Subgroups — #14542632

Order 2176.

1140 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763544	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763542	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763541	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763531	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763528	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763521	C₂	1	2	yes	maximal, complemented
7	#11763508	C₂	1	2	yes	maximal, complemented
8	#11763504	C₂	1	2	yes	maximal, complemented
9	#11763480	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763479	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763457	C₂	1	2	yes	maximal, complemented
12	#11763395	C₂	1	2	yes	maximal, complemented
13	#11763393	C₂	1	2	yes	maximal, complemented
14	#11763377	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763372	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763363	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763358	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763318	C₂	1	2	yes	maximal, complemented
19	#11763317	C₂	1	2	yes	maximal, complemented
20	#11763291	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763288	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#559	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	1	yes	characteristic
25	C₂×#63254	C₂²	1	1	yes	characteristic
26	C₂×#63254	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
28	C₂×#63252	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₁₇	C₂²	1	2	yes	—
30	C₁₇×#127	C₂²	1	1	yes	characteristic
31	C₁₇×#124	C₂²	1	1	yes	characteristic
32	C₁₇×#124	C₂²	1	2	yes	complemented
33	C₁₇×#124	C₂²	1	1	yes	characteristic, complemented
34	C₁₇×#123	C₂²	1	2	yes	complemented
35	C₁₇×#123	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
38	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₇	C₂²	1	2	yes	complemented
41	#10587633	C₂²	1	1	yes	characteristic
42	#10587633	C₂²	1	2	yes	complemented
43	#10587632	C₂²	1	1	yes	characteristic
44	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
45	#10587630	C₂²	1	1	yes	characteristic, complemented
46	#10587630	C₂²	1	1	yes	characteristic, complemented
47	#10587626	C₂²	1	1	yes	characteristic
48	#10587626	C₂²	1	1	yes	characteristic
49	#10587626	C₂²	1	1	yes	characteristic, complemented
50	#10587625	C₂²	1	2	yes	—
51	#10587625	C₂²	1	2	yes	—
52	#10587625	C₂²	1	2	yes	complemented
53	#10587625	C₂²	1	2	yes	complemented
54	#10587624	C₂²	1	2	yes	complemented
55	#10587623	C₂²	1	2	yes	—
56	#10587623	C₂²	1	2	yes	—
57	#10587622	C₂²	1	1	yes	characteristic
58	D₄×Dic₁₇	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
60	#10587616	C₂²	1	2	yes	complemented
61	#10587615	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
