Subgroups — #14542511

Order 2176.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763523	C₂	1	2	yes	maximal, complemented
2	#11763504	C₂	1	2	yes	maximal, complemented
3	#11763502	C₂	1	2	yes	maximal, complemented
4	#11763487	C₂	1	2	yes	maximal, complemented
5	#11763482	C₂	1	2	yes	maximal, complemented
6	#11763457	C₂	1	2	yes	maximal, complemented
7	#11763456	C₂	1	2	yes	maximal, complemented
8	#11763448	C₂	1	2	yes	maximal, complemented
9	#11763439	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763430	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763426	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763412	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763372	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763357	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763356	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763344	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763341	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763319	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763288	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763281	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63254	C₂²	1	1	yes	characteristic
25	C₂×#63254	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₇	C₂²	1	2	yes	—
28	C₂×#63252	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×#127	C₂²	1	1	yes	characteristic, complemented
31	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
32	C₁₇×#123	C₂²	1	2	yes	complemented
33	C₁₇×#123	C₂²	1	2	yes	complemented
34	C₁₇×#121	C₂²	1	1	yes	characteristic
35	C₁₇×#121	C₂²	1	2	yes	complemented
36	C₁₇×#121	C₂²	1	2	yes	complemented
37	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
40	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
41	#10587626	C₂²	1	1	yes	characteristic, complemented
42	#10587625	C₂²	1	2	yes	—
43	#10587625	C₂²	1	2	yes	complemented
44	#10587625	C₂²	1	2	yes	complemented
45	#10587625	C₂²	1	2	yes	complemented
46	#10587624	C₂²	1	1	yes	characteristic
47	#10587624	C₂²	1	2	yes	complemented
48	#10587624	C₂²	1	2	yes	complemented
49	#10587624	C₂²	1	1	yes	characteristic, complemented
50	#10587623	C₂²	1	2	yes	—
51	#10587623	C₂²	1	2	yes	—
52	#10587623	C₂²	1	2	yes	—
53	#10587622	C₂²	1	2	yes	complemented
54	#10587622	C₂²	1	2	yes	complemented
55	#10587622	C₂²	1	1	yes	characteristic, complemented
56	#10587621	C₂²	1	2	yes	complemented
57	D₄×Dic₁₇	C₂²	1	2	yes	complemented
58	D₄×Dic₁₇	C₂²	1	2	yes	complemented
59	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
60	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
