Subgroups — C₆₇×#59378 #30738629

Order 17152.

2212 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2760	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2697	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2576	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2561	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2494	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2463	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2452	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2420	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2408	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2357	C₂	1	2	yes	maximal, complemented
13	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₄×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#121×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#121×C₆₇	C₂²	1	2	yes	—
21	C₂×#120×C₆₇	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
26	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
27	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#401×C₆₇	C₂²	1	4	yes	complemented
29	#397×C₆₇	C₂²	1	4	yes	—
30	#397×C₆₇	C₂²	1	4	yes	complemented
31	#396×C₆₇	C₂²	1	4	yes	complemented
32	#394×C₆₇	C₂²	1	2	yes	—
33	#394×C₆₇	C₂²	1	4	yes	complemented
34	#393×C₆₇	C₂²	1	2	yes	—
35	#393×C₆₇	C₂²	1	4	yes	complemented
36	#393×C₆₇	C₂²	1	2	yes	complemented
37	#392×C₆₇	C₂²	1	2	yes	—
38	#390×C₆₇	C₂²	1	2	yes	—
39	#390×C₆₇	C₂²	1	2	yes	—
40	#390×C₆₇	C₂²	1	2	yes	—
41	#390×C₆₇	C₂²	1	2	yes	—
42	#389×C₆₇	C₂²	1	2	yes	complemented
43	#389×C₆₇	C₂²	1	2	yes	complemented
44	#388×C₆₇	C₂²	1	2	yes	—
45	#388×C₆₇	C₂²	1	4	yes	—
46	#388×C₆₇	C₂²	1	4	yes	complemented
47	#388×C₆₇	C₂²	1	4	yes	complemented
48	#388×C₆₇	C₂²	1	4	yes	complemented
49	#387×C₆₇	C₂²	1	2	yes	complemented
50	#387×C₆₇	C₂²	1	4	yes	complemented
51	#386×C₆₇	C₂²	1	4	yes	—
52	#386×C₆₇	C₂²	1	1	yes	characteristic
53	#386×C₆₇	C₂²	1	4	yes	—
54	#386×C₆₇	C₂²	1	4	yes	complemented
55	#386×C₆₇	C₂²	1	4	yes	complemented
56	#385×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#385×C₆₇	C₂²	1	4	yes	complemented
58	#382×C₆₇	C₂²	1	2	yes	complemented
59	#382×C₆₇	C₂²	1	2	yes	complemented
60	#381×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	#381×C₆₇	C₂²	1	4	yes	complemented
62	#381×C₆₇	C₂²	1	4	yes	complemented
63	#380×C₆₇	C₂²	1	2	yes	—
64	#380×C₆₇	C₂²	1	1	yes	characteristic
65	#380×C₆₇	C₂²	1	2	yes	complemented
66	#379×C₆₇	C₂²	1	2	yes	—
67	#379×C₆₇	C₂²	1	4	yes	—
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
69	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
70	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
75	C₂⁵×C₆₇	C₂³	1	2	yes	—
76	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
77	C₂²×D₄×C₆₇	—	2	8	no	—
78	C₂²×D₄×C₆₇	—	4	2	no	—
79	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
