Subgroups — #17056406

Order 4352.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537733	C₂	1	1	yes	maximal, characteristic, complemented
2	#14537352	C₂	1	1	yes	maximal, characteristic
3	#14529762	C₂	1	1	yes	maximal, characteristic, complemented
4	#14529560	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529538	C₂	1	2	yes	maximal, complemented
6	#14529385	C₂	1	2	yes	maximal, complemented
7	#14529061	C₂	1	2	yes	maximal
8	#14528639	C₂	1	1	yes	maximal, characteristic, complemented
9	#14528631	C₂	1	2	yes	maximal
10	C₄×#10587508	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#3076	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587634	C₂²	1	2	yes	—
13	#11762940	—	2	2	no	—
14	#11762940	—	2	1	no	—
15	Q₈×#3622	—	2	1	no	—
16	C₂×#10587490	C₂²	1	2	yes	—
17	#11762836	—	2	2	no	—
18	#11762836	C₂²	1	2	yes	—
19	#11762836	C₂²	1	2	yes	—
20	#11762833	—	2	1	no	—
21	#11762833	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#3622	—	2	1	no	—
23	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
24	C₂×#10587508	C₂²	1	1	yes	characteristic
25	C₂×#10587508	C₂²	1	1	yes	characteristic
26	#11762765	C₂²	1	2	yes	—
27	C₄×#63223	C₂²	1	1	yes	characteristic
28	C₂×#10587486	C₂²	1	2	yes	—
29	C₄²×Dic₁₇	C₂²	1	1	yes	characteristic
30	#11762574	C₂²	1	2	yes	—
31	#11762568	C₂²	1	1	yes	characteristic
32	#11762568	C₂²	1	2	yes	—
33	#11762568	C₂²	1	2	yes	—
34	#11762568	C₂²	1	1	yes	characteristic
35	#11762563	C₂²	1	2	yes	—
36	C₁₇×#533	C₂²	1	1	yes	characteristic
37	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
38	C₁₇×#479	C₄	1	2	yes	complemented
39	C₁₇×#478	C₄	1	2	yes	complemented
40	C₁₇×#477	C₄	1	1	yes	characteristic, complemented
41	C₁₇×#476	C₄	1	1	yes	characteristic, complemented
42	C₁₇×#475	C₄	1	1	yes	characteristic, complemented
43	C₁₇×#474	C₄	1	1	yes	characteristic, complemented
44	C₁₇×#427	C₂²	1	2	yes	—
45	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₇×#416	C₂²	1	2	yes	—
47	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
49	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₁₇×#125	C₂×C₄	1	2	yes	—
52	C₁₇×C₂²⋊Q₈	—	2	1	no	—
53	C₁₇×C₂²⋊Q₈	—	2	1	no	—
54	C₄×Q₈×C₁₇	—	2	1	no	—
55	C₄×Q₈×C₁₇	—	2	1	no	—
56	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
58	C₄×D₄×C₁₇	—	2	1	no	—
59	C₄×D₄×C₁₇	—	2	1	no	—
60	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
62	C₁₇×#117	—	2	1	no	—
63	C₁₇×#117	C₂³	1	1	yes	characteristic
64	C₁₇×#117	C₂³	1	2	yes	—
65	C₂×C₄²×C₁₇	—	2	1	no	—
66	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
67	#10587634	—	2	4	no	—
68	#10587634	—	4	2	no	—
69	C₂×C₄×Dic₁₇	—	2	1	no	—
70	C₂×C₄×Dic₁₇	—	2	1	no	—
71	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
73	C₂×#63223	—	2	2	no	—
74	C₂×#63223	C₂³	1	1	yes	characteristic
75	C₂×#63223	C₂³	1	2	yes	—
