Subgroups — D₁₇×#3549 #17942122

Order 4352.

8802 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543189	C₂	1	3	yes	maximal, complemented
2	#14543188	C₂	1	4	yes	maximal, complemented
3	#14543187	C₂	1	12	yes	maximal, complemented
4	#14543186	C₂	1	6	yes	maximal, complemented
5	#14543185	C₂	1	6	yes	maximal, complemented
6	D₁₇×H(3,𝔽₄)	C₂	1	4	yes	maximal, complemented
7	D₁₇×#555	C₂	1	6	yes	maximal, complemented
8	D₄²×D₁₇	C₂	1	6	yes	maximal, complemented
9	D₁₇×#535	C₂	1	12	yes	maximal, complemented
10	D₁₇×#532	C₂	1	3	yes	maximal, complemented
11	C₁₇×#3549	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₁₇	C₂²	1	6	yes	complemented
13	C₂²×D₄×D₁₇	C₂²	1	12	yes	complemented
14	#11763552	C₂²	1	24	yes	complemented
15	#11763551	C₂²	1	24	yes	complemented
16	#11763551	C₂²	1	12	yes	complemented
17	#11763525	C₂²	1	6	yes	complemented
18	#11763524	C₂²	1	12	yes	complemented
19	#11763523	C₂²	1	24	yes	complemented
20	#11763522	C₂²	1	24	yes	complemented
21	#11763521	C₂²	1	24	yes	complemented
22	D₄×D₆₈	C₂²	1	12	yes	complemented
23	#11763444	C₂²	1	6	yes	complemented
24	#11763443	C₂²	1	24	yes	complemented
25	D₄×C₂²⋊D₁₇	C₂²	1	24	yes	complemented
26	#11763441	C₂²	1	24	yes	complemented
27	#11763378	C₂²	1	12	yes	complemented
28	#11763377	C₂²	1	24	yes	complemented
29	#11763376	C₂²	1	12	yes	complemented
30	#11763375	C₂²	1	24	yes	complemented
31	#11763375	C₂²	1	24	yes	complemented
32	#11763374	C₂²	1	24	yes	complemented
33	#11763374	C₂²	1	24	yes	complemented
34	#11763373	C₂²	1	12	yes	complemented
35	#11763372	C₂²	1	24	yes	complemented
36	#11763360	C₂²	1	3	yes	complemented
37	#11763359	C₂²	1	3	yes	complemented
38	#11763358	C₂²	1	6	yes	complemented
39	#11763357	C₂²	1	3	yes	complemented
40	#11763356	C₂²	1	12	yes	complemented
41	#11763355	C₂²	1	6	yes	complemented
42	#11763354	C₂²	1	12	yes	complemented
43	C₄⋊Q₈×D₁₇	C₂²	1	3	yes	complemented
44	#127×D₁₇	C₂²	1	3	yes	—
45	#127×D₁₇	C₂²	1	8	yes	complemented
46	#124×D₁₇	C₂²	1	24	yes	complemented
47	#124×D₁₇	C₂²	1	6	yes	complemented
48	#121×D₁₇	C₂²	1	12	yes	complemented
49	#121×D₁₇	C₂²	1	24	yes	complemented
50	#120×D₁₇	C₂²	1	8	yes	complemented
51	#120×D₁₇	C₂²	1	24	yes	complemented
52	C₄×D₄×D₁₇	C₂²	1	12	yes	complemented
53	#117×D₁₇	C₂²	1	12	yes	complemented
54	C₂×C₄²×D₁₇	C₂²	1	1	yes	characteristic, complemented
55	C₁₇×H(3,𝔽₄)	C₂²	1	4	yes	complemented
56	C₁₇×#555	C₂²	1	6	yes	complemented
57	D₄²×C₁₇	C₂²	1	6	yes	complemented
58	C₁₇×#535	C₂²	1	12	yes	complemented
59	C₁₇×#532	C₂²	1	3	yes	complemented
60	C₂⁴×D₁₇	C₂³	1	8	yes	—
61	C₂×#41×C₁₇	C₂³	1	6	yes	complemented
62	C₂²×D₄×C₁₇	C₂³	1	12	yes	complemented
63	C₂²×C₂²⋊D₁₇	C₂³	1	24	yes	complemented
64	#41×D₁₇	—	4	24	no	—
65	C₂×#63256	C₂³	1	6	yes	complemented
