Subgroups — #14542829

Order 2176.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763531	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763514	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763491	C₂	1	2	yes	maximal, complemented
4	#11763488	C₂	1	2	yes	maximal, complemented
5	#11763486	C₂	1	2	yes	maximal, complemented
6	#11763474	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763469	C₂	1	2	yes	maximal, complemented
8	#11763461	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763460	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	#11763432	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763407	C₂	1	2	yes	maximal, complemented
15	#11763405	C₂	1	2	yes	maximal, complemented
16	#11763361	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763339	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763318	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₁₇	C₂	1	2	yes	maximal, complemented
20	#11763291	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763290	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#10587579	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#63256	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₇	C₂²	1	2	yes	complemented
26	C₂×#63252	C₂²	1	1	yes	characteristic
27	C₂×#63252	C₂²	1	2	yes	complemented
28	C₂²×D₆₈	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₇	C₂²	1	2	yes	—
30	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₇×#125	C₂²	1	2	yes	complemented
32	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₇	C₂²	1	2	yes	—
38	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
41	#10587633	C₂²	1	1	yes	characteristic
42	#10587633	C₂²	1	2	yes	complemented
43	#10587632	C₂²	1	2	yes	complemented
44	#10587632	C₂²	1	2	yes	complemented
45	Q₈×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
46	#10587630	C₂²	1	1	yes	characteristic, complemented
47	#10587625	C₂²	1	1	yes	characteristic
48	#10587623	C₂²	1	2	yes	—
49	#10587621	C₂²	1	1	yes	characteristic
50	#10587616	C₂²	1	1	yes	characteristic
51	#10587615	C₂²	1	2	yes	complemented
52	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₇	C₂²	1	2	yes	complemented
57	C₂×#63227	C₂²	1	2	yes	—
58	#10587612	C₂²	1	1	yes	characteristic, complemented
59	#10587610	C₂²	1	2	yes	—
60	#10587610	C₂²	1	1	yes	characteristic
61	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
62	#10587584	C₂²	1	2	yes	complemented
63	#10587584	C₂²	1	2	yes	complemented
64	#10587584	C₂²	1	2	yes	complemented
65	#10587584	C₂²	1	1	yes	characteristic, complemented
66	#10587583	C₂²	1	1	yes	characteristic, complemented
67	#10587583	C₂²	1	2	yes	complemented
68	#10587582	C₂²	1	2	yes	complemented
69	#10587582	C₂²	1	2	yes	complemented
70	#10587582	C₂²	1	2	yes	complemented
71	#10587582	C₂²	1	2	yes	complemented
