Subgroups — #17005243

Order 4352.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538815	C₂	1	1	yes	maximal, characteristic
2	Q₈×#63223	C₂	1	1	yes	maximal, characteristic, complemented
3	#14537527	C₂	1	1	yes	maximal, characteristic
4	#14527671	C₂	1	2	yes	maximal, complemented
5	#14527624	C₂	1	2	yes	maximal, complemented
6	#14527623	C₂	1	2	yes	maximal, complemented
7	#14527581	C₂	1	2	yes	maximal, complemented
8	#14527554	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527236	C₂	1	1	yes	maximal, characteristic
10	C₈×#63223	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10587587	—	2	1	no	—
13	#11763359	C₂²	1	1	yes	characteristic
14	#11763127	C₄	1	2	yes	—
15	#11763094	C₄	1	1	yes	characteristic
16	#11763094	C₄	1	1	yes	characteristic
17	#11763009	C₄	1	1	yes	characteristic
18	#11763009	C₄	1	1	yes	characteristic
19	#11762948	C₄	1	2	yes	—
20	#11762940	—	2	2	no	—
21	#11762940	C₂²	1	2	yes	—
22	Q₈×#3622	C₂²	1	2	yes	—
23	C₄×#63230	C₂²	1	2	yes	—
24	C₄×#63230	C₂²	1	2	yes	—
25	#11762886	C₂²	1	2	yes	—
26	#11762879	—	2	2	no	—
27	#11762874	C₂²	1	2	yes	—
28	#11762862	C₂²	1	1	yes	characteristic
29	#11762833	—	2	1	no	—
30	#11762833	C₂²	1	1	yes	characteristic
31	#11762775	—	2	1	no	—
32	C₄×#63223	—	2	1	no	—
33	C₄×#63223	C₂²	1	1	yes	characteristic
34	#11762559	C₂²	1	2	yes	—
35	#11762559	C₂²	1	2	yes	—
36	#11762538	C₂²	1	2	yes	—
37	#11762538	C₂²	1	2	yes	—
38	#11762531	C₂²	1	2	yes	—
39	C₈×#3622	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
43	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×#63252	—	2	1	no	—
49	C₂²×C₈×C₁₇	—	2	1	no	—
50	C₂²×C₈×C₁₇	—	2	1	no	—
51	C₄×Q₈×C₁₇	—	2	1	no	—
52	C₄×Q₈×C₁₇	—	2	1	no	—
53	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
56	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₇	—	2	1	no	—
60	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
61	C₂×#63230	C₂×C₄	1	2	yes	—
62	C₂×#63230	C₂×C₄	1	2	yes	—
63	#10587616	—	2	1	no	—
64	#10587616	C₂×C₄	1	2	yes	—
65	C₂×#63223	—	2	1	no	—
66	C₂×#63223	D₄	1	1	yes	characteristic
67	C₂×#63223	D₄	1	1	yes	characteristic
68	#10587587	—	4	4	no	—
69	C₂×#63218	—	2	2	no	—
70	C₂×C₈×D₁₇	—	2	2	no	—
71	#10587561	—	2	1	no	—
72	#10587560	C₂×C₄	1	1	yes	characteristic
73	C₄×D₆₈	—	2	1	no	—
74	C₄×D₆₈	C₂³	1	2	yes	—
75	#10587555	C₂×C₄	1	1	yes	characteristic
76	C₁₇×C₄⋊C₈	—	2	1	no	—
77	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₇	—	2	1	no	—
80	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
82	#10587506	C₂×C₄	1	2	yes	—
83	#10587506	C₂×C₄	1	2	yes	—
84	C₂²⋊#3622	C₂×C₄	1	2	yes	—
85	#10587491	—	2	2	no	—
86	#10587491	—	2	2	no	—
87	#10587480	C₂×C₄	1	2	yes	—
88	#10587480	C₂×C₄	1	2	yes	—
89	#10587479	C₂×C₄	1	2	yes	—
90	#10587479	C₂×C₄	1	2	yes	—
91	C₄⋊#3622	—	2	2	no	—
92	C₄⋊#3622	—	2	2	no	—
93	C₄⋊#3622	—	2	1	no	—
94	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
96	C₄⋊#3622	C₂³	1	2	yes	—
97	#10587474	—	2	2	no	—
98	#10587474	D₄	1	2	yes	—
99	C₄×#3622	—	2	2	no	—
100	C₄×#3622	C₂³	1	2	yes	—
101	C₄×#3622	C₂³	1	2	yes	—
102	C₂×Q₈×C₁₇	—	2	1	no	—
103	C₂×Q₈×C₁₇	—	2	2	no	—
104	C₂×Q₈×C₁₇	—	4	1	no	—
105	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₇	—	2	1	no	—
