Subgroups — C₂×#14526681 #16924549

Order 4352.

666 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762862	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762833	C₂	1	1	yes	maximal, characteristic
3	#14526681	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63223	—	2	1	no	—
6	#11762862	—	2	1	no	—
7	#11762862	—	2	1	no	—
8	#11762862	C₄	1	2	yes	—
9	#11762862	C₂²	1	2	yes	—
10	#11762833	—	2	1	no	—
11	#11762833	—	2	1	no	—
12	#11762833	C₄	1	2	yes	—
13	#11762833	C₂²	1	2	yes	—
14	C₂×C₄⋊#3622	—	2	1	no	—
15	C₂×C₄⋊#3622	—	2	1	no	—
16	C₂×C₄⋊#3622	C₄	1	2	yes	—
17	C₂×C₂²⋊#3622	C₄	1	2	yes	—
18	C₂×C₄×#3622	—	2	1	no	—
19	C₂³×C₈×C₁₇	—	2	1	no	—
20	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
22	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
23	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
24	C₂×C₁₇×C₄⋊C₈	C₄	1	2	yes	—
25	C₂×C₁₇×C₄⋊C₈	C₄	1	2	yes	—
26	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₇	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₇	—	2	2	no	—
31	C₂²×C₈×C₁₇	—	2	2	no	—
32	C₂²×C₈×C₁₇	—	2	2	no	—
33	C₂²×C₈×C₁₇	—	4	2	no	—
34	C₂²×C₈×C₁₇	—	4	2	no	—
35	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×#63223	—	2	2	no	—
48	C₂×#63223	—	2	2	no	—
49	C₂×#63223	—	4	2	no	—
50	C₂×#63223	—	4	2	no	—
51	C₂²×#3622	—	2	2	no	—
52	C₂²×#3622	—	2	2	no	—
53	C₁₇×C₄⋊C₈	—	2	2	no	—
54	C₁₇×C₄⋊C₈	—	2	2	no	—
55	C₁₇×C₄⋊C₈	—	2	2	no	—
56	C₁₇×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₂²⋊#3622	—	2	2	no	—
58	C₂²⋊#3622	C₂×C₄	1	4	yes	—
59	C₄⋊#3622	—	2	2	no	—
60	C₄⋊#3622	—	2	2	no	—
61	C₄⋊#3622	—	2	2	no	—
62	C₄⋊#3622	—	2	2	no	—
63	C₄⋊#3622	—	2	2	no	—
64	C₄⋊#3622	C₂×C₄	1	4	yes	—
65	C₄×#3622	—	2	2	no	—
66	C₄×#3622	—	2	2	no	—
67	C₂⁴×C₁₇	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₇	—	2	4	no	—
69	C₂²×C₄×C₁₇	—	4	2	no	—
70	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄⋊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	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	D₈	1	2	yes	—
86	C₂²×C₄×C₁₇	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₁₇	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₁₇	Q₁₆	1	2	yes	—
89	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₈×C₁₇	—	2	4	no	—
93	C₂×C₈×C₁₇	—	4	4	no	—
94	C₂×C₈×C₁₇	—	4	4	no	—
95	C₂×C₈×C₁₇	—	4	2	no	—
96	C₂×C₈×C₁₇	—	4	2	no	—
97	C₄²×C₁₇	C₄²	1	1	yes	characteristic
98	C₄²×C₁₇	C₄²	1	1	yes	characteristic
99	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
113	#63223	—	4	4	no	—
114	#63223	—	4	2	no	—
115	#63223	—	4	2	no	—
116	C₂×#3622	—	2	4	no	—
117	C₂×#3622	—	2	4	no	—
118	C₂×#3622	—	4	4	no	—
119	C₂×#3622	—	4	4	no	—
120	C₂×#1301	—	17	1	no	maximal, Sylow
121	C₂³×C₁₇	—	2	2	no	—
122	C₂³×C₁₇	—	2	2	no	—
