Subgroups — #30826444

Order 17152.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570809	C₂	1	1	yes	maximal, characteristic
2	#22569178	C₂	1	1	yes	maximal, characteristic
3	#22569144	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559103	C₂	1	2	yes	maximal, complemented
5	#22559096	C₂	1	2	yes	maximal, complemented
6	#22559025	C₂	1	2	yes	maximal, complemented
7	#22559024	C₂	1	2	yes	maximal, complemented
8	#22558977	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558675	C₂	1	1	yes	maximal, characteristic
10	#22558490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863930	C₂²	1	1	yes	characteristic
13	#16863802	C₄	1	1	yes	characteristic
14	#16863788	C₄	1	1	yes	characteristic
15	#16863764	C₄	1	1	yes	characteristic
16	#16863758	C₄	1	1	yes	characteristic
17	#16863652	C₄	1	2	yes	—
18	#16863644	C₄	1	2	yes	—
19	#16863527	—	2	1	no	—
20	#16863527	C₂²	1	2	yes	—
21	#16863523	C₂²	1	1	yes	characteristic
22	Q₈×C₆₇⋊C₈	—	2	1	no	—
23	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	—
24	#16863520	C₂²	1	1	yes	characteristic
25	C₄×#11761618	C₂²	1	2	yes	—
26	C₄×#11761615	C₂²	1	2	yes	—
27	#16863473	C₂²	1	1	yes	characteristic
28	#16863464	—	2	1	no	—
29	#16863461	C₂²	1	1	yes	characteristic
30	(C₂²⋊D₆₇)⋊C₈	—	2	1	no	—
31	#16863458	—	2	1	no	—
32	#16863423	—	2	1	no	—
33	#16863420	C₂²	1	1	yes	characteristic
34	#16863353	—	2	1	no	—
35	#16863352	—	2	1	no	—
36	C₄×#11761612	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
38	#16863148	C₂²	1	2	yes	—
39	#16863146	C₂²	1	2	yes	—
40	#16863128	C₂²	1	2	yes	—
41	#16863125	C₂²	1	2	yes	—
42	#16863118	C₂²	1	2	yes	—
43	C₈×C₆₇⋊C₈	C₂²	1	2	yes	—
44	#533×C₆₇	C₂²	1	1	yes	characteristic
45	#432×C₆₇	C₂²	1	1	yes	characteristic
46	#431×C₆₇	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₆₇	C₂²	1	2	yes	—
49	C₂×#11761618	C₂×C₄	1	2	yes	—
50	C₂×#11761615	C₂×C₄	1	2	yes	—
51	C₂×#11761612	—	2	1	no	—
52	C₂×#11761612	C₂×C₄	1	2	yes	—
53	C₂×#11761611	—	2	1	no	—
54	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
55	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
56	C₂×C₈×D₆₇	—	2	1	no	—
57	#14524037	—	2	1	no	—
58	#14524035	C₂×C₄	1	1	yes	characteristic
59	#14524031	C₂×C₄	1	1	yes	characteristic
60	#14524026	—	2	1	no	—
61	#14524022	C₂×C₄	1	1	yes	characteristic
62	#14524017	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
64	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₆₇	—	2	1	no	—
66	#14524000	—	2	1	no	—
67	#14523976	C₂×C₄	1	2	yes	—
68	#14523974	C₂×C₄	1	2	yes	—
69	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
70	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
71	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
72	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
73	Dic₆₇⋊C₈	—	2	1	no	—
74	Dic₆₇⋊C₈	—	2	1	no	—
75	#14523967	C₂×C₄	1	2	yes	—
76	#14523967	C₂×C₄	1	2	yes	—
77	#14523966	C₂×C₄	1	2	yes	—
78	#14523963	C₂×C₄	1	2	yes	—
79	(C₂×D₆₇)⋊C₈	—	2	1	no	—
80	(C₂×D₆₇)⋊C₈	—	2	1	no	—
81	#14523954	—	2	2	no	—
82	#14523954	C₂×C₄	1	1	yes	characteristic
83	#14523954	C₂×C₄	1	1	yes	characteristic
84	#14523953	—	2	1	no	—
85	C₄×C₆₇⋊C₈	—	2	2	no	—
