Subgroups — C₂×#14542941 #17941447

Order 4352.

9542 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14542941	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11763548	C₂	1	3	yes	maximal, complemented
3	C₂×#11763489	C₂	1	3	yes	maximal, complemented
4	C₂×#11763452	C₂	1	6	yes	maximal, complemented
5	C₂×#11763441	C₂	1	3	yes	maximal, complemented
6	C₂×#11763393	C₂	1	6	yes	maximal, complemented
7	C₂×#11763377	C₂	1	3	yes	maximal, complemented
8	C₂×#11763369	C₂	1	3	yes	maximal, complemented
9	C₂×#120×D₁₇	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₇×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₇	C₂²	1	1	yes	characteristic, complemented
12	C₂²×#63256	C₂²	1	3	yes	complemented
13	C₂³×C₂²⋊D₁₇	C₂²	1	3	yes	complemented
14	C₂²×D₄×D₁₇	C₂²	1	3	yes	complemented
15	C₂²×D₄×D₁₇	C₂²	1	6	yes	complemented
16	#11763548	C₂²	1	48	yes	complemented
17	#11763489	C₂²	1	48	yes	complemented
18	#11763452	C₂²	1	96	yes	complemented
19	#11763441	C₂²	1	48	yes	complemented
20	#11763393	C₂²	1	96	yes	complemented
21	#11763377	C₂²	1	48	yes	complemented
22	#11763369	C₂²	1	48	yes	complemented
23	C₂×#10587560	C₂²	1	1	yes	characteristic, complemented
24	C₂×#10587626	C₂²	1	3	yes	complemented
25	C₂×#10587562	C₂²	1	2	yes	complemented
26	C₂×#10587565	C₂²	1	6	yes	complemented
27	C₂×#10587633	C₂²	1	3	yes	complemented
28	C₂×#10587572	C₂²	1	3	yes	complemented
29	C₂×#10587569	C₂²	1	6	yes	complemented
30	C₂×#10587569	C₂²	1	6	yes	complemented
31	C₂×#10587621	C₂²	1	3	yes	complemented
32	C₂×#10587632	C₂²	1	6	yes	complemented
33	C₂×#10587570	C₂²	1	6	yes	complemented
34	C₂×#10587570	C₂²	1	6	yes	complemented
35	C₂×#10587570	C₂²	1	6	yes	complemented
36	C₂×#10587625	C₂²	1	6	yes	complemented
37	C₂×#10587624	C₂²	1	6	yes	complemented
38	C₂×#10587568	C₂²	1	6	yes	complemented
39	C₂×#10587568	C₂²	1	3	yes	complemented
40	C₂×#10587568	C₂²	1	6	yes	complemented
41	C₂×#10587639	C₂²	1	3	yes	complemented
42	C₂×#10587639	C₂²	1	1	yes	characteristic, complemented
43	C₂×#10587623	C₂²	1	3	yes	—
44	C₂×#10587623	C₂²	1	6	yes	complemented
45	#120×D₁₇	C₂²	1	48	yes	complemented
46	C₂×C₄×D₆₈	C₂²	1	6	yes	complemented
47	C₂×#10587567	C₂²	1	6	yes	complemented
48	C₂×#10587558	C₂²	1	3	yes	complemented
49	C₂×C₂²⋊C₄×D₁₇	C₂²	1	3	yes	complemented
50	C₂×C₂²⋊C₄×D₁₇	C₂²	1	6	yes	complemented
51	C₂×C₂²⋊C₄×D₁₇	C₂²	1	3	yes	complemented
52	C₁₇×H(3,𝔽₄)	C₂²	1	16	yes	complemented
53	C₂×C₁₇×#124	C₂²	1	3	yes	complemented
54	C₂×C₁₇×#124	C₂²	1	6	yes	complemented
55	C₂×C₁₇×#120	C₂²	1	3	yes	complemented
56	C₂×C₁₇×#120	C₂²	1	3	yes	complemented
57	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic
58	C₂⁵×C₁₇	C₂³	1	1	yes	characteristic, complemented
59	C₂⁴×D₁₇	—	4	12	no	—
60	C₂⁴×D₁₇	C₂³	1	3	yes	—
61	C₂⁴×D₁₇	C₂³	1	3	yes	—
62	C₂⁴×D₁₇	C₂³	1	3	yes	—
63	C₂⁴×D₁₇	C₂³	1	8	yes	complemented
64	C₂²×Q₈×C₁₇	C₂³	1	3	yes	complemented