61	#10587616	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
64	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
66	C₂×#63227	C₂²	1	2	yes	—
67	#10587612	C₂²	1	2	yes	complemented
68	#10587612	C₂²	1	1	yes	characteristic, complemented
69	#10587610	C₂²	1	1	yes	characteristic, complemented
70	C₂×#63225	C₂²	1	2	yes	complemented
71	#10587584	C₂²	1	2	yes	complemented
72	#10587584	C₂²	1	2	yes	complemented
73	#10587583	C₂²	1	2	yes	—
74	#10587583	C₂²	1	1	yes	characteristic, complemented
75	#10587582	C₂²	1	2	yes	—
76	#10587582	C₂²	1	2	yes	complemented
77	#10587581	C₂²	1	1	yes	characteristic
78	#10587580	C₂²	1	2	yes	complemented
79	#10587579	C₂²	1	2	yes	complemented
80	#10587579	C₂²	1	1	yes	characteristic, complemented
81	#10587578	C₂²	1	1	yes	characteristic
82	#10587578	C₂²	1	1	yes	characteristic
83	#10587578	C₂²	1	1	yes	characteristic
84	#10587578	C₂²	1	2	yes	complemented
85	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
87	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
88	#10587576	C₂²	1	1	yes	characteristic, complemented
89	#10587575	C₂²	1	2	yes	complemented
90	#10587574	C₂²	1	2	yes	complemented
91	#10587574	C₂²	1	1	yes	characteristic, complemented
92	#10587573	C₂²	1	1	yes	characteristic, complemented
93	#10587572	C₂²	1	2	yes	complemented
94	#10587571	C₂²	1	2	yes	complemented
95	#10587571	C₂²	1	2	yes	complemented
96	#10587570	C₂²	1	2	yes	—
97	#10587570	C₂²	1	2	yes	complemented
98	#10587569	C₂²	1	2	yes	—
99	#10587569	C₂²	1	2	yes	complemented
100	#10587569	C₂²	1	2	yes	complemented
101	#10587569	C₂²	1	2	yes	complemented
102	#10587567	C₂²	1	2	yes	—
103	#10587567	C₂²	1	2	yes	complemented
104	#10587567	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
109	#10587565	C₂²	1	2	yes	complemented
110	#10587565	C₂²	1	2	yes	complemented
111	#10587564	C₂²	1	2	yes	complemented
112	#10587563	C₂²	1	1	yes	characteristic, complemented
113	#10587563	C₂²	1	2	yes	complemented
114	#10587563	C₂²	1	1	yes	characteristic, complemented
115	#10587561	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
117	#10587558	C₂²	1	1	yes	characteristic
118	#10587558	C₂²	1	1	yes	characteristic
119	C₄²×D₁₇	C₂²	1	1	yes	characteristic, complemented
120	C₄²×D₁₇	C₂²	1	1	yes	characteristic, complemented
121	#10587555	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₇	C₂³	1	1	yes	characteristic
124	C₂³×D₁₇	C₂³	1	2	yes	—
125	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₇	C₂³	1	2	yes	—
128	C₂×D₄×C₁₇	C₂³	1	2	yes	—
129	C₂×D₄×C₁₇	C₂³	1	2	yes	—
130	C₂×D₄×C₁₇	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
