Subgroups — #22569239

Order 8576.

464 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic
2	#16863472	C₂	1	1	yes	maximal, characteristic, complemented
3	#16863471	C₂	1	1	yes	maximal, characteristic, complemented
4	#16863469	C₂	1	1	yes	maximal, characteristic, complemented
5	#16863468	C₂	1	1	yes	maximal, characteristic, complemented
6	#16863466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	(C₂²⋊D₆₇)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#16863451	C₂	1	1	yes	maximal, characteristic, complemented
10	#16863448	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863359	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863358	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂×D₆₇)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₆₇	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
19	C₂×#11761612	C₂²	1	1	yes	characteristic, complemented
20	C₂×#11761611	C₂²	1	1	yes	characteristic, complemented
21	C₂×#11761611	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
26	D₄×Dic₆₇	C₄	1	1	yes	characteristic
27	#14524005	C₄	1	1	yes	characteristic
28	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
30	(C₂²⋊D₆₇)⋊C₄	C₄	1	1	yes	characteristic
31	(C₂²⋊D₆₇)⋊C₄	C₄	1	1	yes	characteristic
32	C₄⋊C₄×D₆₇	C₄	1	1	yes	characteristic
33	C₂²⋊C₄×D₆₇	C₄	1	1	yes	characteristic
34	C₂²⋊C₄×D₆₇	C₄	1	1	yes	characteristic
35	C₄²×D₆₇	C₂²	1	1	yes	characteristic
36	C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
37	Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
42	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
43	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
44	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	#14523954	C₂²	1	1	yes	characteristic, complemented
50	C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
55	C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×D₆₇	C₂×C₄	1	1	yes	characteristic
61	C₂×D₂₆₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
64	D₄×D₆₇	—	2	4	no	—
65	C₂²×Dic₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₆₇	—	4	1	no	—
68	C₂×C₄×D₆₇	—	4	1	no	—
69	C₂×C₄×D₆₇	—	4	1	no	—
70	C₂×C₄×D₆₇	—	4	1	no	—
71	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
80	#11761612	—	4	1	no	—
81	#11761611	—	4	1	no	—
82	#11761611	—	4	1	no	—
83	C₂×C₆₇⋊C₈	—	4	1	no	—
84	C₂×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₂×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
88	C₈×D₆₇	—	4	1	no	—
89	C₈×D₆₇	—	4	1	no	—
90	C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
91	Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
92	Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
100	C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
101	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
105	M₁₆×C₆₇	—	4	1	no	—
106	C₂×C₈×C₆₇	—	4	1	no	—
107	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₆₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×D₆₇	—	2	2	no	—
