Subgroups — #14537814

Order 2176.

464 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×D₁₇	C₂	1	1	yes	maximal, characteristic
2	#11762885	C₂	1	1	yes	maximal, characteristic, complemented
3	#11762884	C₂	1	1	yes	maximal, characteristic, complemented
4	#11762882	C₂	1	1	yes	maximal, characteristic, complemented
5	#11762881	C₂	1	1	yes	maximal, characteristic, complemented
6	#11762879	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₂²⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#11762872	C₂	1	1	yes	maximal, characteristic, complemented
9	#11762864	C₂	1	1	yes	maximal, characteristic, complemented
10	#11762861	C₂	1	1	yes	maximal, characteristic, complemented
11	#11762772	C₂	1	1	yes	maximal, characteristic, complemented
12	#11762771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#10587491	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₇	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₁₇	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
22	D₄×Dic₁₇	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
25	C₂×#63223	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#3622	C₂²	1	1	yes	characteristic, complemented
27	C₂×#63218	C₂²	1	1	yes	characteristic, complemented
28	C₂×#63218	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic, complemented
31	#10587579	C₄	1	1	yes	characteristic
32	C₄⋊C₄×D₁₇	C₄	1	1	yes	characteristic
33	#10587567	C₄	1	1	yes	characteristic
34	#10587567	C₄	1	1	yes	characteristic
35	C₂²⋊C₄×D₁₇	C₄	1	1	yes	characteristic
36	C₂²⋊C₄×D₁₇	C₄	1	1	yes	characteristic
37	C₄×D₆₈	C₂²	1	1	yes	characteristic
38	C₄²×D₁₇	C₂²	1	1	yes	characteristic
39	C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₇×#97	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊#3622	C₂²	1	1	yes	characteristic, complemented
44	C₂²⋊#3622	C₂²	1	1	yes	characteristic, complemented
45	#10587491	C₂²	1	1	yes	characteristic
46	#10587491	C₂²	1	1	yes	characteristic
47	#10587491	C₂²	1	1	yes	characteristic
48	#10587491	C₂²	1	1	yes	characteristic
49	#10587491	C₂²	1	1	yes	characteristic, complemented
50	#10587491	C₂²	1	1	yes	characteristic, complemented
51	#10587491	C₂²	1	1	yes	characteristic, complemented
52	#10587491	C₂²	1	1	yes	characteristic, complemented
53	#10587485	C₂²	1	1	yes	characteristic, complemented
54	#10587485	C₂²	1	1	yes	characteristic, complemented
55	C₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
56	C₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊#3622	C₂²	1	1	yes	characteristic, complemented
