Subgroups — #14543372

Order 2176.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763555	C₂	1	2	yes	maximal, complemented
2	#11763547	C₂	1	2	yes	maximal, complemented
3	#11763544	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763532	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763510	C₂	1	2	yes	maximal, complemented
6	#11763484	C₂	1	2	yes	maximal, complemented
7	#11763480	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763468	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763468	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763464	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763421	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763414	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763411	C₂	1	2	yes	maximal, complemented
16	#11763407	C₂	1	2	yes	maximal, complemented
17	#11763395	C₂	1	2	yes	maximal, complemented
18	#11763393	C₂	1	2	yes	maximal, complemented
19	#11763385	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763378	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763359	C₂	1	1	yes	maximal, characteristic, complemented
22	#11763343	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63252	C₂²	1	1	yes	characteristic
25	C₂×#63252	C₂²	1	1	yes	characteristic
26	C₂×#63252	C₂²	1	1	yes	characteristic
27	C₂×#63252	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₆₈	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
30	C₁₇×#126	C₂²	1	1	yes	characteristic
31	C₁₇×#126	C₂²	1	1	yes	characteristic, complemented
32	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
33	C₁₇×#124	C₂²	1	1	yes	characteristic
34	C₁₇×#123	C₂²	1	1	yes	characteristic
35	C₁₇×#123	C₂²	1	1	yes	characteristic, complemented
36	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₇×#121	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
41	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
42	C₁₇×#117	C₂²	1	1	yes	characteristic
43	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic, complemented
45	#10587633	C₂²	1	2	yes	complemented
46	#10587632	C₂²	1	2	yes	complemented
47	#10587626	C₂²	1	2	yes	complemented
48	#10587625	C₂²	1	2	yes	—
49	#10587625	C₂²	1	2	yes	complemented
50	#10587624	C₂²	1	2	yes	—
51	#10587623	C₂²	1	2	yes	—
52	#10587623	C₂²	1	2	yes	—
53	#10587616	C₂²	1	1	yes	characteristic
54	#10587616	C₂²	1	1	yes	characteristic
55	#10587616	C₂²	1	1	yes	characteristic, complemented
56	#10587616	C₂²	1	2	yes	complemented
57	#10587616	C₂²	1	2	yes	complemented
58	#10587615	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
60	#10587610	C₂²	1	1	yes	characteristic
61	#10587610	C₂²	1	1	yes	characteristic
62	#10587610	C₂²	1	1	yes	characteristic, complemented
63	#10587584	C₂²	1	2	yes	complemented
64	#10587584	C₂²	1	2	yes	complemented
