Subgroups — #17056400

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	#14538572	C₂	1	1	yes	maximal, characteristic
2	#14537731	C₂	1	1	yes	maximal, characteristic, complemented
3	#14537352	C₂	1	1	yes	maximal, characteristic
4	#14529761	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529559	C₂	1	1	yes	maximal, characteristic, complemented
6	#14529536	C₂	1	2	yes	maximal, complemented
7	#14529386	C₂	1	2	yes	maximal, complemented
8	#14529057	C₂	1	2	yes	maximal
9	#14528637	C₂	1	1	yes	maximal, characteristic, complemented
10	#14528629	C₂	1	2	yes	maximal
11	C₄×C₁₇×#104	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587634	C₂²	1	2	yes	—
13	#11763366	C₂²	1	1	yes	characteristic
14	#11763116	C₄	1	2	yes	complemented
15	#11763109	C₄	1	2	yes	complemented
16	#11763104	C₄	1	1	yes	characteristic, complemented
17	#11763099	C₄	1	1	yes	characteristic, complemented
18	#11763094	C₄	1	1	yes	characteristic, complemented
19	#11763089	C₄	1	1	yes	characteristic, complemented
20	#11762939	—	2	1	no	—
21	#11762937	—	2	2	no	—
22	C₈×Dic₃₄	—	2	1	no	—
23	C₂×#10587493	C₂²	1	2	yes	—
24	#11762845	C₂²	1	2	yes	—
25	#11762837	C₂²	1	2	yes	—
26	#11762836	—	2	2	no	—
27	#11762836	C₂²	1	2	yes	—
28	#11762833	—	2	1	no	—
29	#11762833	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊#3622	—	2	1	no	—
31	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
33	#11762805	C₂²	1	2	yes	—
34	#11762767	C₂²	1	2	yes	—
35	C₂×#10587474	C₂²	1	2	yes	—
36	#11762573	C₂²	1	2	yes	—
37	#11762569	C₂²	1	2	yes	—
38	#11762569	C₂²	1	2	yes	—
39	#11762564	C₂²	1	2	yes	—
40	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
42	C₂×C₁₇×#104	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
44	C₄³×C₁₇	C₂²	1	1	yes	characteristic
45	C₁₇×#339	C₂²	1	1	yes	characteristic
46	C₁₇×#339	C₂²	1	1	yes	characteristic
47	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₁₇	—	2	1	no	—
53	C₄×D₄×C₁₇	—	2	1	no	—
54	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
55	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
56	C₁₇×#117	—	2	1	no	—
57	C₁₇×#117	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₇	—	2	1	no	—
59	C₂×C₄²×C₁₇	—	2	1	no	—
60	C₂×C₄²×C₁₇	—	2	1	no	—
61	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
64	#10587634	—	2	4	no	—
65	#10587634	—	4	2	no	—
66	#10587612	C₂³	1	2	yes	—
67	#10587610	—	2	1	no	—
68	#10587610	—	2	1	no	—
69	C₂×#63223	—	2	2	no	—
70	C₂×#63223	C₂³	1	2	yes	—
71	C₂²×#3622	—	2	2	no	—
72	C₂²×#3622	C₂³	1	2	yes	—
73	C₂²×#3622	C₂³	1	2	yes	—
74	#10587556	C₂×C₄	1	2	yes	—
75	#10587555	C₂×C₄	1	1	yes	characteristic
76	#10587555	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₃₄	—	2	1	no	—
78	C₄×Dic₃₄	—	2	1	no	—
79	C₁₇×#104	—	2	2	no	—
80	C₁₇×#104	Q₈	1	4	yes	complemented
81	C₁₇×#97	—	2	1	no	—
82	C₄×C₈×C₁₇	—	2	1	no	—
83	#10587506	C₂×C₄	1	2	yes	—
84	#10587506	C₂×C₄	1	2	yes	—
85	#10587503	C₂×C₄	1	2	yes	—
86	#10587503	C₂×C₄	1	2	yes	—
87	#10587493	—	4	2	no	—
88	#10587486	—	2	2	no	—
89	#10587485	—	2	2	no	—
