Subgroups — #14543060

Order 2176.

1058 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763551	C₂	1	2	yes	maximal, complemented
2	#11763550	C₂	1	2	yes	maximal, complemented
3	#11763544	C₂	1	2	yes	maximal, complemented
4	#11763527	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763525	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763522	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763484	C₂	1	2	yes	maximal, complemented
8	#11763471	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763469	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763450	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763433	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763431	C₂	1	2	yes	maximal, complemented
14	#11763431	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763425	C₂	1	2	yes	maximal, complemented
16	#11763398	C₂	1	2	yes	maximal, complemented
17	#11763393	C₂	1	2	yes	maximal, complemented
18	#11763382	C₂	1	1	yes	maximal, characteristic, complemented
19	#11763378	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763322	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763321	C₂	1	1	yes	maximal, characteristic, complemented
22	#11763318	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, complemented
26	C₂×#63252	C₂²	1	1	yes	characteristic
27	C₂×#63252	C₂²	1	1	yes	characteristic
28	C₂²×D₆₈	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
30	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₇×#126	C₂²	1	2	yes	complemented
32	C₁₇×#126	C₂²	1	2	yes	complemented
33	C₁₇×#124	C₂²	1	2	yes	—
34	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₄×Q₈×C₁₇	C₂²	1	2	yes	complemented
38	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
40	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
41	#10587633	C₂²	1	1	yes	characteristic, complemented
42	#10587633	C₂²	1	2	yes	complemented
43	#10587633	C₂²	1	2	yes	complemented
44	#10587633	C₂²	1	2	yes	complemented
45	#10587632	C₂²	1	1	yes	characteristic, complemented
46	#10587632	C₂²	1	2	yes	complemented
47	#10587625	C₂²	1	1	yes	characteristic
48	#10587623	C₂²	1	1	yes	characteristic
49	#10587623	C₂²	1	2	yes	—
50	#10587616	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
53	#10587610	C₂²	1	1	yes	characteristic, complemented
54	#10587584	C₂²	1	2	yes	complemented
55	#10587583	C₂²	1	2	yes	complemented
56	#10587583	C₂²	1	1	yes	characteristic, complemented
57	#10587583	C₂²	1	1	yes	characteristic, complemented
58	#10587582	C₂²	1	2	yes	complemented
59	#10587582	C₂²	1	1	yes	characteristic, complemented
60	#10587582	C₂²	1	2	yes	complemented
61	#10587581	C₂²	1	1	yes	characteristic
62	#10587581	C₂²	1	2	yes	—
