Subgroups — C₂×C₆₇×#3492 #30742019

Order 17152.

7910 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3492	C₂	1	32	yes	maximal, direct product factor
2	C₂×#554×C₆₇	C₂	1	4	yes	maximal, complemented
3	C₂×#553×C₆₇	C₂	1	4	yes	maximal, complemented
4	C₂×#552×C₆₇	C₂	1	4	yes	maximal, complemented
5	C₂×#547×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#544×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#539×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#537×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#525×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#525×C₆₇	C₂	1	4	yes	maximal, complemented
11	C₂×#520×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂³×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₇	C₂²	1	2	yes	—
14	C₂²×#41×C₆₇	C₂²	1	4	yes	—
15	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	—
17	#554×C₆₇	C₂²	1	64	yes	complemented
18	#553×C₆₇	C₂²	1	64	yes	complemented
19	#552×C₆₇	C₂²	1	64	yes	complemented
20	#547×C₆₇	C₂²	1	64	yes	complemented
21	#544×C₆₇	C₂²	1	16	yes	complemented
22	#539×C₆₇	C₂²	1	64	yes	complemented
23	#537×C₆₇	C₂²	1	16	yes	complemented
24	C₂×C₄⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
25	C₂×#126×C₆₇	C₂²	1	8	yes	complemented
26	C₂×#125×C₆₇	C₂²	1	8	yes	complemented
27	C₂×#125×C₆₇	C₂²	1	4	yes	complemented
28	#525×C₆₇	C₂²	1	32	yes	complemented
29	#525×C₆₇	C₂²	1	64	yes	complemented
30	C₂×#123×C₆₇	C₂²	1	4	yes	—
31	C₂×#123×C₆₇	C₂²	1	8	yes	—
32	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
33	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	8	yes	complemented
39	C₂×#121×C₆₇	C₂²	1	4	yes	—
40	C₂×#121×C₆₇	C₂²	1	2	yes	—
41	C₂×#121×C₆₇	C₂²	1	4	yes	—
42	C₂×#121×C₆₇	C₂²	1	2	yes	—
43	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
44	C₂×#120×C₆₇	C₂²	1	4	yes	—
45	#520×C₆₇	C₂²	1	32	yes	complemented
46	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
47	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	—
48	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
49	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	—
50	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
51	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
52	C₂×#117×C₆₇	C₂²	1	2	yes	—
53	C₂×#117×C₆₇	C₂²	1	4	yes	—
54	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
55	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
56	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
57	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
58	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
59	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
60	C₂²×C₄⋊C₄×C₆₇	C₂²	1	16	yes	complemented
61	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	complemented
62	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
63	C₂×#41×C₆₇	—	2	16	no	—
64	C₂×#41×C₆₇	—	4	16	no	—
65	C₂×#41×C₆₇	C₂³	1	16	yes	—
66	C₂×#41×C₆₇	C₂³	1	32	yes	—
67	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
68	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
69	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
70	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
71	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
72	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
73	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
74	C₂³×C₄×C₆₇	—	2	8	no	—
75	C₂³×C₄×C₆₇	—	4	8	no	—
76	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
77	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
81	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
82	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
83	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
84	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₆₇	C₂³	1	16	yes	—
86	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
87	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
89	#126×C₆₇	C₂³	1	64	yes	complemented
90	#125×C₆₇	C₂³	1	64	yes	complemented
91	#125×C₆₇	C₂³	1	32	yes	complemented
92	#123×C₆₇	C₂³	1	32	yes	—
93	#123×C₆₇	C₂³	1	64	yes	—
94	#123×C₆₇	C₂³	1	64	yes	complemented
95	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
96	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
97	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
98	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
