Subgroups — #14542847

Order 2176.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763529	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763527	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763515	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763506	C₂	1	2	yes	maximal, complemented
5	#11763495	C₂	1	2	yes	maximal, complemented
6	#11763494	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763488	C₂	1	2	yes	maximal, complemented
8	#11763482	C₂	1	2	yes	maximal, complemented
9	#11763464	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763456	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763456	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763426	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763422	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763402	C₂	1	2	yes	maximal, complemented
15	#11763391	C₂	1	2	yes	maximal, complemented
16	#11763341	C₂	1	2	yes	maximal, complemented
17	#11763340	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763339	C₂	1	1	yes	maximal, characteristic, complemented
19	#126×D₁₇	C₂	1	2	yes	maximal, complemented
20	#11763290	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763281	C₂	1	1	yes	maximal, characteristic, complemented
22	#11763277	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
25	C₂×#63252	C₂²	1	1	yes	characteristic
26	C₂×#63252	C₂²	1	1	yes	characteristic
27	C₁₇×#126	C₂²	1	2	yes	complemented
28	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
29	C₁₇×#123	C₂²	1	2	yes	complemented
30	C₁₇×#121	C₂²	1	1	yes	characteristic
31	C₁₇×#121	C₂²	1	1	yes	characteristic
32	C₁₇×#121	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
36	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
38	#10587625	C₂²	1	1	yes	characteristic
39	#10587624	C₂²	1	2	yes	—
40	#10587624	C₂²	1	2	yes	—
41	#10587624	C₂²	1	2	yes	complemented
42	#10587623	C₂²	1	2	yes	—
43	#10587623	C₂²	1	2	yes	—
44	#10587622	C₂²	1	1	yes	characteristic
45	#10587622	C₂²	1	1	yes	characteristic
46	#10587622	C₂²	1	2	yes	complemented
47	#10587621	C₂²	1	2	yes	complemented
48	#10587621	C₂²	1	1	yes	characteristic, complemented
49	#10587621	C₂²	1	2	yes	complemented
50	D₄×Dic₁₇	C₂²	1	1	yes	characteristic
51	D₄×Dic₁₇	C₂²	1	2	yes	complemented
52	#10587615	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
58	C₂×#63227	C₂²	1	2	yes	—
59	#10587612	C₂²	1	2	yes	complemented
60	#10587612	C₂²	1	2	yes	complemented
61	#10587612	C₂²	1	1	yes	characteristic, complemented
62	#10587610	C₂²	1	1	yes	characteristic, complemented
63	#10587610	C₂²	1	1	yes	characteristic, complemented
64	#10587610	C₂²	1	2	yes	complemented
65	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
66	#10587584	C₂²	1	2	yes	—
67	#10587584	C₂²	1	2	yes	—
68	#10587584	C₂²	1	1	yes	characteristic
69	#10587584	C₂²	1	2	yes	—
