Subgroups — C₂×C₄×#10587696 #17940927

Order 4352.

12378 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587696	C₂	1	1	yes	maximal, characteristic
2	C₄×#10587696	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11763292	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11763291	C₂	1	2	yes	maximal, complemented
5	C₂×#11763289	C₂	1	3	yes	maximal, complemented
6	C₂×#11763283	C₂	1	3	yes	maximal, complemented
7	C₂×#11763281	C₂	1	6	yes	maximal, complemented
8	C₂×C₄×#63256	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#63252	C₂	1	3	yes	maximal, complemented
10	C₂²×C₄×D₆₈	C₂	1	3	yes	maximal, complemented
11	C₂×C₄×D₄×D₁₇	C₂	1	6	yes	maximal, complemented
12	C₂×C₄×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#10587696	C₄	1	32	yes	direct product factor
14	C₂×#10587696	C₂²	1	16	yes	—
15	C₂²×#63256	C₂²	1	2	yes	—
16	C₂²×#63252	C₂²	1	3	yes	—
17	C₂³×D₆₈	C₂²	1	3	yes	—
18	C₂²×D₄×D₁₇	C₂²	1	6	yes	—
19	C₂³×C₄×D₁₇	C₂²	1	6	yes	complemented
20	#11763292	C₂²	1	16	yes	complemented
21	#11763291	C₂²	1	32	yes	complemented
22	#11763289	C₂²	1	48	yes	complemented
23	#11763283	C₂²	1	48	yes	complemented
24	#11763281	C₂²	1	96	yes	complemented
25	C₄×#63256	C₂²	1	32	yes	complemented
26	C₄×#63252	C₂²	1	48	yes	complemented
27	C₂×Q₈×Dic₁₇	C₂²	1	2	yes	complemented
28	C₂×C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×Dic₃₄	C₂²	1	3	yes	complemented
30	C₂×C₄×D₆₈	C₂²	1	6	yes	complemented
31	C₂×C₄×D₆₈	C₂²	1	3	yes	complemented
32	C₂×C₄×D₆₈	C₂²	1	6	yes	complemented
33	C₂×C₄×D₆₈	C₂²	1	6	yes	complemented
34	C₂×C₄×D₆₈	C₂²	1	3	yes	complemented
35	C₂×C₄×D₆₈	C₂²	1	48	yes	complemented
36	C₂×D₄×Dic₁₇	C₂²	1	6	yes	complemented
37	C₂×#10587579	C₂²	1	6	yes	complemented
38	C₂×#10587579	C₂²	1	6	yes	complemented
39	C₂×C₄×C₂²⋊D₁₇	C₂²	1	6	yes	complemented
40	C₂×C₄×C₂²⋊D₁₇	C₂²	1	6	yes	complemented
41	C₂×#10587567	C₂²	1	12	yes	complemented
42	C₄×D₄×D₁₇	C₂²	1	96	yes	complemented
43	C₂×#10587612	C₂²	1	3	yes	complemented
44	C₂×#10587578	C₂²	1	6	yes	complemented
45	C₂×#10587558	C₂²	1	6	yes	complemented
46	C₂²×C₄⋊Dic₁₇	C₂²	1	3	yes	complemented
47	C₂×C₄⋊C₄×D₁₇	C₂²	1	6	yes	complemented
48	C₂²×#63227	C₂²	1	6	yes	complemented
49	C₂×C₂²⋊C₄×D₁₇	C₂²	1	12	yes	complemented
50	C₂×C₄²×D₁₇	C₂²	1	6	yes	complemented
51	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic
52	C₄×#41×C₁₇	C₂²	1	16	yes	complemented
53	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₁₇	C₂²	1	3	yes	complemented
56	C₂×C₄×D₄×C₁₇	C₂²	1	3	yes	complemented
57	C₂×C₁₇×#117	C₂²	1	3	yes	complemented
58	C₂²×C₄²×C₁₇	C₂²	1	3	yes	complemented
59	C₂⁴×D₁₇	C₂³	1	6	yes	—
60	C₂×#41×C₁₇	C₂×C₄	1	16	yes	complemented
61	C₂×#41×C₁₇	C₂³	1	8	yes	—
62	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₇	C₂³	1	3	yes	—
64	C₂³×C₄×C₁₇	C₂³	1	3	yes	—
65	C₂³×C₄×C₁₇	C₂³	1	3	yes	—
66	C₂³×C₄×C₁₇	C₂³	1	3	yes	—
67	C₂²×C₂²⋊D₁₇	C₂³	1	6	yes	—
