Subgroups — #30854383

Order 17152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863514	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863512	C₂	1	1	yes	maximal, characteristic
3	#22568980	C₂	1	1	yes	maximal, characteristic
4	#22568631	C₂	1	2	yes	maximal, complemented
5	#108×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560090	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560048	C₂	1	2	yes	maximal, complemented
8	#22560043	C₂	1	2	yes	maximal, complemented
9	#22560013	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	C₂×#14524051	C₂²	1	2	yes	—
14	C₂×#14524049	C₂²	1	2	yes	—
15	#16863864	C₂²	1	2	yes	—
16	#16863514	C₄	1	8	yes	complemented
17	#16863512	C₄	1	8	yes	complemented
18	#16863490	C₄	1	2	yes	complemented
19	#16863483	C₄	1	4	yes	complemented
20	#16863478	C₄	1	2	yes	complemented
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	C₂×#14523971	C₂²	1	2	yes	—
23	C₂×#14523969	C₂²	1	2	yes	—
24	#16863390	C₂²	1	2	yes	—
25	#16863353	—	2	2	no	—
26	#16863352	C₂²	1	2	yes	—
27	#16863350	—	2	2	no	—
28	#16863348	—	2	2	no	—
29	M₁₆×Dic₆₇	C₂²	1	2	yes	—
30	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₆₇	—	2	2	no	—
36	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
37	#16863160	C₂²	1	2	yes	—
38	#16863155	C₂²	1	2	yes	—
39	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
40	#427×C₆₇	C₂²	1	1	yes	characteristic
41	#405×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
43	#339×C₆₇	C₂²	1	2	yes	—
44	C₂×#11761628	C₂³	1	2	yes	—
45	#14524065	C₂×C₄	1	4	yes	—
46	#14524065	C₂×C₄	1	4	yes	—
47	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
48	C₂×#11761617	C₂×C₄	1	2	yes	—
49	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
50	#14524051	—	2	4	no	—
51	#14524051	C₂×C₄	1	8	yes	complemented
52	#14524049	—	2	4	no	—
53	#14524049	C₂×C₄	1	8	yes	complemented
54	C₂×#11761612	C₂³	1	2	yes	—
55	C₂×#11761611	—	2	2	no	—
56	C₂×#11761611	—	2	2	no	—
57	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₆₇	—	2	2	no	—
60	C₂×C₈×D₆₇	—	2	2	no	—
61	#14524008	C₂×C₄	1	4	yes	—
62	#14524005	C₂×C₄	1	4	yes	—
63	(C₂²⋊D₆₇)⋊C₄	—	2	4	no	—
64	#14524000	—	2	2	no	—
65	C₂×C₄×Dic₆₇	—	2	2	no	—
66	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
68	C₄²×D₆₇	—	2	2	no	—
69	#14523979	C₂×C₄	1	4	yes	complemented
70	#14523971	C₂×C₄	1	8	yes	complemented
71	#14523969	C₂×C₄	1	8	yes	complemented
72	#14523966	C₂×C₄	1	4	yes	—
73	#14523963	C₂×C₄	1	4	yes	—
74	#14523954	—	2	2	no	—
75	#14523953	—	2	2	no	—
76	C₄×C₆₇⋊C₈	—	2	2	no	—
77	C₄×C₆₇⋊C₈	—	2	2	no	—
78	C₈×Dic₆₇	—	2	2	no	—
79	C₈×Dic₆₇	—	2	2	no	—
80	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
81	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
82	C₈×Dic₆₇	C₂×C₄	1	4	yes	complemented
83	C₈×Dic₆₇	D₄	1	1	yes	characteristic
84	C₈×Dic₆₇	D₄	1	1	yes	characteristic
85	C₈×Dic₆₇	D₄	1	1	yes	characteristic
86	C₈×Dic₆₇	D₄	1	1	yes	characteristic
87	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	#117×C₆₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
92	#108×C₆₇	C₂×C₄	1	4	yes	complemented
93	#107×C₆₇	C₂×C₄	1	2	yes	—
94	#106×C₆₇	C₂×C₄	1	2	yes	—
95	#97×C₆₇	—	2	2	no	—
96	C₄×C₈×C₆₇	—	2	2	no	—
97	C₄×C₈×C₆₇	C₂×C₄	1	4	yes	complemented
98	#11761628	—	2	2	no	—
99	#11761628	—	2	2	no	—
