Subgroups — D₄×#41×C₁₇ #14526474

Order 2176.

1648 conjugacy classes of subgroups.

The subgroup lattice has 292 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	2	yes	maximal, complemented
2	C₁₇×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#548	C₂	1	2	yes	maximal, complemented
5	C₁₇×#547	C₂	1	3	yes	maximal, complemented
6	C₁₇×#546	C₂	1	6	yes	maximal, complemented
7	D₄²×C₁₇	C₂	1	3	yes	maximal, complemented
8	C₁₇×#532	C₂	1	3	yes	maximal, complemented
9	C₁₇×#525	C₂	1	6	yes	maximal, complemented
10	C₄×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₁₇	C₂	1	3	yes	maximal, complemented
12	C₂×#41×C₁₇	—	2	16	no	—
13	C₂×#41×C₁₇	C₂²	1	1	yes	characteristic
14	C₂×#41×C₁₇	C₂²	1	6	yes	complemented
15	C₂×#41×C₁₇	C₂²	1	6	yes	complemented
16	C₂×#41×C₁₇	C₂²	1	2	yes	complemented
17	C₂²×Q₈×C₁₇	C₂²	1	2	yes	complemented
18	C₂²×D₄×C₁₇	C₂²	1	3	yes	—
19	C₂²×D₄×C₁₇	C₂²	1	6	yes	complemented
20	C₂³×C₄×C₁₇	C₂²	1	6	yes	complemented
21	C₁₇×C₄⋊Q₈	C₂²	1	3	yes	complemented
22	C₁₇×#127	C₂²	1	3	yes	complemented
23	C₁₇×#124	C₂²	1	6	yes	complemented
24	C₁₇×#123	C₂²	1	12	yes	complemented
25	C₁₇×C₂²⋊Q₈	C₂²	1	6	yes	complemented
26	C₁₇×C₂²⋊Q₈	C₂²	1	6	yes	complemented
27	C₁₇×#121	C₂²	1	6	yes	complemented
28	C₁₇×#121	C₂²	1	6	yes	complemented
29	C₁₇×#121	C₂²	1	6	yes	complemented
30	C₁₇×#121	C₂²	1	6	yes	complemented
31	C₁₇×#120	C₂²	1	12	yes	complemented
32	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
33	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
34	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₇	C₂²	1	3	yes	—
36	C₄×D₄×C₁₇	C₂²	1	6	yes	complemented
37	C₄×D₄×C₁₇	C₂²	1	3	yes	complemented
38	C₄×D₄×C₁₇	C₂²	1	6	yes	complemented
39	C₄×D₄×C₁₇	C₂²	1	3	yes	complemented
40	C₄×D₄×C₁₇	C₂²	1	3	yes	complemented
41	C₄×D₄×C₁₇	C₂²	1	3	yes	complemented
42	C₄×D₄×C₁₇	C₂²	1	6	yes	complemented
43	C₁₇×#117	C₂²	1	3	yes	complemented
44	C₂×C₄⋊C₄×C₁₇	C₂²	1	3	yes	complemented
45	C₂×C₂²⋊C₄×C₁₇	C₂²	1	6	yes	complemented
46	C₂×C₄²×C₁₇	C₂²	1	3	yes	complemented
47	C₂⁴×C₁₇	C₂³	1	6	yes	—
48	#41×C₁₇	—	2	8	no	—
49	#41×C₁₇	—	2	24	no	—
50	#41×C₁₇	—	2	24	no	—
51	#41×C₁₇	D₄	1	8	yes	direct product factor
52	C₂×Q₈×C₁₇	—	2	8	no	—
53	C₂×Q₈×C₁₇	C₂³	1	6	yes	—
54	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
55	C₂×D₄×C₁₇	—	2	24	no	—
