Subgroups — #17040779

Order 4352.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538239	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762929	C₂	1	2	yes	maximal, complemented
3	#14537497	C₂	1	1	yes	maximal, characteristic, complemented
4	#14529703	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529559	C₂	1	1	yes	maximal, characteristic, complemented
6	#14529432	C₂	1	2	yes	maximal, complemented
7	#14529111	C₂	1	2	yes	maximal, complemented
8	#14528804	C₂	1	1	yes	maximal, characteristic, complemented
9	#14528651	C₂	1	1	yes	maximal, characteristic, complemented
10	#14528630	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10587636	C₂²	1	2	yes	—
13	C₂×#10587587	C₂²	1	2	yes	—
14	#11763359	C₂²	1	1	yes	characteristic
15	#11763031	C₄	1	2	yes	complemented
16	#11763024	C₄	1	2	yes	complemented
17	#11763019	C₄	1	1	yes	characteristic, complemented
18	#11763014	C₄	1	1	yes	characteristic, complemented
19	#11763009	C₄	1	1	yes	characteristic, complemented
20	#11763004	C₄	1	1	yes	characteristic, complemented
21	#11762929	—	2	8	no	—
22	#11762888	—	2	1	no	—
23	#11762888	—	2	1	no	—
24	C₈×D₆₈	—	2	1	no	—
25	C₈×D₆₈	—	2	1	no	—
26	C₂×#10587493	C₂²	1	2	yes	—
27	#11762833	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
29	C₂×#10587508	C₂²	1	2	yes	—
30	C₂×#10587496	C₂²	1	2	yes	—
31	C₂×#10587496	C₂²	1	2	yes	—
32	#11762803	C₂²	1	2	yes	—
33	#11762775	C₂²	1	2	yes	—
34	C₂×#10587486	C₂²	1	2	yes	—
35	C₄×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
36	#11762573	C₂²	1	2	yes	—
37	#11762568	C₂²	1	2	yes	—
38	#11762563	C₂²	1	2	yes	—
39	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
41	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
42	C₁₇×#405	—	2	1	no	—
43	C₁₇×#405	—	2	1	no	—
44	C₁₇×#405	C₂²	1	1	yes	characteristic
45	C₁₇×#405	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₁₇	—	2	1	no	—
47	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₁₇	—	2	1	no	—
49	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
50	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
51	C₂×#63252	C₂³	1	2	yes	—
52	C₁₇×#131	—	2	2	no	—
53	C₁₇×#131	—	2	2	no	—
54	C₁₇×#131	—	2	2	no	—
55	C₁₇×#131	D₄	1	4	yes	complemented
56	C₂×M₁₆×C₁₇	—	2	1	no	—
57	C₂×M₁₆×C₁₇	—	2	1	no	—
58	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₇	—	2	1	no	—
61	C₂²×C₈×C₁₇	—	2	1	no	—
62	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₁₇	—	2	1	no	—
67	C₄×D₄×C₁₇	—	2	1	no	—
68	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₁₇×#117	—	2	1	no	—
71	C₁₇×#117	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₇	—	2	1	no	—
73	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
74	#10587636	—	2	4	no	—
75	#10587636	—	2	4	no	—
76	C₂×#63231	C₂×C₄	1	2	yes	—
77	C₂×#63230	C₂×C₄	1	2	yes	—
78	C₂×#63229	C₂×C₄	1	2	yes	—
79	C₂×#63228	C₂×C₄	1	2	yes	—
80	#10587616	—	2	1	no	—
81	#10587616	—	2	1	no	—
82	C₂×C₄⋊Dic₁₇	—	2	1	no	—
83	C₂×C₄×Dic₁₇	C₂³	1	2	yes	—
84	C₂×#63223	C₂³	1	2	yes	—
85	C₂²×#3622	C₂³	1	2	yes	—
86	#10587587	—	2	4	no	—
87	#10587587	—	2	4	no	—
88	C₂×#63218	—	2	2	no	—
89	C₂×C₈×D₁₇	—	2	2	no	—
90	#10587561	C₂×C₄	1	2	yes	—
91	#10587560	C₂×C₄	1	1	yes	characteristic
92	C₄×D₆₈	—	2	1	no	—
93	C₄×D₆₈	—	2	1	no	—