100	#11761628	C₂²×C₄	1	4	yes	—
101	#11761628	C₂²×C₄	1	4	yes	—
102	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
103	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
104	C₂×C₂²⋊D₆₇	—	2	2	no	—
105	C₂²×Dic₆₇	—	2	1	no	—
106	C₂²×Dic₆₇	#41	1	2	yes	—
107	C₂×C₄×D₆₇	—	2	2	no	—
108	C₂×C₄×D₆₇	—	2	4	no	—
109	Dic₂₆₈	C₄²	1	4	yes	complemented
110	#11761617	C₄²	1	8	yes	complemented
111	D₅₃₆	C₄²	1	4	yes	complemented
112	#11761612	—	2	2	no	—
113	#11761612	C₂²×C₄	1	4	yes	—
114	#11761611	—	2	8	no	—
115	#11761611	—	2	8	no	—
116	C₂×C₆₇⋊C₈	—	2	2	no	—
117	C₂×C₆₇⋊C₈	—	2	1	no	—
118	C₂×C₆₇⋊C₈	—	2	1	no	—
119	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₆₇⋊C₈	#41	1	2	yes	—
124	C₈×D₆₇	—	2	8	no	—
125	C₈×D₆₇	—	2	8	no	—
126	Dic₆₇⋊C₄	—	2	4	no	—
127	(C₂×D₆₇)⋊C₄	—	2	4	no	—
128	C₄×Dic₆₇	—	2	8	no	—
129	C₄×Dic₆₇	—	2	1	no	—
130	C₄×Dic₆₇	—	2	4	no	—
131	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
132	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
133	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₇	—	2	1	no	—
136	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
137	M₁₆×C₆₇	—	2	2	no	—
138	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
139	C₂×C₈×C₆₇	—	2	2	no	—
140	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	#41	1	2	yes	—
148	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
149	C₂²⋊C₄×C₆₇	—	2	2	no	—
150	C₄²×C₆₇	—	2	2	no	—
151	C₄²×C₆₇	—	2	1	no	—
152	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
153	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
154	C₂²×D₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
164	C₂²⋊D₆₇	—	2	4	no	—
165	C₂²⋊D₆₇	—	2	4	no	—
166	C₂×Dic₆₇	—	2	4	no	—
167	C₂×Dic₆₇	—	2	2	no	—
168	C₂×Dic₆₇	—	2	2	no	—
169	C₂×Dic₆₇	—	2	4	no	—
170	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
171	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
172	D₂₆₈	—	2	2	no	—
173	D₂₆₈	C₂×C₄²	1	4	yes	—
174	C₄×D₆₇	—	2	4	no	—
175	C₄×D₆₇	—	2	4	no	—
176	C₄×D₆₇	—	4	8	no	—
177	Dic₁₃₄	—	2	2	no	—
178	Dic₁₃₄	C₂×C₄²	1	4	yes	—
179	C₈×C₆₇	—	2	4	no	—
180	C₈×C₆₇	C₂×C₄²	1	2	yes	—
181	C₈×C₆₇	C₂×C₄²	1	2	yes	—
182	C₈×C₆₇	C₄×D₄	1	2	yes	—
183	C₈×C₆₇	C₄×D₄	1	2	yes	—
184	C₆₇⋊C₈	—	2	4	no	—
185	C₆₇⋊C₈	—	2	2	no	—
186	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
187	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
188	C₂²×C₆₇	—	2	2	no	—
189	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
191	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
192	C₂×D₆₇	—	2	4	no	—
193	C₂×D₆₇	—	4	4	no	—
194	C₄×C₆₇	—	2	4	no	—
195	C₄×C₆₇	—	4	4	no	—
196	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
197	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
200	Dic₆₇	—	2	4	no	—
201	Dic₆₇	—	2	2	no	—
202	Dic₆₇	—	2	4	no	—
203	Dic₆₇	#443	1	4	yes	complemented
204	C₄×#443	—	67	1	no	maximal, Sylow
205	C₂×C₆₇	—	2	1	no	—
206	C₂×C₆₇	—	2	1	no	—
207	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
208	C₂×C₆₇	C₂×#443	1	2	yes	—
209	D₆₇	—	4	4	no	—
210	C₂×#443	—	67	1	no	—
211	C₂×#443	—	67	1	no	—
212	C₄×#135	—	67	1	no	—
213	C₄×#131	—	67	2	no	—
214	C₄×#108	—	67	1	no	—
215	#1772	—	67	1	no	—
216	#1772	D₆₇	1	1	yes	characteristic, complemented
217	#1764	—	67	2	no	—
218	#1764	—	67	2	no	—
219	C₄×#104	—	67	2	no	—
220	C₄²×C₈	—	67	1	no	—