56	C₂×D₄×C₁₇	—	2	12	no	—
57	C₂×D₄×C₁₇	C₂³	1	12	yes	—
58	C₂×D₄×C₁₇	C₂³	1	6	yes	—
59	C₂×D₄×C₁₇	C₂³	1	3	yes	—
60	C₂×D₄×C₁₇	C₂³	1	6	yes	—
61	C₂×D₄×C₁₇	C₂³	1	6	yes	—
62	C₂×D₄×C₁₇	C₂³	1	3	yes	—
63	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₇	—	2	24	no	—
65	C₂²×C₄×C₁₇	C₂³	1	6	yes	—
66	C₂²×C₄×C₁₇	C₂³	1	6	yes	—
67	C₂²×C₄×C₁₇	C₂³	1	6	yes	—
68	C₂²×C₄×C₁₇	C₂³	1	3	yes	—
69	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
70	C₂²×C₄×C₁₇	C₂³	1	6	yes	—
71	C₂²×C₄×C₁₇	C₂³	1	3	yes	—
72	C₂²×C₄×C₁₇	C₂³	1	3	yes	—
73	C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
74	C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
75	C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
76	C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
77	C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
78	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
79	C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
80	C₂²⋊C₄×C₁₇	C₂³	1	12	yes	—
81	C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
82	C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
83	C₂²⋊C₄×C₁₇	C₂³	1	6	yes	—
84	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
85	C₄²×C₁₇	C₂³	1	3	yes	—
86	C₄²×C₁₇	C₂³	1	3	yes	—
87	C₄²×C₁₇	C₂³	1	1	yes	characteristic
88	C₄²×C₁₇	C₂³	1	3	yes	—
89	C₂³×C₁₇	—	2	12	no	—
90	C₂³×C₁₇	—	2	12	no	—
91	C₂³×C₁₇	—	4	6	no	—
92	C₂³×C₁₇	C₂⁴	1	6	yes	—
93	C₂³×C₁₇	C₂⁴	1	3	yes	—
94	C₂³×C₁₇	C₂⁴	1	2	yes	—
95	Q₈×C₁₇	—	2	12	no	—
96	Q₈×C₁₇	C₂×D₄	1	4	yes	complemented
97	D₄×C₁₇	—	2	24	no	—
98	D₄×C₁₇	—	2	12	no	—
99	D₄×C₁₇	—	2	12	no	—
100	D₄×C₁₇	—	2	6	no	—
101	D₄×C₁₇	—	4	6	no	—
102	D₄×C₁₇	C₂×D₄	1	12	yes	complemented
103	D₄×C₁₇	#41	1	4	yes	direct product factor
104	C₂×C₄×C₁₇	—	2	12	no	—
105	C₂×C₄×C₁₇	—	2	4	no	—
106	C₂×C₄×C₁₇	—	2	12	no	—
107	C₂×C₄×C₁₇	—	2	12	no	—
108	C₂×C₄×C₁₇	—	2	12	no	—
109	C₂×C₄×C₁₇	—	2	6	no	—
110	C₂×C₄×C₁₇	—	4	3	no	—
111	C₂×C₄×C₁₇	C₂×D₄	1	12	yes	complemented
112	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
113	C₂×C₄×C₁₇	C₂⁴	1	3	yes	—
114	C₂×C₄×C₁₇	C₂⁴	1	3	yes	—
115	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
116	C₂×C₄×C₁₇	C₂⁴	1	6	yes	—
117	C₂×C₄×C₁₇	C₂⁴	1	3	yes	—
118	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
119	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