99	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
100	C₂²⋊Q₈×C₆₇	C₂³	1	64	yes	complemented
101	#121×C₆₇	C₂³	1	32	yes	—
102	#121×C₆₇	C₂³	1	16	yes	—
103	#121×C₆₇	C₂³	1	32	yes	—
104	#121×C₆₇	C₂³	1	16	yes	—
105	#121×C₆₇	C₂³	1	32	yes	complemented
106	#120×C₆₇	C₂³	1	32	yes	—
107	C₄×Q₈×C₆₇	C₂³	1	32	yes	complemented
108	C₄×D₄×C₆₇	C₂³	1	64	yes	—
109	C₄×D₄×C₆₇	C₂³	1	32	yes	—
110	C₄×D₄×C₆₇	C₂³	1	64	yes	—
111	C₄×D₄×C₆₇	C₂³	1	32	yes	—
112	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
113	#117×C₆₇	C₂³	1	16	yes	—
114	#117×C₆₇	C₂³	1	32	yes	—
115	#117×C₆₇	C₂³	1	32	yes	complemented
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
119	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
120	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	complemented
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
141	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
142	C₂⁴×C₆₇	—	2	4	no	—
143	C₂⁴×C₆₇	—	2	4	no	—
144	C₂⁴×C₆₇	—	2	4	no	—
145	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
146	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
147	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
149	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
150	#41×C₆₇	—	2	64	no	—
151	#41×C₆₇	—	4	64	no	—
152	C₂×Q₈×C₆₇	—	2	8	no	—
153	C₂×Q₈×C₆₇	—	4	8	no	—
154	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
155	C₂×Q₈×C₆₇	C₂⁴	1	16	yes	—
156	C₂×D₄×C₆₇	—	2	16	no	—
157	C₂×D₄×C₆₇	—	2	16	no	—
158	C₂×D₄×C₆₇	—	2	16	no	—
159	C₂×D₄×C₆₇	—	2	8	no	—
160	C₂×D₄×C₆₇	—	4	8	no	—
161	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
162	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
163	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
164	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
165	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
166	C₂²×C₄×C₆₇	—	2	4	no	—
167	C₂²×C₄×C₆₇	—	2	16	no	—
168	C₂²×C₄×C₆₇	—	2	8	no	—
169	C₂²×C₄×C₆₇	—	2	8	no	—
170	C₂²×C₄×C₆₇	—	2	16	no	—
171	C₂²×C₄×C₆₇	—	2	32	no	—
172	C₂²×C₄×C₆₇	—	4	4	no	—
173	C₂²×C₄×C₆₇	—	4	8	no	—
174	C₂²×C₄×C₆₇	—	4	4	no	—
175	C₂²×C₄×C₆₇	—	4	32	no	—
176	C₂²×C₄×C₆₇	—	4	16	no	—
177	C₂²×C₄×C₆₇	#41	1	8	yes	complemented
178	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
179	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
180	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
181	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
183	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
191	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	32	yes	—
193	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
195	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
196	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
197	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	—
198	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
199	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	—
200	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
201	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
202	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
203	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
204	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	—
205	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
206	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
207	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
208	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
209	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
210	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
211	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
212	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
213	C₄²×C₆₇	C₂⁴	1	32	yes	—
214	C₄²×C₆₇	C₂⁴	1	16	yes	—
215	C₂³×C₆₇	—	2	32	no	—
216	C₂³×C₆₇	—	2	8	no	—
217	C₂³×C₆₇	—	2	2	no	—
218	C₂³×C₆₇	—	2	2	no	—
219	C₂³×C₆₇	—	2	8	no	—
220	C₂³×C₆₇	—	2	2	no	—
221	C₂³×C₆₇	—	2	2	no	—
222	C₂³×C₆₇	—	2	8	no	—
223	C₂³×C₆₇	—	2	2	no	—
224	C₂³×C₆₇	—	2	2	no	—
225	C₂³×C₆₇	—	2	8	no	—
226	C₂³×C₆₇	—	2	8	no	—
227	C₂³×C₆₇	—	2	8	no	—
228	C₂³×C₆₇	C₂×#41	1	4	yes	—
229	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
230	C₂³×C₆₇	2₋¹⁺⁴	1	4	yes	—
231	C₂³×C₆₇	C₂⁵	1	8	yes	—
232	C₂³×C₆₇	C₂⁵	1	2	yes	—
233	C₂³×C₆₇	C₂⁵	1	2	yes	—
234	C₂³×C₆₇	C₂⁵	1	2	yes	—
235	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
