Subgroups — #14542518

Order 2176.

1142 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763522	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763509	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763506	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763505	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763503	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763489	C₂	1	2	yes	maximal, complemented
7	#11763483	C₂	1	2	yes	maximal, complemented
8	#11763462	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763459	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763452	C₂	1	2	yes	maximal, complemented
11	#11763448	C₂	1	2	yes	maximal, complemented
12	#11763436	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763423	C₂	1	2	yes	maximal, complemented
14	#11763409	C₂	1	2	yes	maximal, complemented
15	#11763375	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763358	C₂	1	2	yes	maximal, complemented
17	#11763337	C₂	1	2	yes	maximal, complemented
18	#11763318	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763289	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763281	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#555	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	2	yes	complemented
25	C₂×#63254	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₇	C₂²	1	2	yes	—
28	C₂×#63252	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic
30	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₇×#124	C₂²	1	2	yes	complemented
32	C₁₇×#124	C₂²	1	2	yes	complemented
33	C₁₇×#121	C₂²	1	1	yes	characteristic
34	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
35	C₁₇×#121	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
38	C₁₇×#117	C₂²	1	2	yes	complemented
39	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
40	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
41	#10587632	C₂²	1	2	yes	—
42	#10587632	C₂²	1	2	yes	complemented
43	#10587630	C₂²	1	2	yes	complemented
44	#10587626	C₂²	1	2	yes	complemented
45	#10587625	C₂²	1	2	yes	—
46	#10587625	C₂²	1	2	yes	complemented
47	#10587625	C₂²	1	1	yes	characteristic, complemented
48	#10587624	C₂²	1	1	yes	characteristic
49	#10587624	C₂²	1	1	yes	characteristic, complemented
50	#10587624	C₂²	1	2	yes	complemented
51	#10587623	C₂²	1	2	yes	—
52	#10587623	C₂²	1	1	yes	characteristic
53	#10587621	C₂²	1	2	yes	complemented
54	#10587621	C₂²	1	2	yes	complemented
55	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
56	#10587616	C₂²	1	1	yes	characteristic
57	#10587616	C₂²	1	1	yes	characteristic, complemented
58	#10587615	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