65	C₂²×D₄×C₁₇	C₂³	1	3	yes	—
66	C₂²×D₄×C₁₇	C₂³	1	6	yes	—
67	C₂²×C₂²⋊D₁₇	—	4	12	no	—
68	C₂²×C₂²⋊D₁₇	C₂³	1	6	yes	—
69	C₂²×C₂²⋊D₁₇	C₂³	1	3	yes	—
70	C₂²×C₂²⋊D₁₇	C₂³	1	3	yes	—
71	C₂²×C₂²⋊D₁₇	C₂³	1	6	yes	—
72	C₂²×C₂²⋊D₁₇	C₂³	1	6	yes	complemented
73	C₂²×C₂²⋊D₁₇	C₂³	1	24	yes	complemented
74	C₂³×Dic₁₇	C₂³	1	3	yes	complemented
75	C₂×#63256	—	4	12	no	—
76	C₂×#63256	C₂³	1	24	yes	complemented
77	C₂×D₄×D₁₇	—	4	12	no	—
78	C₂×D₄×D₁₇	—	4	24	no	—
79	C₂×D₄×D₁₇	C₂³	1	24	yes	complemented
80	C₂×D₄×D₁₇	C₂³	1	48	yes	complemented
81	C₂²×D₆₈	C₂³	1	6	yes	—
82	C₂²×D₆₈	C₂³	1	3	yes	—
83	C₂²×D₆₈	C₂³	1	3	yes	complemented
84	C₂²×C₄×D₁₇	C₂³	1	3	yes	—
85	C₂²×C₄×D₁₇	C₂³	1	6	yes	—
86	C₂²×C₄×D₁₇	C₂³	1	6	yes	complemented
87	C₁₇×#124	C₂³	1	24	yes	complemented
88	C₁₇×#124	C₂³	1	48	yes	complemented
89	C₁₇×#120	C₂³	1	24	yes	complemented
90	C₁₇×#120	C₂³	1	24	yes	complemented
91	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
92	C₂×C₂²⋊C₄×C₁₇	C₂³	1	3	yes	—
93	C₂×C₂²⋊C₄×C₁₇	C₂³	1	3	yes	complemented
94	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	complemented
95	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic, complemented
96	C₂×C₄²×C₁₇	C₂³	1	2	yes	complemented
97	#10587639	C₂³	1	24	yes	complemented
98	#10587639	C₂³	1	8	yes	complemented
99	C₂×C₂²⋊Dic₁₇	C₂³	1	3	yes	—
100	C₂×C₂²⋊Dic₁₇	C₂³	1	6	yes	—
101	C₂×C₂²⋊Dic₁₇	C₂³	1	3	yes	complemented
102	#10587633	C₂³	1	24	yes	complemented
103	#10587632	C₂³	1	48	yes	complemented
104	#10587626	C₂³	1	24	yes	complemented
105	#10587625	C₂³	1	48	yes	complemented
106	#10587624	C₂³	1	48	yes	complemented
107	#10587623	C₂³	1	24	yes	—
108	#10587623	C₂³	1	48	yes	complemented
109	#10587621	C₂³	1	24	yes	complemented
110	C₂×#63227	C₂³	1	6	yes	—
111	C₂×#63227	C₂³	1	6	yes	—
112	C₂×#63227	C₂³	1	6	yes	—
113	C₂×#63227	C₂³	1	6	yes	complemented
114	C₂×C₄⋊Dic₁₇	C₂³	1	6	yes	complemented
115	C₂×#63225	C₂³	1	6	yes	complemented
116	C₂×#63225	C₂³	1	6	yes	complemented
117	C₂×C₄×Dic₁₇	C₂³	1	3	yes	complemented
118	#10587572	C₂³	1	24	yes	complemented
119	#10587570	C₂³	1	48	yes	complemented
120	#10587570	C₂³	1	48	yes	complemented
121	#10587570	C₂³	1	48	yes	complemented
122	#10587569	C₂³	1	48	yes	complemented
123	#10587569	C₂³	1	48	yes	complemented
124	#10587568	C₂³	1	48	yes	complemented
125	#10587568	C₂³	1	24	yes	complemented
126	#10587568	C₂³	1	48	yes	complemented
127	#10587567	C₂³	1	48	yes	complemented
128	C₂²⋊C₄×D₁₇	C₂³	1	48	yes	complemented
129	C₂²⋊C₄×D₁₇	C₂³	1	24	yes	complemented
130	C₂²⋊C₄×D₁₇	C₂³	1	24	yes	complemented
131	#10587565	C₂³	1	48	yes	complemented
132	#10587562	C₂³	1	16	yes	complemented
133	#10587560	C₂³	1	8	yes	complemented
134	C₄×D₆₈	C₂³	1	48	yes	complemented
135	#10587558	C₂³	1	24	yes	complemented
136	C₂⁴×C₁₇	—	4	6	no	—
137	C₂⁴×C₁₇	—	4	6	no	—
138	C₂⁴×C₁₇	C₂⁴	1	3	yes	—
139	C₂⁴×C₁₇	C₂⁴	1	3	yes	—
140	C₂⁴×C₁₇	C₂⁴	1	4	yes	—
141	C₂⁴×C₁₇	C₂⁴	1	4	yes	complemented