70	#10587583	C₂²	1	1	yes	characteristic
71	#10587583	C₂²	1	1	yes	characteristic
72	#10587583	C₂²	1	2	yes	complemented
73	#10587582	C₂²	1	2	yes	complemented
74	#10587582	C₂²	1	2	yes	complemented
75	#10587579	C₂²	1	1	yes	characteristic
76	#10587579	C₂²	1	1	yes	characteristic
77	#10587579	C₂²	1	1	yes	characteristic
78	#10587578	C₂²	1	1	yes	characteristic
79	#10587578	C₂²	1	2	yes	complemented
80	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
81	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
82	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
83	#10587576	C₂²	1	1	yes	characteristic, complemented
84	#10587576	C₂²	1	2	yes	complemented
85	#10587576	C₂²	1	2	yes	complemented
86	#10587575	C₂²	1	2	yes	complemented
87	#10587575	C₂²	1	1	yes	characteristic, complemented
88	#10587574	C₂²	1	1	yes	characteristic, complemented
89	#10587573	C₂²	1	1	yes	characteristic, complemented
90	#10587573	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	1	yes	characteristic
94	#10587571	C₂²	1	2	yes	—
95	#10587571	C₂²	1	1	yes	characteristic
96	#10587569	C₂²	1	2	yes	—
97	#10587569	C₂²	1	2	yes	—
98	#10587569	C₂²	1	2	yes	complemented
99	#10587569	C₂²	1	2	yes	complemented
100	#10587567	C₂²	1	2	yes	—
101	#10587567	C₂²	1	2	yes	complemented
102	#10587567	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
106	#10587565	C₂²	1	2	yes	complemented
107	#10587565	C₂²	1	2	yes	complemented
108	#10587565	C₂²	1	2	yes	complemented
109	#10587565	C₂²	1	2	yes	complemented
110	#10587565	C₂²	1	2	yes	complemented
111	#10587565	C₂²	1	1	yes	characteristic, complemented
112	#10587564	C₂²	1	2	yes	complemented
113	#10587564	C₂²	1	1	yes	characteristic, complemented
114	#10587563	C₂²	1	2	yes	complemented
115	#10587562	C₂²	1	2	yes	—
116	C₄×D₆₈	C₂²	1	1	yes	characteristic
117	#10587558	C₂²	1	1	yes	characteristic
118	#10587558	C₂²	1	2	yes	complemented
119	C₄²×D₁₇	C₂²	1	2	yes	complemented
120	#10587555	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₄	C₂²	1	2	yes	complemented
122	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₇	C₂³	1	2	yes	—
124	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₇	C₂³	1	2	yes	—
126	C₂×D₄×C₁₇	C₂³	1	2	yes	—
127	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₇	C₂³	1	2	yes	—
138	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
139	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
140	D₄×D₁₇	—	2	4	no	—
141	#63252	—	2	4	no	—
142	#63252	—	2	4	no	—
143	C₂×D₆₈	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₇	C₂³	1	2	yes	—
145	C₂×C₄×D₁₇	C₂³	1	2	yes	—
146	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₇	C₂³	1	2	yes	—
148	C₂×C₄×D₁₇	C₂³	1	2	yes	—
149	C₂×C₄×D₁₇	C₂³	1	2	yes	—
150	C₂×C₄×D₁₇	C₂³	1	2	yes	—
151	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
152	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
