no	—
323	C₂²	—	4	8	no	—
324	C₂²	—	4	8	no	—
325	C₂²	#394×C₆₇	1	64	yes	direct product factor
326	C₂²	C₂×#120×C₆₇	1	12	yes	—
327	C₂²	C₂×#121×C₆₇	1	12	yes	—
328	C₂²	C₂×#121×C₆₇	1	24	yes	—
329	C₂²	C₂×#123×C₆₇	1	24	yes	—
330	C₂²	C₂×#124×C₆₇	1	12	yes	—
331	C₂²	C₂³×D₄×C₆₇	1	2	yes	—
332	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
333	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
334	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
335	C₂²	C₂²×#41×C₆₇	1	2	yes	—
336	C₄	—	2	8	no	—
337	C₄	—	2	8	no	—
338	C₄	—	4	4	no	—
339	C₄	—	4	8	no	—
340	C₂	—	4	16	no	—
341	C₂	C₂×#394×C₆₇	1	24	yes	direct product factor
342	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
343	C₂	C₂²×#121×C₆₇	1	1	yes	characteristic
344	C₂	C₂²×#121×C₆₇	1	2	yes	—
345	C₂	C₂²×#123×C₆₇	1	2	yes	—
346	C₂	C₂²×#124×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊C₄×C₆₇	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₆₇	C₂	semidirect
4. C₂³×C₂²⋊C₄×C₆₇	C₂	semidirect
5. C₂×#394×C₆₇	C₂	direct (N × H)
6. C₂²×#95×C₆₇	C₂	semidirect
16. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
19. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
21. #394×C₆₇	C₂²	direct (N × H)
22. C₂×#95×C₆₇	C₂²	semidirect
45. C₂³×C₄×C₆₇	D₄	semidirect
51. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
54. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
55. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
56. #95×C₆₇	C₂³	semidirect
94. C₂²×C₄×C₆₇	C₂×D₄	semidirect
142. C₂×C₄×C₆₇	C₂²×D₄	semidirect
151. C₂²×C₆₇	#394	direct (N × H)
166. C₂²×#394	C₆₇	direct (N × H)
168. C₂×C₆₇	C₂×#394	direct (N × H)
175. C₂³×C₄⋊C₄	C₂×C₆₇	semidirect
176. C₂³×C₂²⋊C₄	C₂×C₆₇	semidirect
177. C₂³×C₂²⋊C₄	C₂×C₆₇	semidirect
178. C₂×#394	C₂×C₆₇	direct (N × H)
179. C₂²×#95	C₂×C₆₇	semidirect
180. C₆₇	C₂²×#394	direct (N × H)
190. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
193. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
194. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
195. #394	C₂²×C₆₇	direct (N × H)
196. C₂×#95	C₂²×C₆₇	semidirect
219. C₂³×C₄	D₄×C₆₇	semidirect
225. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
228. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
229. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
230. #95	C₂³×C₆₇	semidirect
268. C₂²×C₄	C₂×D₄×C₆₇	semidirect
316. C₂×C₄	C₂²×D₄×C₆₇	semidirect
325. C₂²	#394×C₆₇	direct (N × H)
341. C₂	C₂×#394×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×D₄×C₆₇	2
C₂³×C₄⋊C₄×C₆₇	2
C₂³×C₂²⋊C₄×C₆₇	2
C₂×#394×C₆₇	2
C₂²×#95×C₆₇	2
C₂²×#394	67

Subgroups — C22×#394×C67 #30713784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#394×C₆₇ #30713784