Subgroups — C₂×C₁₇×#546 #14526469

Order 2176.

1900 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#546	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₇×#123	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₇×#121	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₇×#120	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₂²⋊C₄×C₁₇	C₂	1	2	yes	maximal, complemented
13	C₂⁵×C₁₇	C₂²	1	2	yes	—
14	C₂×#41×C₁₇	—	2	8	no	—
15	C₂×#41×C₁₇	C₂²	1	8	yes	complemented
16	C₂²×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄×C₁₇	—	2	8	no	—
18	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₇	C₂²	1	2	yes	—
20	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₁₇	C₂²	1	8	yes	complemented
23	C₂²×D₄×C₁₇	C₂²	1	2	yes	complemented
24	C₂²×D₄×C₁₇	C₂²	1	2	yes	complemented
25	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic
26	C₂³×C₄×C₁₇	C₂²	1	2	yes	complemented
27	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₄×C₁₇	C₂²	1	2	yes	complemented
29	C₁₇×#124	C₂²	1	8	yes	complemented
30	C₁₇×#123	C₂²	1	16	yes	complemented
31	C₁₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
32	C₁₇×#121	C₂²	1	8	yes	complemented
33	C₁₇×#121	C₂²	1	16	yes	complemented
34	C₁₇×#120	C₂²	1	16	yes	complemented
35	C₄×D₄×C₁₇	C₂²	1	8	yes	complemented
36	C₄×D₄×C₁₇	C₂²	1	8	yes	complemented
37	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊C₄×C₁₇	C₂²	1	2	yes	complemented
40	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
42	C₂×C₂²⋊C₄×C₁₇	C₂²	1	16	yes	complemented
43	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
45	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
46	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	complemented
48	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic, complemented
49	C₂⁴×C₁₇	—	2	8	no	—
50	C₂⁴×C₁₇	—	2	8	no	—
51	C₂⁴×C₁₇	—	4	4	no	—
52	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
53	C₂⁴×C₁₇	C₂³	1	2	yes	—
54	C₂⁴×C₁₇	C₂³	1	8	yes	—
55	C₂⁴×C₁₇	C₂³	1	2	yes	—
56	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
57	#41×C₁₇	—	2	32	no	—
58	C₂×Q₈×C₁₇	—	2	4	no	—
59	C₂×Q₈×C₁₇	C₂³	1	4	yes	complemented
60	C₂×D₄×C₁₇	—	2	8	no	—
61	C₂×D₄×C₁₇	—	2	8	no	—
62	C₂×D₄×C₁₇	—	2	4	no	—
63	C₂×D₄×C₁₇	—	2	32	no	—
64	C₂×D₄×C₁₇	—	2	4	no	—
65	C₂×D₄×C₁₇	—	4	4	no	—
66	C₂×D₄×C₁₇	D₄	1	8	yes	complemented
67	C₂×D₄×C₁₇	C₂³	1	8	yes	—
68	C₂×D₄×C₁₇	C₂³	1	4	yes	—
69	C₂×D₄×C₁₇	C₂³	1	4	yes	—
70	C₂×D₄×C₁₇	C₂³	1	4	yes	—
71	C₂×D₄×C₁₇	C₂³	1	8	yes	complemented
72	C₂×D₄×C₁₇	C₂³	1	8	yes	complemented
73	C₂²×C₄×C₁₇	—	2	8	no	—
74	C₂²×C₄×C₁₇	—	2	4	no	—
75	C₂²×C₄×C₁₇	—	2	4	no	—
76	C₂²×C₄×C₁₇	—	4	4	no	—
77	C₂²×C₄×C₁₇	C₂³	1	4	yes	—
78	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
