Subgroups — C₂×C₁₇×#2297 #16891768

Order 4352.

6174 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#2297	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₇×#391	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#390	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₇×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₁₇	C₂	1	4	yes	maximal, complemented
9	C₂²×#41×C₁₇	—	2	8	no	—
10	C₂²×#41×C₁₇	—	2	8	no	—
11	C₂²×#41×C₁₇	C₄	1	16	yes	complemented
12	C₂²×#41×C₁₇	C₂²	1	8	yes	—
13	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₇	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₁₇	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×#117	—	2	8	no	—
20	C₂×C₁₇×#117	C₂²	1	8	yes	complemented
21	C₂²×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	8	yes	—
23	C₂²×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₇	—	2	8	no	—
25	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₇	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₇	C₂²	1	8	yes	complemented
29	C₁₇×#391	C₂²	1	16	yes	complemented
30	C₁₇×#390	C₂²	1	16	yes	complemented
31	C₁₇×#386	C₂²	1	32	yes	complemented
32	C₄×C₂²⋊C₄×C₁₇	C₂²	1	32	yes	complemented
33	C₂×C₁₇×#95	C₂²	1	8	yes	—
34	C₂⁵×C₁₇	C₂³	1	2	yes	—
35	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
36	C₂×#41×C₁₇	—	2	128	no	—
37	C₂×#41×C₁₇	—	2	32	no	—
38	C₂×#41×C₁₇	—	2	32	no	—
39	C₂×#41×C₁₇	C₂×C₄	1	64	yes	complemented
40	C₂²×Q₈×C₁₇	—	2	4	no	—
41	C₂²×Q₈×C₁₇	—	2	4	no	—
42	C₂²×Q₈×C₁₇	C₂×C₄	1	8	yes	complemented
43	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
44	C₂²×D₄×C₁₇	—	2	8	no	—
45	C₂²×D₄×C₁₇	—	2	8	no	—
46	C₂²×D₄×C₁₇	—	2	4	no	—
47	C₂²×D₄×C₁₇	—	2	4	no	—
48	C₂²×D₄×C₁₇	C₂×C₄	1	16	yes	—
49	C₂²×D₄×C₁₇	C₂×C₄	1	8	yes	complemented
50	C₂²×D₄×C₁₇	C₂³	1	8	yes	—
51	C₂²×D₄×C₁₇	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₇	—	2	8	no	—
53	C₂³×C₄×C₁₇	—	2	8	no	—
54	C₂³×C₄×C₁₇	—	2	8	no	—
55	C₂³×C₄×C₁₇	—	2	16	no	—
56	C₂³×C₄×C₁₇	C₂×C₄	1	8	yes	—
57	C₂³×C₄×C₁₇	C₂×C₄	1	16	yes	complemented
58	C₂³×C₄×C₁₇	D₄	1	8	yes	—
59	C₂³×C₄×C₁₇	D₄	1	8	yes	—
60	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₇	C₂³	1	8	yes	—
62	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₇	C₂³	1	8	yes	—
64	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
68	C₁₇×#117	—	2	32	no	—
69	C₂×C₄⋊C₄×C₁₇	—	2	8	no	—
70	C₂×C₄⋊C₄×C₁₇	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₁₇	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₁₇	—	2	32	no	—
73	C₂×C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₁₇	C₂³	1	32	yes	—
75	C₂×C₄²×C₁₇	—	2	8	no	—
76	C₂×C₄²×C₁₇	—	2	8	no	—
77	C₂×C₄²×C₁₇	—	2	32	no	—
78	C₂×C₄²×C₁₇	—	2	8	no	—
79	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
80	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