141	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₇	C₂³	1	2	yes	—
143	C₂²×Dic₁₇	C₂³	1	2	yes	—
144	C₂²×Dic₁₇	C₂³	1	2	yes	—
145	#63254	—	2	4	no	—
146	#63254	—	4	4	no	—
147	D₄×D₁₇	—	2	4	no	—
148	D₄×D₁₇	—	4	4	no	—
149	#63252	—	4	4	no	—
150	C₂×D₆₈	C₂³	1	2	yes	—
151	C₂×D₆₈	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₇	—	2	4	no	—
153	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₇	C₂³	1	2	yes	—
159	C₂×C₄×D₁₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₇	C₂³	1	2	yes	—
163	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
164	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
165	C₂×Dic₃₄	C₂³	1	2	yes	—
166	C₂×Dic₃₄	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
170	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
171	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
173	C₂²⋊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	1	yes	characteristic
179	C₄²×C₁₇	C₂³	1	1	yes	characteristic
180	C₄²×C₁₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
190	#63227	C₂³	1	1	yes	characteristic
191	#63227	C₂³	1	1	yes	characteristic
192	#63227	C₂³	1	1	yes	characteristic
193	#63227	C₂³	1	1	yes	characteristic
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	2	yes	—
202	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₇	C₂³	1	2	yes	—
205	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₇	C₂³	1	2	yes	—
208	C₄⋊Dic₁₇	C₂³	1	2	yes	—
209	#63225	C₂³	1	2	yes	—
210	#63225	C₂³	1	1	yes	characteristic
211	#63225	C₂³	1	1	yes	characteristic
212	#63225	C₂³	1	1	yes	characteristic
213	#63225	C₂³	1	1	yes	characteristic
214	#63225	C₂³	1	2	yes	—
215	#63225	C₂³	1	2	yes	—
216	#63225	C₂³	1	2	yes	—
217	#63225	C₂³	1	2	yes	—
218	#63225	C₂³	1	2	yes	—
219	C₄×Dic₁₇	C₂³	1	2	yes	—
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	1	yes	characteristic
225	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₇	C₂³	1	2	yes	—
227	C₄×Dic₁₇	C₂³	1	2	yes	—
228	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₇	C₂⁴	1	2	yes	—
230	C₂³×C₁₇	C₂⁴	1	2	yes	—
231	C₂²×D₁₇	—	2	2	no	—
232	C₂²×D₁₇	—	2	2	no	—
233	C₂²×D₁₇	—	2	4	no	—
234	C₂²×D₁₇	—	4	1	no	—
235	C₂²×D₁₇	—	4	2	no	—
236	C₂²×D₁₇	—	4	2	no	—
237	C₂²×D₁₇	C₂⁴	1	2	yes	—
238	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
240	D₄×C₁₇	—	2	2	no	—
241	D₄×C₁₇	—	2	2	no	—
242	D₄×C₁₇	—	4	2	no	—
243	D₄×C₁₇	—	4	2	no	—
244	D₄×C₁₇	—	4	2	no	—
245	D₄×C₁₇	—	4	2	no	—
246	C₂×C₄×C₁₇	—	2	2	no	—
247	C₂×C₄×C₁₇	—	4	2	no	—
248	C₂×C₄×C₁₇	—	4	2	no	—
249	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₇	—	2	4	no	—
258	C₂²⋊D₁₇	—	2	4	no	—
259	C₂²⋊D₁₇	—	2	4	no	—
260	C₂²⋊D₁₇	—	2	4	no	—
