Subgroups — #2222×D₆₇ #31010390

Order 17152.

638 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#504×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#473×D₆₇	C₂	1	2	yes	maximal
4	#22562335	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562334	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562333	C₂	1	2	yes	maximal, complemented
7	#22562332	C₂	1	2	yes	maximal, complemented
8	#22562331	C₂	1	1	yes	maximal, characteristic, complemented
9	#368×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#362×D₆₇	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2222	C₂	1	1	yes	maximal, characteristic, complemented
12	#137×D₆₇	—	2	2	no	—
13	C₂×Q₁₆×D₆₇	C₂²	1	2	yes	—
14	#131×D₆₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₃₆	C₂²	1	1	yes	characteristic, complemented
16	C₂×#14523989	C₂²	1	2	yes	complemented
17	Q₃₂×D₆₇	—	2	1	no	—
18	Q₃₂×D₆₇	—	2	1	no	—
19	Q₃₂×D₆₇	—	2	1	no	—
20	Q₃₂×D₆₇	—	2	1	no	—
21	#16863814	—	2	1	no	—
22	#16863814	C₂²	1	1	yes	characteristic
23	#16863813	C₂²	1	1	yes	characteristic
24	#16863812	—	2	1	no	—
25	#16863812	C₂²	1	1	yes	characteristic
26	M₃₂×D₆₇	—	2	1	no	—
27	M₃₂×D₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₆₇	—	2	1	no	—
29	C₂×C₁₆×D₆₇	C₂²	1	1	yes	characteristic
30	#16863672	C₂²	1	2	yes	—
31	#16863671	C₂²	1	2	yes	—
32	#16863670	—	2	2	no	—
33	#16863669	—	2	2	no	—
34	#16863668	C₂²	1	2	yes	—
35	#108×D₆₇	C₂²	1	2	yes	—
36	#101×D₆₇	—	2	2	no	—
37	#16863226	C₂²	1	1	yes	characteristic, complemented
38	#16863225	C₂²	1	2	yes	complemented
39	#16863213	C₂²	1	2	yes	complemented
40	#16863212	C₂²	1	2	yes	complemented
41	#16863211	C₂²	1	2	yes	complemented
42	C₂×Q₃₂×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#504×C₆₇	C₂²	1	1	yes	characteristic
44	#473×C₆₇	C₂²	1	2	yes	—
45	#368×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#362×C₆₇	C₂²	1	2	yes	complemented
47	#41×D₆₇	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₆₇	—	2	2	no	—
49	#14524076	—	2	2	no	—
50	#14524075	—	4	2	no	—
51	#14524074	—	2	2	no	—
52	#14524073	—	2	2	no	—
53	#14524072	—	4	2	no	—
54	C₂×Dic₂₆₈	C₂³	1	2	yes	—
55	C₂×#11761618	—	2	2	no	—
56	Q₁₆×D₆₇	—	2	2	no	—
57	Q₁₆×D₆₇	—	2	2	no	—
58	Q₁₆×D₆₇	—	2	2	no	—
59	Q₁₆×D₆₇	—	2	2	no	—
60	Q₁₆×D₆₇	—	4	2	no	—
61	SD₁₆×D₆₇	—	4	2	no	—
62	#14524051	—	2	1	no	—
63	#14524051	D₄	1	1	yes	characteristic
64	#14524050	D₄	1	1	yes	characteristic
65	#14524049	—	2	1	no	—
