Subgroups — #30839736

Order 17152.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570354	C₂	1	2	yes	maximal, complemented
2	C₈×#11761628	C₂	1	1	yes	maximal, characteristic, complemented
3	#22559576	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559571	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559566	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559561	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559554	C₂	1	2	yes	maximal, complemented
8	#22559547	C₂	1	2	yes	maximal, complemented
9	#22558972	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558914	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11761628	C₂²	1	1	yes	characteristic
13	#16863717	—	2	2	no	—
14	#16863678	C₂²	1	2	yes	—
15	#16863673	C₂²	1	2	yes	—
16	#16863593	C₂²	1	2	yes	—
17	#16863588	C₂²	1	2	yes	—
18	#16863539	—	2	2	no	—
19	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
21	#16863506	—	2	2	no	—
22	#16863496	—	2	2	no	—
23	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
24	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₆₇	—	2	1	no	—
26	C₈×C₂²⋊D₆₇	—	2	1	no	—
27	#16863453	C₂²	1	2	yes	—
28	#16863449	C₂²	1	1	yes	characteristic
29	#16863447	—	2	1	no	—
30	C₄×C₈×D₆₇	—	2	1	no	—
31	#16863149	C₂²	1	1	yes	characteristic
32	#16863149	C₂²	1	1	yes	characteristic
33	#16863147	C₂²	1	2	yes	—
34	#16863142	C₂²	1	2	yes	—
35	#16863142	C₂²	1	2	yes	—
36	#16863140	C₂²	1	2	yes	—
37	#16863140	C₂²	1	2	yes	—
38	C₂×#135×C₆₇	—	2	1	no	—
39	C₂×#135×C₆₇	—	2	1	no	—
40	#532×C₆₇	C₂²	1	2	yes	—
41	#495×C₆₇	—	2	1	no	—
42	#495×C₆₇	—	2	1	no	—
43	#494×C₆₇	C₂²	1	1	yes	characteristic
44	#493×C₆₇	C₂²	1	1	yes	characteristic
45	#492×C₆₇	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#11761628	D₄	1	1	yes	characteristic
48	C₂×#11761616	—	2	2	no	—
49	C₂×#11761613	—	2	2	no	—
50	C₂×C₈×D₆₇	—	2	1	no	—
51	C₂×C₈×D₆₇	—	2	1	no	—
52	C₄×Dic₁₃₄	D₄	1	1	yes	characteristic
53	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
54	C₄×D₂₆₈	D₄	1	1	yes	characteristic
55	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₆₇	—	2	1	no	—
57	C₄×C₂²⋊D₆₇	—	2	1	no	—
58	#14524002	D₄	1	1	yes	characteristic
59	#14524000	—	2	1	no	—
60	C₄²×D₆₇	—	2	1	no	—
61	#14523976	—	2	2	no	—
62	#14523974	—	2	2	no	—
63	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
67	Dic₆₇⋊C₈	—	2	1	no	—
68	Dic₆₇⋊C₈	—	2	1	no	—
69	#14523966	—	2	2	no	—
70	#14523964	—	2	2	no	—
71	#14523964	—	2	2	no	—
72	#14523963	—	2	2	no	—
73	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
75	(C₂×D₆₇)⋊C₈	—	2	1	no	—
76	(C₂×D₆₇)⋊C₈	—	2	1	no	—
77	#14523954	—	2	2	no	—
78	C₄×C₆₇⋊C₈	—	2	1	no	—
79	C₈×Dic₆₇	—	2	1	no	—
80	C₈×Dic₆₇	—	2	1	no	—
81	C₂×#41×C₆₇	—	2	2	no	—
82	#135×C₆₇	—	4	4	no	—
83	#135×C₆₇	—	4	4	no	—
84	C₂×Q₁₆×C₆₇	—	2	1	no	—
85	C₂×Q₁₆×C₆₇	—	2	1	no	—
86	C₂×SD₁₆×C₆₇	—	2	2	no	—
87	C₂×SD₁₆×C₆₇	—	2	2	no	—
88	C₂×D₈×C₆₇	—	2	1	no	—
89	C₂×D₈×C₆₇	—	2	1	no	—
90	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
92	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
93	#127×C₆₇	C₂³	1	2	yes	—
94	#124×C₆₇	—	2	2	no	—
95	#121×C₆₇	—	2	2	no	—
96	#121×C₆₇	—	2	2	no	—
97	C₄×D₄×C₆₇	—	2	2	no	—
98	C₄×D₄×C₆₇	—	2	2	no	—
99	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
101	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
102	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
