Subgroups — #14542674

Order 2176.

1040 conjugacy classes of subgroups.

The subgroup lattice has 640 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	#11763544	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763542	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763541	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763533	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763531	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763528	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763486	C₂	1	2	yes	maximal, complemented
9	#11763484	C₂	1	2	yes	maximal, complemented
10	#11763484	C₂	1	2	yes	maximal, complemented
11	#11763483	C₂	1	2	yes	maximal, complemented
12	#11763429	C₂	1	2	yes	maximal, complemented
13	#11763425	C₂	1	2	yes	maximal, complemented
14	#11763384	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763377	C₂	1	1	yes	maximal, characteristic
16	#11763363	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763342	C₂	1	2	yes	maximal, complemented
18	#11763337	C₂	1	2	yes	maximal, complemented
19	#124×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763285	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×#556	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₇	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₇	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×#126	C₂²	1	2	yes	complemented
30	C₁₇×#124	C₂²	1	1	yes	characteristic
31	C₁₇×#124	C₂²	1	1	yes	characteristic
32	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
34	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
35	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
37	C₁₇×#117	C₂²	1	2	yes	complemented
38	#10587633	C₂²	1	1	yes	characteristic
39	#10587633	C₂²	1	1	yes	characteristic
40	#10587633	C₂²	1	2	yes	complemented
41	#10587633	C₂²	1	1	yes	characteristic, complemented
42	#10587632	C₂²	1	1	yes	characteristic
43	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
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	#10587622	C₂²	1	1	yes	characteristic
49	D₄×Dic₁₇	C₂²	1	1	yes	characteristic
50	#10587615	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
53	C₂×#63227	C₂²	1	2	yes	—
54	#10587584	C₂²	1	2	yes	complemented
55	#10587584	C₂²	1	2	yes	complemented
56	#10587584	C₂²	1	2	yes	complemented
57	#10587583	C₂²	1	1	yes	characteristic
58	#10587583	C₂²	1	2	yes	complemented
59	#10587582	C₂²	1	1	yes	characteristic
60	#10587582	C₂²	1	1	yes	characteristic
61	#10587582	C₂²	1	2	yes	complemented
62	#10587582	C₂²	1	2	yes	complemented
63	#10587582	C₂²	1	2	yes	complemented
64	#10587580	C₂²	1	2	yes	—
65	#10587580	C₂²	1	2	yes	—
66	#10587580	C₂²	1	2	yes	complemented