108	C₂²×C₄×C₁₇	—	2	1	no	—
109	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₁₇	—	2	2	no	—
113	#63252	—	4	2	no	—
114	#63252	—	4	2	no	—
115	C₂×D₆₈	—	2	1	no	—
116	C₂×D₆₈	—	2	1	no	—
117	C₂×D₆₈	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₁₇	—	2	2	no	—
119	C₂×Dic₃₄	—	2	1	no	—
120	C₂×C₈×C₁₇	—	2	1	no	—
121	C₂×C₈×C₁₇	—	2	1	no	—
122	C₂×C₈×C₁₇	—	2	1	no	—
123	C₂×C₈×C₁₇	—	2	1	no	—
124	C₂×C₈×C₁₇	—	4	2	no	—
125	C₂×C₈×C₁₇	—	4	2	no	—
126	C₄⋊C₄×C₁₇	—	2	1	no	—
127	C₄⋊C₄×C₁₇	—	2	1	no	—
128	C₄⋊C₄×C₁₇	—	2	1	no	—
129	C₄⋊C₄×C₁₇	—	2	1	no	—
130	C₄⋊C₄×C₁₇	—	2	1	no	—
131	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₁₇	—	2	1	no	—
134	C₄²×C₁₇	—	2	1	no	—
135	C₄²×C₁₇	—	2	1	no	—
136	C₄²×C₁₇	—	2	1	no	—
137	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₇	#41	1	1	yes	characteristic
140	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
141	#63230	—	2	4	no	—
142	#63230	—	4	2	no	—
143	#63227	—	2	2	no	—
144	#63227	—	2	2	no	—
145	C₄⋊Dic₁₇	—	2	1	no	—
146	C₄⋊Dic₁₇	C₂²×C₄	1	2	yes	—
147	#63223	—	2	2	no	—
148	#63223	—	4	2	no	—
149	#63223	SD₁₆	1	4	yes	complemented
150	C₂×#3622	—	2	2	no	—
151	C₂×#3622	C₂²×C₄	1	2	yes	—
152	C₂×#3622	C₂²×C₄	1	2	yes	—
153	C₂×#3622	C₂×D₄	1	2	yes	—
154	C₂×#3622	C₂×D₄	1	2	yes	—
155	#63218	—	4	4	no	—
156	C₈×D₁₇	—	4	4	no	—
157	#17997	—	17	1	no	maximal, Sylow
158	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
159	C₂²×D₁₇	—	2	2	no	—
160	Q₈×C₁₇	—	2	1	no	—
161	Q₈×C₁₇	—	2	1	no	—
162	Q₈×C₁₇	—	2	1	no	—
163	Q₈×C₁₇	—	4	2	no	—
164	Q₈×C₁₇	#131	1	2	yes	complemented
165	C₂×C₄×C₁₇	—	2	1	no	—
166	C₂×C₄×C₁₇	—	2	1	no	—
167	C₂×C₄×C₁₇	—	2	1	no	—
168	C₂×C₄×C₁₇	—	2	1	no	—
169	C₂×C₄×C₁₇	—	2	1	no	—
170	C₂×C₄×C₁₇	—	2	1	no	—
171	C₂×C₄×C₁₇	—	4	1	no	—
172	C₂×C₄×C₁₇	—	4	2	no	—
173	C₂×C₄×C₁₇	—	8	1	no	—
174	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₇	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₁₇	#135	1	2	yes	—
179	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
182	C₂²⋊D₁₇	—	4	4	no	—
183	C₂×Dic₁₇	—	2	2	no	—
184	D₆₈	—	2	2	no	—
185	D₆₈	—	2	2	no	—
186	D₆₈	—	4	2	no	—
187	D₆₈	—	8	1	no	—
188	C₄×D₁₇	—	4	2	no	—
189	C₄×D₁₇	—	4	2	no	—
190	Dic₃₄	—	4	2	no	—
191	C₈×C₁₇	—	2	2	no	—
192	C₈×C₁₇	—	4	1	no	—
193	C₈×C₁₇	—	4	1	no	—
194	C₈×C₁₇	—	4	1	no	—
195	#3622	—	2	2	no	—
196	#3622	—	2	2	no	—
197	#3622	—	2	2	no	—
198	#3622	—	4	2	no	—
199	#3622	C₂×SD₁₆	1	4	yes	—
200	#3103	—	17	1	no	—
201	Q₈×M₁₆	—	17	1	no	—
202	#2935	—	17	1	no	—
203	#1590	—	17	2	no	—
204	#1583	—	17	2	no	—
205	#1582	—	17	2	no	—
206	C₈×SD₁₆	—	17	2	no	—
207	#1570	—	17	1	no	—
208	#1492	—	17	1	no	—
209	C₂×Q₈⋊C₈	D₁₇	1	1	yes	characteristic, complemented
210	C₈×M₁₆	—	17	1	no	—
211	C₂²×C₁₇	—	2	1	no	—
212	C₂²×C₁₇	—	2	1	no	—
213	C₂²×C₁₇	C₄×SD₁₆	1	2	yes	—
214	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂×D₁₇	—	4	2	no	—
216	C₂×D₁₇	—	4	2	no	—
217	C₂×D₁₇	—	4	2	no	—
218	C₄×C₁₇	—	2	1	no	—
219	C₄×C₁₇	—	2	2	no	—
220	C₄×C₁₇	—	2	1	no	—
221	C₄×C₁₇	—	2	1	no	—
222	C₄×C₁₇	—	4	1	no	—
223	C₄×C₁₇	—	4	1	no	—
224	C₄×C₁₇	—	4	1	no	—
225	C₄×C₁₇	C₄×SD₁₆	1	2	yes	—
226	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
