Subgroups — #17004414

Order 4352.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538844	C₂	1	1	yes	maximal, characteristic
2	#14537859	C₂	1	1	yes	maximal, characteristic, complemented
3	#14527662	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527648	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527627	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527613	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527606	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527594	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#63230	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#63228	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527567	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527218	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527182	C₂	1	1	yes	maximal, characteristic, complemented
14	#14527084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#2988	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763359	C₂²	1	1	yes	characteristic
17	#11763133	C₄	1	1	yes	characteristic
18	#11763133	C₄	1	1	yes	characteristic
19	#11763104	C₄	1	1	yes	characteristic
20	#11763099	C₄	1	1	yes	characteristic
21	#11763009	C₄	1	1	yes	characteristic
22	#11763004	C₄	1	1	yes	characteristic
23	#11762954	C₄	1	1	yes	characteristic
24	#11762954	C₄	1	1	yes	characteristic
25	C₄×#63230	C₂²	1	1	yes	characteristic
26	C₄×#63230	C₂²	1	1	yes	characteristic
27	C₄×#63228	C₂²	1	1	yes	characteristic
28	C₄×#63228	C₂²	1	1	yes	characteristic
29	#11762888	C₂²	1	1	yes	characteristic
30	#11762888	C₂²	1	1	yes	characteristic
31	#11762879	—	2	1	no	—
32	#11762879	—	2	1	no	—
33	C₈×D₆₈	C₂²	1	1	yes	characteristic
34	C₈×D₆₈	C₂²	1	1	yes	characteristic
35	#11762866	C₂²	1	1	yes	characteristic
36	#11762862	C₂²	1	1	yes	characteristic
37	#11762862	C₂²	1	1	yes	characteristic
38	#11762774	—	2	1	no	—
39	#11762774	—	2	1	no	—
40	#11762561	C₂²	1	1	yes	characteristic
41	#11762561	C₂²	1	1	yes	characteristic
42	#11762559	C₂²	1	1	yes	characteristic
43	#11762559	C₂²	1	1	yes	characteristic
44	Q₈⋊#3622	C₂²	1	1	yes	characteristic
45	Q₈⋊#3622	C₂²	1	1	yes	characteristic
46	D₄⋊#3622	C₂²	1	1	yes	characteristic
47	D₄⋊#3622	C₂²	1	1	yes	characteristic
48	#11762536	C₂²	1	1	yes	characteristic
49	#11762536	C₂²	1	1	yes	characteristic
50	#11762536	C₂²	1	1	yes	characteristic
51	#11762536	C₂²	1	1	yes	characteristic
52	#11762531	C₂²	1	1	yes	characteristic
53	#11762531	C₂²	1	1	yes	characteristic
54	#11762530	C₂²	1	1	yes	characteristic
55	C₈×#3622	C₂²	1	1	yes	characteristic
56	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
59	C₈×D₄×C₁₇	—	2	1	no	—
60	C₈×D₄×C₁₇	—	2	1	no	—
61	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
63	C₁₇×#431	—	2	1	no	—
64	C₁₇×#431	C₂²	1	1	yes	characteristic
65	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
66	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×#63252	—	2	1	no	—
69	C₂²×C₈×C₁₇	—	2	1	no	—
70	C₂²×C₈×C₁₇	—	2	1	no	—
71	C₂²×C₈×C₁₇	—	2	1	no	—