81	C₂×C₄²×C₁₇	C₂³	1	8	yes	—
82	C₁₇×#95	C₂³	1	32	yes	—
83	C₂⁴×C₁₇	—	2	8	no	—
84	C₂⁴×C₁₇	—	2	4	no	—
85	C₂⁴×C₁₇	—	2	4	no	—
86	C₂⁴×C₁₇	—	2	16	no	—
87	C₂⁴×C₁₇	C₂²×C₄	1	8	yes	—
88	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
89	C₂⁴×C₁₇	C₂×D₄	1	4	yes	—
90	C₂⁴×C₁₇	C₂×D₄	1	4	yes	—
91	C₂⁴×C₁₇	C₂⁴	1	4	yes	—
92	C₂⁴×C₁₇	C₂⁴	1	2	yes	—
93	C₂⁴×C₁₇	C₂⁴	1	1	yes	characteristic
94	#41×C₁₇	—	2	256	no	—
95	C₂×Q₈×C₁₇	—	2	32	no	—
96	C₂×Q₈×C₁₇	—	2	8	no	—
97	C₂×Q₈×C₁₇	—	2	8	no	—
98	C₂×Q₈×C₁₇	C₂²×C₄	1	16	yes	complemented
99	C₂×D₄×C₁₇	—	2	64	no	—
100	C₂×D₄×C₁₇	—	2	16	no	—
101	C₂×D₄×C₁₇	—	2	16	no	—
102	C₂×D₄×C₁₇	—	2	32	no	—
103	C₂×D₄×C₁₇	—	2	8	no	—
104	C₂×D₄×C₁₇	—	2	8	no	—
105	C₂×D₄×C₁₇	C₂²×C₄	1	32	yes	—
106	C₂×D₄×C₁₇	C₂²×C₄	1	16	yes	complemented
107	C₂²×C₄×C₁₇	—	2	64	no	—
108	C₂²×C₄×C₁₇	—	2	4	no	—
109	C₂²×C₄×C₁₇	—	2	4	no	—
110	C₂²×C₄×C₁₇	—	2	16	no	—
111	C₂²×C₄×C₁₇	—	2	8	no	—
112	C₂²×C₄×C₁₇	—	2	8	no	—
113	C₂²×C₄×C₁₇	—	2	64	no	—
114	C₂²×C₄×C₁₇	—	2	16	no	—
115	C₂²×C₄×C₁₇	—	2	16	no	—
116	C₂²×C₄×C₁₇	—	2	32	no	—
117	C₂²×C₄×C₁₇	—	2	8	no	—
118	C₂²×C₄×C₁₇	—	2	16	no	—
119	C₂²×C₄×C₁₇	C₂²⋊C₄	1	64	yes	complemented
120	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
121	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₇	C₂²×C₄	1	16	yes	—
124	C₂²×C₄×C₁₇	C₂²×C₄	1	32	yes	complemented
125	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₇	C₂×D₄	1	16	yes	—
130	C₂²×C₄×C₁₇	C₂×D₄	1	16	yes	—
131	C₂²×C₄×C₁₇	#41	1	16	yes	complemented
132	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
133	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
135	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
137	C₄⋊C₄×C₁₇	—	2	16	no	—
138	C₂²⋊C₄×C₁₇	—	2	16	no	—
139	C₂²⋊C₄×C₁₇	—	2	64	no	—
140	C₄²×C₁₇	—	2	16	no	—
141	C₄²×C₁₇	—	2	16	no	—
142	C₄²×C₁₇	—	2	16	no	—
143	C₂×#2297	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₁₇	—	2	16	no	—
145	C₂³×C₁₇	—	2	16	no	—
146	C₂³×C₁₇	—	2	16	no	—
147	C₂³×C₁₇	—	2	8	no	—
148	C₂³×C₁₇	—	2	16	no	—
149	C₂³×C₁₇	—	2	32	no	—
150	C₂³×C₁₇	—	2	4	no	—
151	C₂³×C₁₇	—	2	4	no	—
152	C₂³×C₁₇	—	2	16	no	—
153	C₂³×C₁₇	—	4	16	no	—
154	C₂³×C₁₇	—	4	16	no	—
155	C₂³×C₁₇	C₂×C₂²⋊C₄	1	16	yes	—
156	C₂³×C₁₇	C₂³×C₄	1	8	yes	—
157	C₂³×C₁₇	C₂³×C₄	1	4	yes	—
158	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
159	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
160	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
161	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
162	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
163	C₂³×C₁₇	C₂×#41	1	8	yes	—
164	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
165	Q₈×C₁₇	—	2	32	no	—
166	D₄×C₁₇	—	2	64	no	—
167	D₄×C₁₇	—	2	32	no	—
168	C₂×C₄×C₁₇	—	2	64	no	—
169	C₂×C₄×C₁₇	—	2	16	no	—
170	C₂×C₄×C₁₇	—	2	32	no	—
171	C₂×C₄×C₁₇	—	2	8	no	—
172	C₂×C₄×C₁₇	—	2	4	no	—
