Subgroups — C₂×#14529572 #17037890

Order 4352.

858 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×#11762857	C₂	1	2	yes	maximal
2	C₂²×#10587490	C₂	1	1	yes	maximal, characteristic
3	C₂×#11762764	C₂	1	1	yes	maximal, characteristic
4	#14529572	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11762580	C₂	1	2	yes	maximal
6	C₂²×C₁₇×#108	C₂	1	1	yes	maximal, characteristic
7	C₂²×#63223	C₂²	1	2	yes	—
8	C₂²×#63223	C₂²	1	1	yes	characteristic
9	C₂×#10587612	C₂²	1	1	yes	characteristic
10	#11762857	—	2	4	no	—
11	#11762857	C₂²	1	8	yes	—
12	C₂×#10587490	C₄	1	4	yes	complemented
13	C₂×#10587490	C₄	1	4	yes	complemented
14	C₂×#10587490	C₂²	1	4	yes	—
15	C₂×#10587493	—	2	4	no	—
16	#11762764	—	2	2	no	—
17	#11762764	C₂²	1	4	yes	—
18	C₂×#10587486	—	2	1	no	—
19	C₂×C₈×Dic₁₇	—	2	1	no	—
20	#11762580	C₂²	1	8	yes	—
21	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
22	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×#108	—	2	1	no	—
24	C₂×C₁₇×#108	—	2	1	no	—
25	C₂×C₁₇×#108	—	2	2	no	—
26	C₂×C₁₇×#108	C₂²	1	4	yes	—
27	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
32	C₂×M₁₆×C₁₇	—	2	2	no	—
33	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
34	C₂²×C₈×C₁₇	—	2	2	no	—
35	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₇	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₇	D₄	1	2	yes	—
40	C₂²×C₈×C₁₇	Q₈	1	2	yes	—
41	C₂²×C₈×C₁₇	Q₈	1	2	yes	—
42	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
43	C₂×C₂²⋊Dic₁₇	Q₈	1	2	yes	—
44	#10587612	—	2	1	no	—
45	#10587612	—	2	1	no	—
46	#10587612	Q₈	1	2	yes	—
47	#10587612	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₁₇	—	2	1	no	—
49	C₂×C₄×Dic₁₇	—	2	1	no	—
50	C₂×#63223	—	2	1	no	—
51	C₂×#63223	—	2	2	no	—
52	C₂×#63223	—	2	1	no	—
53	C₂×#63223	—	2	1	no	—
54	C₂×#63223	—	2	2	no	—
55	C₂×#63223	—	2	2	no	—
56	C₂×#63223	C₂×C₄	1	4	yes	—
57	C₂×#63223	C₂×C₄	1	4	yes	—
58	C₂×#63223	D₄	1	2	yes	—
59	C₂×#63223	D₄	1	2	yes	—
60	C₂×#63223	C₂³	1	4	yes	—
61	C₂×#63223	C₂³	1	2	yes	—
62	C₂²×#3622	—	2	1	no	—
63	C₂²×#3622	—	2	2	no	—
64	C₁₇×#108	—	2	4	no	—
65	C₁₇×#108	—	2	4	no	—
66	#10587493	—	2	16	no	—
67	#10587490	C₂×C₄	1	16	yes	complemented
68	#10587486	—	2	4	no	—
69	C₈×Dic₁₇	—	2	4	no	—
70	C₂⁴×C₁₇	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₇	C₂²×C₄	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×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
85	C₂²×Dic₁₇	—	2	2	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	C₄⋊C₄	1	2	yes	—
94	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
98	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₁₇	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₇	C₂×Q₈	1	4	yes	—
103	C₂²⋊Dic₁₇	—	2	2	no	—
104	C₂²⋊Dic₁₇	C₂×Q₈	1	4	yes	—
105	C₄⋊Dic₁₇	—	2	2	no	—
106	C₄⋊Dic₁₇	—	2	2	no	—
107	C₄×Dic₁₇	—	2	2	no	—
108	C₄×Dic₁₇	—	2	2	no	—
109	#63223	—	2	4	no	—
110	#63223	—	2	4	no	—
111	#63223	—	2	2	no	—
112	#63223	—	2	2	no	—
113	#63223	—	2	2	no	—
114	#63223	—	2	4	no	—
115	#63223	C₂²×C₄	1	8	yes	—
116	#63223	C₂×D₄	1	4	yes	—