63	#10587581	C₂²	1	1	yes	characteristic
64	#10587581	C₂²	1	1	yes	characteristic
65	#10587581	C₂²	1	1	yes	characteristic, complemented
66	#10587581	C₂²	1	1	yes	characteristic, complemented
67	#10587581	C₂²	1	2	yes	complemented
68	#10587581	C₂²	1	2	yes	complemented
69	#10587580	C₂²	1	2	yes	complemented
70	#10587580	C₂²	1	2	yes	complemented
71	#10587580	C₂²	1	1	yes	characteristic, complemented
72	#10587580	C₂²	1	2	yes	complemented
73	#10587580	C₂²	1	2	yes	complemented
74	#10587580	C₂²	1	2	yes	complemented
75	#10587580	C₂²	1	2	yes	complemented
76	#10587579	C₂²	1	2	yes	complemented
77	#10587579	C₂²	1	2	yes	complemented
78	#10587579	C₂²	1	1	yes	characteristic, complemented
79	#10587578	C₂²	1	2	yes	complemented
80	#10587578	C₂²	1	1	yes	characteristic, complemented
81	#10587578	C₂²	1	1	yes	characteristic, complemented
82	#10587574	C₂²	1	1	yes	characteristic, complemented
83	#10587574	C₂²	1	2	yes	complemented
84	#10587573	C₂²	1	1	yes	characteristic, complemented
85	#10587572	C₂²	1	2	yes	complemented
86	#10587571	C₂²	1	2	yes	—
87	#10587571	C₂²	1	2	yes	—
88	#10587571	C₂²	1	2	yes	complemented
89	#10587571	C₂²	1	2	yes	complemented
90	#10587570	C₂²	1	2	yes	—
91	#10587570	C₂²	1	1	yes	characteristic
92	#10587570	C₂²	1	2	yes	complemented
93	#10587570	C₂²	1	2	yes	complemented
94	#10587569	C₂²	1	1	yes	characteristic
95	#10587569	C₂²	1	2	yes	complemented
96	#10587568	C₂²	1	2	yes	—
97	#10587568	C₂²	1	2	yes	—
98	#10587568	C₂²	1	1	yes	characteristic, complemented
99	#10587568	C₂²	1	2	yes	complemented
100	#10587568	C₂²	1	2	yes	complemented
101	#10587568	C₂²	1	2	yes	complemented
102	#10587567	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
104	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	complemented
105	#10587565	C₂²	1	2	yes	complemented
106	#10587564	C₂²	1	1	yes	characteristic, complemented
107	#10587562	C₂²	1	2	yes	complemented
108	#10587562	C₂²	1	2	yes	complemented
109	#10587561	C₂²	1	2	yes	complemented
110	#10587561	C₂²	1	1	yes	characteristic, complemented
111	#10587561	C₂²	1	2	yes	complemented
112	#10587561	C₂²	1	2	yes	complemented
113	#10587561	C₂²	1	2	yes	complemented
114	#10587560	C₂²	1	2	yes	—
115	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₆₈	C₂²	1	2	yes	complemented
117	C₄×D₆₈	C₂²	1	2	yes	complemented
118	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₆₈	C₂²	1	2	yes	complemented
120	#10587558	C₂²	1	2	yes	complemented
121	#10587558	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₃₄	C₂²	1	2	yes	complemented
123	C₂³×D₁₇	C₂³	1	1	yes	characteristic
124	C₂³×D₁₇	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
