Subgroups — #22568898

Order 8576.

520 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	C₂×#14524049	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#16863905	C₂	1	1	yes	maximal, characteristic
4	#16863470	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	#16863464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863421	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863361	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863358	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863350	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11761628	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
18	#14524049	—	2	4	no	—
19	C₂×#11761612	C₂²	1	1	yes	characteristic, complemented
20	C₂×#11761611	C₂²	1	1	yes	characteristic
21	C₂×#11761611	C₂²	1	1	yes	characteristic
22	C₂×#11761611	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₆₇	—	2	4	no	—
25	C₂×C₈×D₆₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×D₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
30	#14524028	C₄	1	1	yes	characteristic
31	#14524025	C₄	1	1	yes	characteristic
32	#14524021	C₄	1	1	yes	characteristic
33	#14524020	C₄	1	1	yes	characteristic
34	#14524016	C₄	1	1	yes	characteristic
35	#14524015	C₄	1	1	yes	characteristic
36	#14524013	C₄	1	1	yes	characteristic
37	#14524011	C₄	1	1	yes	characteristic
38	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
41	#14524000	C₂²	1	1	yes	characteristic
42	C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
46	C₂²⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#14523954	C₂²	1	1	yes	characteristic, complemented
52	#14523953	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₈×C₆₇	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₆₇	C₂×C₄	1	1	yes	characteristic
62	#11761628	—	2	2	no	—
63	#11761628	—	2	2	no	—
64	C₂×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
65	C₂×D₂₆₈	C₂×C₄	1	1	yes	characteristic
66	C₂×D₂₆₈	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×Dic₆₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₆₇	—	2	2	no	—
73	C₂×C₄×D₆₇	—	2	2	no	—
74	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
79	#11761612	—	2	2	no	—
80	#11761611	—	2	2	no	—
81	#11761611	—	2	2	no	—
82	#11761611	—	2	2	no	—
83	C₂×C₆₇⋊C₈	—	2	2	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	—	2	2	no	—
89	C₈×D₆₇	—	2	2	no	—
90	C₈×D₆₇	—	2	2	no	—
91	C₈×D₆₇	—	2	2	no	—
92	C₈×D₆₇	D₄	1	4	yes	complemented
93	C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
94	Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
95	Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
96	Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
97	Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
100	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
101	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
103	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
104	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
105	(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂×C₈×C₆₇	—	2	2	no	—
111	C₂×C₈×C₆₇	—	2	2	no	—
112	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₆₇	—	2	2	no	—
123	C₂²×D₆₇	—	2	2	no	—
124	C₂²×D₆₇	—	2	2	no	—
125	C₂²×D₆₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₆₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₆₇	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	1	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	1	no	—
133	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₆₇	—	2	2	no	—
