Subgroups — #14542738

Order 2176.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763541	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763531	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763521	C₂	1	2	yes	maximal, complemented
4	#11763488	C₂	1	2	yes	maximal, complemented
5	#11763486	C₂	1	2	yes	maximal, complemented
6	Q₈×C₂²⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763469	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763448	C₂	1	2	yes	maximal, complemented
10	#11763447	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763443	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763429	C₂	1	2	yes	maximal, complemented
13	#11763396	C₂	1	2	yes	maximal, complemented
14	#11763393	C₂	1	2	yes	maximal, complemented
15	#11763355	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763346	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763345	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763340	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#10587633	C₂	1	1	yes	maximal, characteristic, complemented
20	#124×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763281	C₂	1	2	yes	maximal, complemented
22	C₄×#63254	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₇	C₂²	1	1	yes	characteristic, complemented
25	C₂²×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#63254	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₇	C₂²	1	2	yes	—
29	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
30	C₂×#63252	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₆₈	C₂²	1	1	yes	characteristic
32	C₁₇×#124	C₂²	1	2	yes	complemented
33	C₁₇×#124	C₂²	1	1	yes	characteristic, complemented
34	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₇×#121	C₂²	1	1	yes	characteristic
37	C₁₇×#121	C₂²	1	2	yes	complemented
38	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
40	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
41	#10587633	C₂²	1	1	yes	characteristic
42	#10587633	C₂²	1	1	yes	characteristic
43	#10587633	C₂²	1	1	yes	characteristic, complemented
44	#10587633	C₂²	1	2	yes	complemented
45	#10587633	C₂²	1	1	yes	characteristic, complemented
46	#10587633	C₂²	1	2	yes	complemented
47	#10587632	C₂²	1	2	yes	complemented
48	#10587632	C₂²	1	1	yes	characteristic, complemented
49	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
50	#10587630	C₂²	1	2	yes	complemented
51	#10587630	C₂²	1	1	yes	characteristic, complemented
52	#10587626	C₂²	1	1	yes	characteristic
53	#10587625	C₂²	1	2	yes	complemented
54	#10587625	C₂²	1	2	yes	complemented
55	#10587625	C₂²	1	2	yes	complemented
56	#10587623	C₂²	1	2	yes	—
57	#10587623	C₂²	1	2	yes	complemented
58	#10587623	C₂²	1	2	yes	complemented
59	#10587622	C₂²	1	1	yes	characteristic, complemented
