Subgroups — C₂×#14543861 #17960552

Order 4352.

554 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587530	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₇⋊#108	C₂	1	1	yes	maximal, characteristic
3	#14543861	C₂	1	4	yes	maximal, direct product factor
4	C₂×#108×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×D₁₇⋊M₁₆	—	2	1	no	—
6	C₂×#10587530	—	2	1	no	—
7	C₂×#10587530	—	2	1	no	—
8	C₂×#10587530	—	2	1	no	—
9	C₂×#10587530	C₄	1	2	yes	—
10	C₂×#10587530	C₄	1	2	yes	—
11	C₂×#10587530	C₂²	1	2	yes	—
12	C₂²×#63216	—	2	1	no	—
13	C₂×#10587536	—	2	1	no	—
14	D₁₇⋊#108	—	2	1	no	—
15	D₁₇⋊#108	—	2	1	no	—
16	D₁₇⋊#108	C₄	1	2	yes	—
17	D₁₇⋊#108	C₂²	1	2	yes	—
18	C₂×#10587535	C₄	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
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	—
26	#108×D₁₇	C₂²	1	2	yes	—
27	C₂×C₁₇×#108	C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₇	D₄	1	1	yes	characteristic
29	C₂×#63247	—	4	1	no	—
30	D₁₇⋊M₁₆	—	2	2	no	—
31	D₁₇⋊M₁₆	—	2	2	no	—
32	D₁₇⋊M₁₆	—	4	1	no	—
33	D₁₇⋊M₁₆	—	4	1	no	—
34	C₂×#63243	—	2	2	no	—
35	C₂×#63242	—	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	C₂×#63216	—	2	2	no	—
59	C₂×#63216	—	2	2	no	—
60	C₂×#63216	—	2	2	no	—
61	#10587536	—	2	2	no	—
62	#10587536	—	2	2	no	—
63	#10587535	—	2	2	no	—
64	#10587535	C₂×C₄	1	4	yes	—
65	#10587530	—	2	2	no	—
66	#10587530	—	2	2	no	—
67	#10587530	—	2	2	no	—
68	#10587530	C₂×C₄	1	4	yes	—
69	C₁₇×#108	—	2	1	no	—
70	C₁₇×#108	C₂×C₄	1	2	yes	—
71	#10587493	—	2	2	no	—
72	#10587493	—	2	2	no	—
73	#10587490	—	2	1	no	—
74	#10587490	C₂×C₄	1	2	yes	—
75	C₂³×D₁₇	Q₁₆	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₁₇	SD₁₆	1	1	yes	characteristic
78	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
84	C₂×C₄×D₁₇	D₈	1	1	yes	characteristic
85	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
86	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₁₇	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₁₇	Q₁₆	1	1	yes	characteristic
89	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
90	#63247	—	4	2	no	—
91	#63247	—	4	2	no	—
92	C₂×#3624	—	4	2	no	—
93	#63243	—	2	4	no	—
94	#63243	—	4	2	no	—
95	#63242	—	4	2	no	—
96	#63242	—	4	2	no	—
97	M₁₆×C₁₇	—	2	2	no	—
98	M₁₆×C₁₇	—	4	1	no	—
99	C₂×C₈×C₁₇	—	4	1	no	—
100	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
101	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
102	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
106	#63223	—	2	2	no	—
107	#63223	—	4	1	no	—
108	C₂×#3622	—	4	1	no	—
109	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
113	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
114	C₂×#3622	C₂×D₄	1	1	yes	characteristic
115	#63218	—	4	2	no	—
116	#63218	—	4	2	no	—