66	#14524049	C₂³	1	1	yes	characteristic
67	M₁₆×D₆₇	—	2	1	no	—
68	M₁₆×D₆₇	—	2	2	no	—
69	M₁₆×D₆₇	D₄	1	1	yes	characteristic
70	C₂×C₈×D₆₇	—	2	1	no	—
71	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
72	Dic₅₃₆	—	2	1	no	—
73	Dic₅₃₆	—	2	1	no	—
74	#14523989	—	2	2	no	—
75	#14523989	—	2	2	no	—
76	#14523983	—	2	1	no	—
77	#14523983	C₂³	1	1	yes	characteristic
78	#14523982	—	2	1	no	—
79	#14523982	—	2	1	no	—
80	#14523982	—	2	1	no	—
81	C₂×C₆₇⋊C₁₆	—	2	1	no	—
82	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
83	C₁₆×D₆₇	—	2	1	no	—
84	C₁₆×D₆₇	—	2	1	no	—
85	C₁₆×D₆₇	—	2	1	no	—
86	C₁₆×D₆₇	D₄	1	1	yes	characteristic
87	C₁₆×D₆₇	D₄	1	1	yes	characteristic
88	C₁₆×D₆₇	D₄	1	1	yes	characteristic
89	C₁₆×D₆₇	D₄	1	1	yes	characteristic
90	#14523979	C₂³	1	2	yes	—
91	#14523978	—	2	2	no	—
92	#14523962	—	2	2	no	—
93	#14523961	—	2	2	no	—
94	#14523961	—	2	2	no	—
95	#137×C₆₇	—	2	2	no	—
96	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
97	#131×C₆₇	C₂³	1	1	yes	characteristic
98	Q₃₂×C₆₇	—	2	1	no	—
99	Q₃₂×C₆₇	—	2	1	no	—
100	M₃₂×C₆₇	—	2	1	no	—
101	M₃₂×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₆₇	—	2	1	no	—
103	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
104	#108×C₆₇	C₂³	1	2	yes	—
105	#101×C₆₇	—	2	2	no	—
106	#11761629	D₈	1	1	yes	characteristic
107	#11761628	—	2	1	no	—
108	#11761628	C₂×D₄	1	1	yes	characteristic
109	#11761627	—	2	1	no	—
110	#11761627	D₈	1	1	yes	characteristic
111	C₂×Dic₁₃₄	—	2	2	no	—
112	C₂×Dic₁₃₄	—	4	2	no	—
113	Q₈×D₆₇	—	4	2	no	—
114	Q₈×D₆₇	—	4	2	no	—
115	Q₈×D₆₇	—	4	2	no	—
116	Q₈×D₆₇	—	4	2	no	—
117	Q₈×D₆₇	D₈	1	1	yes	characteristic
118	D₄×D₆₇	—	2	1	no	—
119	D₄×D₆₇	D₈	1	1	yes	characteristic
120	C₂×C₄×D₆₇	—	2	1	no	—
121	C₂×C₄×D₆₇	—	4	2	no	—
122	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
123	Dic₂₆₈	—	2	2	no	—
124	Dic₂₆₈	—	2	2	no	—
125	Dic₂₆₈	—	4	2	no	—
126	#11761618	—	4	2	no	—
127	#11761618	—	4	2	no	—
128	#11761618	—	4	2	no	—
129	#11761618	—	4	2	no	—
130	#11761617	—	4	2	no	—
131	#11761616	—	4	2	no	—
132	#11761615	—	4	2	no	—
133	#11761612	—	2	1	no	—
134	#11761612	—	2	2	no	—
135	#11761612	C₂×D₄	1	1	yes	characteristic
136	#11761611	—	2	1	no	—
137	#11761611	—	2	1	no	—
138	#11761611	—	2	1	no	—
139	#11761611	—	4	2	no	—
140	C₂×C₆₇⋊C₈	—	2	1	no	—
141	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₈×D₆₇	—	2	1	no	—
143	C₈×D₆₇	—	2	1	no	—
144	C₈×D₆₇	—	2	1	no	—
145	C₈×D₆₇	—	4	2	no	—
146	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