123	C₂³×C₁₇	#95	1	1	yes	characteristic
124	C₂³×C₁₇	#95	1	1	yes	characteristic
125	C₂³×C₁₇	#106	1	2	yes	—
126	C₂³×C₁₇	#107	1	2	yes	—
127	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₇	—	2	2	no	—
129	C₂×C₄×C₁₇	—	2	2	no	—
130	C₂×C₄×C₁₇	—	2	2	no	—
131	C₂×C₄×C₁₇	—	2	2	no	—
132	C₂×C₄×C₁₇	—	2	2	no	—
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	4	1	no	—
136	C₂×C₄×C₁₇	—	4	1	no	—
137	C₂×C₄×C₁₇	—	4	1	no	—
138	C₂×C₄×C₁₇	—	4	1	no	—
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	#95	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	#102	1	2	yes	—
146	C₂×C₄×C₁₇	#102	1	2	yes	—
147	C₂×C₄×C₁₇	#102	1	2	yes	—
148	C₂×C₄×C₁₇	#102	1	2	yes	—
149	C₂×C₄×C₁₇	#103	1	2	yes	—
150	C₂×C₄×C₁₇	#103	1	2	yes	—
151	C₂×C₄×C₁₇	#103	1	2	yes	—
152	C₂×C₄×C₁₇	#103	1	2	yes	—
153	C₂×C₄×C₁₇	#106	1	2	yes	—
154	C₂×C₄×C₁₇	#107	1	2	yes	—
155	C₂×C₄×C₁₇	#108	1	4	yes	—
156	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
166	C₈×C₁₇	—	4	4	no	—
167	#3622	—	4	4	no	—
168	#3622	—	4	4	no	—
169	C₂×#431	—	17	1	no	—
170	C₂×#423	—	17	1	no	—
171	C₂²×C₄⋊C₈	D₁₇	1	1	yes	characteristic
172	#1301	—	17	4	no	—
173	C₂²×C₁₇	—	2	4	no	—
174	C₂²×C₁₇	—	2	4	no	—
175	C₂²×C₁₇	—	2	1	no	—
176	C₂²×C₁₇	—	2	1	no	—
177	C₂²×C₁₇	—	2	1	no	—
178	C₂²×C₁₇	—	2	1	no	—
179	C₂²×C₁₇	#340	1	2	yes	—
180	C₂²×C₁₇	#340	1	2	yes	—
181	C₂²×C₁₇	#341	1	2	yes	—
182	C₂²×C₁₇	#344	1	2	yes	—
183	C₂²×C₁₇	C₂×#95	1	1	yes	characteristic
184	C₂²×C₁₇	C₂×#106	1	1	yes	characteristic
185	C₂²×C₁₇	C₂×#107	1	1	yes	characteristic
186	C₄×C₁₇	—	2	1	no	—
187	C₄×C₁₇	—	2	1	no	—
188	C₄×C₁₇	—	2	1	no	—
189	C₄×C₁₇	—	2	1	no	—
190	C₄×C₁₇	—	2	1	no	—
191	C₄×C₁₇	—	2	1	no	—
192	C₄×C₁₇	#340	1	2	yes	—
193	C₄×C₁₇	#340	1	2	yes	—
194	C₄×C₁₇	#341	1	2	yes	—
195	C₄×C₁₇	C₂×#102	1	1	yes	characteristic
196	C₄×C₁₇	C₂×#102	1	1	yes	characteristic
197	C₄×C₁₇	C₂×#103	1	1	yes	characteristic
198	C₄×C₁₇	C₂×#103	1	1	yes	characteristic
199	C₄×C₁₇	C₂×#108	1	2	yes	—
200	C₂²×M₁₆	—	34	1	no	—
201	C₂³×C₈	—	2	1	no	—
202	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
203	#431	—	17	2	no	—
204	#431	—	17	2	no	—
205	#431	—	34	1	no	—
206	#431	—	34	1	no	—
207	#423	—	17	2	no	—
208	#423	—	17	2	no	—
209	#423	—	34	1	no	—
210	#423	—	34	1	no	—
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	—	2	1	no	—
213	C₂×C₄⋊C₈	—	2	1	no	—
214	C₂×C₄⋊C₈	—	17	2	no	—
215	C₂×C₄⋊C₈	—	34	1	no	—
216	C₂×C₄⋊C₈	—	34	1	no	—
217	C₂×C₄⋊C₈	Dic₁₇	1	2	yes	—
218	C₂×C₄⋊C₈	Dic₁₇	1	2	yes	—
219	C₂×C₄⋊C₈	C₂×D₁₇	1	2	yes	—
220	C₂×C₂²⋊C₈	—	17	2	no	—
221	C₂×C₄×C₈	—	34	1	no	—
222	C₂×C₁₇	—	2	2	no	—
223	C₂×C₁₇	—	2	1	no	—
224	C₂×C₁₇	—	2	1	no	—
225	C₂×C₁₇	#1301	1	4	yes	complemented
226	C₂×C₁₇	C₂×#340	1	1	yes	characteristic
227	C₂×C₁₇	C₂×#341	1	1	yes	characteristic
