Subgroups — C₂×#14543850 #17960523

Order 4352.

614 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763865	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10587533	C₂	1	1	yes	maximal, characteristic
3	#14543850	C₂	1	4	yes	maximal, direct product factor
4	C₂×#108×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊#595	—	2	1	no	—
6	C₂×#10587530	—	2	1	no	—
7	#11763865	—	2	1	no	—
8	#11763865	—	2	1	no	—
9	#11763865	C₄	1	2	yes	complemented
10	#11763865	C₂²	1	2	yes	—
11	C₂×#10587538	—	2	1	no	—
12	C₂×#10587529	C₄	1	2	yes	complemented
13	C₂×#10587533	—	2	1	no	—
14	C₂×#10587533	—	2	1	no	—
15	C₂×#10587533	—	2	1	no	—
16	C₂×#10587533	C₄	1	2	yes	—
17	C₂×#10587533	C₄	1	2	yes	—
18	C₂×#10587533	C₂²	1	2	yes	—
19	C₂×M₁₆×D₁₇	—	2	1	no	—
20	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
21	C₂×#10587490	C₄	1	1	yes	characteristic, complemented
22	C₂×#10587493	—	2	1	no	—
23	#108×D₁₇	—	2	1	no	—
24	#108×D₁₇	—	2	1	no	—
25	#108×D₁₇	C₄	1	2	yes	complemented
26	#108×D₁₇	C₂²	1	2	yes	—
27	C₂×C₁₇×#108	C₄	1	1	yes	characteristic, complemented
28	C₂³×#595	—	4	1	no	—
29	C₂²×C₄×D₁₇	D₄	1	1	yes	characteristic
30	C₂×C₄⋊#595	—	2	2	no	—
31	C₂×C₄⋊#595	—	2	2	no	—
32	C₂×C₄⋊#595	—	2	2	no	—
33	C₂×C₄⋊#595	—	4	1	no	—
34	C₂×C₄⋊#595	—	4	1	no	—
35	C₂×C₄⋊#595	—	4	1	no	—
36	C₂×M₁₆×C₁₇	—	2	1	no	—
37	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×#63223	—	2	1	no	—
39	C₂²×#3622	D₄	1	1	yes	characteristic
40	M₁₆×D₁₇	—	2	2	no	—
41	M₁₆×D₁₇	—	2	2	no	—
42	M₁₆×D₁₇	—	4	1	no	—
43	M₁₆×D₁₇	—	4	1	no	—
44	C₂×#63218	—	4	1	no	—
45	C₂×C₈×D₁₇	—	4	1	no	—
46	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
55	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
57	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
58	#10587538	—	2	2	no	—
59	#10587538	—	2	2	no	—
60	C₂×#63216	—	2	2	no	—
61	#10587533	—	2	2	no	—
62	#10587533	—	2	2	no	—
63	#10587533	—	2	2	no	—
64	#10587533	C₂×C₄	1	4	yes	—
65	#10587530	—	2	2	no	—
66	#10587530	—	2	2	no	—
67	#10587529	—	2	2	no	—
68	#10587529	C₂×C₄	1	4	yes	complemented
69	C₁₇×#108	—	2	1	no	—
70	C₁₇×#108	C₂×C₄	1	2	yes	complemented
71	#10587493	—	2	2	no	—
72	#10587493	—	2	2	no	—
73	#10587490	—	2	1	no	—
74	#10587490	C₂×C₄	1	2	yes	complemented
75	C₂³×D₁₇	SD₁₆	1	1	yes	characteristic
76	C₂²×#595	—	4	2	no	—
77	C₂²×#595	—	4	2	no	—
78	C₂²×#595	—	4	2	no	—
79	C₂²×#595	—	8	4	no	—
80	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₁₇	Q₁₆	1	1	yes	characteristic
82	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
88	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
89	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
90	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