82	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
83	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂³	1	8	yes	complemented
86	C₂²×C₄×C₁₇	C₂³	1	4	yes	complemented
87	C₂²×C₄×C₁₇	C₂³	1	8	yes	complemented
88	C₄⋊C₄×C₁₇	C₂³	1	8	yes	complemented
89	C₄⋊C₄×C₁₇	C₂³	1	4	yes	complemented
90	C₄⋊C₄×C₁₇	C₂³	1	4	yes	complemented
91	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	—
92	C₂²⋊C₄×C₁₇	C₂³	1	4	yes	—
93	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	complemented
94	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	complemented
95	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	complemented
96	C₂²⋊C₄×C₁₇	C₂³	1	8	yes	complemented
97	C₂²⋊C₄×C₁₇	C₂³	1	4	yes	complemented
98	C₄²×C₁₇	C₂³	1	4	yes	complemented
99	C₂³×C₁₇	—	2	2	no	—
100	C₂³×C₁₇	—	2	4	no	—
101	C₂³×C₁₇	—	2	4	no	—
102	C₂³×C₁₇	—	2	2	no	—
103	C₂³×C₁₇	—	2	2	no	—
104	C₂³×C₁₇	—	2	16	no	—
105	C₂³×C₁₇	—	2	4	no	—
106	C₂³×C₁₇	—	2	2	no	—
107	C₂³×C₁₇	—	2	4	no	—
108	C₂³×C₁₇	—	2	16	no	—
109	C₂³×C₁₇	—	2	2	no	—
110	C₂³×C₁₇	—	2	4	no	—
111	C₂³×C₁₇	—	4	8	no	—
112	C₂³×C₁₇	—	4	32	no	—
113	C₂³×C₁₇	C₂×D₄	1	8	yes	—
114	C₂³×C₁₇	#41	1	4	yes	complemented
115	C₂³×C₁₇	C₂⁴	1	4	yes	—
116	C₂³×C₁₇	C₂⁴	1	2	yes	—
117	C₂³×C₁₇	C₂⁴	1	4	yes	—
118	C₂³×C₁₇	C₂⁴	1	2	yes	—
119	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
120	Q₈×C₁₇	—	2	8	no	—
121	D₄×C₁₇	—	2	16	no	—
122	D₄×C₁₇	—	2	16	no	—
123	D₄×C₁₇	—	2	8	no	—
124	D₄×C₁₇	—	2	8	no	—
125	D₄×C₁₇	—	4	8	no	—
126	D₄×C₁₇	C₂×D₄	1	16	yes	complemented
127	C₂×C₄×C₁₇	—	2	2	no	—
128	C₂×C₄×C₁₇	—	2	2	no	—
129	C₂×C₄×C₁₇	—	2	4	no	—
130	C₂×C₄×C₁₇	—	2	16	no	—
131	C₂×C₄×C₁₇	—	2	2	no	—
132	C₂×C₄×C₁₇	—	2	2	no	—
133	C₂×C₄×C₁₇	—	2	4	no	—
134	C₂×C₄×C₁₇	—	2	8	no	—
135	C₂×C₄×C₁₇	—	2	8	no	—
136	C₂×C₄×C₁₇	—	4	8	no	—
137	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	—
138	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
139	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
140	C₂×C₄×C₁₇	C₂⁴	1	4	yes	—
141	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
142	C₂×C₄×C₁₇	C₂⁴	1	4	yes	—
143	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
144	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
145	C₂×#546	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂²×C₁₇	—	2	8	no	—
147	C₂²×C₁₇	—	2	16	no	—
148	C₂²×C₁₇	—	2	2	no	—
149	C₂²×C₁₇	—	2	4	no	—
150	C₂²×C₁₇	—	2	4	no	—
151	C₂²×C₁₇	—	2	2	no	—
152	C₂²×C₁₇	—	2	2	no	—
153	C₂²×C₁₇	—	2	4	no	—
154	C₂²×C₁₇	—	2	2	no	—
155	C₂²×C₁₇	—	2	4	no	—
156	C₂²×C₁₇	—	2	2	no	—
157	C₂²×C₁₇	—	2	4	no	—
158	C₂²×C₁₇	—	4	32	no	—
159	C₂²×C₁₇	—	4	4	no	—
160	C₂²×C₁₇	—	4	8	no	—
161	C₂²×C₁₇	C₂²×D₄	1	8	yes	—
162	C₂²×C₁₇	C₂²×D₄	1	2	yes	—
163	C₂²×C₁₇	C₂×#41	1	2	yes	—