126	C₂×Q₈×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	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
137	#63256	—	4	2	no	—
138	Q₈×D₁₇	—	4	2	no	—
139	#63252	—	4	2	no	—
140	#63252	—	4	2	no	—
141	C₂×D₆₈	—	4	2	no	—
142	C₂×D₆₈	C₂³	1	1	yes	characteristic
143	C₂×D₆₈	C₂³	1	1	yes	characteristic
144	C₂×D₆₈	C₂³	1	2	yes	—
145	C₂×D₆₈	C₂³	1	1	yes	characteristic
146	C₂×D₆₈	C₂³	1	2	yes	—
147	C₂×D₆₈	C₂³	1	2	yes	—
148	C₂×D₆₈	C₂³	1	2	yes	—
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	2	no	—
154	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₇	C₂³	1	2	yes	—
161	C₂×C₄×D₁₇	C₂³	1	2	yes	—
162	C₂×C₄×D₁₇	C₂³	1	2	yes	—
163	C₂×C₄×D₁₇	C₂³	1	2	yes	—
164	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
165	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
166	C₂×Dic₃₄	C₂³	1	2	yes	—
167	C₂×Dic₃₄	C₂³	1	2	yes	—
168	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
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	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
173	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
174	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
176	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
181	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
182	C₄²×C₁₇	C₂³	1	2	yes	—
183	C₄²×C₁₇	C₂³	1	2	yes	—
184	C₄²×C₁₇	C₂³	1	2	yes	—
185	C₄²×C₁₇	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
189	#63227	C₂³	1	2	yes	—
190	#63227	C₂³	1	1	yes	characteristic
191	#63227	C₂³	1	2	yes	—
192	#63227	C₂³	1	1	yes	characteristic
193	#63227	C₂³	1	1	yes	characteristic
194	#63227	C₂³	1	2	yes	—
195	#63227	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
210	#63227	C₂³	1	2	yes	—
211	#63227	C₂³	1	2	yes	—
212	C₄⋊Dic₁₇	C₂³	1	2	yes	—
213	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₁₇	C₂³	1	2	yes	—
215	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
216	#63225	C₂³	1	1	yes	characteristic
217	#63225	C₂³	1	2	yes	—
218	#63225	C₂³	1	1	yes	characteristic
219	#63225	C₂³	1	2	yes	—
220	#63225	C₂³	1	1	yes	characteristic
221	#63225	C₂³	1	1	yes	characteristic
222	#63225	C₂³	1	2	yes	—
223	#63225	C₂³	1	2	yes	—
224	C₄×Dic₁₇	C₂³	1	2	yes	—
225	C₄×Dic₁₇	C₂³	1	2	yes	—
226	C₄×Dic₁₇	C₂³	1	2	yes	—
227	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
228	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₇	—	4	1	no	—
231	C₂²×D₁₇	—	4	1	no	—
232	C₂²×D₁₇	—	4	1	no	—
233	C₂²×D₁₇	—	4	2	no	—
234	C₂²×D₁₇	—	4	2	no	—
235	C₂²×D₁₇	—	4	2	no	—
236	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₇	C₂⁴	1	2	yes	—
240	C₂²×D₁₇	C₂⁴	1	2	yes	—
241	Q₈×C₁₇	—	2	2	no	—
242	Q₈×C₁₇	—	4	2	no	—
243	D₄×C₁₇	—	4	1	no	—
244	C₂×C₄×C₁₇	—	2	2	no	—
245	C₂×C₄×C₁₇	—	2	2	no	—
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	1	yes	characteristic
