Subgroups — #17969736

Order 4352.

810 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545463	C₂	1	2	yes	maximal
2	#14544724	C₂	1	2	yes	maximal, complemented
3	#14544709	C₂	1	2	yes	maximal, complemented
4	#14544664	C₂	1	2	yes	maximal
5	#14544663	C₂	1	2	yes	maximal
6	C₄×#10587536	C₂	1	2	yes	maximal, complemented
7	C₄×#10587535	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
9	#11763832	—	2	2	no	—
10	#11763829	—	2	2	no	—
11	#11763827	—	2	2	no	—
12	#11763826	—	2	2	no	—
13	C₂×#10587536	C₂²	1	4	yes	—
14	C₂×#10587535	C₂²	1	4	yes	—
15	#11763814	C₂²	1	4	yes	—
16	#11763780	C₂²	1	4	yes	—
17	C₄×#63243	C₂²	1	4	yes	—
18	#11763685	C₂²	1	4	yes	—
19	#11763685	C₂²	1	4	yes	—
20	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₁₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×#3622	C₄	1	1	yes	characteristic
24	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
25	C₂×C₈×Dic₁₇	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
28	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
29	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
30	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₇	Q₈	1	1	yes	characteristic
36	C₂²×C₄×D₁₇	Q₈	1	1	yes	characteristic
37	C₂²×C₄×D₁₇	C₂³	1	1	yes	characteristic
38	C₂×#63243	C₂³	1	8	yes	—
39	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
45	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
46	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₇	—	2	4	no	—
48	C₂×C₈×D₁₇	—	2	4	no	—
49	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
57	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₇	D₄	1	1	yes	characteristic
60	C₄²×D₁₇	D₄	1	1	yes	characteristic
61	C₄²×D₁₇	Q₈	1	1	yes	characteristic
62	C₄²×D₁₇	Q₈	1	1	yes	characteristic
63	C₄²×D₁₇	C₂³	1	1	yes	characteristic
64	C₄²×D₁₇	C₂³	1	1	yes	characteristic
65	C₂²⋊#3624	—	2	4	no	—
66	#10587544	—	2	4	no	—
67	#10587544	—	2	4	no	—
68	#10587543	—	2	4	no	—
69	#10587542	—	2	4	no	—
70	C₄×#3624	—	2	4	no	—
71	#10587536	—	2	8	no	—
72	#10587535	—	2	8	no	—
73	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₇	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	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
85	C₄×#3622	C₂×C₄	1	1	yes	characteristic
86	C₄×#3622	C₂×C₄	1	1	yes	characteristic
87	C₄×#3622	C₂×C₄	1	1	yes	characteristic
88	C₄×#3622	C₂×C₄	1	1	yes	characteristic
89	C₂³×D₁₇	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₁₇	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×D₁₇	—	2	4	no	—
97	C₂×C₄×D₁₇	—	2	4	no	—
98	C₂×C₄×D₁₇	—	2	2	no	—
99	C₂×C₄×D₁₇	—	2	2	no	—
100	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
112	C₂×#3624	—	2	8	no	—
113	#63243	—	2	8	no	—
114	#63243	—	2	8	no	—
115	C₂×C₈×C₁₇	—	2	2	no	—
116	C₂×C₈×C₁₇	—	2	2	no	—
117	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
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	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
122	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₇	C₂²×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	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
137	C₂×#3622	—	2	2	no	—
138	C₂×#3622	—	2	2	no	—
139	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
140	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
141	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
142	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
143	C₈×D₁₇	—	2	2	no	—
144	C₈×D₁₇	—	2	2	no	—
145	C₈×D₁₇	—	2	2	no	—
146	C₈×D₁₇	—	2	2	no	—
147	C₈×D₁₇	—	2	2	no	—
148	C₈×D₁₇	—	2	2	no	—
149	C₈×D₁₇	#41	1	4	yes	—
150	C₈×D₁₇	#41	1	4	yes	—
151	#20826	—	17	1	no	maximal, Sylow