65	C₂×#63225	C₂²	1	2	yes	complemented
66	#10587584	C₂²	1	2	yes	complemented
67	#10587583	C₂²	1	1	yes	characteristic
68	#10587582	C₂²	1	1	yes	characteristic
69	#10587582	C₂²	1	1	yes	characteristic
70	#10587582	C₂²	1	2	yes	complemented
71	#10587580	C₂²	1	2	yes	complemented
72	#10587580	C₂²	1	2	yes	complemented
73	#10587579	C₂²	1	1	yes	characteristic
74	#10587579	C₂²	1	2	yes	—
75	#10587579	C₂²	1	1	yes	characteristic, complemented
76	#10587579	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
79	#10587575	C₂²	1	1	yes	characteristic, complemented
80	#10587575	C₂²	1	1	yes	characteristic, complemented
81	#10587574	C₂²	1	1	yes	characteristic, complemented
82	#10587573	C₂²	1	1	yes	characteristic, complemented
83	#10587572	C₂²	1	2	yes	complemented
84	#10587571	C₂²	1	2	yes	complemented
85	#10587571	C₂²	1	2	yes	complemented
86	#10587570	C₂²	1	2	yes	—
87	#10587570	C₂²	1	2	yes	—
88	#10587570	C₂²	1	2	yes	—
89	#10587570	C₂²	1	2	yes	—
90	#10587570	C₂²	1	2	yes	complemented
91	#10587570	C₂²	1	2	yes	complemented
92	#10587569	C₂²	1	2	yes	complemented
93	#10587569	C₂²	1	2	yes	complemented
94	#10587568	C₂²	1	2	yes	—
95	#10587568	C₂²	1	2	yes	—
96	#10587567	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	#10587567	C₂²	1	2	yes	complemented
101	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
102	#10587565	C₂²	1	2	yes	complemented
103	#10587565	C₂²	1	2	yes	complemented
104	#10587564	C₂²	1	2	yes	complemented
105	#10587563	C₂²	1	2	yes	complemented
106	#10587563	C₂²	1	2	yes	complemented
107	#10587562	C₂²	1	2	yes	complemented
108	#10587561	C₂²	1	1	yes	characteristic
109	#10587561	C₂²	1	1	yes	characteristic, complemented
110	#10587560	C₂²	1	1	yes	characteristic
111	C₄×D₆₈	C₂²	1	1	yes	characteristic
112	C₄×D₆₈	C₂²	1	2	yes	—
113	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
114	#10587558	C₂²	1	1	yes	characteristic
115	#10587558	C₂²	1	1	yes	characteristic
116	#10587558	C₂²	1	2	yes	complemented
117	#10587558	C₂²	1	2	yes	complemented
118	C₄²×D₁₇	C₂²	1	1	yes	characteristic
119	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
126	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₇	C₂³	1	2	yes	—
129	C₂×D₄×C₁₇	C₂³	1	2	yes	—
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	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	C₂²×Dic₁₇	C₂³	1	2	yes	—
141	C₂²×Dic₁₇	C₂³	1	2	yes	—
142	C₂²×Dic₁₇	C₂³	1	2	yes	—
143	#63256	—	2	4	no	—
144	#63254	—	2	4	no	—
145	#63254	—	4	4	no	—
146	D₄×D₁₇	—	2	4	no	—
147	#63252	—	4	4	no	—
148	C₂×D₆₈	C₂³	1	1	yes	characteristic
149	C₂×D₆₈	C₂³	1	2	yes	—
150	C₂×D₆₈	C₂³	1	1	yes	characteristic
151	C₂×D₆₈	C₂³	1	2	yes	—
152	C₂×D₆₈	C₂³	1	2	yes	—
153	C₂×C₄×D₁₇	—	4	4	no	—
154	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₇	C₂³	1	2	yes	—
156	C₂×C₄×D₁₇	C₂³	1	2	yes	—
