Subgroups — #17966344

Order 4352.

762 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	#14545460	C₂	1	2	yes	maximal
2	#14544346	C₂	1	2	yes	maximal, complemented
3	#14544344	C₂	1	2	yes	maximal, complemented
4	#14544341	C₂	1	2	yes	maximal, complemented
5	#14544338	C₂	1	2	yes	maximal, complemented
6	#14544333	C₂	1	2	yes	maximal, complemented
7	#14544331	C₂	1	2	yes	maximal, complemented
8	C₂²×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
9	#11763830	C₂²	1	4	yes	—
10	#11763829	—	2	2	no	—
11	#11763826	—	2	2	no	—
12	#11763825	C₂²	1	4	yes	—
13	#11763812	C₂²	1	4	yes	—
14	#11763779	—	2	2	no	—
15	C₄×#63247	—	2	2	no	—
16	#11763673	C₂²	1	4	yes	complemented
17	#11763672	C₂²	1	4	yes	complemented
18	#11763671	C₂²	1	4	yes	complemented
19	#11763670	C₂²	1	4	yes	complemented
20	C₂³×#3622	C₄	1	1	yes	characteristic
21	C₂²×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
23	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
24	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
25	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
26	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
27	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
28	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
34	C₂³×C₈×C₁₇	C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×Dic₁₇	D₄	1	1	yes	characteristic
37	C₂³×Dic₁₇	Q₈	1	1	yes	characteristic
38	C₂×#63247	—	2	4	no	—
39	C₂²×C₈×C₁₇	—	2	4	no	—
40	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₇	Q₈	1	1	yes	characteristic
53	C₂×C₄×Dic₁₇	Q₈	1	1	yes	characteristic
54	C₂×C₄×Dic₁₇	Q₈	1	1	yes	characteristic
55	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
58	C₂²×#3622	—	2	4	no	—
59	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
60	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
61	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
62	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
63	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
64	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
65	C₂²⋊#3624	—	2	4	no	—
66	C₂²⋊#3624	—	2	4	no	—
67	#10587544	—	2	4	no	—
68	#10587542	—	2	4	no	—
69	C₄⋊#3624	C₂³	1	8	yes	—
70	C₄×#3624	—	2	4	no	—
71	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
84	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
85	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
86	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
87	C₂⁴×C₁₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	—	2	2	no	—
89	C₂²×C₄×C₁₇	—	2	2	no	—
90	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₇	—	2	4	no	—
97	C₂²×Dic₁₇	—	2	4	no	—
98	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₁₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×Dic₁₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×Dic₁₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
108	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
109	C₂²×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
110	#63247	—	4	8	no	—
111	C₂×#3624	—	2	8	no	—
112	C₂×C₈×C₁₇	—	2	2	no	—