142	C₂³×D₁₇	—	2	24	no	—
143	C₂³×D₁₇	—	2	12	no	—
144	C₂³×D₁₇	—	2	12	no	—
145	C₂³×D₁₇	—	4	48	no	—
146	C₂³×D₁₇	—	4	6	no	—
147	C₂³×D₁₇	—	4	12	no	—
148	C₂³×D₁₇	—	4	12	no	—
149	C₂³×D₁₇	—	4	64	no	—
150	C₂³×D₁₇	C₂⁴	1	3	yes	—
151	C₂³×D₁₇	C₂⁴	1	1	yes	characteristic
152	C₂³×D₁₇	C₂⁴	1	12	yes	—
153	C₂³×D₁₇	C₂⁴	1	3	yes	—
154	C₂³×D₁₇	C₂⁴	1	12	yes	—
155	C₂³×D₁₇	C₂⁴	1	12	yes	—
156	C₂×Q₈×C₁₇	—	4	6	no	—
157	C₂×Q₈×C₁₇	C₂⁴	1	12	yes	complemented
158	C₂×D₄×C₁₇	—	4	6	no	—
159	C₂×D₄×C₁₇	—	4	12	no	—
160	C₂×D₄×C₁₇	C₂⁴	1	12	yes	—
161	C₂×D₄×C₁₇	C₂⁴	1	24	yes	—
162	C₂²×C₄×C₁₇	C₂⁴	1	6	yes	—
163	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
164	C₂×C₂²⋊D₁₇	—	2	24	no	—
165	C₂×C₂²⋊D₁₇	—	4	6	no	—
166	C₂×C₂²⋊D₁₇	—	4	6	no	—
167	C₂×C₂²⋊D₁₇	—	4	12	no	—
168	C₂×C₂²⋊D₁₇	—	4	12	no	—
169	C₂×C₂²⋊D₁₇	—	4	48	no	—
170	C₂×C₂²⋊D₁₇	C₂⁴	1	24	yes	—
171	C₂×C₂²⋊D₁₇	C₂⁴	1	24	yes	—
172	C₂×C₂²⋊D₁₇	C₂⁴	1	12	yes	—
173	C₂×C₂²⋊D₁₇	C₂⁴	1	12	yes	—
174	C₂×C₂²⋊D₁₇	C₂⁴	1	24	yes	complemented
175	C₂²×Dic₁₇	—	4	6	no	—
176	C₂²×Dic₁₇	C₂⁴	1	3	yes	—
177	C₂²×Dic₁₇	C₂⁴	1	6	yes	—
178	C₂²×Dic₁₇	C₂⁴	1	12	yes	complemented
179	#63256	—	4	48	no	—
180	D₄×D₁₇	—	4	48	no	—
181	D₄×D₁₇	—	4	96	no	—
182	C₂×D₆₈	—	2	24	no	—
183	C₂×D₆₈	—	4	6	no	—
184	C₂×D₆₈	—	4	6	no	—
185	C₂×D₆₈	C₂⁴	1	24	yes	—
186	C₂×D₆₈	C₂⁴	1	12	yes	—
187	C₂×D₆₈	C₂⁴	1	12	yes	complemented
188	C₂×C₄×D₁₇	—	2	12	no	—
189	C₂×C₄×D₁₇	—	4	12	no	—
190	C₂×C₄×D₁₇	—	4	12	no	—
191	C₂×C₄×D₁₇	C₂⁴	1	12	yes	—
192	C₂×C₄×D₁₇	C₂⁴	1	24	yes	—
193	C₂×C₄×D₁₇	C₂⁴	1	24	yes	complemented
194	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
195	C₂²⋊C₄×C₁₇	C₂⁴	1	12	yes	—
196	C₂²⋊C₄×C₁₇	C₂⁴	1	12	yes	complemented
197	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	complemented
198	C₄²×C₁₇	C₂⁴	1	4	yes	complemented
199	C₄²×C₁₇	C₂⁴	1	8	yes	complemented
200	C₂²⋊Dic₁₇	C₂⁴	1	12	yes	—
201	C₂²⋊Dic₁₇	C₂⁴	1	24	yes	—
202	C₂²⋊Dic₁₇	C₂⁴	1	12	yes	complemented
203	#63227	C₂⁴	1	24	yes	—
204	#63227	C₂⁴	1	24	yes	—
205	#63227	C₂⁴	1	24	yes	—
206	#63227	C₂⁴	1	24	yes	complemented
207	C₄⋊Dic₁₇	C₂⁴	1	24	yes	complemented
208	#63225	C₂⁴	1	24	yes	complemented
209	#63225	C₂⁴	1	24	yes	complemented
210	C₄×Dic₁₇	C₂⁴	1	12	yes	complemented
211	C₂×#3532	—	17	1	no	maximal, Sylow
212	C₂³×C₁₇	—	2	6	no	—
213	C₂³×C₁₇	—	2	12	no	—
214	C₂³×C₁₇	—	2	6	no	—
215	C₂³×C₁₇	—	2	12	no	—
216	C₂³×C₁₇	—	4	12	no	—
217	C₂³×C₁₇	—	4	12	no	—
218	C₂³×C₁₇	—	4	16	no	—
219	C₂³×C₁₇	—	8	8	no	—
220	C₂³×C₁₇	C₂⁵	1	6	yes	—
221	C₂³×C₁₇	C₂⁵	1	6	yes	—
222	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
223	C₂²×D₁₇	—	2	12	no	—
224	C₂²×D₁₇	—	2	12	no	—
225	C₂²×D₁₇	—	2	6	no	—
226	C₂²×D₁₇	—	2	6	no	—
227	C₂²×D₁₇	—	2	48	no	—
228	C₂²×D₁₇	—	2	24	no	—
229	C₂²×D₁₇	—	2	24	no	—
230	C₂²×D₁₇	—	4	12	no	—
231	C₂²×D₁₇	—	4	24	no	—
232	C₂²×D₁₇	—	4	48	no	—
233	C₂²×D₁₇	—	4	24	no	—
234	C₂²×D₁₇	—	4	48	no	—
235	C₂²×D₁₇	—	4	128	no	—
236	C₂²×D₁₇	—	8	24	no	—