76	C₂×#63223	C₂³	1	1	yes	characteristic
77	C₂²×#3622	—	2	2	no	—
78	C₂²×#3622	C₂³	1	2	yes	—
79	C₁₇×#107	C₂×C₄	1	2	yes	—
80	C₁₇×#107	C₂×C₄	1	2	yes	—
81	C₁₇×#106	C₂×C₄	1	2	yes	—
82	C₁₇×#106	C₂×C₄	1	2	yes	—
83	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
86	C₁₇×#103	C₂×C₄	1	2	yes	—
87	C₁₇×#103	C₂×C₄	1	2	yes	—
88	C₁₇×#102	C₂×C₄	1	2	yes	—
89	C₁₇×#102	C₂×C₄	1	2	yes	—
90	#10587508	—	2	2	no	—
91	#10587508	Q₈	1	4	yes	complemented
92	#10587490	—	4	2	no	—
93	#10587486	—	4	2	no	—
94	C₄⋊#3622	—	2	2	no	—
95	C₄⋊#3622	—	2	2	no	—
96	C₄⋊#3622	—	2	2	no	—
97	C₄⋊#3622	—	2	2	no	—
98	C₄⋊#3622	—	2	1	no	—
99	C₄⋊#3622	—	2	1	no	—
100	C₄⋊#3622	D₄	1	1	yes	characteristic
101	C₄⋊#3622	D₄	1	1	yes	characteristic
102	C₄⋊#3622	D₄	1	2	yes	—
103	#10587474	—	2	2	no	—
104	#10587474	—	2	1	no	—
105	C₄×#3622	—	2	2	no	—
106	C₄×#3622	—	2	1	no	—
107	#41×C₁₇	—	2	1	no	—
108	#41×C₁₇	—	2	1	no	—
109	#41×C₁₇	C₂×Q₈	1	2	yes	—
110	#41×C₁₇	#41	1	2	yes	—
111	C₂×Q₈×C₁₇	—	2	1	no	—
112	C₂×Q₈×C₁₇	—	2	1	no	—
113	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₇	—	2	1	no	—
115	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₇	—	2	1	no	—
117	C₂²×C₄×C₁₇	—	2	1	no	—
118	C₂²×C₄×C₁₇	—	2	1	no	—
119	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
122	C₂²×Dic₁₇	—	2	1	no	—
123	C₂²×Dic₁₇	—	2	1	no	—
124	C₂×C₈×C₁₇	—	2	2	no	—
125	C₂×C₈×C₁₇	—	2	2	no	—
126	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₁₇	—	2	2	no	—
129	C₄⋊C₄×C₁₇	—	2	2	no	—
130	C₄⋊C₄×C₁₇	—	2	1	no	—
131	C₄⋊C₄×C₁₇	—	2	1	no	—
132	C₄⋊C₄×C₁₇	—	2	1	no	—
133	C₄⋊C₄×C₁₇	—	2	1	no	—
134	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₁₇	—	2	2	no	—
139	C₂²⋊C₄×C₁₇	—	2	1	no	—
140	C₂²⋊C₄×C₁₇	—	2	1	no	—
141	C₂²⋊C₄×C₁₇	—	2	1	no	—
142	C₄²×C₁₇	—	2	1	no	—
143	C₄²×C₁₇	—	2	1	no	—
144	C₄²×C₁₇	—	2	2	no	—
145	C₄²×C₁₇	—	2	1	no	—
146	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₁₇	—	2	1	no	—
151	C₄×Dic₁₇	—	2	1	no	—
152	C₄×Dic₁₇	—	2	1	no	—
153	C₄×Dic₁₇	—	4	2	no	—
154	C₄×Dic₁₇	—	4	2	no	—
155	C₄×Dic₁₇	C₂×Q₈	1	2	yes	—
156	#63223	—	2	1	no	—
157	#63223	—	2	1	no	—
158	#63223	—	2	2	no	—
159	#63223	—	2	1	no	—
160	#63223	—	2	2	no	—
161	#63223	—	4	4	no	—
162	#63223	C₂×Q₈	1	2	yes	—
163	C₂×#3622	—	2	1	no	—
164	C₂×#3622	—	2	2	no	—
165	C₂×#3622	—	2	2	no	—
166	C₂×#3622	—	2	1	no	—
167	C₂×#3622	—	2	2	no	—
168	C₂×#3622	—	4	4	no	—
169	C₂×#3622	C₂×D₄	1	2	yes	—
170	C₂×#3622	C₂×D₄	1	2	yes	—
171	#22983	—	17	1	no	maximal, Sylow
172	C₂³×C₁₇	—	2	1	no	—
173	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
174	Q₈×C₁₇	—	2	1	no	—
175	Q₈×C₁₇	—	4	2	no	—
176	Q₈×C₁₇	—	8	1	no	—
177	Q₈×C₁₇	C₄×Q₈	1	2	yes	—
178	D₄×C₁₇	—	2	2	no	—
179	D₄×C₁₇	—	2	2	no	—
180	D₄×C₁₇	—	2	1	no	—
181	D₄×C₁₇	C₄×Q₈	1	2	yes	—
182	C₂×C₄×C₁₇	—	2	1	no	—
183	C₂×C₄×C₁₇	—	2	2	no	—
184	C₂×C₄×C₁₇	—	2	2	no	—