94	#10587555	C₂×C₄	1	1	yes	characteristic
95	C₁₇×#97	—	2	1	no	—
96	C₁₇×#97	—	2	1	no	—
97	C₁₇×#97	—	2	1	no	—
98	C₄×C₈×C₁₇	—	2	1	no	—
99	C₄×C₈×C₁₇	—	2	1	no	—
100	C₄×C₈×C₁₇	—	2	1	no	—
101	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
102	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
105	#10587508	—	2	4	no	—
106	#10587502	—	2	1	no	—
107	#10587496	—	2	4	no	—
108	#10587496	—	2	4	no	—
109	#10587493	—	2	4	no	—
110	#10587491	—	2	2	no	—
111	#10587491	—	2	2	no	—
112	#10587486	—	2	4	no	—
113	#10587481	C₂×C₄	1	2	yes	—
114	#10587481	C₂×C₄	1	2	yes	—
115	#10587480	C₂×C₄	1	2	yes	—
116	#10587480	C₂×C₄	1	2	yes	—
117	C₄⋊#3622	—	2	1	no	—
118	C₄⋊#3622	—	2	1	no	—
119	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
120	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
121	C₄⋊#3622	C₂×C₄	1	2	yes	—
122	#41×C₁₇	—	2	1	no	—
123	#41×C₁₇	—	2	1	no	—
124	#41×C₁₇	C₂×D₄	1	2	yes	—
125	#41×C₁₇	#41	1	2	yes	—
126	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×D₄×C₁₇	—	2	1	no	—
128	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	—	2	1	no	—
130	C₂²×C₄×C₁₇	—	2	1	no	—
131	C₂²×C₄×C₁₇	—	2	1	no	—
132	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₇	—	2	2	no	—
136	C₂²×Dic₁₇	—	2	2	no	—
137	#63252	—	2	2	no	—
138	#63252	—	2	2	no	—
139	#63252	—	2	2	no	—
140	#63252	—	2	2	no	—
141	C₂×D₆₈	—	2	1	no	—
142	C₂×D₆₈	—	2	1	no	—
143	C₂×D₆₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄×D₁₇	—	2	2	no	—
145	C₂×Dic₃₄	C₂²×C₄	1	2	yes	—
146	M₁₆×C₁₇	—	2	4	no	—
147	M₁₆×C₁₇	—	2	1	no	—
148	M₁₆×C₁₇	—	2	1	no	—
149	M₁₆×C₁₇	—	2	4	no	—
150	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
151	M₁₆×C₁₇	#41	1	2	yes	—
152	C₂×C₈×C₁₇	—	2	4	no	—
153	C₂×C₈×C₁₇	—	2	1	no	—
154	C₂×C₈×C₁₇	—	2	1	no	—
155	C₂×C₈×C₁₇	—	2	1	no	—
156	C₂×C₈×C₁₇	—	2	1	no	—
157	C₂×C₈×C₁₇	—	2	4	no	—
158	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₇	#41	1	2	yes	—
164	C₄⋊C₄×C₁₇	—	2	1	no	—
165	C₄⋊C₄×C₁₇	—	2	1	no	—
166	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₇	—	2	1	no	—
169	C₂²⋊C₄×C₁₇	—	2	1	no	—
170	C₂²⋊C₄×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	—	2	1	no	—
172	C₄²×C₁₇	—	2	1	no	—
173	C₄²×C₁₇	—	2	1	no	—
174	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
178	#63231	—	2	4	no	—
179	#63230	—	2	4	no	—
180	#63229	—	2	4	no	—
181	#63228	—	2	4	no	—
182	#63227	—	2	2	no	—
183	#63227	—	2	2	no	—
184	C₄⋊Dic₁₇	—	2	1	no	—
185	C₄⋊Dic₁₇	—	2	1	no	—
186	C₄⋊Dic₁₇	—	4	2	no	—
187	C₄×Dic₁₇	—	2	2	no	—
188	C₄×Dic₁₇	—	2	2	no	—
189	#63223	—	2	2	no	—
190	#63223	—	2	2	no	—
191	C₂×#3622	—	2	2	no	—
192	C₂×#3622	—	2	2	no	—
193	C₂×#3622	—	2	2	no	—
194	C₂×#3622	C₂²×C₄	1	2	yes	—
195	C₂×#3622	C₂²×C₄	1	2	yes	—
196	#63218	—	4	4	no	—
197	C₈×D₁₇	—	4	4	no	—
198	#21518	—	17	1	no	maximal, Sylow
199	C₂³×C₁₇	—	2	1	no	—
200	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
201	C₂²×D₁₇	—	2	2	no	—
202	Q₈×C₁₇	—	2	1	no	—
203	Q₈×C₁₇	C₄×D₄	1	2	yes	—
204	D₄×C₁₇	—	2	2	no	—
205	D₄×C₁₇	—	2	2	no	—
206	D₄×C₁₇	—	2	1	no	—
207	D₄×C₁₇	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₁₇	—	2	1	no	—
209	C₂×C₄×C₁₇	—	2	2	no	—
210	C₂×C₄×C₁₇	—	2	2	no	—
211	C₂×C₄×C₁₇	—	2	2	no	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	—	4	1	no	—