66	C₂×Q₈×D₁₇	C₂³	1	6	yes	—
67	C₂×#63254	C₂³	1	12	yes	complemented
68	C₂×#63254	C₂³	1	6	yes	complemented
69	C₂×D₄×D₁₇	—	4	48	no	—
70	C₂×D₄×D₁₇	C₂³	1	12	yes	—
71	C₂×D₄×D₁₇	C₂³	1	6	yes	—
72	C₂×D₄×D₁₇	C₂³	1	24	yes	—
73	C₂×D₄×D₁₇	C₂³	1	12	yes	—
74	C₂×D₄×D₁₇	C₂³	1	24	yes	complemented
75	C₂×D₄×D₁₇	C₂³	1	24	yes	complemented
76	C₂×#63252	C₂³	1	6	yes	complemented
77	C₂×#63252	C₂³	1	12	yes	complemented
78	C₂²×D₆₈	C₂³	1	12	yes	complemented
79	C₂²×C₄×D₁₇	C₂³	1	3	yes	—
80	C₂²×C₄×D₁₇	C₂³	1	12	yes	—
81	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	complemented
82	C₁₇×#127	C₂³	1	3	yes	—
83	C₁₇×#127	C₂³	1	8	yes	complemented
84	C₁₇×#124	C₂³	1	6	yes	complemented
85	C₁₇×#124	C₂³	1	24	yes	complemented
86	C₁₇×#121	C₂³	1	12	yes	complemented
87	C₁₇×#121	C₂³	1	24	yes	complemented
88	C₁₇×#120	C₂³	1	8	yes	complemented
89	C₁₇×#120	C₂³	1	24	yes	complemented
90	C₄×D₄×C₁₇	C₂³	1	12	yes	complemented
91	C₁₇×#117	C₂³	1	12	yes	complemented
92	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic, complemented
93	#10587639	C₂³	1	24	yes	complemented
94	#10587639	C₂³	1	8	yes	complemented
95	#10587633	C₂³	1	24	yes	complemented
96	#10587633	C₂³	1	6	yes	complemented
97	#10587630	C₂³	1	6	yes	complemented
98	#10587626	C₂³	1	12	yes	—
99	#10587626	C₂³	1	6	yes	—
100	#10587626	C₂³	1	24	yes	complemented
101	#10587626	C₂³	1	24	yes	complemented
102	#10587625	C₂³	1	48	yes	complemented
103	#10587625	C₂³	1	24	yes	complemented
104	#10587624	C₂³	1	24	yes	complemented
105	#10587624	C₂³	1	12	yes	complemented
106	#10587623	C₂³	1	48	yes	complemented
107	#10587623	C₂³	1	24	yes	complemented
108	#10587623	C₂³	1	24	yes	complemented
109	#10587622	C₂³	1	24	yes	complemented
110	#10587622	C₂³	1	6	yes	complemented
111	D₄×Dic₁₇	C₂³	1	12	yes	complemented
112	#10587616	C₂³	1	24	yes	complemented
113	#10587616	C₂³	1	12	yes	complemented
114	C₄×C₂²⋊D₁₇	C₂³	1	24	yes	complemented
115	#10587612	C₂³	1	12	yes	complemented
116	C₂×C₄×Dic₁₇	C₂³	1	3	yes	complemented
117	#10587581	C₂³	1	24	yes	complemented
118	#10587581	C₂³	1	12	yes	complemented
119	#10587579	C₂³	1	12	yes	complemented
120	#10587578	C₂³	1	24	yes	complemented
121	C₄⋊C₄×D₁₇	C₂³	1	12	yes	—
122	#10587574	C₂³	1	12	yes	complemented
123	#10587571	C₂³	1	48	yes	complemented
124	#10587571	C₂³	1	48	yes	complemented
125	#10587571	C₂³	1	24	yes	complemented
126	#10587570	C₂³	1	48	yes	complemented
127	#10587570	C₂³	1	24	yes	complemented
128	#10587568	C₂³	1	24	yes	complemented
129	#10587568	C₂³	1	48	yes	complemented
130	#10587568	C₂³	1	24	yes	complemented
131	#10587567	C₂³	1	24	yes	complemented
132	C₂²⋊C₄×D₁₇	C₂³	1	24	yes	—
133	C₂²⋊C₄×D₁₇	C₂³	1	24	yes	—
134	#10587563	C₂³	1	24	yes	complemented
135	#10587561	C₂³	1	24	yes	complemented