261	C₂²⋊D₁₇	—	4	2	no	—
262	C₂²⋊D₁₇	—	4	2	no	—
263	C₂²⋊D₁₇	—	4	2	no	—
264	C₂×Dic₁₇	—	2	2	no	—
265	C₂×Dic₁₇	—	2	4	no	—
266	C₂×Dic₁₇	—	4	2	no	—
267	C₂×Dic₁₇	—	4	2	no	—
268	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₇	C₂⁴	1	2	yes	—
271	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₇	C₂⁴	1	2	yes	—
273	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₇	C₂⁴	1	2	yes	—
275	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
277	D₆₈	—	2	4	no	—
278	D₆₈	—	2	2	no	—
279	C₄×D₁₇	—	2	2	no	—
280	C₄×D₁₇	—	2	2	no	—
281	C₄×D₁₇	—	2	2	no	—
282	C₄×D₁₇	—	2	2	no	—
283	C₄×D₁₇	—	2	2	no	—
284	C₄×D₁₇	—	4	2	no	—
285	C₄×D₁₇	—	4	1	no	—
286	C₄×D₁₇	—	4	1	no	—
287	C₄×D₁₇	—	4	2	no	—
288	C₄×D₁₇	—	4	2	no	—
289	C₄×D₁₇	#41	1	4	yes	complemented
290	Dic₃₄	—	2	2	no	—
291	Dic₃₄	—	4	2	no	—
292	Dic₃₄	—	4	2	no	—
293	#3494	—	17	1	no	maximal, Sylow
294	C₂²×C₁₇	—	2	2	no	—
295	C₂²×C₁₇	—	2	1	no	—
296	C₂²×C₁₇	—	2	2	no	—
297	C₂²×C₁₇	—	2	2	no	—
298	C₂²×C₁₇	—	2	2	no	—
299	C₂²×C₁₇	—	2	1	no	—
300	C₂²×C₁₇	—	2	2	no	—
301	C₂²×C₁₇	—	2	2	no	—
302	C₂²×C₁₇	—	2	1	no	—
303	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
304	C₂×D₁₇	—	2	1	no	—
305	C₂×D₁₇	—	2	1	no	—
306	C₂×D₁₇	—	2	1	no	—
307	C₂×D₁₇	—	2	1	no	—
308	C₂×D₁₇	—	2	2	no	—
309	C₂×D₁₇	—	2	2	no	—
310	C₂×D₁₇	—	2	2	no	—
311	C₂×D₁₇	—	4	4	no	—
312	C₂×D₁₇	—	8	4	no	—
313	C₂×D₁₇	C₂×#41	1	2	yes	—
314	C₂×D₁₇	H(5,𝔽₂)	1	2	yes	—
315	C₄×C₁₇	—	2	1	no	—
316	C₄×C₁₇	—	2	1	no	—
317	C₄×C₁₇	—	2	2	no	—
318	C₄×C₁₇	—	2	1	no	—
319	C₄×C₁₇	—	2	1	no	—
320	C₄×C₁₇	—	2	2	no	—
321	C₄×C₁₇	—	2	1	no	—
322	C₄×C₁₇	C₂×#41	1	2	yes	—
323	Dic₁₇	—	2	2	no	—
324	Dic₁₇	—	2	1	no	—
325	Dic₁₇	—	2	1	no	—
326	Dic₁₇	—	2	2	no	—
327	Dic₁₇	—	2	2	no	—
328	Dic₁₇	—	2	1	no	—
329	Dic₁₇	—	2	1	no	—
330	Dic₁₇	—	2	1	no	—
331	Dic₁₇	C₂×#41	1	2	yes	—
332	#555	—	17	2	no	—
333	#553	—	17	2	no	—
334	#553	—	17	2	no	—
335	#551	—	17	2	no	—
336	#551	—	17	2	no	—
337	#547	—	17	2	no	—
338	#546	—	17	2	no	—
339	#546	—	17	2	no	—
340	#544	—	17	1	no	—
341	#542	—	17	1	no	—
342	#542	—	17	1	no	—
343	#540	—	17	1	no	—
344	#540	D₁₇	1	1	yes	characteristic, complemented
345	#535	—	17	1	no	—
346	#532	—	17	1	no	—
347	#532	—	17	1	no	—
348	#529	—	17	1	no	—
349	#529	—	17	1	no	—
350	#525	—	17	1	no	—
351	C₂×#121	—	17	1	no	—
352	#520	—	17	1	no	—
353	#518	—	17	1	no	—
354	C₂×#117	—	17	1	no	—
355	C₂×C₁₇	—	4	1	no	—
356	C₂×C₁₇	—	4	2	no	—
357	C₂×C₁₇	—	4	2	no	—
358	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
359	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₁₇	#585	1	1	yes	characteristic
361	D₁₇	—	2	2	no	—
362	D₁₇	—	2	2	no	—
363	D₁₇	—	4	2	no	—
364	C₂×#41	—	17	1	no	—
365	C₂×#41	—	17	2	no	—