237	C₂²×D₁₇	H(5,𝔽₂)	1	12	yes	—
238	C₂²×D₁₇	C₂⁵	1	6	yes	—
239	C₂²×D₁₇	C₂⁵	1	2	yes	—
240	C₂²×D₁₇	C₂⁵	1	6	yes	—
241	Q₈×C₁₇	—	4	12	no	—
242	D₄×C₁₇	—	4	12	no	—
243	D₄×C₁₇	—	4	24	no	—
244	C₂×C₄×C₁₇	—	2	6	no	—
245	C₂×C₄×C₁₇	—	2	12	no	—
246	C₂×C₄×C₁₇	C₂⁵	1	12	yes	—
247	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
248	C₂²⋊D₁₇	—	2	48	no	—
249	C₂²⋊D₁₇	—	4	12	no	—
250	C₂²⋊D₁₇	—	4	12	no	—
251	C₂²⋊D₁₇	—	4	24	no	—
252	C₂²⋊D₁₇	—	4	24	no	—
253	C₂×Dic₁₇	—	2	6	no	—
254	C₂×Dic₁₇	—	2	12	no	—
255	C₂×Dic₁₇	—	4	12	no	—
256	C₂×Dic₁₇	C₂⁵	1	6	yes	—
257	C₂×Dic₁₇	C₂⁵	1	12	yes	—
258	D₆₈	—	2	48	no	—
259	D₆₈	—	4	12	no	—
260	D₆₈	—	4	12	no	—
261	C₄×D₁₇	—	2	24	no	—
262	C₄×D₁₇	—	4	24	no	—
263	C₄×D₁₇	—	4	24	no	—
264	#3532	—	17	32	no	—
265	C₂×H(3,𝔽₄)	D₁₇	1	1	yes	characteristic, complemented
266	C₂×#560	—	17	3	no	—
267	C₂×#551	—	17	3	no	—
268	C₂×#546	—	17	6	no	—
269	C₂×D₄²	—	17	3	no	—
270	C₂×#538	—	17	6	no	—
271	C₂×#535	—	17	3	no	—
272	C₂×#534	—	17	3	no	—
273	C₂²×#120	—	17	3	no	—
274	C₂²×C₁₇	—	2	6	no	—
275	C₂²×C₁₇	—	2	12	no	—
276	C₂²×C₁₇	—	2	6	no	—
277	C₂²×C₁₇	—	2	12	no	—
278	C₂²×C₁₇	—	4	16	no	—
279	C₂²×C₁₇	—	4	12	no	—
280	C₂²×C₁₇	—	4	12	no	—
281	C₂²×C₁₇	—	8	8	no	—
282	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	6	yes	—
283	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
284	C₂×D₁₇	—	2	12	no	—
285	C₂×D₁₇	—	2	24	no	—
286	C₂×D₁₇	—	2	12	no	—
287	C₂×D₁₇	—	2	6	no	—
288	C₂×D₁₇	—	2	6	no	—
289	C₂×D₁₇	—	4	48	no	—
290	C₂×D₁₇	—	4	48	no	—
291	C₂×D₁₇	—	4	4	no	—
292	C₂×D₁₇	—	4	12	no	—
293	C₂×D₁₇	—	8	24	no	—
294	C₂×D₁₇	C₂×H(5,𝔽₂)	1	12	yes	—
295	C₄×C₁₇	—	2	6	no	—
296	C₄×C₁₇	—	2	12	no	—
297	Dic₁₇	—	2	6	no	—
298	Dic₁₇	—	2	12	no	—
299	C₂⁶	—	17	1	no	—
300	C₂²×#41	—	17	3	no	—
301	C₂³×D₄	—	17	3	no	—
302	C₂³×D₄	—	17	3	no	—
303	C₂³×D₄	—	17	6	no	—
304	H(3,𝔽₄)	C₂×D₁₇	1	16	yes	complemented
305	#560	—	17	48	no	—
306	#551	—	17	48	no	—
307	#546	—	17	96	no	—
308	D₄²	—	17	48	no	—
309	#538	—	17	96	no	—
310	#535	—	17	48	no	—
311	#534	—	17	48	no	—
312	C₂×#127	—	17	3	no	—
313	C₂×#127	—	17	1	no	—
314	C₂×#126	—	17	6	no	—
315	C₂×#126	—	17	2	no	—
316	C₂×#124	—	17	3	no	—
317	C₂×#124	C₂×D₁₇	1	3	yes	complemented
318	C₂×#124	C₂×D₁₇	1	6	yes	complemented
319	C₂×#123	—	17	3	no	—
320	C₂×#123	—	17	6	no	—
321	C₂×#123	—	17	6	no	—
322	C₂×#123	—	17	3	no	—
323	C₂×C₂²⋊Q₈	—	17	6	no	—
324	C₂×#121	—	17	6	no	—
325	C₂×#121	—	17	6	no	—
326	C₂×#121	—	17	6	no	—
327	C₂×#121	—	17	6	no	—
328	C₂×#121	—	17	6	no	—
329	C₂×#120	—	17	3	no	—
330	C₂×#120	—	17	1	no	—
331	C₂×#120	—	17	3	no	—
332	C₂×#120	—	17	6	no	—
333	C₂×#120	—	17	48	no	—
334	C₂×#120	—	17	6	no	—
335	C₂×#120	—	17	3	no	—
336	C₂×#120	—	17	6	no	—
337	C₂×#120	C₂×D₁₇	1	3	yes	complemented
338	C₂×#120	C₂×D₁₇	1	3	yes	complemented
339	C₂×C₄×D₄	—	17	6	no	—
340	C₂×C₄×D₄	—	17	6	no	—
341	C₂×#117	—	17	3	no	—
342	C₂²×C₂²⋊C₄	—	17	3	no	—
343	C₂²×C₂²⋊C₄	—	17	6	no	—
344	C₂²×C₂²⋊C₄	—	17	3	no	—