136	#10587561	C₂³	1	6	yes	complemented
137	#10587560	C₂³	1	3	yes	—
138	#10587560	C₂³	1	8	yes	complemented
139	C₄×D₆₈	C₂³	1	12	yes	complemented
140	#10587558	C₂³	1	24	yes	complemented
141	C₄²×D₁₇	C₂³	1	3	yes	—
142	C₄²×D₁₇	C₂³	1	1	yes	characteristic
143	C₄²×D₁₇	C₂³	1	8	yes	—
144	C₄²×D₁₇	C₂³	1	3	yes	complemented
145	C₄²×D₁₇	C₂³	1	1	yes	characteristic, complemented
146	#10587555	C₂³	1	3	yes	complemented
147	C₂⁴×C₁₇	C₂⁴	1	8	yes	—
148	C₂³×D₁₇	—	4	48	no	—
149	C₂³×D₁₇	C₂⁴	1	1	yes	characteristic
150	C₂³×D₁₇	C₂⁴	1	12	yes	—
151	C₂³×D₁₇	C₂⁴	1	24	yes	—
152	#41×C₁₇	—	4	12	no	—
153	C₂×Q₈×C₁₇	C₂⁴	1	6	yes	—
154	C₂×D₄×C₁₇	—	4	24	no	—
155	C₂×D₄×C₁₇	C₂⁴	1	12	yes	—
156	C₂×D₄×C₁₇	C₂⁴	1	6	yes	—
157	C₂×D₄×C₁₇	C₂⁴	1	24	yes	—
158	C₂×D₄×C₁₇	C₂⁴	1	12	yes	—
159	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
160	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
161	C₂×C₂²⋊D₁₇	—	4	48	no	—
162	C₂×C₂²⋊D₁₇	C₂⁴	1	24	yes	—
163	C₂×C₂²⋊D₁₇	C₂⁴	1	12	yes	—
164	C₂×C₂²⋊D₁₇	C₂⁴	1	12	yes	—
165	C₂×C₂²⋊D₁₇	C₂⁴	1	12	yes	—
166	C₂×C₂²⋊D₁₇	C₂⁴	1	48	yes	—
167	C₂²×Dic₁₇	C₂⁴	1	3	yes	—
168	C₂²×Dic₁₇	C₂⁴	1	12	yes	—
169	#63256	—	4	12	no	—
170	Q₈×D₁₇	—	4	12	no	—
171	#63254	—	4	24	no	—
172	#63254	—	4	12	no	—
173	D₄×D₁₇	—	2	48	no	—
174	D₄×D₁₇	—	4	48	no	—
175	D₄×D₁₇	—	4	48	no	—
176	D₄×D₁₇	—	4	48	no	—
177	D₄×D₁₇	—	4	24	no	—
178	D₄×D₁₇	—	4	12	no	—
179	#63252	—	4	24	no	—
180	#63252	—	4	12	no	—
181	C₂×D₆₈	—	4	24	no	—
182	C₂×D₆₈	C₂⁴	1	12	yes	—
183	C₂×D₆₈	C₂⁴	1	24	yes	—
184	C₂×D₆₈	C₂⁴	1	6	yes	—
185	C₂×D₆₈	C₂⁴	1	12	yes	—
186	C₂×C₄×D₁₇	—	2	48	no	—
187	C₂×C₄×D₁₇	—	2	12	no	—
188	C₂×C₄×D₁₇	C₂⁴	1	3	yes	—
189	C₂×C₄×D₁₇	C₂⁴	1	12	yes	—
190	C₂×C₄×D₁₇	C₂⁴	1	12	yes	—
191	C₂×C₄×D₁₇	C₂⁴	1	3	yes	—
192	C₂×C₄×D₁₇	C₂⁴	1	12	yes	—
193	C₂×C₄×D₁₇	C₂⁴	1	3	yes	—
194	C₂×C₄×D₁₇	C₂⁴	1	3	yes	—
195	C₂×Dic₃₄	C₂⁴	1	6	yes	—
196	C₂×Dic₃₄	C₂⁴	1	12	yes	—
197	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
198	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
199	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
200	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
201	C₄²×C₁₇	C₂⁴	1	8	yes	—
202	C₄²×C₁₇	C₂⁴	1	3	yes	—
203	C₂²⋊Dic₁₇	C₂⁴	1	24	yes	—
204	C₂²⋊Dic₁₇	C₂⁴	1	24	yes	—
205	#63227	C₂⁴	1	48	yes	—
206	#63227	C₂⁴	1	24	yes	—
207	#63227	C₂⁴	1	24	yes	—
208	C₄⋊Dic₁₇	C₂⁴	1	12	yes	—
209	#63225	C₂⁴	1	24	yes	—
210	C₄×Dic₁₇	C₂⁴	1	3	yes	—
211	C₄×Dic₁₇	C₂⁴	1	3	yes	—
212	C₄×Dic₁₇	C₂⁴	1	6	yes	—
213	C₄×Dic₁₇	C₂⁴	1	24	yes	—
214	C₂×#3549	—	17	1	no	maximal, Sylow
215	C₂³×C₁₇	—	4	24	no	—
216	C₂³×C₁₇	C₂⁵	1	12	yes	—
217	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
218	C₂²×D₁₇	—	2	6	no	—
219	C₂²×D₁₇	—	2	24	no	—
220	C₂²×D₁₇	—	2	48	no	—
221	C₂²×D₁₇	—	4	24	no	—
222	C₂²×D₁₇	—	4	48	no	—
