Subgroups — #17052163

Order 4352.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14529508	C₂	1	1	yes	maximal, characteristic, complemented
2	#14529503	C₂	1	1	yes	maximal, characteristic, complemented
3	#14529350	C₂	1	1	yes	maximal, characteristic, complemented
4	#14529343	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529343	C₂	1	1	yes	maximal, characteristic, complemented
6	#14529343	C₂	1	1	yes	maximal, characteristic, complemented
7	#14528768	C₂	1	1	yes	maximal, characteristic
8	#14528768	C₂	1	1	yes	maximal, characteristic
9	#14528764	C₂	1	1	yes	maximal, characteristic
10	#14528659	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×#3622	C₂	1	1	yes	maximal, characteristic, complemented
12	#14528550	C₂	1	1	yes	maximal, characteristic
13	#14528550	C₂	1	1	yes	maximal, characteristic
14	C₄×C₂²⋊#3622	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#2296	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊#3622	C₂²	1	1	yes	characteristic
26	C₂×#10587474	C₂²	1	1	yes	characteristic
27	C₂×#10587474	C₂²	1	1	yes	characteristic
28	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
29	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
30	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
31	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
32	#11762564	C₂²	1	1	yes	characteristic
33	#11762564	C₂²	1	1	yes	characteristic
34	#11762564	C₂²	1	1	yes	characteristic
35	#11762564	C₂²	1	1	yes	characteristic
36	#11762564	C₂²	1	1	yes	characteristic
37	#11762564	C₂²	1	1	yes	characteristic
38	#11762564	C₂²	1	1	yes	characteristic
39	#11762564	C₂²	1	1	yes	characteristic
40	#11762564	C₂²	1	1	yes	characteristic
41	#11762564	C₂²	1	1	yes	characteristic
42	#11762564	C₂²	1	1	yes	characteristic
43	#11762564	C₂²	1	1	yes	characteristic
44	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
45	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
47	C₁₇×#389	C₄	1	1	yes	characteristic
48	C₁₇×#389	C₄	1	1	yes	characteristic
49	C₁₇×#389	C₄	1	1	yes	characteristic
50	C₁₇×#389	C₄	1	1	yes	characteristic
51	C₁₇×#385	C₄	1	1	yes	characteristic
52	C₁₇×#385	C₄	1	1	yes	characteristic
53	C₁₇×#385	C₄	1	1	yes	characteristic
54	C₁₇×#385	C₄	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
59	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₁₇×#117	—	2	2	no	—
63	C₁₇×#117	—	2	2	no	—
64	C₁₇×#117	—	4	1	no	—
65	C₁₇×#117	—	4	1	no	—
66	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₇	—	4	1	no	—
83	C₂×C₄²×C₁₇	—	4	1	no	—
84	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
92	C₂²×#3622	C₂³	1	1	yes	characteristic
93	C₂²×#3622	C₂³	1	1	yes	characteristic
94	C₂²×#3622	C₂³	1	1	yes	characteristic
95	C₂²×#3622	C₂³	1	1	yes	characteristic
96	C₂²×#3622	C₂³	1	1	yes	characteristic
97	C₂²×#3622	C₂³	1	1	yes	characteristic
98	C₂²×#3622	C₂³	1	1	yes	characteristic
99	C₂²×#3622	C₂³	1	1	yes	characteristic
100	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
101	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
102	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