251	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₇	—	4	2	no	—
256	C₂²⋊D₁₇	—	4	1	no	—
257	C₂²⋊D₁₇	—	4	1	no	—
258	C₂²⋊D₁₇	—	4	1	no	—
259	C₂²⋊D₁₇	—	4	2	no	—
260	C₂²⋊D₁₇	—	4	1	no	—
261	C₂×Dic₁₇	—	4	1	no	—
262	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
269	D₆₈	—	2	2	no	—
270	D₆₈	—	2	2	no	—
271	D₆₈	—	4	2	no	—
272	D₆₈	—	4	2	no	—
273	D₆₈	—	4	2	no	—
274	D₆₈	—	4	1	no	—
275	D₆₈	—	4	2	no	—
276	D₆₈	—	4	2	no	—
277	D₆₈	—	4	2	no	—
278	D₆₈	—	4	1	no	—
279	D₆₈	—	4	2	no	—
280	C₄×D₁₇	—	2	2	no	—
281	C₄×D₁₇	—	2	2	no	—
282	C₄×D₁₇	—	2	2	no	—
283	C₄×D₁₇	—	4	1	no	—
284	C₄×D₁₇	—	4	1	no	—
285	C₄×D₁₇	—	4	2	no	—
286	C₄×D₁₇	—	4	2	no	—
287	C₄×D₁₇	—	4	2	no	—
288	C₄×D₁₇	—	4	2	no	—
289	C₄×D₁₇	—	4	2	no	—
290	Dic₃₄	—	2	2	no	—
291	Dic₃₄	—	4	2	no	—
292	Dic₃₄	—	4	1	no	—
293	Dic₃₄	—	4	2	no	—
294	#3540	—	17	1	no	maximal, Sylow
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	—	2	1	no	—
301	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
302	C₂×D₁₇	—	2	1	no	—
303	C₂×D₁₇	—	2	1	no	—
304	C₂×D₁₇	—	2	1	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	1	no	—
310	C₂×D₁₇	—	2	1	no	—
311	C₂×D₁₇	—	2	1	no	—
312	C₂×D₁₇	—	2	1	no	—
313	C₂×D₁₇	—	2	2	no	—
314	C₂×D₁₇	—	2	1	no	—
315	C₂×D₁₇	—	2	1	no	—
316	C₂×D₁₇	—	2	2	no	—
317	C₂×D₁₇	—	4	4	no	—
318	C₂×D₁₇	—	8	4	no	—
319	C₄×C₁₇	—	2	2	no	—
320	C₄×C₁₇	—	2	1	no	—
321	C₄×C₁₇	—	2	1	no	—
322	C₄×C₁₇	—	2	2	no	—
323	C₄×C₁₇	—	2	1	no	—
324	C₄×C₁₇	—	2	2	no	—
325	C₄×C₁₇	—	2	2	no	—
326	C₄×C₁₇	—	2	1	no	—
327	C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
328	Dic₁₇	—	2	2	no	—
329	Dic₁₇	—	2	1	no	—
330	Dic₁₇	—	2	1	no	—
331	Dic₁₇	—	2	1	no	—
332	Dic₁₇	—	2	1	no	—
333	Dic₁₇	—	2	2	no	—
334	Dic₁₇	—	2	1	no	—
335	H(3,𝔽₄)	—	17	2	no	—
336	#560	—	17	2	no	—
337	#559	—	17	2	no	—
338	#556	—	17	1	no	—
339	#556	D₁₇	1	1	yes	characteristic, complemented
340	#555	—	17	1	no	—
341	#555	—	17	1	no	—
342	#551	—	17	2	no	—
343	#548	—	17	1	no	—
344	#548	—	17	1	no	—
345	#546	—	17	1	no	—
346	#546	—	17	1	no	—
347	#542	—	17	1	no	—
348	#542	—	17	2	no	—
349	#542	—	17	1	no	—
350	#542	—	17	2	no	—
351	#538	—	17	2	no	—
352	#538	—	17	2	no	—
353	#536	—	17	1	no	—
354	#535	—	17	1	no	—
355	#525	—	17	1	no	—
356	#525	—	17	1	no	—
357	#525	—	17	1	no	—
358	C₂×C₁₇	—	4	1	no	—
359	C₂×C₁₇	—	4	1	no	—
360	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₁₇	#585	1	1	yes	characteristic
362	C₂×C₁₇	#585	1	1	yes	characteristic
363	D₁₇	—	4	1	no	—
364	D₁₇	—	4	1	no	—
365	D₁₇	—	4	1	no	—
366	D₁₇	—	4	2	no	—
367	D₁₇	—	4	2	no	—
368	C₂×#41	—	17	1	no	—
369	C₂×#41	—	17	1	no	—
370	C₂×#41	—	17	1	no	—
371	C₂²×Q₈	—	17	1	no	—
372	C₂²×D₄	—	17	1	no	—
373	C₂³×C₄	—	17	1	no	—
374	C₄⋊Q₈	—	17	2	no	—
375	C₄⋊Q₈	—	17	1	no	—