86	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₆₇⋊C₈	D₄	1	1	yes	characteristic
88	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
89	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
90	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
91	C₈×Dic₆₇	—	2	1	no	—
92	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
94	#125×C₆₇	—	2	1	no	—
95	C₂²⋊Q₈×C₆₇	—	2	1	no	—
96	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₆₇	—	2	1	no	—
98	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
99	#117×C₆₇	—	2	1	no	—
100	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₆₇	—	2	1	no	—
102	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₆₇	—	2	1	no	—
105	C₂²⋊C₈×C₆₇	—	2	1	no	—
106	#97×C₆₇	—	2	1	no	—
107	C₄×C₈×C₆₇	C₂³	1	2	yes	—
108	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₆₇	—	2	1	no	—
111	C₂×C₄×D₆₇	—	2	1	no	—
112	#11761618	—	2	4	no	—
113	#11761615	—	2	4	no	—
114	#11761612	—	2	4	no	—
115	#11761612	—	4	2	no	—
116	#11761611	—	4	2	no	—
117	C₂×C₆₇⋊C₈	—	2	2	no	—
118	C₂×C₆₇⋊C₈	—	2	2	no	—
119	C₂×C₆₇⋊C₈	—	4	1	no	—
120	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
122	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
126	C₈×D₆₇	—	4	2	no	—
127	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
129	Dic₆₇⋊C₄	—	2	1	no	—
130	Dic₆₇⋊C₄	—	2	1	no	—
131	Dic₆₇⋊C₄	—	2	1	no	—
132	Dic₆₇⋊C₄	—	2	1	no	—
133	C₂²⋊Dic₆₇	—	2	1	no	—
134	(C₂×D₆₇)⋊C₄	—	2	1	no	—
135	(C₂×D₆₇)⋊C₄	—	2	1	no	—
136	(C₂×D₆₇)⋊C₄	—	2	1	no	—
137	(C₂×D₆₇)⋊C₄	—	2	1	no	—
138	C₄×Dic₆₇	—	2	1	no	—
139	C₂×Q₈×C₆₇	—	2	1	no	—
140	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
144	C₂×C₈×C₆₇	—	2	1	no	—
145	C₂×C₈×C₆₇	—	2	1	no	—
146	C₂×C₈×C₆₇	—	2	2	no	—
147	C₄⋊C₄×C₆₇	—	2	1	no	—
148	C₄⋊C₄×C₆₇	—	2	1	no	—
149	C₄⋊C₄×C₆₇	—	2	1	no	—
150	C₄⋊C₄×C₆₇	—	2	2	no	—
151	C₄⋊C₄×C₆₇	—	2	2	no	—
152	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₆₇	—	2	2	no	—
154	C₄²×C₆₇	—	2	2	no	—
155	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₆₇	#41	1	1	yes	characteristic
158	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
159	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₆₇	—	2	1	no	—
161	Q₈×C₆₇	—	2	2	no	—
162	Q₈×C₆₇	—	2	2	no	—
163	Q₈×C₆₇	—	4	2	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	—	2	1	no	—
166	C₂×C₄×C₆₇	—	2	1	no	—
167	C₂×C₄×C₆₇	—	2	2	no	—
168	C₂×C₄×C₆₇	—	2	2	no	—
169	C₂×C₄×C₆₇	—	4	1	no	—
170	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₆₇	—	4	2	no	—
177	C₂×Dic₆₇	—	2	1	no	—
178	C₂×Dic₆₇	—	2	1	no	—
179	C₂×Dic₆₇	—	2	1	no	—
180	D₂₆₈	—	2	2	no	—
181	C₄×D₆₇	—	4	1	no	—
182	C₄×D₆₇	—	4	1	no	—
183	Dic₁₃₄	—	2	2	no	—
184	C₈×C₆₇	—	4	2	no	—
185	C₈×C₆₇	—	4	1	no	—
186	C₈×C₆₇	—	4	1	no	—
187	C₆₇⋊C₈	—	2	2	no	—
188	C₆₇⋊C₈	—	2	1	no	—
189	C₆₇⋊C₈	—	2	1	no	—
190	C₆₇⋊C₈	—	2	1	no	—
191	C₆₇⋊C₈	—	4	2	no	—
192	C₆₇⋊C₈	#131	1	4	yes	—
193	C₆₇⋊C₈	#137	1	2	yes	—
194	C₂²×C₆₇	—	2	1	no	—
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	—	2	1	no	—
197	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×D₆₇	—	4	1	no	—
199	C₂×D₆₇	—	4	1	no	—
200	C₂×D₆₇	—	4	1	no	—
201	C₄×C₆₇	—	2	1	no	—
202	C₄×C₆₇	—	2	1	no	—
203	C₄×C₆₇	—	2	1	no	—
204	C₄×C₆₇	—	2	1	no	—
205	C₄×C₆₇	—	4	2	no	—
206	C₄×C₆₇	—	4	2	no	—