58	#10587474	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×D₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
67	C₂²×Dic₁₇	C₂×C₄	1	1	yes	characteristic
68	D₄×D₁₇	—	2	4	no	—
69	C₂×D₆₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₁₇	—	4	1	no	—
71	C₂×C₄×D₁₇	—	4	1	no	—
72	C₂×C₄×D₁₇	—	4	1	no	—
73	C₂×C₄×D₁₇	—	4	1	no	—
74	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
83	M₁₆×C₁₇	—	4	1	no	—
84	C₂×C₈×C₁₇	—	4	1	no	—
85	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
92	C₄²×C₁₇	C₂³	1	1	yes	characteristic
93	C₂²⋊Dic₁₇	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₁₇	C₂×C₄	1	1	yes	characteristic
95	#63227	C₂×C₄	1	1	yes	characteristic
96	#63227	C₂×C₄	1	1	yes	characteristic
97	#63227	C₂×C₄	1	1	yes	characteristic
98	#63227	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Dic₁₇	C₂×C₄	1	1	yes	characteristic
100	#63225	C₂×C₄	1	1	yes	characteristic
101	#63225	C₂×C₄	1	1	yes	characteristic
102	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
103	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
105	#63223	—	4	1	no	—
106	C₂×#3622	—	4	1	no	—
107	C₂×#3622	C₂³	1	1	yes	characteristic
108	C₂×#3622	C₂³	1	1	yes	characteristic
109	C₂×#3622	C₂³	1	1	yes	characteristic
110	C₂×#3622	C₂³	1	1	yes	characteristic
111	#63218	—	4	1	no	—
112	#63218	—	4	1	no	—
113	C₈×D₁₇	—	4	1	no	—
114	C₈×D₁₇	—	4	1	no	—
115	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×D₁₇	—	2	2	no	—
118	C₂²×D₁₇	—	2	2	no	—
119	C₂²×D₁₇	—	2	2	no	—
120	C₂²×D₁₇	—	2	2	no	—
121	C₂²×D₁₇	—	4	1	no	—
122	C₂²×D₁₇	—	4	1	no	—
123	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
126	D₄×C₁₇	—	2	2	no	—
127	C₂×C₄×C₁₇	—	2	1	no	—
128	C₂×C₄×C₁₇	—	2	1	no	—
129	C₂×C₄×C₁₇	—	2	1	no	—
130	C₂×C₄×C₁₇	—	2	1	no	—
131	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
136	C₂²⋊D₁₇	—	2	2	no	—
137	C₂²⋊D₁₇	M₁₆	1	4	yes	complemented
138	C₂×Dic₁₇	—	4	1	no	—
139	C₂×Dic₁₇	—	4	1	no	—
140	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
145	D₆₈	—	2	2	no	—
146	C₄×D₁₇	—	2	2	no	—
147	C₄×D₁₇	—	2	1	no	—
148	C₄×D₁₇	—	2	1	no	—
149	C₄×D₁₇	—	2	1	no	—
150	C₄×D₁₇	—	2	1	no	—
151	C₄×D₁₇	—	2	1	no	—
152	C₄×D₁₇	—	2	1	no	—
153	C₄×D₁₇	—	2	2	no	—
154	C₄×D₁₇	—	4	1	no	—
155	C₄×D₁₇	—	4	1	no	—
156	C₄×D₁₇	—	4	1	no	—
157	C₄×D₁₇	—	4	1	no	—
158	C₈×C₁₇	—	2	1	no	—
159	C₈×C₁₇	—	2	1	no	—
160	C₈×C₁₇	—	2	1	no	—
161	C₈×C₁₇	—	2	1	no	—
162	#3622	—	2	1	no	—
163	#3622	—	2	1	no	—
164	#3622	—	2	1	no	—
165	#3622	—	2	1	no	—
166	#2974	—	17	1	no	maximal, Sylow
167	C₂²×C₁₇	—	2	1	no	—
168	C₂²×C₁₇	—	2	1	no	—
169	C₂²×C₁₇	—	2	1	no	—
170	C₂²×C₁₇	—	2	1	no	—