80	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
81	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
82	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
89	C₄⋊Q₈×C₆₇	—	4	2	no	—
90	#123×C₆₇	—	2	4	no	—
91	C₂²⋊Q₈×C₆₇	—	4	8	no	—
92	#121×C₆₇	—	2	8	no	—
93	#120×C₆₇	—	2	8	no	—
94	C₄×D₄×C₆₇	—	2	8	no	—
95	C₄×D₄×C₆₇	—	4	4	no	—
96	C₄×D₄×C₆₇	—	4	2	no	—
97	C₄×D₄×C₆₇	—	4	8	no	—
98	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₆₇	—	4	8	no	—
108	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₆₇	—	4	2	no	—
127	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
130	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
132	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
133	#95×C₆₇	C₂³	1	2	yes	—
134	#95×C₆₇	C₂³	1	2	yes	—
135	#95×C₆₇	C₂³	1	2	yes	—
136	#95×C₆₇	C₂³	1	4	yes	—
137	#95×C₆₇	C₂³	1	2	yes	—
138	#95×C₆₇	C₂³	1	4	yes	—
139	#95×C₆₇	C₂³	1	4	yes	—
140	#95×C₆₇	C₂³	1	2	yes	—
141	#95×C₆₇	C₂³	1	2	yes	—
142	#95×C₆₇	C₂³	1	4	yes	—
143	#95×C₆₇	C₂³	1	4	yes	—
144	#95×C₆₇	C₂³	1	2	yes	—
145	#95×C₆₇	C₂³	1	4	yes	—
146	#95×C₆₇	C₂³	1	4	yes	—
147	C₂⁴×C₆₇	—	2	4	no	—
148	C₂⁴×C₆₇	—	2	8	no	—
149	C₂⁴×C₆₇	—	4	4	no	—
150	C₂⁴×C₆₇	—	4	2	no	—
151	C₂⁴×C₆₇	—	4	2	no	—
152	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
153	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
154	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
155	C₂×Q₈×C₆₇	—	4	4	no	—
156	C₂×Q₈×C₆₇	—	4	2	no	—
157	C₂×D₄×C₆₇	—	2	8	no	—
158	C₂×D₄×C₆₇	—	2	8	no	—
159	C₂×D₄×C₆₇	—	2	8	no	—
160	C₂×D₄×C₆₇	—	2	4	no	—
161	C₂×D₄×C₆₇	—	2	4	no	—
162	C₂×D₄×C₆₇	—	4	1	no	—
163	C₂×D₄×C₆₇	—	4	4	no	—
164	C₂×D₄×C₆₇	—	4	2	no	—
165	C₂×D₄×C₆₇	—	4	1	no	—
166	C₂×D₄×C₆₇	—	4	16	no	—
167	C₂×D₄×C₆₇	#41	1	8	yes	—
168	C₂×D₄×C₆₇	#41	1	4	yes	—
169	C₂²×C₄×C₆₇	—	2	2	no	—
170	C₂²×C₄×C₆₇	—	2	8	no	—
171	C₂²×C₄×C₆₇	—	2	4	no	—
172	C₂²×C₄×C₆₇	—	2	4	no	—
173	C₂²×C₄×C₆₇	—	2	2	no	—
174	C₂²×C₄×C₆₇	—	2	4	no	—
175	C₂²×C₄×C₆₇	—	2	2	no	—
176	C₂²×C₄×C₆₇	—	2	8	no	—
177	C₂²×C₄×C₆₇	—	4	1	no	—
178	C₂²×C₄×C₆₇	—	4	1	no	—
179	C₂²×C₄×C₆₇	—	4	1	no	—
180	C₂²×C₄×C₆₇	—	4	4	no	—
181	C₂²×C₄×C₆₇	—	4	4	no	—
182	C₂²×C₄×C₆₇	—	4	4	no	—
183	C₂²×C₄×C₆₇	—	4	4	no	—
184	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
196	C₄⋊C₄×C₆₇	—	2	4	no	—
197	C₄⋊C₄×C₆₇	—	2	4	no	—
198	C₄⋊C₄×C₆₇	—	2	4	no	—
199	C₄⋊C₄×C₆₇	—	2	8	no	—
200	C₄⋊C₄×C₆₇	—	2	4	no	—
201	C₄⋊C₄×C₆₇	—	2	4	no	—
202	C₄⋊C₄×C₆₇	—	4	1	no	—
203	C₄⋊C₄×C₆₇	—	4	4	no	—
204	C₄⋊C₄×C₆₇	—	4	2	no	—
205	C₂²⋊C₄×C₆₇	—	2	8	no	—
206	C₂²⋊C₄×C₆₇	—	2	4	no	—
207	C₂²⋊C₄×C₆₇	—	2	8	no	—
208	C₂²⋊C₄×C₆₇	—	2	2	no	—
209	C₂²⋊C₄×C₆₇	—	2	4	no	—
210	C₂²⋊C₄×C₆₇	—	2	8	no	—
211	C₂²⋊C₄×C₆₇	—	2	4	no	—
212	C₂²⋊C₄×C₆₇	—	2	8	no	—
213	C₂²⋊C₄×C₆₇	—	4	4	no	—
214	C₂²⋊C₄×C₆₇	—	4	4	no	—
215	C₂²⋊C₄×C₆₇	—	4	4	no	—
216	C₂²⋊C₄×C₆₇	—	4	1	no	—
217	C₂²⋊C₄×C₆₇	—	4	4	no	—
218	C₂²⋊C₄×C₆₇	—	4	1	no	—
219	C₂²⋊C₄×C₆₇	—	4	1	no	—