103	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
104	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
105	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
106	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊#3622	—	2	2	no	—
109	C₂²⋊#3622	—	2	2	no	—
110	C₂²⋊#3622	—	2	2	no	—
111	C₂²⋊#3622	Q₈	1	4	yes	—
112	C₄⋊#3622	—	2	2	no	—
113	C₄⋊#3622	—	2	2	no	—
114	C₄⋊#3622	—	4	1	no	—
115	C₄⋊#3622	—	4	1	no	—
116	C₄⋊#3622	—	4	1	no	—
117	C₄⋊#3622	—	4	1	no	—
118	#10587474	—	2	2	no	—
119	#10587474	—	4	1	no	—
120	C₄×#3622	—	2	2	no	—
121	C₄×#3622	—	4	1	no	—
122	C₄×#3622	—	4	1	no	—
123	C₄×#3622	—	4	1	no	—
124	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₇	—	2	1	no	—
126	C₂²×C₄×C₁₇	—	2	1	no	—
127	C₂²×C₄×C₁₇	—	2	1	no	—
128	C₂²×C₄×C₁₇	—	2	1	no	—
129	C₂²×C₄×C₁₇	—	2	2	no	—
130	C₂²×C₄×C₁₇	—	2	2	no	—
131	C₂²×C₄×C₁₇	—	2	2	no	—
132	C₂²×C₄×C₁₇	—	4	1	no	—
133	C₂²×C₄×C₁₇	—	4	1	no	—
134	C₂²×C₄×C₁₇	—	4	1	no	—
135	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₇	C₂×Q₈	1	2	yes	—
149	C₂²×C₄×C₁₇	#41	1	2	yes	—
150	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₁₇	—	2	2	no	—
152	C₄⋊C₄×C₁₇	—	2	2	no	—
153	C₄⋊C₄×C₁₇	—	2	2	no	—
154	C₄⋊C₄×C₁₇	—	2	2	no	—
155	C₄⋊C₄×C₁₇	—	2	2	no	—
156	C₄⋊C₄×C₁₇	—	2	2	no	—
157	C₄⋊C₄×C₁₇	—	2	2	no	—
158	C₄⋊C₄×C₁₇	—	2	2	no	—
159	C₄⋊C₄×C₁₇	—	4	1	no	—
160	C₄⋊C₄×C₁₇	—	4	1	no	—
161	C₄⋊C₄×C₁₇	—	4	1	no	—
162	C₄⋊C₄×C₁₇	—	4	1	no	—
163	C₂²⋊C₄×C₁₇	—	2	2	no	—
164	C₂²⋊C₄×C₁₇	—	2	2	no	—
165	C₂²⋊C₄×C₁₇	—	4	1	no	—
166	C₂²⋊C₄×C₁₇	—	4	1	no	—
167	C₄²×C₁₇	—	2	1	no	—
168	C₄²×C₁₇	—	2	1	no	—
169	C₄²×C₁₇	—	2	1	no	—
170	C₄²×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	—	2	1	no	—
175	C₄²×C₁₇	—	2	1	no	—
176	C₄²×C₁₇	—	2	1	no	—
177	C₄²×C₁₇	—	4	1	no	—
178	C₄²×C₁₇	—	4	1	no	—
179	C₄²×C₁₇	#41	1	2	yes	—
180	C₄²×C₁₇	#41	1	2	yes	—
181	C₂×#3622	—	2	1	no	—
182	C₂×#3622	—	2	1	no	—
183	C₂×#3622	—	2	1	no	—
184	C₂×#3622	—	2	1	no	—
185	C₂×#3622	—	2	1	no	—
186	C₂×#3622	—	2	1	no	—
187	C₂×#3622	—	2	1	no	—
188	C₂×#3622	—	2	1	no	—
189	C₂×#3622	—	2	1	no	—
190	C₂×#3622	—	2	1	no	—
191	C₂×#3622	—	2	1	no	—
192	C₂×#3622	—	2	1	no	—
193	C₂×#3622	—	2	1	no	—
194	C₂×#3622	—	2	1	no	—
195	C₂×#3622	—	2	1	no	—
196	C₂×#3622	—	2	1	no	—
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	—	2	1	no	—
199	C₂×#3622	—	2	1	no	—
200	C₂×#3622	—	2	1	no	—
201	C₂×#3622	—	2	1	no	—
202	C₂×#3622	—	2	1	no	—
203	C₂×#3622	C₂×Q₈	1	2	yes	—
204	C₂×#3622	C₂×Q₈	1	2	yes	—
205	#22630	—	17	1	no	maximal, Sylow
206	C₂³×C₁₇	—	2	1	no	—
207	C₂³×C₁₇	—	2	1	no	—
208	C₂³×C₁₇	—	2	1	no	—
209	C₂³×C₁₇	—	2	1	no	—
210	C₂³×C₁₇	—	2	1	no	—
211	C₂³×C₁₇	—	2	1	no	—
212	C₂³×C₁₇	C₄×Q₈	1	2	yes	—
213	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₇	—	2	1	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	2	no	—
227	C₂×C₄×C₁₇	—	2	2	no	—
228	C₂×C₄×C₁₇	—	2	2	no	—
229	C₂×C₄×C₁₇	—	2	2	no	—
230	C₂×C₄×C₁₇	—	2	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	1	no	—
233	C₂×C₄×C₁₇	—	2	1	no	—
234	C₂×C₄×C₁₇	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	1	no	—
236	C₂×C₄×C₁₇	—	2	1	no	—
237	C₂×C₄×C₁₇	—	2	1	no	—
