Subgroups — #30827593

Order 17152.

654 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570769	C₂	1	1	yes	maximal, characteristic
2	#22569158	C₂	1	1	yes	maximal, characteristic, complemented
3	#22568952	C₂	1	1	yes	maximal, characteristic
4	#22559096	C₂	1	2	yes	maximal, complemented
5	#22559049	C₂	1	2	yes	maximal, complemented
6	#22559048	C₂	1	2	yes	maximal, complemented
7	#22559006	C₂	1	2	yes	maximal, complemented
8	C₂×#16863146	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558609	C₂	1	1	yes	maximal, characteristic
10	#22558490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1481	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	—	2	1	no	—
13	#16863946	C₂²	1	1	yes	characteristic
14	#16863792	C₄	1	1	yes	characteristic
15	#16863770	C₄	1	1	yes	characteristic
16	#16863746	C₄	1	1	yes	characteristic
17	#16863744	C₄	1	1	yes	characteristic
18	#16863627	C₄	1	2	yes	—
19	#16863627	C₄	1	2	yes	—
20	#16863527	—	2	2	no	—
21	#16863527	C₂²	1	2	yes	—
22	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	—
23	C₄×#11761615	C₂²	1	2	yes	—
24	C₄×#11761615	C₂²	1	2	yes	—
25	#16863473	C₂²	1	2	yes	—
26	#16863466	—	2	2	no	—
27	#16863461	C₂²	1	2	yes	—
28	#16863423	—	2	1	no	—
29	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
30	#16863362	—	2	1	no	—
31	#16863352	—	2	1	no	—
32	C₄×#11761612	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
34	#16863146	C₂²	1	1	yes	characteristic
35	#16863146	C₂²	1	1	yes	characteristic
36	#16863146	C₂²	1	1	yes	characteristic
37	#16863146	C₂²	1	1	yes	characteristic
38	#16863125	C₂²	1	2	yes	—
39	#16863125	C₂²	1	2	yes	—
40	#16863118	C₂²	1	2	yes	—
41	C₈×C₆₇⋊C₈	C₂²	1	2	yes	—
42	#533×C₆₇	C₂²	1	1	yes	characteristic
43	#431×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
46	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
47	C₂×#11761628	—	2	1	no	—
48	C₂×#11761615	C₂×C₄	1	2	yes	—
49	C₂×#11761615	C₂×C₄	1	2	yes	—
50	#14524049	—	4	4	no	—
51	C₂×#11761612	D₄	1	1	yes	characteristic
52	C₂×#11761612	D₄	1	1	yes	characteristic
53	C₂×#11761611	—	2	2	no	—
54	C₂²×C₆₇⋊C₈	—	2	1	no	—
55	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₆₇	—	2	2	no	—
58	#14524043	C₂×C₄	1	1	yes	characteristic
59	#14524040	C₂×C₄	1	1	yes	characteristic
60	#14524031	—	2	1	no	—
61	#14524017	—	2	1	no	—
62	#14524017	C₂×C₄	1	2	yes	—
63	C₄×D₂₆₈	—	2	1	no	—
64	C₄×D₂₆₈	C₂³	1	2	yes	—
65	#14523974	C₂×C₄	1	2	yes	—
66	#14523974	C₂×C₄	1	2	yes	—
67	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
68	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
69	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
70	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
72	#14523967	C₂×C₄	1	2	yes	—
73	#14523967	C₂×C₄	1	2	yes	—
74	#14523963	C₂×C₄	1	2	yes	—
75	#14523963	C₂×C₄	1	2	yes	—
76	(C₂×D₆₇)⋊C₈	—	2	2	no	—
77	(C₂×D₆₇)⋊C₈	—	2	2	no	—
78	#14523954	—	2	2	no	—
79	#14523954	D₄	1	2	yes	—
80	C₄×C₆₇⋊C₈	—	2	2	no	—
81	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
86	C₂²×C₈×C₆₇	—	2	1	no	—
87	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
89	#125×C₆₇	—	2	1	no	—
90	C₂²⋊Q₈×C₆₇	—	2	1	no	—