185	C₂×C₄×C₁₇	—	2	2	no	—
186	C₂×C₄×C₁₇	—	2	1	no	—
187	C₂×C₄×C₁₇	—	2	1	no	—
188	C₂×C₄×C₁₇	—	2	2	no	—
189	C₂×C₄×C₁₇	—	2	2	no	—
190	C₂×C₄×C₁₇	—	4	1	no	—
191	C₂×C₄×C₁₇	—	4	2	no	—
192	C₂×C₄×C₁₇	—	8	1	no	—
193	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×Dic₁₇	—	2	2	no	—
204	C₂×Dic₁₇	—	2	2	no	—
205	C₂×Dic₁₇	—	4	1	no	—
206	C₂×Dic₁₇	—	4	1	no	—
207	C₂×Dic₁₇	—	4	1	no	—
208	C₂×Dic₁₇	—	4	1	no	—
209	C₈×C₁₇	—	2	2	no	—
210	C₈×C₁₇	—	2	2	no	—
211	#3622	—	2	2	no	—
212	#3622	—	2	2	no	—
213	#3622	—	2	2	no	—
214	#3622	—	4	2	no	—
215	#3622	—	4	1	no	—
216	#3076	D₁₇	1	1	yes	characteristic
217	#2962	—	17	1	no	—
218	#2906	—	17	1	no	—
219	#1994	—	17	1	no	—
220	#1950	—	17	1	no	—
221	#1946	—	17	2	no	—
222	#1922	—	17	2	no	—
223	#1866	—	17	2	no	—
224	#1767	—	17	1	no	—
225	#1765	—	17	2	no	—
226	C₄×#104	—	17	1	no	—
227	C₂²×C₁₇	—	2	1	no	—
228	C₂²×C₁₇	—	2	1	no	—
229	C₂²×C₁₇	—	2	2	no	—
230	C₂²×C₁₇	—	4	1	no	—
231	C₂²×C₁₇	—	4	1	no	—
232	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂²×C₁₇	#552	1	1	yes	characteristic
234	C₂²×C₁₇	#554	1	1	yes	characteristic
235	C₄×C₁₇	—	2	2	no	—
236	C₄×C₁₇	—	2	1	no	—
237	C₄×C₁₇	—	2	1	no	—
238	C₄×C₁₇	—	2	1	no	—
239	C₄×C₁₇	—	4	1	no	—
240	C₄×C₁₇	—	4	2	no	—
241	C₄×C₁₇	—	4	1	no	—
242	C₄×C₁₇	—	4	2	no	—
243	C₄×C₁₇	#444	1	2	yes	—
244	C₄×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
245	C₄×C₁₇	#520	1	1	yes	characteristic
246	C₄×C₁₇	#546	1	1	yes	characteristic
247	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
248	Dic₁₇	—	4	2	no	—
249	Dic₁₇	—	4	2	no	—
250	C₂×#131	—	17	2	no	—
251	#533	C₂×D₁₇	1	1	yes	characteristic
252	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
253	#479	Dic₁₇	1	2	yes	complemented
254	#478	Dic₁₇	1	2	yes	complemented
255	#477	Dic₁₇	1	1	yes	characteristic, complemented
256	#476	Dic₁₇	1	1	yes	characteristic, complemented
257	#475	Dic₁₇	1	1	yes	characteristic, complemented
258	#474	Dic₁₇	1	1	yes	characteristic, complemented
259	#446	—	34	2	no	—
260	#446	—	34	1	no	—
261	C₈×Q₈	—	34	1	no	—
262	C₂×#108	—	17	2	no	—
263	#427	C₂×D₁₇	1	2	yes	—
264	#424	—	17	2	no	—
265	#424	—	17	2	no	—
266	#424	—	34	2	no	—
267	#423	—	17	1	no	—
268	#423	—	34	1	no	—
269	C₂×C₄⋊C₈	—	17	1	no	—
270	C₂×C₄⋊C₈	—	34	1	no	—
271	C₂×C₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
272	C₂×#104	—	17	1	no	—
273	C₂×#104	—	17	1	no	—
274	#416	C₂×D₁₇	1	2	yes	—
275	#405	—	17	2	no	—
276	C₄×M₁₆	—	17	1	no	—
277	C₂×#97	—	17	2	no	—
278	C₄³	—	17	1	no	—
279	#341	—	17	2	no	—
280	#339	—	17	2	no	—
281	#339	—	17	1	no	—
282	#339	—	17	1	no	—
283	#339	—	17	2	no	—
284	#336	—	17	2	no	—
285	C₂×C₁₇	—	2	1	no	—
286	C₂×C₁₇	—	2	1	no	—
287	C₂×C₁₇	—	4	2	no	—
288	C₂×C₁₇	#2360	1	1	yes	characteristic
289	C₂×C₁₇	C₂×#444	1	1	yes	characteristic
290	C₂×C₁₇	#2956	1	1	yes	characteristic
