Subgroups — #17000078

Order 4352.

704 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14537751	C₂	1	1	yes	maximal, characteristic
2	#14537751	C₂	1	1	yes	maximal, characteristic
3	#14527087	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527084	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527084	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527081	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527079	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527079	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527077	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527074	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527073	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527068	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527065	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#63223	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#2922	C₂	1	1	yes	maximal, characteristic
16	#11762940	C₄	1	2	yes	—
17	#11762940	C₄	1	2	yes	—
18	#11762887	C₄	1	2	yes	—
19	#11762887	C₄	1	2	yes	—
20	#11762881	C₄	1	2	yes	—
21	#11762881	C₄	1	2	yes	—
22	#11762881	C₄	1	2	yes	—
23	#11762881	C₄	1	2	yes	—
24	#11762862	C₂²	1	1	yes	characteristic
25	#11762862	C₂²	1	1	yes	characteristic
26	#11762862	C₂²	1	1	yes	characteristic
27	#11762862	C₂²	1	1	yes	characteristic
28	#11762862	C₂²	1	1	yes	characteristic
29	#11762862	C₂²	1	1	yes	characteristic
30	C₄×#63223	C₂²	1	1	yes	characteristic
31	C₄×#63223	C₂²	1	1	yes	characteristic
32	C₄×#63223	C₂²	1	1	yes	characteristic
33	C₄×#63223	C₂²	1	1	yes	characteristic
34	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
35	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
36	#11762531	C₂²	1	1	yes	characteristic
37	#11762531	C₂²	1	1	yes	characteristic
38	#11762531	C₂²	1	1	yes	characteristic
39	#11762531	C₂²	1	1	yes	characteristic
40	#11762531	C₂²	1	1	yes	characteristic
41	#11762531	C₂²	1	1	yes	characteristic
42	#11762531	C₂²	1	1	yes	characteristic
43	#11762531	C₂²	1	1	yes	characteristic
44	#11762530	C₂²	1	1	yes	characteristic
45	#11762530	C₂²	1	1	yes	characteristic
46	#11762530	C₂²	1	1	yes	characteristic
47	#11762530	C₂²	1	1	yes	characteristic
48	C₈×#3622	C₂²	1	1	yes	characteristic
49	C₈×#3622	C₂²	1	1	yes	characteristic
50	C₈×#3622	C₂²	1	1	yes	characteristic
51	C₈×#3622	C₂²	1	1	yes	characteristic
52	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
53	C₁₇×#433	C₄	1	2	yes	—
54	C₁₇×#433	C₄	1	2	yes	—
55	C₁₇×#431	C₂²	1	1	yes	characteristic
56	C₁₇×#431	C₂²	1	1	yes	characteristic
57	C₁₇×#431	C₂²	1	1	yes	characteristic
58	C₁₇×#431	C₂²	1	1	yes	characteristic
59	C₁₇×#424	C₄	1	2	yes	—
60	C₁₇×#408	C₄	1	2	yes	—
61	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
63	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
64	C₂×M₁₆×C₁₇	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
66	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
67	C₄×Q₈×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	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
