Subgroups — #17053786

Order 4352.

752 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537450	C₂	1	1	yes	maximal, characteristic, complemented
2	#14537352	C₂	1	1	yes	maximal, characteristic, complemented
3	#14529490	C₂	1	2	yes	maximal, complemented
4	#14529385	C₂	1	2	yes	maximal, complemented
5	#14529113	C₂	1	2	yes	maximal
6	#14528922	C₂	1	1	yes	maximal, characteristic, complemented
7	#14528804	C₂	1	1	yes	maximal, characteristic, complemented
8	#14528804	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#14528624	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₇×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587634	C₂²	1	2	yes	—
13	#11762870	—	2	2	no	—
14	#11762866	—	2	1	no	—
15	#11762862	—	2	1	no	—
16	#11762836	—	2	2	no	—
17	#11762836	C₂²	1	2	yes	—
18	#11762833	—	2	1	no	—
19	#11762833	C₂²	1	1	yes	characteristic
20	#11762833	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#3622	—	2	1	no	—
22	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
23	C₂×#10587508	C₂²	1	2	yes	—
24	C₂×#10587508	C₂²	1	2	yes	—
25	#11762776	C₂²	1	2	yes	—
26	#11762765	C₂²	1	2	yes	—
27	C₂×C₈×Dic₁₇	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
29	#11762574	C₂²	1	2	yes	—
30	#11762574	C₂²	1	2	yes	—
31	#11762568	C₂²	1	2	yes	—
32	#11762568	C₂²	1	2	yes	—
33	#11762563	C₂²	1	2	yes	—
34	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
35	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
36	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
38	C₄×Q₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
39	C₄×SD₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
40	C₄×SD₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
41	C₄×SD₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
42	C₄×SD₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
43	C₄×D₈×C₁₇	C₄	1	1	yes	characteristic, complemented
44	C₄×D₈×C₁₇	C₄	1	1	yes	characteristic, complemented
45	C₁₇×#427	C₂²	1	1	yes	characteristic
46	C₁₇×#416	C₂²	1	1	yes	characteristic
47	C₁₇×#416	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
50	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
51	C₁₇×#135	—	2	2	no	—
52	C₁₇×#135	—	2	2	no	—
53	C₂×Q₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×D₈×C₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
59	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄×C₁₇	—	2	1	no	—
64	C₄×D₄×C₁₇	—	2	1	no	—
65	C₄×D₄×C₁₇	—	2	1	no	—
66	C₄×D₄×C₁₇	—	2	1	no	—
67	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
71	C₁₇×#117	—	2	1	no	—
72	C₁₇×#117	—	2	1	no	—
73	C₁₇×#117	C₂³	1	1	yes	characteristic
74	C₁₇×#117	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₇	—	2	1	no	—
76	C₂×C₄²×C₁₇	—	2	1	no	—
77	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
78	#10587634	—	2	4	no	—
79	#10587634	—	4	2	no	—
80	C₂×C₄⋊Dic₁₇	—	2	1	no	—
81	C₂×C₄×Dic₁₇	C₂³	1	2	yes	—
82	C₂×#63223	—	2	2	no	—
83	C₂×#63223	C₂³	1	2	yes	—
84	C₂×#63223	C₂³	1	2	yes	—
85	C₂²×#3622	—	2	2	no	—
86	C₂²×#3622	C₂³	1	2	yes	—
87	C₁₇×#107	C₂×C₄	1	1	yes	characteristic
88	C₁₇×#107	C₂×C₄	1	1	yes	characteristic
89	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
90	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
91	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