236	Q₈×C₆₇	—	2	16	no	—
237	Q₈×C₆₇	—	4	16	no	—
238	D₄×C₆₇	—	2	32	no	—
239	D₄×C₆₇	—	2	32	no	—
240	D₄×C₆₇	—	2	32	no	—
241	D₄×C₆₇	—	2	16	no	—
242	D₄×C₆₇	—	4	16	no	—
243	C₂×C₄×C₆₇	—	2	8	no	—
244	C₂×C₄×C₆₇	—	2	4	no	—
245	C₂×C₄×C₆₇	—	2	8	no	—
246	C₂×C₄×C₆₇	—	2	8	no	—
247	C₂×C₄×C₆₇	—	2	8	no	—
248	C₂×C₄×C₆₇	—	2	32	no	—
249	C₂×C₄×C₆₇	—	2	8	no	—
250	C₂×C₄×C₆₇	—	2	8	no	—
251	C₂×C₄×C₆₇	—	2	16	no	—
252	C₂×C₄×C₆₇	—	2	16	no	—
253	C₂×C₄×C₆₇	—	2	32	no	—
254	C₂×C₄×C₆₇	—	4	8	no	—
255	C₂×C₄×C₆₇	—	4	16	no	—
256	C₂×C₄×C₆₇	—	4	8	no	—
257	C₂×C₄×C₆₇	—	4	32	no	—
258	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
259	C₂×C₄×C₆₇	C₂×#41	1	16	yes	complemented
260	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
261	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
262	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
263	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
264	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
265	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
266	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
267	C₂²×C₆₇	—	2	32	no	—
268	C₂²×C₆₇	—	2	2	no	—
269	C₂²×C₆₇	—	2	2	no	—
270	C₂²×C₆₇	—	2	2	no	—
271	C₂²×C₆₇	—	2	2	no	—
272	C₂²×C₆₇	—	2	2	no	—
273	C₂²×C₆₇	—	2	2	no	—
274	C₂²×C₆₇	—	2	8	no	—
275	C₂²×C₆₇	—	2	8	no	—
276	C₂²×C₆₇	—	2	8	no	—
277	C₂²×C₆₇	—	2	8	no	—
278	C₂²×C₆₇	—	2	8	no	—
279	C₂²×C₆₇	—	2	8	no	—
280	C₂²×C₆₇	—	4	16	no	—
281	C₂²×C₆₇	C₂²×#41	1	4	yes	—
282	C₂²×C₆₇	C₂²×#41	1	2	yes	—
283	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
284	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
286	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
287	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
288	C₄×C₆₇	—	2	4	no	—
289	C₄×C₆₇	—	2	8	no	—
290	C₄×C₆₇	—	2	8	no	—
291	C₄×C₆₇	—	2	8	no	—
292	C₄×C₆₇	—	2	8	no	—
293	C₄×C₆₇	—	2	8	no	—
294	C₄×C₆₇	C₂²×#41	1	8	yes	—
295	C₂×#3492	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂×C₆₇	—	2	4	no	—
297	C₂×C₆₇	—	2	4	no	—
298	C₂×C₆₇	—	2	4	no	—
299	C₂×C₆₇	—	4	8	no	—
300	C₂×C₆₇	#3492	1	4	yes	direct product factor
301	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
302	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
304	#3492	C₂×C₆₇	1	32	yes	direct product factor
305	C₂×#554	C₂×C₆₇	1	4	yes	complemented
306	C₂×#553	C₂×C₆₇	1	4	yes	complemented
307	C₂×#552	C₂×C₆₇	1	4	yes	complemented
308	C₂×#547	C₂×C₆₇	1	4	yes	complemented
309	C₂×#544	C₂×C₆₇	1	1	yes	characteristic, complemented
310	C₂×#539	C₂×C₆₇	1	4	yes	complemented
311	C₂×#537	C₂×C₆₇	1	1	yes	characteristic, complemented
312	C₂×#525	C₂×C₆₇	1	2	yes	complemented
313	C₂×#525	C₂×C₆₇	1	4	yes	complemented
314	C₂×#520	C₂×C₆₇	1	2	yes	complemented
315	C₂³×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
316	C₆₇	C₂×#3492	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²×#41	C₂²×C₆₇	1	2	yes	—
318	C₂²×#41	C₂²×C₆₇	1	4	yes	—
319	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
320	C₂⁴×C₄	C₂²×C₆₇	1	2	yes	—
321	#554	C₂²×C₆₇	1	64	yes	complemented
322	#553	C₂²×C₆₇	1	64	yes	complemented
323	#552	C₂²×C₆₇	1	64	yes	complemented
324	#547	C₂²×C₆₇	1	64	yes	complemented
325	#544	C₂²×C₆₇	1	16	yes	complemented
326	#539	C₂²×C₆₇	1	64	yes	complemented
327	#537	C₂²×C₆₇	1	16	yes	complemented
328	C₂×C₄⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
329	C₂×#126	C₂²×C₆₇	1	8	yes	complemented
330	C₂×#125	C₂²×C₆₇	1	8	yes	complemented
331	C₂×#125	C₂²×C₆₇	1	4	yes	complemented
332	#525	C₂²×C₆₇	1	32	yes	complemented
333	#525	C₂²×C₆₇	1	64	yes	complemented
334	C₂×#123	C₂²×C₆₇	1	4	yes	—
335	C₂×#123	C₂²×C₆₇	1	8	yes	—
336	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
337	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
338	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
339	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
340	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
341	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
342	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	8	yes	complemented
343	C₂×#121	C₂²×C₆₇	1	4	yes	—
344	C₂×#121	C₂²×C₆₇	1	2	yes	—
345	C₂×#121	C₂²×C₆₇	1	4	yes	—
346	C₂×#121	C₂²×C₆₇	1	2	yes	—
347	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
348	C₂×#120	C₂²×C₆₇	1	4	yes	—
349	#520	C₂²×C₆₇	1	32	yes	complemented