117	C₈×D₁₇	—	4	2	no	—
118	C₈×D₁₇	—	4	2	no	—
119	C₈×D₁₇	C₄²	1	1	yes	characteristic
120	C₈×D₁₇	C₄²	1	1	yes	characteristic
121	C₈×D₁₇	C₂²⋊C₄	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	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
132	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
134	C₈×D₁₇	C₂×Q₈	1	1	yes	characteristic
135	#63216	—	2	4	no	—
136	C₂×#1388	—	17	1	no	maximal, Sylow
137	C₂³×C₁₇	#103	1	1	yes	characteristic
138	C₂²×D₁₇	—	4	2	no	—
139	C₂²×D₁₇	#103	1	1	yes	characteristic
140	C₂²×D₁₇	#103	1	1	yes	characteristic
141	C₂²×D₁₇	#103	1	1	yes	characteristic
142	C₂²×D₁₇	#107	1	1	yes	characteristic
143	C₂²×D₁₇	#107	1	1	yes	characteristic
144	C₂²×D₁₇	C₂×Q₁₆	1	1	yes	characteristic
145	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
148	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
149	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×Dic₁₇	#102	1	1	yes	characteristic
152	C₂×Dic₁₇	#102	1	1	yes	characteristic
153	C₂×Dic₁₇	#103	1	1	yes	characteristic
154	C₂×Dic₁₇	#106	1	1	yes	characteristic
155	C₂×Dic₁₇	#106	1	1	yes	characteristic
156	C₂×Dic₁₇	C₂×SD₁₆	1	1	yes	characteristic
157	C₄×D₁₇	#95	1	1	yes	characteristic
158	C₄×D₁₇	#95	1	1	yes	characteristic
159	C₄×D₁₇	#102	1	1	yes	characteristic
160	C₄×D₁₇	#102	1	1	yes	characteristic
161	C₄×D₁₇	#102	1	1	yes	characteristic
162	C₄×D₁₇	#102	1	1	yes	characteristic
163	C₄×D₁₇	#103	1	1	yes	characteristic
164	C₄×D₁₇	#103	1	1	yes	characteristic
165	C₄×D₁₇	#106	1	1	yes	characteristic
166	C₄×D₁₇	#106	1	1	yes	characteristic
167	C₄×D₁₇	#107	1	1	yes	characteristic
168	C₄×D₁₇	#107	1	1	yes	characteristic
169	C₄×D₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₄×D₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₄×D₁₇	C₂×D₈	1	1	yes	characteristic
172	C₄×D₁₇	C₂×SD₁₆	1	1	yes	characteristic
173	#3624	—	4	4	no	—
174	C₈×C₁₇	—	4	2	no	—
175	C₈×C₁₇	#95	1	1	yes	characteristic
176	C₈×C₁₇	#95	1	1	yes	characteristic
177	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
178	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	#3622	—	4	2	no	—
180	#3622	#95	1	1	yes	characteristic
181	#3622	#95	1	1	yes	characteristic
182	#3622	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×M₃₂	—	17	1	no	—
185	C₂²×#108	—	17	1	no	—
186	C₂²×#108	—	17	1	no	—
187	#1388	—	17	4	no	—
188	C₂²×C₁₇	—	2	2	no	—
189	C₂²×C₁₇	#340	1	1	yes	characteristic
190	C₂²×C₁₇	#340	1	1	yes	characteristic
191	C₂²×C₁₇	C₂×#103	1	1	yes	characteristic
192	C₂×D₁₇	—	2	2	no	—
193	C₂×D₁₇	—	2	2	no	—
194	C₂×D₁₇	—	4	1	no	—
195	C₂×D₁₇	—	4	1	no	—
196	C₂×D₁₇	—	4	1	no	—
197	C₂×D₁₇	—	4	1	no	—
198	C₂×D₁₇	#340	1	1	yes	characteristic
199	C₂×D₁₇	#340	1	1	yes	characteristic
200	C₂×D₁₇	C₂×#103	1	1	yes	characteristic