90	#10587485	—	2	2	no	—
91	C₈×Dic₁₇	—	2	2	no	—
92	#10587479	C₂×C₄	1	2	yes	—
93	#10587479	C₂×C₄	1	2	yes	—
94	#10587478	C₂×C₄	1	2	yes	—
95	#10587478	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#3622	C₂×C₄	1	2	yes	—
103	C₄⋊#3622	D₄	1	1	yes	characteristic
104	C₄⋊#3622	D₄	1	1	yes	characteristic
105	C₄⋊#3622	D₄	1	2	yes	—
106	#10587474	—	4	2	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	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₇	—	2	1	no	—
113	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₇	—	2	1	no	—
115	C₂²×C₄×C₁₇	—	2	1	no	—
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	C₂×Dic₃₄	—	2	1	no	—
123	C₂×Dic₃₄	—	2	1	no	—
124	M₁₆×C₁₇	—	2	1	no	—
125	M₁₆×C₁₇	—	2	1	no	—
126	M₁₆×C₁₇	—	2	1	no	—
127	M₁₆×C₁₇	C₂×Q₈	1	2	yes	—
128	C₂×C₈×C₁₇	—	2	1	no	—
129	C₂×C₈×C₁₇	—	2	1	no	—
130	C₄⋊C₄×C₁₇	—	2	1	no	—
131	C₄⋊C₄×C₁₇	—	2	1	no	—
132	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₁₇	—	2	1	no	—
135	C₂²⋊C₄×C₁₇	—	2	1	no	—
136	C₂²⋊C₄×C₁₇	—	2	1	no	—
137	C₄²×C₁₇	—	2	1	no	—
138	C₄²×C₁₇	—	2	1	no	—
139	C₄²×C₁₇	—	2	1	no	—
140	C₄²×C₁₇	—	2	1	no	—
141	C₄²×C₁₇	—	2	1	no	—
142	C₄²×C₁₇	—	2	1	no	—
143	C₄²×C₁₇	—	4	2	no	—
144	C₄²×C₁₇	—	4	2	no	—
145	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₇	C₂×Q₈	1	2	yes	—
150	C₂²⋊Dic₁₇	—	2	2	no	—
151	C₄⋊Dic₁₇	—	2	1	no	—
152	C₄⋊Dic₁₇	—	2	1	no	—
153	C₄⋊Dic₁₇	C₂²×C₄	1	2	yes	—
154	C₄⋊Dic₁₇	C₂²×C₄	1	2	yes	—
155	#63225	—	2	2	no	—
156	#63225	—	2	2	no	—
157	C₄×Dic₁₇	—	2	2	no	—
158	#63223	—	2	2	no	—
159	#63223	—	2	2	no	—
160	#63223	—	4	4	no	—
161	C₂×#3622	—	2	2	no	—
162	C₂×#3622	—	2	2	no	—
163	C₂×#3622	—	2	2	no	—
164	C₂×#3622	—	2	2	no	—
165	C₂×#3622	—	2	2	no	—
166	C₂×#3622	—	4	4	no	—
167	C₂×#3622	C₂²×C₄	1	2	yes	—
168	C₂×#3622	C₂²×C₄	1	2	yes	—
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	C₄×Q₈	1	2	yes	—
176	D₄×C₁₇	—	2	2	no	—
177	D₄×C₁₇	—	2	2	no	—
178	D₄×C₁₇	—	2	1	no	—
179	D₄×C₁₇	C₄×Q₈	1	2	yes	—
180	C₂×C₄×C₁₇	—	2	1	no	—
181	C₂×C₄×C₁₇	—	2	2	no	—
182	C₂×C₄×C₁₇	—	2	2	no	—
183	C₂×C₄×C₁₇	—	2	2	no	—
184	C₂×C₄×C₁₇	—	2	2	no	—
185	C₂×C₄×C₁₇	—	2	1	no	—
186	C₂×C₄×C₁₇	—	2	1	no	—
187	C₂×C₄×C₁₇	—	2	2	no	—
188	C₂×C₄×C₁₇	—	4	1	no	—
189	C₂×C₄×C₁₇	—	4	1	no	—
190	C₂×C₄×C₁₇	—	4	1	no	—
191	C₂×C₄×C₁₇	—	4	1	no	—
192	C₂×C₄×C₁₇	—	4	1	no	—
193	C₂×C₄×C₁₇	—	4	2	no	—
194	C₂×C₄×C₁₇	—	8	1	no	—
195	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
205	C₂×Dic₁₇	—	2	2	no	—
206	C₂×Dic₁₇	—	2	2	no	—
207	Dic₃₄	—	4	2	no	—
208	Dic₃₄	—	8	1	no	—
209	C₈×C₁₇	—	2	2	no	—
210	C₈×C₁₇	—	4	1	no	—
211	#3622	—	2	2	no	—
212	#3622	—	2	2	no	—
213	#3622	—	2	2	no	—
214	#3622	—	2	2	no	—
215	#3622	—	4	2	no	—
216	#3076	—	17	1	no	—
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	D₁₇	1	1	yes	characteristic
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	2	no	—
240	C₄×C₁₇	—	4	2	no	—
241	C₄×C₁₇	—	4	1	no	—
242	C₄×C₁₇	—	4	1	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	—	17	1	no	—
252	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
253	#479	—	17	2	no	—
