Subgroups — #17018235

Order 4352.

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	#14539212	C₂	1	1	yes	maximal, characteristic, complemented
2	#14538935	C₂	1	2	yes	maximal, complemented
3	#14528154	C₂	1	1	yes	maximal, characteristic, complemented
4	#14528149	C₂	1	1	yes	maximal, characteristic, complemented
5	#14528144	C₂	1	1	yes	maximal, characteristic, complemented
6	#14528139	C₂	1	1	yes	maximal, characteristic, complemented
7	#14528132	C₂	1	2	yes	maximal, complemented
8	#14528125	C₂	1	2	yes	maximal, complemented
9	#14527547	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527487	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10587590	—	2	1	no	—
13	C₂×#10587590	—	2	1	no	—
14	#11763359	C₂²	1	2	yes	—
15	#11763193	—	2	1	no	—
16	#11763193	—	2	1	no	—
17	#11763189	C₂²	1	1	yes	characteristic
18	#11763186	C₂²	1	1	yes	characteristic
19	#11763182	C₂²	1	2	yes	—
20	#11763133	—	2	2	no	—
21	#11763094	C₂²	1	2	yes	—
22	#11763089	C₂²	1	2	yes	—
23	#11763009	C₂²	1	2	yes	—
24	#11763004	C₂²	1	2	yes	—
25	#11762954	—	2	2	no	—
26	#11762919	—	2	2	no	—
27	#11762907	—	2	2	no	—
28	#11762866	C₂²	1	2	yes	—
29	#11762562	C₂²	1	1	yes	characteristic
30	#11762562	C₂²	1	1	yes	characteristic
31	#11762560	C₂²	1	2	yes	—
32	#11762556	C₂²	1	2	yes	—
33	#11762556	C₂²	1	2	yes	—
34	#11762552	C₂²	1	2	yes	—
35	#11762552	C₂²	1	2	yes	—
36	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₇	—	2	1	no	—
40	C₈×D₄×C₁₇	—	2	1	no	—
41	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
43	C₁₇×#431	—	2	1	no	—
44	C₁₇×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₁₇	—	2	1	no	—
46	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
48	C₂×#63252	—	2	2	no	—
49	C₂²×C₈×C₁₇	—	2	1	no	—
50	C₂²×C₈×C₁₇	—	2	1	no	—
51	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₇	—	2	1	no	—
56	C₄×D₄×C₁₇	—	2	1	no	—
57	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
58	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
59	C₁₇×#117	—	2	1	no	—
60	C₁₇×#117	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₇	—	2	1	no	—
62	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
63	C₂×#63230	—	2	2	no	—
64	C₂×#63228	—	2	2	no	—
65	#10587616	—	2	2	no	—
66	#10587616	—	2	2	no	—
67	C₂×Dic₆₈	—	2	1	no	—
68	C₂×Dic₆₈	—	2	1	no	—
69	#10587590	—	4	4	no	—
70	#10587590	—	4	4	no	—
71	C₂×D₁₃₆	—	2	1	no	—
72	C₂×D₁₃₆	—	2	1	no	—
73	C₂×#63219	—	2	2	no	—
74	C₂×#63219	—	2	2	no	—
75	#10587561	—	2	2	no	—
76	#10587560	C₂³	1	2	yes	—
77	C₄×D₆₈	—	2	2	no	—
78	C₄×D₆₈	—	2	2	no	—
79	#10587555	C₂³	1	2	yes	—
80	C₁₇×C₄⋊C₈	—	2	1	no	—
81	C₁₇×C₄⋊C₈	—	2	1	no	—
82	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₇×C₂²⋊C₈	—	2	1	no	—
85	C₁₇×C₂²⋊C₈	—	2	1	no	—
86	C₁₇×C₂²⋊C₈	—	2	1	no	—
87	C₄×C₈×C₁₇	—	2	1	no	—
88	C₄×C₈×C₁₇	—	2	1	no	—
89	C₄×C₈×C₁₇	—	2	1	no	—
90	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
94	#10587506	—	2	2	no	—
95	#10587503	—	2	2	no	—
96	C₂²⋊#3622	—	2	2	no	—
97	#10587480	—	2	2	no	—
98	#10587480	—	2	2	no	—
99	#10587479	—	2	2	no	—
100	#10587478	—	2	2	no	—
101	C₄⋊#3622	C₂³	1	2	yes	—
102	C₄⋊#3622	C₂³	1	2	yes	—
103	#10587474	—	2	2	no	—
104	#41×C₁₇	—	2	2	no	—
105	#41×C₁₇	—	2	2	no	—
106	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₁₇	—	2	1	no	—