207	C₄×C₆₇	C₂×#131	1	2	yes	—
208	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
209	C₄×C₆₇	#575	1	1	yes	characteristic
210	Dic₆₇	—	4	1	no	—
211	Dic₆₇	—	4	1	no	—
212	Dic₆₇	—	4	1	no	—
213	#17967	—	67	1	no	maximal, Sylow
214	C₂×C₆₇	—	4	1	no	—
215	C₂×C₆₇	#2931	1	1	yes	characteristic
216	C₂×C₆₇	C₄×#137	1	1	yes	characteristic
217	C₂×C₆₇	#2955	1	1	yes	characteristic
218	D₆₇	—	8	1	no	—
219	#3172	—	67	1	no	—
220	#2966	—	67	1	no	—
221	#2960	—	67	1	no	—
222	#1591	—	67	2	no	—
223	#1590	—	67	2	no	—
224	#1579	—	67	2	no	—
225	SD₁₆⋊C₈	—	67	2	no	—
226	#1569	—	67	1	no	—
227	#1497	D₆₇	1	1	yes	characteristic, complemented
228	#1495	—	67	1	no	—
229	C₈×M₁₆	—	67	1	no	—
230	C₆₇	#17967	1	1	yes	characteristic, complemented, Sylow
231	#533	C₂×D₆₇	1	1	yes	characteristic
232	#529	—	67	1	no	—
233	#501	—	67	1	no	—
234	#497	—	67	1	no	—
235	#491	—	67	1	no	—
236	#489	—	67	1	no	—
237	#470	—	67	2	no	—
238	#468	—	67	2	no	—
239	#446	—	67	2	no	—
240	#446	—	67	1	no	—
241	#446	—	134	1	no	—
242	C₈×Q₈	—	67	2	no	—
243	C₈×Q₈	—	67	1	no	—
244	C₈×Q₈	—	134	1	no	—
245	C₄×Q₁₆	—	67	2	no	—
246	C₄×SD₁₆	—	67	2	no	—
247	#436	—	67	1	no	—
248	#435	—	134	1	no	—
249	C₈×D₄	—	67	1	no	—
250	C₈×D₄	—	134	1	no	—
251	#433	—	134	1	no	—
252	#432	C₂×D₆₇	1	1	yes	characteristic
253	#431	C₂×D₆₇	1	1	yes	characteristic
254	#424	—	134	1	no	—
255	#423	—	67	1	no	—
256	#405	—	134	1	no	—
257	#405	—	134	1	no	—
258	C₄×M₁₆	—	67	1	no	—
259	C₂×C₄×C₈	—	67	1	no	—
260	#335	—	67	2	no	—
261	#334	—	67	2	no	—
262	Q₈⋊C₈	—	67	2	no	—
263	Q₈⋊C₈	C₂×D₆₇	1	2	yes	—
264	Q₈⋊C₈	C₂×D₆₇	1	2	yes	—
265	D₄⋊C₈	—	67	2	no	—
266	#322	—	67	2	no	—
267	C₈²	—	67	2	no	—
268	C₂×Q₁₆	—	67	2	no	—
269	C₂×SD₁₆	—	67	2	no	—
270	C₂×M₁₆	—	67	2	no	—
271	C₂×M₁₆	—	134	1	no	—
272	C₂×M₁₆	—	134	1	no	—
273	C₂²×C₈	—	67	1	no	—
274	C₂²×C₈	—	67	1	no	—
275	C₂²×C₈	—	134	1	no	—
276	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
278	#126	—	134	1	no	—
279	#125	—	2	1	no	—
280	#125	—	67	1	no	—
281	#124	—	67	1	no	—
282	#123	—	134	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	67	1	no	—
285	C₂²⋊Q₈	C₄×D₆₇	1	2	yes	—
286	#121	—	67	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	67	1	no	—
289	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
290	C₄×D₄	—	67	1	no	—
291	C₄×D₄	—	134	1	no	—
292	#117	—	2	1	no	—
293	#117	—	134	1	no	—
294	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
295	#107	—	67	2	no	—
296	#106	—	67	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	67	2	no	—
299	C₄⋊C₈	—	134	2	no	—
300	C₄⋊C₈	—	134	2	no	—
301	C₄⋊C₈	—	134	1	no	—
302	C₄⋊C₈	—	134	1	no	—
303	C₄⋊C₈	—	134	1	no	—
304	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
306	#103	—	67	2	no	—
307	#103	—	67	2	no	—
308	#103	—	67	2	no	—
309	#102	—	67	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	134	1	no	—
313	C₂²⋊C₈	—	134	1	no	—
314	#97	—	2	1	no	—
315	#97	—	67	1	no	—
316	#97	—	67	1	no	—
317	#97	—	134	2	no	—
318	#97	—	134	1	no	—
319	C₄×C₈	—	67	1	no	—
320	C₄×C₈	—	67	1	no	—
321	C₄×C₈	—	67	1	no	—
322	C₄×C₈	—	67	2	no	—
323	C₄×C₈	—	67	1	no	—
324	C₄×C₈	—	134	2	no	—
325	C₄×C₈	—	134	1	no	—
326	C₄×C₈	C₂²×D₆₇	1	2	yes	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	67	1	no	—
