Subgroups — #30875532

Order 17152.

710 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568980	C₂	1	1	yes	maximal, characteristic
2	#22568873	C₂	1	2	yes	maximal, complemented
3	#22561102	C₂	1	1	yes	maximal, characteristic
4	#22561100	C₂	1	1	yes	maximal, characteristic
5	#22560857	C₂	1	2	yes	maximal, complemented
6	#22560855	C₂	1	2	yes	maximal, complemented
7	#22560379	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560228	C₂	1	2	yes	maximal, complemented
9	#22560095	C₂	1	1	yes	maximal, characteristic, complemented
10	#22560077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	#16863864	C₂²	1	2	yes	—
14	#16863490	C₄	1	1	yes	characteristic, complemented
15	#16863490	C₄	1	1	yes	characteristic, complemented
16	#16863483	C₄	1	2	yes	complemented
17	#16863483	C₄	1	2	yes	complemented
18	#16863478	C₄	1	1	yes	characteristic, complemented
19	#16863478	C₄	1	1	yes	characteristic, complemented
20	#16863458	—	2	2	no	—
21	#16863455	—	2	2	no	—
22	#16863451	—	2	2	no	—
23	#16863447	—	2	2	no	—
24	C₂×#14523979	C₂²	1	1	yes	characteristic
25	C₂×#14523978	C₂²	1	2	yes	—
26	#16863419	C₂²	1	2	yes	—
27	C₂×Dic₆₇⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×#14523971	C₂²	1	2	yes	—
29	C₂×#14523969	C₂²	1	2	yes	—
30	#16863390	C₂²	1	2	yes	—
31	#16863364	C₂²	1	2	yes	—
32	#16863362	C₂²	1	2	yes	—
33	#16863352	C₂²	1	2	yes	—
34	C₂×#14523953	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
36	C₄×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
37	#16863155	C₂²	1	2	yes	—
38	#16863151	C₂²	1	1	yes	characteristic
39	#16863150	C₂²	1	1	yes	characteristic
40	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
41	#427×C₆₇	C₂²	1	1	yes	characteristic
42	#405×C₆₇	C₂²	1	2	yes	—
43	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
44	#339×C₆₇	C₂²	1	2	yes	—
45	C₂×#11761628	C₂³	1	2	yes	—
46	#14524065	—	2	2	no	—
47	#14524065	—	2	2	no	—
48	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
49	C₂×#11761617	C₂×C₄	1	2	yes	—
50	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
51	C₂×#11761612	C₂³	1	2	yes	—
52	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
54	#14524008	C₂×C₄	1	2	yes	—
55	#14524008	C₂×C₄	1	2	yes	—
56	#14524005	C₂×C₄	1	2	yes	—
57	#14524005	C₂×C₄	1	2	yes	—
58	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
59	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
60	#14524000	—	2	2	no	—
61	C₂×Dic₆₇⋊C₄	—	2	1	no	—
62	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
64	C₄²×D₆₇	—	2	2	no	—
65	#14523979	—	2	2	no	—
66	#14523978	—	4	2	no	—
67	Dic₆₇⋊C₈	—	2	2	no	—
68	Dic₆₇⋊C₈	—	2	2	no	—
69	Dic₆₇⋊C₈	D₄	1	2	yes	—
70	Dic₆₇⋊C₈	D₄	1	2	yes	—
71	#14523971	—	4	2	no	—
72	#14523969	—	4	2	no	—