92	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
93	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
94	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
96	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
97	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
98	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
103	#10587508	—	2	4	no	—
104	#10587508	—	4	2	no	—
105	#10587502	—	2	1	no	—
106	C₂²⋊#3622	—	2	2	no	—
107	C₂²⋊#3622	—	2	2	no	—
108	C₈×Dic₁₇	—	4	2	no	—
109	C₄⋊#3622	—	2	2	no	—
110	C₄⋊#3622	—	2	2	no	—
111	C₄⋊#3622	—	2	1	no	—
112	C₄⋊#3622	—	2	1	no	—
113	C₄⋊#3622	—	2	1	no	—
114	C₄⋊#3622	—	2	1	no	—
115	C₄⋊#3622	D₄	1	1	yes	characteristic
116	C₄⋊#3622	D₄	1	1	yes	characteristic
117	C₄⋊#3622	D₄	1	2	yes	—
118	#10587474	—	2	2	no	—
119	C₄×#3622	—	2	2	no	—
120	#41×C₁₇	—	2	1	no	—
121	#41×C₁₇	—	2	1	no	—
122	#41×C₁₇	—	2	1	no	—
123	#41×C₁₇	—	2	1	no	—
124	#41×C₁₇	—	2	1	no	—
125	#41×C₁₇	—	2	1	no	—
126	#41×C₁₇	#41	1	2	yes	—
127	#41×C₁₇	#41	1	2	yes	—
128	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₄×C₁₇	—	2	1	no	—
131	C₂×D₄×C₁₇	—	2	1	no	—
132	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×D₄×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	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	2	1	no	—
139	C₂²×C₄×C₁₇	—	2	1	no	—
140	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
143	C₂²×Dic₁₇	—	2	2	no	—
144	Q₁₆×C₁₇	—	2	2	no	—
145	SD₁₆×C₁₇	—	2	2	no	—
146	SD₁₆×C₁₇	—	2	2	no	—
147	D₈×C₁₇	—	2	2	no	—
148	C₂×C₈×C₁₇	—	2	1	no	—
149	C₂×C₈×C₁₇	—	2	1	no	—
150	C₂×C₈×C₁₇	—	2	1	no	—
151	C₂×C₈×C₁₇	—	2	1	no	—
152	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₁₇	—	2	1	no	—
157	C₄⋊C₄×C₁₇	—	2	1	no	—
158	C₄⋊C₄×C₁₇	—	2	1	no	—
159	C₄⋊C₄×C₁₇	—	2	1	no	—
160	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
161	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
162	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²⋊C₄×C₁₇	—	2	1	no	—
165	C₂²⋊C₄×C₁₇	—	2	1	no	—
166	C₂²⋊C₄×C₁₇	—	2	1	no	—
167	C₂²⋊C₄×C₁₇	—	2	1	no	—
168	C₂²⋊C₄×C₁₇	—	2	1	no	—
169	C₂²⋊C₄×C₁₇	—	2	1	no	—
170	C₄²×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	—	2	1	no	—
172	C₄²×C₁₇	—	2	1	no	—
173	C₄²×C₁₇	—	2	1	no	—
174	C₄²×C₁₇	—	2	1	no	—
175	C₄²×C₁₇	—	2	1	no	—
176	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
180	C₄⋊Dic₁₇	—	2	4	no	—
181	C₄×Dic₁₇	—	2	2	no	—
182	C₄×Dic₁₇	—	2	2	no	—
183	#63223	—	2	2	no	—
184	#63223	—	2	2	no	—
185	#63223	—	2	2	no	—
186	#63223	—	2	2	no	—
187	#63223	—	4	4	no	—
188	C₂×#3622	—	2	2	no	—
189	C₂×#3622	—	2	2	no	—
190	C₂×#3622	—	2	2	no	—
191	C₂×#3622	—	2	2	no	—
192	C₂×#3622	—	4	4	no	—
193	C₂×#3622	C₂×D₄	1	2	yes	—
194	C₂×#3622	C₂×D₄	1	2	yes	—
195	#22783	—	17	1	no	maximal, Sylow
196	C₂³×C₁₇	—	2	1	no	—
197	C₂³×C₁₇	—	2	1	no	—
198	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
199	Q₈×C₁₇	—	2	1	no	—
200	Q₈×C₁₇	—	2	1	no	—
201	Q₈×C₁₇	—	2	1	no	—
202	Q₈×C₁₇	#117	1	2	yes	—
203	D₄×C₁₇	—	2	2	no	—
204	D₄×C₁₇	—	2	2	no	—
205	D₄×C₁₇	—	2	1	no	—
206	D₄×C₁₇	—	2	1	no	—
207	D₄×C₁₇	—	2	1	no	—
208	D₄×C₁₇	—	4	1	no	—
209	D₄×C₁₇	—	4	1	no	—
210	D₄×C₁₇	#117	1	2	yes	—
211	C₂×C₄×C₁₇	—	2	1	no	—
212	C₂×C₄×C₁₇	—	2	2	no	—
213	C₂×C₄×C₁₇	—	2	2	no	—
214	C₂×C₄×C₁₇	—	2	2	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	4	1	no	—