91	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
92	C₂×C₄×D₁₇	Q₁₆	1	1	yes	characteristic
93	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
94	C₄⋊#595	—	2	4	no	—
95	C₄⋊#595	—	4	2	no	—
96	C₄⋊#595	—	4	2	no	—
97	C₄⋊#595	—	4	2	no	—
98	M₁₆×C₁₇	—	2	2	no	—
99	M₁₆×C₁₇	—	4	1	no	—
100	C₂×C₈×C₁₇	—	4	1	no	—
101	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
102	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
103	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
107	#63223	—	2	2	no	—
108	#63223	—	4	1	no	—
109	C₂×#3622	—	4	1	no	—
110	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
114	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
115	C₂×#3622	C₂×D₄	1	1	yes	characteristic
116	#63218	—	4	2	no	—
117	#63218	—	4	2	no	—
118	C₈×D₁₇	—	4	2	no	—
119	C₈×D₁₇	—	4	2	no	—
120	C₈×D₁₇	C₄²	1	1	yes	characteristic
121	C₈×D₁₇	C₄²	1	1	yes	characteristic
122	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
135	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
136	#63216	—	2	4	no	—
137	C₂×#1383	—	17	1	no	maximal, Sylow
138	C₂³×C₁₇	#103	1	1	yes	characteristic
139	C₂²×D₁₇	—	2	4	no	—
140	C₂²×D₁₇	#102	1	1	yes	characteristic
141	C₂²×D₁₇	#102	1	1	yes	characteristic
142	C₂²×D₁₇	#103	1	1	yes	characteristic
143	C₂²×D₁₇	#106	1	1	yes	characteristic
144	C₂²×D₁₇	#106	1	1	yes	characteristic
145	C₂²×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×#595	—	4	4	no	—
147	C₂×#595	—	8	4	no	—
148	C₂×#595	—	8	4	no	—
149	C₂×#595	—	8	4	no	—
150	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
152	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
153	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
154	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×Dic₁₇	#103	1	1	yes	characteristic
157	C₂×Dic₁₇	#103	1	1	yes	characteristic
158	C₂×Dic₁₇	#103	1	1	yes	characteristic
159	C₂×Dic₁₇	#107	1	1	yes	characteristic
160	C₂×Dic₁₇	#107	1	1	yes	characteristic
161	C₂×Dic₁₇	C₂×Q₁₆	1	1	yes	characteristic
162	C₄×D₁₇	#95	1	1	yes	characteristic
163	C₄×D₁₇	#95	1	1	yes	characteristic
164	C₄×D₁₇	#102	1	1	yes	characteristic
165	C₄×D₁₇	#102	1	1	yes	characteristic
166	C₄×D₁₇	#102	1	1	yes	characteristic
167	C₄×D₁₇	#102	1	1	yes	characteristic
168	C₄×D₁₇	#103	1	1	yes	characteristic
169	C₄×D₁₇	#103	1	1	yes	characteristic
170	C₄×D₁₇	#106	1	1	yes	characteristic
171	C₄×D₁₇	#106	1	1	yes	characteristic
172	C₄×D₁₇	#107	1	1	yes	characteristic
173	C₄×D₁₇	#107	1	1	yes	characteristic
174	C₄×D₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₄×D₁₇	C₂×D₈	1	1	yes	characteristic
177	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
178	C₈×C₁₇	—	4	2	no	—
179	C₈×C₁₇	#95	1	1	yes	characteristic
180	C₈×C₁₇	#95	1	1	yes	characteristic
