Subgroups — C₂×C₆₇×#3507 #30742028

Order 17152.

7130 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3507	C₂	1	32	yes	maximal, direct product factor
2	C₂×#559×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#557×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#556×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#556×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×#554×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#552×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#539×C₆₇	C₂	1	4	yes	maximal, complemented
9	C₂×#536×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#529×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#520×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₆₇	C₂²	1	2	yes	—
16	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
17	#559×C₆₇	C₂²	1	32	yes	complemented
18	#557×C₆₇	C₂²	1	32	yes	complemented
19	#556×C₆₇	C₂²	1	32	yes	complemented
20	#556×C₆₇	C₂²	1	64	yes	complemented
21	#554×C₆₇	C₂²	1	32	yes	complemented
22	#552×C₆₇	C₂²	1	64	yes	complemented
23	#539×C₆₇	C₂²	1	64	yes	complemented
24	#536×C₆₇	C₂²	1	32	yes	complemented
25	#533×C₆₇	C₂²	1	16	yes	complemented
26	#532×C₆₇	C₂²	1	16	yes	—
27	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₆₇	C₂²	1	4	yes	—
31	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
32	#529×C₆₇	C₂²	1	64	yes	complemented
33	C₂×#126×C₆₇	C₂²	1	8	yes	—
34	C₂×#126×C₆₇	C₂²	1	8	yes	—
35	C₂×#125×C₆₇	C₂²	1	4	yes	—
36	C₂×#125×C₆₇	C₂²	1	2	yes	—
37	C₂×#125×C₆₇	C₂²	1	8	yes	—
38	C₂×#124×C₆₇	C₂²	1	4	yes	—
39	C₂×#124×C₆₇	C₂²	1	2	yes	—
40	C₂×#124×C₆₇	C₂²	1	4	yes	—
41	C₂×#123×C₆₇	C₂²	1	8	yes	—
42	C₂×#123×C₆₇	C₂²	1	8	yes	—
43	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
44	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
45	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
46	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
47	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	8	yes	—
48	C₂×#121×C₆₇	C₂²	1	2	yes	—
49	C₂×#121×C₆₇	C₂²	1	2	yes	—
50	#520×C₆₇	C₂²	1	32	yes	complemented
51	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
52	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
53	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
54	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
55	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
56	C₂×C₄×Q₈×C₆₇	C₂²	1	4	yes	—
57	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
58	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
59	C₂×C₄×Q₈×C₆₇	C₂²	1	16	yes	complemented
60	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	—
61	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
62	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
63	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
64	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
65	C₂×#117×C₆₇	C₂²	1	2	yes	—
66	C₂×#117×C₆₇	C₂²	1	4	yes	—
67	C₂×#117×C₆₇	C₂²	1	8	yes	—
68	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
69	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
70	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
71	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
72	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×#41×C₆₇	—	2	16	no	—
74	C₂×#41×C₆₇	C₂³	1	16	yes	—
75	C₂²×Q₈×C₆₇	—	2	8	no	—
76	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
77	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
78	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
79	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
80	C₂²×Q₈×C₆₇	C₂³	1	8	yes	—
81	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
82	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
83	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
84	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
85	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
89	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
94	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
95	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
96	C₄⋊Q₈×C₆₇	C₂³	1	32	yes	—
97	#127×C₆₇	C₂³	1	8	yes	—
98	#126×C₆₇	C₂³	1	64	yes	—
99	#126×C₆₇	C₂³	1	64	yes	—