117	C₂×#3622	—	2	4	no	—
118	C₂×#3622	—	2	4	no	—
119	C₂×#3622	—	2	2	no	—
120	C₂×#3622	—	2	2	no	—
121	C₂×#3622	—	2	2	no	—
122	C₂×#3622	—	2	4	no	—
123	C₂×#1953	—	17	1	no	maximal, Sylow
124	C₂³×C₁₇	—	4	2	no	—
125	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
126	C₂³×C₁₇	C₄×Q₈	1	1	yes	characteristic
127	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂³×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
129	C₂³×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
130	C₂³×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
131	C₂³×C₁₇	C₂²×Q₈	1	1	yes	characteristic
132	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₇	C₂×C₄⋊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	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
141	C₂×C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
143	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
145	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
146	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂×C₄×C₁₇	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
149	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
150	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
151	C₂×C₄×C₁₇	#125	1	1	yes	characteristic
152	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₁₇	—	2	4	no	—
161	C₂×Dic₁₇	—	4	4	no	—
162	C₈×C₁₇	—	4	4	no	—
163	C₈×C₁₇	C₂×C₄⋊C₄	1	4	yes	—
164	C₈×C₁₇	C₂×C₄⋊C₄	1	4	yes	—
165	#3622	—	2	8	no	—
166	#3622	—	2	4	no	—
167	C₂×#430	—	17	2	no	—
168	C₂²×#108	—	17	1	no	—
169	C₂²×#108	D₁₇	1	1	yes	characteristic
170	C₂×#405	—	17	1	no	—
171	#1953	—	17	8	no	—
172	C₂×#344	—	17	2	no	—
173	C₂²×C₁₇	—	2	2	no	—
174	C₂²×C₁₇	—	2	2	no	—
175	C₂²×C₁₇	—	2	2	no	—
176	C₂²×C₁₇	—	4	1	no	—
177	C₂²×C₁₇	—	4	1	no	—
178	C₂²×C₁₇	—	4	1	no	—
179	C₂²×C₁₇	—	4	1	no	—
180	C₂²×C₁₇	#389	1	1	yes	characteristic
181	C₂²×C₁₇	#389	1	1	yes	characteristic
182	C₂²×C₁₇	#389	1	1	yes	characteristic
183	C₂²×C₁₇	#389	1	1	yes	characteristic
184	C₂²×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
185	C₂²×C₁₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
186	C₂²×C₁₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
187	C₄×C₁₇	#389	1	1	yes	characteristic
188	C₄×C₁₇	#389	1	1	yes	characteristic
189	C₄×C₁₇	#389	1	1	yes	characteristic
190	C₄×C₁₇	#389	1	1	yes	characteristic
191	C₄×C₁₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
192	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₁₇	C₂×#121	1	1	yes	characteristic
194	C₄×C₁₇	C₂×#125	1	1	yes	characteristic
195	Dic₁₇	—	4	4	no	—
196	C₂²×M₁₆	—	17	1	no	—
197	C₂²×M₁₆	—	17	2	no	—
198	C₂²×M₁₆	C₂×D₁₇	1	2	yes	—
199	C₂³×C₈	C₂×D₁₇	1	1	yes	characteristic
200	C₂×#117	—	17	1	no	—
201	#430	—	17	8	no	—
202	#430	—	34	4	no	—
203	C₂×#108	—	2	1	no	—
204	C₂×#108	—	2	1	no	—
205	C₂×#108	—	2	2	no	—
206	C₂×#108	—	17	4	no	—
207	C₂×#108	—	17	4	no	—
208	C₂×#108	—	17	4	no	—
209	C₂×#108	—	34	4	no	—
210	C₂×#108	C₂×D₁₇	1	4	yes	—
211	#405	—	17	4	no	—
212	#405	—	34	2	no	—
213	C₂×#97	—	34	1	no	—
214	C₂×C₄×C₈	—	34	1	no	—
215	#344	—	17	8	no	—