91	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₆₇	—	2	1	no	—
93	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
94	#117×C₆₇	—	2	1	no	—
95	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₆₇	—	2	1	no	—
97	C₄⋊C₈×C₆₇	—	2	1	no	—
98	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
100	C₂²⋊C₈×C₆₇	—	2	1	no	—
101	C₄×C₈×C₆₇	C₂³	1	2	yes	—
102	#11761628	—	4	2	no	—
103	#11761628	—	4	2	no	—
104	C₂×Dic₁₃₄	—	2	1	no	—
105	C₂×D₂₆₈	—	2	1	no	—
106	C₂×D₂₆₈	—	2	1	no	—
107	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
108	C₂×C₂²⋊D₆₇	—	2	2	no	—
109	C₂×C₄×D₆₇	—	2	2	no	—
110	#11761615	—	2	4	no	—
111	#11761615	—	4	2	no	—
112	#11761612	—	2	2	no	—
113	#11761612	SD₁₆	1	4	yes	complemented
114	#11761611	—	4	4	no	—
115	C₂×C₆₇⋊C₈	—	2	2	no	—
116	C₂×C₆₇⋊C₈	—	2	1	no	—
117	C₂×C₆₇⋊C₈	—	2	1	no	—
118	C₂×C₆₇⋊C₈	—	4	1	no	—
119	C₂×C₆₇⋊C₈	—	4	2	no	—
120	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
125	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
126	C₈×D₆₇	—	4	4	no	—
127	C₄⋊Dic₆₇	—	2	1	no	—
128	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
129	(C₂×D₆₇)⋊C₄	—	2	2	no	—
130	(C₂×D₆₇)⋊C₄	—	2	2	no	—
131	C₂×Q₈×C₆₇	—	2	1	no	—
132	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
136	C₂×C₈×C₆₇	—	2	1	no	—
137	C₂×C₈×C₆₇	—	2	1	no	—
138	C₂×C₈×C₆₇	—	2	2	no	—
139	C₂×C₈×C₆₇	—	4	2	no	—
140	C₄⋊C₄×C₆₇	—	2	1	no	—
141	C₄⋊C₄×C₆₇	—	2	1	no	—
142	C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₄⋊C₄×C₆₇	—	2	2	no	—
144	C₄⋊C₄×C₆₇	—	2	2	no	—
145	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂²⋊C₄×C₆₇	—	2	2	no	—
147	C₄²×C₆₇	—	2	2	no	—
148	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₇	#41	1	1	yes	characteristic
151	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
152	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
153	C₂²×D₆₇	—	2	2	no	—
154	Q₈×C₆₇	—	2	2	no	—
155	Q₈×C₆₇	—	2	2	no	—
156	Q₈×C₆₇	—	8	1	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	4	1	no	—
162	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₆₇	#135	1	2	yes	—
167	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₆₇	—	4	4	no	—
171	C₂×Dic₆₇	—	2	2	no	—
172	D₂₆₈	—	2	2	no	—
173	D₂₆₈	—	2	2	no	—
174	D₂₆₈	—	4	2	no	—
175	D₂₆₈	—	8	1	no	—
176	C₄×D₆₇	—	4	2	no	—
177	C₄×D₆₇	—	4	2	no	—
178	Dic₁₃₄	—	4	2	no	—
179	C₈×C₆₇	—	4	2	no	—
180	C₈×C₆₇	—	4	1	no	—
181	C₈×C₆₇	—	4	1	no	—
182	C₆₇⋊C₈	—	2	1	no	—
183	C₆₇⋊C₈	—	2	1	no	—
184	C₆₇⋊C₈	—	2	1	no	—
185	C₆₇⋊C₈	—	2	2	no	—
186	C₆₇⋊C₈	—	4	1	no	—
187	C₆₇⋊C₈	—	4	1	no	—
188	C₆₇⋊C₈	#131	1	2	yes	complemented
189	C₆₇⋊C₈	C₂×SD₁₆	1	4	yes	—
190	C₂²×C₆₇	—	2	1	no	—
191	C₂²×C₆₇	—	2	1	no	—
192	C₂²×C₆₇	C₄×SD₁₆	1	2	yes	—
193	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₆₇	—	4	2	no	—
195	C₂×D₆₇	—	4	2	no	—
196	C₂×D₆₇	—	4	2	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	2	1	no	—
199	C₄×C₆₇	—	2	1	no	—
200	C₄×C₆₇	—	4	2	no	—
201	C₄×C₆₇	—	4	2	no	—
202	C₄×C₆₇	C₄×SD₁₆	1	2	yes	—
203	C₄×C₆₇	C₂×#131	1	1	yes	characteristic
204	C₄×C₆₇	#568	1	1	yes	characteristic
205	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
206	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
207	Dic₆₇	—	4	2	no	—
208	#18067	—	67	1	no	maximal, Sylow
