Subgroups — C₂×#14543835 #17960487

Order 4352.

586 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587538	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10587538	C₂	1	1	yes	maximal, characteristic
3	#14543835	C₂	1	4	yes	maximal, direct product factor
4	C₂×#11762767	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587538	—	2	1	no	—
6	C₂×#10587538	—	2	1	no	—
7	C₂×#10587538	—	2	1	no	—
8	C₂×#10587538	—	2	1	no	—
9	C₂×#10587538	—	2	1	no	—
10	C₂×#10587538	—	2	1	no	—
11	C₂×#10587538	—	2	1	no	—
12	C₂×#10587538	C₄	1	2	yes	complemented
13	C₂×#10587538	C₄	1	2	yes	complemented
14	C₂×#10587538	C₄	1	2	yes	complemented
15	C₂×#10587538	C₂²	1	2	yes	—
16	C₂×#10587538	C₂²	1	2	yes	—
17	C₂²×#63216	—	2	1	no	—
18	C₂²×#63216	C₄	1	2	yes	complemented
19	C₂³×#3622	C₂²	1	1	yes	characteristic
20	C₂×#10587612	C₄	1	1	yes	characteristic
21	#11762767	—	2	1	no	—
22	#11762767	—	2	1	no	—
23	#11762767	C₄	1	2	yes	—
24	#11762767	C₂²	1	2	yes	—
25	C₂×#10587486	—	2	1	no	—
26	C₂×C₈×Dic₁₇	—	2	1	no	—
27	C₂²×M₁₆×C₁₇	C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₂×M₁₆×C₁₇	—	2	1	no	—
30	C₂×M₁₆×C₁₇	—	2	1	no	—
31	C₂×M₁₆×C₁₇	—	2	1	no	—
32	C₂×M₁₆×C₁₇	C₈	1	2	yes	—
33	C₂×M₁₆×C₁₇	C₈	1	2	yes	—
34	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₇	—	2	1	no	—
36	C₂×C₂²⋊Dic₁₇	C₈	1	2	yes	—
37	#10587612	—	2	1	no	—
38	#10587612	—	2	1	no	—
39	#10587612	C₈	1	2	yes	—
40	#10587612	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊Dic₁₇	—	2	1	no	—
42	C₂×C₄×Dic₁₇	—	2	1	no	—
43	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
44	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
45	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
46	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
47	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
48	C₂²×#3622	D₄	1	1	yes	characteristic
49	C₂²×#3622	D₄	1	1	yes	characteristic
50	C₂²×#3622	D₄	1	1	yes	characteristic
51	C₂²×#3622	D₄	1	1	yes	characteristic
52	C₂²×#3622	D₄	1	1	yes	characteristic
53	C₂²×#3622	D₄	1	1	yes	characteristic
54	C₂²×#3622	Q₈	1	1	yes	characteristic
55	C₂²×#3622	Q₈	1	1	yes	characteristic
56	C₂²×#3622	C₂³	1	1	yes	characteristic
57	#10587538	—	2	2	no	—
58	#10587538	—	2	2	no	—
59	#10587538	—	2	2	no	—
60	#10587538	—	2	2	no	—
61	#10587538	—	2	2	no	—
62	#10587538	—	2	2	no	—
63	#10587538	—	2	2	no	—
64	#10587538	C₂×C₄	1	4	yes	complemented
65	C₂×#63216	—	2	2	no	—
66	C₂×#63216	—	2	2	no	—
67	C₂×#63216	—	2	2	no	—
68	C₂×#63216	—	2	2	no	—
69	C₂×#63216	—	2	2	no	—
70	C₂×#63216	C₂×C₄	1	4	yes	complemented
71	#10587486	—	2	2	no	—
72	#10587486	—	2	2	no	—
73	C₈×Dic₁₇	—	2	2	no	—
74	C₈×Dic₁₇	—	2	2	no	—
75	C₂⁴×C₁₇	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂²⋊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	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	M₁₆	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	M₁₆	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	M₁₆	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	M₁₆	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₁₇	—	2	2	no	—
91	M₁₆×C₁₇	—	2	2	no	—
92	M₁₆×C₁₇	—	2	2	no	—
93	M₁₆×C₁₇	—	2	2	no	—
94	M₁₆×C₁₇	C₂×C₈	1	4	yes	—
95	C₂×C₈×C₁₇	—	2	2	no	—
96	C₂×C₈×C₁₇	—	2	2	no	—
97	C₂×C₈×C₁₇	—	2	2	no	—
98	C₂²⋊Dic₁₇	—	2	2	no	—