350	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
351	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	—
352	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
353	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	—
354	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
355	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
356	C₂×#117	C₂²×C₆₇	1	2	yes	—
357	C₂×#117	C₂²×C₆₇	1	4	yes	—
358	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
359	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
360	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
361	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
362	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
363	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
364	C₂²×C₄⋊C₄	C₂²×C₆₇	1	16	yes	complemented
365	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	complemented
366	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
367	C₂×#41	—	2	16	no	—
368	C₂×#41	—	4	16	no	—
369	C₂×#41	C₂³×C₆₇	1	16	yes	—
370	C₂×#41	C₂³×C₆₇	1	32	yes	—
371	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
372	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
373	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
374	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
375	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
376	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
377	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
378	C₂³×C₄	—	2	8	no	—
379	C₂³×C₄	—	4	8	no	—
380	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
381	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
382	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
383	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₆₇	1	8	yes	—
385	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
386	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
387	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
388	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
389	C₂³×C₄	C₂³×C₆₇	1	16	yes	—
390	C₂³×C₄	C₂³×C₆₇	1	8	yes	—
391	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
392	C₄⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
393	#126	C₂³×C₆₇	1	64	yes	complemented
394	#125	C₂³×C₆₇	1	64	yes	complemented
395	#125	C₂³×C₆₇	1	32	yes	complemented
396	#123	C₂³×C₆₇	1	32	yes	—
397	#123	C₂³×C₆₇	1	64	yes	—
398	#123	C₂³×C₆₇	1	64	yes	complemented
399	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
400	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
401	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
402	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
403	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
404	C₂²⋊Q₈	C₂³×C₆₇	1	64	yes	complemented
405	#121	C₂³×C₆₇	1	32	yes	—
406	#121	C₂³×C₆₇	1	16	yes	—
407	#121	C₂³×C₆₇	1	32	yes	—
408	#121	C₂³×C₆₇	1	16	yes	—
409	#121	C₂³×C₆₇	1	32	yes	complemented
410	#120	C₂³×C₆₇	1	32	yes	—
411	C₄×Q₈	C₂³×C₆₇	1	32	yes	complemented
412	C₄×D₄	C₂³×C₆₇	1	64	yes	—
413	C₄×D₄	C₂³×C₆₇	1	32	yes	—
414	C₄×D₄	C₂³×C₆₇	1	64	yes	—
415	C₄×D₄	C₂³×C₆₇	1	32	yes	—
416	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
417	#117	C₂³×C₆₇	1	16	yes	—
418	#117	C₂³×C₆₇	1	32	yes	—
419	#117	C₂³×C₆₇	1	32	yes	complemented
420	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
423	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
424	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
425	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
426	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
427	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
428	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
430	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
432	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
433	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
435	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	complemented
437	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
444	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
445	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
450	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
451	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
453	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
454	#41	—	2	64	no	—
455	#41	—	4	64	no	—
456	C₂×Q₈	—	2	8	no	—
