Subgroups — C₂×#14526896 #16949255

Order 4352.

554 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587490	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10587490	C₂	1	1	yes	maximal, characteristic
3	#14526896	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₇×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63223	—	2	1	no	—
6	C₂²×#63223	—	2	1	no	—
7	C₂×#10587490	—	2	1	no	—
8	C₂×#10587490	—	2	1	no	—
9	C₂×#10587490	—	2	1	no	—
10	C₂×#10587490	—	2	1	no	—
11	C₂×#10587490	—	2	1	no	—
12	C₂×#10587490	—	2	1	no	—
13	C₂×#10587490	C₄	1	2	yes	—
14	C₂×#10587490	C₄	1	2	yes	—
15	C₂×#10587490	C₄	1	2	yes	—
16	C₂×#10587490	C₄	1	2	yes	—
17	C₂×#10587490	C₂²	1	2	yes	—
18	C₂×#10587490	C₂²	1	2	yes	—
19	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×M₃₂	—	2	1	no	—
21	C₂×C₁₇×M₃₂	—	2	1	no	—
22	C₂×C₁₇×M₃₂	—	2	1	no	—
23	C₂×C₁₇×M₃₂	C₄	1	2	yes	—
24	C₂×C₁₇×M₃₂	C₄	1	2	yes	—
25	C₂×C₁₇×M₃₂	C₂²	1	2	yes	—
26	C₂²×C₁₆×C₁₇	—	2	1	no	—
27	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₇	Q₈	1	1	yes	characteristic
40	C₂²×C₈×C₁₇	Q₈	1	1	yes	characteristic
41	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
42	C₂×#63223	—	2	2	no	—
43	C₂×#63223	—	2	2	no	—
44	C₂×#63223	—	2	2	no	—
45	C₂×#63223	—	2	2	no	—
46	C₂×#63223	—	2	2	no	—
47	C₂×#63223	—	2	2	no	—
48	C₂×#63223	—	4	1	no	—
49	C₂×#63223	—	4	1	no	—
50	C₂×#63223	—	4	1	no	—
51	C₂×#63223	—	4	1	no	—
52	C₂×#63223	—	4	1	no	—
53	C₂×#63223	—	4	1	no	—
54	C₂²×#3622	—	4	1	no	—
55	C₂²×#3622	—	4	1	no	—
56	C₁₇×M₃₂	—	2	2	no	—
57	C₁₇×M₃₂	—	2	2	no	—
58	C₁₇×M₃₂	—	2	2	no	—
59	C₁₇×M₃₂	C₂×C₄	1	4	yes	—
60	C₂×C₁₆×C₁₇	—	2	2	no	—
61	C₂×C₁₆×C₁₇	—	2	2	no	—
62	C₂×C₁₆×C₁₇	—	2	2	no	—
63	#10587490	—	2	2	no	—
64	#10587490	—	2	2	no	—
65	#10587490	—	2	2	no	—
66	#10587490	—	2	2	no	—
67	#10587490	—	2	2	no	—
68	#10587490	—	2	2	no	—
69	#10587490	C₂×C₄	1	4	yes	—
70	#10587490	C₂×C₄	1	4	yes	—
71	C₂⁴×C₁₇	Q₁₆	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	D₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	D₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	SD₁₆	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	SD₁₆	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	SD₁₆	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	SD₁₆	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	Q₁₆	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
86	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
87	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
88	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
89	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
90	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₇	C₄⋊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	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
114	#63223	—	2	4	no	—
115	#63223	—	2	4	no	—
116	#63223	—	4	2	no	—
117	#63223	—	4	2	no	—
118	#63223	—	4	2	no	—
119	#63223	—	4	2	no	—
120	#63223	—	4	2	no	—
121	#63223	—	4	2	no	—
122	C₂×#3622	—	4	2	no	—
123	C₂×#3622	—	4	2	no	—
124	C₂×#3622	—	4	2	no	—
125	C₂×#3622	—	4	2	no	—
126	C₂×#3622	—	4	2	no	—
127	C₂×#3622	—	4	2	no	—
128	C₁₆×C₁₇	—	2	4	no	—
129	C₂×#1388	—	17	1	no	maximal, Sylow
130	C₂³×C₁₇	—	4	2	no	—
131	C₂³×C₁₇	#103	1	1	yes	characteristic
132	C₂³×C₁₇	#103	1	1	yes	characteristic
133	C₂³×C₁₇	#103	1	1	yes	characteristic