152	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×D₁₇	—	2	2	no	—
154	C₂²×D₁₇	—	2	2	no	—
155	C₂²×D₁₇	—	2	2	no	—
156	C₂²×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×D₁₇	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₇	—	2	2	no	—
159	C₂×C₄×C₁₇	—	2	1	no	—
160	C₂×C₄×C₁₇	—	2	1	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×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
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	#108	1	4	yes	complemented
171	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₁₇	C₂²×D₄	1	1	yes	characteristic
177	C₄×D₁₇	—	2	2	no	—
178	C₄×D₁₇	—	2	2	no	—
179	C₄×D₁₇	—	2	1	no	—
180	C₄×D₁₇	—	2	1	no	—
181	C₄×D₁₇	—	2	2	no	—
182	C₄×D₁₇	—	2	2	no	—
183	C₄×D₁₇	—	2	2	no	—
184	C₄×D₁₇	—	2	2	no	—
185	C₄×D₁₇	—	2	2	no	—
186	C₄×D₁₇	—	2	2	no	—
187	C₄×D₁₇	—	2	2	no	—
188	C₄×D₁₇	#108	1	4	yes	complemented
189	C₄×D₁₇	C₂×#41	1	2	yes	—
190	C₄×D₁₇	C₂×#41	1	2	yes	—
191	#3624	—	4	8	no	—
192	C₈×C₁₇	—	2	1	no	—
193	C₈×C₁₇	—	2	1	no	—
194	C₈×C₁₇	#117	1	2	yes	—
195	C₈×C₁₇	#117	1	2	yes	—
196	#3622	—	2	1	no	—
197	#3622	—	2	1	no	—
198	#3622	#117	1	2	yes	—
199	#3622	#117	1	2	yes	—
200	#2920	—	17	2	no	—
201	C₂²×C₄×C₈	—	17	1	no	—
202	#1848	—	17	2	no	—
203	#1837	—	17	2	no	—
204	#1810	—	17	2	no	—
205	#1810	—	17	2	no	—
206	C₄×#108	—	17	2	no	—
207	C₄×#108	—	17	2	no	—
208	C₂²×C₁₇	—	2	1	no	—
209	C₂²×C₁₇	—	2	1	no	—
210	C₂²×C₁₇	C₂×#108	1	2	yes	—
211	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₂×D₁₇	—	2	8	no	—
213	C₂×D₁₇	—	2	1	no	—
214	C₂×D₁₇	—	2	1	no	—
215	C₂×D₁₇	—	2	1	no	—
216	C₂×D₁₇	—	2	1	no	—
217	C₂×D₁₇	C₂×#108	1	2	yes	—
218	C₂×D₁₇	#533	1	2	yes	—
219	C₄×C₁₇	—	2	1	no	—
220	C₄×C₁₇	—	2	1	no	—
221	C₄×C₁₇	—	2	1	no	—
222	C₄×C₁₇	—	2	1	no	—
223	C₄×C₁₇	C₂×#108	1	2	yes	—
224	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
225	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
226	Dic₁₇	—	2	1	no	—
227	Dic₁₇	—	2	1	no	—
228	Dic₁₇	C₂×#108	1	2	yes	—
229	Dic₁₇	C₂×#108	1	2	yes	—
230	Dic₁₇	C₂×#108	1	2	yes	—
231	Dic₁₇	#532	1	2	yes	—
232	C₂³×C₈	—	17	1	no	—
233	C₂³×C₈	—	17	1	no	—
234	C₂²×C₄²	—	17	1	no	—
235	#432	—	34	2	no	—
236	#432	—	34	2	no	—
237	#431	—	34	2	no	—
238	#431	—	34	2	no	—
239	C₂×#108	—	17	4	no	—
240	C₂×#108	—	17	4	no	—
241	#423	—	17	4	no	—
242	#407	—	17	4	no	—
243	C₄×M₁₆	—	17	4	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	C₂×C₄×C₈	—	17	1	no	—
252	C₂×C₄×C₈	—	17	1	no	—
253	C₂×C₄×C₈	—	17	1	no	—
254	C₂×C₄×C₈	—	17	1	no	—
255	C₂×C₄×C₈	#595	1	1	yes	characteristic
256	#341	—	17	4	no	—
257	#341	—	17	4	no	—
258	C₂×C₁₇	—	2	2	no	—
259	C₂×C₁₇	#2285	1	1	yes	characteristic
260	C₂×C₁₇	C₂²×#108	1	1	yes	characteristic
261	C₂×C₁₇	C₂²×#108	1	1	yes	characteristic
262	D₁₇	—	2	2	no	—
263	D₁₇	—	2	2	no	—
264	C₂³×C₄	—	17	1	no	—
265	C₂³×C₄	—	17	1	no	—
266	C₂³×C₄	—	17	1	no	—
267	C₂×M₁₆	—	17	8	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	—	17	1	no	—
273	C₂²×C₈	—	17	1	no	—
274	C₂²×C₈	—	17	1	no	—
275	C₂²×C₈	—	17	1	no	—
276	C₂²×C₈	—	17	1	no	—
277	C₂²×C₈	—	17	1	no	—
278	C₂²×C₈	—	34	4	no	—
279	C₂²×C₈	—	34	4	no	—
280	C₂²×C₈	C₂×#595	1	1	yes	characteristic
281	C₂²×C₈	C₂×#595	1	1	yes	characteristic
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	C₂×C₄²	—	17	1	no	—
292	C₂×C₄²	—	17	1	no	—
293	C₂×C₄²	C₂×#595	1	1	yes	characteristic
294	#108	—	34	8	no	—
295	#108	—	34	8	no	—
296	C₄⋊C₈	—	34	4	no	—
297	C₄⋊C₈	—	34	4	no	—
298	C₂²⋊C₈	—	34	4	no	—
299	C₂²⋊C₈	—	34	4	no	—
300	#97	—	34	4	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	—	17	1	no	—
313	C₄×C₈	—	34	4	no	—
314	C₄×C₈	C₂×#595	1	1	yes	characteristic
315	C₄×C₈	C₂×#595	1	1	yes	characteristic
316	C₄×C₈	C₂×#595	1	1	yes	characteristic
