Subgroups — #30859090

Order 17152.

764 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568860	C₂	1	1	yes	maximal, characteristic, complemented
2	#22568637	C₂	1	1	yes	maximal, characteristic, complemented
3	#22560859	C₂	1	2	yes	maximal, complemented
4	#22560810	C₂	1	2	yes	maximal, complemented
5	#22560538	C₂	1	2	yes	maximal
6	#22560486	C₂	1	2	yes	maximal, complemented
7	C₄×#14523979	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560019	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560019	C₂	1	1	yes	maximal, characteristic, complemented
10	#22559960	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	2	yes	—
13	#16863457	—	2	2	no	—
14	#16863453	—	2	1	no	—
15	#16863453	—	2	1	no	—
16	C₂×#14523979	C₂²	1	2	yes	—
17	#16863423	C₂²	1	2	yes	—
18	C₂×#14523970	C₂²	1	2	yes	—
19	C₂×#14523970	C₂²	1	2	yes	—
20	#16863363	C₂²	1	2	yes	—
21	#16863352	—	2	2	no	—
22	#16863352	C₂²	1	2	yes	—
23	C₄×#11761612	—	2	1	no	—
24	C₄×#11761612	C₂²	1	1	yes	characteristic
25	C₄×#11761612	C₂²	1	1	yes	characteristic
26	C₂×#14523954	—	2	1	no	—
27	C₂×#14523954	C₂²	1	1	yes	characteristic
28	#16863242	C₂²	1	1	yes	characteristic
29	#16863161	C₂²	1	2	yes	—
30	#16863155	C₂²	1	2	yes	—
31	#16863155	C₂²	1	2	yes	—
32	#16863150	C₂²	1	2	yes	—
33	#16863150	C₂²	1	2	yes	—
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
35	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
36	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₆₇	C₄	1	2	yes	complemented
38	C₄×SD₁₆×C₆₇	C₄	1	2	yes	complemented
39	C₄×SD₁₆×C₆₇	C₄	1	2	yes	complemented
40	C₄×D₈×C₆₇	C₄	1	2	yes	complemented
41	#427×C₆₇	C₂²	1	1	yes	characteristic
42	#416×C₆₇	C₂²	1	1	yes	characteristic
43	#416×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
45	#14524050	—	2	4	no	—
46	#14524050	—	2	4	no	—
47	C₂×#11761612	—	2	2	no	—
48	C₂×#11761612	C₂³	1	2	yes	—
49	C₂×#11761612	C₂³	1	2	yes	—
50	C₂²×C₆₇⋊C₈	—	2	2	no	—
51	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
52	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
53	#14523979	—	2	4	no	—
54	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
55	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
56	#14523970	—	2	4	no	—
57	#14523970	—	2	4	no	—
58	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
60	#14523954	—	2	2	no	—
61	#14523954	—	2	1	no	—
62	#14523954	—	2	1	no	—
63	#14523954	D₄	1	1	yes	characteristic
64	#14523954	D₄	1	1	yes	characteristic
65	#14523954	D₄	1	2	yes	—
66	C₄×C₆₇⋊C₈	—	2	2	no	—
67	C₄×C₆₇⋊C₈	—	2	1	no	—
68	C₄×C₆₇⋊C₈	—	2	1	no	—
69	C₆₇⋊#95	—	2	2	no	—
70	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
71	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
72	#135×C₆₇	—	2	4	no	—
73	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
75	C₂×SD₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
76	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
79	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
80	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
81	C₄×D₄×C₆₇	—	2	2	no	—
82	C₄×D₄×C₆₇	—	2	2	no	—
83	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
84	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
