Subgroups — #17003307

Order 4352.

778 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11762862	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#63223	C₂	1	1	yes	maximal, characteristic
3	#14527537	C₂	1	4	yes	maximal, complemented
4	#14527534	C₂	1	4	yes	maximal, complemented
5	#14527530	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₇×#431	C₂	1	1	yes	maximal, characteristic
7	C₂²×#63223	C₄	1	1	yes	characteristic
8	C₂²×#63223	C₄	1	1	yes	characteristic
9	#11762862	—	2	1	no	—
10	#11762862	—	2	1	no	—
11	#11762862	C₂²	1	2	yes	—
12	#11762862	C₂²	1	2	yes	—
13	C₂×C₄⋊#3622	C₂²	1	2	yes	—
14	C₂×C₂²⋊#3622	—	2	1	no	—
15	C₄×#63223	C₄	1	2	yes	—
16	C₄×#63223	C₄	1	2	yes	—
17	C₄×#63223	C₂²	1	2	yes	—
18	C₄×#63223	C₂²	1	2	yes	—
19	C₂×#10587474	C₄	1	2	yes	—
20	C₂×C₄×#3622	—	2	1	no	—
21	C₂×C₄×#3622	C₂²	1	2	yes	—
22	#11762561	C₂²	1	8	yes	complemented
23	#11762559	C₂²	1	8	yes	complemented
24	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
25	C₁₇×#431	—	2	1	no	—
26	C₁₇×#431	—	2	1	no	—
27	C₁₇×#431	C₂²	1	2	yes	—
28	C₁₇×#431	C₂²	1	2	yes	—
29	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
30	C₂×C₁₇×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₁₇	—	2	1	no	—
32	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₇	Q₈	1	1	yes	characteristic
35	C₂²×C₈×C₁₇	—	2	2	no	—
36	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
43	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
48	C₂×#63223	—	2	4	no	—
49	C₂×#63223	C₈	1	8	yes	complemented
50	C₂×#63223	C₂×C₄	1	2	yes	—
51	C₂×#63223	C₂×C₄	1	2	yes	—
52	C₂×#63223	C₂×C₄	1	2	yes	—
53	C₂×#63223	C₂×C₄	1	2	yes	—
54	C₂²×#3622	—	2	2	no	—
55	C₂²×#3622	C₂×C₄	1	2	yes	—
56	C₂²×#3622	C₂×C₄	1	2	yes	—
57	C₁₇×C₄⋊C₈	—	2	2	no	—
58	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
59	C₁₇×C₂²⋊C₈	—	2	2	no	—
60	C₁₇×C₂²⋊C₈	—	2	2	no	—
61	C₄×C₈×C₁₇	—	2	2	no	—
62	C₄×C₈×C₁₇	—	2	2	no	—
63	C₂²⋊#3622	—	2	2	no	—
64	C₂²⋊#3622	—	2	2	no	—
65	C₄⋊#3622	—	2	2	no	—
66	C₄⋊#3622	C₂³	1	4	yes	—
67	#10587474	C₂×C₄	1	4	yes	—
68	#10587474	C₂×C₄	1	4	yes	—
69	C₄×#3622	—	2	2	no	—
70	C₄×#3622	—	2	2	no	—
71	C₄×#3622	C₂×C₄	1	4	yes	—
72	C₄×#3622	C₂³	1	4	yes	—
73	C₂⁴×C₁₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	—	4	2	no	—
75	C₂²×C₄×C₁₇	—	4	2	no	—
76	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
86	C₂²×C₄×C₁₇	M₁₆	1	4	yes	—
87	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₈×C₁₇	—	2	4	no	—
97	C₂×C₈×C₁₇	—	4	4	no	—
98	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₁₇	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
114	#63223	—	2	4	no	—
115	#63223	—	2	4	no	—
116	#63223	C₂×C₈	1	8	yes	complemented
117	#63223	C₂×C₈	1	8	yes	complemented
118	C₂×#3622	—	2	4	no	—
119	C₂×#3622	—	2	4	no	—
120	C₂×#3622	—	4	4	no	—
121	C₂×#3622	C₂×C₈	1	8	yes	complemented
122	C₂×#3622	C₂²×C₄	1	4	yes	—
123	C₂×#3622	C₂²×C₄	1	4	yes	—
124	#17787	—	17	1	no	maximal, Sylow
125	C₂³×C₁₇	—	4	1	no	—
126	C₂³×C₁₇	—	4	1	no	—
127	C₂³×C₁₇	C₄⋊C₈	1	4	yes	—
128	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₇	—	2	2	no	—
132	C₂×C₄×C₁₇	—	2	2	no	—
133	C₂×C₄×C₁₇	—	2	2	no	—
134	C₂×C₄×C₁₇	—	2	2	no	—
135	C₂×C₄×C₁₇	—	2	2	no	—
136	C₂×C₄×C₁₇	—	2	2	no	—
137	C₂×C₄×C₁₇	—	4	1	no	—
138	C₂×C₄×C₁₇	—	4	1	no	—
139	C₂×C₄×C₁₇	—	4	1	no	—
140	C₂×C₄×C₁₇	—	4	1	no	—
141	C₂×C₄×C₁₇	—	4	1	no	—
142	C₂×C₄×C₁₇	—	4	1	no	—
143	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
144	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
145	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
146	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₁₇	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