68	C₂³×Dic₁₇	C₂³	1	6	yes	—
69	#10587696	C₂×C₄	1	256	yes	direct product factor
70	C₂×#63256	C₂×C₄	1	32	yes	complemented
71	C₂×#63256	C₂³	1	16	yes	—
72	C₂×D₄×D₁₇	C₂×C₄	1	96	yes	complemented
73	C₂×D₄×D₁₇	C₂³	1	48	yes	—
74	C₂×#63252	C₂×C₄	1	48	yes	complemented
75	C₂×#63252	C₂³	1	24	yes	—
76	C₂²×D₆₈	C₂×C₄	1	48	yes	complemented
77	C₂²×D₆₈	C₂³	1	6	yes	—
78	C₂²×D₆₈	C₂³	1	3	yes	—
79	C₂²×D₆₈	C₂³	1	24	yes	—
80	C₂²×C₄×D₁₇	—	4	24	no	—
81	C₂²×C₄×D₁₇	C₂³	1	6	yes	—
82	C₂²×C₄×D₁₇	C₂³	1	6	yes	—
83	C₂²×C₄×D₁₇	C₂³	1	12	yes	—
84	C₂²×C₄×D₁₇	C₂³	1	6	yes	—
85	C₂²×C₄×D₁₇	C₂³	1	48	yes	complemented
86	C₂²×Dic₃₄	C₂³	1	1	yes	characteristic
87	C₄×Q₈×C₁₇	C₂³	1	8	yes	complemented
88	C₄×Q₈×C₁₇	C₂³	1	8	yes	complemented
89	C₄×D₄×C₁₇	C₂³	1	24	yes	complemented
90	C₄×D₄×C₁₇	C₂³	1	24	yes	complemented
91	C₁₇×#117	C₂³	1	24	yes	complemented
92	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
93	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
94	C₂×C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
95	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
97	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
98	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
99	C₂×C₄²×C₁₇	C₂³	1	24	yes	complemented
100	C₂×C₂²⋊Dic₁₇	C₂³	1	6	yes	—
101	Q₈×Dic₁₇	C₂³	1	16	yes	complemented
102	D₄×Dic₁₇	C₂³	1	48	yes	complemented
103	C₄×C₂²⋊D₁₇	C₂³	1	48	yes	complemented
104	C₄×C₂²⋊D₁₇	C₂³	1	48	yes	complemented
105	C₂×#63227	C₂³	1	6	yes	—
106	C₂×#63227	C₂³	1	12	yes	—
107	C₂×#63227	C₂³	1	6	yes	—
108	C₂×#63227	C₂³	1	48	yes	complemented
109	#10587612	C₂³	1	24	yes	complemented
110	C₂×C₄⋊Dic₁₇	C₂³	1	6	yes	—
111	C₂×C₄⋊Dic₁₇	C₂³	1	3	yes	—
112	C₂×C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊Dic₁₇	C₂³	1	24	yes	complemented
114	C₂×#63225	C₂³	1	6	yes	—
115	C₂×#63225	C₂³	1	2	yes	—
116	C₂×C₄×Dic₁₇	C₂³	1	2	yes	—
117	C₂×C₄×Dic₁₇	C₂³	1	6	yes	—
118	C₂×C₄×Dic₁₇	C₂³	1	6	yes	—
119	#10587579	C₂³	1	48	yes	complemented
120	#10587579	C₂³	1	48	yes	complemented
121	#10587578	C₂³	1	48	yes	complemented
122	C₄⋊C₄×D₁₇	C₂³	1	48	yes	complemented
123	#10587567	C₂³	1	96	yes	complemented
124	C₂²⋊C₄×D₁₇	C₂³	1	96	yes	complemented
125	C₄×D₆₈	C₂³	1	48	yes	complemented
126	C₄×D₆₈	C₂³	1	24	yes	complemented
127	C₄×D₆₈	C₂³	1	48	yes	complemented
128	C₄×D₆₈	C₂³	1	48	yes	complemented
129	C₄×D₆₈	C₂³	1	24	yes	complemented
130	#10587558	C₂³	1	48	yes	complemented
131	C₄²×D₁₇	C₂³	1	48	yes	complemented
132	C₄×Dic₃₄	C₂³	1	8	yes	complemented
133	C₄×Dic₃₄	C₂³	1	24	yes	complemented
134	C₂⁴×C₁₇	C₂⁴	1	3	yes	—
135	C₂³×D₁₇	—	4	12	no	—
136	C₂³×D₁₇	—	4	12	no	—
137	C₂³×D₁₇	C₂²×C₄	1	48	yes	complemented
138	C₂³×D₁₇	C₂⁴	1	6	yes	—
139	C₂³×D₁₇	C₂⁴	1	24	yes	—
140	#41×C₁₇	C₂²×C₄	1	64	yes	complemented
141	C₂×Q₈×C₁₇	C₂²×C₄	1	8	yes	complemented
142	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
143	C₂×D₄×C₁₇	C₂²×C₄	1	24	yes	complemented