181	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
182	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	#3622	—	4	2	no	—
184	#3622	#95	1	1	yes	characteristic
185	#3622	#95	1	1	yes	characteristic
186	#3622	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×M₃₂	—	17	1	no	—
189	C₂²×#108	—	17	1	no	—
190	C₂²×#106	—	17	1	no	—
191	#1383	—	17	4	no	—
192	C₂²×C₁₇	—	2	2	no	—
193	C₂²×C₁₇	#340	1	1	yes	characteristic
194	C₂²×C₁₇	#340	1	1	yes	characteristic
195	C₂²×C₁₇	C₂×#103	1	1	yes	characteristic
196	C₂×D₁₇	—	2	2	no	—
197	C₂×D₁₇	—	2	2	no	—
198	C₂×D₁₇	—	2	2	no	—
199	C₂×D₁₇	—	2	2	no	—
200	C₂×D₁₇	—	2	2	no	—
201	C₂×D₁₇	#340	1	1	yes	characteristic
202	C₂×D₁₇	#340	1	1	yes	characteristic
203	C₂×D₁₇	#365	1	4	yes	—
204	C₂×D₁₇	C₂×#102	1	1	yes	characteristic
205	C₂×D₁₇	C₂×#106	1	1	yes	characteristic
206	#595	—	8	4	no	—
207	C₄×C₁₇	#340	1	1	yes	characteristic
208	C₄×C₁₇	#340	1	1	yes	characteristic
209	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
210	C₄×C₁₇	C₂×#102	1	1	yes	characteristic
211	Dic₁₇	#340	1	1	yes	characteristic
212	Dic₁₇	#340	1	1	yes	characteristic
213	Dic₁₇	C₂×#103	1	1	yes	characteristic
214	Dic₁₇	C₂×#107	1	1	yes	characteristic
215	C₂²×M₁₆	—	34	1	no	—
216	C₂³×C₈	—	17	1	no	—
217	C₂²×C₄⋊C₄	—	34	1	no	—
218	C₂×M₃₂	—	17	2	no	—
219	C₂×M₃₂	—	17	2	no	—
220	C₂×M₃₂	—	34	1	no	—
221	C₂×M₃₂	—	34	1	no	—
222	C₂×M₃₂	—	34	1	no	—
223	C₂×M₃₂	—	34	1	no	—
224	C₂²×C₁₆	—	17	2	no	—
225	C₂×#108	—	17	1	no	—
226	C₂×#108	—	17	2	no	—
227	C₂×#108	—	17	2	no	—
228	C₂×#108	—	34	1	no	—
229	C₂×#108	—	34	1	no	—
230	C₂×#108	—	34	1	no	—
231	C₂×#108	#595	1	1	yes	characteristic, complemented
232	C₂×#106	—	17	2	no	—
233	C₂×#106	—	17	2	no	—
234	C₂×#106	—	17	2	no	—
235	C₂×#106	—	34	1	no	—
236	C₂×#106	—	34	1	no	—
237	C₂×#106	—	34	1	no	—
238	C₂×C₁₇	—	2	1	no	—
239	C₂×C₁₇	—	2	1	no	—
240	C₂×C₁₇	#1383	1	2	yes	complemented
241	C₂×C₁₇	C₂×#340	1	1	yes	characteristic
242	D₁₇	—	2	1	no	—
243	D₁₇	—	2	1	no	—
244	D₁₇	#1383	1	2	yes	complemented
245	D₁₇	C₂×#365	1	2	yes	—
246	C₂³×C₄	—	17	1	no	—
247	C₂³×C₄	—	68	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	34	2	no	—
250	C₂×M₁₆	—	34	2	no	—
251	C₂×M₁₆	—	34	1	no	—
252	C₂×M₁₆	—	68	1	no	—
253	C₂×M₁₆	—	68	1	no	—
254	C₂×M₁₆	—	68	1	no	—
255	C₂²×C₈	—	17	1	no	—
256	C₂²×C₈	—	17	1	no	—
257	C₂²×C₈	—	17	1	no	—
258	C₂²×C₈	—	17	1	no	—
259	C₂²×C₈	—	17	1	no	—
260	C₂²×C₈	—	17	1	no	—
261	C₂²×C₈	—	17	1	no	—
262	C₂²×C₈	—	17	1	no	—
263	C₂²×C₈	—	17	1	no	—
264	C₂²×C₈	—	17	1	no	—
265	C₂²×C₈	—	17	1	no	—
266	C₂²×C₈	—	17	1	no	—
267	C₂²×C₈	—	17	1	no	—
268	C₂²×C₈	—	68	1	no	—
269	C₂²×C₈	C₂×#595	1	1	yes	characteristic
270	C₂×C₄⋊C₄	—	34	2	no	—
271	C₂×C₄⋊C₄	—	34	2	no	—
272	C₂×C₄⋊C₄	—	34	2	no	—