223	C₂²×D₁₇	—	8	64	no	—
224	C₂²×D₁₇	C₂⁵	1	1	yes	characteristic
225	C₂²×D₁₇	C₂⁵	1	12	yes	—
226	C₂²×D₁₇	C₂⁵	1	1	yes	characteristic
227	Q₈×C₁₇	—	4	6	no	—
228	D₄×C₁₇	—	2	24	no	—
229	D₄×C₁₇	—	4	24	no	—
230	D₄×C₁₇	—	4	6	no	—
231	D₄×C₁₇	—	4	12	no	—
232	C₂×C₄×C₁₇	—	2	24	no	—
233	C₂×C₄×C₁₇	—	2	6	no	—
234	C₂×C₄×C₁₇	C₂⁵	1	3	yes	—
235	C₂×C₄×C₁₇	C₂⁵	1	12	yes	—
236	C₂×C₄×C₁₇	C₂⁵	1	3	yes	—
237	C₂²⋊D₁₇	—	2	48	no	—
238	C₂²⋊D₁₇	—	4	12	no	—
239	C₂²⋊D₁₇	—	4	12	no	—
240	C₂²⋊D₁₇	—	4	12	no	—
241	C₂²⋊D₁₇	—	4	48	no	—
242	C₂×Dic₁₇	—	2	6	no	—
243	C₂×Dic₁₇	—	2	24	no	—
244	C₂×Dic₁₇	C₂⁵	1	3	yes	—
245	C₂×Dic₁₇	C₂⁵	1	12	yes	—
246	C₂×Dic₁₇	C₂⁵	1	3	yes	—
247	D₆₈	—	2	24	no	—
248	D₆₈	—	4	24	no	—
249	D₆₈	—	4	6	no	—
250	D₆₈	—	4	12	no	—
251	C₄×D₁₇	—	2	24	no	—
252	C₄×D₁₇	—	2	6	no	—
253	C₄×D₁₇	—	2	6	no	—
254	C₄×D₁₇	—	2	24	no	—
255	C₄×D₁₇	—	2	24	no	—
256	C₄×D₁₇	—	2	6	no	—
257	C₄×D₁₇	H(5,𝔽₂)	1	12	yes	—
258	Dic₃₄	—	4	12	no	—
259	Dic₃₄	—	4	6	no	—
260	#3549	—	17	4	no	—
261	#3549	—	17	6	no	—
262	#3549	—	17	6	no	—
263	#3549	—	17	12	no	—
264	#3549	—	17	3	no	—
265	#3549	D₁₇	1	1	yes	characteristic, direct product factor
266	C₂×H(3,𝔽₄)	—	17	4	no	—
267	C₂×#555	—	17	6	no	—
268	C₂×D₄²	—	17	6	no	—
269	C₂×#535	—	17	12	no	—
270	C₂×#532	—	17	3	no	—
271	C₂²×C₁₇	—	2	3	no	—
272	C₂²×C₁₇	—	2	12	no	—
273	C₂²×C₁₇	—	2	24	no	—
274	C₂²×C₁₇	—	8	16	no	—
275	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
276	C₂×D₁₇	—	2	3	no	—
277	C₂×D₁₇	—	2	12	no	—
278	C₂×D₁₇	—	2	24	no	—
279	C₂×D₁₇	—	4	4	no	—
280	C₂×D₁₇	—	4	48	no	—
281	C₂×D₁₇	—	8	48	no	—
282	C₂×D₁₇	C₂×H(5,𝔽₂)	1	6	yes	—
283	C₄×C₁₇	—	2	3	no	—
284	C₄×C₁₇	—	2	12	no	—
285	C₄×C₁₇	C₂×H(5,𝔽₂)	1	6	yes	—
286	Dic₁₇	—	2	3	no	—
287	Dic₁₇	—	2	12	no	—
288	Dic₁₇	C₂×H(5,𝔽₂)	1	6	yes	—
289	C₂²×#41	—	17	6	no	—
290	C₂³×D₄	—	17	12	no	—
291	H(3,𝔽₄)	—	17	24	no	—
292	H(3,𝔽₄)	—	17	12	no	—
293	H(3,𝔽₄)	—	17	24	no	—
294	H(3,𝔽₄)	C₂×D₁₇	1	4	yes	complemented
295	#555	—	17	6	no	—
296	#555	—	17	24	no	—
297	#555	—	17	24	no	—
298	#555	—	17	12	no	—
299	#555	—	17	24	no	—
300	#555	C₂×D₁₇	1	6	yes	complemented
301	D₄²	—	17	24	no	—
302	D₄²	—	17	6	no	—
303	D₄²	—	17	24	no	—
304	D₄²	—	17	24	no	—
305	D₄²	—	17	12	no	—
306	D₄²	C₂×D₁₇	1	6	yes	complemented
307	#535	—	17	12	no	—
308	#535	—	17	12	no	—
309	#535	—	17	24	no	—
310	#535	—	17	24	no	—
311	#535	—	17	24	no	—
312	#535	—	17	24	no	—
313	#535	—	17	24	no	—
314	#535	—	17	24	no	—
315	#535	—	17	12	no	—
316	#535	C₂×D₁₇	1	12	yes	complemented
317	#532	—	17	6	no	—
318	#532	—	17	3	no	—
319	#532	—	17	3	no	—
320	#532	—	17	6	no	—
321	#532	—	17	12	no	—
322	#532	—	17	12	no	—
323	#532	—	17	3	no	—
324	#532	C₂×D₁₇	1	3	yes	complemented
325	C₂×C₄⋊Q₈	—	17	3	no	—
326	C₂×#127	—	17	3	no	—
327	C₂×#127	—	17	8	no	—
328	C₂×#124	—	17	6	no	—