139	C₂²⋊D₆₇	—	2	2	no	—
140	C₂²⋊D₆₇	—	2	2	no	—
141	C₂²⋊D₆₇	—	2	2	no	—
142	C₂×Dic₆₇	—	2	2	no	—
143	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
148	D₂₆₈	—	2	2	no	—
149	D₂₆₈	—	2	2	no	—
150	C₄×D₆₇	—	2	2	no	—
151	C₄×D₆₇	—	2	1	no	—
152	C₄×D₆₇	—	2	1	no	—
153	C₄×D₆₇	—	2	1	no	—
154	C₄×D₆₇	—	2	1	no	—
155	C₄×D₆₇	—	2	2	no	—
156	C₄×D₆₇	C₂×D₄	1	2	yes	—
157	C₄×D₆₇	#41	1	2	yes	—
158	Dic₁₃₄	—	2	2	no	—
159	C₈×C₆₇	—	2	1	no	—
160	C₈×C₆₇	—	2	1	no	—
161	C₈×C₆₇	—	2	1	no	—
162	C₈×C₆₇	C₂×D₄	1	2	yes	—
163	C₆₇⋊C₈	—	2	1	no	—
164	C₆₇⋊C₈	—	2	1	no	—
165	C₆₇⋊C₈	—	2	1	no	—
166	C₆₇⋊C₈	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
172	C₂²×C₆₇	#131	1	2	yes	complemented
173	C₂²×C₆₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₆₇	—	2	8	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	—	2	1	no	—
181	C₂×D₆₇	—	2	1	no	—
182	C₂×D₆₇	C₄×D₄	1	2	yes	—
183	C₂×D₆₇	#131	1	2	yes	complemented
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	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₆₇	C₂×#41	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	C₄×D₄	1	2	yes	—
195	C₂×C₆₇	—	2	2	no	—
196	C₂×C₆₇	—	4	1	no	—
197	C₂×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×C₆₇	C₂×#131	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	#2929	—	67	1	no	maximal, Sylow
204	C₆₇	#2929	1	1	yes	characteristic, complemented, Sylow
205	C₂×#131	—	67	1	no	—
206	C₂³×C₈	—	67	1	no	—
207	#525	—	67	1	no	—
208	#435	—	67	1	no	—
209	#435	—	67	1	no	—
210	#435	—	67	1	no	—
211	#435	—	67	1	no	—
212	C₈×D₄	—	67	1	no	—
213	C₈×D₄	—	67	1	no	—
214	C₈×D₄	—	67	1	no	—
215	C₈×D₄	D₆₇	1	1	yes	characteristic, complemented
216	#424	—	67	1	no	—
217	#408	—	67	1	no	—
218	#407	—	67	1	no	—
219	#405	—	67	1	no	—
220	C₂×#41	—	67	1	no	—
221	C₂³×C₄	—	67	1	no	—
222	#131	—	134	4	no	—
223	C₂×M₁₆	—	67	1	no	—
224	C₂×M₁₆	—	67	1	no	—
225	C₂×M₁₆	—	67	1	no	—
226	C₂×M₁₆	—	67	1	no	—
227	C₂²×C₈	—	67	1	no	—
228	C₂²×C₈	—	67	1	no	—
229	C₂²×C₈	—	67	1	no	—
230	C₂²×C₈	—	67	1	no	—
231	C₂²×C₈	—	67	1	no	—
232	C₂²×C₈	—	67	1	no	—
233	C₂²×C₈	—	134	4	no	—
234	C₂²×C₈	C₂×D₆₇	1	1	yes	characteristic
235	C₂²×C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
236	#123	—	67	1	no	—
237	#123	—	67	1	no	—
238	C₂²⋊Q₈	—	67	1	no	—
239	C₂²⋊Q₈	—	67	1	no	—
240	#121	—	67	1	no	—
241	#121	—	67	1	no	—
242	#120	—	67	1	no	—
243	#120	—	67	1	no	—
244	C₄×D₄	—	67	1	no	—
245	C₄×D₄	—	67	1	no	—
246	C₄×D₄	—	67	1	no	—
247	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
248	#117	—	67	1	no	—
249	C₄⋊C₈	—	67	1	no	—
250	C₄⋊C₈	—	67	1	no	—
251	C₄⋊C₈	—	67	1	no	—
252	C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
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	—	67	1	no	—
258	C₂²⋊C₈	—	67	1	no	—
259	C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
261	#97	—	67	1	no	—
262	#97	—	67	1	no	—
263	C₄×C₈	—	67	1	no	—
264	C₄×C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
265	C₂⁴	—	67	1	no	—
266	#41	—	134	2	no	—
267	#41	—	134	2	no	—
268	C₂×Q₈	—	67	1	no	—
269	C₂×D₄	—	67	1	no	—
270	C₂×D₄	—	67	1	no	—
271	C₂×D₄	—	67	1	no	—
272	C₂×D₄	—	67	1	no	—
273	C₂×D₄	—	67	1	no	—
274	C₂×D₄	—	67	1	no	—
275	C₂×D₄	C₄×D₆₇	1	1	yes	characteristic
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	—	134	2	no	—
283	C₂²×C₄	—	134	2	no	—
284	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
286	M₁₆	—	134	2	no	—
287	M₁₆	—	134	2	no	—
288	M₁₆	—	134	2	no	—
289	M₁₆	—	134	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	67	1	no	—
293	C₂×C₈	—	67	4	no	—
294	C₂×C₈	—	67	1	no	—
295	C₂×C₈	—	67	1	no	—
