Subgroups — #16940270

Order 4352.

730 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587490	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762764	C₂	1	1	yes	maximal, characteristic
3	C₂×#11762579	C₂	1	2	yes	maximal
4	#14528494	C₂	1	2	yes	maximal
5	C₂×C₁₇×#427	C₂	1	1	yes	maximal, characteristic
6	C₂²×#63223	C₂²	1	2	yes	—
7	C₂²×#63223	C₂²	1	1	yes	characteristic
8	C₂×#10587612	C₂²	1	1	yes	characteristic
9	C₂×#10587490	—	2	1	no	—
10	C₂×#10587490	—	2	1	no	—
11	C₂×#10587490	—	2	2	no	—
12	C₂×#10587490	C₄	1	4	yes	complemented
13	#11762764	—	2	1	no	—
14	#11762764	—	2	1	no	—
15	#11762764	C₄	1	2	yes	complemented
16	#11762764	C₄	1	2	yes	complemented
17	C₂×#10587486	—	2	1	no	—
18	C₂×C₈×Dic₁₇	—	2	1	no	—
19	#11762579	—	2	4	no	—
20	#11762569	—	2	4	no	—
21	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×#117	C₂²	1	2	yes	—
23	C₁₇×#427	—	2	2	no	—
24	C₁₇×#427	C₄	1	4	yes	complemented
25	C₂×C₁₇×#107	—	2	1	no	—
26	C₂×C₁₇×#106	—	2	1	no	—
27	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
28	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₇	D₄	1	2	yes	—
37	C₂²×C₈×C₁₇	Q₈	1	2	yes	—
38	C₁₇×#117	—	2	2	no	—
39	C₁₇×#117	—	2	2	no	—
40	C₁₇×#117	—	2	2	no	—
41	C₁₇×#117	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
43	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
44	C₂×C₄²×C₁₇	—	2	2	no	—
45	C₂×C₂²⋊Dic₁₇	—	2	1	no	—
46	#10587612	—	2	1	no	—
47	#10587612	—	2	1	no	—
48	#10587612	C₂×C₄	1	2	yes	—
49	#10587612	D₄	1	2	yes	—
50	C₂×C₄⋊Dic₁₇	Q₈	1	2	yes	—
51	C₂×C₄×Dic₁₇	—	2	1	no	—
52	C₂×#63223	—	2	1	no	—
53	C₂×#63223	—	2	2	no	—
54	C₂×#63223	—	2	2	no	—
55	C₂×#63223	—	2	2	no	—
56	C₂×#63223	—	2	2	no	—
57	C₂×#63223	—	2	1	no	—
58	C₂×#63223	—	2	1	no	—
59	C₂×#63223	—	2	2	no	—
60	C₂×#63223	C₂×C₄	1	4	yes	—
61	C₂×#63223	C₂×C₄	1	2	yes	—
62	C₂×#63223	D₄	1	2	yes	—
63	C₂×#63223	Q₈	1	2	yes	—
64	C₂²×#3622	—	2	1	no	—
65	C₂²×#3622	—	2	2	no	—
66	C₁₇×#107	—	2	4	no	—
67	C₁₇×#106	—	2	4	no	—
68	#10587490	—	2	4	no	—
69	#10587490	—	2	4	no	—
70	#10587486	—	2	2	no	—
71	#10587486	—	2	2	no	—
72	C₈×Dic₁₇	—	2	2	no	—
73	C₈×Dic₁₇	—	2	2	no	—
74	C₂⁴×C₁₇	#41	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	—	4	2	no	—
76	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
90	C₂²×Dic₁₇	—	2	2	no	—
91	C₂×C₈×C₁₇	C₄²	1	2	yes	—
92	C₂×C₈×C₁₇	C₄²	1	2	yes	—
93	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
94	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
100	C₂×C₈×C₁₇	C₂²⋊C₄	1	2	yes	—
101	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
102	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
103	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
104	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
105	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
106	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
107	C₄⋊C₄×C₁₇	—	2	4	no	—
108	C₄⋊C₄×C₁₇	—	4	2	no	—
109	C₂²⋊C₄×C₁₇	—	2	4	no	—
110	C₂²⋊C₄×C₁₇	—	4	2	no	—
111	C₄²×C₁₇	—	2	4	no	—
112	C₄²×C₁₇	—	4	2	no	—
113	C₂²⋊Dic₁₇	—	2	2	no	—
114	C₂²⋊Dic₁₇	—	2	2	no	—
115	C₄⋊Dic₁₇	—	2	2	no	—
116	C₄⋊Dic₁₇	C₄⋊C₄	1	4	yes	—
117	C₄×Dic₁₇	—	2	2	no	—
118	C₄×Dic₁₇	—	2	2	no	—
119	#63223	—	2	2	no	—