238	C₂×C₄×C₁₇	—	2	1	no	—
239	C₂×C₄×C₁₇	—	2	1	no	—
240	C₂×C₄×C₁₇	—	2	1	no	—
241	C₂×C₄×C₁₇	—	2	1	no	—
242	C₂×C₄×C₁₇	—	2	1	no	—
243	C₂×C₄×C₁₇	—	2	1	no	—
244	C₂×C₄×C₁₇	—	2	1	no	—
245	C₂×C₄×C₁₇	—	2	1	no	—
246	C₂×C₄×C₁₇	—	2	1	no	—
247	C₂×C₄×C₁₇	—	2	1	no	—
248	C₂×C₄×C₁₇	—	2	1	no	—
249	C₂×C₄×C₁₇	—	2	1	no	—
250	C₂×C₄×C₁₇	—	2	1	no	—
251	C₂×C₄×C₁₇	—	4	4	no	—
252	C₂×C₄×C₁₇	—	4	4	no	—
253	C₂×C₄×C₁₇	#117	1	2	yes	—
254	C₂×C₄×C₁₇	#117	1	2	yes	—
255	C₂×C₄×C₁₇	C₄×Q₈	1	2	yes	—
256	C₂×C₄×C₁₇	#131	1	2	yes	—
257	C₂×C₄×C₁₇	#131	1	2	yes	—
258	C₂×C₄×C₁₇	#131	1	2	yes	—
259	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
265	#3622	—	2	2	no	—
266	#3622	—	2	2	no	—
267	#3622	—	4	1	no	—
268	#3622	—	4	1	no	—
269	#3622	—	4	1	no	—
270	#3622	—	4	1	no	—
271	#3622	—	4	1	no	—
272	#3622	—	4	1	no	—
273	#2296	D₁₇	1	1	yes	characteristic
274	#1940	—	17	1	no	—
275	#1939	—	17	1	no	—
276	#1917	—	17	1	no	—
277	#1916	—	17	1	no	—
278	#1916	—	17	1	no	—
279	#1916	—	17	1	no	—
280	#1798	—	17	1	no	—
281	#1798	—	17	1	no	—
282	#1797	—	17	1	no	—
283	#1771	—	17	1	no	—
284	C₈×C₄⋊C₄	—	17	1	no	—
285	#1750	—	17	1	no	—
286	#1750	—	17	1	no	—
287	C₄×C₂²⋊C₈	—	17	1	no	—
288	C₂²×C₁₇	—	2	2	no	—
289	C₂²×C₁₇	—	2	2	no	—
290	C₂²×C₁₇	—	2	2	no	—
291	C₂²×C₁₇	—	4	1	no	—
292	C₂²×C₁₇	—	4	1	no	—
293	C₂²×C₁₇	—	4	1	no	—
294	C₂²×C₁₇	—	4	1	no	—
295	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
296	C₂²×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
297	C₂²×C₁₇	#518	1	1	yes	characteristic
298	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
299	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
300	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
301	C₂²×C₁₇	#568	1	1	yes	characteristic
302	C₄×C₁₇	—	2	2	no	—
303	C₄×C₁₇	—	2	2	no	—
304	C₄×C₁₇	—	2	2	no	—
305	C₄×C₁₇	—	2	2	no	—
306	C₄×C₁₇	—	2	2	no	—
307	C₄×C₁₇	—	2	2	no	—
308	C₄×C₁₇	—	4	1	no	—
309	C₄×C₁₇	—	4	1	no	—
310	C₄×C₁₇	—	4	1	no	—
311	C₄×C₁₇	—	4	1	no	—
312	C₄×C₁₇	—	4	1	no	—
313	C₄×C₁₇	—	4	1	no	—
314	C₄×C₁₇	—	4	1	no	—
315	C₄×C₁₇	#553	1	1	yes	characteristic
316	C₄×C₁₇	#553	1	1	yes	characteristic
317	C₄×C₁₇	#554	1	1	yes	characteristic
318	C₄×C₁₇	#554	1	1	yes	characteristic
319	C₂×#117	C₂×D₁₇	1	1	yes	characteristic
320	C₂×#117	C₂×D₁₇	1	1	yes	characteristic
321	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
322	C₂×C₄⋊C₈	—	17	1	no	—
323	C₂×C₄⋊C₈	—	17	1	no	—
324	C₂×C₄⋊C₈	—	17	1	no	—
325	C₂×C₄⋊C₈	—	17	1	no	—
326	C₂×C₄⋊C₈	—	17	1	no	—
327	C₂×C₄⋊C₈	—	17	1	no	—
328	C₂×C₂²⋊C₈	—	17	1	no	—
329	C₂×C₂²⋊C₈	—	17	1	no	—
330	C₂×C₂²⋊C₈	—	17	1	no	—
331	C₂×C₂²⋊C₈	—	17	1	no	—
332	C₂×#97	—	17	1	no	—
333	C₂×#97	—	17	1	no	—
334	C₂×C₄×C₈	—	17	1	no	—
335	C₂×C₄×C₈	—	17	1	no	—
336	C₂×C₄×C₈	—	17	1	no	—
337	C₂×C₄×C₈	—	17	1	no	—
338	#389	Dic₁₇	1	1	yes	characteristic
339	#389	Dic₁₇	1	1	yes	characteristic
340	#389	Dic₁₇	1	1	yes	characteristic
341	#389	Dic₁₇	1	1	yes	characteristic
342	#385	Dic₁₇	1	1	yes	characteristic
343	#385	Dic₁₇	1	1	yes	characteristic
344	#385	Dic₁₇	1	1	yes	characteristic
345	#385	Dic₁₇	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