72	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₁₇	—	2	1	no	—
75	C₄×D₄×C₁₇	—	2	1	no	—
76	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
77	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₁₇×#117	—	2	1	no	—
79	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₇	—	2	1	no	—
81	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
82	C₂×#63230	C₂×C₄	1	1	yes	characteristic
83	C₂×#63230	C₂×C₄	1	1	yes	characteristic
84	C₂×#63228	C₂×C₄	1	1	yes	characteristic
85	C₂×#63228	C₂×C₄	1	1	yes	characteristic
86	#10587616	—	2	1	no	—
87	#10587616	C₂×C₄	1	1	yes	characteristic
88	#10587616	C₂×C₄	1	1	yes	characteristic
89	C₂×#63218	—	2	1	no	—
90	C₂×#63218	—	2	1	no	—
91	C₂×C₈×D₁₇	—	2	1	no	—
92	C₂×C₈×D₁₇	—	2	1	no	—
93	#10587561	—	2	1	no	—
94	#10587560	C₂×C₄	1	1	yes	characteristic
95	C₄×D₆₈	—	2	1	no	—
96	C₄×D₆₈	C₂³	1	1	yes	characteristic
97	C₄×D₆₈	C₂³	1	1	yes	characteristic
98	#10587555	C₂×C₄	1	1	yes	characteristic
99	C₁₇×C₄⋊C₈	—	2	1	no	—
100	C₁₇×C₄⋊C₈	—	2	1	no	—
101	C₁₇×C₄⋊C₈	—	2	1	no	—
102	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
103	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₁₇×C₂²⋊C₈	—	2	1	no	—
107	C₁₇×C₂²⋊C₈	—	2	1	no	—
108	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
109	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
110	C₄×C₈×C₁₇	—	2	1	no	—
111	C₄×C₈×C₁₇	—	2	1	no	—
112	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
114	#10587506	C₂×C₄	1	1	yes	characteristic
115	#10587506	C₂×C₄	1	1	yes	characteristic
116	#10587503	C₂×C₄	1	1	yes	characteristic
117	#10587503	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#3622	—	2	1	no	—
119	C₂²⋊#3622	—	2	1	no	—
120	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
121	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
122	#10587491	—	2	1	no	—
123	#10587491	—	2	1	no	—
124	#10587491	—	2	1	no	—
125	#10587491	—	2	1	no	—
126	#10587480	C₂×C₄	1	1	yes	characteristic
127	#10587480	C₂×C₄	1	1	yes	characteristic
128	#10587480	C₂×C₄	1	1	yes	characteristic
129	#10587480	C₂×C₄	1	1	yes	characteristic
130	#10587479	C₂×C₄	1	1	yes	characteristic
131	#10587479	C₂×C₄	1	1	yes	characteristic
132	#10587478	C₂×C₄	1	1	yes	characteristic
133	#10587478	C₂×C₄	1	1	yes	characteristic
134	C₄⋊#3622	—	2	1	no	—
135	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
136	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
137	C₄⋊#3622	C₂³	1	1	yes	characteristic
138	C₄⋊#3622	C₂³	1	1	yes	characteristic
139	#10587474	—	2	1	no	—
140	C₄×#3622	C₂³	1	1	yes	characteristic
141	C₄×#3622	C₂³	1	1	yes	characteristic
142	C₄×#3622	C₂³	1	1	yes	characteristic
143	C₄×#3622	C₂³	1	1	yes	characteristic
144	#41×C₁₇	—	2	2	no	—
145	#41×C₁₇	—	2	2	no	—
146	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₇	—	2	1	no	—
148	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	—	2	1	no	—
150	C₂²×C₄×C₁₇	—	2	1	no	—
151	C₂²×C₄×C₁₇	—	2	1	no	—
152	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