120	D₄×#41	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂²×C₁₇	—	2	2	no	—
122	C₂²×C₁₇	—	2	3	no	—
123	C₂²×C₁₇	—	2	3	no	—
124	C₂²×C₁₇	—	2	2	no	—
125	C₂²×C₁₇	—	2	6	no	—
126	C₂²×C₁₇	—	2	6	no	—
127	C₂²×C₁₇	—	2	6	no	—
128	C₂²×C₁₇	—	4	24	no	—
129	C₂²×C₁₇	C₂²×D₄	1	6	yes	—
130	C₂²×C₁₇	C₂×#41	1	4	yes	complemented
131	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
132	C₄×C₁₇	—	2	2	no	—
133	C₄×C₁₇	—	2	6	no	—
134	C₄×C₁₇	—	2	3	no	—
135	C₄×C₁₇	—	2	1	no	—
136	C₄×C₁₇	—	2	3	no	—
137	C₄×C₁₇	C₂²×D₄	1	2	yes	—
138	C₄×C₁₇	C₂²×D₄	1	6	yes	—
139	C₄×C₁₇	C₂×#41	1	2	yes	complemented
140	C₂²×#41	C₂×C₁₇	1	2	yes	complemented
141	#550	C₂×C₁₇	1	1	yes	characteristic, complemented
142	D₄×Q₈	C₂×C₁₇	1	1	yes	characteristic, complemented
143	#548	C₂×C₁₇	1	2	yes	complemented
144	#547	C₂×C₁₇	1	3	yes	complemented
145	#546	C₂×C₁₇	1	6	yes	complemented
146	D₄²	C₂×C₁₇	1	3	yes	complemented
147	#532	C₂×C₁₇	1	3	yes	complemented
148	#525	C₂×C₁₇	1	6	yes	complemented
149	C₄×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
150	C₂×C₄×D₄	C₂×C₁₇	1	3	yes	complemented
151	C₂×C₁₇	—	2	4	no	—
152	C₂×C₁₇	—	2	6	no	—
153	C₂×C₁₇	—	4	6	no	—
154	C₂×C₁₇	C₂³×D₄	1	1	yes	characteristic
155	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
156	C₂×C₁₇	#585	1	1	yes	characteristic
157	C₂×#41	—	2	16	no	—
158	C₂×#41	C₂²×C₁₇	1	1	yes	characteristic
159	C₂×#41	C₂²×C₁₇	1	6	yes	complemented
160	C₂×#41	C₂²×C₁₇	1	6	yes	complemented
161	C₂×#41	C₂²×C₁₇	1	2	yes	complemented
162	C₂²×Q₈	C₂²×C₁₇	1	2	yes	complemented
163	C₂²×D₄	C₂²×C₁₇	1	3	yes	—
164	C₂²×D₄	C₂²×C₁₇	1	6	yes	complemented
165	C₂³×C₄	C₂²×C₁₇	1	6	yes	complemented
166	C₄⋊Q₈	C₂²×C₁₇	1	3	yes	complemented
167	#127	C₂²×C₁₇	1	3	yes	complemented
168	#124	C₂²×C₁₇	1	6	yes	complemented
169	#123	C₂²×C₁₇	1	12	yes	complemented
170	C₂²⋊Q₈	C₂²×C₁₇	1	6	yes	complemented
171	C₂²⋊Q₈	C₂²×C₁₇	1	6	yes	complemented
172	#121	C₂²×C₁₇	1	6	yes	complemented
173	#121	C₂²×C₁₇	1	6	yes	complemented
174	#121	C₂²×C₁₇	1	6	yes	complemented
175	#121	C₂²×C₁₇	1	6	yes	complemented
176	#120	C₂²×C₁₇	1	12	yes	complemented
177	C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
178	C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
179	C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
180	C₄×D₄	C₂²×C₁₇	1	3	yes	—