100	#125×C₆₇	C₂³	1	32	yes	—
101	#125×C₆₇	C₂³	1	16	yes	—
102	#125×C₆₇	C₂³	1	64	yes	—
103	#124×C₆₇	C₂³	1	32	yes	—
104	#124×C₆₇	C₂³	1	16	yes	—
105	#124×C₆₇	C₂³	1	32	yes	—
106	#123×C₆₇	C₂³	1	64	yes	—
107	#123×C₆₇	C₂³	1	64	yes	—
108	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
109	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
110	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
111	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
112	C₂²⋊Q₈×C₆₇	C₂³	1	64	yes	—
113	#121×C₆₇	C₂³	1	16	yes	—
114	#121×C₆₇	C₂³	1	16	yes	—
115	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
116	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
117	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
118	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
119	C₄×Q₈×C₆₇	C₂³	1	32	yes	—
120	C₄×Q₈×C₆₇	C₂³	1	32	yes	—
121	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
122	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
123	C₄×D₄×C₆₇	C₂³	1	64	yes	—
124	C₄×D₄×C₆₇	C₂³	1	32	yes	—
125	C₄×D₄×C₆₇	C₂³	1	32	yes	—
126	C₄×D₄×C₆₇	C₂³	1	16	yes	—
127	C₄×D₄×C₆₇	C₂³	1	16	yes	—
128	#117×C₆₇	C₂³	1	16	yes	—
129	#117×C₆₇	C₂³	1	32	yes	—
130	#117×C₆₇	C₂³	1	64	yes	—
131	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
155	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
156	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₇	C₂³	1	16	yes	—
162	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
163	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
164	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
165	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
166	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
167	#41×C₆₇	—	2	64	no	—
168	C₂×Q₈×C₆₇	—	2	8	no	—
169	C₂×Q₈×C₆₇	—	2	8	no	—
170	C₂×Q₈×C₆₇	—	2	32	no	—
171	C₂×Q₈×C₆₇	—	2	8	no	—
172	C₂×Q₈×C₆₇	—	2	8	no	—
173	C₂×Q₈×C₆₇	—	4	4	no	—
174	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
175	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
176	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
177	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
178	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
179	C₂×D₄×C₆₇	—	2	16	no	—
180	C₂×D₄×C₆₇	—	2	8	no	—
181	C₂×D₄×C₆₇	—	2	8	no	—
182	C₂×D₄×C₆₇	—	4	4	no	—
183	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
184	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
185	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
186	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
187	C₂²×C₄×C₆₇	—	2	8	no	—
188	C₂²×C₄×C₆₇	—	2	16	no	—
189	C₂²×C₄×C₆₇	—	2	4	no	—
190	C₂²×C₄×C₆₇	—	4	4	no	—
191	C₂²×C₄×C₆₇	—	4	16	no	—
192	C₂²×C₄×C₆₇	—	4	2	no	—
193	C₂²×C₄×C₆₇	#41	1	8	yes	—
194	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
196	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
197	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
206	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₆₇	C₂⁴	1	32	yes	—
208	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
213	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
214	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
215	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	—
216	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
217	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
218	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
219	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
220	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	—
221	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
222	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
223	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
224	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
225	C₄⋊C₄×C₆₇	C₂⁴	1	32	yes	—
226	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
227	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
228	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
229	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
230	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
231	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
232	C₂²⋊C₄×C₆₇	C₂⁴	1	32	yes	—