155	C₂×C₂²⋊D₁₇	—	2	1	no	—
156	C₂×C₂²⋊D₁₇	—	2	1	no	—
157	#63252	—	8	1	no	—
158	#63252	—	8	1	no	—
159	C₂×D₆₈	—	2	1	no	—
160	C₂×D₆₈	—	2	1	no	—
161	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₁₇	—	2	1	no	—
164	C₂×C₄×D₁₇	—	2	1	no	—
165	C₂×Dic₃₄	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	—	8	1	no	—
169	C₂×C₈×C₁₇	—	8	1	no	—
170	C₂×C₈×C₁₇	—	8	1	no	—
171	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₁₇	—	2	1	no	—
176	C₄⋊C₄×C₁₇	—	2	1	no	—
177	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²⋊C₄×C₁₇	—	2	1	no	—
180	C₂²⋊C₄×C₁₇	—	2	1	no	—
181	C₂²⋊C₄×C₁₇	—	2	1	no	—
182	C₄²×C₁₇	—	2	1	no	—
183	C₄²×C₁₇	—	2	1	no	—
184	C₄²×C₁₇	—	2	1	no	—
185	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₁₇	#41	1	1	yes	characteristic
188	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
189	#63230	—	2	2	no	—
190	#63230	—	2	2	no	—
191	#63228	—	2	2	no	—
192	#63228	—	2	2	no	—
193	#63227	—	2	1	no	—
194	#63227	—	2	1	no	—
195	#63227	—	2	1	no	—
196	#63227	—	2	1	no	—
197	C₄⋊Dic₁₇	—	2	1	no	—
198	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
199	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
200	C₂×#3622	—	2	1	no	—
201	C₂×#3622	—	2	1	no	—
202	C₂×#3622	—	2	1	no	—
203	C₂×#3622	—	2	1	no	—
204	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
205	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
206	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
207	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
208	#63218	—	8	1	no	—
209	#63218	—	8	1	no	—
210	C₈×D₁₇	—	8	1	no	—
211	C₈×D₁₇	—	8	1	no	—
212	#17920	—	17	1	no	maximal, Sylow
213	C₂³×C₁₇	—	2	1	no	—
214	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
215	C₂²×D₁₇	—	2	1	no	—
216	C₂²×D₁₇	—	2	1	no	—
217	Q₈×C₁₇	—	2	1	no	—
218	Q₈×C₁₇	#131	1	2	yes	—
219	D₄×C₁₇	—	2	4	no	—
220	D₄×C₁₇	—	2	1	no	—
221	D₄×C₁₇	#131	1	2	yes	—
222	C₂×C₄×C₁₇	—	2	4	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	1	no	—
227	C₂×C₄×C₁₇	—	2	1	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	2	1	no	—
230	C₂×C₄×C₁₇	—	4	1	no	—
231	C₂×C₄×C₁₇	—	4	1	no	—
232	C₂×C₄×C₁₇	—	4	1	no	—
233	C₂×C₄×C₁₇	—	8	1	no	—
234	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
240	C₂²⋊D₁₇	—	8	1	no	—
241	C₂²⋊D₁₇	—	8	1	no	—
242	C₂×Dic₁₇	—	2	1	no	—
243	C₂×Dic₁₇	—	2	1	no	—
244	D₆₈	—	2	1	no	—
245	D₆₈	—	2	1	no	—
246	D₆₈	—	2	1	no	—
247	D₆₈	—	2	1	no	—
248	D₆₈	—	8	1	no	—
249	D₆₈	—	8	1	no	—
250	C₄×D₁₇	—	4	1	no	—
251	C₄×D₁₇	—	4	1	no	—
252	C₄×D₁₇	—	4	1	no	—
253	C₄×D₁₇	—	4	1	no	—
254	Dic₃₄	—	8	1	no	—
255	C₈×C₁₇	—	2	1	no	—
256	C₈×C₁₇	—	2	1	no	—
257	C₈×C₁₇	—	2	1	no	—
258	C₈×C₁₇	—	2	1	no	—
259	C₈×C₁₇	—	4	1	no	—
260	C₈×C₁₇	—	4	1	no	—
261	#3622	—	2	1	no	—
262	#3622	—	2	1	no	—
263	#3622	—	2	1	no	—
264	#3622	—	2	1	no	—
265	#3622	—	4	1	no	—
266	#3622	—	4	1	no	—
267	#3622	—	4	1	no	—
268	#3622	—	4	1	no	—
269	#3106	—	17	1	no	—
270	#2988	D₁₇	1	1	yes	characteristic, complemented
271	#2981	—	17	1	no	—
272	#1588	—	17	1	no	—
273	#1586	—	17	1	no	—
274	#1583	—	17	1	no	—