60	#10587621	C₂²	1	2	yes	complemented
61	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
62	D₄×Dic₁₇	C₂²	1	2	yes	complemented
63	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
64	#10587616	C₂²	1	1	yes	characteristic
65	#10587615	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
71	C₂×#63227	C₂²	1	2	yes	complemented
72	C₂×#63227	C₂²	1	2	yes	complemented
73	C₂×#63227	C₂²	1	2	yes	complemented
74	#10587610	C₂²	1	2	yes	complemented
75	#10587610	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
78	#10587584	C₂²	1	2	yes	complemented
79	#10587584	C₂²	1	2	yes	complemented
80	#10587584	C₂²	1	2	yes	complemented
81	#10587582	C₂²	1	2	yes	complemented
82	#10587582	C₂²	1	2	yes	complemented
83	#10587581	C₂²	1	1	yes	characteristic
84	#10587580	C₂²	1	2	yes	complemented
85	#10587580	C₂²	1	2	yes	complemented
86	#10587579	C₂²	1	1	yes	characteristic
87	#10587579	C₂²	1	2	yes	complemented
88	#10587578	C₂²	1	1	yes	characteristic, complemented
89	#10587578	C₂²	1	2	yes	complemented
90	#10587576	C₂²	1	1	yes	characteristic, complemented
91	#10587573	C₂²	1	1	yes	characteristic, complemented
92	#10587573	C₂²	1	1	yes	characteristic, complemented
93	#10587572	C₂²	1	2	yes	complemented
94	#10587572	C₂²	1	2	yes	complemented
95	#10587571	C₂²	1	2	yes	complemented
96	#10587571	C₂²	1	2	yes	complemented
97	#10587571	C₂²	1	2	yes	complemented
98	#10587571	C₂²	1	2	yes	complemented
99	#10587570	C₂²	1	2	yes	—
100	#10587570	C₂²	1	2	yes	complemented
101	#10587570	C₂²	1	2	yes	complemented
102	#10587569	C₂²	1	2	yes	complemented
103	#10587568	C₂²	1	2	yes	—
104	#10587567	C₂²	1	1	yes	characteristic
105	#10587567	C₂²	1	2	yes	complemented
106	#10587567	C₂²	1	2	yes	complemented
107	#10587567	C₂²	1	1	yes	characteristic, complemented
108	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
111	#10587565	C₂²	1	2	yes	complemented
112	#10587563	C₂²	1	2	yes	complemented
113	#10587563	C₂²	1	1	yes	characteristic, complemented
114	#10587563	C₂²	1	1	yes	characteristic, complemented
115	#10587562	C₂²	1	2	yes	complemented
116	#10587561	C₂²	1	1	yes	characteristic
117	C₄×D₆₈	C₂²	1	2	yes	complemented
118	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
119	#10587558	C₂²	1	2	yes	complemented
120	#10587558	C₂²	1	2	yes	complemented
121	C₄²×D₁₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₇	C₂³	1	2	yes	—
124	C₂³×D₁₇	C₂³	1	2	yes	—
125	#41×C₁₇	—	4	2	no	—
126	C₂×Q₈×C₁₇	—	4	2	no	—
127	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₇	C₂³	1	2	yes	—
130	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₇	C₂³	1	2	yes	—
132	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₇	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
145	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₇	C₂³	1	2	yes	—