164	C₂²×C₁₇	C₂×#41	1	4	yes	complemented
165	C₂²×C₁₇	H(5,𝔽₂)	1	2	yes	—
166	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
167	C₄×C₁₇	—	2	2	no	—
168	C₄×C₁₇	—	2	2	no	—
169	C₄×C₁₇	—	2	4	no	—
170	C₄×C₁₇	—	2	2	no	—
171	C₄×C₁₇	—	2	2	no	—
172	C₄×C₁₇	—	2	4	no	—
173	C₄×C₁₇	C₂²×D₄	1	4	yes	—
174	C₂²×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
175	C₂³×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
176	#546	C₂×C₁₇	1	16	yes	direct product factor
177	C₂×#124	C₂×C₁₇	1	1	yes	characteristic, complemented
178	C₂×#123	C₂×C₁₇	1	2	yes	complemented
179	C₂×C₂²⋊Q₈	C₂×C₁₇	1	1	yes	characteristic, complemented
180	C₂×#121	C₂×C₁₇	1	1	yes	characteristic, complemented
181	C₂×#121	C₂×C₁₇	1	2	yes	complemented
182	C₂×#120	C₂×C₁₇	1	2	yes	complemented
183	C₂×C₄×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
184	C₂×C₄×D₄	C₂×C₁₇	1	1	yes	characteristic, complemented
185	C₂²×C₂²⋊C₄	C₂×C₁₇	1	2	yes	complemented
186	C₂×C₁₇	—	2	4	no	—
187	C₂×C₁₇	—	2	8	no	—
188	C₂×C₁₇	—	4	2	no	—
189	C₂×C₁₇	—	4	4	no	—
190	C₂×C₁₇	#546	1	4	yes	direct product factor
191	C₂×C₁₇	C₂³×D₄	1	1	yes	characteristic
192	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
193	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
194	C₂⁵	C₂²×C₁₇	1	2	yes	—
195	C₂×#41	—	2	8	no	—
196	C₂×#41	C₂²×C₁₇	1	8	yes	complemented
197	C₂²×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
198	C₂²×D₄	—	2	8	no	—
199	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
200	C₂²×D₄	C₂²×C₁₇	1	2	yes	—
201	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
202	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
203	C₂²×D₄	C₂²×C₁₇	1	8	yes	complemented
204	C₂²×D₄	C₂²×C₁₇	1	2	yes	complemented
205	C₂²×D₄	C₂²×C₁₇	1	2	yes	complemented
206	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic
207	C₂³×C₄	C₂²×C₁₇	1	2	yes	complemented
208	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
209	C₂³×C₄	C₂²×C₁₇	1	2	yes	complemented
210	#124	C₂²×C₁₇	1	8	yes	complemented
211	#123	C₂²×C₁₇	1	16	yes	complemented
212	C₂²⋊Q₈	C₂²×C₁₇	1	8	yes	complemented
213	#121	C₂²×C₁₇	1	8	yes	complemented
214	#121	C₂²×C₁₇	1	16	yes	complemented
215	#120	C₂²×C₁₇	1	16	yes	complemented
216	C₄×D₄	C₂²×C₁₇	1	8	yes	complemented
217	C₄×D₄	C₂²×C₁₇	1	8	yes	complemented
218	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
219	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
220	C₂×C₄⋊C₄	C₂²×C₁₇	1	2	yes	complemented
221	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂²×C₁₇	1	16	yes	complemented
224	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
225	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
226	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
