Subgroups — #14542850

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	#11763533	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763528	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763520	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763511	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763504	C₂	1	2	yes	maximal, complemented
6	#11763501	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763493	C₂	1	2	yes	maximal, complemented
8	#11763486	C₂	1	2	yes	maximal, complemented
9	#11763482	C₂	1	2	yes	maximal, complemented
10	#11763461	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763456	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763452	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763417	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763400	C₂	1	2	yes	maximal, complemented
15	#11763393	C₂	1	2	yes	maximal, complemented
16	#11763341	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763338	C₂	1	2	yes	maximal, complemented
18	#11763337	C₂	1	1	yes	maximal, characteristic, complemented
19	#126×D₁₇	C₂	1	2	yes	maximal, complemented
20	#11763289	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763281	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#63256	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
26	C₂×#63252	C₂²	1	1	yes	characteristic
27	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₇×#126	C₂²	1	2	yes	complemented
29	C₁₇×#124	C₂²	1	1	yes	characteristic
30	C₁₇×#124	C₂²	1	2	yes	complemented
31	C₁₇×#123	C₂²	1	2	yes	complemented
32	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₇×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
37	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
38	#10587633	C₂²	1	2	yes	—
39	#10587632	C₂²	1	1	yes	characteristic
40	#10587632	C₂²	1	2	yes	complemented
41	#10587632	C₂²	1	2	yes	complemented
42	Q₈×Dic₁₇	C₂²	1	2	yes	complemented
43	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
44	#10587630	C₂²	1	1	yes	characteristic, complemented
45	#10587625	C₂²	1	2	yes	complemented
46	#10587624	C₂²	1	2	yes	—
47	#10587624	C₂²	1	1	yes	characteristic
48	#10587623	C₂²	1	2	yes	—
49	#10587622	C₂²	1	1	yes	characteristic
50	D₄×Dic₁₇	C₂²	1	1	yes	characteristic
51	D₄×Dic₁₇	C₂²	1	2	yes	complemented
52	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
56	C₂×#63227	C₂²	1	2	yes	—
57	#10587612	C₂²	1	2	yes	complemented
58	C₂×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic, complemented
59	#10587584	C₂²	1	2	yes	—
60	#10587584	C₂²	1	2	yes	—
61	#10587584	C₂²	1	2	yes	—
62	#10587584	C₂²	1	1	yes	characteristic
63	#10587584	C₂²	1	2	yes	complemented
64	#10587583	C₂²	1	1	yes	characteristic
65	#10587583	C₂²	1	1	yes	characteristic, complemented
66	#10587583	C₂²	1	2	yes	complemented
67	#10587582	C₂²	1	1	yes	characteristic, complemented
68	#10587580	C₂²	1	1	yes	characteristic
69	#10587580	C₂²	1	2	yes	complemented
70	#10587579	C₂²	1	1	yes	characteristic
71	#10587579	C₂²	1	1	yes	characteristic
72	#10587579	C₂²	1	2	yes	complemented
73	#10587578	C₂²	1	1	yes	characteristic