148	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
150	Q₈×D₁₇	—	4	2	no	—
151	#63254	—	2	4	no	—
152	D₄×D₁₇	—	2	8	no	—
153	D₄×D₁₇	—	4	2	no	—
154	#63252	—	4	2	no	—
155	C₂×D₆₈	—	4	2	no	—
156	C₂×D₆₈	C₂³	1	1	yes	characteristic
157	C₂×D₆₈	C₂³	1	1	yes	characteristic
158	C₂×D₆₈	C₂³	1	2	yes	—
159	C₂×D₆₈	C₂³	1	2	yes	—
160	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₇	C₂³	1	2	yes	—
162	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₇	C₂³	1	2	yes	—
164	C₂×C₄×D₁₇	C₂³	1	2	yes	—
165	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₁₇	C₂³	1	2	yes	—
167	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
168	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
169	C₂×Dic₃₄	C₂³	1	2	yes	—
170	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
172	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
178	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
180	C₄²×C₁₇	C₂³	1	1	yes	characteristic
181	C₄²×C₁₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
188	#63227	C₂³	1	2	yes	—
189	#63227	C₂³	1	2	yes	—
190	#63227	C₂³	1	2	yes	—
191	#63227	C₂³	1	2	yes	—
192	#63227	C₂³	1	2	yes	—
193	#63227	C₂³	1	2	yes	—
194	#63227	C₂³	1	2	yes	—
195	#63227	C₂³	1	2	yes	—
196	#63227	C₂³	1	2	yes	—
197	#63227	C₂³	1	2	yes	—
198	#63227	C₂³	1	2	yes	—
199	#63227	C₂³	1	2	yes	—
200	#63227	C₂³	1	2	yes	—
201	#63227	C₂³	1	1	yes	characteristic
202	#63227	C₂³	1	1	yes	characteristic
203	#63227	C₂³	1	2	yes	—
204	#63227	C₂³	1	2	yes	—
205	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₇	C₂³	1	2	yes	—
207	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₇	C₂³	1	2	yes	—
209	#63225	C₂³	1	1	yes	characteristic
210	#63225	C₂³	1	1	yes	characteristic
211	#63225	C₂³	1	2	yes	—
212	#63225	C₂³	1	2	yes	—
213	#63225	C₂³	1	2	yes	—
214	#63225	C₂³	1	2	yes	—
215	#63225	C₂³	1	2	yes	—
216	#63225	C₂³	1	2	yes	—
217	#63225	C₂³	1	1	yes	characteristic
218	#63225	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₇	C₂³	1	2	yes	—
225	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
228	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₇	C₂³	1	2	yes	—
230	C₂³×C₁₇	C₂⁴	1	2	yes	—
231	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₇	—	2	4	no	—
234	C₂²×D₁₇	—	2	4	no	—
235	C₂²×D₁₇	—	4	2	no	—
236	C₂²×D₁₇	—	4	2	no	—
237	C₂²×D₁₇	—	4	2	no	—
238	C₂²×D₁₇	—	4	2	no	—
239	C₂²×D₁₇	C₂⁴	1	2	yes	—
240	C₂²×D₁₇	C₂⁴	1	2	yes	—
241	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
242	Q₈×C₁₇	—	2	2	no	—
243	Q₈×C₁₇	—	2	2	no	—
244	Q₈×C₁₇	—	4	2	no	—
245	D₄×C₁₇	—	2	4	no	—
246	D₄×C₁₇	—	2	2	no	—
247	D₄×C₁₇	—	2	2	no	—
248	D₄×C₁₇	—	4	2	no	—
249	C₂×C₄×C₁₇	—	2	2	no	—
250	C₂×C₄×C₁₇	—	2	2	no	—
251	C₂×C₄×C₁₇	—	4	2	no	—
252	C₂×C₄×C₁₇	—	4	2	no	—
253	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
261	C₂²⋊D₁₇	—	2	2	no	—