61	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
63	C₂×#63227	C₂²	1	2	yes	—
64	#10587612	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic, complemented
66	#10587584	C₂²	1	2	yes	complemented
67	#10587582	C₂²	1	2	yes	—
68	#10587582	C₂²	1	1	yes	characteristic, complemented
69	#10587581	C₂²	1	1	yes	characteristic
70	#10587581	C₂²	1	1	yes	characteristic, complemented
71	#10587580	C₂²	1	1	yes	characteristic
72	#10587580	C₂²	1	2	yes	complemented
73	#10587580	C₂²	1	2	yes	complemented
74	#10587579	C₂²	1	1	yes	characteristic, complemented
75	#10587578	C₂²	1	1	yes	characteristic
76	#10587578	C₂²	1	1	yes	characteristic
77	#10587578	C₂²	1	1	yes	characteristic, complemented
78	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
79	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
80	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
81	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
82	#10587576	C₂²	1	1	yes	characteristic, complemented
83	#10587575	C₂²	1	2	yes	complemented
84	#10587574	C₂²	1	1	yes	characteristic, complemented
85	#10587571	C₂²	1	2	yes	complemented
86	#10587571	C₂²	1	2	yes	complemented
87	#10587570	C₂²	1	2	yes	—
88	#10587570	C₂²	1	2	yes	complemented
89	#10587570	C₂²	1	2	yes	complemented
90	#10587570	C₂²	1	2	yes	complemented
91	#10587570	C₂²	1	1	yes	characteristic, complemented
92	#10587569	C₂²	1	1	yes	characteristic
93	#10587569	C₂²	1	2	yes	complemented
94	#10587569	C₂²	1	2	yes	complemented
95	#10587569	C₂²	1	2	yes	complemented
96	#10587568	C₂²	1	2	yes	—
97	#10587568	C₂²	1	1	yes	characteristic
98	#10587567	C₂²	1	2	yes	—
99	#10587567	C₂²	1	2	yes	complemented
100	#10587567	C₂²	1	2	yes	complemented
101	#10587567	C₂²	1	2	yes	complemented
102	#10587567	C₂²	1	2	yes	complemented
103	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
106	#10587565	C₂²	1	2	yes	complemented
107	#10587565	C₂²	1	2	yes	complemented
108	#10587564	C₂²	1	2	yes	complemented
109	#10587564	C₂²	1	1	yes	characteristic, complemented
110	#10587563	C₂²	1	2	yes	complemented
111	#10587562	C₂²	1	2	yes	complemented
112	#10587561	C₂²	1	2	yes	complemented
113	C₄×D₆₈	C₂²	1	2	yes	—
114	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₆₈	C₂²	1	2	yes	complemented
117	#10587558	C₂²	1	2	yes	—
118	#10587558	C₂²	1	1	yes	characteristic
119	#10587558	C₂²	1	2	yes	complemented
120	C₄²×D₁₇	C₂²	1	2	yes	complemented
121	#10587556	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	2	yes	—
126	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₇	C₂³	1	2	yes	—
128	C₂×D₄×C₁₇	C₂³	1	2	yes	—
129	C₂×D₄×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	2	yes	—
133	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₇	C₂³	1	2	yes	—