74	#10587578	C₂²	1	2	yes	complemented
75	#10587578	C₂²	1	2	yes	complemented
76	#10587578	C₂²	1	1	yes	characteristic, complemented
77	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
78	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
79	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
80	#10587576	C₂²	1	2	yes	complemented
81	#10587576	C₂²	1	1	yes	characteristic, complemented
82	#10587576	C₂²	1	1	yes	characteristic, complemented
83	#10587575	C₂²	1	1	yes	characteristic, complemented
84	#10587575	C₂²	1	2	yes	complemented
85	#10587572	C₂²	1	2	yes	—
86	#10587572	C₂²	1	2	yes	complemented
87	#10587571	C₂²	1	1	yes	characteristic
88	#10587570	C₂²	1	2	yes	—
89	#10587570	C₂²	1	1	yes	characteristic
90	#10587570	C₂²	1	2	yes	complemented
91	#10587569	C₂²	1	2	yes	—
92	#10587569	C₂²	1	2	yes	—
93	#10587569	C₂²	1	2	yes	complemented
94	#10587569	C₂²	1	1	yes	characteristic, complemented
95	#10587569	C₂²	1	2	yes	complemented
96	#10587568	C₂²	1	2	yes	—
97	#10587567	C₂²	1	2	yes	—
98	#10587567	C₂²	1	2	yes	complemented
99	#10587567	C₂²	1	2	yes	complemented
100	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
101	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
103	#10587565	C₂²	1	2	yes	complemented
104	#10587565	C₂²	1	2	yes	complemented
105	#10587565	C₂²	1	2	yes	complemented
106	#10587565	C₂²	1	2	yes	complemented
107	#10587565	C₂²	1	1	yes	characteristic, complemented
108	#10587564	C₂²	1	2	yes	complemented
109	#10587563	C₂²	1	2	yes	complemented
110	#10587563	C₂²	1	2	yes	complemented
111	#10587562	C₂²	1	2	yes	—
112	C₄×D₆₈	C₂²	1	1	yes	characteristic
113	C₄×D₆₈	C₂²	1	1	yes	characteristic
114	C₄×D₆₈	C₂²	1	1	yes	characteristic
115	C₄×D₆₈	C₂²	1	2	yes	complemented
116	#10587558	C₂²	1	1	yes	characteristic
117	C₄²×D₁₇	C₂²	1	2	yes	complemented
118	C₄²×D₁₇	C₂²	1	1	yes	characteristic, complemented
119	#10587556	C₂²	1	2	yes	complemented
120	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₇	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₇	C₂³	1	2	yes	—
126	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₇	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₇	C₂³	1	2	yes	—
136	C₂²×Dic₁₇	C₂³	1	2	yes	—
137	#63256	—	2	4	no	—
138	D₄×D₁₇	—	2	4	no	—
139	#63252	—	2	4	no	—
140	C₂×D₆₈	C₂³	1	2	yes	—
141	C₂×D₆₈	C₂³	1	1	yes	characteristic
142	C₂×D₆₈	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₇	C₂³	1	2	yes	—
144	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₇	C₂³	1	2	yes	—
148	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₇	C₂³	1	2	yes	—
150	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₇	C₂³	1	2	yes	—
152	C₂×C₄×D₁₇	C₂³	1	2	yes	—
153	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
154	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
160	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
162	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
166	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
169	C₄²×C₁₇	C₂³	1	1	yes	characteristic
170	C₄²×C₁₇	C₂³	1	2	yes	—
171	C₄²×C₁₇	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