273	C₂×C₄⋊C₄	—	68	1	no	—
274	C₂×C₄⋊C₄	—	68	1	no	—
275	C₂×C₄⋊C₄	—	68	1	no	—
276	M₃₂	—	34	2	no	—
277	M₃₂	—	34	2	no	—
278	M₃₂	—	34	2	no	—
279	M₃₂	—	34	2	no	—
280	C₂×C₁₆	—	17	4	no	—
281	C₂×C₁₆	—	34	2	no	—
282	C₂×C₁₆	—	34	2	no	—
283	#108	—	2	1	no	—
284	#108	—	17	2	no	—
285	#108	—	34	2	no	—
286	#108	—	34	2	no	—
287	#108	—	34	1	no	—
288	#108	C₂×#595	1	2	yes	complemented
289	#106	—	17	4	no	—
290	#106	—	34	2	no	—
291	#106	—	34	2	no	—
292	#106	—	34	2	no	—
293	C₁₇	C₂×#1383	1	1	yes	characteristic, complemented, Sylow
294	C₂⁴	—	17	1	no	—
295	C₂²×C₄	—	17	1	no	—
296	C₂²×C₄	—	17	1	no	—
297	C₂²×C₄	—	17	1	no	—
298	C₂²×C₄	—	17	1	no	—
299	C₂²×C₄	—	17	1	no	—
300	C₂²×C₄	—	17	1	no	—
301	C₂²×C₄	—	17	1	no	—
302	C₂²×C₄	—	17	1	no	—
303	C₂²×C₄	—	17	1	no	—
304	C₂²×C₄	—	17	1	no	—
305	C₂²×C₄	—	17	1	no	—
306	C₂²×C₄	—	17	1	no	—
307	C₂²×C₄	—	17	1	no	—
308	C₂²×C₄	—	68	2	no	—
309	C₂²×C₄	—	68	2	no	—
310	C₂²×C₄	—	68	2	no	—
311	C₂²×C₄	—	136	4	no	—
312	C₂²×C₄	C₂²⋊#595	1	1	yes	characteristic
313	M₁₆	—	2	2	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	—	34	2	no	—
316	M₁₆	—	68	2	no	—
317	M₁₆	—	68	2	no	—
318	M₁₆	—	68	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	17	1	no	—
321	C₂×C₈	—	17	1	no	—
322	C₂×C₈	—	17	1	no	—
323	C₂×C₈	—	17	1	no	—
324	C₂×C₈	—	17	1	no	—
325	C₂×C₈	—	17	1	no	—
326	C₂×C₈	—	17	1	no	—
327	C₂×C₈	—	17	1	no	—
328	C₂×C₈	—	17	1	no	—
329	C₂×C₈	—	17	1	no	—
330	C₂×C₈	—	17	1	no	—
331	C₂×C₈	—	17	1	no	—
332	C₂×C₈	—	17	1	no	—
333	C₂×C₈	—	17	1	no	—
334	C₂×C₈	—	17	1	no	—
335	C₂×C₈	—	17	1	no	—
336	C₂×C₈	—	17	1	no	—
337	C₂×C₈	—	17	1	no	—
338	C₂×C₈	—	17	1	no	—
339	C₂×C₈	—	17	1	no	—
340	C₂×C₈	—	17	1	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	68	2	no	—
343	C₂×C₈	—	68	2	no	—
344	C₂×C₈	—	68	1	no	—
345	C₂×C₈	C₄×#595	1	1	yes	characteristic
346	C₂×C₈	C₄×#595	1	1	yes	characteristic
347	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
348	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
349	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
350	C₂×C₈	C₂²×#595	1	1	yes	characteristic
351	C₄⋊C₄	—	34	4	no	—
352	C₄⋊C₄	—	68	2	no	—
353	C₄⋊C₄	—	68	2	no	—
354	C₄⋊C₄	—	68	2	no	—
355	C₁₆	—	34	4	no	—
356	C₂³	—	17	1	no	—
357	C₂³	—	17	1	no	—
358	C₂³	—	17	1	no	—
359	C₂³	—	17	1	no	—
360	C₂³	—	17	1	no	—
361	C₂³	—	17	1	no	—
362	C₂³	—	34	4	no	—
363	C₂³	#10587549	1	1	yes	characteristic
364	C₂×C₄	—	17	1	no	—
365	C₂×C₄	—	17	1	no	—
366	C₂×C₄	—	17	1	no	—
367	C₂×C₄	—	17	1	no	—
368	C₂×C₄	—	17	1	no	—
369	C₂×C₄	—	17	1	no	—
370	C₂×C₄	—	17	1	no	—
371	C₂×C₄	—	17	1	no	—
372	C₂×C₄	—	17	1	no	—
373	C₂×C₄	—	17	1	no	—
374	C₂×C₄	—	17	1	no	—
375	C₂×C₄	—	17	1	no	—
376	C₂×C₄	—	17	1	no	—
377	C₂×C₄	—	17	1	no	—
378	C₂×C₄	—	17	1	no	—
379	C₂×C₄	—	17	1	no	—