72	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
74	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
75	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
76	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
80	C₂×#63223	C₂×C₄	1	2	yes	—
81	C₂×#63223	C₂×C₄	1	2	yes	—
82	C₂×#63223	C₂×C₄	1	2	yes	—
83	C₂×#63223	C₂×C₄	1	2	yes	—
84	C₂²×#3622	C₂×C₄	1	2	yes	—
85	C₂²×#3622	C₂×C₄	1	2	yes	—
86	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
89	C₁₇×C₄⋊C₈	C₂×C₄	1	2	yes	—
90	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₇×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₁₇×#97	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
100	C₂²⋊#3622	C₂×C₄	1	2	yes	—
101	C₂²⋊#3622	C₂×C₄	1	2	yes	—
102	C₂²⋊#3622	C₂×C₄	1	2	yes	—
103	C₂²⋊#3622	C₂×C₄	1	2	yes	—
104	C₂²⋊#3622	C₂×C₄	1	2	yes	—
105	C₂²⋊#3622	C₂×C₄	1	2	yes	—
106	C₄⋊#3622	C₂×C₄	1	2	yes	—
107	C₄⋊#3622	C₂×C₄	1	2	yes	—
108	C₄⋊#3622	C₂×C₄	1	2	yes	—
109	C₄⋊#3622	C₂×C₄	1	2	yes	—
110	C₄⋊#3622	C₂×C₄	1	2	yes	—
111	C₄⋊#3622	C₂×C₄	1	2	yes	—
112	#10587474	C₂×C₄	1	2	yes	—
113	#10587474	C₂×C₄	1	2	yes	—
114	#10587474	C₂×C₄	1	2	yes	—
115	#10587474	C₂×C₄	1	2	yes	—
116	C₄×#3622	C₂×C₄	1	2	yes	—
117	C₄×#3622	C₂×C₄	1	2	yes	—
118	C₄×#3622	C₂³	1	1	yes	characteristic
119	C₄×#3622	C₂³	1	1	yes	characteristic
120	C₄×#3622	C₂³	1	1	yes	characteristic
121	C₄×#3622	C₂³	1	1	yes	characteristic
122	C₄×#3622	C₂³	1	1	yes	characteristic
123	C₄×#3622	C₂³	1	1	yes	characteristic
124	C₄×#3622	C₂³	1	1	yes	characteristic
125	C₄×#3622	C₂³	1	1	yes	characteristic
126	#41×C₁₇	—	4	2	no	—
127	C₂×Q₈×C₁₇	C₄²	1	1	yes	characteristic
128	C₂×D₄×C₁₇	C₄²	1	1	yes	characteristic
129	C₂×D₄×C₁₇	C₄²	1	1	yes	characteristic
130	C₂×D₄×C₁₇	C₄²	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
140	M₁₆×C₁₇	—	4	2	no	—
141	C₂×C₈×C₁₇	—	4	2	no	—
142	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
146	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
147	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
148	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
149	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
150	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
151	C₄⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
152	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
153	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
154	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
155	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
156	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
157	C₂²⋊C₄×C₁₇	C₄²	1	1	yes	characteristic
158	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
168	#63223	—	2	4	no	—
169	#63223	—	2	4	no	—
170	#63223	—	4	2	no	—
171	#63223	—	4	2	no	—
172	C₂×#3622	—	2	4	no	—
173	C₂×#3622	—	4	2	no	—
174	C₂×#3622	C₂²×C₄	1	2	yes	—
175	C₂×#3622	C₂²×C₄	1	2	yes	—
176	C₂×#3622	C₂²×C₄	1	2	yes	—
177	C₂×#3622	C₂²×C₄	1	2	yes	—
178	C₂×#3622	C₂²×C₄	1	2	yes	—
179	C₂×#3622	C₂²×C₄	1	2	yes	—
180	C₂×#3622	C₂²×C₄	1	2	yes	—