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	#63227	C₂³	1	1	yes	characteristic
179	#63227	C₂³	1	1	yes	characteristic
180	#63227	C₂³	1	1	yes	characteristic
181	#63227	C₂³	1	2	yes	—
182	#63227	C₂³	1	2	yes	—
183	#63227	C₂³	1	1	yes	characteristic
184	#63227	C₂³	1	2	yes	—
185	#63227	C₂³	1	2	yes	—
186	#63227	C₂³	1	2	yes	—
187	#63227	C₂³	1	2	yes	—
188	#63227	C₂³	1	1	yes	characteristic
189	#63227	C₂³	1	2	yes	—
190	#63227	C₂³	1	2	yes	—
191	#63227	C₂³	1	2	yes	—
192	#63227	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₇	C₂³	1	2	yes	—
197	C₄⋊Dic₁₇	C₂³	1	2	yes	—
198	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₇	C₂³	1	2	yes	—
200	C₄⋊Dic₁₇	C₂³	1	2	yes	—
201	C₄⋊Dic₁₇	C₂³	1	2	yes	—
202	C₄⋊Dic₁₇	C₂³	1	2	yes	—
203	#63225	C₂³	1	2	yes	—
204	#63225	C₂³	1	1	yes	characteristic
205	#63225	C₂³	1	2	yes	—
206	#63225	C₂³	1	1	yes	characteristic
207	#63225	C₂³	1	1	yes	characteristic
208	#63225	C₂³	1	2	yes	—
209	#63225	C₂³	1	2	yes	—
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	1	yes	characteristic
215	#63225	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₇	C₂³	1	2	yes	—
219	C₄×Dic₁₇	C₂³	1	2	yes	—
220	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₇	C₂³	1	2	yes	—
222	C₄×Dic₁₇	C₂³	1	2	yes	—
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	C₂²×D₁₇	—	2	4	no	—
228	C₂²×D₁₇	—	4	2	no	—
229	C₂²×D₁₇	—	4	2	no	—
230	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₇	C₂⁴	1	2	yes	—
233	Q₈×C₁₇	—	2	2	no	—
234	Q₈×C₁₇	—	4	2	no	—
235	D₄×C₁₇	—	2	2	no	—
236	D₄×C₁₇	—	4	2	no	—
237	C₂×C₄×C₁₇	—	2	2	no	—
238	C₂×C₄×C₁₇	—	4	2	no	—
239	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₁₇	—	2	4	no	—
249	C₂²⋊D₁₇	—	2	4	no	—
250	C₂²⋊D₁₇	—	4	1	no	—
251	C₂²⋊D₁₇	—	4	1	no	—
252	C₂²⋊D₁₇	—	4	2	no	—
253	C₂×Dic₁₇	—	4	2	no	—
254	C₂×Dic₁₇	—	4	2	no	—
255	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₇	C₂⁴	1	2	yes	—
258	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₇	C₂⁴	1	2	yes	—
262	C₂×Dic₁₇	C₂⁴	1	2	yes	—
263	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
264	D₆₈	—	2	4	no	—
265	D₆₈	—	4	1	no	—
266	D₆₈	#41	1	4	yes	—
267	C₄×D₁₇	—	2	4	no	—
268	C₄×D₁₇	—	2	4	no	—
269	C₄×D₁₇	—	2	2	no	—
270	C₄×D₁₇	—	2	2	no	—
271	C₄×D₁₇	—	4	1	no	—
272	C₄×D₁₇	—	4	1	no	—
273	C₄×D₁₇	—	4	2	no	—
274	C₄×D₁₇	—	4	2	no	—
275	C₄×D₁₇	—	4	2	no	—
276	C₄×D₁₇	—	4	2	no	—
277	Dic₃₄	—	2	2	no	—
278	Dic₃₄	—	4	1	no	—
279	#3521	—	17	1	no	maximal, Sylow
280	C₂²×C₁₇	—	2	1	no	—
281	C₂²×C₁₇	—	2	2	no	—
282	C₂²×C₁₇	—	2	1	no	—
283	C₂²×C₁₇	—	2	2	no	—
284	C₂²×C₁₇	—	2	1	no	—
285	C₂²×C₁₇	—	2	2	no	—
286	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
287	C₂×D₁₇	—	2	2	no	—
288	C₂×D₁₇	—	2	2	no	—
289	C₂×D₁₇	—	2	1	no	—
290	C₂×D₁₇	—	2	1	no	—
291	C₂×D₁₇	—	2	1	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	2	no	—
299	C₄×C₁₇	—	2	1	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	—	2	1	no	—
305	C₄×C₁₇	C₂×#41	1	2	yes	—
306	Dic₁₇	—	2	2	no	—
307	Dic₁₇	—	2	1	no	—
308	Dic₁₇	—	2	1	no	—
309	Dic₁₇	—	2	1	no	—
310	Dic₁₇	—	2	1	no	—
311	Dic₁₇	—	2	1	no	—
312	Dic₁₇	—	2	1	no	—
313	Dic₁₇	—	2	2	no	—
314	Dic₁₇	—	2	2	no	—