173	C₂×C₄×C₁₇	—	2	4	no	—
174	C₂×C₄×C₁₇	—	2	8	no	—
175	C₂×C₄×C₁₇	—	2	64	no	—
176	C₂×C₄×C₁₇	—	2	8	no	—
177	C₂×C₄×C₁₇	—	2	16	no	—
178	C₂×C₄×C₁₇	—	4	16	no	—
179	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	16	yes	—
180	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	16	yes	—
181	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	64	yes	complemented
182	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
183	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
184	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
185	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
188	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₁₇	C₂×#41	1	16	yes	complemented
190	C₂³×#41	C₂×C₁₇	1	1	yes	characteristic
191	C₂²×#117	C₂×C₁₇	1	1	yes	characteristic, complemented
192	C₂³×C₄²	C₂×C₁₇	1	1	yes	characteristic, complemented
193	#2297	C₂×C₁₇	1	16	yes	direct product factor
194	C₂×#391	C₂×C₁₇	1	2	yes	complemented
195	C₂×#390	C₂×C₁₇	1	2	yes	complemented
196	C₂×#386	C₂×C₁₇	1	4	yes	complemented
197	C₂×C₄×C₂²⋊C₄	C₂×C₁₇	1	4	yes	complemented
198	C₂²×C₁₇	—	2	8	no	—
199	C₂²×C₁₇	—	2	8	no	—
200	C₂²×C₁₇	—	2	8	no	—
201	C₂²×C₁₇	—	2	32	no	—
202	C₂²×C₁₇	—	2	8	no	—
203	C₂²×C₁₇	—	2	16	no	—
204	C₂²×C₁₇	—	4	8	no	—
205	C₂²×C₁₇	—	4	8	no	—
206	C₂²×C₁₇	—	4	32	no	—
207	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	8	yes	—
208	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	4	yes	—
209	C₂²×C₁₇	C₄×#41	1	8	yes	—
210	C₂²×C₁₇	#525	1	8	yes	—
211	C₂²×C₁₇	#532	1	8	yes	—
212	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
213	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
214	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
215	C₂²×C₁₇	C₂²×#41	1	4	yes	—
216	C₄×C₁₇	—	2	8	no	—
217	C₄×C₁₇	—	2	16	no	—
218	C₄×C₁₇	—	4	8	no	—
219	C₄×C₁₇	C₂²×C₂²⋊C₄	1	8	yes	—
220	C₄×C₁₇	C₂²×C₂²⋊C₄	1	8	yes	—
221	C₂²×#41	—	2	8	no	—
222	C₂²×#41	—	2	8	no	—
223	C₂²×#41	C₄×C₁₇	1	16	yes	complemented
224	C₂²×#41	C₂²×C₁₇	1	8	yes	—
225	C₂³×Q₈	C₂²×C₁₇	1	1	yes	characteristic
226	C₂³×D₄	C₂²×C₁₇	1	2	yes	—
227	C₂³×D₄	C₂²×C₁₇	1	1	yes	characteristic
228	C₂⁴×C₄	C₂²×C₁₇	1	2	yes	—
229	C₂⁴×C₄	C₂²×C₁₇	1	2	yes	—
230	C₂⁴×C₄	C₂²×C₁₇	1	1	yes	characteristic
231	C₂×#117	—	2	8	no	—
232	C₂×#117	C₂²×C₁₇	1	8	yes	complemented
233	C₂²×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₁₇	1	8	yes	—
236	C₂²×C₄²	—	2	8	no	—
237	C₂²×C₄²	C₂²×C₁₇	1	2	yes	—
238	C₂²×C₄²	C₂²×C₁₇	1	2	yes	—
239	C₂²×C₄²	C₂²×C₁₇	1	2	yes	—
240	C₂²×C₄²	C₂²×C₁₇	1	8	yes	complemented
241	#391	C₂²×C₁₇	1	16	yes	complemented
242	#390	C₂²×C₁₇	1	16	yes	complemented
243	#386	C₂²×C₁₇	1	32	yes	complemented
244	C₄×C₂²⋊C₄	C₂²×C₁₇	1	32	yes	complemented
245	C₂×#95	C₂²×C₁₇	1	8	yes	—
246	C₂×C₁₇	—	2	8	no	—
247	C₂×C₁₇	—	4	8	no	—
248	C₂×C₁₇	#2297	1	8	yes	direct product factor