144	C₂×D₄×C₁₇	C₂⁴	1	12	yes	—
145	C₂²×C₄×C₁₇	—	2	12	no	—
146	C₂²×C₄×C₁₇	—	4	6	no	—
147	C₂²×C₄×C₁₇	C₂²×C₄	1	24	yes	complemented
148	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
149	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
150	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
151	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
153	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
155	C₂²×C₄×C₁₇	C₂⁴	1	12	yes	—
156	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
157	C₂×C₂²⋊D₁₇	C₂²×C₄	1	48	yes	complemented
158	C₂×C₂²⋊D₁₇	C₂⁴	1	24	yes	—
159	C₂²×Dic₁₇	—	4	12	no	—
160	C₂²×Dic₁₇	C₂⁴	1	6	yes	—
161	C₂²×Dic₁₇	C₂⁴	1	2	yes	—
162	C₂²×Dic₁₇	C₂⁴	1	24	yes	—
163	C₂²×Dic₁₇	C₂⁴	1	2	yes	—
164	#63256	C₂²×C₄	1	128	yes	complemented
165	D₄×D₁₇	C₂²×C₄	1	384	yes	complemented
166	#63252	C₂²×C₄	1	192	yes	complemented
167	C₂×D₆₈	C₂²×C₄	1	24	yes	complemented
168	C₂×D₆₈	C₂²×C₄	1	48	yes	complemented
169	C₂×D₆₈	C₂²×C₄	1	192	yes	complemented
170	C₂×D₆₈	C₂⁴	1	12	yes	—
171	C₂×D₆₈	C₂⁴	1	24	yes	—
172	C₂×C₄×D₁₇	—	2	24	no	—
173	C₂×C₄×D₁₇	—	4	96	no	—
174	C₂×C₄×D₁₇	—	4	24	no	—
175	C₂×C₄×D₁₇	—	4	12	no	—
176	C₂×C₄×D₁₇	C₂²×C₄	1	48	yes	complemented
177	C₂×C₄×D₁₇	C₂⁴	1	24	yes	—
178	C₂×C₄×D₁₇	C₂⁴	1	48	yes	—
179	C₂×C₄×D₁₇	C₂⁴	1	24	yes	—
180	C₂×C₄×D₁₇	C₂⁴	1	24	yes	—
181	C₂×Dic₃₄	C₂²×C₄	1	8	yes	complemented
182	C₂×Dic₃₄	C₂⁴	1	4	yes	—
183	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
184	C₄⋊C₄×C₁₇	C₂⁴	1	12	yes	—
185	C₂²⋊C₄×C₁₇	C₂⁴	1	24	yes	—
186	C₄²×C₁₇	C₂⁴	1	4	yes	—
187	C₄²×C₁₇	C₂⁴	1	12	yes	—
188	C₄²×C₁₇	C₂⁴	1	12	yes	—
189	C₄²×C₁₇	C₂⁴	1	12	yes	—
190	C₂²⋊Dic₁₇	C₂⁴	1	24	yes	—
191	#63227	C₂⁴	1	24	yes	—
192	#63227	C₂⁴	1	24	yes	—
193	#63227	C₂⁴	1	48	yes	—
194	C₄⋊Dic₁₇	C₂⁴	1	12	yes	—
195	C₄⋊Dic₁₇	C₂⁴	1	4	yes	—
196	C₄⋊Dic₁₇	C₂⁴	1	24	yes	—
197	#63225	C₂⁴	1	8	yes	—
198	#63225	C₂⁴	1	24	yes	—
199	C₄×Dic₁₇	C₂⁴	1	8	yes	—
200	C₄×Dic₁₇	C₂⁴	1	24	yes	—
201	C₄×Dic₁₇	C₂⁴	1	24	yes	—
202	C₂×C₄×H(5,𝔽₂)	—	17	1	no	maximal, Sylow
203	C₂³×C₁₇	—	2	6	no	—
204	C₂³×C₁₇	—	2	6	no	—
205	C₂³×C₁₇	C₂³×C₄	1	12	yes	—
206	C₂³×C₁₇	C₂⁵	1	6	yes	—
207	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
208	C₂²×D₁₇	—	2	12	no	—
209	C₂²×D₁₇	—	2	12	no	—
210	C₂²×D₁₇	—	4	24	no	—
211	C₂²×D₁₇	—	4	96	no	—
212	C₂²×D₁₇	—	4	24	no	—
213	C₂²×D₁₇	C₂³×C₄	1	24	yes	—
214	C₂²×D₁₇	C₂³×C₄	1	96	yes	complemented
215	C₂²×D₁₇	C₂⁵	1	12	yes	—
216	Q₈×C₁₇	C₂³×C₄	1	16	yes	complemented
217	D₄×C₁₇	C₂³×C₄	1	48	yes	complemented
218	C₂×C₄×C₁₇	—	2	6	no	—
219	C₂×C₄×C₁₇	—	2	6	no	—
220	C₂×C₄×C₁₇	—	2	2	no	—
221	C₂×C₄×C₁₇	—	2	24	no	—
222	C₂×C₄×C₁₇	—	4	12	no	—
223	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
224	C₂×C₄×C₁₇	C₂³×C₄	1	12	yes	—
225	C₂×C₄×C₁₇	C₂³×C₄	1	48	yes	complemented
226	C₂×C₄×C₁₇	H(5,𝔽₂)	1	4	yes	complemented
227	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
228	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