108	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₇	—	2	1	no	—
110	C₂²×C₄×C₁₇	—	2	1	no	—
111	C₂²×C₄×C₁₇	—	2	1	no	—
112	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₇	—	4	2	no	—
116	#63252	—	4	4	no	—
117	#63252	—	4	4	no	—
118	C₂×D₆₈	—	2	2	no	—
119	C₂×D₆₈	—	2	2	no	—
120	C₂×D₆₈	—	2	2	no	—
121	C₂×C₄×D₁₇	—	4	2	no	—
122	C₂×Dic₃₄	—	2	2	no	—
123	C₂×C₈×C₁₇	—	2	2	no	—
124	C₂×C₈×C₁₇	—	2	2	no	—
125	C₂×C₈×C₁₇	—	2	1	no	—
126	C₂×C₈×C₁₇	—	2	1	no	—
127	C₂×C₈×C₁₇	—	4	2	no	—
128	C₂×C₈×C₁₇	—	4	2	no	—
129	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₁₇	—	2	1	no	—
134	C₄⋊C₄×C₁₇	—	2	1	no	—
135	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
137	C₂²⋊C₄×C₁₇	—	2	1	no	—
138	C₂²⋊C₄×C₁₇	—	2	1	no	—
139	C₂²⋊C₄×C₁₇	—	2	1	no	—
140	C₄²×C₁₇	—	2	1	no	—
141	C₄²×C₁₇	—	2	1	no	—
142	C₄²×C₁₇	—	2	1	no	—
143	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₇	#41	1	1	yes	characteristic
146	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
147	#63230	—	4	4	no	—
148	#63228	—	4	4	no	—
149	#63227	—	4	2	no	—
150	#63227	—	4	2	no	—
151	C₄⋊Dic₁₇	—	2	2	no	—
152	C₄⋊Dic₁₇	—	2	2	no	—
153	C₂×#3622	—	2	2	no	—
154	C₂×#3622	—	2	2	no	—
155	Dic₆₈	—	4	2	no	—
156	Dic₆₈	—	4	2	no	—
157	D₁₃₆	—	4	2	no	—
158	D₁₃₆	—	4	2	no	—
159	#63219	—	4	4	no	—
160	#63219	—	4	4	no	—
161	#19269	—	17	1	no	maximal, Sylow
162	C₂³×C₁₇	—	2	1	no	—
163	C₂³×C₁₇	#121	1	1	yes	characteristic
164	C₂²×D₁₇	—	4	2	no	—
165	Q₈×C₁₇	—	2	1	no	—
166	Q₈×C₁₇	#135	1	2	yes	complemented
167	D₄×C₁₇	—	2	4	no	—
168	D₄×C₁₇	—	2	1	no	—
169	D₄×C₁₇	#135	1	2	yes	complemented
170	C₂×C₄×C₁₇	—	2	4	no	—
171	C₂×C₄×C₁₇	—	2	1	no	—
172	C₂×C₄×C₁₇	—	2	1	no	—
173	C₂×C₄×C₁₇	—	2	1	no	—
174	C₂×C₄×C₁₇	—	2	1	no	—
175	C₂×C₄×C₁₇	—	2	1	no	—
176	C₂×C₄×C₁₇	—	2	1	no	—
177	C₂×C₄×C₁₇	—	2	1	no	—
178	C₂×C₄×C₁₇	—	4	1	no	—
179	C₂×C₄×C₁₇	—	4	2	no	—
180	C₂×C₄×C₁₇	—	4	1	no	—
181	C₂×C₄×C₁₇	—	4	1	no	—
182	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
188	C₂²⋊D₁₇	—	8	4	no	—
189	C₂×Dic₁₇	—	4	2	no	—
190	D₆₈	—	4	2	no	—
191	D₆₈	—	4	2	no	—
192	D₆₈	—	4	2	no	—
193	D₆₈	—	4	2	no	—
194	D₆₈	—	8	2	no	—
195	C₄×D₁₇	—	8	4	no	—
196	Dic₃₄	—	4	2	no	—
197	Dic₃₄	—	4	2	no	—
198	C₈×C₁₇	—	2	1	no	—
199	C₈×C₁₇	—	2	1	no	—
200	C₈×C₁₇	—	4	1	no	—
201	C₈×C₁₇	—	4	1	no	—
202	C₈×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
203	C₈×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
204	#3622	—	4	2	no	—
205	#3622	—	4	2	no	—
206	#3147	—	17	1	no	—
207	#3115	—	17	2	no	—
208	C₈×#41	D₁₇	1	1	yes	characteristic, complemented
209	#1670	—	17	1	no	—
210	#1669	—	17	1	no	—
211	#1668	—	17	1	no	—
212	#1667	—	17	1	no	—
213	#1666	—	17	2	no	—
214	#1665	—	17	2	no	—
215	#1568	—	17	1	no	—
216	#1553	—	17	2	no	—
217	C₂²×C₁₇	—	2	1	no	—
218	C₂²×C₁₇	—	2	1	no	—
219	C₂²×C₁₇	—	2	2	no	—
220	C₂²×C₁₇	—	2	1	no	—
221	C₂²×C₁₇	—	4	1	no	—
222	C₂²×C₁₇	—	4	1	no	—
223	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
224	C₂×D₁₇	—	8	2	no	—
225	C₂×D₁₇	—	8	2	no	—
226	C₂×D₁₇	—	8	2	no	—
227	C₄×C₁₇	—	2	1	no	—
228	C₄×C₁₇	—	2	1	no	—
229	C₄×C₁₇	—	2	2	no	—
230	C₄×C₁₇	—	2	1	no	—
231	C₄×C₁₇	—	2	1	no	—
232	C₄×C₁₇	—	4	1	no	—
233	C₄×C₁₇	—	4	1	no	—
234	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
235	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