65	#10587583	C₂²	1	2	yes	complemented
66	#10587583	C₂²	1	2	yes	complemented
67	#10587582	C₂²	1	2	yes	complemented
68	#10587582	C₂²	1	2	yes	complemented
69	#10587581	C₂²	1	2	yes	—
70	#10587581	C₂²	1	2	yes	—
71	#10587580	C₂²	1	2	yes	—
72	#10587580	C₂²	1	2	yes	—
73	#10587580	C₂²	1	2	yes	complemented
74	#10587580	C₂²	1	2	yes	complemented
75	#10587580	C₂²	1	2	yes	complemented
76	#10587580	C₂²	1	2	yes	complemented
77	#10587579	C₂²	1	2	yes	complemented
78	#10587579	C₂²	1	2	yes	complemented
79	#10587578	C₂²	1	2	yes	complemented
80	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
81	#10587575	C₂²	1	2	yes	complemented
82	#10587575	C₂²	1	2	yes	complemented
83	#10587572	C₂²	1	2	yes	complemented
84	#10587572	C₂²	1	2	yes	complemented
85	#10587571	C₂²	1	2	yes	—
86	#10587571	C₂²	1	2	yes	complemented
87	#10587570	C₂²	1	2	yes	—
88	#10587570	C₂²	1	2	yes	—
89	#10587570	C₂²	1	2	yes	complemented
90	#10587570	C₂²	1	2	yes	complemented
91	#10587570	C₂²	1	2	yes	complemented
92	#10587570	C₂²	1	2	yes	complemented
93	#10587569	C₂²	1	2	yes	—
94	#10587569	C₂²	1	2	yes	complemented
95	#10587568	C₂²	1	2	yes	—
96	#10587568	C₂²	1	2	yes	—
97	#10587567	C₂²	1	2	yes	complemented
98	#10587567	C₂²	1	2	yes	complemented
99	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
100	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
101	#10587565	C₂²	1	2	yes	—
102	#10587565	C₂²	1	2	yes	—
103	#10587562	C₂²	1	2	yes	complemented
104	#10587561	C₂²	1	1	yes	characteristic
105	#10587561	C₂²	1	1	yes	characteristic
106	#10587561	C₂²	1	1	yes	characteristic
107	#10587561	C₂²	1	1	yes	characteristic
108	#10587561	C₂²	1	1	yes	characteristic, complemented
109	#10587560	C₂²	1	1	yes	characteristic
110	#10587560	C₂²	1	1	yes	characteristic
111	C₄×D₆₈	C₂²	1	1	yes	characteristic
112	C₄×D₆₈	C₂²	1	1	yes	characteristic
113	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₆₈	C₂²	1	2	yes	complemented
115	C₄×D₆₈	C₂²	1	2	yes	complemented
116	#10587558	C₂²	1	2	yes	complemented
117	#10587556	C₂²	1	1	yes	characteristic, complemented
118	#10587555	C₂²	1	1	yes	characteristic, complemented
119	#10587555	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×D₄×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	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
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	#63252	—	4	2	no	—
142	#63252	—	4	2	no	—
143	#63252	—	4	2	no	—
144	#63252	—	4	2	no	—
145	C₂×D₆₈	—	4	2	no	—
146	C₂×D₆₈	C₂³	1	1	yes	characteristic
147	C₂×D₆₈	C₂³	1	1	yes	characteristic
148	C₂×D₆₈	C₂³	1	1	yes	characteristic
149	C₂×D₆₈	C₂³	1	2	yes	—
150	C₂×D₆₈	C₂³	1	2	yes	—
151	C₂×D₆₈	C₂³	1	2	yes	—
152	C₂×D₆₈	C₂³	1	2	yes	—
153	C₂×D₆₈	C₂³	1	2	yes	—
154	C₂×C₄×D₁₇	C₂³	1	2	yes	—
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×Dic₃₄	—	4	2	no	—