104	#11761628	—	2	2	no	—
105	#11761628	—	2	2	no	—
106	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
107	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₆₇	—	2	1	no	—
109	C₂×C₄×D₆₇	—	2	1	no	—
110	C₂×C₄×D₆₇	—	2	1	no	—
111	C₂×C₄×D₆₇	—	2	1	no	—
112	#11761616	—	4	4	no	—
113	#11761613	—	4	4	no	—
114	C₂×C₆₇⋊C₈	—	2	1	no	—
115	C₂×C₆₇⋊C₈	—	2	1	no	—
116	C₂×C₆₇⋊C₈	—	2	2	no	—
117	C₂×C₆₇⋊C₈	—	2	2	no	—
118	C₈×D₆₇	—	4	2	no	—
119	C₈×D₆₇	—	4	2	no	—
120	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
122	Dic₆₇⋊C₄	—	2	1	no	—
123	Dic₆₇⋊C₄	—	2	1	no	—
124	C₂²⋊Dic₆₇	—	2	1	no	—
125	(C₂×D₆₇)⋊C₄	—	2	1	no	—
126	(C₂×D₆₇)⋊C₄	—	2	1	no	—
127	C₄×Dic₆₇	—	2	1	no	—
128	C₄×Dic₆₇	—	2	1	no	—
129	C₄×Dic₆₇	—	2	1	no	—
130	#41×C₆₇	—	4	4	no	—
131	#41×C₆₇	—	4	4	no	—
132	C₂×Q₈×C₆₇	—	2	2	no	—
133	C₂×D₄×C₆₇	—	2	2	no	—
134	C₂×D₄×C₆₇	—	2	2	no	—
135	C₂×D₄×C₆₇	—	2	2	no	—
136	C₂×D₄×C₆₇	—	4	2	no	—
137	C₂²×C₄×C₆₇	—	4	2	no	—
138	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
141	Q₁₆×C₆₇	—	4	2	no	—
142	Q₁₆×C₆₇	—	4	2	no	—
143	SD₁₆×C₆₇	—	4	4	no	—
144	SD₁₆×C₆₇	—	4	4	no	—
145	D₈×C₆₇	—	4	2	no	—
146	D₈×C₆₇	—	4	2	no	—
147	C₂×C₈×C₆₇	—	2	2	no	—
148	C₂×C₈×C₆₇	—	2	2	no	—
149	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
153	C₄⋊C₄×C₆₇	—	2	2	no	—
154	C₄⋊C₄×C₆₇	—	2	2	no	—
155	C₂²⋊C₄×C₆₇	—	4	2	no	—
156	C₂²⋊C₄×C₆₇	—	4	2	no	—
157	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₆₇	#41	1	1	yes	characteristic
160	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
161	C₂³×C₆₇	—	4	2	no	—
162	C₂³×C₆₇	#121	1	1	yes	characteristic
163	C₂²×D₆₇	—	2	1	no	—
164	Q₈×C₆₇	—	4	2	no	—
165	Q₈×C₆₇	—	4	2	no	—
166	D₄×C₆₇	—	4	2	no	—
167	D₄×C₆₇	—	4	2	no	—
168	D₄×C₆₇	—	4	2	no	—
169	D₄×C₆₇	—	4	2	no	—
170	D₄×C₆₇	—	8	2	no	—
171	D₄×C₆₇	—	8	4	no	—
172	C₂×C₄×C₆₇	—	2	1	no	—
173	C₂×C₄×C₆₇	—	2	1	no	—
174	C₂×C₄×C₆₇	—	2	1	no	—
175	C₂×C₄×C₆₇	—	2	1	no	—
176	C₂×C₄×C₆₇	—	4	1	no	—
177	C₂×C₄×C₆₇	—	4	2	no	—
178	C₂×C₄×C₆₇	—	8	4	no	—
179	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
180	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
181	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
182	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
185	C₂²⋊D₆₇	—	2	4	no	—
186	C₂×Dic₆₇	—	2	1	no	—
187	C₂×Dic₆₇	—	2	1	no	—
188	C₂×Dic₆₇	—	2	1	no	—
189	D₂₆₈	—	2	1	no	—
190	D₂₆₈	#135	1	2	yes	complemented
191	C₄×D₆₇	—	2	4	no	—
192	C₄×D₆₇	—	4	2	no	—
193	C₄×D₆₇	—	4	1	no	—
194	C₄×D₆₇	—	4	1	no	—
195	Dic₁₃₄	—	2	1	no	—
196	Dic₁₃₄	#135	1	2	yes	complemented
197	C₈×C₆₇	—	2	1	no	—
198	C₈×C₆₇	—	2	1	no	—
199	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
200	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
201	C₆₇⋊C₈	—	4	2	no	—
202	C₆₇⋊C₈	—	4	2	no	—
203	C₆₇⋊C₈	—	4	1	no	—
204	C₆₇⋊C₈	—	4	1	no	—
205	C₂²×C₆₇	—	2	1	no	—
206	C₂²×C₆₇	—	2	1	no	—
207	C₂²×C₆₇	—	2	1	no	—
208	C₂²×C₆₇	—	8	2	no	—
209	C₂²×C₆₇	—	8	2	no	—
210	C₂²×C₆₇	—	8	2	no	—
211	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
212	C₂×D₆₇	—	2	2	no	—
213	C₂×D₆₇	—	4	1	no	—
214	C₂×D₆₇	—	4	1	no	—
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	2	1	no	—
217	C₄×C₆₇	—	2	1	no	—
218	C₄×C₆₇	—	2	1	no	—
219	C₄×C₆₇	—	8	2	no	—
220	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
221	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
222	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	Dic₆₇	—	2	2	no	—