249	C₂×C₁₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₁₇	C₂×C₄×#41	1	2	yes	—
251	C₂×C₁₇	C₂×#525	1	2	yes	—
252	C₂×C₁₇	C₂×#532	1	2	yes	—
253	C₂⁵	C₂³×C₁₇	1	2	yes	—
254	C₂⁵	C₂³×C₁₇	1	1	yes	characteristic
255	C₂×#41	—	2	128	no	—
256	C₂×#41	—	2	32	no	—
257	C₂×#41	—	2	32	no	—
258	C₂×#41	C₂×C₄×C₁₇	1	64	yes	complemented
259	C₂²×Q₈	—	2	4	no	—
260	C₂²×Q₈	—	2	4	no	—
261	C₂²×Q₈	C₂×C₄×C₁₇	1	8	yes	complemented
262	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	2	8	no	—
265	C₂²×D₄	—	2	4	no	—
266	C₂²×D₄	—	2	4	no	—
267	C₂²×D₄	C₂×C₄×C₁₇	1	16	yes	—
268	C₂²×D₄	C₂×C₄×C₁₇	1	8	yes	complemented
269	C₂²×D₄	C₂³×C₁₇	1	8	yes	—
270	C₂²×D₄	C₂³×C₁₇	1	4	yes	—
271	C₂³×C₄	—	2	8	no	—
272	C₂³×C₄	—	2	8	no	—
273	C₂³×C₄	—	2	8	no	—
274	C₂³×C₄	—	2	16	no	—
275	C₂³×C₄	C₂×C₄×C₁₇	1	8	yes	—
276	C₂³×C₄	C₂×C₄×C₁₇	1	16	yes	complemented
277	C₂³×C₄	D₄×C₁₇	1	8	yes	—
278	C₂³×C₄	D₄×C₁₇	1	8	yes	—
279	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
280	C₂³×C₄	C₂³×C₁₇	1	8	yes	—
281	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
282	C₂³×C₄	C₂³×C₁₇	1	8	yes	—
283	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
284	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
286	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
287	#117	—	2	32	no	—
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₇	1	8	yes	—
290	C₂×C₂²⋊C₄	—	2	8	no	—
291	C₂×C₂²⋊C₄	—	2	32	no	—
292	C₂×C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₇	1	32	yes	—
294	C₂×C₄²	—	2	8	no	—
295	C₂×C₄²	—	2	8	no	—
296	C₂×C₄²	—	2	8	no	—
297	C₂×C₄²	—	2	32	no	—
298	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
299	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
300	C₂×C₄²	C₂³×C₁₇	1	8	yes	—
301	#95	C₂³×C₁₇	1	32	yes	—
302	C₁₇	C₂×#2297	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	—	2	8	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	—	2	16	no	—
307	C₂⁴	C₂²×C₄×C₁₇	1	8	yes	—
308	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
309	C₂⁴	C₂×D₄×C₁₇	1	4	yes	—
310	C₂⁴	C₂×D₄×C₁₇	1	4	yes	—
311	C₂⁴	C₂⁴×C₁₇	1	4	yes	—
312	C₂⁴	C₂⁴×C₁₇	1	2	yes	—
313	C₂⁴	C₂⁴×C₁₇	1	1	yes	characteristic
314	#41	—	2	256	no	—
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	2	8	no	—
317	C₂×Q₈	—	2	32	no	—
318	C₂×Q₈	C₂²×C₄×C₁₇	1	16	yes	complemented
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	64	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	2	32	no	—
325	C₂×D₄	C₂²×C₄×C₁₇	1	32	yes	—
326	C₂×D₄	C₂²×C₄×C₁₇	1	16	yes	complemented
327	C₂²×C₄	—	2	64	no	—
328	C₂²×C₄	—	2	16	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	16	no	—
334	C₂²×C₄	—	2	16	no	—
335	C₂²×C₄	—	2	32	no	—
336	C₂²×C₄	—	2	64	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	C₂²⋊C₄×C₁₇	1	64	yes	complemented
340	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