181	C₄×D₄	C₂²×C₁₇	1	6	yes	complemented
182	C₄×D₄	C₂²×C₁₇	1	3	yes	complemented
183	C₄×D₄	C₂²×C₁₇	1	6	yes	complemented
184	C₄×D₄	C₂²×C₁₇	1	3	yes	complemented
185	C₄×D₄	C₂²×C₁₇	1	3	yes	complemented
186	C₄×D₄	C₂²×C₁₇	1	3	yes	complemented
187	C₄×D₄	C₂²×C₁₇	1	6	yes	complemented
188	#117	C₂²×C₁₇	1	3	yes	complemented
189	C₂×C₄⋊C₄	C₂²×C₁₇	1	3	yes	complemented
190	C₂×C₂²⋊C₄	C₂²×C₁₇	1	6	yes	complemented
191	C₂×C₄²	C₂²×C₁₇	1	3	yes	complemented
192	C₁₇	D₄×#41	1	1	yes	characteristic, direct product factor, Sylow
193	C₂⁴	C₂³×C₁₇	1	6	yes	—
194	#41	—	2	8	no	—
195	#41	—	2	24	no	—
196	#41	—	2	24	no	—
197	#41	D₄×C₁₇	1	8	yes	direct product factor
198	C₂×Q₈	—	2	8	no	—
199	C₂×Q₈	C₂³×C₁₇	1	6	yes	—
200	C₂×Q₈	C₂³×C₁₇	1	1	yes	characteristic
201	C₂×D₄	—	2	24	no	—
202	C₂×D₄	—	2	12	no	—
203	C₂×D₄	C₂³×C₁₇	1	6	yes	—
204	C₂×D₄	C₂³×C₁₇	1	3	yes	—
205	C₂×D₄	C₂³×C₁₇	1	12	yes	—
206	C₂×D₄	C₂³×C₁₇	1	6	yes	—
207	C₂×D₄	C₂³×C₁₇	1	6	yes	—
208	C₂×D₄	C₂³×C₁₇	1	3	yes	—
209	C₂×D₄	C₂³×C₁₇	1	1	yes	characteristic
210	C₂²×C₄	—	2	24	no	—
211	C₂²×C₄	C₂³×C₁₇	1	3	yes	—
212	C₂²×C₄	C₂³×C₁₇	1	6	yes	—
213	C₂²×C₄	C₂³×C₁₇	1	2	yes	—
214	C₂²×C₄	C₂³×C₁₇	1	6	yes	—
215	C₂²×C₄	C₂³×C₁₇	1	6	yes	—
216	C₂²×C₄	C₂³×C₁₇	1	6	yes	—
217	C₂²×C₄	C₂³×C₁₇	1	3	yes	—
218	C₂²×C₄	C₂³×C₁₇	1	3	yes	—
219	C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
220	C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
221	C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
222	C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
223	C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
224	C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
225	C₂²⋊C₄	C₂³×C₁₇	1	2	yes	—
226	C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
227	C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
228	C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
229	C₂²⋊C₄	C₂³×C₁₇	1	6	yes	—
230	C₂²⋊C₄	C₂³×C₁₇	1	12	yes	—
231	C₄²	C₂³×C₁₇	1	1	yes	characteristic
232	C₄²	C₂³×C₁₇	1	3	yes	—
233	C₄²	C₂³×C₁₇	1	3	yes	—
234	C₄²	C₂³×C₁₇	1	3	yes	—
235	C₂³	—	2	12	no	—
236	C₂³	—	2	12	no	—
237	C₂³	—	4	6	no	—
238	C₂³	C₂⁴×C₁₇	1	6	yes	—
239	C₂³	C₂⁴×C₁₇	1	3	yes	—
240	C₂³	C₂⁴×C₁₇	1	2	yes	—
241	Q₈	—	2	12	no	—
242	Q₈	C₂×D₄×C₁₇	1	4	yes	complemented
243	D₄	—	2	24	no	—
244	D₄	—	2	12	no	—
245	D₄	—	2	12	no	—
246	D₄	—	2	6	no	—
