Subgroups — C₂×#14526614 #16923739

Order 4352.

678 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762862	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10587474	C₂	1	1	yes	maximal, characteristic
3	#14526614	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
5	C₂³×#3622	C₄	1	2	yes	—
6	#11762862	—	2	1	no	—
7	#11762862	—	2	1	no	—
8	#11762862	C₄	1	2	yes	—
9	#11762862	C₂²	1	2	yes	—
10	C₂×C₄⋊#3622	—	2	1	no	—
11	C₂×C₂²⋊#3622	—	2	1	no	—
12	C₂×#10587474	—	2	1	no	—
13	C₂×#10587474	—	2	1	no	—
14	C₂×#10587474	—	2	1	no	—
15	C₂×#10587474	—	2	1	no	—
16	C₂×#10587474	C₄	1	2	yes	—
17	C₂×#10587474	C₂²	1	2	yes	—
18	C₂×C₄×#3622	C₄	1	2	yes	—
19	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#431	—	2	1	no	—
21	C₁₇×#431	—	2	1	no	—
22	C₁₇×#431	C₄	1	2	yes	—
23	C₁₇×#431	C₂²	1	2	yes	—
24	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
25	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
26	C₂×C₄×C₈×C₁₇	C₄	1	2	yes	—
27	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₇	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₇	—	2	2	no	—
31	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	D₄	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	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
43	C₂²×#3622	—	2	2	no	—
44	C₂²×#3622	—	2	2	no	—
45	C₂²×#3622	—	2	2	no	—
46	C₂²×#3622	—	2	4	no	—
47	C₂²×#3622	C₈	1	8	yes	complemented
48	C₂²×#3622	C₂×C₄	1	4	yes	—
49	C₁₇×C₄⋊C₈	—	2	2	no	—
50	C₁₇×C₄⋊C₈	—	2	2	no	—
51	C₁₇×C₂²⋊C₈	—	2	2	no	—
52	C₁₇×C₂²⋊C₈	—	2	2	no	—
53	C₄×C₈×C₁₇	—	2	2	no	—
54	C₄×C₈×C₁₇	C₂×C₄	1	4	yes	—
55	C₂²⋊#3622	—	2	2	no	—
56	C₂²⋊#3622	—	2	2	no	—
57	C₄⋊#3622	—	2	2	no	—
58	C₄⋊#3622	—	2	2	no	—
59	#10587474	—	2	2	no	—
60	#10587474	—	2	2	no	—
61	#10587474	—	2	2	no	—
62	#10587474	—	2	2	no	—
63	C₄×#3622	—	2	2	no	—
64	C₄×#3622	C₂×C₄	1	4	yes	—
65	C₂⁴×C₁₇	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₇	—	4	2	no	—
67	C₂²×C₄×C₁₇	—	4	2	no	—
68	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₁₇	M₁₆	1	4	yes	—
85	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₈×C₁₇	—	2	4	no	—
89	C₂×C₈×C₁₇	—	4	4	no	—
90	C₄²×C₁₇	C₄²	1	1	yes	characteristic
91	C₄²×C₁₇	C₄²	1	1	yes	characteristic
92	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₇	C₂²⋊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	C₄⋊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	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
106	C₂×#3622	—	2	8	no	—
107	C₂×#3622	—	2	8	no	—
108	C₂×#3622	—	2	4	no	—
109	C₂×#3622	—	2	4	no	—
110	C₂×#3622	—	2	4	no	—
111	C₂×#3622	—	4	4	no	—
112	C₂×#3622	C₂×C₈	1	8	yes	complemented
113	C₂×#1275	—	17	1	no	maximal, Sylow
114	C₂³×C₁₇	—	2	2	no	—
115	C₂³×C₁₇	—	2	2	no	—
116	C₂³×C₁₇	#95	1	1	yes	characteristic
117	C₂³×C₁₇	#95	1	1	yes	characteristic
118	C₂³×C₁₇	C₄⋊C₈	1	4	yes	—
119	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₁₇	—	2	2	no	—
121	C₂×C₄×C₁₇	—	2	2	no	—
122	C₂×C₄×C₁₇	—	2	2	no	—
123	C₂×C₄×C₁₇	—	2	2	no	—
124	C₂×C₄×C₁₇	—	4	1	no	—
125	C₂×C₄×C₁₇	—	4	1	no	—
126	C₂×C₄×C₁₇	—	4	1	no	—
127	C₂×C₄×C₁₇	—	4	1	no	—
128	C₂×C₄×C₁₇	—	4	1	no	—
129	C₂×C₄×C₁₇	—	4	1	no	—
130	C₂×C₄×C₁₇	—	4	1	no	—
131	C₂×C₄×C₁₇	—	4	1	no	—
132	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
133	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
134	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
135	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