220	C₂²⋊C₄×C₆₇	—	4	4	no	—
221	C₂²⋊C₄×C₆₇	—	4	4	no	—
222	C₂²⋊C₄×C₆₇	—	4	4	no	—
223	C₄²×C₆₇	—	2	4	no	—
224	C₄²×C₆₇	—	2	4	no	—
225	C₄²×C₆₇	—	2	2	no	—
226	C₄²×C₆₇	—	4	2	no	—
227	C₄²×C₆₇	—	4	2	no	—
228	C₄²×C₆₇	—	4	4	no	—
229	C₂³×C₆₇	—	2	4	no	—
230	C₂³×C₆₇	—	2	2	no	—
231	C₂³×C₆₇	—	2	2	no	—
232	C₂³×C₆₇	—	2	4	no	—
233	C₂³×C₆₇	—	2	2	no	—
234	C₂³×C₆₇	—	2	4	no	—
235	C₂³×C₆₇	—	2	4	no	—
236	C₂³×C₆₇	—	2	2	no	—
237	C₂³×C₆₇	—	2	1	no	—
238	C₂³×C₆₇	—	2	1	no	—
239	C₂³×C₆₇	—	2	4	no	—
240	C₂³×C₆₇	—	2	1	no	—
241	C₂³×C₆₇	—	2	4	no	—
242	C₂³×C₆₇	—	2	1	no	—
243	C₂³×C₆₇	—	4	8	no	—
244	C₂³×C₆₇	—	4	16	no	—
245	C₂³×C₆₇	—	8	4	no	—
246	C₂³×C₆₇	—	8	8	no	—
247	C₂³×C₆₇	—	8	4	no	—
248	C₂³×C₆₇	C₂×#41	1	2	yes	—
249	C₂³×C₆₇	C₂×#41	1	8	yes	—
250	C₂³×C₆₇	C₂×#41	1	2	yes	—
251	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
252	Q₈×C₆₇	—	8	4	no	—
253	D₄×C₆₇	—	2	16	no	—
254	D₄×C₆₇	—	4	4	no	—
255	D₄×C₆₇	—	4	16	no	—
256	D₄×C₆₇	—	4	8	no	—
257	C₂×C₄×C₆₇	—	2	2	no	—
258	C₂×C₄×C₆₇	—	2	1	no	—
259	C₂×C₄×C₆₇	—	2	2	no	—
260	C₂×C₄×C₆₇	—	2	1	no	—
261	C₂×C₄×C₆₇	—	2	2	no	—
262	C₂×C₄×C₆₇	—	2	2	no	—
263	C₂×C₄×C₆₇	—	2	2	no	—
264	C₂×C₄×C₆₇	—	2	2	no	—
265	C₂×C₄×C₆₇	—	2	4	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	4	no	—
268	C₂×C₄×C₆₇	—	2	4	no	—
269	C₂×C₄×C₆₇	—	2	2	no	—
270	C₂×C₄×C₆₇	—	2	2	no	—
271	C₂×C₄×C₆₇	—	2	1	no	—
272	C₂×C₄×C₆₇	—	2	1	no	—
273	C₂×C₄×C₆₇	—	2	4	no	—
274	C₂×C₄×C₆₇	—	2	4	no	—
275	C₂×C₄×C₆₇	—	2	2	no	—
276	C₂×C₄×C₆₇	—	2	2	no	—
277	C₂×C₄×C₆₇	—	2	4	no	—
278	C₂×C₄×C₆₇	—	2	2	no	—
279	C₂×C₄×C₆₇	—	2	4	no	—
280	C₂×C₄×C₆₇	—	2	4	no	—
281	C₂×C₄×C₆₇	—	2	1	no	—
282	C₂×C₄×C₆₇	—	2	4	no	—
283	C₂×C₄×C₆₇	—	2	2	no	—
284	C₂×C₄×C₆₇	—	2	2	no	—
285	C₂×C₄×C₆₇	—	4	4	no	—
286	C₂×C₄×C₆₇	—	4	4	no	—
287	C₂×C₄×C₆₇	—	4	4	no	—
288	C₂×C₄×C₆₇	—	4	4	no	—
289	C₂×C₄×C₆₇	—	8	8	no	—
290	C₂×C₄×C₆₇	—	8	8	no	—
291	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
292	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
293	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
294	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
295	C₂²×C₆₇	—	2	8	no	—
296	C₂²×C₆₇	—	2	4	no	—
297	C₂²×C₆₇	—	2	8	no	—
298	C₂²×C₆₇	—	2	4	no	—
299	C₂²×C₆₇	—	2	2	no	—
300	C₂²×C₆₇	—	2	2	no	—
301	C₂²×C₆₇	—	2	8	no	—
302	C₂²×C₆₇	—	4	1	no	—
303	C₂²×C₆₇	—	4	1	no	—
304	C₂²×C₆₇	—	4	4	no	—
305	C₂²×C₆₇	—	4	4	no	—
306	C₂²×C₆₇	—	4	2	no	—
307	C₂²×C₆₇	—	4	4	no	—
308	C₂²×C₆₇	—	4	2	no	—
309	C₂²×C₆₇	—	4	1	no	—
310	C₂²×C₆₇	—	4	4	no	—
311	C₂²×C₆₇	—	4	1	no	—
312	C₂²×C₆₇	—	8	16	no	—
313	C₂²×C₆₇	C₂²×#41	1	2	yes	—
314	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
315	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
317	C₂²×C₆₇	#585	1	1	yes	characteristic
318	C₄×C₆₇	—	2	2	no	—
319	C₄×C₆₇	—	2	4	no	—
320	C₄×C₆₇	—	4	1	no	—
321	C₄×C₆₇	—	4	1	no	—
322	C₄×C₆₇	—	4	2	no	—
323	C₄×C₆₇	—	4	4	no	—
324	C₄×C₆₇	—	4	2	no	—
325	C₄×C₆₇	—	4	4	no	—