144	C₂²×Dic₁₇	C₂³	1	2	yes	—
145	#63256	—	4	4	no	—
146	#63254	—	4	4	no	—
147	D₄×D₁₇	—	2	4	no	—
148	D₄×D₁₇	—	4	4	no	—
149	#63252	—	2	4	no	—
150	C₂×D₆₈	C₂³	1	1	yes	characteristic
151	C₂×D₆₈	C₂³	1	2	yes	—
152	C₂×D₆₈	C₂³	1	1	yes	characteristic
153	C₂×D₆₈	C₂³	1	1	yes	characteristic
154	C₂×D₆₈	C₂³	1	2	yes	—
155	C₂×C₄×D₁₇	—	2	4	no	—
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	1	yes	characteristic
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×C₄×D₁₇	C₂³	1	2	yes	—
165	C₂×C₄×D₁₇	C₂³	1	2	yes	—
166	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
167	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
168	C₂×Dic₃₄	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
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	2	yes	—
181	C₄²×C₁₇	C₂³	1	2	yes	—
182	C₄²×C₁₇	C₂³	1	2	yes	—
183	C₄²×C₁₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
190	#63227	C₂³	1	2	yes	—
191	#63227	C₂³	1	1	yes	characteristic
192	#63227	C₂³	1	2	yes	—
193	#63227	C₂³	1	1	yes	characteristic
194	#63227	C₂³	1	2	yes	—
195	#63227	C₂³	1	2	yes	—
196	#63227	C₂³	1	2	yes	—
197	#63227	C₂³	1	1	yes	characteristic
198	#63227	C₂³	1	2	yes	—
199	#63227	C₂³	1	1	yes	characteristic
200	#63227	C₂³	1	1	yes	characteristic
201	#63227	C₂³	1	2	yes	—
202	#63227	C₂³	1	1	yes	characteristic
203	#63227	C₂³	1	2	yes	—
204	#63227	C₂³	1	2	yes	—
205	C₄⋊Dic₁₇	C₂³	1	2	yes	—
206	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
209	C₄⋊Dic₁₇	C₂³	1	2	yes	—
210	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
211	#63225	C₂³	1	2	yes	—
212	#63225	C₂³	1	2	yes	—
213	#63225	C₂³	1	2	yes	—
214	#63225	C₂³	1	2	yes	—
215	#63225	C₂³	1	2	yes	—
216	#63225	C₂³	1	2	yes	—
217	#63225	C₂³	1	1	yes	characteristic
218	#63225	C₂³	1	1	yes	characteristic
219	#63225	C₂³	1	1	yes	characteristic
220	#63225	C₂³	1	2	yes	—
221	#63225	C₂³	1	1	yes	characteristic
222	#63225	C₂³	1	2	yes	—
223	C₄×Dic₁₇	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	2	yes	—
230	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₇	—	2	2	no	—
232	C₂²×D₁₇	—	2	2	no	—
233	C₂²×D₁₇	—	2	4	no	—
234	C₂²×D₁₇	—	4	1	no	—
235	C₂²×D₁₇	—	4	2	no	—
236	C₂²×D₁₇	—	4	2	no	—
237	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
238	C₂²×D₁₇	C₂⁴	1	2	yes	—
239	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
241	Q₈×C₁₇	—	4	2	no	—
242	D₄×C₁₇	—	2	2	no	—
243	D₄×C₁₇	—	4	2	no	—
244	D₄×C₁₇	—	4	2	no	—
245	D₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	—	2	2	no	—
247	C₂×C₄×C₁₇	—	2	2	no	—
248	C₂×C₄×C₁₇	—	4	2	no	—
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	1	yes	characteristic
253	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₇	—	2	2	no	—
258	C₂²⋊D₁₇	—	2	4	no	—