159	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
160	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
164	C₈×C₁₇	—	4	4	no	—
165	#3622	—	2	4	no	—
166	#3622	—	4	4	no	—
167	#3622	C₂²×C₈	1	8	yes	—
168	C₂×#431	—	17	1	no	—
169	C₂×#431	D₁₇	1	1	yes	characteristic
170	C₂×C₄×M₁₆	—	17	1	no	—
171	#1565	—	17	4	no	—
172	#1565	—	17	4	no	—
173	#1564	—	17	4	no	—
174	C₂²×C₁₇	—	2	1	no	—
175	C₂²×C₁₇	—	2	1	no	—
176	C₂²×C₁₇	—	2	1	no	—
177	C₂²×C₁₇	—	2	1	no	—
178	C₂²×C₁₇	—	2	1	no	—
179	C₂²×C₁₇	—	2	1	no	—
180	C₂²×C₁₇	—	4	4	no	—
181	C₂²×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
182	C₂²×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
183	C₂²×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
184	C₂²×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₄×C₁₇	—	2	1	no	—
186	C₄×C₁₇	—	2	1	no	—
187	C₄×C₁₇	—	2	1	no	—
188	C₄×C₁₇	—	2	1	no	—
189	C₄×C₁₇	—	2	1	no	—
190	C₄×C₁₇	—	2	1	no	—
191	C₄×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
192	C₄×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
193	C₄×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
194	C₄×C₁₇	#430	1	2	yes	—
195	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
196	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
197	C₄×C₁₇	#575	1	2	yes	—
198	C₂²×M₁₆	—	17	1	no	—
199	C₂²×M₁₆	—	17	1	no	—
200	C₂²×C₄²	C₂×D₁₇	1	1	yes	characteristic
201	#431	—	2	1	no	—
202	#431	—	2	1	no	—
203	#431	—	17	2	no	—
204	#431	—	17	2	no	—
205	#431	—	34	1	no	—
206	#431	—	34	1	no	—
207	#431	C₂×D₁₇	1	2	yes	—
208	#431	C₂×D₁₇	1	2	yes	—
209	C₂×C₄⋊C₈	—	17	2	no	—
210	C₂×C₄⋊C₈	C₂×D₁₇	1	2	yes	—
211	C₂×C₂²⋊C₈	—	2	1	no	—
212	C₂×C₂²⋊C₈	—	34	1	no	—
213	C₄×M₁₆	—	17	2	no	—
214	C₄×M₁₆	—	17	2	no	—
215	C₄×M₁₆	—	17	2	no	—
216	C₄×M₁₆	—	17	2	no	—
217	C₂×#97	—	17	2	no	—
218	C₂×C₄×C₈	—	2	1	no	—
219	C₂×C₄×C₈	—	17	2	no	—
220	C₂×C₄×C₈	—	34	1	no	—
221	#335	—	17	8	no	—
222	#334	—	17	8	no	—
223	C₂×C₁₇	—	2	2	no	—
224	C₂×C₁₇	—	2	2	no	—
225	C₂×C₁₇	—	2	2	no	—
226	C₂×C₁₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
227	C₂×C₁₇	#2911	1	1	yes	characteristic
228	C₂×C₁₇	C₂×#430	1	1	yes	characteristic
229	C₂³×C₄	Dic₃₄	1	1	yes	characteristic
230	C₂³×C₄	C₄×D₁₇	1	1	yes	characteristic
231	C₂³×C₄	C₂²⋊D₁₇	1	1	yes	characteristic
232	C₂×M₁₆	—	17	2	no	—
233	C₂×M₁₆	—	17	2	no	—
234	C₂×M₁₆	—	17	8	no	—
235	C₂×M₁₆	—	17	2	no	—
236	C₂×M₁₆	—	17	2	no	—
237	C₂×M₁₆	—	34	4	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	17	2	no	—
240	C₂²×C₈	—	17	2	no	—
241	C₂²×C₈	—	34	2	no	—
242	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
243	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
244	C₂×C₄²	Dic₃₄	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₁₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₁₇	1	1	yes	characteristic
251	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
253	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	17	4	no	—
256	C₄⋊C₈	—	34	2	no	—
257	C₄⋊C₈	C₂²×D₁₇	1	4	yes	—
258	C₂²⋊C₈	—	2	2	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	34	2	no	—
261	C₂²⋊C₈	—	34	2	no	—
262	#97	—	17	4	no	—
263	#97	—	17	4	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₄×C₈	—	17	4	no	—
267	C₄×C₈	—	17	4	no	—
268	C₄×C₈	—	34	2	no	—
269	C₄×C₈	—	34	2	no	—
270	C₁₇	#17787	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	#63225	1	1	yes	characteristic
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	C₈×D₁₇	1	4	yes	—
275	C₂²×C₄	#63218	1	4	yes	—
276	C₂²×C₄	#63225	1	1	yes	characteristic
277	C₂²×C₄	#63225	1	1	yes	characteristic
278	C₂²×C₄	#63225	1	1	yes	characteristic
279	C₂²×C₄	#63225	1	1	yes	characteristic
280	C₂²×C₄	#63225	1	1	yes	characteristic
281	C₂²×C₄	#63225	1	1	yes	characteristic