73	#14523966	C₂×C₄	1	2	yes	—
74	#14523966	C₂×C₄	1	2	yes	—
75	#14523963	C₂×C₄	1	2	yes	—
76	#14523963	C₂×C₄	1	2	yes	—
77	(C₂×D₆₇)⋊C₈	—	2	2	no	—
78	(C₂×D₆₇)⋊C₈	—	2	2	no	—
79	(C₂×D₆₇)⋊C₈	—	2	2	no	—
80	(C₂×D₆₇)⋊C₈	—	2	2	no	—
81	#14523954	—	2	2	no	—
82	#14523953	—	2	2	no	—
83	C₄×C₆₇⋊C₈	—	2	2	no	—
84	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
88	C₆₇⋊#95	—	2	1	no	—
89	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
90	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	#117×C₆₇	C₂³	1	2	yes	—
93	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
94	#108×C₆₇	—	2	2	no	—
95	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
96	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
97	#106×C₆₇	C₂×C₄	1	2	yes	—
98	#97×C₆₇	—	2	2	no	—
99	#97×C₆₇	—	2	2	no	—
100	C₄×C₈×C₆₇	—	2	2	no	—
101	#11761628	—	2	2	no	—
102	#11761628	—	2	2	no	—
103	#11761628	—	2	2	no	—
104	#11761628	—	2	2	no	—
105	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
106	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
107	C₂×C₂²⋊D₆₇	—	2	2	no	—
108	C₂²×Dic₆₇	—	2	1	no	—
109	C₂²×Dic₆₇	#41	1	1	yes	characteristic
110	C₂²×Dic₆₇	#41	1	1	yes	characteristic
111	C₂×C₄×D₆₇	—	2	2	no	—
112	C₂×C₄×D₆₇	—	2	2	no	—
113	C₂×C₄×D₆₇	—	2	2	no	—
114	Dic₂₆₈	—	2	2	no	—
115	#11761617	—	2	4	no	—
116	D₅₃₆	—	2	2	no	—
117	#11761612	—	2	2	no	—
118	#11761612	—	2	2	no	—
119	C₂×C₆₇⋊C₈	—	2	1	no	—
120	C₂×C₆₇⋊C₈	—	2	1	no	—
121	C₂×C₆₇⋊C₈	—	2	1	no	—
122	C₂×C₆₇⋊C₈	—	2	1	no	—
123	C₂×C₆₇⋊C₈	—	2	2	no	—
124	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
127	Dic₆₇⋊C₄	—	2	2	no	—
128	Dic₆₇⋊C₄	—	2	2	no	—
129	Dic₆₇⋊C₄	—	4	2	no	—
130	(C₂×D₆₇)⋊C₄	—	2	2	no	—
131	(C₂×D₆₇)⋊C₄	—	2	2	no	—
132	C₄×Dic₆₇	—	2	2	no	—
133	C₄×Dic₆₇	—	2	2	no	—
134	C₄×Dic₆₇	—	2	1	no	—
135	C₄×Dic₆₇	—	2	1	no	—
136	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	—	2	1	no	—
141	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
142	M₁₆×C₆₇	—	2	2	no	—
143	M₁₆×C₆₇	—	2	2	no	—
144	C₂×C₈×C₆₇	—	2	1	no	—
145	C₂×C₈×C₆₇	—	2	1	no	—
146	C₂×C₈×C₆₇	—	2	2	no	—
147	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₆₇	#41	1	2	yes	—
151	C₂×C₈×C₆₇	#41	1	2	yes	—
152	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
153	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
154	C₂²⋊C₄×C₆₇	—	2	2	no	—
155	C₄²×C₆₇	—	2	2	no	—
156	C₄²×C₆₇	—	2	1	no	—
157	C₄²×C₆₇	—	2	1	no	—
158	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
159	C₂²×D₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	2	no	—
162	C₂×C₄×C₆₇	—	4	1	no	—
163	C₂×C₄×C₆₇	—	4	1	no	—
164	C₂×C₄×C₆₇	—	4	1	no	—
165	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
171	C₂²⋊D₆₇	—	4	2	no	—
172	C₂²⋊D₆₇	—	4	2	no	—
173	C₂×Dic₆₇	—	2	2	no	—