215	C₂×C₄×C₁₇	—	4	2	no	—
216	C₂×C₄×C₁₇	—	4	2	no	—
217	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
227	C₂²⋊D₁₇	—	4	2	no	—
228	C₂²⋊D₁₇	—	4	2	no	—
229	C₂×Dic₁₇	—	2	2	no	—
230	C₂×Dic₁₇	—	4	2	no	—
231	C₂×Dic₁₇	—	4	2	no	—
232	C₂×Dic₁₇	—	4	2	no	—
233	D₆₈	—	2	2	no	—
234	D₆₈	—	2	2	no	—
235	D₆₈	—	4	2	no	—
236	D₆₈	—	4	2	no	—
237	C₄×D₁₇	—	4	2	no	—
238	C₄×D₁₇	—	4	2	no	—
239	Dic₃₄	—	2	2	no	—
240	Dic₃₄	—	2	2	no	—
241	C₈×C₁₇	—	2	2	no	—
242	C₈×C₁₇	—	2	1	no	—
243	C₈×C₁₇	—	2	2	no	—
244	C₈×C₁₇	—	2	1	no	—
245	C₈×C₁₇	#121	1	2	yes	—
246	C₈×C₁₇	#121	1	2	yes	—
247	#3622	—	2	2	no	—
248	#3622	—	2	2	no	—
249	#3622	—	4	2	no	—
250	#3035	—	17	1	no	—
251	C₂×#444	—	17	2	no	—
252	#2931	—	17	1	no	—
253	C₄×#131	D₁₇	1	1	yes	characteristic, complemented
254	#1980	—	17	1	no	—
255	#1950	—	17	1	no	—
256	#1929	—	17	2	no	—
257	#1876	—	17	2	no	—
258	#1806	—	17	1	no	—
259	#1770	—	17	1	no	—
260	#1765	—	17	2	no	—
261	C₂²×C₁₇	—	2	1	no	—
262	C₂²×C₁₇	—	2	1	no	—
263	C₂²×C₁₇	—	2	2	no	—
264	C₂²×C₁₇	—	4	1	no	—
265	C₂²×C₁₇	—	4	1	no	—
266	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₁₇	#529	1	1	yes	characteristic
268	C₂²×C₁₇	#532	1	1	yes	characteristic
269	C₂×D₁₇	—	4	2	no	—
270	C₂×D₁₇	—	4	2	no	—
271	C₂×D₁₇	—	4	2	no	—
272	C₄×C₁₇	—	2	1	no	—
273	C₄×C₁₇	—	2	1	no	—
274	C₄×C₁₇	—	2	1	no	—
275	C₄×C₁₇	—	2	2	no	—
276	C₄×C₁₇	—	4	1	no	—
277	C₄×C₁₇	—	4	1	no	—
278	C₄×C₁₇	#444	1	2	yes	complemented
279	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
280	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
281	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
282	C₄×C₁₇	#525	1	1	yes	characteristic
283	Dic₁₇	—	4	2	no	—
284	Dic₁₇	—	8	2	no	—
285	C₂×#135	—	17	2	no	—
286	C₂×#131	—	17	2	no	—
287	C₂×#131	C₂×D₁₇	1	1	yes	characteristic
288	C₂×#131	C₂×D₁₇	1	1	yes	characteristic
289	#532	—	17	1	no	—
290	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
291	#464	—	17	2	no	—
292	#463	—	17	2	no	—
293	#462	—	17	1	no	—
294	#461	—	17	1	no	—
295	#460	—	17	1	no	—
296	#459	—	17	1	no	—
297	#444	—	34	8	no	—
298	#436	—	34	1	no	—
299	#436	—	34	1	no	—
300	C₈×D₄	—	34	1	no	—
301	C₈×D₄	—	34	1	no	—
302	C₂×#108	—	17	2	no	—
303	#423	—	17	1	no	—
304	C₂×C₄⋊C₈	—	17	1	no	—
305	C₂×#104	—	17	2	no	—
306	C₂×#104	—	17	2	no	—
307	C₂×#104	—	17	2	no	—
308	#416	—	17	2	no	—
309	#408	—	17	2	no	—
310	#405	—	2	1	no	—
311	#405	—	2	1	no	—
312	#405	C₂×D₁₇	1	1	yes	characteristic
313	#405	C₂×D₁₇	1	1	yes	characteristic
314	C₄×M₁₆	—	2	1	no	—
315	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
316	C₂×#97	—	17	2	no	—
317	C₂×C₄×C₈	—	2	1	no	—
318	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
319	C₄×C₄⋊C₄	—	17	1	no	—
320	#341	—	17	2	no	—
321	#339	—	17	2	no	—
322	#336	—	17	2	no	—
323	C₂×C₁₇	—	2	1	no	—
324	C₂×C₁₇	—	2	1	no	—
325	C₂×C₁₇	—	4	2	no	—
326	C₂×C₁₇	C₄×#121	1	1	yes	characteristic
327	C₂×C₁₇	C₂×#444	1	1	yes	characteristic
328	C₂×C₁₇	#2955	1	1	yes	characteristic
329	D₁₇	—	8	2	no	—
330	C₂×#41	—	17	2	no	—
331	C₂×#41	C₂²×D₁₇	1	1	yes	characteristic
332	#135	—	34	4	no	—
333	#135	—	34	4	no	—
334	C₂×Q₁₆	—	17	2	no	—
335	C₂×SD₁₆	—	17	2	no	—
336	C₂×SD₁₆	—	17	2	no	—
337	C₂×D₈	—	17	2	no	—
338	#131	—	2	2	no	—
339	#131	—	2	2	no	—
340	#131	—	2	2	no	—