72	#10587582	C₂²	1	2	yes	complemented
73	#10587581	C₂²	1	1	yes	characteristic
74	#10587581	C₂²	1	2	yes	—
75	#10587580	C₂²	1	2	yes	—
76	#10587580	C₂²	1	2	yes	—
77	#10587580	C₂²	1	2	yes	complemented
78	#10587580	C₂²	1	2	yes	complemented
79	#10587580	C₂²	1	2	yes	complemented
80	#10587579	C₂²	1	1	yes	characteristic
81	#10587579	C₂²	1	1	yes	characteristic
82	#10587579	C₂²	1	2	yes	—
83	#10587579	C₂²	1	1	yes	characteristic
84	#10587579	C₂²	1	1	yes	characteristic
85	#10587579	C₂²	1	2	yes	—
86	#10587579	C₂²	1	1	yes	characteristic
87	#10587579	C₂²	1	2	yes	complemented
88	#10587578	C₂²	1	2	yes	complemented
89	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
91	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
92	C₄⋊C₄×D₁₇	C₂²	1	2	yes	complemented
93	#10587575	C₂²	1	1	yes	characteristic, complemented
94	#10587575	C₂²	1	2	yes	complemented
95	#10587575	C₂²	1	2	yes	complemented
96	#10587574	C₂²	1	1	yes	characteristic, complemented
97	#10587574	C₂²	1	1	yes	characteristic, complemented
98	#10587573	C₂²	1	2	yes	complemented
99	#10587573	C₂²	1	1	yes	characteristic, complemented
100	#10587573	C₂²	1	1	yes	characteristic, complemented
101	#10587572	C₂²	1	1	yes	characteristic
102	#10587571	C₂²	1	1	yes	characteristic, complemented
103	#10587571	C₂²	1	2	yes	complemented
104	#10587570	C₂²	1	2	yes	—
105	#10587570	C₂²	1	2	yes	complemented
106	#10587569	C₂²	1	2	yes	complemented
107	#10587569	C₂²	1	2	yes	complemented
108	#10587568	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₇	C₂²	1	2	yes	—
111	#10587565	C₂²	1	1	yes	characteristic, complemented
112	#10587564	C₂²	1	1	yes	characteristic
113	#10587564	C₂²	1	2	yes	—
114	#10587563	C₂²	1	2	yes	—
115	#10587562	C₂²	1	2	yes	complemented
116	#10587561	C₂²	1	1	yes	characteristic
117	C₄×D₆₈	C₂²	1	1	yes	characteristic
118	C₄×D₆₈	C₂²	1	2	yes	complemented
119	#10587558	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	1	yes	characteristic, complemented
123	C₂³×D₁₇	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₇	C₂³	1	2	yes	—
126	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₇	C₂³	1	2	yes	—
135	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
137	#63256	—	2	4	no	—
138	Q₈×D₁₇	—	4	4	no	—
139	#63252	—	2	4	no	—
140	#63252	—	4	4	no	—
141	C₂×D₆₈	—	2	4	no	—
142	C₂×D₆₈	C₂³	1	1	yes	characteristic
143	C₂×D₆₈	C₂³	1	2	yes	—
144	C₂×D₆₈	C₂³	1	2	yes	—
145	C₂×D₆₈	C₂³	1	2	yes	—
146	C₂×D₆₈	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₇	—	4	4	no	—
148	C₂×C₄×D₁₇	C₂³	1	2	yes	—
149	C₂×C₄×D₁₇	C₂³	1	2	yes	—
150	C₂×C₄×D₁₇	C₂³	1	2	yes	—
151	C₂×C₄×D₁₇	C₂³	1	2	yes	—
152	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₇	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×Dic₃₄	C₂³	1	1	yes	characteristic
159	C₂×Dic₃₄	C₂³	1	2	yes	—