118	C₂²×D₆₇	—	2	2	no	—
119	C₂²×D₆₇	—	2	2	no	—
120	C₂²×D₆₇	—	2	2	no	—
121	C₂²×D₆₇	—	4	1	no	—
122	C₂²×D₆₇	—	4	1	no	—
123	C₂²×D₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₆₇	C₂²×C₄	1	1	yes	characteristic
126	D₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	1	no	—
128	C₂×C₄×C₆₇	—	2	1	no	—
129	C₂×C₄×C₆₇	—	2	1	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
136	C₂²⋊D₆₇	—	2	2	no	—
137	C₂²⋊D₆₇	M₁₆	1	4	yes	complemented
138	C₂×Dic₆₇	—	4	1	no	—
139	C₂×Dic₆₇	—	4	1	no	—
140	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
145	D₂₆₈	—	2	2	no	—
146	C₄×D₆₇	—	2	2	no	—
147	C₄×D₆₇	—	2	1	no	—
148	C₄×D₆₇	—	2	1	no	—
149	C₄×D₆₇	—	2	1	no	—
150	C₄×D₆₇	—	2	1	no	—
151	C₄×D₆₇	—	2	1	no	—
152	C₄×D₆₇	—	2	1	no	—
153	C₄×D₆₇	—	2	2	no	—
154	C₄×D₆₇	—	4	1	no	—
155	C₄×D₆₇	—	4	1	no	—
156	C₄×D₆₇	—	4	1	no	—
157	C₄×D₆₇	—	4	1	no	—
158	C₈×C₆₇	—	2	1	no	—
159	C₈×C₆₇	—	2	1	no	—
160	C₈×C₆₇	—	2	1	no	—
161	C₈×C₆₇	—	2	1	no	—
162	C₆₇⋊C₈	—	2	1	no	—
163	C₆₇⋊C₈	—	2	1	no	—
164	C₆₇⋊C₈	—	2	1	no	—
165	C₆₇⋊C₈	—	2	1	no	—
166	C₂²×C₆₇	—	2	1	no	—
167	C₂²×C₆₇	—	2	1	no	—
168	C₂²×C₆₇	—	2	1	no	—
169	C₂²×C₆₇	—	2	1	no	—
170	C₂²×C₆₇	—	2	1	no	—
171	C₂²×C₆₇	C₂×M₁₆	1	2	yes	—
172	C₂²×C₆₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×D₆₇	—	2	1	no	—
174	C₂×D₆₇	—	2	1	no	—
175	C₂×D₆₇	—	2	1	no	—
176	C₂×D₆₇	—	2	1	no	—
177	C₂×D₆₇	—	2	1	no	—
178	C₂×D₆₇	—	2	1	no	—
179	C₂×D₆₇	—	2	1	no	—
180	C₂×D₆₇	—	4	4	no	—
181	C₂×D₆₇	—	4	4	no	—
182	C₂×D₆₇	C₂×M₁₆	1	2	yes	—
183	C₂×D₆₇	#131	1	2	yes	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	2	1	no	—
186	C₄×C₆₇	—	2	1	no	—
187	C₄×C₆₇	—	2	1	no	—
188	C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
189	C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
190	Dic₆₇	—	2	1	no	—
191	Dic₆₇	—	2	1	no	—
192	Dic₆₇	—	2	1	no	—
193	Dic₆₇	—	2	1	no	—
194	Dic₆₇	C₂×M₁₆	1	2	yes	—
195	C₂×C₆₇	—	2	2	no	—
196	C₂×C₆₇	—	4	1	no	—
197	C₂×C₆₇	#518	1	1	yes	characteristic
198	C₂×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
199	C₂×C₆₇	C₂×#131	1	1	yes	characteristic
200	D₆₇	—	2	2	no	—
201	D₆₇	—	2	2	no	—
202	D₆₇	—	4	1	no	—
203	#2974	—	67	1	no	maximal, Sylow
204	C₆₇	#2974	1	1	yes	characteristic, complemented, Sylow
205	C₂×C₄×D₄	—	67	1	no	—
206	#436	—	67	1	no	—
207	#436	—	67	1	no	—
208	#435	—	67	1	no	—
209	#435	—	67	1	no	—
210	#435	—	67	1	no	—
211	#435	D₆₇	1	1	yes	characteristic, complemented
212	C₈×D₄	—	67	1	no	—
213	C₈×D₄	—	67	1	no	—
214	#432	—	67	1	no	—
215	#431	—	67	1	no	—
216	#407	—	67	1	no	—
217	#407	—	67	1	no	—
218	C₂×C₂²⋊C₈	—	67	1	no	—
219	C₂×C₂²⋊C₈	—	67	1	no	—
220	C₂²×D₄	—	67	1	no	—
221	C₂³×C₄	—	67	1	no	—
222	C₂³×C₄	—	67	1	no	—
223	C₂×M₁₆	—	67	1	no	—
224	C₂×M₁₆	—	67	1	no	—
225	C₂×M₁₆	—	67	1	no	—
226	C₂×M₁₆	C₂×D₆₇	1	1	yes	characteristic, complemented
227	C₂²×C₈	—	67	1	no	—
228	C₂²×C₈	—	67	1	no	—
229	C₂²×C₈	—	67	1	no	—
230	C₂²×C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