376	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
377	#127	—	17	2	no	—
378	#126	—	17	2	no	—
379	#126	—	17	2	no	—
380	#126	—	17	2	no	—
381	#126	—	17	2	no	—
382	#126	C₂×D₁₇	1	2	yes	complemented
383	#126	C₂×D₁₇	1	2	yes	complemented
384	#124	—	17	2	no	—
385	#124	—	17	1	no	—
386	#124	—	17	2	no	—
387	#124	—	17	2	no	—
388	#124	—	17	2	no	—
389	#124	—	17	2	no	—
390	#124	—	17	2	no	—
391	#124	—	17	2	no	—
392	#124	—	17	2	no	—
393	#124	—	17	2	no	—
394	#124	—	17	1	no	—
395	#124	—	17	2	no	—
396	#124	—	17	2	no	—
397	#124	C₂×D₁₇	1	2	yes	—
398	#123	—	17	2	no	—
399	#123	—	17	1	no	—
400	#123	—	17	2	no	—
401	#123	—	17	2	no	—
402	#123	—	17	2	no	—
403	#123	—	17	2	no	—
404	#123	—	17	2	no	—
405	#123	—	17	2	no	—
406	#123	—	17	1	no	—
407	#123	—	17	2	no	—
408	C₂²⋊Q₈	—	17	1	no	—
409	C₂²⋊Q₈	—	17	2	no	—
410	C₂²⋊Q₈	—	17	1	no	—
411	C₂²⋊Q₈	—	17	1	no	—
412	C₂²⋊Q₈	—	17	1	no	—
413	C₂²⋊Q₈	—	17	1	no	—
414	C₂²⋊Q₈	—	17	2	no	—
415	C₂²⋊Q₈	—	17	2	no	—
416	C₂²⋊Q₈	—	17	2	no	—
417	C₂²⋊Q₈	—	17	1	no	—
418	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
419	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
420	#121	—	17	1	no	—
421	#121	—	17	1	no	—
422	#121	—	17	1	no	—
423	#121	—	17	1	no	—
424	#121	—	17	1	no	—
425	#121	—	17	1	no	—
426	#121	—	17	1	no	—
427	#121	—	17	2	no	—
428	#121	—	17	2	no	—
429	#121	—	17	2	no	—
430	#121	—	17	1	no	—
431	#121	—	17	2	no	—
432	#121	—	17	2	no	—
433	#121	—	17	2	no	—
434	#120	—	17	1	no	—
435	#120	—	17	2	no	—
436	#120	—	17	1	no	—
437	#120	—	17	2	no	—
438	#120	—	17	2	no	—
439	#120	—	17	2	no	—
440	#120	—	17	2	no	—
441	#120	—	17	2	no	—
442	C₄×Q₈	—	17	1	no	—
443	C₄×Q₈	—	17	2	no	—
444	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
445	C₄×Q₈	C₂×D₁₇	1	2	yes	complemented
446	C₄×D₄	—	17	1	no	—
447	C₄×D₄	—	17	1	no	—
448	C₄×D₄	—	17	2	no	—
449	C₄×D₄	—	17	2	no	—
450	C₄×D₄	—	17	1	no	—
451	C₄×D₄	—	17	2	no	—
452	C₄×D₄	—	17	2	no	—
453	C₄×D₄	—	17	1	no	—
454	C₄×D₄	—	17	2	no	—
455	C₄×D₄	—	17	2	no	—
456	C₄×D₄	—	17	1	no	—
457	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
458	#117	—	17	1	no	—
459	#117	—	17	1	no	—
460	#117	—	17	2	no	—
461	#117	—	17	1	no	—
462	#117	—	17	2	no	—
463	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
464	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
465	C₂×C₂²⋊C₄	—	17	2	no	—
466	C₂×C₂²⋊C₄	—	17	2	no	—
467	C₁₇	#3540	1	1	yes	characteristic, complemented, Sylow
468	C₂⁴	—	17	2	no	—
469	C₂⁴	—	17	1	no	—
470	#41	—	68	2	no	—
471	#41	—	68	2	no	—
472	#41	—	68	2	no	—
473	C₂×Q₈	—	17	1	no	—
474	C₂×Q₈	—	17	2	no	—
475	C₂×Q₈	—	17	2	no	—
476	C₂×Q₈	—	17	1	no	—
477	C₂×Q₈	—	68	2	no	—
478	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
479	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