134	C₂³×C₁₇	#103	1	1	yes	characteristic
135	C₂³×C₁₇	#107	1	1	yes	characteristic
136	C₂³×C₁₇	#107	1	1	yes	characteristic
137	C₂³×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
138	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
143	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
144	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
145	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
146	C₂×C₄×C₁₇	#102	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	#102	1	1	yes	characteristic
150	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
151	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
152	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
153	C₂×C₄×C₁₇	#103	1	1	yes	characteristic
154	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
155	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
156	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
157	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
158	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
159	C₂×C₄×C₁₇	#107	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
166	C₈×C₁₇	#95	1	1	yes	characteristic
167	C₈×C₁₇	#95	1	1	yes	characteristic
168	C₈×C₁₇	#95	1	1	yes	characteristic
169	C₈×C₁₇	#95	1	1	yes	characteristic
170	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
171	C₈×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	#3622	—	4	4	no	—
175	#3622	—	4	4	no	—
176	C₂²×M₃₂	D₁₇	1	1	yes	characteristic
177	C₂²×#108	—	17	1	no	—
178	C₂²×#108	—	17	1	no	—
179	#1388	—	17	4	no	—
180	C₂²×C₁₇	—	2	2	no	—
181	C₂²×C₁₇	—	2	2	no	—
182	C₂²×C₁₇	—	2	2	no	—
183	C₂²×C₁₇	—	4	1	no	—
184	C₂²×C₁₇	—	4	1	no	—
185	C₂²×C₁₇	—	4	1	no	—
186	C₂²×C₁₇	—	4	1	no	—
187	C₂²×C₁₇	#340	1	1	yes	characteristic
188	C₂²×C₁₇	#340	1	1	yes	characteristic
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	C₂²×C₁₇	C₂×#103	1	1	yes	characteristic
193	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
194	C₄×C₁₇	#340	1	1	yes	characteristic
195	C₄×C₁₇	#340	1	1	yes	characteristic
196	C₄×C₁₇	#340	1	1	yes	characteristic
197	C₄×C₁₇	#340	1	1	yes	characteristic
198	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
199	C₄×C₁₇	C₂×#102	1	1	yes	characteristic
200	C₄×C₁₇	C₂×#102	1	1	yes	characteristic
201	C₄×C₁₇	C₂×#106	1	1	yes	characteristic
202	C₂²×M₁₆	—	34	1	no	—
203	C₂²×M₁₆	—	34	1	no	—
204	C₂³×C₈	C₂×D₁₇	1	1	yes	characteristic
205	C₂×M₃₂	—	2	1	no	—
206	C₂×M₃₂	—	2	1	no	—
207	C₂×M₃₂	—	2	1	no	—
208	C₂×M₃₂	Dic₁₇	1	2	yes	—
209	C₂×M₃₂	Dic₁₇	1	2	yes	—
210	C₂×M₃₂	C₂×D₁₇	1	2	yes	—
211	C₂²×C₁₆	—	2	1	no	—
212	C₂×#108	—	17	2	no	—
213	C₂×#108	—	17	2	no	—
214	C₂×#108	—	17	2	no	—
215	C₂×#108	—	17	2	no	—
216	C₂×#108	—	17	2	no	—
217	C₂×#108	—	17	2	no	—
218	C₂×#108	—	34	1	no	—
219	C₂×#108	—	34	1	no	—
220	C₂×#108	—	34	1	no	—
221	C₂×#108	—	34	1	no	—
222	C₂×#108	—	34	1	no	—
223	C₂×#108	—	34	1	no	—
224	C₂×C₁₇	—	2	1	no	—
225	C₂×C₁₇	—	2	1	no	—
226	C₂×C₁₇	—	2	1	no	—
227	C₂×C₁₇	—	2	1	no	—
228	C₂×C₁₇	—	2	1	no	—
229	C₂×C₁₇	—	2	1	no	—
230	C₂×C₁₇	#1388	1	2	yes	complemented
231	C₂×C₁₇	C₂×#340	1	1	yes	characteristic
232	C₂³×C₄	D₆₈	1	1	yes	characteristic
233	C₂×M₁₆	—	34	2	no	—
234	C₂×M₁₆	—	34	2	no	—
235	C₂×M₁₆	—	34	2	no	—
236	C₂×M₁₆	—	34	2	no	—
237	C₂×M₁₆	—	34	2	no	—
238	C₂×M₁₆	—	34	2	no	—
239	C₂×M₁₆	—	68	1	no	—
240	C₂×M₁₆	—	68	1	no	—
