Subgroups — #30748733

Order 17152.

524 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	#22560238	C₂	1	1	yes	maximal, characteristic, complemented
2	#22560234	C₂	1	1	yes	maximal, characteristic, complemented
3	#22560197	C₂	1	2	yes	maximal
4	#22558077	C₂	1	2	yes	maximal, complemented
5	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#14523977	—	2	1	no	—
7	C₂×#14523975	—	2	1	no	—
8	C₂×#14523958	—	2	2	no	—
9	#16863256	C₂²	1	2	yes	—
10	#16863256	C₂²	1	2	yes	—
11	#16863163	—	2	2	no	—
12	#16863159	—	2	1	no	—
13	#16863159	—	2	1	no	—
14	C₂²×M₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
15	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
17	#435×C₆₇	—	2	1	no	—
18	#435×C₆₇	—	2	1	no	—
19	#435×C₆₇	—	2	1	no	—
20	#435×C₆₇	—	2	1	no	—
21	C₂×C₄⋊C₈×C₆₇	C₄	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊C₈×C₆₇	C₄	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#97×C₆₇	C₄	1	1	yes	characteristic, complemented
25	C₂×C₄⋊Dic₆₇	—	2	2	no	—
26	C₂×C₄⋊Dic₆₇	—	2	2	no	—
27	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
28	C₂×C₂²⋊Dic₆₇	—	2	2	no	—
29	#14523977	—	4	2	no	—
30	#14523975	—	4	2	no	—
31	#14523958	—	4	4	no	—
32	C₆₇⋊#95	—	2	2	no	—
33	C₆₇⋊#95	—	2	2	no	—
34	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₆₇	—	2	1	no	—
38	C₂×M₁₆×C₆₇	—	2	1	no	—
39	C₂×M₁₆×C₆₇	—	4	2	no	—
40	C₂²×C₈×C₆₇	—	4	2	no	—
41	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
49	C₄×D₄×C₆₇	—	2	1	no	—
50	C₄×D₄×C₆₇	—	2	1	no	—
51	C₄×D₄×C₆₇	—	2	1	no	—
52	C₄×D₄×C₆₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₇	Q₈	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₆₇	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₄⋊C₈×C₆₇	—	2	1	no	—
58	C₄⋊C₈×C₆₇	—	2	1	no	—
59	C₂²⋊C₈×C₆₇	—	2	1	no	—
60	C₂²⋊C₈×C₆₇	—	2	1	no	—
61	C₂²⋊C₈×C₆₇	—	2	1	no	—
62	C₂²⋊C₈×C₆₇	—	2	1	no	—
63	#97×C₆₇	—	2	1	no	—
64	#97×C₆₇	—	2	1	no	—
65	C₂²×Dic₆₇	—	4	2	no	—
66	C₂²×Dic₆₇	—	4	2	no	—
67	C₄⋊Dic₆₇	—	4	2	no	—
68	C₄⋊Dic₆₇	—	4	2	no	—
69	C₄⋊Dic₆₇	—	4	2	no	—
70	C₄⋊Dic₆₇	—	4	2	no	—
71	C₂²⋊Dic₆₇	—	4	2	no	—
72	C₂²⋊Dic₆₇	—	4	2	no	—
73	C₂²⋊Dic₆₇	—	4	2	no	—
74	C₂²⋊Dic₆₇	—	4	2	no	—
75	C₂⁴×C₆₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₆₇	—	2	1	no	—
78	C₂×D₄×C₆₇	—	2	1	no	—
79	C₂×D₄×C₆₇	—	2	2	no	—
80	C₂×D₄×C₆₇	—	2	2	no	—
81	C₂²×C₄×C₆₇	—	2	1	no	—
82	C₂²×C₄×C₆₇	—	2	1	no	—
83	C₂²×C₄×C₆₇	—	4	1	no	—
84	C₂²×C₄×C₆₇	—	4	1	no	—
85	C₂²×C₄×C₆₇	—	4	1	no	—
86	C₂²×C₄×C₆₇	—	4	1	no	—
87	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
96	M₁₆×C₆₇	—	4	2	no	—
97	M₁₆×C₆₇	—	4	2	no	—
98	C₂×C₈×C₆₇	—	2	2	no	—
99	C₂×C₈×C₆₇	—	2	2	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	2	1	no	—
102	C₂×C₈×C₆₇	—	2	1	no	—
103	C₂×C₈×C₆₇	—	4	1	no	—
104	C₂×C₈×C₆₇	—	4	1	no	—
105	C₂×C₈×C₆₇	—	4	1	no	—
106	C₂×C₈×C₆₇	—	4	1	no	—
107	C₂×C₈×C₆₇	—	4	1	no	—
108	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₄⋊C₄×C₆₇	—	2	1	no	—
113	C₄⋊C₄×C₆₇	—	2	1	no	—
114	C₂²⋊C₄×C₆₇	—	2	1	no	—
115	C₂²⋊C₄×C₆₇	—	2	1	no	—
116	C₂²⋊C₄×C₆₇	—	2	1	no	—
117	C₂²⋊C₄×C₆₇	—	2	1	no	—
118	C₄²×C₆₇	—	2	1	no	—
119	C₄²×C₆₇	—	2	1	no	—
120	C₂³×C₆₇	—	2	1	no	—
121	C₂³×C₆₇	—	2	2	no	—
122	C₂³×C₆₇	—	4	1	no	—
123	C₂³×C₆₇	—	4	1	no	—
124	C₂³×C₆₇	—	4	1	no	—
125	C₂³×C₆₇	—	4	1	no	—
126	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂³×C₆₇	#121	1	1	yes	characteristic
128	C₂³×C₆₇	#121	1	1	yes	characteristic
129	C₂³×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
130	C₂³×C₆₇	#137	1	2	yes	—
131	D₄×C₆₇	—	4	2	no	—
132	D₄×C₆₇	—	4	1	no	—
133	D₄×C₆₇	—	4	1	no	—