227	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic, complemented
228	C₂×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	complemented
229	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic, complemented
230	C₁₇	C₂×#546	1	1	yes	characteristic, direct product factor, Sylow
231	C₂⁴	—	2	8	no	—
232	C₂⁴	—	2	8	no	—
233	C₂⁴	—	4	4	no	—
234	C₂⁴	C₂³×C₁₇	1	2	yes	—
235	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
236	C₂⁴	C₂³×C₁₇	1	8	yes	—
237	C₂⁴	C₂³×C₁₇	1	2	yes	—
238	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
239	#41	—	2	32	no	—
240	C₂×Q₈	—	2	4	no	—
241	C₂×Q₈	C₂³×C₁₇	1	4	yes	complemented
242	C₂×D₄	—	2	8	no	—
243	C₂×D₄	—	2	8	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	2	32	no	—
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	4	4	no	—
248	C₂×D₄	D₄×C₁₇	1	8	yes	complemented
249	C₂×D₄	C₂³×C₁₇	1	4	yes	—
250	C₂×D₄	C₂³×C₁₇	1	8	yes	—
251	C₂×D₄	C₂³×C₁₇	1	4	yes	—
252	C₂×D₄	C₂³×C₁₇	1	4	yes	—
253	C₂×D₄	C₂³×C₁₇	1	8	yes	complemented
254	C₂×D₄	C₂³×C₁₇	1	8	yes	complemented
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
260	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
261	C₂²×C₄	C₂³×C₁₇	1	2	yes	—
262	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₁₇	1	2	yes	—
264	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₁₇	1	4	yes	—
266	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
267	C₂²×C₄	C₂³×C₁₇	1	8	yes	complemented
268	C₂²×C₄	C₂³×C₁₇	1	4	yes	complemented
269	C₂²×C₄	C₂³×C₁₇	1	8	yes	complemented
270	C₄⋊C₄	C₂³×C₁₇	1	4	yes	complemented
271	C₄⋊C₄	C₂³×C₁₇	1	4	yes	complemented
272	C₄⋊C₄	C₂³×C₁₇	1	8	yes	complemented
273	C₂²⋊C₄	C₂³×C₁₇	1	4	yes	—
274	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	—
275	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	complemented
276	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	complemented
277	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	complemented
278	C₂²⋊C₄	C₂³×C₁₇	1	4	yes	complemented
279	C₂²⋊C₄	C₂³×C₁₇	1	8	yes	complemented
280	C₄²	C₂³×C₁₇	1	4	yes	complemented
281	C₂³	—	2	2	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	4	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	16	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	4	no	—
293	C₂³	—	4	8	no	—
294	C₂³	—	4	32	no	—
295	C₂³	C₂×D₄×C₁₇	1	8	yes	—
296	C₂³	#41×C₁₇	1	4	yes	complemented
297	C₂³	C₂⁴×C₁₇	1	4	yes	—
298	C₂³	C₂⁴×C₁₇	1	2	yes	—
299	C₂³	C₂⁴×C₁₇	1	4	yes	—
300	C₂³	C₂⁴×C₁₇	1	2	yes	—
301	C₂³	C₂⁴×C₁₇	1	1	yes	characteristic
302	Q₈	—	2	8	no	—
303	D₄	—	2	16	no	—
304	D₄	—	2	16	no	—
305	D₄	—	2	8	no	—
306	D₄	—	2	8	no	—
307	D₄	—	4	8	no	—
308	D₄	C₂×D₄×C₁₇	1	16	yes	complemented