262	C₂²⋊D₁₇	—	2	4	no	—
263	C₂²⋊D₁₇	—	4	2	no	—
264	C₂²⋊D₁₇	—	4	2	no	—
265	C₂²⋊D₁₇	—	4	2	no	—
266	C₂²⋊D₁₇	—	4	2	no	—
267	C₂²⋊D₁₇	#41	1	4	yes	complemented
268	C₂×Dic₁₇	—	2	2	no	—
269	C₂×Dic₁₇	—	2	2	no	—
270	C₂×Dic₁₇	—	4	1	no	—
271	C₂×Dic₁₇	—	4	1	no	—
272	C₂×Dic₁₇	—	4	2	no	—
273	C₂×Dic₁₇	C₂⁴	1	2	yes	—
274	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₇	C₂⁴	1	2	yes	—
279	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
282	D₆₈	—	2	4	no	—
283	D₆₈	—	2	2	no	—
284	D₆₈	—	2	2	no	—
285	D₆₈	—	4	2	no	—
286	C₄×D₁₇	—	2	2	no	—
287	C₄×D₁₇	—	2	2	no	—
288	C₄×D₁₇	—	2	4	no	—
289	C₄×D₁₇	—	4	1	no	—
290	C₄×D₁₇	—	4	2	no	—
291	C₄×D₁₇	—	4	2	no	—
292	C₄×D₁₇	—	4	2	no	—
293	Dic₃₄	—	2	2	no	—
294	Dic₃₄	—	2	2	no	—
295	Dic₃₄	—	4	2	no	—
296	#3514	—	17	1	no	maximal, Sylow
297	C₂²×C₁₇	—	2	1	no	—
298	C₂²×C₁₇	—	2	1	no	—
299	C₂²×C₁₇	—	2	1	no	—
300	C₂²×C₁₇	—	2	2	no	—
301	C₂²×C₁₇	—	2	1	no	—
302	C₂²×C₁₇	—	2	2	no	—
303	C₂²×C₁₇	—	2	1	no	—
304	C₂²×C₁₇	—	2	2	no	—
305	C₂²×C₁₇	C₂×#41	1	2	yes	—
306	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
307	C₂×D₁₇	—	2	1	no	—
308	C₂×D₁₇	—	2	1	no	—
309	C₂×D₁₇	—	2	2	no	—
310	C₂×D₁₇	—	2	2	no	—
311	C₂×D₁₇	—	2	2	no	—
312	C₂×D₁₇	—	2	2	no	—
313	C₂×D₁₇	—	2	2	no	—
314	C₂×D₁₇	—	2	2	no	—
315	C₂×D₁₇	—	8	4	no	—
316	C₂×D₁₇	—	8	4	no	—
317	C₂×D₁₇	C₂×#41	1	2	yes	—
318	C₄×C₁₇	—	2	1	no	—
319	C₄×C₁₇	—	2	2	no	—
320	C₄×C₁₇	—	2	2	no	—
321	C₄×C₁₇	—	2	1	no	—
322	C₄×C₁₇	—	2	1	no	—
323	C₄×C₁₇	—	2	2	no	—
324	C₄×C₁₇	—	2	1	no	—
325	C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
326	Dic₁₇	—	2	1	no	—
327	Dic₁₇	—	2	1	no	—
328	Dic₁₇	—	2	2	no	—
329	Dic₁₇	—	2	1	no	—
330	Dic₁₇	—	2	1	no	—
331	Dic₁₇	—	2	2	no	—
332	Dic₁₇	—	2	1	no	—
333	Dic₁₇	—	2	1	no	—
334	Dic₁₇	C₂×#41	1	2	yes	—
335	#559	—	17	1	no	—
336	#556	—	17	1	no	—
337	#555	—	17	2	no	—
338	#551	—	17	2	no	—
339	#551	—	17	2	no	—
340	D₄×Q₈	—	17	1	no	—
341	#548	—	17	1	no	—
342	#548	D₁₇	1	1	yes	characteristic, complemented
343	#546	—	17	1	no	—
344	#546	—	17	2	no	—
345	#546	—	17	1	no	—
346	D₄²	—	17	1	no	—
347	#542	—	17	2	no	—
348	#538	—	17	2	no	—
349	#538	—	17	2	no	—
350	#532	—	17	1	no	—
351	#529	—	17	1	no	—
352	#529	—	17	1	no	—
353	#529	—	17	1	no	—
354	C₂×#124	—	17	1	no	—
355	C₂×#124	—	17	1	no	—
356	#518	—	17	2	no	—
357	C₄×#41	—	17	1	no	—
358	C₂×C₁₇	—	2	2	no	—
359	C₂×C₁₇	—	4	2	no	—
360	C₂×C₁₇	—	4	1	no	—
361	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
362	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₁₇	#585	1	1	yes	characteristic
364	D₁₇	—	2	2	no	—
365	D₁₇	—	4	2	no	—
366	D₁₇	—	4	2	no	—
367	C₂×#41	—	17	1	no	—
368	C₂×#41	—	17	1	no	—
369	C₂×#41	C₂×D₁₇	1	1	yes	characteristic, complemented
370	C₂²×Q₈	—	17	1	no	—
371	C₂²×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
372	C₂²×D₄	—	17	2	no	—
373	C₂²×D₄	—	17	1	no	—
374	C₂²×D₄	—	17	1	no	—
