Subgroups — C₂×C₄×C₁₇×C₂²⋊Q₈ #16891774

Order 4352.

3854 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₄×C₁₇	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂³	C₂⁵×C₁₇
socle	C₂⁴×C₁₇	C₂⁴
prime radical	C₂⁵×C₁₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₁₇	C₂	semidirect
4. C₄×C₁₇×C₂²⋊Q₈	C₂	direct (N × H)
5. C₂×C₁₇×#391	C₂	semidirect
6. C₂×C₁₇×#389	C₂	semidirect
7. C₂×C₁₇×#387	C₂	semidirect
10. C₂×C₄×C₄⋊C₄×C₁₇	C₂	semidirect
11. C₂×C₄×C₄⋊C₄×C₁₇	C₂	semidirect
17. C₂×C₁₇×C₂²⋊Q₈	C₄	direct (N × H)
20. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
37. C₁₇×#391	C₂²	semidirect
38. C₁₇×#389	C₂²	semidirect
39. C₁₇×#387	C₂²	semidirect
42. C₄×C₄⋊C₄×C₁₇	C₂²	semidirect
43. C₄×C₄⋊C₄×C₁₇	C₂²	semidirect
53. C₂²×Q₈×C₁₇	C₂×C₄	semidirect
63. C₂³×C₄×C₁₇	Q₈	semidirect
77. C₁₇×C₂²⋊Q₈	C₂×C₄	direct (N × H)
83. C₂×C₄⋊C₄×C₁₇	C₂×C₄	semidirect
84. C₂×C₄⋊C₄×C₁₇	C₂×C₄	semidirect
125. C₂×Q₈×C₁₇	C₂²×C₄	semidirect
164. C₂²×C₄×C₁₇	C₂×Q₈	semidirect
182. C₄⋊C₄×C₁₇	C₂²×C₄	semidirect
183. C₄⋊C₄×C₁₇	C₂²×C₄	semidirect
192. C₂×C₄×C₂²⋊Q₈	C₁₇	direct (N × H)
203. C₂³×C₁₇	C₄×Q₈	semidirect
246. C₂×C₄×C₁₇	C₂²⋊Q₈	direct (N × H)
260. C₂²×C₄×Q₈	C₂×C₁₇	semidirect
262. C₄×C₂²⋊Q₈	C₂×C₁₇	direct (N × H)
263. C₂×#391	C₂×C₁₇	semidirect
264. C₂×#389	C₂×C₁₇	semidirect
265. C₂×#387	C₂×C₁₇	semidirect
268. C₂×C₄×C₄⋊C₄	C₂×C₁₇	semidirect
269. C₂×C₄×C₄⋊C₄	C₂×C₁₇	semidirect
280. C₂²×C₁₇	C₂×C₄×Q₈	semidirect
302. C₄×C₁₇	C₂×C₂²⋊Q₈	direct (N × H)
307. C₂×C₂²⋊Q₈	C₄×C₁₇	direct (N × H)
310. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
327. #391	C₂²×C₁₇	semidirect
328. #389	C₂²×C₁₇	semidirect
329. #387	C₂²×C₁₇	semidirect
332. C₄×C₄⋊C₄	C₂²×C₁₇	semidirect
333. C₄×C₄⋊C₄	C₂²×C₁₇	semidirect
341. C₂×C₁₇	C₄×C₂²⋊Q₈	direct (N × H)
352. C₂²×Q₈	C₂×C₄×C₁₇	semidirect
362. C₂³×C₄	Q₈×C₁₇	semidirect
376. C₂²⋊Q₈	C₂×C₄×C₁₇	direct (N × H)
382. C₂×C₄⋊C₄	C₂×C₄×C₁₇	semidirect
383. C₂×C₄⋊C₄	C₂×C₄×C₁₇	semidirect
412. C₁₇	C₂×C₄×C₂²⋊Q₈	direct (N × H)
425. C₂×Q₈	C₂²×C₄×C₁₇	semidirect
464. C₂²×C₄	C₂×Q₈×C₁₇	semidirect
482. C₄⋊C₄	C₂²×C₄×C₁₇	semidirect
483. C₄⋊C₄	C₂²×C₄×C₁₇	semidirect
502. C₂³	C₄×Q₈×C₁₇	semidirect
545. C₂×C₄	C₁₇×C₂²⋊Q₈	direct (N × H)
567. C₂²	C₂×C₄×Q₈×C₁₇	semidirect
589. C₄	C₂×C₁₇×C₂²⋊Q₈	direct (N × H)
591. C₂	C₄×C₁₇×C₂²⋊Q₈	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×C₁₇×C₂²⋊Q₈	2
C₂²×C₄×Q₈×C₁₇	2
C₂³×C₄²×C₁₇	2
C₄×C₁₇×C₂²⋊Q₈	2
C₂×C₁₇×#391	2
C₂×C₁₇×#389	2
C₂×C₁₇×#387	2
C₂×C₁₇×#385	2
C₂×C₁₇×#380	2
C₂×C₄×C₄⋊C₄×C₁₇	2
C₂×C₄×C₂²⋊C₄×C₁₇	2
C₂×C₄×C₂²⋊Q₈	17

Subgroups — C2×C4×C17×C22⋊Q8 #16891774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₇×C₂²⋊Q₈ #16891774