231	C₄×D₄	—	67	1	no	—
232	C₄×D₄	—	67	1	no	—
233	C₄×D₄	—	67	1	no	—
234	C₄×D₄	—	67	1	no	—
235	C₄×D₄	—	67	1	no	—
236	C₄×D₄	—	67	1	no	—
237	C₄×D₄	—	67	1	no	—
238	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	67	1	no	—
240	C₂×C₂²⋊C₄	—	67	1	no	—
241	C₂×C₂²⋊C₄	—	67	1	no	—
242	C₂×C₄²	—	67	1	no	—
243	C₄⋊C₈	—	67	1	no	—
244	C₄⋊C₈	—	67	1	no	—
245	C₄⋊C₈	—	67	1	no	—
246	C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
247	C₂²⋊C₈	—	67	1	no	—
248	C₂²⋊C₈	—	67	1	no	—
249	C₂²⋊C₈	—	67	1	no	—
250	C₂²⋊C₈	—	67	1	no	—
251	C₂²⋊C₈	—	67	1	no	—
252	C₂²⋊C₈	—	67	1	no	—
253	C₂²⋊C₈	—	67	1	no	—
254	C₂²⋊C₈	—	67	1	no	—
255	C₂²⋊C₈	—	67	1	no	—
256	C₂²⋊C₈	—	67	1	no	—
257	C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
258	C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
259	#97	—	67	1	no	—
260	#97	C₂×D₆₇	1	1	yes	characteristic, complemented
261	C₄×C₈	—	67	1	no	—
262	C₄×C₈	—	67	1	no	—
263	C₂⁴	—	67	1	no	—
264	C₂⁴	—	67	1	no	—
265	C₂×D₄	—	67	1	no	—
266	C₂×D₄	—	67	1	no	—
267	C₂×D₄	—	67	1	no	—
268	C₂×D₄	—	134	4	no	—
269	C₂×D₄	C₄×D₆₇	1	1	yes	characteristic
270	C₂²×C₄	—	268	1	no	—
271	C₂²×C₄	—	268	1	no	—
272	C₂²×C₄	—	268	1	no	—
273	C₂²×C₄	—	268	1	no	—
274	C₂²×C₄	—	67	1	no	—
275	C₂²×C₄	—	67	1	no	—
276	C₂²×C₄	—	67	1	no	—
277	C₂²×C₄	—	67	1	no	—
278	C₂²×C₄	—	67	1	no	—
279	C₂²×C₄	—	67	1	no	—
280	C₂²×C₄	—	67	1	no	—
281	C₂²×C₄	—	67	1	no	—
282	C₂²×C₄	—	67	1	no	—
283	C₂²×C₄	—	67	1	no	—
284	C₂²×C₄	—	67	1	no	—
285	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
287	M₁₆	—	4	1	no	—
288	M₁₆	—	268	1	no	—
289	M₁₆	—	268	1	no	—
290	M₁₆	—	268	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	268	1	no	—
293	C₂×C₈	—	268	1	no	—
294	C₂×C₈	—	268	1	no	—
295	C₂×C₈	—	67	1	no	—
296	C₂×C₈	—	67	1	no	—
297	C₂×C₈	—	67	1	no	—
298	C₂×C₈	—	67	1	no	—
299	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
301	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
302	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
303	C₄⋊C₄	—	67	1	no	—
304	C₄⋊C₄	—	67	1	no	—
305	C₄⋊C₄	—	67	1	no	—
306	C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
307	C₂²⋊C₄	—	67	1	no	—
308	C₂²⋊C₄	—	67	1	no	—
309	C₂²⋊C₄	—	67	1	no	—
310	C₂²⋊C₄	—	67	1	no	—
311	C₂²⋊C₄	—	67	1	no	—
312	C₂²⋊C₄	—	67	1	no	—
313	C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
314	C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
315	C₄²	—	67	1	no	—
316	C₄²	—	67	1	no	—
317	C₄²	—	67	1	no	—
318	C₄²	C₂²×D₆₇	1	1	yes	characteristic
319	C₂³	—	268	1	no	—
320	C₂³	—	268	1	no	—
321	C₂³	—	67	1	no	—
322	C₂³	—	67	1	no	—
323	C₂³	—	67	1	no	—
324	C₂³	—	134	2	no	—
325	C₂³	—	134	2	no	—
326	C₂³	—	134	2	no	—
327	C₂³	—	134	2	no	—
328	C₂³	C₂×C₄×D₆₇	1	1	yes	characteristic
329	C₂³	C₂×C₄×D₆₇	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	67	4	no	—
332	D₄	—	134	2	no	—
333	D₄	—	134	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	268	1	no	—
339	C₂×C₄	—	268	1	no	—