160	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
161	C₂×Dic₃₄	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
163	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
164	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
166	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
168	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₇	C₂³	1	2	yes	—
173	C₂²⋊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	C₄²×C₁₇	C₂³	1	2	yes	—
177	C₄²×C₁₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
183	#63227	C₂³	1	2	yes	—
184	#63227	C₂³	1	1	yes	characteristic
185	#63227	C₂³	1	2	yes	—
186	#63227	C₂³	1	2	yes	—
187	#63227	C₂³	1	1	yes	characteristic
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	#63227	C₂³	1	2	yes	—
196	#63227	C₂³	1	2	yes	—
197	#63227	C₂³	1	2	yes	—
198	#63227	C₂³	1	1	yes	characteristic
199	#63227	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₇	C₂³	1	2	yes	—
203	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₇	C₂³	1	2	yes	—
205	C₄⋊Dic₁₇	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	1	yes	characteristic
210	#63225	C₂³	1	2	yes	—
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	1	yes	characteristic
217	#63225	C₂³	1	1	yes	characteristic
218	#63225	C₂³	1	2	yes	—
219	#63225	C₂³	1	2	yes	—
220	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₇	C₂³	1	2	yes	—
223	C₄×Dic₁₇	C₂³	1	2	yes	—
224	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₇	C₂³	1	2	yes	—
226	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
231	C₂²×D₁₇	—	2	4	no	—
232	C₂²×D₁₇	—	4	2	no	—
233	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₇	C₂⁴	1	2	yes	—
235	C₂²×D₁₇	C₂⁴	1	2	yes	—
236	Q₈×C₁₇	—	2	2	no	—
237	Q₈×C₁₇	—	4	2	no	—
238	D₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	2	no	—
240	C₂×C₄×C₁₇	—	2	2	no	—
241	C₂×C₄×C₁₇	—	4	2	no	—
242	C₂×C₄×C₁₇	—	4	2	no	—
243	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₁₇	—	2	2	no	—
253	C₂²⋊D₁₇	—	2	4	no	—
254	C₂²⋊D₁₇	—	2	2	no	—
255	C₂²⋊D₁₇	—	4	2	no	—
256	C₂×Dic₁₇	—	2	2	no	—
257	C₂×Dic₁₇	—	2	2	no	—
258	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₇	C₂⁴	1	2	yes	—
261	C₂×Dic₁₇	C₂⁴	1	2	yes	—
262	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
267	D₆₈	—	2	4	no	—
268	D₆₈	—	2	4	no	—
269	D₆₈	—	2	2	no	—
270	D₆₈	—	4	2	no	—
271	D₆₈	#41	1	4	yes	complemented
272	C₄×D₁₇	—	2	4	no	—
273	C₄×D₁₇	—	2	4	no	—
274	C₄×D₁₇	—	2	2	no	—
275	C₄×D₁₇	—	2	4	no	—
276	C₄×D₁₇	—	2	4	no	—
277	C₄×D₁₇	—	4	2	no	—
278	C₄×D₁₇	—	4	2	no	—
279	C₄×D₁₇	—	4	2	no	—
280	C₄×D₁₇	—	4	2	no	—
281	C₄×D₁₇	—	4	2	no	—
282	Dic₃₄	—	2	2	no	—
283	Dic₃₄	—	2	4	no	—
284	Dic₃₄	—	2	2	no	—
285	Dic₃₄	—	4	2	no	—
286	#3520	—	17	1	no	maximal, Sylow
287	C₂²×C₁₇	—	2	1	no	—
288	C₂²×C₁₇	—	2	1	no	—
289	C₂²×C₁₇	—	2	1	no	—
290	C₂²×C₁₇	—	2	1	no	—
291	C₂²×C₁₇	—	2	1	no	—