341	#131	—	34	4	no	—
342	#131	—	34	4	no	—
343	#131	D₆₈	1	4	yes	complemented
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	17	2	no	—
347	C₂×M₁₆	—	34	2	no	—
348	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
349	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	17	2	no	—
353	C₂²×C₈	—	34	2	no	—
354	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
356	C₄⋊Q₈	—	17	1	no	—
357	#127	—	17	1	no	—
358	#124	—	17	2	no	—
359	#121	—	34	1	no	—
360	#121	—	34	1	no	—
361	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
362	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	34	1	no	—
366	C₄×D₄	—	34	1	no	—
367	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
368	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	C₂²×D₁₇	1	1	yes	characteristic
371	C₂×C₄⋊C₄	—	34	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	17	2	no	—
374	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
375	#108	—	34	4	no	—
376	C₄⋊C₈	—	17	1	no	—
377	C₄⋊C₈	—	17	1	no	—
378	C₄⋊C₈	—	17	2	no	—
379	C₄⋊C₈	—	34	1	no	—
380	C₄⋊C₈	—	34	1	no	—
381	#104	—	34	4	no	—
382	#104	—	34	4	no	—
383	#104	—	34	4	no	—
384	#103	—	17	2	no	—
385	#103	—	17	2	no	—
386	#102	—	17	2	no	—
387	#102	—	17	2	no	—
388	C₂²⋊C₈	—	34	2	no	—
389	C₂²⋊C₈	—	34	2	no	—
390	#97	—	2	1	no	—
391	#97	—	2	1	no	—
392	#97	—	2	1	no	—
393	#97	—	34	4	no	—
394	C₄×C₈	—	2	1	no	—
395	C₄×C₈	—	2	1	no	—
396	C₄×C₈	—	2	1	no	—
397	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
398	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
399	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
400	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
401	#95	—	34	1	no	—
402	C₁₇	#21518	1	1	yes	characteristic, complemented, Sylow
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	34	2	no	—
406	#41	—	34	2	no	—
407	#41	—	34	2	no	—
408	#41	—	34	2	no	—
409	#41	C₂×D₆₈	1	2	yes	—
410	#41	#63252	1	2	yes	—
411	C₂×Q₈	—	17	2	no	—
412	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	17	2	no	—
415	C₂×D₄	—	34	2	no	—
416	C₂×D₄	—	34	1	no	—
417	C₂×D₄	—	34	1	no	—
418	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	34	2	no	—
423	C₂²×C₄	—	34	2	no	—
424	C₂²×C₄	#63252	1	1	yes	characteristic
425	C₂²×C₄	#63252	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
427	Q₁₆	—	34	4	no	—
428	SD₁₆	—	34	4	no	—
429	SD₁₆	—	34	4	no	—
430	D₈	—	34	4	no	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	1	no	—
433	M₁₆	—	2	1	no	—
434	M₁₆	—	2	4	no	—
435	M₁₆	—	34	2	no	—
436	M₁₆	—	34	2	no	—
437	M₁₆	—	68	4	no	—
438	M₁₆	C₂×D₆₈	1	2	yes	—
439	M₁₆	#63252	1	2	yes	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	—	17	2	no	—
447	C₂×C₈	—	17	2	no	—
448	C₂×C₈	—	34	2	no	—
449	C₂×C₈	—	34	2	no	—
450	C₂×C₈	—	34	2	no	—
451	C₂×C₈	—	68	4	no	—
452	C₂×C₈	C₂×D₆₈	1	2	yes	—
453	C₂×C₈	#63252	1	2	yes	—
454	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
455	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
456	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
457	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	34	1	no	—
461	C₄⋊C₄	—	34	1	no	—
462	C₄⋊C₄	—	68	2	no	—
463	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
464	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	34	2	no	—