99	C₂²⋊Dic₁₇	C₂×C₈	1	4	yes	—
100	C₄⋊Dic₁₇	—	2	2	no	—
101	C₄⋊Dic₁₇	—	2	2	no	—
102	C₄×Dic₁₇	—	2	2	no	—
103	C₄×Dic₁₇	—	2	2	no	—
104	C₂×#3622	C₄²	1	1	yes	characteristic
105	C₂×#3622	C₄²	1	1	yes	characteristic
106	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×#3622	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
117	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
118	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
119	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
120	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
121	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
122	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
123	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
124	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
125	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
126	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
127	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
128	C₂×#3622	C₂×D₄	1	1	yes	characteristic
129	C₂×#3622	C₂×D₄	1	1	yes	characteristic
130	C₂×#3622	C₂×D₄	1	1	yes	characteristic
131	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
132	#63216	—	2	4	no	—
133	#63216	—	2	4	no	—
134	C₂×#1378	—	17	1	no	maximal, Sylow
135	C₂³×C₁₇	—	4	2	no	—
136	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
137	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
138	C₂³×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
139	C₂³×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
140	C₂³×C₁₇	C₄⋊C₈	1	1	yes	characteristic
141	C₂³×C₁₇	C₄⋊C₈	1	1	yes	characteristic
142	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₇	#95	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	C₄×C₈	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
149	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
150	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
151	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
152	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
162	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
170	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
171	C₂×Dic₁₇	—	2	4	no	—
172	C₂×Dic₁₇	—	4	4	no	—
173	C₈×C₁₇	—	2	4	no	—
174	#3622	#95	1	1	yes	characteristic
175	#3622	#95	1	1	yes	characteristic
176	#3622	#95	1	1	yes	characteristic
177	#3622	#95	1	1	yes	characteristic
178	#3622	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	#3622	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
181	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×M₃₂	—	17	1	no	—
183	C₂²×M₃₂	—	17	1	no	—
184	C₂×#405	—	17	1	no	—
185	#1378	—	17	4	no	—
186	C₂²×C₁₇	—	2	2	no	—
187	C₂²×C₁₇	—	2	2	no	—
188	C₂²×C₁₇	—	2	2	no	—
189	C₂²×C₁₇	—	4	1	no	—
190	C₂²×C₁₇	—	4	1	no	—
191	C₂²×C₁₇	—	4	1	no	—
192	C₂²×C₁₇	—	4	1	no	—
193	C₂²×C₁₇	#336	1	1	yes	characteristic
194	C₂²×C₁₇	#336	1	1	yes	characteristic
195	C₂²×C₁₇	#336	1	1	yes	characteristic
196	C₂²×C₁₇	#336	1	1	yes	characteristic
197	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
198	C₂²×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
199	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
200	C₄×C₁₇	#336	1	1	yes	characteristic
201	C₄×C₁₇	#336	1	1	yes	characteristic