315	#556	—	17	1	no	—
316	#556	—	17	1	no	—
317	#554	—	17	1	no	—
318	#553	—	17	2	no	—
319	#553	—	17	1	no	—
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	D₁₇	1	1	yes	characteristic, complemented
328	#541	—	17	1	no	—
329	#539	—	17	2	no	—
330	#538	—	17	2	no	—
331	#529	—	17	2	no	—
332	#529	—	17	1	no	—
333	#529	—	17	1	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	C₂²×#41	1	1	yes	characteristic
341	C₂×C₁₇	#585	1	1	yes	characteristic
342	C₂×C₁₇	#585	1	1	yes	characteristic
343	D₁₇	—	2	4	no	—
344	D₁₇	—	4	1	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	C₂×D₁₇	1	1	yes	characteristic, complemented
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	2	no	—
359	#126	—	17	1	no	—
360	#126	—	17	2	no	—
361	#126	—	17	2	no	—
362	#126	C₂×D₁₇	1	2	yes	complemented
363	#125	—	17	1	no	—
364	#125	—	17	1	no	—
365	#125	—	17	2	no	—
366	#125	—	17	2	no	—
367	#125	—	17	1	no	—
368	#125	—	17	2	no	—
369	#124	—	17	2	no	—
370	#124	—	17	1	no	—
371	#124	—	17	1	no	—
372	#124	C₂×D₁₇	1	1	yes	characteristic
373	#124	C₂×D₁₇	1	2	yes	complemented
374	#123	—	17	1	no	—
375	#123	—	17	2	no	—
376	#123	—	17	2	no	—
377	#123	—	17	2	no	—
378	#123	—	17	2	no	—
379	#123	—	17	1	no	—
380	#123	—	17	2	no	—
381	#123	—	17	2	no	—
382	#123	—	17	2	no	—
383	#123	C₂×D₁₇	1	2	yes	complemented
384	C₂²⋊Q₈	—	17	2	no	—
385	C₂²⋊Q₈	—	17	2	no	—
386	C₂²⋊Q₈	—	17	1	no	—
387	C₂²⋊Q₈	—	17	1	no	—
388	C₂²⋊Q₈	—	17	1	no	—
389	C₂²⋊Q₈	—	17	2	no	—
390	C₂²⋊Q₈	—	17	1	no	—
391	C₂²⋊Q₈	—	17	2	no	—
392	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
393	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	complemented
394	#121	—	17	1	no	—
395	#121	—	17	2	no	—
396	#121	—	17	2	no	—
397	#121	—	17	1	no	—
398	#121	—	17	2	no	—
399	#121	—	17	2	no	—
400	#121	C₂×D₁₇	1	1	yes	characteristic
401	#120	—	17	2	no	—
402	#120	—	17	2	no	—
403	C₄×Q₈	—	17	1	no	—
404	C₄×Q₈	—	17	2	no	—
405	C₄×Q₈	—	17	1	no	—
406	C₄×Q₈	—	17	1	no	—
407	C₄×Q₈	—	17	1	no	—
408	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
409	C₄×D₄	—	17	1	no	—
410	C₄×D₄	—	17	2	no	—
411	C₄×D₄	—	17	2	no	—
412	C₄×D₄	—	17	1	no	—
413	C₄×D₄	—	17	1	no	—
414	C₄×D₄	—	17	2	no	—
415	C₄×D₄	—	17	1	no	—
416	C₄×D₄	—	17	2	no	—
417	C₄×D₄	—	17	1	no	—
418	C₄×D₄	—	17	2	no	—
419	C₄×D₄	—	17	2	no	—
420	C₄×D₄	—	17	2	no	—
421	C₄×D₄	—	17	1	no	—
422	C₄×D₄	—	17	2	no	—
423	C₄×D₄	—	17	1	no	—
424	C₄×D₄	—	17	1	no	—
425	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
426	#117	—	17	2	no	—
427	#117	—	17	2	no	—
428	#117	—	17	1	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	1	no	—
436	C₂×C₄⋊C₄	—	17	2	no	—
437	C₂×C₄⋊C₄	—	17	2	no	—
438	C₂×C₄⋊C₄	—	17	2	no	—
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	2	no	—
444	C₂×C₄²	—	17	1	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	C₂²×D₁₇	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
453	C₂×D₄	—	17	2	no	—
454	C₂×D₄	—	17	2	no	—
455	C₂×D₄	—	17	1	no	—
456	C₂×D₄	—	17	2	no	—
457	C₂×D₄	—	17	1	no	—
458	C₂×D₄	—	17	1	no	—
459	C₂×D₄	—	17	2	no	—
460	C₂×D₄	—	17	1	no	—
461	C₂×D₄	—	34	4	no	—
462	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
463	C₂×D₄	C₂²×D₁₇	1	2	yes	—