162	C₂×Dic₃₄	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	2	yes	—
166	C₄⋊C₄×C₁₇	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	1	yes	characteristic
170	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
176	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
177	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
178	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
179	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
180	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
181	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
182	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
184	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
185	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
186	C₄²×C₁₇	C₂³	1	1	yes	characteristic
187	C₄²×C₁₇	C₂³	1	1	yes	characteristic
188	C₄²×C₁₇	C₂³	1	1	yes	characteristic
189	C₄²×C₁₇	C₂³	1	1	yes	characteristic
190	C₄²×C₁₇	C₂³	1	1	yes	characteristic
191	C₄²×C₁₇	C₂³	1	1	yes	characteristic
192	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
193	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
194	C₂²⋊Dic₁₇	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	#63227	C₂³	1	2	yes	—
203	#63227	C₂³	1	2	yes	—
204	#63227	C₂³	1	2	yes	—
205	#63227	C₂³	1	2	yes	—
206	#63227	C₂³	1	2	yes	—
207	#63227	C₂³	1	2	yes	—
208	#63227	C₂³	1	2	yes	—
209	#63227	C₂³	1	2	yes	—
210	#63227	C₂³	1	2	yes	—
211	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₇	C₂³	1	2	yes	—
214	C₄⋊Dic₁₇	C₂³	1	2	yes	—
215	C₄⋊Dic₁₇	C₂³	1	2	yes	—
216	C₄⋊Dic₁₇	C₂³	1	2	yes	—
217	#63225	C₂³	1	2	yes	—
218	#63225	C₂³	1	2	yes	—
219	#63225	C₂³	1	2	yes	—
220	#63225	C₂³	1	2	yes	—
221	#63225	C₂³	1	2	yes	—
222	#63225	C₂³	1	2	yes	—
223	#63225	C₂³	1	2	yes	—
224	#63225	C₂³	1	2	yes	—
225	C₄×Dic₁₇	C₂³	1	2	yes	—
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	1	yes	characteristic
230	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₇	—	4	2	no	—
232	C₂²×D₁₇	—	4	2	no	—
233	C₂²×D₁₇	—	4	2	no	—
234	C₂²×D₁₇	C₂⁴	1	2	yes	—
235	C₂²×D₁₇	C₂⁴	1	2	yes	—
236	C₂²×D₁₇	C₂⁴	1	2	yes	—
237	Q₈×C₁₇	—	4	1	no	—
238	D₄×C₁₇	—	4	1	no	—
239	D₄×C₁₇	—	4	1	no	—
240	D₄×C₁₇	—	4	1	no	—
241	C₂×C₄×C₁₇	—	2	2	no	—
242	C₂×C₄×C₁₇	—	2	2	no	—
243	C₂×C₄×C₁₇	—	2	2	no	—
244	C₂×C₄×C₁₇	—	4	1	no	—
245	C₂×C₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
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	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	1	yes	characteristic
255	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₁₇	—	4	2	no	—
259	C₂²⋊D₁₇	—	4	2	no	—
260	C₂²⋊D₁₇	—	4	2	no	—
261	C₂²⋊D₁₇	—	4	2	no	—
262	C₂²⋊D₁₇	—	4	2	no	—
263	C₂²⋊D₁₇	—	4	2	no	—
264	C₂²⋊D₁₇	—	4	2	no	—
265	C₂×Dic₁₇	—	4	2	no	—
266	C₂×Dic₁₇	C₂⁴	1	2	yes	—
267	C₂×Dic₁₇	C₂⁴	1	2	yes	—
268	C₂×Dic₁₇	C₂⁴	1	2	yes	—
269	C₂×Dic₁₇	C₂⁴	1	2	yes	—