366	C₂×#41	—	17	2	no	—
367	C₂²×D₄	—	17	1	no	—
368	C₂²×D₄	—	17	2	no	—
369	C₂³×C₄	—	17	1	no	—
370	C₄⋊Q₈	—	17	1	no	—
371	C₄⋊Q₈	—	17	2	no	—
372	C₄⋊Q₈	—	17	1	no	—
373	#127	—	17	1	no	—
374	#127	C₂×D₁₇	1	1	yes	characteristic, complemented
375	#126	—	17	2	no	—
376	#126	—	17	2	no	—
377	#126	—	17	2	no	—
378	#126	—	17	2	no	—
379	#125	—	17	1	no	—
380	#125	—	17	2	no	—
381	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
382	#124	—	17	1	no	—
383	#124	—	17	2	no	—
384	#124	—	17	2	no	—
385	#124	—	17	2	no	—
386	#124	—	17	2	no	—
387	#124	—	17	1	no	—
388	#123	—	17	2	no	—
389	#123	—	17	2	no	—
390	#123	—	17	2	no	—
391	#123	—	17	2	no	—
392	#123	—	17	2	no	—
393	#123	—	17	2	no	—
394	#123	—	17	2	no	—
395	#123	C₂×D₁₇	1	2	yes	complemented
396	#123	C₂×D₁₇	1	2	yes	complemented
397	C₂²⋊Q₈	—	17	1	no	—
398	C₂²⋊Q₈	—	17	1	no	—
399	C₂²⋊Q₈	—	17	2	no	—
400	C₂²⋊Q₈	—	17	2	no	—
401	C₂²⋊Q₈	—	17	2	no	—
402	C₂²⋊Q₈	—	17	2	no	—
403	#121	—	17	1	no	—
404	#121	—	17	2	no	—
405	#121	—	17	1	no	—
406	#121	—	17	2	no	—
407	#121	—	17	2	no	—
408	#121	—	17	2	no	—
409	#121	—	17	2	no	—
410	#121	—	17	2	no	—
411	#121	—	17	1	no	—
412	#121	—	17	1	no	—
413	#121	—	17	2	no	—
414	#121	—	17	2	no	—
415	#121	C₂×D₁₇	1	1	yes	characteristic
416	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
417	#121	C₂×D₁₇	1	2	yes	complemented
418	#121	C₂×D₁₇	1	2	yes	complemented
419	#120	—	17	2	no	—
420	#120	—	17	2	no	—
421	#120	—	17	2	no	—
422	C₄×Q₈	—	17	1	no	—
423	C₄×Q₈	—	17	1	no	—
424	C₄×D₄	—	17	1	no	—
425	C₄×D₄	—	17	1	no	—
426	C₄×D₄	—	17	2	no	—
427	C₄×D₄	—	17	2	no	—
428	C₄×D₄	—	17	2	no	—
429	C₄×D₄	—	17	2	no	—
430	C₄×D₄	—	17	2	no	—
431	C₄×D₄	—	17	2	no	—
432	C₄×D₄	—	17	1	no	—
433	C₄×D₄	—	17	2	no	—
434	C₄×D₄	—	17	2	no	—
435	C₄×D₄	—	17	2	no	—
436	C₄×D₄	—	17	2	no	—
437	C₄×D₄	—	17	1	no	—
438	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
439	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
440	#117	—	17	1	no	—
441	#117	—	17	2	no	—
442	#117	—	17	1	no	—
443	#117	—	17	1	no	—
444	#117	—	17	1	no	—
445	#117	—	17	2	no	—
446	#117	—	17	1	no	—
447	#117	—	17	1	no	—
448	#117	—	17	2	no	—
449	#117	—	17	1	no	—
450	#117	—	17	1	no	—
451	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
452	C₂×C₄⋊C₄	—	17	2	no	—
453	C₂×C₄⋊C₄	—	17	1	no	—
454	C₂×C₄⋊C₄	—	17	1	no	—
455	C₂×C₄⋊C₄	—	17	1	no	—
456	C₂×C₂²⋊C₄	—	17	2	no	—
457	C₂×C₂²⋊C₄	—	17	1	no	—
458	C₂×C₂²⋊C₄	—	17	1	no	—
459	C₂×C₂²⋊C₄	—	17	2	no	—
460	C₂×C₂²⋊C₄	—	17	2	no	—
461	C₂×C₄²	—	17	1	no	—
462	C₂×C₄²	—	17	1	no	—
463	C₁₇	#3494	1	1	yes	characteristic, complemented, Sylow
464	C₂⁴	—	17	1	no	—
465	C₂⁴	—	17	2	no	—
466	#41	—	34	4	no	—
467	#41	—	68	4	no	—