329	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
330	C₂×D₄	—	67	1	no	—
331	C₂×D₄	—	134	1	no	—
332	C₂²×C₄	—	134	1	no	—
333	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
335	C₂²×C₄	#11761627	1	1	yes	characteristic
336	Q₁₆	—	134	4	no	—
337	SD₁₆	—	134	4	no	—
338	M₁₆	—	268	2	no	—
339	M₁₆	—	268	2	no	—
340	M₁₆	—	134	4	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	268	2	no	—
345	C₂×C₈	—	268	1	no	—
346	C₂×C₈	—	67	2	no	—
347	C₂×C₈	—	67	1	no	—
348	C₂×C₈	—	67	2	no	—
349	C₂×C₈	—	67	1	no	—
350	C₂×C₈	—	67	1	no	—
351	C₂×C₈	—	67	1	no	—
352	C₂×C₈	—	134	2	no	—
353	C₂×C₈	—	134	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	67	1	no	—
360	C₄⋊C₄	—	67	1	no	—
361	C₄⋊C₄	—	134	1	no	—
362	C₄⋊C₄	—	134	1	no	—
363	C₄⋊C₄	—	134	1	no	—
364	C₄⋊C₄	—	134	1	no	—
365	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	134	1	no	—
368	C₂²⋊C₄	—	134	1	no	—
369	C₂²⋊C₄	—	134	1	no	—
370	C₂²⋊C₄	—	134	1	no	—
371	C₂²⋊C₄	—	134	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	134	1	no	—
374	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
375	C₄²	D₄×D₆₇	1	1	yes	characteristic
376	C₄²	#11761627	1	1	yes	characteristic
377	C₄²	C₂³×D₆₇	1	1	yes	characteristic
378	C₂³	—	134	1	no	—
379	C₂³	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	134	2	no	—
384	D₄	—	268	2	no	—
385	D₄	—	134	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	268	1	no	—
393	C₂×C₄	—	268	1	no	—
394	C₂×C₄	—	134	1	no	—
395	C₂×C₄	—	134	1	no	—
396	C₂×C₄	—	134	1	no	—
397	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
398	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
399	C₂×C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	268	2	no	—
407	C₈	—	67	4	no	—
408	C₈	—	67	2	no	—
409	C₈	—	134	2	no	—
410	C₈	—	134	1	no	—
411	C₈	—	134	1	no	—
412	C₈	—	134	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	268	1	no	—
417	C₂²	—	268	1	no	—
418	C₂²	—	268	1	no	—
419	C₂²	C₂×(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	268	1	no	—
427	C₄	—	268	1	no	—
428	C₄	—	268	1	no	—
429	C₄	#131×D₆₇	1	2	yes	—
430	C₄	#137×D₆₇	1	1	yes	characteristic
431	C₄	#16864195	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	536	1	no	—
434	C₂	#22568917	1	1	yes	characteristic
435	C₂	#22569024	1	1	yes	characteristic
436	C₂	#22569108	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×#1497	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#14524017	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1497	D₆₇
hypocenter	C₆₇	#17967
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1497

Complements

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

N	H ≅ G/N	type
3. #22569144	C₂	semidirect
4. #22559103	C₂	semidirect
5. #22559096	C₂	semidirect
6. #22559025	C₂	semidirect
7. #22559024	C₂	semidirect
8. #22558977	C₂	semidirect
10. #22558490	C₂	semidirect
11. C₆₇×#1497	C₂	semidirect
227. #1497	D₆₇	semidirect
230. C₆₇	#17967	semidirect

Maximal subgroups

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

subgroup	index
#22570809	2
#22569178	2
#22569144	2
#22559103	2
#22559096	2
#22559025	2
#22559024	2
#22558977	2
#22558675	2
#22558490	2
C₆₇×#1497	2
#17967	67