113	C₂×C₈×C₁₇	—	2	2	no	—
114	C₂×C₈×C₁₇	—	2	2	no	—
115	C₂×C₈×C₁₇	—	2	2	no	—
116	C₂×C₈×C₁₇	—	2	2	no	—
117	C₂×C₈×C₁₇	M₁₆	1	4	yes	complemented
118	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
135	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
136	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₁₇	C₂⁴	1	1	yes	characteristic
138	C₂×#3622	—	2	2	no	—
139	C₂×#3622	—	2	2	no	—
140	C₂×#3622	—	2	2	no	—
141	C₂×#3622	—	2	2	no	—
142	C₂×#3622	—	2	2	no	—
143	C₂×#3622	M₁₆	1	4	yes	complemented
144	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
145	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
146	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
147	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
148	#17793	—	17	1	no	maximal, Sylow
149	C₂³×C₁₇	—	2	2	no	—
150	C₂³×C₁₇	—	2	2	no	—
151	C₂³×C₁₇	—	2	2	no	—
152	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₇	—	2	2	no	—
156	C₂×C₄×C₁₇	—	2	1	no	—
157	C₂×C₄×C₁₇	—	2	1	no	—
158	C₂×C₄×C₁₇	—	2	1	no	—
159	C₂×C₄×C₁₇	—	2	1	no	—
160	C₂×C₄×C₁₇	—	2	2	no	—
161	C₂×C₄×C₁₇	—	2	2	no	—
162	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
166	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
167	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×Dic₁₇	—	2	2	no	—
169	C₂×Dic₁₇	—	2	2	no	—
170	C₂×Dic₁₇	—	2	2	no	—
171	C₂×Dic₁₇	—	2	2	no	—
172	C₂×Dic₁₇	—	2	2	no	—
173	C₂×Dic₁₇	—	2	2	no	—
174	C₂×Dic₁₇	—	2	2	no	—
175	C₂×Dic₁₇	—	2	2	no	—
176	C₂×Dic₁₇	—	2	2	no	—
177	C₂×Dic₁₇	—	2	2	no	—
178	C₂×Dic₁₇	#108	1	4	yes	—
179	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₁₇	#135	1	4	yes	—
186	C₂×Dic₁₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×Dic₁₇	C₂²×Q₈	1	1	yes	characteristic
188	#3624	—	4	8	no	—
189	C₈×C₁₇	—	2	1	no	—
190	C₈×C₁₇	—	2	1	no	—
191	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
192	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
193	#3622	—	2	1	no	—
194	#3622	—	2	1	no	—
195	#3622	C₂×M₁₆	1	2	yes	—
196	#3622	C₂×M₁₆	1	2	yes	—
197	#2920	—	17	2	no	—
198	C₂²×C₄×C₈	—	17	1	no	—
199	#1568	—	17	2	no	—
200	#1568	—	17	2	no	—
201	#1567	—	17	2	no	—
202	#1566	—	17	2	no	—
203	#1564	—	17	2	no	—
204	#1564	—	17	2	no	—
205	C₂²×C₁₇	—	2	8	no	—
206	C₂²×C₁₇	—	2	1	no	—
207	C₂²×C₁₇	—	2	1	no	—
208	C₂²×C₁₇	—	2	1	no	—
209	C₂²×C₁₇	—	2	1	no	—
210	C₂²×C₁₇	—	2	1	no	—
211	C₂²×C₁₇	—	2	1	no	—
212	C₂²×C₁₇	#423	1	2	yes	—
213	C₂²×C₁₇	#427	1	2	yes	—
214	C₂²×C₁₇	C₂×#108	1	2	yes	—
215	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₄×C₁₇	—	2	1	no	—
217	C₄×C₁₇	—	2	1	no	—
218	C₄×C₁₇	#423	1	2	yes	—
219	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
220	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
221	Dic₁₇	—	2	1	no	—
222	Dic₁₇	—	2	1	no	—
223	Dic₁₇	—	2	1	no	—
224	Dic₁₇	—	2	1	no	—
225	Dic₁₇	#427	1	2	yes	—
226	Dic₁₇	C₂×#108	1	2	yes	—
227	Dic₁₇	C₂×#108	1	2	yes	—
228	Dic₁₇	C₂×#135	1	2	yes	—
229	C₂³×C₈	—	17	1	no	—
230	C₂³×C₈	#595	1	1	yes	characteristic
231	C₂²×C₄²	—	17	1	no	—
232	#432	—	17	4	no	—
233	#432	—	34	2	no	—
234	#431	—	17	4	no	—
235	#431	—	34	2	no	—
236	#423	—	17	4	no	—