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	16	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	C₂×D₄×C₁₇	1	4	yes	—
320	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
321	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
322	C₂×C₄	C₂⁴×C₁₇	1	4	yes	—
323	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
324	C₂×C₄	C₂⁴×C₁₇	1	4	yes	—
325	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
326	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
327	C₂²	—	2	8	no	—
328	C₂²	—	2	16	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	4	32	no	—
340	C₂²	—	4	8	no	—
341	C₂²	—	4	4	no	—
342	C₂²	C₂²×D₄×C₁₇	1	8	yes	—
343	C₂²	C₂²×D₄×C₁₇	1	2	yes	—
344	C₂²	C₂×#41×C₁₇	1	2	yes	—
345	C₂²	C₂×#41×C₁₇	1	4	yes	complemented
346	C₂²	C₁₇×H(5,𝔽₂)	1	2	yes	—
347	C₂²	C₂⁵×C₁₇	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	C₂²×D₄×C₁₇	1	4	yes	—
355	C₂	—	2	4	no	—
356	C₂	—	2	8	no	—
357	C₂	—	4	4	no	—
358	C₂	—	4	2	no	—
359	C₂	C₁₇×#546	1	4	yes	direct product factor
360	C₂	C₂³×D₄×C₁₇	1	1	yes	characteristic
361	C₂	C₂²×#41×C₁₇	1	1	yes	characteristic
362	C₂	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×C₁₇	C₂	semidirect
2. C₂³×D₄×C₁₇	C₂	semidirect
3. C₁₇×#546	C₂	direct (N × H)
4. C₂×C₁₇×#124	C₂	semidirect
5. C₂×C₁₇×#123	C₂	semidirect
6. C₂×C₁₇×C₂²⋊Q₈	C₂	semidirect
7. C₂×C₁₇×#121	C₂	semidirect
8. C₂×C₁₇×#121	C₂	semidirect
9. C₂×C₁₇×#120	C₂	semidirect
10. C₂×C₄×D₄×C₁₇	C₂	semidirect
11. C₂×C₄×D₄×C₁₇	C₂	semidirect
12. C₂²×C₂²⋊C₄×C₁₇	C₂	semidirect
15. C₂×#41×C₁₇	C₂²	semidirect
16. C₂²×Q₈×C₁₇	C₂²	semidirect
22. C₂²×D₄×C₁₇	C₂²	semidirect
23. C₂²×D₄×C₁₇	C₂²	semidirect
24. C₂²×D₄×C₁₇	C₂²	semidirect
26. C₂³×C₄×C₁₇	C₂²	semidirect
27. C₂³×C₄×C₁₇	C₂²	semidirect
28. C₂³×C₄×C₁₇	C₂²	semidirect
29. C₁₇×#124	C₂²	semidirect
30. C₁₇×#123	C₂²	semidirect
31. C₁₇×C₂²⋊Q₈	C₂²	semidirect
32. C₁₇×#121	C₂²	semidirect
33. C₁₇×#121	C₂²	semidirect
34. C₁₇×#120	C₂²	semidirect
35. C₄×D₄×C₁₇	C₂²	semidirect
36. C₄×D₄×C₁₇	C₂²	semidirect
37. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
38. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
39. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
42. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
43. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
44. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
45. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
46. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
48. C₂×C₄²×C₁₇	C₂²	semidirect
59. C₂×Q₈×C₁₇	C₂³	semidirect
66. C₂×D₄×C₁₇	D₄	semidirect
71. C₂×D₄×C₁₇	C₂³	semidirect
72. C₂×D₄×C₁₇	C₂³	semidirect
85. C₂²×C₄×C₁₇	C₂³	semidirect
86. C₂²×C₄×C₁₇	C₂³	semidirect
87. C₂²×C₄×C₁₇	C₂³	semidirect
88. C₄⋊C₄×C₁₇	C₂³	semidirect
89. C₄⋊C₄×C₁₇	C₂³	semidirect