67	#10587580	C₂²	1	2	yes	complemented
68	#10587580	C₂²	1	2	yes	complemented
69	#10587580	C₂²	1	2	yes	complemented
70	#10587579	C₂²	1	2	yes	—
71	#10587579	C₂²	1	1	yes	characteristic
72	#10587579	C₂²	1	2	yes	complemented
73	#10587579	C₂²	1	1	yes	characteristic, complemented
74	#10587578	C₂²	1	2	yes	—
75	#10587578	C₂²	1	1	yes	characteristic
76	#10587578	C₂²	1	2	yes	complemented
77	#10587578	C₂²	1	2	yes	complemented
78	#10587575	C₂²	1	1	yes	characteristic, complemented
79	#10587575	C₂²	1	1	yes	characteristic, complemented
80	#10587574	C₂²	1	1	yes	characteristic, complemented
81	#10587573	C₂²	1	1	yes	characteristic, complemented
82	#10587573	C₂²	1	2	yes	complemented
83	#10587572	C₂²	1	2	yes	complemented
84	#10587571	C₂²	1	2	yes	—
85	#10587571	C₂²	1	2	yes	—
86	#10587571	C₂²	1	2	yes	complemented
87	#10587571	C₂²	1	2	yes	complemented
88	#10587570	C₂²	1	2	yes	—
89	#10587570	C₂²	1	2	yes	—
90	#10587569	C₂²	1	2	yes	complemented
91	#10587569	C₂²	1	2	yes	complemented
92	#10587568	C₂²	1	2	yes	—
93	#10587568	C₂²	1	2	yes	—
94	#10587567	C₂²	1	2	yes	—
95	#10587567	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
99	#10587565	C₂²	1	2	yes	complemented
100	#10587565	C₂²	1	2	yes	complemented
101	#10587564	C₂²	1	2	yes	complemented
102	#10587563	C₂²	1	2	yes	complemented
103	#10587562	C₂²	1	2	yes	complemented
104	#10587561	C₂²	1	1	yes	characteristic
105	#10587561	C₂²	1	2	yes	complemented
106	#10587561	C₂²	1	1	yes	characteristic, complemented
107	#10587560	C₂²	1	1	yes	characteristic
108	C₄×D₆₈	C₂²	1	2	yes	—
109	C₄×D₆₈	C₂²	1	1	yes	characteristic
110	C₄×D₆₈	C₂²	1	2	yes	complemented
111	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
112	#10587558	C₂²	1	2	yes	—
113	#10587558	C₂²	1	1	yes	characteristic
114	#10587558	C₂²	1	1	yes	characteristic
115	#10587558	C₂²	1	2	yes	complemented
116	C₄²×D₁₇	C₂²	1	1	yes	characteristic
117	C₄²×D₁₇	C₂²	1	2	yes	complemented
118	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
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	2	yes	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×Q₈×C₁₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
132	C₂²×Dic₁₇	C₂³	1	2	yes	—
133	#63256	—	2	4	no	—
134	Q₈×D₁₇	—	2	4	no	—
135	D₄×D₁₇	—	2	4	no	—
136	C₂×D₆₈	C₂³	1	1	yes	characteristic
137	C₂×D₆₈	C₂³	1	2	yes	—
138	C₂×D₆₈	C₂³	1	1	yes	characteristic
139	C₂×D₆₈	C₂³	1	2	yes	—
140	C₂×D₆₈	C₂³	1	2	yes	—
141	C₂×C₄×D₁₇	C₂³	1	2	yes	—
142	C₂×C₄×D₁₇	C₂³	1	2	yes	—
143	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₇	C₂³	1	2	yes	—
146	C₂×C₄×D₁₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₇	C₂³	1	2	yes	—
148	C₂×C₄×D₁₇	C₂³	1	2	yes	—
149	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