229	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
230	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
231	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
232	C₂×C₄×C₁₇	C₂⁵	1	2	yes	—
233	C₂²⋊D₁₇	C₂³×C₄	1	96	yes	complemented
234	C₂×Dic₁₇	—	2	12	no	—
235	C₂×Dic₁₇	—	2	4	no	—
236	C₂×Dic₁₇	—	4	24	no	—
237	C₂×Dic₁₇	C₂³×C₄	1	8	yes	—
238	C₂×Dic₁₇	C₂⁵	1	4	yes	—
239	C₂×Dic₁₇	C₂⁵	1	12	yes	—
240	C₂×Dic₁₇	C₂⁵	1	4	yes	—
241	D₆₈	C₂³×C₄	1	48	yes	complemented
242	D₆₈	C₂³×C₄	1	96	yes	complemented
243	C₄×D₁₇	—	2	48	no	—
244	C₄×D₁₇	—	4	48	no	—
245	C₄×D₁₇	—	4	24	no	—
246	C₄×D₁₇	C₂³×C₄	1	96	yes	complemented
247	Dic₃₄	C₂³×C₄	1	16	yes	complemented
248	C₂²×H(5,𝔽₂)	—	17	1	no	—
249	C₄×H(5,𝔽₂)	—	17	32	no	—
250	C₂×#520	—	17	1	no	—
251	C₂×#520	—	17	2	no	—
252	C₂×#520	—	17	3	no	—
253	C₂×#518	—	17	6	no	—
254	C₂×#518	—	17	3	no	—
255	C₂×C₄×#41	—	17	3	no	—
256	C₂×C₄×#41	—	17	2	no	—
257	C₂×C₄×#41	D₁₇	1	1	yes	characteristic, complemented
258	C₂²×C₄×D₄	—	17	3	no	—
259	C₂²×C₄×D₄	—	17	6	no	—
260	C₂²×C₁₇	—	2	6	no	—
261	C₂²×C₁₇	—	2	6	no	—
262	C₂²×C₁₇	—	2	24	no	—
263	C₂²×C₁₇	C₂⁴×C₄	1	12	yes	—
264	C₂²×C₁₇	C₂⁴×C₄	1	2	yes	—
265	C₂²×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
266	C₂²×C₁₇	#585	1	2	yes	—
267	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
268	C₂×D₁₇	—	2	12	no	—
269	C₂×D₁₇	—	2	12	no	—
270	C₂×D₁₇	—	2	48	no	—
271	C₂×D₁₇	—	4	96	no	—
272	C₂×D₁₇	C₂⁴×C₄	1	24	yes	—
273	C₄×C₁₇	—	2	6	no	—
274	C₄×C₁₇	—	2	6	no	—
275	C₄×C₁₇	—	2	2	no	—
276	C₄×C₁₇	C₂⁴×C₄	1	4	yes	—
277	C₄×C₁₇	C₂⁴×C₄	1	12	yes	—
278	C₄×C₁₇	C₂×H(5,𝔽₂)	1	4	yes	complemented
279	Dic₁₇	—	2	12	no	—
280	Dic₁₇	—	2	4	no	—
281	Dic₁₇	C₂⁴×C₄	1	8	yes	—
282	C₂×H(5,𝔽₂)	—	17	32	no	—
283	C₂×H(5,𝔽₂)	—	17	16	no	—
284	C₂²×#41	—	17	2	no	—
285	C₂²×#41	—	17	3	no	—
286	C₂²×#41	C₂×D₁₇	1	1	yes	characteristic
287	C₂³×D₄	—	17	6	no	—
288	C₂³×D₄	—	17	3	no	—
289	C₂⁴×C₄	—	17	6	no	—
290	#520	—	17	16	no	—
291	#520	—	17	32	no	—
292	#520	—	17	48	no	—
293	#518	—	17	96	no	—
294	#518	—	17	48	no	—
295	C₄×#41	—	17	32	no	—
296	C₄×#41	—	17	48	no	—
297	C₄×#41	C₂×D₁₇	1	16	yes	complemented
298	C₂×C₄×Q₈	—	17	2	no	—
299	C₂×C₄×Q₈	—	17	1	no	—
300	C₂×C₄×Q₈	—	17	3	no	—
301	C₂×C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
302	C₂×C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
303	C₂×C₄×D₄	—	17	6	no	—
304	C₂×C₄×D₄	—	17	6	no	—
305	C₂×C₄×D₄	—	17	6	no	—
306	C₂×C₄×D₄	—	17	96	no	—
307	C₂×C₄×D₄	—	17	6	no	—
308	C₂×C₄×D₄	—	17	6	no	—
309	C₂×C₄×D₄	—	17	12	no	—
310	C₂×C₄×D₄	—	17	3	no	—
311	C₂×C₄×D₄	—	17	6	no	—
312	C₂×C₄×D₄	—	17	6	no	—
313	C₂×C₄×D₄	—	17	6	no	—
314	C₂×C₄×D₄	—	17	3	no	—
315	C₂×C₄×D₄	—	17	48	no	—
316	C₂×C₄×D₄	C₂×D₁₇	1	3	yes	complemented
317	C₂×C₄×D₄	C₂×D₁₇	1	3	yes	complemented
318	C₂×#117	—	17	3	no	—
319	C₂×#117	—	17	6	no	—
320	C₂×#117	—	17	6	no	—
321	C₂×#117	C₂×D₁₇	1	3	yes	complemented
322	C₂²×C₄⋊C₄	—	17	3	no	—