221	C₂×C₄×C₁₇	—	4	1	no	—
222	C₂×C₄×C₁₇	—	4	1	no	—
223	C₂×C₄×C₁₇	—	4	2	no	—
224	C₂×C₄×C₁₇	—	4	2	no	—
225	C₂×C₄×C₁₇	—	8	1	no	—
226	C₂×C₄×C₁₇	—	8	1	no	—
227	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×Dic₁₇	—	2	4	no	—
238	C₂×Dic₁₇	—	4	2	no	—
239	C₂×Dic₁₇	—	4	2	no	—
240	C₈×C₁₇	—	2	1	no	—
241	C₈×C₁₇	—	2	1	no	—
242	C₈×C₁₇	—	2	1	no	—
243	C₈×C₁₇	—	2	1	no	—
244	#3622	—	2	2	no	—
245	#3622	—	2	2	no	—
246	#3622	—	4	2	no	—
247	#3622	—	4	2	no	—
248	C₄×#135	D₁₇	1	1	yes	characteristic
249	#2925	—	17	1	no	—
250	#2906	—	17	1	no	—
251	#1937	—	17	2	no	—
252	#1922	—	17	2	no	—
253	#1876	—	17	2	no	—
254	#1837	—	17	1	no	—
255	#1806	—	17	1	no	—
256	#1806	—	17	1	no	—
257	C₈×C₄⋊C₄	—	17	1	no	—
258	#1764	—	17	2	no	—
259	C₂²×C₁₇	—	2	1	no	—
260	C₂²×C₁₇	—	2	1	no	—
261	C₂²×C₁₇	—	2	2	no	—
262	C₂²×C₁₇	—	4	1	no	—
263	C₂²×C₁₇	—	4	1	no	—
264	C₂²×C₁₇	—	4	1	no	—
265	C₂²×C₁₇	—	4	1	no	—
266	C₂²×C₁₇	—	4	1	no	—
267	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂²×C₁₇	#552	1	1	yes	characteristic
269	C₂²×C₁₇	#553	1	1	yes	characteristic
270	C₄×C₁₇	—	2	2	no	—
271	C₄×C₁₇	—	2	1	no	—
272	C₄×C₁₇	—	2	1	no	—
273	C₄×C₁₇	—	2	1	no	—
274	C₄×C₁₇	—	4	1	no	—
275	C₄×C₁₇	—	4	1	no	—
276	C₄×C₁₇	—	4	1	no	—
277	C₄×C₁₇	—	4	1	no	—
278	C₄×C₁₇	—	4	1	no	—
279	C₄×C₁₇	#443	1	2	yes	—
280	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
281	C₄×C₁₇	#520	1	1	yes	characteristic
282	C₄×C₁₇	#546	1	1	yes	characteristic
283	C₄×C₁₇	#548	1	1	yes	characteristic
284	Dic₁₇	—	4	4	no	—
285	C₂×#135	C₂×D₁₇	1	1	yes	characteristic
286	C₂×#131	—	17	2	no	—
287	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
288	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
289	C₄×Q₁₆	Dic₁₇	1	1	yes	characteristic, complemented
290	C₄×Q₁₆	Dic₁₇	1	1	yes	characteristic, complemented
291	C₄×SD₁₆	Dic₁₇	1	1	yes	characteristic, complemented
292	C₄×SD₁₆	Dic₁₇	1	1	yes	characteristic, complemented
293	C₄×SD₁₆	Dic₁₇	1	1	yes	characteristic, complemented
294	C₄×SD₁₆	Dic₁₇	1	1	yes	characteristic, complemented
295	C₄×D₈	Dic₁₇	1	1	yes	characteristic, complemented
296	C₄×D₈	Dic₁₇	1	1	yes	characteristic, complemented
297	#433	—	34	2	no	—
298	#432	—	34	1	no	—
299	#431	—	34	1	no	—
300	#427	C₂×D₁₇	1	1	yes	characteristic
301	#424	—	17	2	no	—
302	#424	—	34	2	no	—
303	#423	—	17	1	no	—
304	#423	—	17	1	no	—
305	#423	—	34	1	no	—
306	C₂×C₄⋊C₈	—	17	1	no	—
307	C₂×C₄⋊C₈	—	34	1	no	—
308	C₂×#104	—	17	2	no	—
309	C₂×#104	—	17	2	no	—
310	#416	C₂×D₁₇	1	1	yes	characteristic
311	#416	C₂×D₁₇	1	1	yes	characteristic
312	#408	—	17	2	no	—
313	#405	—	17	2	no	—
314	C₂×C₄×C₈	—	17	2	no	—
315	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
316	C₄×C₄⋊C₄	—	17	1	no	—
317	#341	—	17	2	no	—
318	#341	—	17	2	no	—
319	#339	—	17	2	no	—
320	#339	—	17	2	no	—
321	#336	—	17	2	no	—
322	C₂×C₁₇	—	2	1	no	—
323	C₂×C₁₇	—	2	1	no	—
324	C₂×C₁₇	—	4	2	no	—
325	C₂×C₁₇	—	8	1	no	—
326	C₂×C₁₇	#2352	1	1	yes	characteristic
327	C₂×C₁₇	C₂×#443	1	1	yes	characteristic
328	C₂×C₁₇	#2957	1	1	yes	characteristic
329	C₂×#41	C₂²×D₁₇	1	1	yes	characteristic
330	C₂×#41	C₂²×D₁₇	1	1	yes	characteristic
331	#135	—	2	2	no	—
332	#135	—	2	2	no	—
333	C₂×Q₁₆	C₂×Dic₁₇	1	1	yes	characteristic
334	C₂×SD₁₆	C₂×Dic₁₇	1	1	yes	characteristic
335	C₂×SD₁₆	C₂×Dic₁₇	1	1	yes	characteristic
336	C₂×D₈	C₂×Dic₁₇	1	1	yes	characteristic