375	C₄⋊Q₈	—	17	1	no	—
376	C₄⋊Q₈	—	17	2	no	—
377	#127	—	17	1	no	—
378	#126	—	17	2	no	—
379	#126	—	17	2	no	—
380	#126	—	17	2	no	—
381	#126	—	17	2	no	—
382	#126	—	17	2	no	—
383	#125	—	17	1	no	—
384	#124	—	17	1	no	—
385	#124	—	17	1	no	—
386	#124	—	17	2	no	—
387	#124	—	17	1	no	—
388	#124	—	17	1	no	—
389	#124	—	17	2	no	—
390	#124	—	17	1	no	—
391	#124	—	17	2	no	—
392	#124	—	17	2	no	—
393	#124	—	17	2	no	—
394	#124	—	17	2	no	—
395	#124	—	17	1	no	—
396	#124	C₂×D₁₇	1	1	yes	characteristic, complemented
397	#124	C₂×D₁₇	1	2	yes	complemented
398	#123	—	17	2	no	—
399	#123	—	17	2	no	—
400	#123	—	17	2	no	—
401	#123	—	17	2	no	—
402	#123	—	17	2	no	—
403	#123	—	17	2	no	—
404	#123	—	17	2	no	—
405	C₂²⋊Q₈	—	17	1	no	—
406	C₂²⋊Q₈	—	17	2	no	—
407	C₂²⋊Q₈	—	17	1	no	—
408	C₂²⋊Q₈	—	17	2	no	—
409	C₂²⋊Q₈	—	17	2	no	—
410	C₂²⋊Q₈	—	17	2	no	—
411	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
412	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	complemented
413	#121	—	17	2	no	—
414	#121	—	17	2	no	—
415	#121	—	17	2	no	—
416	#121	—	17	1	no	—
417	#121	—	17	1	no	—
418	#121	—	17	2	no	—
419	#121	—	17	2	no	—
420	#121	—	17	2	no	—
421	#121	C₂×D₁₇	1	1	yes	characteristic
422	#121	C₂×D₁₇	1	2	yes	complemented
423	#120	—	17	2	no	—
424	#120	—	17	2	no	—
425	#120	—	17	2	no	—
426	#120	—	17	2	no	—
427	C₄×Q₈	—	17	1	no	—
428	C₄×Q₈	—	17	1	no	—
429	C₄×Q₈	—	17	1	no	—
430	C₄×Q₈	—	17	1	no	—
431	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
432	C₄×D₄	—	17	1	no	—
433	C₄×D₄	—	17	2	no	—
434	C₄×D₄	—	17	1	no	—
435	C₄×D₄	—	17	1	no	—
436	C₄×D₄	—	17	1	no	—
437	C₄×D₄	—	17	2	no	—
438	C₄×D₄	—	17	2	no	—
439	C₄×D₄	—	17	2	no	—
440	C₄×D₄	—	17	2	no	—
441	C₄×D₄	—	17	1	no	—
442	C₄×D₄	—	17	1	no	—
443	C₄×D₄	—	17	1	no	—
444	C₄×D₄	—	17	2	no	—
445	C₄×D₄	—	17	2	no	—
446	C₄×D₄	—	17	2	no	—
447	C₄×D₄	—	17	1	no	—
448	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
449	C₄×D₄	C₂×D₁₇	1	2	yes	complemented
450	#117	—	17	1	no	—
451	#117	—	17	2	no	—
452	#117	—	17	1	no	—
453	#117	—	17	1	no	—
454	#117	—	17	2	no	—
455	#117	—	17	2	no	—
456	#117	—	17	2	no	—
457	C₂×C₂²⋊C₄	—	17	2	no	—
458	C₂×C₂²⋊C₄	—	17	2	no	—
459	C₂×C₂²⋊C₄	—	17	2	no	—
460	C₂×C₂²⋊C₄	—	17	2	no	—
461	C₂×C₂²⋊C₄	—	17	2	no	—
462	C₂×C₂²⋊C₄	—	17	2	no	—
463	C₂×C₄²	—	17	1	no	—
464	C₂×C₄²	—	17	1	no	—
465	C₂×C₄²	—	17	1	no	—
466	C₁₇	#3514	1	1	yes	characteristic, complemented, Sylow
467	C₂⁴	—	17	2	no	—
468	C₂⁴	—	17	2	no	—
469	#41	—	4	2	no	—
470	#41	—	34	4	no	—
471	#41	—	68	2	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	17	1	no	—
474	C₂×Q₈	—	17	1	no	—
475	C₂×Q₈	—	17	2	no	—
476	C₂×Q₈	—	68	2	no	—
477	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
478	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
479	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
480	C₂×D₄	—	17	1	no	—