209	C₂×C₆₇	—	2	2	no	—
210	C₂×C₆₇	#2935	1	1	yes	characteristic
211	C₂×C₆₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
212	C₂×C₆₇	#2957	1	1	yes	characteristic
213	D₆₇	—	8	2	no	—
214	#3167	—	67	1	no	—
215	#2962	—	67	1	no	—
216	#2935	—	67	1	no	—
217	#1590	—	67	2	no	—
218	#1583	—	67	2	no	—
219	#1582	—	67	2	no	—
220	C₈×SD₁₆	—	67	2	no	—
221	C₂×#334	—	67	1	no	—
222	#1481	D₆₇	1	1	yes	characteristic, complemented
223	#1480	—	67	1	no	—
224	C₈×M₁₆	—	67	1	no	—
225	C₆₇	#18067	1	1	yes	characteristic, complemented, Sylow
226	C₂×#131	—	134	1	no	—
227	#533	C₂×D₆₇	1	1	yes	characteristic
228	#532	—	67	1	no	—
229	#498	—	67	1	no	—
230	#492	—	67	1	no	—
231	#487	—	67	1	no	—
232	#486	—	67	1	no	—
233	#465	—	67	2	no	—
234	#465	—	67	2	no	—
235	#446	—	67	2	no	—
236	#446	—	134	2	no	—
237	C₈×Q₈	—	67	2	no	—
238	C₄×SD₁₆	—	67	2	no	—
239	C₄×SD₁₆	—	67	2	no	—
240	#436	—	67	2	no	—
241	#435	—	134	2	no	—
242	C₈×D₄	—	67	2	no	—
243	#431	C₂×D₆₇	1	1	yes	characteristic
244	#424	—	134	1	no	—
245	C₂×C₄⋊C₈	—	67	1	no	—
246	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
247	#408	—	134	1	no	—
248	#405	—	134	1	no	—
249	C₄×M₁₆	—	67	1	no	—
250	C₂×C₄×C₈	—	67	1	no	—
251	#334	—	67	1	no	—
252	#334	—	67	1	no	—
253	#334	—	67	1	no	—
254	#334	—	67	1	no	—
255	Q₈⋊C₈	C₂×D₆₇	1	2	yes	—
256	Q₈⋊C₈	C₂×D₆₇	1	2	yes	—
257	D₄⋊C₈	—	67	2	no	—
258	D₄⋊C₈	—	67	2	no	—
259	#322	—	67	2	no	—
260	C₈²	—	67	2	no	—
261	C₂×#41	—	134	1	no	—
262	C₂×SD₁₆	—	67	2	no	—
263	C₂×SD₁₆	—	67	2	no	—
264	#131	—	268	4	no	—
265	C₂×M₁₆	—	67	1	no	—
266	C₂×M₁₆	—	67	1	no	—
267	C₂×M₁₆	—	134	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	67	1	no	—
270	C₂²×C₈	—	67	1	no	—
271	C₂²×C₈	—	134	2	no	—
272	C₂²×C₈	—	134	1	no	—
273	C₄⋊Q₈	—	67	1	no	—
274	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
275	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
276	#127	—	67	1	no	—
277	#125	—	2	1	no	—
278	#124	—	134	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	C₄×D₆₇	1	2	yes	—
281	#121	—	67	2	no	—
282	#121	—	134	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
285	C₄×D₄	—	67	2	no	—
286	C₄×D₄	—	134	1	no	—
287	#117	—	2	1	no	—
288	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
289	#106	—	67	2	no	—
290	#106	—	67	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	67	1	no	—
294	C₄⋊C₈	—	67	1	no	—
295	C₄⋊C₈	—	134	2	no	—
296	C₄⋊C₈	—	134	2	no	—
297	C₄⋊C₈	—	134	1	no	—
298	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
300	#103	—	67	2	no	—
301	#103	—	67	2	no	—
302	#102	—	67	2	no	—
303	#102	—	67	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	134	2	no	—
306	C₂²⋊C₈	—	134	2	no	—
307	#97	—	67	2	no	—
308	#97	—	134	2	no	—
309	C₄×C₈	—	67	1	no	—
310	C₄×C₈	—	67	1	no	—
311	C₄×C₈	—	67	1	no	—
312	C₄×C₈	—	67	2	no	—
313	C₄×C₈	—	67	1	no	—
314	C₄×C₈	—	134	2	no	—
315	C₄×C₈	C₂²×D₆₇	1	2	yes	—
316	#41	—	268	2	no	—
317	#41	—	268	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	134	1	no	—
320	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
321	C₂×D₄	—	67	2	no	—
322	C₂×D₄	—	134	2	no	—
323	C₂×D₄	—	134	1	no	—
324	C₂×D₄	—	134	1	no	—
325	C₂²×C₄	—	134	2	no	—
