Subgroups — #16940260

Order 4352.

774 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587489	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762764	C₂	1	1	yes	maximal, characteristic
3	C₂×#11762577	C₂	1	2	yes	maximal
4	#14528504	C₂	1	2	yes	maximal
5	C₂²×C₁₇×#108	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63223	C₂²	1	1	yes	characteristic
7	C₂×#10587612	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₇	C₂²	1	2	yes	—
9	C₂×#10587489	—	2	1	no	—
10	C₂×#10587489	—	2	1	no	—
11	C₂×#10587489	—	2	2	no	—
12	C₂×#10587489	C₄	1	4	yes	complemented
13	#11762764	—	2	2	no	—
14	#11762764	C₄	1	4	yes	complemented
15	C₂×#10587486	—	2	1	no	—
16	C₂×C₈×Dic₁₇	—	2	1	no	—
17	#11762577	—	2	4	no	—
18	#11762572	—	2	4	no	—
19	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
20	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×#108	—	2	2	no	—
22	C₂×C₁₇×#108	—	2	2	no	—
23	C₂×C₁₇×#108	C₄	1	4	yes	complemented
24	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₇	—	2	2	no	—
26	C₂×M₁₆×C₁₇	—	2	2	no	—
27	C₂×M₁₆×C₁₇	—	2	2	no	—
28	C₂×M₁₆×C₁₇	—	2	2	no	—
29	C₂×M₁₆×C₁₇	—	2	2	no	—
30	C₂×M₁₆×C₁₇	—	2	2	no	—
31	C₂×M₁₆×C₁₇	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₇	—	2	2	no	—
33	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₇	D₄	1	2	yes	—
39	C₂²×C₈×C₁₇	D₄	1	2	yes	—
40	C₂²×C₈×C₁₇	Q₈	1	2	yes	—
41	C₂×C₂²⋊Dic₁₇	—	2	1	no	—
42	#10587612	—	2	1	no	—
43	#10587612	—	2	1	no	—
44	#10587612	C₂×C₄	1	2	yes	—
45	#10587612	Q₈	1	2	yes	—
46	C₂×C₄⋊Dic₁₇	—	2	2	no	—
47	C₂×C₄⋊Dic₁₇	—	2	2	no	—
48	C₂×C₄⋊Dic₁₇	—	2	2	no	—
49	C₂×C₄⋊Dic₁₇	—	2	2	no	—
50	C₂×C₄⋊Dic₁₇	—	2	2	no	—
51	C₂×C₄⋊Dic₁₇	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊Dic₁₇	D₄	1	2	yes	—
53	C₂×C₄×Dic₁₇	—	2	1	no	—
54	C₂×#63223	—	2	1	no	—
55	C₂×#63223	—	2	1	no	—
56	C₂×#63223	—	2	1	no	—
57	C₂×#63223	C₂×C₄	1	2	yes	—
58	C₂×#63223	D₄	1	2	yes	—
59	C₂×#63223	Q₈	1	2	yes	—
60	C₂²×#3622	—	2	1	no	—
61	C₁₇×#108	—	2	8	no	—
62	#10587489	—	2	4	no	—
63	#10587489	—	2	4	no	—
64	#10587486	—	2	4	no	—
65	C₈×Dic₁₇	—	2	4	no	—
66	C₂⁴×C₁₇	#41	1	1	yes	characteristic
67	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
81	C₂²×Dic₁₇	—	2	2	no	—
82	C₂²×Dic₁₇	—	2	4	no	—
83	C₂²×Dic₁₇	—	4	2	no	—
84	C₂²×Dic₁₇	—	4	2	no	—
85	C₂²×Dic₁₇	—	8	4	no	—
86	M₁₆×C₁₇	—	2	4	no	—
87	M₁₆×C₁₇	—	2	4	no	—
88	M₁₆×C₁₇	—	4	2	no	—
89	M₁₆×C₁₇	—	4	2	no	—
90	C₂×C₈×C₁₇	—	2	4	no	—
91	C₂×C₈×C₁₇	—	4	2	no	—
92	C₂×C₈×C₁₇	—	4	2	no	—
93	C₂×C₈×C₁₇	C₄²	1	4	yes	—
94	C₂×C₈×C₁₇	C₂²⋊C₄	1	4	yes	—
95	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
98	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
99	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
101	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
102	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
103	C₂²⋊Dic₁₇	—	2	2	no	—
104	C₂²⋊Dic₁₇	—	2	2	no	—
105	C₄⋊Dic₁₇	—	2	2	no	—
106	C₄⋊Dic₁₇	—	2	4	no	—
107	C₄⋊Dic₁₇	—	2	4	no	—
108	C₄⋊Dic₁₇	—	4	2	no	—
109	C₄⋊Dic₁₇	—	4	2	no	—
110	C₄⋊Dic₁₇	C₄⋊C₄	1	4	yes	—
