Subgroups — #17039262

Order 4352.

780 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537417	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#63223	C₂	1	1	yes	maximal, characteristic
3	#14529560	C₂	1	4	yes	maximal, complemented
4	#14528991	C₂	1	4	yes	maximal
5	C₄×#10587490	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
7	C₂²×#63223	C₂²	1	2	yes	—
8	#11762866	—	2	1	no	—
9	#11762866	—	2	1	no	—
10	#11762862	—	2	1	no	—
11	#11762862	—	2	1	no	—
12	C₂×#10587490	C₂²	1	8	yes	—
13	#11762833	C₂²	1	2	yes	—
14	#11762773	C₂²	1	2	yes	—
15	C₄×#63223	—	2	1	no	—
16	C₄×#63223	—	2	1	no	—
17	C₄×#63223	C₂²	1	2	yes	—
18	C₄×#63223	C₂²	1	2	yes	—
19	C₄×#63223	C₂²	1	2	yes	—
20	C₂×#10587474	—	2	1	no	—
21	C₂×C₄×#3622	—	2	1	no	—
22	#11762574	C₂²	1	8	yes	—
23	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
24	C₁₇×#431	C₄	1	2	yes	—
25	C₁₇×#431	C₄	1	2	yes	—
26	C₁₇×#431	C₄	1	2	yes	—
27	C₁₇×#431	C₄	1	2	yes	—
28	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
31	C₂³×C₄×C₁₇	Q₈	1	1	yes	characteristic
32	C₂³×C₄×C₁₇	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
35	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×#63223	—	2	8	no	—
48	C₂×#63223	—	2	2	no	—
49	C₂×#63223	C₂³	1	4	yes	—
50	C₂×#63223	C₂³	1	4	yes	—
51	C₂²×#3622	—	2	2	no	—
52	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
53	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
55	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	—
56	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
57	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
58	C₂²⋊#3622	—	2	2	no	—
59	C₂²⋊#3622	—	2	2	no	—
60	#10587490	—	2	16	no	—
61	C₄⋊#3622	—	2	2	no	—
62	C₄⋊#3622	—	2	2	no	—
63	#10587474	—	2	2	no	—
64	#10587474	—	2	2	no	—
65	#10587474	—	2	2	no	—
66	C₄×#3622	—	2	2	no	—
67	C₄×#3622	—	2	2	no	—
68	C₄×#3622	—	2	2	no	—
69	C₂⁴×C₁₇	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₁₇	—	2	4	no	—
71	C₂²×C₄×C₁₇	—	2	4	no	—
72	C₂²×C₄×C₁₇	—	4	2	no	—
73	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
91	C₂×C₈×C₁₇	—	2	8	no	—
92	C₂×C₈×C₁₇	C₂²×C₄	1	8	yes	—
93	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
109	#63223	—	2	8	no	—
110	#63223	—	2	4	no	—
111	#63223	—	2	8	no	—
112	#63223	#41	1	8	yes	—
113	C₂×#3622	—	2	8	no	—
114	C₂×#3622	—	2	4	no	—
115	C₂×#3622	—	2	4	no	—
116	#21370	—	17	1	no	maximal, Sylow
117	C₂³×C₁₇	—	2	2	no	—
118	C₂³×C₁₇	—	2	2	no	—
119	C₂³×C₁₇	—	4	1	no	—
120	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₇	C₂²×Q₈	1	1	yes	characteristic
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	2	2	no	—
125	C₂×C₄×C₁₇	—	2	2	no	—
126	C₂×C₄×C₁₇	—	2	2	no	—
127	C₂×C₄×C₁₇	—	2	2	no	—
128	C₂×C₄×C₁₇	—	2	2	no	—
129	C₂×C₄×C₁₇	—	2	2	no	—
130	C₂×C₄×C₁₇	—	2	2	no	—
131	C₂×C₄×C₁₇	—	2	2	no	—
132	C₂×C₄×C₁₇	—	2	2	no	—
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	—	4	1	no	—
137	C₂×C₄×C₁₇	—	4	1	no	—
138	C₂×C₄×C₁₇	—	4	1	no	—
139	C₂×C₄×C₁₇	#108	1	4	yes	complemented
140	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
153	C₈×C₁₇	—	2	8	no	—
154	#3622	—	2	8	no	—
155	#3622	—	4	4	no	—
156	#2920	—	17	1	no	—
157	C₂×#431	D₁₇	1	1	yes	characteristic
158	C₂×C₄×M₁₆	—	17	1	no	—
159	#1950	—	17	4	no	—
160	#1855	—	17	4	no	—
161	C₄×#108	—	17	4	no	—
162	C₂²×C₁₇	—	2	1	no	—
163	C₂²×C₁₇	—	2	1	no	—
164	C₂²×C₁₇	—	2	1	no	—
165	C₂²×C₁₇	—	2	1	no	—
166	C₂²×C₁₇	—	2	1	no	—
167	C₂²×C₁₇	—	2	1	no	—
168	C₂²×C₁₇	—	2	1	no	—
169	C₂²×C₁₇	—	4	4	no	—
170	C₂²×C₁₇	C₂×#108	1	2	yes	—
171	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
172	C₂²×C₁₇	#533	1	2	yes	—
173	C₄×C₁₇	—	2	1	no	—
174	C₄×C₁₇	—	2	1	no	—
175	C₄×C₁₇	—	2	1	no	—
176	C₄×C₁₇	—	2	1	no	—
177	C₄×C₁₇	—	2	1	no	—
178	C₄×C₁₇	—	2	1	no	—
179	C₄×C₁₇	—	2	1	no	—
180	C₄×C₁₇	C₂×#108	1	2	yes	—
181	C₄×C₁₇	C₂×#108	1	2	yes	—
182	C₄×C₁₇	#430	1	2	yes	—
183	C₄×C₁₇	C₄×#41	1	2	yes	—
184	C₄×C₁₇	#525	1	2	yes	—
185	C₂²×M₁₆	—	17	2	no	—
186	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
187	#432	—	34	1	no	—
188	#432	—	34	1	no	—
189	#431	—	34	1	no	—
190	#431	—	34	1	no	—
191	#431	Dic₁₇	1	2	yes	—
192	#431	Dic₁₇	1	2	yes	—
193	#431	Dic₁₇	1	2	yes	—
194	#431	Dic₁₇	1	2	yes	—
195	C₂×#108	—	17	8	no	—
196	#423	—	17	2	no	—
197	C₂×C₄⋊C₈	C₂×D₁₇	1	2	yes	—
198	#407	—	17	2	no	—
199	C₂×C₂²⋊C₈	C₂×D₁₇	1	2	yes	—
200	C₄×M₁₆	—	17	2	no	—
201	C₄×M₁₆	—	17	2	no	—
202	C₄×M₁₆	—	17	2	no	—
203	C₄×M₁₆	—	34	1	no	—