464	C₂²×C₄	—	17	2	no	—
465	C₂²×C₄	—	17	2	no	—
466	C₂²×C₄	—	17	2	no	—
467	C₂²×C₄	—	17	1	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	1	no	—
473	C₂²×C₄	—	17	1	no	—
474	C₂²×C₄	—	17	2	no	—
475	C₂²×C₄	—	17	2	no	—
476	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
478	C₄⋊C₄	—	17	2	no	—
479	C₄⋊C₄	—	17	1	no	—
480	C₄⋊C₄	—	17	1	no	—
481	C₄⋊C₄	—	17	1	no	—
482	C₄⋊C₄	—	17	2	no	—
483	C₄⋊C₄	—	17	2	no	—
484	C₄⋊C₄	—	17	1	no	—
485	C₄⋊C₄	—	17	2	no	—
486	C₄⋊C₄	—	17	2	no	—
487	C₄⋊C₄	—	17	2	no	—
488	C₄⋊C₄	—	17	2	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	1	no	—
497	C₄⋊C₄	—	17	2	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	2	no	—
513	C₂²⋊C₄	—	17	1	no	—
514	C₂²⋊C₄	—	17	1	no	—
515	C₂²⋊C₄	—	17	2	no	—
516	C₂²⋊C₄	—	17	1	no	—
517	C₂²⋊C₄	—	17	1	no	—
518	C₂²⋊C₄	—	17	1	no	—
519	C₂²⋊C₄	—	17	2	no	—
520	C₂²⋊C₄	—	17	2	no	—
521	C₂²⋊C₄	—	17	2	no	—
522	C₂²⋊C₄	—	17	2	no	—
523	C₂²⋊C₄	—	17	2	no	—
524	C₂²⋊C₄	—	17	2	no	—
525	C₂²⋊C₄	—	17	2	no	—
526	C₂²⋊C₄	—	17	1	no	—
527	C₂²⋊C₄	—	17	2	no	—
528	C₂²⋊C₄	—	17	1	no	—
529	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
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	2	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	1	no	—
545	C₄²	C₂²×D₁₇	1	1	yes	characteristic
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	—	17	1	no	—
551	C₂³	—	34	4	no	—
552	C₂³	—	68	2	no	—
553	C₂³	—	68	2	no	—
554	C₂³	C₂³×D₁₇	1	2	yes	—
555	C₂³	C₂³×D₁₇	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	34	2	no	—
559	Q₈	—	68	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	17	4	no	—
563	D₄	—	34	4	no	—
564	D₄	—	34	4	no	—
565	D₄	—	34	4	no	—
566	D₄	—	68	1	no	—
567	D₄	—	68	1	no	—
568	D₄	—	68	2	no	—
569	D₄	—	68	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	17	1	no	—
573	C₂×C₄	—	17	1	no	—
574	C₂×C₄	—	17	2	no	—
575	C₂×C₄	—	17	2	no	—
576	C₂×C₄	—	17	1	no	—
577	C₂×C₄	—	17	1	no	—
578	C₂×C₄	—	17	1	no	—
579	C₂×C₄	—	17	1	no	—
580	C₂×C₄	—	17	2	no	—
581	C₂×C₄	—	34	4	no	—
582	C₂×C₄	—	34	4	no	—
583	C₂×C₄	—	34	2	no	—
584	C₂×C₄	—	34	2	no	—
585	C₂×C₄	—	68	1	no	—
586	C₂×C₄	—	68	2	no	—
587	C₂×C₄	—	68	2	no	—
588	C₂×C₄	—	68	2	no	—
589	C₂×C₄	—	68	1	no	—
590	C₂×C₄	—	68	2	no	—
591	C₂×C₄	—	68	2	no	—
592	C₂×C₄	—	68	2	no	—
593	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
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	2	yes	—
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	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	17	4	no	—
609	C₂²	—	34	2	no	—
610	C₂²	—	34	2	no	—
611	C₂²	—	34	1	no	—
612	C₂²	—	34	1	no	—
613	C₂²	—	34	1	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	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	34	1	no	—
628	C₄	—	34	1	no	—
629	C₄	—	34	2	no	—
630	C₄	—	34	1	no	—
631	C₄	—	34	1	no	—
632	C₄	—	34	2	no	—
633	C₄	—	34	2	no	—
634	C₄	—	34	1	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	—	34	4	no	—
640	C₂	—	68	1	no	—
641	C₂	—	68	1	no	—
642	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
643	C₂	#11763644	1	1	yes	characteristic
644	C₂	#11763646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#542	C₂