111	C₄×Dic₁₇	—	2	2	no	—
112	C₄×Dic₁₇	—	2	2	no	—
113	#63223	—	2	2	no	—
114	#63223	—	2	2	no	—
115	#63223	—	2	2	no	—
116	#63223	C₄⋊C₄	1	4	yes	—
117	C₂×#3622	—	2	2	no	—
118	C₂×#3622	—	2	2	no	—
119	C₂×#3622	—	2	2	no	—
120	#10870	—	17	1	no	maximal, Sylow
121	C₂³×C₁₇	—	2	2	no	—
122	C₂³×C₁₇	—	2	2	no	—
123	C₂³×C₁₇	#117	1	1	yes	characteristic
124	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
125	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
126	C₂³×C₁₇	#121	1	1	yes	characteristic
127	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂³×C₁₇	#124	1	1	yes	characteristic
129	C₂³×C₁₇	#125	1	1	yes	characteristic
130	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₇	#117	1	1	yes	characteristic
140	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
153	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
154	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×Dic₁₇	—	2	4	no	—
159	C₂×Dic₁₇	—	4	2	no	—
160	C₂×Dic₁₇	—	4	2	no	—
161	C₂×Dic₁₇	—	4	4	no	—
162	C₂×Dic₁₇	—	8	4	no	—
163	C₂×Dic₁₇	—	8	4	no	—
164	C₂×Dic₁₇	—	8	4	no	—
165	C₈×C₁₇	—	4	4	no	—
166	C₈×C₁₇	#95	1	4	yes	—
167	C₈×C₁₇	#95	1	4	yes	—
168	#3622	—	2	4	no	—
169	C₂²×#108	D₁₇	1	1	yes	characteristic
170	C₂²×#107	—	17	1	no	—
171	C₂×#405	—	17	1	no	—
172	C₂×#343	—	17	2	no	—
173	#1736	—	17	2	no	—
174	C₂²×C₁₇	—	2	2	no	—
175	C₂²×C₁₇	—	2	2	no	—
176	C₂²×C₁₇	—	2	2	no	—
177	C₂²×C₁₇	—	2	2	no	—
178	C₂²×C₁₇	—	2	1	no	—
179	C₂²×C₁₇	—	2	1	no	—
180	C₂²×C₁₇	—	2	1	no	—
181	C₂²×C₁₇	—	2	1	no	—
182	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₁₇	#380	1	1	yes	characteristic
184	C₂²×C₁₇	#382	1	1	yes	characteristic
185	C₂²×C₁₇	#389	1	1	yes	characteristic
186	C₂²×C₁₇	#389	1	1	yes	characteristic
187	C₂²×C₁₇	#390	1	1	yes	characteristic
188	C₂²×C₁₇	#391	1	1	yes	characteristic
189	C₂²×C₁₇	#472	1	2	yes	—
190	C₂²×C₁₇	#473	1	2	yes	—
191	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
192	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
193	C₄×C₁₇	#380	1	1	yes	characteristic
194	C₄×C₁₇	#384	1	1	yes	characteristic
195	C₄×C₁₇	#389	1	1	yes	characteristic
196	C₄×C₁₇	#389	1	1	yes	characteristic
197	C₄×C₁₇	#390	1	1	yes	characteristic
198	C₄×C₁₇	#391	1	1	yes	characteristic
199	Dic₁₇	—	4	4	no	—
200	Dic₁₇	—	8	4	no	—
201	C₂²×M₁₆	—	17	1	no	—
202	C₂²×M₁₆	C₂×D₁₇	1	2	yes	—
203	C₂³×C₈	C₂×D₁₇	1	1	yes	characteristic
204	C₂×#117	—	17	1	no	—
205	C₂²×C₄⋊C₄	—	17	2	no	—
206	C₂×#108	—	2	2	no	—
207	C₂×#108	—	2	2	no	—
208	C₂×#108	Dic₁₇	1	4	yes	complemented
209	C₂×#107	—	17	4	no	—
210	C₂×#107	—	34	1	no	—
211	C₂×#107	—	34	1	no	—
212	C₂×#107	—	34	2	no	—
213	#405	—	17	4	no	—
214	#405	—	34	2	no	—
215	C₂×#97	—	34	1	no	—
216	C₂×C₄×C₈	—	34	1	no	—
217	#343	—	34	4	no	—
218	#340	—	34	4	no	—
219	C₂×C₁₇	—	2	1	no	—
220	C₂×C₁₇	—	2	1	no	—
221	C₂×C₁₇	—	2	1	no	—
222	C₂×C₁₇	—	2	1	no	—
223	C₂×C₁₇	C₄⋊#95	1	1	yes	characteristic
224	C₂×C₁₇	#1816	1	2	yes	—
225	C₂×C₁₇	#1952	1	2	yes	—
226	C₂×C₁₇	#1978	1	1	yes	characteristic
227	C₂×C₁₇	#1979	1	1	yes	characteristic