241	C₂×M₁₆	—	68	1	no	—
242	C₂×M₁₆	—	68	1	no	—
243	C₂×M₁₆	—	68	1	no	—
244	C₂×M₁₆	—	68	1	no	—
245	C₂²×C₈	—	68	1	no	—
246	C₂²×C₈	—	68	1	no	—
247	C₂²×C₈	Dic₃₄	1	1	yes	characteristic
248	C₂²×C₈	Dic₃₄	1	1	yes	characteristic
249	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
250	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
251	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
252	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
253	C₂²×C₈	D₆₈	1	1	yes	characteristic
254	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
255	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
257	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
258	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
259	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
261	M₃₂	—	2	2	no	—
262	M₃₂	—	2	2	no	—
263	M₃₂	—	2	2	no	—
264	M₃₂	C₂×Dic₁₇	1	4	yes	—
265	C₂×C₁₆	—	2	2	no	—
266	C₂×C₁₆	—	2	2	no	—
267	C₂×C₁₆	—	2	2	no	—
268	#108	—	17	4	no	—
269	#108	—	17	4	no	—
270	#108	—	34	2	no	—
271	#108	—	34	2	no	—
272	#108	—	34	2	no	—
273	#108	—	34	2	no	—
274	#108	—	34	2	no	—
275	#108	—	34	2	no	—
276	C₁₇	C₂×#1388	1	1	yes	characteristic, complemented, Sylow
277	C₂⁴	Dic₆₈	1	1	yes	characteristic
278	C₂²×C₄	#63219	1	1	yes	characteristic
279	C₂²×C₄	#63219	1	1	yes	characteristic
280	C₂²×C₄	#63219	1	1	yes	characteristic
281	C₂²×C₄	#63219	1	1	yes	characteristic
282	C₂²×C₄	D₁₃₆	1	1	yes	characteristic
283	C₂²×C₄	D₁₃₆	1	1	yes	characteristic
284	C₂²×C₄	Dic₆₈	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
286	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
287	C₂²×C₄	#63227	1	1	yes	characteristic
288	C₂²×C₄	#63227	1	1	yes	characteristic
289	C₂²×C₄	#63227	1	1	yes	characteristic
290	C₂²×C₄	#63227	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
292	M₁₆	—	34	4	no	—
293	M₁₆	—	34	4	no	—
294	M₁₆	—	68	2	no	—
295	M₁₆	—	68	2	no	—
296	M₁₆	—	68	2	no	—
297	M₁₆	—	68	2	no	—
298	M₁₆	—	68	2	no	—
299	M₁₆	—	68	2	no	—
300	C₂×C₈	—	68	2	no	—
301	C₂×C₈	—	68	2	no	—
302	C₂×C₈	—	68	2	no	—
303	C₂×C₈	—	68	2	no	—
304	C₂×C₈	—	68	2	no	—
305	C₂×C₈	—	68	2	no	—
306	C₂×C₈	C₄×Dic₁₇	1	1	yes	characteristic
307	C₂×C₈	C₄×Dic₁₇	1	1	yes	characteristic
308	C₂×C₈	C₄×Dic₁₇	1	1	yes	characteristic
309	C₂×C₈	C₄×Dic₁₇	1	1	yes	characteristic
310	C₂×C₈	#63225	1	1	yes	characteristic
311	C₂×C₈	#63225	1	1	yes	characteristic
312	C₂×C₈	#63225	1	1	yes	characteristic
313	C₂×C₈	#63225	1	1	yes	characteristic
314	C₂×C₈	#63225	1	1	yes	characteristic
315	C₂×C₈	#63225	1	1	yes	characteristic
316	C₂×C₈	#63225	1	1	yes	characteristic
317	C₂×C₈	#63225	1	1	yes	characteristic
318	C₂×C₈	C₄⋊Dic₁₇	1	1	yes	characteristic
319	C₂×C₈	C₄⋊Dic₁₇	1	1	yes	characteristic
320	C₂×C₈	#63227	1	1	yes	characteristic
321	C₂×C₈	#63227	1	1	yes	characteristic
322	C₂×C₈	#63227	1	1	yes	characteristic
323	C₂×C₈	#63227	1	1	yes	characteristic
324	C₂×C₈	C₂²⋊Dic₁₇	1	1	yes	characteristic
325	C₂×C₈	C₂²⋊Dic₁₇	1	1	yes	characteristic
326	C₂×C₈	C₂²⋊Dic₁₇	1	1	yes	characteristic
327	C₂×C₈	C₂²⋊Dic₁₇	1	1	yes	characteristic
328	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
330	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
331	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
332	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
334	C₁₆	—	2	4	no	—
335	C₂³	—	4	2	no	—