181	C₂×#3622	C₂²×C₄	1	2	yes	—
182	#17340	—	17	1	no	maximal, Sylow
183	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
184	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
185	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
186	Q₈×C₁₇	—	4	1	no	—
187	D₄×C₁₇	—	4	1	no	—
188	D₄×C₁₇	—	4	1	no	—
189	D₄×C₁₇	—	4	1	no	—
190	C₂×C₄×C₁₇	—	2	2	no	—
191	C₂×C₄×C₁₇	—	2	2	no	—
192	C₂×C₄×C₁₇	—	2	2	no	—
193	C₂×C₄×C₁₇	—	2	2	no	—
194	C₂×C₄×C₁₇	—	2	2	no	—
195	C₂×C₄×C₁₇	—	2	2	no	—
196	C₂×C₄×C₁₇	—	2	2	no	—
197	C₂×C₄×C₁₇	—	2	2	no	—
198	C₂×C₄×C₁₇	—	2	2	no	—
199	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
202	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
203	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
204	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
208	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
211	C₈×C₁₇	—	2	2	no	—
212	C₈×C₁₇	—	2	2	no	—
213	C₈×C₁₇	—	2	2	no	—
214	C₈×C₁₇	—	2	2	no	—
215	#3622	—	2	2	no	—
216	#3622	—	2	2	no	—
217	#3622	—	2	2	no	—
218	#3622	—	2	2	no	—
219	#3622	—	2	2	no	—
220	#3622	—	2	2	no	—
221	#3622	—	2	2	no	—
222	#3622	#131	1	4	yes	—
223	#2965	—	17	1	no	—
224	#2965	—	17	1	no	—
225	#2922	D₁₇	1	1	yes	characteristic
226	#1455	—	17	1	no	—
227	#1454	—	17	1	no	—
228	#1454	—	17	1	no	—
229	#1453	—	17	1	no	—
230	#1453	—	17	1	no	—
231	#1453	—	17	1	no	—
232	#1452	—	17	1	no	—
233	#1451	—	17	1	no	—
234	#1451	—	17	1	no	—
235	#1450	—	17	1	no	—
236	C₈×M₁₆	—	17	1	no	—
237	C₈×M₁₆	—	17	1	no	—
238	C₂²×C₁₇	—	2	1	no	—
239	C₂²×C₁₇	—	2	1	no	—
240	C₂²×C₁₇	—	2	1	no	—
241	C₂²×C₁₇	—	2	1	no	—
242	C₂²×C₁₇	—	2	1	no	—
243	C₂²×C₁₇	—	2	1	no	—
244	C₂²×C₁₇	—	2	1	no	—
245	C₂²×C₁₇	—	2	1	no	—
246	C₂²×C₁₇	—	2	1	no	—
247	C₂²×C₁₇	C₂²×C₄²	1	1	yes	characteristic
248	C₄×C₁₇	—	2	1	no	—
249	C₄×C₁₇	—	2	1	no	—
250	C₄×C₁₇	—	2	1	no	—
251	C₄×C₁₇	—	2	1	no	—
252	C₄×C₁₇	—	2	1	no	—
253	C₄×C₁₇	—	2	1	no	—
254	C₄×C₁₇	—	2	1	no	—
255	C₄×C₁₇	—	2	1	no	—
256	C₄×C₁₇	—	2	1	no	—
257	C₄×C₁₇	C₂×#131	1	2	yes	—
258	C₄×C₁₇	#568	1	2	yes	—
259	C₄×C₁₇	#568	1	2	yes	—
260	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
261	#446	—	17	2	no	—
262	#446	—	17	2	no	—
263	#436	—	17	2	no	—
264	#436	—	17	2	no	—
265	#435	—	17	2	no	—
266	#435	—	17	2	no	—
267	#435	—	17	2	no	—
268	#435	—	17	2	no	—
269	#433	Dic₁₇	1	2	yes	—
270	#433	Dic₁₇	1	2	yes	—
271	#431	—	17	1	no	—
272	#431	—	17	1	no	—
273	#431	—	17	1	no	—
274	#431	—	17	1	no	—
275	#431	—	17	1	no	—
276	#431	—	17	1	no	—
277	#431	C₂×D₁₇	1	1	yes	characteristic
278	#431	C₂×D₁₇	1	1	yes	characteristic
279	#431	C₂×D₁₇	1	1	yes	characteristic
280	#431	C₂×D₁₇	1	1	yes	characteristic
281	#424	Dic₁₇	1	2	yes	—
282	#408	Dic₁₇	1	2	yes	—
283	C₄×M₁₆	—	17	1	no	—
284	C₄×M₁₆	—	17	1	no	—
285	C₄×M₁₆	—	17	1	no	—
286	C₄×M₁₆	—	17	1	no	—
287	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
288	C₂×C₄×C₈	—	17	1	no	—
289	C₂×C₄×C₈	—	17	1	no	—
290	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
291	#322	—	17	1	no	—
292	#322	—	17	1	no	—
293	#322	—	17	1	no	—
294	#322	—	17	1	no	—
295	#322	—	17	1	no	—