233	C₄²×C₆₇	C₂⁴	1	16	yes	—
234	C₄²×C₆₇	C₂⁴	1	4	yes	—
235	C₄²×C₆₇	C₂⁴	1	4	yes	—
236	C₄²×C₆₇	C₂⁴	1	16	yes	—
237	C₄²×C₆₇	C₂⁴	1	4	yes	—
238	C₄²×C₆₇	C₂⁴	1	4	yes	—
239	C₄²×C₆₇	C₂⁴	1	32	yes	—
240	C₄²×C₆₇	C₂⁴	1	16	yes	—
241	C₂³×C₆₇	—	2	2	no	—
242	C₂³×C₆₇	—	2	2	no	—
243	C₂³×C₆₇	—	2	8	no	—
244	C₂³×C₆₇	—	2	8	no	—
245	C₂³×C₆₇	—	2	8	no	—
246	C₂³×C₆₇	C₂×#41	1	4	yes	—
247	C₂³×C₆₇	C₂⁵	1	8	yes	—
248	C₂³×C₆₇	C₂⁵	1	2	yes	—
249	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
250	Q₈×C₆₇	—	2	16	no	—
251	Q₈×C₆₇	—	2	16	no	—
252	Q₈×C₆₇	—	2	16	no	—
253	Q₈×C₆₇	—	2	16	no	—
254	Q₈×C₆₇	—	4	8	no	—
255	D₄×C₆₇	—	2	32	no	—
256	D₄×C₆₇	—	2	16	no	—
257	D₄×C₆₇	—	2	16	no	—
258	D₄×C₆₇	—	4	8	no	—
259	C₂×C₄×C₆₇	—	2	8	no	—
260	C₂×C₄×C₆₇	—	2	16	no	—
261	C₂×C₄×C₆₇	—	2	8	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	8	no	—
264	C₂×C₄×C₆₇	—	2	8	no	—
265	C₂×C₄×C₆₇	—	2	8	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	2	no	—
268	C₂×C₄×C₆₇	—	2	32	no	—
269	C₂×C₄×C₆₇	—	2	8	no	—
270	C₂×C₄×C₆₇	—	4	8	no	—
271	C₂×C₄×C₆₇	—	4	32	no	—
272	C₂×C₄×C₆₇	—	4	4	no	—
273	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
274	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
275	C₂×C₄×C₆₇	C₂×#41	1	16	yes	—
276	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
277	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
278	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
279	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
280	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
281	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
282	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
283	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
284	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
285	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
286	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
287	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
288	C₂²×C₆₇	—	2	2	no	—
289	C₂²×C₆₇	—	2	2	no	—
290	C₂²×C₆₇	—	2	8	no	—
291	C₂²×C₆₇	—	2	8	no	—
292	C₂²×C₆₇	—	2	8	no	—
293	C₂²×C₆₇	—	2	8	no	—
294	C₂²×C₆₇	—	4	16	no	—
295	C₂²×C₆₇	C₂²×#41	1	4	yes	—
296	C₂²×C₆₇	C₂²×#41	1	2	yes	—
297	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
298	C₂²×C₆₇	#585	1	2	yes	—
299	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
300	C₄×C₆₇	—	2	8	no	—
301	C₄×C₆₇	—	2	8	no	—
302	C₄×C₆₇	—	2	2	no	—
303	C₄×C₆₇	—	2	8	no	—
304	C₄×C₆₇	—	2	8	no	—
305	C₄×C₆₇	—	2	8	no	—
306	C₄×C₆₇	—	2	2	no	—
307	C₄×C₆₇	—	2	2	no	—
308	C₄×C₆₇	C₂²×#41	1	4	yes	—
309	C₄×C₆₇	C₂²×#41	1	4	yes	—
310	C₄×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
311	C₂×#3507	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂×C₆₇	—	2	4	no	—
313	C₂×C₆₇	—	4	8	no	—
314	C₂×C₆₇	#3507	1	4	yes	direct product factor
315	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
316	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
318	#3507	C₂×C₆₇	1	32	yes	direct product factor
319	C₂×#559	C₂×C₆₇	1	2	yes	complemented
320	C₂×#557	C₂×C₆₇	1	2	yes	complemented
321	C₂×#556	C₂×C₆₇	1	2	yes	complemented
322	C₂×#556	C₂×C₆₇	1	4	yes	complemented
323	C₂×#554	C₂×C₆₇	1	2	yes	complemented
324	C₂×#552	C₂×C₆₇	1	4	yes	complemented
325	C₂×#539	C₂×C₆₇	1	4	yes	complemented
326	C₂×#536	C₂×C₆₇	1	2	yes	complemented
327	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
328	C₂×#532	C₂×C₆₇	1	1	yes	characteristic
329	C₂×#529	C₂×C₆₇	1	4	yes	complemented
330	C₂×#520	C₂×C₆₇	1	2	yes	complemented
331	C₂²×C₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
332	C₆₇	C₂×#3507	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²×#41	C₂²×C₆₇	1	2	yes	—
334	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
335	#559	C₂²×C₆₇	1	32	yes	complemented
336	#557	C₂²×C₆₇	1	32	yes	complemented
337	#556	C₂²×C₆₇	1	32	yes	complemented
338	#556	C₂²×C₆₇	1	64	yes	complemented
339	#554	C₂²×C₆₇	1	32	yes	complemented
340	#552	C₂²×C₆₇	1	64	yes	complemented
341	#539	C₂²×C₆₇	1	64	yes	complemented
342	#536	C₂²×C₆₇	1	32	yes	complemented
343	#533	C₂²×C₆₇	1	16	yes	complemented
344	#532	C₂²×C₆₇	1	16	yes	—
345	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
346	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