228	C₂³×C₄	—	34	2	no	—
229	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	17	2	no	—
236	C₂×M₁₆	—	17	2	no	—
237	C₂×M₁₆	—	17	2	no	—
238	C₂×M₁₆	—	34	1	no	—
239	C₂×M₁₆	—	34	1	no	—
240	C₂×M₁₆	—	34	1	no	—
241	C₂×M₁₆	C₂×Dic₁₇	1	4	yes	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	34	1	no	—
244	C₂²×C₈	Dic₃₄	1	2	yes	—
245	C₂²×C₈	C₄×D₁₇	1	2	yes	—
246	C₂²×C₈	C₄×D₁₇	1	2	yes	—
247	C₂²×C₈	D₆₈	1	1	yes	characteristic
248	C₂²×C₈	D₆₈	1	1	yes	characteristic
249	C₂²×C₈	C₂×Dic₁₇	1	2	yes	—
250	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
251	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
252	#117	—	17	2	no	—
253	#117	—	17	2	no	—
254	#117	—	34	1	no	—
255	#117	—	34	1	no	—
256	C₂×C₄⋊C₄	—	17	2	no	—
257	C₂×C₄⋊C₄	—	17	4	no	—
258	C₂×C₄⋊C₄	—	34	2	no	—
259	C₂×C₄⋊C₄	—	34	2	no	—
260	C₂×C₄⋊C₄	—	34	2	no	—
261	C₂×C₄⋊C₄	—	34	2	no	—
262	C₂×C₄⋊C₄	—	34	2	no	—
263	C₂×C₂²⋊C₄	—	34	1	no	—
264	C₂×C₄²	—	34	1	no	—
265	#108	—	2	8	no	—
266	#107	—	34	4	no	—
267	#107	—	34	4	no	—
268	#97	—	34	4	no	—
269	C₄×C₈	—	34	4	no	—
270	C₁₇	#10870	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	#63256	1	1	yes	characteristic
272	C₂²×C₄	—	34	2	no	—
273	C₂²×C₄	—	34	4	no	—
274	C₂²×C₄	—	68	2	no	—
275	C₂²×C₄	—	68	2	no	—
276	C₂²×C₄	—	136	4	no	—
277	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
281	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
282	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
283	C₂²×C₄	#63254	1	1	yes	characteristic
284	C₂²×C₄	#63254	1	1	yes	characteristic
285	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
286	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
287	C₂²×C₄	#63256	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
291	M₁₆	—	2	4	no	—
292	M₁₆	—	2	4	no	—
293	M₁₆	—	4	2	no	—
294	M₁₆	—	4	2	no	—
295	M₁₆	—	17	4	no	—
296	M₁₆	—	34	2	no	—
297	M₁₆	—	34	2	no	—
298	M₁₆	—	34	2	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	34	2	no	—
303	C₂×C₈	—	34	2	no	—
304	C₂×C₈	—	34	2	no	—
305	C₂×C₈	C₄×Dic₁₇	1	4	yes	—
306	C₂×C₈	#63225	1	4	yes	—
307	C₂×C₈	#63225	1	4	yes	—
308	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
309	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
310	C₂×C₈	#63227	1	2	yes	—
311	C₂×C₈	#63227	1	2	yes	—
312	C₂×C₈	#63227	1	2	yes	—
313	C₂×C₈	#63227	1	2	yes	—
314	C₂×C₈	C₂²⋊Dic₁₇	1	4	yes	—
315	C₄⋊C₄	—	17	4	no	—
316	C₄⋊C₄	—	34	2	no	—
317	C₄⋊C₄	—	34	4	no	—
318	C₄⋊C₄	—	34	4	no	—
319	C₄⋊C₄	—	68	2	no	—
320	C₄⋊C₄	—	68	2	no	—
321	C₂²⋊C₄	—	34	2	no	—
322	C₂²⋊C₄	—	34	2	no	—
323	C₄²	—	34	2	no	—
324	C₄²	—	34	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	#10587576	1	1	yes	characteristic
328	C₂³	#10587578	1	1	yes	characteristic
329	C₂³	#10587579	1	1	yes	characteristic
330	C₂³	#10587581	1	1	yes	characteristic
331	C₂³	Q₈×Dic₁₇	1	1	yes	characteristic
332	C₂³	#10587632	1	1	yes	characteristic
333	C₂³	#10587633	1	1	yes	characteristic
334	C₂×C₄	—	34	4	no	—
335	C₂×C₄	—	68	2	no	—
336	C₂×C₄	—	68	2	no	—
337	C₂×C₄	—	68	4	no	—