147	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
148	C₈×D₆₇	#41	1	1	yes	characteristic
149	C₈×D₆₇	#41	1	1	yes	characteristic
150	C₆₇⋊C₁₆	—	2	1	no	—
151	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
152	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
153	#41×C₆₇	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₆₇	—	2	2	no	—
155	Q₁₆×C₆₇	—	2	2	no	—
156	Q₁₆×C₆₇	—	2	2	no	—
157	Q₁₆×C₆₇	—	4	2	no	—
158	SD₁₆×C₆₇	—	4	2	no	—
159	M₁₆×C₆₇	—	2	1	no	—
160	M₁₆×C₆₇	—	2	2	no	—
161	M₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₆₇	—	2	1	no	—
163	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
164	C₁₆×C₆₇	—	2	1	no	—
165	C₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
166	C₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×D₆₇	—	2	1	no	—
168	C₂²×D₆₇	#135	1	1	yes	characteristic
169	Q₈×C₆₇	—	4	2	no	—
170	Q₈×C₆₇	—	4	2	no	—
171	Q₈×C₆₇	C₂×D₈	1	1	yes	characteristic
172	D₄×C₆₇	—	2	1	no	—
173	D₄×C₆₇	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	4	2	no	—
176	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
177	C₂²⋊D₆₇	—	2	1	no	—
178	C₂²⋊D₆₇	—	2	1	no	—
179	C₂²⋊D₆₇	—	2	1	no	—
180	C₂×Dic₆₇	—	2	1	no	—
181	C₂×Dic₆₇	—	4	2	no	—
182	C₂×Dic₆₇	#135	1	1	yes	characteristic
183	D₂₆₈	—	2	1	no	—
184	D₂₆₈	C₂×D₈	1	1	yes	characteristic
185	C₄×D₆₇	—	2	1	no	—
186	C₄×D₆₇	—	2	1	no	—
187	C₄×D₆₇	—	2	1	no	—
188	C₄×D₆₇	—	8	2	no	—
189	C₄×D₆₇	—	8	2	no	—
190	C₄×D₆₇	#121	1	1	yes	characteristic
191	C₄×D₆₇	#121	1	1	yes	characteristic
192	C₄×D₆₇	C₂×D₈	1	1	yes	characteristic
193	C₄×D₆₇	C₂×D₈	1	1	yes	characteristic
194	Dic₁₃₄	—	2	1	no	—
195	Dic₁₃₄	—	4	2	no	—
196	Dic₁₃₄	—	4	2	no	—
197	Dic₁₃₄	—	8	2	no	—
198	Dic₁₃₄	—	8	2	no	—
199	Dic₁₃₄	C₂×D₈	1	1	yes	characteristic
200	C₈×C₆₇	—	2	1	no	—
201	C₈×C₆₇	—	4	2	no	—
202	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
204	C₆₇⋊C₈	—	2	1	no	—
205	C₆₇⋊C₈	—	4	2	no	—
206	C₆₇⋊C₈	#121	1	1	yes	characteristic
207	C₆₇⋊C₈	#121	1	1	yes	characteristic
208	C₂²×C₆₇	—	2	1	no	—
209	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
210	C₂×D₆₇	—	2	2	no	—
211	C₂×D₆₇	—	2	1	no	—
212	C₂×D₆₇	—	4	2	no	—
213	C₂×D₆₇	#466	1	1	yes	characteristic
214	C₂×D₆₇	#466	1	1	yes	characteristic
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	8	2	no	—
217	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
218	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
219	Dic₆₇	—	2	1	no	—
220	Dic₆₇	—	8	2	no	—