90. C₄⋊C₄×C₁₇	C₂³	semidirect
93. C₂²⋊C₄×C₁₇	C₂³	semidirect
94. C₂²⋊C₄×C₁₇	C₂³	semidirect
95. C₂²⋊C₄×C₁₇	C₂³	semidirect
96. C₂²⋊C₄×C₁₇	C₂³	semidirect
97. C₂²⋊C₄×C₁₇	C₂³	semidirect
98. C₄²×C₁₇	C₂³	semidirect
114. C₂³×C₁₇	#41	semidirect
126. D₄×C₁₇	C₂×D₄	semidirect
145. C₂×#546	C₁₇	direct (N × H)
164. C₂²×C₁₇	C₂×#41	semidirect
174. C₂²×#41	C₂×C₁₇	semidirect
175. C₂³×D₄	C₂×C₁₇	semidirect
176. #546	C₂×C₁₇	direct (N × H)
177. C₂×#124	C₂×C₁₇	semidirect
178. C₂×#123	C₂×C₁₇	semidirect
179. C₂×C₂²⋊Q₈	C₂×C₁₇	semidirect
180. C₂×#121	C₂×C₁₇	semidirect
181. C₂×#121	C₂×C₁₇	semidirect
182. C₂×#120	C₂×C₁₇	semidirect
183. C₂×C₄×D₄	C₂×C₁₇	semidirect
184. C₂×C₄×D₄	C₂×C₁₇	semidirect
185. C₂²×C₂²⋊C₄	C₂×C₁₇	semidirect
190. C₂×C₁₇	#546	direct (N × H)
196. C₂×#41	C₂²×C₁₇	semidirect
197. C₂²×Q₈	C₂²×C₁₇	semidirect
203. C₂²×D₄	C₂²×C₁₇	semidirect
204. C₂²×D₄	C₂²×C₁₇	semidirect
205. C₂²×D₄	C₂²×C₁₇	semidirect
207. C₂³×C₄	C₂²×C₁₇	semidirect
208. C₂³×C₄	C₂²×C₁₇	semidirect
209. C₂³×C₄	C₂²×C₁₇	semidirect
210. #124	C₂²×C₁₇	semidirect
211. #123	C₂²×C₁₇	semidirect
212. C₂²⋊Q₈	C₂²×C₁₇	semidirect
213. #121	C₂²×C₁₇	semidirect
214. #121	C₂²×C₁₇	semidirect
215. #120	C₂²×C₁₇	semidirect
216. C₄×D₄	C₂²×C₁₇	semidirect
217. C₄×D₄	C₂²×C₁₇	semidirect
218. C₂×C₄⋊C₄	C₂²×C₁₇	semidirect
219. C₂×C₄⋊C₄	C₂²×C₁₇	semidirect
220. C₂×C₄⋊C₄	C₂²×C₁₇	semidirect
223. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
224. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
225. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
226. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
227. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
228. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
229. C₂×C₄²	C₂²×C₁₇	semidirect
230. C₁₇	C₂×#546	direct (N × H)
241. C₂×Q₈	C₂³×C₁₇	semidirect
248. C₂×D₄	D₄×C₁₇	semidirect
253. C₂×D₄	C₂³×C₁₇	semidirect
254. C₂×D₄	C₂³×C₁₇	semidirect
267. C₂²×C₄	C₂³×C₁₇	semidirect
268. C₂²×C₄	C₂³×C₁₇	semidirect
269. C₂²×C₄	C₂³×C₁₇	semidirect
270. C₄⋊C₄	C₂³×C₁₇	semidirect
271. C₄⋊C₄	C₂³×C₁₇	semidirect
272. C₄⋊C₄	C₂³×C₁₇	semidirect
275. C₂²⋊C₄	C₂³×C₁₇	semidirect
276. C₂²⋊C₄	C₂³×C₁₇	semidirect
277. C₂²⋊C₄	C₂³×C₁₇	semidirect
278. C₂²⋊C₄	C₂³×C₁₇	semidirect
279. C₂²⋊C₄	C₂³×C₁₇	semidirect
280. C₄²	C₂³×C₁₇	semidirect
296. C₂³	#41×C₁₇	semidirect
308. D₄	C₂×D₄×C₁₇	semidirect
345. C₂²	C₂×#41×C₁₇	semidirect
359. C₂	C₁₇×#546	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×#41×C₁₇	2
C₂³×D₄×C₁₇	2
C₁₇×#546	2
C₂×C₁₇×#124	2
C₂×C₁₇×#123	2
C₂×C₁₇×C₂²⋊Q₈	2
C₂×C₁₇×#121	2
C₂×C₁₇×#120	2
C₂×C₄×D₄×C₁₇	2
C₂²×C₂²⋊C₄×C₁₇	2
C₂×#546	17

Subgroups — C2×C17×#546 #14526469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#546 #14526469