157	C₂×C₄×D₁₇	C₂³	1	2	yes	—
158	C₂×C₄×D₁₇	C₂³	1	2	yes	—
159	C₂×C₄×D₁₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₇	C₂³	1	2	yes	—
161	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
163	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
164	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
165	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
166	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
171	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
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	2	yes	—
178	C₄²×C₁₇	C₂³	1	1	yes	characteristic
179	C₄²×C₁₇	C₂³	1	1	yes	characteristic
180	C₄²×C₁₇	C₂³	1	2	yes	—
181	C₄²×C₁₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
186	#63227	C₂³	1	1	yes	characteristic
187	#63227	C₂³	1	1	yes	characteristic
188	#63227	C₂³	1	1	yes	characteristic
189	#63227	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₇	C₂³	1	2	yes	—
205	#63225	C₂³	1	1	yes	characteristic
206	#63225	C₂³	1	1	yes	characteristic
207	#63225	C₂³	1	1	yes	characteristic
208	#63225	C₂³	1	2	yes	—
209	#63225	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
215	#63225	C₂³	1	1	yes	characteristic
216	#63225	C₂³	1	2	yes	—
217	#63225	C₂³	1	2	yes	—
218	#63225	C₂³	1	2	yes	—
219	#63225	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	2	yes	—
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	2	yes	—
229	C₂³×C₁₇	C₂⁴	1	2	yes	—
230	C₂²×D₁₇	—	2	4	no	—
231	C₂²×D₁₇	—	4	2	no	—
232	C₂²×D₁₇	—	4	2	no	—
233	C₂²×D₁₇	C₂⁴	1	2	yes	—
234	C₂²×D₁₇	C₂⁴	1	2	yes	—
235	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
236	Q₈×C₁₇	—	2	2	no	—
237	Q₈×C₁₇	—	4	1	no	—
238	D₄×C₁₇	—	2	2	no	—
239	D₄×C₁₇	—	2	2	no	—
240	D₄×C₁₇	—	4	2	no	—
241	D₄×C₁₇	—	4	2	no	—
242	C₂×C₄×C₁₇	—	4	2	no	—
243	C₂×C₄×C₁₇	—	4	2	no	—
244	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₁₇	—	2	4	no	—
254	C₂²⋊D₁₇	—	2	4	no	—
255	C₂²⋊D₁₇	—	2	4	no	—
256	C₂²⋊D₁₇	—	4	2	no	—
257	C₂²⋊D₁₇	—	4	2	no	—
258	C₂²⋊D₁₇	—	4	2	no	—
259	C₂²⋊D₁₇	—	4	2	no	—
260	C₂²⋊D₁₇	—	4	2	no	—
261	C₂×Dic₁₇	—	2	4	no	—
262	C₂×Dic₁₇	—	2	4	no	—
263	C₂×Dic₁₇	—	4	2	no	—
264	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₇	C₂⁴	1	2	yes	—
266	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₇	C₂⁴	1	2	yes	—
269	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
273	D₆₈	—	2	4	no	—
274	D₆₈	—	2	2	no	—
275	D₆₈	—	2	2	no	—
276	D₆₈	—	4	2	no	—
277	D₆₈	—	4	2	no	—
278	C₄×D₁₇	—	2	4	no	—
279	C₄×D₁₇	—	2	2	no	—
280	C₄×D₁₇	—	2	4	no	—
281	C₄×D₁₇	—	4	2	no	—
282	C₄×D₁₇	—	4	2	no	—
283	C₄×D₁₇	—	4	1	no	—
284	C₄×D₁₇	—	4	2	no	—
285	C₄×D₁₇	—	4	2	no	—
286	C₄×D₁₇	#41	1	4	yes	complemented
287	Dic₃₄	—	2	2	no	—
288	Dic₃₄	—	2	2	no	—
289	Dic₃₄	—	2	2	no	—
290	Dic₃₄	—	4	1	no	—
291	#3506	—	17	1	no	maximal, Sylow
292	C₂²×C₁₇	—	2	2	no	—
