Subgroups — C₆₇×#32884 #30712135

Order 17152.

3994 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#449×C₆₇	C₂	1	3	yes	maximal, complemented
3	C₂×#447×C₆₇	C₂	1	3	yes	maximal, complemented
4	C₆₇×#2615	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1788	C₂	1	3	yes	maximal, complemented
6	C₆₇×#1786	C₂	1	3	yes	maximal, complemented
7	C₆₇×#1780	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(5,𝔽₂)×C₆₇	—	2	12	no	—
9	C₂×H(5,𝔽₂)×C₆₇	—	2	12	no	—
10	C₂²×#41×C₆₇	—	2	1	no	—
11	C₂²×#41×C₆₇	C₂²	1	3	yes	—
12	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₆₇	—	2	3	no	—
14	C₂³×D₄×C₆₇	C₂²	1	3	yes	—
15	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
16	C₂²×D₈×C₆₇	C₂²	1	3	yes	complemented
17	C₂×#121×C₆₇	C₂²	1	3	yes	complemented
18	#449×C₆₇	—	2	12	no	—
19	#447×C₆₇	—	2	12	no	—
20	C₂×#103×C₆₇	C₂²	1	3	yes	complemented
21	C₂×#102×C₆₇	C₂²	1	3	yes	complemented
22	C₂×#102×C₆₇	C₂²	1	6	yes	complemented
23	C₂×C₂²⋊C₈×C₆₇	C₂²	1	3	yes	complemented
24	C₂×C₂²⋊C₈×C₆₇	C₂²	1	3	yes	complemented
25	#393×C₆₇	—	2	1	no	—
26	#392×C₆₇	—	2	3	no	—
27	#380×C₆₇	C₂²	1	3	yes	complemented
28	C₂⁵×C₆₇	—	2	3	no	—
29	H(5,𝔽₂)×C₆₇	—	2	32	no	—
30	H(5,𝔽₂)×C₆₇	—	2	96	no	—
31	C₂×#41×C₆₇	—	2	24	no	—
32	C₂×#41×C₆₇	—	2	12	no	—
33	C₂×#41×C₆₇	—	2	12	no	—
34	C₂×#41×C₆₇	—	2	6	no	—
35	C₂×#41×C₆₇	—	2	6	no	—
36	C₂×#41×C₆₇	—	2	6	no	—
37	C₂×#41×C₆₇	D₄	1	12	yes	complemented
38	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₆₇	—	2	48	no	—
41	C₂²×D₄×C₆₇	—	2	24	no	—
42	C₂²×D₄×C₆₇	—	2	3	no	—
43	C₂²×D₄×C₆₇	—	2	12	no	—
44	C₂²×D₄×C₆₇	—	2	12	no	—
45	C₂²×D₄×C₆₇	—	2	3	no	—
46	C₂²×D₄×C₆₇	—	2	3	no	—
47	C₂²×D₄×C₆₇	—	2	6	no	—
48	C₂²×D₄×C₆₇	D₄	1	3	yes	—
49	C₂²×D₄×C₆₇	D₄	1	12	yes	complemented
50	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
52	C₂³×C₄×C₆₇	—	2	3	no	—
53	C₂³×C₄×C₆₇	C₂³	1	3	yes	—
54	C₂×SD₁₆×C₆₇	—	2	6	no	—
55	C₂×D₈×C₆₇	—	2	6	no	—
56	C₂×D₈×C₆₇	—	2	12	no	—
57	C₂²×C₈×C₆₇	C₂³	1	3	yes	—
58	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
59	#121×C₆₇	—	2	6	no	—
60	#121×C₆₇	—	2	6	no	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	3	yes	—