350	#336	—	17	1	no	—
351	#336	—	17	1	no	—
352	#336	—	17	1	no	—
353	#336	—	17	1	no	—
354	#336	—	17	1	no	—
355	#336	—	17	1	no	—
356	#336	—	17	1	no	—
357	#336	—	17	1	no	—
358	#336	—	17	1	no	—
359	#336	—	17	1	no	—
360	#336	—	17	1	no	—
361	#336	—	17	1	no	—
362	C₂×C₁₇	—	4	2	no	—
363	C₂×C₁₇	#2345	1	1	yes	characteristic
364	C₂×C₁₇	#2922	1	1	yes	characteristic
365	C₂×C₁₇	#2925	1	1	yes	characteristic
366	C₂×C₁₇	#2960	1	1	yes	characteristic
367	C₂×C₁₇	#2962	1	1	yes	characteristic
368	C₂×C₁₇	#2976	1	1	yes	characteristic
369	C₂×C₁₇	#2977	1	1	yes	characteristic
370	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
371	C₂³×C₄	C₂×Dic₁₇	1	1	yes	characteristic
372	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
373	C₂²×C₈	—	17	1	no	—
374	C₂²×C₈	—	17	1	no	—
375	C₂²×C₈	—	17	1	no	—
376	C₂²×C₈	—	17	1	no	—
377	C₂²×C₈	—	17	1	no	—
378	C₂²×C₈	—	17	1	no	—
379	C₂²×C₈	—	17	1	no	—
380	C₂²×C₈	—	17	1	no	—
381	#117	—	2	2	no	—
382	#117	—	2	2	no	—
383	#117	—	4	1	no	—
384	#117	—	4	1	no	—
385	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	C₂×Dic₁₇	1	1	yes	characteristic
401	C₂×C₄²	—	4	1	no	—
402	C₂×C₄²	—	4	1	no	—
403	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
404	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
405	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
406	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
407	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
408	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
409	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
410	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
411	C₄⋊C₈	—	34	2	no	—
412	C₄⋊C₈	—	34	2	no	—
413	C₄⋊C₈	—	68	1	no	—
414	C₄⋊C₈	—	68	1	no	—
415	C₄⋊C₈	—	68	1	no	—
416	C₄⋊C₈	—	68	1	no	—
417	C₂²⋊C₈	—	17	4	no	—
418	C₂²⋊C₈	—	34	2	no	—
419	C₂²⋊C₈	—	34	2	no	—
420	C₂²⋊C₈	—	34	2	no	—
421	#97	—	34	2	no	—
422	#97	—	68	1	no	—
423	C₄×C₈	—	34	2	no	—
424	C₄×C₈	—	68	1	no	—
425	C₄×C₈	—	68	1	no	—
426	C₄×C₈	—	68	1	no	—
427	#95	C₂×Dic₁₇	1	1	yes	characteristic
428	#95	C₂×Dic₁₇	1	1	yes	characteristic
429	#95	C₂×Dic₁₇	1	1	yes	characteristic
430	#95	C₂×Dic₁₇	1	1	yes	characteristic
431	#95	C₂×Dic₁₇	1	1	yes	characteristic
432	#95	C₂×Dic₁₇	1	1	yes	characteristic
433	#95	C₂×Dic₁₇	1	1	yes	characteristic
434	#95	C₂×Dic₁₇	1	1	yes	characteristic
435	C₁₇	#22630	1	1	yes	characteristic, complemented, Sylow
436	C₂⁴	C₂²×Dic₁₇	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	Q₈×D₁₇	1	2	yes	—
448	C₂²×C₄	#63256	1	2	yes	—
449	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
450	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
451	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
452	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
453	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
454	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
455	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
456	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
462	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
463	C₂×C₈	—	17	2	no	—
464	C₂×C₈	—	17	2	no	—