347	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
348	C₂×C₄⋊Q₈	C₂²×C₆₇	1	4	yes	—
349	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
350	#529	C₂²×C₆₇	1	64	yes	complemented
351	C₂×#126	C₂²×C₆₇	1	8	yes	—
352	C₂×#126	C₂²×C₆₇	1	8	yes	—
353	C₂×#125	C₂²×C₆₇	1	4	yes	—
354	C₂×#125	C₂²×C₆₇	1	2	yes	—
355	C₂×#125	C₂²×C₆₇	1	8	yes	—
356	C₂×#124	C₂²×C₆₇	1	4	yes	—
357	C₂×#124	C₂²×C₆₇	1	2	yes	—
358	C₂×#124	C₂²×C₆₇	1	4	yes	—
359	C₂×#123	C₂²×C₆₇	1	8	yes	—
360	C₂×#123	C₂²×C₆₇	1	8	yes	—
361	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
364	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	8	yes	—
366	C₂×#121	C₂²×C₆₇	1	2	yes	—
367	C₂×#121	C₂²×C₆₇	1	2	yes	—
368	#520	C₂²×C₆₇	1	32	yes	complemented
369	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
370	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
371	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
372	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
373	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
374	C₂×C₄×Q₈	C₂²×C₆₇	1	4	yes	—
375	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
376	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
377	C₂×C₄×Q₈	C₂²×C₆₇	1	16	yes	complemented
378	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	—
379	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
380	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
381	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
383	C₂×#117	C₂²×C₆₇	1	2	yes	—
384	C₂×#117	C₂²×C₆₇	1	4	yes	—
385	C₂×#117	C₂²×C₆₇	1	8	yes	—
386	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
388	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
389	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
390	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
391	C₂×#41	—	2	16	no	—
392	C₂×#41	C₂³×C₆₇	1	16	yes	—
393	C₂²×Q₈	—	2	8	no	—
394	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
395	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
396	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
397	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
398	C₂²×Q₈	C₂³×C₆₇	1	8	yes	—
399	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
400	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
401	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
402	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
403	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
404	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
405	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
406	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
408	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₆₇	1	8	yes	—
410	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
411	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
412	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
413	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
414	C₄⋊Q₈	C₂³×C₆₇	1	32	yes	—
415	#127	C₂³×C₆₇	1	8	yes	—
416	#126	C₂³×C₆₇	1	64	yes	—
417	#126	C₂³×C₆₇	1	64	yes	—
418	#125	C₂³×C₆₇	1	32	yes	—
419	#125	C₂³×C₆₇	1	16	yes	—
420	#125	C₂³×C₆₇	1	64	yes	—
421	#124	C₂³×C₆₇	1	32	yes	—
422	#124	C₂³×C₆₇	1	16	yes	—
423	#124	C₂³×C₆₇	1	32	yes	—
424	#123	C₂³×C₆₇	1	64	yes	—
425	#123	C₂³×C₆₇	1	64	yes	—
426	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
427	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
428	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
429	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
430	C₂²⋊Q₈	C₂³×C₆₇	1	64	yes	—
431	#121	C₂³×C₆₇	1	16	yes	—
432	#121	C₂³×C₆₇	1	16	yes	—
433	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
434	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
435	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
436	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
437	C₄×Q₈	C₂³×C₆₇	1	32	yes	—
438	C₄×Q₈	C₂³×C₆₇	1	32	yes	—
439	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
440	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
441	C₄×D₄	C₂³×C₆₇	1	64	yes	—
442	C₄×D₄	C₂³×C₆₇	1	32	yes	—
443	C₄×D₄	C₂³×C₆₇	1	32	yes	—
444	C₄×D₄	C₂³×C₆₇	1	16	yes	—
445	C₄×D₄	C₂³×C₆₇	1	16	yes	—