153	C₂×Dic₃₄	C₂³	1	2	yes	—
154	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
162	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
163	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
168	C₄²×C₁₇	C₂³	1	1	yes	characteristic
169	C₄²×C₁₇	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
181	#63227	C₂³	1	1	yes	characteristic
182	#63227	C₂³	1	1	yes	characteristic
183	#63227	C₂³	1	2	yes	—
184	#63227	C₂³	1	2	yes	—
185	#63227	C₂³	1	2	yes	—
186	#63227	C₂³	1	1	yes	characteristic
187	#63227	C₂³	1	2	yes	—
188	#63227	C₂³	1	2	yes	—
189	#63227	C₂³	1	1	yes	characteristic
190	#63227	C₂³	1	2	yes	—
191	#63227	C₂³	1	2	yes	—
192	C₄⋊Dic₁₇	C₂³	1	2	yes	—
193	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₇	C₂³	1	2	yes	—
195	C₄⋊Dic₁₇	C₂³	1	2	yes	—
196	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₇	C₂³	1	2	yes	—
200	C₄⋊Dic₁₇	C₂³	1	2	yes	—
201	#63225	C₂³	1	1	yes	characteristic
202	#63225	C₂³	1	2	yes	—
203	#63225	C₂³	1	1	yes	characteristic
204	#63225	C₂³	1	1	yes	characteristic
205	#63225	C₂³	1	1	yes	characteristic
206	#63225	C₂³	1	1	yes	characteristic
207	#63225	C₂³	1	2	yes	—
208	#63225	C₂³	1	2	yes	—
209	#63225	C₂³	1	2	yes	—
210	#63225	C₂³	1	2	yes	—
211	#63225	C₂³	1	2	yes	—
212	#63225	C₂³	1	2	yes	—
213	#63225	C₂³	1	1	yes	characteristic
214	#63225	C₂³	1	2	yes	—
215	C₄×Dic₁₇	C₂³	1	2	yes	—
216	C₄×Dic₁₇	C₂³	1	2	yes	—
217	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₇	C₂³	1	2	yes	—
221	C₄×Dic₁₇	C₂³	1	2	yes	—
222	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₇	C₂³	1	2	yes	—
225	C₂³×C₁₇	C₂⁴	1	2	yes	—
226	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₇	—	2	4	no	—
229	C₂²×D₁₇	—	4	2	no	—
230	C₂²×D₁₇	—	4	2	no	—
231	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₇	C₂⁴	1	2	yes	—
233	D₄×C₁₇	—	2	2	no	—
234	D₄×C₁₇	—	4	2	no	—
235	D₄×C₁₇	—	4	1	no	—
236	D₄×C₁₇	—	4	2	no	—
237	C₂×C₄×C₁₇	—	2	2	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	4	2	no	—
240	C₂×C₄×C₁₇	—	4	2	no	—
241	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₇	—	2	4	no	—
250	C₂²⋊D₁₇	—	2	4	no	—
251	C₂²⋊D₁₇	—	2	4	no	—
252	C₂²⋊D₁₇	—	4	1	no	—
253	C₂²⋊D₁₇	—	4	1	no	—
254	C₂×Dic₁₇	—	4	2	no	—
255	C₂×Dic₁₇	—	4	1	no	—
256	C₂×Dic₁₇	—	4	1	no	—
257	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₇	C₂⁴	1	2	yes	—
260	C₂×Dic₁₇	C₂⁴	1	2	yes	—
261	C₂×Dic₁₇	C₂⁴	1	2	yes	—
262	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
267	D₆₈	#41	1	4	yes	—
268	C₄×D₁₇	—	2	4	no	—
269	C₄×D₁₇	—	2	4	no	—
270	C₄×D₁₇	—	2	2	no	—
271	C₄×D₁₇	—	4	2	no	—
272	C₄×D₁₇	—	4	2	no	—
273	C₄×D₁₇	—	4	2	no	—
274	C₄×D₁₇	—	4	2	no	—
275	Dic₃₄	—	2	2	no	—
276	Dic₃₄	—	2	2	no	—
277	Dic₃₄	—	4	2	no	—
278	Dic₃₄	—	4	1	no	—
279	#3521	—	17	1	no	maximal, Sylow
280	C₂²×C₁₇	—	2	1	no	—
281	C₂²×C₁₇	—	2	1	no	—
282	C₂²×C₁₇	—	2	2	no	—
283	C₂²×C₁₇	—	2	1	no	—
284	C₂²×C₁₇	—	2	1	no	—