62	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	3	no	—
64	#103×C₆₇	—	2	6	no	—
65	#102×C₆₇	—	2	6	no	—
66	#102×C₆₇	—	2	12	no	—
67	C₂²⋊C₈×C₆₇	—	2	6	no	—
68	C₂²⋊C₈×C₆₇	—	2	6	no	—
69	#95×C₆₇	—	2	3	no	—
70	C₂⁴×C₆₇	—	2	24	no	—
71	C₂⁴×C₆₇	—	2	3	no	—
72	C₂⁴×C₆₇	—	2	12	no	—
73	C₂⁴×C₆₇	—	2	1	no	—
74	C₂⁴×C₆₇	—	8	3	no	—
75	C₂⁴×C₆₇	—	8	6	no	—
76	C₂⁴×C₆₇	—	8	3	no	—
77	C₂⁴×C₆₇	C₂×D₄	1	3	yes	—
78	#41×C₆₇	—	2	64	no	—
79	#41×C₆₇	—	2	48	no	—
80	#41×C₆₇	—	2	8	no	—
81	#41×C₆₇	—	2	24	no	—
82	#41×C₆₇	—	2	24	no	—
83	#41×C₆₇	—	2	24	no	—
84	C₂×Q₈×C₆₇	—	2	6	no	—
85	C₂×Q₈×C₆₇	—	2	3	no	—
86	C₂×Q₈×C₆₇	C₂×D₄	1	6	yes	—
87	C₂×D₄×C₆₇	—	2	24	no	—
88	C₂×D₄×C₆₇	—	2	24	no	—
89	C₂×D₄×C₆₇	—	2	192	no	—
90	C₂×D₄×C₆₇	—	2	24	no	—
91	C₂×D₄×C₆₇	—	2	24	no	—
92	C₂×D₄×C₆₇	—	2	12	no	—
93	C₂×D₄×C₆₇	—	2	12	no	—
94	C₂×D₄×C₆₇	—	2	48	no	—
95	C₂×D₄×C₆₇	—	2	6	no	—
96	C₂×D₄×C₆₇	—	2	12	no	—
97	C₂×D₄×C₆₇	—	2	6	no	—
98	C₂×D₄×C₆₇	—	2	3	no	—
99	C₂×D₄×C₆₇	—	2	3	no	—
100	C₂×D₄×C₆₇	—	2	3	no	—
101	C₂×D₄×C₆₇	—	4	6	no	—
102	C₂×D₄×C₆₇	—	8	6	no	—
103	C₂×D₄×C₆₇	C₂×D₄	1	6	yes	—
104	C₂×D₄×C₆₇	C₂×D₄	1	12	yes	—
105	C₂²×C₄×C₆₇	—	2	24	no	—
106	C₂²×C₄×C₆₇	—	2	1	no	—
107	C₂²×C₄×C₆₇	—	2	12	no	—
108	C₂²×C₄×C₆₇	—	2	6	no	—
109	C₂²×C₄×C₆₇	—	2	6	no	—
110	C₂²×C₄×C₆₇	—	2	3	no	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	3	yes	—
112	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	6	yes	—
114	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
115	SD₁₆×C₆₇	—	4	4	no	—
116	D₈×C₆₇	—	4	12	no	—
117	C₂×C₈×C₆₇	—	2	6	no	—
118	C₂×C₈×C₆₇	—	2	3	no	—
119	C₂×C₈×C₆₇	—	2	3	no	—
120	C₄⋊C₄×C₆₇	—	2	3	no	—
121	C₄⋊C₄×C₆₇	—	2	3	no	—
122	C₂²⋊C₄×C₆₇	—	4	6	no	—
123	C₂²⋊C₄×C₆₇	—	8	3	no	—
124	C₂³×C₆₇	—	2	48	no	—
125	C₂³×C₆₇	—	2	6	no	—
126	C₂³×C₆₇	—	2	12	no	—
127	C₂³×C₆₇	—	2	6	no	—
128	C₂³×C₆₇	—	2	3	no	—
129	C₂³×C₆₇	—	2	6	no	—
130	C₂³×C₆₇	—	2	3	no	—
131	C₂³×C₆₇	—	4	3	no	—
132	C₂³×C₆₇	—	4	6	no	—
133	C₂³×C₆₇	—	4	3	no	—
134	C₂³×C₆₇	—	4	3	no	—
135	C₂³×C₆₇	—	4	3	no	—
136	C₂³×C₆₇	—	4	1	no	—
137	C₂³×C₆₇	—	8	12	no	—
138	C₂³×C₆₇	—	8	12	no	—
139	C₂³×C₆₇	—	8	24	no	—
140	C₂³×C₆₇	—	8	24	no	—