292	C₂²×C₁₇	2₋¹⁺⁴	1	2	yes	—
293	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
294	C₂×D₁₇	—	2	2	no	—
295	C₂×D₁₇	—	2	2	no	—
296	C₂×D₁₇	—	2	1	no	—
297	C₂×D₁₇	—	2	2	no	—
298	C₂×D₁₇	—	2	2	no	—
299	C₂×D₁₇	—	2	1	no	—
300	C₂×D₁₇	—	2	1	no	—
301	C₂×D₁₇	—	2	2	no	—
302	C₂×D₁₇	—	4	8	no	—
303	C₂×D₁₇	C₂×#41	1	4	yes	—
304	C₄×C₁₇	—	2	1	no	—
305	C₄×C₁₇	—	2	2	no	—
306	C₄×C₁₇	—	2	1	no	—
307	C₄×C₁₇	—	2	1	no	—
308	C₄×C₁₇	—	2	2	no	—
309	C₄×C₁₇	—	2	2	no	—
310	C₄×C₁₇	—	2	2	no	—
311	C₄×C₁₇	—	2	1	no	—
312	C₄×C₁₇	C₂×#41	1	2	yes	—
313	Dic₁₇	—	2	2	no	—
314	Dic₁₇	—	2	1	no	—
315	Dic₁₇	—	2	1	no	—
316	Dic₁₇	—	2	2	no	—
317	Dic₁₇	—	2	1	no	—
318	Dic₁₇	—	2	1	no	—
319	Dic₁₇	—	2	1	no	—
320	Dic₁₇	—	2	1	no	—
321	Dic₁₇	H(5,𝔽₂)	1	2	yes	—
322	#556	—	17	1	no	—
323	#554	—	17	1	no	—
324	#554	D₁₇	1	1	yes	characteristic, complemented
325	#552	—	17	2	no	—
326	#551	—	17	2	no	—
327	#551	—	17	2	no	—
328	D₄×Q₈	—	17	1	no	—
329	#548	—	17	2	no	—
330	#547	—	17	1	no	—
331	#547	—	17	1	no	—
332	#546	—	17	1	no	—
333	#546	—	17	1	no	—
334	#542	—	17	1	no	—
335	#542	—	17	1	no	—
336	#539	—	17	2	no	—
337	#539	—	17	2	no	—
338	#533	—	17	1	no	—
339	#529	—	17	1	no	—
340	#525	—	17	2	no	—
341	C₂×C₂²⋊Q₈	—	17	2	no	—
342	#520	—	17	1	no	—
343	#520	—	17	1	no	—
344	C₂×C₄×D₄	—	17	1	no	—
345	C₂×C₁₇	—	2	2	no	—
346	C₂×C₁₇	—	4	1	no	—
347	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
348	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
350	D₁₇	—	2	4	no	—
351	D₁₇	—	4	1	no	—
352	D₁₇	—	4	2	no	—
353	C₂×#41	—	17	1	no	—
354	C₂×#41	—	17	1	no	—
355	C₂×#41	—	17	2	no	—
356	C₂²×Q₈	—	17	2	no	—
357	C₂²×D₄	—	17	1	no	—
358	C₂³×C₄	—	17	2	no	—
359	C₄⋊Q₈	—	17	1	no	—
360	C₄⋊Q₈	—	17	1	no	—
361	C₄⋊Q₈	—	17	1	no	—
362	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
363	#126	—	17	1	no	—
364	#126	—	17	2	no	—
365	#126	—	17	2	no	—
366	#126	—	17	2	no	—
367	#126	—	17	1	no	—
368	#126	—	17	2	no	—
369	#125	—	17	1	no	—
370	#125	—	17	2	no	—
371	#125	—	17	2	no	—
372	#125	C₂×D₁₇	1	2	yes	complemented
373	#124	—	17	1	no	—
374	#124	—	17	2	no	—
375	#124	—	17	1	no	—
376	#124	—	17	2	no	—
377	#124	—	17	1	no	—
378	#123	—	17	1	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	#123	—	17	1	no	—
387	#123	—	17	2	no	—
388	C₂²⋊Q₈	—	17	2	no	—
389	C₂²⋊Q₈	—	17	2	no	—
390	C₂²⋊Q₈	—	17	2	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	—	17	2	no	—
396	C₂²⋊Q₈	—	17	2	no	—
397	C₂²⋊Q₈	—	17	2	no	—
398	C₂²⋊Q₈	—	17	1	no	—
399	C₂²⋊Q₈	—	17	1	no	—
400	C₂²⋊Q₈	—	17	2	no	—
401	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	—
402	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
403	C₂²⋊Q₈	C₂×D₁₇	1	2	yes	complemented
404	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
405	#121	—	17	1	no	—
406	#121	—	17	1	no	—
407	#121	—	17	2	no	—
408	#121	—	17	1	no	—
409	#121	—	17	2	no	—
410	#121	—	17	2	no	—