85	#117×C₆₇	—	2	1	no	—
86	#117×C₆₇	—	2	1	no	—
87	#117×C₆₇	C₂³	1	1	yes	characteristic
88	#117×C₆₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₆₇	—	2	1	no	—
90	C₂×C₄²×C₆₇	—	2	1	no	—
91	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
92	#107×C₆₇	C₂×C₄	1	2	yes	—
93	#106×C₆₇	C₂×C₄	1	2	yes	—
94	#103×C₆₇	C₂×C₄	1	2	yes	—
95	#103×C₆₇	C₂×C₄	1	2	yes	—
96	#102×C₆₇	C₂×C₄	1	2	yes	—
97	#102×C₆₇	C₂×C₄	1	2	yes	—
98	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
100	C₂²×Dic₆₇	—	2	2	no	—
101	#11761612	—	2	8	no	—
102	#11761612	—	2	2	no	—
103	#11761612	—	2	2	no	—
104	#11761612	—	2	2	no	—
105	#11761612	#41	1	4	yes	—
106	C₂×C₆₇⋊C₈	—	2	8	no	—
107	C₂×C₆₇⋊C₈	—	2	2	no	—
108	C₂×C₆₇⋊C₈	—	2	2	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₂×C₆₇⋊C₈	—	2	2	no	—
111	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
112	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
113	C₄×Dic₆₇	—	2	2	no	—
114	C₄×Dic₆₇	—	2	2	no	—
115	#41×C₆₇	—	2	2	no	—
116	#41×C₆₇	—	2	2	no	—
117	#41×C₆₇	—	2	2	no	—
118	#41×C₆₇	#41	1	4	yes	—
119	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₆₇	—	2	1	no	—
122	C₂×D₄×C₆₇	—	2	1	no	—
123	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₇	—	2	1	no	—
126	C₂²×C₄×C₆₇	—	2	1	no	—
127	C₂²×C₄×C₆₇	—	2	2	no	—
128	C₂²×C₄×C₆₇	—	2	2	no	—
129	C₂²×C₄×C₆₇	#41	1	2	yes	—
130	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₆₇	—	2	2	no	—
132	SD₁₆×C₆₇	—	2	2	no	—
133	SD₁₆×C₆₇	—	2	2	no	—
134	D₈×C₆₇	—	2	2	no	—
135	C₂×C₈×C₆₇	—	2	2	no	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₆₇	—	2	2	no	—
141	C₄⋊C₄×C₆₇	—	2	2	no	—
142	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₆₇	—	2	1	no	—
145	C₂²⋊C₄×C₆₇	—	2	1	no	—
146	C₂²⋊C₄×C₆₇	—	2	2	no	—
147	C₂²⋊C₄×C₆₇	—	2	2	no	—
148	C₄²×C₆₇	—	2	2	no	—
149	C₄²×C₆₇	—	2	2	no	—
150	C₄²×C₆₇	—	2	1	no	—
151	C₄²×C₆₇	—	2	1	no	—
152	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
153	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
155	C₂³×C₆₇	—	2	1	no	—
156	C₂³×C₆₇	—	2	1	no	—
157	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
158	Q₈×C₆₇	—	2	1	no	—
159	Q₈×C₆₇	—	2	1	no	—
160	Q₈×C₆₇	—	2	1	no	—
161	Q₈×C₆₇	#117	1	2	yes	—
162	D₄×C₆₇	—	2	4	no	—
163	D₄×C₆₇	—	2	1	no	—
164	D₄×C₆₇	—	2	1	no	—
165	D₄×C₆₇	—	2	1	no	—
166	D₄×C₆₇	—	4	2	no	—
167	D₄×C₆₇	#117	1	2	yes	—
168	C₂×C₄×C₆₇	—	2	1	no	—
169	C₂×C₄×C₆₇	—	2	4	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	4	2	no	—
174	C₂×C₄×C₆₇	—	4	2	no	—
175	C₂×C₄×C₆₇	—	8	2	no	—
176	C₂×C₄×C₆₇	—	8	2	no	—
177	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
182	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
183	C₂×Dic₆₇	—	4	4	no	—
184	C₂×Dic₆₇	—	4	2	no	—
185	C₈×C₆₇	—	2	1	no	—
186	C₈×C₆₇	—	2	1	no	—
187	C₈×C₆₇	—	2	2	no	—
188	C₆₇⋊C₈	—	2	2	no	—
189	C₆₇⋊C₈	—	2	4	no	—
190	C₆₇⋊C₈	—	2	2	no	—
191	C₆₇⋊C₈	—	4	2	no	—
192	C₂²×C₆₇	—	2	2	no	—
193	C₂²×C₆₇	—	2	2	no	—
194	C₂²×C₆₇	—	4	2	no	—
195	C₂²×C₆₇	—	4	2	no	—
196	C₂²×C₆₇	—	4	1	no	—
197	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₆₇	#529	1	2	yes	—
199	C₄×C₆₇	—	2	2	no	—
200	C₄×C₆₇	—	2	2	no	—
201	C₄×C₆₇	—	2	2	no	—
202	C₄×C₆₇	—	4	2	no	—
203	C₄×C₆₇	—	4	2	no	—
204	C₄×C₆₇	—	4	1	no	—