468	#41	—	68	4	no	—
469	C₂×Q₈	—	17	1	no	—
470	C₂×Q₈	—	17	2	no	—
471	C₂×Q₈	—	17	2	no	—
472	C₂×D₄	—	17	2	no	—
473	C₂×D₄	—	17	2	no	—
474	C₂×D₄	—	17	2	no	—
475	C₂×D₄	—	17	2	no	—
476	C₂×D₄	—	17	2	no	—
477	C₂×D₄	—	17	2	no	—
478	C₂×D₄	—	17	2	no	—
479	C₂×D₄	—	17	1	no	—
480	C₂×D₄	—	17	2	no	—
481	C₂×D₄	—	34	4	no	—
482	C₂×D₄	—	68	4	no	—
483	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₁₇	1	2	yes	—
486	C₂×D₄	C₂²×D₁₇	1	2	yes	—
487	C₂×D₄	C₂²×D₁₇	1	2	yes	—
488	C₂×D₄	C₂²×D₁₇	1	2	yes	—
489	C₂²×C₄	—	17	1	no	—
490	C₂²×C₄	—	17	2	no	—
491	C₂²×C₄	—	17	1	no	—
492	C₂²×C₄	—	17	2	no	—
493	C₂²×C₄	—	17	2	no	—
494	C₂²×C₄	—	17	1	no	—
495	C₂²×C₄	—	17	1	no	—
496	C₂²×C₄	—	17	1	no	—
497	C₂²×C₄	—	17	1	no	—
498	C₂²×C₄	—	17	1	no	—
499	C₂²×C₄	—	17	1	no	—
500	C₂²×C₄	—	17	1	no	—
501	C₂²×C₄	—	17	2	no	—
502	C₂²×C₄	—	17	2	no	—
503	C₂²×C₄	—	17	2	no	—
504	C₂²×C₄	—	34	4	no	—
505	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
507	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
508	C₄⋊C₄	—	17	1	no	—
509	C₄⋊C₄	—	17	2	no	—
510	C₄⋊C₄	—	17	1	no	—
511	C₄⋊C₄	—	17	1	no	—
512	C₄⋊C₄	—	17	1	no	—
513	C₄⋊C₄	—	17	1	no	—
514	C₄⋊C₄	—	17	1	no	—
515	C₄⋊C₄	—	17	1	no	—
516	C₄⋊C₄	—	17	2	no	—
517	C₄⋊C₄	—	17	2	no	—
518	C₄⋊C₄	—	17	2	no	—
519	C₄⋊C₄	—	17	1	no	—
520	C₄⋊C₄	—	17	2	no	—
521	C₄⋊C₄	—	17	2	no	—
522	C₄⋊C₄	—	17	2	no	—
523	C₄⋊C₄	—	17	2	no	—
524	C₄⋊C₄	—	17	2	no	—
525	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
530	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
531	C₂²⋊C₄	—	17	1	no	—
532	C₂²⋊C₄	—	17	1	no	—
533	C₂²⋊C₄	—	17	2	no	—
534	C₂²⋊C₄	—	17	2	no	—
535	C₂²⋊C₄	—	17	2	no	—
536	C₂²⋊C₄	—	17	2	no	—
537	C₂²⋊C₄	—	17	2	no	—
538	C₂²⋊C₄	—	17	2	no	—
539	C₂²⋊C₄	—	17	2	no	—
540	C₂²⋊C₄	—	17	1	no	—
541	C₂²⋊C₄	—	17	1	no	—
542	C₂²⋊C₄	—	17	2	no	—
543	C₂²⋊C₄	—	17	1	no	—
544	C₂²⋊C₄	—	17	1	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	2	no	—
552	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
558	C₄²	—	17	1	no	—
559	C₄²	—	17	1	no	—
560	C₄²	—	17	1	no	—
561	C₄²	—	17	1	no	—
562	C₄²	—	17	1	no	—
563	C₄²	—	17	1	no	—
564	C₄²	—	17	2	no	—
565	C₄²	—	17	2	no	—
566	C₄²	—	17	2	no	—
567	C₄²	C₂²×D₁₇	1	1	yes	characteristic
568	C₄²	C₂²×D₁₇	1	1	yes	characteristic
569	C₂³	—	17	1	no	—
570	C₂³	—	17	1	no	—
571	C₂³	—	17	2	no	—
572	C₂³	—	34	2	no	—
573	C₂³	—	34	2	no	—
574	C₂³	—	34	4	no	—
575	C₂³	—	68	1	no	—
576	C₂³	—	68	2	no	—
577	C₂³	—	68	2	no	—
578	C₂³	C₂³×D₁₇	1	1	yes	characteristic
579	C₂³	C₂³×D₁₇	1	2	yes	—
580	C₂³	C₂³×D₁₇	1	2	yes	—
581	Q₈	—	34	2	no	—
582	Q₈	—	68	2	no	—
583	Q₈	—	68	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	34	4	no	—
591	D₄	—	34	4	no	—