338	C₂×C₄	—	136	4	no	—
339	C₂×C₄	—	136	4	no	—
340	C₂×C₄	—	136	4	no	—
341	C₂×C₄	#10587573	1	1	yes	characteristic
342	C₂×C₄	#10587573	1	1	yes	characteristic
343	C₂×C₄	#10587574	1	1	yes	characteristic
344	C₂×C₄	#10587574	1	1	yes	characteristic
345	C₂×C₄	#10587576	1	1	yes	characteristic
346	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
347	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
348	C₂×C₄	#10587578	1	1	yes	characteristic
349	C₂×C₄	#10587579	1	1	yes	characteristic
350	C₂×C₄	#10587581	1	1	yes	characteristic
351	C₂×C₄	#10587583	1	1	yes	characteristic
352	C₂×C₄	#10587583	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×Dic₁₇	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×C₄⋊Dic₁₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#63227	1	1	yes	characteristic
358	C₂×C₄	C₂×#63227	1	1	yes	characteristic
359	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
360	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
361	C₂×C₄	#10587622	1	1	yes	characteristic
362	C₂×C₄	#10587624	1	1	yes	characteristic
363	C₂×C₄	#10587624	1	1	yes	characteristic
364	C₂×C₄	#10587626	1	1	yes	characteristic
365	C₂×C₄	#10587630	1	1	yes	characteristic
366	C₂×C₄	Q₈×Dic₁₇	1	1	yes	characteristic
367	C₂×C₄	#10587632	1	1	yes	characteristic
368	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
369	C₈	—	4	4	no	—
370	C₈	—	34	4	no	—
371	C₈	#10587502	1	4	yes	—
372	C₈	#10587502	1	4	yes	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	C₄⋊C₄×Dic₁₇	1	1	yes	characteristic
382	C₂²	#11762666	1	1	yes	characteristic
383	C₂²	#11762674	1	1	yes	characteristic
384	C₂²	#11762705	1	1	yes	characteristic
385	C₂²	#11762708	1	1	yes	characteristic
386	C₂²	#11762710	1	1	yes	characteristic
387	C₂²	#11762716	1	1	yes	characteristic
388	C₂²	#11763080	1	2	yes	—
389	C₂²	#11763085	1	2	yes	—
390	C₄	—	68	4	no	—
391	C₄	—	136	4	no	—
392	C₄	C₂×#10587502	1	1	yes	characteristic
393	C₄	C₄⋊C₄×Dic₁₇	1	1	yes	characteristic
394	C₄	#11762666	1	1	yes	characteristic
395	C₄	#11762678	1	1	yes	characteristic
396	C₄	#11762705	1	1	yes	characteristic
397	C₄	#11762708	1	1	yes	characteristic
398	C₄	#11762712	1	1	yes	characteristic
399	C₄	#11762714	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	#14527013	1	1	yes	characteristic
405	C₂	#14528845	1	2	yes	—
406	C₂	#14529570	1	2	yes	—
407	C₂	#14529692	1	1	yes	characteristic
408	C₂	#14529697	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10587581
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₇
Fitting	C₂²×C₁₇×#108	C₂
socle	C₂³×C₁₇	#121
prime radical	C₂⁴×C₁₇	#41
cosocle	C₂³×C₄×C₁₇	C₂³
hypercenter	C₂²×#108	D₁₇
hypocenter	C₁₇	#10870
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
12. C₂×#10587489	C₄	semidirect
14. #11762764	C₄	semidirect
23. C₂×C₁₇×#108	C₄	semidirect
208. C₂×#108	Dic₁₇	semidirect
270. C₁₇	#10870	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10587489	2
C₂×#11762764	2
C₂×#11762577	2
#14528504	2
C₂²×C₁₇×#108	2
#10870	17