457	C₂×Q₈	—	4	8	no	—
458	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
459	C₂×Q₈	C₂⁴×C₆₇	1	16	yes	—
460	C₂×D₄	—	2	16	no	—
461	C₂×D₄	—	2	16	no	—
462	C₂×D₄	—	2	16	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	4	8	no	—
465	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
466	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
467	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
468	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
469	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	16	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	2	16	no	—
475	C₂²×C₄	—	2	32	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	8	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	32	no	—
480	C₂²×C₄	—	4	16	no	—
481	C₂²×C₄	#41×C₆₇	1	8	yes	complemented
482	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
489	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
490	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
491	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
493	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
494	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
495	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
496	C₂²×C₄	C₂⁴×C₆₇	1	32	yes	—
497	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
499	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
500	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
501	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	—
502	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
503	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	—
504	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
505	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
506	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
507	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
508	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	—
509	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
510	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
511	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
512	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
513	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
514	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
515	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
516	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
517	C₄²	C₂⁴×C₆₇	1	32	yes	—
518	C₄²	C₂⁴×C₆₇	1	16	yes	—
519	C₂³	—	2	32	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	8	no	—
530	C₂³	—	2	8	no	—
531	C₂³	—	2	8	no	—
532	C₂³	C₂×#41×C₆₇	1	4	yes	—
533	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
534	C₂³	2₋¹⁺⁴×C₆₇	1	4	yes	—
535	C₂³	C₂⁵×C₆₇	1	8	yes	—
536	C₂³	C₂⁵×C₆₇	1	2	yes	—
537	C₂³	C₂⁵×C₆₇	1	2	yes	—
538	C₂³	C₂⁵×C₆₇	1	2	yes	—
539	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
540	Q₈	—	2	16	no	—
541	Q₈	—	4	16	no	—
542	D₄	—	2	32	no	—
543	D₄	—	2	32	no	—
544	D₄	—	2	32	no	—
545	D₄	—	2	16	no	—
546	D₄	—	4	16	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	32	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	16	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	32	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	4	16	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	—	4	32	no	—
562	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
563	C₂×C₄	C₂×#41×C₆₇	1	16	yes	complemented
564	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
565	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
566	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
567	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
568	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
569	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
570	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
571	C₂²	—	2	32	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	8	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	8	no	—
582	C₂²	—	2	8	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	4	16	no	—
585	C₂²	C₂²×#41×C₆₇	1	4	yes	—
586	C₂²	C₂²×#41×C₆₇	1	2	yes	—
587	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
588	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
589	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
590	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