592	D₄	—	34	4	no	—
593	D₄	—	34	4	no	—
594	D₄	—	34	4	no	—
595	D₄	—	34	2	no	—
596	D₄	—	68	2	no	—
597	D₄	—	68	2	no	—
598	D₄	—	68	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	17	1	no	—
603	C₂×C₄	—	17	4	no	—
604	C₂×C₄	—	17	1	no	—
605	C₂×C₄	—	17	1	no	—
606	C₂×C₄	—	17	2	no	—
607	C₂×C₄	—	17	1	no	—
608	C₂×C₄	—	17	1	no	—
609	C₂×C₄	—	17	1	no	—
610	C₂×C₄	—	17	2	no	—
611	C₂×C₄	—	17	2	no	—
612	C₂×C₄	—	34	2	no	—
613	C₂×C₄	—	34	2	no	—
614	C₂×C₄	—	34	2	no	—
615	C₂×C₄	—	34	2	no	—
616	C₂×C₄	—	34	2	no	—
617	C₂×C₄	—	34	4	no	—
618	C₂×C₄	—	34	2	no	—
619	C₂×C₄	—	68	2	no	—
620	C₂×C₄	—	68	2	no	—
621	C₂×C₄	—	68	1	no	—
622	C₂×C₄	—	68	2	no	—
623	C₂×C₄	—	68	1	no	—
624	C₂×C₄	—	68	2	no	—
625	C₂×C₄	—	68	2	no	—
626	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₇	1	2	yes	—
631	C₂×C₄	C₂³×D₁₇	1	2	yes	—
632	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	17	2	no	—
644	C₂²	—	17	2	no	—
645	C₂²	—	34	1	no	—
646	C₂²	—	34	1	no	—
647	C₂²	—	34	1	no	—
648	C₂²	—	34	1	no	—
649	C₂²	—	34	2	no	—
650	C₂²	—	34	2	no	—
651	C₂²	—	34	2	no	—
652	C₂²	—	68	4	no	—
653	C₂²	—	136	4	no	—
654	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	17	2	no	—
663	C₄	—	34	1	no	—
664	C₄	—	34	2	no	—
665	C₄	—	34	1	no	—
666	C₄	—	34	1	no	—
667	C₄	—	34	2	no	—
668	C₄	—	34	2	no	—
669	C₄	—	34	1	no	—
670	C₄	—	34	1	no	—
671	C₄	#41×D₁₇	1	2	yes	—
672	C₂	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	34	2	no	—
676	C₂	—	34	2	no	—
677	C₂	—	68	2	no	—
678	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
679	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
680	C₂	#11763644	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#540	C₂
hypercenter	#540	D₁₇
hypocenter	C₁₇	#3494
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #11763523	C₂	semidirect
2. #11763504	C₂	semidirect
3. #11763502	C₂	semidirect
4. #11763487	C₂	semidirect
5. #11763482	C₂	semidirect
6. #11763457	C₂	semidirect
7. #11763456	C₂	semidirect
8. #11763448	C₂	semidirect
9. #11763439	C₂	semidirect
10. #11763430	C₂	semidirect
11. #11763426	C₂	semidirect
12. #11763412	C₂	semidirect
13. #11763372	C₂	semidirect
14. #11763357	C₂	semidirect
15. #11763356	C₂	semidirect
16. #11763344	C₂	semidirect
17. #11763341	C₂	semidirect
18. #11763319	C₂	semidirect
19. #121×D₁₇	C₂	semidirect
20. #11763288	C₂	semidirect
21. #11763281	C₂	semidirect
22. #117×D₁₇	C₂	semidirect
23. C₁₇×#540	C₂	semidirect
25. C₂×#63254	C₂²	semidirect
28. C₂×#63252	C₂²	semidirect
30. C₁₇×#127	C₂²	semidirect
31. C₁₇×#125	C₂²	semidirect
32. C₁₇×#123	C₂²	semidirect
33. C₁₇×#123	C₂²	semidirect
35. C₁₇×#121	C₂²	semidirect
36. C₁₇×#121	C₂²	semidirect