285	C₂²×C₁₇	—	2	2	no	—
286	C₂²×C₁₇	—	2	1	no	—
287	C₂²×C₁₇	—	2	2	no	—
288	C₂²×C₁₇	—	2	1	no	—
289	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
290	C₂×D₁₇	—	2	2	no	—
291	C₂×D₁₇	—	2	2	no	—
292	C₂×D₁₇	—	2	1	no	—
293	C₂×D₁₇	—	2	1	no	—
294	C₂×D₁₇	—	2	1	no	—
295	C₂×D₁₇	—	8	4	no	—
296	C₂×D₁₇	C₂×#41	1	4	yes	—
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	1	no	—
299	C₄×C₁₇	—	2	2	no	—
300	C₄×C₁₇	—	2	1	no	—
301	C₄×C₁₇	—	2	1	no	—
302	C₄×C₁₇	—	2	2	no	—
303	C₄×C₁₇	—	2	2	no	—
304	C₄×C₁₇	C₂×#41	1	2	yes	—
305	Dic₁₇	—	2	2	no	—
306	Dic₁₇	—	2	2	no	—
307	Dic₁₇	—	2	1	no	—
308	Dic₁₇	—	2	1	no	—
309	Dic₁₇	—	2	1	no	—
310	Dic₁₇	—	2	2	no	—
311	Dic₁₇	—	2	1	no	—
312	Dic₁₇	—	2	1	no	—
313	Dic₁₇	—	2	1	no	—
314	Dic₁₇	—	2	1	no	—
315	#556	—	17	1	no	—
316	#556	—	17	1	no	—
317	#554	—	17	1	no	—
318	#553	—	17	2	no	—
319	#553	D₁₇	1	1	yes	characteristic, complemented
320	#552	—	17	2	no	—
321	#552	—	17	1	no	—
322	#551	—	17	2	no	—
323	#551	—	17	2	no	—
324	#547	—	17	1	no	—
325	#546	—	17	1	no	—
326	#546	—	17	1	no	—
327	#542	—	17	1	no	—
328	#541	—	17	1	no	—
329	#539	—	17	2	no	—
330	#538	—	17	2	no	—
331	#529	—	17	1	no	—
332	#529	—	17	1	no	—
333	#529	—	17	2	no	—
334	C₂×#126	—	17	2	no	—
335	#520	—	17	1	no	—
336	#518	—	17	1	no	—
337	C₄×#41	—	17	1	no	—
338	C₂×C₁₇	—	4	2	no	—
339	C₂×C₁₇	—	4	1	no	—
340	C₂×C₁₇	—	4	1	no	—
341	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
342	C₂×C₁₇	#585	1	1	yes	characteristic
343	C₂×C₁₇	#585	1	1	yes	characteristic
344	D₁₇	—	2	4	no	—
345	D₁₇	—	4	1	no	—
346	C₂×#41	—	17	1	no	—
347	C₂×#41	—	17	1	no	—
348	C₂²×D₄	—	17	1	no	—
349	C₄⋊Q₈	—	17	1	no	—
350	C₄⋊Q₈	—	17	1	no	—
351	#126	—	17	1	no	—
352	#126	—	17	2	no	—
353	#126	—	17	2	no	—
354	#126	—	17	2	no	—
355	#126	—	17	2	no	—
356	#126	—	17	2	no	—
357	#126	—	17	2	no	—
358	#126	—	17	1	no	—
359	#126	—	17	2	no	—
360	#126	—	17	2	no	—
361	#126	—	17	2	no	—
362	#126	C₂×D₁₇	1	2	yes	complemented
363	#125	—	17	2	no	—
364	#125	—	17	1	no	—
365	#125	—	17	1	no	—
366	#125	—	17	2	no	—
367	#125	—	17	2	no	—
368	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
369	#124	—	17	2	no	—
370	#124	—	17	1	no	—
371	#124	—	17	1	no	—
372	#124	—	17	1	no	—
373	#124	—	17	2	no	—
374	#123	—	17	2	no	—
375	#123	—	17	1	no	—
376	#123	—	17	2	no	—
377	#123	—	17	2	no	—
378	#123	—	17	2	no	—
379	#123	—	17	2	no	—
380	#123	—	17	1	no	—
381	#123	—	17	2	no	—
382	#123	—	17	2	no	—
383	#123	C₂×D₁₇	1	2	yes	complemented
384	C₂²⋊Q₈	—	17	1	no	—
385	C₂²⋊Q₈	—	17	2	no	—
386	C₂²⋊Q₈	—	17	1	no	—
387	C₂²⋊Q₈	—	17	2	no	—
388	C₂²⋊Q₈	—	17	2	no	—
389	C₂²⋊Q₈	—	17	2	no	—
390	C₂²⋊Q₈	—	17	1	no	—
391	C₂²⋊Q₈	—	17	1	no	—
392	C₂²⋊Q₈	—	17	1	no	—
393	C₂²⋊Q₈	—	17	2	no	—
394	#121	—	17	1	no	—
395	#121	—	17	2	no	—
396	#121	—	17	2	no	—
397	#121	—	17	2	no	—
398	#121	C₂×D₁₇	1	1	yes	characteristic
399	#121	C₂×D₁₇	1	1	yes	characteristic