205	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
206	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
207	C₄×C₆₇	#525	1	2	yes	—
208	Dic₆₇	—	8	2	no	—
209	#21140	—	67	1	no	maximal, Sylow
210	C₂×C₆₇	—	2	2	no	—
211	C₂×C₆₇	—	4	2	no	—
212	C₂×C₆₇	—	8	1	no	—
213	C₂×C₆₇	#2290	1	1	yes	characteristic
214	C₂×C₆₇	#2957	1	2	yes	—
215	C₄×#135	D₆₇	1	1	yes	characteristic
216	#2923	—	67	1	no	—
217	#2875	—	67	1	no	—
218	#1929	—	67	2	no	—
219	#1922	—	67	2	no	—
220	#1876	—	67	2	no	—
221	#1866	—	67	2	no	—
222	C₄×#108	—	67	1	no	—
223	#1759	—	67	1	no	—
224	#1759	—	67	1	no	—
225	#1746	—	67	1	no	—
226	C₆₇	#21140	1	1	yes	characteristic, complemented, Sylow
227	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
228	C₂×#131	—	67	2	no	—
229	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
230	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
231	C₄×Q₁₆	Dic₆₇	1	2	yes	complemented
232	C₄×SD₁₆	Dic₆₇	1	2	yes	complemented
233	C₄×SD₁₆	Dic₆₇	1	2	yes	complemented
234	C₄×D₈	Dic₆₇	1	2	yes	complemented
235	#433	—	134	2	no	—
236	#432	—	134	1	no	—
237	#432	—	134	1	no	—
238	C₂×#108	—	67	2	no	—
239	#427	C₂×D₆₇	1	1	yes	characteristic
240	#424	—	67	2	no	—
241	C₂×#104	—	67	2	no	—
242	C₂×#104	—	67	2	no	—
243	#416	C₂×D₆₇	1	1	yes	characteristic
244	#416	C₂×D₆₇	1	1	yes	characteristic
245	#408	—	67	2	no	—
246	#405	—	67	2	no	—
247	#405	—	134	2	no	—
248	C₄×M₁₆	—	67	1	no	—
249	C₄×M₁₆	—	67	1	no	—
250	C₄×M₁₆	—	134	1	no	—
251	C₂×#97	—	67	1	no	—
252	C₂×#97	—	134	1	no	—
253	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
254	#376	—	67	1	no	—
255	#341	—	67	2	no	—
256	#339	—	67	2	no	—
257	#339	—	67	2	no	—
258	#336	—	67	2	no	—
259	#336	—	67	2	no	—
260	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
261	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
262	#135	—	2	4	no	—
263	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
265	C₂×SD₁₆	C₂×Dic₆₇	1	1	yes	characteristic
266	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
267	#131	—	134	4	no	—
268	#131	—	134	4	no	—
269	C₂×M₁₆	—	67	2	no	—
270	C₂×M₁₆	—	67	2	no	—
271	C₂×M₁₆	—	134	2	no	—
272	C₂²×C₈	—	67	2	no	—
273	C₂²×C₈	—	134	2	no	—
274	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
276	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
277	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
281	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	C₂²×D₆₇	1	1	yes	characteristic
285	#117	C₂²×D₆₇	1	1	yes	characteristic
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	67	2	no	—
289	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
290	#108	—	134	4	no	—
291	#107	C₂×Dic₆₇	1	2	yes	—
292	#106	C₂×Dic₆₇	1	2	yes	—
293	C₄⋊C₈	—	134	2	no	—
294	C₄⋊C₈	—	134	2	no	—
295	#104	—	134	4	no	—
296	#104	—	134	4	no	—
297	#103	C₂×Dic₆₇	1	2	yes	—
298	#103	C₂×Dic₆₇	1	2	yes	—
299	#102	C₂×Dic₆₇	1	2	yes	—
300	#102	C₂×Dic₆₇	1	2	yes	—
301	C₂²⋊C₈	—	134	2	no	—
302	C₂²⋊C₈	—	134	2	no	—
303	#97	—	67	1	no	—
304	#97	—	67	1	no	—
305	#97	—	67	2	no	—
306	#97	—	134	2	no	—
307	#97	—	134	1	no	—
308	#97	—	134	1	no	—
309	C₄×C₈	—	134	2	no	—
310	C₄×C₈	—	134	1	no	—
311	C₄×C₈	—	134	1	no	—
312	C₄×C₈	C₂×Dic₆₇	1	2	yes	—
313	C₄×C₈	C₂×Dic₆₇	1	2	yes	—