227	C₄×C₁₇	#568	1	1	yes	characteristic
228	C₄×C₁₇	C₂²×SD₁₆	1	1	yes	characteristic
229	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
230	Dic₁₇	—	4	2	no	—
231	C₂×#131	—	34	1	no	—
232	#532	—	17	1	no	—
233	C₂×C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic
234	#481	—	17	2	no	—
235	#475	—	17	1	no	—
236	#475	—	17	1	no	—
237	#460	—	17	1	no	—
238	#460	—	17	1	no	—
239	#448	—	17	2	no	—
240	#446	—	17	2	no	—
241	#446	—	34	2	no	—
242	C₈×Q₈	—	17	2	no	—
243	C₄×SD₁₆	—	17	2	no	—
244	C₄×SD₁₆	—	17	2	no	—
245	#436	—	17	2	no	—
246	#435	—	34	2	no	—
247	C₈×D₄	—	17	2	no	—
248	#431	—	17	1	no	—
249	#423	—	17	1	no	—
250	#423	—	34	1	no	—
251	C₂×C₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
252	#408	—	34	1	no	—
253	C₄×M₁₆	—	17	1	no	—
254	C₄×M₁₆	—	34	1	no	—
255	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
256	#334	—	17	2	no	—
257	#334	—	17	2	no	—
258	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
259	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
260	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
261	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
262	D₄⋊C₈	—	17	2	no	—
263	D₄⋊C₈	—	17	2	no	—
264	#322	—	17	2	no	—
265	C₈²	—	17	2	no	—
266	C₂×C₁₇	—	2	2	no	—
267	C₂×C₁₇	#2933	1	1	yes	characteristic
268	C₂×C₁₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
269	C₂×C₁₇	#2956	1	1	yes	characteristic
270	D₁₇	—	8	2	no	—
271	C₂×#41	—	34	1	no	—
272	C₂²×Q₈	C₄×D₁₇	1	1	yes	characteristic
273	C₂×SD₁₆	—	17	2	no	—
274	C₂×SD₁₆	—	17	2	no	—
275	#131	—	68	4	no	—
276	C₂×M₁₆	—	17	1	no	—
277	C₂×M₁₆	—	17	1	no	—
278	C₂×M₁₆	—	34	2	no	—
279	C₂×M₁₆	—	34	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	34	2	no	—
283	C₄⋊Q₈	—	17	1	no	—
284	#127	—	17	1	no	—
285	#124	—	34	1	no	—
286	#121	—	17	2	no	—
287	#121	—	34	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
291	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
292	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
294	C₄×D₄	—	17	2	no	—
295	C₄×D₄	—	34	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	C₄×D₁₇	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
300	#106	—	17	2	no	—
301	#106	—	17	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	—	17	1	no	—
304	C₄⋊C₈	—	17	1	no	—
305	C₄⋊C₈	—	17	2	no	—
306	C₄⋊C₈	—	34	2	no	—
307	C₄⋊C₈	—	34	2	no	—
308	C₄⋊C₈	—	34	1	no	—
309	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
310	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
311	#103	—	17	2	no	—
312	#103	—	17	2	no	—
313	#102	—	17	2	no	—
314	#102	—	17	2	no	—
315	C₂²⋊C₈	—	17	2	no	—
316	C₂²⋊C₈	—	34	2	no	—
317	C₂²⋊C₈	—	34	2	no	—
318	#97	—	17	2	no	—
319	#97	—	34	2	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	17	2	no	—
322	C₄×C₈	—	17	2	no	—
323	C₄×C₈	—	34	2	no	—
324	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
326	C₁₇	#17997	1	1	yes	characteristic, complemented, Sylow
327	#41	—	68	2	no	—
328	#41	—	68	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	34	1	no	—
333	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
334	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
335	C₂×D₄	—	17	2	no	—