hypercenter	#542	D₁₇
hypocenter	C₁₇	#3521
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #11763533	C₂	semidirect
2. #11763528	C₂	semidirect
3. #11763520	C₂	semidirect
4. #11763511	C₂	semidirect
5. #11763504	C₂	semidirect
6. #11763501	C₂	semidirect
7. #11763493	C₂	semidirect
8. #11763486	C₂	semidirect
9. #11763482	C₂	semidirect
10. #11763461	C₂	semidirect
11. #11763456	C₂	semidirect
12. #11763452	C₂	semidirect
13. #11763417	C₂	semidirect
14. #11763400	C₂	semidirect
15. #11763393	C₂	semidirect
16. #11763341	C₂	semidirect
17. #11763338	C₂	semidirect
18. #11763337	C₂	semidirect
19. #126×D₁₇	C₂	semidirect
20. #11763289	C₂	semidirect
21. #11763281	C₂	semidirect
22. C₄×#63256	C₂	semidirect
23. C₁₇×#542	C₂	semidirect
27. C₁₇×C₄⋊Q₈	C₂²	semidirect
28. C₁₇×#126	C₂²	semidirect
30. C₁₇×#124	C₂²	semidirect
31. C₁₇×#123	C₂²	semidirect
32. C₁₇×C₂²⋊Q₈	C₂²	semidirect
33. C₁₇×C₂²⋊Q₈	C₂²	semidirect
35. C₄×Q₈×C₁₇	C₂²	semidirect
37. C₁₇×#117	C₂²	semidirect
40. #10587632	C₂²	semidirect
41. #10587632	C₂²	semidirect
42. Q₈×Dic₁₇	C₂²	semidirect
43. Q₈×Dic₁₇	C₂²	semidirect
44. #10587630	C₂²	semidirect
45. #10587625	C₂²	semidirect
51. D₄×Dic₁₇	C₂²	semidirect
54. C₄×C₂²⋊D₁₇	C₂²	semidirect
55. C₄×C₂²⋊D₁₇	C₂²	semidirect
57. #10587612	C₂²	semidirect
58. C₂×C₄⋊Dic₁₇	C₂²	semidirect
63. #10587584	C₂²	semidirect
65. #10587583	C₂²	semidirect
66. #10587583	C₂²	semidirect
67. #10587582	C₂²	semidirect
69. #10587580	C₂²	semidirect
72. #10587579	C₂²	semidirect
74. #10587578	C₂²	semidirect
75. #10587578	C₂²	semidirect
76. #10587578	C₂²	semidirect
77. C₄⋊C₄×D₁₇	C₂²	semidirect
78. C₄⋊C₄×D₁₇	C₂²	semidirect
79. C₄⋊C₄×D₁₇	C₂²	semidirect
80. #10587576	C₂²	semidirect
81. #10587576	C₂²	semidirect
82. #10587576	C₂²	semidirect
83. #10587575	C₂²	semidirect
84. #10587575	C₂²	semidirect
86. #10587572	C₂²	semidirect
90. #10587570	C₂²	semidirect
93. #10587569	C₂²	semidirect
94. #10587569	C₂²	semidirect
95. #10587569	C₂²	semidirect
98. #10587567	C₂²	semidirect
99. #10587567	C₂²	semidirect
103. #10587565	C₂²	semidirect
104. #10587565	C₂²	semidirect
105. #10587565	C₂²	semidirect
106. #10587565	C₂²	semidirect
107. #10587565	C₂²	semidirect
108. #10587564	C₂²	semidirect
109. #10587563	C₂²	semidirect
110. #10587563	C₂²	semidirect
115. C₄×D₆₈	C₂²	semidirect
117. C₄²×D₁₇	C₂²	semidirect
118. C₄²×D₁₇	C₂²	semidirect
119. #10587556	C₂²	semidirect
120. C₄×Dic₃₄	C₂²	semidirect
121. C₄×Dic₃₄	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
327. #542	D₁₇	semidirect
350. C₄⋊Q₈	C₂×D₁₇	semidirect
362. #126	C₂×D₁₇	semidirect
373. #124	C₂×D₁₇	semidirect
383. #123	C₂×D₁₇	semidirect
392. C₂²⋊Q₈	C₂×D₁₇	semidirect
393. C₂²⋊Q₈	C₂×D₁₇	semidirect
408. C₄×Q₈	C₂×D₁₇	semidirect
434. #117	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
#11763533	2
#11763528	2
#11763520	2
#11763511	2
#11763504	2
#11763501	2
#11763493	2
#11763486	2
#11763482	2
#11763461	2
#11763456	2
#11763452	2
#11763417	2
#11763400	2
#11763393	2
#11763341	2
#11763338	2
#11763337	2
#126×D₁₇	2
#11763289	2
#11763281	2
C₄×#63256	2
C₁₇×#542	2
#3521	17