174	C₂×Dic₆₇	—	2	2	no	—
175	C₂×Dic₆₇	—	4	1	no	—
176	C₂×Dic₆₇	—	4	1	no	—
177	C₂×Dic₆₇	—	4	1	no	—
178	C₂×Dic₆₇	—	4	1	no	—
179	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
180	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
181	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
182	C₂×Dic₆₇	C₄×D₄	1	1	yes	characteristic
183	D₂₆₈	—	2	2	no	—
184	D₂₆₈	—	2	2	no	—
185	C₄×D₆₇	—	4	2	no	—
186	C₄×D₆₇	—	4	2	no	—
187	C₄×D₆₇	—	4	4	no	—
188	C₄×D₆₇	—	8	2	no	—
189	Dic₁₃₄	—	2	2	no	—
190	Dic₁₃₄	—	2	2	no	—
191	C₈×C₆₇	—	2	2	no	—
192	C₈×C₆₇	—	4	2	no	—
193	C₈×C₆₇	#117	1	2	yes	—
194	C₈×C₆₇	#117	1	2	yes	—
195	C₆₇⋊C₈	—	2	1	no	—
196	C₆₇⋊C₈	—	2	1	no	—
197	C₆₇⋊C₈	—	2	2	no	—
198	C₆₇⋊C₈	—	4	2	no	—
199	C₂²×C₆₇	—	2	1	no	—
200	C₂²×C₆₇	—	2	1	no	—
201	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₆₇	#555	1	1	yes	characteristic
203	C₂²×C₆₇	#556	1	1	yes	characteristic
204	C₂×D₆₇	—	4	2	no	—
205	C₂×D₆₇	—	4	2	no	—
206	C₂×D₆₇	—	4	2	no	—
207	C₄×C₆₇	—	4	2	no	—
208	C₄×C₆₇	—	4	2	no	—
209	C₄×C₆₇	—	8	1	no	—
210	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
211	C₄×C₆₇	#520	1	1	yes	characteristic
212	C₄×C₆₇	#547	1	1	yes	characteristic
213	C₄×C₆₇	#550	1	1	yes	characteristic
214	Dic₆₇	—	2	1	no	—
215	Dic₆₇	—	2	1	no	—
216	Dic₆₇	—	2	1	no	—
217	Dic₆₇	—	4	2	no	—
218	Dic₆₇	—	8	1	no	—
219	Dic₆₇	#444	1	2	yes	—
220	#22803	—	67	1	no	maximal, Sylow
221	C₂×C₆₇	—	2	1	no	—
222	C₂×C₆₇	—	2	1	no	—
223	C₂×C₆₇	#2354	1	1	yes	characteristic
224	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
225	C₂×C₆₇	#2957	1	1	yes	characteristic
226	D₆₇	—	8	2	no	—
227	C₄×#135	—	67	1	no	—
228	#2925	—	67	2	no	—
229	#1975	—	67	1	no	—
230	#1975	—	67	1	no	—
231	#1929	—	67	2	no	—
232	#1929	—	67	2	no	—
233	#1848	—	67	1	no	—
234	#1806	—	67	2	no	—
235	#1773	—	67	1	no	—
236	#1773	D₆₇	1	1	yes	characteristic, complemented
237	#1770	—	67	1	no	—
238	C₆₇	#22803	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	—	67	1	no	—
240	C₄×#41	—	67	2	no	—
241	C₄×Q₁₆	—	67	1	no	—
242	C₄×Q₁₆	—	67	1	no	—
243	C₄×SD₁₆	—	67	2	no	—
244	C₄×SD₁₆	—	67	2	no	—
245	C₄×D₈	—	67	1	no	—
246	C₄×D₈	—	67	1	no	—
247	#433	—	134	2	no	—
248	#433	—	134	2	no	—
249	#432	—	134	2	no	—
250	#431	—	134	2	no	—
251	C₂×#108	—	67	2	no	—
252	C₂×#108	—	67	1	no	—
253	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
254	#427	C₂×D₆₇	1	1	yes	characteristic
255	#423	—	67	2	no	—
256	C₂×C₄⋊C₈	—	67	1	no	—
257	C₂×#104	—	67	2	no	—
258	C₂×#104	—	67	2	no	—
259	#416	—	67	2	no	—
260	#408	—	67	2	no	—
261	#408	—	67	2	no	—
262	#405	—	67	2	no	—
263	#405	C₂×D₆₇	1	2	yes	—
264	C₂×#97	—	67	1	no	—
265	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
266	C₂×C₄×C₈	—	67	1	no	—
267	C₄×C₄⋊C₄	—	67	1	no	—
268	#339	—	67	2	no	—