270	C₂×Dic₁₇	C₂⁴	1	2	yes	—
271	D₆₈	—	2	2	no	—
272	D₆₈	—	2	2	no	—
273	D₆₈	—	2	2	no	—
274	D₆₈	—	4	2	no	—
275	D₆₈	—	4	2	no	—
276	D₆₈	—	4	2	no	—
277	D₆₈	—	4	2	no	—
278	D₆₈	—	4	2	no	—
279	C₄×D₁₇	—	4	2	no	—
280	C₄×D₁₇	—	4	2	no	—
281	C₄×D₁₇	—	4	2	no	—
282	C₄×D₁₇	—	4	2	no	—
283	C₄×D₁₇	—	4	2	no	—
284	C₄×D₁₇	—	4	2	no	—
285	C₄×D₁₇	—	4	2	no	—
286	Dic₃₄	—	2	2	no	—
287	Dic₃₄	—	2	2	no	—
288	Dic₃₄	—	2	2	no	—
289	Dic₃₄	—	4	2	no	—
290	#3562	—	17	1	no	maximal, Sylow
291	C₂²×C₁₇	—	2	1	no	—
292	C₂²×C₁₇	—	2	1	no	—
293	C₂²×C₁₇	—	2	1	no	—
294	C₂²×C₁₇	—	2	1	no	—
295	C₂²×C₁₇	—	2	1	no	—
296	C₂²×C₁₇	—	2	1	no	—
297	C₂²×C₁₇	—	2	1	no	—
298	C₂²×C₁₇	—	2	1	no	—
299	C₂²×C₁₇	—	2	1	no	—
300	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
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	—	2	2	no	—
308	C₂×D₁₇	—	2	2	no	—
309	C₂×D₁₇	—	2	2	no	—
310	C₂×D₁₇	—	8	4	no	—
311	C₄×C₁₇	—	2	1	no	—
312	C₄×C₁₇	—	2	1	no	—
313	C₄×C₁₇	—	2	1	no	—
314	C₄×C₁₇	—	2	1	no	—
315	C₄×C₁₇	—	2	1	no	—
316	C₄×C₁₇	—	2	1	no	—
317	C₄×C₁₇	—	2	1	no	—
318	C₄×C₁₇	—	2	1	no	—
319	C₄×C₁₇	—	2	1	no	—
320	C₄×C₁₇	—	2	1	no	—
321	C₄×C₁₇	—	2	1	no	—
322	C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
323	Dic₁₇	—	2	2	no	—
324	Dic₁₇	—	2	2	no	—
325	Dic₁₇	—	2	2	no	—
326	Dic₁₇	—	2	2	no	—
327	Dic₁₇	—	2	2	no	—
328	#562	—	17	2	no	—
329	#560	—	17	2	no	—
330	#559	—	17	1	no	—
331	#556	—	17	1	no	—
332	#553	—	17	2	no	—
333	#551	—	17	2	no	—
334	#550	—	17	1	no	—
335	#548	—	17	1	no	—
336	#548	—	17	1	no	—
337	#547	—	17	1	no	—
338	#546	—	17	1	no	—
339	#546	—	17	1	no	—
340	#541	—	17	1	no	—
341	#540	—	17	2	no	—
342	#540	—	17	1	no	—
343	#539	—	17	2	no	—
344	#538	—	17	2	no	—
345	#538	—	17	2	no	—
346	#536	—	17	1	no	—
347	#535	—	17	1	no	—
348	#532	—	17	1	no	—
349	#529	—	17	1	no	—
350	#529	D₁₇	1	1	yes	characteristic, complemented
351	C₂×C₁₇	—	4	1	no	—
352	C₂×C₁₇	—	4	1	no	—
353	C₂×C₁₇	—	4	1	no	—
354	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₁₇	#585	1	1	yes	characteristic
356	C₂×C₁₇	#585	1	1	yes	characteristic
357	D₁₇	—	4	2	no	—
358	D₁₇	—	4	2	no	—
359	D₁₇	—	4	2	no	—
360	C₂×#41	—	17	1	no	—
361	C₂×#41	—	17	1	no	—
362	C₂×#41	—	17	1	no	—
363	C₂×#41	—	17	1	no	—
364	C₂²×Q₈	—	17	1	no	—
365	C₂²×D₄	—	17	1	no	—
366	C₄⋊Q₈	—	17	1	no	—
367	C₄⋊Q₈	—	17	1	no	—
368	#127	—	17	2	no	—
369	#127	—	17	1	no	—
370	#127	—	17	1	no	—
371	#126	—	17	2	no	—
372	#126	—	17	2	no	—
373	#126	—	17	2	no	—
374	#126	—	17	2	no	—
375	#126	—	17	2	no	—
376	#126	C₂×D₁₇	1	1	yes	characteristic
377	#126	C₂×D₁₇	1	1	yes	characteristic, complemented
378	#125	—	17	2	no	—
379	#125	—	17	2	no	—
380	#125	—	17	1	no	—
381	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
382	#124	—	17	2	no	—
383	#124	—	17	2	no	—
384	#124	—	17	2	no	—
385	#124	—	17	1	no	—
386	#124	—	17	1	no	—
387	#124	—	17	1	no	—
388	#124	—	17	1	no	—
389	#124	—	17	1	no	—