345	C₂×C₁₇	—	4	6	no	—
346	C₂×C₁₇	—	4	6	no	—
347	C₂×C₁₇	#3532	1	4	yes	complemented
348	C₂×C₁₇	C₂²×H(5,𝔽₂)	1	3	yes	—
349	D₁₇	—	2	12	no	—
350	D₁₇	—	4	2	no	—
351	D₁₇	—	4	6	no	—
352	C₂⁵	—	17	3	no	—
353	C₂⁵	—	17	3	no	—
354	C₂⁵	—	17	3	no	—
355	C₂⁵	—	17	8	no	—
356	C₂⁵	—	68	12	no	—
357	C₂⁵	C₂²×D₁₇	1	1	yes	characteristic
358	C₂⁵	C₂²×D₁₇	1	1	yes	characteristic, complemented
359	C₂×#41	—	17	24	no	—
360	C₂×#41	—	68	12	no	—
361	C₂²×Q₈	C₂²×D₁₇	1	3	yes	complemented
362	C₂²×D₄	—	17	6	no	—
363	C₂²×D₄	—	17	3	no	—
364	C₂²×D₄	—	17	3	no	—
365	C₂²×D₄	—	17	6	no	—
366	C₂²×D₄	—	17	6	no	—
367	C₂²×D₄	—	17	24	no	—
368	C₂²×D₄	—	17	24	no	—
369	C₂²×D₄	—	17	48	no	—
370	C₂²×D₄	—	17	6	no	—
371	C₂²×D₄	—	17	3	no	—
372	C₂²×D₄	—	17	3	no	—
373	C₂²×D₄	—	68	12	no	—
374	C₂²×D₄	—	68	24	no	—
375	C₂²×D₄	—	68	12	no	—
376	C₂²×D₄	C₂²×D₁₇	1	6	yes	—
377	C₂²×D₄	C₂²×D₁₇	1	3	yes	—
378	C₂³×C₄	—	17	3	no	—
379	C₂³×C₄	—	17	3	no	—
380	C₂³×C₄	—	17	6	no	—
381	C₂³×C₄	—	17	6	no	—
382	#127	—	17	24	no	—
383	#127	—	17	8	no	—
384	#126	—	17	48	no	—
385	#126	—	17	16	no	—
386	#124	—	17	24	no	—
387	#124	C₂²×D₁₇	1	24	yes	complemented
388	#124	C₂²×D₁₇	1	48	yes	complemented
389	#123	—	17	24	no	—
390	#123	—	17	48	no	—
391	#123	—	17	24	no	—
392	#123	—	17	48	no	—
393	C₂²⋊Q₈	—	17	48	no	—
394	#121	—	17	48	no	—
395	#121	—	17	48	no	—
396	#121	—	17	48	no	—
397	#121	—	17	48	no	—
398	#121	—	17	48	no	—
399	#120	—	17	24	no	—
400	#120	—	17	8	no	—
401	#120	—	17	48	no	—
402	#120	—	17	24	no	—
403	#120	—	17	48	no	—
404	#120	—	17	24	no	—
405	#120	—	17	48	no	—
406	#120	C₂²×D₁₇	1	24	yes	complemented
407	#120	C₂²×D₁₇	1	24	yes	complemented
408	C₄×D₄	—	17	48	no	—
409	C₄×D₄	—	17	48	no	—
410	#117	—	17	24	no	—
411	C₂×C₄⋊C₄	—	17	6	no	—
412	C₂×C₄⋊C₄	—	17	6	no	—
413	C₂×C₄⋊C₄	—	17	6	no	—
414	C₂×C₂²⋊C₄	—	17	3	no	—
415	C₂×C₂²⋊C₄	—	17	6	no	—
416	C₂×C₂²⋊C₄	—	17	3	no	—
417	C₂×C₂²⋊C₄	—	17	6	no	—
418	C₂×C₂²⋊C₄	—	17	6	no	—
419	C₂×C₂²⋊C₄	—	17	6	no	—
420	C₂×C₂²⋊C₄	—	17	6	no	—
421	C₂×C₂²⋊C₄	—	17	24	no	—
422	C₂×C₂²⋊C₄	—	17	48	no	—
423	C₂×C₂²⋊C₄	—	17	24	no	—
424	C₂×C₂²⋊C₄	C₂²×D₁₇	1	6	yes	—
425	C₂×C₂²⋊C₄	C₂²×D₁₇	1	3	yes	—
426	C₂×C₂²⋊C₄	C₂²×D₁₇	1	3	yes	complemented
427	C₂×C₂²⋊C₄	C₂²×D₁₇	1	6	yes	complemented
428	C₂×C₄²	—	17	3	no	—
429	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic, complemented
430	C₂×C₄²	C₂²×D₁₇	1	2	yes	complemented
431	C₁₇	C₂×#3532	1	1	yes	characteristic, complemented, Sylow
432	C₂⁴	—	4	6	no	—
433	C₂⁴	—	4	6	no	—
434	C₂⁴	—	17	3	no	—
435	C₂⁴	—	17	1	no	—
436	C₂⁴	—	17	3	no	—
437	C₂⁴	—	17	12	no	—
438	C₂⁴	—	17	12	no	—
439	C₂⁴	—	17	12	no	—
440	C₂⁴	—	34	24	no	—
441	C₂⁴	—	34	12	no	—
442	C₂⁴	—	34	12	no	—
443	C₂⁴	—	68	6	no	—
444	C₂⁴	—	68	12	no	—
445	C₂⁴	—	68	12	no	—
446	C₂⁴	—	68	48	no	—
447	C₂⁴	—	68	64	no	—
448	C₂⁴	C₂³×D₁₇	1	3	yes	—
449	C₂⁴	C₂³×D₁₇	1	3	yes	—
450	C₂⁴	C₂³×D₁₇	1	4	yes	—
451	C₂⁴	C₂³×D₁₇	1	4	yes	complemented
452	#41	—	68	48	no	—