411	#120	—	17	2	no	—
412	#120	—	17	2	no	—
413	C₄×Q₈	—	17	1	no	—
414	C₄×Q₈	—	17	1	no	—
415	C₄×Q₈	—	17	1	no	—
416	C₄×Q₈	—	17	2	no	—
417	C₄×Q₈	—	17	1	no	—
418	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
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	1	no	—
425	C₄×D₄	—	17	2	no	—
426	C₄×D₄	—	17	1	no	—
427	C₄×D₄	—	17	1	no	—
428	C₄×D₄	—	17	1	no	—
429	C₄×D₄	—	17	2	no	—
430	C₄×D₄	—	17	1	no	—
431	C₄×D₄	—	17	2	no	—
432	C₄×D₄	—	17	2	no	—
433	C₄×D₄	—	17	1	no	—
434	C₄×D₄	C₂×D₁₇	1	2	yes	—
435	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
436	#117	—	17	1	no	—
437	#117	—	17	2	no	—
438	#117	—	17	2	no	—
439	#117	—	17	1	no	—
440	#117	—	17	2	no	—
441	#117	—	17	2	no	—
442	C₂×C₄⋊C₄	—	17	2	no	—
443	C₂×C₄⋊C₄	—	17	2	no	—
444	C₂×C₄⋊C₄	—	17	1	no	—
445	C₂×C₄⋊C₄	—	17	2	no	—
446	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
448	C₂×C₂²⋊C₄	—	17	2	no	—
449	C₂×C₂²⋊C₄	—	17	2	no	—
450	C₂×C₂²⋊C₄	—	17	2	no	—
451	C₂×C₄²	—	17	1	no	—
452	C₁₇	#3520	1	1	yes	characteristic, complemented, Sylow
453	C₂⁴	—	17	2	no	—
454	#41	—	34	4	no	—
455	#41	—	34	4	no	—
456	#41	—	68	4	no	—
457	C₂×Q₈	—	17	1	no	—
458	C₂×Q₈	—	17	1	no	—
459	C₂×Q₈	—	17	2	no	—
460	C₂×Q₈	—	17	2	no	—
461	C₂×Q₈	—	68	4	no	—
462	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₁₇	1	2	yes	—
464	C₂×D₄	—	17	1	no	—
465	C₂×D₄	—	17	2	no	—
466	C₂×D₄	—	17	1	no	—
467	C₂×D₄	—	17	2	no	—
468	C₂×D₄	—	17	1	no	—
469	C₂×D₄	—	17	2	no	—
470	C₂×D₄	—	17	2	no	—
471	C₂×D₄	—	17	1	no	—
472	C₂×D₄	—	17	2	no	—
473	C₂×D₄	—	34	4	no	—
474	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
475	C₂²×C₄	—	17	1	no	—
476	C₂²×C₄	—	17	1	no	—
477	C₂²×C₄	—	17	2	no	—
478	C₂²×C₄	—	17	2	no	—
479	C₂²×C₄	—	17	1	no	—
480	C₂²×C₄	—	17	2	no	—
481	C₂²×C₄	—	17	2	no	—
482	C₂²×C₄	—	17	2	no	—
483	C₂²×C₄	—	17	2	no	—
484	C₂²×C₄	—	17	2	no	—
485	C₂²×C₄	—	17	2	no	—
486	C₂²×C₄	—	17	2	no	—
487	C₂²×C₄	—	68	4	no	—
488	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
491	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
492	C₄⋊C₄	—	17	1	no	—
493	C₄⋊C₄	—	17	1	no	—
494	C₄⋊C₄	—	17	2	no	—
495	C₄⋊C₄	—	17	1	no	—
496	C₄⋊C₄	—	17	2	no	—
497	C₄⋊C₄	—	17	1	no	—
498	C₄⋊C₄	—	17	2	no	—
499	C₄⋊C₄	—	17	2	no	—
500	C₄⋊C₄	—	17	2	no	—
501	C₄⋊C₄	—	17	2	no	—
502	C₄⋊C₄	—	17	1	no	—
503	C₄⋊C₄	—	17	1	no	—
504	C₄⋊C₄	—	17	1	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	2	no	—
510	C₄⋊C₄	—	17	1	no	—
511	C₄⋊C₄	—	17	1	no	—
512	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
517	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₇	1	2	yes	—
522	C₂²⋊C₄	—	17	1	no	—
523	C₂²⋊C₄	—	17	2	no	—
524	C₂²⋊C₄	—	17	1	no	—
525	C₂²⋊C₄	—	17	1	no	—
526	C₂²⋊C₄	—	17	1	no	—
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	1	no	—
538	C₂²⋊C₄	—	17	1	no	—
539	C₂²⋊C₄	—	17	2	no	—
540	C₂²⋊C₄	—	17	2	no	—
541	C₂²⋊C₄	—	17	1	no	—