293	C₂²×C₁₇	—	2	2	no	—
294	C₂²×C₁₇	—	2	2	no	—
295	C₂²×C₁₇	—	2	2	no	—
296	C₂²×C₁₇	—	2	2	no	—
297	C₂²×C₁₇	—	2	2	no	—
298	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
299	C₂×D₁₇	—	2	1	no	—
300	C₂×D₁₇	—	2	1	no	—
301	C₂×D₁₇	—	2	2	no	—
302	C₂×D₁₇	—	2	2	no	—
303	C₂×D₁₇	—	2	2	no	—
304	C₂×D₁₇	—	2	2	no	—
305	C₂×D₁₇	—	2	2	no	—
306	C₂×D₁₇	—	2	2	no	—
307	C₂×D₁₇	—	4	8	no	—
308	C₂×D₁₇	C₂×#41	1	2	yes	—
309	C₄×C₁₇	—	2	2	no	—
310	C₄×C₁₇	—	2	1	no	—
311	C₄×C₁₇	—	2	1	no	—
312	C₄×C₁₇	—	2	1	no	—
313	C₄×C₁₇	—	2	2	no	—
314	C₄×C₁₇	—	2	1	no	—
315	C₄×C₁₇	—	2	1	no	—
316	C₄×C₁₇	—	2	1	no	—
317	C₄×C₁₇	C₂×#41	1	2	yes	—
318	Dic₁₇	—	2	2	no	—
319	Dic₁₇	—	2	1	no	—
320	Dic₁₇	—	2	1	no	—
321	Dic₁₇	—	2	2	no	—
322	Dic₁₇	—	2	1	no	—
323	Dic₁₇	—	2	1	no	—
324	Dic₁₇	—	2	1	no	—
325	Dic₁₇	C₂×#41	1	2	yes	—
326	Dic₁₇	H(5,𝔽₂)	1	2	yes	—
327	#559	—	17	1	no	—
328	#559	—	17	1	no	—
329	#559	—	17	1	no	—
330	#559	D₁₇	1	1	yes	characteristic, complemented
331	#556	—	17	1	no	—
332	#556	—	17	1	no	—
333	#555	—	17	2	no	—
334	#553	—	17	2	no	—
335	#553	—	17	2	no	—
336	#550	—	17	1	no	—
337	#550	—	17	1	no	—
338	#547	—	17	2	no	—
339	#538	—	17	2	no	—
340	#538	—	17	2	no	—
341	#535	—	17	1	no	—
342	#535	—	17	1	no	—
343	#533	—	17	1	no	—
344	#532	—	17	1	no	—
345	#525	—	17	2	no	—
346	#525	—	17	2	no	—
347	#520	—	17	1	no	—
348	#520	—	17	1	no	—
349	C₂×C₄×D₄	—	17	1	no	—
350	C₂×C₁₇	—	4	2	no	—
351	C₂×C₁₇	—	4	2	no	—
352	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
353	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₁₇	#585	1	1	yes	characteristic
355	D₁₇	—	2	2	no	—
356	D₁₇	—	4	2	no	—
357	D₁₇	—	4	2	no	—
358	C₂×#41	—	17	1	no	—
359	C₂×#41	—	17	1	no	—
360	C₂×#41	—	17	2	no	—
361	C₂×#41	—	17	2	no	—
362	C₂²×D₄	—	17	1	no	—
363	C₂³×C₄	—	17	2	no	—
364	C₄⋊Q₈	—	17	1	no	—
365	C₄⋊Q₈	—	17	1	no	—
366	C₄⋊Q₈	—	17	1	no	—
367	#127	—	17	1	no	—
368	#127	—	17	1	no	—
369	#127	—	17	1	no	—
370	#127	—	17	1	no	—
371	#127	C₂×D₁₇	1	1	yes	characteristic
372	#126	—	17	2	no	—
373	#126	—	17	2	no	—
374	#126	—	17	2	no	—
375	#126	—	17	2	no	—
376	#125	—	17	1	no	—
377	#125	—	17	1	no	—
378	#124	—	17	1	no	—
379	#124	—	17	2	no	—
380	#124	—	17	1	no	—
381	#124	—	17	2	no	—
382	#124	—	17	2	no	—
383	#124	—	17	1	no	—
384	#124	—	17	1	no	—
385	#124	C₂×D₁₇	1	1	yes	characteristic
386	#124	C₂×D₁₇	1	1	yes	characteristic, complemented
387	#124	C₂×D₁₇	1	2	yes	complemented
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	C₂×D₁₇	1	2	yes	complemented
395	#123	C₂×D₁₇	1	2	yes	complemented
396	C₂²⋊Q₈	—	17	1	no	—
397	C₂²⋊Q₈	—	17	1	no	—
398	C₂²⋊Q₈	—	17	1	no	—
399	C₂²⋊Q₈	—	17	2	no	—
400	C₂²⋊Q₈	—	17	1	no	—
401	C₂²⋊Q₈	—	17	2	no	—
402	#121	—	17	2	no	—
403	#121	—	17	2	no	—
404	#121	—	17	2	no	—
405	#121	—	17	2	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	2	no	—
412	#121	—	17	2	no	—