390	#124	C₂×D₁₇	1	1	yes	characteristic
391	#123	—	17	2	no	—
392	#123	—	17	2	no	—
393	#123	—	17	2	no	—
394	#123	—	17	2	no	—
395	#123	—	17	2	no	—
396	#123	—	17	2	no	—
397	#123	—	17	2	no	—
398	#123	—	17	2	no	—
399	#123	—	17	2	no	—
400	#123	—	17	2	no	—
401	#123	—	17	2	no	—
402	#123	C₂×D₁₇	1	1	yes	characteristic
403	#123	C₂×D₁₇	1	1	yes	characteristic, complemented
404	C₂²⋊Q₈	—	17	2	no	—
405	C₂²⋊Q₈	—	17	1	no	—
406	C₂²⋊Q₈	—	17	1	no	—
407	C₂²⋊Q₈	—	17	1	no	—
408	C₂²⋊Q₈	—	17	2	no	—
409	C₂²⋊Q₈	—	17	2	no	—
410	C₂²⋊Q₈	—	17	2	no	—
411	C₂²⋊Q₈	—	17	2	no	—
412	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
413	#121	—	17	2	no	—
414	#121	—	17	2	no	—
415	#121	—	17	2	no	—
416	#121	—	17	1	no	—
417	#121	—	17	2	no	—
418	#121	—	17	2	no	—
419	#121	—	17	1	no	—
420	#121	—	17	1	no	—
421	#121	—	17	2	no	—
422	#121	—	17	2	no	—
423	#121	—	17	2	no	—
424	#121	—	17	2	no	—
425	#121	—	17	2	no	—
426	#121	—	17	2	no	—
427	#121	—	17	2	no	—
428	#121	—	17	2	no	—
429	#121	C₂×D₁₇	1	1	yes	characteristic
430	#120	—	17	2	no	—
431	#120	—	17	2	no	—
432	#120	—	17	2	no	—
433	#120	—	17	2	no	—
434	C₄×Q₈	—	17	1	no	—
435	C₄×Q₈	—	17	1	no	—
436	C₄×Q₈	—	17	1	no	—
437	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
438	C₄×D₄	—	17	2	no	—
439	C₄×D₄	—	17	2	no	—
440	C₄×D₄	—	17	2	no	—
441	C₄×D₄	—	17	2	no	—
442	C₄×D₄	—	17	2	no	—
443	C₄×D₄	—	17	1	no	—
444	C₄×D₄	—	17	2	no	—
445	C₄×D₄	—	17	2	no	—
446	C₄×D₄	—	17	1	no	—
447	C₄×D₄	—	17	1	no	—
448	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
449	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
450	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
451	#117	—	17	2	no	—
452	#117	—	17	2	no	—
453	#117	C₂×D₁₇	1	1	yes	characteristic
454	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	17	2	no	—
456	C₂×C₂²⋊C₄	—	17	2	no	—
457	C₂×C₂²⋊C₄	—	17	2	no	—
458	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic, complemented
459	C₁₇	#3562	1	1	yes	characteristic, complemented, Sylow
460	C₂⁴	—	17	2	no	—
461	#41	—	68	2	no	—
462	#41	—	68	2	no	—
463	#41	—	68	2	no	—
464	#41	—	68	2	no	—
465	C₂×Q₈	—	17	1	no	—
466	C₂×Q₈	—	17	1	no	—
467	C₂×Q₈	—	17	1	no	—
468	C₂×Q₈	—	17	2	no	—
469	C₂×Q₈	—	68	2	no	—
470	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
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	1	no	—
481	C₂×D₄	—	17	2	no	—
482	C₂×D₄	—	17	2	no	—
483	C₂×D₄	—	17	2	no	—
484	C₂×D₄	—	17	2	no	—
485	C₂×D₄	—	17	2	no	—
486	C₂×D₄	—	68	2	no	—
487	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
490	C₂²×C₄	—	17	2	no	—
491	C₂²×C₄	—	17	2	no	—
492	C₂²×C₄	—	17	2	no	—
493	C₂²×C₄	—	17	2	no	—
494	C₂²×C₄	—	17	2	no	—
495	C₂²×C₄	—	17	2	no	—
496	C₂²×C₄	—	17	2	no	—
497	C₂²×C₄	—	17	2	no	—
498	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
503	C₄⋊C₄	—	17	2	no	—
504	C₄⋊C₄	—	17	2	no	—
505	C₄⋊C₄	—	17	2	no	—