400	#121	C₂×D₁₇	1	2	yes	complemented
401	#120	—	17	2	no	—
402	#120	—	17	2	no	—
403	C₄×Q₈	—	17	1	no	—
404	C₄×Q₈	—	17	1	no	—
405	C₄×Q₈	—	17	1	no	—
406	C₄×Q₈	—	17	1	no	—
407	C₄×Q₈	—	17	2	no	—
408	C₄×Q₈	—	17	1	no	—
409	C₄×D₄	—	17	1	no	—
410	C₄×D₄	—	17	2	no	—
411	C₄×D₄	—	17	2	no	—
412	C₄×D₄	—	17	2	no	—
413	C₄×D₄	—	17	2	no	—
414	C₄×D₄	—	17	1	no	—
415	C₄×D₄	—	17	1	no	—
416	C₄×D₄	—	17	1	no	—
417	C₄×D₄	—	17	1	no	—
418	C₄×D₄	—	17	1	no	—
419	C₄×D₄	—	17	2	no	—
420	C₄×D₄	—	17	2	no	—
421	C₄×D₄	—	17	2	no	—
422	C₄×D₄	—	17	1	no	—
423	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
424	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
425	C₄×D₄	C₂×D₁₇	1	2	yes	complemented
426	#117	—	17	1	no	—
427	#117	—	17	2	no	—
428	#117	—	17	2	no	—
429	#117	—	17	1	no	—
430	#117	—	17	2	no	—
431	#117	—	17	2	no	—
432	#117	—	17	2	no	—
433	#117	—	17	1	no	—
434	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
435	C₂×C₄⋊C₄	—	17	2	no	—
436	C₂×C₄⋊C₄	—	17	2	no	—
437	C₂×C₄⋊C₄	—	17	2	no	—
438	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
439	C₂×C₂²⋊C₄	—	17	2	no	—
440	C₂×C₂²⋊C₄	—	17	2	no	—
441	C₂×C₂²⋊C₄	—	17	2	no	—
442	C₂×C₂²⋊C₄	—	17	2	no	—
443	C₂×C₄²	—	17	1	no	—
444	C₂×C₄²	—	17	2	no	—
445	C₁₇	#3521	1	1	yes	characteristic, complemented, Sylow
446	C₂⁴	—	17	2	no	—
447	#41	—	34	4	no	—
448	#41	—	34	4	no	—
449	C₂×Q₈	—	17	1	no	—
450	C₂×Q₈	—	17	1	no	—
451	C₂×Q₈	—	17	1	no	—
452	C₂×Q₈	—	17	2	no	—
453	C₂×D₄	—	17	2	no	—
454	C₂×D₄	—	17	2	no	—
455	C₂×D₄	—	17	2	no	—
456	C₂×D₄	—	17	1	no	—
457	C₂×D₄	—	17	1	no	—
458	C₂×D₄	—	17	1	no	—
459	C₂×D₄	—	34	4	no	—
460	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₁₇	1	2	yes	—
462	C₂×D₄	C₂²×D₁₇	1	2	yes	—
463	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
464	C₂²×C₄	—	17	1	no	—
465	C₂²×C₄	—	17	1	no	—
466	C₂²×C₄	—	17	2	no	—
467	C₂²×C₄	—	17	2	no	—
468	C₂²×C₄	—	17	2	no	—
469	C₂²×C₄	—	17	1	no	—
470	C₂²×C₄	—	17	2	no	—
471	C₂²×C₄	—	17	2	no	—
472	C₂²×C₄	—	17	2	no	—
473	C₂²×C₄	—	17	2	no	—
474	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
477	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
478	C₄⋊C₄	—	17	1	no	—
479	C₄⋊C₄	—	17	1	no	—
480	C₄⋊C₄	—	17	2	no	—
481	C₄⋊C₄	—	17	2	no	—
482	C₄⋊C₄	—	17	2	no	—
483	C₄⋊C₄	—	17	2	no	—
484	C₄⋊C₄	—	17	2	no	—
485	C₄⋊C₄	—	17	2	no	—
486	C₄⋊C₄	—	17	2	no	—
487	C₄⋊C₄	—	17	1	no	—
488	C₄⋊C₄	—	17	1	no	—
489	C₄⋊C₄	—	17	1	no	—
490	C₄⋊C₄	—	17	1	no	—
491	C₄⋊C₄	—	17	1	no	—
492	C₄⋊C₄	—	17	2	no	—
493	C₄⋊C₄	—	17	2	no	—
494	C₄⋊C₄	—	17	2	no	—
495	C₄⋊C₄	—	17	2	no	—
496	C₄⋊C₄	—	17	2	no	—
497	C₄⋊C₄	—	17	1	no	—
498	C₄⋊C₄	—	17	1	no	—
499	C₄⋊C₄	—	17	1	no	—
500	C₄⋊C₄	—	17	2	no	—
501	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
508	C₂²⋊C₄	—	17	2	no	—
509	C₂²⋊C₄	—	17	2	no	—
510	C₂²⋊C₄	—	17	2	no	—
511	C₂²⋊C₄	—	17	1	no	—
512	C₂²⋊C₄	—	17	1	no	—
513	C₂²⋊C₄	—	17	1	no	—
514	C₂²⋊C₄	—	17	2	no	—