413	#121	—	17	2	no	—
414	#120	—	17	2	no	—
415	#120	—	17	2	no	—
416	#120	—	17	2	no	—
417	#120	—	17	2	no	—
418	C₄×Q₈	—	17	1	no	—
419	C₄×Q₈	—	17	1	no	—
420	C₄×Q₈	—	17	1	no	—
421	C₄×Q₈	—	17	1	no	—
422	C₄×Q₈	—	17	1	no	—
423	C₄×Q₈	—	17	1	no	—
424	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
425	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
426	C₄×D₄	—	17	1	no	—
427	C₄×D₄	—	17	1	no	—
428	C₄×D₄	—	17	2	no	—
429	C₄×D₄	—	17	2	no	—
430	C₄×D₄	—	17	2	no	—
431	C₄×D₄	—	17	1	no	—
432	C₄×D₄	—	17	2	no	—
433	C₄×D₄	—	17	1	no	—
434	C₄×D₄	—	17	2	no	—
435	C₄×D₄	—	17	2	no	—
436	C₄×D₄	—	17	2	no	—
437	C₄×D₄	—	17	2	no	—
438	C₄×D₄	—	17	2	no	—
439	C₄×D₄	—	17	2	no	—
440	C₄×D₄	—	17	1	no	—
441	C₄×D₄	—	17	2	no	—
442	C₄×D₄	—	17	1	no	—
443	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
444	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
445	C₄×D₄	C₂×D₁₇	1	2	yes	complemented
446	#117	—	17	2	no	—
447	#117	—	17	2	no	—
448	#117	—	17	1	no	—
449	#117	—	17	1	no	—
450	#117	—	17	2	no	—
451	#117	—	17	2	no	—
452	C₂×C₄⋊C₄	—	17	2	no	—
453	C₂×C₄⋊C₄	—	17	1	no	—
454	C₂×C₄⋊C₄	—	17	2	no	—
455	C₂×C₂²⋊C₄	—	17	2	no	—
456	C₂×C₄²	—	17	1	no	—
457	C₁₇	#3506	1	1	yes	characteristic, complemented, Sylow
458	C₂⁴	—	17	2	no	—
459	#41	—	34	4	no	—
460	#41	—	34	4	no	—
461	#41	—	68	4	no	—
462	#41	—	68	4	no	—
463	C₂×Q₈	—	17	1	no	—
464	C₂×Q₈	—	17	1	no	—
465	C₂×Q₈	—	17	1	no	—
466	C₂×Q₈	—	17	1	no	—
467	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
469	C₂×D₄	—	17	2	no	—
470	C₂×D₄	—	17	2	no	—
471	C₂×D₄	—	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	1	no	—
479	C₂×D₄	—	17	1	no	—
480	C₂×D₄	—	17	2	no	—
481	C₂×D₄	—	17	2	no	—
482	C₂×D₄	—	34	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	C₂²×C₄	—	17	1	no	—
488	C₂²×C₄	—	17	2	no	—
489	C₂²×C₄	—	17	2	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	2	no	—
496	C₂²×C₄	—	17	2	no	—
497	C₂²×C₄	—	17	2	no	—
498	C₂²×C₄	—	17	2	no	—
499	C₂²×C₄	—	68	4	no	—
500	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
502	C₄⋊C₄	—	17	2	no	—
503	C₄⋊C₄	—	17	1	no	—
504	C₄⋊C₄	—	17	1	no	—
505	C₄⋊C₄	—	17	1	no	—
506	C₄⋊C₄	—	17	2	no	—
507	C₄⋊C₄	—	17	2	no	—
508	C₄⋊C₄	—	17	2	no	—
509	C₄⋊C₄	—	17	1	no	—
510	C₄⋊C₄	—	17	1	no	—
511	C₄⋊C₄	—	17	2	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	1	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	C₂²×D₁₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
527	C₂²⋊C₄	—	17	2	no	—
528	C₂²⋊C₄	—	17	2	no	—
529	C₂²⋊C₄	—	17	2	no	—
530	C₂²⋊C₄	—	17	2	no	—
531	C₂²⋊C₄	—	17	2	no	—
532	C₂²⋊C₄	—	17	2	no	—
533	C₂²⋊C₄	—	17	1	no	—
534	C₂²⋊C₄	—	17	1	no	—
535	C₂²⋊C₄	—	17	1	no	—
536	C₂²⋊C₄	—	17	1	no	—
537	C₂²⋊C₄	—	17	2	no	—
538	C₂²⋊C₄	—	17	2	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	C₂²×D₁₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