329	C₂×#124	—	17	24	no	—
330	C₂×#121	—	17	12	no	—
331	C₂×#121	—	17	24	no	—
332	C₂×#120	—	17	8	no	—
333	C₂×#120	—	17	24	no	—
334	C₂×C₄×D₄	—	17	12	no	—
335	C₂×#117	—	17	12	no	—
336	C₂²×C₄²	—	17	1	no	—
337	C₂×C₁₇	—	4	12	no	—
338	C₂×C₁₇	—	4	1	no	—
339	C₂×C₁₇	C₂²×H(5,𝔽₂)	1	3	yes	—
340	D₁₇	—	4	1	no	—
341	D₁₇	—	4	12	no	—
342	D₁₇	#3549	1	4	yes	direct product factor
343	C₂⁵	—	17	8	no	—
344	C₂×#41	—	17	6	no	—
345	C₂×#41	—	17	12	no	—
346	C₂×#41	—	17	6	no	—
347	C₂×#41	—	17	12	no	—
348	C₂×#41	—	17	6	no	—
349	C₂×#41	—	68	24	no	—
350	C₂×#41	C₂²×D₁₇	1	6	yes	complemented
351	C₂²×Q₈	—	17	6	no	—
352	C₂²×D₄	—	17	24	no	—
353	C₂²×D₄	—	17	12	no	—
354	C₂²×D₄	—	17	6	no	—
355	C₂²×D₄	—	17	24	no	—
356	C₂²×D₄	—	17	12	no	—
357	C₂²×D₄	—	17	24	no	—
358	C₂²×D₄	—	17	24	no	—
359	C₂²×D₄	—	17	12	no	—
360	C₂²×D₄	—	68	48	no	—
361	C₂²×D₄	C₂²×D₁₇	1	12	yes	complemented
362	C₂³×C₄	—	17	12	no	—
363	C₂³×C₄	—	17	3	no	—
364	C₄⋊Q₈	—	17	6	no	—
365	C₄⋊Q₈	—	17	12	no	—
366	C₄⋊Q₈	—	17	3	no	—
367	C₄⋊Q₈	C₂²×D₁₇	1	3	yes	complemented
368	#127	—	17	6	no	—
369	#127	—	17	12	no	—
370	#127	—	17	24	no	—
371	#127	—	17	24	no	—
372	#127	—	17	3	no	—
373	#127	—	17	8	no	—
374	#127	C₂²×D₁₇	1	3	yes	—
375	#127	C₂²×D₁₇	1	8	yes	complemented
376	#124	—	17	6	no	—
377	#124	—	17	24	no	—
378	#124	—	17	6	no	—
379	#124	—	17	24	no	—
380	#124	—	17	24	no	—
381	#124	—	17	48	no	—
382	#124	—	17	48	no	—
383	#124	—	17	6	no	—
384	#124	—	17	24	no	—
385	#124	C₂²×D₁₇	1	6	yes	complemented
386	#124	C₂²×D₁₇	1	24	yes	complemented
387	#121	—	17	12	no	—
388	#121	—	17	24	no	—
389	#121	—	17	24	no	—
390	#121	—	17	48	no	—
391	#121	—	17	12	no	—
392	#121	—	17	24	no	—
393	#121	—	17	12	no	—
394	#121	—	17	24	no	—
395	#121	—	17	24	no	—
396	#121	—	17	48	no	—
397	#121	C₂²×D₁₇	1	12	yes	complemented
398	#121	C₂²×D₁₇	1	24	yes	complemented
399	#120	—	17	8	no	—
400	#120	—	17	24	no	—
401	#120	—	17	24	no	—
402	#120	—	17	24	no	—
403	#120	—	17	48	no	—
404	#120	—	17	24	no	—
405	#120	—	17	48	no	—
406	#120	—	17	24	no	—
407	#120	C₂²×D₁₇	1	8	yes	complemented
408	#120	C₂²×D₁₇	1	24	yes	complemented
409	C₄×D₄	—	17	12	no	—
410	C₄×D₄	—	17	24	no	—
411	C₄×D₄	—	17	12	no	—
412	C₄×D₄	—	17	24	no	—
413	C₄×D₄	—	17	12	no	—
414	C₄×D₄	C₂²×D₁₇	1	12	yes	complemented
415	#117	—	17	12	no	—
416	#117	—	17	24	no	—
417	#117	—	17	24	no	—
418	#117	—	17	24	no	—
419	#117	C₂²×D₁₇	1	12	yes	complemented
420	C₂×C₄⋊C₄	—	17	12	no	—
421	C₂×C₂²⋊C₄	—	17	24	no	—
422	C₂×C₂²⋊C₄	—	17	24	no	—
423	C₂×C₄²	—	17	3	no	—
424	C₂×C₄²	—	17	8	no	—
425	C₂×C₄²	—	17	3	no	—
426	C₂×C₄²	—	17	1	no	—
427	C₂×C₄²	—	17	1	no	—
428	C₂×C₄²	—	17	3	no	—
429	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic, complemented
430	C₁₇	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