326	C₄×C₆₇	—	4	2	no	—
327	C₄×C₆₇	—	4	4	no	—
328	C₄×C₆₇	—	4	1	no	—
329	C₄×C₆₇	#551	1	4	yes	—
330	#59378	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₂×C₆₇	—	4	2	no	—
332	C₂×C₆₇	—	4	8	no	—
333	C₂×C₆₇	—	4	2	no	—
334	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
335	C₂×C₆₇	#3481	1	2	yes	—
336	C₂×C₆₇	#3505	1	1	yes	characteristic
337	C₂×C₆₇	#3514	1	2	yes	—
338	C₂×C₆₇	#3537	1	1	yes	characteristic
339	#2760	C₂×C₆₇	1	2	yes	complemented
340	#2697	C₂×C₆₇	1	2	yes	complemented
341	#2576	C₂×C₆₇	1	4	yes	complemented
342	#2563	C₂×C₆₇	1	1	yes	characteristic, complemented
343	#2561	C₂×C₆₇	1	4	yes	complemented
344	#2494	C₂×C₆₇	1	2	yes	complemented
345	#2463	C₂×C₆₇	1	2	yes	complemented
346	#2452	C₂×C₆₇	1	2	yes	complemented
347	#2420	C₂×C₆₇	1	2	yes	complemented
348	#2408	C₂×C₆₇	1	1	yes	characteristic
349	#2358	C₂×C₆₇	1	2	yes	complemented
350	#2357	C₂×C₆₇	1	2	yes	complemented
351	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
352	C₄×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
353	C₄×#121	C₂×C₆₇	1	2	yes	complemented
354	C₆₇	#59378	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
356	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
357	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
358	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
359	C₂×#121	C₂²×C₆₇	1	2	yes	—
360	C₂×#120	C₂²×C₆₇	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
362	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
363	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
364	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
365	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
366	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
367	#401	C₂²×C₆₇	1	4	yes	complemented
368	#397	C₂²×C₆₇	1	4	yes	—
369	#397	C₂²×C₆₇	1	4	yes	complemented
370	#396	C₂²×C₆₇	1	4	yes	complemented
371	#394	C₂²×C₆₇	1	2	yes	—
372	#394	C₂²×C₆₇	1	4	yes	complemented
373	#393	C₂²×C₆₇	1	2	yes	—
374	#393	C₂²×C₆₇	1	4	yes	complemented
375	#393	C₂²×C₆₇	1	2	yes	complemented
376	#392	C₂²×C₆₇	1	2	yes	—
377	#390	C₂²×C₆₇	1	2	yes	—
378	#390	C₂²×C₆₇	1	2	yes	—
379	#390	C₂²×C₆₇	1	2	yes	—
380	#390	C₂²×C₆₇	1	2	yes	—
381	#389	C₂²×C₆₇	1	2	yes	complemented
382	#389	C₂²×C₆₇	1	2	yes	complemented
383	#388	C₂²×C₆₇	1	2	yes	—
384	#388	C₂²×C₆₇	1	4	yes	—
385	#388	C₂²×C₆₇	1	4	yes	complemented
386	#388	C₂²×C₆₇	1	4	yes	complemented
387	#388	C₂²×C₆₇	1	4	yes	complemented
388	#387	C₂²×C₆₇	1	2	yes	complemented
389	#387	C₂²×C₆₇	1	4	yes	complemented
390	#386	C₂²×C₆₇	1	4	yes	—
391	#386	C₂²×C₆₇	1	4	yes	—
392	#386	C₂²×C₆₇	1	1	yes	characteristic
393	#386	C₂²×C₆₇	1	4	yes	complemented
394	#386	C₂²×C₆₇	1	4	yes	complemented
395	#385	C₂²×C₆₇	1	4	yes	complemented
396	#385	C₂²×C₆₇	1	1	yes	characteristic, complemented
397	#382	C₂²×C₆₇	1	2	yes	complemented
398	#382	C₂²×C₆₇	1	2	yes	complemented