150	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
151	C₂×Dic₃₄	C₂³	1	2	yes	—
152	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
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	2	yes	—
157	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
158	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
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	C₄⋊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	2	yes	—
168	C₄²×C₁₇	C₂³	1	1	yes	characteristic
169	C₄²×C₁₇	C₂³	1	1	yes	characteristic
170	C₄²×C₁₇	C₂³	1	2	yes	—
171	C₄²×C₁₇	C₂³	1	2	yes	—
172	C₄²×C₁₇	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	#63227	C₂³	1	1	yes	characteristic
177	#63227	C₂³	1	2	yes	—
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	2	yes	—
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	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	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₇	C₂³	1	2	yes	—
199	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₇	C₂³	1	2	yes	—
201	#63225	C₂³	1	2	yes	—
202	#63225	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
208	#63225	C₂³	1	1	yes	characteristic
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	2	yes	—
214	#63225	C₂³	1	2	yes	—
215	C₄×Dic₁₇	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	2	yes	—
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	2	yes	—
225	C₂³×C₁₇	C₂⁴	1	2	yes	—
226	C₂²×D₁₇	—	2	4	no	—
227	C₂²×D₁₇	—	4	2	no	—
228	C₂²×D₁₇	—	4	2	no	—
229	C₂²×D₁₇	C₂⁴	1	2	yes	—
230	C₂²×D₁₇	C₂⁴	1	2	yes	—
231	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
232	Q₈×C₁₇	—	2	2	no	—
233	Q₈×C₁₇	—	2	2	no	—
234	Q₈×C₁₇	—	4	1	no	—
235	D₄×C₁₇	—	2	2	no	—
236	C₂×C₄×C₁₇	—	4	2	no	—
237	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
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	2	yes	—
244	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₁₇	—	2	4	no	—
248	C₂²⋊D₁₇	—	4	2	no	—
249	C₂²⋊D₁₇	—	4	2	no	—
250	C₂×Dic₁₇	—	4	2	no	—
251	C₂×Dic₁₇	C₂⁴	1	2	yes	—
252	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₇	C₂⁴	1	2	yes	—
256	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
260	D₆₈	—	2	4	no	—
261	D₆₈	—	2	2	no	—
262	D₆₈	—	2	2	no	—
263	D₆₈	—	4	2	no	—
264	D₆₈	—	4	2	no	—
265	C₄×D₁₇	—	2	4	no	—
266	C₄×D₁₇	—	2	4	no	—
267	C₄×D₁₇	—	4	1	no	—
268	C₄×D₁₇	—	4	2	no	—
269	C₄×D₁₇	—	4	1	no	—
270	C₄×D₁₇	—	4	2	no	—
271	C₄×D₁₇	—	4	2	no	—
272	C₄×D₁₇	—	4	2	no	—
273	C₄×D₁₇	#41	1	4	yes	—
274	Dic₃₄	—	2	2	no	—
275	Dic₃₄	—	2	4	no	—
276	Dic₃₄	—	4	1	no	—
277	Dic₃₄	—	4	1	no	—
278	Dic₃₄	—	4	1	no	—
279	#3510	—	17	1	no	maximal, Sylow
280	C₂²×C₁₇	—	2	2	no	—
281	C₂²×C₁₇	—	2	2	no	—
282	C₂²×C₁₇	—	2	2	no	—