337	#131	—	34	4	no	—
338	#131	—	68	2	no	—
339	C₂×M₁₆	—	17	2	no	—
340	C₂×M₁₆	—	17	2	no	—
341	C₂×M₁₆	—	34	2	no	—
342	C₂²×C₈	—	17	2	no	—
343	C₂²×C₈	—	34	2	no	—
344	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
346	C₄×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
347	C₄×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
348	C₄×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
349	C₄×Q₈	C₂×Dic₁₇	1	1	yes	characteristic
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	C₂×Dic₁₇	1	1	yes	characteristic
355	C₄×D₄	C₂×Dic₁₇	1	1	yes	characteristic
356	C₄×D₄	C₂×Dic₁₇	1	1	yes	characteristic
357	C₄×D₄	C₂×Dic₁₇	1	1	yes	characteristic
358	#117	—	2	1	no	—
359	#117	—	2	1	no	—
360	#117	C₂²×D₁₇	1	1	yes	characteristic
361	#117	C₂²×D₁₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	—	34	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	17	2	no	—
366	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
367	#107	C₂×Dic₁₇	1	1	yes	characteristic
368	#107	C₂×Dic₁₇	1	1	yes	characteristic
369	#106	C₂×Dic₁₇	1	1	yes	characteristic
370	#106	C₂×Dic₁₇	1	1	yes	characteristic
371	C₄⋊C₈	—	17	1	no	—
372	C₄⋊C₈	—	17	1	no	—
373	C₄⋊C₈	—	17	2	no	—
374	C₄⋊C₈	—	34	2	no	—
375	C₄⋊C₈	—	34	2	no	—
376	C₄⋊C₈	—	34	1	no	—
377	C₄⋊C₈	—	34	1	no	—
378	C₄⋊C₈	—	34	1	no	—
379	C₄⋊C₈	—	34	1	no	—
380	#104	—	34	4	no	—
381	#104	—	68	2	no	—
382	#103	C₂×Dic₁₇	1	1	yes	characteristic
383	#103	C₂×Dic₁₇	1	1	yes	characteristic
384	#103	C₂×Dic₁₇	1	1	yes	characteristic
385	#103	C₂×Dic₁₇	1	1	yes	characteristic
386	#102	C₂×Dic₁₇	1	1	yes	characteristic
387	#102	C₂×Dic₁₇	1	1	yes	characteristic
388	#102	C₂×Dic₁₇	1	1	yes	characteristic
389	#102	C₂×Dic₁₇	1	1	yes	characteristic
390	C₂²⋊C₈	—	34	2	no	—
391	C₂²⋊C₈	—	34	2	no	—
392	#97	—	34	2	no	—
393	C₄×C₈	—	34	2	no	—
394	C₄×C₈	—	68	2	no	—
395	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
396	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
397	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
398	C₄×C₈	C₂×Dic₁₇	1	1	yes	characteristic
399	#95	—	34	1	no	—
400	C₁₇	#22783	1	1	yes	characteristic, complemented, Sylow
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	2	1	no	—
406	#41	—	2	1	no	—
407	#41	#63252	1	2	yes	—
408	#41	#63252	1	2	yes	—
409	C₂×Q₈	C₂²×Dic₁₇	1	1	yes	characteristic
410	C₂×Q₈	C₂²×Dic₁₇	1	1	yes	characteristic
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	C₂²×Dic₁₇	1	1	yes	characteristic
414	C₂×D₄	C₂²×Dic₁₇	1	1	yes	characteristic
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	34	2	no	—
422	C₂²×C₄	#63254	1	1	yes	characteristic
423	C₂²×C₄	#63254	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
425	Q₁₆	—	2	2	no	—
426	SD₁₆	—	2	2	no	—
427	SD₁₆	—	2	2	no	—
428	D₈	—	2	2	no	—
429	M₁₆	—	34	2	no	—
430	M₁₆	—	34	2	no	—
431	M₁₆	—	34	2	no	—
432	M₁₆	—	34	2	no	—
433	M₁₆	—	68	4	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	17	2	no	—
439	C₂×C₈	—	17	2	no	—
440	C₂×C₈	—	34	2	no	—
441	C₂×C₈	—	34	2	no	—
442	C₂×C₈	—	34	2	no	—
443	C₂×C₈	—	34	2	no	—
444	C₂×C₈	—	68	4	no	—
445	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
446	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
447	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
448	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	34	4	no	—