237	#407	—	34	2	no	—
238	C₄×M₁₆	—	34	2	no	—
239	C₂×C₄×C₈	—	17	1	no	—
240	C₂×C₄×C₈	—	17	1	no	—
241	C₂×C₄×C₈	—	17	1	no	—
242	C₂×C₄×C₈	—	17	1	no	—
243	C₂×C₄×C₈	—	17	1	no	—
244	C₂×C₄×C₈	—	17	1	no	—
245	C₂×C₄×C₈	—	17	1	no	—
246	C₂×C₄×C₈	—	17	1	no	—
247	C₂×C₄×C₈	—	17	1	no	—
248	C₂×C₄×C₈	—	17	1	no	—
249	C₂×C₄×C₈	—	17	1	no	—
250	C₂×C₄×C₈	—	17	1	no	—
251	#335	—	17	4	no	—
252	#335	—	17	4	no	—
253	#334	—	17	4	no	—
254	#334	—	17	4	no	—
255	C₂×C₁₇	—	2	2	no	—
256	C₂×C₁₇	—	2	2	no	—
257	C₂×C₁₇	—	2	2	no	—
258	C₂×C₁₇	C₂×#423	1	1	yes	characteristic
259	C₂×C₁₇	C₂×#427	1	1	yes	characteristic
260	C₂×C₁₇	C₂²×#108	1	1	yes	characteristic
261	C₂³×C₄	—	17	1	no	—
262	C₂³×C₄	—	17	1	no	—
263	C₂³×C₄	C₂×#595	1	1	yes	characteristic
264	C₂×M₁₆	—	34	4	no	—
265	C₂²×C₈	—	2	4	no	—
266	C₂²×C₈	—	17	1	no	—
267	C₂²×C₈	—	17	1	no	—
268	C₂²×C₈	—	17	1	no	—
269	C₂²×C₈	—	17	1	no	—
270	C₂²×C₈	—	17	1	no	—
271	C₂²×C₈	—	17	1	no	—
272	C₂²×C₈	—	34	4	no	—
273	C₂²×C₈	C₂×#595	1	1	yes	characteristic
274	C₂²×C₈	C₂×#595	1	1	yes	characteristic
275	C₂²×C₈	C₂×#595	1	1	yes	characteristic
276	C₂²×C₈	C₂×#595	1	1	yes	characteristic
277	C₂²×C₈	C₂×#595	1	1	yes	characteristic
278	C₂²×C₈	C₂×#595	1	1	yes	characteristic
279	C₂×C₄²	—	17	1	no	—
280	C₂×C₄²	—	17	1	no	—
281	C₂×C₄²	—	17	1	no	—
282	C₂×C₄²	—	17	1	no	—
283	C₂×C₄²	—	17	1	no	—
284	C₂×C₄²	—	17	1	no	—
285	C₂×C₄²	—	17	1	no	—
286	C₂×C₄²	—	17	1	no	—
287	C₂×C₄²	—	17	1	no	—
288	C₂×C₄²	—	17	1	no	—
289	C₂×C₄²	—	17	1	no	—
290	C₂×C₄²	—	17	1	no	—
291	C₄⋊C₈	—	17	8	no	—
292	C₄⋊C₈	—	34	4	no	—
293	C₂²⋊C₈	—	34	4	no	—
294	C₂²⋊C₈	—	34	4	no	—
295	#97	—	34	4	no	—
296	C₄×C₈	—	17	1	no	—
297	C₄×C₈	—	17	1	no	—
298	C₄×C₈	—	17	1	no	—
299	C₄×C₈	—	17	1	no	—
300	C₄×C₈	—	17	1	no	—
301	C₄×C₈	—	17	1	no	—
302	C₄×C₈	—	17	1	no	—
303	C₄×C₈	—	17	1	no	—
304	C₄×C₈	—	17	1	no	—
305	C₄×C₈	—	17	1	no	—
306	C₄×C₈	—	17	1	no	—
307	C₄×C₈	—	17	1	no	—
308	C₄×C₈	—	17	1	no	—
309	C₄×C₈	—	17	1	no	—
310	C₄×C₈	—	17	1	no	—
311	C₄×C₈	—	17	1	no	—
312	C₄×C₈	—	34	4	no	—
313	C₁₇	#17793	1	1	yes	characteristic, complemented, Sylow
314	C₂⁴	C₄⋊#595	1	1	yes	characteristic
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	17	1	no	—
318	C₂²×C₄	—	17	1	no	—
319	C₂²×C₄	—	17	1	no	—
320	C₂²×C₄	—	17	1	no	—
321	C₂²×C₄	—	17	1	no	—
322	C₂²×C₄	—	17	1	no	—
323	C₂²×C₄	—	17	1	no	—
324	C₂²×C₄	—	17	1	no	—
325	C₂²×C₄	—	17	1	no	—
326	C₂²×C₄	—	17	1	no	—
327	C₂²×C₄	—	17	1	no	—
328	C₂²×C₄	—	17	1	no	—
329	C₂²×C₄	—	34	4	no	—
330	C₂²×C₄	—	34	4	no	—
331	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
332	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
333	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
334	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
335	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
336	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
337	M₁₆	—	68	8	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	17	4	no	—
344	C₂×C₈	—	17	1	no	—
345	C₂×C₈	—	17	1	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	17	1	no	—
348	C₂×C₈	—	34	2	no	—
349	C₂×C₈	—	34	2	no	—
350	C₂×C₈	—	34	2	no	—