37. C₁₇×#121	C₂²	semidirect
38. C₄×D₄×C₁₇	C₂²	semidirect
39. C₄×D₄×C₁₇	C₂²	semidirect
40. C₁₇×#117	C₂²	semidirect
41. #10587626	C₂²	semidirect
43. #10587625	C₂²	semidirect
44. #10587625	C₂²	semidirect
45. #10587625	C₂²	semidirect
47. #10587624	C₂²	semidirect
48. #10587624	C₂²	semidirect
49. #10587624	C₂²	semidirect
53. #10587622	C₂²	semidirect
54. #10587622	C₂²	semidirect
55. #10587622	C₂²	semidirect
56. #10587621	C₂²	semidirect
57. D₄×Dic₁₇	C₂²	semidirect
58. D₄×Dic₁₇	C₂²	semidirect
59. D₄×Dic₁₇	C₂²	semidirect
60. D₄×Dic₁₇	C₂²	semidirect
63. C₄×C₂²⋊D₁₇	C₂²	semidirect
64. C₄×C₂²⋊D₁₇	C₂²	semidirect
65. C₄×C₂²⋊D₁₇	C₂²	semidirect
67. #10587612	C₂²	semidirect
68. #10587612	C₂²	semidirect
69. #10587610	C₂²	semidirect
70. C₂×#63225	C₂²	semidirect
71. #10587584	C₂²	semidirect
72. #10587584	C₂²	semidirect
74. #10587583	C₂²	semidirect
76. #10587582	C₂²	semidirect
78. #10587580	C₂²	semidirect
79. #10587579	C₂²	semidirect
80. #10587579	C₂²	semidirect
84. #10587578	C₂²	semidirect
86. C₄⋊C₄×D₁₇	C₂²	semidirect
87. C₄⋊C₄×D₁₇	C₂²	semidirect
88. #10587576	C₂²	semidirect
89. #10587575	C₂²	semidirect
90. #10587574	C₂²	semidirect
91. #10587574	C₂²	semidirect
92. #10587573	C₂²	semidirect
93. #10587572	C₂²	semidirect
94. #10587571	C₂²	semidirect
95. #10587571	C₂²	semidirect
97. #10587570	C₂²	semidirect
99. #10587569	C₂²	semidirect
100. #10587569	C₂²	semidirect
101. #10587569	C₂²	semidirect
103. #10587567	C₂²	semidirect
104. #10587567	C₂²	semidirect
109. #10587565	C₂²	semidirect
110. #10587565	C₂²	semidirect
111. #10587564	C₂²	semidirect
112. #10587563	C₂²	semidirect
113. #10587563	C₂²	semidirect
114. #10587563	C₂²	semidirect
115. #10587561	C₂²	semidirect
116. C₄×D₆₈	C₂²	semidirect
119. C₄²×D₁₇	C₂²	semidirect
120. C₄²×D₁₇	C₂²	semidirect
121. #10587555	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
289. C₄×D₁₇	#41	semidirect
344. #540	D₁₇	semidirect
374. #127	C₂×D₁₇	semidirect
381. #125	C₂×D₁₇	semidirect
395. #123	C₂×D₁₇	semidirect
396. #123	C₂×D₁₇	semidirect
416. #121	C₂×D₁₇	semidirect
417. #121	C₂×D₁₇	semidirect
418. #121	C₂×D₁₇	semidirect
438. C₄×D₄	C₂×D₁₇	semidirect
439. C₄×D₄	C₂×D₁₇	semidirect
451. #117	C₂×D₁₇	semidirect
463. C₁₇	#3494	semidirect

Maximal subgroups

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

subgroup	index
#11763523	2
#11763504	2
#11763502	2
#11763487	2
#11763482	2
#11763457	2
#11763456	2
#11763448	2
#11763439	2
#11763430	2
#11763426	2
#11763412	2
#11763372	2
#11763357	2
#11763356	2
#11763344	2
#11763341	2
#11763319	2
#121×D₁₇	2
#11763288	2
#11763281	2
#117×D₁₇	2
C₁₇×#540	2
#3494	17