259	C₂²⋊D₁₇	—	2	2	no	—
260	C₂²⋊D₁₇	—	2	2	no	—
261	C₂²⋊D₁₇	—	2	4	no	—
262	C₂²⋊D₁₇	—	4	2	no	—
263	C₂²⋊D₁₇	—	4	1	no	—
264	C₂²⋊D₁₇	—	4	2	no	—
265	C₂²⋊D₁₇	—	4	2	no	—
266	C₂×Dic₁₇	—	2	2	no	—
267	C₂×Dic₁₇	—	4	2	no	—
268	C₂×Dic₁₇	—	4	2	no	—
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	2	yes	—
273	C₂×Dic₁₇	C₂⁴	1	2	yes	—
274	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₇	C₂⁴	1	2	yes	—
276	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
277	D₆₈	—	2	2	no	—
278	D₆₈	—	2	4	no	—
279	D₆₈	—	2	2	no	—
280	D₆₈	—	2	2	no	—
281	D₆₈	—	4	2	no	—
282	C₄×D₁₇	—	2	2	no	—
283	C₄×D₁₇	—	2	4	no	—
284	C₄×D₁₇	—	2	2	no	—
285	C₄×D₁₇	—	2	2	no	—
286	C₄×D₁₇	—	2	2	no	—
287	C₄×D₁₇	—	4	2	no	—
288	C₄×D₁₇	—	4	2	no	—
289	C₄×D₁₇	—	4	2	no	—
290	C₄×D₁₇	—	4	2	no	—
291	C₄×D₁₇	—	4	2	no	—
292	C₄×D₁₇	#41	1	4	yes	complemented
293	Dic₃₄	—	2	2	no	—
294	Dic₃₄	—	4	2	no	—
295	#3494	—	17	1	no	maximal, Sylow
296	C₂²×C₁₇	—	2	1	no	—
297	C₂²×C₁₇	—	2	1	no	—
298	C₂²×C₁₇	—	2	2	no	—
299	C₂²×C₁₇	—	2	1	no	—
300	C₂²×C₁₇	—	2	2	no	—
301	C₂²×C₁₇	—	2	1	no	—
302	C₂²×C₁₇	—	2	1	no	—
303	C₂²×C₁₇	—	2	2	no	—
304	C₂²×C₁₇	—	2	1	no	—
305	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
306	C₂×D₁₇	—	2	1	no	—
307	C₂×D₁₇	—	2	1	no	—
308	C₂×D₁₇	—	2	1	no	—
309	C₂×D₁₇	—	2	1	no	—
310	C₂×D₁₇	—	2	1	no	—
311	C₂×D₁₇	—	2	2	no	—
312	C₂×D₁₇	—	2	1	no	—
313	C₂×D₁₇	—	2	2	no	—
314	C₂×D₁₇	—	2	2	no	—
315	C₂×D₁₇	—	2	1	no	—
316	C₂×D₁₇	—	4	4	no	—
317	C₂×D₁₇	—	8	4	no	—
318	C₂×D₁₇	C₂×#41	1	2	yes	—
319	C₂×D₁₇	H(5,𝔽₂)	1	2	yes	—
320	C₄×C₁₇	—	2	1	no	—
321	C₄×C₁₇	—	2	1	no	—
322	C₄×C₁₇	—	2	2	no	—
323	C₄×C₁₇	—	2	2	no	—
324	C₄×C₁₇	—	2	1	no	—
325	C₄×C₁₇	—	2	2	no	—
326	C₄×C₁₇	—	2	1	no	—
327	C₄×C₁₇	C₂×#41	1	2	yes	—
328	Dic₁₇	—	2	1	no	—
329	Dic₁₇	—	2	1	no	—
330	Dic₁₇	—	2	1	no	—
331	Dic₁₇	—	2	2	no	—
332	Dic₁₇	—	2	2	no	—
333	Dic₁₇	—	2	1	no	—
334	Dic₁₇	—	2	2	no	—
335	Dic₁₇	C₂×#41	1	2	yes	—
336	#555	—	17	1	no	—
337	#555	D₁₇	1	1	yes	characteristic, complemented
338	#553	—	17	1	no	—
339	#553	—	17	1	no	—
340	#553	—	17	1	no	—
341	#553	—	17	1	no	—
342	#551	—	17	2	no	—
343	#551	—	17	2	no	—
344	#547	—	17	1	no	—
345	#547	—	17	1	no	—
346	#546	—	17	2	no	—
347	#546	—	17	2	no	—
348	#544	—	17	1	no	—
349	#542	—	17	2	no	—
350	#540	—	17	2	no	—
351	#535	—	17	1	no	—
352	#532	—	17	2	no	—
353	#529	—	17	2	no	—
354	#525	—	17	1	no	—
355	C₂×#121	—	17	1	no	—
356	#520	—	17	1	no	—
357	#518	—	17	1	no	—
358	C₂×#117	—	17	1	no	—
359	C₂×C₁₇	—	4	1	no	—
360	C₂×C₁₇	—	4	2	no	—
361	C₂×C₁₇	—	4	1	no	—
362	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
363	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂×C₁₇	#585	1	1	yes	characteristic
365	D₁₇	—	2	2	no	—
366	D₁₇	—	2	2	no	—
367	D₁₇	—	4	1	no	—
368	D₁₇	—	4	2	no	—