431	C₂⁴	—	17	12	no	—
432	C₂⁴	—	17	1	no	—
433	C₂⁴	—	17	24	no	—
434	C₂⁴	—	68	48	no	—
435	C₂⁴	C₂³×D₁₇	1	8	yes	—
436	#41	—	4	12	no	—
437	#41	—	68	24	no	—
438	#41	—	68	12	no	—
439	#41	—	68	24	no	—
440	#41	—	68	12	no	—
441	#41	—	68	12	no	—
442	C₂×Q₈	—	17	12	no	—
443	C₂×Q₈	—	17	6	no	—
444	C₂×Q₈	—	68	12	no	—
445	C₂×Q₈	C₂³×D₁₇	1	6	yes	—
446	C₂×D₄	—	4	24	no	—
447	C₂×D₄	—	17	24	no	—
448	C₂×D₄	—	17	12	no	—
449	C₂×D₄	—	17	48	no	—
450	C₂×D₄	—	17	12	no	—
451	C₂×D₄	—	17	12	no	—
452	C₂×D₄	—	17	12	no	—
453	C₂×D₄	—	17	6	no	—
454	C₂×D₄	—	17	24	no	—
455	C₂×D₄	—	17	12	no	—
456	C₂×D₄	—	34	48	no	—
457	C₂×D₄	—	68	24	no	—
458	C₂×D₄	—	68	48	no	—
459	C₂×D₄	—	68	48	no	—
460	C₂×D₄	—	68	48	no	—
461	C₂×D₄	—	68	24	no	—
462	C₂×D₄	—	68	12	no	—
463	C₂×D₄	—	68	48	no	—
464	C₂×D₄	C₂³×D₁₇	1	12	yes	—
465	C₂×D₄	C₂³×D₁₇	1	6	yes	—
466	C₂×D₄	C₂³×D₁₇	1	24	yes	—
467	C₂×D₄	C₂³×D₁₇	1	12	yes	—
468	C₂²×C₄	—	17	3	no	—
469	C₂²×C₄	—	17	3	no	—
470	C₂²×C₄	—	17	12	no	—
471	C₂²×C₄	—	17	3	no	—
472	C₂²×C₄	—	17	12	no	—
473	C₂²×C₄	—	17	3	no	—
474	C₂²×C₄	—	17	3	no	—
475	C₂²×C₄	—	17	12	no	—
476	C₂²×C₄	—	17	12	no	—
477	C₂²×C₄	—	34	48	no	—
478	C₂²×C₄	—	34	12	no	—
479	C₂²×C₄	C₂³×D₁₇	1	3	yes	—
480	C₂²×C₄	C₂³×D₁₇	1	12	yes	—
481	C₄⋊C₄	—	17	24	no	—
482	C₄⋊C₄	—	17	12	no	—
483	C₄⋊C₄	C₂³×D₁₇	1	12	yes	—
484	C₂²⋊C₄	—	17	24	no	—
485	C₂²⋊C₄	—	17	24	no	—
486	C₂²⋊C₄	—	17	48	no	—
487	C₂²⋊C₄	—	17	24	no	—
488	C₂²⋊C₄	—	17	24	no	—
489	C₂²⋊C₄	C₂³×D₁₇	1	24	yes	—
490	C₂²⋊C₄	C₂³×D₁₇	1	24	yes	—
491	C₄²	—	17	3	no	—
492	C₄²	—	17	6	no	—
493	C₄²	—	17	3	no	—
494	C₄²	—	17	24	no	—
495	C₄²	C₂³×D₁₇	1	3	yes	—
496	C₄²	C₂³×D₁₇	1	1	yes	characteristic
497	C₄²	C₂³×D₁₇	1	8	yes	—
498	C₂³	—	4	24	no	—
499	C₂³	—	17	1	no	—
500	C₂³	—	17	12	no	—
501	C₂³	—	17	1	no	—
502	C₂³	—	34	6	no	—
503	C₂³	—	34	24	no	—
504	C₂³	—	34	48	no	—
505	C₂³	—	68	24	no	—
506	C₂³	—	68	48	no	—
507	C₂³	—	136	64	no	—
508	C₂³	C₂⁴×D₁₇	1	12	yes	—
509	C₂³	C₂⁴×D₁₇	1	1	yes	characteristic
510	Q₈	—	4	6	no	—
511	Q₈	—	68	12	no	—
512	Q₈	—	68	6	no	—
513	D₄	—	2	24	no	—
514	D₄	—	4	24	no	—
515	D₄	—	4	12	no	—
516	D₄	—	4	6	no	—
517	D₄	—	34	48	no	—
518	D₄	—	34	24	no	—
519	D₄	—	68	24	no	—
520	D₄	—	68	12	no	—
521	D₄	—	68	6	no	—
522	D₄	—	68	48	no	—
523	D₄	—	68	12	no	—
524	D₄	—	68	12	no	—
525	D₄	—	68	12	no	—
526	C₂×C₄	—	2	24	no	—
527	C₂×C₄	—	2	6	no	—
528	C₂×C₄	—	17	3	no	—
529	C₂×C₄	—	17	12	no	—
530	C₂×C₄	—	17	3	no	—
531	C₂×C₄	—	17	12	no	—
532	C₂×C₄	—	34	24	no	—
533	C₂×C₄	—	34	6	no	—
534	C₂×C₄	—	34	24	no	—
535	C₂×C₄	—	34	6	no	—
536	C₂×C₄	—	34	24	no	—
537	C₂×C₄	—	34	6	no	—
538	C₂×C₄	—	34	24	no	—
539	C₂×C₄	—	34	6	no	—
540	C₂×C₄	C₂⁴×D₁₇	1	3	yes	—
541	C₂×C₄	C₂⁴×D₁₇	1	12	yes	—
542	C₂×C₄	C₂⁴×D₁₇	1	3	yes	—
543	C₂²	—	2	3	no	—
544	C₂²	—	2	12	no	—
545	C₂²	—	2	24	no	—