254	#478	—	17	2	no	—
255	#477	—	17	1	no	—
256	#476	—	17	1	no	—
257	#475	—	17	1	no	—
258	#474	—	17	1	no	—
259	#446	—	34	1	no	—
260	#446	—	34	2	no	—
261	C₈×Q₈	—	34	1	no	—
262	C₂×#108	—	17	2	no	—
263	#427	—	17	2	no	—
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	—	17	1	no	—
271	C₂×C₄⋊C₈	—	34	1	no	—
272	C₂×#104	C₂×D₁₇	1	1	yes	characteristic
273	C₂×#104	C₂×D₁₇	1	1	yes	characteristic
274	#416	—	17	2	no	—
275	#405	—	17	2	no	—
276	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
277	C₂×#97	—	17	2	no	—
278	C₄³	C₂×D₁₇	1	1	yes	characteristic
279	#341	—	17	2	no	—
280	#339	—	17	2	no	—
281	#339	—	17	2	no	—
282	#339	C₂×D₁₇	1	1	yes	characteristic
283	#339	C₂×D₁₇	1	1	yes	characteristic
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	2	no	—
295	C₂×M₁₆	—	34	2	no	—
296	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
297	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
298	C₂²×C₈	—	17	2	no	—
299	C₂²×C₈	—	17	2	no	—
300	C₂²×C₈	—	34	2	no	—
301	C₄⋊Q₈	—	17	1	no	—
302	C₄⋊Q₈	—	17	1	no	—
303	#125	—	17	2	no	—
304	C₂²⋊Q₈	—	34	1	no	—
305	C₂²⋊Q₈	—	34	1	no	—
306	C₄×Q₈	—	34	1	no	—
307	C₄×Q₈	—	34	1	no	—
308	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
309	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
313	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
314	#117	—	2	1	no	—
315	#117	—	17	2	no	—
316	#117	C₂²×D₁₇	1	1	yes	characteristic
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
321	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
323	#108	—	68	2	no	—
324	#107	—	17	2	no	—
325	#107	—	17	2	no	—
326	#106	—	17	2	no	—
327	#106	—	17	2	no	—
328	C₄⋊C₈	—	17	1	no	—
329	C₄⋊C₈	—	17	1	no	—
330	C₄⋊C₈	—	17	2	no	—
331	C₄⋊C₈	—	17	1	no	—
332	C₄⋊C₈	—	17	1	no	—
333	C₄⋊C₈	—	17	2	no	—
334	C₄⋊C₈	—	34	2	no	—
335	C₄⋊C₈	—	34	2	no	—
336	C₄⋊C₈	—	34	2	no	—
337	C₄⋊C₈	—	34	2	no	—
338	C₄⋊C₈	—	34	1	no	—
339	C₄⋊C₈	—	34	1	no	—
340	#104	—	2	2	no	—
341	#104	Dic₃₄	1	4	yes	complemented
342	#103	—	17	2	no	—
343	#103	—	17	2	no	—
344	#102	—	17	2	no	—
345	#102	—	17	2	no	—
346	#97	—	2	1	no	—
347	#97	—	34	2	no	—
348	#97	—	68	2	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	34	2	no	—
351	C₁₇	#22983	1	1	yes	characteristic, complemented, Sylow
352	#41	—	2	1	no	—
353	#41	—	2	1	no	—
354	#41	C₂×Dic₃₄	1	2	yes	—
355	#41	#63252	1	2	yes	—
356	C₂×Q₈	—	34	1	no	—
357	C₂×Q₈	—	34	1	no	—
358	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂×C₄×D₁₇	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	—	2	1	no	—
365	C₂²×C₄	—	2	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	—	2	1	no	—
370	M₁₆	—	2	1	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	34	2	no	—
373	M₁₆	—	34	2	no	—
374	M₁₆	—	68	4	no	—
375	M₁₆	C₂×Dic₃₄	1	2	yes	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	17	2	no	—
379	C₂×C₈	—	17	2	no	—
380	C₂×C₈	—	17	2	no	—
381	C₂×C₈	—	17	2	no	—
382	C₂×C₈	—	34	2	no	—
383	C₂×C₈	—	34	2	no	—
384	C₂×C₈	—	34	2	no	—
385	C₂×C₈	—	34	2	no	—
386	C₂×C₈	—	34	2	no	—