399	#381	C₂²×C₆₇	1	4	yes	complemented
400	#381	C₂²×C₆₇	1	4	yes	complemented
401	#381	C₂²×C₆₇	1	1	yes	characteristic, complemented
402	#380	C₂²×C₆₇	1	2	yes	—
403	#380	C₂²×C₆₇	1	1	yes	characteristic
404	#380	C₂²×C₆₇	1	2	yes	complemented
405	#379	C₂²×C₆₇	1	2	yes	—
406	#379	C₂²×C₆₇	1	4	yes	—
407	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
408	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
409	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
410	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
412	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
413	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
414	C₂⁵	C₂³×C₆₇	1	2	yes	—
415	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
416	C₂²×D₄	—	2	8	no	—
417	C₂²×D₄	—	4	2	no	—
418	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
419	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
420	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
421	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
426	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
427	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
428	C₄⋊Q₈	—	4	2	no	—
429	#123	—	2	4	no	—
430	C₂²⋊Q₈	—	4	8	no	—
431	#121	—	2	8	no	—
432	#120	—	2	8	no	—
433	C₄×D₄	—	2	8	no	—
434	C₄×D₄	—	4	4	no	—
435	C₄×D₄	—	4	2	no	—
436	C₄×D₄	—	4	8	no	—
437	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
446	C₂×C₂²⋊C₄	—	4	8	no	—
447	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
465	C₂×C₄²	—	4	2	no	—
466	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
468	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
469	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
470	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
471	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
472	#95	C₂³×C₆₇	1	2	yes	—
473	#95	C₂³×C₆₇	1	2	yes	—
474	#95	C₂³×C₆₇	1	2	yes	—
475	#95	C₂³×C₆₇	1	4	yes	—
476	#95	C₂³×C₆₇	1	2	yes	—
477	#95	C₂³×C₆₇	1	4	yes	—
478	#95	C₂³×C₆₇	1	4	yes	—
479	#95	C₂³×C₆₇	1	2	yes	—
480	#95	C₂³×C₆₇	1	2	yes	—
481	#95	C₂³×C₆₇	1	4	yes	—
482	#95	C₂³×C₆₇	1	4	yes	—
483	#95	C₂³×C₆₇	1	2	yes	—
484	#95	C₂³×C₆₇	1	4	yes	—
485	#95	C₂³×C₆₇	1	4	yes	—
486	C₂⁴	—	2	4	no	—
487	C₂⁴	—	2	8	no	—
488	C₂⁴	—	4	4	no	—
489	C₂⁴	—	4	2	no	—
490	C₂⁴	—	4	2	no	—
491	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
492	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
493	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
494	C₂×Q₈	—	4	4	no	—
495	C₂×Q₈	—	4	2	no	—
496	C₂×D₄	—	2	8	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	8	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	4	1	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	—	4	16	no	—
506	C₂×D₄	#41×C₆₇	1	8	yes	—
507	C₂×D₄	#41×C₆₇	1	4	yes	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	8	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	8	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	—	4	1	no	—