141	C₂³×C₆₇	#120	1	6	yes	—
142	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₆₇	—	2	8	no	—
144	Q₈×C₆₇	—	2	6	no	—
145	Q₈×C₆₇	#120	1	4	yes	—
146	D₄×C₆₇	—	2	48	no	—
147	D₄×C₆₇	—	2	24	no	—
148	D₄×C₆₇	—	2	48	no	—
149	D₄×C₆₇	—	2	6	no	—
150	D₄×C₆₇	—	2	12	no	—
151	D₄×C₆₇	—	4	3	no	—
152	D₄×C₆₇	—	4	1	no	—
153	D₄×C₆₇	—	8	12	no	—
154	D₄×C₆₇	#120	1	12	yes	—
155	C₂×C₄×C₆₇	—	2	48	no	—
156	C₂×C₄×C₆₇	—	2	6	no	—
157	C₂×C₄×C₆₇	—	2	6	no	—
158	C₂×C₄×C₆₇	—	2	6	no	—
159	C₂×C₄×C₆₇	—	2	6	no	—
160	C₂×C₄×C₆₇	—	2	12	no	—
161	C₂×C₄×C₆₇	—	4	3	no	—
162	C₂×C₄×C₆₇	—	4	6	no	—
163	C₂×C₄×C₆₇	#120	1	6	yes	—
164	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
165	C₂×C₄×C₆₇	C₂²×D₄	1	3	yes	—
166	C₈×C₆₇	—	4	3	no	—
167	C₈×C₆₇	—	4	1	no	—
168	C₂²×C₆₇	—	2	6	no	—
169	C₂²×C₆₇	—	2	12	no	—
170	C₂²×C₆₇	—	2	6	no	—
171	C₂²×C₆₇	—	2	6	no	—
172	C₂²×C₆₇	—	4	6	no	—
173	C₂²×C₆₇	—	4	12	no	—
174	C₂²×C₆₇	—	4	6	no	—
175	C₂²×C₆₇	—	4	6	no	—
176	C₂²×C₆₇	—	4	12	no	—
177	C₂²×C₆₇	—	4	6	no	—
178	C₂²×C₆₇	—	8	48	no	—
179	C₂²×C₆₇	—	8	1	no	—
180	C₂²×C₆₇	—	8	3	no	—
181	C₂²×C₆₇	—	8	3	no	—
182	C₂²×C₆₇	C₂×#120	1	3	yes	—
183	C₂²×C₆₇	#576	1	3	yes	—
184	C₂²×C₆₇	#577	1	1	yes	characteristic
185	C₄×C₆₇	—	2	4	no	—
186	C₄×C₆₇	—	2	6	no	—
187	C₄×C₆₇	—	8	3	no	—
188	C₄×C₆₇	C₂×#120	1	1	yes	characteristic
189	C₄×C₆₇	C₂×#120	1	3	yes	—
190	#32884	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂×C₆₇	—	4	6	no	—
192	C₂×C₆₇	—	4	12	no	—
193	C₂×C₆₇	—	16	1	no	—
194	C₂×C₆₇	#2846	1	1	yes	characteristic
195	C₂×C₆₇	#3008	1	3	yes	—
196	C₂×C₆₇	#3012	1	3	yes	—
197	C₂²×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
198	C₂×#449	C₂×C₆₇	1	3	yes	complemented
199	C₂×#447	C₂×C₆₇	1	3	yes	complemented
200	#2615	C₂×C₆₇	1	1	yes	characteristic, complemented
201	#1788	C₂×C₆₇	1	3	yes	complemented
202	#1786	C₂×C₆₇	1	3	yes	complemented
203	#1780	C₂×C₆₇	1	1	yes	characteristic, complemented
204	C₆₇	#32884	1	1	yes	characteristic, direct product factor, Sylow
205	C₂×H(5,𝔽₂)	—	2	12	no	—
206	C₂×H(5,𝔽₂)	—	2	12	no	—
207	C₂²×#41	—	2	1	no	—
208	C₂²×#41	C₂²×C₆₇	1	3	yes	—
209	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