446	#117	C₂³×C₆₇	1	16	yes	—
447	#117	C₂³×C₆₇	1	32	yes	—
448	#117	C₂³×C₆₇	1	64	yes	—
449	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
453	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
456	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
457	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
458	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
461	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
466	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
473	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
474	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
475	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
476	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
479	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₆₇	1	16	yes	—
482	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
483	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
484	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
485	#41	—	2	64	no	—
486	C₂×Q₈	—	2	8	no	—
487	C₂×Q₈	—	2	8	no	—
488	C₂×Q₈	—	2	32	no	—
489	C₂×Q₈	—	2	8	no	—
490	C₂×Q₈	—	2	8	no	—
491	C₂×Q₈	—	4	4	no	—
492	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
493	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
494	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
495	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
496	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
497	C₂×D₄	—	2	16	no	—
498	C₂×D₄	—	2	8	no	—
499	C₂×D₄	—	2	8	no	—
500	C₂×D₄	—	4	4	no	—
501	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
502	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
503	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
504	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
505	C₂²×C₄	—	2	8	no	—
506	C₂²×C₄	—	2	16	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	4	4	no	—
509	C₂²×C₄	—	4	16	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	#41×C₆₇	1	8	yes	—
512	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
516	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
517	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
519	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
521	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
523	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
524	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₆₇	1	32	yes	—
526	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
530	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
531	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
532	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
533	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	—
534	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
535	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
536	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
537	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
538	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	—
539	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
540	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
541	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
542	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
543	C₄⋊C₄	C₂⁴×C₆₇	1	32	yes	—
544	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
545	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
546	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
547	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
548	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
549	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
550	C₂²⋊C₄	C₂⁴×C₆₇	1	32	yes	—
551	C₄²	C₂⁴×C₆₇	1	16	yes	—
552	C₄²	C₂⁴×C₆₇	1	4	yes	—
553	C₄²	C₂⁴×C₆₇	1	4	yes	—
554	C₄²	C₂⁴×C₆₇	1	16	yes	—
555	C₄²	C₂⁴×C₆₇	1	4	yes	—
556	C₄²	C₂⁴×C₆₇	1	4	yes	—
557	C₄²	C₂⁴×C₆₇	1	32	yes	—
558	C₄²	C₂⁴×C₆₇	1	16	yes	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	8	no	—
562	C₂³	—	2	8	no	—
563	C₂³	—	2	8	no	—
564	C₂³	C₂×#41×C₆₇	1	4	yes	—
565	C₂³	C₂⁵×C₆₇	1	8	yes	—
566	C₂³	C₂⁵×C₆₇	1	2	yes	—
567	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
568	Q₈	—	2	16	no	—
569	Q₈	—	2	16	no	—
570	Q₈	—	2	16	no	—