202	C₄×C₁₇	#336	1	1	yes	characteristic
203	C₄×C₁₇	#336	1	1	yes	characteristic
204	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
205	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
206	C₄×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
207	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
208	Dic₁₇	—	4	4	no	—
209	C₂²×M₁₆	#595	1	1	yes	characteristic
210	C₂³×C₈	—	17	1	no	—
211	C₂×#117	—	17	1	no	—
212	C₂×M₃₂	—	17	2	no	—
213	C₂×M₃₂	—	17	2	no	—
214	C₂×M₃₂	—	17	2	no	—
215	C₂×M₃₂	—	17	2	no	—
216	C₂×M₃₂	—	17	2	no	—
217	C₂×M₃₂	—	34	1	no	—
218	C₂×M₃₂	—	34	1	no	—
219	C₂×M₃₂	—	34	1	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	C₂²×C₁₆	—	34	1	no	—
226	#405	—	17	2	no	—
227	#405	—	17	2	no	—
228	#405	—	34	1	no	—
229	#405	—	34	1	no	—
230	C₂×#97	—	34	1	no	—
231	C₂×C₄×C₈	—	34	1	no	—
232	C₂×C₁₇	—	2	1	no	—
233	C₂×C₁₇	—	2	1	no	—
234	C₂×C₁₇	—	2	1	no	—
235	C₂×C₁₇	—	2	1	no	—
236	C₂×C₁₇	—	2	1	no	—
237	C₂×C₁₇	—	2	1	no	—
238	C₂×C₁₇	#1378	1	2	yes	complemented
239	C₂×C₁₇	C₂×#336	1	1	yes	characteristic
240	C₂³×C₄	C₂×#595	1	1	yes	characteristic
241	C₂×M₁₆	—	2	1	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	#3624	1	2	yes	—
245	C₂×M₁₆	#3624	1	2	yes	—
246	C₂×M₁₆	C₂×#595	1	2	yes	—
247	C₂²×C₈	—	2	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	—	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	#117	—	17	2	no	—
263	#117	—	17	2	no	—
264	#117	—	34	1	no	—
265	#117	—	34	1	no	—
266	C₂×C₄⋊C₄	—	34	1	no	—
267	C₂×C₂²⋊C₄	—	17	2	no	—
268	C₂×C₄²	—	34	1	no	—
269	M₃₂	—	17	4	no	—
270	M₃₂	—	34	2	no	—
271	M₃₂	—	34	2	no	—
272	M₃₂	—	34	2	no	—
273	M₃₂	—	34	2	no	—
274	M₃₂	—	34	2	no	—
275	M₃₂	—	34	2	no	—
276	M₃₂	—	34	2	no	—
277	C₂×C₁₆	—	17	4	no	—
278	C₂×C₁₆	—	34	2	no	—
279	C₂×C₁₆	—	34	2	no	—
280	C₂×C₁₆	—	34	2	no	—
281	C₂×C₁₆	—	34	2	no	—
282	C₂×C₁₆	—	34	2	no	—
283	#97	—	34	2	no	—
284	#97	—	34	2	no	—
285	C₄×C₈	—	34	2	no	—
286	C₄×C₈	—	34	2	no	—
287	C₁₇	C₂×#1378	1	1	yes	characteristic, complemented, Sylow
288	C₂⁴	#63242	1	1	yes	characteristic
289	C₂²×C₄	—	34	2	no	—
290	C₂²×C₄	#63242	1	1	yes	characteristic
291	C₂²×C₄	#63243	1	1	yes	characteristic
292	C₂²×C₄	#63243	1	1	yes	characteristic
293	C₂²×C₄	C₄×#595	1	1	yes	characteristic
294	C₂²×C₄	C₄×#595	1	1	yes	characteristic
295	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
296	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
297	C₂²×C₄	C₂×#3624	1	1	yes	characteristic
298	C₂²×C₄	C₂×#3624	1	1	yes	characteristic
299	C₂²×C₄	#63247	1	1	yes	characteristic
300	C₂²×C₄	#63247	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊#595	1	1	yes	characteristic
302	C₂²×C₄	C₂²⋊#595	1	1	yes	characteristic
303	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	C₂×#3624	1	4	yes	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	17	1	no	—
312	C₂×C₈	—	17	1	no	—
313	C₂×C₈	—	17	1	no	—
314	C₂×C₈	—	17	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	—	17	1	no	—
338	C₂×C₈	—	17	1	no	—
339	C₄⋊C₄	—	34	2	no	—
340	C₄⋊C₄	—	34	2	no	—
341	C₂²⋊C₄	—	17	4	no	—
342	C₂²⋊C₄	—	34	2	no	—
343	C₄²	—	34	2	no	—
344	C₄²	—	34	2	no	—
345	C₁₆	—	34	4	no	—
346	C₁₆	—	34	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₄×#3624	1	1	yes	characteristic
349	C₂³	C₄×#3624	1	1	yes	characteristic