542	C₂²⋊C₄	—	17	2	no	—
543	C₂²⋊C₄	—	17	1	no	—
544	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₁₇	1	2	yes	—
548	C₄²	—	17	1	no	—
549	C₄²	—	17	1	no	—
550	C₄²	—	17	1	no	—
551	C₄²	—	17	1	no	—
552	C₄²	—	17	2	no	—
553	C₄²	—	17	2	no	—
554	C₄²	—	17	2	no	—
555	C₄²	—	17	1	no	—
556	C₄²	C₂²×D₁₇	1	2	yes	—
557	C₄²	C₂²×D₁₇	1	1	yes	characteristic
558	C₂³	—	17	2	no	—
559	C₂³	—	17	2	no	—
560	C₂³	—	17	1	no	—
561	C₂³	—	34	4	no	—
562	C₂³	—	34	4	no	—
563	C₂³	—	68	2	no	—
564	C₂³	C₂³×D₁₇	1	1	yes	characteristic
565	C₂³	C₂³×D₁₇	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	34	2	no	—
569	Q₈	—	34	4	no	—
570	Q₈	—	34	2	no	—
571	Q₈	—	68	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	17	4	no	—
574	D₄	—	34	4	no	—
575	D₄	—	34	4	no	—
576	D₄	—	34	2	no	—
577	D₄	—	34	4	no	—
578	D₄	—	34	2	no	—
579	D₄	—	34	2	no	—
580	D₄	—	68	2	no	—
581	D₄	—	68	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	17	1	no	—
587	C₂×C₄	—	17	1	no	—
588	C₂×C₄	—	17	1	no	—
589	C₂×C₄	—	17	1	no	—
590	C₂×C₄	—	17	2	no	—
591	C₂×C₄	—	17	1	no	—
592	C₂×C₄	—	17	1	no	—
593	C₂×C₄	—	17	2	no	—
594	C₂×C₄	—	17	1	no	—
595	C₂×C₄	—	34	4	no	—
596	C₂×C₄	—	34	4	no	—
597	C₂×C₄	—	34	4	no	—
598	C₂×C₄	—	34	4	no	—
599	C₂×C₄	—	34	2	no	—
600	C₂×C₄	—	34	2	no	—
601	C₂×C₄	—	34	2	no	—
602	C₂×C₄	—	68	2	no	—
603	C₂×C₄	—	68	2	no	—
604	C₂×C₄	—	68	2	no	—
605	C₂×C₄	—	68	2	no	—
606	C₂×C₄	—	68	2	no	—
607	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₇	1	2	yes	—
609	C₂×C₄	C₂³×D₁₇	1	2	yes	—
610	C₂×C₄	C₂³×D₁₇	1	2	yes	—
611	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₇	1	2	yes	—
615	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	17	4	no	—
622	C₂²	—	34	2	no	—
623	C₂²	—	34	2	no	—
624	C₂²	—	34	1	no	—
625	C₂²	—	34	2	no	—
626	C₂²	—	34	2	no	—
627	C₂²	—	34	1	no	—
628	C₂²	—	34	1	no	—
629	C₂²	—	34	2	no	—
630	C₂²	—	68	8	no	—
631	C₂²	#10587694	1	2	yes	—
632	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	17	2	no	—
642	C₄	—	34	1	no	—
643	C₄	—	34	2	no	—
644	C₄	—	34	1	no	—
645	C₄	—	34	2	no	—
646	C₄	—	34	1	no	—
647	C₄	—	34	1	no	—
648	C₄	—	34	1	no	—
649	C₄	—	34	1	no	—
650	C₄	#41×D₁₇	1	2	yes	—
651	C₂	—	2	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	34	4	no	—
654	C₂	—	68	2	no	—
655	C₂	—	68	1	no	—
656	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
657	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
658	C₂	C₂×#10587694	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#554	C₂
hypercenter	#554	D₁₇
hypocenter	C₁₇	#3520
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #11763531	C₂	semidirect
2. #11763514	C₂	semidirect
3. #11763491	C₂	semidirect
4. #11763488	C₂	semidirect
5. #11763486	C₂	semidirect
6. #11763474	C₂	semidirect
7. #11763469	C₂	semidirect
8. #11763461	C₂	semidirect
9. #11763460	C₂	semidirect
10. #11763455	C₂	semidirect