204	C₄×M₁₆	—	34	1	no	—
205	C₂×#97	—	34	1	no	—
206	C₂×C₄×C₈	—	34	1	no	—
207	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
208	#341	—	17	8	no	—
209	C₂×C₁₇	—	2	2	no	—
210	C₂×C₁₇	—	2	2	no	—
211	C₂×C₁₇	—	4	1	no	—
212	C₂×C₁₇	#2296	1	1	yes	characteristic
213	C₂×C₁₇	C₂²×#108	1	1	yes	characteristic
214	C₂×C₁₇	C₂×#430	1	1	yes	characteristic
215	C₂³×C₄	Dic₃₄	1	1	yes	characteristic
216	C₂³×C₄	Dic₃₄	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
218	C₂×M₁₆	—	17	4	no	—
219	C₂×M₁₆	—	17	4	no	—
220	C₂×M₁₆	—	34	8	no	—
221	C₂×M₁₆	—	34	2	no	—
222	C₂²×C₈	—	34	2	no	—
223	C₂²×C₈	C₂²×D₁₇	1	4	yes	—
224	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
225	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
226	C₂×C₄²	D₆₈	1	1	yes	characteristic
227	C₂×C₄²	D₆₈	1	1	yes	characteristic
228	C₂×C₄²	D₆₈	1	1	yes	characteristic
229	C₂×C₄²	D₆₈	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
236	#108	—	34	16	no	—
237	C₄⋊C₈	—	34	2	no	—
238	C₄⋊C₈	—	34	2	no	—
239	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
240	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
241	C₂²⋊C₈	—	34	2	no	—
242	C₂²⋊C₈	—	34	2	no	—
243	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
244	C₂²⋊C₈	C₂×Dic₁₇	1	4	yes	—
245	#97	—	34	2	no	—
246	#97	—	34	2	no	—
247	#97	—	34	2	no	—
248	C₄×C₈	—	34	2	no	—
249	C₄×C₈	—	34	2	no	—
250	C₄×C₈	—	34	2	no	—
251	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
252	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
253	C₁₇	#21370	1	1	yes	characteristic, complemented, Sylow
254	C₂⁴	C₂×Dic₃₄	1	1	yes	characteristic
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
260	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
261	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
269	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
274	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
275	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
276	M₁₆	—	17	8	no	—
277	M₁₆	—	34	8	no	—
278	M₁₆	—	34	4	no	—
279	M₁₆	—	34	8	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	34	8	no	—
282	C₂×C₈	—	34	4	no	—
283	C₂×C₈	—	34	4	no	—
284	C₂×C₈	C₂²×Dic₁₇	1	8	yes	—
285	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
286	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
287	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
292	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
293	C₄²	C₂×D₆₈	1	1	yes	characteristic
294	C₄²	C₂×D₆₈	1	1	yes	characteristic
295	C₄²	C₂×D₆₈	1	1	yes	characteristic
296	C₄²	C₂×D₆₈	1	1	yes	characteristic
297	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
298	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
299	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
300	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	4	1	no	—
304	C₂³	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
305	C₂³	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
306	C₂³	C₂²×Dic₃₄	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	#10587490	1	4	yes	complemented
324	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
335	C₂×C₄	#41×D₁₇	1	4	yes	—
336	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	34	8	no	—
339	C₈	—	68	4	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	4	no	—
348	C₂²	C₂×#10587490	1	2	yes	—
349	C₂²	C₂²×C₄⋊Dic₁₇	1	1	yes	characteristic
350	C₂²	#11763362	1	2	yes	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	C₂×#10587490	1	2	yes	—
359	C₄	C₂×#10587490	1	2	yes	—
360	C₄	#11762858	1	2	yes	—
361	C₄	#41×Dic₁₇	1	2	yes	—
362	C₄	#11763321	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	4	1	no	—
366	C₂	#14531268	1	1	yes	characteristic
367	C₂	C₂²×#10587490	1	1	yes	characteristic
368	C₂	C₂×#11762858	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₆₈
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₂×C₁₇×#431	C₂
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₂×#431	D₁₇
hypocenter	C₁₇	#21370
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14529560	C₂	semidirect
5. C₄×#10587490	C₂	semidirect
139. C₂×C₄×C₁₇	#108	semidirect
253. C₁₇	#21370	semidirect
323. C₂×C₄	#10587490	semidirect

Maximal subgroups

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

subgroup	index
#14537417	2
C₂×C₄×#63223	2
#14529560	2
#14528991	2
C₄×#10587490	2
C₂×C₁₇×#431	2
#21370	17