480	C₂×D₄	—	17	1	no	—
481	C₂×D₄	—	17	2	no	—
482	C₂×D₄	—	17	1	no	—
483	C₂×D₄	—	17	1	no	—
484	C₂×D₄	—	17	1	no	—
485	C₂×D₄	—	17	2	no	—
486	C₂×D₄	—	17	1	no	—
487	C₂×D₄	—	17	1	no	—
488	C₂×D₄	—	17	2	no	—
489	C₂×D₄	—	17	2	no	—
490	C₂×D₄	—	17	2	no	—
491	C₂×D₄	—	17	1	no	—
492	C₂×D₄	—	17	2	no	—
493	C₂×D₄	—	17	2	no	—
494	C₂×D₄	—	17	2	no	—
495	C₂×D₄	—	17	1	no	—
496	C₂×D₄	—	17	2	no	—
497	C₂×D₄	—	68	2	no	—
498	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
499	C₂²×C₄	—	17	1	no	—
500	C₂²×C₄	—	17	1	no	—
501	C₂²×C₄	—	17	1	no	—
502	C₂²×C₄	—	17	1	no	—
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	2	no	—
509	C₂²×C₄	—	17	1	no	—
510	C₂²×C₄	—	68	2	no	—
511	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
513	C₄⋊C₄	—	17	1	no	—
514	C₄⋊C₄	—	17	1	no	—
515	C₄⋊C₄	—	17	1	no	—
516	C₄⋊C₄	—	17	1	no	—
517	C₄⋊C₄	—	17	1	no	—
518	C₄⋊C₄	—	17	2	no	—
519	C₄⋊C₄	—	17	2	no	—
520	C₄⋊C₄	—	17	1	no	—
521	C₄⋊C₄	—	17	2	no	—
522	C₄⋊C₄	—	17	2	no	—
523	C₄⋊C₄	—	17	2	no	—
524	C₄⋊C₄	—	17	2	no	—
525	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
530	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
532	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
533	C₂²⋊C₄	—	17	1	no	—
534	C₂²⋊C₄	—	17	2	no	—
535	C₂²⋊C₄	—	17	1	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	1	no	—
544	C₂²⋊C₄	—	17	1	no	—
545	C₂²⋊C₄	—	17	2	no	—
546	C₂²⋊C₄	—	17	1	no	—
547	C₂²⋊C₄	—	17	1	no	—
548	C₂²⋊C₄	—	17	1	no	—
549	C₂²⋊C₄	—	17	2	no	—
550	C₂²⋊C₄	—	17	2	no	—
551	C₂²⋊C₄	—	17	2	no	—
552	C₂²⋊C₄	—	17	2	no	—
553	C₂²⋊C₄	—	17	2	no	—
554	C₂²⋊C₄	—	17	2	no	—
555	C₂²⋊C₄	—	17	2	no	—
556	C₂²⋊C₄	—	17	1	no	—
557	C₂²⋊C₄	—	17	2	no	—
558	C₂²⋊C₄	—	17	2	no	—
559	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
565	C₄²	—	17	2	no	—
566	C₄²	—	17	2	no	—
567	C₄²	—	17	1	no	—
568	C₄²	—	17	2	no	—
569	C₄²	C₂²×D₁₇	1	2	yes	—
570	C₄²	C₂²×D₁₇	1	1	yes	characteristic
571	C₄²	C₂²×D₁₇	1	2	yes	—
572	C₄²	C₂²×D₁₇	1	2	yes	—
573	C₂³	—	17	1	no	—
574	C₂³	—	17	1	no	—
575	C₂³	—	17	2	no	—
576	C₂³	—	17	2	no	—
577	C₂³	—	17	1	no	—
578	C₂³	—	68	1	no	—
579	C₂³	—	68	1	no	—
580	C₂³	—	68	1	no	—
581	C₂³	—	68	2	no	—
582	C₂³	—	68	2	no	—
583	C₂³	—	68	2	no	—
584	C₂³	C₂³×D₁₇	1	1	yes	characteristic
585	C₂³	C₂³×D₁₇	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	34	2	no	—
589	Q₈	—	68	2	no	—
590	Q₈	—	68	1	no	—
591	Q₈	—	68	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	34	2	no	—
594	D₄	—	34	2	no	—
595	D₄	—	68	2	no	—
596	D₄	—	68	1	no	—
597	D₄	—	68	2	no	—
598	D₄	—	68	2	no	—
599	D₄	—	68	2	no	—
600	D₄	—	68	2	no	—
601	D₄	—	68	1	no	—
602	D₄	—	68	2	no	—
603	D₄	—	68	2	no	—
604	D₄	—	68	1	no	—
605	D₄	—	68	1	no	—
606	D₄	—	68	2	no	—
607	D₄	—	68	1	no	—