296	#322	—	17	1	no	—
297	#322	—	17	1	no	—
298	#322	—	17	1	no	—
299	#322	—	17	1	no	—
300	#322	—	17	1	no	—
301	#322	—	17	1	no	—
302	#322	—	17	1	no	—
303	C₈²	—	17	1	no	—
304	C₈²	—	17	1	no	—
305	C₈²	—	17	1	no	—
306	C₈²	—	17	1	no	—
307	C₂×C₁₇	—	4	1	no	—
308	C₂×C₁₇	—	4	1	no	—
309	C₂×C₁₇	—	4	1	no	—
310	C₂×C₁₇	#2873	1	1	yes	characteristic
311	C₂×C₁₇	C₄×#131	1	1	yes	characteristic
312	C₂×C₁₇	#2875	1	1	yes	characteristic
313	C₂×#41	C₂×Dic₁₇	1	1	yes	characteristic
314	C₂×M₁₆	—	17	2	no	—
315	C₂×M₁₆	—	17	2	no	—
316	C₂×M₁₆	—	17	2	no	—
317	C₂×M₁₆	—	17	2	no	—
318	C₂×M₁₆	C₂×Dic₁₇	1	2	yes	—
319	C₂²×C₈	—	17	2	no	—
320	C₂²×C₈	—	17	2	no	—
321	C₂²×C₈	C₂×Dic₁₇	1	2	yes	—
322	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
323	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
324	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
325	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
326	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
327	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
328	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
329	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
330	#117	C₂×Dic₁₇	1	1	yes	characteristic
331	#117	C₂×Dic₁₇	1	1	yes	characteristic
332	#117	C₂×Dic₁₇	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
335	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
336	C₄⋊C₈	—	17	2	no	—
337	C₄⋊C₈	—	17	2	no	—
338	C₄⋊C₈	—	17	2	no	—
339	C₄⋊C₈	—	17	2	no	—
340	C₄⋊C₈	—	17	2	no	—
341	C₄⋊C₈	—	17	2	no	—
342	C₄⋊C₈	C₂×Dic₁₇	1	2	yes	—
343	C₄⋊C₈	C₂×Dic₁₇	1	2	yes	—
344	C₄⋊C₈	C₂×Dic₁₇	1	2	yes	—
345	C₄⋊C₈	C₂×Dic₁₇	1	2	yes	—
346	C₂²⋊C₈	—	17	2	no	—
347	C₂²⋊C₈	—	17	2	no	—
348	C₂²⋊C₈	—	17	2	no	—
349	C₂²⋊C₈	—	17	2	no	—
350	C₂²⋊C₈	—	17	2	no	—
351	C₂²⋊C₈	—	17	2	no	—
352	C₂²⋊C₈	C₂×Dic₁₇	1	2	yes	—
353	C₂²⋊C₈	C₂×Dic₁₇	1	2	yes	—
354	C₂²⋊C₈	C₂×Dic₁₇	1	2	yes	—
355	C₂²⋊C₈	C₂×Dic₁₇	1	2	yes	—
356	#97	—	17	2	no	—
357	#97	—	17	2	no	—
358	#97	—	17	2	no	—
359	#97	—	17	2	no	—
360	#97	C₂×Dic₁₇	1	2	yes	—
361	C₄×C₈	—	17	2	no	—
362	C₄×C₈	—	17	2	no	—
363	C₄×C₈	—	17	1	no	—
364	C₄×C₈	—	17	1	no	—
365	C₄×C₈	—	17	1	no	—
366	C₄×C₈	—	17	1	no	—
367	C₄×C₈	—	17	1	no	—
368	C₄×C₈	—	17	1	no	—
369	C₄×C₈	—	17	1	no	—
370	C₄×C₈	—	17	1	no	—
371	C₄×C₈	C₂×Dic₁₇	1	2	yes	—
372	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
376	C₁₇	#17340	1	1	yes	characteristic, complemented, Sylow
377	#41	—	4	2	no	—
378	C₂×Q₈	C₄×Dic₁₇	1	1	yes	characteristic
379	C₂×D₄	C₄×Dic₁₇	1	1	yes	characteristic
380	C₂×D₄	C₄×Dic₁₇	1	1	yes	characteristic
381	C₂×D₄	C₄×Dic₁₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
391	M₁₆	—	4	2	no	—
392	M₁₆	—	34	4	no	—
393	M₁₆	—	34	4	no	—
394	M₁₆	—	68	2	no	—
395	M₁₆	—	68	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	—	17	2	no	—
398	C₂×C₈	—	17	2	no	—
399	C₂×C₈	—	17	2	no	—
400	C₂×C₈	—	17	2	no	—
401	C₂×C₈	—	17	2	no	—
402	C₂×C₈	—	17	2	no	—
403	C₂×C₈	—	17	2	no	—
404	C₂×C₈	—	17	2	no	—
405	C₂×C₈	—	34	4	no	—
406	C₂×C₈	—	68	2	no	—
407	C₂×C₈	C₂²×Dic₁₇	1	2	yes	—
408	C₂×C₈	C₂²×Dic₁₇	1	2	yes	—