454	C₄⋊C₄	C₂²×Dic₁₇	1	1	yes	characteristic
455	C₄⋊C₄	C₂²×Dic₁₇	1	1	yes	characteristic
456	C₄⋊C₄	C₂²×Dic₁₇	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×Dic₁₇	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	34	2	no	—
471	C₄²	—	34	2	no	—
472	C₄²	D₄×D₁₇	1	1	yes	characteristic
473	C₄²	D₄×D₁₇	1	1	yes	characteristic
474	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
475	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	C₂×#63254	1	1	yes	characteristic
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	#10587612	1	2	yes	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	2	1	no	—
487	D₄	—	2	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	#10587612	1	2	yes	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	8	1	no	—
506	C₂×C₄	—	8	1	no	—
507	C₂×C₄	—	34	4	no	—
508	C₂×C₄	—	68	2	no	—
509	C₂×C₄	—	68	2	no	—
510	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
511	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
512	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
513	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
514	C₂×C₄	C₂×#63252	1	1	yes	characteristic
515	C₂×C₄	C₂×#63252	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
517	C₂×C₄	#10587696	1	1	yes	characteristic
518	C₂×C₄	#10587697	1	1	yes	characteristic
519	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	34	2	no	—
525	C₈	—	34	2	no	—
526	C₈	—	68	2	no	—
527	C₈	—	68	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	C₂×D₄×Dic₁₇	1	1	yes	characteristic
537	C₂²	#11763499	1	1	yes	characteristic
538	C₂²	#11763505	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	68	4	no	—
549	C₄	#11762926	1	2	yes	—
550	C₄	C₂×#10587612	1	1	yes	characteristic
551	C₄	#11763292	1	1	yes	characteristic
552	C₄	#11763455	1	1	yes	characteristic
553	C₄	#11763468	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	1	no	—
558	C₂	#14531713	1	1	yes	characteristic
559	C₂	C₂×#11762926	1	1	yes	characteristic
560	C₂	#14537701	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×#135	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×C₁₇×#135	C₂²
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₄×#135	D₁₇
hypocenter	C₁₇	#22783
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #14537450	C₂	semidirect
2. #14537352	C₂	semidirect
3. #14529490	C₂	semidirect
4. #14529385	C₂	semidirect
6. #14528922	C₂	semidirect
7. #14528804	C₂	semidirect
8. #14528804	C₂	semidirect
9. C₈×C₄⋊Dic₁₇	C₂	semidirect
10. #14528624	C₂	semidirect
37. C₄×Q₁₆×C₁₇	C₄	semidirect
38. C₄×Q₁₆×C₁₇	C₄	semidirect
39. C₄×SD₁₆×C₁₇	C₄	semidirect
40. C₄×SD₁₆×C₁₇	C₄	semidirect
41. C₄×SD₁₆×C₁₇	C₄	semidirect
42. C₄×SD₁₆×C₁₇	C₄	semidirect
43. C₄×D₈×C₁₇	C₄	semidirect
44. C₄×D₈×C₁₇	C₄	semidirect
289. C₄×Q₁₆	Dic₁₇	semidirect
290. C₄×Q₁₆	Dic₁₇	semidirect
291. C₄×SD₁₆	Dic₁₇	semidirect
292. C₄×SD₁₆	Dic₁₇	semidirect
293. C₄×SD₁₆	Dic₁₇	semidirect
294. C₄×SD₁₆	Dic₁₇	semidirect
295. C₄×D₈	Dic₁₇	semidirect
296. C₄×D₈	Dic₁₇	semidirect
400. C₁₇	#22783	semidirect

Maximal subgroups

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

subgroup	index
#14537450	2
#14537352	2
#14529490	2
#14529385	2
#14529113	2
#14528922	2
#14528804	2
C₈×C₄⋊Dic₁₇	2
#14528624	2
C₄×C₁₇×#135	2
#22783	17