518	C₂²×C₄	—	4	1	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	—	4	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	8	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	4	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	2	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	4	no	—
567	C₄²	—	4	2	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	4	16	no	—
584	C₂³	—	8	4	no	—
585	C₂³	—	8	8	no	—
586	C₂³	—	8	4	no	—
587	C₂³	C₂×#41×C₆₇	1	2	yes	—
588	C₂³	C₂×#41×C₆₇	1	8	yes	—
589	C₂³	C₂×#41×C₆₇	1	2	yes	—
590	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
591	Q₈	—	8	4	no	—
592	D₄	—	2	16	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	8	no	—
595	D₄	—	4	16	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	8	8	no	—
629	C₂×C₄	—	8	8	no	—
630	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
631	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
632	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
633	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
634	C₂²	—	2	8	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	8	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	8	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	4	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	8	16	no	—
652	C₂²	C₂²×#41×C₆₇	1	2	yes	—
653	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
654	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
655	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
656	C₂²	#585×C₆₇	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	2	no	—
659	C₄	—	4	4	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	2	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	4	no	—
668	C₄	#551×C₆₇	1	4	yes	—
669	C₂	—	4	2	no	—
670	C₂	—	4	8	no	—
671	C₂	—	4	2	no	—
672	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
673	C₂	C₆₇×#3481	1	2	yes	—
674	C₂	C₆₇×#3505	1	1	yes	characteristic
675	C₂	C₆₇×#3514	1	2	yes	—
676	C₂	C₆₇×#3537	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2408	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2760	C₂	semidirect
2. C₆₇×#2697	C₂	semidirect
3. C₆₇×#2576	C₂	semidirect
4. C₆₇×#2563	C₂	semidirect
5. C₆₇×#2561	C₂	semidirect
6. C₆₇×#2494	C₂	semidirect
7. C₆₇×#2463	C₂	semidirect
8. C₆₇×#2452	C₂	semidirect
9. C₆₇×#2420	C₂	semidirect
11. C₆₇×#2358	C₂	semidirect
12. C₆₇×#2357	C₂	semidirect
13. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
14. C₄×#123×C₆₇	C₂	semidirect
15. C₄×#121×C₆₇	C₂	semidirect
17. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
19. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
25. C₂×C₄×D₄×C₆₇	C₂²	semidirect
27. C₂²×C₄²×C₆₇	C₂²	semidirect
28. #401×C₆₇	C₂²	semidirect
30. #397×C₆₇	C₂²	semidirect