275	#1581	—	17	1	no	—
276	#1580	—	17	1	no	—
277	SD₁₆⋊C₈	—	17	1	no	—
278	C₈×SD₁₆	—	17	1	no	—
279	C₈×D₈	—	17	1	no	—
280	#1573	—	17	1	no	—
281	#1488	—	17	1	no	—
282	#1480	—	17	1	no	—
283	#1454	—	17	1	no	—
284	C₂²×C₁₇	—	2	1	no	—
285	C₂²×C₁₇	—	2	2	no	—
286	C₂²×C₁₇	—	2	1	no	—
287	C₂²×C₁₇	—	2	1	no	—
288	C₂²×C₁₇	—	4	1	no	—
289	C₂²×C₁₇	—	4	1	no	—
290	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×D₁₇	—	4	1	no	—
292	C₂×D₁₇	—	4	1	no	—
293	C₂×D₁₇	—	4	1	no	—
294	C₂×D₁₇	—	4	1	no	—
295	C₂×D₁₇	—	4	1	no	—
296	C₂×D₁₇	—	4	1	no	—
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	2	no	—
299	C₄×C₁₇	—	2	1	no	—
300	C₄×C₁₇	—	2	1	no	—
301	C₄×C₁₇	—	2	1	no	—
302	C₄×C₁₇	—	4	1	no	—
303	C₄×C₁₇	—	4	1	no	—
304	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
305	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
306	C₄×C₁₇	#576	1	1	yes	characteristic
307	C₄×C₁₇	#577	1	1	yes	characteristic
308	Dic₁₇	—	4	1	no	—
309	Dic₁₇	—	4	1	no	—
310	#532	—	17	1	no	—
311	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
312	#482	—	17	1	no	—
313	#482	—	17	1	no	—
314	#477	—	17	1	no	—
315	#476	—	17	1	no	—
316	#460	—	17	1	no	—
317	#459	—	17	1	no	—
318	#449	—	17	1	no	—
319	#449	—	17	1	no	—
320	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
321	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
322	C₄×SD₁₆	—	17	1	no	—
323	C₄×SD₁₆	—	17	1	no	—
324	C₄×D₈	—	17	1	no	—
325	C₄×D₈	—	17	1	no	—
326	#436	—	17	1	no	—
327	#436	—	17	1	no	—
328	#435	—	34	1	no	—
329	#435	—	34	1	no	—
330	C₈×D₄	—	2	1	no	—
331	C₈×D₄	—	2	1	no	—
332	C₈×D₄	—	17	1	no	—
333	C₈×D₄	—	17	1	no	—
334	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
335	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
336	#432	—	17	1	no	—
337	#431	—	2	1	no	—
338	#431	—	17	1	no	—
339	#431	—	17	1	no	—
340	#431	C₂×D₁₇	1	1	yes	characteristic
341	C₂×C₄⋊C₈	—	2	1	no	—
342	C₂×C₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
343	#408	—	34	1	no	—
344	#408	—	34	1	no	—
345	#335	—	17	1	no	—
346	#335	—	17	1	no	—
347	#334	—	17	1	no	—
348	#334	—	17	1	no	—
349	Q₈⋊C₈	—	17	1	no	—
350	Q₈⋊C₈	—	17	1	no	—
351	D₄⋊C₈	—	17	1	no	—
352	D₄⋊C₈	—	17	1	no	—
353	D₄⋊C₈	—	17	1	no	—
354	D₄⋊C₈	—	17	1	no	—
355	D₄⋊C₈	—	17	1	no	—
356	D₄⋊C₈	—	17	1	no	—
357	#322	—	17	1	no	—
358	#322	—	17	1	no	—
359	#322	—	17	1	no	—
360	C₈²	—	17	1	no	—
361	C₂×C₁₇	—	4	1	no	—
362	C₂×C₁₇	—	4	2	no	—
363	C₂×C₁₇	#2929	1	1	yes	characteristic
364	C₂×C₁₇	#2946	1	1	yes	characteristic
365	C₂×C₁₇	#2957	1	1	yes	characteristic
366	D₁₇	—	8	1	no	—
367	D₁₇	—	8	1	no	—
368	C₂×#41	—	34	1	no	—
369	C₂×#41	C₄×D₁₇	1	1	yes	characteristic
370	C₂×SD₁₆	—	17	1	no	—
371	C₂×SD₁₆	—	17	1	no	—
372	C₂×D₈	—	17	1	no	—
373	C₂×D₈	—	17	1	no	—
374	C₂×M₁₆	—	34	1	no	—
375	C₂×M₁₆	—	34	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	34	1	no	—
380	C₂²×C₈	—	34	1	no	—
381	C₄⋊Q₈	—	17	1	no	—
382	#127	—	17	1	no	—
383	#124	—	34	1	no	—
384	#121	—	17	1	no	—
385	#121	—	17	1	no	—
386	#121	—	34	1	no	—
387	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