283	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
284	C₂×D₁₇	—	2	1	no	—
285	C₂×D₁₇	—	2	1	no	—
286	C₂×D₁₇	—	2	2	no	—
287	C₂×D₁₇	—	2	2	no	—
288	C₂×D₁₇	—	2	2	no	—
289	C₂×D₁₇	—	2	2	no	—
290	C₂×D₁₇	—	2	2	no	—
291	C₂×D₁₇	—	2	2	no	—
292	C₂×D₁₇	—	8	4	no	—
293	C₂×D₁₇	C₂×#41	1	2	yes	—
294	C₄×C₁₇	—	2	2	no	—
295	C₄×C₁₇	—	2	2	no	—
296	C₄×C₁₇	—	2	1	no	—
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	1	no	—
299	C₄×C₁₇	—	2	1	no	—
300	C₄×C₁₇	—	2	2	no	—
301	C₄×C₁₇	—	2	1	no	—
302	C₄×C₁₇	—	2	1	no	—
303	C₄×C₁₇	C₂×#41	1	2	yes	—
304	Dic₁₇	—	2	2	no	—
305	Dic₁₇	—	2	1	no	—
306	Dic₁₇	—	2	1	no	—
307	Dic₁₇	—	2	1	no	—
308	Dic₁₇	—	2	1	no	—
309	Dic₁₇	—	2	1	no	—
310	Dic₁₇	—	2	1	no	—
311	Dic₁₇	—	2	2	no	—
312	Dic₁₇	C₂×#41	1	2	yes	—
313	#559	—	17	1	no	—
314	#559	—	17	1	no	—
315	#559	—	17	1	no	—
316	#559	—	17	1	no	—
317	#556	—	17	1	no	—
318	#556	—	17	1	no	—
319	#556	—	17	1	no	—
320	#556	D₁₇	1	1	yes	characteristic, complemented
321	#551	—	17	2	no	—
322	#551	—	17	2	no	—
323	#551	—	17	2	no	—
324	#551	—	17	2	no	—
325	#542	—	17	2	no	—
326	#542	—	17	2	no	—
327	#536	—	17	1	no	—
328	#535	—	17	1	no	—
329	#533	—	17	1	no	—
330	#529	—	17	2	no	—
331	#529	—	17	2	no	—
332	C₂×#124	—	17	1	no	—
333	#519	—	17	1	no	—
334	#518	—	17	1	no	—
335	C₄×#41	—	17	1	no	—
336	C₂×C₁₇	—	4	2	no	—
337	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
338	C₂×C₁₇	#585	1	1	yes	characteristic
339	C₂×C₁₇	#585	1	1	yes	characteristic
340	D₁₇	—	2	2	no	—
341	D₁₇	—	4	2	no	—
342	D₁₇	—	4	2	no	—
343	C₂×#41	—	17	1	no	—
344	C₂²×Q₈	—	17	1	no	—
345	C₂²×D₄	—	17	1	no	—
346	C₄⋊Q₈	—	17	1	no	—
347	C₄⋊Q₈	—	17	1	no	—
348	C₄⋊Q₈	—	17	1	no	—
349	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
350	#127	—	17	1	no	—
351	#127	—	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	C₂×D₁₇	1	2	yes	complemented
359	#126	C₂×D₁₇	1	2	yes	complemented
360	#125	—	17	1	no	—
361	#125	—	17	1	no	—
362	#124	—	17	1	no	—
363	#124	—	17	1	no	—
364	#124	—	17	1	no	—
365	#124	—	17	2	no	—
366	#124	—	17	1	no	—
367	#124	—	17	2	no	—
368	#124	—	17	2	no	—
369	#124	—	17	2	no	—
370	#124	—	17	2	no	—
371	#124	—	17	1	no	—
372	#124	—	17	1	no	—
373	#124	—	17	2	no	—
374	#124	C₂×D₁₇	1	1	yes	characteristic
375	#124	C₂×D₁₇	1	1	yes	characteristic
376	#123	—	17	2	no	—
377	#123	—	17	2	no	—
378	#123	—	17	2	no	—
379	#123	—	17	2	no	—
380	#123	—	17	2	no	—
381	#123	—	17	2	no	—
382	#123	—	17	2	no	—
383	#123	—	17	2	no	—
384	#123	—	17	2	no	—
385	#123	—	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	1	no	—
390	C₂²⋊Q₈	—	17	1	no	—
391	C₂²⋊Q₈	—	17	1	no	—
392	C₂²⋊Q₈	—	17	2	no	—
393	C₂²⋊Q₈	—	17	2	no	—
394	C₂²⋊Q₈	—	17	2	no	—
395	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	complemented
396	#121	—	17	2	no	—
397	#121	—	17	2	no	—