369	C₂×#41	—	17	2	no	—
370	C₂×#41	—	17	2	no	—
371	C₂×#41	—	17	1	no	—
372	C₂²×D₄	—	17	1	no	—
373	C₂²×D₄	—	17	2	no	—
374	C₂³×C₄	—	17	1	no	—
375	C₄⋊Q₈	—	17	2	no	—
376	C₄⋊Q₈	—	17	1	no	—
377	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
378	#127	—	17	2	no	—
379	#126	—	17	2	no	—
380	#126	—	17	2	no	—
381	#126	—	17	2	no	—
382	#126	—	17	2	no	—
383	#125	—	17	2	no	—
384	#125	—	17	1	no	—
385	#125	—	17	1	no	—
386	#124	—	17	2	no	—
387	#124	—	17	2	no	—
388	#124	—	17	2	no	—
389	#124	C₂×D₁₇	1	2	yes	complemented
390	#124	C₂×D₁₇	1	2	yes	complemented
391	#123	—	17	2	no	—
392	#123	—	17	2	no	—
393	#123	—	17	2	no	—
394	#123	—	17	1	no	—
395	#123	—	17	2	no	—
396	#123	—	17	2	no	—
397	#123	—	17	1	no	—
398	#123	—	17	2	no	—
399	#123	—	17	2	no	—
400	#123	—	17	2	no	—
401	C₂²⋊Q₈	—	17	2	no	—
402	C₂²⋊Q₈	—	17	2	no	—
403	C₂²⋊Q₈	—	17	1	no	—
404	C₂²⋊Q₈	—	17	2	no	—
405	C₂²⋊Q₈	—	17	1	no	—
406	C₂²⋊Q₈	—	17	2	no	—
407	#121	—	17	2	no	—
408	#121	—	17	1	no	—
409	#121	—	17	1	no	—
410	#121	—	17	1	no	—
411	#121	—	17	2	no	—
412	#121	—	17	2	no	—
413	#121	—	17	1	no	—
414	#121	—	17	1	no	—
415	#121	—	17	1	no	—
416	#121	—	17	1	no	—
417	#121	—	17	2	no	—
418	#121	—	17	1	no	—
419	#121	—	17	2	no	—
420	#121	—	17	2	no	—
421	#121	—	17	2	no	—
422	#121	C₂×D₁₇	1	1	yes	characteristic
423	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
424	#121	C₂×D₁₇	1	2	yes	complemented
425	#120	—	17	1	no	—
426	#120	—	17	2	no	—
427	#120	—	17	1	no	—
428	#120	—	17	2	no	—
429	C₄×Q₈	—	17	2	no	—
430	C₄×D₄	—	17	1	no	—
431	C₄×D₄	—	17	2	no	—
432	C₄×D₄	—	17	1	no	—
433	C₄×D₄	—	17	1	no	—
434	C₄×D₄	—	17	2	no	—
435	C₄×D₄	—	17	1	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	2	no	—
441	C₄×D₄	—	17	1	no	—
442	C₄×D₄	—	17	2	no	—
443	C₄×D₄	—	17	1	no	—
444	C₄×D₄	—	17	2	no	—
445	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
446	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
447	#117	—	17	1	no	—
448	#117	—	17	1	no	—
449	#117	—	17	1	no	—
450	#117	—	17	1	no	—
451	#117	—	17	2	no	—
452	#117	—	17	2	no	—
453	#117	—	17	1	no	—
454	#117	—	17	2	no	—
455	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
456	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
457	#117	C₂×D₁₇	1	2	yes	complemented
458	C₂×C₄⋊C₄	—	17	1	no	—
459	C₂×C₄⋊C₄	—	17	1	no	—
460	C₂×C₄⋊C₄	—	17	1	no	—
461	C₂×C₄⋊C₄	—	17	1	no	—
462	C₂×C₄⋊C₄	—	17	1	no	—
463	C₂×C₂²⋊C₄	—	17	2	no	—
464	C₂×C₂²⋊C₄	—	17	2	no	—
465	C₂×C₂²⋊C₄	—	17	2	no	—
466	C₂×C₂²⋊C₄	—	17	2	no	—
467	C₂×C₄²	—	17	2	no	—
468	C₁₇	#3494	1	1	yes	characteristic, complemented, Sylow
469	C₂⁴	—	17	1	no	—
470	C₂⁴	—	17	2	no	—
471	#41	—	34	4	no	—
472	#41	—	68	4	no	—
473	#41	—	68	4	no	—
474	C₂×Q₈	—	17	1	no	—
475	C₂×Q₈	—	17	2	no	—