120	#63223	—	2	2	no	—
121	#63223	—	2	2	no	—
122	#63223	—	2	4	no	—
123	#63223	—	2	4	no	—
124	#63223	—	4	2	no	—
125	#63223	—	4	2	no	—
126	#63223	C₄⋊C₄	1	4	yes	—
127	C₂×#3622	—	2	2	no	—
128	C₂×#3622	—	2	2	no	—
129	C₂×#3622	—	2	2	no	—
130	C₂×#3622	—	2	4	no	—
131	C₂×#3622	—	4	2	no	—
132	C₂×#3622	—	4	2	no	—
133	#10872	—	17	1	no	maximal, Sylow
134	C₂³×C₁₇	—	4	2	no	—
135	C₂³×C₁₇	#117	1	1	yes	characteristic
136	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
137	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
138	C₂³×C₁₇	#121	1	1	yes	characteristic
139	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂³×C₁₇	#124	1	1	yes	characteristic
141	C₂³×C₁₇	#125	1	1	yes	characteristic
142	C₂×C₄×C₁₇	—	4	4	no	—
143	C₂×C₄×C₁₇	—	8	4	no	—
144	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂×C₂²⋊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	#117	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₇	#124	1	1	yes	characteristic
167	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
168	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
169	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
172	C₂×Dic₁₇	—	2	4	no	—
173	C₂×Dic₁₇	—	4	4	no	—
174	C₈×C₁₇	#95	1	2	yes	—
175	C₈×C₁₇	#95	1	2	yes	—
176	C₈×C₁₇	#95	1	2	yes	—
177	C₈×C₁₇	#95	1	2	yes	—
178	#3622	—	2	4	no	—
179	#3622	—	4	4	no	—
180	C₂²×#108	—	17	1	no	—
181	C₂×#427	D₁₇	1	1	yes	characteristic
182	C₂×#405	—	17	1	no	—
183	C₂×#344	—	17	2	no	—
184	#1733	—	17	2	no	—
185	C₂²×C₁₇	—	2	2	no	—
186	C₂²×C₁₇	—	2	2	no	—
187	C₂²×C₁₇	—	2	2	no	—
188	C₂²×C₁₇	—	4	1	no	—
189	C₂²×C₁₇	—	4	1	no	—
190	C₂²×C₁₇	—	4	1	no	—
191	C₂²×C₁₇	—	4	1	no	—
192	C₂²×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₁₇	#380	1	1	yes	characteristic
194	C₂²×C₁₇	#382	1	1	yes	characteristic
195	C₂²×C₁₇	#389	1	1	yes	characteristic
196	C₂²×C₁₇	#389	1	1	yes	characteristic
197	C₂²×C₁₇	#390	1	1	yes	characteristic
198	C₂²×C₁₇	#391	1	1	yes	characteristic
199	C₄×C₁₇	—	8	4	no	—
200	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
201	C₄×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
202	C₄×C₁₇	#380	1	1	yes	characteristic
203	C₄×C₁₇	#384	1	1	yes	characteristic
204	C₄×C₁₇	#389	1	1	yes	characteristic
205	C₄×C₁₇	#389	1	1	yes	characteristic
206	C₄×C₁₇	#390	1	1	yes	characteristic
207	C₄×C₁₇	#391	1	1	yes	characteristic
208	Dic₁₇	—	4	4	no	—
209	C₂²×M₁₆	—	17	1	no	—
210	C₂²×M₁₆	—	17	2	no	—
211	C₂³×C₈	C₂×D₁₇	1	1	yes	characteristic
212	C₂×#117	—	17	1	no	—
213	C₂×#117	C₂×D₁₇	1	2	yes	—
214	C₂×#108	—	17	4	no	—
215	C₂×#108	—	34	1	no	—
216	C₂×#108	—	34	1	no	—
217	C₂×#108	—	34	2	no	—
218	#427	—	2	2	no	—
219	#427	Dic₁₇	1	4	yes	complemented
220	C₂×#107	—	2	1	no	—
221	C₂×#106	—	2	1	no	—
222	#405	—	17	2	no	—
223	#405	—	17	2	no	—
224	#405	—	34	1	no	—
225	#405	—	34	1	no	—
226	C₂×#97	—	34	1	no	—
227	C₂×C₄×C₈	—	34	1	no	—
228	#344	—	34	4	no	—
229	#339	—	34	4	no	—
230	C₂×C₁₇	—	2	1	no	—
231	C₂×C₁₇	—	2	1	no	—
232	C₂×C₁₇	—	2	1	no	—
233	C₂×C₁₇	—	2	1	no	—
234	C₂×C₁₇	—	2	1	no	—
235	C₂×C₁₇	—	2	1	no	—
236	C₂×C₁₇	C₄⋊#95	1	1	yes	characteristic
237	C₂×C₁₇	#1814	1	2	yes	—
238	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