31. #396×C₆₇	C₂²	semidirect
33. #394×C₆₇	C₂²	semidirect
35. #393×C₆₇	C₂²	semidirect
36. #393×C₆₇	C₂²	semidirect
42. #389×C₆₇	C₂²	semidirect
43. #389×C₆₇	C₂²	semidirect
46. #388×C₆₇	C₂²	semidirect
47. #388×C₆₇	C₂²	semidirect
48. #388×C₆₇	C₂²	semidirect
49. #387×C₆₇	C₂²	semidirect
50. #387×C₆₇	C₂²	semidirect
54. #386×C₆₇	C₂²	semidirect
55. #386×C₆₇	C₂²	semidirect
56. #385×C₆₇	C₂²	semidirect
57. #385×C₆₇	C₂²	semidirect
58. #382×C₆₇	C₂²	semidirect
59. #382×C₆₇	C₂²	semidirect
60. #381×C₆₇	C₂²	semidirect
61. #381×C₆₇	C₂²	semidirect
62. #381×C₆₇	C₂²	semidirect
65. #380×C₆₇	C₂²	semidirect
68. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
69. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
70. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
330. #59378	C₆₇	direct (N × H)
339. #2760	C₂×C₆₇	semidirect
340. #2697	C₂×C₆₇	semidirect
341. #2576	C₂×C₆₇	semidirect
342. #2563	C₂×C₆₇	semidirect
343. #2561	C₂×C₆₇	semidirect
344. #2494	C₂×C₆₇	semidirect
345. #2463	C₂×C₆₇	semidirect
346. #2452	C₂×C₆₇	semidirect
347. #2420	C₂×C₆₇	semidirect
349. #2358	C₂×C₆₇	semidirect
350. #2357	C₂×C₆₇	semidirect
351. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
352. C₄×#123	C₂×C₆₇	semidirect
353. C₄×#121	C₂×C₆₇	semidirect
354. C₆₇	#59378	direct (N × H)
356. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
358. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
364. C₂×C₄×D₄	C₂²×C₆₇	semidirect
366. C₂²×C₄²	C₂²×C₆₇	semidirect
367. #401	C₂²×C₆₇	semidirect
369. #397	C₂²×C₆₇	semidirect
370. #396	C₂²×C₆₇	semidirect
372. #394	C₂²×C₆₇	semidirect
374. #393	C₂²×C₆₇	semidirect
375. #393	C₂²×C₆₇	semidirect
381. #389	C₂²×C₆₇	semidirect
382. #389	C₂²×C₆₇	semidirect
385. #388	C₂²×C₆₇	semidirect
386. #388	C₂²×C₆₇	semidirect
387. #388	C₂²×C₆₇	semidirect
388. #387	C₂²×C₆₇	semidirect
389. #387	C₂²×C₆₇	semidirect
393. #386	C₂²×C₆₇	semidirect
394. #386	C₂²×C₆₇	semidirect
395. #385	C₂²×C₆₇	semidirect
396. #385	C₂²×C₆₇	semidirect
397. #382	C₂²×C₆₇	semidirect
398. #382	C₂²×C₆₇	semidirect
399. #381	C₂²×C₆₇	semidirect
400. #381	C₂²×C₆₇	semidirect
401. #381	C₂²×C₆₇	semidirect
404. #380	C₂²×C₆₇	semidirect
407. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
408. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
409. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
411. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
412. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
413. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2760	2
C₆₇×#2697	2
C₆₇×#2576	2
C₆₇×#2563	2
C₆₇×#2561	2
C₆₇×#2494	2
C₆₇×#2463	2
C₆₇×#2452	2
C₆₇×#2420	2
C₆₇×#2408	2
C₆₇×#2358	2
C₆₇×#2357	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×#123×C₆₇	2
C₄×#121×C₆₇	2
#59378	67

Subgroups — C67×#59378 #30738629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59378 #30738629