398	#120	—	17	2	no	—
399	#120	—	17	2	no	—
400	C₄×Q₈	—	17	1	no	—
401	C₄×Q₈	—	17	1	no	—
402	C₄×Q₈	—	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	—	17	1	no	—
409	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
410	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
411	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
412	C₄×D₄	—	17	1	no	—
413	C₄×D₄	—	17	2	no	—
414	C₄×D₄	—	17	2	no	—
415	C₄×D₄	—	17	2	no	—
416	C₄×D₄	—	17	1	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	2	no	—
422	C₄×D₄	—	17	1	no	—
423	C₄×D₄	—	17	1	no	—
424	C₄×D₄	—	17	2	no	—
425	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
426	#117	—	17	1	no	—
427	#117	—	17	2	no	—
428	#117	—	17	2	no	—
429	#117	—	17	2	no	—
430	#117	—	17	2	no	—
431	#117	—	17	1	no	—
432	#117	—	17	1	no	—
433	#117	—	17	2	no	—
434	#117	—	17	2	no	—
435	#117	C₂×D₁₇	1	2	yes	complemented
436	C₂×C₂²⋊C₄	—	17	2	no	—
437	C₂×C₂²⋊C₄	—	17	2	no	—
438	C₂×C₂²⋊C₄	—	17	2	no	—
439	C₂×C₂²⋊C₄	—	17	2	no	—
440	C₂×C₄²	—	17	1	no	—
441	C₂×C₄²	—	17	2	no	—
442	C₁₇	#3510	1	1	yes	characteristic, complemented, Sylow
443	C₂⁴	—	17	2	no	—
444	#41	—	34	4	no	—
445	C₂×Q₈	—	17	2	no	—
446	C₂×Q₈	—	17	1	no	—
447	C₂×Q₈	—	17	1	no	—
448	C₂×Q₈	—	17	1	no	—
449	C₂×Q₈	—	17	1	no	—
450	C₂×Q₈	—	34	4	no	—
451	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
454	C₂×D₄	—	17	2	no	—
455	C₂×D₄	—	17	2	no	—
456	C₂×D₄	—	17	2	no	—
457	C₂×D₄	—	17	2	no	—
458	C₂×D₄	—	17	1	no	—
459	C₂×D₄	—	17	1	no	—
460	C₂×D₄	—	17	2	no	—
461	C₂×D₄	—	17	2	no	—
462	C₂×D₄	—	34	4	no	—
463	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
464	C₂²×C₄	—	17	1	no	—
465	C₂²×C₄	—	17	2	no	—
466	C₂²×C₄	—	17	2	no	—
467	C₂²×C₄	—	17	2	no	—
468	C₂²×C₄	—	17	1	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	2	yes	—
475	C₄⋊C₄	—	17	1	no	—
476	C₄⋊C₄	—	17	1	no	—
477	C₄⋊C₄	—	17	1	no	—
478	C₄⋊C₄	—	17	1	no	—
479	C₄⋊C₄	—	17	1	no	—
480	C₄⋊C₄	—	17	1	no	—
481	C₄⋊C₄	—	17	2	no	—
482	C₄⋊C₄	—	17	1	no	—
483	C₄⋊C₄	—	17	1	no	—
484	C₄⋊C₄	—	17	2	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	1	no	—
493	C₄⋊C₄	—	17	1	no	—
494	C₄⋊C₄	—	17	1	no	—
495	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
497	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
498	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
503	C₂²⋊C₄	—	17	2	no	—
504	C₂²⋊C₄	—	17	2	no	—
505	C₂²⋊C₄	—	17	2	no	—
506	C₂²⋊C₄	—	17	2	no	—
507	C₂²⋊C₄	—	17	1	no	—
508	C₂²⋊C₄	—	17	1	no	—
509	C₂²⋊C₄	—	17	2	no	—
510	C₂²⋊C₄	—	17	2	no	—
511	C₂²⋊C₄	—	17	2	no	—
512	C₂²⋊C₄	—	17	2	no	—
513	C₂²⋊C₄	—	17	2	no	—
514	C₂²⋊C₄	—	17	2	no	—
515	C₂²⋊C₄	—	17	1	no	—
516	C₂²⋊C₄	—	17	1	no	—
517	C₂²⋊C₄	—	17	2	no	—