11. #11763450	C₂	semidirect
12. #11763433	C₂	semidirect
13. #11763432	C₂	semidirect
14. #11763407	C₂	semidirect
15. #11763405	C₂	semidirect
16. #11763361	C₂	semidirect
17. #11763339	C₂	semidirect
18. #11763318	C₂	semidirect
19. C₂²⋊Q₈×D₁₇	C₂	semidirect
20. #11763291	C₂	semidirect
21. #11763290	C₂	semidirect
22. C₂×#10587579	C₂	semidirect
23. C₁₇×#554	C₂	semidirect
25. C₂×Q₈×D₁₇	C₂²	semidirect
27. C₂×#63252	C₂²	semidirect
30. C₁₇×C₄⋊Q₈	C₂²	semidirect
31. C₁₇×#125	C₂²	semidirect
34. C₁₇×C₂²⋊Q₈	C₂²	semidirect
35. C₁₇×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₇	C₂²	semidirect
40. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
42. #10587633	C₂²	semidirect
43. #10587632	C₂²	semidirect
44. #10587632	C₂²	semidirect
45. Q₈×Dic₁₇	C₂²	semidirect
46. #10587630	C₂²	semidirect
51. #10587615	C₂²	semidirect
54. C₄×C₂²⋊D₁₇	C₂²	semidirect
55. C₄×C₂²⋊D₁₇	C₂²	semidirect
56. C₄×C₂²⋊D₁₇	C₂²	semidirect
58. #10587612	C₂²	semidirect
62. #10587584	C₂²	semidirect
63. #10587584	C₂²	semidirect
64. #10587584	C₂²	semidirect
65. #10587584	C₂²	semidirect
66. #10587583	C₂²	semidirect
67. #10587583	C₂²	semidirect
68. #10587582	C₂²	semidirect
69. #10587582	C₂²	semidirect
70. #10587582	C₂²	semidirect
71. #10587582	C₂²	semidirect
72. #10587582	C₂²	semidirect
77. #10587580	C₂²	semidirect
78. #10587580	C₂²	semidirect
79. #10587580	C₂²	semidirect
87. #10587579	C₂²	semidirect
88. #10587578	C₂²	semidirect
89. C₄⋊C₄×D₁₇	C₂²	semidirect
90. C₄⋊C₄×D₁₇	C₂²	semidirect
91. C₄⋊C₄×D₁₇	C₂²	semidirect
92. C₄⋊C₄×D₁₇	C₂²	semidirect
93. #10587575	C₂²	semidirect
94. #10587575	C₂²	semidirect
95. #10587575	C₂²	semidirect
96. #10587574	C₂²	semidirect
97. #10587574	C₂²	semidirect
98. #10587573	C₂²	semidirect
99. #10587573	C₂²	semidirect
100. #10587573	C₂²	semidirect
102. #10587571	C₂²	semidirect
103. #10587571	C₂²	semidirect
105. #10587570	C₂²	semidirect
106. #10587569	C₂²	semidirect
107. #10587569	C₂²	semidirect
111. #10587565	C₂²	semidirect
115. #10587562	C₂²	semidirect
118. C₄×D₆₈	C₂²	semidirect
119. #10587558	C₂²	semidirect
120. #10587558	C₂²	semidirect
121. #10587558	C₂²	semidirect
122. C₄×Dic₃₄	C₂²	semidirect
271. D₆₈	#41	semidirect
324. #554	D₁₇	semidirect
362. C₄⋊Q₈	C₂×D₁₇	semidirect
372. #125	C₂×D₁₇	semidirect
403. C₂²⋊Q₈	C₂×D₁₇	semidirect
404. C₂²⋊Q₈	C₂×D₁₇	semidirect
418. C₄×Q₈	C₂×D₁₇	semidirect
447. C₂×C₄⋊C₄	C₂×D₁₇	semidirect
452. C₁₇	#3520	semidirect

Maximal subgroups

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

subgroup	index
#11763531	2
#11763514	2
#11763491	2
#11763488	2
#11763486	2
#11763474	2
#11763469	2
#11763461	2
#11763460	2
#11763455	2
#11763450	2
#11763433	2
#11763432	2
#11763407	2
#11763405	2
#11763361	2
#11763339	2
#11763318	2
C₂²⋊Q₈×D₁₇	2
#11763291	2
#11763290	2
C₂×#10587579	2
C₁₇×#554	2
#3520	17