247	D₄	—	4	6	no	—
248	D₄	C₂×D₄×C₁₇	1	12	yes	complemented
249	D₄	#41×C₁₇	1	4	yes	direct product factor
250	C₂×C₄	—	2	12	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	12	no	—
253	C₂×C₄	—	2	12	no	—
254	C₂×C₄	—	2	12	no	—
255	C₂×C₄	—	2	6	no	—
256	C₂×C₄	—	4	3	no	—
257	C₂×C₄	C₂×D₄×C₁₇	1	12	yes	complemented
258	C₂×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
259	C₂×C₄	C₂⁴×C₁₇	1	3	yes	—
260	C₂×C₄	C₂⁴×C₁₇	1	3	yes	—
261	C₂×C₄	C₂⁴×C₁₇	1	2	yes	—
262	C₂×C₄	C₂⁴×C₁₇	1	6	yes	—
263	C₂×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
264	C₂×C₄	C₂⁴×C₁₇	1	3	yes	—
265	C₂×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
266	C₂²	—	2	2	no	—
267	C₂²	—	2	3	no	—
268	C₂²	—	2	3	no	—
269	C₂²	—	2	2	no	—
270	C₂²	—	2	6	no	—
271	C₂²	—	2	6	no	—
272	C₂²	—	2	6	no	—
273	C₂²	—	4	24	no	—
274	C₂²	C₂²×D₄×C₁₇	1	6	yes	—
275	C₂²	C₂×#41×C₁₇	1	4	yes	complemented
276	C₂²	C₂⁵×C₁₇	1	1	yes	characteristic
277	C₄	—	2	2	no	—
278	C₄	—	2	6	no	—
279	C₄	—	2	3	no	—
280	C₄	—	2	1	no	—
281	C₄	—	2	3	no	—
282	C₄	C₂²×D₄×C₁₇	1	2	yes	—
283	C₄	C₂²×D₄×C₁₇	1	6	yes	—
284	C₄	C₂×#41×C₁₇	1	2	yes	complemented
285	C₂	—	2	4	no	—
286	C₂	—	2	6	no	—
287	C₂	—	4	6	no	—
288	C₂	C₂³×D₄×C₁₇	1	1	yes	characteristic
289	C₂	C₂²×#41×C₁₇	1	1	yes	characteristic
290	C₂	C₁₇×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₁₇×#550	C₂	semidirect
3. D₄×Q₈×C₁₇	C₂	semidirect
4. C₁₇×#548	C₂	semidirect
5. C₁₇×#547	C₂	semidirect
6. C₁₇×#546	C₂	semidirect
7. D₄²×C₁₇	C₂	semidirect
8. C₁₇×#532	C₂	semidirect
9. C₁₇×#525	C₂	semidirect
10. C₄×#41×C₁₇	C₂	semidirect
11. C₂×C₄×D₄×C₁₇	C₂	semidirect
14. C₂×#41×C₁₇	C₂²	semidirect
15. C₂×#41×C₁₇	C₂²	semidirect
16. C₂×#41×C₁₇	C₂²	semidirect
17. C₂²×Q₈×C₁₇	C₂²	semidirect
19. C₂²×D₄×C₁₇	C₂²	semidirect
20. C₂³×C₄×C₁₇	C₂²	semidirect
21. C₁₇×C₄⋊Q₈	C₂²	semidirect
22. C₁₇×#127	C₂²	semidirect
23. C₁₇×#124	C₂²	semidirect
24. C₁₇×#123	C₂²	semidirect
25. C₁₇×C₂²⋊Q₈	C₂²	semidirect
26. C₁₇×C₂²⋊Q₈	C₂²	semidirect
27. C₁₇×#121	C₂²	semidirect
28. C₁₇×#121	C₂²	semidirect
29. C₁₇×#121	C₂²	semidirect
30. C₁₇×#121	C₂²	semidirect
31. C₁₇×#120	C₂²	semidirect
32. C₄×Q₈×C₁₇	C₂²	semidirect
33. C₄×Q₈×C₁₇	C₂²	semidirect
36. C₄×D₄×C₁₇	C₂²	semidirect
37. C₄×D₄×C₁₇	C₂²	semidirect
38. C₄×D₄×C₁₇	C₂²	semidirect
39. C₄×D₄×C₁₇	C₂²	semidirect