546	C₂²	—	8	16	no	—
547	C₂²	—	17	6	no	—
548	C₂²	—	34	3	no	—
549	C₂²	—	34	12	no	—
550	C₂²	—	34	24	no	—
551	C₂²	—	68	48	no	—
552	C₂²	—	68	4	no	—
553	C₂²	—	136	48	no	—
554	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
555	C₄	—	2	12	no	—
556	C₄	—	2	3	no	—
557	C₄	—	17	6	no	—
558	C₄	—	34	12	no	—
559	C₄	—	34	3	no	—
560	C₄	H(5,𝔽₂)×D₁₇	1	6	yes	—
561	C₂	—	4	12	no	—
562	C₂	—	4	1	no	—
563	C₂	—	17	4	no	—
564	C₂	—	68	12	no	—
565	C₂	—	68	1	no	—
566	C₂	C₂×H(5,𝔽₂)×D₁₇	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁶
Fitting	C₁₇×#3549	C₂
hypercenter	#3549	D₁₇
hypocenter	C₁₇	C₂×#3549
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #3549

Complements

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

N	H ≅ G/N	type
1. #14543189	C₂	semidirect
2. #14543188	C₂	semidirect
3. #14543187	C₂	semidirect
4. #14543186	C₂	semidirect
5. #14543185	C₂	semidirect
6. D₁₇×H(3,𝔽₄)	C₂	semidirect
7. D₁₇×#555	C₂	semidirect
8. D₄²×D₁₇	C₂	semidirect
9. D₁₇×#535	C₂	semidirect
10. D₁₇×#532	C₂	semidirect
11. C₁₇×#3549	C₂	semidirect
12. C₂×#41×D₁₇	C₂²	semidirect
13. C₂²×D₄×D₁₇	C₂²	semidirect
14. #11763552	C₂²	semidirect
15. #11763551	C₂²	semidirect
16. #11763551	C₂²	semidirect
17. #11763525	C₂²	semidirect
18. #11763524	C₂²	semidirect
19. #11763523	C₂²	semidirect
20. #11763522	C₂²	semidirect
21. #11763521	C₂²	semidirect
22. D₄×D₆₈	C₂²	semidirect
23. #11763444	C₂²	semidirect
24. #11763443	C₂²	semidirect
25. D₄×C₂²⋊D₁₇	C₂²	semidirect
26. #11763441	C₂²	semidirect
27. #11763378	C₂²	semidirect
28. #11763377	C₂²	semidirect
29. #11763376	C₂²	semidirect
30. #11763375	C₂²	semidirect
31. #11763375	C₂²	semidirect
32. #11763374	C₂²	semidirect
33. #11763374	C₂²	semidirect
34. #11763373	C₂²	semidirect
35. #11763372	C₂²	semidirect
36. #11763360	C₂²	semidirect
37. #11763359	C₂²	semidirect
38. #11763358	C₂²	semidirect
39. #11763357	C₂²	semidirect
40. #11763356	C₂²	semidirect
41. #11763355	C₂²	semidirect
42. #11763354	C₂²	semidirect
43. C₄⋊Q₈×D₁₇	C₂²	semidirect
45. #127×D₁₇	C₂²	semidirect
46. #124×D₁₇	C₂²	semidirect
47. #124×D₁₇	C₂²	semidirect
48. #121×D₁₇	C₂²	semidirect
49. #121×D₁₇	C₂²	semidirect
50. #120×D₁₇	C₂²	semidirect
51. #120×D₁₇	C₂²	semidirect
52. C₄×D₄×D₁₇	C₂²	semidirect
53. #117×D₁₇	C₂²	semidirect
54. C₂×C₄²×D₁₇	C₂²	semidirect
55. C₁₇×H(3,𝔽₄)	C₂²	semidirect
56. C₁₇×#555	C₂²	semidirect
57. D₄²×C₁₇	C₂²	semidirect
58. C₁₇×#535	C₂²	semidirect
59. C₁₇×#532	C₂²	semidirect
61. C₂×#41×C₁₇	C₂³	semidirect
62. C₂²×D₄×C₁₇	C₂³	semidirect
63. C₂²×C₂²⋊D₁₇	C₂³	semidirect
65. C₂×#63256	C₂³	semidirect
67. C₂×#63254	C₂³	semidirect
68. C₂×#63254	C₂³	semidirect
74. C₂×D₄×D₁₇	C₂³	semidirect
75. C₂×D₄×D₁₇	C₂³	semidirect
76. C₂×#63252	C₂³	semidirect