518	C₂²⋊C₄	—	17	2	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	C₂²×D₁₇	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
530	C₄²	—	17	1	no	—
531	C₄²	—	17	2	no	—
532	C₄²	—	17	2	no	—
533	C₄²	—	17	1	no	—
534	C₄²	—	17	1	no	—
535	C₄²	—	17	2	no	—
536	C₄²	—	17	2	no	—
537	C₄²	—	17	2	no	—
538	C₄²	—	17	1	no	—
539	C₄²	—	17	1	no	—
540	C₄²	C₂²×D₁₇	1	2	yes	—
541	C₄²	C₂²×D₁₇	1	1	yes	characteristic
542	C₄²	C₂²×D₁₇	1	2	yes	—
543	C₄²	C₂²×D₁₇	1	1	yes	characteristic
544	C₄²	C₂²×D₁₇	1	1	yes	characteristic
545	C₂³	—	17	1	no	—
546	C₂³	—	17	2	no	—
547	C₂³	—	17	2	no	—
548	C₂³	—	34	4	no	—
549	C₂³	—	68	2	no	—
550	C₂³	—	68	2	no	—
551	C₂³	C₂³×D₁₇	1	2	yes	—
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	34	4	no	—
556	Q₈	—	34	2	no	—
557	Q₈	—	68	1	no	—
558	Q₈	—	68	1	no	—
559	Q₈	—	68	1	no	—
560	D₄	—	2	2	no	—
561	D₄	—	34	4	no	—
562	D₄	—	34	4	no	—
563	D₄	—	34	2	no	—
564	D₄	—	34	2	no	—
565	D₄	—	68	2	no	—
566	D₄	—	68	2	no	—
567	D₄	—	68	2	no	—
568	D₄	—	68	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	17	1	no	—
571	C₂×C₄	—	17	4	no	—
572	C₂×C₄	—	17	1	no	—
573	C₂×C₄	—	17	2	no	—
574	C₂×C₄	—	17	1	no	—
575	C₂×C₄	—	17	1	no	—
576	C₂×C₄	—	17	2	no	—
577	C₂×C₄	—	17	1	no	—
578	C₂×C₄	—	17	1	no	—
579	C₂×C₄	—	17	1	no	—
580	C₂×C₄	—	34	4	no	—
581	C₂×C₄	—	34	4	no	—
582	C₂×C₄	—	68	2	no	—
583	C₂×C₄	—	68	2	no	—
584	C₂×C₄	—	68	1	no	—
585	C₂×C₄	—	68	2	no	—
586	C₂×C₄	—	68	1	no	—
587	C₂×C₄	—	68	2	no	—
588	C₂×C₄	—	68	2	no	—
589	C₂×C₄	C₂³×D₁₇	1	2	yes	—
590	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₇	1	2	yes	—
593	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₇	1	2	yes	—
595	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	17	2	no	—
603	C₂²	—	34	1	no	—
604	C₂²	—	34	1	no	—
605	C₂²	—	34	2	no	—
606	C₂²	—	34	2	no	—
607	C₂²	—	34	2	no	—
608	C₂²	—	34	2	no	—
609	C₂²	—	34	2	no	—
610	C₂²	—	34	2	no	—
611	C₂²	—	136	4	no	—
612	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	17	2	no	—
623	C₄	—	34	2	no	—
624	C₄	—	34	1	no	—
625	C₄	—	34	1	no	—
626	C₄	—	34	1	no	—
627	C₄	—	34	2	no	—
628	C₄	—	34	1	no	—
629	C₄	—	34	1	no	—
630	C₄	—	34	1	no	—
631	C₄	#41×D₁₇	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	34	2	no	—
634	C₂	—	68	2	no	—
635	C₂	—	68	2	no	—
636	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
637	C₂	#11763645	1	1	yes	characteristic
638	C₂	#11763646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#556	C₂
prime radical	#11763377	C₂
hypercenter	#556	D₁₇
hypocenter	C₁₇	#3510
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #11763544	C₂	semidirect
2. #11763544	C₂	semidirect
3. #11763542	C₂	semidirect
4. #11763541	C₂	semidirect
5. #11763533	C₂	semidirect
6. #11763531	C₂	semidirect
7. #11763528	C₂	semidirect
8. #11763486	C₂	semidirect
9. #11763484	C₂	semidirect