476	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
477	C₂×D₄	—	17	1	no	—
478	C₂×D₄	—	17	2	no	—
479	C₂×D₄	—	17	1	no	—
480	C₂×D₄	—	17	1	no	—
481	C₂×D₄	—	17	2	no	—
482	C₂×D₄	—	17	1	no	—
483	C₂×D₄	—	17	2	no	—
484	C₂×D₄	—	17	2	no	—
485	C₂×D₄	—	17	2	no	—
486	C₂×D₄	—	17	1	no	—
487	C₂×D₄	—	17	1	no	—
488	C₂×D₄	—	17	1	no	—
489	C₂×D₄	—	17	2	no	—
490	C₂×D₄	—	17	2	no	—
491	C₂×D₄	—	34	4	no	—
492	C₂×D₄	—	68	4	no	—
493	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
494	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
495	C₂×D₄	C₂²×D₁₇	1	2	yes	—
496	C₂×D₄	C₂²×D₁₇	1	2	yes	—
497	C₂²×C₄	—	17	1	no	—
498	C₂²×C₄	—	17	1	no	—
499	C₂²×C₄	—	17	2	no	—
500	C₂²×C₄	—	17	2	no	—
501	C₂²×C₄	—	17	1	no	—
502	C₂²×C₄	—	17	2	no	—
503	C₂²×C₄	—	17	1	no	—
504	C₂²×C₄	—	17	1	no	—
505	C₂²×C₄	—	17	1	no	—
506	C₂²×C₄	—	17	2	no	—
507	C₂²×C₄	—	17	2	no	—
508	C₂²×C₄	—	17	2	no	—
509	C₂²×C₄	—	17	2	no	—
510	C₂²×C₄	—	17	2	no	—
511	C₂²×C₄	—	34	4	no	—
512	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
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	2	no	—
521	C₄⋊C₄	—	17	2	no	—
522	C₄⋊C₄	—	17	2	no	—
523	C₄⋊C₄	—	17	1	no	—
524	C₄⋊C₄	—	17	1	no	—
525	C₄⋊C₄	—	17	1	no	—
526	C₄⋊C₄	—	17	2	no	—
527	C₄⋊C₄	—	17	2	no	—
528	C₄⋊C₄	—	17	2	no	—
529	C₄⋊C₄	—	17	2	no	—
530	C₄⋊C₄	—	17	2	no	—
531	C₄⋊C₄	—	17	1	no	—
532	C₄⋊C₄	—	17	1	no	—
533	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
537	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
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	1	no	—
543	C₂²⋊C₄	—	17	1	no	—
544	C₂²⋊C₄	—	17	2	no	—
545	C₂²⋊C₄	—	17	1	no	—
546	C₂²⋊C₄	—	17	1	no	—
547	C₂²⋊C₄	—	17	2	no	—
548	C₂²⋊C₄	—	17	2	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	1	no	—
555	C₂²⋊C₄	—	17	1	no	—
556	C₂²⋊C₄	—	17	1	no	—
557	C₂²⋊C₄	—	17	2	no	—
558	C₂²⋊C₄	—	17	1	no	—
559	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
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	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
566	C₄²	—	17	2	no	—
567	C₄²	—	17	2	no	—
568	C₄²	—	17	2	no	—
569	C₄²	—	17	2	no	—
570	C₄²	—	17	1	no	—
571	C₄²	C₂²×D₁₇	1	2	yes	—
572	C₄²	C₂²×D₁₇	1	1	yes	characteristic
573	C₄²	C₂²×D₁₇	1	2	yes	—
574	C₂³	—	17	1	no	—
575	C₂³	—	17	1	no	—
576	C₂³	—	17	2	no	—
577	C₂³	—	17	1	no	—
578	C₂³	—	34	2	no	—
579	C₂³	—	34	2	no	—
580	C₂³	—	34	4	no	—
581	C₂³	—	68	1	no	—
582	C₂³	—	68	2	no	—
583	C₂³	—	68	2	no	—
584	C₂³	C₂³×D₁₇	1	1	yes	characteristic
585	C₂³	C₂³×D₁₇	1	2	yes	—
586	C₂³	C₂³×D₁₇	1	1	yes	characteristic
587	Q₈	—	4	2	no	—
588	Q₈	—	34	2	no	—
589	Q₈	—	68	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	1	no	—
594	D₄	—	34	4	no	—
595	D₄	—	34	2	no	—
596	D₄	—	34	2	no	—
597	D₄	—	34	4	no	—