551	C₄²	—	17	1	no	—
552	C₄²	—	17	1	no	—
553	C₄²	—	17	1	no	—
554	C₄²	—	17	2	no	—
555	C₄²	—	17	2	no	—
556	C₄²	—	17	2	no	—
557	C₄²	—	17	1	no	—
558	C₄²	—	17	1	no	—
559	C₄²	C₂²×D₁₇	1	1	yes	characteristic
560	C₄²	C₂²×D₁₇	1	2	yes	—
561	C₄²	C₂²×D₁₇	1	1	yes	characteristic
562	C₄²	C₂²×D₁₇	1	1	yes	characteristic
563	C₂³	—	17	1	no	—
564	C₂³	—	17	2	no	—
565	C₂³	—	17	2	no	—
566	C₂³	—	34	4	no	—
567	C₂³	—	68	2	no	—
568	C₂³	—	68	2	no	—
569	C₂³	C₂³×D₁₇	1	2	yes	—
570	C₂³	C₂³×D₁₇	1	2	yes	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	34	2	no	—
574	Q₈	—	34	2	no	—
575	Q₈	—	34	2	no	—
576	Q₈	—	68	1	no	—
577	D₄	—	2	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	34	4	no	—
582	D₄	—	34	4	no	—
583	D₄	—	34	4	no	—
584	D₄	—	34	4	no	—
585	D₄	—	34	2	no	—
586	D₄	—	34	2	no	—
587	D₄	—	68	2	no	—
588	D₄	—	68	2	no	—
589	D₄	—	68	2	no	—
590	D₄	—	68	2	no	—
591	D₄	—	68	2	no	—
592	D₄	—	68	2	no	—
593	D₄	—	68	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	17	1	no	—
597	C₂×C₄	—	17	1	no	—
598	C₂×C₄	—	17	4	no	—
599	C₂×C₄	—	17	1	no	—
600	C₂×C₄	—	17	1	no	—
601	C₂×C₄	—	17	2	no	—
602	C₂×C₄	—	17	1	no	—
603	C₂×C₄	—	17	2	no	—
604	C₂×C₄	—	17	1	no	—
605	C₂×C₄	—	17	1	no	—
606	C₂×C₄	—	34	2	no	—
607	C₂×C₄	—	34	4	no	—
608	C₂×C₄	—	34	4	no	—
609	C₂×C₄	—	34	4	no	—
610	C₂×C₄	—	34	4	no	—
611	C₂×C₄	—	68	2	no	—
612	C₂×C₄	—	68	2	no	—
613	C₂×C₄	—	68	2	no	—
614	C₂×C₄	—	68	2	no	—
615	C₂×C₄	—	68	1	no	—
616	C₂×C₄	—	68	2	no	—
617	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₇	1	2	yes	—
620	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₇	1	2	yes	—
622	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	17	2	no	—
633	C₂²	—	34	1	no	—
634	C₂²	—	34	1	no	—
635	C₂²	—	34	2	no	—
636	C₂²	—	34	2	no	—
637	C₂²	—	34	2	no	—
638	C₂²	—	34	2	no	—
639	C₂²	—	34	2	no	—
640	C₂²	—	34	2	no	—
641	C₂²	—	68	8	no	—
642	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	17	2	no	—
652	C₄	—	17	2	no	—
653	C₄	—	34	2	no	—
654	C₄	—	34	2	no	—
655	C₄	—	34	1	no	—
656	C₄	—	34	1	no	—
657	C₄	—	34	1	no	—
658	C₄	—	34	1	no	—
659	C₄	—	34	1	no	—
660	C₄	#41×D₁₇	1	2	yes	—
661	C₂	—	4	2	no	—
662	C₂	—	4	2	no	—
663	C₂	—	34	2	no	—
664	C₂	—	68	2	no	—
665	C₂	—	68	2	no	—
666	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
667	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
668	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#559	C₂
hypercenter	#559	D₁₇
hypocenter	C₁₇	#3506
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. #11763544	C₂	semidirect
2. #11763542	C₂	semidirect
3. #11763541	C₂	semidirect
4. #11763531	C₂	semidirect
5. #11763528	C₂	semidirect
6. #11763521	C₂	semidirect
7. #11763508	C₂	semidirect
8. #11763504	C₂	semidirect
9. #11763480	C₂	semidirect
10. #11763479	C₂	semidirect
11. #11763457	C₂	semidirect