317	C₄×C₈	C₂×#595	1	1	yes	characteristic
318	C₁₇	#20826	1	1	yes	characteristic, complemented, Sylow
319	C₂⁴	—	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	—	17	1	no	—
330	C₂²×C₄	—	17	1	no	—
331	C₂²×C₄	—	17	1	no	—
332	C₂²×C₄	—	17	1	no	—
333	C₂²×C₄	—	17	1	no	—
334	C₂²×C₄	—	17	1	no	—
335	C₂²×C₄	—	34	2	no	—
336	C₂²×C₄	—	34	2	no	—
337	C₂²×C₄	—	34	4	no	—
338	C₂²×C₄	—	34	4	no	—
339	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
340	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
341	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
342	M₁₆	—	34	8	no	—
343	M₁₆	—	34	8	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	17	1	no	—
348	C₂×C₈	—	17	4	no	—
349	C₂×C₈	—	17	4	no	—
350	C₂×C₈	—	17	1	no	—
351	C₂×C₈	—	17	1	no	—
352	C₂×C₈	—	34	2	no	—
353	C₂×C₈	—	34	2	no	—
354	C₂×C₈	—	34	2	no	—
355	C₂×C₈	—	34	2	no	—
356	C₂×C₈	—	34	2	no	—
357	C₂×C₈	—	34	2	no	—
358	C₂×C₈	—	34	2	no	—
359	C₂×C₈	—	34	2	no	—
360	C₂×C₈	—	34	8	no	—
361	C₂×C₈	C₂²×#595	1	1	yes	characteristic
362	C₂×C₈	C₂²×#595	1	1	yes	characteristic
363	C₂×C₈	C₂²×#595	1	1	yes	characteristic
364	C₂×C₈	C₂²×#595	1	1	yes	characteristic
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	C₄²	—	17	1	no	—
376	C₄²	—	17	1	no	—
377	C₄²	C₄⋊#595	1	1	yes	characteristic
378	C₄²	C₄⋊#595	1	1	yes	characteristic
379	C₄²	C₂²×#595	1	1	yes	characteristic
380	C₄²	C₂²×#595	1	1	yes	characteristic
381	C₂³	—	17	1	no	—
382	C₂³	—	17	1	no	—
383	C₂³	—	34	2	no	—
384	C₂³	—	34	2	no	—
385	C₂³	—	34	2	no	—
386	C₂³	C₂×C₄⋊#595	1	1	yes	characteristic
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	17	4	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	4	no	—
397	C₂×C₄	—	17	2	no	—
398	C₂×C₄	—	17	2	no	—
399	C₂×C₄	—	17	1	no	—
400	C₂×C₄	—	17	1	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	—	34	2	no	—
409	C₂×C₄	—	34	2	no	—
410	C₂×C₄	—	34	2	no	—
411	C₂×C₄	—	34	2	no	—
412	C₂×C₄	—	34	1	no	—
413	C₂×C₄	—	34	1	no	—
414	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
415	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
418	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
419	C₂×C₄	C₂³×#595	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	17	2	no	—
423	C₈	—	17	2	no	—
424	C₈	—	34	1	no	—
425	C₈	—	34	1	no	—
426	C₈	—	68	8	no	—
427	C₈	#10587677	1	2	yes	—
428	C₈	#10587677	1	2	yes	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	17	2	no	—
432	C₂²	—	17	2	no	—
433	C₂²	—	34	8	no	—
434	C₂²	—	34	1	no	—
435	C₂²	—	34	1	no	—
436	C₂²	—	34	1	no	—
437	C₂²	—	34	1	no	—
438	C₂²	D₁₇⋊#108	1	2	yes	—
439	C₂²	C₂²×C₄⋊#595	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	17	2	no	—
445	C₄	—	17	2	no	—
446	C₄	—	17	2	no	—
447	C₄	—	17	2	no	—
448	C₄	—	34	1	no	—
449	C₄	—	34	1	no	—
450	C₄	D₁₇⋊#108	1	2	yes	—
451	C₄	C₂×#10587677	1	1	yes	characteristic
452	C₄	C₂×#10587677	1	1	yes	characteristic
453	C₂	—	2	2	no	—
454	C₂	—	34	2	no	—
455	C₂	—	34	2	no	—
456	C₂	#14545233	1	1	yes	characteristic
457	C₂	C₂×D₁₇⋊#108	1	1	yes	characteristic
458	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	C₂×C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₇	C₂×Q₈
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	#20826
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14544724	C₂	semidirect
3. #14544709	C₂	semidirect
6. C₄×#10587536	C₂	semidirect
7. C₄×#10587535	C₂	semidirect
170. C₂×Dic₁₇	#108	semidirect
188. C₄×D₁₇	#108	semidirect
318. C₁₇	#20826	semidirect

Maximal subgroups

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

subgroup	index
#14545463	2
#14544724	2
#14544709	2
#14544664	2
#14544663	2
C₄×#10587536	2
C₄×#10587535	2
C₂×C₄×C₈×D₁₇	2
#20826	17