388	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	17	1	no	—
392	C₄×D₄	—	17	1	no	—
393	C₄×D₄	—	34	1	no	—
394	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
395	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
396	#117	—	2	1	no	—
397	#117	C₄×D₁₇	1	1	yes	characteristic
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
400	#107	—	17	1	no	—
401	#107	—	17	1	no	—
402	#106	—	17	1	no	—
403	#106	—	17	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	2	1	no	—
407	C₄⋊C₈	—	17	1	no	—
408	C₄⋊C₈	—	17	1	no	—
409	C₄⋊C₈	—	17	1	no	—
410	C₄⋊C₈	—	17	1	no	—
411	C₄⋊C₈	—	34	1	no	—
412	C₄⋊C₈	C₂²⋊D₁₇	1	1	yes	characteristic
413	C₄⋊C₈	C₂²⋊D₁₇	1	1	yes	characteristic
414	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
416	#103	—	17	1	no	—
417	#103	—	17	1	no	—
418	#102	—	17	1	no	—
419	#102	—	17	1	no	—
420	#102	—	17	1	no	—
421	#102	—	17	1	no	—
422	#102	—	17	1	no	—
423	#102	—	17	1	no	—
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	17	1	no	—
427	C₂²⋊C₈	—	17	1	no	—
428	C₂²⋊C₈	—	34	1	no	—
429	C₂²⋊C₈	—	34	1	no	—
430	C₂²⋊C₈	—	34	1	no	—
431	C₂²⋊C₈	—	34	1	no	—
432	C₂²⋊C₈	—	34	1	no	—
433	C₂²⋊C₈	—	34	1	no	—
434	C₂²⋊C₈	C₂²⋊D₁₇	1	1	yes	characteristic
435	C₂²⋊C₈	C₂²⋊D₁₇	1	1	yes	characteristic
436	#97	—	34	1	no	—
437	C₄×C₈	—	2	1	no	—
438	C₄×C₈	—	2	1	no	—
439	C₄×C₈	—	17	1	no	—
440	C₄×C₈	—	17	1	no	—
441	C₄×C₈	—	17	1	no	—
442	C₄×C₈	—	17	1	no	—
443	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
444	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
445	C₁₇	#17920	1	1	yes	characteristic, complemented, Sylow
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	136	1	no	—
449	#41	—	136	1	no	—
450	C₂×Q₈	—	34	1	no	—
451	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	17	1	no	—
454	C₂×D₄	—	17	1	no	—
455	C₂×D₄	—	34	1	no	—
456	C₂×D₄	—	34	1	no	—
457	C₂×D₄	—	34	1	no	—
458	C₂×D₄	—	34	1	no	—
459	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	34	1	no	—
464	C₂²×C₄	—	34	1	no	—
465	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
466	C₂²×C₄	#63252	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
468	SD₁₆	—	34	2	no	—
469	SD₁₆	—	34	2	no	—
470	D₈	—	34	2	no	—
471	D₈	—	34	2	no	—
472	M₁₆	—	136	1	no	—
473	M₁₆	—	136	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	8	1	no	—
477	C₂×C₈	—	8	1	no	—
478	C₂×C₈	—	8	1	no	—
479	C₂×C₈	—	17	1	no	—
480	C₂×C₈	—	17	1	no	—
481	C₂×C₈	—	17	1	no	—
482	C₂×C₈	—	17	1	no	—
483	C₂×C₈	—	34	1	no	—
484	C₂×C₈	—	34	1	no	—
485	C₂×C₈	—	34	1	no	—
486	C₂×C₈	—	34	1	no	—
487	C₂×C₈	—	136	1	no	—
488	C₂×C₈	—	136	1	no	—
489	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
490	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
491	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
492	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	17	1	no	—
496	C₄⋊C₄	—	17	1	no	—
497	C₄⋊C₄	—	34	1	no	—
498	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
499	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	34	1	no	—