225	Dic₆₇	—	4	1	no	—
226	Dic₆₇	—	4	1	no	—
227	#19269	—	67	1	no	maximal, Sylow
228	C₂×C₆₇	—	4	1	no	—
229	C₂×C₆₇	—	16	2	no	—
230	C₂×C₆₇	#3038	1	1	yes	characteristic
231	C₂×C₆₇	#3050	1	1	yes	characteristic
232	C₂×C₆₇	#3067	1	1	yes	characteristic
233	D₆₇	—	4	2	no	—
234	#3147	D₆₇	1	1	yes	characteristic, complemented
235	#3115	—	67	2	no	—
236	C₈×#41	—	67	1	no	—
237	#1670	—	67	1	no	—
238	#1669	—	67	1	no	—
239	#1668	—	67	1	no	—
240	#1667	—	67	1	no	—
241	#1666	—	67	2	no	—
242	#1665	—	67	2	no	—
243	#1568	—	67	1	no	—
244	#1553	—	67	2	no	—
245	C₆₇	#19269	1	1	yes	characteristic, complemented, Sylow
246	C₂×#135	—	2	1	no	—
247	C₂×#135	—	2	1	no	—
248	#532	C₂×D₆₇	1	2	yes	—
249	C₄×#41	—	67	1	no	—
250	#495	—	2	1	no	—
251	#495	—	2	1	no	—
252	#494	C₂×D₆₇	1	1	yes	characteristic
253	#493	C₂×D₆₇	1	1	yes	characteristic
254	#492	C₂×D₆₇	1	2	yes	—
255	#482	—	134	2	no	—
256	#475	—	67	2	no	—
257	#474	—	67	2	no	—
258	#460	—	67	2	no	—
259	#459	—	67	2	no	—
260	#449	—	134	2	no	—
261	C₈×Q₈	—	67	1	no	—
262	C₈×Q₈	—	67	1	no	—
263	#442	—	134	2	no	—
264	#440	—	134	2	no	—
265	C₈×D₄	—	67	1	no	—
266	C₈×D₄	—	67	1	no	—
267	C₈×D₄	—	134	1	no	—
268	C₈×D₄	—	134	1	no	—
269	#432	—	67	2	no	—
270	#431	—	67	1	no	—
271	#431	—	134	1	no	—
272	C₂×C₄×C₈	—	134	1	no	—
273	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
274	#335	—	67	1	no	—
275	#335	—	67	1	no	—
276	#334	—	67	2	no	—
277	#332	—	67	2	no	—
278	#332	—	67	2	no	—
279	#331	—	67	2	no	—
280	#331	—	67	2	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	67	1	no	—
283	#135	—	4	4	no	—
284	#135	—	4	4	no	—
285	C₂×Q₁₆	—	2	1	no	—
286	C₂×Q₁₆	—	2	1	no	—
287	C₂×SD₁₆	—	2	2	no	—
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	134	2	no	—
290	C₂×D₈	—	2	1	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×D₈	—	134	2	no	—
293	C₂²×C₈	—	134	1	no	—
294	C₂²×C₈	—	134	1	no	—
295	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
297	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
298	#127	C₂²×D₆₇	1	2	yes	—
299	#124	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	C₄×Q₈	—	67	1	no	—
303	C₄×Q₈	—	67	1	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	67	1	no	—
307	C₄×D₄	—	67	1	no	—
308	C₄×D₄	—	134	1	no	—
309	C₄×D₄	—	134	1	no	—
310	#117	—	67	1	no	—
311	#117	—	134	1	no	—
312	C₂×C₄²	—	134	1	no	—
313	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
314	#107	—	134	2	no	—
315	#106	—	134	2	no	—
316	C₄⋊C₈	—	67	1	no	—
317	C₄⋊C₈	—	67	1	no	—
318	C₄⋊C₈	—	67	2	no	—
319	C₄⋊C₈	—	67	2	no	—
320	C₄⋊C₈	—	134	1	no	—
321	C₄⋊C₈	—	134	1	no	—
322	#103	—	134	2	no	—
323	#102	—	134	2	no	—
324	#102	—	134	2	no	—
325	#102	—	134	2	no	—
326	C₂²⋊C₈	—	134	2	no	—
327	C₂²⋊C₈	—	134	1	no	—
328	C₂²⋊C₈	—	134	1	no	—
329	C₂²⋊C₈	—	134	1	no	—
330	#97	—	134	2	no	—
331	C₄×C₈	—	134	1	no	—
332	C₄×C₈	—	134	1	no	—
333	C₄×C₈	—	134	1	no	—
334	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
335	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	#41	—	134	2	no	—
341	#41	—	134	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	67	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	67	1	no	—
349	C₂×D₄	—	134	1	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	134	1	no	—
352	C₂²×C₄	—	134	1	no	—
353	C₂²×C₄	—	134	1	no	—
354	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
356	C₂²×C₄	#11761627	1	1	yes	characteristic