216	C₂×C₁₇	—	2	1	no	—
217	C₂×C₁₇	—	2	1	no	—
218	C₂×C₁₇	—	2	1	no	—
219	C₂×C₁₇	—	2	1	no	—
220	C₂×C₁₇	—	2	1	no	—
221	C₂×C₁₇	—	2	1	no	—
222	C₂×C₁₇	#1953	1	2	yes	complemented
223	C₂×C₁₇	C₂×#389	1	1	yes	characteristic
224	C₂³×C₄	C₂²×D₁₇	1	1	yes	characteristic
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	2	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	17	4	no	—
231	C₂×M₁₆	—	17	4	no	—
232	C₂×M₁₆	—	17	2	no	—
233	C₂×M₁₆	—	17	2	no	—
234	C₂×M₁₆	—	17	4	no	—
235	C₂×M₁₆	—	17	2	no	—
236	C₂×M₁₆	—	34	2	no	—
237	C₂×M₁₆	—	34	1	no	—
238	C₂×M₁₆	—	34	1	no	—
239	C₂×M₁₆	—	34	2	no	—
240	C₂×M₁₆	—	34	2	no	—
241	C₂×M₁₆	—	34	1	no	—
242	C₂×M₁₆	C₂²×D₁₇	1	4	yes	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	34	2	no	—
245	C₂²×C₈	—	34	1	no	—
246	C₂²×C₈	Dic₃₄	1	2	yes	—
247	C₂²×C₈	Dic₃₄	1	2	yes	—
248	C₂²×C₈	C₄×D₁₇	1	2	yes	—
249	C₂²×C₈	C₄×D₁₇	1	2	yes	—
250	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
251	C₂²×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
252	C₂²×C₈	C₂²⋊D₁₇	1	2	yes	—
253	C₂²×C₈	C₂²×D₁₇	1	2	yes	—
254	#117	—	17	2	no	—
255	#117	—	17	2	no	—
256	#117	—	34	1	no	—
257	#117	—	34	1	no	—
258	C₂×C₄⋊C₄	—	34	1	no	—
259	C₂×C₂²⋊C₄	—	17	2	no	—
260	C₂×C₄²	—	34	1	no	—
261	#108	—	2	4	no	—
262	#108	—	2	4	no	—
263	#108	—	17	16	no	—
264	#108	—	34	16	no	—
265	#97	—	34	4	no	—
266	C₄×C₈	—	34	4	no	—
267	C₁₇	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
268	C₂⁴	Q₈×D₁₇	1	1	yes	characteristic
269	C₂²×C₄	—	34	2	no	—
270	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₃₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
274	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
275	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
276	C₂²×C₄	#63254	1	1	yes	characteristic
277	C₂²×C₄	#63254	1	1	yes	characteristic
278	C₂²×C₄	Q₈×D₁₇	1	1	yes	characteristic
279	C₂²×C₄	#63256	1	1	yes	characteristic
280	C₂²×C₄	#63256	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
283	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	4	2	no	—
288	M₁₆	—	17	8	no	—
289	M₁₆	—	17	4	no	—
290	M₁₆	—	34	2	no	—
291	M₁₆	—	34	4	no	—
292	M₁₆	—	34	4	no	—
293	M₁₆	—	34	4	no	—
294	M₁₆	—	34	2	no	—
295	M₁₆	—	34	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	34	4	no	—
300	C₂×C₈	—	34	2	no	—
301	C₂×C₈	—	34	4	no	—
302	C₂×C₈	—	34	4	no	—
303	C₂×C₈	—	34	2	no	—
304	C₂×C₈	—	34	2	no	—
305	C₂×C₈	#63225	1	2	yes	—
306	C₂×C₈	#63225	1	2	yes	—
307	C₂×C₈	#63225	1	2	yes	—
308	C₂×C₈	#63225	1	2	yes	—
309	C₂×C₈	#63225	1	4	yes	—
310	C₂×C₈	#63225	1	4	yes	—
311	C₂×C₈	C₂×Dic₃₄	1	4	yes	—
312	C₂×C₈	C₂×C₄×D₁₇	1	4	yes	—
313	C₂×C₈	C₂×C₂²⋊D₁₇	1	2	yes	—
314	C₂×C₈	C₂×C₂²⋊D₁₇	1	2	yes	—
315	C₄⋊C₄	—	34	2	no	—
316	C₄⋊C₄	—	34	2	no	—
317	C₂²⋊C₄	—	17	4	no	—
318	C₂²⋊C₄	—	34	2	no	—
319	C₄²	—	34	2	no	—
320	C₄²	—	34	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	#10587573	1	1	yes	characteristic
323	C₂³	#10587573	1	1	yes	characteristic
324	C₂³	#10587574	1	1	yes	characteristic
325	C₂³	#10587574	1	1	yes	characteristic
326	C₂³	#10587632	1	1	yes	characteristic