221	Dic₆₇	#466	1	1	yes	characteristic
222	Dic₆₇	#466	1	1	yes	characteristic
223	C₂×#2222	—	67	1	no	maximal, Sylow
224	C₂×C₆₇	—	2	1	no	—
225	C₂×C₆₇	—	4	1	no	—
226	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
227	D₆₇	—	2	1	no	—
228	D₆₇	—	4	1	no	—
229	D₆₇	#2222	1	2	yes	direct product factor
230	C₂²×Q₃₂	—	67	1	no	—
231	C₂×#504	—	67	1	no	—
232	C₂×#473	—	67	2	no	—
233	#2222	—	67	1	no	—
234	#2222	—	67	1	no	—
235	#2222	—	67	2	no	—
236	#2222	—	67	1	no	—
237	#2222	—	67	2	no	—
238	#2222	D₆₇	1	1	yes	characteristic, direct product factor
239	C₂×#368	—	67	1	no	—
240	C₂×#362	—	67	2	no	—
241	C₆₇	C₂×#2222	1	1	yes	characteristic, complemented, Sylow
242	C₂×#137	—	134	2	no	—
243	C₂²×Q₁₆	—	67	2	no	—
244	C₂×#131	—	67	1	no	—
245	C₂×Q₃₂	—	67	2	no	—
246	C₂×Q₃₂	—	67	1	no	—
247	C₂×Q₃₂	—	134	1	no	—
248	C₂×Q₃₂	—	134	1	no	—
249	C₂×Q₃₂	—	134	1	no	—
250	C₂×Q₃₂	—	134	1	no	—
251	C₂×Q₃₂	C₂×D₆₇	1	1	yes	characteristic, complemented
252	#504	—	67	1	no	—
253	#504	—	67	1	no	—
254	#504	—	67	1	no	—
255	#504	—	134	1	no	—
256	#504	—	134	1	no	—
257	#504	C₂×D₆₇	1	1	yes	characteristic
258	C₂×M₃₂	—	67	1	no	—
259	C₂×M₃₂	—	134	1	no	—
260	C₂²×C₁₆	—	67	1	no	—
261	C₂²×C₁₆	—	134	1	no	—
262	#473	—	67	2	no	—
263	#473	—	67	2	no	—
264	#473	—	67	2	no	—
265	#473	—	134	2	no	—
266	#473	—	134	2	no	—
267	#473	C₂×D₆₇	1	2	yes	—
268	C₂×#108	—	67	2	no	—
269	C₂×#101	—	134	2	no	—
270	#368	—	67	1	no	—
271	#368	—	67	2	no	—
272	#368	C₂×D₆₇	1	1	yes	characteristic, complemented
273	#362	—	67	2	no	—
274	#362	—	67	2	no	—
275	#362	—	67	2	no	—
276	#362	C₂×D₆₇	1	2	yes	complemented
277	C₂×#41	—	67	1	no	—
278	C₂²×Q₈	—	134	2	no	—
279	#137	—	2	2	no	—
280	#137	—	268	2	no	—
281	#137	—	268	2	no	—
282	#137	—	134	2	no	—
283	#137	—	134	2	no	—
284	#137	—	134	2	no	—
285	C₂×Q₁₆	—	268	2	no	—
286	C₂×Q₁₆	—	67	2	no	—
287	C₂×Q₁₆	—	134	2	no	—
288	C₂×Q₁₆	—	134	2	no	—
289	C₂×Q₁₆	—	134	2	no	—
290	C₂×Q₁₆	—	134	2	no	—
291	C₂×Q₁₆	—	134	2	no	—
292	C₂×Q₁₆	C₂²×D₆₇	1	2	yes	—
293	C₂×SD₁₆	—	268	2	no	—
294	#131	—	67	1	no	—
295	#131	—	67	1	no	—
296	#131	—	67	1	no	—
297	#131	—	134	1	no	—
298	#131	—	134	1	no	—
299	#131	C₂²×D₆₇	1	1	yes	characteristic
300	C₂×M₁₆	—	67	1	no	—
301	C₂×M₁₆	—	134	2	no	—
302	C₂×M₁₆	—	134	1	no	—
303	C₂²×C₈	—	67	1	no	—
304	C₂²×C₈	—	134	1	no	—
305	Q₃₂	—	2	1	no	—
306	Q₃₂	—	2	1	no	—
307	Q₃₂	—	134	2	no	—
308	Q₃₂	—	134	2	no	—
309	Q₃₂	—	134	1	no	—
310	Q₃₂	—	134	1	no	—
311	M₃₂	—	2	1	no	—
312	M₃₂	—	67	1	no	—