323	C₂²×C₄⋊C₄	—	17	6	no	—
324	C₂²×C₂²⋊C₄	—	17	6	no	—
325	C₂²×C₂²⋊C₄	—	17	12	no	—
326	C₂²×C₄²	—	17	6	no	—
327	C₂²×C₄²	C₂×D₁₇	1	3	yes	complemented
328	C₂×C₁₇	—	2	12	no	—
329	C₂×C₁₇	C₄×H(5,𝔽₂)	1	4	yes	complemented
330	C₂×C₁₇	C₂⁵×C₄	1	1	yes	characteristic
331	C₂×C₁₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₁₇	C₂×#585	1	1	yes	characteristic
333	D₁₇	—	2	24	no	—
334	C₂⁵	—	17	6	no	—
335	H(5,𝔽₂)	—	17	256	no	—
336	C₂×#41	—	17	32	no	—
337	C₂×#41	—	17	16	no	—
338	C₂×#41	—	17	48	no	—
339	C₂×#41	—	17	24	no	—
340	C₂×#41	C₄×D₁₇	1	16	yes	complemented
341	C₂×#41	C₂²×D₁₇	1	8	yes	—
342	C₂²×Q₈	—	17	1	no	—
343	C₂²×Q₈	C₂²×D₁₇	1	1	yes	characteristic
344	C₂²×D₄	—	17	6	no	—
345	C₂²×D₄	—	17	96	no	—
346	C₂²×D₄	—	17	48	no	—
347	C₂²×D₄	—	17	48	no	—
348	C₂²×D₄	—	17	6	no	—
349	C₂²×D₄	—	17	3	no	—
350	C₂²×D₄	—	17	24	no	—
351	C₂²×D₄	C₂²×D₁₇	1	3	yes	—
352	C₂³×C₄	—	17	6	no	—
353	C₂³×C₄	—	17	6	no	—
354	C₂³×C₄	—	17	6	no	—
355	C₂³×C₄	—	17	6	no	—
356	C₂³×C₄	—	17	12	no	—
357	C₂³×C₄	—	17	48	no	—
358	C₂³×C₄	—	68	24	no	—
359	C₂³×C₄	C₂²×D₁₇	1	3	yes	—
360	C₂³×C₄	C₂²×D₁₇	1	3	yes	—
361	C₂³×C₄	C₂²×D₁₇	1	3	yes	—
362	C₄×Q₈	—	17	16	no	—
363	C₄×Q₈	—	17	8	no	—
364	C₄×Q₈	—	17	24	no	—
365	C₄×Q₈	C₂²×D₁₇	1	8	yes	complemented
366	C₄×Q₈	C₂²×D₁₇	1	8	yes	complemented
367	C₄×D₄	—	17	48	no	—
368	C₄×D₄	—	17	48	no	—
369	C₄×D₄	—	17	48	no	—
370	C₄×D₄	—	17	48	no	—
371	C₄×D₄	—	17	48	no	—
372	C₄×D₄	—	17	96	no	—
373	C₄×D₄	—	17	48	no	—
374	C₄×D₄	—	17	24	no	—
375	C₄×D₄	—	17	48	no	—
376	C₄×D₄	—	17	48	no	—
377	C₄×D₄	—	17	24	no	—
378	C₄×D₄	C₂²×D₁₇	1	24	yes	complemented
379	C₄×D₄	C₂²×D₁₇	1	24	yes	complemented
380	#117	—	17	24	no	—
381	#117	—	17	48	no	—
382	#117	—	17	48	no	—
383	#117	C₂²×D₁₇	1	24	yes	complemented
384	C₂×C₄⋊C₄	—	17	6	no	—
385	C₂×C₄⋊C₄	—	17	6	no	—
386	C₂×C₄⋊C₄	—	17	3	no	—
387	C₂×C₄⋊C₄	—	17	24	no	—
388	C₂×C₄⋊C₄	—	17	2	no	—
389	C₂×C₄⋊C₄	—	17	1	no	—
390	C₂×C₄⋊C₄	—	17	48	no	—
391	C₂×C₄⋊C₄	C₂²×D₁₇	1	3	yes	—
392	C₂×C₄⋊C₄	C₂²×D₁₇	1	3	yes	—
393	C₂×C₂²⋊C₄	—	17	6	no	—
394	C₂×C₂²⋊C₄	—	17	6	no	—
395	C₂×C₂²⋊C₄	—	17	12	no	—
396	C₂×C₂²⋊C₄	—	17	6	no	—
397	C₂×C₂²⋊C₄	—	17	48	no	—
398	C₂×C₂²⋊C₄	—	17	96	no	—
399	C₂×C₂²⋊C₄	C₂²×D₁₇	1	6	yes	—
400	C₂×C₄²	—	17	6	no	—
401	C₂×C₄²	—	17	6	no	—
402	C₂×C₄²	—	17	2	no	—
403	C₂×C₄²	—	17	48	no	—
404	C₂×C₄²	C₂²×D₁₇	1	3	yes	—
405	C₂×C₄²	C₂²×D₁₇	1	3	yes	—
406	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
407	C₂×C₄²	C₂²×D₁₇	1	3	yes	—
408	C₂×C₄²	C₂²×D₁₇	1	24	yes	complemented
409	C₁₇	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
410	C₂⁴	—	17	6	no	—
411	C₂⁴	—	17	48	no	—
412	C₂⁴	—	17	24	no	—
413	C₂⁴	—	68	12	no	—
414	C₂⁴	—	68	12	no	—
415	C₂⁴	C₂³×D₁₇	1	3	yes	—
416	#41	—	17	128	no	—
417	#41	—	17	192	no	—
418	#41	C₂×C₄×D₁₇	1	64	yes	complemented
419	C₂×Q₈	—	17	8	no	—
420	C₂×Q₈	—	17	4	no	—
421	C₂×Q₈	C₂×C₄×D₁₇	1	8	yes	complemented
422	C₂×Q₈	C₂³×D₁₇	1	4	yes	—
423	C₂×D₄	—	17	48	no	—