171	C₂²×C₁₇	—	2	1	no	—
172	C₂²×C₁₇	C₂×M₁₆	1	2	yes	—
173	C₂²×C₁₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₁₇	—	2	1	no	—
175	C₂×D₁₇	—	2	1	no	—
176	C₂×D₁₇	—	2	1	no	—
177	C₂×D₁₇	—	2	1	no	—
178	C₂×D₁₇	—	2	1	no	—
179	C₂×D₁₇	—	2	1	no	—
180	C₂×D₁₇	—	2	1	no	—
181	C₂×D₁₇	—	4	4	no	—
182	C₂×D₁₇	—	4	4	no	—
183	C₂×D₁₇	C₂×M₁₆	1	2	yes	—
184	C₂×D₁₇	#131	1	2	yes	—
185	C₄×C₁₇	—	2	1	no	—
186	C₄×C₁₇	—	2	1	no	—
187	C₄×C₁₇	—	2	1	no	—
188	C₄×C₁₇	—	2	1	no	—
189	C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
190	C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
191	Dic₁₇	—	2	1	no	—
192	Dic₁₇	—	2	1	no	—
193	Dic₁₇	—	2	1	no	—
194	Dic₁₇	—	2	1	no	—
195	Dic₁₇	C₂×M₁₆	1	2	yes	—
196	C₂×C₄×D₄	—	17	1	no	—
197	#436	—	17	1	no	—
198	#436	—	17	1	no	—
199	#435	—	17	1	no	—
200	#435	—	17	1	no	—
201	#435	—	17	1	no	—
202	#435	D₁₇	1	1	yes	characteristic, complemented
203	C₈×D₄	—	17	1	no	—
204	C₈×D₄	—	17	1	no	—
205	#432	—	17	1	no	—
206	#431	—	17	1	no	—
207	#407	—	17	1	no	—
208	#407	—	17	1	no	—
209	C₂×C₂²⋊C₈	—	17	1	no	—
210	C₂×C₂²⋊C₈	—	17	1	no	—
211	C₂×C₁₇	—	2	2	no	—
212	C₂×C₁₇	—	4	1	no	—
213	C₂×C₁₇	#518	1	1	yes	characteristic
214	C₂×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
215	C₂×C₁₇	C₂×#131	1	1	yes	characteristic
216	D₁₇	—	2	2	no	—
217	D₁₇	—	2	2	no	—
218	D₁₇	—	4	1	no	—
219	C₂²×D₄	—	17	1	no	—
220	C₂³×C₄	—	17	1	no	—
221	C₂³×C₄	—	17	1	no	—
222	C₂×M₁₆	—	17	1	no	—
223	C₂×M₁₆	—	17	1	no	—
224	C₂×M₁₆	—	17	1	no	—
225	C₂×M₁₆	C₂×D₁₇	1	1	yes	characteristic, complemented
226	C₂²×C₈	—	17	1	no	—
227	C₂²×C₈	—	17	1	no	—
228	C₂²×C₈	—	17	1	no	—
229	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic, complemented
230	C₄×D₄	—	17	1	no	—
231	C₄×D₄	—	17	1	no	—
232	C₄×D₄	—	17	1	no	—
233	C₄×D₄	—	17	1	no	—
234	C₄×D₄	—	17	1	no	—
235	C₄×D₄	—	17	1	no	—
236	C₄×D₄	—	17	1	no	—
237	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
238	C₂×C₄⋊C₄	—	17	1	no	—
239	C₂×C₂²⋊C₄	—	17	1	no	—
240	C₂×C₂²⋊C₄	—	17	1	no	—
241	C₂×C₄²	—	17	1	no	—
242	C₄⋊C₈	—	17	1	no	—
243	C₄⋊C₈	—	17	1	no	—
244	C₄⋊C₈	—	17	1	no	—
245	C₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic, complemented
246	C₂²⋊C₈	—	17	1	no	—
247	C₂²⋊C₈	—	17	1	no	—
248	C₂²⋊C₈	—	17	1	no	—
249	C₂²⋊C₈	—	17	1	no	—
250	C₂²⋊C₈	—	17	1	no	—
251	C₂²⋊C₈	—	17	1	no	—
252	C₂²⋊C₈	—	17	1	no	—
253	C₂²⋊C₈	—	17	1	no	—
254	C₂²⋊C₈	—	17	1	no	—
255	C₂²⋊C₈	—	17	1	no	—
256	C₂²⋊C₈	C₂×D₁₇	1	1	yes	characteristic, complemented
257	C₂²⋊C₈	C₂×D₁₇	1	1	yes	characteristic, complemented
258	#97	—	17	1	no	—
259	#97	C₂×D₁₇	1	1	yes	characteristic, complemented