504	C₂²⋊C₄	—	34	1	no	—
505	C₂²⋊C₄	—	34	1	no	—
506	C₂²⋊C₄	—	34	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
511	C₄²	#63252	1	1	yes	characteristic
512	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
513	C₄²	C₂³×D₁₇	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	34	1	no	—
516	C₂³	—	34	1	no	—
517	C₂³	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	136	1	no	—
520	Q₈	#10587587	1	2	yes	—
521	D₄	—	2	4	no	—
522	D₄	—	2	1	no	—
523	D₄	—	34	1	no	—
524	D₄	—	34	1	no	—
525	D₄	—	34	1	no	—
526	D₄	—	34	1	no	—
527	D₄	—	136	1	no	—
528	D₄	—	136	1	no	—
529	D₄	—	136	1	no	—
530	D₄	—	136	1	no	—
531	D₄	#10587587	1	2	yes	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	8	1	no	—
544	C₂×C₄	—	34	1	no	—
545	C₂×C₄	—	34	1	no	—
546	C₂×C₄	—	68	1	no	—
547	C₂×C₄	—	68	1	no	—
548	C₂×C₄	—	68	1	no	—
549	C₂×C₄	—	68	1	no	—
550	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
551	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
552	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
554	C₂×C₄	C₂×#63252	1	1	yes	characteristic
555	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	34	1	no	—
563	C₈	—	34	1	no	—
564	C₈	—	34	1	no	—
565	C₈	—	34	1	no	—
566	C₈	—	68	1	no	—
567	C₈	—	68	1	no	—
568	C₈	—	68	1	no	—
569	C₈	—	68	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	68	1	no	—
577	C₂²	—	68	1	no	—
578	C₂²	—	68	1	no	—
579	C₂²	—	68	1	no	—
580	C₂²	—	68	1	no	—
581	C₂²	—	68	1	no	—
582	C₂²	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	68	1	no	—
591	C₄	—	68	1	no	—
592	C₄	C₂×#10587587	1	1	yes	characteristic
593	C₄	C₂×#10587587	1	1	yes	characteristic
594	C₄	#11763612	1	1	yes	characteristic
595	C₄	#11763617	1	1	yes	characteristic
596	C₂	—	4	1	no	—
597	C₂	—	4	2	no	—
598	C₂	—	136	1	no	—
599	C₂	—	136	1	no	—
600	C₂	#14537478	1	1	yes	characteristic
601	C₂	#14537612	1	1	yes	characteristic
602	C₂	#14537699	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#2988	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#14538844	C₂
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#2988	D₁₇
hypocenter	C₁₇	#17920
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2988

Complements

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

N	H ≅ G/N	type
2. #14537859	C₂	semidirect
3. #14527662	C₂	semidirect
4. #14527648	C₂	semidirect
5. #14527627	C₂	semidirect
6. #14527613	C₂	semidirect
7. #14527606	C₂	semidirect
8. #14527594	C₂	semidirect
9. C₈×#63230	C₂	semidirect
10. C₈×#63228	C₂	semidirect
11. #14527567	C₂	semidirect
12. #14527218	C₂	semidirect
13. #14527182	C₂	semidirect
14. #14527084	C₂	semidirect
15. C₁₇×#2988	C₂	semidirect
270. #2988	D₁₇	semidirect
445. C₁₇	#17920	semidirect

Maximal subgroups

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

subgroup	index
#14538844	2
#14537859	2
#14527662	2
#14527648	2
#14527627	2
#14527613	2
#14527606	2
#14527594	2
C₈×#63230	2
C₈×#63228	2
#14527567	2
#14527218	2
#14527182	2
#14527084	2
C₁₇×#2988	2
#17920	17