598	D₄	—	34	2	no	—
599	D₄	—	34	4	no	—
600	D₄	—	34	2	no	—
601	D₄	—	34	2	no	—
602	D₄	—	34	2	no	—
603	D₄	—	68	2	no	—
604	D₄	—	68	2	no	—
605	D₄	—	68	1	no	—
606	D₄	—	68	2	no	—
607	D₄	—	68	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	17	1	no	—
612	C₂×C₄	—	17	4	no	—
613	C₂×C₄	—	17	1	no	—
614	C₂×C₄	—	17	2	no	—
615	C₂×C₄	—	17	2	no	—
616	C₂×C₄	—	17	1	no	—
617	C₂×C₄	—	17	1	no	—
618	C₂×C₄	—	17	2	no	—
619	C₂×C₄	—	17	1	no	—
620	C₂×C₄	—	34	2	no	—
621	C₂×C₄	—	34	2	no	—
622	C₂×C₄	—	34	4	no	—
623	C₂×C₄	—	34	2	no	—
624	C₂×C₄	—	34	2	no	—
625	C₂×C₄	—	34	2	no	—
626	C₂×C₄	—	68	2	no	—
627	C₂×C₄	—	68	2	no	—
628	C₂×C₄	—	68	2	no	—
629	C₂×C₄	—	68	2	no	—
630	C₂×C₄	—	68	2	no	—
631	C₂×C₄	—	68	2	no	—
632	C₂×C₄	—	68	2	no	—
633	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₇	1	2	yes	—
635	C₂×C₄	C₂³×D₁₇	1	2	yes	—
636	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₇	1	2	yes	—
640	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	17	2	no	—
651	C₂²	—	17	2	no	—
652	C₂²	—	34	1	no	—
653	C₂²	—	34	1	no	—
654	C₂²	—	34	1	no	—
655	C₂²	—	34	1	no	—
656	C₂²	—	34	1	no	—
657	C₂²	—	34	2	no	—
658	C₂²	—	34	1	no	—
659	C₂²	—	34	2	no	—
660	C₂²	—	34	2	no	—
661	C₂²	—	34	1	no	—
662	C₂²	—	68	4	no	—
663	C₂²	—	136	4	no	—
664	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	2	no	—
672	C₄	—	17	2	no	—
673	C₄	—	34	1	no	—
674	C₄	—	34	1	no	—
675	C₄	—	34	2	no	—
676	C₄	—	34	2	no	—
677	C₄	—	34	1	no	—
678	C₄	—	34	1	no	—
679	C₄	—	34	2	no	—
680	C₄	#41×D₁₇	1	2	yes	—
681	C₂	—	4	1	no	—
682	C₂	—	4	2	no	—
683	C₂	—	4	1	no	—
684	C₂	—	34	2	no	—
685	C₂	—	34	2	no	—
686	C₂	—	68	2	no	—
687	C₂	—	68	1	no	—
688	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
689	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
690	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#555	C₂
hypercenter	#555	D₁₇
hypocenter	C₁₇	#3494
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #11763522	C₂	semidirect
2. #11763509	C₂	semidirect
3. #11763506	C₂	semidirect
4. #11763505	C₂	semidirect
5. #11763503	C₂	semidirect
6. #11763489	C₂	semidirect
7. #11763483	C₂	semidirect
8. #11763462	C₂	semidirect
9. #11763459	C₂	semidirect
10. #11763452	C₂	semidirect
11. #11763448	C₂	semidirect
12. #11763436	C₂	semidirect
13. #11763423	C₂	semidirect
14. #11763409	C₂	semidirect
15. #11763375	C₂	semidirect
16. #11763358	C₂	semidirect
17. #11763337	C₂	semidirect
18. #11763318	C₂	semidirect
19. #121×D₁₇	C₂	semidirect
20. #11763289	C₂	semidirect
21. #11763281	C₂	semidirect
22. #117×D₁₇	C₂	semidirect
23. C₁₇×#555	C₂	semidirect
24. C₂×#63256	C₂²	semidirect
25. C₂×#63254	C₂²	semidirect
30. C₁₇×C₄⋊Q₈	C₂²	semidirect
31. C₁₇×#124	C₂²	semidirect
32. C₁₇×#124	C₂²	semidirect