608	D₄	—	68	2	no	—
609	D₄	—	68	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	17	1	no	—
613	C₂×C₄	—	17	2	no	—
614	C₂×C₄	—	17	1	no	—
615	C₂×C₄	—	17	1	no	—
616	C₂×C₄	—	17	1	no	—
617	C₂×C₄	—	17	2	no	—
618	C₂×C₄	—	17	1	no	—
619	C₂×C₄	—	34	2	no	—
620	C₂×C₄	—	34	2	no	—
621	C₂×C₄	—	34	2	no	—
622	C₂×C₄	—	68	1	no	—
623	C₂×C₄	—	68	1	no	—
624	C₂×C₄	—	68	2	no	—
625	C₂×C₄	—	68	2	no	—
626	C₂×C₄	—	68	2	no	—
627	C₂×C₄	—	68	2	no	—
628	C₂×C₄	—	68	2	no	—
629	C₂×C₄	—	68	1	no	—
630	C₂×C₄	C₂³×D₁₇	1	2	yes	—
631	C₂×C₄	C₂³×D₁₇	1	2	yes	—
632	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₁₇	1	2	yes	—
634	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₇	1	2	yes	—
638	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	34	1	no	—
646	C₂²	—	34	1	no	—
647	C₂²	—	34	1	no	—
648	C₂²	—	34	2	no	—
649	C₂²	—	34	2	no	—
650	C₂²	—	34	2	no	—
651	C₂²	—	34	1	no	—
652	C₂²	—	34	1	no	—
653	C₂²	—	34	1	no	—
654	C₂²	—	34	2	no	—
655	C₂²	—	34	2	no	—
656	C₂²	—	34	1	no	—
657	C₂²	—	34	1	no	—
658	C₂²	—	34	1	no	—
659	C₂²	—	34	2	no	—
660	C₂²	—	68	4	no	—
661	C₂²	—	136	4	no	—
662	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	2	no	—
671	C₄	—	34	1	no	—
672	C₄	—	34	1	no	—
673	C₄	—	34	1	no	—
674	C₄	—	34	2	no	—
675	C₄	—	34	1	no	—
676	C₄	—	34	2	no	—
677	C₄	—	34	1	no	—
678	C₄	#10587696	1	2	yes	—
679	C₂	—	4	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	68	1	no	—
682	C₂	—	68	1	no	—
683	C₂	—	68	2	no	—
684	C₂	—	68	2	no	—
685	C₂	—	68	1	no	—
686	C₂	C₂×#10587696	1	1	yes	characteristic
687	C₂	#11763645	1	1	yes	characteristic
688	C₂	#11763646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#556	C₂
hypercenter	#556	D₁₇
hypocenter	C₁₇	#3540
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. #11763551	C₂	semidirect
2. #11763550	C₂	semidirect
3. #11763544	C₂	semidirect
4. #11763527	C₂	semidirect
5. #11763525	C₂	semidirect
6. #11763522	C₂	semidirect
7. #11763484	C₂	semidirect
8. #11763471	C₂	semidirect
9. #11763469	C₂	semidirect
10. #11763455	C₂	semidirect
11. #11763450	C₂	semidirect
12. #11763433	C₂	semidirect
13. #11763431	C₂	semidirect
14. #11763431	C₂	semidirect
15. #11763425	C₂	semidirect
16. #11763398	C₂	semidirect
17. #11763393	C₂	semidirect
18. #11763382	C₂	semidirect
19. #11763378	C₂	semidirect
20. #11763322	C₂	semidirect
21. #11763321	C₂	semidirect
22. #11763318	C₂	semidirect
23. C₁₇×#556	C₂	semidirect
25. C₂×Q₈×D₁₇	C₂²	semidirect
28. C₂²×D₆₈	C₂²	semidirect
29. C₂²×C₄×D₁₇	C₂²	semidirect
30. C₁₇×C₄⋊Q₈	C₂²	semidirect
31. C₁₇×#126	C₂²	semidirect
32. C₁₇×#126	C₂²	semidirect
34. C₁₇×C₂²⋊Q₈	C₂²	semidirect
35. C₁₇×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₇	C₂²	semidirect
37. C₄×Q₈×C₁₇	C₂²	semidirect