424	C₂×D₄	—	17	24	no	—
425	C₂×D₄	—	17	384	no	—
426	C₂×D₄	—	17	48	no	—
427	C₂×D₄	—	17	24	no	—
428	C₂×D₄	—	17	192	no	—
429	C₂×D₄	—	17	24	no	—
430	C₂×D₄	—	17	12	no	—
431	C₂×D₄	C₂×C₄×D₁₇	1	24	yes	complemented
432	C₂×D₄	C₂³×D₁₇	1	12	yes	—
433	C₂²×C₄	—	2	12	no	—
434	C₂²×C₄	—	4	6	no	—
435	C₂²×C₄	—	17	2	no	—
436	C₂²×C₄	—	17	48	no	—
437	C₂²×C₄	—	17	24	no	—
438	C₂²×C₄	—	17	2	no	—
439	C₂²×C₄	—	17	6	no	—
440	C₂²×C₄	—	17	24	no	—
441	C₂²×C₄	—	17	24	no	—
442	C₂²×C₄	—	17	24	no	—
443	C₂²×C₄	—	17	48	no	—
444	C₂²×C₄	—	34	24	no	—
445	C₂²×C₄	—	68	96	no	—
446	C₂²×C₄	—	68	12	no	—
447	C₂²×C₄	—	68	24	no	—
448	C₂²×C₄	—	68	12	no	—
449	C₂²×C₄	C₂×C₄×D₁₇	1	24	yes	complemented
450	C₂²×C₄	C₂³×D₁₇	1	3	yes	—
451	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
452	C₂²×C₄	C₂³×D₁₇	1	3	yes	—
453	C₂²×C₄	C₂³×D₁₇	1	12	yes	—
454	C₂²×C₄	C₂³×D₁₇	1	12	yes	—
455	C₂²×C₄	C₂³×D₁₇	1	3	yes	—
456	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
457	C₂²×C₄	C₂³×D₁₇	1	12	yes	—
458	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
459	C₄⋊C₄	—	17	24	no	—
460	C₄⋊C₄	—	17	24	no	—
461	C₄⋊C₄	—	17	12	no	—
462	C₄⋊C₄	—	17	8	no	—
463	C₄⋊C₄	—	17	4	no	—
464	C₄⋊C₄	C₂³×D₁₇	1	12	yes	—
465	C₄⋊C₄	C₂³×D₁₇	1	12	yes	—
466	C₂²⋊C₄	—	17	24	no	—
467	C₂²⋊C₄	—	17	24	no	—
468	C₂²⋊C₄	—	17	48	no	—
469	C₂²⋊C₄	—	17	24	no	—
470	C₂²⋊C₄	C₂³×D₁₇	1	24	yes	—
471	C₄²	—	17	8	no	—
472	C₄²	—	17	24	no	—
473	C₄²	—	17	24	no	—
474	C₄²	C₂³×D₁₇	1	12	yes	—
475	C₄²	C₂³×D₁₇	1	4	yes	—
476	C₄²	C₂³×D₁₇	1	12	yes	—
477	C₄²	C₂³×D₁₇	1	12	yes	—
478	C₂³	—	2	6	no	—
479	C₂³	—	2	6	no	—
480	C₂³	—	17	24	no	—
481	C₂³	—	17	12	no	—
482	C₂³	—	17	96	no	—
483	C₂³	—	34	12	no	—
484	C₂³	—	34	12	no	—
485	C₂³	—	68	24	no	—
486	C₂³	—	68	96	no	—
487	C₂³	—	68	24	no	—
488	C₂³	C₂²×C₄×D₁₇	1	12	yes	—
489	C₂³	C₂⁴×D₁₇	1	6	yes	—
490	C₂³	C₂⁴×D₁₇	1	1	yes	characteristic
491	Q₈	—	17	16	no	—
492	Q₈	C₂²×C₄×D₁₇	1	16	yes	complemented
493	D₄	—	17	96	no	—
494	D₄	—	17	96	no	—
495	D₄	—	17	48	no	—
496	D₄	C₂²×C₄×D₁₇	1	48	yes	complemented
497	C₂×C₄	—	2	6	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	6	no	—
500	C₂×C₄	—	2	24	no	—
501	C₂×C₄	—	4	12	no	—
502	C₂×C₄	—	17	8	no	—
503	C₂×C₄	—	17	4	no	—
504	C₂×C₄	—	17	96	no	—
505	C₂×C₄	—	17	4	no	—
506	C₂×C₄	—	17	12	no	—
507	C₂×C₄	—	34	12	no	—
508	C₂×C₄	—	34	4	no	—
509	C₂×C₄	—	34	48	no	—
510	C₂×C₄	—	68	48	no	—
511	C₂×C₄	—	68	24	no	—
512	C₂×C₄	—	68	24	no	—
513	C₂×C₄	C₂²×C₄×D₁₇	1	12	yes	—
514	C₂×C₄	C₂²×C₄×D₁₇	1	4	yes	—
515	C₂×C₄	C₂²×C₄×D₁₇	1	48	yes	complemented
516	C₂×C₄	#10587696	1	4	yes	direct product factor
517	C₂×C₄	C₂⁴×D₁₇	1	6	yes	—
518	C₂×C₄	C₂⁴×D₁₇	1	2	yes	—
519	C₂×C₄	C₂⁴×D₁₇	1	6	yes	—
520	C₂×C₄	C₂⁴×D₁₇	1	6	yes	—
521	C₂×C₄	C₂⁴×D₁₇	1	2	yes	—
522	C₂×C₄	C₂⁴×D₁₇	1	2	yes	—
523	C₂²	—	2	24	no	—
524	C₂²	—	2	6	no	—
525	C₂²	—	2	6	no	—
526	C₂²	—	17	24	no	—
527	C₂²	—	34	48	no	—
528	C₂²	—	34	12	no	—
529	C₂²	—	34	12	no	—
530	C₂²	—	68	96	no	—