453	C₂×Q₈	—	4	6	no	—
454	C₂×Q₈	C₂³×D₁₇	1	12	yes	complemented
455	C₂×D₄	—	4	6	no	—
456	C₂×D₄	—	4	12	no	—
457	C₂×D₄	—	17	24	no	—
458	C₂×D₄	—	17	12	no	—
459	C₂×D₄	—	17	12	no	—
460	C₂×D₄	—	17	24	no	—
461	C₂×D₄	—	17	24	no	—
462	C₂×D₄	—	17	24	no	—
463	C₂×D₄	—	17	12	no	—
464	C₂×D₄	—	17	12	no	—
465	C₂×D₄	—	34	24	no	—
466	C₂×D₄	—	34	24	no	—
467	C₂×D₄	—	68	6	no	—
468	C₂×D₄	—	68	6	no	—
469	C₂×D₄	—	68	48	no	—
470	C₂×D₄	—	68	6	no	—
471	C₂×D₄	—	68	6	no	—
472	C₂×D₄	—	68	12	no	—
473	C₂×D₄	—	68	12	no	—
474	C₂×D₄	—	68	96	no	—
475	C₂×D₄	—	68	48	no	—
476	C₂×D₄	C₂³×D₁₇	1	24	yes	—
477	C₂×D₄	C₂³×D₁₇	1	12	yes	—
478	C₂²×C₄	—	17	6	no	—
479	C₂²×C₄	—	17	3	no	—
480	C₂²×C₄	—	17	12	no	—
481	C₂²×C₄	—	17	12	no	—
482	C₂²×C₄	—	17	24	no	—
483	C₂²×C₄	—	17	24	no	—
484	C₂²×C₄	—	34	12	no	—
485	C₂²×C₄	—	68	12	no	—
486	C₂²×C₄	—	68	12	no	—
487	C₂²×C₄	—	68	6	no	—
488	C₂²×C₄	C₂³×D₁₇	1	3	yes	—
489	C₂²×C₄	C₂³×D₁₇	1	6	yes	—
490	C₄⋊C₄	—	17	24	no	—
491	C₄⋊C₄	—	17	24	no	—
492	C₄⋊C₄	—	17	24	no	—
493	C₂²⋊C₄	—	17	12	no	—
494	C₂²⋊C₄	—	17	24	no	—
495	C₂²⋊C₄	—	17	12	no	—
496	C₂²⋊C₄	—	17	24	no	—
497	C₂²⋊C₄	—	17	24	no	—
498	C₂²⋊C₄	—	17	24	no	—
499	C₂²⋊C₄	—	17	24	no	—
500	C₂²⋊C₄	C₂³×D₁₇	1	24	yes	—
501	C₂²⋊C₄	C₂³×D₁₇	1	12	yes	—
502	C₂²⋊C₄	C₂³×D₁₇	1	12	yes	complemented
503	C₂²⋊C₄	C₂³×D₁₇	1	24	yes	complemented
504	C₄²	—	17	12	no	—
505	C₄²	C₂³×D₁₇	1	4	yes	complemented
506	C₄²	C₂³×D₁₇	1	8	yes	complemented
507	C₂³	—	2	6	no	—
508	C₂³	—	2	12	no	—
509	C₂³	—	2	6	no	—
510	C₂³	—	2	12	no	—
511	C₂³	—	4	12	no	—
512	C₂³	—	4	12	no	—
513	C₂³	—	4	16	no	—
514	C₂³	—	8	8	no	—
515	C₂³	—	17	12	no	—
516	C₂³	—	17	6	no	—
517	C₂³	—	17	2	no	—
518	C₂³	—	17	6	no	—
519	C₂³	—	34	48	no	—
520	C₂³	—	34	24	no	—
521	C₂³	—	34	24	no	—
522	C₂³	—	34	12	no	—
523	C₂³	—	34	12	no	—
524	C₂³	—	34	6	no	—
525	C₂³	—	34	6	no	—
526	C₂³	—	68	12	no	—
527	C₂³	—	68	24	no	—
528	C₂³	—	68	24	no	—
529	C₂³	—	68	48	no	—
530	C₂³	—	68	48	no	—
531	C₂³	—	68	128	no	—
532	C₂³	—	136	24	no	—
533	C₂³	C₂⁴×D₁₇	1	6	yes	—
534	C₂³	C₂⁴×D₁₇	1	6	yes	—
535	C₂³	C₂⁴×D₁₇	1	1	yes	characteristic
536	Q₈	—	4	12	no	—
537	D₄	—	4	12	no	—
538	D₄	—	4	24	no	—
539	D₄	—	34	48	no	—
540	D₄	—	34	48	no	—
541	D₄	—	68	12	no	—
542	D₄	—	68	12	no	—
543	D₄	—	68	12	no	—
544	D₄	—	68	12	no	—
545	D₄	—	68	24	no	—
546	D₄	—	68	24	no	—
547	C₂×C₄	—	2	6	no	—
548	C₂×C₄	—	2	12	no	—
549	C₂×C₄	—	17	12	no	—
550	C₂×C₄	—	17	6	no	—
551	C₂×C₄	—	34	24	no	—
552	C₂×C₄	—	34	6	no	—
553	C₂×C₄	—	34	12	no	—
554	C₂×C₄	—	68	24	no	—
555	C₂×C₄	—	68	24	no	—
556	C₂×C₄	—	68	12	no	—
557	C₂×C₄	C₂⁴×D₁₇	1	6	yes	—
558	C₂×C₄	C₂⁴×D₁₇	1	12	yes	—
559	C₂²	—	2	6	no	—
560	C₂²	—	2	12	no	—
561	C₂²	—	2	6	no	—
562	C₂²	—	2	12	no	—
563	C₂²	—	4	16	no	—
564	C₂²	—	4	12	no	—
565	C₂²	—	4	12	no	—
566	C₂²	—	8	8	no	—
567	C₂²	—	17	12	no	—
568	C₂²	—	34	24	no	—
569	C₂²	—	34	12	no	—
570	C₂²	—	34	12	no	—
571	C₂²	—	34	6	no	—
572	C₂²	—	34	6	no	—
573	C₂²	—	68	48	no	—