327	C₂³	#10587632	1	1	yes	characteristic
328	C₂³	C₂×Q₈×D₁₇	1	1	yes	characteristic
329	C₂×C₄	—	34	4	no	—
330	C₂×C₄	—	68	4	no	—
331	C₂×C₄	#10587573	1	1	yes	characteristic
332	C₂×C₄	#10587573	1	1	yes	characteristic
333	C₂×C₄	#10587574	1	1	yes	characteristic
334	C₂×C₄	#10587574	1	1	yes	characteristic
335	C₂×C₄	#10587576	1	1	yes	characteristic
336	C₂×C₄	#10587576	1	1	yes	characteristic
337	C₂×C₄	#10587576	1	1	yes	characteristic
338	C₂×C₄	#10587576	1	1	yes	characteristic
339	C₂×C₄	#10587579	1	1	yes	characteristic
340	C₂×C₄	#10587579	1	1	yes	characteristic
341	C₂×C₄	#10587579	1	1	yes	characteristic
342	C₂×C₄	#10587579	1	1	yes	characteristic
343	C₂×C₄	C₂×#63225	1	1	yes	characteristic
344	C₂×C₄	C₂×#63225	1	1	yes	characteristic
345	C₂×C₄	C₂×#63225	1	1	yes	characteristic
346	C₂×C₄	C₂×#63225	1	1	yes	characteristic
347	C₂×C₄	#10587624	1	1	yes	characteristic
348	C₂×C₄	#10587624	1	1	yes	characteristic
349	C₂×C₄	#10587624	1	1	yes	characteristic
350	C₂×C₄	#10587624	1	1	yes	characteristic
351	C₂×C₄	#10587632	1	1	yes	characteristic
352	C₂×C₄	#10587632	1	1	yes	characteristic
353	C₂×C₄	C₂²×Dic₃₄	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
356	C₂×C₄	C₂×#63254	1	1	yes	characteristic
357	C₂×C₄	C₂×#63256	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
359	C₈	—	4	4	no	—
360	C₈	—	34	8	no	—
361	C₈	—	34	4	no	—
362	C₈	C₂×#63225	1	4	yes	—
363	C₈	C₂×#63225	1	4	yes	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	#11762705	1	1	yes	characteristic
372	C₂²	#11762705	1	1	yes	characteristic
373	C₂²	#11762705	1	1	yes	characteristic
374	C₂²	#11762705	1	1	yes	characteristic
375	C₂²	C₂×#10587573	1	1	yes	characteristic
376	C₂²	C₂×#10587632	1	1	yes	characteristic
377	C₂²	C₂×#10587574	1	1	yes	characteristic
378	C₄	—	68	4	no	—
379	C₄	#11762705	1	1	yes	characteristic
380	C₄	#11762705	1	1	yes	characteristic
381	C₄	#11762705	1	1	yes	characteristic
382	C₄	#11762705	1	1	yes	characteristic
383	C₄	C₂²×#63225	1	1	yes	characteristic
384	C₄	C₂×#10587579	1	1	yes	characteristic
385	C₄	C₂×#10587624	1	1	yes	characteristic
386	C₄	C₂×#10587576	1	1	yes	characteristic
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	#14529572	1	2	yes	direct product factor
394	C₂	C₂×#11762705	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10587624
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₂²×C₁₇×#108	C₂
socle	C₂²×C₁₇	#389
prime radical	C₂⁴×C₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	C₂²×#108	D₁₇
hypocenter	C₁₇	C₂×#1953
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
4. #14529572	C₂	direct (N × H)
12. C₂×#10587490	C₄	semidirect
13. C₂×#10587490	C₄	semidirect
67. #10587490	C₂×C₄	semidirect
222. C₂×C₁₇	#1953	semidirect
267. C₁₇	C₂×#1953	semidirect
393. C₂	#14529572	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11762857	2
C₂²×#10587490	2
C₂×#11762764	2
#14529572	2
C₂×#11762580	2
C₂²×C₁₇×#108	2
C₂×#1953	17

Subgroups — C2×#14529572 #17037890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14529572 #17037890