134	C₂×C₄×C₆₇	—	2	1	no	—
135	C₂×C₄×C₆₇	—	2	1	no	—
136	C₂×C₄×C₆₇	—	2	1	no	—
137	C₂×C₄×C₆₇	—	2	1	no	—
138	C₂×C₄×C₆₇	—	2	1	no	—
139	C₂×C₄×C₆₇	—	2	1	no	—
140	C₂×C₄×C₆₇	—	2	1	no	—
141	C₂×C₄×C₆₇	—	2	1	no	—
142	C₂×C₄×C₆₇	—	2	1	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	4	1	no	—
145	C₂×C₄×C₆₇	—	4	1	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	4	1	no	—
149	C₂×C₄×C₆₇	—	4	1	no	—
150	C₂×C₄×C₆₇	—	4	1	no	—
151	C₂×C₄×C₆₇	—	4	1	no	—
152	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×Dic₆₇	—	8	2	no	—
157	C₂×Dic₆₇	—	8	2	no	—
158	C₂×Dic₆₇	—	8	2	no	—
159	C₂×Dic₆₇	—	8	2	no	—
160	C₂×Dic₆₇	—	8	2	no	—
161	C₂×Dic₆₇	—	8	2	no	—
162	C₈×C₆₇	—	2	1	no	—
163	C₈×C₆₇	—	2	1	no	—
164	C₈×C₆₇	—	2	1	no	—
165	C₈×C₆₇	—	4	1	no	—
166	C₈×C₆₇	—	4	1	no	—
167	C₈×C₆₇	#99	1	2	yes	complemented
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	—	2	1	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	—	4	2	no	—
175	C₂²×C₆₇	—	4	2	no	—
176	C₂²×C₆₇	—	4	1	no	—
177	C₂²×C₆₇	—	4	1	no	—
178	C₂²×C₆₇	—	4	1	no	—
179	C₂²×C₆₇	—	8	2	no	—
180	C₂²×C₆₇	#380	1	1	yes	characteristic
181	C₂²×C₆₇	#428	1	2	yes	—
182	C₂²×C₆₇	#468	1	2	yes	—
183	C₂²×C₆₇	#469	1	1	yes	characteristic
184	C₂²×C₆₇	#470	1	1	yes	characteristic
185	C₄×C₆₇	—	2	1	no	—
186	C₄×C₆₇	—	2	1	no	—
187	C₄×C₆₇	—	2	1	no	—
188	C₄×C₆₇	—	4	1	no	—
189	C₄×C₆₇	—	4	1	no	—
190	C₄×C₆₇	—	4	1	no	—
191	C₄×C₆₇	C₂×#99	1	1	yes	characteristic
192	C₄×C₆₇	#410	1	1	yes	characteristic
193	Dic₆₇	—	16	2	no	—
194	Dic₆₇	—	16	2	no	—
195	#8610	—	67	1	no	maximal, Sylow
196	C₂×C₆₇	—	2	1	no	—
197	C₂×C₆₇	—	2	2	no	—
198	C₂×C₆₇	—	2	2	no	—
199	C₂×C₆₇	—	2	1	no	—
200	C₂×C₆₇	—	8	1	no	—
201	C₂×C₆₇	#1799	1	1	yes	characteristic
202	C₂×C₆₇	#1809	1	1	yes	characteristic
203	C₂×C₆₇	#1812	1	1	yes	characteristic
204	C₂×#435	D₆₇	1	1	yes	characteristic
205	#1808	—	67	1	no	—
206	#1807	—	67	1	no	—
207	#1799	—	67	2	no	—
208	#1289	—	67	2	no	—
209	C₆₇	#8610	1	1	yes	characteristic, complemented, Sylow
210	C₂²×M₁₆	Dic₆₇	1	1	yes	characteristic, complemented
211	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
213	#435	—	2	1	no	—
214	#435	—	2	1	no	—
215	#435	—	2	1	no	—
216	#435	—	2	1	no	—
217	C₂×#107	—	134	1	no	—
218	C₂×#106	—	134	1	no	—
219	C₂×C₄⋊C₈	Dic₆₇	1	1	yes	characteristic, complemented
220	C₂×#99	—	134	2	no	—
221	C₂×C₂²⋊C₈	Dic₆₇	1	1	yes	characteristic, complemented
222	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
223	C₂×#97	Dic₆₇	1	1	yes	characteristic, complemented
224	#380	—	67	2	no	—
225	#380	—	67	2	no	—
226	#342	—	134	2	no	—
227	#340	—	134	1	no	—
228	#340	—	134	1	no	—
229	C₂²×D₄	D₂₆₈	1	1	yes	characteristic
230	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
231	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	—	4	2	no	—
235	C₂²×C₈	—	4	2	no	—
236	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
237	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
238	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
239	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
240	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
241	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
242	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
243	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	134	2	no	—
249	C₂×C₄⋊C₄	—	134	2	no	—
250	C₂×C₄⋊C₄	Dic₁₃₄	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	134	2	no	—
252	C₂×C₂²⋊C₄	—	134	2	no	—
253	C₂×C₂²⋊C₄	Dic₁₃₄	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	D₂₆₈	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