506	C₄⋊C₄	—	17	2	no	—
507	C₄⋊C₄	—	17	2	no	—
508	C₄⋊C₄	—	17	1	no	—
509	C₄⋊C₄	—	17	1	no	—
510	C₄⋊C₄	—	17	2	no	—
511	C₄⋊C₄	—	17	2	no	—
512	C₄⋊C₄	—	17	2	no	—
513	C₄⋊C₄	—	17	2	no	—
514	C₄⋊C₄	—	17	2	no	—
515	C₄⋊C₄	—	17	2	no	—
516	C₄⋊C₄	—	17	2	no	—
517	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
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	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	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	—	17	2	no	—
546	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
556	C₄²	—	17	2	no	—
557	C₄²	—	17	2	no	—
558	C₄²	—	17	2	no	—
559	C₄²	C₂²×D₁₇	1	1	yes	characteristic
560	C₄²	C₂²×D₁₇	1	1	yes	characteristic
561	C₄²	C₂²×D₁₇	1	1	yes	characteristic
562	C₄²	C₂²×D₁₇	1	1	yes	characteristic
563	C₄²	C₂²×D₁₇	1	1	yes	characteristic
564	C₄²	C₂²×D₁₇	1	1	yes	characteristic
565	C₂³	—	17	2	no	—
566	C₂³	—	17	2	no	—
567	C₂³	—	17	2	no	—
568	C₂³	—	68	2	no	—
569	C₂³	—	68	2	no	—
570	C₂³	—	68	2	no	—
571	C₂³	C₂³×D₁₇	1	1	yes	characteristic
572	C₂³	C₂³×D₁₇	1	1	yes	characteristic
573	C₂³	C₂³×D₁₇	1	1	yes	characteristic
574	Q₈	—	4	1	no	—
575	Q₈	—	34	2	no	—
576	Q₈	—	34	2	no	—
577	Q₈	—	34	2	no	—
578	Q₈	—	68	2	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	34	2	no	—
583	D₄	—	34	2	no	—
584	D₄	—	34	2	no	—
585	D₄	—	68	2	no	—
586	D₄	—	68	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	D₄	—	68	2	no	—
595	D₄	—	68	2	no	—
596	D₄	—	68	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	17	2	no	—
603	C₂×C₄	—	17	2	no	—
604	C₂×C₄	—	17	2	no	—
605	C₂×C₄	—	17	2	no	—
606	C₂×C₄	—	17	2	no	—
607	C₂×C₄	—	68	2	no	—
608	C₂×C₄	—	68	2	no	—
609	C₂×C₄	—	68	2	no	—
610	C₂×C₄	—	68	2	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	C₂³×D₁₇	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
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	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	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	—	34	2	no	—
642	C₂²	—	34	2	no	—
643	C₂²	—	34	2	no	—
644	C₂²	—	34	2	no	—
645	C₂²	—	136	4	no	—
646	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	34	2	no	—
659	C₄	—	34	2	no	—
660	C₄	—	34	2	no	—
661	C₄	—	34	2	no	—
662	C₄	—	34	2	no	—
663	C₄	#10587696	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	68	2	no	—
668	C₂	—	68	2	no	—
669	C₂	—	68	2	no	—
670	C₂	C₂×#10587696	1	1	yes	characteristic
671	C₂	#11763645	1	1	yes	characteristic
672	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#529	C₂
hypercenter	#529	D₁₇
hypocenter	C₁₇	#3562
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #11763555	C₂	semidirect
2. #11763547	C₂	semidirect
3. #11763544	C₂	semidirect
4. #11763532	C₂	semidirect
5. #11763510	C₂	semidirect
6. #11763484	C₂	semidirect
7. #11763480	C₂	semidirect
8. #11763468	C₂	semidirect
9. #11763468	C₂	semidirect