515	C₂²⋊C₄	—	17	2	no	—
516	C₂²⋊C₄	—	17	2	no	—
517	C₂²⋊C₄	—	17	1	no	—
518	C₂²⋊C₄	—	17	2	no	—
519	C₂²⋊C₄	—	17	1	no	—
520	C₂²⋊C₄	—	17	1	no	—
521	C₂²⋊C₄	—	17	2	no	—
522	C₂²⋊C₄	—	17	1	no	—
523	C₂²⋊C₄	—	17	1	no	—
524	C₂²⋊C₄	—	17	2	no	—
525	C₂²⋊C₄	—	17	2	no	—
526	C₂²⋊C₄	—	17	2	no	—
527	C₂²⋊C₄	—	17	2	no	—
528	C₂²⋊C₄	—	17	2	no	—
529	C₂²⋊C₄	—	17	2	no	—
530	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
536	C₄²	—	17	1	no	—
537	C₄²	—	17	1	no	—
538	C₄²	—	17	1	no	—
539	C₄²	—	17	2	no	—
540	C₄²	—	17	1	no	—
541	C₄²	—	17	2	no	—
542	C₄²	—	17	2	no	—
543	C₄²	—	17	2	no	—
544	C₄²	—	17	2	no	—
545	C₄²	—	17	1	no	—
546	C₄²	C₂²×D₁₇	1	2	yes	—
547	C₄²	C₂²×D₁₇	1	1	yes	characteristic
548	C₂³	—	17	2	no	—
549	C₂³	—	17	1	no	—
550	C₂³	—	34	4	no	—
551	C₂³	—	68	2	no	—
552	C₂³	—	68	2	no	—
553	C₂³	C₂³×D₁₇	1	2	yes	—
554	C₂³	C₂³×D₁₇	1	1	yes	characteristic
555	C₂³	C₂³×D₁₇	1	1	yes	characteristic
556	Q₈	—	34	2	no	—
557	Q₈	—	34	2	no	—
558	Q₈	—	68	1	no	—
559	Q₈	—	68	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	2	no	—
564	D₄	—	17	4	no	—
565	D₄	—	34	4	no	—
566	D₄	—	34	4	no	—
567	D₄	—	34	4	no	—
568	D₄	—	68	1	no	—
569	D₄	—	68	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	17	1	no	—
575	C₂×C₄	—	17	1	no	—
576	C₂×C₄	—	17	1	no	—
577	C₂×C₄	—	17	1	no	—
578	C₂×C₄	—	17	2	no	—
579	C₂×C₄	—	17	2	no	—
580	C₂×C₄	—	17	1	no	—
581	C₂×C₄	—	17	1	no	—
582	C₂×C₄	—	17	1	no	—
583	C₂×C₄	—	17	2	no	—
584	C₂×C₄	—	34	4	no	—
585	C₂×C₄	—	34	4	no	—
586	C₂×C₄	—	34	2	no	—
587	C₂×C₄	—	68	2	no	—
588	C₂×C₄	—	68	2	no	—
589	C₂×C₄	—	68	2	no	—
590	C₂×C₄	—	68	2	no	—
591	C₂×C₄	—	68	1	no	—
592	C₂×C₄	—	68	1	no	—
593	C₂×C₄	—	68	2	no	—
594	C₂×C₄	C₂³×D₁₇	1	2	yes	—
595	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₇	1	2	yes	—
597	C₂×C₄	C₂³×D₁₇	1	2	yes	—
598	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	17	4	no	—
612	C₂²	—	34	2	no	—
613	C₂²	—	34	2	no	—
614	C₂²	—	34	1	no	—
615	C₂²	—	34	1	no	—
616	C₂²	—	34	1	no	—
617	C₂²	—	136	4	no	—
618	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	34	1	no	—
627	C₄	—	34	2	no	—
628	C₄	—	34	2	no	—
629	C₄	—	34	1	no	—
630	C₄	—	34	1	no	—
631	C₄	—	34	1	no	—
632	C₄	—	34	1	no	—
633	C₄	—	34	1	no	—
634	C₄	—	34	2	no	—
635	C₄	—	34	1	no	—
636	C₄	#41×D₁₇	1	2	yes	—
637	C₂	—	4	2	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	1	no	—
640	C₂	—	34	4	no	—
641	C₂	—	68	1	no	—
642	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
643	C₂	#11763644	1	1	yes	characteristic
644	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#553	C₂
hypercenter	#553	D₁₇
hypocenter	C₁₇	#3521
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #11763529	C₂	semidirect
2. #11763527	C₂	semidirect
3. #11763515	C₂	semidirect
4. #11763506	C₂	semidirect
5. #11763495	C₂	semidirect
6. #11763494	C₂	semidirect
7. #11763488	C₂	semidirect
8. #11763482	C₂	semidirect
9. #11763464	C₂	semidirect