296	C₂×C₈	—	67	1	no	—
297	C₂×C₈	—	134	2	no	—
298	C₂×C₈	—	134	2	no	—
299	C₂×C₈	—	134	2	no	—
300	C₂×C₈	—	134	2	no	—
301	C₂×C₈	—	134	2	no	—
302	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
306	C₄⋊C₄	—	67	1	no	—
307	C₄⋊C₄	—	67	1	no	—
308	C₄⋊C₄	—	67	1	no	—
309	C₄⋊C₄	—	67	1	no	—
310	C₄⋊C₄	—	67	1	no	—
311	C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
312	C₂²⋊C₄	—	67	1	no	—
313	C₂²⋊C₄	—	67	1	no	—
314	C₂²⋊C₄	—	67	1	no	—
315	C₂²⋊C₄	—	67	1	no	—
316	C₂²⋊C₄	—	67	1	no	—
317	C₂²⋊C₄	—	67	1	no	—
318	C₂²⋊C₄	—	67	1	no	—
319	C₂²⋊C₄	—	67	1	no	—
320	C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
322	C₄²	—	67	1	no	—
323	C₄²	C₂²×D₆₇	1	1	yes	characteristic
324	C₂³	—	67	1	no	—
325	C₂³	—	67	1	no	—
326	C₂³	—	67	1	no	—
327	C₂³	—	134	2	no	—
328	C₂³	—	134	2	no	—
329	C₂³	—	134	2	no	—
330	C₂³	C₂×C₄×D₆₇	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₆₇	1	1	yes	characteristic
332	Q₈	—	134	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	134	2	no	—
335	D₄	—	134	2	no	—
336	D₄	—	134	2	no	—
337	D₄	—	134	2	no	—
338	D₄	—	134	2	no	—
339	D₄	—	134	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	67	1	no	—
345	C₂×C₄	—	67	2	no	—
346	C₂×C₄	—	67	2	no	—
347	C₂×C₄	—	67	1	no	—
348	C₂×C₄	—	67	1	no	—
349	C₂×C₄	—	67	1	no	—
350	C₂×C₄	—	67	1	no	—
351	C₂×C₄	—	134	2	no	—
352	C₂×C₄	—	134	2	no	—
353	C₂×C₄	—	134	2	no	—
354	C₂×C₄	—	134	1	no	—
355	C₂×C₄	—	134	1	no	—
356	C₂×C₄	—	134	1	no	—
357	C₂×C₄	—	134	1	no	—
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	C₂×C₄×D₆₇	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	67	2	no	—
367	C₈	—	134	1	no	—
368	C₈	—	134	1	no	—
369	C₈	—	134	1	no	—
370	C₈	D₄×D₆₇	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	67	2	no	—
377	C₂²	—	67	2	no	—
378	C₂²	—	134	8	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	#14524049	1	2	yes	complemented
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	C₂×D₄×D₆₇	1	1	yes	characteristic
398	C₄	#41×D₆₇	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	C₄×D₄×D₆₇	1	1	yes	characteristic
405	C₂	#131×D₆₇	1	1	yes	characteristic
406	C₂	C₂×#14524049	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₆₇
commutator, socle	C₂²×C₆₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₆₇
Fitting	C₈×D₄×C₆₇	C₂
hypercenter	C₈×D₄	D₆₇
hypocenter	C₆₇	#2929
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#14524049	C₂	semidirect
2. C₂²×C₈×D₆₇	C₂	semidirect
4. #16863470	C₂	semidirect
5. #16863468	C₂	semidirect
6. #16863466	C₂	semidirect
7. #16863464	C₂	semidirect
8. C₈×D₂₆₈	C₂	semidirect
9. C₈×C₂²⋊D₆₇	C₂	semidirect
10. C₈×C₂²⋊D₆₇	C₂	semidirect
11. #16863421	C₂	semidirect
12. #16863361	C₂	semidirect
13. #16863358	C₂	semidirect
14. #16863350	C₂	semidirect
15. C₈×D₄×C₆₇	C₂	semidirect
19. C₂×#11761612	C₂²	semidirect
22. C₂×#11761611	C₂²	semidirect
29. C₂×C₈×D₆₇	C₂²	semidirect
42. C₄⋊(C₆₇⋊C₈)	C₂²	semidirect
43. Dic₆₇⋊C₈	C₂²	semidirect
44. Dic₆₇⋊C₈	C₂²	semidirect
46. C₂²⋊(C₆₇⋊C₈)	C₂²	semidirect
49. (C₂×D₆₇)⋊C₈	C₂²	semidirect
50. (C₂×D₆₇)⋊C₈	C₂²	semidirect
51. #14523954	C₂²	semidirect
52. #14523953	C₂²	semidirect
53. C₈×Dic₆₇	C₂²	semidirect
55. C₂²×C₈×C₆₇	C₂²	semidirect
57. C₄⋊C₈×C₆₇	C₂²	semidirect
59. C₂²⋊C₈×C₆₇	C₂²	semidirect
60. C₄×C₈×C₆₇	C₂²	semidirect
92. C₈×D₆₇	D₄	semidirect
172. C₂²×C₆₇	#131	semidirect
183. C₂×D₆₇	#131	semidirect
204. C₆₇	#2929	semidirect
215. C₈×D₄	D₆₇	semidirect
235. C₂²×C₈	C₂×D₆₇	semidirect
252. C₄⋊C₈	C₂×D₆₇	semidirect
260. C₂²⋊C₈	C₂×D₆₇	semidirect
264. C₄×C₈	C₂×D₆₇	semidirect
386. C₂²	#14524049	semidirect