210	C₂³×D₄	—	2	3	no	—
211	C₂³×D₄	C₂²×C₆₇	1	3	yes	—
212	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
213	C₂²×D₈	C₂²×C₆₇	1	3	yes	complemented
214	C₂×#121	C₂²×C₆₇	1	3	yes	complemented
215	#449	—	2	12	no	—
216	#447	—	2	12	no	—
217	C₂×#103	C₂²×C₆₇	1	3	yes	complemented
218	C₂×#102	C₂²×C₆₇	1	6	yes	complemented
219	C₂×#102	C₂²×C₆₇	1	3	yes	complemented
220	C₂×C₂²⋊C₈	C₂²×C₆₇	1	3	yes	complemented
221	C₂×C₂²⋊C₈	C₂²×C₆₇	1	3	yes	complemented
222	#393	—	2	1	no	—
223	#392	—	2	3	no	—
224	#380	C₂²×C₆₇	1	3	yes	complemented
225	C₂⁵	—	2	3	no	—
226	H(5,𝔽₂)	—	2	32	no	—
227	H(5,𝔽₂)	—	2	96	no	—
228	C₂×#41	—	2	24	no	—
229	C₂×#41	—	2	12	no	—
230	C₂×#41	—	2	12	no	—
231	C₂×#41	—	2	6	no	—
232	C₂×#41	—	2	6	no	—
233	C₂×#41	—	2	6	no	—
234	C₂×#41	D₄×C₆₇	1	12	yes	complemented
235	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
237	C₂²×D₄	—	2	48	no	—
238	C₂²×D₄	—	2	24	no	—
239	C₂²×D₄	—	2	3	no	—
240	C₂²×D₄	—	2	12	no	—
241	C₂²×D₄	—	2	12	no	—
242	C₂²×D₄	—	2	3	no	—
243	C₂²×D₄	—	2	3	no	—
244	C₂²×D₄	—	2	6	no	—
245	C₂²×D₄	D₄×C₆₇	1	3	yes	—
246	C₂²×D₄	D₄×C₆₇	1	12	yes	complemented
247	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
248	C₂²×D₄	C₂³×C₆₇	1	3	yes	—
249	C₂³×C₄	—	2	3	no	—
250	C₂³×C₄	C₂³×C₆₇	1	3	yes	—
251	C₂×SD₁₆	—	2	6	no	—
252	C₂×D₈	—	2	12	no	—
253	C₂×D₈	—	2	6	no	—
254	C₂²×C₈	C₂³×C₆₇	1	3	yes	—
255	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
256	#121	—	2	6	no	—
257	#121	—	2	6	no	—
258	C₂×C₄⋊C₄	C₂³×C₆₇	1	3	yes	—
259	C₂×C₂²⋊C₄	—	2	3	no	—
260	C₂×C₂²⋊C₄	—	2	3	no	—
261	#103	—	2	6	no	—
262	#102	—	2	12	no	—
263	#102	—	2	6	no	—
264	C₂²⋊C₈	—	2	6	no	—
265	C₂²⋊C₈	—	2	6	no	—
266	#95	—	2	3	no	—
267	C₂⁴	—	2	24	no	—
268	C₂⁴	—	2	3	no	—
269	C₂⁴	—	2	12	no	—
270	C₂⁴	—	2	1	no	—
271	C₂⁴	—	8	3	no	—
272	C₂⁴	—	8	6	no	—
273	C₂⁴	—	8	3	no	—
274	C₂⁴	C₂×D₄×C₆₇	1	3	yes	—
275	#41	—	2	64	no	—
276	#41	—	2	48	no	—
277	#41	—	2	8	no	—
278	#41	—	2	24	no	—
279	#41	—	2	24	no	—
280	#41	—	2	24	no	—
281	C₂×Q₈	—	2	6	no	—
282	C₂×Q₈	—	2	3	no	—
283	C₂×Q₈	C₂×D₄×C₆₇	1	6	yes	—
284	C₂×D₄	—	2	24	no	—
285	C₂×D₄	—	2	24	no	—