341	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
342	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
343	C₂²×C₄	C₂²×C₄×C₁₇	1	16	yes	—
344	C₂²×C₄	C₂²×C₄×C₁₇	1	32	yes	complemented
345	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
346	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
347	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
348	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
349	C₂²×C₄	C₂×D₄×C₁₇	1	16	yes	—
350	C₂²×C₄	C₂×D₄×C₁₇	1	16	yes	—
351	C₂²×C₄	#41×C₁₇	1	16	yes	complemented
352	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
353	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
355	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
357	C₄⋊C₄	—	2	16	no	—
358	C₂²⋊C₄	—	2	16	no	—
359	C₂²⋊C₄	—	2	64	no	—
360	C₄²	—	2	16	no	—
361	C₄²	—	2	16	no	—
362	C₄²	—	2	16	no	—
363	C₂³	—	2	16	no	—
364	C₂³	—	2	16	no	—
365	C₂³	—	2	16	no	—
366	C₂³	—	2	8	no	—
367	C₂³	—	2	16	no	—
368	C₂³	—	2	32	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	16	no	—
372	C₂³	—	4	16	no	—
373	C₂³	—	4	16	no	—
374	C₂³	C₂×C₂²⋊C₄×C₁₇	1	16	yes	—
375	C₂³	C₂³×C₄×C₁₇	1	8	yes	—
376	C₂³	C₂³×C₄×C₁₇	1	4	yes	—
377	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
378	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
379	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
380	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
381	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
382	C₂³	C₂×#41×C₁₇	1	8	yes	—
383	C₂³	C₂⁵×C₁₇	1	1	yes	characteristic
384	Q₈	—	2	32	no	—
385	D₄	—	2	64	no	—
386	D₄	—	2	32	no	—
387	C₂×C₄	—	2	64	no	—
388	C₂×C₄	—	2	16	no	—
389	C₂×C₄	—	2	32	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	64	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	4	16	no	—
398	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	16	yes	—
399	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	16	yes	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	64	yes	complemented
401	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
402	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
403	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
405	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
406	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
408	C₂×C₄	C₂×#41×C₁₇	1	16	yes	complemented
409	C₂²	—	2	32	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	2	16	no	—
415	C₂²	—	4	32	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	8	no	—
418	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	8	yes	—
419	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	4	yes	—
420	C₂²	C₄×#41×C₁₇	1	8	yes	—
421	C₂²	C₁₇×#525	1	8	yes	—
422	C₂²	C₁₇×#532	1	8	yes	—
423	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