313	M₃₂	—	134	1	no	—
314	M₃₂	—	134	1	no	—
315	M₃₂	—	134	1	no	—
316	M₃₂	—	134	1	no	—
317	M₃₂	C₂²×D₆₇	1	1	yes	characteristic
318	C₂×C₁₆	—	2	1	no	—
319	C₂×C₁₆	—	67	1	no	—
320	C₂×C₁₆	—	67	1	no	—
321	C₂×C₁₆	—	67	1	no	—
322	C₂×C₁₆	—	67	1	no	—
323	C₂×C₁₆	—	67	1	no	—
324	C₂×C₁₆	—	134	1	no	—
325	C₂×C₁₆	—	134	1	no	—
326	C₂×C₁₆	—	134	1	no	—
327	C₂×C₁₆	—	134	1	no	—
328	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
329	#108	—	67	2	no	—
330	#108	—	134	2	no	—
331	#108	C₂²×D₆₇	1	2	yes	—
332	#101	—	2	2	no	—
333	#101	—	134	2	no	—
334	#101	—	134	2	no	—
335	#101	—	134	2	no	—
336	#41	—	67	1	no	—
337	#41	—	67	1	no	—
338	#41	—	67	1	no	—
339	#41	—	134	1	no	—
340	#41	—	134	1	no	—
341	#41	D₄×D₆₇	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	268	2	no	—
344	C₂×Q₈	—	268	2	no	—
345	C₂×Q₈	—	268	2	no	—
346	C₂×Q₈	—	268	2	no	—
347	C₂×Q₈	—	268	2	no	—
348	C₂×Q₈	—	67	1	no	—
349	C₂×Q₈	—	134	2	no	—
350	C₂×D₄	—	67	1	no	—
351	C₂×D₄	—	134	1	no	—
352	C₂²×C₄	—	268	2	no	—
353	C₂²×C₄	—	67	1	no	—
354	C₂²×C₄	—	134	1	no	—
355	Q₁₆	—	2	2	no	—
356	Q₁₆	—	2	2	no	—
357	Q₁₆	—	4	2	no	—
358	Q₁₆	—	268	2	no	—
359	Q₁₆	—	268	2	no	—
360	Q₁₆	—	268	2	no	—
361	Q₁₆	—	268	2	no	—
362	Q₁₆	—	268	2	no	—
363	Q₁₆	—	134	2	no	—
364	Q₁₆	—	134	2	no	—
365	SD₁₆	—	4	2	no	—
366	SD₁₆	—	268	2	no	—
367	SD₁₆	—	268	2	no	—
368	SD₁₆	—	268	2	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	268	2	no	—
372	M₁₆	—	67	1	no	—
373	M₁₆	—	134	1	no	—
374	M₁₆	—	134	1	no	—
375	M₁₆	—	134	2	no	—
376	M₁₆	—	134	1	no	—
377	M₁₆	—	134	1	no	—
378	M₁₆	D₄×D₆₇	1	1	yes	characteristic
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	268	2	no	—
381	C₂×C₈	—	67	1	no	—
382	C₂×C₈	—	67	1	no	—
383	C₂×C₈	—	67	1	no	—
384	C₂×C₈	—	67	1	no	—
385	C₂×C₈	—	67	1	no	—
386	C₂×C₈	—	134	1	no	—
387	C₂×C₈	—	134	1	no	—
388	C₂×C₈	—	134	1	no	—
389	C₂×C₈	—	134	1	no	—
390	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
391	C₁₆	—	2	1	no	—
392	C₁₆	—	67	1	no	—
393	C₁₆	—	67	1	no	—
394	C₁₆	—	134	1	no	—
395	C₁₆	D₄×D₆₇	1	1	yes	characteristic
396	C₁₆	D₄×D₆₇	1	1	yes	characteristic
397	C₂³	—	67	1	no	—
398	C₂³	—	134	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	268	2	no	—
402	Q₈	—	268	2	no	—
403	Q₈	—	536	2	no	—
404	Q₈	—	536	2	no	—
405	Q₈	—	67	1	no	—
406	Q₈	—	134	1	no	—
407	Q₈	D₈×D₆₇	1	1	yes	characteristic
408	D₄	—	2	1	no	—
409	D₄	—	67	1	no	—
410	D₄	—	134	1	no	—
411	D₄	—	134	1	no	—
412	D₄	—	134	1	no	—
413	D₄	—	134	1	no	—