12. #11763395	C₂	semidirect
13. #11763393	C₂	semidirect
14. #11763377	C₂	semidirect
15. #11763372	C₂	semidirect
16. #11763363	C₂	semidirect
17. #11763358	C₂	semidirect
18. #11763318	C₂	semidirect
19. #11763317	C₂	semidirect
20. #11763291	C₂	semidirect
21. #11763288	C₂	semidirect
22. C₄×D₄×D₁₇	C₂	semidirect
23. C₁₇×#559	C₂	semidirect
26. C₂×#63254	C₂²	semidirect
28. C₂×#63252	C₂²	semidirect
32. C₁₇×#124	C₂²	semidirect
33. C₁₇×#124	C₂²	semidirect
34. C₁₇×#123	C₂²	semidirect
35. C₁₇×#123	C₂²	semidirect
36. C₄×Q₈×C₁₇	C₂²	semidirect
37. C₄×Q₈×C₁₇	C₂²	semidirect
39. C₄×D₄×C₁₇	C₂²	semidirect
40. C₄×D₄×C₁₇	C₂²	semidirect
42. #10587633	C₂²	semidirect
44. Q₈×Dic₁₇	C₂²	semidirect
45. #10587630	C₂²	semidirect
46. #10587630	C₂²	semidirect
49. #10587626	C₂²	semidirect
52. #10587625	C₂²	semidirect
53. #10587625	C₂²	semidirect
54. #10587624	C₂²	semidirect
59. D₄×Dic₁₇	C₂²	semidirect
60. #10587616	C₂²	semidirect
61. #10587615	C₂²	semidirect
64. C₄×C₂²⋊D₁₇	C₂²	semidirect
65. C₂×#63225	C₂²	semidirect
66. #10587584	C₂²	semidirect
70. #10587582	C₂²	semidirect
71. #10587580	C₂²	semidirect
72. #10587580	C₂²	semidirect
75. #10587579	C₂²	semidirect
76. #10587579	C₂²	semidirect
78. C₄⋊C₄×D₁₇	C₂²	semidirect
79. #10587575	C₂²	semidirect
80. #10587575	C₂²	semidirect
81. #10587574	C₂²	semidirect
82. #10587573	C₂²	semidirect
83. #10587572	C₂²	semidirect
84. #10587571	C₂²	semidirect
85. #10587571	C₂²	semidirect
90. #10587570	C₂²	semidirect
91. #10587570	C₂²	semidirect
92. #10587569	C₂²	semidirect
93. #10587569	C₂²	semidirect
98. #10587567	C₂²	semidirect
99. #10587567	C₂²	semidirect
100. #10587567	C₂²	semidirect
102. #10587565	C₂²	semidirect
103. #10587565	C₂²	semidirect
104. #10587564	C₂²	semidirect
105. #10587563	C₂²	semidirect
106. #10587563	C₂²	semidirect
107. #10587562	C₂²	semidirect
109. #10587561	C₂²	semidirect
113. C₄×D₆₈	C₂²	semidirect
116. #10587558	C₂²	semidirect
117. #10587558	C₂²	semidirect
119. C₄×Dic₃₄	C₂²	semidirect
120. C₄×Dic₃₄	C₂²	semidirect
121. C₄×Dic₃₄	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
286. C₄×D₁₇	#41	semidirect
330. #559	D₁₇	semidirect
386. #124	C₂×D₁₇	semidirect
387. #124	C₂×D₁₇	semidirect
394. #123	C₂×D₁₇	semidirect
395. #123	C₂×D₁₇	semidirect
424. C₄×Q₈	C₂×D₁₇	semidirect
425. C₄×Q₈	C₂×D₁₇	semidirect
444. C₄×D₄	C₂×D₁₇	semidirect
445. C₄×D₄	C₂×D₁₇	semidirect
457. C₁₇	#3506	semidirect

Maximal subgroups

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

subgroup	index
#11763544	2
#11763542	2
#11763541	2
#11763531	2
#11763528	2
#11763521	2
#11763508	2
#11763504	2
#11763480	2
#11763479	2
#11763457	2
#11763395	2
#11763393	2
#11763377	2
#11763372	2
#11763363	2
#11763358	2
#11763318	2
#11763317	2
#11763291	2
#11763288	2
C₄×D₄×D₁₇	2
C₁₇×#559	2
#3506	17