269	#339	C₂×D₆₇	1	2	yes	—
270	#336	—	67	1	no	—
271	#336	—	67	1	no	—
272	C₂×#41	—	67	2	no	—
273	#135	—	134	2	no	—
274	#135	—	134	2	no	—
275	C₂×Q₁₆	—	67	1	no	—
276	C₂×SD₁₆	—	67	2	no	—
277	C₂×D₈	—	67	1	no	—
278	C₂×M₁₆	—	67	2	no	—
279	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
280	C₂²×C₈	—	67	1	no	—
281	C₂²×C₈	—	67	1	no	—
282	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
284	C₄×Q₈	—	67	2	no	—
285	C₄×Q₈	—	67	2	no	—
286	C₄×D₄	—	67	2	no	—
287	C₄×D₄	—	67	2	no	—
288	C₄×D₄	—	134	2	no	—
289	C₄×D₄	—	134	2	no	—
290	#117	—	134	2	no	—
291	#117	C₂²×D₆₇	1	2	yes	—
292	C₂×C₄⋊C₄	—	134	1	no	—
293	C₂×C₄²	—	67	1	no	—
294	C₂×C₄²	—	67	1	no	—
295	C₂×C₄²	—	134	2	no	—
296	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
297	#108	—	2	2	no	—
298	#108	—	268	2	no	—
299	#108	—	134	2	no	—
300	#107	C₄×D₆₇	1	1	yes	characteristic
301	#107	C₄×D₆₇	1	1	yes	characteristic
302	#106	C₄×D₆₇	1	2	yes	—
303	C₄⋊C₈	—	67	2	no	—
304	C₄⋊C₈	—	67	2	no	—
305	C₄⋊C₈	—	134	2	no	—
306	C₄⋊C₈	—	134	2	no	—
307	#104	—	268	2	no	—
308	#104	—	268	2	no	—
309	#103	—	67	2	no	—
310	#103	—	67	2	no	—
311	#102	—	67	2	no	—
312	#102	—	67	2	no	—
313	C₂²⋊C₈	—	134	2	no	—
314	C₂²⋊C₈	—	134	2	no	—
315	C₂²⋊C₈	—	134	2	no	—
316	C₂²⋊C₈	—	134	2	no	—
317	#97	—	2	2	no	—
318	#97	—	2	2	no	—
319	#97	—	134	2	no	—
320	#97	—	134	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	67	1	no	—
323	C₄×C₈	—	67	1	no	—
324	C₄×C₈	—	67	1	no	—
325	C₄×C₈	—	67	1	no	—
326	C₄×C₈	—	134	2	no	—
327	#95	—	134	1	no	—
328	#41	—	134	2	no	—
329	#41	—	134	2	no	—
330	#41	—	134	2	no	—
331	#41	—	134	2	no	—
332	C₂×Q₈	—	67	2	no	—
333	C₂×D₄	—	67	2	no	—
334	C₂×D₄	—	134	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	67	1	no	—
337	C₂²×C₄	—	67	1	no	—
338	C₂²×C₄	—	134	2	no	—
339	C₂²×C₄	—	134	2	no	—
340	C₂²×C₄	—	134	1	no	—
341	C₂²×C₄	—	134	2	no	—
342	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
343	Q₁₆	—	134	2	no	—
344	SD₁₆	—	134	4	no	—
345	D₈	—	134	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	134	2	no	—
349	M₁₆	—	134	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	67	1	no	—
354	C₂×C₈	—	67	1	no	—
355	C₂×C₈	—	67	2	no	—
356	C₂×C₈	—	134	2	no	—
357	C₂×C₈	—	134	1	no	—
358	C₂×C₈	—	134	1	no	—
359	C₂×C₈	—	134	1	no	—
360	C₂×C₈	—	134	1	no	—
361	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
362	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
363	C₂×C₈	D₄×D₆₇	1	2	yes	—
364	C₂×C₈	#11761628	1	2	yes	—
365	C₂×C₈	#11761628	1	2	yes	—
366	C₄⋊C₄	—	268	2	no	—
367	C₄⋊C₄	—	134	2	no	—
368	C₄⋊C₄	—	134	2	no	—
369	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
370	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	134	2	no	—