380	C₂×C₄	—	17	1	no	—
381	C₂×C₄	—	17	1	no	—
382	C₂×C₄	—	17	1	no	—
383	C₂×C₄	—	17	1	no	—
384	C₂×C₄	—	17	1	no	—
385	C₂×C₄	—	17	1	no	—
386	C₂×C₄	—	68	4	no	—
387	C₂×C₄	—	136	4	no	—
388	C₂×C₄	—	136	4	no	—
389	C₂×C₄	—	136	4	no	—
390	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
391	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
392	C₂×C₄	#10587547	1	1	yes	characteristic
393	C₂×C₄	#10587547	1	1	yes	characteristic
394	C₂×C₄	#10587549	1	1	yes	characteristic
395	C₂×C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	—	17	1	no	—
398	C₈	—	17	1	no	—
399	C₈	—	17	1	no	—
400	C₈	—	17	1	no	—
401	C₈	—	68	2	no	—
402	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
403	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
404	C₈	C₂×C₄×#595	1	1	yes	characteristic
405	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
406	C₂²	—	2	2	no	—
407	C₂²	—	17	1	no	—
408	C₂²	—	17	1	no	—
409	C₂²	—	17	4	no	—
410	C₂²	—	17	1	no	—
411	C₂²	—	17	1	no	—
412	C₂²	—	34	2	no	—
413	C₂²	—	34	2	no	—
414	C₂²	—	34	2	no	—
415	C₂²	—	34	2	no	—
416	C₂²	—	34	2	no	—
417	C₂²	#11763682	1	1	yes	characteristic
418	C₂²	#11763682	1	1	yes	characteristic
419	C₂²	C₂×#10587549	1	1	yes	characteristic
420	C₄	—	17	1	no	—
421	C₄	—	17	1	no	—
422	C₄	—	17	1	no	—
423	C₄	—	17	1	no	—
424	C₄	—	136	4	no	—
425	C₄	#11763682	1	1	yes	characteristic
426	C₄	#11763682	1	1	yes	characteristic
427	C₄	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
428	C₄	C₂×#10587547	1	1	yes	characteristic
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	17	2	no	—
432	C₂	—	17	2	no	—
433	C₂	—	34	1	no	—
434	C₂	—	34	1	no	—
435	C₂	#14543850	1	2	yes	direct product factor
436	C₂	C₂×#11763682	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11763682
commutator	C₈×C₁₇	C₂×C₄²
Frattini	C₂×C₈	C₂²×#595
Fitting	C₂×C₁₇×#108	C₄
socle	C₂²×C₁₇	#340
prime radical	C₂³×D₁₇	SD₁₆
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	C₂×#108	#595
hypocenter	C₁₇	C₂×#1383
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
3. #14543850	C₂	direct (N × H)
9. #11763865	C₄	semidirect
12. C₂×#10587529	C₄	semidirect
21. C₂×#10587490	C₄	semidirect
25. #108×D₁₇	C₄	semidirect
27. C₂×C₁₇×#108	C₄	semidirect
68. #10587529	C₂×C₄	semidirect
70. C₁₇×#108	C₂×C₄	semidirect
74. #10587490	C₂×C₄	semidirect
231. C₂×#108	#595	semidirect
240. C₂×C₁₇	#1383	semidirect
244. D₁₇	#1383	semidirect
288. #108	C₂×#595	semidirect
293. C₁₇	C₂×#1383	semidirect
435. C₂	#14543850	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×#11763865	2
C₂²×#10587533	2
#14543850	2
C₂×#108×D₁₇	2
C₂×#1383	17

Subgroups — C2×#14543850 #17960523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543850 #17960523