10. #11763484	C₂	semidirect
11. #11763483	C₂	semidirect
12. #11763429	C₂	semidirect
13. #11763425	C₂	semidirect
14. #11763384	C₂	semidirect
16. #11763363	C₂	semidirect
17. #11763342	C₂	semidirect
18. #11763337	C₂	semidirect
19. #124×D₁₇	C₂	semidirect
20. #11763285	C₂	semidirect
21. #11763281	C₂	semidirect
22. C₄×#63256	C₂	semidirect
23. C₁₇×#556	C₂	semidirect
27. C₁₇×C₄⋊Q₈	C₂²	semidirect
28. C₁₇×#126	C₂²	semidirect
29. C₁₇×#126	C₂²	semidirect
32. C₁₇×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₁₇	C₂²	semidirect
34. C₄×Q₈×C₁₇	C₂²	semidirect
35. C₄×Q₈×C₁₇	C₂²	semidirect
37. C₁₇×#117	C₂²	semidirect
40. #10587633	C₂²	semidirect
41. #10587633	C₂²	semidirect
43. Q₈×Dic₁₇	C₂²	semidirect
44. Q₈×Dic₁₇	C₂²	semidirect
45. #10587630	C₂²	semidirect
46. #10587630	C₂²	semidirect
50. #10587615	C₂²	semidirect
52. C₄×C₂²⋊D₁₇	C₂²	semidirect
54. #10587584	C₂²	semidirect
55. #10587584	C₂²	semidirect
56. #10587584	C₂²	semidirect
58. #10587583	C₂²	semidirect
61. #10587582	C₂²	semidirect
62. #10587582	C₂²	semidirect
63. #10587582	C₂²	semidirect
66. #10587580	C₂²	semidirect
67. #10587580	C₂²	semidirect
68. #10587580	C₂²	semidirect
69. #10587580	C₂²	semidirect
72. #10587579	C₂²	semidirect
73. #10587579	C₂²	semidirect
76. #10587578	C₂²	semidirect
77. #10587578	C₂²	semidirect
78. #10587575	C₂²	semidirect
79. #10587575	C₂²	semidirect
80. #10587574	C₂²	semidirect
81. #10587573	C₂²	semidirect
82. #10587573	C₂²	semidirect
83. #10587572	C₂²	semidirect
86. #10587571	C₂²	semidirect
87. #10587571	C₂²	semidirect
90. #10587569	C₂²	semidirect
91. #10587569	C₂²	semidirect
95. #10587567	C₂²	semidirect
99. #10587565	C₂²	semidirect
100. #10587565	C₂²	semidirect
101. #10587564	C₂²	semidirect
102. #10587563	C₂²	semidirect
103. #10587562	C₂²	semidirect
105. #10587561	C₂²	semidirect
106. #10587561	C₂²	semidirect
110. C₄×D₆₈	C₂²	semidirect
111. C₄×D₆₈	C₂²	semidirect
115. #10587558	C₂²	semidirect
117. C₄²×D₁₇	C₂²	semidirect
118. C₄×Dic₃₄	C₂²	semidirect
119. C₄×Dic₃₄	C₂²	semidirect
120. C₄×Dic₃₄	C₂²	semidirect
121. C₄×Dic₃₄	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
320. #556	D₁₇	semidirect
349. C₄⋊Q₈	C₂×D₁₇	semidirect
358. #126	C₂×D₁₇	semidirect
359. #126	C₂×D₁₇	semidirect
395. C₂²⋊Q₈	C₂×D₁₇	semidirect
409. C₄×Q₈	C₂×D₁₇	semidirect
410. C₄×Q₈	C₂×D₁₇	semidirect
411. C₄×Q₈	C₂×D₁₇	semidirect
435. #117	C₂×D₁₇	semidirect
442. C₁₇	#3510	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
#11763533	2
#11763531	2
#11763528	2
#11763486	2
#11763484	2
#11763483	2
#11763429	2
#11763425	2
#11763384	2
#11763377	2
#11763363	2
#11763342	2
#11763337	2
#124×D₁₇	2
#11763285	2
#11763281	2
C₄×#63256	2
C₁₇×#556	2
#3510	17