481	C₂×D₄	—	17	1	no	—
482	C₂×D₄	—	17	2	no	—
483	C₂×D₄	—	17	2	no	—
484	C₂×D₄	—	17	2	no	—
485	C₂×D₄	—	17	2	no	—
486	C₂×D₄	—	17	2	no	—
487	C₂×D₄	—	17	2	no	—
488	C₂×D₄	—	17	1	no	—
489	C₂×D₄	—	17	1	no	—
490	C₂×D₄	—	17	2	no	—
491	C₂×D₄	—	34	8	no	—
492	C₂×D₄	—	68	2	no	—
493	C₂×D₄	—	68	2	no	—
494	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₁₇	1	2	yes	—
496	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₁₇	1	2	yes	—
498	C₂²×C₄	—	17	1	no	—
499	C₂²×C₄	—	17	1	no	—
500	C₂²×C₄	—	17	1	no	—
501	C₂²×C₄	—	17	1	no	—
502	C₂²×C₄	—	17	2	no	—
503	C₂²×C₄	—	17	1	no	—
504	C₂²×C₄	—	17	1	no	—
505	C₂²×C₄	—	17	2	no	—
506	C₂²×C₄	—	17	1	no	—
507	C₂²×C₄	—	17	2	no	—
508	C₂²×C₄	—	17	2	no	—
509	C₂²×C₄	—	17	2	no	—
510	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
513	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
514	C₄⋊C₄	—	17	1	no	—
515	C₄⋊C₄	—	17	2	no	—
516	C₄⋊C₄	—	17	2	no	—
517	C₄⋊C₄	—	17	2	no	—
518	C₄⋊C₄	—	17	1	no	—
519	C₄⋊C₄	—	17	1	no	—
520	C₄⋊C₄	—	17	1	no	—
521	C₄⋊C₄	—	17	1	no	—
522	C₄⋊C₄	—	17	2	no	—
523	C₄⋊C₄	—	17	2	no	—
524	C₄⋊C₄	—	17	1	no	—
525	C₄⋊C₄	—	17	2	no	—
526	C₄⋊C₄	—	17	2	no	—
527	C₄⋊C₄	—	17	2	no	—
528	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
532	C₂²⋊C₄	—	17	2	no	—
533	C₂²⋊C₄	—	17	2	no	—
534	C₂²⋊C₄	—	17	2	no	—
535	C₂²⋊C₄	—	17	1	no	—
536	C₂²⋊C₄	—	17	1	no	—
537	C₂²⋊C₄	—	17	2	no	—
538	C₂²⋊C₄	—	17	1	no	—
539	C₂²⋊C₄	—	17	2	no	—
540	C₂²⋊C₄	—	17	2	no	—
541	C₂²⋊C₄	—	17	2	no	—
542	C₂²⋊C₄	—	17	2	no	—
543	C₂²⋊C₄	—	17	2	no	—
544	C₂²⋊C₄	—	17	2	no	—
545	C₂²⋊C₄	—	17	2	no	—
546	C₂²⋊C₄	—	17	2	no	—
547	C₂²⋊C₄	—	17	2	no	—
548	C₂²⋊C₄	—	17	2	no	—
549	C₂²⋊C₄	—	17	2	no	—
550	C₂²⋊C₄	—	17	2	no	—
551	C₂²⋊C₄	—	17	1	no	—
552	C₂²⋊C₄	—	17	2	no	—
553	C₂²⋊C₄	—	17	2	no	—
554	C₂²⋊C₄	—	17	2	no	—
555	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
559	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
561	C₄²	—	17	1	no	—
562	C₄²	—	17	1	no	—
563	C₄²	—	17	1	no	—
564	C₄²	—	17	1	no	—
565	C₄²	—	17	1	no	—
566	C₄²	—	17	1	no	—
567	C₄²	—	17	1	no	—
568	C₄²	—	17	1	no	—
569	C₄²	—	17	1	no	—
570	C₄²	—	17	2	no	—
571	C₄²	—	17	2	no	—
572	C₄²	C₂²×D₁₇	1	1	yes	characteristic
573	C₄²	C₂²×D₁₇	1	2	yes	—
574	C₂³	—	17	1	no	—
575	C₂³	—	17	2	no	—
576	C₂³	—	17	2	no	—
577	C₂³	—	34	4	no	—
578	C₂³	—	34	4	no	—
579	C₂³	—	68	2	no	—
580	C₂³	—	68	2	no	—
581	C₂³	—	68	2	no	—
582	C₂³	—	68	2	no	—
583	C₂³	C₂³×D₁₇	1	2	yes	—
584	C₂³	C₂³×D₁₇	1	1	yes	characteristic
585	C₂³	C₂³×D₁₇	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	34	2	no	—
590	Q₈	—	34	2	no	—
591	Q₈	—	68	2	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	2	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	17	4	no	—
597	D₄	—	34	4	no	—
598	D₄	—	34	4	no	—
599	D₄	—	34	2	no	—
600	D₄	—	34	2	no	—
601	D₄	—	34	2	no	—
602	D₄	—	68	2	no	—