387	C₂×C₈	—	68	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	17	2	no	—
391	C₄⋊C₄	—	17	2	no	—
392	C₄⋊C₄	—	34	2	no	—
393	C₄⋊C₄	—	34	2	no	—
394	C₄⋊C₄	—	34	1	no	—
395	C₄⋊C₄	—	34	1	no	—
396	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
397	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	34	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	4	2	no	—
409	C₄²	—	4	2	no	—
410	C₄²	—	34	2	no	—
411	C₄²	C₂×Dic₃₄	1	2	yes	—
412	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
413	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
414	C₄²	D₄×D₁₇	1	1	yes	characteristic
415	C₄²	D₄×D₁₇	1	1	yes	characteristic
416	C₂³	—	2	1	no	—
417	C₂³	C₂×#63254	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	68	2	no	—
420	Q₈	—	136	1	no	—
421	Q₈	C₄×Dic₃₄	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	C₄×Dic₃₄	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	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	8	1	no	—
441	C₂×C₄	—	34	2	no	—
442	C₂×C₄	—	34	2	no	—
443	C₂×C₄	#10587567	1	1	yes	characteristic
444	C₂×C₄	#10587567	1	1	yes	characteristic
445	C₂×C₄	#10587567	1	1	yes	characteristic
446	C₂×C₄	#10587567	1	1	yes	characteristic
447	C₂×C₄	C₂²×Dic₃₄	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
449	C₂×C₄	C₂×#63252	1	1	yes	characteristic
450	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
451	C₂×C₄	#10587696	1	1	yes	characteristic
452	C₂×C₄	#10587697	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	4	1	no	—
455	C₈	—	34	2	no	—
456	C₈	—	34	2	no	—
457	C₈	—	34	2	no	—
458	C₈	—	34	2	no	—
459	C₈	—	68	2	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×#10587567	1	1	yes	characteristic
466	C₂²	#11763499	1	1	yes	characteristic
467	C₂²	#11763516	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	68	2	no	—
477	C₄	—	68	2	no	—
478	C₄	#11762928	1	2	yes	—
479	C₄	C₂×C₄×Dic₃₄	1	1	yes	characteristic
480	C₄	#11763289	1	1	yes	characteristic
481	C₄	#11763455	1	1	yes	characteristic
482	C₄	D₄×Dic₃₄	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	#14531787	1	1	yes	characteristic
487	C₂	C₂×#11762928	1	1	yes	characteristic
488	C₂	#14537690	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	C₄×C₁₇×#104	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×#41×C₁₇	C₂³
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄×#104	D₁₇
hypocenter	C₁₇	#22983
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
2. #14537731	C₂	semidirect
4. #14529761	C₂	semidirect
5. #14529559	C₂	semidirect
6. #14529536	C₂	semidirect
7. #14529386	C₂	semidirect
9. #14528637	C₂	semidirect
14. #11763116	C₄	semidirect
15. #11763109	C₄	semidirect
16. #11763104	C₄	semidirect
17. #11763099	C₄	semidirect
18. #11763094	C₄	semidirect
19. #11763089	C₄	semidirect
80. C₁₇×#104	Q₈	semidirect
341. #104	Dic₃₄	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
#14538572	2
#14537731	2
#14537352	2
#14529761	2
#14529559	2
#14529536	2
#14529386	2
#14529057	2
#14528637	2
#14528629	2
C₄×C₁₇×#104	2
#22983	17