291	C₂×#41	C₂²×D₁₇	1	1	yes	characteristic
292	#131	—	34	4	no	—
293	#131	—	68	2	no	—
294	C₂×M₁₆	—	17	1	no	—
295	C₂×M₁₆	—	17	2	no	—
296	C₂×M₁₆	—	17	1	no	—
297	C₂×M₁₆	—	34	2	no	—
298	C₂²×C₈	—	17	2	no	—
299	C₂²×C₈	—	34	2	no	—
300	C₂²×C₈	C₂²×D₁₇	1	2	yes	—
301	C₄⋊Q₈	C₂×Dic₁₇	1	1	yes	characteristic
302	C₄⋊Q₈	C₂×Dic₁₇	1	1	yes	characteristic
303	#125	C₂×Dic₁₇	1	2	yes	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
309	C₄×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₂×Dic₁₇	1	1	yes	characteristic
313	C₄×D₄	C₂×Dic₁₇	1	1	yes	characteristic
314	#117	—	2	1	no	—
315	#117	C₂²×D₁₇	1	1	yes	characteristic
316	#117	C₂²×D₁₇	1	2	yes	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	17	1	no	—
319	C₂×C₄²	—	17	1	no	—
320	C₂×C₄²	—	34	1	no	—
321	C₂×C₄²	—	34	1	no	—
322	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
323	#108	—	68	2	no	—
324	#107	C₂×Dic₁₇	1	2	yes	—
325	#107	C₂×Dic₁₇	1	2	yes	—
326	#106	C₂×Dic₁₇	1	2	yes	—
327	#106	C₂×Dic₁₇	1	2	yes	—
328	C₄⋊C₈	—	17	1	no	—
329	C₄⋊C₈	—	17	1	no	—
330	C₄⋊C₈	—	17	2	no	—
331	C₄⋊C₈	—	34	2	no	—
332	C₄⋊C₈	—	34	2	no	—
333	C₄⋊C₈	—	34	2	no	—
334	C₄⋊C₈	—	34	2	no	—
335	C₄⋊C₈	—	34	1	no	—
336	C₄⋊C₈	—	34	1	no	—
337	C₄⋊C₈	C₂×Dic₁₇	1	1	yes	characteristic
338	C₄⋊C₈	C₂×Dic₁₇	1	1	yes	characteristic
339	C₄⋊C₈	C₂×Dic₁₇	1	2	yes	—
340	#104	—	17	4	no	—
341	#104	—	34	2	no	—
342	#103	C₂×Dic₁₇	1	2	yes	—
343	#103	C₂×Dic₁₇	1	2	yes	—
344	#102	C₂×Dic₁₇	1	2	yes	—
345	#102	C₂×Dic₁₇	1	2	yes	—
346	#97	—	34	2	no	—
347	#97	—	34	1	no	—
348	#97	—	68	2	no	—
349	C₄×C₈	—	34	2	no	—
350	C₄×C₈	—	34	1	no	—
351	C₁₇	#22983	1	1	yes	characteristic, complemented, Sylow
352	#41	—	2	1	no	—
353	#41	—	2	1	no	—
354	#41	Q₈×D₁₇	1	2	yes	—
355	#41	#63256	1	2	yes	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	C₂²×Dic₁₇	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂²×Dic₁₇	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	34	1	no	—
365	C₂²×C₄	—	34	1	no	—
366	C₂²×C₄	#63254	1	1	yes	characteristic
367	C₂²×C₄	#63254	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
369	M₁₆	—	17	2	no	—
370	M₁₆	—	34	1	no	—
371	M₁₆	—	34	1	no	—
372	M₁₆	—	34	2	no	—
373	M₁₆	—	34	1	no	—
374	M₁₆	—	34	2	no	—
375	M₁₆	—	68	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	17	2	no	—
379	C₂×C₈	—	17	2	no	—
380	C₂×C₈	—	34	1	no	—
381	C₂×C₈	—	34	2	no	—
382	C₂×C₈	—	34	2	no	—
383	C₂×C₈	—	34	1	no	—
384	C₂×C₈	—	34	2	no	—
385	C₂×C₈	—	68	4	no	—
386	C₂×C₈	C₂²×Dic₁₇	1	2	yes	—
387	C₂×C₈	C₂²×Dic₁₇	1	2	yes	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	C₂²×Dic₁₇	1	2	yes	—
395	C₄⋊C₄	C₂²×Dic₁₇	1	2	yes	—
396	C₄⋊C₄	C₂²×Dic₁₇	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×Dic₁₇	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	17	2	no	—
407	C₄²	—	34	1	no	—
408	C₄²	—	34	1	no	—
409	C₄²	—	34	1	no	—