239	C₂×M₁₆	—	17	2	no	—
240	C₂×M₁₆	—	17	2	no	—
241	C₂×M₁₆	—	17	2	no	—
242	C₂×M₁₆	—	17	4	no	—
243	C₂×M₁₆	—	34	1	no	—
244	C₂×M₁₆	—	34	1	no	—
245	C₂×M₁₆	—	34	1	no	—
246	C₂×M₁₆	—	34	2	no	—
247	C₂×M₁₆	—	34	2	no	—
248	C₂×M₁₆	—	34	2	no	—
249	C₂×M₁₆	—	34	2	no	—
250	C₂×M₁₆	—	34	2	no	—
251	C₂²×C₈	—	34	1	no	—
252	C₂²×C₈	—	34	2	no	—
253	C₂²×C₈	Dic₃₄	1	2	yes	—
254	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
255	C₂²×C₈	C₄×D₁₇	1	1	yes	characteristic
256	C₂²×C₈	C₄×D₁₇	1	2	yes	—
257	C₂²×C₈	D₆₈	1	1	yes	characteristic
258	C₂²×C₈	D₆₈	1	1	yes	characteristic
259	C₂²×C₈	C₂×Dic₁₇	1	2	yes	—
260	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
261	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
262	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	—	17	2	no	—
267	#117	—	17	2	no	—
268	#117	—	34	1	no	—
269	#117	—	34	1	no	—
270	#117	C₂×Dic₁₇	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	17	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	34	1	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	34	1	no	—
277	#108	—	34	4	no	—
278	#108	—	34	4	no	—
279	#107	—	2	4	no	—
280	#106	—	2	4	no	—
281	#97	—	34	2	no	—
282	#97	—	34	2	no	—
283	C₄×C₈	—	34	2	no	—
284	C₄×C₈	—	34	2	no	—
285	C₁₇	#10872	1	1	yes	characteristic, complemented, Sylow
286	C₂⁴	#63254	1	1	yes	characteristic
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	34	2	no	—
289	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
293	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
294	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
295	C₂²×C₄	#63254	1	1	yes	characteristic
296	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
297	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
298	C₂²×C₄	#63256	1	1	yes	characteristic
299	C₂²×C₄	#63256	1	1	yes	characteristic
300	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
303	M₁₆	—	17	4	no	—
304	M₁₆	—	34	2	no	—
305	M₁₆	—	34	2	no	—
306	M₁₆	—	34	2	no	—
307	M₁₆	—	34	4	no	—
308	M₁₆	—	34	4	no	—
309	M₁₆	—	68	2	no	—
310	M₁₆	—	68	2	no	—
311	C₂×C₈	—	34	2	no	—
312	C₂×C₈	—	34	2	no	—
313	C₂×C₈	—	34	2	no	—
314	C₂×C₈	—	34	4	no	—
315	C₂×C₈	—	68	2	no	—
316	C₂×C₈	—	68	2	no	—
317	C₂×C₈	C₄×Dic₁₇	1	2	yes	—
318	C₂×C₈	C₄×Dic₁₇	1	2	yes	—
319	C₂×C₈	#63225	1	2	yes	—
320	C₂×C₈	#63225	1	2	yes	—
321	C₂×C₈	#63225	1	2	yes	—
322	C₂×C₈	#63225	1	2	yes	—
323	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
324	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
325	C₂×C₈	#63227	1	1	yes	characteristic
326	C₂×C₈	#63227	1	1	yes	characteristic
327	C₂×C₈	#63227	1	1	yes	characteristic
328	C₂×C₈	#63227	1	1	yes	characteristic
329	C₂×C₈	#63227	1	2	yes	—
330	C₂×C₈	#63227	1	2	yes	—
331	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
332	C₂×C₈	C₂²⋊Dic₁₇	1	2	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	17	4	no	—
336	C₄⋊C₄	—	34	2	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	34	2	no	—
340	C₂²⋊C₄	—	34	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	34	2	no	—
344	C₄²	—	34	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	#10587573	1	1	yes	characteristic
347	C₂³	#10587576	1	1	yes	characteristic