260	C₄×C₈	—	17	1	no	—
261	C₄×C₈	—	17	1	no	—
262	C₁₇	#2974	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	17	1	no	—
264	C₂⁴	—	17	1	no	—
265	C₂×D₄	—	17	1	no	—
266	C₂×D₄	—	17	1	no	—
267	C₂×D₄	—	17	1	no	—
268	C₂×D₄	—	34	4	no	—
269	C₂×D₄	C₄×D₁₇	1	1	yes	characteristic
270	C₂²×C₄	—	17	1	no	—
271	C₂²×C₄	—	17	1	no	—
272	C₂²×C₄	—	17	1	no	—
273	C₂²×C₄	—	17	1	no	—
274	C₂²×C₄	—	17	1	no	—
275	C₂²×C₄	—	17	1	no	—
276	C₂²×C₄	—	17	1	no	—
277	C₂²×C₄	—	17	1	no	—
278	C₂²×C₄	—	17	1	no	—
279	C₂²×C₄	—	17	1	no	—
280	C₂²×C₄	—	17	1	no	—
281	C₂²×C₄	—	68	1	no	—
282	C₂²×C₄	—	68	1	no	—
283	C₂²×C₄	—	68	1	no	—
284	C₂²×C₄	—	68	1	no	—
285	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
287	M₁₆	—	4	1	no	—
288	M₁₆	—	68	1	no	—
289	M₁₆	—	68	1	no	—
290	M₁₆	—	68	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	17	1	no	—
293	C₂×C₈	—	17	1	no	—
294	C₂×C₈	—	17	1	no	—
295	C₂×C₈	—	17	1	no	—
296	C₂×C₈	—	68	1	no	—
297	C₂×C₈	—	68	1	no	—
298	C₂×C₈	—	68	1	no	—
299	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
301	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
302	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
303	C₄⋊C₄	—	17	1	no	—
304	C₄⋊C₄	—	17	1	no	—
305	C₄⋊C₄	—	17	1	no	—
306	C₄⋊C₄	C₄×D₁₇	1	1	yes	characteristic
307	C₂²⋊C₄	—	17	1	no	—
308	C₂²⋊C₄	—	17	1	no	—
309	C₂²⋊C₄	—	17	1	no	—
310	C₂²⋊C₄	—	17	1	no	—
311	C₂²⋊C₄	—	17	1	no	—
312	C₂²⋊C₄	—	17	1	no	—
313	C₂²⋊C₄	C₄×D₁₇	1	1	yes	characteristic
314	C₂²⋊C₄	C₄×D₁₇	1	1	yes	characteristic
315	C₄²	—	17	1	no	—
316	C₄²	—	17	1	no	—
317	C₄²	—	17	1	no	—
318	C₄²	C₂²×D₁₇	1	1	yes	characteristic
319	C₂³	—	17	1	no	—
320	C₂³	—	17	1	no	—
321	C₂³	—	17	1	no	—
322	C₂³	—	34	2	no	—
323	C₂³	—	34	2	no	—
324	C₂³	—	34	2	no	—
325	C₂³	—	34	2	no	—
326	C₂³	—	68	1	no	—
327	C₂³	—	68	1	no	—
328	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
329	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	17	4	no	—
332	D₄	—	34	2	no	—
333	D₄	—	34	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	17	1	no	—
339	C₂×C₄	—	17	1	no	—
340	C₂×C₄	—	17	1	no	—
341	C₂×C₄	—	17	1	no	—
342	C₂×C₄	—	17	1	no	—
343	C₂×C₄	—	34	2	no	—
344	C₂×C₄	—	34	2	no	—
345	C₂×C₄	—	34	1	no	—
346	C₂×C₄	—	34	1	no	—
347	C₂×C₄	—	34	1	no	—
348	C₂×C₄	—	34	1	no	—
349	C₂×C₄	—	34	1	no	—
350	C₂×C₄	—	34	1	no	—
351	C₂×C₄	—	68	1	no	—
352	C₂×C₄	—	68	1	no	—
353	C₂×C₄	—	68	1	no	—
354	C₂×C₄	—	68	1	no	—
355	C₂×C₄	—	68	1	no	—
356	C₂×C₄	—	68	1	no	—
357	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	34	1	no	—
367	C₈	—	34	1	no	—
368	C₈	—	34	1	no	—
369	C₈	—	34	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	17	2	no	—