10. #11763464	C₂	semidirect
11. #11763455	C₂	semidirect
12. #11763455	C₂	semidirect
13. #11763421	C₂	semidirect
14. #11763414	C₂	semidirect
15. #11763411	C₂	semidirect
16. #11763407	C₂	semidirect
17. #11763395	C₂	semidirect
18. #11763393	C₂	semidirect
19. #11763385	C₂	semidirect
20. #11763378	C₂	semidirect
21. #11763359	C₂	semidirect
22. #11763343	C₂	semidirect
23. C₁₇×#529	C₂	semidirect
27. C₂×#63252	C₂²	semidirect
29. C₂²×Dic₃₄	C₂²	semidirect
31. C₁₇×#126	C₂²	semidirect
32. C₁₇×#125	C₂²	semidirect
35. C₁₇×#123	C₂²	semidirect
36. C₁₇×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₇	C₂²	semidirect
41. C₄×D₄×C₁₇	C₂²	semidirect
43. C₁₇×#117	C₂²	semidirect
44. C₂×C₄²×C₁₇	C₂²	semidirect
45. #10587633	C₂²	semidirect
46. #10587632	C₂²	semidirect
47. #10587626	C₂²	semidirect
49. #10587625	C₂²	semidirect
55. #10587616	C₂²	semidirect
56. #10587616	C₂²	semidirect
57. #10587616	C₂²	semidirect
58. #10587615	C₂²	semidirect
59. C₄×C₂²⋊D₁₇	C₂²	semidirect
62. #10587610	C₂²	semidirect
63. #10587584	C₂²	semidirect
64. #10587584	C₂²	semidirect
65. #10587583	C₂²	semidirect
66. #10587583	C₂²	semidirect
67. #10587582	C₂²	semidirect
68. #10587582	C₂²	semidirect
73. #10587580	C₂²	semidirect
74. #10587580	C₂²	semidirect
75. #10587580	C₂²	semidirect
76. #10587580	C₂²	semidirect
77. #10587579	C₂²	semidirect
78. #10587579	C₂²	semidirect
79. #10587578	C₂²	semidirect
80. C₄⋊C₄×D₁₇	C₂²	semidirect
81. #10587575	C₂²	semidirect
82. #10587575	C₂²	semidirect
83. #10587572	C₂²	semidirect
84. #10587572	C₂²	semidirect
86. #10587571	C₂²	semidirect
89. #10587570	C₂²	semidirect
90. #10587570	C₂²	semidirect
91. #10587570	C₂²	semidirect
92. #10587570	C₂²	semidirect
94. #10587569	C₂²	semidirect
97. #10587567	C₂²	semidirect
98. #10587567	C₂²	semidirect
103. #10587562	C₂²	semidirect
108. #10587561	C₂²	semidirect
113. C₄×D₆₈	C₂²	semidirect
114. C₄×D₆₈	C₂²	semidirect
115. C₄×D₆₈	C₂²	semidirect
116. #10587558	C₂²	semidirect
117. #10587556	C₂²	semidirect
118. #10587555	C₂²	semidirect
119. #10587555	C₂²	semidirect
120. C₄×Dic₃₄	C₂²	semidirect
121. C₄×Dic₃₄	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
350. #529	D₁₇	semidirect
377. #126	C₂×D₁₇	semidirect
381. #125	C₂×D₁₇	semidirect
403. #123	C₂×D₁₇	semidirect
412. C₂²⋊Q₈	C₂×D₁₇	semidirect
437. C₄×Q₈	C₂×D₁₇	semidirect
450. C₄×D₄	C₂×D₁₇	semidirect
454. #117	C₂×D₁₇	semidirect
458. C₂×C₄²	C₂×D₁₇	semidirect
459. C₁₇	#3562	semidirect

Maximal subgroups

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

subgroup	index
#11763555	2
#11763547	2
#11763544	2
#11763532	2
#11763510	2
#11763484	2
#11763480	2
#11763468	2
#11763464	2
#11763455	2
#11763421	2
#11763414	2
#11763411	2
#11763407	2
#11763395	2
#11763393	2
#11763385	2
#11763378	2
#11763359	2
#11763343	2
C₁₇×#529	2
#3562	17