373	C₂²⋊C₄	—	134	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	67	1	no	—
378	C₄²	—	67	1	no	—
379	C₄²	—	67	1	no	—
380	C₄²	—	67	1	no	—
381	C₄²	—	134	2	no	—
382	C₄²	—	134	2	no	—
383	C₄²	—	134	1	no	—
384	C₄²	—	134	1	no	—
385	C₂³	—	134	2	no	—
386	C₂³	#41×D₆₇	1	1	yes	characteristic
387	Q₈	—	134	2	no	—
388	Q₈	—	134	2	no	—
389	D₄	—	268	2	no	—
390	D₄	—	268	2	no	—
391	D₄	—	134	2	no	—
392	D₄	—	134	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	268	4	no	—
399	C₂×C₄	—	268	2	no	—
400	C₂×C₄	—	268	2	no	—
401	C₂×C₄	—	268	1	no	—
402	C₂×C₄	—	268	1	no	—
403	C₂×C₄	—	268	1	no	—
404	C₂×C₄	—	268	1	no	—
405	C₂×C₄	—	536	2	no	—
406	C₂×C₄	—	67	1	no	—
407	C₂×C₄	—	67	1	no	—
408	C₂×C₄	—	67	1	no	—
409	C₂×C₄	—	67	1	no	—
410	C₂×C₄	—	134	2	no	—
411	C₂×C₄	—	134	2	no	—
412	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
415	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
416	C₂×C₄	#14524089	1	1	yes	characteristic
417	C₂×C₄	#14524091	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	268	2	no	—
421	C₈	—	134	2	no	—
422	C₈	—	134	1	no	—
423	C₈	—	134	1	no	—
424	C₈	#14524000	1	2	yes	—
425	C₈	#14524000	1	2	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	268	2	no	—
429	C₂²	—	268	2	no	—
430	C₂²	—	268	2	no	—
431	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
432	C₂²	#16864109	1	1	yes	characteristic
433	C₂²	#16864118	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	268	2	no	—
438	C₄	—	536	1	no	—
439	C₄	—	67	2	no	—
440	C₄	—	134	1	no	—
441	C₄	—	134	1	no	—
442	C₄	—	134	1	no	—
443	C₄	C₂×#14524000	1	1	yes	characteristic
444	C₄	#16863878	1	1	yes	characteristic
445	C₄	#16864047	1	1	yes	characteristic
446	C₄	#16864067	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	536	2	no	—
450	C₂	#22563154	1	1	yes	characteristic
451	C₂	#444×D₆₇	1	1	yes	characteristic
452	C₂	#22569123	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1773	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1773	D₆₇
hypocenter	C₆₇	#22803
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
2. #22568873	C₂	semidirect
5. #22560857	C₂	semidirect
6. #22560855	C₂	semidirect
7. #22560379	C₂	semidirect
8. #22560228	C₂	semidirect
9. #22560095	C₂	semidirect
10. #22560077	C₂	semidirect
11. C₆₇×#1773	C₂	semidirect
14. #16863490	C₄	semidirect
15. #16863490	C₄	semidirect
16. #16863483	C₄	semidirect
17. #16863483	C₄	semidirect
18. #16863478	C₄	semidirect
19. #16863478	C₄	semidirect
236. #1773	D₆₇	semidirect
238. C₆₇	#22803	semidirect

Maximal subgroups

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

subgroup	index
#22568980	2
#22568873	2
#22561102	2
#22561100	2
#22560857	2
#22560855	2
#22560379	2
#22560228	2
#22560095	2
#22560077	2
C₆₇×#1773	2
#22803	67