236	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	Dic₁₇	—	8	2	no	—
239	C₂×#135	—	34	1	no	—
240	C₂×#135	—	34	1	no	—
241	#532	—	17	2	no	—
242	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
243	#495	—	34	1	no	—
244	#495	—	34	1	no	—
245	#494	—	17	1	no	—
246	#493	—	17	1	no	—
247	#492	—	17	2	no	—
248	#482	—	34	2	no	—
249	#475	—	17	2	no	—
250	#474	—	17	2	no	—
251	#460	—	17	2	no	—
252	#459	—	17	2	no	—
253	#449	—	34	2	no	—
254	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
255	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
256	#442	—	34	2	no	—
257	#440	—	34	2	no	—
258	C₈×D₄	—	2	1	no	—
259	C₈×D₄	—	2	1	no	—
260	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
261	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
262	#432	—	17	2	no	—
263	#431	—	2	1	no	—
264	#431	C₂×D₁₇	1	1	yes	characteristic
265	C₂×C₄×C₈	—	2	1	no	—
266	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
267	#335	—	17	1	no	—
268	#335	—	17	1	no	—
269	#334	—	17	2	no	—
270	#332	—	17	2	no	—
271	#332	—	17	2	no	—
272	#331	—	17	2	no	—
273	#331	—	17	2	no	—
274	C₂×C₁₇	—	4	1	no	—
275	C₂×C₁₇	—	4	2	no	—
276	C₂×C₁₇	#3038	1	1	yes	characteristic
277	C₂×C₁₇	#3050	1	1	yes	characteristic
278	C₂×C₁₇	#3067	1	1	yes	characteristic
279	D₁₇	—	16	2	no	—
280	C₂×#41	—	34	2	no	—
281	C₂×#41	D₆₈	1	1	yes	characteristic
282	#135	—	68	4	no	—
283	#135	—	68	4	no	—
284	C₂×Q₁₆	—	34	1	no	—
285	C₂×Q₁₆	—	34	1	no	—
286	C₂×SD₁₆	—	34	2	no	—
287	C₂×SD₁₆	—	34	2	no	—
288	C₂×SD₁₆	—	34	2	no	—
289	C₂×D₈	—	34	2	no	—
290	C₂×D₈	—	34	1	no	—
291	C₂×D₈	—	34	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
295	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
296	C₄⋊Q₈	—	17	2	no	—
297	#127	—	17	2	no	—
298	#124	—	34	2	no	—
299	#121	—	34	2	no	—
300	#121	—	34	2	no	—
301	C₄×Q₈	D₆₈	1	1	yes	characteristic
302	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	34	2	no	—
306	C₄×D₄	—	34	2	no	—
307	C₄×D₄	D₆₈	1	1	yes	characteristic
308	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
309	#117	—	2	1	no	—
310	#117	D₆₈	1	1	yes	characteristic
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
313	#107	—	34	2	no	—
314	#106	—	34	2	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	17	2	no	—
318	C₄⋊C₈	—	17	2	no	—
319	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
320	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
321	#103	—	34	2	no	—
322	#102	—	34	2	no	—
323	#102	—	34	2	no	—
324	#102	—	34	2	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	34	2	no	—
329	#97	—	34	2	no	—
330	C₄×C₈	—	2	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
334	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
335	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
337	C₁₇	#19269	1	1	yes	characteristic, complemented, Sylow
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	68	4	no	—
341	#41	—	68	4	no	—
342	C₂×Q₈	—	34	2	no	—
343	C₂×Q₈	C₂×D₆₈	1	1	yes	characteristic
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	34	2	no	—
346	C₂×D₄	—	34	2	no	—
347	C₂×D₄	—	34	2	no	—
348	C₂×D₄	—	68	2	no	—
349	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	68	2	no	—
354	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
355	C₂²×C₄	#63252	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