603	D₄	—	68	2	no	—
604	D₄	—	68	2	no	—
605	D₄	—	68	2	no	—
606	D₄	—	68	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	17	1	no	—
612	C₂×C₄	—	17	1	no	—
613	C₂×C₄	—	17	1	no	—
614	C₂×C₄	—	17	1	no	—
615	C₂×C₄	—	17	1	no	—
616	C₂×C₄	—	17	1	no	—
617	C₂×C₄	—	17	1	no	—
618	C₂×C₄	—	17	2	no	—
619	C₂×C₄	—	17	2	no	—
620	C₂×C₄	—	34	4	no	—
621	C₂×C₄	—	34	2	no	—
622	C₂×C₄	—	34	2	no	—
623	C₂×C₄	—	34	2	no	—
624	C₂×C₄	—	34	2	no	—
625	C₂×C₄	—	68	2	no	—
626	C₂×C₄	—	68	2	no	—
627	C₂×C₄	—	68	1	no	—
628	C₂×C₄	—	68	2	no	—
629	C₂×C₄	—	68	1	no	—
630	C₂×C₄	—	68	2	no	—
631	C₂×C₄	—	68	1	no	—
632	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₇	1	2	yes	—
637	C₂×C₄	C₂³×D₁₇	1	2	yes	—
638	C₂×C₄	C₂³×D₁₇	1	2	yes	—
639	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	17	2	no	—
649	C₂²	—	34	1	no	—
650	C₂²	—	34	1	no	—
651	C₂²	—	34	2	no	—
652	C₂²	—	34	2	no	—
653	C₂²	—	34	2	no	—
654	C₂²	—	34	2	no	—
655	C₂²	—	34	2	no	—
656	C₂²	—	34	2	no	—
657	C₂²	—	136	4	no	—
658	C₂²	—	136	4	no	—
659	C₂²	#41×D₁₇	1	2	yes	—
660	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
661	C₄	—	2	2	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	17	2	no	—
669	C₄	—	34	1	no	—
670	C₄	—	34	1	no	—
671	C₄	—	34	1	no	—
672	C₄	—	34	2	no	—
673	C₄	—	34	1	no	—
674	C₄	—	34	1	no	—
675	C₄	—	34	2	no	—
676	C₄	—	34	1	no	—
677	C₄	#10587691	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	34	2	no	—
682	C₂	—	68	2	no	—
683	C₂	—	68	2	no	—
684	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
685	C₂	C₂×#10587691	1	1	yes	characteristic
686	C₂	#11763646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#548	C₂
hypercenter	#548	D₁₇
hypocenter	C₁₇	#3514
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #11763541	C₂	semidirect
2. #11763531	C₂	semidirect
3. #11763521	C₂	semidirect
4. #11763488	C₂	semidirect
5. #11763486	C₂	semidirect
6. Q₈×C₂²⋊D₁₇	C₂	semidirect
7. #11763469	C₂	semidirect
8. #11763455	C₂	semidirect
9. #11763448	C₂	semidirect
10. #11763447	C₂	semidirect
11. #11763443	C₂	semidirect
12. #11763429	C₂	semidirect
13. #11763396	C₂	semidirect
14. #11763393	C₂	semidirect
15. #11763355	C₂	semidirect
16. #11763346	C₂	semidirect
17. #11763345	C₂	semidirect
18. #11763340	C₂	semidirect
19. C₂×#10587633	C₂	semidirect
20. #124×D₁₇	C₂	semidirect
21. #11763281	C₂	semidirect
22. C₄×#63254	C₂	semidirect
23. C₁₇×#548	C₂	semidirect
24. C₂×#41×C₁₇	C₂²	semidirect
25. C₂²×Q₈×C₁₇	C₂²	semidirect
26. C₂×Q₈×D₁₇	C₂²	semidirect
30. C₂×#63252	C₂²	semidirect
32. C₁₇×#124	C₂²	semidirect
33. C₁₇×#124	C₂²	semidirect
34. C₁₇×C₂²⋊Q₈	C₂²	semidirect
35. C₁₇×C₂²⋊Q₈	C₂²	semidirect
37. C₁₇×#121	C₂²	semidirect
38. C₄×Q₈×C₁₇	C₂²	semidirect
39. C₄×D₄×C₁₇	C₂²	semidirect
40. C₄×D₄×C₁₇	C₂²	semidirect
43. #10587633	C₂²	semidirect
44. #10587633	C₂²	semidirect