424	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
425	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
426	C₂²	C₂²×#41×C₁₇	1	4	yes	—
427	C₄	—	2	8	no	—
428	C₄	—	2	16	no	—
429	C₄	—	4	8	no	—
430	C₄	C₂²×C₂²⋊C₄×C₁₇	1	8	yes	—
431	C₄	C₂²×C₂²⋊C₄×C₁₇	1	8	yes	—
432	C₂	—	2	8	no	—
433	C₂	—	4	8	no	—
434	C₂	C₁₇×#2297	1	8	yes	direct product factor
435	C₂	C₂³×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
436	C₂	C₂×C₄×#41×C₁₇	1	2	yes	—
437	C₂	C₂×C₁₇×#525	1	2	yes	—
438	C₂	C₂×C₁₇×#532	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₇	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
socle	C₂⁴×C₁₇	C₂⁴
prime radical	C₂³×#41×C₁₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₇×#117	C₂	semidirect
3. C₂³×C₄²×C₁₇	C₂	semidirect
4. C₁₇×#2297	C₂	direct (N × H)
5. C₂×C₁₇×#391	C₂	semidirect
6. C₂×C₁₇×#390	C₂	semidirect
7. C₂×C₁₇×#386	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₁₇	C₂	semidirect
11. C₂²×#41×C₁₇	C₄	semidirect
20. C₂×C₁₇×#117	C₂²	semidirect
28. C₂²×C₄²×C₁₇	C₂²	semidirect
29. C₁₇×#391	C₂²	semidirect
30. C₁₇×#390	C₂²	semidirect
31. C₁₇×#386	C₂²	semidirect
32. C₄×C₂²⋊C₄×C₁₇	C₂²	semidirect
39. C₂×#41×C₁₇	C₂×C₄	semidirect
42. C₂²×Q₈×C₁₇	C₂×C₄	semidirect
49. C₂²×D₄×C₁₇	C₂×C₄	semidirect
57. C₂³×C₄×C₁₇	C₂×C₄	semidirect
98. C₂×Q₈×C₁₇	C₂²×C₄	semidirect
106. C₂×D₄×C₁₇	C₂²×C₄	semidirect
119. C₂²×C₄×C₁₇	C₂²⋊C₄	semidirect
124. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
131. C₂²×C₄×C₁₇	#41	semidirect
143. C₂×#2297	C₁₇	direct (N × H)
181. C₂×C₄×C₁₇	C₂×C₂²⋊C₄	semidirect
189. C₂×C₄×C₁₇	C₂×#41	semidirect
191. C₂²×#117	C₂×C₁₇	semidirect
192. C₂³×C₄²	C₂×C₁₇	semidirect
193. #2297	C₂×C₁₇	direct (N × H)
194. C₂×#391	C₂×C₁₇	semidirect
195. C₂×#390	C₂×C₁₇	semidirect
196. C₂×#386	C₂×C₁₇	semidirect
197. C₂×C₄×C₂²⋊C₄	C₂×C₁₇	semidirect
223. C₂²×#41	C₄×C₁₇	semidirect
232. C₂×#117	C₂²×C₁₇	semidirect
240. C₂²×C₄²	C₂²×C₁₇	semidirect
241. #391	C₂²×C₁₇	semidirect
242. #390	C₂²×C₁₇	semidirect
243. #386	C₂²×C₁₇	semidirect
244. C₄×C₂²⋊C₄	C₂²×C₁₇	semidirect
248. C₂×C₁₇	#2297	direct (N × H)
258. C₂×#41	C₂×C₄×C₁₇	semidirect
261. C₂²×Q₈	C₂×C₄×C₁₇	semidirect
268. C₂²×D₄	C₂×C₄×C₁₇	semidirect
276. C₂³×C₄	C₂×C₄×C₁₇	semidirect
302. C₁₇	C₂×#2297	direct (N × H)
318. C₂×Q₈	C₂²×C₄×C₁₇	semidirect
326. C₂×D₄	C₂²×C₄×C₁₇	semidirect
339. C₂²×C₄	C₂²⋊C₄×C₁₇	semidirect
344. C₂²×C₄	C₂²×C₄×C₁₇	semidirect
351. C₂²×C₄	#41×C₁₇	semidirect
400. C₂×C₄	C₂×C₂²⋊C₄×C₁₇	semidirect
408. C₂×C₄	C₂×#41×C₁₇	semidirect
434. C₂	C₁₇×#2297	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₇	2
C₂²×C₁₇×#117	2
C₂³×C₄²×C₁₇	2
C₁₇×#2297	2
C₂×C₁₇×#391	2
C₂×C₁₇×#390	2
C₂×C₁₇×#386	2
C₂×C₄×C₂²⋊C₄×C₁₇	2
C₂×#2297	17

Subgroups — C2×C17×#2297 #16891768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#2297 #16891768