336	C₂³	#10587487	1	1	yes	characteristic
337	C₂³	#10587487	1	1	yes	characteristic
338	C₂³	#10587487	1	1	yes	characteristic
339	C₂³	#10587487	1	1	yes	characteristic
340	C₂³	#10587489	1	1	yes	characteristic
341	C₂³	#10587489	1	1	yes	characteristic
342	C₂³	C₂×Dic₆₈	1	1	yes	characteristic
343	C₂×C₄	#10587487	1	1	yes	characteristic
344	C₂×C₄	#10587487	1	1	yes	characteristic
345	C₂×C₄	#10587487	1	1	yes	characteristic
346	C₂×C₄	#10587487	1	1	yes	characteristic
347	C₂×C₄	#10587488	1	1	yes	characteristic
348	C₂×C₄	#10587488	1	1	yes	characteristic
349	C₂×C₄	#10587488	1	1	yes	characteristic
350	C₂×C₄	#10587488	1	1	yes	characteristic
351	C₂×C₄	#10587489	1	1	yes	characteristic
352	C₂×C₄	#10587489	1	1	yes	characteristic
353	C₂×C₄	#10587492	1	1	yes	characteristic
354	C₂×C₄	#10587492	1	1	yes	characteristic
355	C₂×C₄	#10587492	1	1	yes	characteristic
356	C₂×C₄	#10587492	1	1	yes	characteristic
357	C₂×C₄	#10587492	1	1	yes	characteristic
358	C₂×C₄	#10587492	1	1	yes	characteristic
359	C₂×C₄	#10587492	1	1	yes	characteristic
360	C₂×C₄	#10587492	1	1	yes	characteristic
361	C₂×C₄	#10587502	1	1	yes	characteristic
362	C₂×C₄	#10587502	1	1	yes	characteristic
363	C₂×C₄	#10587502	1	1	yes	characteristic
364	C₂×C₄	#10587502	1	1	yes	characteristic
365	C₂×C₄	C₂×#63219	1	1	yes	characteristic
366	C₂×C₄	C₂×#63219	1	1	yes	characteristic
367	C₂×C₄	C₂×D₁₃₆	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
369	C₂×C₄	C₂×#63227	1	1	yes	characteristic
370	C₂×C₄	C₂×#63227	1	1	yes	characteristic
371	C₈	—	68	4	no	—
372	C₈	—	68	4	no	—
373	C₈	#10587502	1	1	yes	characteristic
374	C₈	#10587502	1	1	yes	characteristic
375	C₈	#10587502	1	1	yes	characteristic
376	C₈	#10587502	1	1	yes	characteristic
377	C₈	C₂×C₄×Dic₁₇	1	1	yes	characteristic
378	C₈	C₂×#63225	1	1	yes	characteristic
379	C₈	C₂×#63225	1	1	yes	characteristic
380	C₈	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	#11762572	1	1	yes	characteristic
389	C₂²	#11762572	1	1	yes	characteristic
390	C₂²	#11762572	1	1	yes	characteristic
391	C₂²	#11762572	1	1	yes	characteristic
392	C₂²	C₂×#10587487	1	1	yes	characteristic
393	C₂²	C₂×#10587487	1	1	yes	characteristic
394	C₂²	C₂×#10587489	1	1	yes	characteristic
395	C₄	#11762572	1	1	yes	characteristic
396	C₄	#11762572	1	1	yes	characteristic
397	C₄	#11762572	1	1	yes	characteristic
398	C₄	#11762572	1	1	yes	characteristic
399	C₄	C₂×#10587502	1	1	yes	characteristic
400	C₄	C₂×#10587492	1	1	yes	characteristic
401	C₄	C₂×#10587492	1	1	yes	characteristic
402	C₄	C₂×#10587488	1	1	yes	characteristic
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	#14526896	1	2	yes	direct product factor
410	C₂	C₂×#11762572	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10587492
commutator	C₈×C₁₇	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₂²×C₁₇×M₃₂	C₂
socle	C₂²×C₁₇	#340
prime radical	C₂⁴×C₁₇	Q₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	C₂²×M₃₂	D₁₇
hypocenter	C₁₇	C₂×#1388
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
3. #14526896	C₂	direct (N × H)
230. C₂×C₁₇	#1388	semidirect
276. C₁₇	C₂×#1388	semidirect
409. C₂	#14526896	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×#10587490	2
#14526896	2
C₂²×C₁₇×M₃₂	2
C₂×#1388	17

Subgroups — C2×#14526896 #16949255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14526896 #16949255