357	Q₁₆	—	68	2	no	—
358	Q₁₆	—	68	2	no	—
359	SD₁₆	—	68	4	no	—
360	SD₁₆	—	68	4	no	—
361	SD₁₆	—	68	4	no	—
362	D₈	—	68	2	no	—
363	D₈	—	68	4	no	—
364	D₈	—	68	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	34	2	no	—
372	C₂×C₈	—	34	2	no	—
373	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
374	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
375	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
376	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	34	2	no	—
380	C₄⋊C₄	—	34	2	no	—
381	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
382	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	68	2	no	—
387	C₂²⋊C₄	—	68	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	C₂×D₆₈	1	1	yes	characteristic
392	C₄²	#63252	1	1	yes	characteristic
393	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
394	C₄²	C₂³×D₁₇	1	1	yes	characteristic
395	C₂³	—	2	1	no	—
396	C₂³	—	68	2	no	—
397	C₂³	#10587616	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	68	2	no	—
400	Q₈	—	68	2	no	—
401	Q₈	#10587590	1	2	yes	complemented
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	68	2	no	—
405	D₄	—	68	2	no	—
406	D₄	—	68	2	no	—
407	D₄	—	68	2	no	—
408	D₄	—	136	2	no	—
409	D₄	—	136	4	no	—
410	D₄	#10587590	1	2	yes	complemented
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	68	2	no	—
424	C₂×C₄	—	136	4	no	—
425	C₂×C₄	#10587616	1	1	yes	characteristic
426	C₂×C₄	#10587616	1	1	yes	characteristic
427	C₂×C₄	#10587616	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
429	C₂×C₄	C₂×#63252	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	68	2	no	—
436	C₈	—	68	2	no	—
437	C₈	#10587635	1	2	yes	—
438	C₈	#10587635	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	136	2	no	—
446	C₂²	—	136	2	no	—
447	C₂²	—	136	2	no	—
448	C₂²	C₂×#10587616	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	—	2	2	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	136	2	no	—
457	C₄	C₂×#10587590	1	1	yes	characteristic
458	C₄	C₂×#10587590	1	1	yes	characteristic
459	C₄	C₂×#10587635	1	1	yes	characteristic
460	C₄	C₂×#10587635	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	272	2	no	—
464	C₂	#14538264	1	1	yes	characteristic
465	C₂	#14538365	1	1	yes	characteristic
466	C₂	#14538504	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10587616
commutator, cosocle	C₄²×C₁₇	C₂⁴
Frattini	C₄²	C₂³×D₁₇
Fitting	C₈×#41×C₁₇	C₂
socle	C₂²×C₁₇	C₂×#121
hypercenter	C₈×#41	D₁₇
hypocenter	C₁₇	#19269
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #14539212	C₂	semidirect
2. #14538935	C₂	semidirect
3. #14528154	C₂	semidirect
4. #14528149	C₂	semidirect
5. #14528144	C₂	semidirect
6. #14528139	C₂	semidirect
7. #14528132	C₂	semidirect
8. #14528125	C₂	semidirect
9. #14527547	C₂	semidirect
10. #14527487	C₂	semidirect
11. C₈×#41×C₁₇	C₂	semidirect
166. Q₈×C₁₇	#135	semidirect
169. D₄×C₁₇	#135	semidirect
208. C₈×#41	D₁₇	semidirect
337. C₁₇	#19269	semidirect
401. Q₈	#10587590	semidirect
410. D₄	#10587590	semidirect

Maximal subgroups

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

subgroup	index
#14539212	2
#14538935	2
#14528154	2
#14528149	2
#14528144	2
#14528139	2
#14528132	2
#14528125	2
#14527547	2
#14527487	2
C₈×#41×C₁₇	2
#19269	17