314	#95	—	134	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	#11761628	1	4	yes	—
319	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
320	C₂×Q₈	C₂²×Dic₆₇	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
324	C₂×D₄	C₂²×Dic₆₇	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	134	2	no	—
330	C₂²×C₄	#11761627	1	2	yes	—
331	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
332	Q₁₆	—	2	2	no	—
333	SD₁₆	—	2	2	no	—
334	SD₁₆	—	2	2	no	—
335	D₈	—	2	2	no	—
336	M₁₆	—	67	4	no	—
337	M₁₆	—	134	2	no	—
338	M₁₆	—	134	2	no	—
339	M₁₆	—	134	8	no	—
340	M₁₆	—	134	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	67	2	no	—
344	C₂×C₈	—	67	2	no	—
345	C₂×C₈	—	134	2	no	—
346	C₂×C₈	—	134	8	no	—
347	C₂×C₈	—	134	2	no	—
348	C₂×C₈	—	134	2	no	—
349	C₂×C₈	—	134	2	no	—
350	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
351	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
352	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	134	2	no	—
366	C₄²	—	134	2	no	—
367	C₄²	C₂²×Dic₆₇	1	2	yes	—
368	C₄²	D₄×D₆₇	1	1	yes	characteristic
369	C₄²	D₄×D₆₇	1	1	yes	characteristic
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	C₂×#11761627	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	—	2	1	no	—
375	Q₈	—	2	1	no	—
376	Q₈	#14524002	1	2	yes	—
377	D₄	—	2	4	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	1	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	#14524002	1	2	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	268	4	no	—
393	C₂×C₄	—	268	2	no	—
394	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
395	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
396	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
398	C₂×C₄	#41×D₆₇	1	2	yes	—
399	C₂×C₄	C₂×#11761628	1	2	yes	—
400	C₈	—	2	1	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	2	no	—
403	C₈	—	268	2	no	—
404	C₈	—	134	2	no	—
405	C₈	—	134	2	no	—
406	C₈	—	134	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
413	C₂²	#16863926	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	536	2	no	—
421	C₄	C₂×#14524002	1	1	yes	characteristic
422	C₄	#41×Dic₆₇	1	1	yes	characteristic
423	C₄	#16863905	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	#22562654	1	1	yes	characteristic
428	C₂	#22569126	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₄×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#135	D₆₇
hypocenter	C₆₇	#21140
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22568860	C₂	semidirect
2. #22568637	C₂	semidirect
3. #22560859	C₂	semidirect
4. #22560810	C₂	semidirect
6. #22560486	C₂	semidirect
7. C₄×#14523979	C₂	semidirect
8. #22560019	C₂	semidirect
9. #22560019	C₂	semidirect
10. #22559960	C₂	semidirect
37. C₄×Q₁₆×C₆₇	C₄	semidirect
38. C₄×SD₁₆×C₆₇	C₄	semidirect
39. C₄×SD₁₆×C₆₇	C₄	semidirect
40. C₄×D₈×C₆₇	C₄	semidirect
226. C₆₇	#21140	semidirect
231. C₄×Q₁₆	Dic₆₇	semidirect
232. C₄×SD₁₆	Dic₆₇	semidirect
233. C₄×SD₁₆	Dic₆₇	semidirect
234. C₄×D₈	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568860	2
#22568637	2
#22560859	2
#22560810	2
#22560538	2
#22560486	2
C₄×#14523979	2
#22560019	2
#22559960	2
C₄×#135×C₆₇	2
#21140	67