201	C₂×D₁₇	C₂×#107	1	1	yes	characteristic
202	C₄×C₁₇	#340	1	1	yes	characteristic
203	C₄×C₁₇	#340	1	1	yes	characteristic
204	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
205	C₄×C₁₇	C₂×#102	1	1	yes	characteristic
206	Dic₁₇	#340	1	1	yes	characteristic
207	Dic₁₇	#340	1	1	yes	characteristic
208	Dic₁₇	C₂×#102	1	1	yes	characteristic
209	Dic₁₇	C₂×#106	1	1	yes	characteristic
210	C₂²×M₁₆	—	34	1	no	—
211	C₂²×M₁₆	—	34	1	no	—
212	C₂³×C₈	—	17	1	no	—
213	C₂×M₃₂	—	17	2	no	—
214	C₂×M₃₂	—	17	2	no	—
215	C₂×M₃₂	—	17	2	no	—
216	C₂×M₃₂	—	34	1	no	—
217	C₂×M₃₂	—	34	1	no	—
218	C₂×M₃₂	—	34	1	no	—
219	C₂²×C₁₆	—	34	1	no	—
220	C₂×#108	—	17	2	no	—
221	C₂×#108	—	17	2	no	—
222	C₂×#108	—	17	2	no	—
223	C₂×#108	—	17	1	no	—
224	C₂×#108	—	17	2	no	—
225	C₂×#108	—	17	2	no	—
226	C₂×#108	—	34	1	no	—
227	C₂×#108	—	34	1	no	—
228	C₂×#108	—	34	1	no	—
229	C₂×#108	—	34	1	no	—
230	C₂×#108	—	34	1	no	—
231	C₂×#108	—	34	1	no	—
232	C₂×#108	#595	1	1	yes	characteristic
233	C₂×C₁₇	—	2	1	no	—
234	C₂×C₁₇	—	2	1	no	—
235	C₂×C₁₇	#1388	1	2	yes	complemented
236	C₂×C₁₇	C₂×#340	1	1	yes	characteristic
237	D₁₇	—	2	1	no	—
238	D₁₇	—	2	1	no	—
239	D₁₇	—	2	1	no	—
240	D₁₇	—	2	1	no	—
241	C₂³×C₄	—	17	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	34	2	no	—
244	C₂×M₁₆	—	34	2	no	—
245	C₂×M₁₆	—	34	2	no	—
246	C₂×M₁₆	—	34	2	no	—
247	C₂×M₁₆	—	34	2	no	—
248	C₂×M₁₆	—	34	1	no	—
249	C₂×M₁₆	—	68	1	no	—
250	C₂×M₁₆	—	68	1	no	—
251	C₂×M₁₆	—	68	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	—	68	1	no	—
270	C₂²×C₈	C₂×#595	1	1	yes	characteristic
271	M₃₂	—	17	4	no	—
272	M₃₂	—	34	2	no	—
273	M₃₂	—	34	2	no	—
274	M₃₂	—	34	2	no	—
275	C₂×C₁₆	—	34	2	no	—
276	C₂×C₁₆	—	34	2	no	—
277	C₂×C₁₆	—	34	2	no	—
278	#108	—	2	1	no	—
279	#108	—	17	4	no	—
280	#108	—	17	2	no	—
281	#108	—	34	2	no	—
282	#108	—	34	2	no	—
283	#108	—	34	2	no	—
284	#108	—	34	2	no	—
285	#108	—	34	2	no	—
286	#108	—	34	1	no	—
287	#108	C₂×#595	1	2	yes	—
288	C₁₇	C₂×#1388	1	1	yes	characteristic, complemented, Sylow
289	C₂⁴	—	17	1	no	—
290	C₂²×C₄	—	17	1	no	—
291	C₂²×C₄	—	17	1	no	—
292	C₂²×C₄	—	17	1	no	—
293	C₂²×C₄	—	17	1	no	—
294	C₂²×C₄	—	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	C₂²⋊#595	1	1	yes	characteristic
304	M₁₆	—	2	2	no	—
305	M₁₆	—	4	1	no	—
306	M₁₆	—	34	4	no	—
307	M₁₆	—	34	2	no	—
308	M₁₆	—	68	2	no	—
309	M₁₆	—	68	2	no	—
310	M₁₆	—	68	2	no	—
311	M₁₆	—	68	2	no	—
312	M₁₆	—	68	2	no	—
313	M₁₆	—	68	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	17	1	no	—
316	C₂×C₈	—	17	1	no	—
317	C₂×C₈	—	17	1	no	—
318	C₂×C₈	—	17	1	no	—
319	C₂×C₈	—	17	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	—	68	2	no	—
338	C₂×C₈	—	68	2	no	—
339	C₂×C₈	—	68	2	no	—
340	C₂×C₈	—	68	2	no	—
341	C₂×C₈	—	68	2	no	—
342	C₂×C₈	—	68	1	no	—