34. C₁₇×#121	C₂²	semidirect
35. C₁₇×#121	C₂²	semidirect
36. C₄×D₄×C₁₇	C₂²	semidirect
37. C₄×D₄×C₁₇	C₂²	semidirect
38. C₁₇×#117	C₂²	semidirect
39. C₁₇×#117	C₂²	semidirect
40. C₁₇×#117	C₂²	semidirect
42. #10587632	C₂²	semidirect
43. #10587630	C₂²	semidirect
44. #10587626	C₂²	semidirect
46. #10587625	C₂²	semidirect
47. #10587625	C₂²	semidirect
49. #10587624	C₂²	semidirect
50. #10587624	C₂²	semidirect
53. #10587621	C₂²	semidirect
54. #10587621	C₂²	semidirect
55. D₄×Dic₁₇	C₂²	semidirect
57. #10587616	C₂²	semidirect
58. #10587615	C₂²	semidirect
59. C₄×C₂²⋊D₁₇	C₂²	semidirect
60. C₄×C₂²⋊D₁₇	C₂²	semidirect
61. C₄×C₂²⋊D₁₇	C₂²	semidirect
62. C₄×C₂²⋊D₁₇	C₂²	semidirect
64. #10587612	C₂²	semidirect
65. C₂×C₄⋊Dic₁₇	C₂²	semidirect
66. #10587584	C₂²	semidirect
68. #10587582	C₂²	semidirect
70. #10587581	C₂²	semidirect
72. #10587580	C₂²	semidirect
73. #10587580	C₂²	semidirect
74. #10587579	C₂²	semidirect
77. #10587578	C₂²	semidirect
79. C₄⋊C₄×D₁₇	C₂²	semidirect
80. C₄⋊C₄×D₁₇	C₂²	semidirect
81. C₄⋊C₄×D₁₇	C₂²	semidirect
82. #10587576	C₂²	semidirect
83. #10587575	C₂²	semidirect
84. #10587574	C₂²	semidirect
85. #10587571	C₂²	semidirect
86. #10587571	C₂²	semidirect
88. #10587570	C₂²	semidirect
89. #10587570	C₂²	semidirect
90. #10587570	C₂²	semidirect
91. #10587570	C₂²	semidirect
93. #10587569	C₂²	semidirect
94. #10587569	C₂²	semidirect
95. #10587569	C₂²	semidirect
99. #10587567	C₂²	semidirect
100. #10587567	C₂²	semidirect
101. #10587567	C₂²	semidirect
102. #10587567	C₂²	semidirect
106. #10587565	C₂²	semidirect
107. #10587565	C₂²	semidirect
108. #10587564	C₂²	semidirect
109. #10587564	C₂²	semidirect
110. #10587563	C₂²	semidirect
111. #10587562	C₂²	semidirect
112. #10587561	C₂²	semidirect
114. C₄×D₆₈	C₂²	semidirect
115. C₄×D₆₈	C₂²	semidirect
116. C₄×D₆₈	C₂²	semidirect
119. #10587558	C₂²	semidirect
120. C₄²×D₁₇	C₂²	semidirect
121. #10587556	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
292. C₄×D₁₇	#41	semidirect
337. #555	D₁₇	semidirect
377. C₄⋊Q₈	C₂×D₁₇	semidirect
389. #124	C₂×D₁₇	semidirect
390. #124	C₂×D₁₇	semidirect
423. #121	C₂×D₁₇	semidirect
424. #121	C₂×D₁₇	semidirect
445. C₄×D₄	C₂×D₁₇	semidirect
446. C₄×D₄	C₂×D₁₇	semidirect
455. #117	C₂×D₁₇	semidirect
456. #117	C₂×D₁₇	semidirect
457. #117	C₂×D₁₇	semidirect
468. C₁₇	#3494	semidirect

Maximal subgroups

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

subgroup	index
#11763522	2
#11763509	2
#11763506	2
#11763505	2
#11763503	2
#11763489	2
#11763483	2
#11763462	2
#11763459	2
#11763452	2
#11763448	2
#11763436	2
#11763423	2
#11763409	2
#11763375	2
#11763358	2
#11763337	2
#11763318	2
#121×D₁₇	2
#11763289	2
#11763281	2
#117×D₁₇	2
C₁₇×#555	2
#3494	17