39. C₁₇×#117	C₂²	semidirect
40. C₁₇×#117	C₂²	semidirect
41. #10587633	C₂²	semidirect
42. #10587633	C₂²	semidirect
43. #10587633	C₂²	semidirect
44. #10587633	C₂²	semidirect
45. #10587632	C₂²	semidirect
46. #10587632	C₂²	semidirect
52. C₄×C₂²⋊D₁₇	C₂²	semidirect
53. #10587610	C₂²	semidirect
54. #10587584	C₂²	semidirect
55. #10587583	C₂²	semidirect
56. #10587583	C₂²	semidirect
57. #10587583	C₂²	semidirect
58. #10587582	C₂²	semidirect
59. #10587582	C₂²	semidirect
60. #10587582	C₂²	semidirect
65. #10587581	C₂²	semidirect
66. #10587581	C₂²	semidirect
67. #10587581	C₂²	semidirect
68. #10587581	C₂²	semidirect
69. #10587580	C₂²	semidirect
70. #10587580	C₂²	semidirect
71. #10587580	C₂²	semidirect
72. #10587580	C₂²	semidirect
73. #10587580	C₂²	semidirect
74. #10587580	C₂²	semidirect
75. #10587580	C₂²	semidirect
76. #10587579	C₂²	semidirect
77. #10587579	C₂²	semidirect
78. #10587579	C₂²	semidirect
79. #10587578	C₂²	semidirect
80. #10587578	C₂²	semidirect
81. #10587578	C₂²	semidirect
82. #10587574	C₂²	semidirect
83. #10587574	C₂²	semidirect
84. #10587573	C₂²	semidirect
85. #10587572	C₂²	semidirect
88. #10587571	C₂²	semidirect
89. #10587571	C₂²	semidirect
92. #10587570	C₂²	semidirect
93. #10587570	C₂²	semidirect
95. #10587569	C₂²	semidirect
98. #10587568	C₂²	semidirect
99. #10587568	C₂²	semidirect
100. #10587568	C₂²	semidirect
101. #10587568	C₂²	semidirect
102. #10587567	C₂²	semidirect
103. C₂²⋊C₄×D₁₇	C₂²	semidirect
104. C₂²⋊C₄×D₁₇	C₂²	semidirect
105. #10587565	C₂²	semidirect
106. #10587564	C₂²	semidirect
107. #10587562	C₂²	semidirect
108. #10587562	C₂²	semidirect
109. #10587561	C₂²	semidirect
110. #10587561	C₂²	semidirect
111. #10587561	C₂²	semidirect
112. #10587561	C₂²	semidirect
113. #10587561	C₂²	semidirect
115. C₄×D₆₈	C₂²	semidirect
116. C₄×D₆₈	C₂²	semidirect
117. C₄×D₆₈	C₂²	semidirect
118. C₄×D₆₈	C₂²	semidirect
119. C₄×D₆₈	C₂²	semidirect
120. #10587558	C₂²	semidirect
121. #10587558	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
339. #556	D₁₇	semidirect
376. C₄⋊Q₈	C₂×D₁₇	semidirect
382. #126	C₂×D₁₇	semidirect
383. #126	C₂×D₁₇	semidirect
418. C₂²⋊Q₈	C₂×D₁₇	semidirect
419. C₂²⋊Q₈	C₂×D₁₇	semidirect
444. C₄×Q₈	C₂×D₁₇	semidirect
445. C₄×Q₈	C₂×D₁₇	semidirect
463. #117	C₂×D₁₇	semidirect
464. #117	C₂×D₁₇	semidirect
467. C₁₇	#3540	semidirect

Maximal subgroups

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

subgroup	index
#11763551	2
#11763550	2
#11763544	2
#11763527	2
#11763525	2
#11763522	2
#11763484	2
#11763471	2
#11763469	2
#11763455	2
#11763450	2
#11763433	2
#11763431	2
#11763425	2
#11763398	2
#11763393	2
#11763382	2
#11763378	2
#11763322	2
#11763321	2
#11763318	2
C₁₇×#556	2
#3540	17