221	C₆₇	C₄×#443	1	1	yes	characteristic, complemented, Sylow
222	C₂×#135	—	67	1	no	—
223	C₂×#131	—	67	2	no	—
224	C₂×#131	—	67	2	no	—
225	C₄×#41	—	67	2	no	—
226	#443	—	67	8	no	—
227	#443	—	67	8	no	—
228	C₄×Q₁₆	—	67	2	no	—
229	C₄×SD₁₆	—	67	4	no	—
230	C₄×D₈	—	67	2	no	—
231	C₂×#108	—	67	1	no	—
232	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
233	#427	C₂×D₆₇	1	1	yes	characteristic
234	C₂×#104	—	67	2	no	—
235	C₂×#104	—	67	2	no	—
236	#416	—	67	2	no	—
237	#405	—	67	2	no	—
238	#405	—	134	2	no	—
239	#405	—	134	2	no	—
240	#405	C₂×D₆₇	1	2	yes	—
241	C₄×M₁₆	—	67	2	no	—
242	C₄×M₁₆	—	134	2	no	—
243	C₂×C₄×C₈	—	67	1	no	—
244	C₂×C₄×C₈	—	67	1	no	—
245	C₂×C₄×C₈	—	67	1	no	—
246	C₂×C₄×C₈	—	67	1	no	—
247	C₂×C₄×C₈	—	67	1	no	—
248	C₂×C₄×C₈	—	134	2	no	—
249	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
250	C₄³	—	67	1	no	—
251	#341	—	67	2	no	—
252	#339	—	67	2	no	—
253	#339	C₂×D₆₇	1	2	yes	—
254	C₂×#41	—	67	2	no	—
255	#135	—	67	4	no	—
256	#135	—	67	4	no	—
257	C₂×Q₁₆	—	67	1	no	—
258	C₂×SD₁₆	—	67	2	no	—
259	C₂×D₈	—	67	1	no	—
260	#131	—	67	8	no	—
261	#131	—	67	8	no	—
262	#131	—	134	4	no	—
263	#131	—	134	4	no	—
264	C₂×M₁₆	—	67	2	no	—
265	C₂×M₁₆	—	134	2	no	—
266	C₂×M₁₆	—	134	2	no	—
267	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
268	C₂²×C₈	—	67	1	no	—
269	C₂²×C₈	—	67	1	no	—
270	C₂²×C₈	—	134	2	no	—
271	C₂²×C₈	—	134	2	no	—
272	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
273	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
274	C₄×Q₈	—	67	4	no	—
275	C₄×D₄	—	67	4	no	—
276	C₄×D₄	—	134	4	no	—
277	#117	—	134	2	no	—
278	#117	C₂²×D₆₇	1	2	yes	—
279	C₂×C₄²	—	67	1	no	—
280	C₂×C₄²	—	67	1	no	—
281	C₂×C₄²	—	134	2	no	—
282	C₂×C₄²	—	134	2	no	—
283	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
284	#108	—	67	4	no	—
285	#108	C₄×D₆₇	1	4	yes	complemented
286	#107	C₄×D₆₇	1	2	yes	—
287	#106	C₄×D₆₇	1	2	yes	—
288	#104	—	67	8	no	—
289	#104	—	67	8	no	—
290	#103	—	67	4	no	—
291	#102	—	67	4	no	—
292	#97	—	2	2	no	—
293	#97	—	134	2	no	—
294	#97	—	134	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	67	2	no	—
297	C₄×C₈	—	67	2	no	—
298	C₄×C₈	—	67	4	no	—
299	C₄×C₈	—	67	1	no	—
300	C₄×C₈	—	67	1	no	—
301	C₄×C₈	—	67	1	no	—
302	C₄×C₈	—	67	1	no	—
303	C₄×C₈	—	134	2	no	—
304	C₄×C₈	—	134	2	no	—
305	C₄×C₈	—	134	2	no	—
306	C₄×C₈	—	134	2	no	—
307	C₄×C₈	C₄×D₆₇	1	4	yes	complemented
308	#41	—	67	4	no	—
309	#41	—	67	4	no	—
310	#41	—	134	2	no	—
311	#41	—	134	2	no	—
312	C₂×Q₈	—	67	2	no	—
313	C₂×D₄	—	67	2	no	—
314	C₂×D₄	—	134	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	67	2	no	—
317	C₂²×C₄	—	134	4	no	—
318	C₂²×C₄	—	134	1	no	—
319	C₂²×C₄	—	134	2	no	—
320	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
321	Q₁₆	—	67	4	no	—
322	SD₁₆	—	67	8	no	—
323	D₈	—	67	4	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	67	4	no	—
326	M₁₆	—	134	8	no	—
327	M₁₆	—	134	2	no	—
328	M₁₆	—	134	8	no	—
329	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	67	2	no	—
332	C₂×C₈	—	67	1	no	—
333	C₂×C₈	—	67	1	no	—
334	C₂×C₈	—	67	2	no	—
335	C₂×C₈	—	67	2	no	—
336	C₂×C₈	—	134	8	no	—
337	C₂×C₈	—	134	2	no	—
338	C₂×C₈	—	134	1	no	—
339	C₂×C₈	—	134	1	no	—
340	C₂×C₈	—	134	8	no	—
341	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
342	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