77. C₂×#63252	C₂³	semidirect
78. C₂²×D₆₈	C₂³	semidirect
81. C₁₇×C₄⋊Q₈	C₂³	semidirect
83. C₁₇×#127	C₂³	semidirect
84. C₁₇×#124	C₂³	semidirect
85. C₁₇×#124	C₂³	semidirect
86. C₁₇×#121	C₂³	semidirect
87. C₁₇×#121	C₂³	semidirect
88. C₁₇×#120	C₂³	semidirect
89. C₁₇×#120	C₂³	semidirect
90. C₄×D₄×C₁₇	C₂³	semidirect
91. C₁₇×#117	C₂³	semidirect
92. C₂×C₄²×C₁₇	C₂³	semidirect
93. #10587639	C₂³	semidirect
94. #10587639	C₂³	semidirect
95. #10587633	C₂³	semidirect
96. #10587633	C₂³	semidirect
97. #10587630	C₂³	semidirect
100. #10587626	C₂³	semidirect
101. #10587626	C₂³	semidirect
102. #10587625	C₂³	semidirect
103. #10587625	C₂³	semidirect
104. #10587624	C₂³	semidirect
105. #10587624	C₂³	semidirect
106. #10587623	C₂³	semidirect
107. #10587623	C₂³	semidirect
108. #10587623	C₂³	semidirect
109. #10587622	C₂³	semidirect
110. #10587622	C₂³	semidirect
111. D₄×Dic₁₇	C₂³	semidirect
112. #10587616	C₂³	semidirect
113. #10587616	C₂³	semidirect
114. C₄×C₂²⋊D₁₇	C₂³	semidirect
115. #10587612	C₂³	semidirect
116. C₂×C₄×Dic₁₇	C₂³	semidirect
117. #10587581	C₂³	semidirect
118. #10587581	C₂³	semidirect
119. #10587579	C₂³	semidirect
120. #10587578	C₂³	semidirect
122. #10587574	C₂³	semidirect
123. #10587571	C₂³	semidirect
124. #10587571	C₂³	semidirect
125. #10587571	C₂³	semidirect
126. #10587570	C₂³	semidirect
127. #10587570	C₂³	semidirect
128. #10587568	C₂³	semidirect
129. #10587568	C₂³	semidirect
130. #10587568	C₂³	semidirect
131. #10587567	C₂³	semidirect
134. #10587563	C₂³	semidirect
135. #10587561	C₂³	semidirect
136. #10587561	C₂³	semidirect
138. #10587560	C₂³	semidirect
139. C₄×D₆₈	C₂³	semidirect
140. #10587558	C₂³	semidirect
144. C₄²×D₁₇	C₂³	semidirect
145. C₄²×D₁₇	C₂³	semidirect
146. #10587555	C₂³	semidirect
265. #3549	D₁₇	direct (N × H)
294. H(3,𝔽₄)	C₂×D₁₇	semidirect
300. #555	C₂×D₁₇	semidirect
306. D₄²	C₂×D₁₇	semidirect
316. #535	C₂×D₁₇	semidirect
324. #532	C₂×D₁₇	semidirect
342. D₁₇	#3549	direct (N × H)
350. C₂×#41	C₂²×D₁₇	semidirect
361. C₂²×D₄	C₂²×D₁₇	semidirect
367. C₄⋊Q₈	C₂²×D₁₇	semidirect
375. #127	C₂²×D₁₇	semidirect
385. #124	C₂²×D₁₇	semidirect
386. #124	C₂²×D₁₇	semidirect
397. #121	C₂²×D₁₇	semidirect
398. #121	C₂²×D₁₇	semidirect
407. #120	C₂²×D₁₇	semidirect
408. #120	C₂²×D₁₇	semidirect
414. C₄×D₄	C₂²×D₁₇	semidirect
419. #117	C₂²×D₁₇	semidirect
429. C₂×C₄²	C₂²×D₁₇	semidirect
430. C₁₇	C₂×#3549	semidirect

Maximal subgroups

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

subgroup	index
#14543189	2
#14543188	2
#14543187	2
#14543186	2
#14543185	2
D₁₇×H(3,𝔽₄)	2
D₁₇×#555	2
D₄²×D₁₇	2
D₁₇×#535	2
D₁₇×#532	2
C₁₇×#3549	2
C₂×#3549	17

Subgroups — D17×#3549 #17942122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×#3549 #17942122