40. C₄×D₄×C₁₇	C₂²	semidirect
41. C₄×D₄×C₁₇	C₂²	semidirect
42. C₄×D₄×C₁₇	C₂²	semidirect
43. C₁₇×#117	C₂²	semidirect
44. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
45. C₂×C₂²⋊C₄×C₁₇	C₂²	semidirect
46. C₂×C₄²×C₁₇	C₂²	semidirect
51. #41×C₁₇	D₄	direct (N × H)
96. Q₈×C₁₇	C₂×D₄	semidirect
102. D₄×C₁₇	C₂×D₄	semidirect
103. D₄×C₁₇	#41	direct (N × H)
111. C₂×C₄×C₁₇	C₂×D₄	semidirect
120. D₄×#41	C₁₇	direct (N × H)
130. C₂²×C₁₇	C₂×#41	semidirect
139. C₄×C₁₇	C₂×#41	semidirect
140. C₂²×#41	C₂×C₁₇	semidirect
141. #550	C₂×C₁₇	semidirect
142. D₄×Q₈	C₂×C₁₇	semidirect
143. #548	C₂×C₁₇	semidirect
144. #547	C₂×C₁₇	semidirect
145. #546	C₂×C₁₇	semidirect
146. D₄²	C₂×C₁₇	semidirect
147. #532	C₂×C₁₇	semidirect
148. #525	C₂×C₁₇	semidirect
149. C₄×#41	C₂×C₁₇	semidirect
150. C₂×C₄×D₄	C₂×C₁₇	semidirect
159. C₂×#41	C₂²×C₁₇	semidirect
160. C₂×#41	C₂²×C₁₇	semidirect
161. C₂×#41	C₂²×C₁₇	semidirect
162. C₂²×Q₈	C₂²×C₁₇	semidirect
164. C₂²×D₄	C₂²×C₁₇	semidirect
165. C₂³×C₄	C₂²×C₁₇	semidirect
166. C₄⋊Q₈	C₂²×C₁₇	semidirect
167. #127	C₂²×C₁₇	semidirect
168. #124	C₂²×C₁₇	semidirect
169. #123	C₂²×C₁₇	semidirect
170. C₂²⋊Q₈	C₂²×C₁₇	semidirect
171. C₂²⋊Q₈	C₂²×C₁₇	semidirect
172. #121	C₂²×C₁₇	semidirect
173. #121	C₂²×C₁₇	semidirect
174. #121	C₂²×C₁₇	semidirect
175. #121	C₂²×C₁₇	semidirect
176. #120	C₂²×C₁₇	semidirect
177. C₄×Q₈	C₂²×C₁₇	semidirect
178. C₄×Q₈	C₂²×C₁₇	semidirect
181. C₄×D₄	C₂²×C₁₇	semidirect
182. C₄×D₄	C₂²×C₁₇	semidirect
183. C₄×D₄	C₂²×C₁₇	semidirect
184. C₄×D₄	C₂²×C₁₇	semidirect
185. C₄×D₄	C₂²×C₁₇	semidirect
186. C₄×D₄	C₂²×C₁₇	semidirect
187. C₄×D₄	C₂²×C₁₇	semidirect
188. #117	C₂²×C₁₇	semidirect
189. C₂×C₄⋊C₄	C₂²×C₁₇	semidirect
190. C₂×C₂²⋊C₄	C₂²×C₁₇	semidirect
191. C₂×C₄²	C₂²×C₁₇	semidirect
192. C₁₇	D₄×#41	direct (N × H)
197. #41	D₄×C₁₇	direct (N × H)
242. Q₈	C₂×D₄×C₁₇	semidirect
248. D₄	C₂×D₄×C₁₇	semidirect
249. D₄	#41×C₁₇	direct (N × H)
257. C₂×C₄	C₂×D₄×C₁₇	semidirect
275. C₂²	C₂×#41×C₁₇	semidirect
284. C₄	C₂×#41×C₁₇	semidirect

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
C₁₇×#550	2
D₄×Q₈×C₁₇	2
C₁₇×#548	2
C₁₇×#547	2
C₁₇×#546	2
D₄²×C₁₇	2
C₁₇×#532	2
C₁₇×#525	2
C₄×#41×C₁₇	2
C₂×C₄×D₄×C₁₇	2
D₄×#41	17

Subgroups — D4×#41×C17 #14526474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#41×C₁₇ #14526474