344	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
345	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
346	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
347	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
348	C₂×C₈	#11761629	1	2	yes	—
349	C₄⋊C₄	—	134	4	no	—
350	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	134	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	67	2	no	—
356	C₄²	—	67	1	no	—
357	C₄²	—	67	1	no	—
358	C₄²	—	67	2	no	—
359	C₄²	—	134	4	no	—
360	C₄²	—	134	8	no	—
361	C₄²	—	134	1	no	—
362	C₄²	C₂×C₄×D₆₇	1	2	yes	—
363	C₂³	—	134	2	no	—
364	C₂³	#41×D₆₇	1	1	yes	characteristic
365	Q₈	—	67	4	no	—
366	Q₈	—	134	2	no	—
367	D₄	—	67	4	no	—
368	D₄	—	134	4	no	—
369	D₄	—	134	4	no	—
370	D₄	—	134	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	268	8	no	—
375	C₂×C₄	—	67	2	no	—
376	C₂×C₄	—	67	2	no	—
377	C₂×C₄	—	134	4	no	—
378	C₂×C₄	—	134	4	no	—
379	C₂×C₄	—	134	2	no	—
380	C₂×C₄	—	134	2	no	—
381	C₂×C₄	—	134	4	no	—
382	C₂×C₄	—	134	4	no	—
383	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
387	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
388	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
389	C₈	—	2	4	no	—
390	C₈	—	67	2	no	—
391	C₈	—	67	2	no	—
392	C₈	—	134	4	no	—
393	C₈	—	134	2	no	—
394	C₈	C₄²×D₆₇	1	2	yes	—
395	C₈	C₄²×D₆₇	1	2	yes	—
396	C₈	#14524005	1	2	yes	—
397	C₈	#14524005	1	2	yes	—
398	C₂²	—	2	2	no	—
399	C₂²	—	268	4	no	—
400	C₂²	—	134	4	no	—
401	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
402	C₂²	#16863864	1	1	yes	characteristic
403	C₂²	C₄×#11761629	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	67	4	no	—
407	C₄	—	134	4	no	—
408	C₄	—	134	2	no	—
409	C₄	—	134	4	no	—
410	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
411	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
412	C₄	C₂×#14524005	1	1	yes	characteristic
413	C₄	C₄×#11761629	1	1	yes	characteristic
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	268	4	no	—
417	C₂	C₄×#14524005	1	1	yes	characteristic
418	C₂	#443×D₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1772	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1772	D₆₇
hypocenter	C₆₇	C₄×#443
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
4. #22568631	C₂	semidirect
5. #108×Dic₆₇	C₂	semidirect
6. #22560090	C₂	semidirect
7. #22560048	C₂	semidirect
8. #22560043	C₂	semidirect
9. #22560013	C₂	semidirect
10. C₄×C₈×Dic₆₇	C₂	semidirect
11. C₆₇×#1772	C₂	semidirect
16. #16863514	C₄	semidirect
17. #16863512	C₄	semidirect
18. #16863490	C₄	semidirect
19. #16863483	C₄	semidirect
20. #16863478	C₄	semidirect
51. #14524051	C₂×C₄	semidirect
53. #14524049	C₂×C₄	semidirect
69. #14523979	C₂×C₄	semidirect
70. #14523971	C₂×C₄	semidirect
71. #14523969	C₂×C₄	semidirect
82. C₈×Dic₆₇	C₂×C₄	semidirect
92. #108×C₆₇	C₂×C₄	semidirect
97. C₄×C₈×C₆₇	C₂×C₄	semidirect
109. Dic₂₆₈	C₄²	semidirect
110. #11761617	C₄²	semidirect
111. D₅₃₆	C₄²	semidirect
203. Dic₆₇	#443	semidirect
216. #1772	D₆₇	semidirect
221. C₆₇	C₄×#443	semidirect
285. #108	C₄×D₆₇	semidirect
307. C₄×C₈	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863514	2
C₂×#16863512	2
#22568980	2
#22568631	2
#108×Dic₆₇	2
#22560090	2
#22560048	2
#22560043	2
#22560013	2
C₄×C₈×Dic₆₇	2
C₆₇×#1772	2
C₄×#443	67