45. #10587633	C₂²	semidirect
46. #10587633	C₂²	semidirect
47. #10587632	C₂²	semidirect
48. #10587632	C₂²	semidirect
49. Q₈×Dic₁₇	C₂²	semidirect
50. #10587630	C₂²	semidirect
51. #10587630	C₂²	semidirect
53. #10587625	C₂²	semidirect
54. #10587625	C₂²	semidirect
55. #10587625	C₂²	semidirect
57. #10587623	C₂²	semidirect
58. #10587623	C₂²	semidirect
59. #10587622	C₂²	semidirect
60. #10587621	C₂²	semidirect
61. D₄×Dic₁₇	C₂²	semidirect
62. D₄×Dic₁₇	C₂²	semidirect
63. D₄×Dic₁₇	C₂²	semidirect
65. #10587615	C₂²	semidirect
68. C₄×C₂²⋊D₁₇	C₂²	semidirect
69. C₄×C₂²⋊D₁₇	C₂²	semidirect
70. C₄×C₂²⋊D₁₇	C₂²	semidirect
71. C₂×#63227	C₂²	semidirect
72. C₂×#63227	C₂²	semidirect
73. C₂×#63227	C₂²	semidirect
74. #10587610	C₂²	semidirect
75. #10587610	C₂²	semidirect
76. C₂×C₄×Dic₁₇	C₂²	semidirect
77. C₂×C₄×Dic₁₇	C₂²	semidirect
78. #10587584	C₂²	semidirect
79. #10587584	C₂²	semidirect
80. #10587584	C₂²	semidirect
81. #10587582	C₂²	semidirect
82. #10587582	C₂²	semidirect
84. #10587580	C₂²	semidirect
85. #10587580	C₂²	semidirect
87. #10587579	C₂²	semidirect
88. #10587578	C₂²	semidirect
89. #10587578	C₂²	semidirect
90. #10587576	C₂²	semidirect
91. #10587573	C₂²	semidirect
92. #10587573	C₂²	semidirect
93. #10587572	C₂²	semidirect
94. #10587572	C₂²	semidirect
95. #10587571	C₂²	semidirect
96. #10587571	C₂²	semidirect
97. #10587571	C₂²	semidirect
98. #10587571	C₂²	semidirect
100. #10587570	C₂²	semidirect
101. #10587570	C₂²	semidirect
102. #10587569	C₂²	semidirect
105. #10587567	C₂²	semidirect
106. #10587567	C₂²	semidirect
107. #10587567	C₂²	semidirect
108. C₂²⋊C₄×D₁₇	C₂²	semidirect
109. C₂²⋊C₄×D₁₇	C₂²	semidirect
110. C₂²⋊C₄×D₁₇	C₂²	semidirect
111. #10587565	C₂²	semidirect
112. #10587563	C₂²	semidirect
113. #10587563	C₂²	semidirect
114. #10587563	C₂²	semidirect
115. #10587562	C₂²	semidirect
117. C₄×D₆₈	C₂²	semidirect
118. C₄×D₆₈	C₂²	semidirect
119. #10587558	C₂²	semidirect
120. #10587558	C₂²	semidirect
121. C₄²×D₁₇	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
267. C₂²⋊D₁₇	#41	semidirect
342. #548	D₁₇	semidirect
369. C₂×#41	C₂×D₁₇	semidirect
371. C₂²×Q₈	C₂×D₁₇	semidirect
396. #124	C₂×D₁₇	semidirect
397. #124	C₂×D₁₇	semidirect
411. C₂²⋊Q₈	C₂×D₁₇	semidirect
412. C₂²⋊Q₈	C₂×D₁₇	semidirect
422. #121	C₂×D₁₇	semidirect
431. C₄×Q₈	C₂×D₁₇	semidirect
448. C₄×D₄	C₂×D₁₇	semidirect
449. C₄×D₄	C₂×D₁₇	semidirect
466. C₁₇	#3514	semidirect

Maximal subgroups

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

subgroup	index
#11763541	2
#11763531	2
#11763521	2
#11763488	2
#11763486	2
Q₈×C₂²⋊D₁₇	2
#11763469	2
#11763455	2
#11763448	2
#11763447	2
#11763443	2
#11763429	2
#11763396	2
#11763393	2
#11763355	2
#11763346	2
#11763345	2
#11763340	2
C₂×#10587633	2
#124×D₁₇	2
#11763281	2
C₄×#63254	2
C₁₇×#548	2
#3514	17