350	C₂³	#10587543	1	1	yes	characteristic
351	C₂³	#10587543	1	1	yes	characteristic
352	C₂³	#10587544	1	1	yes	characteristic
353	C₂³	#10587544	1	1	yes	characteristic
354	C₂³	C₂×#63242	1	1	yes	characteristic
355	C₂×C₄	—	34	4	no	—
356	C₂×C₄	—	68	4	no	—
357	C₂×C₄	C₄×#3624	1	1	yes	characteristic
358	C₂×C₄	C₄×#3624	1	1	yes	characteristic
359	C₂×C₄	C₄⋊#3624	1	1	yes	characteristic
360	C₂×C₄	C₄⋊#3624	1	1	yes	characteristic
361	C₂×C₄	C₄⋊#3624	1	1	yes	characteristic
362	C₂×C₄	C₄⋊#3624	1	1	yes	characteristic
363	C₂×C₄	#10587542	1	1	yes	characteristic
364	C₂×C₄	#10587542	1	1	yes	characteristic
365	C₂×C₄	#10587542	1	1	yes	characteristic
366	C₂×C₄	#10587542	1	1	yes	characteristic
367	C₂×C₄	#10587543	1	1	yes	characteristic
368	C₂×C₄	#10587543	1	1	yes	characteristic
369	C₂×C₄	#10587544	1	1	yes	characteristic
370	C₂×C₄	#10587544	1	1	yes	characteristic
371	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
372	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
374	C₂×C₄	(C₂×#595)⋊C₄	1	1	yes	characteristic
375	C₂×C₄	C₂²⋊#3624	1	1	yes	characteristic
376	C₂×C₄	C₂²⋊#3624	1	1	yes	characteristic
377	C₂×C₄	C₂²⋊#3624	1	1	yes	characteristic
378	C₂×C₄	C₂²⋊#3624	1	1	yes	characteristic
379	C₂×C₄	C₂×#63243	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
382	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
383	C₂×C₄	C₂×#63247	1	1	yes	characteristic
384	C₂×C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	17	1	no	—
387	C₈	—	17	1	no	—
388	C₈	—	17	1	no	—
389	C₈	—	17	1	no	—
390	C₈	—	17	1	no	—
391	C₈	—	17	1	no	—
392	C₈	—	17	1	no	—
393	C₈	—	17	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	#11763675	1	1	yes	characteristic
402	C₂²	#11763675	1	1	yes	characteristic
403	C₂²	#11763675	1	1	yes	characteristic
404	C₂²	#11763675	1	1	yes	characteristic
405	C₂²	C₂×C₄×#3624	1	1	yes	characteristic
406	C₂²	C₂×#10587543	1	1	yes	characteristic
407	C₂²	C₂×#10587544	1	1	yes	characteristic
408	C₄	—	68	4	no	—
409	C₄	#11763675	1	1	yes	characteristic
410	C₄	#11763675	1	1	yes	characteristic
411	C₄	#11763675	1	1	yes	characteristic
412	C₄	#11763675	1	1	yes	characteristic
413	C₄	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
414	C₄	C₂×#10587542	1	1	yes	characteristic
415	C₄	C₂×C₂²⋊#3624	1	1	yes	characteristic
416	C₄	C₂×C₄⋊#3624	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	#14543835	1	2	yes	direct product factor
424	C₂	C₂×#11763675	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×#595)⋊C₄
commutator	C₂²×C₁₇	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₂²×M₁₆×C₁₇	C₄
socle	C₂²×C₁₇	#336
prime radical	C₂⁴×C₁₇	C₂×C₈
cosocle	C₂²×#3622	C₂³
hypercenter	C₂²×M₁₆	#595
hypocenter	C₁₇	C₂×#1378
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
3. #14543835	C₂	direct (N × H)
12. C₂×#10587538	C₄	semidirect
13. C₂×#10587538	C₄	semidirect
14. C₂×#10587538	C₄	semidirect
18. C₂²×#63216	C₄	semidirect
64. #10587538	C₂×C₄	semidirect
70. C₂×#63216	C₂×C₄	semidirect
238. C₂×C₁₇	#1378	semidirect
287. C₁₇	C₂×#1378	semidirect
423. C₂	#14543835	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×#10587538	2
#14543835	2
C₂×#11762767	2
C₂×#1378	17

Subgroups — C2×#14543835 #17960487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543835 #17960487