531	C₂²	C₂³×C₄×D₁₇	1	12	yes	—
532	C₂²	C₂³×C₄×D₁₇	1	2	yes	—
533	C₂²	C₂×#10587696	1	2	yes	—
534	C₂²	#11763645	1	2	yes	—
535	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
536	C₄	—	2	6	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	6	no	—
539	C₄	—	17	8	no	—
540	C₄	—	34	12	no	—
541	C₄	—	34	4	no	—
542	C₄	C₂³×C₄×D₁₇	1	12	yes	—
543	C₄	C₂³×C₄×D₁₇	1	4	yes	—
544	C₄	C₂×#10587696	1	4	yes	direct product factor
545	C₂	—	2	12	no	—
546	C₂	—	34	24	no	—
547	C₂	C₄×#10587696	1	4	yes	direct product factor
548	C₂	C₂⁴×C₄×D₁₇	1	1	yes	characteristic
549	C₂	C₂²×#10587696	1	1	yes	characteristic
550	C₂	C₂×#11763645	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₇
commutator	C₂×C₁₇	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₇
Fitting	C₂×C₄×#41×C₁₇	C₂
socle	C₂³×C₁₇	C₂⁵
prime radical	C₂²×#10587696	C₂
cosocle	C₂²×C₁₇	C₂⁶
hypercenter	C₂×C₄×#41	D₁₇
hypocenter	C₁₇	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₄×#10587696	C₂	direct (N × H)
3. C₂×#11763292	C₂	semidirect
4. C₂×#11763291	C₂	semidirect
5. C₂×#11763289	C₂	semidirect
6. C₂×#11763283	C₂	semidirect
7. C₂×#11763281	C₂	semidirect
8. C₂×C₄×#63256	C₂	semidirect
9. C₂×C₄×#63252	C₂	semidirect
10. C₂²×C₄×D₆₈	C₂	semidirect
11. C₂×C₄×D₄×D₁₇	C₂	semidirect
12. C₂×C₄×#41×C₁₇	C₂	semidirect
13. C₂×#10587696	C₄	direct (N × H)
19. C₂³×C₄×D₁₇	C₂²	semidirect
20. #11763292	C₂²	semidirect
21. #11763291	C₂²	semidirect
22. #11763289	C₂²	semidirect
23. #11763283	C₂²	semidirect
24. #11763281	C₂²	semidirect
25. C₄×#63256	C₂²	semidirect
26. C₄×#63252	C₂²	semidirect
27. C₂×Q₈×Dic₁₇	C₂²	semidirect
28. C₂×C₄×Dic₃₄	C₂²	semidirect
29. C₂×C₄×Dic₃₄	C₂²	semidirect
30. C₂×C₄×D₆₈	C₂²	semidirect
31. C₂×C₄×D₆₈	C₂²	semidirect
32. C₂×C₄×D₆₈	C₂²	semidirect
33. C₂×C₄×D₆₈	C₂²	semidirect
34. C₂×C₄×D₆₈	C₂²	semidirect
35. C₂×C₄×D₆₈	C₂²	semidirect
36. C₂×D₄×Dic₁₇	C₂²	semidirect
37. C₂×#10587579	C₂²	semidirect
38. C₂×#10587579	C₂²	semidirect
39. C₂×C₄×C₂²⋊D₁₇	C₂²	semidirect
40. C₂×C₄×C₂²⋊D₁₇	C₂²	semidirect
41. C₂×#10587567	C₂²	semidirect
42. C₄×D₄×D₁₇	C₂²	semidirect
43. C₂×#10587612	C₂²	semidirect
44. C₂×#10587578	C₂²	semidirect
45. C₂×#10587558	C₂²	semidirect
46. C₂²×C₄⋊Dic₁₇	C₂²	semidirect
47. C₂×C₄⋊C₄×D₁₇	C₂²	semidirect
48. C₂²×#63227	C₂²	semidirect
49. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
50. C₂×C₄²×D₁₇	C₂²	semidirect
52. C₄×#41×C₁₇	C₂²	semidirect
53. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
54. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
55. C₂×C₄×D₄×C₁₇	C₂²	semidirect
56. C₂×C₄×D₄×C₁₇	C₂²	semidirect
57. C₂×C₁₇×#117	C₂²	semidirect
58. C₂²×C₄²×C₁₇	C₂²	semidirect
60. C₂×#41×C₁₇	C₂×C₄	semidirect
69. #10587696	C₂×C₄	direct (N × H)
70. C₂×#63256	C₂×C₄	semidirect
72. C₂×D₄×D₁₇	C₂×C₄	semidirect
74. C₂×#63252	C₂×C₄	semidirect
76. C₂²×D₆₈	C₂×C₄	semidirect
85. C₂²×C₄×D₁₇	C₂³	semidirect
87. C₄×Q₈×C₁₇	C₂³	semidirect