136	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
137	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
139	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
140	C₂×C₄×C₁₇	#97	1	2	yes	—
141	C₂×C₄×C₁₇	#97	1	2	yes	—
142	C₂×C₄×C₁₇	C₂²⋊C₈	1	4	yes	—
143	C₂×C₄×C₁₇	C₂²⋊C₈	1	4	yes	—
144	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
145	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
153	C₈×C₁₇	—	4	4	no	—
154	#3622	—	2	8	no	—
155	#3622	—	4	4	no	—
156	C₂×#431	—	17	1	no	—
157	C₂×#431	D₁₇	1	1	yes	characteristic
158	C₂²×#97	—	17	1	no	—
159	#1275	—	17	4	no	—
160	C₂²×C₁₇	—	2	1	no	—
161	C₂²×C₁₇	—	2	1	no	—
162	C₂²×C₁₇	—	2	1	no	—
163	C₂²×C₁₇	—	2	1	no	—
164	C₂²×C₁₇	—	2	8	no	—
165	C₂²×C₁₇	#336	1	2	yes	—
166	C₂²×C₁₇	#336	1	2	yes	—
167	C₂²×C₁₇	H(3,ℤ/4)	1	2	yes	—
168	C₂²×C₁₇	#338	1	2	yes	—
169	C₂²×C₁₇	C₂×#95	1	1	yes	characteristic
170	C₂²×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
171	C₄×C₁₇	—	2	1	no	—
172	C₄×C₁₇	—	2	1	no	—
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	#336	1	2	yes	—
180	C₄×C₁₇	#336	1	2	yes	—
181	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
182	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
183	C₄×C₁₇	C₂×C₂²⋊C₈	1	2	yes	—
184	C₂³×C₈	—	17	2	no	—
185	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
186	#431	—	2	1	no	—
187	#431	—	2	1	no	—
188	#431	—	17	2	no	—
189	#431	—	17	2	no	—
190	#431	—	34	1	no	—
191	#431	—	34	1	no	—
192	#431	Dic₁₇	1	2	yes	—
193	#431	C₂×D₁₇	1	2	yes	—
194	C₂×C₄⋊C₈	—	2	1	no	—
195	C₂×C₄⋊C₈	—	34	1	no	—
196	C₂×C₂²⋊C₈	—	2	1	no	—
197	C₂×C₂²⋊C₈	—	34	1	no	—
198	C₂×#97	—	17	2	no	—
199	C₂×#97	—	17	2	no	—
200	C₂×#97	—	34	1	no	—
201	C₂×#97	—	34	1	no	—
202	C₂×#97	—	34	1	no	—
203	C₂×#97	—	34	1	no	—
204	C₂×C₄×C₈	—	17	2	no	—
205	C₂×C₄×C₈	Dic₁₇	1	2	yes	—
206	C₂×C₁₇	—	2	2	no	—
207	C₂×C₁₇	—	2	2	no	—
208	C₂×C₁₇	#1275	1	4	yes	complemented
209	C₂×C₁₇	C₂×#336	1	1	yes	characteristic
210	C₂×C₁₇	C₂×H(3,ℤ/4)	1	1	yes	characteristic
211	C₂×C₁₇	C₂×#338	1	1	yes	characteristic
212	C₂³×C₄	Dic₃₄	1	1	yes	characteristic
213	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	17	4	no	—
217	C₂²×C₈	—	17	8	no	—
218	C₂²×C₈	—	34	4	no	—
219	C₂²×C₈	—	34	2	no	—
220	C₂²×C₈	—	34	2	no	—
221	C₂²×C₈	—	34	2	no	—
222	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
226	C₂×C₄²	D₆₈	1	1	yes	characteristic
227	C₂×C₄²	D₆₈	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	34	2	no	—
237	C₄⋊C₈	—	34	2	no	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	—	34	2	no	—
241	C₂²⋊C₈	—	34	2	no	—
242	#97	—	34	2	no	—
243	#97	—	34	2	no	—
244	#97	—	34	2	no	—
245	#97	—	34	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	17	4	no	—
248	C₄×C₈	—	34	2	no	—
249	C₄×C₈	C₂×Dic₁₇	1	4	yes	—
250	C₁₇	C₂×#1275	1	1	yes	characteristic, complemented, Sylow
251	C₂⁴	#63225	1	1	yes	characteristic
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₈×D₁₇	1	4	yes	—
255	C₂²×C₄	#63218	1	4	yes	—
256	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
258	C₂²×C₄	#63225	1	1	yes	characteristic
259	C₂²×C₄	#63225	1	1	yes	characteristic
260	C₂²×C₄	#63225	1	1	yes	characteristic
261	C₂²×C₄	#63225	1	1	yes	characteristic
262	C₂²×C₄	#63225	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	#63227	1	1	yes	characteristic
266	C₂²×C₄	#63227	1	1	yes	characteristic
267	C₂²×C₄	#63227	1	1	yes	characteristic
268	C₂²×C₄	#63227	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	4	4	no	—