326	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
328	C₂²×C₄	#11761627	1	1	yes	characteristic
329	SD₁₆	—	268	2	no	—
330	SD₁₆	—	134	4	no	—
331	M₁₆	—	268	4	no	—
332	M₁₆	—	67	4	no	—
333	M₁₆	—	134	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	268	4	no	—
339	C₂×C₈	—	268	2	no	—
340	C₂×C₈	—	268	1	no	—
341	C₂×C₈	—	67	1	no	—
342	C₂×C₈	—	67	2	no	—
343	C₂×C₈	—	67	1	no	—
344	C₂×C₈	—	67	1	no	—
345	C₂×C₈	—	67	1	no	—
346	C₂×C₈	—	67	2	no	—
347	C₂×C₈	—	134	1	no	—
348	C₂×C₈	—	134	1	no	—
349	C₂×C₈	—	134	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	67	2	no	—
356	C₄⋊C₄	—	134	1	no	—
357	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	134	2	no	—
360	C₂²⋊C₄	—	134	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
363	C₄²	D₄×D₆₇	1	1	yes	characteristic
364	C₄²	#11761627	1	1	yes	characteristic
365	C₄²	C₂³×D₆₇	1	1	yes	characteristic
366	C₂³	—	134	2	no	—
367	C₂³	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	268	2	no	—
372	D₄	—	268	4	no	—
373	D₄	—	268	2	no	—
374	D₄	—	536	1	no	—
375	D₄	—	134	2	no	—
376	D₄	—	134	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	268	2	no	—
383	C₂×C₄	—	268	2	no	—
384	C₂×C₄	—	134	2	no	—
385	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
386	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
387	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	SD₁₆×D₆₇	1	2	yes	—
389	C₂×C₄	#14524066	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
392	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	268	1	no	—
397	C₈	—	268	1	no	—
398	C₈	—	67	2	no	—
399	C₈	—	67	4	no	—
400	C₈	—	134	1	no	—
401	C₈	—	134	1	no	—
402	C₈	—	134	1	no	—
403	C₈	—	134	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	268	2	no	—
407	C₂²	—	268	2	no	—
408	C₂²	—	268	2	no	—
409	C₂²	#16863481	1	2	yes	—
410	C₂²	C₂×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	268	2	no	—
417	C₄	#16863481	1	2	yes	—
418	C₄	#131×D₆₇	1	1	yes	characteristic
419	C₄	#16864161	1	1	yes	characteristic
420	C₄	C₂×SD₁₆×D₆₇	1	1	yes	characteristic
421	C₄	C₂×#14524066	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	536	2	no	—
424	C₂	#22568949	1	1	yes	characteristic
425	C₂	C₂×#16863481	1	1	yes	characteristic
426	C₂	#22569122	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1481	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#16863946	C₂²
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1481	D₆₇
hypocenter	C₆₇	#18067
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

Complements

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

N	H ≅ G/N	type
2. #22569158	C₂	semidirect
4. #22559096	C₂	semidirect
5. #22559049	C₂	semidirect
6. #22559048	C₂	semidirect
7. #22559006	C₂	semidirect
8. C₂×#16863146	C₂	semidirect
10. #22558490	C₂	semidirect
11. C₆₇×#1481	C₂	semidirect
113. #11761612	SD₁₆	semidirect
188. C₆₇⋊C₈	#131	semidirect
222. #1481	D₆₇	semidirect
225. C₆₇	#18067	semidirect

Maximal subgroups

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

subgroup	index
#22570769	2
#22569158	2
#22568952	2
#22559096	2
#22559049	2
#22559048	2
#22559006	2
C₂×#16863146	2
#22558609	2
#22558490	2
C₆₇×#1481	2
#18067	67