574	C₂²	—	68	48	no	—
575	C₂²	—	68	4	no	—
576	C₂²	—	68	12	no	—
577	C₂²	—	136	24	no	—
578	C₂²	H(5,𝔽₂)×D₁₇	1	6	yes	—
579	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
580	C₄	—	2	6	no	—
581	C₄	—	2	12	no	—
582	C₄	—	34	6	no	—
583	C₄	—	34	12	no	—
584	C₂	—	4	6	no	—
585	C₂	—	4	6	no	—
586	C₂	—	34	12	no	—
587	C₂	—	68	2	no	—
588	C₂	—	68	6	no	—
589	C₂	#14542941	1	4	yes	direct product factor
590	C₂	C₂×H(5,𝔽₂)×D₁₇	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₇
commutator, cosocle	C₂²×C₁₇	C₂⁶
Frattini	C₂²	C₂⁵×D₁₇
Fitting	C₂×C₁₇×H(3,𝔽₄)	C₂
socle	C₂³×C₁₇	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₁₇
hypocenter	C₁₇	C₂×#3532
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #14542941	C₂	direct (N × H)
2. C₂×#11763548	C₂	semidirect
3. C₂×#11763489	C₂	semidirect
4. C₂×#11763452	C₂	semidirect
5. C₂×#11763441	C₂	semidirect
6. C₂×#11763393	C₂	semidirect
7. C₂×#11763377	C₂	semidirect
8. C₂×#11763369	C₂	semidirect
9. C₂×#120×D₁₇	C₂	semidirect
10. C₂×C₁₇×H(3,𝔽₄)	C₂	semidirect
11. C₂⁵×D₁₇	C₂²	semidirect
12. C₂²×#63256	C₂²	semidirect
13. C₂³×C₂²⋊D₁₇	C₂²	semidirect
14. C₂²×D₄×D₁₇	C₂²	semidirect
15. C₂²×D₄×D₁₇	C₂²	semidirect
16. #11763548	C₂²	semidirect
17. #11763489	C₂²	semidirect
18. #11763452	C₂²	semidirect
19. #11763441	C₂²	semidirect
20. #11763393	C₂²	semidirect
21. #11763377	C₂²	semidirect
22. #11763369	C₂²	semidirect
23. C₂×#10587560	C₂²	semidirect
24. C₂×#10587626	C₂²	semidirect
25. C₂×#10587562	C₂²	semidirect
26. C₂×#10587565	C₂²	semidirect
27. C₂×#10587633	C₂²	semidirect
28. C₂×#10587572	C₂²	semidirect
29. C₂×#10587569	C₂²	semidirect
30. C₂×#10587569	C₂²	semidirect
31. C₂×#10587621	C₂²	semidirect
32. C₂×#10587632	C₂²	semidirect
33. C₂×#10587570	C₂²	semidirect
34. C₂×#10587570	C₂²	semidirect
35. C₂×#10587570	C₂²	semidirect
36. C₂×#10587625	C₂²	semidirect
37. C₂×#10587624	C₂²	semidirect
38. C₂×#10587568	C₂²	semidirect
39. C₂×#10587568	C₂²	semidirect
40. C₂×#10587568	C₂²	semidirect
41. C₂×#10587639	C₂²	semidirect
42. C₂×#10587639	C₂²	semidirect
44. C₂×#10587623	C₂²	semidirect
45. #120×D₁₇	C₂²	semidirect
46. C₂×C₄×D₆₈	C₂²	semidirect
47. C₂×#10587567	C₂²	semidirect
48. C₂×#10587558	C₂²	semidirect
49. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
50. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
51. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
52. C₁₇×H(3,𝔽₄)	C₂²	semidirect
53. C₂×C₁₇×#124	C₂²	semidirect
54. C₂×C₁₇×#124	C₂²	semidirect
55. C₂×C₁₇×#120	C₂²	semidirect
56. C₂×C₁₇×#120	C₂²	semidirect
58. C₂⁵×C₁₇	C₂³	semidirect
63. C₂⁴×D₁₇	C₂³	semidirect
64. C₂²×Q₈×C₁₇	C₂³	semidirect
72. C₂²×C₂²⋊D₁₇	C₂³	semidirect
73. C₂²×C₂²⋊D₁₇	C₂³	semidirect
74. C₂³×Dic₁₇	C₂³	semidirect
76. C₂×#63256	C₂³	semidirect
79. C₂×D₄×D₁₇	C₂³	semidirect
80. C₂×D₄×D₁₇	C₂³	semidirect
83. C₂²×D₆₈	C₂³	semidirect
86. C₂²×C₄×D₁₇	C₂³	semidirect
87. C₁₇×#124	C₂³	semidirect