256	#107	—	268	2	no	—
257	#106	—	268	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	#99	—	268	4	no	—
261	C₂²⋊C₈	—	2	1	no	—
262	C₂²⋊C₈	—	2	1	no	—
263	C₂²⋊C₈	—	2	1	no	—
264	C₂²⋊C₈	—	2	1	no	—
265	#97	—	2	1	no	—
266	#97	—	2	1	no	—
267	#95	—	134	2	no	—
268	#95	—	134	2	no	—
269	C₂⁴	C₄⋊Dic₆₇	1	1	yes	characteristic
270	C₂⁴	C₂×D₂₆₈	1	1	yes	characteristic
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	268	2	no	—
282	C₂²×C₄	—	268	2	no	—
283	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
284	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
290	C₂²×C₄	#11761628	1	1	yes	characteristic
291	C₂²×C₄	#11761628	1	1	yes	characteristic
292	M₁₆	—	4	2	no	—
293	M₁₆	—	4	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
305	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
306	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
307	C₂×C₈	C₂²⋊Dic₆₇	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	268	2	no	—
311	C₄⋊C₄	—	268	2	no	—
312	C₄⋊C₄	—	268	2	no	—
313	C₄⋊C₄	—	268	2	no	—
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	268	2	no	—
319	C₂²⋊C₄	—	268	2	no	—
320	C₂²⋊C₄	—	268	2	no	—
321	C₂²⋊C₄	—	268	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
331	C₂³	#14524017	1	1	yes	characteristic
332	C₂³	#14524017	1	1	yes	characteristic
333	C₂³	#14524071	1	2	yes	—
334	C₂³	#14524076	1	2	yes	—
335	D₄	—	4	2	no	—
336	D₄	—	4	1	no	—
337	D₄	—	4	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	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	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	536	2	no	—
357	C₂×C₄	—	536	2	no	—
358	C₂×C₄	—	536	2	no	—
359	C₂×C₄	—	536	2	no	—
360	C₂×C₄	—	536	2	no	—
361	C₂×C₄	—	536	2	no	—
362	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
363	C₂×C₄	#14524002	1	1	yes	characteristic
364	C₂×C₄	#14524022	1	1	yes	characteristic
365	C₂×C₄	#14524022	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	1	no	—
371	C₈	#14523958	1	2	yes	complemented
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	8	2	no	—
384	C₂²	#16863256	1	1	yes	characteristic
385	C₂²	#16863438	1	2	yes	—
386	C₂²	#16863642	1	2	yes	—
387	C₂²	#16863649	1	1	yes	characteristic
388	C₂²	#16863654	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	1072	2	no	—
396	C₄	—	1072	2	no	—
397	C₄	C₂×#14523958	1	1	yes	characteristic
398	C₄	#16863370	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	2	2	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	1	no	—
404	C₂	#22560197	1	1	yes	characteristic
405	C₂	#22560242	1	1	yes	characteristic
406	C₂	#22560255	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863256
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₂×#435×C₆₇	C₂
socle	C₂²×C₆₇	#380
prime radical	C₂²×D₄×C₆₇	D₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₂×#435	D₆₇
hypocenter	C₆₇	#8610
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
1. #22560238	C₂	semidirect
2. #22560234	C₂	semidirect
4. #22558077	C₂	semidirect
14. C₂²×M₁₆×C₆₇	C₄	semidirect
21. C₂×C₄⋊C₈×C₆₇	C₄	semidirect
22. C₂×C₂²⋊C₈×C₆₇	C₄	semidirect
24. C₂×#97×C₆₇	C₄	semidirect
167. C₈×C₆₇	#99	semidirect
209. C₆₇	#8610	semidirect
210. C₂²×M₁₆	Dic₆₇	semidirect
219. C₂×C₄⋊C₈	Dic₆₇	semidirect
221. C₂×C₂²⋊C₈	Dic₆₇	semidirect
223. C₂×#97	Dic₆₇	semidirect
371. C₈	#14523958	semidirect

Maximal subgroups

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

subgroup	index
#22560238	2
#22560234	2
#22560197	2
#22558077	2
C₂×#435×C₆₇	2
#8610	67