10. #11763456	C₂	semidirect
11. #11763456	C₂	semidirect
12. #11763426	C₂	semidirect
13. #11763422	C₂	semidirect
14. #11763402	C₂	semidirect
15. #11763391	C₂	semidirect
16. #11763341	C₂	semidirect
17. #11763340	C₂	semidirect
18. #11763339	C₂	semidirect
19. #126×D₁₇	C₂	semidirect
20. #11763290	C₂	semidirect
21. #11763281	C₂	semidirect
22. #11763277	C₂	semidirect
23. C₁₇×#553	C₂	semidirect
27. C₁₇×#126	C₂²	semidirect
28. C₁₇×#125	C₂²	semidirect
29. C₁₇×#123	C₂²	semidirect
32. C₁₇×#121	C₂²	semidirect
34. C₄×D₄×C₁₇	C₂²	semidirect
35. C₄×D₄×C₁₇	C₂²	semidirect
36. C₁₇×#117	C₂²	semidirect
37. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
41. #10587624	C₂²	semidirect
46. #10587622	C₂²	semidirect
47. #10587621	C₂²	semidirect
48. #10587621	C₂²	semidirect
49. #10587621	C₂²	semidirect
51. D₄×Dic₁₇	C₂²	semidirect
56. C₄×C₂²⋊D₁₇	C₂²	semidirect
57. C₄×C₂²⋊D₁₇	C₂²	semidirect
59. #10587612	C₂²	semidirect
60. #10587612	C₂²	semidirect
61. #10587612	C₂²	semidirect
62. #10587610	C₂²	semidirect
63. #10587610	C₂²	semidirect
64. #10587610	C₂²	semidirect
65. C₂×C₄×Dic₁₇	C₂²	semidirect
72. #10587583	C₂²	semidirect
73. #10587582	C₂²	semidirect
74. #10587582	C₂²	semidirect
79. #10587578	C₂²	semidirect
80. C₄⋊C₄×D₁₇	C₂²	semidirect
81. C₄⋊C₄×D₁₇	C₂²	semidirect
82. C₄⋊C₄×D₁₇	C₂²	semidirect
83. #10587576	C₂²	semidirect
84. #10587576	C₂²	semidirect
85. #10587576	C₂²	semidirect
86. #10587575	C₂²	semidirect
87. #10587575	C₂²	semidirect
88. #10587574	C₂²	semidirect
89. #10587573	C₂²	semidirect
90. #10587573	C₂²	semidirect
91. #10587573	C₂²	semidirect
92. #10587573	C₂²	semidirect
98. #10587569	C₂²	semidirect
99. #10587569	C₂²	semidirect
101. #10587567	C₂²	semidirect
102. #10587567	C₂²	semidirect
106. #10587565	C₂²	semidirect
107. #10587565	C₂²	semidirect
108. #10587565	C₂²	semidirect
109. #10587565	C₂²	semidirect
110. #10587565	C₂²	semidirect
111. #10587565	C₂²	semidirect
112. #10587564	C₂²	semidirect
113. #10587564	C₂²	semidirect
114. #10587563	C₂²	semidirect
118. #10587558	C₂²	semidirect
119. C₄²×D₁₇	C₂²	semidirect
120. #10587555	C₂²	semidirect
121. C₄×Dic₃₄	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
319. #553	D₁₇	semidirect
362. #126	C₂×D₁₇	semidirect
368. #125	C₂×D₁₇	semidirect
383. #123	C₂×D₁₇	semidirect
400. #121	C₂×D₁₇	semidirect
424. C₄×D₄	C₂×D₁₇	semidirect
425. C₄×D₄	C₂×D₁₇	semidirect
434. #117	C₂×D₁₇	semidirect
438. C₂×C₄⋊C₄	C₂×D₁₇	semidirect
445. C₁₇	#3521	semidirect

Maximal subgroups

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

subgroup	index
#11763529	2
#11763527	2
#11763515	2
#11763506	2
#11763495	2
#11763494	2
#11763488	2
#11763482	2
#11763464	2
#11763456	2
#11763426	2
#11763422	2
#11763402	2
#11763391	2
#11763341	2
#11763340	2
#11763339	2
#126×D₁₇	2
#11763290	2
#11763281	2
#11763277	2
C₁₇×#553	2
#3521	17