88. C₁₇×#124	C₂³	semidirect
89. C₁₇×#120	C₂³	semidirect
90. C₁₇×#120	C₂³	semidirect
93. C₂×C₂²⋊C₄×C₁₇	C₂³	semidirect
94. C₂×C₂²⋊C₄×C₁₇	C₂³	semidirect
95. C₂×C₄²×C₁₇	C₂³	semidirect
96. C₂×C₄²×C₁₇	C₂³	semidirect
97. #10587639	C₂³	semidirect
98. #10587639	C₂³	semidirect
101. C₂×C₂²⋊Dic₁₇	C₂³	semidirect
102. #10587633	C₂³	semidirect
103. #10587632	C₂³	semidirect
104. #10587626	C₂³	semidirect
105. #10587625	C₂³	semidirect
106. #10587624	C₂³	semidirect
108. #10587623	C₂³	semidirect
109. #10587621	C₂³	semidirect
113. C₂×#63227	C₂³	semidirect
114. C₂×C₄⋊Dic₁₇	C₂³	semidirect
115. C₂×#63225	C₂³	semidirect
116. C₂×#63225	C₂³	semidirect
117. C₂×C₄×Dic₁₇	C₂³	semidirect
118. #10587572	C₂³	semidirect
119. #10587570	C₂³	semidirect
120. #10587570	C₂³	semidirect
121. #10587570	C₂³	semidirect
122. #10587569	C₂³	semidirect
123. #10587569	C₂³	semidirect
124. #10587568	C₂³	semidirect
125. #10587568	C₂³	semidirect
126. #10587568	C₂³	semidirect
127. #10587567	C₂³	semidirect
128. C₂²⋊C₄×D₁₇	C₂³	semidirect
129. C₂²⋊C₄×D₁₇	C₂³	semidirect
130. C₂²⋊C₄×D₁₇	C₂³	semidirect
131. #10587565	C₂³	semidirect
132. #10587562	C₂³	semidirect
133. #10587560	C₂³	semidirect
134. C₄×D₆₈	C₂³	semidirect
135. #10587558	C₂³	semidirect
141. C₂⁴×C₁₇	C₂⁴	semidirect
157. C₂×Q₈×C₁₇	C₂⁴	semidirect
174. C₂×C₂²⋊D₁₇	C₂⁴	semidirect
178. C₂²×Dic₁₇	C₂⁴	semidirect
187. C₂×D₆₈	C₂⁴	semidirect
193. C₂×C₄×D₁₇	C₂⁴	semidirect
196. C₂²⋊C₄×C₁₇	C₂⁴	semidirect
197. C₂²⋊C₄×C₁₇	C₂⁴	semidirect
198. C₄²×C₁₇	C₂⁴	semidirect
199. C₄²×C₁₇	C₂⁴	semidirect
202. C₂²⋊Dic₁₇	C₂⁴	semidirect
206. #63227	C₂⁴	semidirect
207. C₄⋊Dic₁₇	C₂⁴	semidirect
208. #63225	C₂⁴	semidirect
209. #63225	C₂⁴	semidirect
210. C₄×Dic₁₇	C₂⁴	semidirect
265. C₂×H(3,𝔽₄)	D₁₇	semidirect
304. H(3,𝔽₄)	C₂×D₁₇	semidirect
317. C₂×#124	C₂×D₁₇	semidirect
318. C₂×#124	C₂×D₁₇	semidirect
337. C₂×#120	C₂×D₁₇	semidirect
338. C₂×#120	C₂×D₁₇	semidirect
347. C₂×C₁₇	#3532	semidirect
358. C₂⁵	C₂²×D₁₇	semidirect
361. C₂²×Q₈	C₂²×D₁₇	semidirect
387. #124	C₂²×D₁₇	semidirect
388. #124	C₂²×D₁₇	semidirect
406. #120	C₂²×D₁₇	semidirect
407. #120	C₂²×D₁₇	semidirect
426. C₂×C₂²⋊C₄	C₂²×D₁₇	semidirect
427. C₂×C₂²⋊C₄	C₂²×D₁₇	semidirect
429. C₂×C₄²	C₂²×D₁₇	semidirect
430. C₂×C₄²	C₂²×D₁₇	semidirect
431. C₁₇	C₂×#3532	semidirect
451. C₂⁴	C₂³×D₁₇	semidirect
454. C₂×Q₈	C₂³×D₁₇	semidirect
502. C₂²⋊C₄	C₂³×D₁₇	semidirect
503. C₂²⋊C₄	C₂³×D₁₇	semidirect
505. C₄²	C₂³×D₁₇	semidirect
506. C₄²	C₂³×D₁₇	semidirect
589. C₂	#14542941	direct (N × H)

Maximal subgroups

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

subgroup	index
#14542941	2
C₂×#11763548	2
C₂×#11763489	2
C₂×#11763452	2
C₂×#11763441	2
C₂×#11763393	2
C₂×#11763377	2
C₂×#11763369	2
C₂×#120×D₁₇	2
C₂×C₁₇×H(3,𝔽₄)	2
C₂×#3532	17

Subgroups — C2×#14542941 #17941447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14542941 #17941447