282	C₂²×C₄	#63225	1	1	yes	characteristic
283	C₂²×C₄	#63225	1	1	yes	characteristic
284	C₂²×C₄	#63225	1	1	yes	characteristic
285	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
286	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
294	M₁₆	—	17	8	no	—
295	M₁₆	—	17	8	no	—
296	M₁₆	—	34	4	no	—
297	M₁₆	—	34	4	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	17	4	no	—
301	C₂×C₈	—	17	8	no	—
302	C₂×C₈	—	17	4	no	—
303	C₂×C₈	—	34	4	no	—
304	C₂×C₈	—	34	4	no	—
305	C₂×C₈	—	68	4	no	—
306	C₄²	#63225	1	1	yes	characteristic
307	C₄²	#63225	1	1	yes	characteristic
308	C₄²	#63225	1	1	yes	characteristic
309	C₄²	#63225	1	1	yes	characteristic
310	C₄²	#63225	1	1	yes	characteristic
311	C₄²	#63225	1	1	yes	characteristic
312	C₄²	C₂×Dic₃₄	1	1	yes	characteristic
313	C₄²	C₂×Dic₃₄	1	1	yes	characteristic
314	C₄²	C₂×Dic₃₄	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
317	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
318	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
319	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
320	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
321	C₄²	C₂³×D₁₇	1	1	yes	characteristic
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	#10587485	1	4	yes	—
325	C₂³	C₂×#63225	1	1	yes	characteristic
326	C₂³	C₂×#63225	1	1	yes	characteristic
327	C₂³	C₂×#63225	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	#10587485	1	4	yes	—
341	C₂×C₄	#10587485	1	4	yes	—
342	C₂×C₄	#10587485	1	4	yes	—
343	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
344	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₁₇	1	2	yes	—
346	C₂×C₄	C₂×#63218	1	2	yes	—
347	C₂×C₄	C₂×#63218	1	2	yes	—
348	C₂×C₄	C₂×#63218	1	2	yes	—
349	C₂×C₄	C₂×#63225	1	1	yes	characteristic
350	C₂×C₄	C₂×#63225	1	1	yes	characteristic
351	C₂×C₄	C₂×#63225	1	1	yes	characteristic
352	C₂×C₄	C₂×#63225	1	1	yes	characteristic
353	C₂×C₄	C₂×#63225	1	1	yes	characteristic
354	C₂×C₄	C₂×#63225	1	1	yes	characteristic
355	C₂×C₄	C₂×#63225	1	1	yes	characteristic
356	C₂×C₄	C₂×#63225	1	1	yes	characteristic
357	C₂×C₄	C₂×#63225	1	1	yes	characteristic
358	C₂×C₄	C₂²×Dic₃₄	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
361	C₈	—	4	4	no	—
362	C₈	—	17	8	no	—
363	C₈	—	34	4	no	—
364	C₈	—	68	4	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	4	no	—
372	C₂²	C₂×#10587485	1	2	yes	—
373	C₂²	C₂×#10587485	1	2	yes	—
374	C₂²	C₂×#10587485	1	2	yes	—
375	C₂²	C₂²×#63225	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	C₂×#10587485	1	2	yes	—
383	C₄	C₂×#10587485	1	2	yes	—
384	C₄	C₂×#10587485	1	2	yes	—
385	C₄	#11762857	1	2	yes	—
386	C₄	C₂²×C₈×D₁₇	1	1	yes	characteristic
387	C₄	C₂²×#63218	1	1	yes	characteristic
388	C₄	#11763607	1	2	yes	—
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	2	2	no	—
392	C₂	C₂²×#10587485	1	1	yes	characteristic
393	C₂	#14537373	1	1	yes	characteristic
394	C₂	C₂×#11762857	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₇
commutator	C₄×C₁₇	C₂³×C₈
Frattini	C₄²	C₂³×D₁₇
Fitting	C₂×C₁₇×#431	C₂
socle	C₂²×C₁₇	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₇	C₄⋊C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	C₂×#431	D₁₇
hypocenter	C₁₇	#17787
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #14527537	C₂	semidirect
4. #14527534	C₂	semidirect
5. #14527530	C₂	semidirect
22. #11762561	C₂²	semidirect
23. #11762559	C₂²	semidirect
49. C₂×#63223	C₈	semidirect
116. #63223	C₂×C₈	semidirect
117. #63223	C₂×C₈	semidirect
121. C₂×#3622	C₂×C₈	semidirect
270. C₁₇	#17787	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11762862	2
C₂×C₄×#63223	2
#14527537	2
#14527534	2
#14527530	2
C₂×C₁₇×#431	2
#17787	17