286	C₂×D₄	—	2	192	no	—
287	C₂×D₄	—	2	24	no	—
288	C₂×D₄	—	2	24	no	—
289	C₂×D₄	—	2	12	no	—
290	C₂×D₄	—	2	12	no	—
291	C₂×D₄	—	2	48	no	—
292	C₂×D₄	—	2	6	no	—
293	C₂×D₄	—	2	12	no	—
294	C₂×D₄	—	2	6	no	—
295	C₂×D₄	—	2	3	no	—
296	C₂×D₄	—	2	3	no	—
297	C₂×D₄	—	2	3	no	—
298	C₂×D₄	—	4	6	no	—
299	C₂×D₄	—	8	6	no	—
300	C₂×D₄	C₂×D₄×C₆₇	1	6	yes	—
301	C₂×D₄	C₂×D₄×C₆₇	1	12	yes	—
302	C₂²×C₄	—	2	24	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	12	no	—
305	C₂²×C₄	—	2	6	no	—
306	C₂²×C₄	—	2	6	no	—
307	C₂²×C₄	—	2	3	no	—
308	C₂²×C₄	C₂×D₄×C₆₇	1	3	yes	—
309	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
310	C₂²×C₄	C₂×D₄×C₆₇	1	6	yes	—
311	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
312	SD₁₆	—	4	4	no	—
313	D₈	—	4	12	no	—
314	C₂×C₈	—	2	6	no	—
315	C₂×C₈	—	2	3	no	—
316	C₂×C₈	—	2	3	no	—
317	C₄⋊C₄	—	2	3	no	—
318	C₄⋊C₄	—	2	3	no	—
319	C₂²⋊C₄	—	4	6	no	—
320	C₂²⋊C₄	—	8	3	no	—
321	C₂³	—	2	48	no	—
322	C₂³	—	2	6	no	—
323	C₂³	—	2	12	no	—
324	C₂³	—	2	6	no	—
325	C₂³	—	2	3	no	—
326	C₂³	—	2	6	no	—
327	C₂³	—	2	3	no	—
328	C₂³	—	4	6	no	—
329	C₂³	—	4	3	no	—
330	C₂³	—	4	3	no	—
331	C₂³	—	4	3	no	—
332	C₂³	—	4	3	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	8	12	no	—
335	C₂³	—	8	12	no	—
336	C₂³	—	8	24	no	—
337	C₂³	—	8	24	no	—
338	C₂³	#120×C₆₇	1	6	yes	—
339	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
340	Q₈	—	2	8	no	—
341	Q₈	—	2	6	no	—
342	Q₈	#120×C₆₇	1	4	yes	—
343	D₄	—	2	48	no	—
344	D₄	—	2	24	no	—
345	D₄	—	2	48	no	—
346	D₄	—	2	6	no	—
347	D₄	—	2	12	no	—
348	D₄	—	4	3	no	—
349	D₄	—	4	1	no	—
350	D₄	—	8	12	no	—
351	D₄	#120×C₆₇	1	12	yes	—
352	C₂×C₄	—	2	48	no	—
353	C₂×C₄	—	2	6	no	—
354	C₂×C₄	—	2	6	no	—
355	C₂×C₄	—	2	6	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	12	no	—
358	C₂×C₄	—	4	3	no	—
359	C₂×C₄	—	4	6	no	—
360	C₂×C₄	#120×C₆₇	1	6	yes	—
361	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
362	C₂×C₄	C₂²×D₄×C₆₇	1	3	yes	—
363	C₈	—	4	3	no	—
364	C₈	—	4	1	no	—
365	C₂²	—	2	6	no	—
366	C₂²	—	2	6	no	—
367	C₂²	—	2	12	no	—
368	C₂²	—	2	6	no	—
369	C₂²	—	4	6	no	—
370	C₂²	—	4	12	no	—
371	C₂²	—	4	6	no	—
372	C₂²	—	4	6	no	—