228	C₂×C₁₇	C₂×#344	1	1	yes	characteristic
229	C₂³×C₄	Dic₃₄	1	1	yes	characteristic
230	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
231	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
232	C₂×M₁₆	—	34	2	no	—
233	C₂×M₁₆	—	34	2	no	—
234	C₂×M₁₆	—	68	2	no	—
235	C₂×M₁₆	—	68	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	4	2	no	—
240	C₂²×C₈	—	4	2	no	—
241	C₂²×C₈	—	34	2	no	—
242	C₂²×C₈	—	34	2	no	—
243	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
247	C₂×C₄²	D₆₈	1	1	yes	characteristic
248	C₂×C₄²	D₆₈	1	1	yes	characteristic
249	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
254	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	17	4	no	—
259	C₄⋊C₈	—	34	2	no	—
260	C₄⋊C₈	—	34	2	no	—
261	C₄⋊C₈	—	34	2	no	—
262	C₄⋊C₈	—	34	2	no	—
263	C₄⋊C₈	—	34	2	no	—
264	C₄⋊C₈	C₂×Dic₁₇	1	4	yes	—
265	C₂²⋊C₈	—	17	4	no	—
266	C₂²⋊C₈	—	34	2	no	—
267	C₄×C₈	—	34	2	no	—
268	C₄×C₈	—	34	2	no	—
269	C₁₇	C₂×#1301	1	1	yes	characteristic, complemented, Sylow
270	C₂⁴	#63225	1	1	yes	characteristic
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
274	C₂²×C₄	C₄×Dic₁₇	1	1	yes	characteristic
275	C₂²×C₄	#63225	1	1	yes	characteristic
276	C₂²×C₄	#63225	1	1	yes	characteristic
277	C₂²×C₄	#63225	1	1	yes	characteristic
278	C₂²×C₄	#63225	1	1	yes	characteristic
279	C₂²×C₄	#63225	1	1	yes	characteristic
280	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊Dic₁₇	1	1	yes	characteristic
282	C₂²×C₄	#63227	1	1	yes	characteristic
283	C₂²×C₄	#63227	1	1	yes	characteristic
284	C₂²×C₄	#63227	1	1	yes	characteristic
285	C₂²×C₄	#63227	1	1	yes	characteristic
286	C₂²×C₄	#63228	1	2	yes	—
287	C₂²×C₄	#63229	1	2	yes	—
288	C₂²×C₄	#63230	1	2	yes	—
289	C₂²×C₄	#63231	1	2	yes	—
290	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
295	M₁₆	—	68	4	no	—
296	M₁₆	—	68	2	no	—
297	M₁₆	—	68	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	34	4	no	—
304	C₂×C₈	—	34	4	no	—
305	C₂×C₈	—	68	4	no	—
306	C₂×C₈	—	68	4	no	—
307	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
308	C₄²	C₄×Dic₁₇	1	1	yes	characteristic
309	C₄²	#63225	1	1	yes	characteristic
310	C₄²	#63225	1	1	yes	characteristic
311	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
312	C₄²	C₄⋊Dic₁₇	1	1	yes	characteristic
313	C₄²	#63227	1	1	yes	characteristic
314	C₄²	#63227	1	1	yes	characteristic
315	C₄²	#63227	1	1	yes	characteristic
316	C₄²	#63227	1	1	yes	characteristic
317	C₄²	C₂²⋊Dic₁₇	1	1	yes	characteristic
318	C₄²	C₂²⋊Dic₁₇	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
320	C₄²	C₂×D₆₈	1	1	yes	characteristic
321	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
322	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	#10587478	1	2	yes	—