343	C₂×C₈	C₄×#595	1	1	yes	characteristic
344	C₂×C₈	C₄×#595	1	1	yes	characteristic
345	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
346	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
347	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
348	C₂×C₈	C₂²×#595	1	1	yes	characteristic
349	C₁₆	—	34	4	no	—
350	C₂³	—	17	1	no	—
351	C₂³	—	17	1	no	—
352	C₂³	—	17	1	no	—
353	C₂³	—	17	1	no	—
354	C₂³	—	17	1	no	—
355	C₂³	—	17	1	no	—
356	C₂³	—	68	2	no	—
357	C₂³	#10587549	1	1	yes	characteristic
358	C₂×C₄	—	17	1	no	—
359	C₂×C₄	—	17	1	no	—
360	C₂×C₄	—	17	1	no	—
361	C₂×C₄	—	17	1	no	—
362	C₂×C₄	—	17	1	no	—
363	C₂×C₄	—	17	1	no	—
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	(C₂×#595)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
382	C₂×C₄	#10587547	1	1	yes	characteristic
383	C₂×C₄	#10587547	1	1	yes	characteristic
384	C₂×C₄	#10587549	1	1	yes	characteristic
385	C₂×C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	17	1	no	—
388	C₈	—	17	1	no	—
389	C₈	—	17	1	no	—
390	C₈	—	17	1	no	—
391	C₈	—	68	4	no	—
392	C₈	—	68	2	no	—
393	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
394	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
395	C₈	C₂×C₄×#595	1	1	yes	characteristic
396	C₈	C₂×C₄⋊#595	1	1	yes	characteristic
397	C₂²	—	2	2	no	—
398	C₂²	—	17	1	no	—
399	C₂²	—	17	1	no	—
400	C₂²	—	17	1	no	—
401	C₂²	—	17	1	no	—
402	C₂²	—	34	2	no	—
403	C₂²	—	34	2	no	—
404	C₂²	—	68	1	no	—
405	C₂²	—	68	1	no	—
406	C₂²	—	68	1	no	—
407	C₂²	—	68	1	no	—
408	C₂²	#11763682	1	1	yes	characteristic
409	C₂²	#11763682	1	1	yes	characteristic
410	C₂²	C₂×#10587549	1	1	yes	characteristic
411	C₄	—	17	1	no	—
412	C₄	—	17	1	no	—
413	C₄	—	17	1	no	—
414	C₄	—	17	1	no	—
415	C₄	#11763682	1	1	yes	characteristic
416	C₄	#11763682	1	1	yes	characteristic
417	C₄	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
418	C₄	C₂×#10587547	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	34	1	no	—
422	C₂	—	34	1	no	—
423	C₂	—	34	1	no	—
424	C₂	—	34	1	no	—
425	C₂	#14543861	1	2	yes	direct product factor
426	C₂	C₂×#11763682	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10587547
commutator	C₈×C₁₇	C₂×C₄²
Frattini	C₂×C₈	C₂²×#595
Fitting	C₂×C₁₇×#108	C₄
socle	C₂²×C₁₇	#340
prime radical	C₂³×D₁₇	Q₁₆
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	C₂×#108	#595
hypocenter	C₁₇	C₂×#1388
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
3. #14543861	C₂	direct (N × H)
235. C₂×C₁₇	#1388	semidirect
288. C₁₇	C₂×#1388	semidirect
425. C₂	#14543861	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#10587530	2
C₂×D₁₇⋊#108	2
#14543861	2
C₂×#108×D₁₇	2
C₂×#1388	17

Subgroups — C2×#14543861 #17960552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543861 #17960552