469	C₂²⋊C₄	—	34	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	34	2	no	—
474	C₄²	—	34	2	no	—
475	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
476	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
477	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
478	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	34	2	no	—
481	C₂³	C₂×#63252	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	34	2	no	—
484	Q₈	—	34	2	no	—
485	Q₈	C₄×D₆₈	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	—	34	2	no	—
490	D₄	—	34	2	no	—
491	D₄	—	68	2	no	—
492	D₄	—	68	2	no	—
493	D₄	—	68	2	no	—
494	D₄	—	68	2	no	—
495	D₄	C₄×D₆₈	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	34	2	no	—
506	C₂×C₄	—	68	2	no	—
507	C₂×C₄	—	68	2	no	—
508	C₂×C₄	—	68	2	no	—
509	C₂×C₄	—	68	2	no	—
510	C₂×C₄	—	68	2	no	—
511	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
512	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
513	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
514	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
517	C₂×C₄	C₂×#63252	1	1	yes	characteristic
518	C₂×C₄	C₂×#63252	1	1	yes	characteristic
519	C₂×C₄	C₂×#63252	1	1	yes	characteristic
520	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	1	no	—
525	C₈	—	34	2	no	—
526	C₈	—	34	2	no	—
527	C₈	—	68	2	no	—
528	C₈	#10587616	1	2	yes	—
529	C₈	#10587616	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	68	2	no	—
536	C₂²	—	68	2	no	—
537	C₂²	—	68	2	no	—
538	C₂²	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
539	C₂²	#11763343	1	1	yes	characteristic
540	C₂²	#11763359	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	68	2	no	—
548	C₄	—	136	2	no	—
549	C₄	#11762929	1	2	yes	complemented
550	C₄	C₂×C₄×D₆₈	1	1	yes	characteristic
551	C₄	C₄×#63252	1	1	yes	characteristic
552	C₄	C₂×#10587616	1	1	yes	characteristic
553	C₄	#11763320	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	136	2	no	—
558	C₂	C₄×#10587616	1	1	yes	characteristic
559	C₂	C₂×#11762929	1	1	yes	characteristic
560	C₂	#14537685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₄×C₁₇×#131	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#14538239	C₂
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄×#131	D₁₇
hypocenter	C₁₇	#21518
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. C₂×#11762929	C₂	semidirect
3. #14537497	C₂	semidirect
4. #14529703	C₂	semidirect
5. #14529559	C₂	semidirect
6. #14529432	C₂	semidirect
7. #14529111	C₂	semidirect
8. #14528804	C₂	semidirect
9. #14528651	C₂	semidirect
10. #14528630	C₂	semidirect
11. C₄×C₁₇×#131	C₂	semidirect
15. #11763031	C₄	semidirect
16. #11763024	C₄	semidirect
17. #11763019	C₄	semidirect
18. #11763014	C₄	semidirect
19. #11763009	C₄	semidirect
20. #11763004	C₄	semidirect
55. C₁₇×#131	D₄	semidirect
253. C₄×#131	D₁₇	semidirect
278. C₄×C₁₇	#444	semidirect
343. #131	D₆₈	semidirect
402. C₁₇	#21518	semidirect
549. C₄	#11762929	semidirect

Maximal subgroups

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

subgroup	index
#14538239	2
C₂×#11762929	2
#14537497	2
#14529703	2
#14529559	2
#14529432	2
#14529111	2
#14528804	2
#14528651	2
#14528630	2
C₄×C₁₇×#131	2
#21518	17