373	C₂²	—	4	12	no	—
374	C₂²	—	4	6	no	—
375	C₂²	—	8	48	no	—
376	C₂²	—	8	3	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	3	no	—
379	C₂²	C₂×#120×C₆₇	1	3	yes	—
380	C₂²	#576×C₆₇	1	3	yes	—
381	C₂²	#577×C₆₇	1	1	yes	characteristic
382	C₄	—	2	4	no	—
383	C₄	—	2	6	no	—
384	C₄	—	8	3	no	—
385	C₄	C₂×#120×C₆₇	1	1	yes	characteristic
386	C₄	C₂×#120×C₆₇	1	3	yes	—
387	C₂	—	4	6	no	—
388	C₂	—	4	12	no	—
389	C₂	—	16	1	no	—
390	C₂	C₆₇×#2846	1	1	yes	characteristic
391	C₂	C₆₇×#3008	1	3	yes	—
392	C₂	C₆₇×#3012	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×H(5,𝔽₂)×C₆₇	C₂	semidirect
2. C₂×#449×C₆₇	C₂	semidirect
3. C₂×#447×C₆₇	C₂	semidirect
4. C₆₇×#2615	C₂	semidirect
5. C₆₇×#1788	C₂	semidirect
6. C₆₇×#1786	C₂	semidirect
7. C₆₇×#1780	C₂	semidirect
15. C₂²×SD₁₆×C₆₇	C₂²	semidirect
16. C₂²×D₈×C₆₇	C₂²	semidirect
17. C₂×#121×C₆₇	C₂²	semidirect
20. C₂×#103×C₆₇	C₂²	semidirect
21. C₂×#102×C₆₇	C₂²	semidirect
22. C₂×#102×C₆₇	C₂²	semidirect
23. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
24. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
27. #380×C₆₇	C₂²	semidirect
37. C₂×#41×C₆₇	D₄	semidirect
49. C₂²×D₄×C₆₇	D₄	semidirect
190. #32884	C₆₇	direct (N × H)
197. C₂²×H(5,𝔽₂)	C₂×C₆₇	semidirect
198. C₂×#449	C₂×C₆₇	semidirect
199. C₂×#447	C₂×C₆₇	semidirect
200. #2615	C₂×C₆₇	semidirect
201. #1788	C₂×C₆₇	semidirect
202. #1786	C₂×C₆₇	semidirect
203. #1780	C₂×C₆₇	semidirect
204. C₆₇	#32884	direct (N × H)
212. C₂²×SD₁₆	C₂²×C₆₇	semidirect
213. C₂²×D₈	C₂²×C₆₇	semidirect
214. C₂×#121	C₂²×C₆₇	semidirect
217. C₂×#103	C₂²×C₆₇	semidirect
218. C₂×#102	C₂²×C₆₇	semidirect
219. C₂×#102	C₂²×C₆₇	semidirect
220. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
221. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
224. #380	C₂²×C₆₇	semidirect
234. C₂×#41	D₄×C₆₇	semidirect
246. C₂²×D₄	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₆₇	2
C₂×#449×C₆₇	2
C₂×#447×C₆₇	2
C₆₇×#2615	2
C₆₇×#1788	2
C₆₇×#1786	2
C₆₇×#1780	2
#32884	67

Subgroups — C67×#32884 #30712135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#32884 #30712135