336	C₂×D₄	—	34	2	no	—
337	C₂×D₄	—	34	1	no	—
338	C₂×D₄	—	34	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	34	2	no	—
342	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
344	C₂²×C₄	#63254	1	1	yes	characteristic
345	SD₁₆	—	34	4	no	—
346	SD₁₆	—	68	2	no	—
347	M₁₆	—	17	4	no	—
348	M₁₆	—	34	2	no	—
349	M₁₆	—	68	4	no	—
350	M₁₆	—	68	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	17	2	no	—
358	C₂×C₈	—	17	2	no	—
359	C₂×C₈	—	17	2	no	—
360	C₂×C₈	—	17	2	no	—
361	C₂×C₈	—	34	2	no	—
362	C₂×C₈	—	68	4	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	17	2	no	—
369	C₄⋊C₄	—	34	1	no	—
370	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
371	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
372	C₂²⋊C₄	—	34	2	no	—
373	C₂²⋊C₄	—	34	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
379	C₄²	D₄×D₁₇	1	1	yes	characteristic
380	C₄²	#63254	1	1	yes	characteristic
381	C₄²	C₂³×D₁₇	1	1	yes	characteristic
382	C₂³	—	34	2	no	—
383	C₂³	#10587567	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	68	2	no	—
389	Q₈	#10587587	1	2	yes	complemented
390	D₄	—	34	2	no	—
391	D₄	—	34	2	no	—
392	D₄	—	68	4	no	—
393	D₄	—	68	2	no	—
394	D₄	—	136	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	34	2	no	—
405	C₂×C₄	—	68	2	no	—
406	C₂×C₄	—	68	2	no	—
407	C₂×C₄	#10587567	1	1	yes	characteristic
408	C₂×C₄	#10587567	1	1	yes	characteristic
409	C₂×C₄	#10587567	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₁₇	1	2	yes	—
411	C₂×C₄	#10587605	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#63254	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	17	4	no	—
420	C₈	—	34	2	no	—
421	C₈	—	34	2	no	—
422	C₈	—	34	2	no	—
423	C₈	—	68	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	68	2	no	—
427	C₂²	—	68	2	no	—
428	C₂²	—	68	2	no	—
429	C₂²	#11762894	1	2	yes	—
430	C₂²	C₂×#10587567	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	68	2	no	—
439	C₄	#11762894	1	2	yes	—
440	C₄	C₂×#10587587	1	1	yes	characteristic
441	C₄	#11763575	1	1	yes	characteristic
442	C₄	C₂×SD₁₆×D₁₇	1	1	yes	characteristic
443	C₄	C₂×#10587605	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	136	2	no	—
446	C₂	#14537505	1	1	yes	characteristic
447	C₂	C₂×#11762894	1	1	yes	characteristic
448	C₂	#14537690	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₂×C₁₇×Q₈⋊C₈	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#11763359	C₂²
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₁₇
hypocenter	C₁₇	#17997
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#63223	C₂	semidirect
4. #14527671	C₂	semidirect
5. #14527624	C₂	semidirect
6. #14527623	C₂	semidirect
7. #14527581	C₂	semidirect
8. #14527554	C₂	semidirect
10. C₈×#63223	C₂	semidirect
11. C₂×C₁₇×Q₈⋊C₈	C₂	semidirect
149. #63223	SD₁₆	semidirect
164. Q₈×C₁₇	#131	semidirect
209. C₂×Q₈⋊C₈	D₁₇	semidirect
326. C₁₇	#17997	semidirect
389. Q₈	#10587587	semidirect

Maximal subgroups

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

subgroup	index
#14538815	2
Q₈×#63223	2
#14537527	2
#14527671	2
#14527624	2
#14527623	2
#14527581	2
#14527554	2
#14527236	2
C₈×#63223	2
C₂×C₁₇×Q₈⋊C₈	2
#17997	17