409	C₂×C₈	C₂²×Dic₁₇	1	2	yes	—
410	C₂×C₈	C₂²×Dic₁₇	1	2	yes	—
411	C₄⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
412	C₄⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
413	C₄⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
414	C₄⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
415	C₄⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
416	C₄⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
417	C₂²⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
418	C₂²⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
419	C₂²⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
420	C₂²⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
421	C₂²⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
422	C₂²⋊C₄	C₄×Dic₁₇	1	1	yes	characteristic
423	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
425	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
426	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
428	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
429	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
430	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
431	C₄²	C₂²×Dic₁₇	1	1	yes	characteristic
432	C₄²	C₂³×D₁₇	1	1	yes	characteristic
433	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
434	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
435	C₂³	C₂×C₄×Dic₁₇	1	1	yes	characteristic
436	Q₈	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
457	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
460	C₂×C₄	C₂³×Dic₁₇	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	17	4	no	—
466	C₈	—	34	2	no	—
467	C₈	—	34	2	no	—
468	C₈	—	34	2	no	—
469	C₈	—	34	2	no	—
470	C₈	—	34	2	no	—
471	C₈	—	34	2	no	—
472	C₈	—	34	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	C₂²×C₄×Dic₁₇	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	#131×D₁₇	1	2	yes	—
493	C₄	#11763574	1	2	yes	—
494	C₄	#11763576	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	#14537203	1	1	yes	characteristic
499	C₂	#131×Dic₁₇	1	1	yes	characteristic
500	C₂	#14537210	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₄²
Fitting	C₁₇×#2922	C₂
prime radical	C₂×#41×C₁₇	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#2922	D₁₇
hypocenter	C₁₇	#17340
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ #2922

Complements

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

N	H ≅ G/N	type
3. #14527087	C₂	semidirect
4. #14527084	C₂	semidirect
5. #14527084	C₂	semidirect
6. #14527081	C₂	semidirect
7. #14527079	C₂	semidirect
8. #14527079	C₂	semidirect
9. #14527077	C₂	semidirect
10. #14527074	C₂	semidirect
11. #14527073	C₂	semidirect
12. #14527068	C₂	semidirect
13. #14527065	C₂	semidirect
14. C₈×#63223	C₂	semidirect
376. C₁₇	#17340	semidirect

Maximal subgroups

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

subgroup	index
#14537751	2
#14527087	2
#14527084	2
#14527081	2
#14527079	2
#14527077	2
#14527074	2
#14527073	2
#14527068	2
#14527065	2
C₈×#63223	2
C₁₇×#2922	2
#17340	17