351	C₂×C₈	—	34	2	no	—
352	C₂×C₈	—	34	2	no	—
353	C₂×C₈	—	34	8	no	—
354	C₂×C₈	#63247	1	4	yes	complemented
355	C₂×C₈	C₂²×#595	1	1	yes	characteristic
356	C₂×C₈	C₂²×#595	1	1	yes	characteristic
357	C₂×C₈	C₂²×#595	1	1	yes	characteristic
358	C₂×C₈	C₂²×#595	1	1	yes	characteristic
359	C₄²	—	17	1	no	—
360	C₄²	—	17	1	no	—
361	C₄²	—	17	1	no	—
362	C₄²	—	17	1	no	—
363	C₄²	—	17	1	no	—
364	C₄²	—	17	1	no	—
365	C₄²	—	17	1	no	—
366	C₄²	—	17	1	no	—
367	C₄²	—	17	1	no	—
368	C₄²	—	17	1	no	—
369	C₄²	—	17	1	no	—
370	C₄²	—	17	1	no	—
371	C₄²	—	17	1	no	—
372	C₄²	—	17	1	no	—
373	C₄²	—	17	1	no	—
374	C₄²	—	17	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
379	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
380	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	17	4	no	—
389	C₂×C₄	—	17	4	no	—
390	C₂×C₄	—	17	1	no	—
391	C₂×C₄	—	17	1	no	—
392	C₂×C₄	—	17	1	no	—
393	C₂×C₄	—	17	1	no	—
394	C₂×C₄	—	17	1	no	—
395	C₂×C₄	—	17	1	no	—
396	C₂×C₄	—	17	1	no	—
397	C₂×C₄	—	17	1	no	—
398	C₂×C₄	—	34	2	no	—
399	C₂×C₄	—	34	2	no	—
400	C₂×C₄	—	34	2	no	—
401	C₂×C₄	—	34	2	no	—
402	C₂×C₄	—	34	2	no	—
403	C₂×C₄	—	34	2	no	—
404	C₂×C₄	—	34	2	no	—
405	C₂×C₄	—	34	2	no	—
406	C₂×C₄	—	34	2	no	—
407	C₂×C₄	—	34	2	no	—
408	C₂×C₄	D₁₇⋊M₁₆	1	2	yes	—
409	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
412	C₂×C₄	C₂×#63247	1	2	yes	—
413	C₂×C₄	C₂³×#595	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	2	1	no	—
416	C₈	—	17	2	no	—
417	C₈	—	17	2	no	—
418	C₈	—	34	1	no	—
419	C₈	—	34	1	no	—
420	C₈	—	68	8	no	—
421	C₈	C₂×#63247	1	2	yes	—
422	C₈	C₂×#63247	1	2	yes	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	#11763812	1	2	yes	—
431	C₂²	#11763819	1	2	yes	—
432	C₂²	D₁₇⋊#108	1	2	yes	—
433	C₂²	C₂²×C₄⋊#595	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	17	2	no	—
437	C₄	—	17	2	no	—
438	C₄	—	17	2	no	—
439	C₄	—	17	2	no	—
440	C₄	—	34	1	no	—
441	C₄	—	34	1	no	—
442	C₄	—	34	1	no	—
443	C₄	—	34	1	no	—
444	C₄	#11763812	1	2	yes	—
445	C₄	C₂²×#63247	1	1	yes	characteristic
446	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	C₂×#11763812	1	1	yes	characteristic
451	C₂	C₂×#11763819	1	1	yes	characteristic
452	C₂	C₂×D₁₇⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#595
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×#595
Fitting	C₂³×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₇	C₄⋊C₄
cosocle	C₄×Dic₁₇	C₂⁴
hypercenter	C₂³×C₈	#595
hypocenter	C₁₇	#17793
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. #14544346	C₂	semidirect
3. #14544344	C₂	semidirect
4. #14544341	C₂	semidirect
5. #14544338	C₂	semidirect
6. #14544333	C₂	semidirect
7. #14544331	C₂	semidirect
16. #11763673	C₂²	semidirect
17. #11763672	C₂²	semidirect
18. #11763671	C₂²	semidirect
19. #11763670	C₂²	semidirect
117. C₂×C₈×C₁₇	M₁₆	semidirect
143. C₂×#3622	M₁₆	semidirect
313. C₁₇	#17793	semidirect
354. C₂×C₈	#63247	semidirect

Maximal subgroups

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

subgroup	index
#14545460	2
#14544346	2
#14544344	2
#14544341	2
#14544338	2
#14544333	2
#14544331	2
C₂²×C₈×Dic₁₇	2
#17793	17