591	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	2	8	no	—
595	C₄	—	2	8	no	—
596	C₄	—	2	8	no	—
597	C₄	—	2	8	no	—
598	C₄	C₂²×#41×C₆₇	1	8	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	2	4	no	—
601	C₂	—	2	4	no	—
602	C₂	—	4	8	no	—
603	C₂	C₆₇×#3492	1	4	yes	direct product factor
604	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
605	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
606	C₂	C₂²×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3492	C₂	direct (N × H)
2. C₂×#554×C₆₇	C₂	semidirect
3. C₂×#553×C₆₇	C₂	semidirect
4. C₂×#552×C₆₇	C₂	semidirect
5. C₂×#547×C₆₇	C₂	semidirect
6. C₂×#544×C₆₇	C₂	semidirect
7. C₂×#539×C₆₇	C₂	semidirect
8. C₂×#537×C₆₇	C₂	semidirect
9. C₂×#525×C₆₇	C₂	semidirect
10. C₂×#525×C₆₇	C₂	semidirect
11. C₂×#520×C₆₇	C₂	semidirect
12. C₂³×C₄⋊C₄×C₆₇	C₂	semidirect
17. #554×C₆₇	C₂²	semidirect
18. #553×C₆₇	C₂²	semidirect
19. #552×C₆₇	C₂²	semidirect
20. #547×C₆₇	C₂²	semidirect
21. #544×C₆₇	C₂²	semidirect
22. #539×C₆₇	C₂²	semidirect
23. #537×C₆₇	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
25. C₂×#126×C₆₇	C₂²	semidirect
26. C₂×#125×C₆₇	C₂²	semidirect
27. C₂×#125×C₆₇	C₂²	semidirect
28. #525×C₆₇	C₂²	semidirect
29. #525×C₆₇	C₂²	semidirect
32. C₂×#123×C₆₇	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
38. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
43. C₂×#121×C₆₇	C₂²	semidirect
45. #520×C₆₇	C₂²	semidirect
46. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
51. C₂×C₄×D₄×C₆₇	C₂²	semidirect
54. C₂×#117×C₆₇	C₂²	semidirect
60. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
61. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
88. C₄⋊Q₈×C₆₇	C₂³	semidirect
89. #126×C₆₇	C₂³	semidirect
90. #125×C₆₇	C₂³	semidirect
91. #125×C₆₇	C₂³	semidirect
94. #123×C₆₇	C₂³	semidirect
99. C₂²⋊Q₈×C₆₇	C₂³	semidirect
100. C₂²⋊Q₈×C₆₇	C₂³	semidirect
105. #121×C₆₇	C₂³	semidirect
107. C₄×Q₈×C₆₇	C₂³	semidirect
112. C₄×D₄×C₆₇	C₂³	semidirect
115. #117×C₆₇	C₂³	semidirect
132. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
177. C₂²×C₄×C₆₇	#41	semidirect
259. C₂×C₄×C₆₇	C₂×#41	semidirect
295. C₂×#3492	C₆₇	direct (N × H)
300. C₂×C₆₇	#3492	direct (N × H)
304. #3492	C₂×C₆₇	direct (N × H)
305. C₂×#554	C₂×C₆₇	semidirect
306. C₂×#553	C₂×C₆₇	semidirect
307. C₂×#552	C₂×C₆₇	semidirect
308. C₂×#547	C₂×C₆₇	semidirect
309. C₂×#544	C₂×C₆₇	semidirect
310. C₂×#539	C₂×C₆₇	semidirect
311. C₂×#537	C₂×C₆₇	semidirect
312. C₂×#525	C₂×C₆₇	semidirect
313. C₂×#525	C₂×C₆₇	semidirect
314. C₂×#520	C₂×C₆₇	semidirect
315. C₂³×C₄⋊C₄	C₂×C₆₇	semidirect
316. C₆₇	C₂×#3492	direct (N × H)
321. #554	C₂²×C₆₇	semidirect
322. #553	C₂²×C₆₇	semidirect
323. #552	C₂²×C₆₇	semidirect
324. #547	C₂²×C₆₇	semidirect
325. #544	C₂²×C₆₇	semidirect
326. #539	C₂²×C₆₇	semidirect
327. #537	C₂²×C₆₇	semidirect
328. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
329. C₂×#126	C₂²×C₆₇	semidirect
330. C₂×#125	C₂²×C₆₇	semidirect
331. C₂×#125	C₂²×C₆₇	semidirect
332. #525	C₂²×C₆₇	semidirect
333. #525	C₂²×C₆₇	semidirect
336. C₂×#123	C₂²×C₆₇	semidirect
341. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
342. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
347. C₂×#121	C₂²×C₆₇	semidirect
349. #520	C₂²×C₆₇	semidirect
350. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
355. C₂×C₄×D₄	C₂²×C₆₇	semidirect
358. C₂×#117	C₂²×C₆₇	semidirect
364. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
365. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
392. C₄⋊Q₈	C₂³×C₆₇	semidirect
393. #126	C₂³×C₆₇	semidirect
394. #125	C₂³×C₆₇	semidirect
395. #125	C₂³×C₆₇	semidirect
398. #123	C₂³×C₆₇	semidirect
403. C₂²⋊Q₈	C₂³×C₆₇	semidirect
404. C₂²⋊Q₈	C₂³×C₆₇	semidirect
409. #121	C₂³×C₆₇	semidirect
411. C₄×Q₈	C₂³×C₆₇	semidirect
416. C₄×D₄	C₂³×C₆₇	semidirect
419. #117	C₂³×C₆₇	semidirect
436. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
481. C₂²×C₄	#41×C₆₇	semidirect
563. C₂×C₄	C₂×#41×C₆₇	semidirect
603. C₂	C₆₇×#3492	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3492	2
C₂×#554×C₆₇	2
C₂×#553×C₆₇	2
C₂×#552×C₆₇	2
C₂×#547×C₆₇	2
C₂×#544×C₆₇	2
C₂×#539×C₆₇	2
C₂×#537×C₆₇	2
C₂×#525×C₆₇	2
C₂×#520×C₆₇	2
C₂³×C₄⋊C₄×C₆₇	2
C₂×#3492	67

Subgroups — C2×C67×#3492 #30742019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3492 #30742019