348	C₂³	#10587578	1	1	yes	characteristic
349	C₂³	#10587583	1	1	yes	characteristic
350	C₂³	D₄×Dic₁₇	1	1	yes	characteristic
351	C₂³	#10587622	1	1	yes	characteristic
352	C₂³	#10587624	1	1	yes	characteristic
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	—	34	4	no	—
356	C₂×C₄	—	68	4	no	—
357	C₂×C₄	#10587573	1	1	yes	characteristic
358	C₂×C₄	#10587574	1	1	yes	characteristic
359	C₂×C₄	#10587574	1	1	yes	characteristic
360	C₂×C₄	#10587576	1	1	yes	characteristic
361	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
362	C₂×C₄	C₄⋊C₄×D₁₇	1	1	yes	characteristic
363	C₂×C₄	#10587578	1	1	yes	characteristic
364	C₂×C₄	#10587579	1	1	yes	characteristic
365	C₂×C₄	#10587579	1	1	yes	characteristic
366	C₂×C₄	#10587581	1	1	yes	characteristic
367	C₂×C₄	#10587581	1	1	yes	characteristic
368	C₂×C₄	#10587583	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
370	C₂×C₄	C₂×#63225	1	1	yes	characteristic
371	C₂×C₄	C₂×#63225	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#63227	1	1	yes	characteristic
374	C₂×C₄	C₂×#63227	1	1	yes	characteristic
375	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
376	C₂×C₄	#10587624	1	1	yes	characteristic
377	C₂×C₄	#10587626	1	1	yes	characteristic
378	C₂×C₄	#10587630	1	1	yes	characteristic
379	C₂×C₄	Q₈×Dic₁₇	1	1	yes	characteristic
380	C₂×C₄	Q₈×Dic₁₇	1	1	yes	characteristic
381	C₂×C₄	#10587632	1	1	yes	characteristic
382	C₂×C₄	#10587632	1	1	yes	characteristic
383	C₂×C₄	#10587633	1	1	yes	characteristic
384	C₂×C₄	C₂×C₂²⋊Dic₁₇	1	1	yes	characteristic
385	C₈	—	34	4	no	—
386	C₈	—	68	4	no	—
387	C₈	#10587502	1	2	yes	—
388	C₈	#10587502	1	2	yes	—
389	C₈	#10587502	1	2	yes	—
390	C₈	#10587502	1	2	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	C₄⋊C₄×Dic₁₇	1	1	yes	characteristic
399	C₂²	#11762666	1	1	yes	characteristic
400	C₂²	#11762674	1	1	yes	characteristic
401	C₂²	#11762705	1	1	yes	characteristic
402	C₂²	#11762708	1	1	yes	characteristic
403	C₂²	#11762712	1	1	yes	characteristic
404	C₂²	#11762714	1	1	yes	characteristic
405	C₄	—	8	4	no	—
406	C₄	—	68	4	no	—
407	C₄	C₂×#10587502	1	1	yes	characteristic
408	C₄	C₄⋊C₄×Dic₁₇	1	1	yes	characteristic
409	C₄	#11762666	1	1	yes	characteristic
410	C₄	#11762678	1	1	yes	characteristic
411	C₄	#11762705	1	1	yes	characteristic
412	C₄	#11762708	1	1	yes	characteristic
413	C₄	#11762710	1	1	yes	characteristic
414	C₄	#11762716	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	2	1	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	#14527013	1	1	yes	characteristic
422	C₂	#14528835	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10587581
commutator	C₂×C₄×C₁₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₇
Fitting	C₂×C₁₇×#427	C₂
socle	C₂²×C₁₇	#380
prime radical	C₂⁴×C₁₇	#41
cosocle	C₂³×C₄×C₁₇	C₂³
hypercenter	C₂×#427	D₁₇
hypocenter	C₁₇	#10872
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
12. C₂×#10587490	C₄	semidirect
15. #11762764	C₄	semidirect
16. #11762764	C₄	semidirect
24. C₁₇×#427	C₄	semidirect
219. #427	Dic₁₇	semidirect
285. C₁₇	#10872	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10587490	2
C₂×#11762764	2
C₂×#11762579	2
#14528494	2
C₂×C₁₇×#427	2
#10872	17