414	D₄	D₈×D₆₇	1	1	yes	characteristic
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	268	2	no	—
418	C₂×C₄	—	536	2	no	—
419	C₂×C₄	—	536	2	no	—
420	C₂×C₄	—	67	1	no	—
421	C₂×C₄	—	67	1	no	—
422	C₂×C₄	—	67	1	no	—
423	C₂×C₄	—	67	1	no	—
424	C₂×C₄	—	67	1	no	—
425	C₂×C₄	—	134	1	no	—
426	C₂×C₄	—	134	1	no	—
427	C₂×C₄	—	134	1	no	—
428	C₂×C₄	—	134	1	no	—
429	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	268	2	no	—
433	C₈	—	67	1	no	—
434	C₈	—	67	1	no	—
435	C₈	—	134	1	no	—
436	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
437	C₈	#41×D₆₇	1	1	yes	characteristic
438	C₂²	—	2	1	no	—
439	C₂²	—	268	2	no	—
440	C₂²	—	67	1	no	—
441	C₂²	—	67	1	no	—
442	C₂²	—	134	2	no	—
443	C₂²	—	134	1	no	—
444	C₂²	#135×D₆₇	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	536	2	no	—
448	C₄	—	67	1	no	—
449	C₄	—	67	1	no	—
450	C₄	—	134	1	no	—
451	C₄	#121×D₆₇	1	1	yes	characteristic
452	C₄	C₂×D₈×D₆₇	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	4	1	no	—
455	C₂	—	268	1	no	—
456	C₂	—	67	2	no	—
457	C₂	—	134	1	no	—
458	C₂	#466×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#466×D₆₇
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#2222	C₂
socle	C₂×C₆₇	C₂×#466
prime radical	#41×D₆₇	D₄
hypercenter	#2222	D₆₇
hypocenter	C₆₇	C₂×#2222
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2222

Complements

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

N	H ≅ G/N	type
1. C₂×Q₃₂×D₆₇	C₂	semidirect
4. #22562335	C₂	semidirect
5. #22562334	C₂	semidirect
6. #22562333	C₂	semidirect
7. #22562332	C₂	semidirect
8. #22562331	C₂	semidirect
9. #368×D₆₇	C₂	semidirect
10. #362×D₆₇	C₂	semidirect
11. C₆₇×#2222	C₂	semidirect
15. C₂×Dic₅₃₆	C₂²	semidirect
16. C₂×#14523989	C₂²	semidirect
37. #16863226	C₂²	semidirect
38. #16863225	C₂²	semidirect
39. #16863213	C₂²	semidirect
40. #16863212	C₂²	semidirect
41. #16863211	C₂²	semidirect
42. C₂×Q₃₂×C₆₇	C₂²	semidirect
45. #368×C₆₇	C₂²	semidirect
46. #362×C₆₇	C₂²	semidirect
229. D₆₇	#2222	direct (N × H)
238. #2222	D₆₇	direct (N × H)
241. C₆₇	C₂×#2222	semidirect
251. C₂×Q₃₂	C₂×D₆₇	semidirect
272. #368	C₂×D₆₇	semidirect
276. #362	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×D₆₇	2
#504×D₆₇	2
#473×D₆₇	2
#22562335	2
#22562334	2
#22562333	2
#22562332	2
#22562331	2
#368×D₆₇	2
#362×D₆₇	2
C₆₇×#2222	2
C₂×#2222	67

Subgroups — #2222×D67 #31010390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2222×D₆₇ #31010390