357	Q₁₆	—	4	2	no	—
358	Q₁₆	—	4	2	no	—
359	SD₁₆	—	4	4	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	268	4	no	—
362	D₈	—	4	2	no	—
363	D₈	—	4	2	no	—
364	D₈	—	268	4	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	268	2	no	—
368	C₂×C₈	—	268	2	no	—
369	C₂×C₈	—	134	2	no	—
370	C₂×C₈	—	134	2	no	—
371	C₂×C₈	—	134	1	no	—
372	C₂×C₈	—	134	1	no	—
373	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
376	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	67	1	no	—
380	C₄⋊C₄	—	67	1	no	—
381	C₄⋊C₄	—	134	1	no	—
382	C₄⋊C₄	—	134	1	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	134	1	no	—
386	C₂²⋊C₄	—	134	1	no	—
387	C₂²⋊C₄	—	134	1	no	—
388	C₄²	—	134	1	no	—
389	C₄²	—	134	1	no	—
390	C₄²	—	134	1	no	—
391	C₄²	D₄×D₆₇	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
393	C₄²	#11761627	1	1	yes	characteristic
394	C₄²	C₂³×D₆₇	1	1	yes	characteristic
395	C₂³	—	4	2	no	—
396	C₂³	—	134	1	no	—
397	C₂³	#14524014	1	1	yes	characteristic
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	67	2	no	—
401	Q₈	—	134	1	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	4	no	—
408	D₄	—	67	2	no	—
409	D₄	—	134	4	no	—
410	D₄	—	134	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	—	268	2	no	—
419	C₂×C₄	—	268	1	no	—
420	C₂×C₄	—	268	1	no	—
421	C₂×C₄	—	134	4	no	—
422	C₂×C₄	—	134	1	no	—
423	C₂×C₄	—	134	1	no	—
424	C₂×C₄	—	134	1	no	—
425	C₂×C₄	#14524014	1	1	yes	characteristic
426	C₂×C₄	#14524014	1	1	yes	characteristic
427	C₂×C₄	#14524014	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
430	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	268	2	no	—
434	C₈	—	268	2	no	—
435	C₈	—	268	1	no	—
436	C₈	—	268	1	no	—
437	C₈	#14524069	1	2	yes	—
438	C₈	#14524069	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	268	1	no	—
446	C₂²	—	268	1	no	—
447	C₂²	—	134	2	no	—
448	C₂²	C₂×#14524014	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	268	1	no	—
455	C₄	—	268	1	no	—
456	C₄	—	134	2	no	—
457	C₄	#135×D₆₇	1	1	yes	characteristic
458	C₄	#135×D₆₇	1	1	yes	characteristic
459	C₄	C₂×#14524069	1	1	yes	characteristic
460	C₄	C₂×#14524069	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	268	2	no	—
463	C₂	—	16	2	no	—
464	C₂	#22569685	1	1	yes	characteristic
465	C₂	#22569786	1	1	yes	characteristic
466	C₂	#22569925	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524014
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#3147	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	#3147	D₆₇
hypocenter	C₆₇	#19269
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3147

Complements

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

N	H ≅ G/N	type
1. #22570354	C₂	semidirect
2. C₈×#11761628	C₂	semidirect
3. #22559576	C₂	semidirect
4. #22559571	C₂	semidirect
5. #22559566	C₂	semidirect
6. #22559561	C₂	semidirect
7. #22559554	C₂	semidirect
8. #22559547	C₂	semidirect
9. #22558972	C₂	semidirect
10. #22558914	C₂	semidirect
11. C₆₇×#3147	C₂	semidirect
190. D₂₆₈	#135	semidirect
196. Dic₁₃₄	#135	semidirect
234. #3147	D₆₇	semidirect
245. C₆₇	#19269	semidirect

Maximal subgroups

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

subgroup	index
#22570354	2
C₈×#11761628	2
#22559576	2
#22559571	2
#22559566	2
#22559561	2
#22559554	2
#22559547	2
#22558972	2
#22558914	2
C₆₇×#3147	2
#19269	67