376	C₂²	—	17	2	no	—
377	C₂²	—	34	1	no	—
378	C₂²	—	34	1	no	—
379	C₂²	—	34	1	no	—
380	C₂²	—	34	1	no	—
381	C₂²	—	34	1	no	—
382	C₂²	—	34	1	no	—
383	C₂²	—	34	1	no	—
384	C₂²	—	68	4	no	—
385	C₂²	—	68	4	no	—
386	C₂²	M₁₆×D₁₇	1	2	yes	—
387	C₂²	C₂²×C₄×D₁₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	17	2	no	—
393	C₄	—	34	1	no	—
394	C₄	—	34	1	no	—
395	C₄	—	34	1	no	—
396	C₄	—	34	1	no	—
397	C₄	#10587691	1	1	yes	characteristic
398	C₄	#10587696	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	34	2	no	—
402	C₂	—	34	2	no	—
403	C₂	—	68	1	no	—
404	C₂	#11763281	1	1	yes	characteristic
405	C₂	C₂×M₁₆×D₁₇	1	1	yes	characteristic
406	C₂	#131×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₇
commutator, socle	C₂²×C₁₇	C₂³×C₄
Fitting	C₁₇×#435	C₂
prime radical	C₂×D₄×D₁₇	C₄
cosocle	C₂×C₄×C₁₇	C₂⁴
hypercenter	#435	D₁₇
hypocenter	C₁₇	#2974
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #11762885	C₂	semidirect
3. #11762884	C₂	semidirect
4. #11762882	C₂	semidirect
5. #11762881	C₂	semidirect
6. #11762879	C₂	semidirect
7. C₈×C₂²⋊D₁₇	C₂	semidirect
8. #11762872	C₂	semidirect
9. #11762864	C₂	semidirect
10. #11762861	C₂	semidirect
11. #11762772	C₂	semidirect
12. #11762771	C₂	semidirect
13. C₂×#10587491	C₂	semidirect
14. C₂²⋊C₈×D₁₇	C₂	semidirect
15. C₁₇×#435	C₂	semidirect
19. C₂×M₁₆×C₁₇	C₂²	semidirect
20. C₂²×C₈×C₁₇	C₂²	semidirect
25. C₂×#63223	C₂²	semidirect
26. C₂²×#3622	C₂²	semidirect
27. C₂×#63218	C₂²	semidirect
28. C₂×#63218	C₂²	semidirect
29. C₂×C₈×D₁₇	C₂²	semidirect
30. C₂×C₈×D₁₇	C₂²	semidirect
39. C₁₇×C₄⋊C₈	C₂²	semidirect
40. C₁₇×C₂²⋊C₈	C₂²	semidirect
41. C₁₇×C₂²⋊C₈	C₂²	semidirect
42. C₁₇×#97	C₂²	semidirect
43. C₂²⋊#3622	C₂²	semidirect
44. C₂²⋊#3622	C₂²	semidirect
49. #10587491	C₂²	semidirect
50. #10587491	C₂²	semidirect
51. #10587491	C₂²	semidirect
52. #10587491	C₂²	semidirect
53. #10587485	C₂²	semidirect
54. #10587485	C₂²	semidirect
55. C₈×Dic₁₇	C₂²	semidirect
56. C₈×Dic₁₇	C₂²	semidirect
57. C₄⋊#3622	C₂²	semidirect
58. #10587474	C₂²	semidirect
137. C₂²⋊D₁₇	M₁₆	semidirect
202. #435	D₁₇	semidirect
225. C₂×M₁₆	C₂×D₁₇	semidirect
229. C₂²×C₈	C₂×D₁₇	semidirect
245. C₄⋊C₈	C₂×D₁₇	semidirect
256. C₂²⋊C₈	C₂×D₁₇	semidirect
257. C₂²⋊C₈	C₂×D₁₇	semidirect
259. #97	C₂×D₁₇	semidirect
262. C₁₇	#2974	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×D₁₇	2
#11762885	2
#11762884	2
#11762882	2
#11762881	2
#11762879	2
C₈×C₂²⋊D₁₇	2
#11762872	2
#11762864	2
#11762861	2
#11762772	2
#11762771	2
C₂×#10587491	2
C₂²⋊C₈×D₁₇	2
C₁₇×#435	2
#2974	17