465	C₂×C₈	—	34	1	no	—
466	C₂×C₈	—	34	1	no	—
467	C₂×C₈	—	34	1	no	—
468	C₂×C₈	—	34	1	no	—
469	C₂×C₈	—	34	1	no	—
470	C₂×C₈	—	34	1	no	—
471	C₂×C₈	—	34	1	no	—
472	C₂×C₈	—	34	1	no	—
473	C₂×C₈	—	34	1	no	—
474	C₂×C₈	—	34	1	no	—
475	C₂×C₈	—	34	1	no	—
476	C₂×C₈	—	34	1	no	—
477	C₂×C₈	—	34	1	no	—
478	C₂×C₈	—	34	1	no	—
479	C₂×C₈	—	34	1	no	—
480	C₂×C₈	—	34	1	no	—
481	C₂×C₈	—	34	1	no	—
482	C₂×C₈	—	34	1	no	—
483	C₂×C₈	—	34	1	no	—
484	C₂×C₈	—	34	1	no	—
485	C₂×C₈	—	34	1	no	—
486	C₂×C₈	—	34	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	4	1	no	—
514	C₄²	—	4	1	no	—
515	C₄²	#63252	1	2	yes	—
516	C₄²	#63252	1	2	yes	—
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	Q₈×Dic₁₇	1	2	yes	—
524	C₂³	C₂³×Dic₁₇	1	1	yes	characteristic
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	#10587612	1	2	yes	—
565	C₂×C₄	#10587612	1	2	yes	—
566	C₂×C₄	Q₈×Dic₁₇	1	2	yes	—
567	C₂×C₄	#10587634	1	2	yes	—
568	C₂×C₄	#10587634	1	2	yes	—
569	C₂×C₄	#10587634	1	2	yes	—
570	C₂×C₄	C₂×#63252	1	1	yes	characteristic
571	C₂×C₄	C₂×#63252	1	1	yes	characteristic
572	C₂×C₄	#10587691	1	1	yes	characteristic
573	C₂×C₄	#10587691	1	1	yes	characteristic
574	C₂×C₄	C₂×Q₈×D₁₇	1	1	yes	characteristic
575	C₂×C₄	C₂×#63256	1	1	yes	characteristic
576	C₈	—	34	2	no	—
577	C₈	—	34	2	no	—
578	C₈	—	68	1	no	—
579	C₈	—	68	1	no	—
580	C₈	—	68	1	no	—
581	C₈	—	68	1	no	—
582	C₈	—	68	1	no	—
583	C₈	—	68	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	C₂×#10587612	1	1	yes	characteristic
592	C₂²	C₂×Q₈×Dic₁₇	1	1	yes	characteristic
593	C₂²	#11763284	1	1	yes	characteristic
594	C₂²	C₂×#10587634	1	1	yes	characteristic
595	C₂²	C₂×#10587634	1	1	yes	characteristic
596	C₂²	C₂×#10587634	1	1	yes	characteristic
597	C₂²	#11763576	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	#11763507	1	1	yes	characteristic
612	C₄	#11763507	1	1	yes	characteristic
613	C₄	#11763514	1	1	yes	characteristic
614	C₄	#11763514	1	1	yes	characteristic
615	C₂	—	4	2	no	—
616	C₂	#14531661	1	1	yes	characteristic
617	C₂	#14537428	1	1	yes	characteristic
618	C₂	#14537450	1	1	yes	characteristic
619	C₂	#14537719	1	1	yes	characteristic
620	C₂	#14537733	1	1	yes	characteristic
621	C₂	#14537832	1	1	yes	characteristic
622	C₂	#14537840	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₇
commutator, socle	C₂³×C₁₇	C₂³×C₄
Fitting	C₁₇×#2296	C₂
prime radical	C₂⁴×C₁₇	C₂²×C₄
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	#2296	D₁₇
hypocenter	C₁₇	#22630
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2296

Complements

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

N	H ≅ G/N	type
1. #14529508	C₂	semidirect
2. #14529503	C₂	semidirect
3. #14529350	C₂	semidirect
4. #14529343	C₂	semidirect
5. #14529343	C₂	semidirect
6. #14529343	C₂	semidirect
10. #14528659	C₂	semidirect
11. C₄⋊C₄×#3622	C₂	semidirect
435. C₁₇	#22630	semidirect

Maximal subgroups

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

subgroup	index
#14529508	2
#14529503	2
#14529350	2
#14529343	2
#14528768	2
#14528764	2
#14528659	2
C₄⋊C₄×#3622	2
#14528550	2
C₄×C₂²⋊#3622	2
C₁₇×#2296	2
#22630	17