340	C₂×C₄	—	268	1	no	—
341	C₂×C₄	—	268	1	no	—
342	C₂×C₄	—	268	1	no	—
343	C₂×C₄	—	268	1	no	—
344	C₂×C₄	—	67	1	no	—
345	C₂×C₄	—	67	1	no	—
346	C₂×C₄	—	67	1	no	—
347	C₂×C₄	—	67	1	no	—
348	C₂×C₄	—	67	1	no	—
349	C₂×C₄	—	134	2	no	—
350	C₂×C₄	—	134	2	no	—
351	C₂×C₄	—	134	1	no	—
352	C₂×C₄	—	134	1	no	—
353	C₂×C₄	—	134	1	no	—
354	C₂×C₄	—	134	1	no	—
355	C₂×C₄	—	134	1	no	—
356	C₂×C₄	—	134	1	no	—
357	C₂×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	134	1	no	—
367	C₈	—	134	1	no	—
368	C₈	—	134	1	no	—
369	C₈	—	134	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	268	4	no	—
376	C₂²	—	268	4	no	—
377	C₂²	—	67	2	no	—
378	C₂²	—	67	2	no	—
379	C₂²	—	134	1	no	—
380	C₂²	—	134	1	no	—
381	C₂²	—	134	1	no	—
382	C₂²	—	134	1	no	—
383	C₂²	—	134	1	no	—
384	C₂²	—	134	1	no	—
385	C₂²	—	134	1	no	—
386	C₂²	M₁₆×D₆₇	1	2	yes	—
387	C₂²	C₂²×C₄×D₆₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	67	2	no	—
393	C₄	—	134	1	no	—
394	C₄	—	134	1	no	—
395	C₄	—	134	1	no	—
396	C₄	—	134	1	no	—
397	C₄	#14524088	1	1	yes	characteristic
398	C₄	#14524089	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	268	1	no	—
402	C₂	—	134	2	no	—
403	C₂	—	134	2	no	—
404	C₂	#16863868	1	1	yes	characteristic
405	C₂	C₂×M₁₆×D₆₇	1	1	yes	characteristic
406	C₂	#131×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₆₇
commutator, socle	C₂²×C₆₇	C₂³×C₄
Fitting	#435×C₆₇	C₂
hypercenter	#435	D₆₇
hypocenter	C₆₇	#2974
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #16863472	C₂	semidirect
3. #16863471	C₂	semidirect
4. #16863469	C₂	semidirect
5. #16863468	C₂	semidirect
6. #16863466	C₂	semidirect
7. C₈×C₂²⋊D₆₇	C₂	semidirect
8. (C₂²⋊D₆₇)⋊C₈	C₂	semidirect
9. #16863451	C₂	semidirect
10. #16863448	C₂	semidirect
11. #16863359	C₂	semidirect
12. #16863358	C₂	semidirect
13. C₂×(C₂×D₆₇)⋊C₈	C₂	semidirect
14. C₂²⋊C₈×D₆₇	C₂	semidirect
15. #435×C₆₇	C₂	semidirect
19. C₂×#11761612	C₂²	semidirect
20. C₂×#11761611	C₂²	semidirect
21. C₂×#11761611	C₂²	semidirect
22. C₂²×C₆₇⋊C₈	C₂²	semidirect
23. C₂×C₈×D₆₇	C₂²	semidirect
24. C₂×C₈×D₆₇	C₂²	semidirect
36. C₄⋊(C₆₇⋊C₈)	C₂²	semidirect
37. Dic₆₇⋊C₈	C₂²	semidirect
38. Dic₆₇⋊C₈	C₂²	semidirect
39. C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
40. C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
45. (C₂×D₆₇)⋊C₈	C₂²	semidirect
46. (C₂×D₆₇)⋊C₈	C₂²	semidirect
47. (C₂×D₆₇)⋊C₈	C₂²	semidirect
48. (C₂×D₆₇)⋊C₈	C₂²	semidirect
49. #14523954	C₂²	semidirect
50. C₈×Dic₆₇	C₂²	semidirect
51. C₈×Dic₆₇	C₂²	semidirect
52. C₂×M₁₆×C₆₇	C₂²	semidirect
53. C₂²×C₈×C₆₇	C₂²	semidirect
55. C₄⋊C₈×C₆₇	C₂²	semidirect
56. C₂²⋊C₈×C₆₇	C₂²	semidirect
57. C₂²⋊C₈×C₆₇	C₂²	semidirect
58. #97×C₆₇	C₂²	semidirect
137. C₂²⋊D₆₇	M₁₆	semidirect
204. C₆₇	#2974	semidirect
211. #435	D₆₇	semidirect
226. C₂×M₁₆	C₂×D₆₇	semidirect
230. C₂²×C₈	C₂×D₆₇	semidirect
246. C₄⋊C₈	C₂×D₆₇	semidirect
257. C₂²⋊C₈	C₂×D₆₇	semidirect
258. C₂²⋊C₈	C₂×D₆₇	semidirect
260. #97	C₂×D₆₇	semidirect