326	C₂³	#10587479	1	2	yes	—
327	C₂³	#10587502	1	1	yes	characteristic
328	C₂³	#10587502	1	1	yes	characteristic
329	C₂³	C₂×#63225	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	#10587478	1	2	yes	—
342	C₂×C₄	#10587479	1	2	yes	—
343	C₂×C₄	#10587480	1	2	yes	—
344	C₂×C₄	#10587480	1	2	yes	—
345	C₂×C₄	#10587481	1	2	yes	—
346	C₂×C₄	#10587481	1	2	yes	—
347	C₂×C₄	#10587490	1	4	yes	—
348	C₂×C₄	#10587502	1	1	yes	characteristic
349	C₂×C₄	#10587502	1	1	yes	characteristic
350	C₂×C₄	#10587502	1	1	yes	characteristic
351	C₂×C₄	#10587502	1	1	yes	characteristic
352	C₂×C₄	#10587502	1	1	yes	characteristic
353	C₂×C₄	#10587502	1	1	yes	characteristic
354	C₂×C₄	#10587503	1	2	yes	—
355	C₂×C₄	#10587503	1	2	yes	—
356	C₂×C₄	#10587506	1	2	yes	—
357	C₂×C₄	#10587506	1	2	yes	—
358	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#63225	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
361	C₂×C₄	C₂×#63227	1	1	yes	characteristic
362	C₂×C₄	C₂×#63227	1	1	yes	characteristic
363	C₂×C₄	C₂×#63228	1	1	yes	characteristic
364	C₂×C₄	C₂×#63229	1	1	yes	characteristic
365	C₂×C₄	C₂×#63230	1	1	yes	characteristic
366	C₂×C₄	C₂×#63231	1	1	yes	characteristic
367	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₈	—	68	4	no	—
370	C₈	—	68	4	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	#11762571	1	2	yes	—
378	C₂²	#11762571	1	2	yes	—
379	C₂²	#11762574	1	2	yes	—
380	C₂²	#11762581	1	2	yes	—
381	C₂²	C₂×#10587502	1	1	yes	characteristic
382	C₂²	C₂×#10587479	1	1	yes	characteristic
383	C₂²	C₂×#10587478	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	#11762571	1	2	yes	—
391	C₄	#11762571	1	2	yes	—
392	C₄	#11762574	1	2	yes	—
393	C₄	C₂×#10587480	1	1	yes	characteristic
394	C₄	C₂×#10587503	1	1	yes	characteristic
395	C₄	C₂×#10587481	1	1	yes	characteristic
396	C₄	C₂×#10587506	1	1	yes	characteristic
397	C₄	C₂×#10587490	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	#14526681	1	4	yes	direct product factor
402	C₂	C₂×#11762571	1	1	yes	characteristic
403	C₂	C₂×#11762574	1	1	yes	characteristic
404	C₂	C₂×#11762581	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#63227
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₂²×C₁₇×C₄⋊C₈	C₂
socle	C₂³×C₁₇	#95
prime radical	C₂⁴×C₁₇	C₄⋊C₄
cosocle	C₂×C₄²×C₁₇	C₂³
hypercenter	C₂²×C₄⋊C₈	D₁₇
hypocenter	C₁₇	C₂×#1301
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #14526681	C₂	direct (N × H)
225. C₂×C₁₇	#1301	semidirect
269. C₁₇	C₂×#1301	semidirect
401. C₂	#14526681	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×#11762862	2
C₂×#11762833	2
#14526681	2
C₂²×C₁₇×C₄⋊C₈	2
C₂×#1301	17

Subgroups — C2×#14526681 #16924549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14526681 #16924549