88. C₄×Q₈×C₁₇	C₂³	semidirect
89. C₄×D₄×C₁₇	C₂³	semidirect
90. C₄×D₄×C₁₇	C₂³	semidirect
91. C₁₇×#117	C₂³	semidirect
99. C₂×C₄²×C₁₇	C₂³	semidirect
101. Q₈×Dic₁₇	C₂³	semidirect
102. D₄×Dic₁₇	C₂³	semidirect
103. C₄×C₂²⋊D₁₇	C₂³	semidirect
104. C₄×C₂²⋊D₁₇	C₂³	semidirect
108. C₂×#63227	C₂³	semidirect
109. #10587612	C₂³	semidirect
113. C₂×C₄⋊Dic₁₇	C₂³	semidirect
119. #10587579	C₂³	semidirect
120. #10587579	C₂³	semidirect
121. #10587578	C₂³	semidirect
122. C₄⋊C₄×D₁₇	C₂³	semidirect
123. #10587567	C₂³	semidirect
124. C₂²⋊C₄×D₁₇	C₂³	semidirect
125. C₄×D₆₈	C₂³	semidirect
126. C₄×D₆₈	C₂³	semidirect
127. C₄×D₆₈	C₂³	semidirect
128. C₄×D₆₈	C₂³	semidirect
129. C₄×D₆₈	C₂³	semidirect
130. #10587558	C₂³	semidirect
131. C₄²×D₁₇	C₂³	semidirect
132. C₄×Dic₃₄	C₂³	semidirect
133. C₄×Dic₃₄	C₂³	semidirect
137. C₂³×D₁₇	C₂²×C₄	semidirect
140. #41×C₁₇	C₂²×C₄	semidirect
141. C₂×Q₈×C₁₇	C₂²×C₄	semidirect
143. C₂×D₄×C₁₇	C₂²×C₄	semidirect
147. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
157. C₂×C₂²⋊D₁₇	C₂²×C₄	semidirect
164. #63256	C₂²×C₄	semidirect
165. D₄×D₁₇	C₂²×C₄	semidirect
166. #63252	C₂²×C₄	semidirect
167. C₂×D₆₈	C₂²×C₄	semidirect
168. C₂×D₆₈	C₂²×C₄	semidirect
169. C₂×D₆₈	C₂²×C₄	semidirect
176. C₂×C₄×D₁₇	C₂²×C₄	semidirect
181. C₂×Dic₃₄	C₂²×C₄	semidirect
214. C₂²×D₁₇	C₂³×C₄	semidirect
216. Q₈×C₁₇	C₂³×C₄	semidirect
217. D₄×C₁₇	C₂³×C₄	semidirect
225. C₂×C₄×C₁₇	C₂³×C₄	semidirect
226. C₂×C₄×C₁₇	H(5,𝔽₂)	semidirect
233. C₂²⋊D₁₇	C₂³×C₄	semidirect
241. D₆₈	C₂³×C₄	semidirect
242. D₆₈	C₂³×C₄	semidirect
246. C₄×D₁₇	C₂³×C₄	semidirect
247. Dic₃₄	C₂³×C₄	semidirect
257. C₂×C₄×#41	D₁₇	semidirect
278. C₄×C₁₇	C₂×H(5,𝔽₂)	semidirect
297. C₄×#41	C₂×D₁₇	semidirect
301. C₂×C₄×Q₈	C₂×D₁₇	semidirect
302. C₂×C₄×Q₈	C₂×D₁₇	semidirect
316. C₂×C₄×D₄	C₂×D₁₇	semidirect
317. C₂×C₄×D₄	C₂×D₁₇	semidirect
321. C₂×#117	C₂×D₁₇	semidirect
327. C₂²×C₄²	C₂×D₁₇	semidirect
329. C₂×C₁₇	C₄×H(5,𝔽₂)	semidirect
340. C₂×#41	C₄×D₁₇	semidirect
365. C₄×Q₈	C₂²×D₁₇	semidirect
366. C₄×Q₈	C₂²×D₁₇	semidirect
378. C₄×D₄	C₂²×D₁₇	semidirect
379. C₄×D₄	C₂²×D₁₇	semidirect
383. #117	C₂²×D₁₇	semidirect
408. C₂×C₄²	C₂²×D₁₇	semidirect
409. C₁₇	C₂×C₄×H(5,𝔽₂)	semidirect
418. #41	C₂×C₄×D₁₇	semidirect
421. C₂×Q₈	C₂×C₄×D₁₇	semidirect
431. C₂×D₄	C₂×C₄×D₁₇	semidirect
449. C₂²×C₄	C₂×C₄×D₁₇	semidirect
492. Q₈	C₂²×C₄×D₁₇	semidirect
496. D₄	C₂²×C₄×D₁₇	semidirect
515. C₂×C₄	C₂²×C₄×D₁₇	semidirect
516. C₂×C₄	#10587696	direct (N × H)
544. C₄	C₂×#10587696	direct (N × H)
547. C₂	C₄×#10587696	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×#10587696	2
C₄×#10587696	2
C₂×#11763292	2
C₂×#11763291	2
C₂×#11763289	2
C₂×#11763283	2
C₂×#11763281	2
C₂×C₄×#63256	2
C₂×C₄×#63252	2
C₂²×C₄×D₆₈	2
C₂×C₄×D₄×D₁₇	2
C₂×C₄×#41×C₁₇	2
C₂×C₄×H(5,𝔽₂)	17

Subgroups — C2×C4×#10587696 #17940927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#10587696 #17940927