410	C₄²	—	68	2	no	—
411	C₄²	—	68	2	no	—
412	C₄²	D₄×D₁₇	1	1	yes	characteristic
413	C₄²	D₄×D₁₇	1	1	yes	characteristic
414	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
415	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
416	C₂³	—	2	1	no	—
417	C₂³	C₂×#63254	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	8	1	no	—
421	Q₈	Q₈×Dic₁₇	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	Q₈×Dic₁₇	1	2	yes	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	34	2	no	—
438	C₂×C₄	—	34	2	no	—
439	C₂×C₄	—	68	1	no	—
440	C₂×C₄	—	68	1	no	—
441	C₂×C₄	—	68	1	no	—
442	C₂×C₄	—	68	1	no	—
443	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
444	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
445	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
446	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
448	C₂×C₄	C₂×Q₈×D₁₇	1	1	yes	characteristic
449	C₂×C₄	C₂×#63256	1	1	yes	characteristic
450	C₂×C₄	#10587696	1	1	yes	characteristic
451	C₂×C₄	#10587697	1	1	yes	characteristic
452	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	34	2	no	—
456	C₈	—	34	2	no	—
457	C₈	—	34	2	no	—
458	C₈	—	68	2	no	—
459	C₈	—	68	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₂×D₄×Dic₁₇	1	1	yes	characteristic
466	C₂²	#11763501	1	1	yes	characteristic
467	C₂²	#11763517	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	68	2	no	—
477	C₄	—	68	2	no	—
478	C₄	#11762931	1	2	yes	—
479	C₄	C₂×Q₈×Dic₁₇	1	1	yes	characteristic
480	C₄	#11763292	1	1	yes	characteristic
481	C₄	#11763450	1	1	yes	characteristic
482	C₄	#11763472	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	#14531793	1	1	yes	characteristic
487	C₂	C₂×#11762931	1	1	yes	characteristic
488	C₂	#14537694	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₁₇×#3076	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×#41×C₁₇	C₂³
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	#3076	D₁₇
hypocenter	C₁₇	#22983
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #14537733	C₂	semidirect
3. #14529762	C₂	semidirect
4. #14529560	C₂	semidirect
5. #14529538	C₂	semidirect
6. #14529385	C₂	semidirect
8. #14528639	C₂	semidirect
38. C₁₇×#479	C₄	semidirect
39. C₁₇×#478	C₄	semidirect
40. C₁₇×#477	C₄	semidirect
41. C₁₇×#476	C₄	semidirect
42. C₁₇×#475	C₄	semidirect
43. C₁₇×#474	C₄	semidirect
91. #10587508	Q₈	semidirect
253. #479	Dic₁₇	semidirect
254. #478	Dic₁₇	semidirect
255. #477	Dic₁₇	semidirect
256. #476	Dic₁₇	semidirect
257. #475	Dic₁₇	semidirect
258. #474	Dic₁₇	semidirect
351. C₁₇	#22983	semidirect

Maximal subgroups

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

subgroup	index
#14537733	2
#14537352	2
#14529762	2
#14529560	2
#14529538	2
#14529385	2
#14529061	2
#14528639	2
#14528631	2
C₄×#10587508	2
C₁₇×#3076	2
#22983	17