276	C₂×C₈	—	17	8	no	—
277	C₂×C₈	—	34	8	no	—
278	C₂×C₈	—	34	8	no	—
279	C₂×C₈	—	34	4	no	—
280	C₂×C₈	—	34	4	no	—
281	C₂×C₈	—	34	4	no	—
282	C₂×C₈	—	68	4	no	—
283	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
284	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
285	C₄²	#63225	1	1	yes	characteristic
286	C₄²	#63225	1	1	yes	characteristic
287	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
289	C₄²	#63227	1	1	yes	characteristic
290	C₄²	#63227	1	1	yes	characteristic
291	C₄²	#63227	1	1	yes	characteristic
292	C₄²	#63227	1	1	yes	characteristic
293	C₄²	C₂²⋊Dic₁₇	1	1	yes	characteristic
294	C₄²	C₂²⋊Dic₁₇	1	1	yes	characteristic
295	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
296	C₄²	C₂×D₆₈	1	1	yes	characteristic
297	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
298	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	#10587485	1	4	yes	—
302	C₂³	#10587502	1	1	yes	characteristic
303	C₂³	#10587502	1	1	yes	characteristic
304	C₂³	C₂×#63225	1	1	yes	characteristic
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	C₈×Dic₁₇	1	2	yes	—
318	C₂×C₄	C₈×Dic₁₇	1	2	yes	—
319	C₂×C₄	#10587485	1	4	yes	—
320	C₂×C₄	#10587486	1	2	yes	—
321	C₂×C₄	#10587486	1	2	yes	—
322	C₂×C₄	#10587491	1	4	yes	—
323	C₂×C₄	#10587491	1	4	yes	—
324	C₂×C₄	#10587502	1	1	yes	characteristic
325	C₂×C₄	#10587502	1	1	yes	characteristic
326	C₂×C₄	#10587502	1	1	yes	characteristic
327	C₂×C₄	#10587502	1	1	yes	characteristic
328	C₂×C₄	#10587502	1	1	yes	characteristic
329	C₂×C₄	#10587502	1	1	yes	characteristic
330	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
331	C₂×C₄	C₂×#63218	1	2	yes	—
332	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
333	C₂×C₄	C₂×#63225	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#63227	1	1	yes	characteristic
336	C₂×C₄	C₂×#63227	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
338	C₈	—	4	4	no	—
339	C₈	—	34	8	no	—
340	C₈	—	68	4	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	#11762563	1	2	yes	—
347	C₂²	#11762563	1	2	yes	—
348	C₂²	#11762565	1	2	yes	—
349	C₂²	#11762567	1	2	yes	—
350	C₂²	C₂×#10587502	1	1	yes	characteristic
351	C₂²	C₂×#10587485	1	2	yes	—
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	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	#11762563	1	2	yes	—
361	C₄	#11762563	1	2	yes	—
362	C₄	C₂×C₈×Dic₁₇	1	1	yes	characteristic
363	C₄	C₂×#10587486	1	1	yes	characteristic
364	C₄	C₂×#10587491	1	2	yes	—
365	C₂	—	2	2	no	—
366	C₂	—	2	2	no	—
367	C₂	#14526614	1	4	yes	direct product factor
368	C₂	C₂×#11762563	1	1	yes	characteristic
369	C₂	C₂×#11762565	1	1	yes	characteristic
370	C₂	C₂×#11762567	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄×Dic₁₇
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂×C₁₇×#431	C₂
socle	C₂³×C₁₇	#95
prime radical	C₂⁴×C₁₇	C₄⋊C₄
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂×#431	D₁₇
hypocenter	C₁₇	C₂×#1275
LCS	G ▷ C₄×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14526614	C₂	direct (N × H)
47. C₂²×#3622	C₈	semidirect
112. C₂×#3622	C₂×C₈	semidirect
208. C₂×C₁₇	#1275	semidirect
250. C₁₇	C₂×#1275	semidirect
367. C₂	#14526614	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11762862	2
C₂²×#10587474	2
#14526614	2
C₂×C₁₇×#431	2
C₂×#1275	17

Subgroups — C2×#14526614 #16923739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14526614 #16923739