571	Q₈	—	2	16	no	—
572	Q₈	—	4	8	no	—
573	D₄	—	2	32	no	—
574	D₄	—	2	16	no	—
575	D₄	—	2	16	no	—
576	D₄	—	4	8	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	16	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	8	no	—
583	C₂×C₄	—	2	8	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	32	no	—
587	C₂×C₄	—	2	8	no	—
588	C₂×C₄	—	4	8	no	—
589	C₂×C₄	—	4	32	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
592	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
593	C₂×C₄	C₂×#41×C₆₇	1	16	yes	—
594	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
595	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
596	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
597	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
598	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
599	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
600	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
601	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
602	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
603	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
604	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
605	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	8	no	—
612	C₂²	—	4	16	no	—
613	C₂²	C₂²×#41×C₆₇	1	4	yes	—
614	C₂²	C₂²×#41×C₆₇	1	2	yes	—
615	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
616	C₂²	#585×C₆₇	1	2	yes	—
617	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
618	C₄	—	2	8	no	—
619	C₄	—	2	8	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	8	no	—
622	C₄	—	2	8	no	—
623	C₄	—	2	8	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	C₂²×#41×C₆₇	1	4	yes	—
627	C₄	C₂²×#41×C₆₇	1	4	yes	—
628	C₄	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
629	C₂	—	2	4	no	—
630	C₂	—	4	8	no	—
631	C₂	C₆₇×#3507	1	4	yes	direct product factor
632	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
633	C₂	C₂²×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
634	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
prime radical	C₂×#532×C₆₇	C₂
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×#3507	C₂	direct (N × H)
2. C₂×#559×C₆₇	C₂	semidirect
3. C₂×#557×C₆₇	C₂	semidirect
4. C₂×#556×C₆₇	C₂	semidirect
5. C₂×#556×C₆₇	C₂	semidirect
6. C₂×#554×C₆₇	C₂	semidirect
7. C₂×#552×C₆₇	C₂	semidirect
8. C₂×#539×C₆₇	C₂	semidirect
9. C₂×#536×C₆₇	C₂	semidirect
10. C₂×#533×C₆₇	C₂	semidirect
12. C₂×#529×C₆₇	C₂	semidirect
13. C₂×#520×C₆₇	C₂	semidirect
14. C₂²×C₄×Q₈×C₆₇	C₂	semidirect
17. #559×C₆₇	C₂²	semidirect
18. #557×C₆₇	C₂²	semidirect
19. #556×C₆₇	C₂²	semidirect
20. #556×C₆₇	C₂²	semidirect
21. #554×C₆₇	C₂²	semidirect
22. #552×C₆₇	C₂²	semidirect
23. #539×C₆₇	C₂²	semidirect
24. #536×C₆₇	C₂²	semidirect
25. #533×C₆₇	C₂²	semidirect
32. #529×C₆₇	C₂²	semidirect
50. #520×C₆₇	C₂²	semidirect
59. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
311. C₂×#3507	C₆₇	direct (N × H)
314. C₂×C₆₇	#3507	direct (N × H)
318. #3507	C₂×C₆₇	direct (N × H)
319. C₂×#559	C₂×C₆₇	semidirect
320. C₂×#557	C₂×C₆₇	semidirect
321. C₂×#556	C₂×C₆₇	semidirect
322. C₂×#556	C₂×C₆₇	semidirect
323. C₂×#554	C₂×C₆₇	semidirect
324. C₂×#552	C₂×C₆₇	semidirect
325. C₂×#539	C₂×C₆₇	semidirect
326. C₂×#536	C₂×C₆₇	semidirect
327. C₂×#533	C₂×C₆₇	semidirect
329. C₂×#529	C₂×C₆₇	semidirect
330. C₂×#520	C₂×C₆₇	semidirect
331. C₂²×C₄×Q₈	C₂×C₆₇	semidirect
332. C₆₇	C₂×#3507	direct (N × H)
335. #559	C₂²×C₆₇	semidirect
336. #557	C₂²×C₆₇	semidirect
337. #556	C₂²×C₆₇	semidirect
338. #556	C₂²×C₆₇	semidirect
339. #554	C₂²×C₆₇	semidirect
340. #552	C₂²×C₆₇	semidirect
341. #539	C₂²×C₆₇	semidirect
342. #536	C₂²×C₆₇	semidirect
343. #533	C₂²×C₆₇	semidirect
350. #529	C₂²×C₆₇	semidirect
368. #520	C₂²×C₆₇	semidirect
377. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
631. C₂	C₆₇×#3507	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×#3507	2
C₂×#559×C₆₇	2
C₂×#557×C₆₇	2
C₂×#556×C₆₇	2
C₂×#554×C₆₇	2
C₂×#552×C₆₇	2
C₂×#539×C₆₇	2
C₂×#536×C₆₇	2
C₂×#533×C₆₇	2
C₂×#532×C₆₇	2
C₂×#529×C₆₇	2
C₂×#520×C₆₇	2
C₂²×C₄×Q₈×C₆₇	2
C₂×#3507	67

Subgroups — C2×C67×#3507 #30742028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3507 #30742028